What is the solution of the system of equations shown below? y = 4x + 4 y
= x^2 - 5x + 18 *

Answers

Answer 1

Answer:

(7, 32) and (2, 12)

Step-by-step explanation:

y = 4x + 4

y = x² - 5x + 18

4x + 4 = x² - 5x + 18

x² - 9x + 14 = 0

14 = (-7)(-2)

-9 = -7 + (-2)

(x - 7)(x - 2)=0

x= 7, x = 2

For x = 7

y = 4x + 4  = 4*7 + 4 = 32

(7, 32)

For x = 2

y = 4x + 4 = 4*2 + 4 = 12

(2, 12)

Check:

y = x² - 5x + 18

(7, 32)

32 = 7² - 5*7 + 18

32= 32 true

(2, 12)

12 = 2² - 5*2 + 18

12 = 12 true

Answer 2

Answer:

(7, 32) and (2, 12)

Step-by-step explanation:


Related Questions

Leigh is going diving and needs to descend to a depth of 360 feet below sea level. She wants to do it in 12 equal descents. How far should she travel in each descent?

Answers

Answer:

30 feet

Step-by-step explanation:

If they are equal, just divide 360 by 12.

360 ÷ 12 = 30

Which number produces a rational number when multiplied by
1/3

Answers

Answer:

Any integer multiplied can give rational number

Step-by-step explanation:

Solve the equation
The equation is -3 = 8x -4y for y​

Answers

Answer:

[tex]y=\frac{3}{4}+2x[/tex]

Step-by-step explanation:

Here are two rectangles.
6 cm
9 cm
8 cm
12 cm
Complete this sentence.
The two rectangles are similar and the scale factor is

Answers

Answer:

3/4

Step-by-step explanation:

Scale factor = 6/8 or 9/12 = 3/4

Pls help with this question.
This recipe makes 16 portions of potato soup.
Richard follows the recipe but wants to make 4 portions.
Complete the amounts of each ingredient that he needs.

Answers

Answer:

24 ml oil

60 g onions

360 g potatoes

400 ml milk

Step-by-step explanation:

The recipe makes 16 portions and you only need 4 portions. Since 16 is 4 times bigger than what you need, just divide everything you've been given by 4.

*you can choose to convert into the correct units of measurement before or after dividing. I converted after dividing. Either way works fine though.

1) 96/4 = 24 ml

2) 240/4 = 60 g

3) 1.44/4 = 0.36 kg

They want it in grams, so times it by 1,000 to convert. this gives you 360 g.

4) 1.6/4 = 0.4 l

They want it in ml, so times it by 1,000 to convert. this gives you 400 ml.

Hope this helped : )

Which of the binomials below is a factor of this
trinomial?
x2 + 13x + 40
O A. x+ 5
O B. X-5
O C. X+4
O D. X-4​

Answers

B is the correct answer

x^2+6x+8=0
someone help me with the equation. i’m super confused and don’t know if i’m doing it right

Answers

Answer:

I think the answer is (x + 4) • (x + 2)

Step-by-step explanation:

First multiply the coefficient of the first term by the constant

Step 2: Find two factors of 8 whose sum equals the coefficient of the middle term 6

Step 3: write the polynomial splitting the middle term using the two factors found in step 2

Step 4:  Add up the first 2 terms, pulling out like factors :

                   x • (x+2)

Add up the last 2 terms, pulling out common factors :

                   4 • (x+2)

Step 5: Add up the four terms in step 4

(x+4)  •  (x+2)

           

Your final answer is (x + 4) • (x + 2)

Evaluate 2(x+1)-3 when x=6

Answers

Answer:

[tex]11[/tex]

Step-by-step explanation:

[tex]2(6+1)-3[/tex]

[tex]2(7)-3[/tex]

[tex]14-3[/tex]

[tex]11[/tex]

Answer:

11

Step-by-step explanation:

1. insert 6 in the x spot

2. add inside of the parenthesis (6+1)=7

3. multiply 2 and 7 to get 14

4. take 3 from 14 to get 11

what is the total amount of sap produced that day?

Answers

Answer:

8 gallons

Step-by-step explanation:

Already a question from another person.

Answer:

5 gallons

Step-by-step explanation:

define the word triangle

Answers

A plane 2-dimensional figure with three straight sides and three angles.

Answer:

The definition of triangle is a plane figure with three straight sides and three angles.

Hope that's work.

