Solve the following system of equations and show all work.
y = -x² + 4
y = 2x + 1
Answers
Answer:
Step-by-step explanation:
The ys have to have the same value. That allows you to equate the right side of each y to each other.
-x^2 + 4 = 2x + 1 Subtract the right side from the left side.
-x^2 + 4 - 2x - 1 = 2x-2x +1 - 1 Combine
-x^2 - 2x + 3 = 0 Multiply both sides by - 1
-1(-x^2 - 2x + 3) = 0*-1 Remove the brackets
x^2 + 2x - 3 Factor
(x - 1)(x + 3 )
x - 1 = 0
x = 1
x + 3 = 0
x = - 3
So the line goes through x = 1 or x = - 3
x = 1
y = 2x + 1
y = 2(1) + 1
y = 3
x = - 3
y = 2(-3) + 1
y = - 6 + 1
y = - 5
Does the graph confirm this? See below.
red: y = -x^2 + 4
green: y = 2x + 1
Yes the graph is in agreement.
Related Questions
what is a point-slope equation of the line with slope -12 that goes through the point (5,3)?
A. y + 3 = 12 ( x + 5)
B. y - 3 = -12 ( x -5 )
C. y - 3 = 12 ( x - 5)
D. y + 3 = -12 ( x + 5 )
Answers
Step-by-step explanation:
Equation of a straight line is given by Y=MX+C
GIVEN POINTS (5, 3) and gradient -12, therefore
in the form of y=mx+c to get the constant, it will be 3=-12(5)+c
3=-60+c
3+60=c
c=63
y=mx+c
y=-12x+63
if anyone is able to help please do :)
Answers
Answer:
49.12?
Step-by-step explanation:
half circle= 4 squared *3.14/2=25.12
triangle=pythagorean theorem to find h=8. 8*6/2= 24
25.12+24=49.12
on squared paper draw the triangle with vertices at (1,1) , (5,3) , (3,5). find the area of the triangle
Answers
Answer:
lol
Step-by-step explanation:
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in the product rule for exponents, what do you do to the coefficients? what do you do to the exponents?
Answers
Answer:
Do not multiply the coefficients and the exponents. Remember, using the Product Rule add the exponents when the bases are the same.
In the product rule of the exponents,
''For same base we can add the exponents of the coefficients.''
What is mean by expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Solve expression by using the product rule for exponents.
Now, We know that;
In the product rule for exponents;
When expression have same base then its exponents are add and the coefficients of expression are written as same as write in expression
Hence, In the product rule of the exponents,
''For same base we can add the exponents of the coefficients.''
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ3
Select the correct answer.
The surface area (SA) of a cube with a as the length of each of its sides is given by the formula SA = 6a2. If the surface area is known, how can
you rewrite the formula to find its side?
ОА va
OB. VSA
OC a = $
OD. =
Answers
Answer:
(A). [tex]\sqrt{\frac{SA}{6} }[/tex]
Step-by-step explanation:
Adult tickets to a play cost $22 tickets for kids cost $15. Tickets for a group of 11 cost a total of $228. How many children and how many adults went to the play?
Answers
Answer:Number of children = 2 and number of adults = 9 attended the play
Step-by-step explanation:
Step 1
Let the number of children be represented as x
and the number of adults in the group be represented as as y
such that the total number of the group that went to the play
= x+y=11--- equation 1
And the total cost paid for the play will be expressed as
15x+ 22y= 228------ equation 2
Step 2-- Solving
x+y=11--- equation 1
15x+ 22y= 228------ equation 2
B y elimination method, multiply equation 1 by 15 to give equation 3 and then subtract from equation 2
15x+ 22y= 228------ equation 2
15x+15Y= 165----- equation 3
7y=63
y= 63/7= 9
y= adults = 9
therefore x = number of children will be
x+y=11
x+ 9=11
x= 11-9= 2
In the group that attended the play, Number of children = 2 and number of adults = 9
Use properties of operations to determine whether or not the expressions (x + 10) + x + 9 and 2(x + 7) + 5 are
equivalent
Answers
Answer:
The expressions are equivalent.
Step-by-step explanation:
We can simplify each expression and compare the results.
(x + 10) + x + 9 = x + 10 + x + 9 = 2x + 19
2(x + 7) + 5 = 2x + 14 + 5 = 2x + 19
2x + 19 = 2x + 19
Answer: The expressions are equivalent.
Can someone help me with these 2 problems thank you
Answers
Answer:
For question 6 there are 3 steps, and for question 7 there are 2 steps
Step-by-step explanation:
Question 6:
step 1. 89 x 2=178
step 2. 89 x 3=267
step 3. 267 + 178=445
Question 7:
step 1. 35 x 3= 105
step 2. 25 x 5= 12
Your're welcome :)
please help me with this problem
Answers
Answer:
vitamin c is the independent variable
Step-by-step explanation:
the amount of vitaman c dose not change but the amount of oranges eaten can change
Which set of ordered pairs is linear? A. {(2, 1), (5, 1), (6, 1)} B. {(–1, 4), (0, 0), (1, 6)} C. {(–3, 5), (1, 0), (2, 4)} D. {(0, 0), (1, 3), (2, 7)}
Answers
Answer:
merhaba ben yeni geledimde adın ne
Will give Brainly! Please help!
Answers
Answer:
The answer is option c.
Hope this helps!
Use the figure to find the measures of the numbered angles. ∠3 = ∘ ∠4 = ∘
Answers
Answer:
Step-by-step explanation:
∠3=95 (corresponding angle)
∠4=180-95
=85
An octagonal prism has...........lateral faces.
8
2
7
5
Answers
Answer:
an octagonal prism has 8 lateral faces
Answer:
8
Step-by-step explanation:
An octagonal prism has 8 lateral faces.
An octagonal prism has 10 faces – 8 lateral faces and 2 bases, 16 vertices, and 24 edges
Avery is buying string and beads to make bracelets for her family and friends. She plans to divide the string into 9-inch pieces to make at least 27 bracelets. What is the minimum amount of string she needs to buy?
Answers
Answer:
243 inches
Step-by-step explanation:
27 bracelets at 9inches each
9x27=243 inches or 20 feet and 1/4 inches of string. Depending on how the string is sold (by the foot, by the inch, yard, etc) will determine her minimum quantity, if you want to get specific.
Write an equation of the line that passes through (2, 1) and is parallel to the line y=2x+7.
Answers
Answer: y=2x-3
Step-by-step explanation:
What fraction is less than 1/2. 3/4,1/6,6/12,4/10,5/8,5/2
Answers
Answer:
1/6 and 4/10
Step-by-step explanation:
1/2 = 0.5 and 0.5 is greater than 1/6 which is 0.166666666667 and 4/10 which is 0.4.
Enter the value of 2 (4x + 3) when x = 3.
Answers
Answer:
30 is your answer
Step-by-step explanation:
2(12+3)
=30
41,692.58
Which number is in the tenths place?
A. 2
B. 5
C. 8
D. 9
Answers
Answer:
5 is in the tenths place
Step-by-step explanation:
2 is in the ones place, 8 is in the hundredths place, and 9 is in the tens place.
Neil has 2 pounds of grapes. He uses some to make a fruit salad. Now Neil has 8 ounces of grapes. How many ounces of grapes does Neil use for the fruit salad?
Answers
Answer:
Neil uses 24 ounces of grapes for the fruit salad.
Step-by-step explanation:
Quantity of grapes = 2 pounds
Use 1 pound = 16 ounces
So,
Quantity of grapes = 2(16) = 32 ounces
Neil uses some grapes to make a fruit salad. Now Neil has 8 ounces of grapes.
Quantity of grapes that Neil use for the fruit salad = [tex]32-8=24[/tex] ounces
Therefore,
Neil uses 24 ounces of grapes for the fruit salad.
Find the missing side of the triangle. Round to the nearest tenth.
A) 5.5
C) 14.1
B) 12.7
D) 9.5
Answers
Which term has the definition "The value that describes the location of a digit within a number, such
as units, tens, hundreds, etc."?
O Repeating Decimal
O Rational Number
O Terminating Decimal
O Place Value
Answers
Answer:
place value is the answer
Answer:
The answer is 'PLACE VALUE'
Step-by-step explanation:
An ice cream company fills containers with 64 ounces of ice cream. The acceptable percentage of error in filling each
ice cream container is 1.5%.
Select all the expressions that could be used to find the greatest number of ounces of ice cream each container can
hold.
64(1.15)
64(1.015)
64(1.5)+64
64-64(1.5)
64(0.015)-64
64+64(0.015)
Answers
Answer:
64(1.015)64+64(0.015)Step-by-step explanation:
The target number is 64 and the error is 1.5%
Possible number is
64 ± 1.5% of 64 = 64 ± 0.015*64
The top limit is:
64 + 64(0.015) or64*(1.015)Correct choices are B and F
64(1.015)
and
64+64(0.015)
PLEASE PLEASE, ANSWER ASAP
Answers
Answer: 16
Step-by-step explanation: 16 is how much the breaking pad is produced per hour because if you divide all of them you get 16 for each of them on the table
Round to the nearest tenth.
x=
y=
Answers
If r = .15, this indicates
Answers
Answer:
Then D=.30
Step-by-step explanation:
Diameter is two times the radius
I think this is correct I'm not to sure
hope this helps :)
35= h(b1+b2) solve for b2
Answers
Answer: look at the picture and I don’t know how to solve for b but I can do h
Step-by-step explanation: hope this help :)
Answer:
i dont know
Step-by-step explanation:
i dont know
what is the answer for 2x=7
Answers
Answer:
x=3.5
the answer is 3.5 because 7 divided by 2 is 3.5
A party cap is in the form of a frustum. The radii of its ends are 10cm and 30 cm. The volume of the cap is 9100. What is the height of the cap?
Answers
Answer:
4.46cm
Step-by-step explanation:
Volume of a frustum is expressed as;
V = (1/3) * π * h * (r₁² + r₂² + (r₁* r₂))
h is the height of the frustum
r₁ and r₂ are the radii of its ends
V is the volume
Given
V = 9100cm₃
r₁ = 10cm
r₂ = 30cm
Substitute
9100 = (1/3) * (3.14) * h * (10² + 30² + (10* 30))
9100 = 1/2(3.14)*h*(100+900+300)
9100 = 1.57*h*(1300)
9100 = 2,041h
h = 9100/2,041
h = 4.46cm
Hence the height of the cap is 4.46cm
Which is greater 2.6 or 2.65 ?
Answers
Answer:
2.65 is greater than 2.6
Step-by-step explanation:
if 65 is greater than 60 than 2.65 is greater than 2.60
Answer:
2.6 > 2.65
Step-by-step explanation:
plz need help
how much black hole required force
solve by using theory of relativity
Answers
Answer:
Solving the Equations of General Relativity for Colliding Black Holes
TOPICS:AstronomyAstrophysicsBlack HoleGeneral RelativityPopularTexas Advanced Computing CenterUniversity Of Texas At Austin
By UNIVERSITY OF TEXAS AT AUSTIN NOVEMBER 8, 2020