The graph shows the relationship between the total cost and the number of erasers bought at the student store. Which of the statements is true?

Answer:

p - q

Step-by-step explanation:

Given the factors

(x + p)(x - q) ← expanding the factors

= x² - qx + px - pq ← collect like terms

= x² + px - qx - pq ← factor out x in each of the x- terms

= x² + (p - q)x - pq

The coefficient of the x- term is p - q

Answer: [tex]AC=10.5[/tex]

Step-by-step explanation:

Assuming that [tex]b=AC[/tex] and given the following equation:

 [tex]tan(55\°)=\frac{15}{b}[/tex]

You need to solve for "b" in order to find the lenght of AC asked in the exercise.

 Therefore, with this procedure you get that the lenght of AC is the following:

[tex]\frac{15}{tan(55\°)}=b[/tex]

[tex]b=AC=10.5[/tex]

Answer:

(x, y ) → (x + 4, y - 3 )

Step-by-step explanation:

A translation of 4 units to the right is a positive shift in the x- direction, that is,

The x- coordinate of the image is the original + 4

A translation of 3 units down is a negative shift in the y- direction, that is

The y- coordinate of the image is the original - 4

Putting the 2 together

(x, y ) → (x + 4, y - 3 )

Answer:

(-2,12)

Step-by-step explanation:

it is the closest because it is only 2 units away

The coordinates of points on the Cartesian plane, are given by a pair of values

Reason:

The given coordinates are; (-6, 0), (-2, -12), (4, 2), (5, 1)

Method:

A point is close to the y-axis where the magnitude x-coordinate value is low

By observation, the coordinates of the point having the lowest magnitude of the x-value, is the point (-2, -12)

Learn more about the Cartesian plane here:

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Answer:

The difference of five times a number and nine

Step-by-step explanation:

The correct option is the difference of five times a number and nine.

Let the number be = x

Five times a number = 5x

Here difference means subtraction:

The difference of five times a number and nine would be 5x-9....

Answer:

D

Step-by-step explanation:

2022 Russian Invasion of Ukr- I mean got it right on Edge 2022

Answer:62

Step-by-step explanation:

F=c+32

C=30

F=30+32

F=62

The Fahrenheit temperature equivalent to 30°C (using the formula  F = C + 32) is  62°F.

The Fahrenheit temperature equivalent to 30°C can be found using the temperature conversion formula F = C + 32, where F is the temperature in Fahrenheit and C is the temperature in Celsius.

To find the temperature in Fahrenheit, substitute 30 for C:

F = 30°C + 32 = 62°F

[tex]\huge{\boxed{4.5}}[/tex]

First, add all the numbers together. [tex]2+2+3+3+3+4+5+6+6+10=\bf{44}[/tex]

Divide by the amount of numbers. [tex]\frac{44}{10}=\boxed{4.4}[/tex]

[tex]4.5[/tex] is the closest, so that is the answer.

Answer:

See attachment

Step-by-step explanation:

The given function is:

[tex]f(x)=3^{x-1}+2[/tex]

This is an exponential function with a horizontal asymptote at  [tex]y=2[/tex]

There is a translation of the form [tex]f(x)=g(x-1)+2[/tex]

The graph of the parent function [tex]g(x)=3^{x}[/tex] is shifted to the right 1 unit and shifted up by 2 units.

See attachment for graph.

Answer:

rectangle, square

Step-by-step explanation:

A rectangle always has 4 congruent angles. A square is a rectangle, so a square always has 4 congruent angles.

A parallelogram and a rhombus may or may not have 4 congruent angles.

Answer: rectangle, square

Answer:

Only a square and rectangle

Step-by-step explanation:

Both have angles of only 90 deg.

Answer:

Step-C. -5x-3y=0 which is the same thing as y= -5/3x + 0.

by-step explanation:

i hope this helps

Answer:

x=-7, y=2

Step-by-step explanation:

You are given the matrix equation

[tex]\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right] \cdot \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}-18\\13\end{array}\right][/tex]

Find the inverse matrix for the matrix

[tex]\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right][/tex]

1. The determinant is

[tex]\left|\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right]\right|=2\cdot 3-(-1)\cdot (-2)=6-2=4[/tex]

2.

[tex]a_{11}=2 \Rightarrow A_{11}=3\\ \\a_{12}=-2 \Rightarrow A_{12}=-(-1)=1\\ \\a_{21}=-1 \Rightarrow A_{21}=-(-2)=2\\ \\a_{22}=3 \Rightarrow A_{22}=2[/tex]

3. Inverse matrix is

[tex]\dfrac{1}{4}\left[\begin{array}{cc}3&1\\2&2\end{array}\right]^T=\dfrac{1}{4}\left[\begin{array}{cc}3&2\\1&2\end{array}\right][/tex]

So, the solution of the equation is

[tex]\left[\begin{array}{c}x\\y\end{array}\right]=\dfrac{1}{4}\left[\begin{array}{cc}3&2\\1&2\end{array}\right]\cdot \left[\begin{array}{c}-18\\13\end{array}\right]=\\ \\=\dfrac{1}{4}\left[\begin{array}{cc}3\cdot(-18)+2\cdot 13\\1\cdot (-18)+2\cdot 13\end{array}\right]=\dfrac{1}{4}\left[\begin{array}{c}-28\\8\end{array}\right]=\left[\begin{array}{c}-7\\2\end{array}\right][/tex]

Answer:

49

Step-by-step explanation:

We are going to use PEMDAS to simplify

[tex]3^3-10+(2 \cdot 4^2)[/tex]

First step is P.

P refers to the parenthesis or anything acting as a grouping symbol.

We notice the following operations there are multiplication and exponents.

According to PEMDAS, after parenthesis we do the exponents so let's do the exponent in the ( ).

[tex]3^3-10+(2 \cdot 16)[/tex]

Now we still have to finish P up. That is we need to do the one last operation in the ( ).

[tex]3^3-10+(32)[/tex]

Nothing left to perform in the () so we can just write:

[tex]3^3-10+32[/tex]

Now there are no more grouping symbols left.

The next letter is E and it stands for exponents so we must evaluate anything we can that has an exponent.

[tex]27-10+32[/tex]

Now after E we have M and D which means to multiply and divide as you the expression from left to right.

There is no multiplication and division so moving on.

A and S means to do the addition and subtraction as it occurs left to right:

[tex]17+32[/tex]

[tex]49[/tex]

Answer:

The correct option is A

Step-by-step explanation:

Lets suppose that the third side is hypotenuse.

We will apply Pythagorean theorem:

c²= a²+b²

where,

a=12 inches

b=15 inches

Now substitute the values in the theorem:

c²=(12)²+(15)²

c²=144+225

c²=369

Take square root on both sides:

√c²=√369

c= 19.2 inches.

Now assume that the third side is a leg:

Here we will find the value of b.

a=12 inches

c= 15 inches.

b= ?

Now substitute the values in the theorem:

c²=a²+b²

(15)²=(12)²+b²

225=144+b²

Move the constant to the L.H.S

225-144=b²

81=b²

Take square root on both sides:

√81=√b²

9=b

Now we will find the difference of the third sides:

19.2-9 = 10.2

Thus the length of the third side is 10.2 inches

The correct option is A....

Answer:

A.

Step-by-step explanation:

Answer:

x> 5

Step-by-step explanation:

x - 8 > -3

Add 8 to each side

x - 8+8 > -3+8

x> 5

Answer:

[tex]\huge \boxed{x>5}[/tex]

Step-by-step explanation:

First, add by 8 from both sides of equation.

[tex]\displaystyle x-8+8>-3+8[/tex]

Simplify, to find the answer.

[tex]-3+8=5[/tex]

[tex]\huge \boxed{x>5}[/tex], which is our answer.

Final answer:

To simplify (f+g)(2) with given functions f(x)=x+1 and g(x)=x^2-x, calculate the functions' values at x=2 and sum them, resulting in (f+g)(2) = 5.

Explanation:

To find and simplify the expression (f+g)(2), you first need to determine the individual functions f(x) and g(x) at the value x = 2, and then sum them.

The function f(x) is given by f(x) = x + 1. At x = 2, f(2) = 2 + 1 = 3.

The function g(x) is given by g(x) = x2 - x. At x = 2, g(2) = 22 - 2 = 4 - 2 = 2.

