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tigry1 [53]
3 years ago
13

How many solutions does the equation have? p−2(4−3p)=2p+7 A.0 B.1 C. Infinitely many

Mathematics
2 answers:
spin [16.1K]3 years ago
7 0
P-8+6p=2p+7
7p-8=2p+7
5p=15
p=3
the answer is 1
Len [333]3 years ago
5 0

Answer:

option:B

Step-by-step explanation:

We are given the equation p-2(4-3p)=2p+7

if we will get a unique value of p on solving the equation then it will have '1' solution.

so on solving for the above equation we have:

p-2\times4-2\times(-3p)=2p+7\\p-8+6p=2p+7\\7p-8=2p+7\\5p=15\\p=3

Hence we get a unique value for 'p'.

so option B is correct.


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Why is it mathematically legal to multiply 2 √ 2 by √ 2 √ 2 in order to rationalize the denominator?
Gala2k [10]
Well if you're referring to rationalizing \bf \cfrac{2}{\sqrt{2}}, which simply means, getting rid of the pesky radical at the bottom

well, it boils down to, hmm say... a quantity or even a polynomial, multiplied times 1, is itself, 2*1=2, 3*1 = 3, ducks*1 = ducks, spaghetti * 1 = spaghetti

or whatever * 1 = whatever
and the value of the multiplicand, doesn't change in anyway, is the same thing before and after the multiplication by 1

now....1 can also be a fraction  \bf \cfrac{2}{2}=1\qquad \cfrac{3}{3}=1\qquad \cfrac{1,000,000}{1,000,000}=1
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\cfrac{ducks}{ducks}=1\qquad \cfrac{spaghetti}{spaghetti}=1\qquad \cfrac{cheese}{cheese}=1
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\cfrac{\textit{the quick fox jumped}}{\textit{the quick fox jumped}}=1\qquad \cfrac{whatever}{whatever}=1

so.. when you're doing \bf \cfrac{2}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\iff \cfrac{2}{\sqrt{2}}\cdot1

and the value multiplicand doesn't change in any way

now, try this in your calculator  \bf \cfrac{2}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{2\sqrt{2}}{\sqrt{2^2}}\implies \cfrac{2\sqrt{2}}{2}\implies \sqrt{2}\\\\
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\textit{check how much is }\cfrac{2}{\sqrt{2}}\textit{ in your calculator}
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\textit{then check how much is }\sqrt{2}\textit{ in it}
6 0
3 years ago
Abigail jogged 10.6 miles in 2.5 hours. What is her jogging speed in miles per hour? A. 4.32 miles/hour B. 4 miles/hour C. 4.24
Lelechka [254]

do miles/hour =

10.6 miles/2.5 hours =

10.6/2.5 =

4.24 miles/hour


5 0
3 years ago
Read 2 more answers
Bruce has $10 in nickels and quarters. The number of nickels is 24 less than twice the number of quarters. How many does he have
STALIN [3.7K]

Answer:

no money

Step-by-step explanation:

he has $10 in change.. he has no money

5 0
3 years ago
20 people applied for a job. Everyone either has a school certificate or diploma or even both. If 14 have school certificates an
STatiana [176]

Given:

Either has a school certificate or diploma or even both = 20 people

Having school certificates = 14

Having diplomas = 11

To find:

The number of people who have a school certificate only.

Solution:

Let A be the set of people who have school certificates and B be the set of people who have diplomas.

According to the given information, we have

n(A)=14

n(B)=11

n(A\cup B)=20

We know that,

n(A\cup B)=n(A)+n(B)-n(A\cap B)

20=14+11-n(A\cap B)

20=25-n(A\cap B)

Subtract both sides by 25.

20-25=-n(A\cap B)

-5=-n(A\cap B)

5=n(A\cap B)

We need to find the number of people who have a school certificate only, i.e. n(A\cap B').

n(A\cap B')=n(A)-n(A\cap B)

n(A\cap B')=14-5

n(A\cap B')=9

Therefore, 9 people have a school certificate only.

3 0
2 years ago
2) WEDNESDAY: Which of the following is NOT a method for solving a quadratic equation?
ozzi

Answer:

line of best fit

Step-by-step explanation:

line of best fit is NOT a method for solving a quadratic equation.

Rest of all the methods are used for solving a quadratic equation.

3 0
3 years ago
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