f(x) = –2² – 9x
Find f(-2)

Answer:

(4 , -25)

Step-by-step explanation:

that is the procedure above

the vertex of the parabola is calculated by the formula                                          

[tex]\displaystyle\ ax^2+bx+c\quad ;\quad \boxed{x_0=\frac{-b}{2a} \ \ ;\quad y_0 =ax_0^2+bx_0+c} \\\\x_0=-\frac{-8}{2} =4 \quad ; \ \ y_0 =16-32-9=-25 \\\\\ \ Answer: Coordinates \ \ of \ the \ vertex \ of \ the \ \ parabola \ \ (4;-25)[/tex]

Answer:

Y= –7.08, 5.08

Step-by-step explanation:

hope ya ready bro.

X=36/Y

replace 36/y instead of X

36/Y–Y=2===> 36–Y²=2Y===> Y²+2Y–36=0

Y1= –1+√37≈ –7.08

Y2= –1–√37≈ 5.08

Answer:

UJ

Step-by-step explanation:

The side that is opposite angle E is  UJ

Since this is a triangle, we use the corners that do not touch the angle, U and J and the segment is the one that connects them

Answer:

Where are the ordered pairs?

Step-by-step explanation:

Answer:

x = -4

Step-by-step explanation:

Plug in -4 into the function and solve for x:

f(x) = 6x + 20

-4 = 6x + 20

-24 = 6x

-4 = x

So, the answer is x = -4

Answer:

[tex]\approx 26.14[/tex]

Step-by-step explanation:

In this problem, one is given a right triangle, with the length of the hypotenuse given and one of the angles in the triangle. One is asked to find the length of one of the legs. In this situation, one can use right-angle trigonometry. Right angle trigonometry has the following ratios,

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

Please note that the sides named (opposite) and (adjacent) are subjective depending on the angle of reference. The side named (hypotenuse) is the side opposite the right angle, its name does not change. In this case, one is given an angle measure and the measurement of the hypotenuse. One is asked to find the length of the side opoosite this angle. One should use the ratio of sine (sin) to achieve this.

[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

Substitute,

[tex]sin(69)=\frac{opposite}{28}[/tex]

Inverse operations,

[tex]28(sin(69))=opposite[/tex]

[tex]26.14\approx opposite[/tex]

Answer:

26.14

Step-by-step explanation:

Answer:

x = 25°

Step-by-step explanation:

3x + 2x + x + 30° = 180°

6x + 30° = 180°

6x = 150°

x =25°

=> 3x = 25 * 3 = 75°

=> 2x = 25 * 2 = 50°

=> x + 30° = 25° + 30° = 55°

Answer:

34

Step-by-step explanation:

First we need to do 2/3*21, which equals 14 as 3 and 21 can be simplified to 1 and 7. 7 * 2/1= 14. Then we add the 20 to 14, 20+14= 34

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{y = \dfrac{2}{3}x + 20}[/tex]

[tex]\mathsf{y =\dfrac{2}{3}(21) + 20}[/tex]

[tex]\mathsf{\dfrac{2}{3}(21) + 20 = y }[/tex]

[tex]\mathsf{\dfrac{2}{3}(21)=\bf14}[/tex]

[tex]\mathsf{14 + 20 = y}[/tex]

[tex]\mathsf{14 + 20 = \bf 34}[/tex]

[tex]\huge\checkmark\boxed{\huge\textsf{y = 34}}\huge\checkmark[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: \bf y = 34}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\huge\text{Amphitrite1040:)}[/tex]

Answer:

In a product like:

a*b = 0

says that one of the two terms (or both) must be zero.

Here we have our equation:

x^2 + 12 = 7x

x^2 + 12 - 7x = 0

Let's try to find an equation like:

(x - a)*(x - b) such that:

(x - a)*(x - b)  = x^2 + 12 - 7x

we get:

x^2 - a*x - b*x  -a*-b = x^2 - 7x + 12

subtracting x^2 in both sides we get:

-(a + b)*x + a*b = -7x + 12

from this, we must have:

-(a + b) = -7

a*b = 12

from the first one, we can see that both a and b must be positive.

