In AABC, b = 620 cm, ZC=106° and ZA=48°. Find the length of a, to the nearest
centimeter.

The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).

What is the right triangle is triangle?

A right triangle is a triangle in which one angle measures 90 degrees. The sides of a right triangle can be used to determine if a triangle is a right triangle using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Using this information, we can determine which of the given sets of side measures could form a right triangle:

A. 61 m, 60 m, 11 m: We can use the Pythagorean theorem to see if these sides could form a right triangle. We'll let the hypotenuse be the side with a length of 61 m, and the other two sides are the ones with lengths of 60 m and 11 m. Plugging these values into the Pythagorean theorem, we get:

(61 m)² = (60 m)² + (11 m)²

61² = 60² + 11²

61² ≠ 60² + 11²

Since the left side does not equal the right side, these sides cannot form a right triangle.

B. 24 in, 34 in, 28 in: Using the Pythagorean theorem, we can see that these sides could form a right triangle:

(34 in)² = (24 in)² + (28 in)²

34² = 24² + 28²

34² = 24² + 28²

The left side equals the right side, so these sides could form a right triangle.

C. 55 ft, 45 ft, 35 ft: Using the Pythagorean theorem, we can see that these sides could form a right triangle:

(55 ft)² = (45 ft)² + (35 ft)²

55² = 45² + 35²

55² = 45² + 35²

The left side equals the right side, so these sides could form a right triangle.

D. 48 cm, 46 cm, 15 cm: Using the Pythagorean theorem, we can see that these sides could not form a right triangle:

(48 cm)² ≠ (46 cm)² + (15 cm)²

48² ≠ 46² + 15²

Since the left side does not equal the right side, these sides cannot form a right triangle.

Hence, The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).

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Answer:

f^-1(x) = 2(x-2)^2 + 1

f^-1(x) = (x+3)^3

Step-by-step explanation:

The inverse of a function is found by switching the roles of the dependent and independent variables. In other words, we can find the inverse of a function by interchanging the x and y values in the equation. So, the inverse of the function f(x) = 2(x-2)^2 + 1 can be written as f^-1(x) = 2(x-2)^2 + 1.

1. To find the inverse function explicitly, we can use the following steps:

2. Replace f(x) with y in the original function to obtain y = 2(x-2)^2 + 1.

3. Solve for x in terms of y to obtain x = +/- sqrt((y-1)/2) + 2.

The inverse function f^-1(x) can then be written as f^-1(x) = +/- sqrt((x-1)/2) + 2.

Note that this inverse function is not a one-to-one function, because for some values of x (namely, x < 1), the function has two possible values of y (i.e. it has two solutions). Therefore, the inverse function is not a function in the strict mathematical sense, but it is still a useful concept in certain contexts.

To find the inverse of a function, we switch the roles of the dependent and independent variables, so the inverse function can be written as x = ^3√y-3.

1. To find the inverse function explicitly, we can use the following steps:

2. Replace y with x in the original function to obtain x = ^3√y-3.

3. Solve for y in terms of x to obtain y = (x+3)^3.

The inverse function can then be written as f^-1(x) = (x+3)^3.

Note that this inverse function is a one-to-one function, meaning that for every value of x, there is only one corresponding value of y. Therefore, the inverse function is a function in the strict mathematical sense.

Answer:

[tex]b = 6\sqrt{2}[/tex]

Step-by-step explanation:

Don't say giving brainiest for work, I will still help you.

Use the Pythagorean Theorem to solve:

[tex]a^2+b^2=c^2[/tex]

A and B refers to the legs, or the shorter sides. C refers to the hypotenuse, or the longest side.

Plug in what you know:

[tex](7)^2+b^2=(11)^2[/tex]

[tex]49 + b^2 = 121[/tex]

Subtract 49 on both sides.

[tex]49 - 49 + b^2 = 121-49[/tex]

[tex]b^2=72[/tex]

Find the square root of both sides.

[tex]\sqrt{b^2} = \sqrt{72}[/tex]

b = [tex]6\sqrt{2}[/tex]

Answer:

please tell me if you get the answer. I need it too!

Answer:

find my dad

Step-by-step explanation:

Answer:

The value of the ratio of crisp wheat cereal to crisp rice cereal is 1/4 to 1 1/2, which can be simplified to 1/4 to 3/2. This means that for every 4 parts of crisp wheat cereal, there are 3 parts of crisp rice cereal. The amount of crisp wheat cereal is therefore less than the amount of crisp rice cereal. Specifically, the amount of crisp wheat cereal is 1/4 * the amount of crisp rice cereal.

Step-by-step explanation:

A graph is a collection of points and the connections between some subset of those points that may or may not be empty in mathematical terms.

The given function is f (x ) = [tex]3e^{2x}[/tex]

1. Domain :

2.Range :

3.Continuity:

4.Behaviour that is either increasing or decreasing:

5.Symmetry:

6.Boundedness:

7.Extrema:

8.Asymptotes:

9.End behaviour :

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Observing the provided figure and using the transformation rule of geometry, The required transformation to map figure H onto figure I is reflection along y=x axis.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

In a mirror line, reflection is a type of transformation that reverses the shape so that each point is at the same distance from the mirror line as its reflected point.

Figure H

Mapped onto figure I

The required transformation:

reflection along y=x.

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Answer:

A and D

Step-by-step explanation:

so sorry im in school

x+y=4

 -y.  -y

x=4-y

4-y-y=2

4-2y=2

-4      -4

-2y= -2

/-2.   /-2

y=1

x+1=4

  -1 -1

x=3

so A and D is correct

Answer:

Below

Step-by-step explanation:

m = slope = rise / run

m = 5 for this equation

rise /run = 5

15 / run = 5

run = 3

Answer:

(sqrt3)/2

Step-by-step explanation:

Sin(x)=opposite/hypotenuse

30, 60, 90 right triangle.

ratio of sides are 1, sqrt3, and 2.

Locate the 60 degree angle on the triangle

The opposite side is sqrt3

The hypotenuse is 2

so its (sqrt3)/2

Answer:

√3/2 or 0.866

Step-by-step explanation:

The values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.

What are the Properties of Angles of a Parallelogram?

A parallelogram is a quadrilateral with equal and parallel opposite sides. There are some special properties of a parallelogram that make it different from the other quadrilaterals.

The consecutive angles are supplementary then,

5y + 7y - 24 = 180

12y = 180 + 24

12y = 204

y = 204/12

y = 17

The opposite angles of a parallelogram are congruent (equal) then,

5y = 4x + 7

5(17) = 4x + 7

85 = 4x + 7

85 -7 = 4x

4x = 78

x = 78/4 = 19.5

x = 19.5

the consecutive angles are supplementary, then

4x + 7 + 3z = 180

4(19.5) + 7 + 3z = 180

78 + 7 + 3z = 180

85 + 3z = 180

3z = 180 - 88

3z = 92

z = 92/3

z = 30.6

All the angles of a parallelogram add up to 360°, then:

4x + 7 + 3z + 5y +7y - 24 = 360

To check is this a parallelogram? put the values of x, y, and z in the above equation:

4(19.5) + 7 + 3(30.6) + 5(17) +7(17) - 24 = 360

356.8 ≠ 360

hence, the values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.

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If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Explanation is given.

Lines that cross the angle under investigation are known as angle bisectors. To "bisect" is to split into two sections of equal size. Therefore, the bisected halves divide the considered angle in half.

According to the angle bisector theorem;

An angle bisector divides the opposing side of a triangle into two portions that are proportionate to the other two sides, according to the angle bisector theorem.

a point is equally far from both sides of an angle if it is on the angle's bisector.

According to the inverse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally far from its sides.

The explanation with diagram is given in the image.

Therefore, If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

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Answer: x = 14/5 or x = 2.8

Step-by-step explanation:

Step 1: Divide both sides of the equation by five: a common nonzero real number.

(5x)/5= 14/5

Step 2: Simplify

x = 14/5

Answer:  BD = 5

Step-by-step explanation:

[tex]a^{2} +12^{2} =13^{2}[/tex]

[tex]a^{2} =13^{2}-12^{2}[/tex]

[tex]a = \sqrt{25}[/tex]

[tex]a = 5[/tex]

Therefore BD = 5

The graph of the function f(x) = x(x - 5)(x - 3) is given by the image shown at the end of the answer.

To draw the sketch of the graph, we need to consider these three following features:

The function in this problem is defined as follows:

f(x) = x(x - 5)(x - 3).

From the factor theorem, the x-intercepts are taken from the linear factors, as follows:

The y-intercept is the value of y when the graph of the function crosses the y-axis, that is, the value of y when x = 0, hence:

f(0) = 0(0 - 5)(0  -3) = 0.

In the problem, we have a cube function, hence:

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The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.

The slope-intercept form a line is given by  

where m is the slope of a line and c is the y-intercept.

Here we use the Slope intercept form to find the line of the equation by using the equation we will draw the graph of the line

Here we have

Slope of line = -4/3

The point of the line

As we know y = mx + c is the line Here m is the slope of the line

From the given data, m = -4/3

=> y = (-4/3)x + c

=> 3y = -4x + 3c

Given that the point on the line is (-6, 2)

=> 3(2) = -4(-6) + 3c

=> 6 = 24 + 3c

=>  3c = 18

=> c = 6

Therefore,

The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.

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There are $21.5 money was spent on a pass and lunch for each student.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that:

The amount spent by school on pass of 40 students and 3 teachers = $546.53

And, the amount spent for the lunch only for students = $351.60

Now,

The money spent for pass of 43 person = $546.53

Then, The amount of pass for each person  = 546.53/43

                                = $12.71

Since, there are 40 student then amount of lunch for each students = ⇒ 351.60/40

⇒ $8.79

Therefore, amount of pass and lunch for each student = 12.71 + 8.79

                              = $21.5

Thus, $21.5 is the required answer.

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The fractions reduced to standard form are -2/5, 1/5, 1/2 and 5/11 for 1), 2), 3), and 4) respectively

To reduce a fraction to standard form, you need to divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). The GCD is the largest number that can be evenly divided into both the numerator and the denominator.

Given:

1) -18/45

The GCD of 18 and 45 is 9. Thus:

-18/45 = -2/5

2) -3/-15

The GCD of 3 and 15 is 3. Thus:

-3/-15 = 1/5

3) 28/56

The GCD of 28 and 56 is 28. Thus:

28/56 = 1/2

4) 45/99

The GCD of 45 and 99 is 9. Thus:

45/99 = 5/11

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1)-6/15

2)1/5

3)1/2

4)5/11

1) -18/45

⇒-6/15

2)-3/-15

⇒-1/-5

⇒1/5

3)28/56

⇒4/8

⇒1/2

4)45/99

⇒15/33

⇒5/11

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yes, z can lie between x and y but z can also lie on another side of x in Number lines.

With an example, define number line?

Number lines in mathematics are horizontal straight lines on which numbers are arranged in equal intervals.

                  A number line can be used to visualize all the numbers in a succession. The endpoints of this line go on forever.

What does the math number line mean?

A horizontal line with uniformly spaced numerical increments is called a number line. How the number on the line can be answered will depend on the numbers that are provided.

                               How a number is used—for example, to plot a point—depends on the question that goes with it.

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Answer:

y = 1/4x - 4

Step-by-step explanation:

4x + y = 3

y = -4x + 3

Perpendicular slope = 1/4

y = 1/4x + b

-3 = 1/4(4) + b

-3 = 1 + b

b = -4

y = 1/4x - 4

Only member B and D will reach their goal.

Given;

Amount to be saved = $285

Total time to save money = 5 weeks

Now,

For member A:

Working hours = 8 per week

per hour earnings = $6.15

Therefore,

The total amount collected

= working hours per week × Total weeks × Earning per hour

= 8 × 5 × 6.15

= $246

For member B:

Working hours = 10 per week

per hour earnings = $5.85

Therefore,

The total amount collected

= working hours per week × Total weeks × Earning per hours

= 10 × 5 × 5.85

= $292.5

For member C:

Working hours = 7 per week

per hour earnings = $7.25

Therefore,

The total amount collected

= working hours per week × Total weeks × Earning per hours

= 7 × 5 × $7.25

= $253.75

For member D:

Working hours = 9 per week

per hour earnings = $6.35

Therefore,

The total amount collected

= working hours per week × Total weeks × Earning per hours

= 9 × 5 × $6.35

= $285.75

Since, the amount earned by member B and D is greater than the goal amount and the amount earned by member A and C is less than the goal amount

therefore,

Only member B and D will reach their goal

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Your question is incomplete. Please find the missing content below:

To be able to go on the band trip, four band members each get a part-time job. Each person has 5 weeks in which to save his or her money. Analyze the four individual plans below and decide which of the four people will reach his or her goal of saving $285? Member A: Works 8 hours per week at $6.15 per hour Member B: Works 10 hours per week at $5.85 per hour Member C: Works 7 hours per week at $7.25 per hour Member D: Works 9 hours per week at $6.35 per hour

Answer:

2,228

Step-by-step explanation:

Each unit will make 13.25 in profit before incorporating the one time cost. This means that 29,521/13.25= the amount needed to break even.

The total amount that Mikaela spent on the paddleboard will be  $449.80.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths.

As per the given,

Original price = $699

The selling price = $699 - 40% of $699

⇒ $699 - 0.40 x $699 = $419.4

The state tax (assuming it applied to the selling price) will be as,

7.25% of $419.4 = (7.25/100) x 419.4 = $30.4065

Final amount = $419.4 + $30.4065 = $449.80

Hence "Mikaela will have spent $449.80 in total on the paddleboard".

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Answer:

Step-by-step explanation:

Answer:

[tex]51.4^{\circ}[/tex]

Step-by-step explanation:

Since this is a right triangle, the cosine formula says

[tex]\cos(x) = \dfrac{5.3}{8.5}[/tex]

[tex]\longrightarrow cos(x) = 0.6235[/tex]

[tex]So\\\\x = \cos^{-1}(0.6235) = 51.4256^{\circ}[/tex]

Rounded to the nearest tenth this would be
[tex]51.4^{\circ}[/tex]

answer : 26

steps

get hypotenuse

a² + b² = c²

7² + 8² = c²

49 + 64 = c²

113 = c²

square root of c is √113 which 10.63

7 + 8 + 10.63 = 25.63

The compound interest received by Matthew Westhoven is $51.80

The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You'll have $110.25 after the second year is over.

Given, the principal amount (P) = $925

Compound interest percentage (r) = 5.5% = 0.055

Time period (t) = 1

Since, it is semiannually compounded (n) = 2*t = 2

Amount (A) = P(1 + r/n)^nt

= 925(1 + 0.055/2)^2

= 925(1.0275)^2

= 925(1.056)

= 976.80

Thus, Interest amount (CI) = A - P

= $976.80 - $925

= $51.80

The compound interest received by Matthew Westhoven is $51.80

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Answer:

The cake cost $6.00

Step-by-step explanation:

Let c = the cost of the cake

Let t =  the cost of the tea

c = 2t

c + 5t = 21  Substitute 2t for c

2t + 5t = 21  Combine like terms

7t = 21  Divide both sides by 7

[tex]\frac{7t}{7}[/tex] = [tex]\frac{21}{7}[/tex]

t = 3  

A cup of tea costs $3.00

c = 2t  Substitute 3 for t

c = 2(3)

c = 6

A cake costs $6.00

Answer:

Cake: £6

Step-by-step explanation:

1c = 2t             Eq. 1

1c + 5t = 21      Eq. 2

c = cost of a cake

t = cost of a cup of tea

Replacing Eq. 1 in Eq 2:

2t + 5t = 21

7t = 21

t = 21/7

t = 3

From Eq. 1:

c = 2t

c = 2*3

c = 6

Check:

From Eq. 2:

c + 5t = 21

6 + 5*3 = 21

6 + 15 = 21

Calculation the variance and standard deviation of the discrete random variable is given by σ² = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex] and standard deviation is the square root of Variance 'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].

As given in the question,

Therefore , the variance and standard deviation of the discrete random variable is calculated with the help of the following formulas:

Variance 'σ²' = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex]  and standard deviation  'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].

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