Solve the inequality.


9p ≥ −72

The correct answer is: O Yes, distance and angle measure are preserved.

When a triangle ABC is reflected across the line y = x, the pre-image and image are congruent.

This is because the line y = x is the perpendicular bisector of the segment joining each corresponding point of the pre-image and image.

Reflection across the line y = x is a type of transformation known as an isometry, which preserves both distance and angle measure.

Here's why:

Distance preservation:

When a point is reflected across the line y = x, the distance between the original point and its reflection remains the same.

This holds true for all corresponding points of the triangle.

Therefore, the distance between any two corresponding points in the pre-image and image triangle will be equal, resulting in distance preservation.

Angle preservation: When a line segment is reflected across the line y = x, the angle between the line segment and the line y = x is preserved. This means that the corresponding angles in the pre-image and image triangle will be congruent.

Since both distance and angle measure are preserved during reflection across the line y = x, the pre-image and image triangles are congruent.

It's important to note that congruence under reflection across a line holds only when the line of reflection is the same for both the pre-image and image.

If the line of reflection were different, the triangles would not be congruent.

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Answer:

58 members of the House of Representatives, and 28 members of the senate.

Step-by-step explanation:

We can find the answer to this by simply subtracting:

86 - 58 = 28

So, there are 58 members of the House of Representatives, and 28 members of the senate.

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All the roots of the polynomial equation that we have in the equation x³ + 6x²+ 9x + 2= 0 are;

x = -1, x = -2, x = -2.

We know that when we talk about a cubic equation, we would be looking at the kind of equation that has the highest power of the variable x in it to be 3.

We know that we can be able to solve the equation by factorization and then when we do that, we would have that;

x³ + 6x²+ 9x + 2= 0 would become  (x+1)(x+2)(x+2) = 0.

Therefore, the solutions to the equation are x = -1, x = -2, x = -2.

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bTo determine the percent of the original price you end up paying after the discounts, we can calculate the final price as a percentage of the original price.

Let's assume the original price of an item is $100.

The first discount reduces the price by 50%, so the price after the first discount is 50% of the original price, which is $100 * 0.5 = $50.

The second discount of 45% is applied to the price after the first discount. The price after the second discount is 45% of $50, which is $50 * 0.45 = $22.50.

Therefore, the final price you end up paying after both discounts is $22.50.\

To find the percent of the original price you end up paying, we divide the final price by the original price and multiply by 100:

Percent of original price = (final price / original price) * 100

In this case, the final price is $22.50 and the original price is $100:

Percent of original price = ($22.50 / $100) * 100

                       = 0.225 * 100

                       = 22.5%

Therefore, you end up paying 22.5% of the original price after the discounts.

It's important to note that the percent of the original price you end up paying will depend on the original price of the item. The calculations above were based on the assumption that the original price was $100. If the original price is different, the resulting percentage will vary accordingly.

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Answer:

Set your calculator to Degree mode.

55^2 = 90^2 + 50^2 - 2(90)(50)cos(C)

3,025 = 10,600 - 9,000cos(C)

-7,575 = -9,000cos(C)

cos(C) = 101/120

C = cos^-1 (101/120) = 32.7°

The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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Answer:

\(\boxed{0}\)

.

Step-by-step explanation:

\(3(2^3 + (4 - 2)^3 - (6 - 2)^2)\)

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

\(= 3(2.2^3 - (2^2)^2)\)

\(= 3(2^4 - 2^4)\)

\(= 3(0)\)

\(= 0\)

Okay so 4x6=24 so now you're gonna take away 200 from 24 which gives you 176

Answer:

$180

Step-by-step explanation:

If the perimeter is 30 yards and each yard costs $6 you times 30 and 6 and you get $180

The equations of the relationship are

A: y = 1/4x

B: y = 2/5x

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

The graph

We can see that the lines pass through the origin

This means that the equations can be represented as

y = mx

Where

m = slope

From the graph. we have

A = (8, 2)

B = (5, 2)

When these points are substituted, we have

A: 8m = 2

B: 5m = 2

When solved, we have

A: m = 1/4

B: m = 2/5

So, the equations are

A: y = 1/4x

B: y = 2/5x

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Answer: 3200 ft^2

Step-by-step explanation:

You have a total area of 4,000 ft^2.

In your plan, you will make two bathrooms (one men's restroom and one women's restroom)

We know that each one of them needs 400ft^2, then the total area needed is two times 400ft^2, or:

2*400ft^2 = 800ft^2

If we subtract this to the total area, we get:

4000ft^2 - 800ft^2 = 3200 ft^2

That is the square feet left for the development of other nonbathroom areas.

Answer:

The three options that result in a difference of squares are:

(x minus y)(x plus y)

(6 minus y)(6 plus y)

(64 y squared + x squared)(64 y squared - x squared)

Answer:

265

Step-by-step explanation:

234+31=265 I use additional

Answer:

13 and 18

Step-by-step explanation:

xy = 234

x + y = 31

Guess and check: go through factors of 234 and find that 18*13=234. 18+13=31 so it satisfies both equations.

Answer:

y = 8x+11

Step-by-step explanation:

The coordination of the points are : (-5,-2) , (3, -1)

Then, the equation is :

\(\frac{y+5}{x+2} =\frac{-5-3}{-2+1} \\\\or,\frac{y+5}{x+2} = 8\\or, y+5=8(x+2)\\or, y = 8x+16-5\\y= 8x+11\)

The period of the sine function representing the position of the band members is 60 feet, and the amplitude is approximately   \(170.3 feet.\)

Since the band members are standing in the shape of a sinusoidal function, we can assume that their positions can be represented by the equation:

\(y = A sin(Bx)\)

where y is the vertical position of a band member, x is the horizontal position on the field, A is the amplitude, and B is the period.

Since Darla is positioned in the exact center of the field, and the person closest to her on the same horizontal line stands 10 yards away, we can assume that the sinusoidal function has a phase shift of 0. This means that the midline of the function passes through the point (0, 0).

To find the amplitude, we need to determine the maximum and minimum heights of the function.

Since the playing area of the football field measures 300 feet by 160 feet, the distance between the two farthest points on the field is the diagonal distance, which can be calculated using the Pythagorean theorem:

\(sqrt(300^2 + 160^2) \approx 340.6 feet\)

Since the distance between the farthest points on the field is equal to the distance between two peaks or two valleys of the sinusoidal function, the amplitude is half of this distance:

\(A = 340.6/2 \approx170.3 feet\)

To find the period, we can use the fact that the distance between two consecutive peaks or valleys is equal to the period of the function.

Since the person closest to Darla stands 10 yards away, or 30 feet away, we can assume that this person is standing at a peak or a valley of the function. This means that the period is twice the distance between Darla and the person closest to her:

\(P = 2(30) = 60 feet\)

Therefore, the period of the sine function representing the position of the band members is 60 feet, and the amplitude is approximately   \(170.3 feet.\)

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The equation (in slope-intercept form) of the line passing through the points with the given coordinates (−2,3) , (−3,2) is y = x + 5

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Hence, let's find the slope of the line using the coordinates (-2, 3) and (-3, 2).

Therefore,

m = 2 - 3 / -3 + 2

m = - 1 / -1

m = 1

Therefore, lets find the y-intercept using (-2, 3)

y = x + b

3 = -2 + b

b = 3 + 2

b = 5

Hence, the equation of the line in slope intercept form is y = x + 5

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Answer:all you need to do is Times everything

Step-by-step explanation:

Answer:

y >= -2x - 5

Step-by-step explanation:

slope = rise / run

slope = -2

y >= -2x - 5

It would be 24.50 x (100+16) % =28.42

Answer:

24.50 x (100+16) % =28.42

Step-by-step explanation:

Answer:

8-(-10)=-8+10=8 your answer is 8

Step-by-step explanation: sorry if its incorrect

Step-by-step explanation:

Given the function

f(x, y) = 5 + x ln(xy − 9) at the point (5, 2)

For the function to be differentiable at the given point, the differential of the function with respect to x and y must be continuous at the point.

Fx is the differential of the function with respect to x.

Using product rule to get f(x):

fx = 0 + x(1/(xy-9)y) + ln(xy-9)

fx = xy(1/(xy-9)) + ln(xy-9)

Substitute point (5, 2) into fx

fx = 5(2)(1/5(2)-9) + ln(5(2)-9)

fx = 10(1/(10-9)) + ln(10-9)

fx = 10(1/1) + ln1

fx = 10 + 0

fx = 10

For fy:

fy = 0 + x²(1/(xy-9))+ 0

fy = x²(1/(xy-9))

Substitute point (5, 2) into fy

fy = 5²(1/(5(2)-9))

fy = 25(1/10-9)

fy = 25(1/1)

fy = 25

Next is to calculate f(5,2)

f(5,2) = 5 + 5 ln(2(5) − 9)

f(5,2) = 5 + 5 ln(10− 9)

f(5,2) = 5 + 5 ln1

f(5,2) = 5 + 5(0)

f(5,2) = 5

Since fx ≠ fy, hence the function is not differentiable at the given point

Answer:

The conditional probability is given by

P(F|E) = P(E and F)/P(E)

P(F|E) = 0.2/0.4

P(F|E) = 0.5

P(F|E) = 50%

Step-by-step explanation:

Recall that the conditional probability is given by

∵ P(B | A) = P(A and B)/P(A)

For the given case,

P(F|E) = P(E and F)/P(E)

Where P(F|E) is the probability of event F occurring given that event E has occurred.

The probability of event E and F is given as

P(E and F) = 0.2

The probability of event E is given as

P(E) = 0.4

So, the conditional probability is

P(F|E) = P(E and F)/P(E)

P(F|E) = 0.2/0.4

P(F|E) = 0.5

P(F|E) = 50%

The amount remaining after 50 years is approximately 45.5% of the Initial amount, A₀.

The given exponential function represents the amount A(t) (in grams) of cesium-137 remaining after t years:

A(t) = A₀ * (1/2)^(t/30)

We are asked to find the initial amount A₀ and the amount remaining after 50 years.

1. Initial amount:

The initial amount, A₀, is the amount of cesium-137 present at t = 0 years. To find A₀, we substitute t = 0 into the equation:

A(0) = A₀ * (1/2)^(0/30)

A(0) = A₀ * 1

Since anything raised to the power of zero is 1, we have A(0) = A₀ * 1, which simplifies to A(0) = A₀.

Therefore, the initial amount of the sample is A₀.

2. Amount after 50 years:

To find the amount remaining after 50 years, we substitute t = 50 into the equation:

A(50) = A₀ * (1/2)^(50/30)

Now we can calculate the amount using the given formula:

A(50) = A₀ * (1/2)^(5/3)

To round the answer to the nearest gram, we evaluate the expression and round the result to the nearest gram:

A(50) = A₀ * 0.455

A(50) ≈ A₀ * 0.455

Therefore, the amount remaining after 50 years is approximately 45.5% of the initial amount, A₀.

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The height of the tree to the nearest tenth of a meter is 73.7m

The angle formed by the line of sight and the horizontal plane for an object above the horizontal.

Given:

base = 13 m

angle of elevation = 53

Using trigonometry

tan 53 = P/B

5.671 = P/ 13

P= 5.671 * 13

P= 73.723

Hence, the height of the tree is 73.7 m.

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Answer:

Step-by-step explanation:

The answer is 33.2

Answer:

33.2

Step-by-step explanation:

332*0.1=33.2