Then we only care for the option with positive values, which is x =3 or x = 4

replacing these in both equations, we get:

-(3 + 4) = -7

3*4 = 12

Both of these equations are true, then we can write our quadratic equation as:

(x - 3)*(x - 4) = x^2 + 12 - 7x

The correct option is the last one.

Answer:

d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The amount of miles increase and the amount of gasoline used increases

Answer:

[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}[/tex]

Step-by-step explanation:

Given

[tex]y=c_1e^x +c_2e^{-x[/tex]

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

[tex]y'(1) =e[/tex]

Required

The solution

Differentiate [tex]y=c_1e^x +c_2e^{-x[/tex]

[tex]y' = c_1e^x - c_2e^{-x}[/tex]

Next, we solve for c1 and c2

[tex]y(1) = 0[/tex] implies that; x = 1 and y = 0

So, we have:

[tex]y=c_1e^x +c_2e^{-x[/tex]

[tex]0 = c_1 * e^1 + c_2 * e^{-1}[/tex]

[tex]0 = c_1 e + \frac{1}{e}c_2[/tex] --- (1)

[tex]y'(1) =e[/tex] implies that: x = 1 and y' = e

So, we have:

[tex]y' = c_1e^x - c_2e^{-x}[/tex]

[tex]e = c_1 * e^1 - c_2 * e^{-1}[/tex]

[tex]e = c_1 e - \frac{1}{e}c_2[/tex] --- (2)

Add (1) and (2)

[tex]0 + e = c_1e + c_1e + \frac{1}{e}c_2 - \frac{1}{e}c_2[/tex]

[tex]e = 2c_1e[/tex]

Divide both sided by e

[tex]1 = 2c_1[/tex]

Divide both sides by 2

[tex]c_1 = \frac{1}{2}[/tex]

Substitute [tex]c_1 = \frac{1}{2}[/tex] in [tex]0 = c_1 e + \frac{1}{e}c_2[/tex]

[tex]0 = \frac{1}{2} e+ \frac{1}{e}c_2[/tex]

Rewrite as:

[tex]\frac{1}{e}c_2 = -\frac{1}{2} e[/tex]

Multiply both sides by e

[tex]c_2 = -\frac{1}{2} e^2[/tex]

So, we have:

[tex]y=c_1e^x +c_2e^{-x[/tex]

[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^2 * e^{-x}[/tex]

[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}[/tex]

Answer:

b

Step-by-step explanation:

Answer:

The explicit formula of that sequence is T - 5

Step-by-step explanation:

Let T represent each term in the sequence. So now try replacing T with each term in the sequence. Like this ;

7 - 5 = 2

2 - 5 = -3

-3 - 5 = -8

hope this helps

Answer:

Sale price = $45.75

Step-by-step explanation:

Original price = $48.41

Percentage Discount = 5.5%

Amount of discount = Percentage Discount × Original price

= 5.5% × $48.41

= 5.5/100 × $48.41

= 0.055 × $48.41

= $2.66255

Sale price = Original price - Amount of discount

= $48.41 - $2.66255

= $45.74745

Approximately,

Sale price = $45.75

Answer:

Step-by-step explanation:

u799

Answer:

60

Step-by-step explanation:

the two angles are equal angle x and the one opposite

=180-40

=120 ÷2

=60

Answer is

z = 70

x = 70

Step-by-step explanation:

z is also equal to x because two sidess are equal

40 + x + x =180

40 + 2x = 180

2x = 140

x =70

so x and z are 70 each

Step-by-step explanation:

SI = PxTxR/100

SI= (13000)(6)(4.7)/100

SI = 366600/100

SI= 3666

Answer:

Step-by-step explanation:

9.7 = [tex]\frac{97}{10}[/tex]

Count the number of places in the decimal number after the decimal point.

Here , there is only one place.

So, multiply and divide by 10. 9.7 *10/1*10 = 97/10

Answer:

Step-by-step explanation:

This is a 30°-60°-90° right triangle.

AC is hypotenuse, AB is opposite side to 30° angle.

We know that in such a triangle the side opposite to 30° angle is half the hypotenuse.

So we have:

Answer:

4x²+2x-2

Step-by-step explanation:

x²-3x+7

+

3x²+5x-9

Answer:

4x² + 2x - 2

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

x² - 3x + 7 + 3x² + 5x - 9

Step 2: Simplify

Answer:

40 and 136

Step-by-step explanation:

The ratio of the 2 numbers = 5 : 17 = 5x : 17x ( x is a multiplier )

One number is 96 more than the other then

17x = 5x + 96 ( subtract 5x from both sides )

12x = 96 ( divide both sides by 12 )

x = 8 , then

5x = 5 × 8 = 40

17x = 17 × 8 = 136

The 2 numbers are 40 and 136

Answer:

p = 0

Step-by-step explanation:

1 - 4p - 2p = 1 - 5p

-6p + 1 = -5p + 1

-p + 1 = 1

-p = 0

p = 0

Answer:

a. 360°

b. 540°

Step-by-step explanation:

a The sum of the exterior angles of any n-sided polygon is always 360°. Therefore:

a + b + c + d + e = 360°

b. Sum of interior angles of an n-sided polygon is given as (n - 2) × 180

The polygon, QRTXW is a 5 sided polygon, therefore n = 5.

Plug in the value of 5 into the equation:

Sum of interior angles of QRTXW = (5 - 2) × 180

= 3 × 180

= 540°

Answer:

m = -1

y intercept = -6

Step-by-step explanation:

The given equation of the line is ,

[tex]\implies y = -x -6[/tex]

We know that the Standard equation of Slope Intercept Form of the line is,

[tex]\implies y = mx + c[/tex]

Where ,

On comparing to the Standard form of the line we get ,

[tex]\implies Slope = -1 [/tex]

[tex]\implies y - intercept= -6 [/tex]

Slope: -1

Hope it helps.

Do comment if you have any query.

Answer:

Step-by-step explanation:

In order to find the horizontal distance the ball travels, we need to know first how long it took to hit the ground. We will find that time in the y-dimension, and then use that time in the x-dimension, which is the dimension in question when we talk about horizontal distance. Here's what we know in the y-dimension:

a = -32 ft/s/s

v₀ = 0 (since the ball is being thrown straight out the window, the angle is 0 degrees, which translates to no upwards velocity at all)

Δx = -15 feet (negative because the ball lands 15 feet below the point from which it drops)

t = ?? sec.

The equation we will use is the one for displacement:

Δx = [tex]v_0t+\frac{1}{2}at^2[/tex] and filling in:

[tex]-15=(0)t+\frac{1}{2}(-32)t^2[/tex] which simplifies down to

[tex]-15=-16t^2[/tex] so

[tex]t=\sqrt{\frac{-15}{-16} }[/tex] so

t = .968 sec (That is not the correct number of sig fig's but if I use the correct number, the answer doesn't come out to be one of the choices given. So I deviate from the rules a bit here out of necessity.)

Now we use that time in the x-dimension. Here's what we know in that dimension specifically:

a = 0 (acceleration in this dimension is always 0)

v₀ = 80 ft/sec

t = .968 sec

Δx = ?? feet

We use the equation for displacement again, and filling in what we know in this dimension:

Δx = [tex](80)(.968) +(0)(.968)^2[/tex] and of course the portion of that after the plus sign goes to 0, leaving us with simply:

Δx = (80)(.968)

Δx = 77.46 feet

Answer:

slope = -2

equation y= -2x -1

y - intercept (0,-1)

Answer:

y-int: -1

Slope: -2/1

Equation: Y=-2/1x-1

Step-by-step explanation:

thank you, you too! :D

Answer:

Solution given:

it is a right angled isosceles triangle

so

perpendicular [p]=base[b]=3

hypotenuse [h]=x

we have

by using Pythagoras law

p²+b²=h²

3²+3²=h²

18=h²

h=[tex]\sqrt{18}[/tex]

x=[tex]\bold{3\sqrt{2}}[/tex]