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3 years ago

What values of P and Q result in an equation with exactly one solution? Px+Q=-19x+18

Mathematics

1 answer:

eduard3 years ago

3 0

Y = mx + b
not sure if this is how you need it done but i hope it helps

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The sum of a number, 1/6 of that number, 2 1/2 of that number, and 7 is 12 1/2. Find the number.

Tema [17]

Answer:

2 $\frac{1}{16}$

Step-by-step explanation:

The question state that; the sum of a number, 1/6 of that number, 2 1/2 of that number, and 7 is 12 1/2. Find the number.

First, we need to interpret and represent this statement mathematically

Let n be the number.

The sum means 'addition'

1/6 of that number is 1/6 of n = 1/6 × n = $\frac{n}{6}$

2 1/2 of that number is 2 1/2 of n = 2 1/2 × n = 5/2 × n = $\frac{5n}{2}$

So the question says that, when we add; $\frac{n}{6}$ , $\frac{5n}{2}$ and 7 all together, the value is 12 1/2

That is;

$\frac{n}{6}$ + $\frac{5n}{2}$ + 7 = 12 1/2

$\frac{n}{6}$ + $\frac{5n}{2}$ + 7 = $\frac{25}{2}$ ( changing 12 1/2 to improper fraction will give $\frac{25}{2}$ )

So we can now go ahead and solve for n

$\frac{n}{6}$ + $\frac{5n}{2}$ + 7 = $\frac{25}{2}$

subtract 7 from both-side of the equation

$\frac{n}{6}$ + $\frac{5n}{2}$ = $\frac{25}{2}$ - 7

$\frac{n + 15n}{6}$ = $\frac{25 -14}{2}$

$\frac{16n}{6}$ = $\frac{11}{2}$

$\frac{16n}{6}$ can be reduced to give us $\frac{8n}{3}$

$\frac{8n}{3}$ = $\frac{11}{2}$

Cross multiply

8n × 2 = 11× 3

16n = 33

Divide both-side of the equation by 16

$\frac{16n}{16}$ = $\frac{33}{16}$

(On the left-hand side of the equation, 16 will cancel-out 16 leaving us with just, while on the right-hand side of the equation 33 will be divided by 16)

n = $\frac{33}{16}$ = $2\frac{1}{16}$

Therefore the number is $2\frac{1}{16}$

5 0

3 years ago

Find an equation for the perpendicular bisector of the line segment whose endpoints are (8,-5)(8,−5) and (4,3)(4,3).

Marysya12 [62]

Answer:

$Correct answer\\y=\frac{1}{2} x-4$

Step-by-step explanation:

$y-\frac{-5+3}{2} =\frac{-1}{\frac{3-(-5)}{4-8} } (x-\frac{4+8}{2} )\\y+1=\frac{1}{2} (x-6)\\y=\frac{1}{2} x-4$

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2 years ago

Juan is saving money for a new car. He has already saved $200 and plans to save $25 per week. This situation can be represented

Marina86 [1]

He would have $400 after 8 weeks.

8 0

3 years ago

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Solve step by step<br>2(p+8)=26

romanna [79]

Answer:

Step-by-step explanation:

$2(p+8)=26\qquad\text{divide both sides by 2}\\\\\dfrac{2\!\!\!\!\diagup^1(p+8)}{2\!\!\!\!\diagup_1}=\dfrac{26\!\!\!\!\!\diagup^{13}}{2\!\!\!\!\diagup_1}\\\\p+8=13\qquad\text{subtract 8 from both sides}\\\\p=5$

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2 years ago

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The side of square whose parimeter is 20m

Lera25 [3.4K]

Take 20 and divide it by 4 and you get 5mm squared .
There are four sides so take the total which is 20 mm and divide it by the sides to get one side.
Answer is 5mm squared

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3 years ago