Mathematics College

Solve the system by substitution.
y=-x^2+2x+10
y=x+4

Answers

Answer 1

Answer:

x=3, y=7

x=-2, y=2

Step-by-step explanation:

System of Equations

We have the following equations:

[tex]y=-x^2+2x+10[/tex]

[tex]y=x+4[/tex]

We'll solve it by substitution. Since the second equation is already solved for y, we use that expression and substitute into the first equation:

[tex]x+4=-x^2+2x+10[/tex]

Since this is a quadratic equation, it's convenient to have all terms to one side:

[tex]x+4+x^2-2x-10=0[/tex]

Simplifying and reordering:

[tex]x^2-x-6=0[/tex]

Factoring:

[tex](x-3)(x+2)=0[/tex]

Solving:

x=3, x=-2

Those yield to two solutions for y:

y=x+4

y=7, y=2

The solutions of the system are:

x=3, y=7

x=-2, y=2

Related Questions

What is the quotient of (-55) divide by 5?

Answers

Answer:

Step-by-step explanation:

✨Answer:✨

-11

✨Step-by-step explanation:✨

-55 ÷ 5 = -11

(Just take the negative sign away and divide)

You pay $25 each month for satellite TV, plus $1.50 for every movie you purchase. Write and solve an equation to find the number of movies purchased during a month with a total bill of $38.50

Answers

$38.50=1.50x+$25 where x is the number of videos ordered during the month

Answer

9 movies

Step-by-step explanation:

$25 - 38.50 = $13.50

13.50/ $1.50 = 9

What is a more economical purchase, a 5-pound box of spaghetti priced at $6.02, or a 1.5-pound box for $1.70?

Answers

The 5 pound box of spaghetti(:

Find the slope in fraction form

Answers

Answer:

-1/3

Step-by-step explanation:

Taking two points on the graph (I took (0,9) and (6,7)

Slope=(y2-y1)/(x2-x1)

(7-9)/(6-0)=-2/6

=-1/3

Answer: 1/3 is right.

Removing which ordered pair will make the relation a function?

Answers

A. (4,3) because that’ll get rid of the 2nd four in the x.

The points D, E, F and G all lie on the same line segment, in that order, such that the ratio of DE:EF:FGDE:EF:FG is equal to 6:5:1.6:5:1. If DG=36,DG=36, find DF.DF.

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

How to round 86.415 to the nearest whole number end point

Answers

You would round this number by rounding each number (until the whole number) from right to left. So it would change from 86.415>86.42>86.4>87.

Hope this helps, if not, comment below please!!!

Answer:

Step-by-step explanation:

I'm not completely sure what this question is asking for. But if you want to round 86.415 to the nearest whole number, it would be 86, since any number less than 5 you would round down, and the 4 in the tenths place is less than 5.

iTunes charges a one time fee of $10 and $ 1 per song . Spotify charges a one time fee of $20 and $0.50 per song. After how many songs will the Spotify membership pay off and in the long run cost you less ?

Answers

Answer:

Step-by-step explanation:

Help easy question......Branliest reward

Answers

Answer:

Step-by-step explanation:

Answer:

y=42.91

Step-by-step explanation:

cos 35=y/53

0.81=y/53

y=0.81*53

y=42.91

t Park Junior High, 10%, or 160, of the students, play a musical instrument. How many students attend the school?

A tape diagram. StartFraction part Over whole EndFraction = StartFraction 10 Over 100 EndFraction = StartFraction 160 Over question mark EndFraction

Which statements are correct? Check all that apply.
The total number of students is 160.
The percent as a part-to-whole ratio is StartFraction 10 Over 100 EndFraction.
The percent as a part-to-whole ratio is StartFraction 160 Over 100 EndFraction
There are 1,600 students in the school.
There are 250 students in the school.

Answers

Answer:

The total number of students is > 160.

The percent as a part-to-whole ratio is StartFraction 10 Over 100 EndFraction.

There are 1,600 students in the school.

Step-by-step explanation:

got is correct

Answer:

2,3,5 for eg. 2020

Step-by-step explanation:

Express missing divisor using power of 10.

6.3 / ____= 0.0063

Answers

you first have to see how many times places the tenths are from the ten thousandths which is 3
so your going to have 3 zeros
so your answer would be 1000
hope that helps

Solve for X
2x + 4 = 10

Answers

Answer:

x = 3

Step-by-step explanation:

2x+4 = 10

2x = 6

x = 3

The ratio of boys to girls is 4:6 in Mrs. Franklin's class. If there are 36 girls, how many boys are there?

Answers

Answer:

Step-by-step explanation:

Lets say 4 boys to 6 girls if there are 36 girls do 4x6 to figure out the ratio of boys would be 24 boys and 36 girls if the other way around it would be 24 girls and 36 boys

A costume designer needs some silver and gold thread for the costumes for a school play. She needs a total of 240 yards. At a store that sells thread by the yard, silver thread costs $0.04 a yard and gold thread costs $0.07 a yard. The designer has $15 to spend on the thread.

How many of each color should she get if she is buying exactly what is needed and spending all of her budget?

Write an equation for the length constraint. Write an equation for the cost constraint. solution

Answers

Answer:

Where s represents silver and g represents gold,

Length constraint: s+g=240

Cost constraint: 0.04s+0.07g=15

s= 60

g=180

Step-by-step explanation:

The measurement of silver and gold threads in yards is given as 60 and 180 respectively.

What is a system of linear equations?

A system of linear equations is a group of equations having same number of variables and degree.

For the n number of variables n number of equations are required.

On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.

The given problem can be solved as follows,

Suppose the number of yards for silver threads be x and that of gold be y.

Then the equation for the total yard is given as,

x + y = 240 (1)

And, the equation for the cost is,

0.04x + 0.07y = 15 (2)

The value of x from equation (1) is x = 240 - y.

Substitute the value of x in equation (2) to obtain,

0.04(240 - y) + 0.07y = 15

=> 9.6 - 0.04y + 0.07y = 15

=> 0.03y = 15 - 9.6

=> 0.03y = 5.4

=> y = 180

Substitute the value of y in x = 240 - y to obtain,

x = 240 - 180 = 60

Hence, the costume designer should get silver and gold thread of 60 yards and 180 yards respectively.

To know more about system of equations click on,

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Evaluate using the order of operations. Enter the answer in simplest form.
3/5+1/7÷3

Answers

Answer:

0.64761904761

Step-by-step explanation:

3/5+1/7 x 1/3 = 3/5+1/21
Your answer is 68/105

Find the GCF of 28p4 and 44p2q.

Answers

4p2

Factors:

28p4 = 1 2 4 7 14 28 p p p p

44p2q = 1 2 4 11 22 44 p p q

Triangle ABC is an obtuse triangle with the obtuse angle at vertex B. Angle A must be

less than 90°.
greater than 90°.
congruent to angle B.
congruent to angle C.

Answers

The correct answer is less than 90°

There are 1200 students in a school 51% of them are female how many are male

Answers

The answer to this question is 612. Your welcome

Answer:

Step-by-step explanation:

588 are boys

1% of 1200 is 12, 50% is 600, add 12 and 600 together, you get 612, subtract it from 1200 and it gives you 588

Logic puzzle,Riddles

You enter a bedroom there are 34 people. You kill 30. How many are in the bedroom?

Answers

Answer:

Step-by-step explanation:

yes

35 including the body.

I need help with this question ! if someone could also explain what the answer is, that would be awesome.

Answers

Answer:

y=3/2x+3

Step-by-step explanation:

The slope is 3/2. The slope is m. We plug 3/2 into our equation.

y=mx+b

y=(3/2)x+b

Now we have to find b.

B is 3 because that's where it crosses the y axis.

