y 2x 3x y The diagram shows a trapezium. All the lengths are in centimetres. The perimeter of the trapezium is P cm. Find a formula, in terms of x and y, for P. Give your answer in its simplest form.​

Y 2x 3x Y The Diagram Shows A Trapezium. All The Lengths Are In Centimetres. The Perimeter Of The Trapezium

Answers

Answer 1

To find:-

The perimeter of the trapezium.

Answer :-

Perimeter: Perimeter is simply the sum of all the side lengths of a figure. Here it is a trapezium so the perimeter would be the sum of all the four sides.

According to the given question , the expressions of the side lengths are , 2x , y , 3x and y .

So the perimeter would be the sum of these four expressions as ,

P = 2x + y + 3x + y

Group like terms ,

P = 2x + 3x + y + y

Add like terms ,

P = 5x + 2y

Also the unit here is centimetres, so the perimeter would be (5x + 2y)cm .

Therefore, the required formula for perimeter is ,

P = (5x + 2y) cm

and we are done!

Answer 2

Answer:

[tex]P=(5x+2y)\; \sf cm[/tex]

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, the perimeter of a trapezium is the sum of its side lengths.

From inspection of the given diagram, the side lengths of the trapezium are:

2x cmy cm3x cmy cm

Therefore, the formula for its perimeter, P, in terms of x and y is:

[tex]\implies P=2x+y+3x+y[/tex]

Simplify by collecting like terms:

[tex]\begin{aligned}\implies P&=2x+y+3x+y\\&=2x+3x+y+y\\&=5x+2y\\\end{aligned}[/tex]

Therefore, the formula, in terms of x and y, for P in its simplest form is:

[tex]P=(5x+2y)\; \sf cm[/tex]


Related Questions

How do I solve? I don’t understand

Answers

Step-by-step explanation:

Use the 110 to find the 70 degree angle   (they form a straight line = 180°)

   then 70 + 64 + R angle = 180°    ( sum of angles of a triangle)

        then  :    R angle = 46°

then the R angle + 2x-10 = 90°    ( because the two lines are perpendicular)

(2x -10)°   + 46 °  = 90 °

x = 27

After solving the problem Is the statement true or false

Answers

Answer:

True

Step-by-step explanation:

Since x = 3 since we are given that f(3) = 16, x = 3.

The equation is:

[tex]f(x) = x^{2} + 2x + 1[/tex]

and x = 3, we can easily sustitute x with 3. When we do so, our equation will look like:

[tex]f(3) = 3^{2} + 2(3) + 1[/tex]

Now, we will solve.

3^2 is = 9

2(3) = 6

Now, we will plug into the equation:

[tex]f(3) = 9 + 6 + 1[/tex]

Combine like terms (constants)

[tex]f(3) = 16[/tex]

-6(4p+5) > 34-8p HELP ASAP

Answers

Answer:

p < -4

Step-by-step explanation:

-6(4p+5) > 34 - 8p

-24p - 30 > 34 - 8p

-16p - 30 > 34

-16p > 64

p < -4

please help fast!! brainliest!! Find the slope of a line perpendicular to the line whose equation is 4x − 6y = −24
Fully simplify your answer.

Answers

The slope of the sole sequence's perpendicular line is [tex]-\frac{3}{2}[/tex].

What is the perpendicular direction?

As two lines meet at right angles, the word "perpendicular" refers to an angle. Every direction, including up and down, across, and side to side, can be faced by a pair of perpendicular lines.

Is a straight line considered to be perpendicular?

A perpendicular is a straight line in mathematics that forms a correct angle (90 °) with another line. In other words, two lines are parallel to one another if they connect at a right angle.

[tex]y = mx + b[/tex], where [tex]m[/tex] is the slope:

[tex]4x - 6y = -24[/tex]

[tex]-6y = -4x - 24[/tex]

[tex]y = (4/6)x + 4[/tex]

[tex]y = (2/3)x + 4[/tex]

So the slope of the given line is [tex]2/3[/tex].

