Type the correct answer in each box. Use numerals instead of words for numbers.
Soccer ball specifications require a diameter of 8.65 inches with an allowable margin of error of 0.05 inch.

Use this information to complete these statements.

The equation that can be used to find d, the diameter of a new soccer ball, is |

| =
.

The minimum possible diameter of a soccer ball is
, and the maximum possible diameter is
.

Reset

The leg measurement will make a right triangle is 21 cm.

The longest side of a right-angled triangle, i.e. the side opposite the right angle, is called the hypotenuse in geometry.

Pythagorean theorem :

If p be the length of the hypotenuse of a right-angled triangle, q and r be the lengths of the other two sides, then

p² = q² + r²

The lengths of the other two sides of the given right-angled triangle are 20 cm and 21 cm. Put these values in the above theorem to get the desired result.

Now, p² = (20)² + (21)²

= 400 + 441 = 841

i.e. p = √(841) = 29

Therefore the length of the hypotenuse is 29 cm. The right angle traingle is 21 cm.

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We can conclude that cosh2x−sinh2x=1.

An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.

To show that cosh2x−sinh2x=1, we can use the identities for cosh2x and sinh2x. The identity for cosh2x is cosh2x=2cosh2x−1 and the identity for sinh2x is sinh2x=2sinh2x−1.

Substituting these identities into the equation cosh2x−sinh2x=1 yields 2cosh2x−1−2sinh2x−1=1. Simplifying this equation yields cosh2x−sinh2x=1, as required. Thus, we can conclude that cosh2x−sinh2x=1.

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Simplifying this equation yields [tex]\cosh^2x-sinh^2x=1[/tex], as required. Thus, we can conclude that [tex]\cosh^2x-sinh^2x=1[/tex].

An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.

We will show that [tex]\cosh^2x-sinh^2x=1[/tex].

Let us consider the expression [tex]\cosh^2x-sinh^2x.[/tex]

Then, [tex]\cosh^2x=(e^2x+e^{-2}x)/2[/tex] and [tex]sinh^2x=(e^2x+e^{-2}x)/2[/tex]

Substituting, we get [tex]\cosh^2x -\sinh^2x=(e^2x+e^{-2}x)/2\ -(e^2x+e^{-2}x)/2[/tex]

Simplifying, we have [tex]\cosh^2x -\sinh^2x=e^2x+e^{-2}x-e^2x+e^{-2}x[/tex]

[tex]=2e^{-2}x\\\\=2(e^{-2}x)\\\\=2[/tex]

Hence, [tex]cosh^2x-sinh^2x=1[/tex]

Therefore, we have shown that [tex]cosh^2x-sinh^2x=1[/tex]

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The correct form of question is Show that cosh2x−sinh2x=1 .

Answer:

  -3

Step-by-step explanation:

You want the graphical solution to x² +6x +9 = 0.

The graph of the expression on the left shows it has a value of 0 when x = -3.

The solution is x = -3.

__

Additional comment

A graphing calculator is very helpful when you want a graphical solution.

If you want to graph this by hand, you can rewrite it as ...

  (x +3)² = 0

The graph of (x +3)² is a graph of the parent function y = x² after it has been shifted left 3 units. The graph will go through points (-5, 4), (-4, 1), (-3, 0), (-2, 1), (-1, 4). Of course the point at (-3, 0) indicates the solution is x=-3.

The best prediction possible for the number of times the spinner will land on green or blue is given as follows:

30 spins.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Out of six regions, three are green and two are blue, hence the probability of one spin resulting in green or blue is given as follows:

p = (3 + 2)/6

p = 5/6.

Thus the expected number out of 36 trials of spins resulting in green or blue is given as follows:

E(X) = 5/6 x 36

E(X) = 30 spins.

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The expression that represents the volume of the cylinder is:

V = π[tex]r^{2}[/tex]h

What is cylinder?

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases. The cylinder can be thought of as a tube or a can. The lateral surface of the cylinder is formed by "unrolling" a rectangular shape along the circumference of the base.

There appears to be a typographical error in the given formula for the volume of a cylinder. The correct formula is:

V = π[tex]r^{2}[/tex]h

where V is the volume of the cylinder, r is the radius of the circular base, and h is the height of the cylinder.

