(y 3 - 4y 2 + 7y - 6) divided by (y - 2)

Answer:

the 6 greens

Answer:

The area of the table is [tex]1,008\ in^{2}[/tex]

Step-by-step explanation:

Let

x----> the length of the rectangular table

y---> the width of the rectangular table

we know that

The perimeter is equal to

[tex]P=2(x+y)[/tex]

[tex]P=132\ in[/tex]

so

[tex]132=2(x+y)[/tex]

[tex]66=x+y[/tex] ------> equation A

[tex]x=1\frac{3}{4}y[/tex]

[tex]x=\frac{1*4+3}{4}y[/tex]

[tex]x=\frac{7}{4}y[/tex] ---> equation B

substitute equation B in equation A and solve for y

[tex]66=\frac{7}{4}y+y[/tex]

[tex]66=\frac{11}{4}y[/tex]

[tex]y=66*4/11=24\ in[/tex]

Find the value of x

[tex]x=\frac{7}{4}(24)=42\ in[/tex]

Find the area of the table

The area is equal to

[tex]A=xy=(42)(24)=1,008\ in^{2}[/tex]

For this case we substitute the value of "[tex]x = 2[/tex]" in each of the inequalities and evaluate:

Option A:

[tex]6x + 20 <29\\6 (2) +20 <29\\12 + 20 <29\\32 <29[/tex]

It is not fulfilled!

Option B:

[tex]7x-10 <11\\7 (2) -10 <11\\14-10 <11\\4 <11[/tex]

Is fulfilled!

Option C:

[tex]14x + 10 <37\\14 (2) +10 <37\\28 + 10 <37\\38 <37[/tex]

It is not fulfilled!

Option D:

[tex]15x-18 <12\\15 (2) -18 <12\\30-18 <12\\12 <12[/tex]

It is not fulfilled!

ANswer:

Option B

Answer:

[tex]\boxed{\text{\$10; \$20}}[/tex]

Step-by-step explanation:

Let t = the price of  a T-shirt

and j = the price of a pair of jeans

You have a system of two equations:

[tex]\begin{cases}(1)& 2t + j = 40\\(2) & 2(0.5t) + 5(0.5j) = 60\end{cases}\\[/tex]

[tex]\begin{array}{lrcll}(3) & t+ 2.5j & = & 60 &\text{Removed parentheses in (2)}\\(4)& 2t + 5j & = & 120 &\text{Multiplied (3) by 2}\\& 4j & = & 80 &\text{Subtracted (4) from (1)}\\(5)& j & = & 20 &\text{Divided each side by 4} \\& 2t + 20& = & 40 & \text{Substituted (5) into (1)} \\&2t & = & 20 & \text{Subtracted 20 from each side}\\& t & = & 20 & \text{Divided each side by 2}\\\end{array}[/tex]

[tex]\text{The price of a T-shirt is \boxed{\textbf{\$10}}}\\\\\text{and the price of a pair of jeans is \boxed{\textbf{\$20}}}\\[/tex]

Check:

[tex]\begin{array}{rclcrcl}2\times10\ + 20 & = & 40 & \qquad &2(0.5\times10) + 5(0.5\times20)&=&60\\20 + 20 & = & 40 & \qquad &2\times5 + 5\times 10& = &60\\40& = & 40 &\qquad &10 + 50 & = & 60\\& & &\qquad &60 & = & 60\\\end{array}[/tex]

OK.

Yes, what do you need help with?

The algebraic expression that expresses how long Julie studied is: 2x.

Algebraic expression can be described as a mathematical statement that uses variables and digits, as well as operation signs.

Number of hours Jake studied = x

Julie studied twice as long as x

Thus, algebraic expression for how long Julie studied would be: 2x.

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If Jake's study time can be represented as 'x', then, given that Julie studied twice as long as Jake, her study time can be represented as '2x'. This is because she studied twice the amount of time that Jake did.

The question describes a relationship between the amount of time Jake studied and the amount of time Julie studied. We know from the question that Julie studied twice as long as Jake did. In mathematical terms, we would represent Jake's studying time as x hours, since we don't have a specified amount. Therefore, because Julie studied twice as long as Jake did, we can represent Julie's studying time as 2x.

Hence, "the algebraic expression for the number of hours that Julie studied is 2x".

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If the denominator is 0, and the numerator ≠ 0, your answer will undefined.

If the numerator is 0, and the denominator is a number, it will always = 0.

So you can set the denominator equal to 0

x + 2 = 0       Find x, so subtract 2 on both sides

x = -2

Answer:

- 494

Step-by-step explanation:

Breaking down the summation into it;s component parts

= 4k - [tex]\frac{3}{2}[/tex] k(k + 1) ← substitute k = 19

= (4 × 19 ) - 1.5 × (19 × 20)

= 76 - (1.5 × 380)

= 76 - 570

= 494

The value of the arithmetic series below is - 494

We have

To break down the summation into its component parts

[tex]S_{19}= 4k - \frac{3}{2} k(k + 1)[/tex]

[tex]= 4k - \frac{3}{2} k(k + 1) .... substitute\ k = 19[/tex]

[tex]= (4 \times 19 ) - 1.5 \times (19 \times 20)[/tex]

[tex]= 76 - (1.5 \times 380)[/tex]

[tex]=76-570[/tex]

= -494

The value of the arithmetic series below is 494.

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Answer:

B.

Step-by-step explanation:

I plugged it into a graphing calculator which got me this.

Answer:

Its 3.5c

Step-by-step explanation:

Let's find the constant of proportionality.

In the proportional relationship between c, the number of cranes, and t, the total time in minutes, one constant of proportionality is the amount of time per crane. It is the number we multiply by the number of cranes to get the total time.

c times ? =t

The constant of proportionality is 3.5 This means we can multiply 3.5 by the number of cranes to get the total time.

Now, let's represent that as an equation.

total time= time per crane X number of cranes

total time

t

​

time per crane×number of cranes

3.5c

​

One correct equation is:

t= 3.5c

Answer:

t = 3.5c

Step-by-step explanation:

This represents a proportional relationship because it is linear (he is folding at a constant rate) and passes through the origin (it would take him 0 minutes to fold 0 cranes). The formula for a proportional relationship is y = kx, where k is the constant of proportionality.

To find k, divide the dependent variable by its corresponding indepent variable. In this example, the amount of minutes is the dependent variable and the amount of cranes is the independent variable.

Using the first row of the table, we get  [tex]k = \frac{17.5}{5} = 3.5[/tex].

Just to confirm our answer, let's try the other values given in the table:

[tex]k = \frac{28}{8} = 3.5\\k = \frac{42}{12} = 3.5[/tex]

So, we get that it takes Terrence 3.5 minutes to make one crane, so t = 3.5c

Find the common ratio, by adding the adults and babies together: 6+5 = 11

Divide the total by that:

44/11 = 4

the common ratio is 4.

Now multiply the given ratios by the common ratio:

Adults = 6 x 4 = 24

Babies = 5 x 4 = 20

There are 20 babies.

Final answer:

To find 65% of a number, use the equation 0.65x = 32.5 and solve for x by dividing both sides by 0.65 to get x = 50.

Explanation:

Sixty-five percent of what number is 32.5?

Let's denote the unknown number as x.

Translate the given information into an equation: 0.65x = 32.5

To solve for x, divide both sides by 0.65 giving x = 32.5 / 0.65 = 50.

Answer:

14.10

Step-by-step explanation:

Quarters are worth .25 of a dollar

40 *.25 = 10

Dimes are worth .10 of a dollar

30 *.10 = 3

Nickels are worth .05 of a dollar

20 *.05 = 1

Pennies are worth .01 of a dollar

10 *.01 = .1

Add this together

10+3+1+.1

14.10

Answer:

P(A) x P(B)

Step-by-step explanation:

If im wrong, im so sorry

P(A | B) is found using the formula P(A AND B) / P(B), which in the context of rolling a dice and looking at events such as rolling a prime number (A) given rolling an odd number (B) would imply looking at the shared outcomes of both events and then calculating the probability.

The Venn diagram question is asking for P(A | B), which is the probability of event A happening given that event B has happened.

The multiplication rule is an important tool to solve this problem, stating that if A and B are independent events, then P(A AND B) = P(A) × P(B).

However, the calculation of P(A | B) is different.

To find P(A | B), which is read as "the probability of A given B," you use the formula P(A AND B) / P(B).

If we consider that A is the event of rolling a prime number (e.g., numbers 2, 3, 5 in a dice) and B is the event of rolling an odd number (e.g., numbers 1, 3, 5), then the outcomes that are both prime and odd (A AND B) would be {3, 5}.

