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4 years ago

A square sheet of paper measures 42 centimeters on each side. What is the length of the diagonal of this paper?

1 answer:

5 0

59.4cm
Use Pythagorean theorem to find the diagonal (^ means exponent)
a^2 + b^2 = c^2
42^2 + 42^2= c^2
1764+1764=c^2
3528=c^2
square root both sides
c= 59.39696962
round and you get 59.4 cm

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Draw the graphs of the equations x – y = 1 and 2x + y = 8. Shade the area bounded by these two lines and y-axis. Also, determine

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Answer:

Using Geometry to answer the question would be the simplest:

Step-by-step explanation:

Remembering the formula for the area of a triangle which is $A=\frac12bh$ . One can then tackle the question by doing the following:

Step 1 Find the y-intercepts

The y-intercepts are found by substituting in $x=0$ .

Which gives you this when you plug it into both equations:

$-y=1\\y=-1\\y=8$

So the y-intercepts for the graphs are $(0,-1)\\$ , and $(0,8)$ respectively.

Now one has to use elimination to solve the problems by adding up the equations we get:

$x-y=1\\2x+y=8\\3x=9\\x=3$

Now to solve for the y component substitute:

$2(3)+y=8\\y=2$

Therefore, the graphs intersect at the following:

$(3,2)$

Now we have our triangle which is accompanied by the graph.

now to solve it we must figure out how long the base is:

$b=8-(-1)\\b=9$

The height must also be accounted for which is the following:

$h=3$

Now the formula can be used:

$A=\frac12bh=\frac12(9)(3)=\frac{27}2\ \text{units}^2$

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3 years ago

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The first hill on a roller coaster is 155 feet tall. The first drop on a second roller coaster is about 11/20 as tall as the fir

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Answer:

85.25

Step-by-step explanation:

155 x (11/20) =85.25 feet

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3 years ago

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Help!!!! Plssss!!! ASAP

zimovet [89]

Answer:

The y-intercept is (0,-26)

Step-by-step explanation:

Given two points P(a,b) and Q(c,d), the line that passes for both points can be found with the expression

$\displaystyle y-b=\frac{d-b}{c-a}(x-a)$

We'll take the first two points P(34,-52) and Q(51,-65) to find

$y=-\frac{13}{17}(x-34)-52\\ \\y=-\frac{13}{17}x-26$

Let's verify if the third point is on the line:

$y=-\frac{13}{17}68-26=-52-26=-78$

It belongs to the line. To find the y-intercept of the line, we set x to 0

$y=-\frac{13}{17}(0)-26=-26$

The y-intercept is (0,-26)

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3 years ago

James delivered 3/8 of the newspaper his route in the first hour and 4/5 of the rest in the second hour. What fraction of the ne

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Answer:

1/2

Step-by-step explanation:

Remaining fraction will be (1-3/8)=5/8

Given that in the second hour he delivered 4/5 of 5/8, then the fraction delivered in the second hour will be:

4/5 of 5/8

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He delivered 1/2 (in fraction)

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3 years ago

Write Each Number As A Power Of 5

Lena [83]

The numbers as powers of 5 are 5^-1, 5^-2, 5^-3 and 5^0

<h3>How to rewrite the numbers as a power of 5?</h3>

The numbers are given as:

• 0.2

• 0.04

• 125^-1

• 15^0

<u>Number 1: 0.2</u>

Express as fraction

1/5

Apply the power rule of indices

5^-1

<u>Number 2: 0.04</u>

Express as fraction

1/25

Express 25 as 5^2

1/5^2

Apply the power rule of indices

5^-2

<u>Number 3: 125^-1</u>

Express as fraction

1/125

Express 125 as 5^3

1/5^3

Apply the power rule of indices

5^-3

<u>Number 4: 15^0</u>

Evaluate the exponent

15^0 = 1

Express 1 as 5^0

15^0 = 5^0

Hence, the numbers as a power of 5 are 5^-1, 5^-2, 5^-3 and 5^0

A square sheet of paper measures 42 centimeters on each side. What is the length of the diagonal of this​ paper?

A square sheet of paper measures 42 centimeters on each side. What is the length of the diagonal of this paper?