The graphs intersect at the points (3, 13) and (-2, -7).
How to determine the intersection of 2 graphsGiven the following equations:
y₁ = x² + 3x - 5 (quadratic equation)
y₂ = 4x + 1 (linear equation)
To find the intersection point(s) of the two graphs, we need to solve their equations simultaneously. By so doing, we'll set the equations equal to each other:
y₁ = y₂
x² + 3x - 5 = 4x + 1
collect the like terms
x² - x - 6 = 0
Now we'll factor the quadratic expression:
(x - 3)(x + 2) = 0
x - 3 = 0 or x + 2 = 0
x = 3 or x = -2
Now we have the points of intersection on the x-axis.
To get the corresponding values on the y-axis, we'll plug each value of x into either of the original equations.
Let's use the first equation:
y₁ = x² + 3x - 5
When x = 3:
y₁ = 3² + 3(3) - 5 = 13
When x = -2:
y₂ = 4x + 1 = 4(-2) + 1 = -7
So the first intersection point is (3, 13) and the second intersection point is (-2, -7).
Therefore, the graphs intersect at the points (3, 13) and (-2, -7).
Learn more about intersection here:
https://brainly.com/question/29185601
#SPJ1
Kyle bought some boxes of donuts. There were 4 donuts in each box, and Kyle bought 76 donuts in all. Write an equation, that when solved, will tell how many boxes, b, of donuts Kyle bought?
Answer:
b=76/4
Step-by-step explanation:
Since there are 4 donuts in each box, and 76 boxes total, then you know that you need to divide the number of donuts by the amount of donuts in each box. b= 19 if u needed that. Cheers
Answer:
The answer is 19 boxes
Step-by-step explanation:
Since there were 4 donuts in each box all you have to do is divide 76 by 4 since there is 76 donuts in all 76 ÷ 4 = 19 boxes (79 equally distributed into 19 boxes)
Find the volume of the prism. Write your answer as a decimal.
6 ft.
9 ft
4.5 ft
helpp plss
Answer:
Step-by-step explanation:
It would be 2.43ft cubed. You first have to multiply 6 x 9 to get 54 and then Do 54 x 4.5 to get 243 ft cubed. Next you have to put it in fraction form 243/100. After that you have to divide 243 by hundred( you can do this by moving the decimal place two places to the left) and you get the answer 2.43 ft cubed
What is the height of a triangle whose base is 36 inches area is 234 Square inches
Answer:
hb will = 3in/ three in
which expression can you substitute for x in 5x+y=8 to solve the system below?
5x+y=8
x+4y=2
Answer:
x =30/19 and y =2/19
Step-by-step explanation:
5x + y = 8
x + 4y = 2
then
5x + y = 8
-5(x +4y =2)
5x + y = 8
-5x - 20y = - 10
0 +y - 20y = -2
- 19y = -2
y = 2/19 then
5x + 2/19 = 8
5x = 152-2/19
5x/5 =150/19 *1/5
x =30/19
If you can buy 48 plaintains for $24 then how many can you buy with $4 ?
Answer:
8 plantains
Step-by-step explanation:
48=$24
x=. $4
192=24x , x= 192÷24= 8
Answer:
8 plantains
Step-by-step explanation:
Cost and number of plantains are in proportion
Number of plantains that can be bought for $ 4 be 'x'
48 : 24 :: x : 4
Product of means = product of extremes
24 * x = 48*4
[tex]x = \frac{48*4}{24}[/tex]
x = 2 * 4
x = 8
How many solutions does this system of equations have? Explain how you know.
Answer:
No solution
Step-by-step explanation:
The given equations are :
9x-3y=-6
3x-y=2.....(1)
5y=15x+10
5y-15x=10
or
y-3x=2 .....(2)
Equations (1) and (2) shows that the lines are parallel. We know that for parallel lines, there is no solution.
What’s the slope ?
Please help I’ll mark u as Brainliest
9514 1404 393
Answer:
5/2 = 2.5
Step-by-step explanation:
The slope is given by ...
m = (y2 -y1)/(x2 -x1)
Using the first two lines in the table, this is ...
m = (10 -5)/(2 -0) = 5/2
The slope of the line is 5/2.
