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

Frank also has an eraser. It has a mass of 3g, and a volume of 1cm3. What is its density?

Answers

0.003 kilograms/ cubic meter

A can run 3 miles in 30 minutes. How long will it take
the runner to run 2.5 miles? Use the diagram to explain.

Answers

Answer:

It will take her about 25 minutes.

Step-by-step explanation:

30 divided by 3 is ten.

It takes ten minutes to run each miles.

I don't have a diagram, but try drawing a graph with the information.  

PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEEEEe

Answers

Answer:

-140 = x

Step-by-step explanation:

Answer:

-140 =x

Step-by-step explanation:

|5x+9|=4x solve for all values of x

Answers

I think The answer is X=0.

Solve for x and y.

(please help asap)

Answers

Answer:

x = 4

y = 1

Step-by-step explanation:

At first, let us find the third angle in the triangle which has a right angle and an acute angle of measure 52°

∵ The sum of the interior angles of a triangle is 180°

∴ 52° + 90° + (6x + 14y)° = 180°

→ Add the like terms

∴ 142° + (6x + 14y) = 180°

→ Subtract 142° from both sides

(6x + 14y)° = 38° ⇒ (1)

→ By using the two triangles

∵ The two triangles are congruent

(15x - 8y) = 52° ⇒ (2)

Now we have a system of equations to solve it

→ Multiply equation (1) by 5 and equation (2) by -2 to make the

   coefficients of x equal in values and different in signs

∵ 5(6x + 14y) = 5(38)

30x + 70y = 190 ⇒ (3)

∵ -2(15x - 8y) = -2(52)

-30x + 16y = -104 ⇒ (4)

→ Add equations (3) and (4) to eliminate x

∵ 86y = 86

→ Divide both sides by 86 to find y

y = 1

→ Substitute the value of y in equation (1) to find x

∵ 6x + 14(1) = 38

∴ 6x + 14 = 38

→ Subtract 14 from both sides

∴ 6x = 24

→ Divide both sides by 6

x = 4

Estimate the sum 59.6 + 51.4

Answers

Answer:

111

Step-by-step explanation:

Answer:

111

Step-by-step explanation:

k(x) = (x + 1)2 – 25
What would this be rewritten in factored form?

Answers

Answer:

[tex]k(x)=(x-4)(x+6)[/tex]

Step-by-step explanation:

[tex]k(x)=(x+1)^2-25\\\\[/tex]

to factorize it you have to remember the difference of squares that says

[tex]a^2-b^2=(a-b)(a+b)[/tex]

so we have

[tex](x+1)^2\\\\(x+1)^2=a^2\\\\25\longrightarrow 5^2\\\\5^2=b^2\\\\[/tex]

and we apply the formula

[tex](x+1)^2-25=[(x+1)-5][(x+1)+5]\\\\=(x+1-5)(x+1+5)\\\\=(x-4)(x+6)[/tex]

so there you have it

[tex]k(x)=(x-4)(x+6)[/tex]

-5(x) = -4x - 11
please help i don’t understand i need to evaluate the function

Answers

Answer:

x=11

Step-by-step explanation:

-5x=-4x-11

-5x+4x=-11

-x=-11

x=11

Round the factors and estimate the products.
a.
656 x 106 -

b. 3,108 x 7,942 -
C.
425 x 9,311 -
what is this i wanna drop out

Answers

Answer:

a. 70,000

b. 24,000,000

c. 3,600,000

Step-by-step explanation:

You round all the numbers and multiply the rounded numbers.

So...

a. 656 = 700

106 = 100

7000*100= 70,000

b. 3108 = 3000

7942 = 8000

3000*8000= 24,000,000

c. 425 = 400

9311 = 9000

400*9000= 3,600,000

Which of the following is not a way to represent the solution of the inequality 3(2x − 1) greater than or equal to 4(2x − 3) − 3? (1 point)

x less than or equal to 6
6 greater than or equal to x
A number line with a closed circle on 6 and shading to the left
A number line with a closed circle on 6 and shading to the right

Answers

Answer:

A number line with a closed circle on 6 and shaded to the right.

Step-by-step explanation:

Answer:a number line with a closed circle on 6 and shading to the right

Step-by-step explanation:I think I’m right! Good luck

What is the equation of the line that passes through the points (−2,4) and (0,3)?

Answers

Answer:

y=-1/2x+3

Step-by-step explanation:

Identify the vertex, the axis of symmetry, the maximum or minimum value, and the domain and range of the function.
f(x)= -(x - 9)2 - 23

Answers

Answer:

thank u

Step-by-step explanation:

Which of the following is the solution to 17 - 2x=-11?
1.)14
2.)-14
3.)-3
4.)3​

Answers

The answer is 14 or number 1

Which division problem does the number line below best illustrate?

A number line going from 0 to 2 in increments of 0.2.

2 divided by one-fifth = 10
1 divided by one-fifth = 10
2 divided by one-tenth = 5
1 divided by one-tenth = 5

Answers

Answer:

A

Step-by-step explanation:

Hope this helps!!!!!!!!!!!!!!!!!!:)

Answer:

is it C OR A

Step-by-step explanation:

Can you solve Please ASAP!

