What are the x-intercepts of the quadratic function? f(x)=x2+2x−24
Answers
Answer:
Just took the test the answers are -6 and 4 for anyone else wondering! :)
Step-by-step explanation:
PS. Use the site called "Desmos" and type your function in the box and just find where it crosses the x axis!
Related Questions
Determine the 10th term 0.1,0.5,2.5
Answers
An=AR^n-1
A(10)=0.1(5)^(10-1)
A(10)=195312.5
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the second equation is substituted into the first equation. 3x + 2y = −21 x − 3y = 4
Answers
[tex] \left \{ {{3x+2y=-21} \atop {x-3y=4}} \right. \\\\ \left \{ {{3x+2y=-21} \atop {x=4+3y}} \right. \\\\ \left \{ {{3(4+3y)+2y=-21} \atop {x=4+3y}} \right. \\\\ \left \{ {{12+9y+2y=-21} \atop {x=4+3y}} \right. \\\\ \left \{ {{12+11y=-21} \atop {x=4+3y}} \right. \\\\ \left \{ {{11y=-21-12} \atop {x=4+3y}} \right. \\\\ \left \{ {{11y=-33} \atop {x=4+3y}} \right. \\\\ \left \{ {{y=-3} \atop {x=4+3(-3)}} \right. \\\\ \left \{ {{y=-3} \atop {x=5}} \right. \\\\ Sol=\{(5,-3)\}\\\\ [/tex]
1400 principal earning 7% compounded monthly after 22 years
Answers
The future value of a $1,400 investment at a 7% interest rate compounded monthly over 22 years using the compound interest formula is $44,923.
The question regards a principal amount of $1,400 earning a 7% interest rate compounded monthly over 22 years. To calculate the future value of this investment, one would typically use the compound interest formula:
[tex]A = P(1 +rn)^n[/tex]
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount ($1,400 in this case).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for in years.
To calculate the future value using our example, you can substitute the given values into the formula:
A = [tex]1400(1+(0.07){12})^{12*22}[/tex] = 44923
After 22 years, the balance in the account with a $1,400 principal earning 7% interest compounded monthly would be approximately $3,808.39. This is calculated using the compound interest formula with the given parameters: principal, interest rate, compounding frequency, and time.
To find the balance in the account after 22 years with a $1,400 principal earning 7% interest compounded monthly, we use the compound interest formula:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
Where:
[tex]- \( A \) is the amount of money accumulated after \( t \) years,- \( P \) is the principal amount (the initial amount of money),- \( r \) is the annual interest rate (in decimal),- \( n \) is the number of times interest is compounded per year, and- \( t \) is the time the money is invested for in years.[/tex]
Given:
[tex]- \( P = $1,400 \),- \( r = 0.07 \) (7% interest rate converted to decimal),- \( n = 12 \) (compounded monthly),- \( t = 22 \) years.[/tex]
Plugging in the values:
[tex]\[ A = 1400 \left(1 + \frac{0.07}{12}\right)^{(12)(22)} \]\[ A = 1400 \left(1 + \frac{0.07}{12}\right)^{264} \]\[ A = 1400 \left(1 + \frac{0.005833}{1}\right)^{264} \]\[ A = 1400 \left(1.005833\right)^{264} \][/tex]
Now, we calculate:
[tex]\[ A \approx 1400 \times 2.72028 \]\[ A \approx $3,808.39 \][/tex]
So, the balance in the account after 22 years would be approximately $3,808.39.
Val rented a bicycle while she was on vacation. A paid a flat rental fee of $55 plus $8.50 each day the total cost was 123 dollars write an equation you can use to find the number of days when she rented to bicycle
Answers
Flat fee= $55
Daily cost= $8.50
d= number of days rented
Total cost equals (the daily cost times the number of days rented) plus the flat fee.
T= (Daily cost)(# Days) + Flat fee
$123= $8.50d + $55
ANSWER: $123= $8.50d + $55
Hope this helps! :)
A segment has endpoints at (3,−4) and (3,−17). How many units long is the segment?
Answers
[tex]\text{The formula of a distance between two points:}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\text{We have the points}\ (3,\ -4)\ \text{and}\ (3,\ -17).\ \text{Substitute:}\\\\d=\sqrt{(3-3)^2+(-17-(-4))^2}=\sqrt{0^2+(-13)^2}=\sqrt{(-13)^2}=13\\\\Answer:\ \boxed{13\ units}[/tex]
If the train that Megan is riding covers 60 miles in 2 hours, how fast is the train traveling?
Answers
60 miles/ 2 hours = 30 miles per hour
Derive the equation of the parabola with a focus at (0, –4) and a directrix of y = 4. (2 points)
A f(x) = –16x2
B f(x) = – x2
C f(x) = x2
D f(x) = 16x2
Answers
Equation of parabola with focus at (0,-4) and directrix is y=4 .
As we know parabola is the locus of all the points such that distance from fixed point on the parabola to fixed line directrix is same.
The parabola is opening downwards.
Let any point on parabola is (x,y).
Distance from focus(0,-4) to (x,y) = [tex]\sqrt{(x-0)^{2} +(y+4) ^{2}}=\sqrt{x^{2}+ (y+4)^{2}}[/tex]
Distance from (x,y) to directrix, y=4 is =[tex]\left | y-4 \right |[/tex]
As these distances are equal.
[tex]\sqrt{x^{2}+ (y+4)^{2}}=\left | y-4 \right |\\{x^{2}+ (y+4)^{2}=(y-4)^{2}[/tex]
→x²+y²+8 y +16 = y² - 8 y+16
→ x² = -8 y - 8 y= -16 y [ Cancelling y² and 16 from L.H.S and R.H.S ]
So , equation of parabola is , x²= - 16 y or f(x)= -x²/16
The Equation of parabola is [tex]f(x)=-\dfrac{x^2}{16}[/tex]
Equation of parabola with focus at [tex](0,-4)[/tex] and directrix is [tex]y=4[/tex] .
Parabola is the locus of all the points such that distance from fixed point on the parabola to fixed line directrix is same.
The parabola is opening downwards.
Let any point on parabola is [tex](x,y)[/tex].
Distance from focus [tex](0,-4)[/tex] to [tex](x,y)[/tex] = [tex]\sqrt{(x-0)^2+(y+4)^2[/tex]
[tex]d=\sqrt{x^2+(y+4)^2[/tex]
Distance from [tex](x,y)[/tex] to directrix, [tex]y=4[/tex] is =[tex]\left | y-4 \right |[/tex]
As these distances are equal.
[tex]\sqrt{x^2+(y+4)^2}=\left | y-4 \right |[/tex]
[tex]d={x^2+(y+4)^2=(y-4)^2[/tex]
[tex]x^2+y^2+8y+16=y^2-8y+16[/tex]
[tex]x^2=-8y-8y[/tex]
[tex]x^2=-16y[/tex]
[tex]y=\dfrac{-x^2}{16}[/tex]
So, the Equation of parabola is [tex]f(x)=-\dfrac{x^2}{16}[/tex]
Learn more about parabola here:
https://brainly.com/question/21685473?referrer=searchResults
Suppose that 1% of the students in a school have head lice and the test for head lice is accurate 75% of the time. What is the probability that a student in the school has head lice, given that the test came back positive?,
Answers
Imagine there are 10,000 students in the school. If 1% have lice, that makes 100 students that have it and 9,900 that don't.
Assume the test was given to all students. Out of the 100 that have lice, only 75 would get a positive test because it is only 75% accurate.
Now, out of the 9,900 student who don't have lice, 25% of them would get a positive test, because the test is only 75% accurate. That is 2,475 false positive tests!!!
So we had a total of 2,550 positive tests, but only 75 of those students actually have lice. 75 out of 2550 is 2.9%.
If the test is positive, there is a 2.9% chance that the subject has head lice.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Assume that the school has 100 students. If 1 student has lice and 99 others don't, that means one student has lice.
Suppose that all students took the test. Only 0.75 of 1 people with lice would have a positive test result because it is only 75% accurate.
Because the test is only 75% accurate, out of the 99 students who do not have lice, 25% would test positive. 24.75 false positive tests are involved here!
So far, 25.50 of our students have had positive tests, although only 0.75 of them truly have lice. 2.9% is 0.75 out of 25.5.
learn more about conditional probability here :
https://brainly.com/question/30144287
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Which are the solutions of this equation 4x2-7x=3x+24
Answers
Answer: x = -3/2 x =4
Answer:
3rd and last choice on ed
Step-by-step explanation:
Solve the single variable equation for n.
4(-n + 4) + 2n = 2n
a. n = 4
b. no solution
c. infinitely many solutions
Answers
-4n + 16 + 2n = 2n
-4n + 16 = 0
-4n = -16
n = 4
answer
a. n = 4
Which is the best estimate for (6.3x10^-2)(9.9x10^-3) written in scientific notation?
Answers
Answer:
[tex]6 \times 10^{-4}.[/tex]Step-by-step explanation:
We are given expression [tex](6.3 \times 10^{-2})(9.9\times 10^{-3})[/tex].
In order to multiply above given expression, we need to multiply 6.3 by 9.9 first.
On multiplying 6.3 by 9.9 , we get 62.37.
Now we would multiply [tex]10^{-2} \ by \ 10^{-3}.[/tex]
Therefore,
[tex]10^{-2} \times 10^{-3}= 10^{-2-3}= 10^{-2-3} = 10^{-5}.[/tex]
Therefore,
[tex](6.3 \times 10^{-2})(9.9\times 10^{-3}) =62.37 \times 10^{-5}[/tex]
Again [tex]62.37 \times 10^{-5}[/tex] could be written as [tex]6.237 \times 10^{-4}[/tex].
Now, [tex]6.237 \times 10^{-4}[/tex] could be round to [tex]6 \times 10^{-4}.[/tex]
Therefore, correct answer is [tex]6 \times 10^{-4}.[/tex]
2. The triangles are similar. write a similarity statement for the triangles.
A. Triangle JKL ~ Triangle NPM
B. Triangle JKL~ Triagle PNM
C. Triangle JKL~ Triangle MNP
D. Triangle JKL~ Triangle PMN
Answers
Answer:
The correct option is C.
Step-by-step explanation:
In triangle JKL and MNP,
[tex]\angle J=\angle M[/tex] (Given)
[tex]\angle L=\angle P=90^{\circ}[/tex] (Given)
According to AA property of similar triangle, two triangles are similar if their two corresponding angles are same.
Here, J is corresponding angle of M, K is corresponding angle of N and L is corresponding angle of P.
Using AA property of similar triangles,
[tex]\triangle JKL\sim \triangle MNP[/tex]
Therefore the correct option is C.
10 POINTS!!! FULL ANSWER WITH FULL STEP BY STEP SOLUTION PLEASE. DO BOTH PARTS OF 1 AND ALL OF 2.
Answers
y = e^x
dy/dx = e^x The f(x) = the differentiated function. Any value that e^x can have, the derivative has the same value. x is contained in all the reals.
One B
y = x*e^x
y' = e^x + xe^x Using the multiplication rule.
You want the slope and the value of the of y to be the same. The slope is y' of the tangent line
xe^x = e^x + xe^x
e^x = 0
This happens only when x is very "small" like x = - 4444444
y = e^x * ln(x) Using the multiplication rule again, we need the slope of the line with is y'
y1 = e^x
y1' = e^x
y2 = ln(x)
y2' = 1/x
y' = e^x*ln(x) + e^x/x So at x = 1 the slope of the line =
y' = e^1*ln(1) + e^1/1
y' = e*0+e = e
y = mx + b
y = ex + b
to find b we use y= e^x ln(x)
e^x ln(x) = e*x + b
e^1 ln(1) = e*1 + b
ln(1) = 0
0 = e + b
b = - e
line equation and answer.
y = e*x - e
PLEASE HELP ASAP!!!
Max is running the concession stand at the local football game. He is selling popcorn and water. Each bag of popcorn costs $1.25 and each bottle of water costs $. 75.
He sold a total of 108 items for a total of $105.00. He needs to report the number of bags of popcorn and bottles of water that were sold.
Determine how many of each item he sold. Be sure to plug your solution back into the equation to verify that it is correct.
