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3 years ago

Use the elimination method to solve the system of equations.3x-5y= -162x+5y=31

Mathematics

1 answer:

Sholpan [36]3 years ago

8 0

5x = 15
x = 3

3(3) - 5y = -16
9 - 5y = -16
5y = -16 - 9
5y = - 25
y = - 5

(3, -5)

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A Ferris wheel has a radius of 48 feet. What is the distance a passenger will travel one time around the Ferris wheel?______ fee

dolphi86 [110]

radius = 48 feet

a = πr²

a = 3.14(48)²

a = 3.14 x 2304

a = 7234.56 feet

a = 7234.6 feet

3 0

3 years ago

1. Find the vertex of the following: y = (x - 4)(x - 10) *

horsena [70]

Answer:

1. (7,-9)

2. (4,0) and (10,0)

3. (3,0) and (-3,0)

4. (0,-9)

5. (-1,-32)

Step-by-step explanation:

To find the vertex use the formula

$\frac{-b}{2a}$

First make the equation into a quadratic equation.

$(x-4)(x-10)\\x^{2} -10x-4x+40\\x^{2} -14x+40$

Now it is in the form

$ax^{2} +bx+c=0$

Now we can substitute the values

$\frac{-(-14)}{2(1)} \\\frac{14}{2} \\7$

Now we have 7 as our x value for the vertex we can substitute for y,

$x^{2} -14x+40=y\\(7)^{2} -14(7)+40=y\\49-98+4=y\\y=-9$

So the vertex for 1 is (7,-9)

To find the intercepts for 2 & 3, they basically already give it to you. You just need to find a value for x for x-4 that will equal it to 0 and another for x for x-10 that will equal it to 0.

$x-4=0\\x=4\\\\x-10=0\\x=10$

4 is slightly different but start the same,

$(x-3)(x+3)\\x^{2}+3x-3x-9\\x^{2}-9$

Here, c (9) just shows the graph move down 9, so the y intercept = 9.

5 is the same process as 1,

$2(x-3)(x+5)\\2(x^{2}+5x-3x-15)\\2(x^{2}+2x-15)\\2x^{2}+4x-30$

Vertex,

$\frac{-(4)}{2(2)} \\\frac{-4}{4} \\-1$

Substitute,

$2x^{2}+4x-30\\2(-1)^{2}+4(-1)-30\\2-4-30\\-32$

So the vertex is (-1,-32)

8 0

3 years ago

The mixed number 3 2/3 comes between 3 and 4 on the number line.

givi [52]

Yes, it’s true, because it’s more than 3, but less than 4

7 0

3 years ago

Kira, goran, & joe sent a total of 90 text messages during the weekend. Goran sent 5 fewer messages than Kira. Joe sent 3 ti

MissTica

Answer:

Kira sent 19 text messages, Goran sent 14 text messages and Joe sent 57 text messages.

Step-by-step explanation:

Let be "k" the number of text messages that Kira sent during the weekend, "g" the number of text messages that Gora sent during the weekend and "j" the number of text messages that Joe sent during the weekend.

We know know that they sent a total of 90 text messages then:

$k+g+j=90$