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scoundrel [369]
2 years ago
14

Solve for w, where w is a real number.

Mathematics
2 answers:
Ber [7]2 years ago
6 0

Answer:

w= 9

Step-by-step explanation:

\sqrt{ - 4w + 61}  = w - 4

Square both sides:

-4w +61= (w -4)²

\boxed{(a - b)^{2}  = a^2 -2ab + b^2 }

Expand:

-4w +61= w² -2(w)(4) +4²

-4w +61= w² -8w +16

Simplify:

w² -8w +16 +4w -61= 0

w² -4w -45= 0

Factorize:

(w -9)(w +5)= 0

w -9= 0 or w +5= 0

w= 9 or w= -5 (reject)

Note:

-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.

<u>Why </u><u>do </u><u>we </u><u>use </u><u>negative </u><u>square </u><u>root?</u>

When solving an equation such as x²= 4,

we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.

In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.

However, back to our question, we did not introduce the square root so we should not consider the negative square root value.

bagirrra123 [75]2 years ago
6 0

Answer: w=9.

Step-by-step explanation:

\sqrt{-4w+61}=w-4

Tolerance range:

\left \{ {{-4w+61\geq 0} \atop {w-4\geq 0}} \right. \ \ \ \ \left \{ {{4w\leq 61\ |:4} \atop {w\geq 4}} \right. \ \ \ \ \left \{ {{w\leq 15,25} \atop {w\geq 4}} \right. \ \ \ \ \Rightarrow\ \ \ \ \\w\in[4;15,25].

Solution:

(\sqrt{-4w+61})^2=(w-4)^2\\-4w+61=w^2-2*w*4+4^2\\-4w+61=w^2-8w+16\\w^2-4w-45=0\\D=(-4)^2-4*1*(-45)\\D=16+4*45\\D=16+180\\D=196.\\\sqrt{D}=\sqrt{196}\\\sqrt{D}=14   \\w_{1,2}=\frac{-(-4)б14}{2} \\w_1=\frac{4-14}{2} \\w_1=\frac{-10}{2} \\w_1=-5\ \notin tolerance\  range.\\w_2=\frac{4+14}{2}\\ w_2=\frac{18}{2} \\w_2=9\ \in tolerance \ range.

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Natalka [10]

Answer:

B) Jack biked 5 miles in 25 minutes and 8 miles in 40 minutes.

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx

The ratio between the two variables is a constant called constant of proportionality k

k=y/x

<u><em>Verify each case</em></u>

A) Julie sold 4 necklaces for $12 and 9 necklaces for $25.

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Multiply in cross

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therefore

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B) Jack biked 5 miles in 25 minutes and 8 miles in 40 minutes.

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Multiply in cross

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therefore

The situation represent a proportional relationship

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\frac{24}{6}=\frac{46}{9}

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7 0
3 years ago
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Answer:

around like 33.50$

Step-by-step explanation:

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7 0
3 years ago
Read 2 more answers
∠ and ∠ are supplementary angles. If ∠ = (2 − 30)° and ∠ = 4, find the measure of the larger angle
Gala2k [10]

Answer:

We get ∠A =40° and ∠B = 140° and ∠B = 140° is measure of larger angle

Step-by-step explanation:

we have  ∠A = (2x − 30)° and ∠B = 4x, and we need to find measure of larger angle. And ∠A and ∠A are supplementary angles.

If the angles are supplementary there sum is equal to 180° i.e ∠A + ∠B = 180°

So,  First we have to find the value of x. and then we can determine larger angle.

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∠A = (70 − 30)°

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and ∠B = 4x

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∠B = 140°

So, we get ∠A =40° and ∠B = 140° and ∠B = 140° is measure of larger angle

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3 years ago
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Luda [366]
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