Find the 78th term of the arithmetic sequence -4, -2, 0, ...−4,−2,0,...

Answer:  Distributive property  a(b+c) = ab + ac

-5(7)x + 7(7) = -35x + 49 (D)

Answer:

t = [tex]\frac{14}{5}[/tex]

Step-by-step explanation:

Parallel lines have equal slopes.

calculate the slope m of PQ and then equate the slope of AB to slope of PQ

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = P (- 2, 4 ) and (x₂, y₂ ) = Q (4, - 1 )

[tex]m_{PQ}[/tex] = [tex]\frac{-1-4}{4-(-2)}[/tex] = [tex]\frac{-5}{4+2}[/tex] = - [tex]\frac{5}{6}[/tex]

now calculate slope of AB

with (x₁, y₁ ) = A (4, - 3 ) and (x₂, y₂ ) = B (t, - 2 )

[tex]m_{AB}[/tex] = [tex]\frac{-2-(-3)}{t-4}[/tex] = [tex]\frac{-2+3}{t-4}[/tex] = [tex]\frac{1}{t-4}[/tex]

equating the slopes gives

[tex]\frac{1}{t-4}[/tex] = - [tex]\frac{5}{6}[/tex] ( cross- multiply )

5(t - 4) = - 6

5t - 20 = - 6 ( add 20 to both sides )

5t = 14 ( divide both sides by 5 )

t = [tex]\frac{14}{5}[/tex]

The solution of the linear system is given by using an arithmetic operation. Then the value of b is 2.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

The linear equation is given below.

–12 + 3b – 1 = –5 – b

The value of b will be given as

Add b both sides, we have

–12 + b + 3b – 1 = –5 – b + b

           –13 + 4b = –5

Add 13 on both sides, we have

13 – 13 + 4b = – 5 + 13

              4b = 8

Divide both sides by 4, we have

b = 2

More about the linear system link is given below.

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Answer:

The fourth option, 2

Answer:

{- 1, 0, 4 }

Step-by-step explanation:

the range is the y- coordinates of the plotted points

the coordinates of the points are

(- 4, - 1 ) , (1, 0 ) , (1, 4 ) with y- coordinates - 1, 0, 4

then range is { - 1, 0, 4 }

Answer:

6:45

Step-by-step explanation: add 45 min to 6:00 and you have your answer

Answer:6:45

Step-by-step explanation: 6:00 + 45minutes would be 6:45

Considering the order of operations, the operation that should be performed last is given by:

B Subtraction.

The operations inside the parenthesis take precedence over every operation. Then, multiplication/division take precedence over sum/subtraction. If there are only multiplication/division or sum/subtraction, the precedence is from left to right.

In this problem, the expression is:

(1 x 2.5) + (52-13) + (6.7 - 5) - (98+8)

Solving the operations inside the parenthesis, the expression will be given by:

2.5 + 30 + 1.7 - 90

Only addition and subtraction, hence the order is from left to right, and the subtraction is done last, hence option B is correct.

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Answer:

x=4 or x= -2

Step-by-step explanation:

(x-1)(x-1)

x(x-1)-1(x-1)

x^2-x-x+1

x^2-2x+1=9

x^2-2x+1-9=0

x^2-2x-8=0

p= -8

s= -2

1------ -8

2------ -4

x^2+2x-4x-8=0

x(x+2)-4(x+2)

(x+2)(x-4)=0

x+2=0

x-4=0

x= -2

or

x=4

Answer:

12.5%

Step-by-step explanation:

900 - 800 = 100

Gotta pay $100 more

100 / 800 = 0.125

Answer:

2 days.

Step-by-step explanation:

Candice has already taken 5 pictures total, so if she needs to have seven in total she will only have to go on vacation for two days.

5/6 x 4/9 = 10/27 as a fraction form. The work for 5/6 times 4/9 as a fraction provides more insight of how to find what is 5/6 times 4/9 in fraction form and the different variations of such problems.

The simplified form of the provided expression of 2 startroot 18 endroot +3 startroot 2 endroot startroot +162 endroot is 18√2.

The simplified form of an equation is the simplest way of expressing the equation, by applying the required operations of mathematics.

The equation provided in the problem is,

[tex]2\sqrt{18}+3\sqrt{2}+\sqrt{162}[/tex]

Let the simplified form of the above expression is n. Thus,

[tex]n=2\sqrt{18}+3\sqrt{2}+\sqrt{162}[/tex]

Rewrite the equation to solve it further as,

[tex]n=2\sqrt{3\times3\times2}+3\sqrt{2}+\sqrt{9\times9\times2}\\n=2\sqrt{3^2\times2}+3\sqrt{2}+\sqrt{9^2\times2}[/tex]

The square of the term cancel out the square root of it. Thus,

[tex]n=2\times3\sqrt{2}+3\sqrt{2}+9\sqrt{2}\\n=6\sqrt{2}+3\sqrt{2}+9\sqrt{2}\\n=(6+3+9)\sqrt{2}\\n=18\sqrt{2}[/tex]

Thus, the simplified form of the provided expression of 2 startroot 18 endroot +3 startroot 2 endroot startroot +162 endroot is 18√2.

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Answer:

Below :)

Step-by-step explanation:

1) 5^2 = 25

2) 12^2 = 144

3) 9^2 = 81

4) 15^2 = 225

5) 8^2 = 64

6) 7^2 = 49

7) 20^2 = 400

8) 13^2 = 169

9) 30^2 = 900

10) 25^2 = 625

Answer: 10 inches

Step-by-step explanation:

Answer:

I think it's 8

Step-by-step explanation:

because if you think of an octagon it has eight sides and the only parallel sides is pn the top of the octagon and the bottom of the octagon

Answer:

x = 9

Step-by-step explanation:

Simplifying

2 + -6(1 + -1x) = 6 + -4(-1x + -2)

2 + (1 * -6 + -1x * -6) = 6 + -4(-1x + -2)

2 + (-6 + 6x) = 6 + -4(-1x + -2)

Combine like terms: 2 + -6 = -4

-4 + 6x = 6 + -4(-1x + -2)

Reorder the terms:

-4 + 6x = 6 + -4(-2 + -1x)

-4 + 6x = 6 + (-2 * -4 + -1x * -4)

-4 + 6x = 6 + (8 + 4x)

Combine like terms: 6 + 8 = 14

-4 + 6x = 14 + 4x

Solving

-4 + 6x = 14 + 4x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4x' to each side of the equation.

-4 + 6x + -4x = 14 + 4x + -4x

Combine like terms: 6x + -4x = 2x

-4 + 2x = 14 + 4x + -4x

Combine like terms: 4x + -4x = 0

-4 + 2x = 14 + 0

-4 + 2x = 14

Add '4' to each side of the equation.

-4 + 4 + 2x = 14 + 4

Combine like terms: -4 + 4 = 0

0 + 2x = 14 + 4

2x = 14 + 4

Combine like terms: 14 + 4 = 18

2x = 18

Divide each side by '2'.

x = 9

Simplifying

x = 9

None of the above. To form a standard triangle, all 3 sides must be of equal length.

The values of the length of the missing sides of triangle is x = 7√2 and y = 7.

Special right triangles are right triangles with three determined interior angles and fixed side ratios. If one side is known in these right-angled triangles, we can find the value of the two missing sides. The 45°- 45°-90° triangle and the 30°- 60°-90° triangle are other names for the two unique right triangles. Before going further, let's review the fundamental characteristics of a right triangle.

One of the angles of a right triangle is 90 degrees, and the total of the other two angles is also 90 degrees. The triangle's hypotenuse, which is the longest side, is the side that faces the right angle.

From the given figure we observe that the two angles are 45 degree and 90 degree.

Using the angle sum property we have:

45 + 90 + third angle = 180

third angle = 45 degrees.

The triangle is thus a 45-45-90 triangle.

The sides of 45-45-90 triangle correspond to the lengths as x : x : x√2.

Here, the angle corresponding to 45 is 7.

Thus, y = 7 and x = 7√2.

Hence, the values of the length of the missing sides of triangle is x = 7√2 and y = 7.

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Answer:3

Step-by-step explanation:

Answer:

432

Step-by-step explanation:

Answer:

I would say that a is NOT an inverse, however b is.

Step-by-step explanation:

If you look at the two tables for a, you can tell that every pair has swapped places (as they should) except 0 and 9. In which in the second table, what should be the 9 in the x row, is just another 0 in its place.

While if you look at the two tables for b, every single pair has been swapped like it should, meaning the second table is the inverse of the first table.

Hope this helps you btw. I'm sorry if it doesn't though.

Answer:

the side s is 18

Step-by-step explanation:

s=?

Area of square(A)=324

Now,

A=s²

324=s²

√(324)=s

s=18

please see analysis

[tex]\left\{\right.{ \triangle}\ RST\cong { \triangle}\ DE[/tex]F

[tex](SSS\ Congruence\ Postulate)[/tex]

[tex]2.\ { \triangle\ CAT\cong { \triangle\ BED\ \left\{\right.Given\left.\ \right\}[/tex]

[tex]\bar{AT}\cong\bar{ED}[/tex]

[tex]\overline{AT}=20[/tex]

[tex]so\ \overline{ED}=20[/tex]

[tex]DE=3x-7=20\rightarrow\ x=9[/tex]

I hope this helps you:)

Step-by-step explanation:

area of triangles

1/2*9*8= 36

area of.rectangle

8*9= 72

36+72=108 square inches

Step-by-step explanation:

the area of a full circle (360°) is

pi×r²

r = 15 ft in our case

the area of a segment of a circle is the corresponding fraction of the whole circle area.

the angle of the shaded area is

360 - 332 = 28°

therefore, the area of the shaded area is

pi×15²×28/360 = pi×225×28/360 = pi×225×7/90 =

= pi×5×7/2 = 54.97787144... ft²

≈ 54.98 ft²

the area of the "ice rink" is the sum of a rectangle and a circle (which is split into 2 halves that are attached to both sides of the rectangle).

the radius of the circle is 7/2 = 3.5 meters.

the length of the rectangle in the middle is

18 - 2×3.5 = 18 - 7 = 11 meters.

so, the area of the rectangle is 11×7 = 77 m²

the area of the circle is

pi×r² = pi×3.5² = pi×12.25 = 38.48451001... m²

that means the total area is

77 + 38.48451001... = 115.48451... m² ≈ 115.48 m²

Answer:

1.91

Step-by-step explanation:

191% means [tex]\sf \frac{191}{100}[/tex]

So to write 191% as a decimal, simply divide it by 100.

To divide a number by 100, move the decimal point to the left by 2 places.

[tex]\sf \implies 191 \div 100=1.91[/tex]

slope formula :  [tex]\bold{ \sf \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

a.                          coordinates : (3,12) and (4,16)

[tex]\sf \rightarrow \dfrac{16-12}{4-3}[/tex]

[tex]\sf \rightarrow \dfrac{4}{1}[/tex]

[tex]\sf \rightarrow 4[/tex]

b.                          coordinates : (1,4) and (3,12)

[tex]\sf \rightarrow \dfrac{12-4}{3-1}[/tex]

[tex]\sf \rightarrow \dfrac{8}{2}[/tex]

[tex]\sf \rightarrow 4[/tex]

⇒ A. Yes. Both slopes are equal to 4

Answer:

Step-by-step explanation:

Answer:

8[tex]\pi[/tex] miles or 25.133 miles

Step-by-step explanation:

your radius is 4 miles.

The area of a circle is A= [tex]\pi r^{2}[/tex]

Therefore, the area of this circle is [tex]4^{2} \pi[/tex], or 16[tex]\pi[/tex]

Half of this area, because what you're looking for is a semi-circle, is:

8[tex]\pi[/tex] (exact) or 25.133 (rounded) miles.

The volume of the stucture made from three rectangular prism is 4080 ft³

Volume is the amount of space occupied by a three dimensional shape or object.

The volume of the rectangular prism = length * width * height = 12 * 10 * 5 = 600 ft³

The volume of the other prism = length * width * height = 10 * 8 * 36 = 2880 ft³

Volume of the structure = 600 ft³ + 600 ft³ + 2880 ft³ = 4080 ft³

The volume of the stucture made from three rectangular prism is 4080 ft³

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