if f(x)=4x+5 what is the value of f(-3)

[tex]n^2 +6n-27 = n^2+6n-27+0\\~\\n^2+6n-27+0 = n^2+6n-27+(3n-3n) \\~\\n^2+6n-27+(3n-3n) = n^2+9n-3n-27\\~\\n^2+9n-3n-27 = n\cdot(n+9)-3\cdot(n+9) \\~\\n\cdot(n+9)-3\cdot(n+9) = (n+9)(n-3)[/tex]

The other side is n-3

Answers:

a = 2 and b = -4

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Explanation:

Let's define the three helper functions

which are drawn from the piecewise function. The g(x) function will change depending on what the input is.

Since we want g(x) to be continuous at x = 1, this must mean the three functions f(x), h(x), j(x) must have the same output value when the input is x = 1.

Because h(x) = 6 is a constant function, the output is always 6 regardless of the input. Therefore, we want f(x) and j(x) to have 6 as their output when x = 1. Or else, the pieces won't connect.

Plug x = 1 into the f(x) function to get

f(x) = ax^2 - b

f(1) = a(1)^2 - b

f(1) = a - b

Set this equal to the desired output of 6 and we end up with the equation a-b = 6. Solving for 'a' leads to a = b+6.

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

We'll use the same idea for j(x)

j(x) = 5ax + b

j(1) = 5a(1) + b

j(1) = 5a + b

5a+b = 6

5(b+6) + b = 6 ... plug in a = b+6; solve for b

5b+30+b = 6

6b+30 = 6

6b = 6-30

6b = -24

b = -24/6

b = -4

Which then leads to,

a = b+6

a = -4+6

a = 2

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

Since a = 2 and b = -4, we go from this

[tex]g(x) = \begin{cases}ax^2-b, \ \ x < 1\\6, \ \ x = 1\\5ax+b, \ \ x > 1\end{cases}[/tex]

to this

[tex]g(x) = \begin{cases}2x^2+4, \ \ x < 1\\6, \ \ x = 1\\10x-4, \ \ x > 1\end{cases}[/tex]

Meaning

f(x) = 2x^2+4 and j(x) = 10x-4

You should find that plugging x = 1 into each of those two functions leads to 6 as the output.

The graph is shown below. Note the red graph f(x) is only drawn when x < 1. Similarly, j(x) is only drawn when x > 1. The orange point represents h(x) which only happens when x = 1. So as the name implies, the piecewise function g(x) is composed of pieces of the three functions f(x), h(x), j(x).

Answer:

15

Step-by-step explanation:

9 squared + 12 squared = x squared

81 + 144 = x

81 + 144 = 225

the sqaure root of 225 = 15

=> 4(7)–2(7+a)=8

Answer:

12500

Step-by-step explanation:

4.5 × 48=216.

12500 Plus 216= 12,716

The value of the invested money becomes $103393.20 after 4 years if the interest rate is 4.5% and compounded annually.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+r)^t[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          t = How long the money is deposited or borrowed (in years)

We have in the question:

p = $12,500

r = 4.5% ⇒ 0.045

t = 4 years ⇒ 4×12 ⇒ 48 months

Put the above values in the formula, we get;

[tex]\rm A = 12500(1+0.045)^4^8[/tex]

A = 12500×8.27145

A = $103393.20

Thus, the value of the invested money becomes $103393.20 after 4 years if the interest rate is 4.5% and compounded annually.

Learn more about the compound interest here:

brainly.com/question/26457073

Answer:

169.6

Step-by-step explanation:

Answer:

502

Step-by-step explanation:

394+108

Answer:

500 is my best answer

Step-by-step explanation:

Answer:

height = 1/4y

Step-by-step explanation:

V(cylinder) = πr²h

V(cone) = πr²h ÷ 3

V(cyl) = πx²y

V(cone) = π(1/2x)²y which simplifies to be πx²y ÷ 4

πx²y = πx²y ÷ 4

if you divide each side by πx² you get:

y = y/4

height is 1/4y

Answer:

5 pears

Step-by-step explanation:

Given that

The  average of 20 pears were sold from Monday to Friday

But after the sales on Saturday and Sunday, the average pears sold per day were increased to 25

We need to determine the number of pears sold on Saturday and sunday

So, it is

= 25 pears - 20 pears

= 5 pears

Answer: [tex]45.11\ mph[/tex]

Step-by-step explanation:

Given

Speed R varies inversely with time T i.e.

[tex]R\propto \dfrac{1}{T}\\\\R=\dfrac{C}{T}\quad [\text{C=constant}][/tex]

when R=58 mph, T=7 s i.e.