Having variables represent the popcorn and the water, so p for popcorn and w for water... I think the equation would be
p + w = 108
and
1.25p + .75w = 105
but after that I get kind of confused...
Answers
Solve the new equation for p.
Use your p solution to plug back into an original equation and solve for w.
Check your solutions by checking them in both original equations.
w= # of waters
QUANTITY EQUATION
p + w= 108
COST EQUATION
$1.25p + $0.75w= $105
STEP 1:
solve for one variable in cost equation
p + w= 108
subtract w from both sides
p= 108 - w
STEP 2:
substitute p=108-w in for p in cost equation
$1.25p + $0.75w= $105
1.25(108-w) + 0.75w= 105
multiply 1.25 by all in parentheses
(1.25*108)+(1.25*-w)+0.75w= 105
135 - 1.25w + 0.75w= 105
combine like terms
135 - 0.5w= 105
subtract 135 from both sides
-0.5w= -30
divide both sides by -0.5
w= 60 water bottles
STEP 3:
substitute w=60 in either equation to find p
1.25p + $0.75w= $105
1.25p + 0.75(60)= 105
1.25p + 45= 105
subtract 45 from both sides
1.25p= 60
divide both sides by 1.25
p= 48 popcorn
CHECK:
p + w= 108
60 + 48= 108
108= 108
ANSWER: There were 60 popcorn sold and 48 waters sold.
Hope this helps! :)
The cake store is having a 25\%25%25, percent off sale on all of its cakes. If the cake you want regularly costs \$9$9dollar sign, 9, how much would you save with the discount?
Answers
9*0.25 = 2.25.
You save $2.25 with the discount.
Answer:
$2.25.
Step by step explanation:
We have been given that the cake store is having a 25% off sale on all of its cakes.
To find our savings with the discount we will find 25% of $9 (regular cost of cake).
[tex]\text{Savings with the discount}=9\times\frac{25}{100}[/tex]
[tex]\text{Savings with the discount}=9\times\frac{1}{4}[/tex]
[tex]\text{Savings with the discount}=\frac{9}{4}=2.25[/tex]
Therefore, we will save $2.25 with the given discount.
will give brainlist
what is the approximate area of the figure
Answers
The rectangle is 8 cm by 14 cm, so that has an area of 112.
Now, add 25 and 112. This will give you about 137.
Answer:
the answer is 137.1
Step-by-step explanation:
Divide the figure into recognizable shapes. Find the area of each shape and add them together.
If two 6-sided number cubes are rolled, what is the probability that you will roll a 1 first and then roll a 5 with the second cube?
Answers
If you were to ask what the odds of getting a 1 and a 5, it would be higher, but the fact that they need to come in that order give you the above answer.
Final answer:
The probability of rolling a 1 first and then rolling a 5 with two 6-sided number cubes is 1/36.
Explanation:
To find the probability of rolling a 1 first and then rolling a 5 with the second cube, we need to consider the probabilities of each event separately. The probability of rolling a 1 on the first cube is 1/6, since there is only one face with a 1 out of six possible outcomes.
The probability of rolling a 5 on the second cube is also 1/6. Since these events are independent, we can multiply their probabilities to find the overall probability:
Probability of rolling a 1 first and then rolling a 5 = (1/6) * (1/6) = 1/36
35 points!
What is the area of this triangle? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answers
Here is the formula for area: ¹⁄₂ • c • b • sin(A)
¹⁄₂ • 11 • 9 • sin63
¹⁄₂ • 99 • sin63
49.5 • sin63
49.5 • .8910065242...
≈44.1
That should be the area of the triangle. The other way to do this is to just start by using the law of cosines, and then finding the height of the triangle, and then using the area formula. I believe the way I showed you is the easier way though. Message me if you have any questions.
Also make sure to include units : 44.1cm²
What is the relative minimum of the function?
Answers
(1,-5)
relative min = -5
Answer:
The required relative minimum is -5
Step-by-step explanation:
Relative minimum is the point where the graph shows its minimum point or the lowest point of the graph.
Like here, we have been given a parabolic shape so, the minimum of this parabola is the coordinate of y in its vertex point.
So, its relative minimum is -5.
