Answer:
The intersection points between the functions are (-4,16) and (2,4)
Step-by-step explanation:
Intersection Between Functions
We are given the functions:
[tex]y=x^2[/tex]
[tex]6x+3y=24[/tex]
To find the intersections between them, we have to solve the system of equations. Let's start by simplifying the second equation by 3:
[tex]2x+y=8[/tex]
Now we substitute [tex]y=x^2[/tex] into this equation:
[tex]2x+x^2=8[/tex]
Solve the quadratic equation by any of the available methods.
Subtract 8:
[tex]2x+x^2-8=0[/tex]
Sort the polynomial:
[tex]x^2+2x-8=0[/tex]
Factor:
[tex](x+4)(x-2)=0[/tex]
Solve:
[tex]x=-4, x=2[/tex]
Now find the y-coordinate of each solution:
[tex]y=x^2=(-4)^2=16[/tex]
The point is (-4,16)
For x=2:
[tex]y=x^2=2^2=4[/tex]
The point is (2,4)
The intersection points between the functions are (-4,16) and (2,4)
Please help‼️
Find the product. Simplify your answer.
-3n-(-3n2-5)
Answer:
-3n-3n2+5
Step-by-step explanation:
You can use Keep Change Change in order to simplify the problem
f(n)= 2n – 2; Find f(2)
Adrianna runs up 4.5 flights of stairs. How far will Arianna have to run down to represent an additive inverse?
Answer:
She needs to run down 4.5 flights of stairs to represent an additive inverse
Step-by-step explanation:
Having an additive inverse means that she will be back at point zero.
The point zero in this context simply refer to her starting point.
So if she has run up 4.5 flights of stairs, then to be back at her starting point, she needs to run down also 4.5 flights of stairs
Given m||n, find the value of x.
Suppose x and y are the number of
students in two classrooms, where x < y.
Compare the expressions using <=, or >
(2x^2) [_?_] (x + y)^2
Answer:
Step-by-step explanation:
G
If 2x−5 = 13, then x=4 true or false
Answer:
False
Step-by-step explanation:
13+5=18
2*4=8
8-5=3
The given solution x=4 is false for 2x-5 = 13.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
2x−5 = 13
Now, for x=4
2(4)- 5
= 8-5
= 3
As, the LHS part of equation is not equal to RHS part.
Hence, the given x=4 is false for 2x-5 = 13
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helppppppppppppp me...............
Answer:
B.
Step-by-step explanation:
Change the denominators to a common one, then change the numerators accordingly. You can also use math///w4y
need help solving matrices answer ASAP
Step-by-step explanation:
Distribute the 6 to the first matrix and add the result of the first matrix to the second matrix
What is the quotient 8 x 10^24/2 x 10^ 8 in scientific notation? Please Help!?!?
Answer:
4x10^6
can you also please mark me as brainliest?
A 2-column table with 8 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3, 4. The second column is labeled f of x with entries negative 2, 0, 2, 2, 0, negative 8, negative 10, negative 20.
Which could be the entire interval over which the function, f(x), is positive?
(–∞, 1)
(–2, 1)
(–∞, 0)
(1, 4)
Answer:
a
Step-by-step explanation:
One week, seventy-two percent of the animals that cam to a veterinary hospital were dogs. If there were 230 animals total, how many were dogs
Answer:
165.6
Step-by-step explanation:
165.6 is 72% of 230
HELP ASAP!!!!!!!! Select the correct answer from each drop-down menu.
The graph of the function y= x^2(x^2 - 6x + 9) has zeros of (0 and -3, -3 and 3, 0 and 3, -3 and 3)
complex zeros.
so the function has (no, two, three, four)
distinct real zeros and (no, two, three, four) complex zeros.
Answer: The answer is
1. 0 and 3
2. Two
3. No
Step-by-step explanation:
I took the test and it's right
The graph of the function has zeros of 0 and 3, two distinct real zeros, and no complex zeros.
What is a function?It is defined as a special type of relationship and they have a predefined domain and range according to the function.