[tex]58=\dfrac{C}{7}\quad \ldots(i)[/tex]

when T=9 s

[tex]R=\dfrac{C}{7}\quad \ldots(ii)[/tex]

Divide (i) and (ii)

[tex]\Rightarrow \dfrac{58}{R}=\dfrac{9}{7}\\\\\Rightarrow R=\dfrac{7}{9}\times 58\\\\\Rightarrow R=45.11\ mph[/tex]

Answer:

and the question is? I'm confused

Answer:

His overtime pay is of $84.00.

Step-by-step explanation:

He is paid double time for overtime.

Basic rate of $7.00, overtime is double, so $7.00*2 = $14.00.

Worked 6 hours overtime:

So his overtime pay is:

$14.00*6 = $84.00

His overtime pay is of $84.00.

Answer:$450 i think?

Step-by-step explanation:

Answer:

[tex]a) \frac{ - 8}{7} [/tex]

[tex]b) \frac{0}{1} [/tex]

[tex]c) \frac{7}{3} [/tex]

hope it helps you:)

This is the transitive property :)

Answer:

A. g=6

Step-by-step explanation:

5g-6=24

5g=30

g=30/5

g=6

Answer:

D, g = -8

Step-by-step explanation:

5 (-8) - 6 => 24

-40 - 6 => 24

-46 is NOT greater than or equal to 24.

Answer:

[tex] - 35{ \bold{.}}( \frac{5}{7} ) \\ = - \frac{175}{7} \\ = 25[/tex]

Answer:

Every Odd Integer is of the form 2q+1

Take 5 as our test odd Number

2(5) + 1 = 11.

This works and Nothing else will from the set of Options.

SO OPTION D IS LEGIT!

Answer: 6.8 inches

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that :

Total amount in cups of green Ooze = 5 cups

From. The dot plot ; The total number of contestants obtained by counting each dot on the plot is 10

Hence ; amout received by each contestants given equal distribution :

5 cups / 10 = 1/2 cups

1/2 cups per contestant.

Answer:

30 strawberry sundaes.

Step-by-step explanation:

We know there is a total of 70 sundaes.

3 sundaes will be strawberry.

4 sundaes will be choclate.

When you add 3 and 4 together, you get 7. This is your total ratio.

So 3/7 of the sundaes are strawberry.

And 4/7 of sundaes are choclate.

We know there is a total of 70 sundaes.

The total ratio we figured out is 7.

If the total sundaes is 70, and the total ration is 7. Then the total sundaes is 10 times bigger than the ratio.

This means we need to multiply the 3 strawberry sundaes and 4 choclate sundaes by 10.

3*10=30

4*10=40

So there are 30 strawberry sundaes and 40 choclate sundaes.

We need to find the strawberry sundae amount, so the answer is 30.

Hope this helps!

Given:

The function is:

[tex]f(x)=-2x+1[/tex]

To find:

a. Slope and Y-intercept.

b. Is the function increasing, decreasing, or constant, justify your answer.

c. Graph the function, label x, and y-intercepts.

Solution:

a. We have,

[tex]f(x)=-2x+1[/tex]                  ...(i)

The slope intercept form of a line is:

[tex]y=mx+b[/tex]                    ...(ii)

Where, m is the slope and b is the y-intercept.

On comparing (i) and (ii), we get

[tex]m=-2,b=1[/tex]

Therefore, the slope of the line is -2 and the y-intercept is 1.

b. If the slope of a linear function is negative, then the function is decreasing.

If the slope of a linear function is positive, then the function is increasing.

If the slope of a linear function is 0, then the function is constant.

The slope of the linear function is negative.

Therefore, the function is decreasing.

c. We have,

[tex]f(x)=-2x+1[/tex]

At [tex]x=0[/tex], we get

[tex]f(0)=-2(0)+1[/tex]

[tex]f(0)=1[/tex]

So, the y-intercept is at (0,1).

At [tex]f(x)=0[/tex], we get

[tex]0=-2x+1[/tex]

[tex]2x=1[/tex]

[tex]x=\dfrac{1}{2}[/tex]

[tex]x=0.5[/tex]

So, the x-intercept is at [tex]\left(0.5,0\right)[/tex].

Plot the points [tex](0,1), \left(0.5,0\right)[/tex] and connect them by a straight line as shown below:

Answer:

use Pisagorth theormi

23²=18²+x²

x²=23²-18²

23²=529

18²=324

x²=205

so the x =√205

its nearly equal 14.3.....

Answer:

B) 9

Step-by-step explanation:

110 + 75 + 11x - 9 + 8x + 13 = 360

19x + 189 = 360

19x (+ 189 - 189) = 360 - 189

19x = 171

19x/19 = 171/19

x = 9