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:
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Amy needs to estimate how many students at her school like online testing. She needs to create a random sample of students. How should Amy collect her sample? Select two that apply.
O Amy should ask every 10th person leaving the school at the end of the day.
O Amy should ask 3 people at every table in the cafeteria
O Amy should ask her 10 closest friends.
O Amy should ask the 35 students in her honors math class
O Amy should ask the 50 students in the computer club.
(2x + y)2 – (3x – 2y)2 + (x – 4y)(x + 4y
11
Answer:
Step-by-step explanation:
(a+ b)² = a² + b² + 2ab
(2x + y)² = (2x)² + y² + 2*2x *y
= 4x² + y² + 4xy
(a- b)² = a² + b² - 2ab
(3x - 2y)² = (3x)² + (2y)² - 2*3x *2y
= 9x² + 4y² - 12xy
(a - b)(a +b) = a² - b²
(x - 4y(x + 4y) = x² - (4y)²
= x² - 16y²
(2x + y)² - (3x - 2y)² + (x - 4y)(x +4y)
= 4x² + y² + 4xy - (9x² + 4y² - 12xy) + x² - 16y²
= 4x² + y² + 4xy - 9x² - 4y² + 12xy + x² - 16y²
= 4x² - 9x² + x² + y² - 4y² - 16y²+ 4xy + 12xy
= -4x² - 19y² + 16xy
HELPPPPPPPPP PLEASEEEE
Answer:
X=17
Step-by-step explanation:
7x-1+5x-23=180
12x-24=180
12x=204
x=17
No LINK Easy math please help is this liner y=2\x +1 explain please too
Answer:
It is not linear
Step-by-step explanation:
If you plug that function into Desmos graphing Calculator, you can see there are two leparate lines and they are not straight.
ALGEBRA
identify the terms, coefficients, and constants in the expression.
5m+9
Answer:
I love algebra anyways
the ans is in the picture with the steps
(hope it helps can i plz have brainlist :D hehe)
Step-by-step explanation:
I need to give the slope but I don’t know how someone help!
Answer:
-4/2
Step-by-step explanation:
rise over run
goes down -4 "rises"
moves over 2 runs
At a candy store each bag holds 0.75 pounds. A box with 12 pounds of candy is being put into ,b, bags. How many bags of candy is this?
Answer:
17 bags is correct
Step-by-step explanation:
12 / 75 is equal to 17.14
Drag the numbers to create three ratios that are equivalent to 4:12. Each number may be used once or not at all.
Answer: 20:60, 12:36, 2:6
Step-by-step explanation: All you need to do is look at the numbers and see which 3 are equivalent to 4:12.
The radius of a circle is changing at the rate of 1/π inches per second. At what rate, in square inches per second, is the circle’s area changing when the radius is 5 inches?
Answer:
10 square inches per second.
Step-by-step explanation:
The radius of the circle is given by the equation:
r(t) = (1/π in/s)*t
Where time in seconds.
Remember that the area of a circle of radius R is written as:
A = π*R^2
Then the area of our circle will be:
A(t) = π*( (1/π in/s)*t)^2 = π*(1/π in/s)^2*(t)^2
Now we want to find the rate of change (the first derivation of the area) when the radius is equal to 5 inches.
Then the first thing we need to do is find the value of t such that the radius is equal to 5 inches.
r(t) = 5 in = (1/ in/s)*t
5in*(π s/in) = t
5*π s = t
So the radius will be equal to 5 inches after 5*π seconds, let's remember that.
Now let's find the first derivate of A(t)
dA(t)/dt = A'(t) = 2*(π*(1/π in/s)^2*t = (2*π*t)*(1/π in/s)^2
Now we need to evaluate this in the time such that the radius is equal to 5 inches, we will get:
A'(5*π s) = (2*π*5*π s)*((1/π in/s)^2
= (10*π^2 s)*(1/π^2 in^2/s^2) = 10 in^2/s
The rate of change is 10 square inches per second.
THIS IS DUE NOW wiil give crown if right Winston bought an encyclopedia priced at $42. Shipping and handling cost anadditional 30% of the price. What was the total cost of the encyclopedia, in cluding shipping and handling?
Answer:$52.60
Step-by-step explanation: You have a initial cost of $42 and you have to add 30 %. When you add the 30 % you get 12.60 more dollars added to the amount. This will then give you an answer of $52.16.
Raja solved the inequality –3x – 5 ≤ 1. His work is shown below. Where did Raja make an error in his calculation? Explain.
Answer:
Raja made an error in d equality sign in d answer
Step-by-step explanation:
-3x< or =6
when dividing both sides by -(negative)3, the sign 4 d answer changes
x > or = -2
A test was done to look at the maximum speed of mopeds. They found that the maximum speed had a normal distribution with a mean of 29 mph and standard deviation of 1.4 mph. Consider randomly selecting a moped.
a. What is the probability that the maximum speed is at most 31 mph?
b. What is the probability that the maximum speed is at least 29.8 mph?
c. What is the probability that maximum speed differs from the mean value by at most 1.5 standard deviations?
d. Suppose we select 49 mopeds, what is the probability that the sample mean will be at least 29.5 mph?
Answer:
C
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!
Addison sells plants. She sold 7 times as many as tomato plants as pepper plants, for a total of 64 plants sold. How many pepper plants did she sell? PLEASE SOMEONE GIVE ME THE ANSWER AHHHH
Answer:
8 pepper plants were sold.
Step-by-step explanation:
Assuming [tex]x=[/tex] the number of pepper plants sold, she sold [tex]7x[/tex] tomato plants and [tex]x[/tex] pepper plants, and since tomato plants sold + pepper plants sold = 64, we can turn this into the equation [tex]7x+x=64[/tex]. To solve this first we combine like terms to get [tex]8x=64[/tex]. Cancel the 8 by dividing both sides by 8 and we get [tex]x=8[/tex], which is the number of pepper plants sold. (We could also multiply x by 7 to get the number of tomato plants sold, which is 56.) Hope this helps!
PS: Please mark brainliest!Find the value of "x"
NO SCAM LINKS.
please reply ASAP PLEASEEEE
Answer:
B
Step-by-step explanation:
Solve if you want cookie!
Step-by-step explanation:
[tex]y = 2x \: \: \: \: x + y = 6 \\ y = 2x \: \: \: \: x = 6 - y \\ y = 2(6 - y) \: \: \: \: x = 6 - y \\ 3y = 12 \: \: \: \: x = 6 - y \\ y = 4 \: \: \: \: x = 2[/tex]
Gimme tha cookie
please help me on this
Answer: 7/8
Step-by-step explanation:
There are 8 tickmarks on the number line, each representing 1/8.
So, the question mark represents 7/8 (since it is one tickmark to the left of 1)
4 more than twice a number is less than the opposite of the number
Answer:
x=1
Step-by-step explanation:
2n+4<-n
:
2n+n+4<0
:
3n<-4
:
n<-4/3
:
0<2
ASAP Please!
Enter the amplitude of the function. f(x)=5cosx
Amplitude of f(x)=5cosx
= 5
what's an amplitude example?The amplitude of a periodic variable is a measure of its change in a single period. The amplitude of a non-periodic signal is its magnitude as compared with a reference value. there are numerous definitions of amplitude, which can be all functions of the magnitude of the differences between the variable's extreme values.
It refers to most displacement from the equilibrium that an object in periodic motion show. as an example, a pendulum swings through its equilibrium point (straight down), and then swings to a maximum distance away from the center.
Learn more about amplitude here
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help help please it due rn?
Answer:
Step-by-step explanation:
E : -5 , -3
F: 2 , -7
Distance = sqrt( ( 2 -(-5)) * ( 2 -(-5)) + (-7 -( -3)) *(-7 -( -3)) )= sqrt ( 49 + 16 ) = sqrt (65)
What is the simplified expression of 14 – 8 + 4 × 11 ÷ 22 + 6 – 11?
Answer:
your answer will be 3
Step-by-step explanation:
Find the simple interest on the following amounts:
a K4000 invested at 6% p.a. for 4 years
b K23 000 invested at 6.5% p.a. for 8 years
K580 borrowed at 5% p.a. for 9 months
inte
с
500
Answer:
a. Simple interest = K960
b. Simple interest = K11,960
c. Simple interest = K261
Step-by-step explanation:
Given the following data;
a. Principal = K4000
Interest rate = 6%
Time = 4 years
To find the simple interest;
Mathematically, simple interest is calculated using this formula;
[tex] S.I = \frac {PRT}{100} [/tex]
Where;
S.I is simple interest.
P is the principal.
R is the interest rate.
T is the time.
Substituting into the equation, we have;
[tex] S.I = \frac {4000*6*4}{100} [/tex]
[tex] S.I = \frac {4000*6*4}{100} [/tex]
[tex] S.I = \frac {96000}{100} [/tex]
S.I = K960
b. Principal = K23 000
Interest rate = 6.5%
Time = 8 years
To find the simple interest;
[tex] S.I = \frac {PRT}{100} [/tex]
Substituting into the formula, we have;
[tex] S.I = \frac {23000*6.5*8}{100} [/tex]
[tex] S.I = \frac {1196000}{100} [/tex]
S.I = K11,960
c. Principal = K580
Interest rate = 5%
Time = 9 months
To find the simple interest;
[tex] S.I = \frac {580*5*9}{100} [/tex]
[tex] S.I = \frac {26100}{100} [/tex]
S.I = K261
The heights, in inches, of five players on a basketball
team are 68, 70, 76, 71, and 70. What is the mean
height, in inches, of these players?
A)76
B)72
C)71
D)70
Answer:
C) 71
Step-by-step explanation:
To find the mean you must first add all the numbers:
68 + 70 + 76 + 71 + 70 = 355.
After that you divide the number you got by how many numbers are in the set.
There are five players so we divide the number by 5
355/5 = 71
Therefore, it is 71.
Find the degree of the polynomial
Answer:
2
degree is highest exponent in equation and 2x² has 2 and is highest
What is the value of y?
Please help!
A pick-up truck is fitted with new tires which have a diameter of 43 inches. How fast will the pick-up truck be moving when the wheels are rotating at 400 revolutions per minute? Express the answer in miles per hour. (mph)
Answer:
v = 51.19 mph
Step-by-step explanation:
The diameter of the tires, d = 43 inches
The angular velocity of the wheels = 400 revolutions per minute
400 revolutions per minute = (400/60) rev/s = 6.67 rev/s
The circumference of the tire is :
C = 2πr
= 2π×21.5
= 135.08 inches
The speed of the truck is given by :
[tex]v=6.67 \times 135.08 \\\\v=900.983\ in/s[/tex]
or
v = 51.19 mph
So, the speed of the truck is equal to 51.19 mph.
Which pair of ratios is proportional?
A. 3 ft : 8 sec and 5 ft : 11 sec
B. 6 yd : 10 mi and 18 yd : 30 mi
C. 3:25 and 5:50
D. 6 in. : 8 min and 3 min : 2 in.
Suppose all the terms of a geometric sequence are
positive, and the common ratio r is between 0 and
1.
Is the sequence increasing of decreasing? Explain.
Answer: the sequence is increasing. The reason it is increasing because its atleaset increasing by one number.
Answer:
Step-by-step explanation:
this is called "monotonically decreasing" as the exponent on the ratio goes up , and the ratio is less than 1 but more than zero, the number gets smaller and smaller.... it approaches zero is what happens.
(10-i)-(12+6i)
.............
Answer:
-2 - 7 i
Srry If Im wrng but Hope this helped :)
Answer:
It is -2-7i
Step-by-step explanation: