Solving systems of equations mastery test

9514 1404 393

Answer:

  17

Step-by-step explanation:

The number of handshakes among n people is n(n -1)/2. Then ...

  n(n -1)/2 = 136

  n(n -1) = 272 = 17×16*

  n = 17

There were 17 people at the party.

_____

* This factoring can be facilitated by recognition that √272 ≈ 16.5, the number midway between the consecutive factors.

Answer:

y=21

Step-by-step explanation:

-3 * -7 = 21

Answer:

21

Step-by-step explanation:

For this question multiply 7  to 3

Problem 7

Consider the general template

g(x) = a*sqrt(x-h) + k

and compare it to the general parent function

f(x) = sqrt(x)

We have the following variables: a, h and k

They are defined as such:

For this problem, we have

Since g(x) = sqrt(x+4)+3 is the same as g(x) = 1*sqrt(x - (-4)) + 3

With a = 1, we know that the curve moves upward. Compared to the parent graph y = sqrt(x), which also goes upward, no reflection has been done over the x axis.

The h = -4 means we shift 4 units to the left

The k = 3 means we shift 3 units up

=====================================================

Problem 8

We'll use the ideas mentioned in problem 7. They'll also be used for problems 9 and 10 as well.

For problem 8, we have

=====================================================

Problem 9

This time we have

=====================================================

Problem 10

So far, all of the 'a' values have been positive 1. This means that there hasn't been any reflection or vertical stretching going on.

This time we have a = -1 instead of a = 1.

So we will reflect over the x axis along with the shiftings similar to the ones that occurred with the previous problems.

Answer:

Step-by-step explanation:

abcd=540

2(5)9a=540

90a=540

a=540/90

a=6

Answer:

Step-by-step explanation:

.CCCCCCCC

If g represents the event of selecting a response from a girl, find the complement of g [P (ḡ)].

Answer:

Step-by-step explanation:

IH:GH = 45:30 = 3:2

JK:GK = 36:GK = 3:2

GK = 24

Answer:

48.3

Step-by-step explanation:

9514 1404 393

Answer:

  1080

Step-by-step explanation:

The first price reduction reduced the price to (1 -20%) = 0.80 times the original. The second price reduction reduced the price to ...

  0.80(1 -25%) = 0.80×0.75 = 0.60

times the original.

The final price was ...

  1800 × 0.60 = 1080

Answer:

Here,

150+10=180

162-180=18

Answer is 18°

Step-by-step explanation:

So the round of nearest tenth is 18°

Hope it will help have a great day at school. ^_^

Answer:

Each book cost $16

Step-by-step explanation:

Step 1: Subtract $13 from 141 to get 128

Step 2: Divide 8 by 128 to get 16

Each book cost $16

Hope this helps

pls mark brainliest!

Answer:

x=405

28.7

x=450

Step-by-step explanation:

Answer:

2h-2=92 and h-2=92-h.

Step-by-step explanation:

Hannah, h, is the older sibling and their ages are consecutive odd integers. This means that Anthony's age will be 2 less than Hannah's, or h-2.

The sum of these would be h+(h-2), giving us the equation h+(h-2)=92.

Combining like terms we would have the first correct choice, 2h-2=92.

Our first equation can be transformed, however, to have (h-2) by itself. To do this, we would subtract h from both sides, giving us h-2=92-h.

The equation that will represent the sum of the age of Hannah and Anthony will be 2x+2=92.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the age of Hannah be x. and Since the age of Hannah and Anthony are two consecutive odd integers, therefore, the age of Anthony will be (x+2).

As it is given that the sum of the ages of the two other person is 92, therefore, the equation that will represent the sum of the age of the two persons can be written as,

[tex]x+(x+2)=92\\\\x+x+2=92\\\\2x+2=92[/tex]

Thus, the equation that will represent the sum of the age of Hannah and Anthony will be 2x+2=92.

Learn more about Equation:

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Answer:

I don't know

Step-by-step explanation:

I really don't know I just tried but don't know sorry

Answer:

its 6 7/8

Step-by-step explanation:

Answer: 211,500

Step-by-step explanation:

Just took the quiz

Answer:

The coordinates of the point are (-4.5,-1).

Step-by-step explanation:

We want to find point T(x,y).

