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3 years ago

12

Find x and y with steps

1 answer:

LuckyWell [14K]3 years ago

7 0

Answer:

x=15, y=12

Step-by-step explanation:

Please see the attached pictures for full solution.

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Alex has a bag of marbles. Each marble is red, blue, or yellow , and the ratio of the red to blue to yellow marbles is 6:10:15.

lesantik [10]

Answer:

There are 150 blue marbles in Alex's bag.

Step-by-step explanation:

Let $x$ , $y$ , $z$ be the quantities of red, blue and yellow marbles, respectively. From statement we derive three rational equations for initial and final ratios:

Initial ratio

$\frac{x}{y} = \frac{6}{10}$ (1)

$\frac{y}{z} = \frac{10}{15}$ (2)

Final ratio

$\frac{x + 10}{z - 25} = \frac{1}{2}$ (3)

After some algebraic handling we get the following system of linear equations:

$x - \frac{3}{5}\cdot y = 0$ (1)

$y - \frac{2}{3}\cdot z = 0$ (2)

$2\cdot (x + 10) = z - 25$

$2\cdot x +20 = z - 25$

$2\cdot x - z = -45$ (3)

The solution of the system of linear equations is:

$x = 90$ , $y = 150$ , $z = 225$

There are 150 blue marbles in Alex's bag.

5 0

3 years ago

The coordinates of the vertices of a polygon are (−5, 1) , (−1, 3) , (2, 3) , (2, −2) , and (−3, −1) .

ozzi

Using the distance formula $d=\sqrt{(x_2-x_1) +(y_2-y_1) }$ Then we assign the points letter for simplicity

$A= (-5.1),B=(-1,3),C=(2,3),D=(2,-2),E=(-3,-1)$ . The distance formula gives us the magnitude between two points hence,

$AB=\sqrt{(-5-(-1))^2+ (-1-3)^2}=\sqrt{16+16}= 5.65$

$BC=\sqrt{(-1-2)^2+(3-3)^2}= \sqrt{9}=3$

$CD=\sqrt{(2-2)^2+((3-(-2))^2} =\sqrt{25}=5$

$DE=\sqrt{(2-(-3))^2+(-2-(-1))^2} =\sqrt{26+1} =5.099$

$AE=\sqrt{(-3-(-5))^2+(-1-1)^2}= \sqrt{4+4} =\sqrt{8}=2.82$

$Perimeter= AB+BC+CD+DE+AE\\Perimeter=5.65+3+5+5.099+2.82=21.57 units$

5 0

3 years ago

Question 1 of 14

lapo4ka [179]

Answer:

c

Step-by-step explanation:

count

3 0

3 years ago

Read 2 more answers

Solve for x: 2x+1= -3x+36

SSSSS [86.1K]

Answer:

x = 7

Step-by-step explanation:

2x + 1 = -3x + 36

2x + 3x + 1 = -3x + 3x +36

5x + 1 = 36

5x + 1 - 1 = 36 - 1

5x = 35

5x/5 = 35/5

x = 7

7 0

4 years ago

Read 2 more answers

5. A sphere has a diameter of 16 inches. What is the<br> volume of the sphere?

oksian1 [2.3K]

Answer:

2144.7 inches³

Step-by-step explanation:

use formula for calculating volume of sphere which is 4/3×π×r3

since diameter is 16 inches we divide it by 2 to get the radius

4 0

2 years ago