So y=3/2x+3

ve spent the whole weekend grading math assignments. I graded 30 students
work this weekend, which is 40% of my class. How many students do I have in
my class?

Answers

Answer:

Step-by-step explanation:

How many students is 1% of the class, 30/40=0.75, so you could do 0.75x100=75, or you could do 0.75x60=45, and 45+30=75.

Which expression has the same sum as the one below?
- 15+6
0.15+6
0-6+(-15)
15+(-6)
6+(-15)

Answers

Answer:

6+(-15)

Step-by-step explanation:

=6+(-15)

=6-15

=-9

6+(-15)

Explanation:
-15+6 = -9

6+(-15)
Remove parentheses
6 - 15

Calculate the difference
6 - 15

Solution
-9
They Both Equal -9

Maggie makes 18 muffins. She is making them for her book group, which has 12 members. If she divides the muffins equally, how many will each person get?

Answers

Answer:

1.5

Step-by-step explanation:

18/12=1.5

solve:4x+3y=20;4x+2y=10 by matrix method

Answers

Answer:

i don't know sorry . and study well to make your future good

Round off to the highest place value of 5658

Answers

Answer:

6000

Step-by-step explanation:

You want to make the 5 a 6 and zero's for the rest. You make the five a six because if the number is 5 or higher you bump it up one number, if it is 4 or lower you don't need to bump it up or down. I hope this helps!

Place values is the value of a digit in relation to its position

5658 approximated to the highest place value is 6000

The number is given as:

[tex]\mathbf{Number = 5658}[/tex]

The number is in thousands; so, the highest place value is thousands

This means that the number must be approximated to thousands.

When 5658 is approximated to the nearest thousands, the approximated value is:

[tex]\mathbf{Approximated = 6000}[/tex]

Hence, 5658 approximated to the highest place value is 6000

Answers

Answer:

24?

Step-by-step explanation:

I need help dudes... DO THIS ASAP AND I'LL MARK YOU THE BRAINlYLIEST!!!! PLUS this question it due in 20 mins sooo

Alex went to the store and purchased red and blue jelly beans. The ratio of red to blue jelly beans is 3 to 7. If 140 jelly beans were in the bag, how many red jelly beans were in the bag?

URGENT!!!

Answers

Answer:

ahhh telll meeeee i have the SAME questio

Step-by-step explanation:

which of the following functions has a range of all real numbers?

Answers

Answer:

Step-by-step explanation:

The dots cannot intersect

Last year a sports team made $2,000,000 in profit, and this year it increased its profits
to $2,500,000. How much money was made on food sales in both years based on how
the sports team makes its profits:
• Programs: 15%
• Food: 40%
• Souvenirs: 25%
• Tickets: 20%

Answers

1,000,000

2,500,000x0.4 (40 as a decimal) = 1,000,000

Drag each description to the correct location on the table. Each description can be used more than once.
Classify each polynomial based on its degree and number of terms.
Polynomial
Name Using Degree
Name Using Number of Terms
5x - 8x
-6- X + 34²
-0.7*²
trinomial
binomial
trinomial
linear
monomial
cubic
quartic
quadratic
quartic
quintic

Answers

Answer:

Cubic-binomial

Quintic-trinomial

Quartic-monomial

Linear-binomial

Quadratic-monomial

Step-by-step explanation:they all in order

The answers are follows:

5x²-8x Cubic binomial

-6-x^5 - 3x² Quintic trinomial

1/3 x^4 Quartic monomial

-0.7x² Quadratic monomial

What is Polynomial?

Polynomials are sums of terms of the form k⋅ xⁿ, where k is any number and n is a positive integer.

According to the table:

5x²-8x Cubic binomial

-6-x^5 - 3x² Quintic trinomial

1/3 x^4 Quartic monomial

-0.7x² Quadratic monomial

Learn more about polynomial here:

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Solve the system by substitution. y=-x^2+2x+10 y=x+4

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Solve the system by substitution.
y=-x^2+2x+10
y=x+4