Adding these two results together, we get (f+g)(2) = f(2) + g(2) = 3 + 2 = 5.

Answer:

[tex]\large\boxed{(b)\ \dfrac{x+2}{x-3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{1}{x+1}+\dfrac{x}{x-3}-\dfrac{-x-5}{x^2-2x-3}=(*)\\\\x^2-2x-3=x^2-3x+x-3=x(x-3)+1(x-3)=(x-3)(x+1)\\\\(*)=\dfrac{1(x-3)}{(x+1)(x-3)}+\dfrac{x(x+1)}{(x+1)(x-3)}+\dfrac{-(-x-5)}{(x+1)(x-3)}\\\\=\dfrac{x-3+x^2+x+x+5}{(x+1)(x-3)}=\dfrac{x^2+(x+x+x)+(-3+5)}{(x+1)(x-3)}\\\\=\dfrac{x^2+3x+2}{(x+1)(x-3)}=\dfrac{x^2+2x+x+2}{(x+1)(x-3)}=\dfrac{x(x+2)+1(x+2)}{(x+1)(x-3)}\\\\=\dfrac{(x+2)(x+1)}{(x+1)(x-3)}\qquad\text{cancel (x + 1)}\\\\=\dfrac{x+2}{x-3}[/tex]

ANSWER

(0, 1), (1,3), (2, 9), (3, 27)

EXPLANATION

For an exponential function, there is a common ratio among the terms.

Therefore we need to examine the y-values of the ordered pairs to see which one has a common ratio.

For the first option, the y-values are:

0,1,8,27

[tex] \frac{27}{8} \ne \frac{8}{1} [/tex]

For the second option, the y-values are:

1,2,5,10

[tex] \frac{10}{5} \ne \frac{5}{2} [/tex]

For the third option, the y-values are:

0,3,6,9

[tex] \frac{9}{6} \ne \frac{6}{3} [/tex]

For the last option, the y-values are:

1,3,9,27

[tex] \frac{27}{9} = \frac{9}{3} = \frac{3}{1} = 3[/tex]

Since there is a common ratio of 3, the set of ordered pairs (0, 1), (1,3), (2, 9), (3, 27) could generate an exponential sequence.

Answer:

Jay needs a 94 on his next test to get an average of 93 on all of his exams.

Step-by-step explanation:

The way test averages work is you take the sum of all of your tests and divide it by the number of tests. So he got an 87 on test 1, a 98 on test 2, and an unknown score on test 3 because he hasn't taken it yet.

Let x = that unknown score. The number of tests is 3. So we set up our equation as:

(87 + 98 + x) / 3

He wants an average of 93 so we set the equation equal to just that.

(87 + 98 + x) / 3 = 93

In order to isolate the numerator equation by itself, we multiply both side by 3. That way the 3 in the denominator on the left side cancels out. You now have:

87 + 98 + x = 93(3)

Simplify:

185 + x = 279

Now to get x by itself, we subtract 185 from both sides:

x = 279 - 185

x = 94

He needs a score of 94 on the next test for the test average that he wants.

Answer:

Mean=10

Step-by-step explanation:

To find the mean of a set of numbers, you need to add all of them up and then divide by the amount of numbers that are in the sequence. In this case...

3+8+10+19=40

Then we need to divide by 4 because there are 4 numbers in the sequence. \

40/4=10

Answer:

The mean is 10

Step-by-step explanation:

The mean is just another word for average.

Add the four numbers together and divide by 4

(3+8+10+19)/4

40/4

10

Answer:

C

Step-by-step explanation:

(-3,0)

I did it in the quiz and the test.

Got it correct.

Answer:

19 x (42 + 58)

Step-by-step explanation:

The common term is 19

Answer : The expression she use can be, [tex]19\times (42+58)[/tex]

Step-by-step explanation :

Distributive property Law : It says that multiplying a number by the group of numbers added together is the same as doing each multiplication separately.  

For example:

3 × (2 + 4) = 3×2 + 3×4

As we are given the expression:

[tex]19\times 42+19\times 58[/tex]

[tex]\Rightarrow 19\times (42+58)[/tex]

Thus, the expression she use can be, [tex]19\times (42+58)[/tex]

Step-by-step explanation:

84 ounces / 27 turtles = 3.111 ounces per turtle

Or in fractional form, 3 ¹/₉ ounces per turtle.

Each turtle gets 3.11 ounces if Each of the 27 turtles in the pet store needs to be fed

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

Each of the 27 turtles in the pet store needs to be fed.

There is one bag of turtle food that weighs 84 ounces.

Each turtle gets the food = 84/27

= 3.11 ounces

Thus, each turtle gets 3.11 ounces if Each of the 27 turtles in the pet store needs to be fed

Learn more about the fraction here:

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[tex]\dfrac{B_x \sqrt{74_x}}{1D_x}+J_x51_x=4G3_x[/tex]

A=10, B=11, C=12, etc.

[tex]\dfrac{11\cdot x^0\cdot \sqrt{7\cdot x^1+4\cdot x^0}}{1\cdot x^1+13\cdot x^0}+19\cdot x^0\cdot (5\cdot x^1+1\cdot x^0)=4\cdot x^2+16\cdot x^1+3\cdot x^0\\\\\dfrac{11\sqrt{7x+4}}{x+13}+19(5x+1)=4x^2+16x+3\\\\\dfrac{11\sqrt{7x+4}}{x+13}+95x+19=4x^2+16x+3\\\\11\sqrt{7x+4}+95x(x+13)+19(x+13)=(4x^2+16x+3)(x+13)\\\\11\sqrt{7x+4}+95x^2+1235x+19x+247=4x^3+52x^2+16x^2+208x+3x+39\\\\11\sqrt{7x+4}=4x^3-27x^2-1043x-208\\\\121(7x+4)=(4x^3-27x^2-1043x-208)^2[/tex]

[tex]121(7x+4)=(4x^3-27x^2-1043x-208)^2\\\\847x+484=16 x^6 - 216 x^5 - 7615 x^4 + 54658 x^3 + 1099081 x^2 + 433888 x + 43264\\\\16 x^6 - 216 x^5 - 7615 x^4 + 54658 x^3 + 1099081 x^2 + 433041 x +42780=0[/tex]

Now, the "only" thing that remains to do is solving the above equation.

While making this problem I only made sure it has a solution. I didn't try to solve it myself and I didn't know it will end up with such "convoluted" polynomial. Sorry to everyone who tried to solve it... m(_ _)m

I think the best way to approach it is using the rational root theorem since we know that [tex]x\in\mathbb{N}[/tex]. Moreover we can deduce that [tex]x\geq19[/tex] since there is [tex]J[/tex] and [tex]J=19[/tex].

After you succesfully solve it, you should get the answer [tex]x=20[/tex].

Answer:

a = -4.

Step-by-step explanation:

If the are perpendicular then the slope of one graph will be - 1 / slope of the other.

Convert each equation to slope-intercept form:

x + 2y + 3 = 0

2y = = -x - 3

y = (-1/2)x - 3/2 (Slope/intercept form)

So the slope of the line perpendicular to this  will be - 1 / (-1/2) = 2.

Consider the other line:

ax + 2y + 3 = 0

2y = -ax - 3

y = (-a/2) x - 3/2 (Slope/intercept form)

So the slope for this line    - a/2 and it equals 2.

-a/2 = 2

-a = 2*2 = 4

a = -4 (answer).

To determine the value of $a$ such that the graph of the equation $ax + 2y + 3 = 0$ is perpendicular to the graph of the equation $x + 2y + 3 = 0$, we'll need to find the slopes of the two lines represented by these equations since two lines are perpendicular if and only if the product of their slopes is $-1$ (the slopes are negative reciprocals of each other).
Let's find the slope of the first line.
The equation of the first line is $x + 2y + 3 = 0$. We can rearrange this to find $y$ in terms of $x$:
\[2y = -x - 3\]
\[y = \frac{-x}{2} - \frac{3}{2}\]
The slope of this line, denoted by $m_1$, is the coefficient of $x$:
\[m_1 = -\frac{1}{2}\]
Now, let's find the slope of the second line.
The equation of the second line is $ax + 2y + 3 = 0$. Rearranging this to solve for $y$ in terms of $x$, we get:
\[2y = -ax - 3\]
\[y = -\frac{a}{2}x - \frac{3}{2}\]
The slope of this line, denoted by $m_2$, is the coefficient of $x$:
\[m_2 = -\frac{a}{2}\]
Now, for the lines to be perpendicular, their slopes must satisfy the following condition:
\[m_1 \cdot m_2 = -1\]
Substituting the known slopes into the equation, we get:
\[-\frac{1}{2} \cdot \left(-\frac{a}{2}\right) = -1\]
\[\frac{a}{4} = -1\]
\[a = -4\]
Therefore, the value of $a$ that ensures the graph of the equation $ax + 2y + 3 = 0$ is perpendicular to the graph of the equation $x + 2y + 3 = 0$ is $a = -4$.

Answer:

The sum is [tex]9,331[/tex]

Step-by-step explanation:

we have

[tex]1,6,36,...[/tex]

we have

[tex]a1=1[/tex]

[tex]a2=6[/tex]

[tex]a3=36[/tex]

Find the common ratio r

[tex]a2/a1=6/1=6[/tex]

[tex]a3/a2=36/6=6[/tex]

The common ratio is r=6

The formula to calculate the sum in a geometric sequence is equal to

[tex]S=a1\frac{(1-r^{n})}{(1-r)}[/tex]

where

n is the number of terms

r is the common ratio

a1 is the first term

we have

[tex]n=6[/tex]

[tex]a1=1[/tex]

[tex]r=6[/tex]

substitute

[tex]S=(1)\frac{(1-(6)^{6})}{(1-6)}[/tex]

[tex]S=\frac{(1-(6)^{6})}{(-5)}[/tex]

[tex]S=9,331[/tex]

Answer:

7776π  or

24,429.02 unit^3 to the nearest  hundredth.

Step-by-step explanation:

The formula for the volume of a sphere is V = 4/3 π r^3   where r is the radius.

Here V = 4/3 * π * 18^3

= 7776π unit^3.

Answer:

7776 pi

Step-by-step explanation:

Answer:

[tex]\boxed{\text{3600 mg}}[/tex]

Step-by-step explanation:

Step 1. Calculate the number of capsules

Marilyn takes 2 capsules per day

[tex]\text{No. of capsules} = \text{90 days} \times \dfrac{\text{2 capsules}}{\text{1 day}} = \text{ 180 capsules}[/tex]

Step 2. Convert capsules to milligrams

There are 20 mg in each capsule.  

[tex]\text{No. of milligrams} = \text{180 capsules} \times \dfrac{\text{20 mg}}{\text{1 capsule}} = \textbf{3600 mg}\\\\\text{Marilyn will take } \boxed{\textbf{3600 mg}} \text{ of Pirixocam}[/tex]

To find the exact value of cos(127.5), we can use the half angle identity for cosine. By substituting the angle into the half angle identity and simplifying, we find that cos(127.5) is approximately ±0.99992.

The cosine function is a trigonometric function that relates the angle of a right triangle to the ratio of the adjacent side to the hypotenuse. To find the exact value of cos(127.5), we can use the half angle identity for cosine. This identity states that cos(θ/2) = ±√((1 + cos(θ))/2), where θ is the original angle.

In this case, we have θ = 255 degrees (since 127.5 is half of 255). Using the half angle identity, we can calculate cos(127.5) as follows:

Therefore, the exact value of cos(127.5) is approximately ±0.99992.

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The slope is [tex]-10[/tex] and the y-intercept is [tex]1[/tex].

This function is written in slope-intercept form, which is [tex]y=mx+b[/tex].  In this form, [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

In this case, [tex]m=-10[/tex] and [tex]b=1[/tex], so those are the answers to this problem.

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have the following equation:

[tex]y = -10x + 1[/tex]

So we have to:

[tex]m = -10\\b = 1[/tex]

Answer:

[tex]m = -10\\b = 1[/tex]

Answer:

Final direction is 45 degrees south of west or  45 degrees west of south.

Step-by-step explanation:

i) You are facing North

Turn 90 degrees left

ii) 90 degrees left to north is west.

Turn around to reverse your direction

iii) On reversing direction you will be facing east.

Turn 45 degrees left

iv) On turning 45 degrees left, you will be facing north east.

 Turn around to reverse your direction

v) On reversing direction you will be facing south west.

Final direction is 45 degrees south of west or  45 degrees west of south.