Graph the function with the given domain. Then identify the range of the function.

1) y = -6; domain: x ≥ 5
2) y = -x - 1; domain: -1 ≤ x ≤ 3

A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC onto ∆A′B′C′ is a reflection across the line x = -3 followed by a reflection across the line y = x.

Given that both triangles are congruent, we can infer or deduce that there were no dilations or contractions. Hence, since we are moving in a clockwise direction, we can submit that this was not a rotation but a reflection.

Hence the first sequence of reflection was such that:

∆ABC reflects onto ∆A′B′C′ across the line x = -3; followed by
a reflection across the line y = x.

Note that in geometry, reflection refers to the mirror image of an image. The line through which an image reflects is called the line of reflection.

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Answer: (f+g)(x) = 6x²- 4x + 6

Step-by-step explanation:

We add f(x) and g(x) together, (4x²-5x+8) + (2x²+x-2)

Add like terms together, (4x²+2x²) + (-5x+x) +(8-2)

We are left with (f+g)(x) = 6x²- 4x + 6

The value of the function  (f - g)(x) is x² + 3x + 5

A function is defined as a relation between a set of inputs having one output each.

In a simpler terms, a function relates input and output.

Therefore, let's solve the function (f - g)(x)

f(x) =  √16x⁴

g(x) = 3x² - 3x - 5

Therefore,

(f - g)(x) = f(x) - g(x)

(f - g)(x) = √16x⁴ - (3x² - 3x - 5)

(f - g)(x) = √16x⁴ - 3x² + 3x + 5

(f - g)(x) = 4x² - 3x² + 3x + 5

Therefore,

(f - g)(x) = x² + 3x + 5

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The proportional equation between y and x^2 is:

y = 3*x^2

We know that y is directly proportional to x^2, then we can write:

y = k*x^2

Where k is the constant of proportionality.

We also know that when x = 10, the value of y is 300, replacing that in the above equation we get:

300 = k*(10)^2

Now we can solve this for k:

300 = k*100

300/100 = k

3 = k

Then the equation is:

y = 3*x^2

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Step-by-step explanation:

so, let's do the multiplications and squaring. and then compare the result with the target.

(x + a)² + b = x² + 2ax + a² + b

and the original expression is

x² - 4x + 19

x² = x² done

2ax = -4x

2a = -4

a = -2

a² + b = 19

(-2)² + b = 19

4 + b = 19

b = 15

so, the result is

(x - 2)² + 15

Answer: (x-2)^2+15

Step-by-step explanation:

Given x^2-4x+19

=here b=-4 and c=19

B=b/2=-4/2=-2

C=c-B^2=19-(-2)^2=19-4-15

so

(x-B)^2+C

(x-2)^2+15

Step-by-step explanation:

I assume our task is to find that point of time, when it reaches the highest point.

and the function is

h(t) = -16t² + 96t + 112

well, a maximum or minimum of a curve (function) is found as a zero solution of the first derivative of the function.

given the nature of the function, the extreme point has to be a maximum (the firecracker goes up and then down again).

h'(t) = -32t + 96

we are looking for the zero :

0 = -32t + 96

32t = 96

t = 3 seconds

so, after 3 seconds, the firecracker reaches its highest point, which is at

-16×3² + 96×3 + 112 = -16×9 + 96×3 + 112 =

= -144 + 288 + 112 = 256 ft

FYI - we know for x = 0 (the starting point) the height of the starting window was 112 ft.

Probability that S assumes a value between 280 and 320 inclusive is 0.853.

S = Σ[tex]X_{i}[/tex] where  [tex]X_{i}[/tex] has a uniform distribution on 1, 2, 3, 4, 5, with mean 3 and variance (25 – 1)/12 = 2 (result known, or calculated via E[[tex]X^{2}[/tex]] = 11, or from book of formulae, p10, with a = 1, b = 5, h = 1).

So S ~ N(300, 200) approximately.

P(280 ≤ S ≤ 320) = [tex]P(\frac{279.5-300}{\sqrt{200} } < Z < \frac{320.5-300}{\sqrt{200} })[/tex]

                           = [tex]P(-1.450 < Z < 1.450)[/tex]

                           = 0.853.

Hence, probability is 0.853.

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The correlation coefficient that is most likely to match a line of best fit of the form y = mx + b for this situation is of:

0.9.

The correlation coefficient is an index that measures correlation between two variables, assuming numeric values between -1 and 1.

If the correlation coefficient is positive, the relation is positive, that is, they are direct proportional. If the correlation coefficient is negative, they are inverse proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the two variables is classified as strong.

In the context of this problem, the variables are listed as follows:

The total price increases with the number of bananas bought, and there is a strong positive relationship between these two variables, hence the coefficient should be greater than 0.6 and the correct option is:

0.9.

The problem is given by the image shown at the end of the answer.

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The correct statement about the model, using proportions, is given as follows:

The model shows that there are 4 pieces that are each 0.75 ft long.

A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in whichever context of the problem.

The application of proportions in this problem is to find the length of each piece, which is obtained as the division of the total length of the model by the number of pieces, hence:

Length of each piece = Total length/number of pieces.

The measures are given as follows:

Hence the length per piece is given by:

3 ft / 4 = 0.75 ft.

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Answer:

answer is 3/4!!! hope this helped

There is not enough evidence to conclude that the mean is less than 14 hours, as the p-value of the test is greater than 0.05, using the t-distribution.

At the null hypothesis, it is tested if the mean is not less than 14 hours, hence:

[tex]H_0: \mu \geq 14[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the mean is less than 14 hours, hence:

[tex]H_1: \mu < 14[/tex]

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which the parameters are defined as follows:

In the context of this problem, the values of these parameters are:

[tex]\overline{x} = 13.5, \mu = 14, s = 3, n = 64[/tex]

Hence the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{13.5 - 14}{\frac{3}{\sqrt{64}}}[/tex]

t = -1.33.

Using a z-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value, with t = -1.33 and 64 - 1 = 63 df, the p-value of the test is of 0.094.

Since the p-value of the test is greater than the significance level of 0.05, there is not enough evidence to conclude that the mean is less than 14 hours.

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a ) The required measure of x = 90°

b ) The height of the right angled triangle = = [tex]\sqrt{244}[/tex]

Given is a triangle with measure 15, 20 and 25

a ) Since a perpendicular is dropped from above

the two angles of x are equal because the angle is bisected by an angle bisector

So to check whether the angle x is a right angled or not

we can use the pythagoras theorem and check if the LHS = RHS or not

LHS = 15² + 20² = 225 + 400 = 625

and RHS = 25² = 625

Since LHS = RHS thus the angle is 90 degrees

b ) The height of the right triangle ;

by using the Pythagoras theorem again

12.5² + h² = 20²  { side 25 is bisected = 12.5 }

h² = 400 - 156.25

h = [tex]\sqrt{244}[/tex]

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The null and alternative hypothesis regarding the test on whether the mean error is of zero is given by the following option:

D. H0: μ = 0 minutes, H1: μ ≠ 0 minutes.

The first step in identifying the hypothesis is to identify the claim tested, given as follows:

The mean prediction error is equals to zero.

At the null hypothesis, it is tested if there is not enough evidence to go against the claim, hence we suppose that the mean is of zero minutes, as follows:

H0: μ = 0 minutes.

At the alternative hypothesis, it is tested if there is enough evidence to reject the null hypothesis, that is, if there is enough evidence to conclude that the mean prediction error is different of zero minutes, hence it is given as follows:

H1: μ ≠ 0 minutes.

Thus option D gives the correct null and alternative hypothesis in the context of this problem.

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Answer:

--------------------------

The equation of line with a slope of 3/2 which passes through point (-4,-2) is y = (3/2)x + 4.

The equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the data in the question;

Point (-4, -2 )

First, we determine the y-intercept 'b'.

Plug the point and slope slope into the equation of line formula and solve for b.

y = mx + b

-2 = (3/2)(-4) + b

-2 = (3)(-2) + b

-2 = -6 + b

b = -2 + 6

b = 4

Now, plug the slope and y-intercept into y = mx + b to determine the equation of the line.

y = mx + b

y = (3/2)x + 4

Therefore, the equation of the line is y = (3/2)x + 4.

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Answer:

Figure A was translated right 4 units and up 2 units

Answer:

Step-by-step explanation

Answer:

6 students

Step-by-step explanation:

[tex]\frac{1}{5} = \frac{x}{30}[/tex]
[tex]30 = 5x[/tex]
[tex]6=x[/tex]

By solving a linear equation, it can be calculated that

There are 4 guppies in  each family

What is a linear equation?

At first it is important to know about equation.

An equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sigh

A one degree equation is known as linear equation.

Here a linear equation needs to be solved

Let the number of guppies in each family be x

Allison has 2 aquariums.

In each aquarium she has 2 families of guppies and 3 tetras.

Total number of fishes Allison have = 2(2x + 3) = 4x + 6

Leigh has 1 aquarium with 10 tetras and 3 families of guppies.

Total number of fishes Leigh have  = 3x + 10

By the problem,

4x + 6 = 3x + 10

4x - 3x = 10 - 6

x = 4

There are 4 guppies in each family

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The plane flies at a speed of 150mph

A plane can fly 300 miles in the same time as it takes a car to go 120 miles

Let the time taken be t

Let the speed of the plane be x

the car travels 90 mph slower than the plane,

Speed of the car is x - 90

Speed = distance / time

Time taken by plane = time taken by car

300/ x = 120/x - 90

300(x - 90) = 120x

300x - 27000 = 120x

300x - 120x = 27000

180x = 27000

x = 27000/180

x = 150

Therefore, the plane flies at a speed of 150mph

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Answer:

------------------------

Correct choice is B.

Answer:

b)  -6

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given the interval is [-2, 0]:

Substitute the endpoints of the interval into the function and solve:

[tex]\begin{aligned}x=-2 \implies f(-2)&=4\left(\dfrac{1}{2}\right)^{-2}\\& = 4(4)\\&=16\end{aligned}[/tex]

[tex]\begin{aligned}x=0 \implies f(0)&=4\left(\dfrac{1}{2}\right)^{0}\\& = 4(1)\\&=4\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\implies\dfrac{f(b)-f(a)}{b-a}&=\dfrac{f(0)-f(-2)}{0-(-2)}\\\\&=\dfrac{4-16}{0+2}\\\\&=\dfrac{-12}{2}\\\\&=-6\end{aligned}[/tex]

Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.

According to the question,

We have the following information:

In 8 years, Estelle's bank account earned $1,270 simple interest at 2.5%.

Now, let's take the principal amount to be $x.

We know that the following formula is used to find simple interest:

Simple interest = (principal*rate*time)/100

(x*2.5*8)/100 = 1270

Using the cross multiplication method:

20x = 127000

x = 127000/20

x = $6350

Hence, Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.

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The probability that a 4 is drawn from from Urn A followed by a 2 from Urn B is  1/40 .

In the question ,

it is given that

the number of balls in Urn A is 8

which are  {1,2,3,4,5,6,7,8}

the probability of getting a 4 from Urn A is (P₁) = 1/8

the number of balls in Urn B is 5 .

which are {1,2,3,4,5}

the probability of getting 2 from Urn B is (P₂) = 1/5

So ,the required probability is = P₁ × P₂

On substituting the values of P₁ and P₂ ,
we get

= 1/8 × 1/5

= 1/40

Therefore , the  required probability is 1/40 .

The given question is incomplete , the complete question is

Find the probability.

Urn A has balls numbered 1 through 8. Urn B has balls numbered 1 through 5. What is the probability that a 4 is drawn from A followed by a 2 from B?

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Answer:

$51,750

Step-by-step explanation: We are going to make x = 3 and we will use the  i=prt equation meaning

Step 1: (45,000)(0.05)(3)= 6750

Step 2: 45,000+ 6750= 51,750

Solution: $ 51,750

2x+3  x-3 those are correct

When quadratic function is subtracted from cubic function, the resultant equation is cubic.

So, It is true.

Function is defined as, In any equation of two variable, we make change in one  accompanied by second.

For example, [tex]F(x)=2x+1[/tex] when we make changes in x , different values of y will obtain.

Quadratic function in which maximum power of variable is two. Similarly, the function which has maximum power on variable is three is called cubic function.

To solve the given problem, let suppose we have,

Quadratic function:[tex]f(x)=x^{2} +x+1[/tex]

Cubic function: [tex]g(x)= x^{3}+x^{2} +x+1[/tex]

According to question,

Subtract quadratic function from cubic function,we get

[tex]g(x)-f(x)=( x^{3}+x^{2}+x+1)-(x^{2} +x+1 )[/tex]

⇒ [tex]h(x)=x^{3} +1[/tex]

It is a cubic function.

Thus, given statement is True.

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⇒[tex]3x^{2} -13x-10\\=3x^{2} -15x+2x-10\\=(3x^{2} -15x)+(2x-10)\\=3x(x-5)+2(x-5)\\=(x-5)(3x+2)[/tex]

⇒The answer is  (x-5)(3x+2)

The given infinite series is divergent.

Given,

[tex]\sum \limits^\infty_{n=1 }{(-1)^{n+1}\frac{3n^2+n+1}{2n^2-1}}[/tex]

it is in the form,

[tex]\sum \limits^\infty_{n=1 }{(-1)^{n+1}\ a_n[/tex]

If the series is convergent then it satisfies,

i)[tex]b_{n+1}\ \leq\ b_n\ for\ all\ n[/tex]

ii)[tex]\lim_{n \to \infty} a_n =0[/tex]

if any of the above condition dissatisfies then the series is divergent

First check the 2nd condition,

[tex]\lim_{n \to \infty}\frac{3n^2+n+1}{2n^2-1}}\\\\= \lim_{n \to \infty}\frac{n^2(3+\frac{1}{n}+\frac{1}{n^2})}{n^2(2-\frac{1}{n^2})}}\\\\=\frac{3+0+0}{2-0}\\\\=\frac{3}{2}[/tex]

Here, [tex]\lim_{n \to \infty} a_n \neq 0[/tex]

Thus, the given series is divergent.

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