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lana66690 [7]
3 years ago
8

A picture measuring 2 inches by 3 inches is placed inside a frame. The width between the picture and the frame is equal around t

he entire picture. If the area of the frame and the picture is 72 square inches, what is the width of the frame? (This is my last question for my homework, so quick help would be appreciated :D).
Mathematics
2 answers:
Burka [1]3 years ago
3 0

Answer:

3 inches

Step-by-step explanation:

(2 + 2x)(3 + 2x) = 72

4x² + 4x + 6x + 6 - 72 = 0

4x² + 10x - 66 = 0

2x² + 5x - 33 = 0

Using quadratic formula:

x = (-5-17)/4, (-5+17)/4

x = 12/4 = 3

gulaghasi [49]3 years ago
3 0

Answer:

3 INCHES

Step-by-step explanation:

Answer:

3 inches

Step-by-step explanation:

(2 + 2x)(3 + 2x) = 72

4x² + 4x + 6x + 6 - 72 = 0

4x² + 10x - 66 = 0

2x² + 5x - 33 = 0

Using quadratic formula:

x = (-5-17)/4, (-5+17)/4

x = 12/4 = 3

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Brainliest if correct please help
ioda

Answer:

Answer: A. 45 feet

Step-by-step explanation:

8 0
3 years ago
The equation d=0.05v2+1.1v models the distance, d, that it takes are car traveling v miles per hour to come to a complete stop.
liq [111]

Answer:

  • <u>Hannah was not speeding because her speed was about 61 mph, which is below the speed limit.</u>

Explanation:

Just to correct some typos, this is the complete question:

<em />

<em>The equation d=0.05v² +  1.1v models the distance, d, that it takes a car traveling at a speed of v miles per hour to come to a complete stop. If Hannah’s car stopped after travelling 250 feet on a highway with a speed limit of 65 mph, was Hannah speeding? Explain using math whether she was speeding and how you know.</em>

<em />

<h2>Solution</h2>

<em />

To find whether Hannah was speeding, you must find the velocity that is solution for the equation:

  • 250=0.05v² +  1.1v

<em />

Write it in standard form:

  • 0.05v² +  1.1v - 250 = 0

Use the quadratic formula:

       v=\dfrac{-1.1\pm\sqrt{(1.1)^2-4(0.05)(-250)}}{2(0.05)}

      v=\dfrac{-1.1\pm 7.1561}{0.1}

       v=60.6\text{ or }v=-82.6

The speed can only be positive; thus, it is about 61 miles per hour, which is below the speed limit of 65mph.

In conclusion, she was not speeding.

5 0
3 years ago
Match the expression on the left with the correct simplified expression on the right.
andriy [413]

Given: The expression below

\begin{gathered} (\frac{(3x^3y^4)^3}{(3x^2y^2)^2})^2 \\ (\frac{(3x^4y^2)^4}{(3x^5y^2)^3})^2 \end{gathered}

To Determine: The matching expression to the given expressions

Solution

Let us simplify each of the expressions using exponents rule

\begin{gathered} Exponent-Rule1=(a^m)^n=a^{m\times n} \\ Exponent-Rule2=(\frac{a^m}{a^n})=a^{m-n} \end{gathered}

Applying the exponent rule 1 above to the given expressions

\begin{gathered} (3x^3y^4)^3=3^3x^{3\times3}y^{4\times3}=27x^9y^{12} \\ (3x^2y^2)^2=3^2x^{2\times2}y^{2\times2}=9x^4y^4 \end{gathered}\begin{gathered} (3x^4y^2)^4=3^4x^{4\times4}y^{2\times4}=81x^{16}y^8 \\ (3x^5y^2)^3=3^3x^{5\times3}y^{2\times3}=27x^{15}y^6 \end{gathered}

Applying the exponent rule 2

\frac{(3x^{3}y^{4})^{3}}{(3x^{2}y^{2})^{2}}=\frac{27x^9y^{12}}{9x^4y^4}=\frac{27}{9}x^{9-4}y^{12-4}=3x^5y^8\frac{(3x^{4}y^{2})^{4}}{(3x^{5}y^{2})^{3}}=\frac{81x^{16}y^8}{27x^{15}y^6}=\frac{81}{27}x^{16-15}y^{8-6}=3xy^2

Let us not apply exponent rule 1 above

(\frac{(3x^{3}y^{4})^{3}}{(3x^{2}y^{2})^{2}})^2=(3x^5y^8)^2=3^2x^{5\times2}y^{8\times2}=9x^{10}y^{16}(\frac{(3x^{4}y^{2})^{4}}{(3x^{5}y^{2})^{3}})^2=(3xy^2)^2=3^2x^2y^{2\times2}=9x^2y^4

Hence, the matching is as shown below

8 0
1 year ago
What is the solution to this inequality 7x -4 &lt; 4 (x+3)​
Naily [24]

Answer:

x < 17/3

Step-by-step explanation:

Perform the indicated multiplication.

We get 7x - 4 < 4x + 12

Combining the x terms, we get:

3x - 4 < 12

Combining the constants, we get:

3x < 16

Solving for x:  x < 17/3

All numbers smaller than 17.3 are solutions to this inequality.

3 0
3 years ago
Jose purchased a delivery van for his business through an online auction. His winning bid for the van was $34,750. In addition,
denpristay [2]

Answer:

Jose's cost basis for the delivery van = $42,410

Step-by-step explanation:

Cost basis of a fixed asset can be described the original value of an asset for tax purposes which includes the purchase price, shipping, installation, sales tax, and other costs incurred that are related to the purchase of the fixed asset and to make it be in conformity with other assets in its class.

Based on this explanation, Jose's cost basis for the delivery van can be calculated as follows:

Jose's cost basis for the delivery van = Winning bid + Shipping costs + Cost of painting to match other fleet vehicles + Sales tax = $34,750 + $1,470 + $1,590 + $4,600 = $42,410

7 0
3 years ago
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