We have a function:
[tex]\rm y= x^2(x^2 - 6x + 9)[/tex]
We can write it as a:
[tex]\rm y= x^2(x^2 - 2(3)(x)+ 3^2)[/tex]
[tex]\rm y = x^2(x-3)^2[/tex]
To find the zeros equate to the function with the zero.
y = 0
[tex]\rm x^2(x-3)^2=0[/tex]
First, take [tex]\rm x^2= 0[/tex] we get:
x = 0
Now
[tex]\rm (x-3)^2=0[/tex]
x - 3 = 0
x = 3
Thus, the graph of the function has zeros of 0 and 3, two distinct real zeros, and no complex zeros.
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Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a \$7.50$7.50dollar sign, 7, point, 50 delivery fee and \$14$14dollar sign, 14 per pizza. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under \$60$60dollar sign, 60. Each pizza is cut into 888 slices, and she wonders how many total slices she can afford. Let P represent the number of pizzas that Jacque buys. ------------------------------------------------------------------------------------ 2) What is the largest number of slices that Jacque can afford?
Answer:
3 pizzas
24 slices.
Step-by-step explanation:
Given:
Delivery fee = $7.50
Charges per pizza = $14
Total money available with Jacque = $60
Number of slices in one pizza = 8
To find:
The number of pizzas, [tex]P[/tex] that Jacque can buy and
The number of slices, that Jacque can afford.
Solution:
Cost of one pizza = $14
Cost of [tex]P[/tex] pizzas = $14 [tex]\times P[/tex]
Out of total money of $60, $7.50 will be used as delivery charge.
Therefore, money that can be used for buying pizza = $60 - $7.50 = $52.50
Now, the money available must be greater than or equal to the cost of [tex]P[/tex] pizzas:
i.e. $52.50 [tex]\geq[/tex] [tex]\$14P[/tex]
[tex]\Rightarrow P = 3[/tex]
A maximum of 3 pizzas can be bought.
Number of slices that Jacque can afford = 3 [tex]\times[/tex] 8 = 24 slices
The revenue for a company producing widgets is given by y = -20x2 - 50x + 200, where x is the price in dollars for each widget. The cost for the production is given by y = 30x - 10. Determine the price that will allow the production of widget to break even.
Answer:
The price is x = $2.779
Step-by-step explanation:
From the question we are told that
The revenue is [tex]y = - 20x^2 - 50 x + 200[/tex]
The cost of production is [tex]y = 30 x - 10[/tex]
Generally at break even point the cost of production is equal to the revenue
So
[tex]-20x^2 -50x + 200 = 30x-10[/tex]
=> [tex]20x^2 +20 -210 = 0[/tex]
Using the quadratic formula to solve this equation we have that
x = $2.779
Answer:
1.81 per widget
Step-by-step explanation:
If you put in the equations in Desmos, you can see where is breaks even
how many solutions does 3x-1=3 have?
Answer:
one solution
Step-by-step explanation:
3x-1=3
Add 1 to each side
3x-1+1=3+1
3x = 4
Divide by 3
3x/3 = 4/3
x = 4/3
There is one solution
Answer:
One solution
Step-by-step explanation:
3x=4
x=4/3
no other answer
The regular price of a Space Invader game is $30, but it is on sale. The discount is $15. What percent discount is this?
Answer:
50%
Step-by-step explanation:
15=30x
x=0.5
x=50%
Answer:
50% Discount
Step-by-step explanation:
So look to get the discount do the math like this:
30 rupees discount is 15 rupees
∴1 rupees discount is 15/30 rupees
∴ 100 rupees discount is 0.2×100 rupees
⇒50 Rupees
∴The Discount is 50%(Ans:)
What is the definition of a pandemic? How does a pandemic differ from an endemic or epidemic? What is the life cycle of the HIV virus once it enters the body? How does the genetic code of the virus change? How does HIV affect the body? How do people become infected with HIV? How does AIDS develop from an HIV infection? What are the current infection rates of HIV across the globe? Where is HIV/AIDS most prevalent? What treatments are currently available for HIV/AIDS? Do some regions of the world have better access to treatments than others? What is the average life expectancy for someone with HIV? Does life expectancy differ around the globe?
Answer:
HIV (human immunodeficiency virus) is a virus that attacks the body’s immune system. If HIV is not treated, it can lead to AIDS (acquired immunodeficiency syndrome). Learning the basics about HIV can keep you healthy and prevent HIV transmission. You can also download materials to share or watch videos on basic information about HIV.
What is HIV?
HIV Overview
HIV (human immunodeficiency virus) is a virus that attacks the body’s immune system. If HIV is not treated, it can lead to AIDS (acquired immunodeficiency syndrome).
