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2 years ago

What is an equation of the line that passes through the points (5,7) and (-5, -1)?

Mathematics

1 answer:

Tema [17]2 years ago

3 0

(-1-7)/(-5-5) = -8/-10 = 4/5

y = mx + c
y = 4x/5 + c
7 = (4/5 x 5) + c
7 - 4 = c
3 = c

y = (4x/5) + 3

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Tell weather -3>-x/5; x =10 is a solution of inequality

chubhunter [2.5K]

Answer: $\begin{bmatrix}\mathrm{Solution:}\:&\:x>15\:\\ \:\mathrm{Interval\:Notation:}&\:\left(15,\:\infty \:\right)\end{bmatrix}$

Step-by-step explanation:

$-3>-\frac{x}{5}$

$-\frac{x}{5}$

$5\left(-\frac{x}{5}\right)$

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3 years ago

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lutik1710 [3]

Answer:

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Step-by-step explanation:

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4 years ago

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A pound of apples costs $1.98 how much will 0.75 pounds cost ?

Alina [70]

Given:

Cost of one pound of apples = $1.98

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The cost of 0.75 pound of apples.

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Cost of one pound = $1.98

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4 years ago

For what values of b are the vectors \langle -46, b, 10 \rangle and \langle b, b^2, b \rangle orthogonal

Jet001 [13]

Answer:

b = 6 or b = -6 (non-zero vectors)

b = 0 (zero vector)

Step-by-step explanation:

Two vectors $\vec{a}=\langle a_1,a_2,a_3\rangle$ and $\vec{b}=\langle b_1,b_2,b_3\rangle$ are orthogonal if their dot product is equal to 0, or in other words

$a_1\cdot b_1+a_2\cdot b_2+a_3\cdot b_3=0$

In your case,

$\vec{a}=\langle -46, b, 10\rangle\\ \\\vec{b}=\langle b,b^2,b\rangle$

Hence, if vectors a and b are orthogonal, then

$-46\cdot b+b\cdot b^2+10\cdot b=0\\ \\-46b+b^3+10b=0\\ \\b^3-36b=0\\ \\b(b^2-36)=0\\ \\b(b-6)(b+6)=0\\ \\b=0\text{ or }b=6\text{ or }b=-6$

Note, then if b = 0, then $\vec{b}=\langle 0,0,0\rangle$ and zero-vector is orthogonal to any other vectors.

Thus, b = 6 or b = -6.

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