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2 years ago

In an arithmetic sequence, the seventh term is −9 and the nineteenth term is 39.

Mathematics

1 answer:

fomenos2 years ago

6 0

Answer:

d = 4

Step-by-step explanation:

a7 = -9

a19 = 39

We know the formula for an arithmetic sequence is

an = a1+d(n-1)

Using the givens:

a7 = -9 = a1 +d(7-1)

a19 = 39 =a1 +d(19-1)

Subtracting these equations

-9 = a1 +d(6)

39 =a1 +d(18)

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

-48 = 0 -12 d

Divide by -12

4 =d

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A square base of a pyramid has the dimensions 5 yards by 5 yards. The height of one of the triangular faces is 12 yards. How can

-Dominant- [34]

Answer:

145 yards squared

Step-by-step explanation:

So the area of the base is area of a square with side length of 5 yards $5*5=25$

The area of one triangular face base times height divided by two and then simply multiplied by 4 because there are 4 triangular faces.

$(\frac{5*12}{2} )*4 = 120$

So the total surface area is $25+120=145$ yards squared

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2 years ago

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Let T:R²->R² be a linear transformation ,and assume that T (1,2)=(-1,1) and T(1,-1)=(2,3)

zavuch27 [327]

Answer:

(-4,-1)

Step-by-step explanation:

We are given T(1,2)=(-1,1) and T(1,-1)=(2,3) and T is a linear transformation.

This implies for scalars a and b that

T(a(1,2)+b(-1,1))=aT(1,2)+bT(-1,1)

T((a,2a)+(-b,b))=a(-1,1)+b(2,3)

T((a-b,2a+b))=(-a,a)+(2b,3b)

T((a-b,2a+b))=(-a+2b,a+3b)

This means we should be able to solve the system below to find a and b for T(3,3):

a-b=3 and 2a+b=3

Add equations to eliminate b and solve for a:

3a=6

Divide 3 on both sides:

a=2

If a-b=3 and a=2, then b=-1.

Plug in a=2, b=-1:

T((a-b,2a+b))=(-a+2b,a+3b)

T((2--1,2×2+-1)=(-2+2×-1,2+3×-1)

T(3,3)=(-4,-1).

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2 years ago

Find the missing side of this right

navik [9.2K]

Answer:

x = 13

Step-by-step explanation:

First start with the blank equation

$a^{2} + b^{2} = c^{2}$

Plug in the legs and hypotenuse. Remember c squared is always the hypotenuse.

$5^{2} + 12^{2} = c^{2}$

Then solve

25 + 144 = $c^{2}$

169 = $c^{2}$

$\sqrt{169} = \sqrt{c^{2} }$

c = 13

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2 years ago

The diner sells bagels for $0.75 each. the bagel shop sells 1 dozen for $7.00. which is the better pric

Varvara68 [4.7K]

The bagel shop has the better price because 1 dozen is 12 bagels and if you multiply 0.75 x 12 = 9.00
so the better price is 7.00

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3 years ago

For an equation 9-3x=21, the first step is

g100num [7]

Answer: A.Subtract 9 from both sides

Step-by-step explanation:

Answer A: Subtract 9 from both sides

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2 years ago

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