Which transformation confirms that rectangle ABCD and rectangle EFGH are similar?

A) Rectangle ABCD is rotated 90° clockwise about the origin and then dilated by a scale factor of 2 with the origin as the center of dilation.

B) Rectangle ABCD is rotated 90° clockwise about the origin and then dilated by a scale factor of 1 2 with the origin as the center of dilation.

C) Rectangle ABCD is rotated 90° counterclockwise about the origin and then dilated by a scale factor of 2 with the origin as the center of dilation.

D) Rectangle ABCD is rotated 90° counterclockwise about the origin and then dilated by a scale factor of 1 2 with the origin as the center of dilation.

Look for any interval where the curve is going uphill as you read it from left to right. The interval your teacher will want is the x interval that corresponds to this upward motion.

Answer:

0.48

Step-by-step explanation:

The problem at hand

[tex]500 = (2)(10^{5x})[/tex]

First divide out 2 on both side of the = sign

[tex]500 = (2)(10^{5x})[/tex]

[tex]\frac{500}{2} = \frac{(2)(10^{5x})}{2}[/tex]

[tex]250 = 10^{5x}[/tex]

Now take the base 10 log on each side of the = sign

[tex]\log_{10} (250) = \log_{10} (10^{5x})[/tex]

Now move the exponent to the left like so

[tex]\log_{10} (250) = 5x \log_{10} (10)[/tex]

Rule you need to know. [tex]\log_a (a) = 1[/tex]

[tex]\log_{10} (250) = 5x (\log_{10} (10))[/tex]

[tex]\log_{10} (250) = 5x(1)[/tex]

[tex]\log_{10} (250) = 5x[/tex]

Now divide 5 from both sides of the equation

[tex]\frac{\log_{10} (250)}{5} = \frac{5x}{5}[/tex]

[tex]\frac{\log_{10} (250)}{5} = x[/tex]

[tex]x = \frac{\log_{10} (250)}{5}[/tex]

[tex]x = 0.4795880017[/tex]

Round to nearest hundredths

[tex]x = 0.48[/tex]

Side Note:

You could approach this problem in a different manner.

For instance, we could have done the following

[tex]x = \frac{\log_{10} (250)}{5(\log_{10} (10))}[/tex]

Also, you did not have to use log with a base 10. You could have used the natural log, which is [tex]\ln_e (x)[/tex]

[tex]x = \frac{\ln_{e} (250)}{5(\ln_{e} (10))}[/tex]

Solving the equation gives 0.48 when rounded to the nearest hundredth.

To solve the equation [tex]500 = (2)(105x)[/tex] , we will first isolate the exponential term. The steps are as follows:

Divide both sides of the equation by 2 to get 250 = 105x.

Take the common logarithm (log) of both sides of the equation to get [tex]log(250) = log(105x).[/tex]

Using logarithmic properties, we have log(250) = 5x log(10)

Now we simplify further since log(10) is 1, so log(250) = 5x.

Divide both sides by 5 to solve for x, which gives [tex]x = log(250) / 5.[/tex]

Using a calculator with a LOG button, we find log(250) approximately equals 2.39794 and, therefore, x is approximately 0.47959 when rounded to five decimal places.

However, we are asked to round x to the nearest hundredth, so the final answer is x = 0.48.

Answer:

C) 115 feet

Step-by-step explanation:

Assuming your setup is correct and the question is asking the height, given that the length of the slant rope is 150 ft, you find x by multiplying the equation by 150:

... 150*sin(50°) = x ≈ 115 ft

Almost any on-line calculator will compute this value. If you don't specifiy the angle is degrees, you will need to verify that it is properly interpreted. (It may be interpreted as radians. Different calculators make different assumptions.)

The Google or Bing search boxes are pretty reliable calculators. Usually * is suitable as the multiplication indicator, and / works for division. They follow the order of operations rigorously, so parentheses are needed for numerators, denominators, and exponents when more than a single number is involved.

_____

There are on-line equation solvers, too. I've found them to be more fussy and less useful. One likes to give irrational results as the ratio of two (large) integers, for example.

Answer:

115 feet

Step-by-step explanation:

Given : A hot-air balloon is tied to the ground with two taut ropes. One rope is directly under the balloon and makes a right angle with the ground. The other rope forms an angle of 50º with the ground.

To Find: What is the height x, to the nearest foot, of the balloon?

Solution:

We are given a set up :

[tex]sin 50 ^{\circ}=\frac{x}{150}[/tex]

Using scientific calculator find the value of sin 50

0.76604

[tex]0.76604=\frac{x}{150}[/tex]

[tex]0.76604 \times 150=x[/tex]

[tex]114.906=x[/tex]

Hence the height of the balloon is 115 feet.

Option C is correct.

Answer:

4 1/2

Step-by-step explanation:

The point is marked at -4 1/2 on the number line. The distance from there to the origin is 4 1/2 units.

(Distances and lengths are always positive—as are values derived from them, such as perimeter or area.)

The distance from 0 to any given point P on a number line is simply the absolute value of the point's coordinate.

The distance from a point to zero on a number line is determined by the absolute value of the point's coordinate. For example, let's say Point P is situated at 5 on a number line. The distance from 0 to Point P would then simply be the absolute value of 5, which is 5 units.

Another example could be if Point P is located at -3 on the number line. In this case, the distance from 0 to Point P is the absolute value of -3, which again, equals 3 units.

So basically, the distance from 0 to any point P on a number line is just the absolute value of the coordinate of that point.

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Answer:

2x

Step-by-step explanation:

You want the sum ...

... Jamie's age + Ana's age

... = x + x

... = 2x

_____

Comment on answer form

For this sort of problem, it isn't clear whether the preferred answer is the sum (x+x) or the simplified sum (2x).

The confidence interval for confidence level of [tex]1-\alpha[/tex] is

[tex]\left(\overline x-Z_{\alpha/2}\dfrac\sigma{\sqrt n},\overline x+Z_{\alpha/2}\dfrac\sigma{\sqrt n}\right)[/tex]

where [tex]\overline x[/tex] is the sample mean, [tex]Z_{\alpha/2}[/tex] is the critical value for the given confidence level, [tex]\sigma[/tex] is the standard deviation of the population, and [tex]n[/tex] is the sample size. The margin of error is the [tex]Z_{\alpha/2}\dfrac\sigma{\sqrt n}[/tex] term.

a) For a confidence level of [tex]1-\alpha=0.90[/tex], we have [tex]Z_{\alpha/2}=Z_{0.05}\approx1.64[/tex]. So in order to have a margin of error of at most 25 points, we have

[tex]1.64\dfrac{250}{\sqrt n}=25\implies n\approx268.96[/tex]

so Raina should collect a sample of at least 269 students.

b) A confidence interval with a higher confidence level would more closely approximate and reflect the population, so it stands to reason that Luke should collect a larger sample than Raina to meet his 99% confidence spec.

c) For a confidence level of [tex]1-\alpha=0.99[/tex], we have [tex]Z_{\alpha/2}=Z_{0.005}\approx2.58[/tex]. Then the margin of error would at most satisfy

[tex]2.58\dfrac{250}{\sqrt n}=25\implies n\approx665.64[/tex]

so that Luke should collect a sample of at least 666 students.

To calculate the sample size required for a given margin of error in a confidence interval, you can use the formula: n = (z * σ) / E. For Raina's 90% confidence interval with a margin of error of 25, she should collect a sample size of 17. Luke's sample size for a 99% confidence interval should be larger than Raina's, and he should collect a minimum sample size of 26.

To calculate the sample size required for a given margin of error in a confidence interval, you can use the formula:

n = (z * σ) / E

Where:
n = sample size
z = z-score corresponding to the desired confidence level
σ = standard deviation of the population
E = margin of error

(a) To find the sample size for Raina's 90% confidence interval with a margin of error of 25, we plug the values into the formula:

n = (1.645 * 250) / 25 = 16.45

Since sample sizes must be whole numbers, Raina should collect a sample size of 17.

(b) Luke's 99% confidence interval will require a larger sample size because the z-score for 99% confidence is larger than for 90% confidence. Therefore, without calculating the actual sample size, we can determine that Luke's sample size should be larger than Raina's.

(c) To calculate the minimum required sample size for Luke's 99% confidence interval, we use the same formula and plug in the values:

n = (2.576 * 250) / 25 = 25.76

Rounding up, Luke should collect a minimum sample size of 26.

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Answer:

Acute

Step-by-step explanation:

The last angle is 71 which is less than 90

Answer:

acute triangle

Step-by-step explanation:

The sum of the two angles given is more than 90°, so the remaining angle is less than 90°. All angles are acute angles, so the triangle is an acute triangle.

Answer: t < 4  hours

Step-by-step explanation:

Renting = $37 + t x $5.70

If $37 + t$5.70 < $59.80

t$5.70 < $59.80 - $37  

t$5.70 < $22.80

t < $22.80/$5.70  

t < 4 hours

[tex]\textit{\textbf{Spymore}}[/tex

Answer:

Option D

Step-by-step explanation:

Its is the last option because all the others fail the vertical line test. The vertical line test says that if you can draw a vertical line through the graph which intersects it at more than 1 point then its NOT a function. For example Option A, a circle, the  vertical axis passes through the graph  at 2 points.

Answer:

D. Option B: Coordinate grid with graph of a curve that passes through point (zero, zero) and is in the first and third quadrants

Step-by-step explanation:

The vertical line test says if a line going straight up and down passes through more than one point of a relation, than the graph is not  a function.

A. Option C: Coordinate grid with graph of a circle centered at point (zero, zero)

A circle fails the vertical line test so it cannot be a function

B. Option D: Coordinate grid with graph of a curve that passes through point (zero, zero) and is in the first and fourth quadrants

This will fail the vertical line test.  The first and fourth quadrants are above each other.

C. Option A: Coordinate grid with graph of vertical line at x equals three

A vertical line will fail the vertical line test

D. Option B: Coordinate grid with graph of a curve that passes through point (zero, zero) and is in the first and third quadrants

This will pass the vertical line test.  The first and third quadrants are diagonal from each other.

Answer:

See below for the graph.

Step-by-step explanation:

A circle or ellipse can be defined using the same sort of equation. Here, we have chosen to use the formulation ...

... ((x -a)/p)^2 +((y -b)/q)^2 -1 = 0

This will be the general form of the equation for an ellipse with center (a, b) and semi-axes p and q, in the x- and y-directions, respectively. When the axes are the same length, the ellipse is a circle.

By defining the function ...

... c(a, b, p, q, x, y) = ((x -a)/p)^2 +((y -b)/q)^2 -1

we can use the same function for all of the circles/ellipses in the figure. The parabola has vertex (0, -6) and a vertical scale factor of -1, so it can be formulated using the vertex form:

... y = k(x -a)^2 +b . . . . . for vertex (a, b) and vertical scale factor k.

_____

The equations

Parabola is a plane curve. The iconic character can be made with the following equation as given below,

We need to draw 3 circles, an ellipse and a parabola, in order to get the desired digram.

For a circle, we only need to know the radius of the circle and the center of the circle,

1. The head(red circle)

The head of the circle is drawn from the origin of the coordinate, while the radius can be found by dividing the length between the points where the circle cuts the x-axis.

[tex]Radius =\dfrac{6-(-6)}{2} = 6[/tex]

Equation of the circle face,

[tex]\text{Equation of the circle face} => {(x-0)^2+(y-0)^2} = 6^2[/tex]

2. The Left Eye (Blue Circle)

3. The Right Eye (Green Circle)

Similarly for the eyes of the diagram,

The right eye = [tex](x-2)^{2}+(y-2)^{2}=1^{2}[/tex]

The left eye = [tex](x+2)^{2}+(y-2)^{2}=1^{2}[/tex]

4.  The Mouth (Purple Ellipse)

The equation of the parabola can be written as,

(x/3)² +(y+2)² -1 = 0

5. The Body (Black Parabola)

The parabola can be made using the equation,

Equation of a parabola

y = a(x-h)² + k

where,

(h, k) are the coordinates of the vertex of the parabola in form (x, y);

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

Therefore, the equation for the body,

Equation of the parabola = [tex]y = -(x-0)^2 -6[/tex]

Learn more about Parabola:

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Answer:

2 + 3i, midpoint is (2,3)

Step-by-step explanation:

we need to find the midpoint between (-1+9i) and B=(5-3i)

To find the midpoint of two points (a+bi)  and (c+di) in a complex plane,  

we apply formula

[tex]\frac{a+c}{2} + \frac{b+d}{2} i[/tex]

A = (-1+9i) and B=(5-3i)

Midpoint for AB is

[tex]\frac{-1+5}{2} + \frac{9+(-3)}{2}i[/tex]

[tex]\frac{4}{2} + \frac{6}{2}i[/tex]

2 + 3i , so midpoint is (2,3)

Answer:

39

Step-by-step explanation:

Use the Pythagorean theorem! So 15^2+36^2=x^2. So x^2=1521 or x=39

Answer:

2.4 * 10^1

Step-by-step explanation:

Divide the two numbers. 4.8 * 10^3 = 4800

4800/200 = 24

Put into scientific notation

24 = 2.4 * 10^1

4.8 * 10^3 is 24 (2.4*10^1) times greater than 200

The total amount raised by the school is 24 times greater than the amount raised by Graham's class.

The amount raised by Graham's class is $200.

The total amount raised by the school is [tex]4.8 * 10^3.[/tex]

To find the number of times greater the total amount raised by the school is compared to Graham's class, we need to divide the total amount raised by the school by the amount raised by Graham's class.

So, we divide 4.8 * 10^3 by 200 to find the number of times greater the total amount raised by the school is compared to Graham's class.

Therefore,

[tex]= 4.8 * 10^3/ 200[/tex]

[tex]= 2.4 * 10^1.[/tex]

Therefore, the total amount raised by the school is 24 times greater than the amount raised by Graham's class.

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Answer: Z.

Step-by-step explanation:

They want you to figure formula then find right graph, but do it fastest way. If it doubles each year, graph can't be straight line, eliminate Y.

A(0) has to be $5, eliminate W. A(1) has to be double A(0), eliminate X. Check: Z shows A(1) is 10, A(2) is 20.

Answer:

The equation is A(x) = 5(2)ˣ and the graph is Graph Z.

Step-by-step explanation:

Equations on compounding interest (which this essentially is) are of the form

A(x) = p(1+r)ˣ, where p is the amount of principal, r is the interest rate and x is the amount of time.

Since Stella begins with $5, the principal is 5.

Since the amount of money doubles each year, this means we add an extra 100%; this makes r equal to 1.

This gives us the equation

A(x) = 5(1+1)ˣ = 5(2)ˣ

This graph will not be linear, as there is not a constant rate of change (there are different amounts added every year).

She begins with $5.  This means the y-intercept of the graph will be 5.

After 1 year, the amount of money doubles; this makes it 10.  The only graph that is not linear and goes through (0, 5) and (1, 10) is graph Z.

Answer:

The percent increase was 48.7.

Step-by-step explanation:

The absolute increase in enrollment is 1084 - 729 = 355. This corresponds to a relative increase of 355/729=0.487 (relative to Aug 2017). The proportion 0.487, expressed in percent: 48.7%

Depending on your current method to exercise, you could solve this using the proportionality method: 355/729 = x/100, then cross-multiply and solve for x. Same thing.

Answer:

C. 26 + 11 - S

Step-by-step explanation:

She had 26 shells

She collected 11 more shells ( that is addition)

26 + 11

Then she gave S shells away ( that is subtraction)

26+11-S

She has 26+11-S

Answer:

C. 26 + 11 - S

Step-by-step explanation:

Nicole has already spent 17 dollars, and will spend c more dollars, for a total of [tex] 17+c [/tex] dollars.

We want this total to be more than 30, so we have

[tex] 17+c>30 [/tex]

Solving this inequality for c yields

[tex] c > 13 [/tex]

The question asks about the additional amount Nicole will need to spend to exceed a total of $30. Given she has already spent $17, the inequality c > 13 represents the additional amount, in dollars, Nicole must spend to meet this requirement. Therefore, Nicole must spend more than $13.

The question is about calculating the possible additional spending of Nicole in order to ensure her total spent will exceed $30. Nicole has already spent $17. As per the condition, set up the inequality which indicates that Nicole will spend more than $30. It's mentioned that we can use c for the additional amount Nicole will spend. Therefore:

17 + c > 30

This inequality can be solved for c by subtracting 17 from both sides:

c > 30 - 17

So,

c > 13

This means Nicole will have to spend more than $13 additionally to ensure her total spending is more than $30.

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1. Area of the original patio: 35 ft^2

The original patio has is a rectangle with length = 7 feet and width = 5 feet. The area of a rectangle is given by the product between length and width:

[tex]A=L \cdot W[/tex]

Therefore, since in this case L=7 and W=5, the area of the original patio is

[tex]A=(7 ft)(5 ft)=35 ft^2[/tex]

2. Area of section A: 7x ft^2

Section A is also a rectangle, with length = 7 feet and width = x. Therefore, the area of this section is equal to:

[tex]A=L\cdot W=(7 feet)(x)=7x[/tex]

3. Area of section B: 5x ft^2

Section B is also a rectangle, with length = x and width = 5 feet. Therefore, the area of this section is equal to:

[tex]A=L\cdot W=(x)(5 feet)=5x[/tex]

4. Area of section C:  [tex]x^2 ft^2[/tex]

Section C is a square, with side equal to x. The area of a square is equal to the square of the length of the side:

[tex]A=L^2[/tex]

therefore, in this case, since L = x, the area of this section is

[tex]A=(x)^2 = x^2[/tex]

5. Total area of the new patio using addition: [tex]x^2 +12x+35[/tex] ft^2

The total area of the new patio is equal to the sum of the four areas calculated in the previous sections:

[tex]A=35 +7x +5x+x^2 = x^2 +12x+35[/tex] ft^2

6. Total area of the new patio using multiplication: [tex]x^2+12x+35[/tex]

The total area of the new patio is equal to the product between the length (7+x) and the width (5+x):

[tex]A=(7+x)(5+x)=35+7x+5x+x^2=x^2+12x+35[/tex] ft^2

7. Yes

As we can see by comparing the area calculated in 5. and the area calculated in 6., the two areas are equal.

8. 80 ft^2

We already have the formula for the area of the new patio:

[tex]A=x^2+12x+35[/tex]

If we substitute x=3, we find the value of the area:

[tex]A=(3)^2+12\cdot 3+35=9+36+35=80[/tex]

Answer:

the answer is 0.760

Divide y by x:

150/10 = 15

135/9 = 15

30 /2 = 15

They all equal 15

This means the constant of proportionality would be y = 15x

The answer is C.

Answer:

Option C is correct

y = 15x

Step-by-step explanation:

Direct variation states that:

[tex]y \propto x[/tex]          ......[1]

then, the equation is in the form of:

[tex]y=kx[/tex], where k is the constant of variation.

From the given table :

consider any points;

x = 9 and y = 135

Substitute these in [1] we have;

[tex]135 = 9k[/tex]

Divide both sides by 9 we have;

15 = k

or

k = 15

then, the equation we have; y = 15x

Therefore,  the constant of proportionality for the table and write in the form y = kx is, y = 15x

Answer:

31) Second number line

32) False

33) x>2

Step-by-step explanation:

31) Since -6<x has only < sign but no = sign, it will be an open dot on top of -6.

Since x≤2 has = sign, it will be a closed dot on top of 2.

So, second number line is the correct option.

32) x < -5 represents all the numbers to the left of -5 on a number line like -6,-7,-8,-9 etc.

Since 4 is on the right side of -5 on the number line, it won't be a solution of the inequality x < -5.

33) x+3 > 5

Subtracting 3 from both the sides of the inequality, we have

x + 3 -3 > 5 - 3

Cancelling out the +3 and -3 from the left side, we have

x > 2

1. The 2nd number line represents the inequality.

Explanation:

In words, the inequality reads "negative six is less than x, which is less than or equal to two". On the number line, the open circle at negative six means that -6 is not a solution to the inequality: -6 < x. The point at positive two means that positive two is a solution to the inequality: x ≤ 2. Therefore, all numbers greater than -6 and less than or equal to +2 are solutions to the inequality. This is shown on the second number line.

2. False

Explanation:

In words, the inequality reads "x is less than negative five". This means that all numbers less than -5 are solutions to the inequality. Positive four is not less than negative five, so it is not a solution to the inequality.

3. x > 2

Explanation:

To solve the inequality, we have to move all the terms that do not contain x to one side. This inequality is simple because it only requires one step: subtraction.

Solve for x: x + 3 > 5

1. Subtract 3 from both sides to get x by itself:

x + 3 - 3 > 5 - 3

2. Simplify

x > 2

x = 77.56 cm

y = 69.71 cm

The mnemonic SOH CAH TOA reminds you that ...

