Need Help ASAP!!!
Which of the following is a key property of the linear parent function?
O A. It is in quadrants I and III.
B. It does not go through the origin.
C. It has a slope of zero.
O D. It is a curved line.

If [tex]a = 0[/tex], then [tex]y = ax^2+bx+c[/tex] turns into [tex]y = 0x^2+bx+c[/tex]. That [tex]0x^2[/tex] term goes away because it turns into 0, and adding 0 onto anything does not change the expression.

So  [tex]y = 0x^2+bx+c[/tex] turns into [tex]y = bx+c[/tex] which is a linear equation (b is the slope, c is the y intercept). It is no longer a quadratic as quadratic equations always graph out a curved parabola.

As an example, you could graph out [tex]y = 0x^2+3x+4[/tex] and note how it's the exact same as [tex]y = 3x+4[/tex], both of which are straight lines through the two points (0,4) and (1,7).

Answer: 49/9

Step-by-step explanation: 42/9 + 7/9 = 49/9

Make first fraction into improper fraction with the same common dominator as 7/9 and add them both

Hope this helps:)

Answer:

49/9

Step-by-step explanation:

Answer:

First blank is 4, second blank is 0

Step-by-step explanation:

divide it :)

Answer:

Yellow box #1=0

Yellow box #1=4

Step-by-step explanation:

Answer:The first one

Step-by-step explanation:

V rectangular prism = Area of the base *5

Answer:

(1,1)

Step-by-step explanation:

x=1

y=1

6(1) + 1=7

6+1=7

Answer:

x=1, y=1

Step-by-step explanation:

Answer:

(See explanation below for further details).

Step-by-step explanation:

Let be a parametric curve represented by [tex]x = 3\cdot t - 5[/tex] and [tex]y = 5\cdot t + 1[/tex], where [tex]t[/tex] is the parametric variable.

The curve is represented graphically with the help of a graphing tool, whose outcome is included in the image attached below. The corresponding rectangular equation is found by eliminating t of each equation.

[tex]t = \frac{x+5}{3}[/tex] and [tex]t = \frac{y-1}{5}[/tex]

[tex]\frac{x+5}{3} = \frac{y-1}{5}[/tex]

[tex]5\cdot (x+5) = 3\cdot (y-1)[/tex]

[tex]5\cdot x +25 = 3\cdot y - 3[/tex]

[tex]5\cdot x -3\cdot y = -28[/tex]

The parametric equations represents a linear function (first-order polynomial).

Answer:

f(x) translate 2 units down to get the function g(x).

Step-by-step explanation:

From the given tables it is clear that the x-values for both tables are -2,-1,2,3,4.

Difference between y-values of both functions are:

[tex]\dfrac{-17}{9}-\dfrac{1}{9}=-2[/tex]

[tex]\dfrac{-5}{3}-\dfrac{1}{3}=-2[/tex]

[tex]7-9=-2[/tex]

[tex]25-27=-2[/tex]

[tex]79-81=-2[/tex]

So, difference between y-values of both functions is constant, i.e., -2.

Now, we get

[tex]g(x)=f(x)-2[/tex]

It means function f(x) shifts 2 units down to get the function g(x).

Therefore, f(x) translate 2 units down to get the function g(x).

Answer: horizontal or vertical stretch

Answer:

Every decade, the number of species decays by a factor of 0.0834.

Step-by-step explanation:

Let be [tex]S(t) = 25,000,000\cdot 0.78^{t}[/tex], [tex]\forall t \geq 0[/tex]. The decay rate per decay is deducted from the following relation:

[tex]\frac{S(t+10)}{S(t)} = \frac{25,000,000\cdot 0.78^{t+10}}{25,000,000\cdot 0.78^{t}}[/tex]

[tex]\frac{S(t+10)}{S(t)} = 0.78^{t+10-t}[/tex]

[tex]\frac{S(t+10)}{S(t)} = 0.78^{10}[/tex]

[tex]\frac{S(t+10)}{S(t)} = 0.0834[/tex]

Every decade, the number of species decays by a factor of 0.0834.

Answer:

28% subtracted

Step-by-step explanation:

khan

Answer:

7.22?

Step-by-step explanation:

Answer:

0.158655253931 or 15.8%

Step-by-step explanation:

Answer: Car-maker C1

Explanation:

The minimum value is visually shown as the tip of the left whisker. For car-maker C1, the min value is 12. For car-maker C2, the min value is 10, which we can see is less than C1's value. So that's why C1 is the answer.

Answer:

C - 3 (negative 64 divided by 8) + 25 =1

Step-by-step explanation:

Answer:

C is correct answer

Step-by-step explanation:

Answer:

slope is m=1. y-intercept is -1

Answer:

Slope is 1 and intercept is -1. Slope can be found by taking the rise and run of 2 points on a graph. and intercept is just when x = 0

Answer:

20*19*18 = 6840

UNLESS...............  

he is allowed to ride the same ride again , over and over....  

then it is 20 x 20 x 20 = 8000

Step-by-step explanation:

Multiply both sides of the ODE

[tex]x'+2tx+5t[/tex]

by [tex]e^{t^2}[/tex]:

[tex]e^{t^2}x'+2te^{t^2}x=5te^{t^2}[/tex]

Now the left side can be condensed as the derivative of a product:

[tex]\left(e^{t^2}x\right)'=5te^{t^2}[/tex]

Integrate both sides, then solve for x :

[tex]e^{t^2}x=\dfrac52e^{t^2}+C[/tex]

[tex]\implies x(t)=\dfrac52+Ce^{-t^2}[/tex]

Given that x(0) = 8, we find

[tex]8=\dfrac52+Ce^0\implies C=\dfrac{11}2[/tex]

so that the particular solution to this IVP is

[tex]\boxed{x(t)=\dfrac{5+11e^{-t^2}}2}[/tex]

Answer:

13

Step-by-step explanation:

factors of 13 : 1, 13

factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

factors of 49: 1, 7, 49

factors of 65: 1, 5, 13, 65

factors of 87: 1, 3, 29, 87

Answer:

1) 2(x-1)^2

2)  y=2(x-1)^2

Step-by-step explanation:

The 1st one is a statement in the terms of x, and the 2nd on is in the slope intercept(graphing) format

Answer:

Option A

Step-by-step explanation:

Given function is,

f(x) = x² + 3x + 5

We have to find the value of f(a + h) so we will substitute (a + h) in place of x, and simplify the expression.

f(a + h) = (a + h)² + 3(a + h) + 5

           = a² + 2ah + h² + 3(a + h) + 5 [(a + b)² = a² + 2ab + b²]

           = a² + 2ah + h² + 3a + 3h + 5

Therefore, Option A will be the answer.

Answer:

2

Step-by-step explanation:

A corresponding angle is in the same position on another parallel line

1 and 2 are both above the parallel line and  to the left of the transversal

1 and 2 are corresponding angles

Answer: Angle 2

Step-by-step explanation:

Corresponding Angles are angles that take up the same spot at independent vertices, with the same transversal.  Both angle 1 and 2 are the top left angles of their vertex.

Hope it helps <3

Answer:

Total bill = $70.80

Step-by-step explanation:

$60 × 0.18 = $10.80

$60 + $10.80 = $70.80

Hope this helps! :)

Answer:

$70.8

Step-by-step explanation:

Since it is 18 percent tax,we need to find 18% of 60$.In order to do that we need to do 60/1 mutiplied by 18/100 and doing the math 18% of 60 =10.8

Now we have to add 60+10.8=$70.8

Thank you and I hope all you have an amazing day.Hope this helps you.Thank you.

Answer:

[tex]\boxed{\sf \ \ \ x = 1 \ \ , \ \ y = 1 \ \ \ }[/tex]

Step-by-step explanation:

hello

we can multiply by 10 both parts of the equations so this is equivalent to

(1) 15x + 8y = 23

(2) 3x - 2y = 1

and we are asked to use the method of substitution

from (2) we can write 3x = 2y + 1

and we substitute 3x in (1) as 15x = 5*3x it comes

5*(2y+1) + 8y = 23

<=> 10y + 5 + 8y = 23

<=> 18y + 5 = 23  let's subtract 5

<=> 18y = 23 - 5 = 18  let's divide by 18

<=> y  =  1

and finally replace y in 3x = 2y + 1

3x = 2*1 + 1 = 3 <=> x = 1 (divide by 3)

so the solution is x = 1, y = 1

hope this helps

Answer:

(1,1)

Step-by-step explanation:

1.5x + 0.8y = 2.3

0.3x − 0.2y = 0.1

I'm going to multiply both of these equations by 10, so we can work with whole numbers.

15x+8y=23

3x-2y=1

We can simplify one of the equations to isolate a variable.

I'm going to isolate y in equation 2.

3x-2y=1

Subtract 3x from both sides.

-2y=-3x+1

Divide both sides by -2.

y=1.5x-0.5

Plug 1.5x-0.5 into the first equation for y.

15x+8(1.5x-0.5)=23

Distribute.

15x+12x-4=23

Combine like terms.

27x-4=23

Add 4 to both sides.

27x=27

Divide both sides by 27.

x=1

Plug that back into original equation to find y.

15(1)+8y=23

15+8y=23

Subtract 15 from both sides.

8y=8

Divide both sides by 8.

y=1

The solution to the system is (1,1).

Answer:

The total number of ways the researcher can select  5 women and 5 men for a study is 7,56,756.

Step-by-step explanation:

The complete question is:

From a group of 10 women and 15 men, a researcher wants to randomly select  5 women and 5 men for a study in how many ways can the study group be selected?

Solution:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

 [tex]{n\choose k}=\frac{n!}{k!\cdot (n-k)!}[/tex]

The number of women in the group: [tex]n_{w}=10[/tex].

The number of women the researcher selects for the study, [tex]k_{w}=5[/tex]

Compute the total number of ways to select 5 women from 10 as follows:

[tex]{n_{w}\choose k_{w}}=\frac{n_{w}!}{k_{w}!\cdot (n_{w}-k_{w})!}=\frac{10!}{5!\cdot (10-5)!}=\frac{10!}{5!\times 5!}=252[/tex]

The number of men in the group: [tex]n_{m}=15[/tex].

The number of men the researcher selects for the study, [tex]k_{m}=5[/tex]

Compute the total number of ways to select 5 men from 15 as follows:

[tex]{n_{m}\choose k_{m}}=\frac{n_{m}!}{k_{m}!\cdot (n_{m}-k_{m})!}=\frac{15!}{5!\cdot (15-5)!}=\frac{15!}{5!\times 10!}=3003[/tex]

Compute the total number of ways the researcher can select  5 women and 5 men for a study as follows:

[tex]{n_{w}\choose k_{w}}\times {n_{m}\choose k_{m}}=252\times 3003=756756[/tex]

Thus, the total number of ways the researcher can select  5 women and 5 men for a study is 7,56,756.

its congruent by HL or RHSaxiom

Answer:

HL

Step-by-step explanation:

[tex] In\: right \triangle 's DAB \: \&\: CBA\\

\angle DAB \cong \angle CBA... (each 90\degree) \\ hypotenuse \: DB \cong hypotenuse \: CA. (given) \\

side AB \cong side BA.. (common) \\

\therefore \triangle DAB \cong \triangle CBA.. (By \: RHS\: or \: HL \: Postulate) [/tex]

Answer:

a. 55 cars

b. 25 cars

Step-by-step explanation:

Let's call the number of cars with stereo systems N(ss), with air conditioners N(ac) and with sun roofs N(sr).

So we have that:

N(ss) = 30

N(ac) = 30

N(sr) = 40

N(ss and ac and sr) = 15

N(at least two) = 30

a.

To find how many cars have at least one option (N(at least one) or N(ss or ac or sr)), we have:

N(ss or ac or sr) = N(ss) + N(ac) + N(sr) - N(ss and ac) - N(ss and sr) - N(ac and sr) + N(ss and ac and sr)

N(ss or ac or sr) = 30 + 30 + 40 - (N(at least two) + 2*N(ss and ac and sr)) + 15

N(ss or ac or sr) = 30 + 30 + 40 - (30 + 2*15) + 15 = 55

b.

The number of cars that have only one option is:

N(only one) = N(at least one) - N(at least two)

N(only one) = 55 - 30 = 25

Answer:

The results of the hypothesis test suggests that there is no difference in productivity level of two warehouses (East Coast and the Midwest Coast).

p-value = 0.0473

Step-by-step explanation:

To perform this test we first define the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, we want to test if there is a difference in productivity level of the two warehouses (East Coast and the Midwest Coast).

Hence, the null hypothesis would be that there isn't significant evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast). That is, there is no difference in the productivity level of two warehouses (East Coast and the Midwest Coast).

The alternative hypothesis is that there is significant evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast).

Mathematically, if the average productivity level of the East Coast group is μ₁, the average productivity level of the Midwest group is μ₂ and the difference in productivity level is μ = μ₂ - μ₁

The null hypothesis is represented as

H₀: μ = 0 or μ₂ = μ₁

The alternative hypothesis is represented as

Hₐ: μ ≠ 0 or μ₂ ≠ μ₁

So, to perform this test, we need to compute the test statistic

Test statistic for 2 sample mean data is given as

Test statistic = (μ₂ - μ₁)/σ

σ = √[(s₂²/n₂) + (s₁²/n₁)]

μ₁ = average productivity level of the East Coast group = 1299 parts shipped

n₁ = sample size of East Coast group surveyed = 35

s₁ = standard deviation of the East Coast group sampled = 350

μ₂ = average productivity level of the Midwest group = 1456 parts shipped

n₂ = sample size of Midwest group surveyed = 35

s₂ = standard deviation of the Midwest group sampled = 297

σ = √[(297²/35) + (350²/35)] = 77.5903160379 = 77.59

We will use the t-distribution as no information on population standard deviation is provided

t = (1456 - 1299) ÷ 77.59

= 2.02

checking the tables for the p-value of this t-statistic

Degree of freedom = df = n₁ + n₂ - 2 = 35 + 35 - 2 = 68

Significance level = 0.01

The hypothesis test uses a two-tailed condition because we're testing in both directions.

p-value (for t = 2.02, at 0.01 significance level, df = 68, with a two tailed condition) = 0.047326

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.01

p-value = 0.047326

0.047326 > 0.01

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that there isn't enough evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast).

Hope this Helps!!!

We assume that we need to simplify the expression in two different ways.

Answer:

One way: Raise both, the numerator and denominator, to the third power, and then simplify the expression.

Second way: Simplify the terms inside parentheses, and then raise the result to the third power.

The result of both ways is the same: [tex] \\8x^{9}[/tex]

Step-by-step explanation:

One way

Raise both, the numerator and denominator, to the third power, and then simplify the expression:

[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]

[tex] \\ (\frac{64x^{5*3}}{8x^{2*3}})[/tex]

[tex] \\ (\frac{64x^{15}}{8x^{6}})[/tex]

[tex] \\ \frac{64}{8}\frac{x^{15}}{x^{6}}[/tex]

[tex] \\8x^{9}[/tex]

This is the first simplification.

Second way

Simplify the terms inside parentheses, and then raise the result to the third power.

[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]

[tex] \\ (\frac{4}{2}*\frac{x^{5}}{x^{2}})^{3}[/tex]

[tex] \\ (2*x^{5-2})^{3}[/tex]

[tex] \\ (2*x^{3})^{3}[/tex]

[tex] \\ (2^{3}*x^{3*3})[/tex]

[tex] \\ (8*x^{9})[/tex]

or [tex] \\ 8x^{9}[/tex].

Answer:

Result = 9b/25 or 36b/100

Step-by-step explanation:

The number is b

step 1

b is decreased by 40%

value of 40% of b = 40/100 *b = 4b/10

New value after this change = b - 40% decreased value of b = b -4b/10

= (10b-4b)/10 = 6b/10

Step 2 The new value obtained is again decreased by 40%

value of 40%  number found in step 1 =  40% of value found in step 1

value of 40%  number found in step 1 =  40/100 * 6b/10 = 24b/100

This value (24b/100) is subtracted from value found in step 1(6b/10) as given that  value obtained is decreased by 40%

new value found after 40% decrease = 6b/10 - 24b/100

new value found after 40% decrease = 60b/100 - 24b/100= 36b/100

new value found after 40% decrease =  36b/100 = 9b/25

Thus, the result of b is decreased by 40% and decreased again by 40% is 9b/25

Hope you understand :)

Answer:

x°=55°

Step-by-step explanation:

90°=35°+x°

90°-35°=x°

55°=x°

therefore, x°=55°

Answer:

56 46 38 2 12

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

I used Desmos

We will see that the y-intercept of g(x) is larger than the y-intercept of f(x).

For a function y = f(x), the y-intercept is the value that takes y when we evaluate in x = 0.

So, for the first function:

[tex]f(x) = (1/5)*|x - 15|[/tex]

The y-intercept is:

[tex]f(0) =  (1/5)*|0 - 15| = 15/5 = 3[/tex]

For the second function:

[tex]g(x) = (x - 2)^2[/tex]

The y-intercept is:

[tex]g(0) = (0 - 2)^2 = (-2)^2 = 4[/tex]

Then we can see that g(x) has a greater y-intercept than f(x).

If you want to learn more about y-intercepts:

https://brainly.com/question/1884491

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