What is the sum of the arithmetic series below 2+5+8+...+56​

Final answer:

A parallelogram is a quadrilateral with parallel and equal sides, but it does not necessarily have any right angles. The greatest number of right angles a parallelogram can have is two, which occurs when the parallelogram is a rectangle.

Explanation:

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. In a parallelogram, the opposite angles are also equal. However, a parallelogram is not required to have any right angles, and in fact, most parallelograms do not have any right angles.

The greatest number of right angles a parallelogram can have is two. This would occur when the parallelogram is a rectangle, which is a special type of parallelogram. A rectangle has opposite sides that are parallel and equal in length, and all four angles are right angles, measuring 90 degrees each.

Therefore, the answer to Sarah's question is that the greatest number of right angles her parallelogram can have is two.

Answer:

The effect of  [tex]\pi[/tex] on the graph is it shift the graph horizontally.                      

Step-by-step explanation:

Given : Function [tex]y=-2-\cos(x-\pi)[/tex]

To find : What effect [tex]\pi[/tex] does have on the basic graph?          

Solution :

Consider the parent function [tex]y=\cos x[/tex]

The graph get transformed into [tex]y=-2-\cos(x-\pi)[/tex]

When there is a change in the x value then horizontal shift happened.

The general form of cosine is [tex]f(x)=A\cos(B(x-C))+D[/tex]

The horizontal shift in this function is C.

Similarly, If we applied in [tex]y=-2-\cos(x-\pi)[/tex] then there is a horizontal shift of [tex]\pi[/tex]

Therefore, The effect of  [tex]\pi[/tex] on the graph is it shift the graph horizontally.      

Answer:

-1

Step-by-step explanation:

3 • 7 = 21

Find two factors of 21 whose sum equals the coefficient of the middle term, which is -1 .

-21 + -1 = -22

-1 + -21 = -22

1 + 21 = 22

21 + 1 = 22

Answer:

Can not be factorized further

Step-by-step explanation:

Here we are asked to factorize the expression [tex]3x^2+x+7[/tex]

In order to factorize a quadratic polynomial , we have to follow the following steps.

step 1. We have to find the product of coefficient of [tex]x^2[/tex] and the constant term. In this case the coefficient of [tex]x^2[/tex] is 3 and constant term is 7. Hence the product is 3*7=21

Step 2: Now we have to find all the possible factors of this product. In our case the factors will be

21=1*21

21=3*7

Step 3: We have to select one pair of those factors such that their sum or difference is equal to the coefficient of middle term that is [tex]x[/tex] . In this case it is 1. And we can see that in our polynomial , none of the pair gives you 1 either as sum or difference.

As there does not exist any such pair , it can not be further factorize.

go 6 to the left of 0 and 10 up from -6

Answer:

About 19 feet

Step-by-step explanation:

You divide 5280 by 275.5 to get feet per rotation.

Answer:

10

Step-by-step explanation:

Divide 2 2/4 cups of raisins by 1/4 cup:

10 cups

-------------

     4

=============

  1 cup

  --------

       4

Invert the divisor and then multiply:

10 cups            4

-------------  ·  ----------  =  10

     4              1 cup

Julie must measure out 10 of these 1/4-cup measures (of raisins).

Final answer:

By applying the Pythagorean theorem, we find that the sum of the squares of the two shorter sides of triangle STV (7 and 11) is not equal to the square of the longest side (14). Therefore, triangle STV is not a right triangle.

Explanation:

To determine if triangle STV with sides of 7, 11, and 14 is a right triangle, we can apply the Pythagorean theorem, a² + b² = c², where c is the hypotenuse (the longest side of the triangle) and a and b are the other two sides. For triangle STV, assume that the side with a length of 14 units is the hypotenuse, and the sides with lengths of 7 and 11 units are the other two sides.

Now, let's calculate:

a² = 7² = 49

b² = 11² = 121

a² + b² = 49 + 121 = 170

c² = 14² = 196

Since 170 does not equal 196, the sums of the squares of the sides do not equal the square of the hypotenuse. Therefore, triangle STV is not a right triangle.

Answer:

cscФ = 13/12

Step-by-step explanation:

∵ The terminal side of the angle Ф passes through point (5/13 , 12/13)

∵ x = 5/13 and y = 12/13

∵ x = cosФ and y = sinФ

∴ cosФ = 5/13

∴ sinФ = 12/13

∵ cscФ = 1/sinФ

∴ cscФ = 1 ÷ 12/13 = 13/12

Answer:

¹²/₇

Step-by-step explanation:

Model ⁴/₇ × 3

Assume that you have three pies, each dived into seven slices.

