lius has 5 over 8 quart of grape juice he pours the same amount in each 5 glasses which equation represents the fraction of a quart of grape juice n that is in each glass

Answers

Answer 1

Answer: so we have to divide 5/8 into 5 equal segments.

5 5
-- ÷ ---
8 1

in order to divide fractions we need to flip the second fraction and change the sign from a divition sign to a multiplication sign

5 1 5
-- × --- = ---
8 5 40

now we just simplify 5/40 is equal to 1/8

each glass gets 1/8 of a quart

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What is the value of pi?
(π)

Answers

The answer to your question is 3.14

3.14 is the value of pi.. lol

Will all parallelograms have diagonals that are line of symmetry

Answers

A parallelogram will always have diagonal lines of symmetry. As if you have a look at a picture of a parallelogram, there are clearly diagonal lines of symmetry.

No, not all, but overall, most of them have diagonal lines of symmetry.

How to find the reference angle of -11pi/3 ?

Answers

$- (11 \pi )/(3) \n \n =- (11*180)/(3) \n \n =- (1980)/(3)$

$=-660$ °

= 60 °

Just replace π by 180°

$\boxed{-(11\pi)/(3)=-(11*180)/(3)=-660^o=60^o}$

Does 2/3x+3/4=8 and 8x=87 have the same solution ?

Answers

(2/3)x + (3/4) = 8
-(3/4) -(3/4)

(2/3)x = 7.25(3/2)
(3/2)

x = 10.875

8x = 87 Divide both sides by 8

x = 10.875

So yes both sides have the same solution

Hope this helps :)

yes it does as far as i can see

Find the inverse of each function1) g (x)= 3+(x-1)^3
4) f (x)=x^3+2
5) f (n)= 5 square root of (-n+1/2)

Answers

to find the inverse
1. replace f(x) or g(x) or f(n) with y
2. switch places of x and y
3. solve for y
4. replace y with f⁻¹(x) or g⁻¹(x) or f⁻¹(n)

1.
g(x)=3+(x-1)^3
replace
y=3+(x-1)^3
switch
x=3+(y-1)^3
solve
x=3+(y-1)^3
subtract 3
x-3=(y-1)^3
cube root both sides
$\sqrt[3]{x-3}$ =y-1
add 1
$\sqrt[3]{x-3}$ +1=y
switch y with g⁻¹(x)
g⁻¹(x)= $\sqrt[3]{x-3}$ +1

4. f(x)=x^3+2
replace with y
y=x^3+2
switch x and y
x=y^3+2
solve for y
x=y^3+2
subtract 2
x-2=y^3
cube roo both sides
$\sqrt[3]{x-2}$ =y
replace with f⁻¹(x)
f⁻¹(x)= $\sqrt[3]{x-2}$

5.
f(n)=5 $√(-n+1/2)$
replace
y=5 $√(-n+1/2)$
switch n and y
n=5 $√(-y+1/2)$
solve for y
n=5 $√(-y+1/2)$
divide both sides by 5
n/5=n= $√(-y+1/2)$
square both sides
$(n^2)/(25)$ =-y+1/2
subtract 1/2 from both sides
$(n^2)/(25)$ - $(1)/(2)$ =-y
multiply both sides by -1
- $(n^2)/(25)$ + $(1)/(2)$ =y
replace with f⁻¹(n)
f⁻¹(n)=- $(n^2)/(25)$ + $(1)/(2)$

1. g⁻¹(x)= $\sqrt[3]{x-3}$ +1
4. f⁻¹(x)= $\sqrt[3]{x-2}$
5. f⁻¹(n)=- $(n^2)/(25)$ + $(1)/(2)$

Suppose the altitude to the hypotenuse of a right triangle bisects the hypotenuse. How does the length of the altitude compare with the lengths of the segments of the hypotenuse?a) The length of the altitude is equal to twice the length of one of the segments of the hypotenuse.
b) The length of the altitude is equal to half the length of one of the segments of the hypotenuse.
c) The length of the altitude is equal to the length of one of the segments of the hypotenuse.
d) The length of the altitude is equal to the sum of the lengths of the segments of the hypotenuse.

Answers

Answer:

Option: C is correct.

c) The length of the altitude is equal to the length of one of the segments of the hypotenuse.

Step-by-step explanation:

By the Right Triangle Altitude Theorem:

The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.

From the figure we could say that:

$AD=√(CD\cdot DB)$

As the hypotenuse is divided into divided into two equal parts since the altitude bisects the hypotenuse of the right triangle.

This means that:

CD=DB

Hence,

$AD=\sqrt{CD^(2)}\n\nAD=CD$

Hence, we could say that:

c) The length of the altitude is equal to the length of one of the segments of the hypotenuse.

1. On a right triangle, how does the length of the median drawn to the ... lengths. D. C. B. A. Triangle ABC is a right triangle with is the median to the ... to the hypotenuse is one-half as long as the hypotenuse, ..... This segment is an altitude to both triangles, with bases. AD and DC. These two segments are equal in length.

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