... Cos = Adjacent/Hypotenuse

so ...

... cos(64°) = (34 cm)/x

... x = (34 cm)/cos(64°) ≈ 77.56 cm

___

It also reminds you ...

... Tan = Opposite/Adjacent

so ...

... tan(64°) = y/(34 cm)

... (34 cm)·tan(64°) = y ≈ 69.71 cm

Answer:

The correct option is D.

Step-by-step explanation:

It is given that events X and Y are two independent events.

Two events are called independent events if the occurrence of one does not affect the probability other. It means

[tex]P(X\text{ and }Y)=P(X)\cdot P(Y)[/tex]

[tex]P(X\cap Y)=P(X)\cdot P(Y)[/tex]          ..... (1)

Therefore option C is correct.

We know that

[tex]P(X|Y)=\frac{P(X\cap Y)}{P(Y)}[/tex]

Using equation (1),

[tex]P(X|Y)=\frac{P(X)\cdot P(Y)}{P(Y)}[/tex]

[tex]P(X|Y)=P(X)[/tex]

Therefore option A is correct.

We know that

[tex]P(Y|X)=\frac{P(X\cap Y)}{P(X)}[/tex]

Using equation (1),

[tex]P(Y|X)=\frac{P(X)\cdot P(Y)}{P(X)}[/tex]

[tex]P(Y|X)=P(Y)[/tex]

Therefore option C is correct.

Since options A, B and C are correct, therefore we can say that correct option is D.

Final answer:

If events X and Y are INDEPENDENT, then option C) P(X and Y) = P(X) x P(Y) is correct.

Explanation:

If events X and Y are INDEPENDENT, then option C) P(X and Y) = P(X) x P(Y) is correct.

For two events to be independent, the probability of their intersection (P(X and Y)) must be equal to the product of their individual probabilities (P(X) x P(Y)).

In other words, if X and Y are independent events, the chance of both X and Y occurring is equal to the chance of X occurring multiplied by the chance of Y occurring.

about 0.380435 hours . . . approximately 22 minutes 49.6 seconds

Start with this equation ...

... 10.5 hours = 27.6 miles

And divide both sides by 27.6

... 10.5/27.6 hours = 1 mile

... 0.380435 hours = 1 mile

[tex]3(x-3)=(3)(x)+(3)(-3)=3x-9\\\\A.\ 3x-6\qquad NOT\\\\B.\ 3x-8-1=3x-9\qquad YES\\\\C.\ x+2x-3=3x-3\qquad NOT\\\\D.\ x-3+x-3+x-3=3x-9\qquad YES[/tex]

A. -2

D. 2

"Expansion" means the magnitude of the scale factor is more than 1. Your choices for that are -2 and 2.

(0.75 and |-0.75| are less than 1.)

Answer: A. −2​  and D. 2

Step-by-step explanation:

A scale factor (k) is number which is used to scale a figure.

It is basically used to either reduce or enlarge the size of the figure

A dilation is transformation which uses scale factor to produce the images of same shape as original but of different size.

From the given options , |-2|>1 and |2|>1 where as |-0.75|=0.75<1 and |0.75|<1

Therefore the scale factors produce a expansion under a dilation of the original image are : -2 and 2.

Hence, the correct options are A. −2​  and D. 2  .

Answer:

D

Step-by-step explanation: 153 divided by 3 = 51

Answer:

D. 153

Step-by-step explanation:

Which number is divisible by 3?

A number is divisible by 3 if you add all the digits and it is divisible by e.

A. 35

3+5 = 8

8/3  has a remainder so it is not divisible by 3

B. 133

1+3+3 = 7

7/3 has a remainder so it is not divisible by 3

C. 103

1+0+3 =4

4/3 has a remainder so it is not divisible by 3

D. 153

1+5+3 =9

9/3 =3  153 is divisible by 3

Answer:

60% increase

Step-by-step explanation:

Percentage increase = (new - old)/ old * 100

We know the new = 4.00

old = 2.50

Lets substitute the values in

Percentage increase = (4-2.5)/2.5 *100

                                   = 1.5/2.5 * 100

                                     =.6*100

                                    =60%