8 is 40% of what number? *

How can you show that two objects are proportional with an equation

V125BC [204]

You can use a plot diagram to plot the points and if they all go straight through the origin then it is proportional :)

5 0

3 years ago

Show all work to factor x^4 − 17x^2 + 16 completely.

Dmitrij [34]

Answer:

$x^{4}-17x^{2} +16$ = (x -1)(x + 1)(x - 4)(x + 4)

Step-by-step explanation:

At first, let us find the first two factors of $x^{4}-17x^{2} +16$

∵ The sign of the last term is positive

∴ The middle signs of the two factors are the same

∵ The sign of the middle term is negative

∴ The middle signs of the two factors are negative

∵ $x^{4}$ = x² × x² ⇒ first terms of the two factors

∵ 16 = -1 × -16 ⇒ second terms of the two factors

∵ x²(-1) + x²(-16) = -x² + -16x² = -17x² ⇒ the value of the middle term

∴ (x² - 1) and (x² - 16) are the factors of $x^{4}-17x^{2} +16$

Now let us factorize each factor

→ The factors of the binomial a² - b² (difference of two squares) are

(a - b) and (a + b)

∵ x² - 1 is the difference of two squares

∴ Its factors are (x - 1) and (x + 1)

∵ x² - 16 is the difference of two squares

∴ Its factors are (x - 4) and (x + 4)

∵ (x -1), (x + 1), (x - 4), and (x + 4) are the factors of (x² - 1) and (x² - 16)

∵ (x² - 1) and (x² - 16) are the factors of $x^{4}-17x^{2} +16$

∴ (x -1), (x + 1), (x - 4), and (x + 4) are the factors of $x^{4}-17x^{2} +16$

∴ $x^{4}-17x^{2} +16$ = (x -1)(x + 1)(x - 4)(x + 4)

8 0

2 years ago

Sarah would like to make a 6 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of a mixture that is 80%

ivolga24 [154]

Answer:

a. The system of equations that models the situation is....

$0.80x+0.50y=3.60\\\\ 0.20x+0.50y=2.40$

b. The solution to the system: x = 2 and y = 4

The amount of 80/20 mixture is 2 pounds and the amount of 50/50 mixture is 4 pounds.

Step-by-step explanation:

Suppose, the amount of 80/20 mixture is $x$ pounds and the amount of 50/50 mixture is $y$ pounds.

So, the amount of peanuts in 80/20 mixture $= 0.80x$ pound and the amount of almonds in 80/20 mixture $=0.20x$ pound.

And the amount of peanuts in 50/50 mixture $=0.50y$ pound and the amount of almonds in 50/50 mixture $=0.50y$ pound.

Now, Sarah would like to make a 6 pounds nut mixture that is 60% peanuts and 40% almonds.

So, the amount of peanuts in that mixture $=(6\times 0.60)=3.60$ pounds

and the amount of almonds in that mixture $=(6 \times 0.40)= 2.40$ pounds.

So, the system of equations will be.........

$0.80x+0.50y=3.60 ...................(1)\\\\ 0.20x+0.50y=2.40...................(2)$

Subtracting equation (2) from equation (1), we will get.....

$(0.80x+0.50y)-(0.20x+0.50y)=3.60-2.40\\ \\ 0.60x=1.20\\ \\ x= \frac{1.20}{0.60}=2$

Now, plugging this $x=2$ into equation (1), we will get......

$0.80(2)+0.50y=3.60\\ \\ 1.60+0.50y=3.60\\ \\ 0.50y=3.60-1.60=2\\ \\ y=\frac{2}{0.50}=4$

So, the amount of 80/20 mixture is 2 pounds and the amount of 50/50 mixture is 4 pounds.

7 0

3 years ago

It is about 350 miles from Ruidoso, New Mexico, to Abilene, Texas. Haruko has already driven 75 miles and made it to Roswell, Ne

kvv77 [185]

Answer:

55 miles per hour

Step-by-step explanation:

Given that:

Distance from Mexico to Texas 350 miles

Miles already traveled = 75 miles

Hence, miles left ;

(350 miles - 75 miles) = 275 miles

To complete 275 miles in 5 hours ;

Speed = distance / time

Speed = 275 / 5

Speed = 55 miles per hour

4 0

3 years ago

Jack wanted to measure the weight of his luggage at the airport before departure. He was surprised to see that it weighed 23.6 k

Alex

Answer:

25.7 is how much his luggage weighs.

Step-by-step explanation:

4 0

2 years ago