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3 years ago

Which is bigger 2/3 or 7/8

2 answers:

5 0

To compare fractions is easier to do if they have the same denominator, so we make both fractions to share the same denominator, for this we need to find the minimum common multiple of 3 an 8 which is 24, hence we multiply and divide (for not alterating it) each fraction for a adequate multiplier:
(2/3)(8/8) = 2*8/3*8 = 16/24
(7/8)(3/3) = 7*3/8*3 = 21/24
Now we can easily compare:
21/24 > <span>16/24
</span><span>21/24 = 7/8 is bigger</span>

Blababa [14]3 years ago

4 0

7/8 is bigger because if you change them to common denominators 2/3 would equal 16/24 and 7/8 would equal to 21/24 and 21/24 is greater than 16/24

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Which number shows the digit 2 with a value ten times the value of the digit 2 in the number 54,267? A. 13,821 B. 18,092 C. 24,1

Flura [38]

Answer:

D. 32,154

Step-by-step explanation:

54,267 can be written as 54267.0

The 2 in 54 267 should be move 1 place to the left to indicate your multiplying by 10

Moving 1 space to the left = Times 10

Moving 2 places to the left = Times 100

Moving 3 places to the left = Times 1000

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3 years ago

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What is the expression though?

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3 years ago

this year a farmer planted 300 acres of corn. this was 1.5 times as many acres as he planted last year. how many acres did he pl

diamong [38]

X • 1.5 = 300

So...

300/ 1.5 = 200

He planted 200 acres last year

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3 years ago

9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

SSSSS [86.1K]

Answer:

Part 4) $r=84\ units$

Part 9) $sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) $sin(\theta)=-\frac{9\sqrt{202}}{202}$

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

$C=2\pi r$

using proportion

$\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}$

simplify

$\frac{r}{180^o}=\frac{56}{120^o}$

solve for r

$r=\frac{56}{120^o}(180^o)$

$r=84\ units$

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

$cos^2(\theta)+sin^2(\theta)=1$

we have

$cos(\theta)=-\frac{2}{3}$

substitute the given value

$(-\frac{2}{3})^2+sin^2(\theta)=1$

$\frac{4}{9}+sin^2(\theta)=1$

$sin^2(\theta)=1-\frac{4}{9}$

$sin^2(\theta)=\frac{5}{9}$

square root both sides

$sin(\theta)=\pm\frac{\sqrt{5}}{3}$

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

$sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?

see the attached figure to better understand the problem

In the right triangle ABC of the figure

$sin(\theta)=\frac{BC}{AC}$

Find the length side AC applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=11^2+9^2$

$AC^2=202$

$AC=\sqrt{202}\ units$

$sin(\theta)=\frac{9}{\sqrt{202}}$

simplify

$sin(\theta)=\frac{9\sqrt{202}}{202}$

Remember that

The point (11,-9) lies in Quadrant IV

then

The value of sin(∅) is negative

therefore

$sin(\theta)=-\frac{9\sqrt{202}}{202}$

5 0

3 years ago

Mary wants to hang a mirror in her room. The mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and

Umnica [9.8K]

Answer:

The quadratic equation used to determine the thickness of frame is $\left(3+2x\right)\times \left(2+2x\right)=7$

Step-by-step explanation:

Refer to the attachment for the diagram.

Consider EFGH as the the frame and ABCD as the mirror which is to be hanged.

Let me the "x" be the thickness of the frame as shown in diagram.

Given that, BC = 3 ft and DC = 2 ft which is the dimensions of the mirror.

Now to calculate the length and width of the frame consider following calculation,

Width of frame HG = x + DC + x

Width of frame HG = x + 2 + x

Width of frame HG = 2 + 2x

2x is the addition of the thickness which is present on both side of mirror

Length of frame FG = x + BC + x

Length of frame FG = x + 3 + x

Length of frame FG = 3 + 2x

Since it is an rectangular frame, so using the formula for area of rectangle

$Area\:of\:rectangle = length \times width$

Given that area of frame is $7\:ft^{2}$

Substituting the value,

$7 = \left(3+2x\right)\times \left(2+2x\right)$

Therefore, the quadratic equation used to determine the thickness of frame is $\left(3+2x\right)\times \left(2+2x\right)=7$

8 0

3 years ago