Solve the following system of equations algebraically:

y = 4x^2 + 17x + 14
y = 2x + 5​

Answers

Answer 1

Answer:

When x = -3  y = -1

When x = -3/4  y = 7/2

Step-by-step explanation:

y = 4x^2 + 17x + 14

y = 2x + 5​

Set each equation equal to each other

4x^2 + 17x + 14  = 2x + 5​

Subtract 2x from each side

4x^2 + 17x-2x + 14  = 2x-2x + 5​

4x^2 + 15x + 14  =  5​

Subtract 5 from each side

4x^2 + 15x + 14-5  =  5​-5

4x^2 + 15x +9  = 0

Factor

(4x+3) ( x+3) =0

Using the zero product property

4x+3 =0    x+3 =0

4x = -3      x=-3

x = -3/4     x=-3

Now we need to find y for each x

x =-3   y = 2x+5  =2(-3)+5 = -6+5 = -1  

When x = -3  y = -1

x = -3/4   y = 2(-3/4) +5 = -3/2 +5 = 7/2

When x = -3/4  y = 7/2


Related Questions

The double number line shows the approximate number of ounces in a certain number of pounds:

Based on the number line, about how many ounces are there in 10 pounds?
Group of answer choices
144 ounces
160 ounces
176 ounces
192 ounces

Answers

Answer:

B- 160

Step-by-Step Explanation:

I did it before and I was rite, so trust me

Answer:

B 160

Step-by-step explanation:

which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"

Answers

Answer:

Let x be that number.

[tex] - 8 \div (x + 3)[/tex]

The quotient is the result of dividing a number by another. In this case, the numbers are - 8 and x + 3.

22+54=y+16 whats the answer

Answers

Answer:

y=60 or 60=y

Step-by-step explanation:

22+54= 76

76=y+16

60=y or the other way around

A restaurant coffee pot holds 3 gallons of coffee. The pot has been filled with 2 gallons of coffee. If the variable c stands for the amount of additional coffee the pot can hold, which of the following units could apply to that variable?

A. yards
B. pounds
C. gallons
D. bushels ​

Answers

C

Because your weight system is gallons in the rest of the question :)

Answer:

gallons

Step-by-step explanation:

15 POINTS!!!HELP!! JUST TELL ME THE FORMULA I NEED TO USE !!!

Answers

Answer: No.

Step-by-step explanation: It's obviously a quiz of some sort. If it's not, then why would it be timed? Please don't do this :(

how to factorise 15x-10x^3

Answers

The answer is 5x(3-2x^2)

How is quadrilateral ABCD related to quadrilateral A'B'C'D' shown below?

Answers

what you put is correct. A’B’C’D’ is what would be shown if you rotate ABCD 90 degrees clockwise

Answer:

i think its a

Step-by-step explanation:

help me pleaseeeeeeeeeeeeeeeeeeeeeee

Answers

A they’re parallel because they have same slope

L.B. Johnson Middle School held a track and field event during the school year. The chess club sold various drink and snack items for the participants and the audience. All together, they sold items 486that totaled .$2,673a.If the chess club sold each item for the same price, calculate the price of each item.

Answers

Answer:

$5.50

Step-by-step explanation:

L.B Johnson middle school held a track and field event

The chess club sold different drinks and snack item for both the audience and participants

They sold 486 items at a total of $2,673

Therefore the price of each item can be calculated as follows

= 2673/486

= 5.50

Hence the price of each item is $5.50

2) If 20 workers can build a house in 45 days, how many more workers are needed
to complete it in 30 days?
А
6
B
15
С
10
D
18

Answers

It’s D 18 if wrong I’m sorry but I took this test as well

Answer:

B

Step-by-step explanation:

Alex bought 2 1/4 pounds of M&Ms and 1.6 pounds of gummy worms. If the M&Ms cost $2 per pound, and the gummy worms cost $ $2.75 per pound, how much did he spend?

Answers

Answer:

Alex paid $8.90 total. $4.50 for the M&Ms and $4.40 for the gummy worms.

Step-by-step explanation:

2 [tex]\frac{1}{4}[/tex] is equivalent to 2.25, and if each pound is worth $2, then you would multiply the cost by each pound bought, shown like this: $2 (2.25) = $4.50 (You are distributing the $2 to find the product).