There is currently no effective cure. Once people get HIV, they have it for life.
But with proper medical care, HIV can be controlled. People with HIV who get effective HIV treatment can live long, healthy lives and protect their partners.
Where did HIV come from?
History of HIV
HIV infection in humans came from a type of chimpanzee in Central Africa.
The chimpanzee version of the virus (called simian immunodeficiency virus, or SIV) was probably passed to humans when humans hunted these chimpanzees for meat and came in contact with their infected blood.
Studies show that HIV may have jumped from chimpanzees to humans as far back as the late 1800s.
Over decades, HIV slowly spread across Africa and later into other parts of the world. We know that the virus has existed in the United States since at least the mid to late 1970s.
To learn more about the history of HIV in the United States and CDC’s response to the epidemic, see CDC’s HIV and AIDS Timeline.
Step-by-step explanation:
Write the converse of this statement.
If two angles are both obtuse, the two angles are equal.
Answer:
If two angles are equal, then they are congruent.
Step-by-step explanation:
Carlos drives 161 kilometers at a speed of 70 kilometers per hour. For how many hours does he drive?
Answer:
2.3 hours
Step-by-step explanation:
161 divided by 70 = 2.3
if Carlos drives 161 kilometers at a speed of 70 kilometers per hour then it takes 2.3 hours to drive.
What is Speed?Speed is the time rate at which an object is moving along a path,
Given,
Carlos drives 161 kilometers at a speed of 70 kilometers per hour
From the given data distance=161 kilometers
Distance is one hundred sixty one kilometers
Speed=70km/hr.
Speed is seventy kilometer per hour.
Speed=Distance/time
70=161/time
Now cross multiply
time=161/70
Time=2.3hrs
Hence, if Carlos drives 161 kilometers at a speed of 70 kilometers per hour then it takes 2.3 hours to drive.
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Casey bought a 15.4 pound turkey and an 11.6 pound ham for Thanksgiving and paid $38.51.
Her friend Jane bought a 10.2 pound turkey and a 7.3 pound ham from the same store and paid
$24.84. Find the cost per pound of turkey and the cost per pound of ham.
Answer:
h = 1.74
t = 1.19
Step-by-step explanation:
15.4t + 11.6h = 38.51
10.2t + 7.3h = 24.84
15.4•t + 11.6•h = 38.51
10.2•t + 7.3•h = 24.84
11.6h+15.4t = 38.51
7.3h+10.2t = 24.84
h = 87
50
= 1.74
t = 119
100
= 1.19
Evaluate 3√-8. Use pencil and paper. Explain how you can check that your result is correct. Show your work.
Answer:
?, the value does not exist because you can't square root a negative value.
Step-by-step explanation:
root 8 can be simplified but in this case, its negative so answer D.N.E.
= 3 x √-8
= D.N.E.
Answer:-2
-2 times -2 times -2 = -8
Lisa is traveling down the highway at 60 miles per hour. Which expression shows the distance she will have traveled after h hours?
A.
60 + h
B.
60 × h
C.
60 - h
D.
60 ÷ h
Answer:
B.
60 x h
Step-by-step explanation:
Because in she can 60 mph so for every hour she can drive 60 miles. And to find out the total miles she can drive in h hours we would have to multiply
PLZ HELP ME! 20 POINTS AND A BRAINLIEST!
Find if they are equal or not: y + 5 = 7 and 5y = 10 PLEASE SHOW STEPS!!!
Answer: They are equal
Step-by-step explanation:
Y+5=7 subtract 5 from both sides
Y=2
5Y=10 divide both sides by 5
Y=2
Simplify the expression by distributing and combining like terms.
Answer:
cOULD BE
Step-by-step explanation:
Step-by-step explanation:
Distribute first: 0.3(-4x+20), multiply 0.3 by -4x and 0.3 by 20, to get -1.2x+6. Then, add -1.2x and 8.8x, which gives you 7.6x.
The final answer is 7.6x-7.
Which equation is the slope-intercept form of the equation of the line that passes through (1, 2) and is parallel to 4x - 2y = 6?
Answer:
The equation of the parallel line is y = 2x
Step-by-step explanation:
The slope-intercept form of the linear equation is:
y = m x + b, where
m is the slope of the line b is the y-intercept (value y at x = 0)Parallel lines have the same slopes and different y-intercepts
∵ The equation of the given line is 4x - 2y = 6
→ To find the slope of this line re-arrange it to be in the
slope-intercept form Subtract 4x from both sides to move x to
the right side
∵ 4x - 4x - 2y = 6 - 4x
∴ -2y = 6 - 4x
→ Divide both sides by -2 to make the coefficient of y = 1
∵ [tex]\frac{-2y}{-2}=\frac{6}{-2}-\frac{4x}{-2}[/tex]
∴ y = -3 - (-2x)
∴ y = -3 + 2x
→ Swithch -3 and 2x
∴ y = 2x - 3
→ Compare it by the form of the equation above to find m
∴ m = 2
∴ The slope of the given line is 2
∵ The two lines are parallel
∴ The slope of the parallel line is 2
→ Substitute it in the form of the equation above
∴ y = 2x + b
→ To find b substitute x and y in the equation by the coordinates
of any point on the line
∵ The line passes through the point (1, 2)
∴ x = 1 and y = 2
∵ 2 = 2(1) + b
∴ 2 = 2 + b
→ Subtract 2 from both sides to find b
∴ 2 - 2 = 2 - 2 + b
∴ 0 = b
∴ y = 2x
The equation of the parallel line is y = 2x
GIVING BRAINLIEST TO WHOEVER ANSWERS FIRST!!!
Based on the graph below, which sequence of transformations is needed to carry ABCD onto its image A'B'CD?
Answer:
The third is correct.
Step-by-step explanation:
Preimage: A(2,3), B(5,6), C(8,6), D(8,3)
Image: A'(-2, 6); B'(-5,3); C'(-8,3); D'(-8,6)
Option 3.
Translation Rotation 180° Clockwise
(x, y-9) (-x,-y)
A(2,3) (2,-6) A' (-2,-6)
B(5,6) (5,-3) B' (-5,3)
C(8,6) (8,-3) C' (-8,3)
D(8,3) (8,-6) D' (-8,6)
Transformation involves changing the position of a shape.
The sequence of transformation is: (d) A translation rule by [tex]\mathbf{(x,y) \to (x, y - 9)}[/tex] and then a 180 degrees clockwise rotation about the origin
The coordinates of the pre-image is:
[tex]\mathbf{A = (2,3)}[/tex]
[tex]\mathbf{B = (5,6)}[/tex]
[tex]\mathbf{C = (8,6)}[/tex]
[tex]\mathbf{D = (8,3)}[/tex]
Of the given sequence of transformations, option (d) is correct.
The proof is as follows.
First, translate ABCD by (x, y - 9)
So, we have:
[tex]\mathbf{(x,y) \to (x, y - 9)}[/tex]
[tex]\mathbf{(2,3) \to (2, -6)}[/tex]
[tex]\mathbf{(5,6) \to (5, -3)}[/tex]
[tex]\mathbf{(8,6) \to (8, -3)}[/tex]
[tex]\mathbf{(8,3) \to (8, -6)}[/tex]
Next, rotate by 180 degrees.
The rule of this transformation is:
[tex]\mathbf{(x,y) \to (-x,-y)}[/tex]
So, we have:
[tex]\mathbf{(2,-6) \to (-2,6)}[/tex]
[tex]\mathbf{(5,-3) \to (-5,3)}[/tex]
[tex]\mathbf{(8,-3) \to (-8,3)}[/tex]
[tex]\mathbf{(8,-6) \to (-8,6)}[/tex]
From the graph, the coordinates of the image are:
[tex]\mathbf{A" = (-2, 6)}[/tex]
[tex]\mathbf{ B" = (-5,3)}[/tex]
[tex]\mathbf{C" = (-8,3)}[/tex]
[tex]\mathbf{D" = (-8,6)}[/tex]
Hence, the sequence of transformation is:
(d) A translation rule by [tex]\mathbf{(x,y) \to (x, y - 9)}[/tex] and then a 180 degrees clockwise rotation about the origin
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the complex solutions of which equation have a real component of 4.
(I'm not sure of what this is asking.)
Answer:
A.
Step-by-step explanation:
I just did this problem and guessed correctly.
The complex solutions of which equation have a real component of 4 is x² - 8x +16 +21 = 0.
What is Complex number?Complex numbers are numbers that consist of two parts — a real number and an imaginary number.
On solving all equation the correct one is x² - 8x +16 = -21.
Using discriminant method calculating the roots
x² - 8x +16 +21 = 0
x² - 8x + 37 = 0
x= -b ± √b² -4ac / 2a
x= 8 ± √ -8² - 4*1 * (37) /2a
x= 8 ± √- 84 / 2
x= 8 ± √2² *(- 21) /2
x=( 8 ± √2² *√21 i)/2
x= 8 / 2 ± 2i√21/2
x= 4 ± √21 i
So, x = 4+ √21 i and x= 4 - √21 i
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A model of the Empire State building is 8 inches high. If the actual Empire State building is 1,200 feet tall, what is the scale factor between the model and the actual building?"
Answer:
Every inch is represents 150 feet
Use the property to complete the statement.
1. Transitive property of Equality: If a=bc and bc=de, then...
2. Substitution Property of Equality: If x = 3c and r = 5x + 7, then..
Answer:
The answer is b and r=5x+7 is 35x
Step-by-step explanation:
Hello, 30 POINTS + BRAINLIEST If correct and has a long explanation. I looked at the same thing in other places but I think those people misread some parts. I will put a parenthesis around the parts you should read carefully. Thank you so much!
Please take notice that it says how long it took him to practice EACH SWIMMING EVENT and not how long he practiced every day. Thank you so so much!
_______________________________________________________
Trayvon recorded the number of minutes he spent practicing each (swimming event) over three days. He recorded his times in the table below.
Trayvon’s Swim Practice Times
Monday Wednesday Friday
Backstroke 12.5 min 15.67 min 9.32 min
Butterfly 14.333 min 12.1 min 10.78 min
Which statement explains how to find the event Trayvon spent more time practicing?
A Compare the sum 12.50 + 15.67 + 9.32 = 37.49 to the sum 14.333 + 12.100 + 10.780 = 37.213; he spent more time practicing the backstroke than the butterfly.
B Compare the sum 12.05 + 15.67 + 9.32 = 37.04 to the sum 14.333 + 12.001 + 10.078 = 36.412; he spent more time practicing the backstroke than the butterfly.
C Compare the sum 12.500 + 14.333 = 26.833 to the sum 15.67 + 12.10 = 27.77 and to the sum 9.32 + 10.78 = 20.1; he spent more time practicing on Wednesday than on the other days.
D Compare the sum 12.005 + 14.333 = 26.338 to the sum 15.67 + 12.01 = 27.68 and to the sum 9.32 + 10.78 = 20.1; he spent more time practicing on Wednesday than on the other days.
Answer:
A
Step-by-step explanation:
We have a table listing the number of minutes Trayvon practiced the Backstroke and Butterfly on Monday, Wednesday, and Friday.
We want to find event that Trayvon spent more time practicing.
To do so, we add up all the minutes of one event and compare this to the total minutes of the other event.
Therefore, we can eliminate options C and D. These two options evaluate the time on Wednesday compared to other days, but we want to do is to find which event did Trayvon spend the longest on.
So, let's add up all the minutes spent doing the Backstroke. Trayvon over the course of the three days spent 12.5 mins, 15.67 mins, and 9.32 mins.
Therefore, the total minutes Trayvon spend practicing the Backstroke is:
[tex]12.5+15.67+9.32=37.49\text{ mins}[/tex]
Now, let's add up all the minutes spent doing the Butterfly. Trayvon spent 14.333 mins, 12.1 mins, and 10.78 mins over the course of three days. So, the total time spent doing the Butterfly is:
[tex]14.333+12.1+10.78=37.213\text{ mins}[/tex]
Trayvon spent a total of 37.49 minutes doing the Backstroke and 37.213 minutes doing the Butterfly.
37.49 is greater than 37.213. So, Trayvon spent more time practicing the Backstroke.
So, our correct answer is A.
There are some number and calculation errors in B.
And we're done!
Answer:
C
Step-by-step explanation:
On Monday he spent 12.5 min on backstroke and 14.33 min on butterfly.
He spent 26.83 min practicing at the Monday event.
On Wednesday: 15.67 min on backstroke and 12.1 min on butterfly.
He spent 27.77 min on practicing at the Wednesday event.
On Friday: 2.32 min on backstroke and 10.78 min on butterfly.
He spent 13.1 on practicing at the Friday event.
So, he spent more time at the Wednesday event.