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2 years ago

11

Which statements verify that the solution set to |x + 3| < 5 is –8 < x < 2? Check all that apply. Substituting a value

into the inequality from the solution set, such as –2, will create a true statement. Substituting a value into the inequality from the solution set, such as 1, will create a false statement. Substituting a value into the inequality not from the solution set, such as 4, will create a true statement. Substituting a value into the inequality not from the solution set, such as 6, will create a false statement. Substituting any value into the inequality will create a true statement.

1 answer:

Vikentia [17]2 years ago

4 0

Answer:

a & d

Step-by-step explanation:

got them right om edge

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Multiply the fraction by both things in the parenthesis.

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3 years ago

Please help.I need all comparing parts, corresponding parts, and the last question in the problem.

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3 years ago

Is the given point interior , exterior, or on the circle k (x+2)2 + (y-3)2 =18 P (8,4)

Mnenie [13.5K]

One way would be to find the distance from the point to the center of the circle and compare it to the radius

for
$(x-h)^2+(y-k)^2=r^2$
the center is (h,k) and the radius is r

and the distance formula is
distance between $(x_1,y_1)$ and $(x_2,y_2)$ is
$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

r=radius
D=distance form (8,4) to center

if r>D, then (8,4) is inside the circle
if r=D, then (8,4) is on the circle
if r<D, then (8,4) is outside the circle

so
$(x+2)^2+(y-3)^2=18$
$(x-(-2))^2+(y-3)^2=(\sqrt{18})^2$
$(x-(-2))^2+(y-3)^2=(3\sqrt{2})^2$

the radius is $3\sqrt{2}$
center is (-2,3)

find distance between (8,4) and (-2,3)

$D=\sqrt{(8-(-2))^2+(4-3)^2}$
$D=\sqrt{(8+2)^2+(1)^2}$
$D=\sqrt{10^2+1}$
$D=\sqrt{100+1}$
$D=\sqrt{101}$

$r=3\sqrt{2}$ ≈4.2
$D=\sqrt{101}$ ≈10.04

do r<D

(8,4) is outside the circle

6 0

3 years ago

2.) A group of kids ate 3/4 of a pizza. If each kid ate a 1/8 piece of the whole pizza, how many kids shared the pizza? *youre a

kirill [66]

6, because 3/4=6/8 so 6 kids ate it if each has 1/8

8 0

3 years ago

This season, Lisa's lacrosse team has won $\frac 23 of their home games (games played at Lisa's school), but just $\frac 25 of t

juin [17]

Answer:

Lisa's team have played 24 home games and 25 away games.

Step-by-step explanation:

Given:

Let $x$ represents games played at home.

also $y$ represent games played away.

Total number of games played = 49

∴ $x+y=49 \ \ \ \ equation \ 1$

Now according to given data:

Number of home games won = $\frac{2}{3}$

Number of away game won = $\frac{2}{5}$

Total games won =26

Hence

$\frac{2}{3}x+\frac{2}{5}y=26\\\\\frac{2\times 5}{3\times 5}x+\frac{2\times 3}{5\times 5}y=26\\\\\frac{10}{15}x+\frac{6}{15}y=26\\\\\frac{10x+6y}{15}=26\\\\10x+6y= 26\times 15\\10x+6y = 390\\2(5x+3y)=390\\5x+3y=\frac{390}{5}\\\\5x+3y=195 \ \ \ \ equation \ 2\\$

Now multiplying equation 1 by 3 we get,

$3(x+y)=3\times49\\3x+3y=147 \ \ \ \ \ equation \ 3\\$

Now Subtracting equation 2 by equation 3 we get,

$(5x+3y=195)-(3x+3y=147)\\2x=48\\x= \frac{48}{2}=24$

Substituting value of x in equation 1 we get.

$x+y=49\\24+y=49\\y=49-24=25$

Hence Lisa's team have played 24 home games and 25 away games.

3 0

3 years ago