What is the equation of a quadratic function whose vertex is (3, 0) and a = 1 and passes through the point (2, 1)? *
a. y = (x + 3)²
b. y = (x + 2)²
c. y = (x - 3)²
d. y = (x - 2)²

Given the roots of a quadratic function 3 and 2, which of the following functions has these roots? *
a. y = x² – 5x + 6 :)
b. y = x² – x + 6
c. y = x² – 5x + 3
d. y = x² + x + 5​

Answer:

y + 5x = -7

Step-by-step explanation:

Hello there?

y + 3 = -5(x + 2)

LHS

Open the brackets

= -5x - 10

RHS remains

Combine the two:

y + 3 = -5 - 10

Collecting the like terms and taking the value of x to the LHS

=> y + 5x = - 7

I hope this helps. Have a nice studies

Answer:

use graphs

Step-by-step explanation:

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Answer:

Step-by-step explanation:

(1+25 /100) (1-20/100) (1-50/100)  <1

5/4 x 4/5 x 1/2 <1

Decrease in volume (in percent)

(1+25 /100) (1-20/100) (1-50/100)  x 100

=48.8%

The exterior angle theorem states that the sum of two opposite interior  angles is equal to the measure of the exterior angle.

The distance SL= 5.77 miles between the boat and the lighthouse after travelling 2.1 miles

According to the conditions given in the problem the exterior angle is 70 degrees and one of the opposite interior angle is 35 degrees.

m∠ L + m∠R= 70°

m∠ L +  35° = 70°

m∠ L = 70°-35°

m∠ L = 35°

If one interior angle is 35 degrees the other must also be 35 degrees to make a total of 70 degrees.

The sum of all angles of the triangle is always equal to 180 degrees.

So the third angle of the triangle will be

180°= 35°+35°+m ∠S

m∠S= 110°

From the triangle

Angle theta= m∠S= 110°

Fy= SL= height

Fx= RS = base

F= RL= hypotenuse

The line SL has to be found out.

Let the Fx= 2.1 miles

Then

Fx= Fcos ∅

But Cos   ∅ =  Cos 110°= -0.342

2.1=  F (-0.342)

F= - 6.140 = hypotenuse

Now the vertical component

Fy= Fsine theta

Fy= - 6.140 sine 110°

Fy= - 6.14×0.94

Fy= -5.77 miles

The negative sign indicates that it is in the opposite direction.

https://brainly.com/question/13729598

We are given two equations, one of which has an isolated variable [tex]x[/tex].

That screams to me that substitution would be a prefered strategy here, compared to elimination, although both work.

That means we'll be substituting our value of [tex]x[/tex], which is given as [tex]-y+3[/tex], into the first equation, [tex]15x+31y=-3[/tex].

[tex]15x+31y=-3[/tex]

[tex]x=-y+3[/tex]

[tex]15(-y+3)+31y=-3[/tex]

[tex]-15y+45+31y=-3[/tex]

[tex]16y=-48[/tex]

[tex]y=-3[/tex]

With this value, we can plug it back into either of the two equations to solve for [tex]x[/tex], I'll be substituting it back into the second equation, since it's easier.

[tex]x=-y+3[/tex]

[tex]y=-3[/tex]

[tex]x=-(-3)+3[/tex]

[tex]x=6[/tex]

So our solution is [tex](6,-3)[/tex], and to check we can plug it back into the first equation.

[tex]15x+31y=-3[/tex]

[tex]15(6)+31(-3)=-3[/tex]

[tex]90-93=-3[/tex]

Which is true, so our solution is correct.

Hope this helps!

Answer:

Step-by-step explanation:

[tex]\begin{cases} 15x+31y=-3 \\\\ x=-y+3 \ \ | \times 15\end{cases} \Leftrightarrow \ominus\begin{cases} 15x+31y=-3 \\\\ 15x=-15y+45 \ \ \end{cases} \Leftrightarrow \\\\\\ 15x-15x+31y=-3-(-15y)-45 \\\\ 31y=15y-48 \\\\ 31y-15y=-48 \\\\ 16y=-48 \ \ |\div 16 \\\\ y=-3 \ \ ; \ \ x=-y+3=3+3=6 \\\\[/tex]

[tex]\huge \boldsymbol{\mathfrak {Unswer}}: x=6 \ \ ; \ \ y=-3[/tex]

Answer:

14 is the mean of boys

Step-by-step explanation:

Answer:

x-2y=7 or y=[tex]\frac{1}{2}x-\frac{7}{2}[/tex]

Step-by-step explanation:

Hi there!

We are given the line 2x-4y=8, and we want to write an equation of the line that is parallel to it and passes through (3, -2)

Parallel lines have the same slope, so it would be a good idea to find the slope of 2x-4y=8

The equation is currently written in standard form (ax+by=c), where a, b, and c are free integer coefficients, but a and b CANNOT be equal to 0, and a CANNOT be negative

In order to find the slope of the line, we can rewrite it in another form; for example, slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

To rewrite the line in this way, we'll need to isolate y on one side.

