Which of the following functions shows the quadratic parent function, F(x)= x2, vertically compressed?
A. G(x) = (2.5x)²
B. G(x) = x²
C. G(x) = (14x)²
D. G(x) = 5x²

Answer:

Brand A

Step-by-step explanation:

If you divide both brands to find how much one can costs, brand B costs more per can.

79 ÷ 3 = 26.34

87 ÷ 4 = 21.75

That being said, if brand B were to sell 4 cans instead of 3 it would be more than brand A's 4 cans. Brand A is cheaper than brand B would be.

Answer:

E represents a number, for this question we need to keep in mind that the product of 1E and E must end in E.

E must be 6.

E = 6

Step-by-step explanation:

16 * 6 = 96

The coordinates of the endpoints of line segments T'V' are; T'(-1, 2) and V'(0, 1).

It follows from the task content that the transformation involved in the formation of the image from the pre-image is dilation by a scale factor of 1/4.

On this note, given that the coordinates of T and V from the task content are; (-4, 8) and (0,4), it follows that the coordinates of the endpoints as required are; T'(-1, 2) and V'(0, 1).

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The correct option is last one  77 degrees.

Therefore the measure angle W is 77 degrees.

Step-by-step explanation:

Given:

Exterior angle = 122°

∠W = (2x-13)°

∠Y= x°

To Find:

∠W = (2x-13)° = ?

Solution:

Exterior Angle Property:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Angle W and Angle Y are the interior angles of Exterior angle 122°.

∴

Substituting the values we get

Now Substitute 'x' in angle W we get

Therefore the measure angle W is 77 degrees.

Step-by-step explanation:

Step-by-step explanation:

so you have the equation: [tex]\sqrt{32x^3y^2z^7}[/tex] which I'm assuming is what you meant to input. and the next step I'm assuming you wrote: [tex]\sqrt{8} * \sqrt{4} * \sqrt{x^2} * \sqrt{y^2} * \sqrt{x} * \sqrt{z^6} * \sqrt{z}[/tex], although I'm not 100% sure, I'm basing this assumption off of step 3. Anyways this will simplify to [tex]2xyz^3\sqrt{8xz}[/tex] which is correct kind of, but since they were asked to FULLY SIMPLIFY, then it's not completely done. This is because 8 has a factor of 4 which is a perfect square. This is because in step 1, the student rewrote 32 as sqrt(8) * sqrt(4) instead of writing it as sqrt(2) * sqrt(16) which is the greatest factor of 32 that is a perfect square. So they could've either done that in step 1, or they could've realized in step 2, that they can further simplify sqrt(8) and then have a step 3 showing that.

Answer:

Step-by-step explanation:

exterior angle of a polygon = 360° ÷ number of sides

The line having the equation, y = -2x + 5, has a slope = -2, and y-intercept = (0, 5). Thus, option A is the best choice.

The slope of a line is the tangent of the angle that the line makes with the positive side of the x-axis.

The y-intercept of a line is the point at which the line intersects the y-axis.

The standard form of a line is y = mx + b, where m represents the slope of the line, and b represents its y-intercept.

In the question, we are asked to identify the slope and the y-intercept of the line whose equation is y = -2x + 5.

Comparing the given equation of the line, y = -2x + 5, with the standard equation of a line, y = mx + b, we can say that,

m = -2, and b = 5.

Representing b as an ordered pair, we get (0, 5), as b represents the y-intercept which is a point on the y-axis, where the x-coordinate is always equal to zero.

Thus, we get the slope = -2, and the y-intercept = (0, 5).

The option representing the answer is option A.

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Answer:

The expression is 42-17-19 OR 42-(17+19).

Step-by-step explanation:

First, we can indicate that we can use subtraction because is giving them away for his birthday.

"He gave one each to the 17 students in his class and to the 19 students in the other third-grade class".

That represents taking away 17 and 19 means that it is subtracting them.

Hope this helps. (:

The required function (f/g)(x) is 3√4x/2x+3 where x ≠ -3/2

Given the functions;

f(x) = ∛4x

g(x) = 2x + 3

We want to find the resulting function (f/g)(x);

(f/g)(x) = f(x)/g(x)

Thus, (f/g)(x) = ∛4x/(2x + 3)

Restriction to the function occurs at the point where the denominator is equal to zero.

Thus;

2x + 3 = 0

2x = -3

x = -3/2

Thus, the required function (f/g)(x) is 3√4x/2x+3 where x ≠ -3/2

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The equation which he have solved is [tex]10/x^{2} -1=15/3x-3[/tex] as in this 1 is the extraneous solution.

Given four equations in which first equation is [tex]10/x^{2} -1=15/3x-3[/tex],second is (x+2)/(x+3)=6x/8, third is (4x-4)/(x+6)=x-1/10, fourth is 4/x-1=x+2/10.

We have to find such a equation which have a valid solution and one extraneous solution.

We have to solve these equation:

[tex]10/x^{2} -1=15/3x-3[/tex]

The above exprssion is not defined for x=1 so 1 is an extraneous solution. Simplifying the above equation by doing cross multiplication.

10(3x-3)=15([tex]x^{2} -1[/tex])

30(x-1)=15(x-1)(x+1)   [We know that [tex]A^{2} -B^{2} =(A+B)(A-B)[/tex]

2=x+1

x=1

In the given equation 1 makes the denominator zero and 1 is the solution of the equation derived from cross multiplication.

Hence the correct equation which Sean solves is option A which is [tex]10/x^{2} -1=15/3x-3[/tex].

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The given question is incomplete as it should include the given figure.

Answer:see photo #15

Step-by-step explanation:

The solution to the inequality: [tex]1.29m\leq 25[/tex]  is m=19.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Value of gift card=$25

Cost of each song=$1.29

Let m be the number of songs purchased.

Then, the required inequality is as follows:

[tex]1.29m\leq 25\\m\leq \frac{25}{1.29}\\ m\leq 19.38[/tex]

The value of m rounded to the nearest whole number is 19.

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Reason:

These angles are both in the same corresponding direction. Both are in the same western corner, or point to the west. If the lines were parallel, then the corresponding angles would be congruent.

Answer:

1:4

2:8

7:28

Step-by-step explanation:

The equation that is true and one that matches the set of ordered pairs of functions is option C. f (0) = 6

Note that a function can be made to be a given set of ordered pairs such as the ordered pairs (2,4), (3,5), (4,6)  can have  input functions of ​​(as domain) 2,3,4 and output functions of ​​(as range) of 4,5,6.

So when you see the ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)} one can see that the option that matches to the set of ordered pairs of functions above is f (0) = 6 value x = 0, f (x) = y = 6, ordered pairs (0.6)

See full question below

The function f (x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)}:Which equation is true?

f(-10)=1

f(2)=-10

f(0)=6

f(1)=-10

The answer choices are :

f (-10) = 1 values ​​x = -10, f (x) = y = 1, ordered pairs (-10,1)

f (2) = - 10 values ​​x = 2, f (x) = y = -10, ordered pairs (2, -10)

f (0) = 6 value x = 0, f (x) = y = 6, ordered pairs (0.6)

f (1) = - 10 values ​​x = 1, f (x) = y = -10, ordered pairs (1, -10)

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Answer:

-8 and 1

Step-by-step explanation:

-8 x 1 is -8

-8+1 is -7

These problems are solved using the trigonometric function. Trigonometric functions provides the ratio of different sides of a right-angle triangle.

The trigonometric function refer to function that are periodic in nature and which lend insight to the relationship between angles and the sides of a triangle that is right angled.

