Points are plotted at (-2, 2), (-2, -4), and (2, -4). A fourth point is drawn such that the four points can be connected to form a rectangle. What is the area of this rectangle?

8 square units
12 square units
16 square units
24 square units

Answer:

[tex] x = \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]   and   [tex] y = \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]

[tex] x = \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]   and   [tex] y = \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]

Step-by-step explanation:

Let the numbers be x and y.

We now have a system of equations.

x + y = 5

xy = -3

Solve the second equation for x.

x = -3/y

Now substitute x in the first equation with -3/y.

-3/y + y = 5

Multiply both sides by y.

-3 + y^2 = 5y

y^2 - 5y - 3 = 0

Use the quadratic formula to solve for y.

[tex] y = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] y = \dfrac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(-3)}}{2(1)} [/tex]

[tex] y = \dfrac{5 \pm \sqrt{25 + 12}}{2} [/tex]

[tex] y = \dfrac{5 \pm \sqrt{37}}{2} [/tex]

[tex] y = \dfrac{5 + \sqrt{37}}{2} [/tex]   or   [tex] y = \dfrac{5 - \sqrt{37}}{2} [/tex]

[tex] y = \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]   or   [tex] y = \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]

We get 2 solutions for y. Now for each solution for y, we need to find a corresponding solution for x.

Solve the first equation for x.

x + y = 5

x = 5 - y

Substitute each y value to find the corresponding x value.

[tex] x = 5 - (\dfrac{5}{2} + \dfrac{\sqrt{37}}{2}) [/tex]

[tex] x = 5 - \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]

[tex] x = \dfrac{10}{2} - \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]

[tex] x = \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]

This give one solution as:

[tex] x = \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]   and   [tex] y = \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]

Now we substitute the other y value to find the other x value.

[tex] x = 5 - (\dfrac{5}{2} - \dfrac{\sqrt{37}}{2}) [/tex]

[tex] x = 5 - \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]

[tex] x = \dfrac{10}{2} - \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]

[tex] x = \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]

This give the second solution as:

[tex] x = \dfrac{5}{2} + \dfrac{\sqrt{37}}{2} [/tex]   and   [tex] y = \dfrac{5}{2} - \dfrac{\sqrt{37}}{2} [/tex]

r1 = -12 and r2 = 12

[tex]\bf 40\pi =\cfrac{5}{18}\pi r^2\implies 40\pi =\cfrac{5\pi r^2}{18}\implies 720\pi =5\pi r^2\implies \cfrac{720\pi }{5\pi }=r^2 \\\\\\ 144=r^2\implies \sqrt{144}=r\implies 12=r[/tex]

Answer:

3n+21

Step-by-step explanation:

3 × n =3n

3 × (+7) = +21

Answer:

Use distributive property.

3(n+7),

3*n + 3*7=

3n + 21

Hope this helps and have a great day!

$3.468.15

I just subtracted 1.89% from $183,500

$3,468.15.

To calculate Patrick's annual property taxes on his new home, we need to apply the property tax rate of 1.89% to the value of the home. The formula to calculate this is:

Property Taxes = Home Value  imes Tax Rate

In this case, Patrick's home value is $183,500 and the tax rate is 1.89%. So, the calculation would be:

Property Taxes = $183,500 times 0.0189

When we perform this multiplication, we get:

Property Taxes = $3,468.15

Therefore, the property taxes on Patrick's new home are $3,468.15.

Answer:wazz up

Step-by-step explanation:

yooo what’s up dude

Answer:

No correlation

Step-by-step explanation:

With the information provided, we have to conclude there is no correlation, since there is no apparent link between the two information.

It would be a positive correlation for example if we knew that the more apples Juan eats, the more he sleeps (or vice-versa).

It could be a negative correlation if we found that the more apples he eats, the less hours of sleep he has (or vice-versa).

But in this instance, we don't have any data indicating there is any form of correlation between those two numbers.

Answer:

B

Step-by-step explanation:

Corresponding angles are not always congruent

Corresponding angles are congruent.

Answer is B.

Answer: Second option.