To find the slope of a line perpendicular to this line, we need to take the negative reciprocal of [tex]2/3[/tex]:

[tex]-1/(2/3) = -3/2[/tex]

Therefore, the slope of a line perpendicular to the given line is [tex]-\frac{3}{2}[/tex].

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What are inequalities?

Answers

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

Answer:

In mathematics, an inequality is a statement that compares two values, indicating that they are not equal, and specifies the relationship between them. In other words, an inequality expresses a relative difference between two values or quantities, rather than an exact equality.

There are different types of inequalities, but the most common ones involve comparisons between numerical values or algebraic expressions using inequality symbols, such as:

Greater than: x > y (read as "x is greater than y")

Less than: x < y (read as "x is less than y")

Greater than or equal to: x ≥ y (read as "x is greater than or equal to y")

Less than or equal to: x ≤ y (read as "x is less than or equal to y")

Inequalities can also involve multiple variables and can be used to describe ranges of values or conditions that must be satisfied. For example, x + y > 5 is an inequality that describes a region of the xy-plane where the sum of x and y is greater than 5.

Inequalities are used extensively in many areas of mathematics, including algebra, calculus, and optimization, and also have applications in other fields such as economics, physics, and engineering.

Step-by-step explanation:

draw a new of a square pyramid for which the base is 2 units long and the height of each triangular face is 5 units>

Answers

After answering the provided question, we can conclude that slant height  of pyramid  [tex]= \sqrt((2/2)^2 + 5^2) = \sqrt(29) = 5.39 units.[/tex]

What exactly is a pyramid?

A pyramid is a polygon formed by connecting points known as bases and polygonal vertices. For each hace and vertex, a triangle known as a face is formed. A cone with a polygonal shape. A pyramid with a floor and n pyramids has n+1 vertices, n+1 vertices, and 2n edges. Every pyramid is dual in nature. A pyramid contains three dimensions. A pyramid is made up of a flat tri face and a polygonal base that come together at a single point known as the vertex. A pyramid is formed by connecting the base and peak. The edges of the base form triangle faces known as sides, which connect to the top.

            /\

          /    \

        /         \

      /______\

         5

         |

         |

         |

         |

         |

         2

The square pyramid in the diagram above has a two-unit-long square base and four five-unit-high triangular faces. The Pythagorean theorem can be used to calculate the slant height of each triangular face:

slant height [tex]= \sqrt((2/2)^2 + 5^2) = \sqrt(29) = 5.39 units.[/tex]

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LI Annexure A shows Rhandzu's grade 11 school timetable for 2023. Learners are given 5 minutes to change from one lesson to the other. Use ANNEXURE A to answer the questions that follow. 1.1.1 Determine how l
ong the second break is. 1.1.2 How many subjects is Rhandzu doing? 1.1.3 Determine the number of days in an eight-day cycle that Rhandzu has Mathematical Literacy. Explain why it is important to schedule breaks on the time-table. 1.1.4​

Answers

The answer of the given question based on determining the second break in the break is  1.1.1 The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long , 1.1.2 Rhandzu is doing 8 subjects , Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle.

What is Sepedi Home Language?

Sepedi is  Bantu language spoken in South Africa by Pedi people. It is one of the 11 official languages of South Africa and is primarily spoken in  northern parts of  country, like Limpopo, Gauteng, and Mpumalanga provinces.

Sepedi is also known as Sesotho sa Leboa and is closely related to Sesotho (Southern Sotho) and Setswana (Tswana). Sepedi Home Language refers to  study of Sepedi as  first language or mother tongue in South African schools. It is an important subject in South African education system, as it helps to preserve and promote use of indigenous languages and cultural heritage.

1.1.1 The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long.

1.1.2 Rhandzu is doing 8 subjects, which are English Home Language, Mathematics, Life Orientation, Physical Sciences, Life Sciences, Agricultural Sciences, Mathematical Literacy, and Sepedi Home Language.

