Isaiah sketches a model of a skateboard ramp. The model has two surfaces on which to skate, represented by sides AB and AD in the diagram.

Triangle A B D is shown. A perpendicular bisector cuts angle B A D to form triangle A B C. Triangle A B C has angle measures 45, 45, and 90 degrees. Triangle A C D has angle measures 60, 30, and 90 degrees.

The steepest side of the model, AB, measures 4 inches. What is the length of the other skating surface, AD?
2 StartRoot 2 EndRoot in.
2 StartRoot 3 EndRoot in.
4 StartRoot 2 EndRoot in.
4 StartRoot 3 EndRoot in.

Answer:

36

Step-by-step explanation:

MC : BC : MB = 1 : √3 : 2

MC : BC = 1 : √3

12 : BC = 1 : √3

BC = 12 : 1/√3

BC = 12 × √3/1

BC = 12 × √3

BC = 12√3

MC : MB = 1 : 2

12 : MB = 1/2

MB = 12 : 1/2

MB = 12 × 2/1

MB = 12 × 2

MB = 24

AB = 2BD

AB = 2CD√3

AB = 2(½BC)√3

AB = 2(½ × 12√3) √3

AB = 2 × 6√3 × √3

AB = 12 × √9

AB = 12 × 3

AB = 36

The sides of the right-angle triangle will be 16 units and 20.30 units. And the missing angle will be 52°.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The side AC will be

tan 38° = 12.5 / AC

      AC = 15.999

      AC ≈ 16 units

Then the side AB will be

AB² = 12.5² + 16²

 AB = 20.30 units

We know that the angle sum is 180 degrees. Then we have

∠A + ∠B + ∠C = 180°

38° + ∠B + 90° = 180°

                  ∠B = 52°

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The area of the enlarged picture on the wall is gotten as; D: 486 in²

The formula for Linear scale factor is;

L.S = Image distance/object distance

Thus, from the attached image, we can find the Linear scale factor as;

L.S = OL'/OL

L.S = 54/ 12

L.S = 9/2

Area scale factor is equal to the square of linear scale factor. Thus;

Area scale factor = (9/2)²

Area scale factor = 81/4

Now,

81/4 = Area of larger rectangle/Area of smaller rectangle

Area of the smaller rectangle = 4 ×6 = 24 in²

Thus;

Area of enlarged picture on wall = (81/4) × 24

Area of enlarged picture on wall = 486 in²

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Answer:

Step-by-step explanation:

its D

Answer:

15

Step-by-step explanation:

→ Write the ratio of men to days to hours

30 : 12 : 8

→ Write the new proportion

24 : x : 8

→ Find the multiple between 30 and 24

1.25

→ Multiply by 12

12 × 1.25 = 15

On the first two pairs you need to write 3 and 4, and 6 and 2.

On the second page we have:

1) 4

2) 2 and 7

3) 1

4) 1 and 3

5) 3.

a) Here we just need to use scientific notation.

For the first case, the numbers that go in the exponent boxes are the same ones that go in the example, which are 4 in the first one and 2 on the second one.

Then, if we want the difference to be 29,400, then we can use 3 on the first box and 6 on the second. OR, because this is an absolute value, we can just invert those.

This is:

6 and 2 on the first two squares, and 3 and 4 on the second two squares.

b) Here we want to make perfect squares.

For example, on the first case we have:

x*2*2

We need to find the value of x such that this is a perfect square. Notice that we can rewrite this as:

x*2*2 = x*4

Then it only is a perfect square if x = 4.

For the second case:

14*x*y

This is only a perfect square if x*y = 14

Then we can use x = 2 and y = 7.

With similar reasoning, on the next box we have:

2*8*x

2*8 = 16, is already a perfect square, so x = 1.

The next one is:

x*3*y

Here we can define x = 3 and y = 1, so we get a perfect square.

Finally:

3*x

Here the only possible value of x is 3.

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Step-by-step explanation:

there are 2 main approaches (in their core they are the same, of course, but they look different) :

1. use one equation to express one variable by the second, and then use this in the second equation to solve for the remaining variable. with that you go back into the first equation and solve for the first variable.

2. multiply both equations by certain factors as needed, then add both results, so that there is one summary equation with only one variable, and then solve for it. then use that in one of the original equations and solve for the second variable.

using 1.

3x + 2y = 1

3x = 1 - 2y

x = (1 - 2y)/3

2x + 7y = 3

2(1 - 2y)/3 + 7y = 3

2(1 - 2y) + 21y = 9

2 - 4y + 21y = 9

17y = 7

y = 7/17

x = (1 - 2y)/3 = (1 - 2×7/17)/3 = (1 - 14/17)/3 =

= (17/17 - 14/17)/3 = 3/17 / 3 = 1/17

using 2.

multiply first equation by 2, the second by -3

6x + 4y = 2

-6x - 21y = -9

----------------------

0 -17y = -7

-17y = -7

17y = 7

y = 7/17

and so on (as under 1.).

Step-by-step explanation:

First, you can multiply the both equation by one of the coefficient of either X or Y as shown above.

Secondly, after doing that you can multiply one of the equations by the negative sign in order for one of the coefficient to cancel out.

From there you can find X

After getting X , you can put the answer you get into any equation of your choice. collect like terms and then you'll find Y.

Hope this helps. If you don't understand use the picture if the solving above for better explanation. Thanks

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What's the equation with a slope of -4 that goes through (-1,1)? find it

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The equation used, here is [tex]\bf{y-y1=m(x-x1)}[/tex].

[tex]\bf{y-1=-4(x-(-1)}[/tex] | simplify after putting in the information given

[tex]\bf{y-1=-4(x+1)}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

                          [tex]\bf{=y-1=-4(x+1)}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

Answer:

The distrubutive property

-9(n-4)

=-9n+36

The number of problems that were on the text was 240 problems.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the total number of problems that were on the text, y represent the time to be spent, hence:

y = x/8

Also:

y - 6 = x/10

x/8 - 6 = x/10

x = 240

The number of problems that were on the text was 240 problems.

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The setup boxes in the synthetic division are (b)

The dividend is given as:

x^3 + 4x^2 + x - 6

The divisor is given as:

x - 2

Set the divisor to 0

x - 2 = 0

Solve for x

x = 2

Remove the variables in the dividend

1 + 4 + 1 - 6

Remove the arithmetic signs

1  4  1 - 6

So, the setup is:

2 | 1  4  1 - 6

Hence, the setup boxes are (b)

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The solution to the system of equation is ( -4.5 , -2)

A system of equation is a set of equations that have a common solution.

The set of equation given are

-2x +4y  = 1

-4x +3y = 12

To find the solution , Elimination Method will be used

Multiplying equation 1 by 2 and then

Subtracting equation 1 by 2

-4x +8y = 2

-4x +3y = 12

+        -       -

5y = -10

y = -2

Substituting this value to determine the value of x

-2x -8 = 1

-2x = 9

x = -4.5

Therefore the solution to the system of equation is ( -4.5 , -2)

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The first quartile of the data set is 28.

From the question, we are to determine the first quartile of the given data set

The first quartile or lower quartile, (Q1), is the value under which 25% of data points are found when they are arranged in increasing order.

The given data set is

14,28,33,42,53,81,97

In the given data set, the first quartile is 28.

Hence, the first quartile of the data set is 28

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Triangle JHK and GHL are congruent based on the angle-angle-angle congruency theorem.

Two triangles are said to be congruent if they have the same shape and angles. The ratio of their corresponding sides are also to be proportional.

Given triangle JHK and GHL are congruent based on the angle-angle-angle congruency theorem.

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Answer:

Distance on the graph is representing the distance from Michelle's home. On her morning jog, Michelle ran to the end of her street, turned around and jogged at a slower pace back home.

The additional information needed to prove both triangles are similar are:

A. ∠B ≅ ∠M

C. △ABC was rotated and dilated by a scale factor between 0 and 1

E. ∠C ≅ ∠L

When a triangle is rotated and dilated by a scale factor, the new triangle formed has the same shape but different size of the original triangle. However, all its corresponding angles remains congruent.

Thus, for triangles ABC and NML to be similar to each other, since we already known each have one congruent right angles, the additional information needed are:

A. ∠B ≅ ∠M

C. △ABC was rotated and dilated by a scale factor between 0 and 1

E. ∠C ≅ ∠L

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The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as risk analysis

Risk analysis is define as the the process of identifying and analyzing potential issues that could negatively impact key business initiatives or projects. This process is done in order to help organizations avoid or mitigate those risks.

So, The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as risk analysis

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Answer:

12stickers

Step-by-step explanation:

that's all I could do.have a nice day.hope it helps.