Step-by-step explanation:

The square root of a number "x" is a number "b" that multiplied by itself is "x":

[tex]b*b=x[/tex]

We know that the square root of 16 is 4 ([tex]\sqrt{16}=4[/tex]) because:

[tex]4*4=16[/tex]

Then [tex]\sqrt{13}[/tex] should be less than 4.

We know that the square root of 9 is 3 ([tex]\sqrt{9}=3[/tex]) because:

[tex]3*3=9[/tex]

Then [tex]\sqrt{13}[/tex] should be greater than 3.

Therefore, the value of  [tex]\sqrt{13}[/tex] is between 3 and 4.

This matches with the second option.

Hello Brainly Student! Your answer is 3 and 4! Hope this helped!!

Answer:

C

Step-by-step explanation:

[tex] \frac{ - 1}{3} \times a = -1[/tex]

then

[tex]a = 3 \: where \: a \: is \: our \: line \: slope[/tex]

Answer:

[tex]\boxed{\text{C. } y - 2 = 3(x - 6)}[/tex]

Step-by-step explanation:

The slope of the perpendicular line m₂ must  be the negative reciprocal of the slope m₁ of the first line.

[tex]m_{2} = -\dfrac{1}{m_{1}} = -\dfrac{1}{-\frac{1}{3}} = 3[/tex]

The only equation with m = 3 is  

[tex]\boxed{\textbf{C. } y - 2 = 3(x - 6)}[/tex]

This is the point slope form of the equation for a straight line through (6, 2) with slope = 3.

Answer:

C. 9P6

Step-by-step explanation:

Given choices are :

A. 8P5

B. 9P1

C. 9P6

D.8P1

Now we need to find about which below is largest when evaluated.

So let's evaluate them using formula:

[tex]nPr=\frac{n!}{\left(n-r\right)!}[/tex]

[tex]8P5=\frac{8!}{\left(8-5\right)!}=\frac{8!}{\left(3\right)!}=6720[/tex]

[tex]9P1=\frac{9!}{\left(9-1\right)!}=\frac{9!}{\left(8\right)!}=9[/tex]

[tex]9P6=\frac{9!}{\left(9-6\right)!}=\frac{9!}{\left(3\right)!}=60480[/tex]

[tex]8P1=\frac{8!}{\left(8-1\right)!}=\frac{8!}{\left(7\right)!}=8[/tex]

Largest value among those numbers is 60480.

Hence correct choice is C. 9P6

Answer:

A. 6

Step-by-step explanation:

f(x) = x² − 12x + 7

To complete the square, we first factor the leading coefficient to make it 1 (which it already is).

Then, we take half the second coefficient, square it, and then add to both sides.  So (-12/2)² = (-6)² = 36.

f(x) + 36 = x² − 12x + 36  + 7

Then we factor the perfect square:

f(x) + 36 = (x − 6)² + 7

Then solve for f(x) by subtracting and simplifying:

f(x) = (x − 6)² + 7 − 36

f(x) = (x − 6)² − 29

So the value of a is 6.

Answer:

9

Step-by-step explanation:

The number of possible lunch combinations of sandwich and juice are 9.

If we have to choose r objects out of n objects and then arrange them among themselves, then we first choose the objects in ⁿCr ways and then arrange them in  ways.

This can be used to find the number of different combinations possible of the sandwiches and juices.

Ways to select the sandwiches from 3 options = ³C₁ = 3!/1!(3-1)!

Ways to select the juice from 3 options = ³C₁ = 3!/1!(3-1)!

= ³C₁ = 3!/1!(3-1)!

Now, the total types of possible lunch combinations that can be created as  3×3=9

Hence, the number of possible lunch combinations of sandwich and juice are 9.

To learn more about the permutation and combination visit:

https://brainly.com/question/28065038.

#SPJ2

The value of the expression for 121 is 11

None.

Distribute the 3 to the (x + 4) to get 3x + 12.

Subtract 3x from both sides to get 12 = 4.

This is not true, so there are no solutions.

Answer:

[tex]d=\sqrt{73}[/tex]

Step-by-step explanation:

Use the distance formula.

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Plug in the points.

8 - 0 = 8

8^2 = 64

5 - 8 = -3

-3^2 = 9

64 + 9 = 73

[tex]d=\sqrt{73}[/tex]

Answer:

the answer is 2.9 x 10^0 and 3.2 x 10^-2

Step-by-step explanation:

10^0 is equal to 1 so 2.9 x 10^0 is really 2.9 times 1 which is less than 3

if i could get brainliest answer that would be great!

10^-2 is a exponential that makes a number go down so 3.2 going down is less than 3

Answer:

C and D

Step-by-step explanation:

A.   2.9 × 10¹ = 2.9 × 10     = 29

B.  3.2 × 10³ = 3.2 × 1000 = 3000

C.  2.9 × 10⁰ = 2.9  × 1      = 2.9

D. 3.2 × 10⁻² = 3.2 × 0.01 = 0.032

Both C and D have values less than 3.

Answer:

Option B f(x) = x + 1

Step-by-step explanation:

The given points are

x        y        Relationship (x & y)

-2      -1        -2 + 1 = -1      

0        1         0 + 1 = 1    

1        2          1 + 1 = 2    

3       4          3 + 1 = 4    

5       6          5 + 1 = 6

As we can see the difference in x and y values of each ordered pairs is one

Therefore, relationship between x & y that can be represented by y = x + 1

Option B f(x) = x + 1 is the answer.

Answer:

The variation equation is

[tex] f = \frac{k.m_1.m_2}{ {r}^{2} } [/tex]

step-by-step explanation:

From the question, the two masses are

[tex]m_1 \: and \: m_2[/tex]

This implies that the product of the two masses

[tex] = m_1 \times m_2 = m_1.m_2[/tex]

Moreover, the force,f varies directly with the products of the two masses

[tex] \implies \: f\propto m_1.m_2....eqn.1[/tex]

Also, the force varies inversely with the square of the distance,r

[tex] \implies \: f\propto \frac{1}{ {r}^{2} }.......eqn.2[/tex]

Joining equation 1 and 2, we got

[tex] \implies \: f\propto \frac{1}{ {r}^{2}} \times m_1.m_2[/tex]

[tex] \implies \: f \propto\frac{m_1.m_2}{ {r}^{2}}[/tex]

But the constant of variation is k

Multiplying the right hand side of the equation by k, we got

[tex] \implies \:f=\frac{k.m_1.m_2}{ {r}^{2}}[/tex]

Answer: Option a) 3

Step-by-step explanation:

The formula for calculating combinations is as follows

[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]

Where "n" is the amount of items in a set and you can choose "r" from them

3C1 reads as: The combination of 1 in 3. You have a set of 3 elements and choose 1 of them.

[tex]n = 3\\\\r = 1[/tex]

So :

[tex]3C1=\frac{3!}{1!(3-1)!}\\\\3C1=\frac{3!}{1!*2!}\\\\3C1=\frac{3*2*1}{1*2*1}\\\\3C1=3[/tex]

All triangles equal 180 degrees.

The answer is 180 degrees.

Answer:

113.09733552923 in2

Step-by-step explanation:

The leash is basically the radius. If the radius is 6...

If you find the area of the circle using the formula πr square. π=3.14. you can do the rest.

Buffalo Bills has the lowest price per wing. To find the answer divide the number of wings by the price to see how much it is per wing.

Buffalo Wild Wings offers the lowest cost per wing at $0.833, compared to $0.875 at Buffalo Bills and $0.85 at Fingers.

Comparing these values, Buffalo Wild Wings offers the lowest cost per wing at $0.833.

Answer: Option B

2 is NOT in the domain of f ° g

Step-by-step explanation:

First we must perform the composition of both functions:

If [tex]g(x) = \sqrt{x-9}[/tex] and not [tex]\sqrt{x} -9[/tex]

[tex]f (x) = 4x + 3\\\\g (x) = \sqrt{x-9}\\\\f (g (x)) = 4 (\sqrt{x-9}) + 3[/tex]

The domain of the composite function will be all real numbers for which the term that is inside the root is greater than zero. When x equals 2, the expression within the root is less than zero

[tex]f (g (x)) = 4 (\sqrt{2-9}) + 3\\\\f (g (x)) = 4 (\sqrt{-7}) + 3[/tex]

The root of -7 does not exist in real numbers, therefore 2 does not belong to the domain of f ° g

The answer is Option B.

Note. If   [tex]g(x) = \sqrt{x}-9[/tex]

So

[tex]f(g(x)) = 4(\sqrt{x})-36 + 3[/tex]   And  2 belongs to the domain of the function

ANSWER

C

E

F

EXPLANATION

The result of the synthetic division is :

3 -1 0

The last number is the remainder which is 0

The first two numbers are the coefficients of the quotient.

Therefore the quotient is 3x -1

Since the remainder is 0, x-4 is a factor of

[tex]f(x) = 3 {x}^{2} - 13x + 4[/tex]

This also means that:

[tex](3 {x}^{2} - 13x + 4) \div (x - 4) = 3x - 1[/tex]

This again means that x=4 is a root of

[tex]f(x) = 3 {x}^{2} - 13x + 4[/tex]

The correct choices are C,E and F.

Answer:

-6 I think

Step-by-step explanation:

Answer:

n = 4, m = 1

Step-by-step explanation:

Given the 2 equations

3m + n = 7 → (1)

m + 2n = 9 → (2)

Rearrange (2) expressing m in terms of n, by subtracting 2n from both sides

m = 9 - 2n → (3)

Substitute m = 9 - 2n into (1)

3(9 - 2n) + n = 7 ← distribute left side

27 - 6n + n = 7 ← simplify left side

27 - 5n = 7 ( subtract 27 from both sides )

- 5n = - 20 ( divide both sides by - 5 )

n = 4

Substitute n = 4 into (3) for corresponding value of m

m = 9 - (2 × 4) = 9 - 8 = 1

Thus m = 1 and n = 4

Answer:

Step-by-step explanation:

[tex]\text{De}\text{finition of logarithm:}\\\\\log_ab=c\iff a^c=b\\\\\text{where}\ a>0\ \wedge\ a\neq1\ \wedge\ b>0\ \wedge\ c\in\mathbb{R}\\===========================\\\\\log_2n=4\iff n=2^4\\\\n=16[/tex]

Answer:

I don't know what answers you were given to your problem but I think the answer is

D) log n =4log2

Sorry if I got it wrong.

Answer:

This is exponential growth

Step-by-step explanation:

The amount by which the function is increasing from point to point is increasing, so it must be a quadratic or exponential function. If it was a quadratic, the amount it increases by would be increasing by a steady amount. (Ex. x^2 increases by how much it increased the last time + 2). But because this is not what the data shows, the function must be exponential.

Answer:  Exponential

Step-by-step explanation:

Find the slope of each tier:

2.654      6.290     14.909     35.335

           ∨             ∨              ∨              

        3.636      8.619        20.426       ← not equal so not linear

                    ∨             ∨

                4.983      11.807                  ← not equal so not quadratic

We have run out of slopes to compare so the options are either exponential or logarithmic.

Refer to the graph below that contains the given coordinates.  Since there is no apparent asymptote, it appears to be exponential.

Answer:

A) −13

Step-by-step explanation:

(x + 6)^2 = 49

Take the square root of each side

sqrt((x + 6)^2) = ±sqrt(49)

x+6 = ±7

Subtract 6 from each side

x+6-6 = -6  ±7

x =-6  ±7

Separating into 2 parts

x = -6+7          x = -6-7

x = 1               x = -13

I believe I did this correctly. Comment to tell me if I didn't.

__________________________________

I got infinite solutions.

For the second problem, I subtracted 9 from both sides. Then I divided them all by -1. They are the same equations.

ANSWER

b) infinite solutions

EXPLANATION

The given system is:

x=3y+9 ...(1)

9-x=-3y...(2)

Put equation (1) into equation (2)

This implies that,

9-(3y+9)=-3y

Expand the parenthesis,

9-3y-9=-3y

-3y=-3y

1=1

This implies that, that the system has infinitely many solutions.