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puteri [66]
3 years ago
5

Use the expression 5x + 2^3 to match the following vocabulary words

Mathematics
1 answer:
sveticcg [70]3 years ago
3 0
A coefficient multiplies a variable. The 5 is a coefficient.
A variable is a letter that stands for a number. The x is a variable.
A base is a number that is raised to an exponent. The 2 is a base.
An exponent is what you raise a base to. The 3 is an exponent.
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Terry and Callie do word processing. For a certain prospectus Callie can prepare it two hours faster than Terry can. If they wor
Dahasolnce [82]

Time taken by jerry alone is 10.1 hours

Time taken by callie alone is 8.1 hours

<u>Solution:</u>

Given:- For a certain prospectus Callie can prepare it two hours faster than Terry can

Let the time taken by Terry be "a" hours

So, the time taken by Callie will be (a-2) hours

Hence, the efficiency of Callie and Terry per hour is \frac{1}{a-2} \text { and } \frac{1}{a} \text { respectively }

If they work together they can do the entire prospectus in five hours

\text {So, } \frac{1}{a-2}+\frac{1}{a}=\frac{1}{5}

On cross-multiplication we get,

\frac{a+(a-2)}{(a-2) \times a}=\frac{1}{5}

\frac{2 a-2}{(a-2) \times a}=\frac{1}{5}

On cross multiplication ,we get

\begin{array}{l}{5 \times(2 a-2)=a \times(a-2)} \\\\ {10 a-10=a^{2}-2 a} \\\\ {a^{2}-2 a-10 a+10=0} \\\\ {a^{2}-12 a+10=0}\end{array}

<em><u>using quadratic formula:-</u></em>

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

x=\frac{12 \pm \sqrt{144-40}}{2}

\begin{array}{l}{x=\frac{12 \pm \sqrt{144-40}}{2}} \\\\ {x=\frac{12 \pm \sqrt{104}}{2}} \\\\ {x=\frac{12 \pm 2 \sqrt{26}}{2}} \\\\ {x=6 \pm \sqrt{26}=6 \pm 5.1} \\\\ {x=10.1 \text { or } x=0.9}\end{array}

If we take a = 0.9, then while calculating time taken by callie = a - 2 we will end up in negative value

Let us take a = 10.1

So time taken by jerry alone = a = 10.1 hours

Time taken by callie alone = a - 2 = 10.1 - 2 = 8.1 hours

3 0
3 years ago
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KengaRu [80]
Yes cookies

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8 0
3 years ago
Convert to the product of multiplication<br>a^2-b^2-4b-4
kirill [66]

a^2-b^2-4b-4 in form of multiplication is  (a-b)(a+b)-4(b+1) .

<u>Step-by-step explanation:</u>

We know that factors are the numbers that are being multiplied together . As 6532*7 = 45724 .Here 6532 & 7 are the factors and 45724 is product of the factors .

Here , we need to convert to the product of multiplication

a^2-b^2-4b-4 or , a^2-b^2-4b-4 :

⇒  a^2-b^2-4b-4

We know by identity that , p^2-q^2 = (p-q)(p+q)

⇒  (a-b)(a+b)-4b-4

Taking common term out as -4 :

⇒  (a-b)(a+b)-4(b+1)

Therefore  , a^2-b^2-4b-4 in form of multiplication is  (a-b)(a+b)-4(b+1) .

7 0
2 years ago
A man who has lost $37 playing roulette in Las Vegas wins $43 playing blackjack. He then loses $44 playing wheel of fortune. Wri
Rina8888 [55]

Answer:

(-37+43)-44=x

Step-by-step explanation:

i put the parentheses only because of PEMDAS. it's a pretty straightfoward question. To put it in an expression however, I'm not sure. Best of luck!

7 0
3 years ago
Grapes cost $1.99 a pound. In a relation, the input is the number of pounds of grapes and the output is the cost.
Gekata [30.6K]

Answer:

$2.19

Step-by-step explanation:

7 0
3 years ago
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