So start by subtracting 2x from both sides

-4y=-2x+8

Divide both sides by -4

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

The slope of the line 1/2, as it's in the place of where m is.

It's also the slope of the line parallel to it.

We can write the equation of the new line in slope-intercept form. Here's what we know so far:

y=[tex]\frac{1}{2}x[/tex]+b (b is a placeholder for the y intercept)

So we'll need to find b.

As the equation passes through the point (3, -2), we can use it to solve for b

Substitute 3 as x and -2 as y:

-2=1/2(3)+b

Multiply

-2=3/2+b

Subtract 3/2 from both sides:

-7/2=b

Substitute -7/2 as b in the equation:

y=[tex]\frac{1}{2}x-\frac{7}{2}[/tex]

The equation can be left as that, or you can convert it back into standard form

Subtract [tex]\frac{1}{2}x[/tex] from both sides, as the variables are on one side.

[tex]-\frac{1}{2}x[/tex]+y=[tex]-\frac{7}{2}[/tex]

Remember that the coefficient in front of x (a) CANNOT be negative, and also the free coefficients a, b, and c CANNOT be fractions.

So in order to clear the fractions and to change the signs, multiply both sides by -2

x-2y=7

Hope this helps!

Answer:

a

Step-by-step explanation:

The transformation from Figure 1 to Figure 2 is:

The transformation of 5 units to the right and 3 units down.

Option C is the correct answer.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

A B C D E has points (-3, 5), (-2, 5), (-1, 4), (-2, 3), and (-5, 3).

A' B' C' D' E' has points (2, 2), (3, 2), (4, 1), (3, 0), and (0, 0).

Now,

A = (-3 + 5, 5 - 3) to A' = (2, 2)

B = (-2 + 5, 5 - 3) to B' = (3, 2)

C = (-1 + 5, 4 - 3) to C' = (4, 1)

D = (-2 + 5, 3 - 3) to A' = (3, 0)

E = (-5 + 5, 3 - 3) to E' = (0, 0)

We see that,

There is a translation of 5 units to the right and  3 units to the down.

Thus,

The transformation of 5 units to the right and 3 units down.

Learn more about translation here:

https://brainly.com/question/12463306

#SPJ1

Answer:

x=

Step-by-step explanation:

Answer:

Do you have a picture that goes with the question that you can post?

Step-by-step explanation:

Answer:

8=4+4

Step-by-step explanation:

If P = (X, Y) is a point in the given square, then X and Y are i.i.d random variables each with distribution

[tex]\displaystyle P(X = x) = \begin{cases}\dfrac14 & \text{if } -2 \le x \le 2 \\ 0 & \text{otherwise}\end{cases}[/tex]

and so the joint density of X and Y is

[tex]\displaystyle P(X = x, Y = y) = \begin{cases}\dfrac1{16} & \text{if }-2 \le x \le 2 \text{ and } -2 \le y \le 2 \\ 0 &\text{otherwise}\end{cases}[/tex]

We want to find P(X² + Y² ≤ 1). Points that satisfy this inequality lie in the set

R = {(x, y) : -1 ≤ x ≤ 1 and -√(1 - x²) ≤ y ≤ √(1 - x²)}

but we can more easily describe the region in polar coordinates by setting

x = r cos(t) and y = r sin(t)

so that the set R is identical to

R' = {(r, t) : 0 ≤ r ≤ 1 and 0 ≤ t ≤ 2π}

Integrate the joint density over R' :

[tex]\displaystyle P(X^2 + Y^2 \le 1) = \iint_R \frac1{16} \, dx \, dy[/tex]

[tex]\displaystyle P(X^2 + Y^2 \le 1) = \iint_{R'} \frac r{16} \, dr \, dt[/tex]

[tex]\displaystyle P(X^2 + Y^2 \le 1) = \int_0^{2\pi} \int_0^1 \frac r{16} \, dr \, dt[/tex]

[tex]\displaystyle P(X^2 + Y^2 \le 1) = \int_0^{2\pi} \frac{1^2 - 0^2}{32} \, dt[/tex]

[tex]\displaystyle P(X^2 + Y^2 \le 1) = \frac1{32} \int_0^{2\pi} dt[/tex]

[tex]\displaystyle P(X^2 + Y^2 \le 1) = \frac{2\pi-0}{32}[/tex]

[tex]\displaystyle P(X^2 + Y^2 \le 1) = \boxed{\frac{\pi}{16}}[/tex]

Answer:

the slop is -1/2 and they y intercept 2

Answer:

that you can define a tangent relationship between a line and an arc. If the adjoining elements change, the tangent relationship is maintained between the elements. Geometric relationships control how a sketch changes when edits are made.