__
As a decimal, that is 2.5.
A circle with a radius of 1 in. is inscribed in a right triangle with legs of 3 in. and 4 in. If a point is randomly chosen within the triangle, what is the probability that the point is NOT also in the circle?
Answer:
P = (6-π)/6Explanation:
Circle Area:
CA = 1²×π
CA ≈ π in²
Triangle Area:
TA = 3×4/2 = 6 in²
Probability:
P(point not in circle) = (6-π)/6 ≈ 0.48 ≈ 47.64%
PLEASE HELP| calculate measure of angle H. round answer right nearest tenth of a degree
9514 1404 393
Answer:
28.1°
Step-by-step explanation:
The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(H) = 8/17
H = arcsin(8/17)
H ≈ 28.1°
x+y+z=9
x-y-z=-1
x-y+z= 21
Which value is not in the solution, (x,y,z), of the
system?
1) -8.
2) ---6
3) 11
4) 4
the answer is (-8) because x=4, y=-6, z=11
These consists of more than 1 equation with unknown variables. The value that is not a solution in (x,y, z)is -8
System of equationsThese consists of more than 1 equation with unknown variables. Given the set of equations
x+y+z=9
x-y-z=-1
x-y+z= 21
Add 1 and 2
2x = 9 - 1
2x = 8
x = 4
Subtract 2 and 3
-2z = -22
z = 11
Determine the value of y
x +y + x = 9
4 + y + 11 = 9
y = 9 - 15
y = -6
Hence the value that is not a solution in (x,y, z)is -8
Learn more on system of equation here: https://brainly.com/question/25976025
#SPJ6
Solve for f(-7)
f(x)=5-x
f(-7)= ?
Answer:
7 f + 5 ??
Step-by-step explanation:
Mountain officials want to build a new ski lift from B to C, as shown in the figure below. The distance from A to C is 1540 feet. They measure angle DAC to be 38º and angle DBC to be 25º. What is the distance from A to B ? Round your answer to the nearest tenth of a foot.
Answer:
there is a 13 degree difference from DBC and DAC
with that you divide 1540 by 13 as you get that 118.461 feet
that means that there is a 118.461 difference from B to C and A to B
so the answer is either 1658.461ft or 1421.539ft I am not sure if that is correct or not but best of luck mate
6 3/4 x 5 + 2 1/4 =?
Answer:
40
Step-by-step explanation:
2
What is the value of x in the equation 3
-18?
-56
-52
52
56
Answer:
sorry
Step-by-step explanation:
plz send full question
Find the total surface area of the cylinder below.
Answer:
83.54 in²
Step-by-step explanation:
Brₐinliest plz
Which ach represents the inequality < -1 + 2x?
Answer:
3rd one
Step-by-step explanation:
is searching online for airline tickets. Two weeks ago, the cost to fly from Boston to Orlando was $220. Now the cost is $370. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Answer:
68% increase and 91% increase
Step-by-step explanation:
220(1+x)=370 -- 220(1+rate increase)=370
1+x=1.68
x=.68
220(1+x)=420 (370+50)=420
1+x=1.909
x=.91
Square 1 has a area of 24 square units if square 2 is half the size what is the ratio of the area of square one to square two?
Answer:
Step-by-step explanation:
I'm going to guess that 1/2 the size means the sides are 1/2 the size.
Square 1 has an area of 24. The sides are s, so the area is found by using s^2
The second square is made from sides that are 1/2 s
Area = 1/2 s * 1/2 s
Area = 1/4 s^2
Area 1 / area 2 = 24 / x^2 = s^2 / 1/4 s^2 = 1/0.25
what is the unknown number in sequence 2
question in picture(explain if u can it helps alot)
Answer:
4z + 2q
Step-by-step explanation:
there is 4 "z" and 2 "q"
Answer:
4z+2q
Step-by-step explanation:
combine like terms
combine all the z’s and all the q’s
Given the angles in the diagram below, what is mZ2?
Answer:
98
Step-by-step explanation:
Hello There!
The angle that has a measure of 82 degrees and the angle labeled "2" are supplementary angles.
This meaning that the sum of the two angles is 180
So to find the missing angle (2) we subtract the given angle (82 in this case) from 180
so ∠2 = 180 - 82
180 - 82 = 98
Hence, the answer is 98°
A recording studio charges musicians an initial fee of $100 to record an album. Studio time cost an additional $1 per minute. Write and graph an equation that models the total cost of recording an album over one afternoon.
Answer:
$340
Step-by-step explanation:
Given data
Inititial fee= $100
cost per minute= $1
Let the total charge for x minutes by y
Hence the expression for the total charges after x minutes is
y= 100+1x
y=100+x
But an after is from 12pm - 4pm= 4 hours
x=4*60
x=240minutes
y=100+240
y=$340
Can I please get help with this
9514 1404 393
Answer:
35x + 20 ≥ 1000x ≥ 28Step-by-step explanation:
The number of filled bags will be 35 for each hour (x) that Jackson works, in addition to those already filled. So, the total number filled after x hours is ...
35x + 20
We want that number to be at least (greater than or equal to) 1000, so the relation is ...
35x +20 ≥ 1000
__
To solve this, we first subtract 20:
35x ≥ 980
Now, we can divide by the coefficient of x.
x ≥ 980/35
x ≥ 28 . . . . . the solution
Answer choices- 4, 64, 240, 116, 68, 105, 480, 400 (20 points)
COMMON CORE REVIEW
1. Find the percent of change from 32 feet to 79 feet. Round to the nearest tenth, if necessary. Then state whether the percent of change is percent of increase or percent of decrease.
2. Factor this expression: 27+108n
3. Factor this expression: 56x + 16
THANKS AGAIN!!
Answer:
146.9
Step-by-step explanation:
I'm not sure of the answer but if I'm wrong tell me I'll continue trying it is a pleasure to help you.
Answer it right and i'll try to give you brainliest.
Answer:
384 cm²
Step-by-step explanation:
Since it is a square pyramid, the total surface area of the pyramid is the area of its square base plus the area of its 4 triangular faces.
[tex]\boxed{area \: of \: triangle = \frac{1}{2} \times base \times height }[/tex]
Area of a triangular face
= ½ ×12 ×10
= 60 cm²
[tex]\boxed{area \: of \: square = side \times side}[/tex]
Base area of pyramid
= 12 ×12
= 144 cm²
∴ Surface area of pyramid
= 4(60) +144
= 240 +144
= 384 cm²
Find the value of x.
A
D
17
8
х
B.
15
O X
120
17
O X
17
120
Answer:
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Step-by-step explanation:
How to figure out square feet of counter tops
Answer:
Chapter Three: Calculate Total Countertop Square Footage
To calculate the total square footage (after placing seams) you will need to follow this formula: “L” x “W” / 144 = s.f. (Length times width divided by 144 = square feet).
12. Dua garis sejajar dipotong oleh sebuah garis
maka jumlah besar sudut dalam sepihak
sama dengan....
a. 360
b270
c180
d.90
Answer:
I do not know the Answer I'm just trying to get my point
Step-by-step explanation:
Thank you
Thank you
2, 6, 10, 15, ...
O Arithmetic
O Geometric
O Neither

Given:
The sequence is:
2, 6, 10, 15,...
To find:
Whether the given sequence is Arithmetic, Geometric, Neither.
Solution:
We have,
2, 6, 10, 15,...
Different between consecutive terms are:
[tex]6-2=4[/tex]
[tex]10-6=4[/tex]
[tex]15-10=5[/tex]
Since [tex]4\neq 5[/tex], therefore the given sequence has no common difference. It means it is not an arithmetic sequence.
Ratio of consecutive terms are:
[tex]\dfrac{6}{2}=3[/tex]
[tex]\dfrac{10}{6}=\dfrac{5}{3}[/tex]
Since [tex]3\neq \dfrac{5}{3}[/tex], therefore the given sequence has no common ratio. It means it is not a geometric sequence.
Since the given sequence is neither arithmetic nor geometric, therefore the correct option is C.