There are only four slices remaining in each pie, that is, there is ⁴/₇ pie in each pie plate

The picture represents ⁴/₇ × 3.  

Model the product

Now, transfer slices to get as many filled pie plates as possible.

Count the total slices.

You have 12 slices, and each slice represents ⅐ of a pie.

You have ¹²/₇  pie.

∴ ⁴/₇ × 3 = ¹²/₇

Answer:

[tex](f\circ g)(3)=-7[/tex]

Step-by-step explanation:

The given functions are;

[tex]f(x)=-2x+7[/tex]

and

[tex]g(x)=x^2-2[/tex]

We need to first of all find [tex](f\circ g)(x)[/tex]

[tex](f\circ g)(x)=f(g(x))[/tex]

[tex](f\circ g)(x)=f(x^2-2)[/tex]

[tex](f\circ g)(x)=-2(x^2-2)+7[/tex]

[tex](f\circ g)(x)=-2x^2+4+7[/tex]

[tex](f\circ g)(x)=-2x^2+11[/tex]

We now plug in x=3

[tex](f\circ g)(3)=-2(3)^2+11[/tex]

[tex](f\circ g)(3)=-18+11[/tex]

[tex](f\circ g)(3)=-7[/tex]

The answer is A. -7 on edge :)

Answer:

1. 50

2. They are congruent

3. They are equidistant

4. No, a chord has endpoints on the edges of a circle while a radius has endpoints on the center of the circle and an edge.

5. Since the chords are not congruent, the lines cannot be congruent.

Step-by-step explanation:

Using Theorem 84, we can find that since CA = BD, the corresponding arcs are congruent. Using this theorem, we can find the answers to the rest of the questions.

Answer:

Step-by-step explanation:

Compounded interest formula is

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where [tex]A[/tex] is the final amount, [tex]P[/tex] is the principal, [tex]r[/tex] is the anual interest in decimal, [tex]n[/tex] is the numer of compounded periods in one year and [tex]t[/tex] is the time in years.

[tex]P=\$800\\r=0.09\\n=1\\t=4[/tex]

Notice that [tex]n=1[/tex], because the interest is compounded anually, if the interest is compounded, then [tex]n=12[/tex], because there would be 12 compound periods in one year.

Then, we replace all these vaules in the formula

[tex]A=P(1+\frac{r}{n})^{nt}\\A=800(1+\frac{0.09}{1})^{1(4)}=800(1.09)^{4}\\ A=1,129.26[/tex]

Therefore, after 4 years, the amount would be $1,129.27.

Answer: 11

Step-by-step explanation:

Add the numbers together to get 68, then divide it by 6 to get your answer! Sorry if I'm wrong!

Mean: 11.3

Median: 12.5

Answer:

see explanation

Step-by-step explanation:

given

[tex]\frac{x8x^2-8}{4x+4}[/tex] , x ≠ - 1

The x ≠ - 1 means that x cannot take the value of - 1 as this would make the denominator equal to zero which would make the fraction undefined.

Factor the numerator/ denominator

8x² - 8 = 8(x² - 1) ← factor out 8 from both terms

x² - 1 ← is a difference of squares, hence

8x² - 8 = 8(x - 1)(x + 1)

4x + 4 = 4(x + 1) ← factor out 4 from both terms

Thus the fraction now simplifies to

[tex]\frac{8(x-1)(x+1)}{4(x+1)}[/tex]

Cancel the 8 and 4 by 4 and cancel the factor (x + 1), leaving

=  2(x - 1) = 2x - 2 ← in the form ax + b

E=20.25x+y is the equation

Larry's earnings, represented by E, when he works x hours and has y dollars in sales, is calculated by his hourly wage ($20.25 per hour) plus an 8% commission on his sales, which results in the equation E = 20.25x + 0.08y.

To calculate Larry's earnings E based on his hourly wage and sales commission, we need to consider both parts of his earnings: his hourly rate and his commission rate. The equation that represents Larry's earnings when he works x hours and has a total of y sales in dollars will include the hourly earnings plus a percentage of his sales.

Larry earns $20.25 per hour, so his earnings from hours worked would be 20.25 times the number of hours worked, which is 20.25x.