Using this formula, the expression that represents the volume of the cylinder is:

V = π[tex]r^{2}[/tex]h

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Answer:

A. February 26th

B. $3,500 - Balance ≈ $6,697.26

C. $2,500 - Balance ≈ $4,263.46

D. $4,284.81

Step-by-step explanation:

a) What is the due date of the loan?

The loan term is given as 317 days, and the loan starts on April 15th. To find the due date, we will add 317 days to April 15th.

April 15th + 317 days = April 15th + (365 days - 48 days) = April 15th + 1 year - 48 days

Subtracting 48 days from April 15th, we get:

Due date = February 26th (of the following year)

b) Calculate the interest due on October 12th and the balance of the loan after the October 12th payment.

First, we need to calculate the number of days between April 15th and October 12th:

April (15 days) + May (31 days) + June (30 days) + July (31 days) + August (31 days) + September (30 days) + October (12 days) = 180 days

Now, we will calculate the interest for 180 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $10,000 × 0.04 × (180 / 365)

Interest ≈ $197.26

Peter will make a payment of $3,500 on October 12th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $10,000 + $197.26 - $3,500

Balance ≈ $6,697.26

c) Calculate the interest due on January 11th and the balance of the loan after the January 11th payment.

First, we need to calculate the number of days between October 12th and January 11th:

October (19 days) + November (30 days) + December (31 days) + January (11 days) = 91 days

Now, we will calculate the interest for 91 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $6,697.26 × 0.04 × (91 / 365)

Interest ≈ $66.20

Peter will make a payment of $2,500 on January 11th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $6,697.26 + $66.20 - $2,500

Balance ≈ $4,263.46

d) Calculate the final payment (interest + principal) Peter must pay on the due date.

First, we need to calculate the number of days between January 11th and February 26th:

January (20 days) + February (26 days) = 46 days

Now, we will calculate the interest for 46 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $4,263.46 × 0.04 × (46 / 365)

Interest ≈ $21.35

Finally, we will calculate the final payment Peter must pay on the due date:

Final payment = Principal + Interest

Final payment = $4,263.46 + $21.35

Final payment ≈ $4,284.81

Answer:2/3

Step-by-step explanation:

its the only possible answer because it needs to have a scale factor below one as A'B'C'D' is smaller than ABCD

Answer: 2/3

Step-by-step explanation:

The corresponding side of AD is A'D'.

AD = 30

A'D' = 20

Scale factor = 2/3 because AD * 2/3 = A'D'

If I'm wrong, please tell me.

Answer:

The figure is omitted--please sketch it to confirm my answer.

Set your calculator to degree mode.

Let h be the height of the flagpole.

[tex] \tan(18) = \frac{h}{80} [/tex]

[tex]h = 80 \tan(18) = 25.994[/tex]

The height of the flagpole is approximately 26.0 meters. #3 is correct.

2x + 2y = 4xy is wrong

2x + 2y = 2(x+y) is correct

3x+4= 7x wrong

4x²+5x = 9x² wrong

3x²+3x²+4x = 6x² + 4x = 2x(3x + 2)

sorry I don't understand this one.....

-4(3x-5) = -12x + 20

Answer:

120

12 10

4 2 5 2

2 2

Answer: Using the given information and the formula ab = cd, we can write:

d = (ab) / c

We are given b = 12 cm and c = 6 cm. To find ab, we can use the Pythagorean theorem:

a^2 + b^2 = c^2

where a is the unknown length we want to find. Substituting the given values, we get:

a^2 + 12^2 = 6^2

a^2 + 144 = 36

a^2 = -108 (which is not a possible solution)

This means that the given values do not form a valid triangle. Therefore, we cannot find the length of segment d using the given information.

Step-by-step explanation:

Given the above prompt on hypothesis testing, we can state that specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.

To determine if there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage, we can conduct a two-sample t-test assuming unequal variances. The null hypothesis is that there is no difference in the average city mileage between the two types of transmissions, and the alternative hypothesis is that there is a difference.

The t-test statistic is calculated as follows:

t = (x1 - x2) / sqrt((s1^2/n1) + (s2^2/n2))

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the values from the given statistics, we get:

t = (16.12 - 19.85) / sqrt((3.85^2/26) + (4.51^2/26))

t = -3.31

Using a significance level of 0.05 and 50 degrees of freedom (approximated by n1+n2-2), the critical t-value is ±2.01.

Since the calculated t-value (-3.31) is less than the critical t-value, we can reject the null hypothesis and conclude that there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage.

Specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached image.

The solution to the system of equations is (23, -72).

The first equation is y = -72, which means that whatever the value of x is, the value of y will always be -72.

Substituting y = -72 in the second equation, we get:

7x + 2(-72) = 20

Simplifying this equation, we get:

7x - 144 = 20

Adding 144 to both sides, we get:

7x = 164

Dividing both sides by 7, we get:

x = 23.428571...

So the solution to the system of equations is the ordered pair (x, y) = (23.428571..., -72).

However, we usually express solutions as ordered pairs of integers, so we can round x to the nearest integer to get:

(x, y) = (23, -72)

Therefore, the solution to the system of equations is (23, -72).

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Sample size and sample standard deviation are the key information needed for a single-sample t-test.

In the event that you need to compare the test cruel with the populace cruel, and you perform a single-sample t-test rather than a z-test, the vital piece of data that will be lost is the populace standard deviation.

Within the z-test, the populace standard deviation is known and the standard mistake of the cruel is calculated utilizing the populace standard deviation.

In a single-sample t-test, the populace standard deviation is obscure, and the standard mistake of the cruel is evaluated from the test standard deviation. 

Therefore, sample size and sample standard deviation are the key information needed for a single-sample t-test. 

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The area of a circle of radius of 0.5 meters is 0.785 square meters.

Remember that for a circle of radius r, the area is:

A = pi*r²

Where pi = 3.14

Here we know that r = 0.5m, then we can input that in the formula for the area that is above, we will get.

A = 3.14*(0.5m)²

A = 3.14*0.25 m²

A = 0.785  m²

That is the area of the circle.

Complete question: Let's say that r is the radius of a circle and A is its area, then: If r=0.5 m, A = ?

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According to the equation, a person who weighs 63 kg is predicted to be approximately 141 centimeters tall.

The equation given is Y = 0.91X - 65.5, where X represents the height in centimeters and Y represents the weight in kilograms. To predict the height of a person who weighs 63 kg, we need to solve for X, the height in centimeters.

To do this, we can plug in the given weight of 63 kg for Y in the equation and then solve for X. So, we have:

63 = 0.91X - 65.5

Adding 65.5 to both sides, we get:

63 + 65.5 = 0.91X

Simplifying, we have:

128.5 = 0.91X

Finally, to solve for X, we divide both sides by 0.91, giving:

X = 141.21

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Let x be the length of the pen and y be the width of the pen.

The total cost of the pen is given by:

Cost = 3x + 5y = 300

3x + 5y = 300

3x = 300 - 5y

x = (300 - 5y)/3

The area of the pen is given by:

Area = xy = (300 - 5y)/3 * y

In the given equation r = 2/5 t "r" is the dependent variable.

In mathematics, a variable is a symbol that represents a quantity that can take on different values. In many cases, variables can be divided into two types: dependent variables and independent variables.

An independent variable is a variable that can be changed freely, and its value is not dependent on any other variable in the equation.

A dependent variable is a variable whose value depends on the value of one or more other variables in the equation

Here we have

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups.

She writes the equation r = 2/5 t to describe the relationship.

In the equation, r = 2/5 t, "t" represents the total number of cups, while "r" represents the number of cups of red paint.

Here "t" is the independent variable because it represents the total number of cups, which can be changed arbitrarily.

The value of "r" depends on the value of "t" because the number of cups of red paint is always 2/5 of the total number of cups.

Therefore,

In the given equation r = 2/5 t "r" is the dependent variable.

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Complete Question:

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups. She writes the equation r = 2/5 t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know.

There are 173 kinda-prime positive integer less than 1000.

To find the number of kinda-prime positive integer less than 1000, we'll follow these steps:

1. Understand the definition of a kinda-prime number: A positive integer is kinda-prime if it has a prime number of positive integer divisors.
2. Determine the number of prime numbers less than 1000: There are 168 prime numbers less than 1000, as given.
3. Determine the possible prime number of divisors: Since 168 is not too large, we only need to consider 2 and 3 as possible prime numbers of divisors for a kinda-prime number.
4. Analyze the cases:

Case 1: Kinda-prime numbers with 2 divisors (prime numbers)
All prime numbers have exactly 2 divisors (1 and itself). Thus, all 168 prime numbers less than 1000 are kinda-prime.

