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3 years ago

Mesha is comparing 1/3 and 3/5 using benchmarks 0 and 1. Which statements are correct? Check a that apply.

Mathematics

2 answers:

avanturin [10]3 years ago

8 0

Answer:

A and C

Step-by-step explanation:

Dennis_Churaev [7]3 years ago

5 0

Answer:

A, C

Step-by-step explanation:

Let's use a different benchmark for this: 1/2. Half of 5 is 2 1/2, so 3/5 is clearly <em>bigger</em> than 1/2 (since 3 is bigger than 2 1/2). Half of 3 is 1 1/2, so 1/3 is clearly <em>smaller</em> than a half (since 1 is smaller than 1 1/2). We have

1/3 < 1/2 < 3/5

Which, of course, implies that <em>1/3 is less than 3/5</em>, and by being smaller, <em>1/3 is closer to 0 than to 1</em>.

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What is the value of m in the figure below in this diagram abd bcd

oee [108]

$\triangle BCA\ \text{and}\ \triangle DCB\ \text{are similar (AAA). Therefore the sides are in proportion:}\\\\\dfrac{BC}{CD}=\dfrac{AC}{BC}\\\\\text{We have}\\\\BC=m\\CD=7\\AC=7+11=18\\\\\text{Substitute:}\\\\\dfrac{m}{7}=\dfrac{18}{m}\qquad\text{cross multiply}\\\\m^2=(7)(18)\\\\m^2=126\to\boxed{m=\sqrt{126}}\to\boxed{A.}$

6 0

3 years ago

A circle is cut into congruent sections and arranged to form a figure that approximates a parallelogram. Find the approximate he

Solnce55 [7]

Answer:

<h2>The height is 3.43 centimeters, approximately.</h2>

Step-by-step explanation:

Notice that there are 16 pieces from the circle, which means each sector has an angle of

$\theta = \frac{360\°}{16}=22.5\°$

Where all sectors have equal area.

Now, the area of the whole circle is $12.25 \pi \ cm^{2}$ , if we use the formula of its area, we'll find the radius of the circle

$A= \pi r^{2}\\ 12.25\pi = \pi r^{2}\\ r=\sqrt{12.25} \approx 3.5$

Notice that each piece works as an isosceles triangle, because each side is the radius, that is, they have the same length. So far, we know the sides of the isosceles triangle and one internal angle.

To find the height of the one piece, we need to use trigonometric reasons, because the height divides a triangle in two equal right triangles.

$cos(11.25\°)=\frac{h}{3.5}\\ h=3.5 \times cos(11.25 \°)\\h \approx 3.43$

Therefore, the height is 3.43 centimeters, approximately.

6 0

3 years ago

Ben is taking guitar classes three times a week for 8eeeks each class will last 1 3/4 hours how many hours will Ben have spent i

Cerrena [4.2K]

Answer:

Step-by-step explanation:

to find the answer to this you would have to ethier convert 1 3/4 to 1.75 or multiply top heavy fractions

converted way

1.75x8= 14 - stays the same

nonconverted way

7/4 x 8/1 = 56/4 = 14

etheir way you get the same answer

8 0

3 years ago

(y - 2)2 = y2 – 6y + 4<br> Is this statement true or false?

trasher [3.6K]

<h3>Answer: False</h3>

==============================================

Explanation:

I'm assuming you meant to type out

(y-2)^2 = y^2-6y+4

This equation is not true for all real numbers because the left hand side expands out like so

(y-2)^2

(y-2)(y-2)

x(y-2) .... let x = y-2

xy-2x

y(x)-2(x)

y(y-2)-2(y-2) ... replace x with y-2

y^2-2y-2y+4

y^2-4y+4

So if the claim was (y-2)^2 = y^2-4y+4, then the claim would be true. However, the right hand side we're given doesn't match up with y^2-4y+4

--------------------------

Another approach is to pick some y value such as y = 2 to find that

(y-2)^2 = y^2-6y+4

(2-2)^2 = 2^2 - 6(2) + 4 .... plug in y = 2

0^2 = 2^2 - 6(2) + 4

0 = 4 - 6(2) + 4

0 = 4 - 12 + 4

0 = -4

We get a false statement. This is one counterexample showing the given equation is not true for all values of y.

6 0

2 years ago

Read 2 more answers

Write the equation of the line graphed below

zimovet [89]

Answer:

y = 5/8x + 12

Step-by-step explanation:

Slope = change in y/change in x

slope = 5/8

Using y = mx + b find b.

y = 5/8x + b

-2 = 5/8(-4) + b

b = 1/2

y = 5/8x + 12

<em>good luck, i hope this helps :)</em>

3 0

3 years ago

Read 2 more answers