Anna has 4 bags of 100 crackers, bags of 10 crackers, and 3 crackers that aren’t in bags. How many crackers does she have

Match the real-world problem to its constant of proportionality.

FrozenT [24]

Real word problem ⇒ constant of proportionality

$4.16 for 4 pounds of bananas ⇒ 1.04

$16.48 for 8 pounds of potatoes ⇒ 2.06

$18.36 for 2 pizzas ⇒ 9.18

2 cups of flour to make 36 cookies ⇒ 18

Solution:

A proportional relationship is one in which two quantities vary directly with each other.

We say the variable y varies directly as x,

if for x ∝ y

then, x = y k

Where "k" is called constant of proportionality

$k = \frac{x}{y}$

$4.16 for 4 pounds of bananas

x = 4.16 and y = 4

$k = \frac{4.16}{4} = 1.04$

Thus constant of proportionality is 1.04

$16.48 for 8 pounds of potatoes

x = 16.48 and y = 8

$k = \frac{16.48}{8} = 2.06$

Thus constant of proportionality is 2.06

$18.36 for 2 pizzas

x = 18.36 and y = 2

$k = \frac{18.36}{2} = 9.18$

Thus constant of proportionality is 9.18

2 cups of flour to make 36 cookies

x = 36 and y = 2

$k = \frac{36}{2} = 18$

Thus constant of proportionality is 18

8 0

3 years ago

Solve the rational equation 1/x-2 - 1/x+3 =1/5

Degger [83]

Answer:

x=0

Step-by-step explanation:

8 0

3 years ago

5. Nathan can join a rock climbing club for $52 a month or a flat rate of

Trava [24]

Answer:

Solution: 9 or more months

Inequality: x > or = 9

Step-by-step explanation:

1. Divide 450 by 52 and you get 8.65...

2. Round up since you can't pay for half a month

4 0

3 years ago

Determine if triangle ABC with coordinates A (0, 2), B (2, 5), and C (−1, 7) is an isosceles triangle. Use evidence to support y

kirill115 [55]

Answer:

The triangle ABC is an isosceles right triangle

Step-by-step explanation:

we have

The coordinates of triangle ABC are

A (0, 2), B (2, 5), and C (−1, 7)

we know that

An isosceles triangle has two equal sides and two equal internal angles

The formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance AB

substitute in the formula

$d=\sqrt{(5-2)^{2}+(2-0)^{2}}$

$d=\sqrt{(3)^{2}+(2)^{2}}$

$dAB=\sqrt{13}\ units$

step 2

Find the distance BC

substitute in the formula

$d=\sqrt{(7-5)^{2}+(-1-2)^{2}}$

$d=\sqrt{(2)^{2}+(-3)^{2}}$

$dBC=\sqrt{13}\ units$

step 3

Find the distance AC

substitute in the formula

$d=\sqrt{(7-2)^{2}+(-1-0)^{2}}$

$d=\sqrt{(5)^{2}+(-1)^{2}}$

$dAC=\sqrt{26}\ units$

step 4

Compare the length sides

$dAB=\sqrt{13}\ units$

$dBC=\sqrt{13}\ units$

$dAC=\sqrt{26}\ units$

$dAB=dBC$

therefore

Is an isosceles triangle

Applying the Pythagoras Theorem

$(AC)^{2} =(AB)^{2}+(BC)^{2}$

substitute

$(\sqrt{26})^{2} =(\sqrt{13})^{2}+(\sqrt{13})^{2}$

$26=13+13$

$26=26$ -----> is true

therefore

Is an isosceles right triangle

8 0

3 years ago

Help plz math is my worst subject i have a lot of over due work

zubka84 [21]

I believe the answer is the first option. 1 to 3 with intervals of 1.
Hope this helps!

5 0

3 years ago