Solve the following system by graphing. If there​ isn't a unique solution to the​ system, state the reason. y=-2x y=2x+4

Answer:

15. [tex] x = 15 [/tex]

17. [tex] c = 13.2 [/tex]

19. [tex] x = 25.8 [/tex]; [tex] y = 12.4 [/tex]

Step-by-step explanation:

15. [tex] 20*6 = 8*x [/tex] (intersecting chord theorem)

Solve for x

[tex] 120 = 8x [/tex]

Divide both sides by 8

[tex] 15 = x [/tex]

[tex] x = 15 [/tex]

17. [tex] (11 + 20)*11 = (13 + c)*13 [/tex] (two secants intersecting theorem)

Solve for c

[tex] 31*11 = 169 + 13c [/tex]

[tex] 341 = 169 + 13c [/tex]

Subtract 169 from each side

[tex] 341 - 169 = 169 + 13c - 169 [/tex]

[tex] 172 = 13c [/tex]

Divide both sides by 13

[tex] \frac{172}{13} = \frac{13c}{13} [/tex]

[tex] 13.2 = c [/tex] (nearest tenth)

19. [tex] (x + 5)*5 = (15 + 7)*7 [/tex] (two secants intersecting theorem)

Solve for x

[tex] 5x + 25 = 22*7 [/tex]

[tex] 5x + 25 = 154 [/tex]

Subtract 25 from each side

[tex] 5x + 25 - 25 = 154 - 25 [/tex]

[tex] 5x = 129 [/tex]

Divide both sides by 5

[tex] \frac{5x}{5} = \frac{129}{5} [/tex]

[tex] x = 25.8 [/tex] (nearest tenth)

[tex] y^2 = 7*(15 + 7) [/tex] (tangent and secant theorem)

Solve for y

[tex] y^2 = 7*22 [/tex]

[tex] y^2 = 154 [/tex]

Take the Square root of both sides

[tex] \sqrt{y^2} = \sqrt{154} [/tex]

[tex] y = \sqrt{154} [/tex]

[tex] y = 12.4 [/tex] (nearest tenth)

Two needed formulas,:

To find the area of a parallelogram, use

A = bh.

To find the area of a semicircle, use

Area = (πr^2)/2.

The area of the parallelogram is 11 x 32 or 352.

The two semicircle have the same measure.

The radius of the semicircle is (1/2)(16) or 8.

Area = (π8^2)/2

Area = 64π ÷ 2

A = 32π

There are two semicircle.

So, the area of both semicircle combined is

2(32π) or 64π.

Area of figure = 64π + 352.

Area of figure = 553.0619298304

We now round to the nearest tenths to get

Area of the figure = 553.06.

Given:

Initial population = 45,000

Decreasing rate = 2%

Time = 5 year

To find:

The population after a period of 5 years.

Solution:

Formula used:

[tex]f(t)=ae^{rt}[/tex]

where, a is initial population, r is rate and t is time.

[tex]r=\dfrac{2}{100}=0.02[/tex]

Decreasing rate represented by -0.02.

Substitute a=45000, r=-0.02 and t=5 in the above formula.

[tex]f(5)=45000e^{-0.02(5)}[/tex]

[tex]f(5)=45000e^{-0.1}[/tex]

[tex]f(5)=45000(0.904837418)[/tex]

[tex]f(5)=40717.68381 [/tex]

Approximate the value to the previous integer.

[tex]f(5)\approx 40717 [/tex]

Therefore, the population after 5 years is 40717.

Answer:

40,718

Step-by-step ex

The population of a city is currently 45,000 and is declining at a rate of 2% each year. Estimate the population after a period of 5 years. Use the formula ƒ(t) = aert. planation:

Answer:

A

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

5 times 4 is 20 divided by 2 is 10 hope this helps

Answer: It's A. -7.

Step-by-step explanation: I've attached an Image of my work.

Answer:

A. -7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define expression

[tex](\frac{7}{8} )(-16)(-7)(\frac{-1}{14} )[/tex]

Step 2: Evaluate

Answer:

$45.34

hope this helps

Answer:

$20.79

Step-by-step explanation:

0.82(6) = 4.92

15.87 + 4.92 = 20.79

Answer: Infinite Solutions

Step-by-step explanation: Make the top x and y values times -2 to cancel all the variables and numbers out to get 0 = 0 so it would be Infinite Solutions.

And if you multiply by 2 you get the exact same equation.

If I am wrong let me know!

Hope this helps!  

Answer:

1/4

Step-by-step explanation:

divide the value in feet by 5280 because 1 mile equals 5280 feet.

Answer:There are 5280 feet in one mile; thus

1320/5280 = 1/4

Step-by-step explanation:

sorry if its not correct }:

Combine like terms

3q^2 − 11q + 8

Answer:

I believe it may be C or D.

C and D are the exact same, but I don't think it is B, seeing as it is an absolute value function. If I'm wrong, please forgive me.

Step-by-step explanation:

Answer:

look it up on Google

Step-by-step explanation:

Answer:

Width = 3 inch and length = 6 inch

Step-by-step explanation:

The width of a frame = x

A frame 3-in longer than it was wide. Length = 3+x

Area of the frame = 18 sq inch

We need to find the the dimensions of the length and width of the frame Zach purchased,

Area of a rectangle is given by : A = lb

[tex]x(3+x)=18\\\\x^2+3x-18=0\\\\x^2+6x-3x-18=0\\\\x(x+6)-3(x+6)=0\\\\x=-6,3[/tex]

Neglecting negative value

Width = 3 inch

Length = 3 + 3 = 6 inch

Hence, the dimensions of the length and width of the frame is 6 inch and 3 inch respectively.

Answer:

3 and a half inches or 3.50 inches

Step-by-step explanation:

if ten feet is 1 inch 30 feet would be 3 inches, 5 feet would make a half a inch since 10 feets divided by 2 is 5. one inch divided by 2 is 0.50 inches (or a half)

there for the answer is 3 and a half inches

Answer:

|0.251 < p < 0.289|

Step-by-step explanation:

Given that:

The proportion of people who like dark chocolate than milk chocolate in a made up poll is 27%

Margin of Error = 1.9%

The conclusion about the proportion p using absolute value inequality ;

Interval :

P ± margin of error

27% ± 1.9%

(27 - 1.9)% ; (27 + 1.9)%

25.1% ; 28.9%

0.251 ; 0.289

Hence,

|0.251 < p < 0.289|

Answer:

Answer. Nestor is actually one of the leaders of the Greeks in the Trojan War which figures prominently in Homer's Iliad. He is absolutely not a character in the novel The Merchant of Venice but he has been referred in the extract because he represents wisdom and good moral judgment.

Hope this helps, have a great day/night, and stay safe!

Answer:

305m+152

Step-by-step explanation:

(8m+4)38

Multiply each term in the parentheses

8m times 38 plus 4 times 38

Multiply 8m times 38

304m plus 4 times 38

Then Multiply 4 times 38

304m+152

That should be your answer, but I could be wrong, therefore I am so sorry if I am. I hope this helps you.

Answer:

A, C, D

Step-by-step explanation:

A. $5.60 per class

$196 divided by 35

B. $6.50 per class

$260 divided by 40

C. $5.00 per class

$250 divided by 50

D. $5.50 per class

$55 divided by 10

E. $7.60 per class

$342 divided by 45

Answer:

65R3

Step-by-step explanation:

260/4 is a whole number, so then there would be a remainder 3. The only one with a r3 is D.

Hope this helps :D

Expression 2(x+1) represents the sum of bob and Jacks age.

An expression is combination of variables, numbers and operators.

Given,

Bob is x years old,

Jack is two years older than bob=x+2

we need to find the sum of jacks age and bobs age

x plus x plus two

x+x+2

Two times of x plus two

2x+2

Take two as common, two times of x plus one

2(x+1)

Hence expression 2(x+1) represents the sum of bob and Jacks age.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ2

No choices given for your question.

9514 1404 393

Answer:

  (9/10)/(2/5) = ratio of work times

  2 1/4 times as long

Step-by-step explanation:

Given:

  2/5 hours work in the morning

  9/10 hours work in the afternoon

Find:

  an equation for how many times as long was afternoon work compared to morning work

  the equation solution

Solution:

  a/m = r . . . . ratio of afternoon work to morning work

  (9/10)/(2/5) = r . . . equation

  (9/10)/(4/10) = r

  9/4 = r = 2 1/4 . . . solution

The builder worked 2 1/4 times as long in the afternoon as in the morning.

Step-by-step explanation:

Here,

No. Of total =600

Let,

no. Of boy=3x

no. Of girls = 5x

By the question,

Number of boys and number oof girls =600

or,3x +5x=600

or, 8x =600

or, x= 600/8

or, x= 75

Again,

No. Of boys =3x

Or, 3 * 75

=225

No. Of girls = 5x

Or, 5 * 75

= 375

Answer:

The LCM of 15, 30, and 105 is 210

Step-by-step explanation:

15, 30, 105

Solution: List the prime factors of each.

15: 3 * 5

30: 3 * 10

105: 3 * 5 * 7

Multiply each factor the greatest number of times it occurs in any of the numbers.

Answer: Hence Pair( x, y) = [ 105/2, 105/2]

Step-by-step explanation:

Given that;

Among all pairs of numbers with a sum of 105;

the pair whose product is maximum = ?

so let pairs of numbers with a sum of 105 be x and y respectively

x + y = 105

let y = 105 - x

now

product = xy =  x( 105 - x ) = 105x - x²

now

p(x) = 105x - x²

for maximum value of p

dp/dx =0

⇒ dp/dx = 105 - 2x = 0

2x = 105

x = 105/2

y + x = 105

y = 105 - x

y = 105 - 105/2 = 105/2

Hence Pair( x, y) = [ 105/2, 105/2]

Given:

Total number of friends = 9

Number of friend to invite = 4

To find:

The number of ways.

Solution:

We know that, total number of ways to select r items from n items is

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

So, the total number of ways to select 4 people from 9 friends is

[tex]^9C_4=\dfrac{9!}{4!(9-4)!}[/tex]

[tex]^9C_4=\dfrac{9!}{4!5!}[/tex]

[tex]^9C_4=\dfrac{9\times 8\times 7\times 6\times 5!}{4\times 3\times 2\times 1\times 5!}[/tex]

[tex]^9C_4=\dfrac{9\times 8\times 7\times 6}{4\times 3\times 2\times 1}[/tex]

Therefore, the required number of ways is [tex]\dfrac{9\times 8\times 7\times 6}{4\times 3\times 2\times 1}[/tex].

Note: All options are incorrect.

Answer: 1234386026

Step-by-step explanation:

Answer:

1,234,386,030

Step-by-step explanation:

Answer:

3/2v

Step-by-step explanation:

v+1/2 is 1.5v or  3/2v.

Hope this helps :D

Answer:

do you have an image for that?

Step-by-step explanation: