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2 years ago

Translate the sentence into an equation.

Mathematics

1 answer:

Klio2033 [76]2 years ago

5 0

Answer:

Step-by-step explanation:

2 times a number, 2y

the sum of that and 9, 2y+9 ‘is’ 7

2y+9=7

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How many solutions are there for the system of equations shown on the graph?

Marianna [84]

No solution did you get it right?

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3 years ago

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Rewrite the expression as a single power with a negative exponent

goblinko [34]

$~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \left(\cfrac{1}{3}\cdot \cfrac{1}{3}\cdot \cfrac{1}{3}\cdot \cfrac{1}{3} \right)^2\implies \left[ \left( \cfrac{1}{3} \right)^4 \right]^2\implies \left( \cfrac{1^4}{3^4} \right)^2 \\\\\\ \left( \cfrac{1^{4\cdot 2}}{3^{4\cdot 2}} \right) \implies \cfrac{1}{3^8} \implies 3^{-8}$

let's recall that

$\begin{array}{llll} 1^1&=&1\\ 1^{10}&=&1\\ 1^{1,000}&=&1\\ 1^{1,000,000,000}&=&1\\ 1^{1,000,000,000,000}&=&1\\ \end{array}$

8 0

2 years ago

a jogger runs 4 miles per hour faster downhill than uphill. if the jogger can run 5 miles downhill in the same time that it take

Serga [27]

Answer: the rate uphill is 6 mph.

The rate downhill is 10 mph

Step-by-step explanation:

Let x represent the rate at which the jogger ran uphill.

The jogger runs 4 miles per hour faster downhill than uphill. This means that speed at which the jogger ran downhill is (x + 4) mph

Time = distance/speed

if the jogger can runs 5 miles downhill, then the time taken to run downhill is

5/(x + 4)

At the same time, the jogger runs 3 miles uphill. It means that the time taken to run uphill is

3/x

Since the time is the same, it means that

5/(x + 4) = 3/x

Cross multiplying, it becomes

5 × x = 3(x + 4)

5x = 3x + 12

5x - 3x = 12

2x = 12

x = 12/2

x = 6

The rate downhill is 6 + 4 = 10 mph

8 0

3 years ago

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On Sunday, Chris bought 5% of the cans from his grocery store in preparation for hurricane Sandy. If he bought 61 cans, how many

Gelneren [198K]

Answer:

1220 cans

Step-by-step explanation:

Let the number of cans be x

<u>5% of x is 61, solve the equation below for x:</u>

x*0.05 = 61
x = 61/0.05
x = 1220 cans

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3 years ago

Sketch the graph of the function f(x) = -(x-4)^3 by indicating how a more basic function has been shifted, reflected, stretched,

irina [24]

Step-by-step explanation:

In the attached images we can see the rigid transformation of the function $f(x) =x^{3}$

1. The basic graph $f(x) =x^{3}$

2. The reflected graph $f(x) = -x^{3}$

3. The displaced graph $f(x) = -(x-4)^{3}$

Reflection: In the expression $f(x) = -(x-4)^{3}$ , the sign - before the parenthesis indicates that the function is reflected in the x axis, for this case the function is even, this means that -f(x) = f(-x) , then the reflection on the x axis is equal to the reflection on the y axis.

Displacement: We observe the term (x-4) of the function $f(x) = -(x-4)^{3}$ and analyze the value -4, where, the sign - indicates displacement to the right and the value 4 indicates the amount that the graph shifted .

3 0

3 years ago