2(2x-20)= -12
6x-20= -12
6x=8
X=8
_
6
Find the mistake

The rate of change of the area of the triangle, in square feet per second, at the instant the bottom of the ladder is 48 feet from the wall is 26 square feet per second.

Let's call the distance between the bottom of the ladder and the wall x. We can express the area of the triangle in terms of x as follows:

Area = (1/2) * 52 * x

The area of the triangle is changing at a rate of 8 square feet per second as x changes at a rate of 8 feet per second. We can find the rate of change of the area with respect to x by taking the derivative of the area expression with respect to x:

d(Area)/dx = (1/2) * 52 = 26

Therefore, the rate of change of the area of the triangle, in square feet per second, at the instant the bottom of the ladder is 48 feet from the wall is 26 square feet per second.

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The value of the shaded area from the rectangle ACDE is approximately 52.124 square centimeters.

In this problem we must calculate the shaded area of the section within the rectangle ACDE, this can be found by the subtracting the area of the region ABDE, which is the combination of the areas of the right triangle ABE and the arc BDE, whose formulas are shown below:

Triangle ABE

S = (1 / 2) · AB · AE

Arc BDE

S = (1 / 2) · α · ED²

Where α is the central angle, in radians.

Rectangle ACDE

S = ED · AE

If we know that AE = 20 cm, ED = 28 cm, α = π / 4 and AB = 20 cm, then the area of the shaded area is:

S = (28 cm) · (20 cm) - (1 / 2) · (π / 4) · (28 cm)² - (1 / 2) · (20 cm) · (20 cm)

S ≈ 52.124 cm²

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The value of y₂, y₃ and y₄ in the linear function are -21, -26 and -31 respectively.

Linear function can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, to find the missing values in the table we have to use the equation of the linear function.

y = mx + b

let's find m.

using (4, -16) and (8, -36)

m = slope = -36 + 16 / 8 - 4

m = -20 / 4

m = -5

Hence, let's find y-intercept using (4, -16).

y = -5x + b

-16 = -5(4) + b

-16 + 20 = b

b = 4

Therefore, the equation is y = -5x + 4.

Let's find y₂, y₃ and y₄

y₂ = -5(5) + 4 = -25 + 4 = - 21

y₃ =  -5(6) + 4 = -30 + 4 = -26

y₄ =  -5(7) + 4 = -35 + 4 = - 31

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The sequences of transformations that could be applied to the parent function are Reflected over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units i.e. Option (4).

What is transformation?

An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation. Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

The two-dimensional shape without any transformations is known as a preimage or inverse image. The transformed figure is shown in the image.

Given, the parent function, f(x) = x

From the given graph, the equation will be

y = -2x + 6

Then, the transformation will be

Shifted up 6 units

Vertical stretch by a factor of 2

Reflected over the y-axis

Hence, the required answer is Option 4.

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The proof that tan(x) sin(x) + cos(x) = sec(x) is represented by the trigonometric equation sec(x) = sec(x)

From the question, we have the following parameters that can be used in our computation:

tan(x) sin(x) + cos(x) = sec(x)

Express tan(x) as sin(x)/cos(x)

So, we have the following representation

sin(x)/cos(x) * sin(x) + cos(x) = sec(x)

Evaluate the products

So, we have the following representation

sin²(x)/cos(x)  + cos(x) = sec(x)

Take the LCM

[sin²(x) + cos²(x)]/cos(x) = sec(x)

Express sin²(x) + cos²(x) as 1

So, we have

1/cos(x) = sec(x)

Evaluate

sec(x) = sec(x)

Hence, the equation has been proved

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Answer:

Step-by-step explanation:

The correlation coefficient between 1 and v(n) is -0.913, and this coefficient indicates a strong negative linear association. The correlation coefficient is a measure of the strength and direction of the relationship between two variables. In this case, the correlation coefficient is -0.913, which indicates a strong negative relationship between 1 and v(n). This means that as the value of 1 increases, the value of v(n) decreases, and vice versa. This relationship is linear, which means that it can be described by a straight line. Overall, the correlation coefficient indicates a strong negative linear association between 1 and v(n).