If event B has already occurred (rolling an odd number), we adjust the sample space accordingly and calculate the probability of A within this new space.

Answer:

Ax = [tex]\left[\begin{array}{cc}-3&-1\\5&1\end{array}\right][/tex] ⇒ 3rd answer

Step-by-step explanation:

Lets revise the Cramer's rule

- If the system of equation is ax + by = c and dx + ey = f

- A is the matrix represent this system of equation

- The first column has the coefficients of x, and

  the second column has the coefficients of y

∴ A = [tex]\left[\begin{array}{cc}a&b\\d&e\end{array}\right][/tex]

- Ax means replace the column of x by the answers of the equation

∴ Ax = [tex]\left[\begin{array}{cc}c&b\\f&e\end{array}\right][/tex]

- Ay means replace the column of y by the answers of the equation

∴ Ay = [tex]\left[\begin{array}{cc}a&c\\d&f\end{array}\right][/tex]

* Now lets solve the problem

∵ 4x - y = -3 and -2x + y = 5

∴ A = [tex]\left[\begin{array}{cc}4&-1\\-2&1\end{array}\right][/tex]

- Replace the column of x by the answer to get Ax

∴ Ax = [tex]\left[\begin{array}{cc}-3&-1\\5&1\end{array}\right][/tex]

* Ax in the system of equation is [tex]\left[\begin{array}{cc}-3&-1\\5&1\end{array}\right][/tex]

Answer:

C

Step-by-step explanation:

Edge2021

Answer:

72

Step-by-step explanation:

He makes 18/30 passes. We need to see how many passes he can make out 120, so we need to see how many times 30 goes into 120.

120/30=4

So 120 is equivalent to 4 30s. Now to find out how many passes he'd make we multiply 18 by 4.

18*4=72

Answer:

Option 4: 0.554

Step-by-step explanation:

As we can see that the intervals and their frequencies are given.

We have to calculate the probability of students' score falling between 70 and 89. It will use the frequency of both intervals 70-79 and 80-89.

So, combined scores of both intervals are:

172+105 = 277

Now to find the probability

= 277/500

=0.554

So option no 4 is the correct answer ..

Answer:

15 hours and 10 min

Step-by-step explanation:

6 1/2 hours on Monday

8 2/3 hours on Tuesday

You have to make the fractions equal to each other so you would have

1/2 x 3 = 3/6

2/3 x 2 = 4/6

Then add them together to get

7/6 or 1 1/6

6+8 = 14

Then add the 1 to 14 to get 15

1/6 of an hour is 10 minutes

Therefore your answer would be 15 hours and 10 minutes

I think it’s a pyramid

The value of x in the expression (5x-15)°, which is the measure of an interior angle of a regular triangle, is 15.

The expression (5x-15)° is given as the measure of one interior angle of a regular triangle. This is a bit complex, as regular triangles, also known as equilateral triangles, only have angles that measure 60° each. Thus, we can set up the equation 5x - 15 = 60.

Solving for x, we get:

So, the value of x that would result in each angle of an regular triangle measuring (5x-15)° is 15.

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Answer:

[tex]\dfrac{1}{12}+\dfrac{1}{15}+\dfrac{1}{x}=\dfrac{1}{6}[/tex]

60 hours

Step-by-step explanation:

John - 12 hours

Rick - 15 hours

Molli - x hours

Together - 6 hours

Each of them can paint:

John - [tex]\frac{1}{12}[/tex] of a room per hour

Rick - [tex]\frac{1}{15}[/tex] of a room per hour

Molli - [tex]\frac{1}{x}[/tex] of a room per hour

Together - [tex]\frac{1}{6}[/tex] of a room per hour

So the equation is

[tex]\dfrac{1}{12}+\dfrac{1}{15}+\dfrac{1}{x}=\dfrac{1}{6}[/tex]

Solve this equation:

[tex]\dfrac{1}{x}=\dfrac{1}{6}-\dfrac{1}{12}-\dfrac{1}{15}\\ \\\dfrac{1}{x}=\dfrac{10-5-4}{60}=\dfrac{1}{60}\\ \\x=60[/tex]

Molli can paint the room in 60 hours.

g(x)=-2

Simplfy: y=-2

x=-9

*Look at where the points intersect

Answer:

x=-9

Step-by-step explanation:

Answer:

using the foil

Step-by-step explanation:

you always have to get rid of the x for example if it is +3x you add it on to get rid of it and you carry on until you have solved x.

Answer:

getting the correct answer

Step-by-step explanation:

Answer:

5.5

Step-by-step explanation:

Of means multiply

13.75 * 2/5

27.5/5

5.5

[tex]\text{Hey there!}[/tex]

[tex]\text{When you come across the word of in mathematics (high learning math at that)}[/tex][tex]\text{, it means to multiply.}[/tex]

[tex]\text{So, your new equation becomes: 13.75}\times\frac{2}{5}\text{multiply those two}[/tex] [tex]\text{numbers.}[/tex]

[tex]\text{The formula to solving for these times of equation is:\ }\frac{b\times c}{d}[/tex]

[tex]\text{So,}\frac{2 \times13.5}{5}[/tex]

[tex]2\times 13.75=27.5[/tex]

[tex]\frac{27.5}{5}=27.5\div5=5.5[/tex]

[tex]\boxed{\boxed{\text{Answer: 5.5}}}\checkmark[/tex]

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

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

C

Explanation:

B=Base Area

In a cylinder, the base area is a circle.

Area Circle=pi r^2

Replace base area with area of circle:

V=pi r^2 H

Answer:

Volume of Cylinder = (pi)(radius^2)(height)

Answer:

5/6

Step-by-step explanation:

Step 1: Find Alicia's share of the gift. To do this, all you have to do is multiply 120 by 2/5, which is 40%. 120 * 40% (0.4) is 48. Alicia's share is $48.

Step 2: Find Jason's share of the gift. In this case, divide 120 by 3. 120/3 is 40. Jason's share is $40.

Step 3: Express the numbers as a fraction and simplify it. 40/48 is the common fraction. Find the GCF of 40 and 48. When you solve for it, the GCF is 8. Divide both the numerator and the denominator by 8. 40/8 is 5/ 48/8 is 6. There. 5/6 is our simplified fraction, which is the ratio.

Answer:

  4 -i

Step-by-step explanation:

For your condition to be met, neither the real part nor the imaginary part can exceed √17 in magnitude. That excludes the first three answer choices.

The magnitude of 4-i is ...

  √(4^2 +(-1)^2) = √17.

Answer:

Step-by-step explanation:

First, we need to know that a complex number, which has a real part and an imaginary part, it's like a vector, where the horizontal coordinate is the real part, and the vertical coordinate is the imaginary part.

So, to find the distances we applied the conventional definition:

[tex]d=\sqrt{r^{2}+i^{2} }[/tex]

Where [tex]r[/tex] refers to the real part and [tex]i[/tex] refers to the imaginary part.

So, we test each answer and see which one gives us the root of 17.

[tex]d=\sqrt{2^{2}+15^{2} }=\sqrt{4+225}=\sqrt{229}[/tex]

[tex]d=\sqrt{17^{2}+1^{2} }=\sqrt{290}[/tex]

[tex]d=\sqrt{20^{2}+(-3)^{2} }=\sqrt{409}[/tex]

[tex]d=\sqrt{4^{2}+(-1)^{2} }=\sqrt{17}[/tex]

Therefore, the right answer is the last one, because the distance is the squared root of 17.

S_n = n(first term + a_n)/2

n = 15

S_15 = 15(2 + a_n)/2

We need a_n.

a_n = first term + d(n - 1)

a_n = 2 + d(15 - 1)

1. Find d.

2. Plug d into expression to find a_n.

3. After finding a_n, plug back into

S_15 = 15(2 + a_n)/2 to find the sum of the first 15 terms.

Take it from here.

Answer: 180 ft2

Step-by-step explanation:

The formula for the area of a rectangle is Area = length X width. Since the length is 20 feet and the width is 9 feet , you multiply 20 X 9, which gives you 180 square feet. Hope this helps!

The reflection that will produce that image would be a reflection across the y-axis

The line segment should be reflected across the y-axis to obtain the desired image with endpoints at (4, -6) and (6, 4).

To find the reflection of the line segment with endpoints (-4,-6) and (-6,4) that will produce an image with endpoints at (4,-6) and (6,4), we can use the formula for reflecting a point in the x-axis or y-axis. The reflection of a point (x, y) in the x-axis is (x, -y) and the reflection of a point (x, y) in the y-axis is (-x, y). Applying these formulas to the given endpoints, we can determine that the reflection in the y-axis will produce the desired image. So, the line segment will be reflected across the y-axis to obtain the image with endpoints at (4, -6) and (6, 4).

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