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Answer:

(2, -5) OR (-2, 5)

Step-by-step explanation:

FOR clockwise 90 degrees you will have x,y becoming y, -x and so therefore 5,2 becomes ( 2, -5)

FOR anticlockwise x,y becomes -y, X and so for anticlockwise is( -2, 5 )

The image of A (5, 2) will be (2, -5) after rotating 90 degrees clockwise and anticlockwise the image will be (-2, 5).

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have:

A (5,2) under R90

R90 means rotating clockwise 90 degrees

The transformation rule:

(x, y) → (y, -x)

(5, 2) → (2, -5)

For anticlockwise:

(x, y) → (-y, x)

(5, 2) → (-2, 5)

Thus, the image of A (5, 2) will be (2, -5) after rotating 90 degrees clockwise and anticlockwise the image will be (-2, 5).

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x=60°, y=15°, angle C is 45°, angle DBC is 105° and angle CBA is 75°.

In the given figure, ∠DBC=7y°, ∠CBA=5y°, ∠C=3y° and ∠D=x°.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Here,

∠DBC+∠CBA=180° (Sum of adjacent angles is 180°)

⇒ 7y°+5y°=180°

⇒ 12y°=180°

⇒ y°=15°

∠DBC=7y°=105°, ∠CBA=5y°=75° and ∠C=3y°=45°

Now, ∠DBC=∠C+∠A

⇒ 105°=45°+∠A

⇒ ∠A=60°

Therefore, x=60°, y=15°, angle C is 45°, angle DBC is 105° and angle CBA is 75°.

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The value after multiplying the given mixed fractions is 7/6   .

In the question ,

it is given that ,

the two mixed fraction are given as \(-2\frac{1}{4}\)  and \(-1\frac{1}{3}\)  ,

we need to find their value after multiplication .

we first convert the mixed fractions into improper fraction ,

So ,

\(-2\frac{1}{4}\) = (-2×4+1)/4 = (-8+1)/4 = -7/4

and

\(-1\frac{1}{3}\) = (-1×3+1)/3 = (-3+1)/3 = -2/3

So , the product of -7/4 and -2/3 is written as

= -7/4 × -2/3

= (-7 × -2)/(4 × 3)

= 14/12

after simplifying ,

= 7/6

Therefore , The value after multiplying the given mixed fractions is 7/6   .

The given question is incomplete , the complete question is

Find the value after multiplying the given mixed fraction \(-2\frac{1}{4} \times -1\frac{1}{3}\)   .

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The probability that she wins the next two matches is 36% or 0.36

How to calculate the probability of two matches?

Given,

She believes that the outcome of each match is independent. So, the outcome of next match does not depend on the previous match, is called independent event.

The probability of winning one match is 0.6

Since the outcome of each match is independent, we easily get the probability of she winning the next two matches by multiplying the probability of she winning per match. So,

Probability she wins the next two matches = 0.6 x 0.6

= 0.36 or 36%

Thus, the probability that she wins the next two matches is 36% or 0.36

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We need derivative of h(t)

\(\\ \sf\longmapsto \dfrac{d}{dx}-16t^2+82t+96\)

\(\\ \sf\longmapsto -32t+82\)

\(\\ \sf\longmapsto h(0)\)

\(\\ \sf\longmapsto -32(0)+82\)

\(\\ \sf\longmapsto 82m\)

Hence

.\(\\ \sf\longmapsto H_{max}=96+82=178m\)

Answer:

\({ \rm{h(t) = 96 + 80t - 16 {t}^{2} }} \\ \\ { \rm{ \frac{dh}{dt} = 0 + 80 - (2 \times 16)t}} \\ \\ { \rm{ \frac{dh}{dt} = - 32t + 80}}\)

• At maximum height, dh/dt is 0

\({ \rm{ - 32t + 80 = 0}} \\ \\ { \rm{ - 32t = - 80}} \\ \\ { \rm{t = 2.5 \: seconds}}\)

• Maximum height = 96 + (80 × 2.5) - (16 × 2.5²)

