Write an equation and solve. Valerie makes a bike ramp in the shape of a right triangle.
The base of the ramp is 4 in more than twice its height, and the length of the incline is 4 in less than three times its height. How high is the ramp?

Answer:

multiply by -3, multiply by -2, multiply by -1, ...

Step-by-step explanation:

Answer:

1. x = 8

2. x = 3

3. x = 25

4. x = 6

5. x = 11

6. x = 3

7. x = 6

8. x = 10

Step-by-step explanation:

Since the opposite sides of a parallelogram are congruent, the length of segment QR is equal to the length of segment PS.

10 = -6 + 2x

Add 6 to each side

10 + 6 = -6 + 6 + 2x

Simplify each side

16 = 2x

Divide both sides by 2

16/2 = 2x/2

Simplify

x = 8

to check if x is correct:

you already know that  segment QR is 10, so your answer needs to be equal to 10

so sement PS is -6x + 2x

-6 + 2x

= -6 + 2(8)

= -6 + 16

= 10

so PS = 10

2. 34x + 5 = 35x + 2

Step 1: Subtract 35x from both sides.

34x + 5 − 35x = 35x + 2 − 35x

−x + 5 = 2

Step 2: Subtract 5 from both sides.

−x + 5 − 5 = 2 − 5

−x = −3

Step 3: Divide both sides by -1.

-x/-1 = -3/-1

Step 4: Simplify

x = 3

3.

115 = 2x + 65

Step 1: Flip the equation.

2x + 65 = 115

Step 2: Subtract 65 from both sides.

2x + 65 − 65 = 115 − 65

2x = 50

Step 3: Divide both sides by 2.

2x/2 = 50/2

x = 25

4.

84 + 16x = 180

84 - 84 + 16x = 180 - 84

16x = 96

16x/16 = 96/16

x = 6

5.

2(3x − 10) = 46

Step 1: Simplify both sides of the equation.

2(3x − 10) = 46

(2)(3x) + (2)(−10 )= 46(Distribute)

6x + −20 = 46

6x − 20 = 46

Step 2: Add 20 to both sides.

6x − 20 + 20 = 46 + 20

6x = 66

Step 3: Divide both sides by 6.

6x/6 = 66/6

x = 11

6. RH = 1/2 FH or RH = 2 × FH

Step 1: Simplify both sides of the equation.

(2)(12)=13x−2

24=13x+−2

24=13x−2

Step 2: Flip the equation.

13x−2=24

Step 3: Add 2 to both sides.

13x−2+2=24+2

13x=26

Step 4: Divide both sides by 13.

13x/13 = 26/13

x = 3

7.

2x+2=3x−4

Step 1: Subtract 3x from both sides.

2x+2−3x=3x−4−3x

−x+2=−4

Step 2: Subtract 2 from both sides.

−x+2−2=−4−2

−x=−6

Step 3: Divide both sides by -1.

-x/-1 = -6/-1

x = 6

8.

2(2x−6)=28

Step 1: Simplify both sides of the equation.

2(2x−6)=28

(2)(2x)+(2)(−6)=28(Distribute)

4x+−12=28

4x−12=28

Step 2: Add 12 to both sides.

4x−12+12=28+12

4x=40

Step 3: Divide both sides by 4.

4x/4 = 40/4

x = 10

Answer:

Option B.

Step-by-step explanation:

The measure of cage is 90 feet by 40 feet.

Length of rope \(=40\sqrt{2}\) foot

It is clear that, length of rope is greater than one side of cage and raw a line which divides the cage in two parts as shown in below figure.

We need to find the shaded area.

By Pythagoras theorem:

\(hypotenuse^2=base^2+perpendicular^2\)

\((40\sqrt{2})^2=(40)^2+perpendicular^2\)

\(3200=1600+perpendicular^2\)

\(3200-1600=perpendicular^2\)

\(1600=perpendicular^2\)

\(40=perpendicular\)

So, it is a square.

From the figure it is clear that the shaded area contains 1/8th part of circle are half part of square.

