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3 years ago

Solve the equation. | 2z - 3| = 4z - 1

1 answer:

6 0

Keeping in mind that, an absolute value expression is in effect a piece-wise, then

$\bf |2z-3|=4z-1\implies 
\begin{cases}
+(2z-3)=4z-1\\
\qquad 2z-3=4z-1\\
\qquad -2=2z\\
\qquad \frac{-2}{2}=z\\
\qquad -1=z\\
----------\\
-(2z-3)=4z-1\\
\qquad -2z+3=4z-1\\
\qquad 4=6z\\
\qquad \frac{4}{6}=z\\\\
\qquad \frac{2}{3}=z
\end{cases}$

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One number is 4 times number another. Their sum is 35. Find the number

jonny [76]

Answer:

Step-by-step explanation:

n+4n=35

5n=35

5n/5=35/5

n=7

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3 years ago

Convert 5 whole number and 7 over 8 into an improper fraction

Len [333]

Answer: 47/8

Step-by-step explanation: To write a mixed number as an improper fraction, first multiply the denominator by the whole number and then add the numerator. Finally, we will put our new number over our old denominator and we have our answer which is 47/8.

Therefore, $5\frac{7}{8}$ can be rewritten as the improper fraction 47/8.

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3 years ago

What is the equation of the quadratic graph with a focus of (8, −8) and a directrix of y = −6?

yarga [219]

The vertex is exactly half way between directrix and focus. In this case the vertex is (8,-7)
(h,k)

P is the distance between the vertex and either the directrix or focus, in this case p = 1.

a = 1/(4p) or 1/(4*1) or 1/4

write the equation in vertex form

y = a(x-h)^2 + k

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3 years ago

Write an inequality that best matches this description

Citrus2011 [14]

Answer:

$x \geq 3(y + z)$

Step-by-step explanation:

I am going to say that:

Mary's amount is x.

Ashley's amount is y.

Oscar's amount is z.

Mary has at least 3 times the amount of cash that ashley and oscar have combined

Ashley's and Oscar's combined amount is y + z.

3 times this amount is 3(y + z).

At least 3 times means that z is equal or greater than 3(y + z).

$x \geq 3(y + z)$

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3 years ago