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3 years ago

Below is an arithmetic sequence.

Mathematics

1 answer:

butalik [34]3 years ago

4 0

Answer:a=1 b=5 c=9

Step-by-step explanation:

-7,-3,a,b,c,...... Is the arithmetic sequence

first term=p=-7

Common difference=d=-7-(-3)=-4

a is the 3rd term=-3+4=1

b Is the 4th term=1+4=5

c is the 5th term=5+4=9

Therefore

a is 1

b is 5

c is 9

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4 pencils and 3 crayons are 20.9 inches. 5 pencils and 4 crayons are 26.5 inches. Each pencil is the same length as the other pe

erastova [34]

Answer:

The length of the pencils is 4.1 inches and for the crayons 1.5 inches

Step-by-step explanation:

We can solve by means of a 2x2 system of equations, we have to:

let "x" be the length of the pencils

let "y" be the length of the crayons

4 * x + 3 * y = 20.9

5 * x + 4 * y = 26.5 => x = (26.5 - 4 * y) / 5

Replacing:

4 * (26.5 - 4 * y) / 5 + 3 * y = 20.9

21.2 - 3.2 * y + 3 * y = 20.9

-0.2 * y = 20.9 - 21.2

y = -0.3 / -0.2

y = 1.5

now for x:

x = (26.5 - 4 * 1.5) / 5

x = 4.1

This means that the length of the pencils is 4.1 inches and for the crayons 1.5 inches

5 0

4 years ago

Prove algebraically that each expression has the same value by evaluating each expression for y=5:

Illusion [34]

Answer:

See explanation

Step-by-step explanation:

Given two expressions

$7(3y-5)-2(10+4y)$

and

$13y-55$

Substitute y = 5 into each expression:

$7(3y-5)-2(10+4y)\\ \\=7(3\cdot 5-5)-2(10+4\cdot 5)\\ \\=7\cdot (15-5)-2\cdot (10+20)\\ \\=7\cdot 10-2\cdot 30\\ \\=70-60\\ \\=10$

$13y-55\\ \\=13\cdot 5-55\\ \\=65-55\\ \\=10$

As you can see the results are the same.

7 0

4 years ago

To the nearest tenth, what is the length of the hypotenuse of an isosceles right triangle with a leg of 7 3 inches? A) 15.7inche

Soloha48 [4]

Very sure it’s C trust the process

4 0

3 years ago

Read 2 more answers

Which is the simplified form of the expression ((p squared) (q Superscript 5 Baseline)) Superscript negative 4 Baseline times ((

Alexus [3.1K]

Answer:

$q^{-30}$

Step-by-step explanation:

Given the expression:

$((p^2) (q ^5)) ^{-4} X ((p ^{-4}) (q^5)) ^{-2}$

First, we open the outer brackets

$=(p^{2X-4}) (q ^{5X-4})X (p ^{-4X-2}) (q^{5X-2})\\\\=(p^{-8}) (q ^{-20})X (p ^{8}) (q^{-10})\\\\$Next, we can collect like terms\\\\=p^{-8}Xp ^{8}Xq ^{-20}Xq ^{-10}\\\\$Applying addition law of indices\\\\=p^{-8+8}Xq^{-20+(-10)}\\\\=p^0 X q^{-30}\\\\=1 X q^{-30}\\\\=q^{-30}$

Therefore:

$((p^2) (q ^5)) ^{-4} X ((p ^{-4}) (q^5)) ^{-2}=q^{-30$

8 0

4 years ago

Read 2 more answers

What is the slant height of a pyramid with a 864 square inch surface area and a 18 inch square base

seropon [69]

To determine the slant height, you will use what you know about surface area of a pyramid.

The surface area of a square Peerman consists of one square, and four congruent triangles.

We know the length of one side on the square base is 18 inches.

The area of the base then would be 324 in.².

Subtract this from the total surface area.

864-324 = 540 in.²

Divide 540 in.² by 4 because there are four congruent triangles.

540/4= 135 in.²

Each triangle is 135 in.². Now use the formula for area of a triangle to solve for the missing slant height.

A = 1/2 x b x h
135 = 1/2 x 18 x h
135 = 9h
h = 15 inches.

The slant height is 15 inches.

6 0

3 years ago