I am going to say that out points are A(-8,-2) and B(6,2)

Since it partitions the segment in a 1:3 ratio, we have that:.

[tex]T - A = \frac{1}{1+3}(B-A)[/tex]

[tex]T - A = \frac{1}{4}(B-A)[/tex]

We apply this to both the x-coordinate and y-coordinate of T.

x-coordinate:

x-coordinate of A: -8

x-coordinate of B: 6

x-coordinate of T: x.

So

[tex]T - A = \frac{1}{4}(B-A)[/tex]

[tex]x - (-8) = \frac{1}{4}(6-(-8))[/tex]

[tex]x + 8 = \frac{14}{4}[/tex]

[tex]x = \frac{14}{4} - 8[/tex]

[tex]x = \frac{14}{4} - \frac{32}{4}[/tex]

[tex]x = -\frac{18}{4}[/tex]

[tex]x = -4.5[/tex]

y-coordinate:

y-coordinate of A: -2

y-coordinate of B: 2

y-coordinate of T: y.

[tex]T - A = \frac{1}{4}(B-A)[/tex]

[tex]y - (-2) = \frac{1}{4}(2-(-2))[/tex]

[tex]y + 2 = 1[/tex]

[tex]y = -1[/tex]

The coordinates of the point are (-4.5,-1).

Answer:

C

Step-by-step explanation:

the line seems to either separate or have multiple y places for 1 x place, making it not continuous at x=0 where this happens

Answer:

b) x= -13

Step-by-step explanation:

Answer:

it's answer is= - 13.175

but it is not in option

so B) - 13

is right

Answer:

Step-by-step explanation:

There is no change in x-coordinate. The line is parallel to y-axis.

Equation of line : x = 5

Answer:

Step-by-step explanation:

100(13/20)=65%

Answer:

one seventh of 14 increased by 12 is 14

Step-by-step explanation:

so my example will use 14, so one seventh of 14 is 14 divided by 7 which is 2 then you just add 12 to 2 which gets you 14

An expression is defined as a set of numbers, variables, and mathematical operations. The given statement "One-seventh of a number, increased by twelve" is written as (x/7)+12.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given statement "One-seventh of a number, increased by twelve" can be written in the form of an expression as shown below.

Hence, The given statement "One-seventh of a number, increased by twelve" is written as (x/7)+12.

Learn more about Expression here:

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Answer:

The midpoint is (3, 3).

Step-by-step explanation:

We are given the two points A(9, 11) and B(-3, -5).

The midpoint is given by:

[tex]\displaystyle M=\Big(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\Big)[/tex]

So:

[tex]\displaystyle M = \Big( \frac{9+(-3) }{2}, \frac{ 11+(-5) }{2} \Big) = (3,3)[/tex]

The midpoint is (3, 3).

We want to show that AM = MB.

We can use the distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

The distance between A(9, 11) and M(3, 3) will then be:

[tex]AM=\sqrt{(9-3)^2+(11-3)^2}=\sqrt{6^2+8^2}=\sqrt{100}=10[/tex]

And the distance between B(-3, -5) and M(3, 3) will be:

[tex]MB = \sqrt{ (3-(-3))^2 + (3-(-5))^2 } = \sqrt{(6)^2+(8)^2} = \sqrt{ 100 } = 10[/tex]

So, AM = MB = 10.

Since AM = MB = 10, AM + MB = 10 + 10 = 20.

So, we want to prove that AB = 20.

By the distance formula:

[tex]AB=\sqrt{(9-(-3))^2+(11-(-5))^2}=\sqrt{12^2+16^2}}=\sqrt{400}=20\stackrel{\checkmark}{=}20[/tex]

Answer:

(a-2b) ×(3+x)

Step-by-step explanation:

plz mark as brainliest

Answer:

72 mins

Step-by-step explanation:

24/4 = 6

So each poster take 6 mins to decorate

12 x 6 = 72

Answer:

111.6

Step-by-step explanation:

Answer:

[tex]Tax~required~to~be~paid = 5.4% (5) = \frac{5.4}{100}(5) = \frac{27}{100}[/tex][tex]~of~(5) = \frac{5.4}{100}(5) = \frac{27}{100} = 0.27~dollars[/tex]

Answer:

-8/15 is less than 10/18 so <

Step-by-step explanation: