Solve the right triangle.
Round your answers to the nearest tenth.

Step-by-step explanation:

2x - 7y = -7

2x + 7 = 7y

y = (2/7)x + 1

the slope of the line is the factor of x : 2/7

FYI that is the ratio y/x and means, when x changes by 7 points to the plus (right) side, then y changes 2 points to the plus (up) side.

the parallel line will have the same slope, of course. just a different y-axis-interception point. that means, the "+" term at the end changes. changes to what ?

well, we use the given point coordinates

-6 = (2/7)×-8 + c

-6 = -16/7 + c

-42/7 = -16/7 + c

-26/7 = c

so, the equation of the parallel line is

y = (2/7)x - 26/7

y = (2/7)×(x - 13)

the perpendicular line is a line that intercepts our original line with a 90 degree angle.

that means its slope will switch x and y of the original line slope and also flips the sign (from + to - or vice versa).

=> the slope of the perpendicular line is -7/2.

the line equation looks like

y = (-7/2)x + c

and again, we use the given point coordinates to find the missing c (y-intercept).

-6 = (-7/2)×-8 + c

-6 = -7×-4 +c

-6 = 28 + c

-34 = c

so, the full equation of the perpendicular line is

y = (-7/2)x - 34

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

The class width of each class is 17.

Class width is the distance between a class's upper and lower bounds (category). It may also refer to one of the following more precisely, depending on the author:

the difference between the upper and lower limits of two (nearby) consecutive classes, or the lowest and higher limits of two classes.

The width of each class in a frequency distribution table must be the same. Due to the fact that you are only working with a single width, this makes calculating the class width relatively simple (as opposed to varying ones).

To find the class width in this, we subtract the lower limits of two consecutive class. i.e.

47 - 30 = 17

64 - 47 = 17

81 - 64 = 17

98 - 81 = 17

So that, The class width of each class is 17.

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The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.

Capacity refers to the product of the length, width, and height of a three-dimensional object or space.

The capacity of an object means the same as its volume.

Olympic-size swimming pools have the following standard dimensions:

Length = 50 m

Width = 25 m

Height = 2 m

Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)

= 660,000 gallons (2,500 x 1,000 ÷ 3.785)

An interval estimate shows the lower and upper limits.

6 x 105 gallons = 630 gallons

Thus, the capacity of the swimming pool is Option B.

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A. 100 gallons to 500 gallons

B. 500 gallons to 1,000 gallons

C. 1,000 gallons to 1,500 gallons

D. 1,500 gallons to 2,000 gallons

The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

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

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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Hello!

4.63 x 10^-3 = 0,00463

we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder.

How to solve the problem ?

The given information states that the cross-sectional areas of a triangular prism and a right cylinder are congruent, and both have a height of 5 units. Based on this information, we can conclude that the volumes of the two shapes may be equal, but we cannot conclude that the volume of the prism is half or twice the volume of the cylinder.

To determine the volumes of the two shapes, we need to know their respective formulas. The volume of a triangular prism is given by V = (1/2)bh, where b is the length of the base of the triangular cross-section and h is the height of the prism. The volume of a right cylinder is given by V = πr²h, where r is the radius of the circular cross-section and h is the height of the cylinder.

Since the cross-sectional areas of the two shapes are congruent, we can assume that their bases are similar. Therefore, the base of the triangular prism must be a triangle with the same area as the circular base of the cylinder. However, without further information about the shape and size of the cross-section, we cannot determine the values of b and r.

Therefore, we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder. The only conclusion that can be made is that the volume of the prism is equal to the volume of the cylinder, assuming that the cross-sectional areas are congruent.

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The trigonometric function on the graph is:

f(x)= -cos(x)

So the correct option is B.

Here we can see the graph of a trigonometric function. We can see that the x-intercept is -1.

Notice that:

sin(0)= 0

cos(0) = 1

So the function can be an inversion over the x-axis of the cosine function, we coulod write this as:

f(x) = -cos(x)

That is the graphed function.

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Answer:

The last one

Step-by-step explanation:

A function is where every x has only one y value.

if there are in total 25 pens, and 14 are black we get that the percent of black pens is

Answer:

a = 5

Step-by-step explanation:

For the quadratic equation

ax² + bx + c = 0,

the discriminant is

b² - 4ac

Here we have ax² - x - 3, so we have

a = a

b = -1

c = -3

b² - 4ac = 61

(-1)² - 4(a)(-3) = 61

1 + 12a = 61

12a = 60

a = 5

The number of pounds of strawberries sold and the number of pounds of grapes sold is 32 and 20 respectively.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given that the selling price of strawberries each pound = $2.50,

The selling price of grapes each pound = $2

The total earning = $160

Let x is the no of a pound of strawberries and y is the no of a pound of grapes sold, then equation will be,

x = y + 12 and 2.50x + 2y= 160

Solve the equation by substitution method;

x = 32 and  y = 20

Therefore, the number of pounds of strawberries sold is 32

the number of pounds of grapes sold is 20.

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Answer:

29 units..

Step-by-step explanation:

well i don't know how to insert an image of the answer...but I did it...its (c): 29 units

Answer:

(6,4)

Thank you and please rate me as brainliest as it will help me to level up

The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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Answer:

\( 2^{2x + 2} = 2^{4x - 4} \)

Step-by-step explanation:

\( 4^{x + 1} = 16^{x - 1} \)

\( 2^{2(x + 1)} = 2^{4(x - 1)} \)

\( 2^{2x + 2} = 2^{4x - 4} \)

Answer:

11449/160000

Step-by-step explanation:

The probability of selecting a single adult that thinks most celebrities are good role models is 214/800 = 107/400

The probability that both do is

(107/400)^2 =. 11449/160000

The inequality and statement about the possible amount of money in the other piggy bank is 0 ≤ PB₂ ≤ 2.69.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Teddy has two piggy banks. The difference in the amount of money between the two banks is no more than $10.

∴ PB₁ + PB₂ ≤ 10.

One piggy bank has $7.31 in it.

∴ 7.31 + PB₂ ≤ 10.

PB₂ ≤ 2.69.

So, The amount in PB₂ can be  0 ≤ PB₂ ≤ 2.69.

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The solutions to the questions are:

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

The housing loses at a rate of 5.4% per year

The "loses at a rate" means that the function decreases with time

So, the function is a decay function

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

The house was worth of 131,000 in 2009

This represents the initial value

So, the initial value is 131,000

This is the decay factor of the function

Recall that

The housing loses at a rate of 5.4% per year

So, we have

Base = 1 - 5.4%

Evaluate

Base = 0.946

We have

Initial = 131000

Base = 0.946

So, the function is

f(x) = 131000(0.946)ˣ

This means that x = 2019 - 2009

x = 10

So, we have

f(10) = 131000(0.946)^10

Evaluate

f(10) = 75193.90

Hence, the value is $75193.90

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Answer:

x = 5

y = 1

Step-by-step explanation:

2x - y = 9

3x + 4y = 19

We multiply the first equation by 4

8x - 4y = 36

3x + 4y = 19

11x = 55

x = 5

Now we put 5 in for x and solve for y

2(5) - y = 9

10 - y = 9

-y = -1

y = 1

Let's Check the answer

2(5) - 1 = 9

10 - 1 = 9

9 = 9

So, x = 5 and y = 1 is the correct answer.

Answer:

36° , 54° , 90°

Step-by-step explanation:

since the triangle is right then one angle is 90°

the ratio of the smaller angles = 3 : 2 = 3x : 2x ( x is a multiplier )

the sum of the 3 angles in the triangle is 180° , that is

3x + 2x + 90 = 180

5x + 90 = 180 ( subtract 90 from both sides )

5x = 90 ( divide both sides by 5 )

x = 18

Then

3x = 3 × 18 = 54°

2x = 2 × 18 = 36°

the 3 angles measure 36° , 54° , 90°

The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?

To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.

The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.

The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.

That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)

The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.

That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,

the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°

The negative sign indicates that the angle is measured below the horizontal line.

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The three solutions are (0, -2), (1, -4) and (3, -4)

Given the equation below expressed as;

-8x - 4y = 8

This can also be expressed as;

-2x - y = 2

If the value of x is zero, then;

-2(0) - y = 2

-y =. 2

y = -2

Hence one of the solution is  (0, -2)

If the value of x is 1, then;

-2(1) - y = 2

-2 - y = 2

y = -(2+2)

y = -4

Hence another of the solution is  (1, -4)

If the value of x is 3, then;

-2(3) - y = 2

-6 -y = 2

-y = -2 + 6

y = -4

Hence another of the solution is  (3, -4)

The three solutions are (0, -2), (1, -4) and (3, -4)

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Given:

The combined event is "Rolling two 3's followed by one 5 on three tosses of a fair die".

Required: Probability of the combined event.

Explanation:

Rolling a die repeatedly more than once are independent events.

Probability of getting a '3' = 1/6

Probability of getting a '5' = 1/6

So, the probability of the combined event

Final Answer: The probability of the combined event is 1/216.

By estimation, 3.9 turns into 4 and 5.3 turns into 5. The answer after estimation is 20 while the real answer is 20.67. Well u see by estimation we get an answer of two places right. So, real answer should also have two places.Place the decimal point after it.y43

Step-by-step explanation: i dont know if I'm right or not

Answer:

Refer to the step-by-step explanation.

Step-by-step explanation:

Come up with a monomial expression and solve it.

A monomial expression is an algebraic expression that consists of a single term. It is an expression that can contain variables, constants, and non-negative integer exponents, but there should be no addition or subtraction between different terms.

Here are a few examples of an monomial expression:

\(\hrulefill\)

Let's work with the monomial expression, 3x²y³z.

To solve this expression, I assume you would like to evaluate it for specific values of the variables x, y, and z. So let x=3, y=2, and z=1.

Plug these values into the expression:

3x²y³z

=> 3(3)²(2)³(1)

=> 3(9)(8)(1)

=> 27(8)(1)

=> 216(1)

=> 216

Thus, the expression is solved.

Answer:

X=1

Step-by-step explanation:

the centre of the quadratic lies at (1,-3)