A scale drawing of a room is shown below. In the drawing, the room is 7 1/2 inches long and 5 inches wide. What is the actual area of the room? Please help

Answers

Answer:

The area of the room is 37.5 square inches.

Step-by-step explanation:

Consider that the room is rectangular in shape.

The dimensions of the rooms are:

Length (l) = 7.5 inches

Breadth (b) = 5 inches

The area of a rectangle is:

Area = l × b

Compute the area of the room as follows:

Area = l × b

        [tex]=7.5\times 5\\=37.5[/tex]

Thus, the area of the room is 37.5 square inches.

Verify sin^4x-sin^2x=cos^4x-cos^2x is an identity. Please dumb it down, i don't get this lesson.

Answers

Answer:

Step-by-step explanation:

cos^2+sin^2 = 1  ( rule)

cos^4x-cos^2x      simplify

- cos^2( -cos^2 +1  )     -cos^2 common

or  -cos^2 ( 1-cos^2)    

since cos^2 + sin^2 = 1

substitute : -cos^2 ( sin^2 )

substitute  :  -(1-sin^2 ) ( sin^2)

multiply : -sin^2 + sin^4 or sin^4 - sin^2

it is verified that sin^4 -sin^2= cos^4-cos^2

hope it helps  

Tony and Tiffany collect semi-precious stones. At the rock hound hut, Tiffany paid $38 for 9 pounds of snowflake obsidian. At the solid rock shop, tony paid $19 for 3 pounds of the same type of the stone. Who made the better buy?

Answers

Answer:

Tiffany made the better buy

Step-by-step explanation:

Based on the information provided within the question it can be said that Tiffany made the better buy in this scenario. Mainly because Tiffany paid a less amount per pound than Tony did. This can be calculated by dividing the total amount each paid by the total amount each of them received, like so...

Tiffany: $38 / 9 = $4.22 per pound

Tony: $19 / 3 = $6.33 per pound

Therefore we can see that Tiffany paid $4.22 per pound and Tony paid $6.33 per pound a whole $2.11 more than Tiffany, thus making Tiffany purchase the better buy.

Solve for x. 2(4x - 1) + 3(3 - 2x) = 0

Answers

Answer:

x=-3.5

Step-by-step explanation:

[tex]2(4x - 1) + 3(3 - 2x) = 0 \\ open \: the \: bracets \: \\ 8x - 2 + 9 - 6x = 0 \\ [/tex]

[tex]collect \: like \: terms. \\ 8x - 6x = 0 + 2 - 9 \\ 2x = - 7[/tex]

[tex]divide \: both \: sides \: of \: the \: equation \: by \: 2 \\ \frac{2x}{2} = \frac{ - 7}{2} \\ x = - \frac{7}{2} or \: x = - 3.5[/tex]

QUESTION 2 of 10: Your house is for sale for $210,000. A realtor will charge you a 3% sales commission. If you choose a "sale by owner"
option by passing a realtor, you will pay no commission, but you will have to pay an attorney an average of $950 at your closing. What will you
save by choosing the sale by owner" option?
a) $1,865
b) $2,150
C) $5,350
d) $9.500

Answers

Answer:

c) $5,350

Step-by-step explanation:

sale price= $210000sales commission= 3% = 3*$210000/100= $6300

The difference between the commission and an attorney

$6300- $950= $5350

Option C is correct

Answer:

C

Step-by-step explanation:

What is the leading coefficient of the polynomial?

5x3 + 17 − 8x5 − 9x4

A) −8
B) −9
C) 17
D) 5

Answers

Answer:

-8

Step-by-step explanation:

Write the polynomial from highest power to smallest

− 8x^5 − 9x^4+5x^3 + 17

The leading coefficient is the first number in front of the highest power

given two consecutive numbers, we are told that twice the first number is twelve more than the second number. What are the two numbers?

Answers

Answer: The numbers are 13 and 14

Step-by-step explanation:

Since they are two consecutive numbers, let the numbers be x and x+1.

We are told that twice the first number is twelve more than the second number. This can be expressed as:

2 × x = x+1+12

2x = x+13

2x-x = 13

x = 13

Since x = 13, x+1 = 13+1 = 14

The numbers are 13 and 14

Which of the following terms have a GCF of 6x^3? Select two options. 12p^3r 27p^4q 45p^3q^6 54p^3 63p^3q^6

Answers

Answer:

A. and D. are correct

Step-by-step explanation:

The correct answers are Option A, Option D.

The terms which have the GCF of [tex]6x^3\\[/tex] are [tex]12p^3r[/tex] and [tex]54p^3[/tex].