The solutions to x in the respective problems is given as follows:

1st.) x = 5 /Sin(30°)

x = 10

!) sin(45°) = 4/x

x = 4/sin(45°)

x = 4√2

I) Cos(45°) = √3 / x

x = √3 / Cos(45°)

x = √6

E) Tan(60°)

= (3√3) / x

x = (3√3) / 3

W) It is to be noted that for right-triangle that is isosceles in nature, the angle made by the legs and the hypotenuse is always 45°.

x = 45°

N) x² + x² = (7√2)²

x = 7

V) Tan(60°) = 7 / x

x = 7√3/3

K) x² + x² = (9)²

x = 9/√2

Y) Sin(60°) = 7√3/x

x = 14

M) Sin(30°) = x/11

x = 11/2

T) Sin(45°) = x/√10

x = √5

A) x + 2x + 90° = 180°

x = 30°

O) Sin(45°) = √2 / x

x = 2

R) Tan(30°) = x / 4

x = 4/√3

= 4√3 / 3

S) Sin(60°) = x / (10/3)

x = (5√3) / 3

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The length of the other leg to the nearest tenth of a foot is 5.7 feet.

What is Pythagorean theorem?

We can use the Pythagorean Theorem to find the length of the other leg

[tex]a^{2} + b^{2} = c^{2}[/tex]

"a" and "c" represent the two legs of the triangle and "b" represents the perpendicular.

So,

      [tex]b^{2} = c^{2} - a^{2}[/tex]

        =  7² - 4²

  b = [tex]\sqrt{49 - 16}[/tex]

  [tex]b = \sqrt{33}[/tex] ⇒ 5.7 feet

Therefore, the length of the other leg to the nearest tenth of a foot is 5.7 feet.

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The sample size suggested by this statement is 664 option second is correct.

It is defined as an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]

Where   Z is the z-score at the confidence interval

            s is the standard deviation

            n is the number of samples.

At 99% confidence Z = 2.576

By using the MOE formula:

0.05 = 2.376×√(0.5(0.5)/n)

After calculating

n = 663.57 ≈ 664

Thus, the sample size suggested by this statement is 664 option second is correct.

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Options 1, 3 and 5. The true statements based on the fact that c and d are parallel are:

The sum of the angles m<4 + m<3 = 180

m<4 + 82 = 180

m<4 = 180 - 82= 98

From the question we have the first as alternate interior angles. The second is corresponding angles and the last option is vertical angles.

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Answer:

-1 <= x <= 1

Step-by-step explanation:

√((1-2x+x^2)+2-2x^2)

= √((1-x)^2 + 2*(1-x)(1+x) )

điều kiện là 1 - x > =0 và 1+x >=0

giải 2 bất phương trình trên ta thu đc kết ququả

71% is the required probability here.

What is a probability simple definition?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

                                        The probability serves as a gauge for the possibility that an event will occur. and a The probability equation is stated by the following notation: P(E) = Number of Favorable Outcomes/Number of Total Outcomes.

The number of customers out of 5 who agree to take the survey here could be modelled as a binomial distribution given as

 x ` Bin (n = 5 , p = 0.22 )

Thus the probability here is computed as

P(X≥ 1) = 1 - P(X = 0) = 1 - (1 - 0.22)⁵

           = 0.71 %

Therefore 71% is the required probability here.

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As per my explanation to (b) above, the largest number of primes that could factor such a number is 4.

Note that  2,3,5 and 7   are the smallest primes, then use the reasoning from

(b) above. we are looking for four exponents, that, when 1 is added to each and all are multiplied together, would equal 20.

But no such integers  k, l, m, and n  exist such that (k + 1)(l + 1)(m + 1) (n + 1)  = 20 where k, l,m, and n ≥ 1 so this number, whatever it is, can't have 4 prime factors

Let's drop 7 out of the mix and suppose it has just 3 prime factors 2, 3, and 5 again we are looking for three exponents,  that, when 1 is added to each and all are multiplied together, would equal 20.  Put another way, we are looking for k, l and m ≥ 1   such that (k + 1)(l + 1)(m + 1) = 20

Note that the  only possibility here  is when we have 2 *2 *5  = 20 and the smallest possible product would be 2^(4 )* 3^(1) * 5^(1) =  2^4 * 3 * 5 = 240

Now......the only remaining possibility is  that this number is composed of the two smallest primes, 2 and 3,  and we are looking for  some k  and l ≥ 1 such that (k + 1)(l + 1) = 20 clearly, the only possibilities  are when k = 4 and l = 5, or vice-versa

So this number would factor as either 2^3 * 3^4   = 648  or 2^4 * 3^3 = 432 and both are > 240.

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The simplest form of the given algebraic expression √(250c³/9d⁶) is; 5c * (√10c)]/3d³

We are given the algebra problems as;

√(250c³/9d⁶)

Now 250c³ can be broken down into 250 = 25c² × 10c

Thus, we now have;

√(250c³/9d⁶) = [√(25c²) * (√10c)]/√9d⁶

When we breakdown the above expression, we have;

5c * (√10c)]/3d³

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Answer:

the answer is a

Step-by-step explanation:

i got it right

When the lightning occurs 4.5 km away then we will hear after 13.5 seconds and if we hear after 1.5 seconds then we are 0.5 km away from lightning.

Given With each km from the lightning 3 seconds passes.

a) The table of values for distances from 0 to 5 km.

     Distances                     Time

            0                              0

            1                               3

            2                              6

            3                               9

            4                               12

            5                                15

b) The graph of lightning is a linear relation because it is increasing constantly by 3 seconds. f(x)=3x

c) When distance =1  , the time be 3 seconds

when distance =4.5  , the time=3*4.5

=13.5 seconds.

d) When time is 3 seconds = 1km

when time =1.5 seconds , the distance be 1/2=0.5 km.

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Since the y-intercept b = 2, hence the equation of the line will be y = -x +2

The formula for calculating the slope of a line is expressed as:

Slope = y2-y1/x2-x1

Given the coordinate points  (0, 2) and (2, 0)

Slope = 0-2/2-0
Slope = -1

Since the y-intercept b = 2, hence the equation of the line will be y = -x +2

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Answer:

c

Step-by-step explanation:

The difference is 2003.

The formula for the sum of the first n even numbers is SE = n^{2} + n, (E standing for even).

The sum of the first n odd numbers is SO = n^{2}, (O standing for odd).

Knowing this, plug 2003 for n,

SE - SO= (2003^{2} + 2003) - (2003^{2}) = 2003

The difference is 2003.

A number that can be divided into two halves, i.e. into two equal parts is called an even number. Even numbers are exactly divisible by 2 which means the remainder will be 0.

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Answer:

12.198

hope it helps

12.198

To round over 7 into 8, the ten-thousandth place needs to be 5 or over, and as we can see the ten-thousandth place is 5.

Since

[tex]17^a = 16 = 4^2 \implies 17^{a/2} = 4[/tex]

it follows that

[tex]17^b = 4 \implies 17^{a/2} = 17^b \implies \dfrac a2 = b \implies a = 2b[/tex]

Then

[tex]2^{a - b} = 2^{2b - b} = 2^b[/tex]

so that

[tex]\dfrac1{2^{a-b}} = 2^{-b}[/tex]

We also have

[tex]17^b = 4 \implies b = \log_{17}(4)[/tex]

so we can go on to say

[tex]\dfrac1{2^{a-b}} = \boxed{2^{-\log_{17}(4)}}[/tex]

The perimeter of the shaded part is: 25.1 cm.

The area of the shaded part is: 36.6 cm².

Area = Area of square - 2(area of square - area of quarter circle) = s² - 2(s² - 1/4πr²).

Parameters given are:

Plug in the values into the equation

Area = 8² - 2(8² - 1/4π(8²)).

Area = 64 - 2(64 - 50.3)

Area = 36.6 cm²

Perimeter = 2(perimeter of quarter circle) = 2(1/4(2πr)) = 2(1/4(2π8)) = 25.1 cm

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