What is the vertex for this function?
y=2x^2−12x+16

(-2, 12)

(-2, 3)

(-12, 36)

(3, -2)

Using an exponential function, it is found that Justin's starting salary was of $50,137.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem, we have that r = 0.037 and A(12) = 77536, hence:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]77536 = A(0)(1.037)^{12}[/tex]

[tex]A(0) = \frac{77536}{(1.037)^{12}}[/tex]

A(0) = 50137.

Justin's starting salary was of $50,137.

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★ Given that,

★ To calculate,

So here we would be using the formula of calculating the midpoint of two points.

Midpoint of two points:-

★ We have :

★ Putting the values :

★ Therefore,

★ Centroid of a triangle :-

★ Distance Formula :-

The linear equation that passes through the two given points is:

y = (1/3)*x + (5/3)

A linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is equal to:

a = (y₂ - y₁)/(x₂ - x₁).

In this case, we know that the line passes through (-2, 1), and (4, 3).

Then the slope is:

a = (3 - 1)/(4 - (-2)) = 2/6 = 1/3

So the line is something like:

y = (1/3)*x + b

To find the value of b, we use the fact that the line passes through the point (4, 3), then:

3 = (1/3)*4 + b

3 - 4/3 = b

5/3 = b

So the line is:

y = (1/3)*x + 5/3

Finally, the x-intercept of the line is the value of x such that y = 0.

0 = (1/3)*x + 5/3

-5/3/(1/3) = x = -5

The graph of the line can be seen below.

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I assume the integral is

[tex]\displaystyle \int x^3 e^{-x} \, dx[/tex]

Integrate by parts with

[tex]u = x^3 \implies du = 3x^2 \, dx[/tex]

[tex]dv = e^{-x} \, dx \implies v = -e^{-x}[/tex]

so that

[tex]\displaystyle \int u \, dv = uv - \int v \, du[/tex]

i.e.

[tex]\displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} + 3 \int x^2 e^{-x} \, dx[/tex]

Integrate by parts again, this time with

[tex]u = x^2 \implies du = 2x \, dx[/tex]

[tex]dv = e^{-x} \, dx \implies v = -e^{-x}[/tex]

and so

[tex]\displaystyle \int x^2 e^{-x} \, dx = -x^2 e^{-x} + 2 \int x e^{-x} \, dx[/tex]

[tex]\implies \displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} + 3 \left(-x^2 e^{-x} + 2 \int x e^{-x} \, dx\right)[/tex]

[tex]\implies \displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} - 3x^2 e^{-x} + 6 \int x e^{-x} \, dx[/tex]

Once more, with

[tex]u = x \implies du = dx[/tex]

[tex]dv = e^{-x} \, dx \implies v = -e^{-x}[/tex]

[tex]\displaystyle \int x e^{-x} \, dx = -xe^{-x} + \int e^{-x} \, dx[/tex]

[tex]\implies \displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} - 3x^2 e^{-x} + 6 \left(-xe^{-x} + \int e^{-x} \, dx\right)[/tex]

[tex]\implies \displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} - 3x^2 e^{-x} -6xe^{-x} + 6 \int e^{-x} \, dx[/tex]

Finally,

[tex]\displaystyle \int e^{-x} \, dx = -e^{-x} + C[/tex]

and so

[tex]\displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} - 3x^2 e^{-x} -6xe^{-x} - 6 e^{-x} + C[/tex]

or equivalently,

[tex]\displaystyle \int x^3 e^{-x} \, dx = \boxed{-(x^3+3x^2+6x+6) e^{-x} + C}[/tex]

We can also approach the integral more generally by considering

[tex]I_n = \displaystyle \int x^n e^{-x} \, dx[/tex]

Integrate by parts with

[tex]u = x^n \implies du = nx^{n-1} \, dx[/tex]

[tex]dv = e^{-x} \, dx \implies v = -e^{-x}[/tex]

Then

[tex]\displaystyle I_n = -x^n e^{-x} + n \int x^{n-1} e^{-x} \, dx = -x^n e^{-x} + n I_{n-1}[/tex]

We can solve the recurrence using the initial "value" [tex]I_0 = -e^{-x}+C[/tex] to find a general formula for [tex]I_n[/tex]. Then we get the integral we want [tex]I_3[/tex] "for free".

The quotient of the expression in form of a + bi is 9/13 - 20/13i

Given the following expressions

1+6i/-3+2i

Rationalizing the given rational complex number, we will have;

= 1+6i/-3+2i * -3-2i/-3-2i

= (1+6i)(-3-2i)/9+4
= -3-2i-18i-12i²/13

Simplify the result to have:

= -3+12-20i/13
= 9-20i/13

Express in the form a + bi

9/13 - 20/13i

Hence the quotient of the expression in form of a + bi is 9/13 - 20/13i

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Answer:

1. The wind has blown all the leaves off the tree.

2. All the leaves have fallen to the ground.

3. My kite is being flown in the wind.

4. A shower of acorns have fallen from the sky

5. A busy squirrel dug for his acorns.

6. In the garden, pumpkins have grown.

7. Yesterday my friend and I rode to the park.

8. We have rode to the skate park.

9. My brother wrote me a letter.

10. He has written a essay.

11. Our neighbor had given us a pie.

12. Mom and Dad have spoken to me about cleaning my room.

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

all angles of a triangle equal to 180, so you just have to subtract those two known angles from 180, and you will get the answer.

Find the value of angle x .

The concept of this question belongs to angles of triangle . We know that the sum of all the three angles of triangle is 180°.

As we know that all the angles of triangle is equal to 180° . So :

Therefore , angle x is of 39° .

Answer:

48

Step-by-step explanation:

180 is the whole thing

So add 25 and 107 to make 132, then 180-132

Answer:

13

Step-by-step explanation:

[tex]\text{determinant of A} =\begin{vmatrix}4&-7\\ 3&-2\end{vmatrix}[/tex]

[tex]\text{determinant of A} =\left( 4\times \left( -2\right) \right) -\left( 3\times \left( -7\right) \right)[/tex]

[tex]\text{determinant of A} =-8+21=13[/tex]

The fraction illustrates that there are 6 red tables.

Fron the information, Julia helps the teacher clean the tables in the classroom she notices that 1/4 of the tables are blue and 3/4 of the table are red.

Therefore, the numbers that are red will be:

= Fraction of red × Total number

= 3/4 × 8

= 6

Therefore there are 6 red tables.

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Answer:

[tex] \frac{1}{9} [/tex]

Step-by-step explanation:

[tex] \frac{3}{11} \times \frac{4}{9} [/tex]

[tex] \frac{12}{108} [/tex]

[tex] \frac{1}{9} [/tex]

Answer: D

Step-by-step explanation:

Adjacent sides of a rectangle are perpendicular. This means that the measure of angle HEF is 90 degrees.

Answer: B

Step-by-step explanation: 3/8 + 1/16 = 0.4375 and 7/16 = 0.4375

Answer:

b.

Step-by-step explanation:

first, you would you would find a common denominator between 3/8 and you will get 6/16. last, you would add 1/16 + 6/16 for your answer of 7/16

Answer:

Step-by-step explanation:

So what you want to know is what are the odds of drawing 4 5 6 out of 13.

P(4 5 6) = 3/13

Odds are a little bit different. You are still getting some idea of how likely an event is.

The formula is  Probabity / ( 1 - Probability)

So The probability = 3/13

1 - probability = 1 - 3/13 = 10/13

probability / (1 - probability ) = 3/13 // 10/13 = 3/13 * 13/10 = 3 / 10 or 3 chances in 10.

I think Probability is more intuitively correct.

Answer:

3/13

Step-by-step explanation:

Answer:

She spent $8.15

Step-by-step explanation:

2 × $2.95 for two pizza = $5.9

$5.9 + an additional $2.25 for a soda = $8.15

Answer: 15.

Step-by-step explanation: To find the slope, you need to use rise/run which is done below if you need a visual look at what I'm saying.  Before we use rise/run, we need two points on the line.  We'll use (2, 80), and (6, 140).  We need to go 60 up and 4 to the right to make the points meet.  Going up or down is the rise and left or right is the run.  Our rise/run is 60/4 or 15 when you divide.  Therefore, 15 is your slope for this equation of a line.

Have a great day! :)

Answer:

r = 18 cm

Step-by-step explanation:

The formula for the circumference of a circle is 2πr.

Hence,

2πr = 36π

r = 18 cm

When you divide by a fraction, flip the second fraction over and change divide to multiply:

17/10 / 11/4 = 17/10 x 4/11

Now multiply straight across:

(17 x 4) / (10 x 11) = 68/110

Simplify:

68/110 = 34/55

Answer: 34/55

Answer:

4 hours

Step-by-step explanation:

the rate of people coming in it 700 per hour

Answer:

Parallel lines never intersect. Perpendicular lines are lines that intersect.