Given data:

To find the greatest common factor (GCF) of the given terms, we need to find the highest power of x that divides into all the terms and the highest power of p that divides into all the terms.

For [tex]12p^3r[/tex] , the highest power of x that divides into this term is [tex]x^0[/tex](since x^0 = 1), and the highest power of p that divides into this term is [tex]p^3[/tex]. Therefore, the GCF is [tex]1 * p^3 = p^3.[/tex]

For 54p^3, the highest power of x that divides into this term is [tex]x^0[/tex] (since x^0 = 1), and the highest power of p that divides into this term is [tex]p^3[/tex]. Therefore, the GCF is [tex]1 * p^3 = p^3.[/tex]

Hence, the terms are [tex]12p^3r[/tex] and [tex]54p^3[/tex].

To learn more about greatest common factor, refer:

https://brainly.com/question/13257989

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VA
How could you use cross products to check the solution
to this proportion?
12 5
30 x
30(5) = (12)(x)
150 = 12x
12.5 = x
the answer is 2x=25. Can someone help me please

Answers

Answer:

don't type the mathematics questions

Answer:150

Step-by-step explanation:

PLEASE ANSWER THIS QUESTION !! WILL GIVE BRAINLIEST !! 15 POINTS !!

Answers

Answer:

The answer is C

Step-by-step explanation:

Please mark me Brainliest

3:15=12:60 then find the sum of the mean​

Answers

Answer:

The means of the proportion 3/15 = 12/60 are 15 and 12. The means of the proportion 3/15 = 12/60 are 15 and 12

The shortest leg of a right triangle measures 9 centimeters and the hypotenuse measures 3 centimeters more than the longer leg. Find the length of the hypotenuse. Use the Pythagorean Theorem Formula.
I'm not sure how to set this up

Answers

Answer:

The triple is 9, 12, 15

The hypotenuse is 15.

Step-by-step explanation:

Pythagorean Theorem Formula: a²+b²=c² where a & b are the short legs and c is the hypotenuse.

9²+b²=(b+3)²

81+b²=(b+3)²

Small list of the Pythagorean Triples that contain 9:

9,12,15

9,40,41

So as you can see, there are only 2 examples in my list that contain 9 in them. The only one that fits our criteria is the triple, 9, 12 and, 15

You don't need to use the Pythagorean Formula for this as I have just proved.

Answer:

12 cm

Step-by-step explanation:

I don't think u have to use the phytagores theorem b/c the hypotenuse is 9+3=12. but if u have to use this.

[tex] {?a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {9}^{2} + {b}^{2} = {9 + 3}^{2} [/tex]

[tex]81 + {b}^{2} = 9(9 + 3) + 3(9 + 3)[/tex]

[tex]81 + {b}^{2} = 81 + 54 + 9[/tex]

[tex]81 + {b}^{2} = 144[/tex]

[tex] {b}^{2} = 144 - 81 = 63[/tex]

[tex] {b}^{2} = \sqrt{53} = b = 7.93[/tex]

so if u found b then u can find c by using the same formula.

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {9}^{2} + {7.93}^{2} = {c}^{2} [/tex]

[tex]81 + 63 = {c}^{2} [/tex]

[tex] {c}^{2} = 81 + 63 = 144[/tex]

[tex] \sqrt{c} = \sqrt{144} [/tex]

[tex]c = 12[/tex]

Observa las figuras y contesta lo siguiente de cada figura ¿cuantos cubos la forman? ¿Cuantos cubos tiene de alto? ¿Cuantos cubos tiene de largo? ¿Cuantos cubos tiene de ancho?

Answers

Answer:

The figures are shown in the image attached.

Figure 1.

Notice that the figure is a cube with side of 3 cubes long. That means the total number of cubes that form the figure are

[tex]V=3^{3}=27[/tex]

27 cubes in total.

Its height is formed by 3 cubes.

Its length is formed by 3 cubes.

Its width is formed by 3 cubes.

Figure 2.

The second figure has:

Its height formed by 5 cubes.

Its length formed by 1 cube.

Its width formed by 3 cubes.

Which gives: [tex]V= 5 \times 1 \times 3 = 15[/tex]

There are 15 cubes in total.

Figure 3.

The third figure has

Its height formed by 3 cubes.

Its length formed by 2 cube.

Its width formed by 3 cubes.

Which gives: [tex]V= 3 \times 2 \times 3 = 18[/tex]

There are 18 cubes in total.

Figure 4.

