Consider the piecewise function shown on the graph, which is composed of three different function types. ----- IMAGE ATTACHED BELOW
Match each piece of the function with its domain.

Answer:

2x^2+x-15

Step-by-step explanation:

foil

Answer:

2x^2 + x - 15

Step-by-step explanation:

using FOIL

(2x - 5)(x + 3)

[(2x ⋅ x) + (2x ⋅ 3) + (-5 ⋅ x) + (-5 ⋅ 3)]

[2x^2 + 6x - 5x - 15]

2x^2 + x - 15

Answer:

Slope is 5/2

y-intercept is 2

Step-by-step explanation:

Turn the equation into slope intercept form [ y = mx +  b ].

2y = 5x + 4

~Divide everything by 2

y = 5/2x + 2

Remember that in slope intercept form, m = slope and b = y-intercept.

Best of Luck!

Answer:

slope: 2.5

y-intercept: 2

Step-by-step explanation:

First isolate the y variable which changes the equation to y=2.5x+2

The equation of a line is mx + b where m is the slope and b and the

y-intercept. Leading us to conclude that 2.5 is the slope and 2 is the y-intercept.

Answer:

y = 25x + 40

Step-by-step explanation:

The electrician charges $25 per hour.

The number of hours is x.

Therefore after x hours the electrician will charge $25x. (multiply the charge by the number of hours $25 * x)

Therefore fee(y) charged by the electrician = $40 + $25x

Hence y = 25x + 40

Answer:

-1

Step-by-step explanation:

Pick two points on the line

(0,2) and (2,0)

Using the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 0-2)/(2-0)

    = -2/2

  = -1

Answer:

-1

Step-by-step explanation:

Use two points on the line to find the slope, using rise over run.

We can use the points (0, 2) and (2, 0).

From the first point to the other, the y value decreases by 2 and the x value increases by 2.

Use rise (change in y value) over run (change in x value):

-2 / 2

= -1

So, the slope is -1.

Answer:7938 inches square

Step-by-step explanation:

multiply everything

Answer:

7938

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

đạo hàm cấp 2 của f(x) rồi thế 0 vào

Answer:

93.6

Step-by-step explanation:

The easiest way for me to complete this was to break it up into parts. I Separated the small triangle and the big triangle. I turned them both into squares and multiplied the dimensions. I then divided those by two and added them together.

Answer:

73.5

Step-by-step explanation:

Answer:

The unknown is 100

Step-by-step explanation:

A straight line is 180 degrees

We have two angles x, and 80

x+80 = 180

x = 180-80

x= 100

Answer:

Step-by-step explanation:

x = 0, 1/5

Answer:

y=-1/7x + 12/7

Step-by-step explanation:

Start by finding the slope

m=(1-0)/(-5-2)

m=-1/7

next plug the slope and the point (-5,1) into point slope formula

y-y1=m(x-x1)

y1=1

x1= -5

m=-1/7

y- 1 = -1/7(x - -5)

y-1=-1/7(x+5)

Distribute -1/7 first

y- 1=-1/7x + 5/7

Add 1 on both sides, but since its a fraction add 7/7

y=-1/7x + (5/7+7/7)

y=-1/7x+12/7

Answer:

Step-by-step explanation:

(-5,1) (2,0)

m=(y-y)/(x-x)

m = (0-1)/2- -5)

m = -1/7

(2,0)

y-0= -1/7 (x-2)

y = -1/7x + 2/7

Answer:

90 i think

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

The diameter is equal to twice the length of the radius

So if the radius is 9 then the diameter is 9 * 2 = 18

Answer:

1) A

B) 5.818 stops

Step-by-step explanation:

Number One is less than or equal to 21 because the person only has 21 dollars, so she can't spend more than 21.

B can be solved through the equation by first subtracting $5, and then dividing 2.75 by 16.

Sampling technique is a way of selecting a sample from a given population. The best way to get a sample of students that represents all 8:00 AM classes is by using a stratified sampling technique.

From the complete question, we can summarize the given data as follows:

[tex]Buildings = 3[/tex] ----3 buildings in the college

[tex]Lecture\ Halls =2[/tex]  ---- 2 lecture halls in each building

[tex]Capacity = 100[/tex] --- 100 students in each lecture hall

Because the students' lecture halls are not in the same building, the best way to get a sample is as follows:

The number of students in each building is:

[tex]Students = Capacity \times Lecture\ Halls[/tex]

[tex]Students = 100 \times 2[/tex]

[tex]Students = 200[/tex]

There are 200 students in each building

The above method is referred to as a stratified sampling technique because the population of the students are divided into groups, before being randomly selected.