Max. height = 196 meters

Answer:

\({ \rm{h(t) = 96 + 80t - 16 {t}^{2} }} \\ \\ { \rm{ \frac{dh}{dt} = 0 + 80 - (2 \times 16)t}} \\ \\ { \rm{ \frac{dh}{dt} = - 32t + 80}}\)

• At maximum height, dh/dt is 0

\({ \rm{ - 32t + 80 = 0}} \\ \\ { \rm{ - 32t = - 80}} \\ \\ { \rm{t = 2.5 \: seconds}}\)

Step-by-step explanation:

A chord is a segment with endpoints on the circle.

A tangent line is a line that touches a circle at only one point.

A diameter is a chord that passes through the center of the circle.

A secant line is a line that touches a circle at two points.

Therefore, AB is a secant line.

The statement related to the diagram is true is that AB is the secant line.

A chord should be treated as the segment that contains the endpoints on the circle. A tangent line refers to the line that touches a circle at only one point. A diameter refer to a chord that passes via the center of the circle. A secant line should be a line that touches a circle at two points.

Hence, The statement related to the diagram is true is that AB is the secant line.

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Answer: 975

Step-by-step explanation: hope this helped!

Answer:

975

Step-by-step explanation:

Create a proportion. Set 75 over 100 equal to x over 1300. Cross multiply to get 75x1300 = 100x. This will get you 97500 equal to 100x. Divide each side by 100 to get x = 975

In an AR (p) scheme the PACF shows p spikes outside the confidence interval is True.

In an AR (p) (autoregressive) scheme, the Partial Autocorrelation Function (PACF) is a plot that shows the correlation between a time series and its lagged values, while controlling for the influence of intermediate lags. The PACF can help identify the order of the autoregressive model.

In an AR (p) scheme, the PACF will typically show p significant spikes outside the confidence interval, indicating the presence of p significant autocorrelations at lags 1, 2, ..., p. These spikes represent the direct effect of each lag on the current value of the time series, while controlling for the influence of other lags.

Therefore, if the PACF shows p spikes outside the confidence interval, it suggests an AR (p) scheme. Hence, the statement is true.

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The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

S = 4a

Step-by-step explanation:

Rosa saves three times as much money as Anna. If a represents Anna's savings, which relationship shows how much money they have saved,

together?

Let

S = Total money they have saved,

together

a = Anna's savings

Rosa saves three times as much money as Anna

Rosa = 3 * a

= 3a

Total savings = Anna's savings + Rosa's savings

S = a + 3a

S = 4a

Answer: y = -3/5x - 6

Step-by-step explanation:

There are a few equations that can be used for this, but the simplest one would be y = mx + b

We are given:

y = -3

m = -3/5 (slope)

x = -5

b = ?

Our equation is this, we are solving for b

==> -3 = -3/5 ( -5) + b

==> -3 = -3/5 ( -5) + b ( multiply the brackets)

==> -3 = 3 + b ( subtract 3 to both sides)

==> -6 = b

Now we can make the desired equation in slope intercept form;

y = -3/5x - 6

Hope this helped! Have a great day :D

Answer:

75$

Step-by-step explanation:

500 x 2.5 x 6 = 7,500

7,500 divided by 100 = 75.

We divide by 100 because " 2.5 " is a decimal.

Answer:

A.x + 5y

Step-by-step explanation:

let 3rd side be z

P=2x+2y+5x-y+z=8x + 6y

7x+y+z=8x+6y

z=8x+6y-7x-y=x+5y (⇒ A)

Answer:

$136

Step-by-step explanation:

100% - 83% = 17%

the 17% is on props.

so, take 17/100 and multiply with $800, which you will get 136.

so the amount of money spent on props is $136

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\)

Option D is the correct answer.

We have,

In this equation, the variable x represents the number of times the square is cut in half, and y represents the surface area of the square.

As x increases, the exponent of 1/2 decreases, causing the value of y to decrease.

This exponential decay accurately represents the idea that the surface area becomes less and less but never reaches zero units²

Thus,

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\).

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The correct equation that would help model the surface area of a square piece of paper as it is repeatedly cut in half is:  \(\(y=36(\frac{1}{2})^x\)\)

As the square is cut in half, the side length of the square is divided by 2, resulting in the area being divided by \(\(2^2 = 4\)\).

Therefore, the equation \(y=36(\frac{1}{2})^x\)\)accurately represents the decreasing surface area of the square as it is repeatedly cut in half.

and, \(\(y=x^2+4x-16\)\)is a quadratic equation that does not represent the decreasing nature of the surface area.

and, \(\(y=-25x^2\)\) is a quadratic equation with a negative coefficient.

and, \(\(y=9(2)^x\)\)represents exponential growth rather than the decreasing nature of the surface area when the square is cut in half.

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The congruent triangles in this problem are given as follows:

Triangles A and B.

Two figures are classified as congruent if their side lengths are the same.

If we rotate triangle B 180º over it's base, we have that it will have a similar format to triangle A, and also with the same side lengths.

Hence the congruent triangles in this problem are given as follows:

Triangles A and B.

With triangle C, no rotation would make it like A and B, with the same side lengths, hence it is not congruent to any of the triangles in this problem.

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Answer:

The number is -2.

Step-by-step explanation:

From the word problem, we can figure out the equation for the unknown number (x).

8x-3=-19

We would then work out the equation to find x.

Add 3 to -19.

8x=-16

Divide -16 by 8.

x=-2

Suppose that 20% of people own dogs, if you pick two people at random,  the probability that they both own a dog is 0.04.

Suppose that 20% of people own dogs.

So the probability of selecting own dogs = 0.20

The probability that a population unit will be included in a sample obtained through probability sampling is known as probability of selection. Each subset of a population has a probability of being chosen in the sample, which is determined by the sampling design.

If you pick two people at random, then the probability that they both own a dog = 0.20 × 0.20

If you pick two people at random, then the probability that they both own a dog = 0.04

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To solve an algebraic equation means to determine the value of the unknown term in the expression. Solving the expression given as \(16x+5=-10\), the value of \(x\) is obtained as \(-\frac{15}{16}\).

To determine the value of the variable \(x\) in this 7th grade math problem, we need to isolate it on one side of the given algebraic equation. This can be done with the help of basic arithmetic operations. The first step is to get rid of the constant on the same side as the variable. To do this, we will subtract \(5\) from both sides of the equation:
\(16x+5-5 =-10-5\)
Simplifying the left side, we get:
\(16x=-15\)
Now, to get the value of \(x\), we need to divide both sides by the coefficient  of \(x\) i.e., \(16\):
\(\frac{16x}{16}=-\frac{15}{16}\)
Simplifying the left side, we get:
\(x=-\frac{15}{16}\)
Therefore, the solution to the math problem \(16x+5=-10\) for 7th grade is \(x=-\frac{15}{16}\).

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The width of the garden is 18 feet. In this case, the length of the diagonal of the rectangular garden is the hypotenuse, and the length and width of the garden are the other two sides. Let's denote the width of the garden as "w".

Given:

Length of the garden = 24 feet

Diagonal of the garden = 30 feet

Using the Pythagorean theorem, we can set up the following equation:

\(24^2\) + \(w^2\) = \(30^2\)

Simplifying:

576 + \(w^2\) = 900

Subtracting 576 from both sides:

\(w^2\) = 900 - 576

\(w^2\) = 324

Taking the square root of both sides:

w = √324

w = 18

So, the width of the garden is 18 feet.

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we have:24² + w² = 30²Solve the equation:576 + w² = 900Subtract 576 from both sides:w² = 324 Take the square root of both sides:w = √324w = 18So, the width of the rectangular garden is 18 feet.

Using the Pythagorean theorem, we can find the width of the garden. If the length is 24 feet and the diagonal is 30 feet, then the width can be found by taking the square root of (30^2 - 24^2), which is approximately 18.97 feet.

Therefore, the garden is about 18.97 feet wide. We can use the Pythagorean theorem to find the width of the rectangular garden.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the diagonal across the garden is the hypotenuse, and the length and width of the garden are the other two sides.

The diagonal is 30 feet, and the length is 24 feet. We need to find the width (w).

The Pythagorean theorem formula is:a² + b² = c²Where 'a' and 'b' are the two shorter sides, and 'c' is the hypotenuse.

In this case, we have:24² + w² = 30²Solve the equation:576 + w² = 900Subtract 576 from both sides:w² = 324Take the square root of both sides:w = √324w = 18So, the width of the rectangular garden is 18 feet.

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The sum of the area of all the rectangles will be 2a + 3a + 4a.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L×W square units

The dimensions of the rectangle are 2 by a, 3 by a, and 4 by a.

The area first rectangle is given as,

⇒ 2 × a

⇒ 2a

The area second rectangle is given as,

⇒ 3 × a

⇒ 3a

The area third rectangle is given as,

⇒ 4 × a

⇒ 4a

The total area of the rectangle will be given as,

A = 2a + 3a + 4a

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Answer: 75%

Step-by-step explanation:

15/20 = 3/4 or 75%

Answer:

3p^3 (-p^4 + 1)

Step-by-step explanation:

The common factor of both -3p^7 and 3p^3 is 3p^3

Divide -3p^7 by 3p^3 and get -p^4

Divide 3p^3 by 3p^3 and get 1

So the factorisation is 3p^3 (-p^4 + 1)

Answer: h>9/2

Step-by-step explanation:

\(Answer:\large\boxed{y=\frac{2}{3} x+6}\)

Step-by-step explanation:

First let's convert 2x - 3y = 12 into \(y = mx + b\)  form.

In order to do this, solve for y.

\(2x-3y=12\)

\(-3y=-2x+12\)

\(y=\frac{2}{3} x-4\)

This shows us that the slope is   \(\boxed{\frac{2}{3}}\)

Now we use the point-slope formula:

\((y-y1)=m(x-x1)\)

where m is the slope and y1 and x1 are the point the line passes through

Using the point (-6,2) and slope, 2/3, we can find the equation:

\((y-2)=\frac{2}{3} (x-(-6))\)

\((y-2)=\frac{2}{3} (x+6)\)

\((y-2)=\frac{2}{3} x+4\)

\(\large\boxed{y=\frac{2}{3} x+6}\)

1) The scenario is described by the inequality: 35  +  12C  ≥  100

2) The minimum amount of classes a customer takes to help Rebekah reach her goal is six.

The initial fee is $35.

$12 additional fee per class

The minimum goal is $100.

C is the number of classes.

One-time initial fee + (added charge per class) multiplied by the number of classes

The scenario is described by the inequality:

35  +  12C  ≥  100

C) To determine the smallest number of courses a customer can take in order for Rebekah to fulfill her goal.

12C  ≥  100 - 35

12C  ≥  65

C   ≥   65 / 12

C  ≥  5.42

The minimum number of courses a customer takes to help Rebekah reach her goal is six.

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The complete question is-

Rebekah manages a yoga studio that charges each customer a one-time initial fee of $35 and an additional fee of 12 per class taken. Rebekah's goal is for each customer to spend at least 100 at the studio, and she wants to know the minimum number of classes a customer needs to take to meet that goal.

Let C represent the number of classes a customer takes.

1) Which inequality describes this scenario?

2) What is the minimum number of classes a customer can take for Rebekah to meet her goal?

The mean number of chocolate bars eaten is given as follows:

3.9 chocolate bars.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

Considering the absolute frequencies, the total number of observations in this problem is given as follows:

19 + 6 + 15 = 40 observations.

The sum of the 40 observations is given as follows:

3 x 19 + 4 x 6 + 5 x 15 = 156.

Then the mean number of chocolate bars eaten is obtained as follows:

156/40 = 3.9 chocolate bars.

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