The numbers of the atoms of each element are;

6 atoms of carbon, 12 atoms of oxygen

12 atoms of hydrogen, 6 atoms of oxygen

6 atoms of carbon, 12 atoms of hydrogen, 6 atoms of oxygen

12 atoms of oxygen

In a chemical reaction, there is the combination of the atoms of the reactants and a consequent recombination as the products are formed. In accordance with the law of the conservation of mass, we know that the number of atoms before reaction must be equal to the number of atoms after reaction.

Now we have to look at the atoms and count up the number of atoms of each element in each of the compounds and this is how we are able to obtain the number of each atom as shown above.

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From the given options, option 2. x= -8 is the correct option. Here, the x is change in height in inches so the, change in height is -8 inches.

A linear equation is simply an equation with the highest degree always being 1. The standard form of a linear equation in one variable is Ax + B = 0. x is a variable in this equation, and A and B are constants. A two-variable linear equation has the standard form Ax + By = C. The variables x and y are variables, their coefficients A and B are variables, and C is a constant.

Given, linear equation is

[tex]4(2x+1)=6x-12\\\\8x+4=6x-12\\\\8x-6x=-4-12\\\\2x=-16\\\\x=-8[/tex]

Hence, the x equals to -8.

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If the snails moves at a constant rate, it will take 25 minutes to travel 55 feet.

We know that the snail travels at a rate of 2.2 feet per minute, so after x minutes, the distance traveled by the snail is:

D = 2.2ft*x

To see how many minutes it takes the snail to travel 55 feet, we need to solve the equation:

55 ft = 2.2ft*x

If we divide both sides by 2.2ft, we will get:

55ft/2.2ft = x

25 = x

So the snail takes 25 minutes to travel the 55 feet.

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The total number of hours that it opens in one week will be 104 hours.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Walmart is open Monday through Saturday from 8:00 AM to 12:00 AM and Sunday from 10:00 AM to 8:00 PM.

From 8:00 AM to 8:00 PM, there are 12 hours and from 8:00 AM to 12:00 AM there are 4 hours. Then the total hours from Monday to Saturday will be calculated as,

⇒ 6 x (12 + 4)

⇒ 6 x 16

⇒ 96 hours

From 10:00 AM to 8:00 PM, there are only 10 hours. Then the total number of hours that it opens in one week will be given as,

⇒ 96 + 8

⇒ 104 hours

The total number of hours that it opens in one week will be 104 hours.

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Answer:

{x = 4

{y = -20

Step-by-step explanation:

{5x - 5y = 120

{y = -7x + 8

5x - 5(-7x +8) = 120

5x + 35x - 40 = 120

40x - 40 = 120

40x = 120 + 40

40x = 160

x = 160/40

(cross out common factor)

x = 4

-----------

x = 4 (next is y)

y = -7 x 4 + 8 (calculate)

y = 20

y = -20

solution of system;

{x = 4

{y = 20

Answer: [tex]2^4 \times 5[/tex]

Step-by-step explanation:

[tex]80=2 \times 40\\\\80=2 \times 2 \times 20\\\\80=2 \times 2 \times 2 \times 10\\\\80=2 \times 2 \times 2 \times 2 \times 5\\\\80=2^4 \times 5[/tex]

Answer:

15.1

Step-by-step explanation:

tan(angle) = opposite/adjacent

tan 37 = AB/20

AB = 20 x tan 37 = 20 x 0.754 = 15.08 or 15.1

Answer:

4,250

Step-by-step explanation:

If 4% of all fans were teenagers, and 100 divided by 4 is 25, simply math of 170 times 25 gives you 4,250

Therefore, the answer is 4,250

Answer:

Total number of people = 4,250

Step-by-step explanation:

4% of 4,250 = 170

Lin needs a 45-meter head start as  Lin will travel 120 meters in 30 seconds, and Diego will travel 165 meters in 30 seconds.

Time = 30 sec

Lin's speed = 4m/s

Diego's speed = 5.5m/s

Distance travelled by ,

Lin = speed * time = 4 * 30

= 120 m

Diego = 5.5 * 30

= 165

Therefore, Diego will travel 45 m more than Lin in 1 sec.

Therefore, the head start should be of 45m.

The most crucial scientific notion is measurement is speed . Base or physical fundamental units are used to quantify a wide range of quantifiable quantities. One such measurable metric is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance.

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

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Answer:

Step-by-step explanation:

the answer is 11/12

Answer:

Makayla's sister has 48 bags of popcorn

Step-by-step explanation:

25/100 = 4

12x4 = 48

12*4

= 48 is the answer

Answer: The Tri-State Pick 3 lottery game offers a choice of several bets, including a "box" bet where you choose a three-digit number and win if the number you choose has the same digits as the winning number, in any order. The expected payoff for a $1 bet on the box is $83.33.

To find this expected value, we need to consider all the possible ways that the winning number could be chosen and calculate the probability of each outcome. Since the winning number is chosen at random, each of the 10 possible digits (0 through 9) is equally likely to be chosen for each of the three positions in the winning number.

Since the box bet pays off if the digits of your chosen number match the digits of the winning number, regardless of their order, the number of winning combinations is equal to the number of ways to arrange the three digits of the winning number. This is equal to 3! (3 factorial), which is equal to 6.

Since there are a total of 10 possible digits for each position and the winning number has three positions, there are a total of 10 x 10 x 10 = 1000 possible winning numbers. Of these, 6 will pay off for a box bet, so the probability of winning a box bet is 6/1000 = 0.006.

Since the expected value of a bet is equal to the probability of winning multiplied by the payoff, the expected value of a $1 bet on the box is 0.006 x $83.33 = $0.05. Therefore, the expected payoff for a $1 bet on the box is $0.05.

The four letter code from the transformations is given as follows:

FB H.

The four letter code is obtained applying the transformations to the given points.

The coordinates of point 1 are given as follows:

(-4,2).

The transformation is a reflection over the x-axis, which has the rule given as follows:

(x,y) ->(x,-y).

Hence the coordinates of the image of point 1 are given as follows:

1'(-4,-2).

Meaning that the first letter is of F.

The coordinates of point 2 are given as follows:

(-2,3).

The transformation is a reflection over the y-axis, which has the rule given as follows:

(x,y) ->(-x,y).

Hence the coordinates of the image of point 2 are given as follows:

2'(2,3)

Meaning that the second letter is of B.

The coordinates of point 4 are given as follows:

(-1,2)

The transformation is a reflection over the line y = x, which has the rule given as follows:

(x,y) ->(y,x).

Hence the coordinates of the image of point 4 are given as follows:

4'(2,-1)

Meaning that the fourth letter is of H.

The third transformation is missing.

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Answer: The answer is y=7x+4

M is the slope and the y-intercept is b

Examples of unit rates are Dollars per pound calories and earnings per hour. The rest is not the unit rate.

What is the unit rate?

An item's unit rate is its price for one of them. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. 70 yards in 10 seconds and 7 yards in 1 second are both ratios, although only the latter is a unit rate.

Earnings per hour are a unit rate since it is calculated for an hour.

Dollars per pound calories is a unit rate.

Serving $25.50 for 5 gallons is not a unit rate, the cost is for 5 gallons. If the cost is for 1 gallon then it will unit rate.

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Answer:

Step-by-step explanation:

The statements that are true regarding undefined terms are;

The reason these statements above are true are as follows:

Examples of undefined terms includes a point, a plane, a line and a set

A point is for representing a position in space. It has no dimensions

Therefore, the statement, A point has no length or width is true

A plane is defined as an interconnected set of points that lay on the same flat surface, and extends infinitely along the surface in all directions

A line is defined as an infinite set of points that are arranged in straight path and extends without end in opposite directions

Therefore, the statement, a line consists of an infinite number of points is true

Therefore, a plane can be considered as being made up of an infinite set of lines that are located on a flat surface

Therefore, the statement, a plane consists of an infinite set of lines is true

Answer:

Its gotta be (6, 5)

Step-by-step explanation:

If we look at the sequence, the x coordinates are 2, -2, 4, -4. In the first & third x coordinates, there is an increment of 2 i. e. first 2 and then 2+2=4 so the fifth x coordinate should be 4+2=6.

The y coordinates are 3, 5, 4, 5. In the first and third y coordinates, there is an increment of 1 i. e. first 3 and then 3+1=4 so the fifth y coordinate should be 4+1=5.

The sequence goes like this

(2, 3), (-2, 5), (4, 4), (-4, 5), (6, 5), (-6, 5), (8, 6), (-8, 5), and so on

Answer:

D)  5x + 10y > 100

Step-by-step explanation:

We know that the sum of x $5 bills and y $10 bills in more than $100:

  5x + 10y > 100

c)  5x + 10y > 100

The sentence did not say equal or greater than (≥).

At the circle's center, the arc's radius and angle are 9 cm and 4/3 radians, respectively.

Any section of a circle's circumference is considered an arc. Remember that the circumference of a circle is its perimeter or distance.

Given the length of the arc is 12cm and the area of the arc is 108 cm Square.

Since the length of the arc = θ × r

Area of the arc (A) =  (θ/360°) × πr2

Substituting values in the formulas

12  = θ × r

108 = θ × r²

comparing both equations

r = 9 cm

θ = 4/3 radian

Therefore, the radius and the angle subtended at the center of the circle by the arc are 9 cm and 4/3 radian respectively.

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By solving a linear equation, it can be calculated that

Each club can order 21.1 cupcakes if they both have the same amount of

money to spend

What is a linear equation?

Equation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by an equal to sign

A one degree equation is called linear equation

Let the number of cupcakes ordered by each club be c

The band would like to order cupcakes from Walmart at a cost of $3.35 per cupcake and a $13.00 order fee

Total amount spent = $(13 + 3.35c)

The orchestra would like to order cupcakes from Publix at $2.90 each

and a $22.50 order fee

Total amount spent = $(22.5 + 2.90c)

By the problem,

The linear equation is

13 + 3.35c = 22.5 + 2.90c

3.35c - 2.90c = 22.5 - 13

0.45c = 9.5

c = 21.1

This solution is not viable as the number of cupcakes must be an integer not a decimal.

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Answer:

1.) 0.25

2.) 0.50

3.) 0.125

4.) 2.25

Step-by-step explanation:

When turning percentages into decimals, you move the decimal point two places to the left.

EX:

25%

25.0 (move the decimal point two places to the left)

2.5

.25

0.25 (add any zeros if necessary)

Hope this helps!!

It doesn't matter where the decimal point is in a percentage, as long as you move the point two places to the left, you are still turning it into a decimal.

Answer:5x+22

there you gooo

Answer:

5x+ 45/2

Step-by-step explanation:

we conclude at the 1% level of significance that the claim is true by accepting H₀

What is Hypothesis?

A hypothesis outlines your expectations for the results of your investigation. It is a speculative, untested response to your research question.

Given,

n = 81

x bar = 7

s= 2

Here, a doctor claims that people are atmost 6 pound over weight

H₀ : μ ≤ 6 versus

H₀ : μ > 6 versus

Now,

The Test Stastistic is

t = x bar - μ / s√n

t = 7-6/2√81

t = 4.5

let ∝ = 0.10, then p value = 0.000

p value >∝

yes, conclude the claim is true by accepting H₀

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