Read more about sampling techniques at:

https://brainly.com/question/9612230

Answer:

To Find F(3) you just have to replace x=3 so:

F(3)= -3^3 + 4×3^2 -2×3 = -27 +4×9 - 6 = -33 + 36 = 3

Answer:

the answer would be (7,5)

You're looking for a solution of the form

[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n[/tex]

Differentiating twice yields

[tex]\displaystyle y' = \sum_{n=0}^\infty n a_n x^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n[/tex]

[tex]\displaystyle y'' = \sum_{n=0}^\infty n(n-1) a_n x^{n-2} = \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n[/tex]

Substitute these series into the DE:

[tex]\displaystyle (x-1) \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n - x \sum_{n=0}^\infty (n+1) a_{n+1} x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]

[tex]\displaystyle \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^{n+1} - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=0}^\infty (n+1) a_{n+1} x^{n+1} + \sum_{n=0}^\infty a_n x^n = 0[/tex]

[tex]\displaystyle \sum_{n=1}^\infty n(n+1) a_{n+1} x^n - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=1}^\infty n a_n x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]

Two of these series start with a linear term, while the other two start with a constant. Remove the constant terms of the latter two series, then condense the remaining series into one:

[tex]\displaystyle a_0-2a_2 + \sum_{n=1}^\infty \bigg(n(n+1)a_{n+1}-(n+1)(n+2)a_{n+2}-na_n+a_n\bigg) x^n = 0[/tex]

which indicates that the coefficients in the series solution are governed by the recurrence,

[tex]\begin{cases}y(0)=a_0 = -7\\y'(0)=a_1 = 3\\(n+1)(n+2)a_{n+2}-n(n+1)a_{n+1}+(n-1)a_n=0&\text{for }n\ge0\end{cases}[/tex]

Use the recurrence to get the first few coefficients:

[tex]\{a_n\}_{n\ge0} = \left\{-7,3,-\dfrac72,-\dfrac76,-\dfrac7{24},-\dfrac7{120},\ldots\right\}[/tex]

You might recognize that each coefficient in the n-th position of the list (starting at n = 0) involving a factor of -7 has a denominator resembling a factorial. Indeed,

-7 = -7/0!

-7/2 = -7/2!

-7/6 = -7/3!

and so on, with only the coefficient in the n = 1 position being the odd one out. So we have

[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n \\\\ y = -\frac7{0!} + 3x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots[/tex]

which looks a lot like the power series expansion for -7eˣ.

Fortunately, we can rewrite the linear term as

3x = 10x - 7x = 10x - 7/1! x

and in doing so, we can condense this solution to

[tex]\displaystyle y = 10x -\frac7{0!} - \frac7{1!}x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots \\\\ \boxed{y = 10x - 7e^x}[/tex]

Just to confirm this solution is valid: we have

y = 10x - 7eˣ   ==>   y (0) = 0 - 7 = -7

y' = 10 - 7eˣ   ==>   y' (0) = 10 - 7 = 3

y'' = -7eˣ

and substituting into the DE gives

-7eˣ (x - 1) - x (10 - 7eˣ ) + (10x - 7eˣ ) = 0

as required.

Answer:

26 and 2

Step-by-step explanation:

Given,

Sum of two even numbers = 54

let one number be x

another number be x +2

x + x +2 = 54

2x + 2 = 54

2x = 54 - 2

2x = 52

x = 52/2

x = 26

Therefore, the numbers are 26 and 26 + 2 = 28..

Answer:

3×(-4)×2

= -24

good day god bless you

Answer:

(−25)(5) = −125; he withdrew $125

-24

Step-by-step explanation:

Because he is withdrawing money, he is deducing money form his account, which makes the $25 negative in the equation. The weeks however, cannot be negative. so the correct answer is (−25)(5) = −125; he withdrew $125.

(3) x (-4) x (2)

(3 x -4) x (2)

(-12) x (2)

(-12 x 2)

-24

hope this helps! if you have any questions, let me know!

Solution :

a). The point estimate of proportion of college graduates among women who work at home,

[tex]$\hat p =\frac{166}{506}$[/tex]

  = 0.3281

99.5% confidence interval

[tex]$=\left( \hat p \pm Z_{0.005/2} \sqrt{\frac{\hat p (1- \hat p)}{n}} \right)$[/tex]

[tex]$=\left( 0.3281 \pm 2.81 \sqrt{\frac{0.3281 \times (1- 0.3281)}{506}} \right)$[/tex]

[tex]$=(0.3281 \pm 0.0586)$[/tex]

[tex]$=(0.2695, 0.3867)$[/tex]

Answer:

length= 125

width= 100

Step-by-step explanation:

let width have a length of x m

therefore length= (x+25)m

perimeter=2(length +width)

p=2((x+25)+x)

p=4x+50

but we have perimeter to be 450,, we equate it to 4x+50 above,

450=4x+50

4x=400

x=100 m

length= 125

width= 100

Answer:

15/17

Step-by-step explanation:

sinA = CB/CA =15/17

Answer:

Step-by-step explanation:

Answer:

a³b

Step-by-step explanation:

(ab²)³/b⁵

= a³b⁶/b⁵

= a³b

Answer:

384 cars

Step-by-step explanation:

To find the total number of spaces in the carpark, we must multiply the number of rows by how many cars they can accommodate:

34 ⋅ 40 = 1360

As you can see, we have 1360 total spaces. Since there are 976 cars parked, and we want to find out how many spaces are left, we have to subtract the amount of cars parked from the total spaces.

1360 - 976 = 384

Therefore, our answer is 384, specifically, 384 cars.

Answer:

384 cars.

Step-by-step explanation:

40 * 34 - 976

= 1360 - 976

= 384.

Answer:

27

Step-by-step explanation: