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3 years ago

Addison's budget is shown in the

Mathematics

1 answer:

Minchanka [31]3 years ago

5 0

Addison spends $1050 on rent.

Step-by-step explanation:

Given,

Addison's budget = $3500

Rent = 30%

Other = 15%

Savings = 30%

Groceries = 25%

Therefore,

Rent = 30% of budget

$Rent=\frac{30}{100}*3500\\Rent=0.30*3500\\Rent=\$1050$

Addison spends $1050 on rent.

Keywords: percentage, multiplication

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Find the Domain of the following exponential and logarithmic equations and solve them:

kakasveta [241]

The base of a logarithm should always be positive and can't be equal to 1, so the domain is 0 < x < 1 or x > 1.

$\log_{\frac1x}243=5$

Write both sides as powers of 1/x :

$\left(\dfrac1x\right)^{\log_{\frac1x}243}=\left(\dfrac1x\right)^5$

Recall that $a^{\log_ab}=b$ , so that

$243=\left(\dfrac1x\right)^5$

$243=\dfrac1{x^5}$

$x^5=\dfrac1{243}$

Take the 5th root of both sides, recalling that 3⁵ = 243, so

$x=\sqrt[5]{\dfrac1{243}}=\boxed{\dfrac13}$

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3 years ago

Points H and F lie on circle c What is the length of line segment GH?

Nina [5.8K]

Answer:

6 units

Step-by-step explanation:

Given: Points H and F lie on circle with center C. EG = 12, EC = 9 and ∠GEC = 90°.

To find: Length of GH.

Sol: EC = CH = 9 (Radius of the same circle are equal)

Now, GC = GH + CH

GC = GH + 9

Now In ΔEGC, using pythagoras theorem,

$(Hypotenuse)^{2} = (Base)^{2} +(Altitude)^{2}$ ......(ΔEGC is a right triangle)

$(GC)^{2} = (GE)^{2} +(EC)^{2}$

$(GH + 9)^{2} = (9)^{2} +(12)^{2}$

$(GH )^{2} + (9)^{2} + 18GH = 81 + 144$

$(GH )^{2} + 81 + 18GH = 81 + 144$

$(GH )^{2} + 18GH = 144$

Now, Let GH = x

$x^{2} +18x = 144$

On rearranging,

$x^{2} +18 x - 144 = 0$

$x^{2} - 6x +24x + 144 = 0$

$x (x-6) + 24 (x - 6) =0$

$(x - 6) (x + 24) = 0$

So x = 6 and x = - 24

∵ x cannot be - 24 as it will not satisfy the property of right triangle.

Therefore, the length of line segment GH = 6 units. so, Option (D) is the correct answer.

3 0

2 years ago

Read 2 more answers

Ms. Nina has 10 lbs of 25% sugar syrup. How much water does she need to add to make 10% sugar syrup?

ryzh [129]

She has 10lbs of 25% syrup... so, in the 10lbs, 25% of that is syrup, the rest, namely the 75% remaining is water or other substances.

let's say she adds "x" lbs of water, to get "y" lbs for the 10% mixture.

how much is 25% of 10lbs? well, (25/100) * 10, or 2.5.

the water has no sugar syrup in it, so is just pure water, so the amoun of syrup in it is 0%, how much is 0% of "x" lbs? well, (0/100) * x, or 0.00x, which is just 0.

how much is 10% of "y" lbs? well (10/100) * y, or 0.10y.

whatever "x" and "y" are, we know that 10 + x = y.

we also know that the syrup amount in that is also 2.5 + 0.00x = 0.10y, thus

$\bf \begin{array}{lccclll}
&\stackrel{lbs}{syrup}&\stackrel{concentration~\%}{syrup}&\stackrel{concentration}{amount}\\
&------&------&------\\
\textit{25\% syrup}&10&0.25&2.5\\
\textit{pur water}&x&0.00&0.00x\\
------&------&------&------\\
\textit{10\% mixture}&y&0.10&0.10y
\end{array}
\\\\\\
\begin{cases}
10+x=\boxed{y}\\
2.5+0.00x=0.10y\\
----------\\
2.5 = 0.10\left( \boxed{10+x} \right)
\end{cases}
\\\\\\
2.5=1 + 0.10x\implies 1.5=0.10x
\\\\\\
\cfrac{1.5}{0.10}=x\implies 15=x$

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Suppose f (x) = x^3 . Find the graph of f (x + 1)

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Answer:

its 3rd graph, the one with (-1,0) point

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Which of the following angles is not congruent to angle 3

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