Answers

Answer:

x = 7/12

Step-by-step explanation:

Write the expression in exponential form with the base of 2

[tex]2x^{3x-3}[/tex]  = [tex]32^{3x-2}[/tex]

[tex]2^{3x-3}[/tex]  = [tex]2^{15x-10}[/tex]

Since the bases are the same, set the exponents equal

x - 3 = 15 - 10

Move variable to the left-hand side and change its sign

3x - 15x - 3 = -10

Move constant the the right-hand side and change its sign

3x - 15x = -10 + 3

Collect like terms

-12x = -10 + 3

Calculate the sum

-12x = -7

Divide both sides o the equation by -12

x = 7/12

Solution

7/12

Alternate form

x = 0.583

An art museum had 275,760 visitors last year. The museum was open every day of the year except for 5 holidays. How many visitors did the museum have each day, on average?​

Answers

Answer:766 people on average because 275,760 divided 360 because 365=1 year 365-5=360 and 275760/360=766

Step-by-step explanation:

Simplify.

xb2aaayx3yyb3xxabby4x2

Answers

Answer:

is that even a real equation?

Uh, I don’t believe this can be simplified...

Tell whether the ratios form proportions
4:20 and 6:30
9/18,3/8

Answers

9514 1404 393

Answer:

yesno

Step-by-step explanation:

1) Each of the ratios can be reduced to 1 : 5, Since both can be reduced to the same ratio, the do form a proportion.

  4 : 20 = 1 : 5

  6 : 30 = 1 : 5

__

2) The first ratio can be reduced to 1/2. The second ratio is not 1/2 and cannot be reduced. Since they are different ratios, they do not form a proportion.

  9/18 = 1/2

  3/8 = 3/8

Three years ago, Jolene bought $500 worth of stock in a software company. Since then the value of her purchase has been increasing at an average rate of 12 1 2 % per year. How much is the stock worth now? (Round each money calculation you make to the nearest cent.)

Answers

Answer:

The stock is worth $702.5.

Step-by-step explanation:

Giving the following information:

Present Value= $500

Number of periods  (n)= 3 years

Growth rate (i)= 12%

To calculate the value of the stock today, we need to use the following formula:

FV= PV*(1+i)^n

FV= 500*(1.12^3)

FV= $702.5

The stock is worth $702.5.

The function r(x) = –0.000345(x – 50)2 + 2.1 can be used to model the curve of a road designed to allow for water to run off in rainstorms depending on the distance from the shoulder of the road, x, in feet. A European firm studying these curves is going to convert feet to meters using the function m(x) = 0.3048x. Which composition can be used to model the curve of the road in terms of meters?

Answers

Answer:

- 0.000105156(x - 50)² + 0.64008

Step-by-step explanation:

Given the curve function model : -0.000345(x - 50)² + 2.1 ; Which is measured in feets :

To convert the curve model in feets to metres +, using the function :

m(x) = 0.3048x

Multiply m(x) by r(x)

Hence,

m(r(x)) = 0.3048(-0.000345(x - 50)² + 2.1)

m(x) = - 0.000105156(x - 50)² + 0.64008 ; measured in meters

Tell whether the equation has one, zero, infinitely many solutions.
3 ( y-2) = 3y - 6

Answers

Answer:

infinitely many solutions

Step-by-step explanation:

Hi there !

3(y - 2) = 3y - 6

3y - 6 = 3y - 6 | + 6

3y = 3y

true ∀ y ∈ R

Good luck  !

3/4 + 5/6 divided by 2/3

Answers

Answer:

2

Step-by-step explanation:

Answer:

Hello

Step-by-step explanation:

The awnser to your question is 2

can u simplify 18/56 into a fraction?

Answers

Answer:

9/28

Step-by-step explanation:

just divide by 2

Answer: 9/28

Steps: 18/56

Factor the number:  8 = 2 · 9

Factor the number:  56 = 2 · 28

Cancel the common factor: 2

9/28

Plz mark brainliest:)

what is the average rate of change for the line graphed in the figure above

Answers

Answer:

5/8

Step-by-step explanation:

I used the slope formula of y2-y1/x2-x1

Amy can run the 150 meter dash in 50 seconds. John can run 1200 meters in 400 seconds. How fast does Amy run. How fast does john run?

Answers

Answer:

Amy and John both run 3 meters in 1 second

Step-by-step explanation:

Amy: 150/50=3 meters in 1 second

John: 1200/400=3 meters in 1 second

Write the equation of the line in slope-intercept form containing the point (2,4) and with a slope of
3/2.

Answers

Answer:

y=3/2x+1

Step-by-step explanation:

y=mx+b is the slope-intercept form

y=3/2x+b

we are looking for b now

plug in the points you provided

2=x, 4=y

4=3/2(2)+b

4=3+b

b=1 which is the intercept

What is the lcm of 12 & 9 pls help im in class and i dont have a clue

Answers

Answer:

36 is the lcm of this question

A fishing boat with two people on it runs out of gas while out in a bay. The people set off an emergency flare from a height of 2 meters above the water. The flare has an initial vertical velocity og 30 meters per second. How long does it take the flare to reach its maximum height? What is that height?

Answers

Answer:

Step-by-step explanation:

time taken to reach the max height is expressed according to the projectile equation;

tmax = u/g

Given u = 30m/s

g is the acceleration due to gravity = 9.81

t = 30/9.81

t = 3.0secs

hence it will take the flare 3.06secs to reach its maximum height.

Max height = u²/2g

Max height = 30²/2(9.81)

Max height = 900/19.62

Max height = 45.87m

If the people set off an emergency flare from a height of 2 meters above the water, the total height will be 45.87 + 2 = 47.87m

we want to factor the following expression 3x^2-16y^5 which pattern can be used to factor the expression U and V are either constant integers or single variable expressions

Answers

Answer: we cant use any patterns

Step-by-step explanation:

can some one plz help me with a queston i posted

Answers

Answer:

ok what is it

Step-by-step explanation:

sureee, which one????
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