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3 years ago

In science class, Farah uses a graduated cylinder with

Mathematics

1 answer:

FromTheMoon [43]3 years ago

7 0

Answer:

47 mL

Step-by-step explanation:

Note each marble increases the height by 3 mL, and we start with 8 mL, so we multiply 3 by 13, and add it to 8

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Write each ratio as a unit rate.

Alja [10]

I hope this helps you

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3 years ago

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Solve for p: p(5-2n) = 5/6-1/3

Hatshy [7]

Factor out P:
p(-3n+5)=½
Divide both sides by -3n+5:
p(-3n+5)^-3n+5

½^-3n+5

p=1^-6n+10

6 0

4 years ago

What is the simplified form of the following expression?

ziro4ka [17]

For this case we must simplify the following expression: $7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {16x}) - 3 (\sqrt [3] {8x})$

We rewrite:

$16x = 2 ^ 3 * 2x\\8x = 2 ^ 3 * x$

We rewrite the expression:

$7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {2 ^ 3 * 2x}) - 3 (\sqrt [3] {2 ^ 3 * x}) =$

By definition of properties of powers and roots we have:

$\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}$

Then, taking the terms of the radical:

$7 (\sqrt [3] {2x}) - 3 (2 \sqrt [3] {2x}) - 3 (2 \sqrt [3] {x}) =\\7 \sqrt [3] {2x} -6 \sqrt [3] {2x} -6 \sqrt [3] {x} =$

We add similar terms:

$\sqrt [3] {2x} -6 \sqrt [3] {x}$

Answer:

Option C

7 0

3 years ago

What is the value of x?

Dafna1 [17]

Answer:

Step-by-step explanation:

We use the concept of similarity to find the value of X.

Δ APR ≡ ΔCDR

∴ AR/CR = PR/DR

(10+x)/x = (15+42)/42

42(10+x) = 57x

420 + 42x = 57x

57x - 42x = 420

15x = 420

x = 420/15

= 28

3 0

3 years ago

Can someone explain this to me please

IrinaVladis [17]

Answer:

c. 36·x

Step-by-step explanation:

Part A

The details of the circle are;

The area of the circle, A = 12·π cm²

The diameter of the circle, d = $\overline {AB}$

Given that $\overline {AB}$ is the diameter of the circle, we have;

The length of the arc AB = Half the the length of the circumference of the circle

Therefore, we have;

A = 12·π = π·d²/4 = π· $\overline {AB}$ ²/4

Therefore;

12 = $\overline {AB}$ ²/4

4 × 12 = $\overline {AB}$ ²

$\overline {AB}$ ² = 48

$\overline {AB}$ = √48 = 4·√3

$\overline {AB}$ = 4·√3

The circumference of the circle, C = π·d = π· $\overline {AB}$

Arc AB = Half the the length of the circumference of the circle = C/2

Arc AB = C/2 = π· $\overline {AB}$ /2

$\overline {AB}$ = 4·√3

∴ C/2 = π·4·√3/2 = 2·√3·π

The length of arc AB = 2·√3·π cm

Part B

The given parameters are;

The length of $\overline {OF}$ = The length of $\overline {FB}$

Angle D = angle B

The radius of the circle = 6·x

The measure of arc EF = 60°

The required information = The perimeter of triangle DOB

We have;

Given that the base angles of the triangles DOB are equal, we have that ΔDOB is an isosceles triangle, therefore;

The length of $\overline {OD}$ = The length of $\overline {OB}$

The length of $\overline {OB}$ = $\overline {OF}$ + $\overline {FB}$ = $\overline {OF}$ + $\overline {OF}$ = 2 × $\overline {OF}$

∴ The length of $\overline {OD}$ = 2 × $\overline {OF}$ = The length of $\overline {OB}$

Given that arc EF = 60°, and the point 'O' is the center of the circle, we have;

∠EOF = The measure of arc EF = 60° = ∠DOB

Therefore, in ΔDOB, we have;

∠D + ∠B = 180° - ∠DOB = 180° - 60° = 120°

∵ ∠D = ∠B, we have;

∠D + ∠B = ∠D + ∠D = 2 × ∠D = 120°

∠D = ∠B = 120°/2 = 60°

All three interior angles of ΔDOB = 60°

∴ ΔDOB is an equilateral triangle and all sides of ΔDOB are equal

Therefore;

The length of $\overline {OD}$ = The length of $\overline {OB}$ = The length of $\overline {DB}$ = 2 × $\overline {OF}$

The perimeter of ΔDOB = The length of $\overline {OD}$ + The length of $\overline {OB}$ + The length of $\overline {DB}$ = 2 × $\overline {OF}$ + 2 × $\overline {OF}$ + 2 × $\overline {OF}$ = 6 × $\overline {OF}$

∴ The perimeter of ΔDOB = 6 × $\overline {OF}$

The radius of the circle = $\overline {OF}$ = 6·x

∴ The perimeter of ΔDOB = 6 × 6·x = 36·x

3 0

3 years ago