The fourth figure has

Its height formed by 1 cubes.

Its length formed by 2 cube.

Its width formed by 7 cubes.

Which gives: [tex]V= 1 \times 2 \times 7 = 14[/tex]

There are 14 cubes in total.

A car with 16 gallons of gas drives 416 miles until the tank is empty. Write a linear equation that describes the amount of gas left in the car, y, after driving x miles.

Answers

It’s somewhere around 110

A 6.5 foot street sign casts a 10-foot shadow while a telephone pole casts a 40-foot shadow. How tall

is the telephone pole?

Answers

Answer:

26

Step-by-step explanation:

10 x 4 = 40

6.5 x 4 = 26

The height of the telephone pole is 26 foot.

What is ratio?

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Shadow of 6.5 foot street sign = 10 foot

Let the height of telephone pole = h foot

According to given condition,

Shadow of h foot telephone pole = 40 foot

Since, 10 foot shadow cast by 6.5 foot street sign

To find the height of the pole,

Use Ratio property,

10/6.5=40/h

⇒h=26 foot

The height of telephone pole is 26 foot

To know more about Ratio on:

https://brainly.com/question/23724140

#SPJ5

A grocery store clerk can scan one product every 1/2 of a second at what rate Can she scan Products

Answers

Answer:

per second or minute or hour?

per second: 2 per second

per minute: 120 per minute

per hour: 7200 per hour

Step-by-step explanation:

two 1/2 seconds per second so 2 products per second. multiply by 60 for per minute is 120. multiply the minute amount by 60 for hour amount aka 7200.

hope this helps! pls mark brainliest! have a good day!

Answer: She scan products at

2 per second.120 per minute. 7200 per hour.

Given that: A grocery store clerk can scan one product every 1/2 of a second.

That means:

Rate = 2 per second.

Rate = (2*60) = 120 per minute.

Rate = (120*60) = 7200 per hour

Learn more: https://brainly.com/question/12049968

1 of 10
Colin buys a tv for £810.
It depreciates at a rate of 3% per year.
How much will it be worth in 3 years?
Give your answer to the nearest penny where appropriate.
7
8
9
q
W
e
r
t
y
u
o

Answers

Answer:

I=72.9

Step-by-step explanation:

I=PRT When P= the principal=810, R=rate=3% and T=time(by year)=3 years

I=810*3/100*3

I=24.3*3

I=72.9

Answer:

Simple interest/Interest = £72.9

Step-by-step explanation:

We have to find the simple interest at this point.

So use the formula:

I = prt or I = p x r x t

I = amount of interest

P = principal amount (810)

R = interest rate (in years) (.03)

T = amount of time in (years) (3)

All we need to do is multiply.

I = (810)(.03)(3)

I = £72.9

Answer correctly !!!!!! Will mark brainliest !!!!!!!!

Answers

Answer:

(x+9)(x+2)

Step-by-step explanation:

x(x+9)+2(x+9)

(x+2)(x+9)

the order of the (---) doesn't matter

How do you solve an standard form/ intercept in y=4x-10 ¿? Help me plzzzz :/

Answers

Answer:

Slope = 8.000/2.000 = 4.000

 x-intercept = 10/4 = 5/2 = 2.50000

 y-intercept = -10/1 = -10.00000

Step-by-step explanation:

y= mx + b is the slope intercept form of a line where m is the slope and b is the y intercept.

Step  1  :   Equation of a Straight Line

Step 2: Graph of a Straight Line

Step 3: Calculate the Y-Intercept

Step 4: Calculate the X-Intercept

Step 5: Calculate the Slope

Hope this helps.

The base of a right circular cone has a radius of 4 inches and a slant height of 9 inches. If the radius and the slant height are multiplied by 6, by what factor is the surface area multiplied? A. 6 B. 36 C. 24 D. 54

Answers

Answer:

Correct option: B -> 36

Step-by-step explanation:

The surface area of a circular cone is given by the formula:

Surface area = pi * radius * (radius + slant height)

If the inicial radius is 4 in and the slant height is 9 in, we have:

Surface area = pi * 4 * (4 + 9) = 52pi in2

The radius and the slant height are multiplied by 6, so we have:

radius = 6 * 4 = 24 in

slant height = 6 * 9 = 54 in

So the new surface area is:

New surface area = pi * 24 * (24 + 54) = 1872pi in2

The factor of the surface areas is:

New surface area / Surface area = 1872pi / 52pi = 36

Correct option: B

Answer:

b

Step-by-step explanation:

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