Additionally, Larry earns a commission of 8% on his sales. To calculate this, you need to convert the percentage to a decimal by dividing by 100 (8% becomes 0.08) and then multiply by the total sales y, resulting in 0.08y.

The total earnings E would therefore be the sum of his hourly earnings and his sales commission, which gives us the equation E = 20.25x + 0.08y.

Answer: {(5,0), (3,4)}

Step-by-step explanation:

You can apply the Substitution method:

- Solve for y from the second equation.

- Substitute into the first equation and solve for x.

Then:

[tex]y=10-2x[/tex]

[tex]x^2+y^2=25\\x^2+(10-2x)^2=25\\[/tex]

(Remember that: [tex](a\±b)^2=a^2\±2ab+b^2[/tex])

[tex]x^2+(10^2-2(10)(2x)+(2x)^2)=25\\x^2+100-40x+4x^2=25\\5x^2-40x+75=0\\x^2-8x+15=0\\(x-5)(x-3)=0\\\\x=5\\x=3[/tex]

Substitute the values obtained into one of the original equation and solve for y:

[tex]2(5)+y=10\\10+y=10\\y=0\\\\2(3)+y=10\\6+y=10\\y=4[/tex]

The solution set is: {(5,0), (3,4)}

|4x-2|=-6 because an absolute value can’t be equal to a negative

Answer:

Option b. degrees Fahrenheit/(mililiters)

Step-by-step explanation:

we know that

The formula to calculate the average rate of change between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have  that

the units of the y-axis are [tex]{\°F}[/tex]

the units of the x-axis are [tex]{ml}[/tex]

therefore

the units of the the average rate of change are

[tex]m=\frac{\°F}{ml}[/tex]

Answer: 8.8pi

Step-by-step explanation:you have to divide 12 by 1.35 then you get your answer.

Answer:

A=bh=24*8=192

V=2(wl+hl+hw)=2·(4·3+15·3+15·4)=234

A=1311(big rectangle ---> (31-12)69)+2(12 x 23 ---> because of the two smaller rectangles=1311+552=1863

Step-by-step explanation:

algebra

Answer:

Part 1) An expression for the area of the inner square is [tex]x^{2}=0.75(20)^{2}[/tex]

Part 2) The area of the entire garden is [tex]400\ ft^{2}[/tex]

Part 3) 75% of the area of the entire garden is [tex]300\ ft^{2}[/tex]

Part 4) The equation is [tex]x^{2}=300[/tex]

Part 5) The solutions of the quadratic equation are [tex]x=(+/-)17.3\ ft[/tex]

Part 6) The solution that best describes the side length of the inner square is [tex]x=17.3\ ft[/tex]

Step-by-step explanation:

Part 1) What is an expression for the area of the inner square?

we know that

The area of the inner square is equal to

[tex]A=x^{2}[/tex]

[tex]A=0.75(20)^{2}[/tex]

so

[tex]x^{2}=0.75(20)^{2}[/tex]

Part 2) What is the area of the entire garden?

The area of the entire garden is

[tex](20)^{2}=400\ ft^{2}[/tex]

Part 3) What is 75% of the area of the entire garden?

we know that

[tex]75\%=75/100=0.75[/tex]

so

[tex]0.75*(400)=300\ ft^{2}[/tex]

Part 4) Write an equation for the area of the inner square using the expressions from Steps 1 and 3

[tex]x^{2}=0.75(20)^{2}[/tex]

[tex]x^{2}=300[/tex]

Part 5) Solve the quadratic equation. Round to the nearest tenth of a foot

we have

[tex]x^{2}=300[/tex]

square root both sides

[tex]x=(+/-)\sqrt{300}[/tex]

[tex]x=(+/-)17.3\ ft[/tex]

Part 6) Which solution to the quadratic equation best describes the side length of the inner square?

[tex]x=(+/-)17.3\ ft[/tex]

so

The solution that best describes the side length of the inner square is

[tex]x=17.3\ ft[/tex]

because

The side length can not be a negative number

28/5x + 328/5 is the answer. I did it and checked. Hope this helped

Answer:

x + 3

Step-by-step explanation:

Factor out the greatest common factor from f(x), which is x²

We get f(x) = x²(x + 3)

The (x + 3) factor is a linear component

Lines are in the form of y = mx + b, here we have y = x + 3

Answer:

b

Step-by-step explanation:

The volume (V) of the triangular prism is

V = area of triangular end × length

area of triangle = [tex]\frac{1}{2}[/tex] × 3.4 × 2.5 = 4.25 in², hence

V = 4.25 × 4.8 = 20.4 in³ → b

Answer: B

Step-by-step explanation:

The volume of a triangular prism can be achieved by the equation:

[tex]V=\frac{1}{2} *l*w*h[/tex]

similar to finding the volume of a regular right triangle, where you have:

[tex]a=\frac{1}{2} b*h[/tex]

Here all you are adding is the dimension of depth by multiplying that depth (l) by the equation for the area.

Answer:

y = 6

Step-by-step explanation:

We are to find the equation of the horizontal line which passes through the point (-4,6).

Since the line is horizontal so the slope will be zero and the equation will be [tex] y = c [/tex] for some constant [tex] c [/tex].

We know that the line passes through the point (-4,6) so the constant [tex] c [/tex] will be 6 at all points on the line.

Therefore, the equation of the horizontal line will be y = 6.

ANSWER

[tex]y = 6[/tex]

EXPLANATION

The equation of a horizontal line passing through:

[tex](x_1,y_1)[/tex]

is given by

[tex]y=y_1[/tex]

The equation of the horizontal line through (-4,6) is

[tex]y = 6[/tex]

1. 6 movies

2. 10 movies

3. The students

4. 10 - 6 = 4

5. For teachers: 9 - 4 =5

For students: 13 - 6 = 7

Answer: x= acb/11 + 32/11

Step-by-step explanation:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

Calculation to finding the value of x:

Given:

[tex]m\ ACB =(11x-32) [/tex]

To find:

x=?

Solution:

[tex]m\ ACB =(11x-32) [/tex]

Given that ABCD is a square,

[tex] \angle ACB = 45[/tex]

Putting the given value in the question:

[tex]\to 45 = 11x-32\\\\ \to 45 + 32= 11x\\\\ \to 77 = 11x\\\\ \to 11x= 77\\\\ \to x=\frac{77}{11}\\\\ \to x=7 [/tex]

Therefore, the final answer is "7".

Learn more:

brainly.com/question/21127280

Answer:

Number C is the rational function

Answer: 0, I think?

Step-by-step explanation: In order to do this equation, we want to get the variable on one side. In order to do this, we add 7 to both sides to cancel out the -7's. Now, we divide 9 on both sides, giving us 0.

Answer:

Step-by-step explanation:

Seven

I imagine that 7 is the one giving you the problem. There are 29 steps between where A is and where B is. The problem is in the directions. If you follow the first direction, there are 29 squares separating them meaning that B and starts on square 31 and A starts on one. If, however, you read on, your find out that B actually starts on 29. Which is it? If you follow the first direction, you get the both land on 13. Here's how.

A's motion is 3 up 1 back. His net motion is that  he moves 2 forward.

B's motion is 5 down and 2 up. His not motion is - 3 each time

A                          B

1                            31

3                            28

5                            25

7                             22

9                             19

11                             16

13                             13

=============================

Let's do it again starting with the second direction

A                              B

1                               29

3                              26

5                               23

7                                20

9                                17

11                                14

13                                11 and they miss  but keep going. You might have to go another round

15                                 8

17                                  5

19                                  2 Now if you try going forward you can't so B uses As  rule.

21                                  4

23                                  6

25                                  8  And these two will never meet on this round.

I think you should follow the first rule.

27                                   10

28                                   12

25                                   14

22                                    16

19                                      18 another miss.    

Well you can carry it on. I would ask your teacher about this one.

Eight

I can give you an answer, but I don't know how you would find it on your own. The smallest number I found was 301

You can see that 2 and 5 do leave a remainder of 1.

You can also see the 301 / 3 leaves a remainder of 1

What about 4? 301 / 4 = 75 with a remainder of 1.

301 / 6 = 50 with a remainder of 1.

301/7 = 43 with no remainder.

What a strange question.

All of these from 2 to 6 divide into 300 evenly. 301 gives a remainder of 1.

But 301 = 7 * 43

Nine

Let the smaller to the 2 angles = x

Therefore the larger one is 3x + 2

The third angle = 90 degrees.

3x + 2 + x + 90 = 180                    Combine like terms on the left.

4x + 92 = 180                                Subtract 92 from both sides.

4x = 180 - 92

4x = 88                                          Divide by 4

x = 88/4

x = 22

So the three angles are

22

66 + 2 = 68

90

This problem seems much easier than the other 2.