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3 years ago

a rectangle has a length if x + 7 centimeters. The perimeter of the rectangle is 23 centimeter. What is the value of x

1 answer:

8 0

$23 = 14 + 2x$
$reasoning \: for \: each \: term \: in \: the \\ \: above \: equation\\ \\ p = 23 \\ 14 = 7 \times 2 \\ 2x = 2 \times x$
$\: \: \: \: \: 23 - 14 \: \: \: \: \: \: \: \: \: \: \: \: \: \: 14 + 2x - 14 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 9 = 2x$
$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 9 \div 2 \: \: \: \: \: \: \: \: \: 2x \div 2 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 4.5 = x$
So, the answer is 4.5

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Points M, N, and P are respectively the midpoints of sides AC , BC , and AB of △ABC. Prove that the area of △MNP is on fourth of

Hunter-Best [27]

Answer:

The area of △MNP is one fourth of the area of △ABC.

Step-by-step explanation:

It is given that the points M, N, and P are the midpoints of sides AC, BC and AB respectively. It means AC, BC and AB are median of the triangle ABC.

Median divides the area of a triangle in two equal parts.

Since the points M, N, and P are the midpoints of sides AC, BC and AB respectively, therefore MN, NP and MP are midsegments of the triangle.

Midsegments are the line segment which are connecting the midpoints of tro sides and parallel to third side. According to midpoint theorem the length of midsegment is half of length of third side.

Since MN, NP and MP are midsegments of the triangle, therefore the length of these sides are half of AB, AC and BC respectively. In triangle ABC and MNP corresponding side are proportional.

$\triangle ABC \sim \triangle NMP$

$MP\parallel BC$

$MP=\frac{BC}{2}$

By the property of similar triangles,

$\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{PM^2}{BC^2}$

$\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{(\frac{BC}{2})^2}{BC^2}$

$\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{1}{4}$

Hence proved.

5 0

3 years ago

What is the distance between points (13,1) and (9,-4)

mariarad [96]

Answer:

5/4

Step-by-step explanation:

y2 -y1 -4-1=-5

x1 -x2 9-13=-4

7 0

2 years ago

Since 2004, the amount of money spent at restaurants in a certain country has increased at a rate of 6% each year. In 2004, a

Stella [2.4K]

$812 billion will be spent at the restaurants if the trend continues.

Explanation

It is given that the amount spent on restaurants increase by 6% every year.

The amount spent on each of the following years can be determined by solving it using the method used to calculate compound interest.

Amount spent in 2004=$510 billion

Annual rate of interest=6%

we have to calculate the amount spent in 2012

number of years n=8

Amount spent= $initial amount*(1+r/100)^{n} \\510(1+6/100)^8\\510*(1+0.06)^8\\510*1.06^8\\=$812 billion$

3 0

3 years ago

24 ⅗ + 43 x (8 ⅕ - 2)

Vilka [71]

Answer: -14/5

Step-by-step explanation:

24 ⅗ + 43 x (8 ⅕ - 2)

= 72/5 + 43 * (8/5 - 2)

= 72/5 + 43 * (8 - 10/5)

= 72/5 + 43 * (-2/5)

= 72/5 - 86/5

= -14/5

8 0

2 years ago

1/4b+1= –1/2b+3<br><br> please help

natita [175]

Answer:

$b = ( - 8)$

Step-by-step explanation:

$\frac{1}{4} b + 1 = \frac{1}{2} b + 3 \\ \frac{1b}{4} - \frac{1b}{2} = 3 - 1 \\ \frac{1b}{4} - \frac{1b \times 2}{2 \times 2} = 2 \\ \frac{1b}{4} - \frac{2b}{4} = 2 \\ \frac{1b - 2b}{4} = 2 \\ \frac{ - b}{4} = 2 \\ - b = 2 \times 4 \\ - b = 8 \\ b =( - 8)$

6 0

2 years ago

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