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belka [17]
2 years ago
5

Cruz's Frame shop makes. a mat by cutting out the inside of a rectangular mat board. Find the length and width of the original m

at if the area of the mat board is 148 square inches. the outside length and with are 2x-1 and x+6 the inside length and width are 2x-5 and x+2
Mathematics
1 answer:
My name is Ann [436]2 years ago
5 0

Answer:

length = 23 inches ; width = 18 inches.

Step-by-step explanation:

Length and width can be found from the following expression after solving for x. The expression is given by :

outside area - inside area = 148 square inches

(2·x - 1)·(x + 6) - (2·x - 5)·(x + 2) = 148  (On substitute length and width expressions. Each area is the product of length and width.)

⇒ 2·x² + 11·x - 6 - (2·x² - x - 10) = 148

⇒ 12·x + 4 = 148 .................(On simplifying the expression)

⇒ 12·x = 144

⇒ x = 12

Then the original length of the mat is given by substituting value of x in outside length expression :

2·x - 1 = 2·12 - 1 = 23 inches

and the original width of the mat is given by :

x + 6 = 12 + 6 = 18 inches

Hence, the overall dimensions of the original mat are 23 inches by 18 inches.

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Miguel spent a total of $60 at the grocery store. Of this amount , he spent $18 on fruit. What percentage of the total did he sp
Paraphin [41]

Answer:

30%

Step-by-step explanation:

A percent can be found by dividing the part by the whole, or

part/whole

In this case, the part is the amount he spent on fruit. The whole is the total amount he spent.

amount spent on fruit/ total amount spent

He spent $18 on fruit, and $60 in total.

$18/ $60

Divide 18 by 60

18/60

0.3

Convert 0.3 to a decimal by multiplying by 100 or moving the deicaml place two spots to the right.

0.3*100=30

0.3--> 3.0 --> 30

30%

He spent 30% on fruit.

4 0
3 years ago
Angle ABC is inscribed in a circle as shown.<br><br>What is the measure, in degrees, of angle ABC?
sladkih [1.3K]

Answer

Find out the measure, in degrees, of angle ABC .

To prove

The relationship between inscribed angles and their arcs

The measure of an inscribed angle is half the measure the intercepted arc.

The formula is  

Measure\ of\ inscribed\ angle = \frac{1}{2}\times measure\ of\ intercepted\ arc

As given in the diagram

The measure of the intercepted arc A to B is 120°.

Put value in the formula

\angle ABC = \frac{1\times 120^{\circ}}{2}

∠ABC = 60°

Therefore the measure of the ∠ABC is 60° .


5 0
3 years ago
-7-4p-(-5) pls answer
Evgesh-ka [11]

Answer:

-7-20p

Step-by-step explanation:

Did it in my head but generally first parentheses so -1 times by -5 is 5... still there so multiply 5 by -4p, after that no more simplifying to be done as you cant combine or simplify a number with a variable to one that doesn't have a variable.

7 0
2 years ago
Question 10 of 10
dangina [55]

Answer:

thanks for the points bye bye for now

Step-by-step explanation:

thanks for the points bye bye for now love u

3 0
2 years ago
The perimeter of a shape is 25.71 cm calculate the value of the radius X takes pie to be 3.142
Mariulka [41]

Answer:

5 cm

Step-by-step explanation:

Given a semicircle with perimeter 25.71 cm, we are required to find the radius of the circle.

Circumference of a Semicircle

=Length of the Circular part+Length of the diameter

=\pi r+2r

If \: \pi=3.142, C=25.71\\Then:\\25.71=3.142r+2r\\r(3.142+2)=25.71\\5.142r=25.71\\r=25.71 \div5.142\\r=5cm

3 0
2 years ago
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