$2.75 (1.6) = $4.40

$4.50 + $4.40  = $8.90

Which expression is equal to 527.471?*
(5x100)+(2x10)+(7x1)+(4x10) + (7x100)+ (1x1,000)
(5x100,000)+(2x10,000)+(7x1,000)+(4x100) + (7x10)+ (1x1)
(5x100)+(2x10)+(7x1)+(4x1/1) + (7x1/10)+ (1x1/100)
(5x100)+(2x10)+(7x1)+(4x1/10) + (7x1/100)+ (1x1/1,000)

Answers

Answer:

Step-by-step explanation:

527.471 =(5 ×100.000) +(2 ×10.000) +(7 ×1.000) +(4 ×100) +(7 ×10) +(1×1)

Answer:

500029301.171

Step-by-step explanation:


6 = m - 16


a) m = 20
b) m = 24
c) m = 22
d) m = 21​

Answers

Answer:

c

Step-by-step explanation:

C; to get m, you isolate it by getting rid of 16. To get rid of 16, you add it to both sides. 16 and 6 is 22 and -16 cancels out 16, so you are left with m=16 :)

Students at the college are allowed to work on campus
no more than 20 hours per week. The jobs that are
available pay different rates, starting from $8.75 an hour.
Students can earn a maximum of $320 per week.
Write at least two inequalities that could represent the
constraints in this situation.

Answers

Answer: theres a website called weegy did you try that?

In which interval is the median?
A sample of 50 students was surveyed about their time
spent in front of a screen (laptop, tablet, phone, etc.).
Each interval contains the left endpoint but not the
right endpoint.
[4,5)
[5,6)
[6,7)
[7,8)
Hours of Screen Time per Day
10
B
Frequency
2
6
8
10 12

Answers

B I think sorry if it’s wrong

Answer:

B is correct! Took the quiz 2021 <3. Yall b safe!

Step-by-step explanation:

John buys two ties that each cost $19.99 he also buys a pair of dress pants that were originally $64 but a discounted by 30% more over he has a coupon for $10 off a purchase of $50 or more purchase finally sales tax is 6% in his state how much did John pay for the ties and pants

Answers

Answer:

Cost of ties and pants = $52.5

Step-by-step explanation:

Total cost of ties = $19.99

cost of dress pants = $64, discountted by 30%

discount on dress pants = 30% of 64 = 0.3 × 64 = $19.2

∴ Discounted price of dress pants = 64 - 19.2 = $44.8

Total cost of ties and dress pants = 19.99 + 44.8 = $64.79

Now, let us apply the coupon

coupon = $10 off every purchase of $50 or more

Purchase amount = $64.79 ;  therefore coupon applies.

Applying coupon

Purchase amount = 64.79 - 10 = $54.79

sale tax = 6% or purchase price

sale tax = 6% × 54.79

sale tax = 0.06 × 54.79 = $3.29

∴ Final cost of ties and dress pants = 54.79 - 3.29 = $52.5

HELP!! please explain how you got the answer too.

Determine whether cach point lies on the graph of the line y = 4.6x -7.

H(0, -7) ​

Answers

Answer:

Point H does lie on the graph y = 4.6x - 7

Step-by-step explanation:

Step 1: Define

y = 4.6x - 7

H(0, -7)

Step 2: Substitute, Evaluate, and Check

-7 = 4.6(0) - 7

-7 = 0 - 7

-7 = -7

Answer:

H(0,-7) does lie on the graph of line y = 4.6x - 7

Step-by-step explanation:

All you have to do is simply plug in the x and y values.

From the point H (0,-7) we can say that

x = 0

y = -7

Now just plug it into the equation.

y = 4.6x - 7

(-7) = 4.6(0) - 7

-7 = -7

Since -7 does equal -7, the point H is on the line of y = 4.6x - 7.

Suppose there is a 1.7f drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on the ground is 49.9f what will be the temperature when the plane reaches am altitude of 4,000ft?? The temperature will be_____F (type an integer or a decimal)

Answers

Answer:

[tex]43.1 ^{\circ}F[/tex]

Step-by-step explanation:

Give that for every 1000 feet increase in the height there is a drop of [tex]1.7 ^{\circ}F[/tex] in temperature.

So, the rate of temperature drop with respect to height, R = 1.7/1000 [tex]^{\circ}F/\text{ft}[/tex].

If the change in height is [tex]\Deltah[/tex][tex]\Delta h[/tex] feet, the temperature drop,

[tex]\Delta T= \Delta h R \;^{\circ}F\cdots(i)[/tex]

The temperature on the ground is 49.9 [tex]^{\circ}F[/tex].

At the ground, the height is 0, so the change in height, \Delta h when the plane reaches an altitude of 4,000 feet, is

\Delta h =4000-0=4000 feet

Now, from equation (i), the temperature drop

[tex]\Delta T= 4000 \times \frac {1.7}{1000}=6.8\;^{\circ}F.[/tex]

Hence, the temperature at an altitude of 4000 feet [tex]= 49.9-6.8=43.1 \;^{\circ}F[/tex].

PLS ANSWER HELP
Thanks

Answers

Its congruent to ELG :)

what is the value of r in the equation r+6=14?

Answers

Answer:

r = 8

Step-by-step explanation:

Given

r + 6 = 14 ( subtract 6 from both sides )

r = 8

You subtract 6 from 14 and you’ll get 8 so r=8

PLEASE HELP ME! I am not sure how to answer this question.​

Answers

Answer:

yes

Step-by-step explanation:

the diagnols are congruent meaning that the diagnol lines in the middle are the same length. So theoretically the left and right lengths are the same, and the top and bottom lengths are the same. The triagles named both have the same base and they're hieght is sbviouysly the same so they would be SSS each of the sides on one triangle coresspondes to the other.

Write the equation of the line that contains the given point and has the given slope.

(–8, –8), slope is 3

Answers

Answer:

y - 8 = 3(x - 8)

Step-by-step explanation:

Point-Slope Form: y + y₁ = m(x + x₁)

x₁ - x coordinate

y₁ - y coordinate

m - slope

Step 1: Define

Point (-8, -8)

Slope m = 3

Step 2: Write in point-slope form

y - 8 = 3(x - 8)

A 5000 seat theater has tickets for sale at 26 and 40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of 153800.

Answers

Answer:

The number of tickets for sale at $26 should be 3300

The number of tickets for sale at $40 should be 1700

Step-by-step explanation:

Use 2 equations to represent the modifiers within the problem:

[tex]5000 = a + b \\ 153800 = 26a + 40b[/tex]

Now you want to find the point at which the variables are changed to make both equations correct, this can be done by graphing and finding the intersection of both lines.

[tex]5000 = 3300 + 1700 \\ 153800 = 26(3300) + 40(1700)[/tex]

Enter the correct answer in the box by replacing the values of m and b.

Answers

Answer:

f(x) = -2x + 5  Plato

Step-by-step explanation:

How are lines KL and MN related?
O The lines intersect at point K.
O The lines are parallel.
O The lines are perpendicular.
O The lines do not have slopes,

Answers

The lines are perpendicular

The lines KL and MN perpendicular to each other.

What is slope?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

If a line passes through two points, then the slope of the line is

m = y2-y1/x2-x1

From the given graph it is clear that coordinates of points on line KL are K(-8,2) and L(6,2).

The slope of line KL is

m = 0

The slope of line KL is 0, it means it is a horizontal line.

From the given graph it is clear that coordinates of points on line MN are M(-4,8) and N(-4,-6).

The slope of line MN is

m = 1/0

The slope of line MN is 1/0 or undefined, it means it is a vertical line.

We know that vertical and horizontal lines are perpendicular to each other.

Therefore the lines KL and MN perpendicular to each other.

To learn more on slope click:

brainly.com/question/3605446

#SPJ7

What’s the correct mathematical expression for 2 groups of z

Answers

Answer:

2z = 2 groups of z

HAVING BAD DAY

Stanley practices his running, swimming and biking every day. During these practices he runs at 9 mph, bikes at 16 mph and swims at 2.5 mph. Yesterday he ran for half an hour longer than he swam, and his biking time was twice his running time. How long did Stanley run, swim, and bike yesterday if the total distance he covered was 64 miles?

In terms of t, how long did Stanley bike yesterday?

Answers

Answer:

16

Step-by-step explanation:

(2(t3+0.5))=16(2t3+t1)

Answer:

1+2*t

Step-by-step explanation:

I checked it and it seemed right. I think it is. Test it and tell me if wrong. if it is wrong I WILL EDIT THIS

Apply a 90 degree rotation to the point (1, 2)

Answers

Answer:

(-1,2)

Step-by-step explanation:

90 degree rotation from (a,b) is (-a,b)

3/4 change 3/4 to a decimal show work

Answers

Answer:

0.75

Step-by-step explanation:

You just need to convert 3/4 into a decimal.

For example: If you get 3 out of 4 problems right on a quiz, in percent form it will be a 75%, in decimal form 0.75 because you'll move the percent sign 2 spaces to the left. That will then be a decimal if you're converting 75% to 0.75.

3 divided by 4 is also going to give you 0.75. Because, a "fraction slash" is the dividing point. So,

3/4 = 0.75

3x-100 what does x equal?

Answers

Yes it’s 33.33 repeating
Other Questions
Match these items.1. maximum number of electrons = 2 2. maximum number of electrons = 6 3. maximum number of electrons = 10 4. maximum number of electrons = 14 fpds What must a single-celled organism do before it can reproduce Find the average rate of change of g(x)=3x^2 ver the interval [-5, -3]. The midpoint of xy is located at the origin How do I factor x ^5x^ 4+3x3 The respiratory system controls __________, and the circulatory systems controls __________. (5 points)antibodies; digestionbreathing; blood flowmuscles; bonesnerves; senses A football team lost 3 yards on their first play. On the second play, 10 yards were gained. On the third play the quarterback got tackled behind the line of scrimmage and lost 6 yards. What was their net gain or loss after the three plays? (URGENT!! PLS HELP) The color of paint used to paint a race car includes a mixture of yellow and green paint. Scotty wants to lighten the color by increasing the amount of yellow paint 30%. If a new mixture contains 3.9 liters of yellow paint, how many liters of yellow paint did he use in the previous mixture? A spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute. Find the rates of change of the radius when r = 70 centimeters and r = 95 centimeters. Ten moles of hydrogen are allowed to react with 6 moles of oxygen. How much water will beobtained from reaction on complete consumption of one gas? A car starts from rest and accelerates for 2.9 swith an acceleration of 2 m/s2.How far does it travel?Answer in units of m. Obesity rates in this country have changed from what to whathow?1 in 2 to 1 in 31 in 3 to 1 in 41 in 4 to 1 in 51 in 4 to 1 in 3 what is Philosopher whose ideas shaped the Chinese civilization term Travel journalism is a type of reporting that provides both facts and subjective impressions of the place that the author describes. As literary nonfiction, travel journalism often uses literary techniques that include a story-like narrative structure, sensory language, figures of speech, sensory language, and subjective opinions about the location.options:TrueFalse if a ramp is 12 meters long has a mechanical advantage of 6 whats its height brainly HELPP! What two poetic words originated in Italy but became popular among poets writing in English?A. Villanelle B. Sonnet C. Renga D. Haiku Why does/doesnt history matter? Give examples on why or why not. A black bear in Washington may spend up to five months in hibernation, while a black bear in Florida may spend only four weeks. Which of the following explains why there is such a big difference in their hibernation periods?A.Florida does not have a cold winter season, and food is available all year long.B.The bear in Florida must feed more often than the bear in Washington.C.There are more places to hibernate in Washington than in Florida.D.It rains much more in Florida, and the bear cannot stay asleep.PLZ HELP FAST. PLEASE MIDDLE SCHOOL MATH NEED HELP!!!! THIS IS URGENT 13 POINTS TO FULL ANSWER!!!I bought 7 1/3 pounds of apples from Store A and 9 2/6 pounds of apples from Store B. I made apple sauce using 2 1/2 pounds of apples, how many pounds do I have left? From 24 grams to 96 grams ( percent change )