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2 years ago

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Which system of equations below has no solution? A. y = 4x + 5 and y = 4x – 5 B. y = 4x + 5 and 2y = 8x + 10 C. y = 4x + 5 and y

= One-fourthx + 5 D. y = 4x + 5 and y = 8x + 10

1 answer:

Stels [109]2 years ago

8 0

Answer: A y=4x -5 and y=4x+5

Step-by-step explanation:

They have no solutions because they have the same slopes but different y intercepts. That works with any equation.

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Complete the table of values

Agata [3.3K]

Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify!

You need to know three exponent rules to simplify these expressions:
1) The negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example, $3^{-2} =
\frac{1}{3^{2} }$ .
2) Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example, $(\frac{3}{4}) ^{3} = \frac{ 3^{3} }{4^{3} }$ .
3) The zero exponent rule<span> says that any number raised to zero is 1. For example, $3^{0} = 1$ .
</span>

Back to the Problem:
Problem 1
The x-values are in the left column. The title of the right column tells you that the function is $y = 4^{-x}$ . The x-values are:
<span>1) x = 0
</span>Plug this into $y = 4^{-x}$ to find letter a:
$y = 4^{-x}\\
y = 4^{-0}\\
y = 4^{0}\\
y = 1$
<span>
2) x = 2
</span>Plug this into $y = 4^{-x}$ to find letter b:
$y = 4^{-x}\\ 
y = 4^{-2}\\ 
y = \frac{1}{4^{2}} \\ 
y= \frac{1}{16}$
<span>
3) x = 4
</span>Plug this into $y = 4^{-x}$ to find letter c:
$y = 4^{-x}\\ 
y = 4^{-4}\\ 
y = \frac{1}{4^{4}} \\ 
y= \frac{1}{256}$
<span>

Problem 2
</span>The x-values are in the left column. The title of the right column tells you that the function is $y = (\frac{2}{3})^x$ . The x-values are:
<span>1) x = 0
</span>Plug this into $y = (\frac{2}{3})^x$ to find letter d:
$y = (\frac{2}{3})^x\\
y = (\frac{2}{3})^0\\
y = 1$
<span>
2) x = 2
</span>Plug this into $y = (\frac{2}{3})^x$ to find letter e:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^2\\ y = \frac{2^2}{3^2}\\
y = \frac{4}{9}$
<span>
3) x = 4
</span>Plug this into $y = (\frac{2}{3})^x$ to find letter f:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^4\\ y = \frac{2^4}{3^4}\\ y = \frac{16}{81}$
<span>
-------

Answers:
a = 1
b = </span> $\frac{1}{16}$ <span>
c = </span> $\frac{1}{256}$
d = 1
e = $\frac{4}{9}$
f = $\frac{16}{81}$

5 0

2 years ago

70.18 divided by 0.9 round the answer to the nearest hundredth

storchak [24]

Answer:

77.98

Step-by-step explanation:

4 0

1 year ago

Read 2 more answers

Brody is purchasing some tools for his workshop. He has a budget of $120 and needs to buy at least 14 tools. Each hammer costs $

STatiana [176]

Answer:

For this case, the first thing we must do is define variables:

x: number of hammers

y: number of wrenches

We write the system of inequations:

10x + 6y <= 120

x + y> = 14

Step-by-step explanation:

5 0

2 years ago

Simplify the square root of four over the cubed root of four. four raised to the five sixths power four raised to the one sixth

romanna [79]

Answer:

$(B)4^{1/6}$

Four raised to the one-sixth power

Step-by-step explanation:

We want to simplify: $\dfrac{\sqrt{4} }{\sqrt[3]{4} }$

First, we apply the fractional law of indices to each term.

$\text{If } a^{1/x}=\sqrt[x]{a},$ then:\\\sqrt{4}=4^{1/2}\\\sqrt[3]{4}=4^{1/3}$

We then have:

$\dfrac{\sqrt{4} }{\sqrt[3]{4} }=\dfrac{4^{1/2} }{4^{1/3} }\\$Applying the division law of indices: \dfrac{a^m }{a^n }=a^{m-n}\\\dfrac{4^{1/2} }{4^{1/3} }=4^{1/2-1/3}\\\\=4^{1/6}$

The correct option is B.

7 0

2 years ago

2.14x - 42.9 for x = 22.4 ?<br> A. -18.36<br> B. 5.026<br> C. 47.939<br> D. 90.839

Fynjy0 [20]

Answer:

Step-by-step explanation:

Your answer would be B., because you would multiply

2.14 x 22.4 =

47.939

then you will subtract that by 42.9

47.939 - 42.9 =

5.026

7 0

2 years ago