Case 2: Kinda-prime numbers with 3 divisors
Let N be a kinda-prime number with 3 divisors. Then, N = p^2 for some prime number p. To find the suitable prime numbers p, we need[tex]p^2 < 1000[/tex]. The prime numbers that meet this condition are 2, 3, 5, 7, and 11 (since 13^2 = 169 > 1000). Therefore, there are 5 additional kinda-prime numbers ([tex]2^2, 3^2, 5^2, 7^2, and 11^2[/tex]).

5. Add the total number of kinda-prime numbers from both cases: 168 + 5 = 173.

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[tex]$(\pi(1000)-1)+11=\boxed{177}$[/tex] "kind a-prime" positive integers less than $1000$.

Let [tex]$n$[/tex] be a positive integer with[tex]$k$[/tex] positive integer divisors.

If [tex]$k$[/tex] is prime, then.

[tex]$n$[/tex] is a "kind a-prime" integer.

[tex]$k$[/tex] must be of the form.

[tex]$k=p$[/tex] or [tex]$k=p^2$[/tex] for some prime [tex]$p$[/tex].

If [tex]$k=p$[/tex], then [tex]$n$[/tex] must be of the form.

[tex]$p^{p-1}$[/tex] for some prime [tex]$p$[/tex]. Since [tex]$p < 1000$[/tex], there are.

[tex]$\pi(1000)$[/tex]possible values of [tex]$p$[/tex].

[tex]$p=2$[/tex] gives [tex]$2^1$[/tex], which is not prime, so we have to subtract.

[tex]$1$[/tex] from [tex]$\pi(1000)$[/tex] to get the number of possible.

[tex]$p$[/tex].

[tex]$\pi(1000)-1$[/tex] values of [tex]$p$[/tex] that give a "kind a-prime" integer of this form.

If [tex]$k=p^2$[/tex], then [tex]$n$[/tex] must be of the form.

[tex]$p^{p^2-1}$[/tex] for some prime[tex]$p$[/tex].

There are.

[tex]$\pi(31)=11$[/tex] primes less than [tex]$31$[/tex], and each of them gives a different "kind a-prime" integer of this form.

Since [tex]$31^5 > 1000$[/tex], no primes larger than [tex]$31$[/tex]can be used to form a "kind a-prime" integer of this form.

[tex]$11$[/tex] possible values of [tex]$p$[/tex] that give a "kind a-prime" integer of this form.

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The height of the kite is approximately 68.4 ft.

To solve the problem, we can use trigonometry. We know that the string is the hypotenuse of a right triangle, with the height of the kite as one of the legs. The angle of elevation, which is the angle between the string and the ground, is also given. We can use the tangent function to find the height of the kite:

tan(46°) = height / 94

Solving for height, we get:

height = 94 * tan(46°)

Using a calculator, we get:

height ≈ 68.4 ft

Therefore, the height of the kite is approximately 68.4 ft.

We use the given angle of elevation and the length of the string to set up a right triangle with the height of the kite as one of the legs. Then, we use the tangent function to relate the angle to the height of the kite. Finally, we solve for the height using a calculator and round to the nearest tenth as requested.

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Complete Question:

A kite flying in the air has a 94-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is 46 °. Find the height of the kite. Round your answer to the nearest tenth.

Lin plans to swim 12 laps and has already swum 9.75 laps, so the number of laps she has left to swim can be found by subtracting 9.75 from 12:

y = 12 - 9.75

Simplifying the right side:

y = 2.25

Therefore, Lin has 2.25 laps left to swim.

Answer: Monique's error is likely due to rounding the surface area to two decimal places, which led to an inaccurate result.

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is approximately 3.14.

To find the correct surface area, we need to know the values of r and h. Without this information, we cannot calculate the exact surface area.

However, we can use Monique's estimate to estimate the values of r and h.

1001.66 = 2πr^2 + 2πrh

Dividing both sides by 2π, we get:

500.83 = r^2 + rh

We don't know the exact values of r and h, but we know that the surface area should be greater than 1001.66 square feet. Therefore, we can assume that the radius and height must be greater than a certain value.

For example, if we assume that the radius is at least 5 feet, we can solve for the minimum value of h:

500.83 = 5^2 + 5h

495.83 = 5h

h = 99.166

So if the radius is 5 feet and the height is 99.166 feet, the surface area would be:

S = 2π(5^2) + 2π(5)(99.166)

S = 1570.8 square feet

This is greater than Monique's estimate of 1001.66 square feet, indicating that her estimate was too low due to rounding.

Step-by-step explanation:

The total length of the beads on one braid is 8.11 centimeters

Keyana places 7 beads on one braid, and each bead is 1.03 centimeters long. So, the total length of these 7 beads would be 7 multiplied by 1.03, which is equal to 7.21 centimeters.

To find the total length of the beads on one braid, we need to evaluate the expression:

7 x 1.03 + 0.9

Multiplying 7 by 1.03 gives us:

7 x 1.03 = 7.21

Then, adding 0.9 gives us:

7.21 + 0.9 = 8.11

Therefore, the total length of the beads on one braid is 8.11 centimeters.

So, the correct answer is B.8.11 centimeters.

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It will take 10 years to double the amount.

Given that, the amount $1400 to double if it is invested at 7% interest compounded monthly, we need to calculate the time,

[tex]A = P(1+r/n)^{nt}[/tex]

[tex]2800 = 1400(1+0.0058)^{12t}[/tex]

[tex]2= (1.0058)^{12t[/tex]

㏒ 2 = 12t ㏒ (1.0058)

0.03 = 12t (0.0025)

12t = 120

t = 10

Hence, it will take 10 years to double the amount.

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The next four equivalent fractions of 8/13 are:

Equivalent fractions are fractions that represent the same value but have different numerator and denominator. To find equivalent fractions of 8/13, we can multiply both the numerator and the denominator by the same non-zero integer.

In this case, we multiplied the numerator and denominator by 2, 3, 4, and 5, respectively, to obtain the next four equivalent fractions: 16/26, 24/39, 32/52, and 40/65. These fractions have different numerators and denominators, but they are equivalent to 8/13 as they represent the same value or amount.

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Answer: 6 3/7

Step-by-step explanation:

9/1 x 5/7

If we multiply the numerators and denominators, we get 45/7 or 6 3/7 as a mixed number.

Answer:

[tex]\frac{45}{7}[/tex] or 6.4285

Step-by-step explanation:

First, multiply 9 and 5, which gives you 45.

9(5)=45

Then, divide 45 by 7.

45/7=6.4285

That gives  you  [tex]\frac{45}{7}[/tex] or 6.4285

Hope this helps!

Okay, here are the steps to find the minimum value of P:

1) Given: |z|=|w|=1 (z and w are complex numbers with unit modulus)

|z+w|=sqrt(2)

Find z and w such that these conditions are satisfied.

Possible solutions:

z = 1, w = i (or vice versa)

z = i, w = 1 (or vice versa)

2) Substitute into P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|

For the cases:

z = 1, w = i: P = |-1-4+2(1+i)i| = |-5+2i| = sqrt(25+4) = 5

z = i, w = 1: P = |1-\frac{4}{i}+2(1+\frac{1}{i})i| = |-3+2i| = sqrt(9+4) = 5

3) The minimum value of P is 5.

So in summary, the minimum value of

P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|

is 5.

Let me know if you have any other questions!

The distance of the object from the helicopter is 698 ft.

Distance is the length between two points.

To calculate how far the object is above the helicopter, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for H

Hence, the distance is 698 ft.

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Answer: positive 2

Step-by-step explanation:

1. The expression √b means "the square root of b".

2. The radical symbol (√) stands for the exponent 1/2.

3. The number or expression under the radical symbol is called the radicand.

A radicand is the number or expression underneath a radical symbol (√). It is the number or expression that is being operated on by the root. The square root of the radicand is the result of the operation.

The expression √6 represents the square root of 6. This is the value of x that, when multiplied with itself, results in 6.

The square root of 6 is equal to 2.44948974, which is the positive solution to the equation x² = 6.

The radical symbol (√) indicates that the expression is a root and the number or expression under the radical symbol is called the radicand, which is 6 in this case.

The exponent of the radical symbol is 1/2, which implies that the expression is a square root.

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Answer:

x = 10

Step-by-step explanation:

Angle form is = 90°

therefore

5x + 25 + x + 5 = 90

6x + 30 = 90

6x = 90-30

6x = 60

6x/6 = 60/6

x = 10