Step-by-step explanation:

i took this i guess and it was gud

Answer:

the slope is 1/4. the equation would be y=1/4x-7 I think

Step-by-step explanation:

Answer:

the width of the rectangle is 15 inches ...

and the length is 3 inches

Answer:

180.

Step-by-step explanation:

to find this, you multiply 36 by 5, which gets you 180.

keyword: times

Answer:

-2

Step-by-step explanation:

rise over run = 4/-2 = -2

Answer:

y-8= -11/6 (x+6)

Step-by-step explanation:

Answer:

Gilbert Stuart's portrait of George Washington The U.S. Constitution

Step-by-step explanation:

Answer:  Gilbert Stuart's portrait of George Washington

The Declaration of Independence

Step-by-step explanation:

Answer:

75/96 or in its simplest form, 25/32

Step-by-step explanation:

1. Convert both fractions into improper fractions

2. Use KFC

15/8 ÷ 12/5 = 15/8 × 5/12

Hope this help!

Answer:

0.01miles/day

Step-by-step explanation:

1: Convert 9cm to miles

[tex]9cm*(\frac{1m}{100cm})*(\frac{1km}{1000m})*(\frac{1mile}{1.609km})=0.000055935miles[/tex]

2: Convert 5.5 minutes to days

[tex]5.5minutes*(\frac{1hour}{60minutes})*(\frac{1day}{24hours})=0.003819444 days[/tex]

3. Set miles over days

[tex]\frac{0.000055935miles}{0.003819444days}[/tex]

4: Divide to get the answer

0.014644 miles/day

5: Round to get the final answer

0.01 miles/day

Answer:

Step-by-step explanation:

Area of the semicircle = pi * r^2 / 2

d = 8

r = d/ 2

r = 8/2 = 4 inches

Area = pi * 4^2 / 2

Area = 3.14 * 8

Area = 25.12 square inches

Area of the triangle

Area = 1/2 * b * h

b = 8

h = 3

Area = 1/2 * 8 * 3

Area = 12 square inches

Total area = 25.12 + 12

Total area = 37.12 square inches

Answer:

its normall

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since it is given that it is quadratic it is of the form   f(n)=an^2 + bn+c.

Since we know a few terms we can plug in to get some equations:

f(1)= a +b+c = 7

f(2)=4a+2b+c = 16

f(3)=9a+3b+c = 31

Now you've got yourself a system of three equations which I trust you can solve.

I will say that I'm not sure that this is the most efficient solution(check out the link below which might have a better solve).

Here are some nice explanations with the "real" math notation for a slightly different but related problem:

https://math.stackexchange.com/questions/2345256/how-to-find-the-nth-term-of-quadratic-sequences

Good luck!

Answer:

B. BD and point E

Step-by-step explanation:

BD and point E is the only choice with both of them lying on the plane, the others lie on other planes

Answer:

x is 10.

..............

Using the percentage method, the amount that Mitch's employer is going to withhold is $29.979

Now, the amount subject to withholding from his total wage payment is;

Provided that the weekly taxable wage is more than $195 but not up to $645; Then, by using the percentage method, the Federal income tax can be computed as:

Therefore, we can conclude that the amount that Mitch's employer is going to withhold is $29.979

Learn more about taxable income here:

https://brainly.com/question/17347618?referrer=searchResults

Answer:

Wrong order!

Step-by-step explanation:

There's a reason why coordinates are called an "ordered pair", and for every point (a, b) a is the x coordinate and b is the y coordinate. The calculations are correct, the way reporting them are not: the point should be (3.0) and (0,2) - in fact, all points on the x axis are of the form (p, 0) and all points on the y axis of the form (0,q)

Answer:

y=x-1

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through the points (7, 6) and (-2, -3)

There are 3 ways to write the equation of the line:

The most common (and usually, the easiest way) would be slope-intercept form, so let's write it that way

First, we'll need to find the slope of the line

The slope can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We have two points, which is needed, but let's label their values in order to avoid any confusion:

[tex]x_1= 7\\y_1=6\\x_2=-2\\y_2=-3[/tex]

Now substitute these values into the formula to find the slope (m):

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-3-6}{-2-7}[/tex]

Subtract the numbers

m=[tex]\frac{-9}{-9}[/tex]

Divide

m=1

The slope of the line is 1

So far, we can write the equation of the line as this:

y=1x+b, or y=x+b

We'll need to find b

As the equation passes through both (7,6) and (-2, -3), we can use either one of them to solve for b

Taking (7, 6) for instance, substitute 7 as x and 6 as y:

6=1(7)+b

Multiply

6=7+b

Subtract 7 from both sides

-1=b

Now substitute -1 as b:

y=x-1

Hope this helps!