The equation in point slope form is y-1 = 1/4(x - 12)

The formula for calculating the equation of a line is expressed as;

y = mx + b

m is the slope

b is the intercept

Slope = 1+3/12+4

Slope = 4/16

Slope = 1/4

For the intercept

1 = 1/4(12) + b

b = 1 - 3

b = -2

Hence the equation in point slope form is y-1 = 1/4(x - 12)

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The standard form is:

4y - x = -8

We know that the point-slope equation of the line is:

y - 1 = (1/4)*(x - 12)

Expanding the right side, we get:

y - 1 = (1/4)*x - 3

Now we can move the term with x to the left side:

y - (1/4)*x = +1 - 3

y - (1/4)*x = -2

Now we can multiply both sides by 4:

4y - x = -8

This is the standard form of the linear equation.

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If Jay spends 40 at the store, the number of points he will earn is; 10 points

Let the number of rewards points a customer earns be y

Let the amount of money, in dollars, that the customer spends at the store be x.

Since the number of rewards points a customer earns varies directly with the amount of money, in dollars, that the customer spends at the store, then we can say that;

y ∝ x

Thus;

y = kx

where k is the constant of proportionality.

We are given x = 15 when y = $60. Thus;

60 = 15k

k = 60/15

k = 4

If Jay spends $40, it means the number of points will be;

40 = 4x

40/4 = x

x = 10 points.

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The height of the wall from the question is 13.27ft

The theorem states that the square of the longest side is equal to the sum of square of other two sides.

From the given question

Hypotenuse (ladder length) = 15ft

Adjacent = 7feet

Required

Height of the wall H

According to the theorem

15² = 7² + H²

H² = 225 - 49

H² = 176

H = 13.27feet

Hence the height of the wall from the question is 13.27ft

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Answer:

I think it's C

Step-by-step explanation:

Hope it helps

Answer:

[tex]\frac{(20x+12)}{2}[/tex] and [tex]\sqrt{100x^2+36}[/tex]

Step-by-step explanation:

The expression 2(5x + 3) equals 10x + 6

One other way to get 10x + 6

[tex]\frac{(20x+12)}{2}[/tex]

finally, you could do:

[tex]\sqrt{100x^2+36}[/tex]

Answer:

= ax + b ln x - c/x + C

Step-by-step explanation:

Recall:

integral a dx = ax + C

integral 1/x dx = ln x + C

integral x^(n) = [x^(n +1)]/(n + 1) + C

Also:

c = variable in this problem

C = constant you add when you integrate

Separate each term of the numerator and set it over the denominator.

integral (ax^2 + bx + c)/x^2 dx =

integral [(ax^2)/x^2 + (bx)/x^2 + c/x^2] dx

Simplify each term and separate into the sum of 3 integrals.

= integral (a dx) + integral (b/x dx) + integral (c/x^-2) dx

= ax + b ln x + (cx^-1)/(-1) + C

= ax + b ln x - c/x + C

Answer:

-b

Step-by-step explanation:

Hello!

Rate of income tax = Tax paid / Monthly income

⇒ Rate = 8,000 / 40,000

⇒ Rate = 0.2

⇒ Rate = 20%

∴ The rate of income tax is 20%.

The other equality which must be stated by Jose is that angles BAC and BAE are congruent and their measures are equal.

It follows from the task content that Jose is trying to prove the congruence of both triangles by means of the Side-Angle-Side congruence theorem.

It therefore follows that since, Jose has identified that the ratio of corresponding sides are equal as indicated in the task content, the equality which Jose has to state is the angle congruence equality.

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Answer:

9x ^ 6 -9x ^ 2-2x + 1

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

Answer:1\6

Step-by-step explanation:

Answer:

  2.36 liters

Step-by-step explanation:

The volume Janet wants is 1/3 of 1/2 of the volume of a sphere with radius 15 cm. The formula for the volume of a sphere is given.

The water volume is ...

  V = (1/3)(1/2)(4/3π)(15 cm)³ = 750π cm³ ≈ 2356 cm³

There are 1000 cm³ in 1 liter, so Janet needs about ...

  2356 cm³/(1000 cm³/L) = 2.356 L

Janet should put about 2.36 liters of water in the fish tank.

Answer:

it is all I could.

Hope it helps

The second transformation is a rotation about point H.

It should be noted that a congruent triangle simply means when two triangles have the same sides and the same angles.

As two rigid transformations, to map ΔHJK to ΔLMN.

The first is a translation of vertex H to vertex L, and the second transformation is a rotation about point H.

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Answer:

B. a rotation about point H

Step-by-step explanation:

got it correct on my quiz