Step-by-step explanation:

Hope this helps.

Answer:

Perpendicular lines meet at a 90 degree angle while parallel lines will never touch

Step-by-step explanation:

Answer:

Area of square: 9/16 m²

Step-by-step explanation:

We are given:

The area of the square is the side multiplied by the same side. Therefore,

Using the exponents property, [(a/b)² = (a²/b²)]:

Therefore, the area of the square is 9/16 m².

Answer:

[tex]\huge\boxed{\bf{Area_{square} = \frac{9}{16}m^2}}[/tex]

Step-by-step explanation:

Given : -

To Find : -

Ans : -

$\sf \to Area_{square} = (side\:length)^2$

$\sf \to Area_{square} = (\frac{3}{4}m)^2$

$\sf \to Area_{square} = (\frac{3}{4}m*\frac{3}{4})$

$\sf \to Area_{square} = (\frac{3*3}{4*4}m^2)$

$\sf \to Area_{square} = \frac{9}{16}m^2$

[tex]\:[/tex]

$\huge\colorbox{skyblue}{BlackPain}$

[tex]\cfrac{42}{70}~~ = ~~\cfrac{u}{55}\implies \cfrac{(14)3}{(14)5}~~ = ~~\cfrac{u}{55}\implies \cfrac{3}{5}=\cfrac{u}{55}\implies \cfrac{3(55)}{5}=u \\\\\\ 3\cdot \cfrac{55}{5}=u \implies 3\cdot 11=u\implies 33=u[/tex]

Answer:

see explanation

Step-by-step explanation:

(3)

Parallel lines have equal slopes

the equation of a line in sloipe- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{4}[/tex] x + 5 ⇒ m = [tex]\frac{1}{4}[/tex]

y = 4x + 5 ⇒ m = 4

y = - 4x + 5 ⇒ m = - 4

y = - 4x - 9 ⇒ m = - 4

the 3rd and 4th options have equal slopes and are parallel

(4)

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]

y = [tex]\frac{1}{6}[/tex] x + 4 ⇒ m = [tex]\frac{1}{6}[/tex]

y = - [tex]\frac{1}{6}[/tex] x + 5 ⇒ m = - [tex]\frac{1}{6}[/tex]

y = [tex]\frac{1}{6}[/tex] x + 3 ⇒ m = [tex]\frac{1}{6}[/tex]

y = 6x + 3 ⇒ m = 6

note that a slope of m = 6 , has a perpendicular slope of

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{6}[/tex]

the 2nd and 4th lines are perpendicular

Answer:

She needs 40.4 feet of wood.

Step-by-step explanation:

➾ She had 8 pieces of wood that are 6.2 feet each, so total length of wood she had = 8×6.2

= 49.6feet.

➾She needs total 90feet. of wood and she had already 49.6 feet of wood.

So, now wood she needed = 90-49.6

= 40.4feet.

____________________________

Hope it helps you:)

Answer:

She needs 40.4 feet of wood

Step-by-step explanation:

Given :-

To find:-

Solution:-

Amount of wood she needs more :-

Wood she wanted to complete project — Wood she already have

by putting the value ,

90 feet — 8 × 6.2 feet

= 40.4 feet

Answer:

1 page in 4 sec.

Step-by-step explanation:

To find the rate in lowest terms, divide the 14 pages by 56 seconds and find the simplest fraction.

14/56 = 1/4 in simplest terms.

This means the rate is 1 page in 4 seconds.

Answer:

Revenue was 55,614 the year before

Step-by-step explanation:

Decay Formula: y = a*(1-r)^x

So:

y = 89700 * (1-0.38)^1

y = 55614

well, their total revenue last year was "x", which oddly enough is 100%.  Now, this year's revenue is 38% more than that, well, 100% + 38% = 138%, and we also know that it's 89700, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 89700& 138 \end{array} \implies \cfrac{x}{89700}=\cfrac{100}{138}\implies \cfrac{x}{89700}=\cfrac{50}{69} \\\\\\ 69x=4485000\implies x=\cfrac{4485000}{69}\implies x=65000[/tex]

Answer:

45/28

Step-by-step explanation:

6/7+3/4

The least common multiple of 7 and 4 is 28.

Convert 6/7 and 3/4 to fractions with the denominator of 28

24/28+21/28

Since the denominators are now the same, add the numorators to get 45/28