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2 years ago

an equation for the line perpendicular to the line 4x + 8y = 7 having the same y -intercept as −3x + 5y = −2

1 answer:

8 0

4x + 8y = 7
8y = -4x + 7
y = -1/2x + 7/8 this equation has slope = -1/2

line perpendicular to the line 4x + 8y = 7, so the slope = 2

same y -intercept as −3x + 5y = −2
 y intercept means x = 0
 5y = −2
y = -2/5
so
b = -2/5

answer:
equation:

y = 2x - 2/5

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mylen [45]

B and C are absurd; if a series converges, it must have a sum, but if a series diverges, it cannot have a sum.

Now, notice that

$\dfrac12+\dfrac29+\dfrac4{27}+\dfrac8{81}+\cdots=\dfrac12+\dfrac{2^{2-1}}{3^2}+\dfrac{2^{3-1}}{3^3}+\dfrac{2^{4-1}}{3^4}+\cdots$

That is, we can write the sum more compactly as

$\dfrac12+\dfrac12\displaystyle\sum_{n=1}^\infty\left(\frac23\right)^n$

The series is geometric with common ratio $\dfrac23$ , so the series converges (and thereby has a sum), so the answer is D.

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2 years ago

Find the area of this parallelogram

IgorLugansk [536]

Answer:

Area of parallelogram= base × perpendicular height

base= 20cm height= 13

Area= 20cm×13cm

Area= 260cm²

Therefore the area of the parallelogram is 260cm²

5 0

2 years ago

10.) state whether the given side lengths can form a triangle

Verizon [17]

Answer:

A. 5,8,12, side lengths can form a triangle.

B. 20, 18, 2, side lengths can not form a triangle.

C. 15, 26 , 9, side lengths can not form a triangle.

D. 4.75, 12.25, 16.25, side lengths can form a triangle.

Step-by-step explanation:

We are given three sides in options A, B , C and D.

We need to check if the given sides would form a triangle or not.

Note: Sum of two sides is always greater than third sides in a triangle.

So, we need to check the sum of two sides of given sides length to check if sum is greater than third side length.

A. 5,8,12.

5+8 is greater than 12.

5+12 is greater than 8.

12+8 is greater than 5.

Therefore A. 5,8,12, side lengths can form a triangle.

B. 20, 18, 2

18+2 is not greater than 20.

Therefore B. 20, 18, 2, side lengths can not form a triangle.

C. 15, 26 , 9

15+9 is less than 26.

Therefore C. 15, 26 , 9, side lengths can not form a triangle.

D. 4.75, 12.25, 16.25.

4.75+12.25 is greater than 16.25.

4.75+16.25 is greater than 12.25.

12.25+16.25 is greater than 4.75.

Therefore D. 4.75, 12.25, 16.25, side lengths can form a triangle.

3 0

3 years ago

What are the solutions to the quadratic equation x^2-16=0

maks197457 [2]

Good evening.

This is a incomplete quadratic equation, because it does not have the term bx. Therefore, we can solve this faster with the following strategy:

$\mathsf{x^2 - 16 = 0}$

Add 16 to both sides:

$\mathsf{x^2 - 16 + 16 = 0 + 16}\\ \\ \mathsf{x^2 = 16}$

Take the square root:

$\mathsf{\sqrt {x^2} = \pm\sqrt{16}}\\ \\ \mathsf{\boxed{\mathsf{x = \pm4} }}$

Therefore:

$\boxed{\boxed{\mathsf{S=\{-4, \ +4\}}}}$

4 0

3 years ago

Write 12/root2 + root18 in the form broot2 where b is an interger

katrin2010 [14]

$\dfrac{12}{\sqrt 2} + \sqrt{18}\\\\\\=\dfrac{12 + \sqrt{18 \times 2}}{\sqrt 2}\\\\\\=\dfrac{12+\sqrt{9 \times 4}}{\sqrt 2}\\\\\\=\dfrac{12+3 \times 2}{\sqrt 2}\\\\\\=\dfrac{18}{\sqrt 2}\\\\\\=\dfrac{18\sqrt 2}{\left(\sqrt 2\right)^2}\\\\\\=\dfrac{18\sqrt 2}2\\\\\\=9\sqrt 2$

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2 years ago