1.1.3 Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle. Therefore, in an eight-day cycle, Rhandzu would have Mathematical Literacy on Day 3, Day 7, Day 3 again, and Day 7 again.

It is important to schedule breaks on the time-table because they allow students to rest and recharge between lessons. Breaks can also help students to stay focused and engaged during lessons by giving them time to process and reflect on what they have learned. Additionally, breaks can provide opportunities for social interaction and physical activity, which can have a positive impact on students' well-being and academic performance.

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The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long , Rhandzu is doing 8 subjects , Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle.

What is Sepedi Home Language?

Sepedi is  Bantu language spoken in South Africa by Pedi people. It is one of the 11 official languages of South Africa and is primarily spoken in  northern parts of  country, like Limpopo, Gauteng, and Mpumalanga provinces.

Sepedi is also known as Sesotho sa Leboa and is closely related to Sesotho (Southern Sotho) and Setswana (Tswana). Sepedi Home Language refers to  study of Sepedi as  first language or mother tongue in South African schools. It is an important subject in South African education system, as it helps to preserve and promote use of indigenous languages and cultural heritage.

1.1.1 The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long.

1.1.2 Rhandzu is doing 8 subjects, which are English Home Language, Mathematics, Life Orientation, Physical Sciences, Life Sciences, Agricultural Sciences, Mathematical Literacy, and Sepedi Home Language.

1.1.3 Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle. Therefore, in an eight-day cycle, Rhandzu would have Mathematical Literacy on Day 3, Day 7, Day 3 again, and Day 7 again.

It is important to schedule breaks on the time-table because they allow students to rest and recharge between lessons. Breaks can also help students to stay focused and engaged during lessons by giving them time to process and reflect on what they have learned. Additionally, breaks can provide opportunities for social interaction and physical activity, which can have a positive impact on students' well-being and academic performance.

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GUYS PLEASE HELP MATH!!

Answers

Answer:

4.3

Step-by-step explanation:

The sides of a triangle have lengths
7.5,11
, and
x
. If
x
is an integer, what is the least possible value of
x
? A. 1 B. 2 C. 3 D. 4 E. 5

Answers

If x is an integer, the least possible value of x is 4. So the option D is correct.

The triangle's third side should be less than the sum of the other two sides and more than the difference of the other two sides.

11 - 7.5 < x < 11 + 7.5

Simplify

3.5 < x < 18.5

So the value of the x is between 3.5 and 18.5.

From the option the value 4 and 5 lies between 3.5 and 18.5.

As we have to determine the least possible value of x, so the value of x should be 4. So the option D is correct.

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The complete question is:

The sides of a triangle have lengths 7.5, 11, and x. If x is an integer, what is the least possible value of x?

A. 1

B. 2

C. 3

D. 4

E. 5

Question 1: 10 pts

A triangle has a base length of 2ac² and a height 6 centimeters more than the base

length. Find the area of the triangle if a = 4 and c = 2.

608 cm²

224 cm²

1,216 cm²

576 cm²

Answers

The area of the triangle with the given base and height where a = 4 and c = 2 is: 608 cm²

What is the Area of a Triangle?

Area = 1/2(base)(height).

Given the parameters:

Base length = 2ac² cmHeight = 2ac² + 6 cm

If a = 4 and c = 2, then:

Area = 1/2(base)(height) = 1/2(2ac²)(2ac² + 6)

Area = 1/2(2 × 4 × 2²)(2 × 4 × 2² + 6)

Area = 1/2(32)(38)

Area = 608 cm²

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for a given positive integer n, output all the perfect numbers between 1 and n, one number in each line.

Answers

Perfect numbers between 1 and n (where n is a positive integer) are 6, 28, 496, 8128.

A positive integer that is the sum of its appropriate divisors is referred to as a perfect number. The sum of the lowest perfect number, 6, is made up of the digits 1, 2, and 3. The digits 28, 496, and 8,128 are also ideal.

Perfect numbers are whole numbers that are equal to the sum of their positive divisors, excluding the number itself. Examples of perfect numbers include 6 (1 + 2 + 3 = 6), 28 (1 + 2 + 4 + 7 + 14 = 28) and 496 (1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496).

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The complete question is:

What are all the perfect numbers between 1 and n (where n is a positive integer)?

Question 15 (2 points)
A standard deck of cards contains 4 suits of the same 13 cards. The contents of a
standard deck are shown below:

Standard deck of 52 cards
4 suits (CLUBS SPADES, HEARTS, DIAMONDS)
13 CLUBS
13 SPADES
13 HEARTS
DIAMONDS

If a card is drawn at random from the deck, what is the probability it is a jack or ten?

0
4/52- 1/13
8/52 = 2/13
48/52- 12/13

Answers

Answer: 2/13

Step-by-step explanation:

There are four jacks and four tens in a standard deck of 52 cards. However, the jack of spades and the ten of spades are counted twice since they are both a jack and a ten. Therefore, there are 8 cards that are either a jack or a ten, and the probability of drawing one of these cards at random is:

P(Jack or Ten) = 8/52 = 2/13

So the answer is 2/13.

Step-by-step explanation:

a probability is airways the ratio

desired cases / totally possible cases

in each of the 4 suits there is one Jack and one 10.

that means in the whole deck of cards we have

4×2 = 8 desired cases.

the totally possible cases are the whole deck = 52.

so, the probability to draw a Jack or a Ten is

8/52 = 2/13

two random vectors follow the same distribution does this mean every marginalized variables have to follow the same distribution

Answers

Yes. they can in fact, more than two independent variables can have the same distribution. Two random vectors follow the same distribution, which means that each marginalized variable must follow the same distribution.

In probability theory and statistics, the marginal distribution of a subset of a set of random variables is the probability distribution of the variables contained in that subset. It gives the probability of different values ​​of variables in the subset without reference to the values ​​of other variables. This contrasts with conditional distributions, which give probabilities based on the values ​​of other variables.

The marginal variables are the variables of the subset of variables which are retained. These concepts are "marginal" because they can be found by adding the values ​​of the rows or columns of a table and writing the sum in the blank space of the table.

The distribution of the marginal variable (marginal distribution) is obtained by marginalizing the distribution of the suppressed variable (that is, focusing on the sum in the margin), and the suppressed variable is called marginalized.

Complete Question:

If two random variables have the same PDF/PMF, then does this mean they have the same distribution?

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Determine the interval(s) over which the graph of f left parenthesis x right parenthesis equals short dash x to the power of 6 minus 6 x to the power of 5 plus 12 x minus 2 is concave up or concave down.

Answers

Answer:

gdiduusuehfuehvv

Step-by-step explanation:

bbzbhshxhdhhd are the best and my mom I WINNNNNN you want it to be over with you guys to come in and your mom are doing ghhdhhsuwuwhsh and your family are doing well and your family are doing well and your family are doing well and your family are doing well and your family and my wife was the best and I WINNNNNN and my mom are doing ghhdhhsuwuwhsh and what is the only ones I WINNNNNN with the kids I WINNNNNN and I will be over and I can do i and eat early for you and Darshanie and I WINNNNNN and my friend and your mom and my mom ever had a great day I love ever and your mom are the kids I will get you a great mom and I will send you a link and I WINNNNNN with the only ones I WINNNNNN with you don't need me I can get it and I will be over and your mom and your mom I will send it out tomorrow night I will send it out tomorrow night with you guys and I can send the best ones that have to do i I will send you and Darshanie and your mom I will send it and your family and I WINNNNNN and my friend are doing errands to run out to do i you guys and I WINNNNNN you want me I will send you and Darshanie is done now we have a great day for a great mom I will be over there and I WINNNNNN you and everyone and my friend and my friend and what time do the kids have a whole new world we live together I will be home tomorrow night with the only one that has to wait until the way home tomorrow morning to run out of wo you guys to run out with the best ones that w with the kids I will get you guys want me when we good day for you it

Please check the image for directions, Five stars, and like. Thank you

Answers

The measure of HI based on the given diagram is 70 units.

What is a triangle mid segment?

A triangle mid segment is the line joining the midpoint of any two sides of the triangle which is parallel to the third side and is also half of the length of the third side.

HI = 3x + 5

EF = -3x + 55

So,

HI = 1/2(EF)

3x + 5 = 1/2(-3x + 55)

3x + 5 = (-3x + 55) / 2

cross product

2(3x + 5) = -3x + 55

open parenthesis

6x + 10 = - 3x + 55

6x + 3x = 55 - 10

9x = 45

divide both sides by 9

x = 45/9

x = 5

Therefore, the measure of HI and EF are;

HI = 3x + 5

= 3(5) + 55

= 15 + 55

= 70

EF = -3x + 55

= -3(5) + 55

= -15 + 55

= 40

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if the sum of a number and eight is doubled​, the result is seven less than the number. Find the number.

Answers

Answer:

Step-by-step explanation:

Let's call the number we're looking for "x".

The problem tells us that "if the sum of a number and eight is doubled, the result is seven less than the number", which can be translated into an equation:

2(x+8) = x-7

Now let's solve for x:

2x + 16 = x - 7

2x - x = -7 - 16

x = -23

Therefore, the number we're looking for is -23.

Drag each tile to its equivalent measure, rounded to the nearest tenth.
Options: 19.8, 10.2, 22.7, 15.4

Measure Equivalent
4 in. _____ Cm
7 kg _____lb
6 gal _____L
65 ft _____ m

Answers

The correct matches are: 4 in. → 10.2 cm   ,   7 kg → 15.4 lb

6 gal → 22.7 L   and  65 ft → 19.8 m.

What are conversions?

Conversions refer to the process of changing a measurement from one unit to another unit that measures the same quantity.

For example, converting distance from miles to kilometers, or converting weight from pounds to kilograms.

Here are the conversions:

1 inch = 2.54 cm (approx.)

1 kg = 2.205 lb (approx.)

1 gal = 3.785 L (approx.)

1 ft = 0.3048 m (approx.)

Using these conversions, we can find the equivalent measures:

4 in. → 4 × 2.54 = 10.16 ≈ 10.2 cm

7 kg → 7 × 2.205 = 15.435 ≈ 15.4 lb

6 gal → 6 × 3.785 = 22.71 ≈ 22.7 L

65 ft → 65 × 0.3048 = 19.812 ≈ 19.8 m

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find the absolute minimuym value of the function over the clsoed triangular region d having vertices g

Answers

The absolute maximum is 56 and absolute minimum values is 24 of a function f given by f(x) = 2x³−15x² + 36x +1 on the interval [1, 5] .

A function is defined as a relationship between a set of inputs, each having an output. In short, a function is a relationship between inputs where each input relates to exactly one output. Each function has a domain and a password domain or scope. Functions are usually denoted by f(x), where x is the input.

Given that:

f(x) = 2x³ −15x²+ 36x+ 1

f'(x) = 6x² −30x + 36

Putting f'(x) = 0

⇒ 6x² − 30x+ 36 = 0

⇒ x² −5x+6 = 0

⇒ (x−2)(x−3) = 0

⇒ x=2 or 3

We are given interval [1,5]

Hence, calculating f(x) at 2, 3, 1, 5,

f(2) = 29

f(3) = 28

f(1) = 24

f(5) = 56

Hence, absolute maximum value is 56 at x=5.

Absolute minimum value is 24 at x=1.

Complete Question:

Find the absolute maximum and absolute minimum values  of a function f given by f(x)=2x³−15x² + 36x +1 on the interval [1, 5] .

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Jane has been practicing sewing, and she wants to make a rectangular blanket to give as a gift to her best friend. So that the blanket is not too small, Jane decides the blanket will have an area of approximately 40 square feet, or 5,760 square inches. She also wants the blanket to be 18 inches longer than it is wide to have room to embroider her friend's name along one edge.
To the nearest tenth of an inch, what is the width of the blanket?

Answers

The width of the blanket to the nearest tenth of an inch is approximately 67.4 inches.

What is width in rectangle ?

In a rectangle, the width refers to the measurement of the shorter side of the rectangle, which is perpendicular to its length.

Let x be the width of the blanket in inches. Then the length of the blanket is x + 18 inches.

The area of the blanket is given by:

Area = Length x Width

5760 sq inches = (x + 18) inches * x inches

Expanding the right-hand side and solving for x, we get:

[tex]x^2 + 18x - 5760 = 0[/tex]

We can solve this quadratic equation using the quadratic formula:

[tex]x = (-b \pm \sqrt{(b^2 - 4ac)}) / 2a[/tex]

where a = 1, b = 18, and c = -5760. Plugging in these values, we get:

[tex]x = (-18 \pm \sqrt{(18^2 - 4(1)(-5760))}) / 2(1)[/tex]

[tex]x = (-18 \pm \sqrt{(18^2 + 23040)}) / 2[/tex]

x ≈ 67.42 or x ≈ -85.42

Since the width cannot be negative, the width of the blanket to the nearest tenth of an inch is approximately 67.4 inches.

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valuate the triple integral. $\int\!\!\int\!\!\int e {\color{red}} y \,dv$, where e is bounded by the planes $ x

Answers

The final answer is $\frac{1}{12}$.

We need to evaluate the triple integral $\iiint e y , dv$ over the region $e$ bounded by the planes $x = 0$, $y = 0$, $z = 0$, $x + y + z = 1$, and $x + y = 2$.

To evaluate this triple integral, we can use the limits of integration obtained by considering the intersection of the planes. From the plane equations $x+y+z=1$ and $x+y=2$, we can solve for $z$ and $x$ in terms of $y$ to obtain the limits:

0≤z≤1−x−yand0≤x≤2−y.

Since $e$ is bounded by the planes $x=0$ and $y=0$, we have $0 \leq x \leq 2-y$ and $0 \leq y \leq 2$. Thus, we can set up the triple integral as follows:

Next, integrating with respect to $x$, we obtain∫

02[22−22]

02−∫ 02 [eyx− 2eyx 2 − 2ey 2 x​ ] 02−ydy.Simplifying this expression, we get

∫02(2−522+32)

.∫ 02​ (2ey− 25​ ey 2 + 2ey 3 )dy.

Evaluating the integral, we get the final answer of $\frac{1}{12}$.

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question:-Evaluate the triple integral $\int!!\int!!\int e y ,dv$, where $e$ is bounded by the planes $x = 0$, $y = 0$, $z = 0$, $x + y + z = 1$ and $x + y = 2$.

What is the value of 2/2 exponent -3

Answers

Answer:1

Step-by-step explanation:

2/2=1

1^-3=1

1/1times1times1

Answer:

1

Step-by-step explanation:

[tex]\frac{2}{2}[/tex] = 1

[tex]1^{-3}[/tex] To make a negative exponent positive, put it under one.

[tex]\frac{1}{1^{3} }[/tex] = [tex]\frac{1}{1}[/tex] = 1

Helping in the name of Jesus.

Proofs help ASAP…….$;$3$3

Answers

IM TRYING TO SOLVE THIS THE ONLY THING I GOT RIGHT NOW IS a to d is 180

3. Factor 72x³ +72x² +18x.

Answers

The expression's fully factored form is:[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{2} + 1)(x + 1)[/tex]

Factored value is what?

Factored Value, also known as "trended value," is the base annual value plus a yearly inflation factor based on a variation in the cost if live that is not to exceed 2% and is set by the State Agency of Equalization.

What is a factored expression example?

Rewriting an expression as the sum of factors is referred to as factor expressions or factoring. For instance, 3x + 12y may be expressed as 3 (x + 4y), which is a straightforward equation. The computations get simpler in this method. Three or (x + 4y) were examples of factors.

We can factor out [tex]18x[/tex] from each term to simplify the expression:

[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{3} + 4x^{2} + 1)[/tex]

An expression enclosed in parentheses can now be calculated by grouping or factoring.

[tex]4x^{3} + 4x^{2} + 1 = (4x^{2} + 1)(x + 1)[/tex]

The expression's properly factored version has the following result,

[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{2} + 1)(x + 1)[/tex]

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To purchase $13200 worth of machinery for her business, Nicole made a down payment of 1200 and took out a business loan for the rest. After 3 years of paying monthly payments of 365.07, she finally paid off the loan.


(a) What was the total amount Nicole ended up paying for the machinery (including the down payment and monthly payments)?

(b) How much interest did Nicole pay on the loan?

Answers

The answer of the given question based on the compound interest to find  total amount Nicole ended up paying for the machinery and the interest did Nicole pay on the loan is (A) the total amount Nicole ended up paying for the machinery is $14,342.52. (B) Nicole paid $2,342.52 in interest on the loan.

What is Compound interest?

Compound interest is type of interest that is calculated not only on initial principal amount but also on accumulated interest from previous periods. In other words,  interest earned in each period is added to  principal amount, and  interest for the next period is calculated on  new, larger principal amount.

Compound interest can be thought of as "interest on interest" and is used in many financial transactions, like loans, investments, and savings accounts.

(a) The total amount Nicole ended up paying for the machinery is the sum of her down payment and all of her monthly loan payments over the 3-year period. We can calculate this as follows:

Total amount paid = Down payment + (Monthly payment x Number of payments)

Total amount paid = 1200 + (365.07 x 36)

Total amount paid = 1200 + 13142.52

Total amount paid = $14,342.52

Therefore, the total amount Nicole ended up paying for the machinery is $14,342.52.

(b) To calculate how much interest Nicole paid on the loan, we first need to calculate the total amount of the loan. We can do this by subtracting her down payment from the total cost of the machinery:

Total loan amount = Total cost of machinery - Down payment

Total loan amount = $13,200 - $1,200

Total loan amount = $12,000

Next, we can calculate the total amount of interest paid over the 3-year period by subtracting the total loan amount from the total amount paid:

Total interest paid = Total amount paid - Total loan amount

Total interest paid = $14,342.52 - $12,000

Total interest paid = $2,342.52

Therefore, Nicole paid $2,342.52 in interest on the loan.

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right triangle that i’m confused on please help

Answers

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Mason earns $8.10 per hour and worked 40 hours. Noah earns $10.80 per hour. How many hours would Noah need to work to equal Mason’s earnings over 40 hours?

Answers

Answer:

Noah would need to work 30 hours to equal Mason's earning for 40 hours

Step-by-step explanation:

Mason;

8.10 x 40 = 324

324 ÷ 10.80 = 30 hours.

Helping in the name of Jesus.

Answer:

30 hours

Step-by-step explanation:

40 times 8.10 is 324 and 324 divided by 10.8 is 30 hours

A boat is heading towards a lighthouse, whose beacon-light is 148 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 8 degrees. What is the ships horizontal distance from the lighthouse(and the shore)? Round your answer to the nearest hundredth of a foot if necessary.

Answers

We can use trigonometry to solve this problem. Let's call the horizontal distance from the boat to the lighthouse "x". We can use the tangent function to find x:

tangent(8 degrees) = opposite / adjacent

tangent(8 degrees) = 148 / x

To solve for x, we can rearrange the equation:

x = 148 / tangent(8 degrees)

x ≈ 1041.87 feet

So the ship's horizontal distance from the lighthouse (and the shore) is approximately 1041.87 feet or 1041.87 rounded to the nearest hundredth of a foot if necessary.

Answer:

Your answer is 1053.07

Hope I helped!

Step-by-step explanation:

On a certain weekday, the rate at which vehicles cross a bridge is modeled by the differentiable function R for 0 ≤ t ≤ 12, where R(t) is measured in vehicles per hour and t is the number of hours since 7:00 a.m. (t = 0). Values of R(t) for selected values of t are given in the table above.

Answers

The approximate value of R'(5) is -716 vehicles per hour per hour.

To approximate Rʹ(5), we can use the formula for the average rate of change

Rʹ(5) ≈ (R(6) - R(4))/(6-4)

We use the values given in the table to get

R(6) = 3010 vehicles per hour

R(4) = 3442 vehicles per hour

Therefore, Rʹ(5) ≈ (3010 - 3442)/(6-4) = -716 vehicles per hour per hour.

So, the approximate rate of change of the rate at which vehicles cross the bridge at 5:00 a.m. is -716 vehicles per hour per hour. This means that the rate at which vehicles cross the bridge is decreasing at a rate of 716 vehicles per hour every hour around 5:00 a.m.

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The given question is incomplete, the complete question is:

On a certain weekday, the rate at which vehicles cross a bridge is modeled by the differentiable function R for 0 ≤ t ≤ 12, where R(t) is measured in vehicles per hour and t is the number of hours since 7:00 a.m. (t = 0). Values of R(t) for selected values of t are given in the table above. t(hours) 0 2 4 6 8 10 12 R(t) (vehicle per hours ) 2935 3653 3442 3010 3604 1986 2201 . Use the data in the table to approximate Rʹ(5)

You run 3 laps around a rectangular field. The field is 100 meters long and 97 meters wide. How many meters do you run?

Answers

The distance around the rectangular field can be calculated using the formula:

distance = 2(length + width)

In this case, the length is 100 meters and the width is 97 meters. So the distance around the field is:

distance = 2(100 + 97) = 2(197) = 394 meters

Since you run 3 laps around the field, the total distance you run is:

total distance = 3 × distance around the field
total distance = 3 × 394 meters
total distance = 1182 meters

Therefore, you run 1182 meters in total.

i need the answer to this question

Answers

The measure of angle BAC is 55°, which is closest to option B (50°).

What is a tangent angle?

The ratio of the length of the side directly opposite an acute angle to the side directly adjacent to the angle is known as the tangent in trigonometry. Only triangles with straight angles can have this.

Let's give the angles shown in the diagram the following labels:

Angle ACD = 55°

Angle ABD = 35°

Angle BCD = 90°

To determine the size of angle ABC, we can use the knowledge that a triangle's total angles equal 180°. Because the straight line formed by angles ABD and BCD, we have:

[tex]Angle ABC = 180° - Angles ABD and BCD.[/tex]

[tex]Angle ABC = 180° - 35° - 90°Angle ABC = 55°[/tex]

Given that triangle ABC has two angles, we can use the knowledge that a triangle's total of angles equals 180° to determine the size of angle BAC:

[tex]Angle BAC = 180° - Angle ABC - Angle ACBAngle BAC = 180° - 55° - 70°Angle BAC = 55°[/tex]

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It is most similar to option B (50°) when the angle BAC is 55°.

What is a tangent angle?

The tangent in trigonometry is the length of the side directly opposite an acute angle divided by the length of the side directly next to the angle.

This property can only be found in triangles with straight angles.

Let's give the angles shown in the diagram the following labels:

Angle ACD = 55°

Angle ABD = 35°

Angle BCD = 90°

We can use the fact that a triangle's total number of angles is 180° to calculate the size of angle ABC. due to the fact that the straight line created by angles ABD and BCD

Triangle ABC has two angles, so we can use the fact that a triangle's sum of angles is 180° to calculate the size of angle BAC.

Therefore, the BAC measurement is 55°, which is closest to option B's 50°.C is 55°, which is closest to option B (50°).

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