Area of circle is

\(A_1=\pi r^2\)

\(A_1=\pi (40\sqrt{2})^2\)

\(A_1=3200\pi\)

Area of square is

\(A_2=a^2\)

\(A_2=(40)^2\)

\(A_2=1600\)

Area of shaded portion is

\(A=\dfrac{A_1}{8}+\dfrac{A_2}{2}\)

\(A=\dfrac{3200\pi}{8}+\dfrac{1600}{2}\)

\(A=400\pi+800\)

\(A=400(\pi+2)\)

The required area is \(400(\pi+2)\) sq. ft.

Therefore, the correct option is B.

Answer:

x^2−8x+16

Step-by-step explanation:

Answer:

x^2 - 8x + 16

Step-by-step explanation:

(x-4) (x-4)

your multiplying the first parentheses by the second

x^2 -4x -4x +16

-4x -4x = -8x

x^2 -8x + 16

Answer: B) 19

Step-by-step explanation:

To solve this problem, simply plug in -4 for x:

\(f(x)=x^{2} +3\\f(x)=(-4)^{2} +3\\f(x)=16+3\\f(x)=19\)

Hope it helps :) and let me know if you want me to elaborate/explain further

Answer:

D. -13

Step-by-step explanation:

If you substitute -4 in for x you get -4^2+3, so when you simplify you get -16+3 which equals -13.

f(x)=x^2+3

f(-4)= -4^2+3

f(-4)= -16+3

f(-4)= -13

The element that orients readers by previewing the structure of the report is "Organization."

Organizing a report effectively helps readers understand the flow of information and the logical structure of the content. By providing an overview of the organization, readers can anticipate the main sections, their sequence, and the connections between them.

The organization element typically includes headings, subheadings, and a clear hierarchy of information. It outlines the main sections and subsections of the report, indicating how they are related and how they contribute to the overall message or argument.

In addition to the organization element, the other options listed—Definitions of key terms and Sources and methods—also play important roles in a report. Definitions of key terms clarify terminology and provide a common understanding, while Sources and methods explain the sources of information and the methods used in the report's research or analysis. However, in the context of previewing the structure, the Organization element specifically serves this purpose.

to learn more about organization click here:brainly.com/question/12825206

#SPJ11

In general, for any binary number x, the function f(x) replaces the first bit with "00".

The correct description of the function f(x) is that it performs a bitwise operation on x where it replaces the first bit with "00".

In binary representation, each digit in a number is called a bit. For example, the number 101 can be represented in binary as "1 0 1", where each digit is a bit.

When we apply the function f(x) to the number 101, it replaces the first bit (which is "1") with "00". So, the resulting number is 0001.

To know more about number visit:

brainly.com/question/3589540

#SPJ11

The required measure of the angle x is given as 117.38°.

A triangle is given with a measure of.
a = 50, b = 55 and c = 90ft

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
Apply cosine formula,
c² = a² + b² -2abcosx
Substitute the value in the above expression,
90² = 50² + 55² - 2×50×55×cosx
cosx = -0.46
x = cos⁻¹[-0.46]
x = 117.38°

Hence, as a result, the measure of the angle x is 117.38°.

Learn more about triangles here:
https://brainly.com/question/2773823

#SPJ1

Answer:

36

Step-by-step explanation:

Let Brandon's age be b. We can write 4b = b + 27 which gives us b = 9. Because Michael is 4 times as old as Brandon, he is 9 * 4 = 36 years old.

Answer:

36

Step-by-step explanation:

Micheal is 4 times as old as Brandon.

y = 4x

Micheal is also 27 years older than Brandon.

y = x +27

Y represents Micheal's age, and x represents Brandon's age.

Since both equations above are equal to the same value, y, you can set the two equations equal to each other.  Solve for x.

4x = x + 27

3x = 27

x = 9

Brandon is 9 years old.  

Plug Brandon's age into one of the equation to solve for Micheal's age.

y = x + 27

y = 9 + 27

y = 36

Micheal is 36 years old.

Answer:

the bigger rectangle = 30 x 5

Step-by-step explanation:

divide the bigger width by the smaller width to find the rate of change (2.5) and multiply both numbers (length and width) to get the larger rectangle.

Answer:

30

Step-by-step explanation:

30

Answer: The exponent

Step-by-step explanation:

\(In\ \boxed{a(b^x))}\)

a is the coefficient,

b is the base

x is the exponent

If something is written in its simplest radical form, that means that you have already found all possible roots and eliminated any radicals from the denominator of a fraction. ... For example, if your fraction is 2/√7, multiply by √7/√7 to get 2√7/√49. This will simplify to 2√7/7.  hope this helps

Answer:

Square roots are the opposite of “squaring” a number, or multiplying it by itself. For example, three squared is nine (3 2 = 9), so the square root of nine is three. In symbols, this is √9 = 3. The “√” symbol tells you to take the square root of a number, and you can find this on most calculators.

Step-by-step explanation:

hope it helps

Answer:

The answer is quad 1 and quad 2 are congruent because quad 2 can be created rotating and then translating quad 1

Step-by-step explanation:

Answer:

y≤-2x=+1

Step-by-step explanation:

this will definitely on coordinate plan.

Kindly completed your question as it seem unfinished

95% confidence interval : 30713 persons to 32433 persons.

The confidence interval is the mean of your estimate plus and minus the change in that estimate. This is the range of values ​​within which, with a certain level of confidence, you would expect your estimate to fall if you retest. In statistics, confidence levels are another way of describing probabilities.

According to the Question:

n = 100

x = 31,578

σ = 4413

class interval = 95% = 0.95

To construct a 95% confidence interval, we use the formula:

                          x ± z(σ/ √n)

α = 1 - CL = 1 - 0.95 =0.05

From the z score, Z(0.05) = Z (0.05/2) = Z 0.0025

Confidence Interval = X± 8 = X - 8= X+8

= (31578-865.34, 31578+ 865.34)

= (php 30713, php 32443)

Therefore, At 95% confidence interval There are 30713 person 32443 person.

Learn more about Interval:

https://brainly.com/question/13708942

#SPJ4

The statement is true: A number

\(�\)

c is an eigenvalue of an

\(�×�n×n matrix �A if and only if the equation (�−��)�=0(A−cI)x=0\)has a nontrivial solution.

To justify this answer, let's consider the reasoning:

Definition of Eigenvalue:

An eigenvalue of a matrix

\(�A is a number �c such that there exists a non-zero vector �x�=��Ax=cx.\)

Rewriting the Eigenvalue Equation:

The equation

\(��=��\)

Ax=cx can be rearranged as

\((�−��)�=0\)

(A−cI)x=0, where

�

I is the

\(��\)

n×n identity matrix.

Nontrivial Solution:

For the equation

\((�−��)�=0\)

(A−cI)x=0 to have a nontrivial solution, there must exist a non-zero vector

�

x such that

\((�−��)�=0(A−cI)x=0.Non-Zero Vector �x:If (�−��)�=0\)

(A−cI)x=0 has a nontrivial solution, it means that there exists a non-zero vector

�

x that is in the null space (kernel) of

\((�−��)(A−cI), i.e., �≠0x=0 and (�−��)�=0(A−cI)x=0.\)

Null Space and Eigenvalues:

The null space of

\((�−��)\)

(A−cI) contains all vectors

\(�x such that (�−��)�=0(A−cI)x=0.\) Therefore, if there exists a non-zero vector

�

x in the null space, it implies that

�

c is an eigenvalue of

�

A.

Conversely, if

�

c is an eigenvalue of

�

A, then there exists a non-zero vector �

x that satisfies

(\(�−��)�=0(A−cI)x=0. This implies that (�−��)\)(A−cI) is singular, and hence,

\((�−��)�=0(A−cI)x=0 has a nontrivial solution.\)

Based on these justifications, we can conclude that the statement is true: a number

\(�c is an eigenvalue of an �×�n×n matrix �A\) if and only if the equation

\((�−��)�=0\)

(A−cI)x=0 has a nontrivial solution.

Learn more about eigenvalue here:

https://brainly.com/question/14415841

#SPJ11

Answer: perpendicular lines

Step-by-step explanation: try Desmos :) its a life saver ;)

Answer: Yes

Step-by-step explanation:

Yes area should be right because you are finidng how much it covers which would be area. A way I used to remember it was you looking for the AREA it covers so that awnser is area! Hope that helped!

Answer:

\(720^o=4\pi\)

Step-by-step explanation:

Given : \(720^o\)

To Find : What is 720° converted to radians?

Solution :

1 degree = \(\frac{\pi }{180}\) \(radian\)

So, \(720^o=\frac{\pi }{180} *720\)

\(720^o=4\pi\)

So, Option D is true

Hence \(720^o=4\pi\)

Hello!

The perimeter is the sum of all sides of the figure. As we know, this is rectangular parking with a length equal to 69m. Look at the figure below:

As we know the definition of the perimeter, we can sum all sides, look:

Answer for A:

width of the parking lot = 58m.

We'll solve it in a similar way.

The area of a rectangle is obtained using the formula:

Replacing the values, we'll obtain:

Answer for B:

length of the pool = 78m.

Answer:

y = 3x + 9

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 7 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes , then

y = 3x + c ← is the partial equation

to find c substitute (- 6, - 9 ) into the partial equation

- 9 = - 18 + c ⇒ c = - 9 + 18 = 9

y = 3x + 9 ← equation of parallel line

Answer:

a

Step-by-step explanation:

I go it right on my test

;)

Answer:

36

Step-by-step explanation:

so 50% is half so you have to multiply the number by two to get 36 Have a great day!

Answer:

31/100. it cannot be simplified.

Step-by-step explanation:

The probability of failing both and passing just physics is 1.45 when student has a 75% probability of passing physics and an 80% chance of passing arithmetic.

Given that,

A student has a 75% probability of passing physics and an 80% chance of passing arithmetic. Let's say there is a 10% chance that the kid will fail math and physics. are math and physics grades independent.

We have to determine the probability of failing both and passing just physics.

We know that,

Let A represent students passes in physics

Let B represent math's students.

P(A) = 0.75

P(B) = 0.8

P(A∩B)=0.1

P(A∪B)= P(A)+P(B)-P(A∩B)

=0.75+0.8-0.1

=1.45

Therefore, The probability of failing both and passing just physics is 1.45 when student has a 75% probability of passing physics and an 80% chance of passing arithmetic.

To learn more about probability visit: https://brainly.com/question/11234923

#SPJ4

Minimum percentage: 96% of the data set lies between 50 and 100.

The value of k:

Mean – (k) (sd) = lower limit

75 – 5K - 50

75 – 50 = 5k

25 = 5k

K = 5

For the percentage, we are using:

1 – 1/k^2.

1 - 1/ 25 = 24/25 = 96%

You can learn more about Percentage from:

https://brainly.com/question/2155156

#SPJ4

To find the surface area of the figure, we need to consider the individual surfaces and add them together.

First, let's identify the surfaces of the figure:

The lateral surface area of the larger prism (excluding the base)

The two bases of the larger prism

The lateral surface area of the smaller prism (excluding the base)

The two bases of the smaller prism

The lateral surface area of a prism is given by the formula: perimeter of the base multiplied by the height.

The bases of the prisms are rectangles, so their areas can be calculated by multiplying the length by the width.

To find the missing prism's surface area, we need to consider that it is a smaller prism nested inside the larger prism. The lateral surface area and bases of the missing prism should also be included.

Once we have calculated the individual surface areas, we add them together to find the total surface area of the figure.

Without specific measurements or dimensions of the figure, it is not possible to provide a numerical answer. Please provide the necessary measurements or dimensions to calculate the surface area.

Learn more about surface here

https://brainly.com/question/16519513

#SPJ11