Two f-18s are catapulted off an aircraft carrier and fly on courses that diverge at a 60° angle. if each flies at a constant rate of 500 mph, after how many hrs will the fighters be 1200 mi apart?
Answers
First draw a picture of an angle of 60 degrees. The vertex is the starting point of the plane and they are flying away from it.
If you drew points for the new positions of the plane and connected them, you would have triangle. The planes are flying at the same speed, so they would be isosceles triangles. And since the vertex angle is 60 degrees, the other angles have to be 60 as well. This makes it an equilateral triangles, meaning all the sides are the same.
So the distance between the planes is equal to the distance that they have flow.
Simply divide 1200 by 500 to get 2.4 hours.
Line segment AC has endpoints A (-1,-3.5) and C (5,-1). Point B is on line segment AC and is located at (0.2,-3). What is the ratio of AB/BC
Answers
The distance between two points can be thought of as a line.
To find the length of this line, you can use the distance formula:
d = √ (x2 - x1) ^ 2 + (y2 - y1) ^ 2
We have then:
AC distance:
AC = root ((5 - (-1)) ^ 2 + (-1 - (-3.5)) ^ 2) = 6.5 units
AB distance:
AB = root ((0.2 - (-1)) ^ 2 + (-3 - (-3.5)) ^ 2) = 1.3 units
BC distance:
BC = 6.5-1.3 = 5.2 units
Answer:
The ratio is:
AB / BC = (1.3) / (5.2)
Answer:
AB/BC = (1.3) / (5.2). Hope this helps :)
Step-by-step explanation:
A cup of coffee contains 130 mg of caffeine. If caffeine is eliminated from the body at a rate of 11% per hour, how much caffeine will remain in the body after 3 hours?
Write the exponential function and solve.
a.
4072-06-01-04-00_files/i0260000.jpg; 184 mg
b.
4072-06-01-04-00_files/i0260001.jpg; about 346 mg
c.
4072-06-01-04-00_files/i0260002.jpg; less than 1 mg
d.
4072-06-01-04-00_files/i0260003.jpg; about 92 mg
Answers
y(t) = a*e^(kt)
---
now:
130 mg
---
one hour from intake:
130 * (1 - 0.11) = 115.7 mg
---
y(1) = 115.7 = 130*e^(k(1))
115.7 = 130*e^k
115.7/130 = e^k
ln( 115.7/130 ) = ln( e^k )
ln( 115.7/130 ) = k
k = -0.1165338
---
three hours from intake:
y(3) = 130*e^(3k)
y(3) = 91.64597
---
answer:
three hours after drinking a cup of coffee, 91.6 mg of caffeine will remain in the body
Javier is 175% heavier than his brother. If Javier’s brother weighs 80 pounds, how much does Javier weigh?
Answers
Let us say weight of Javier is x pounds.
Weight of his bother = 80 pounds
Javier is 175 % or 1.75 times heavier than his brother.
So Javier's weight = x pounds= 1.75 *80 = 140 pounds.
Answer: Javier's weight is 140 pounds.
Help please! Math Nation Section 6 Test Yourself Practice Tool.
Answers
Answer: D) [tex]y=-5(x-5)^2+1125[/tex]
Step-by-step explanation:
Let x be the number of $2 increases in price and y be the revenue.
By using the given table , lets check all the options
A) [tex]y=(x+5)^2-1125[/tex]
For x=1, y=1045
[tex]y=(1+5)^2-1125=36-1125=-1089\\\\But\ 1045\neq-1089[/tex]
B) [tex]y=(x-5)^2+1125[/tex]
For x=1, y=1045
[tex]y=(1-5)^2+1125=14+1125=1139\\\But\ 1045\neq1139[/tex]
C) [tex]y=-5(x+5)^2-1125[/tex]
[tex]y=-5(1+5)^2-1125=-5(36)-1125=-1305\\\\But\ 1045\neq-1305[/tex]
D) [tex]y=-5(x-5)^2+1125[/tex]
[tex]y=-5(1-5)^2+1125=-5(16)+1125=1045[/tex]
Hence, this is the quadratic equation that models the data.
Based on the table of values, an equation of the quadratic that models the data is: D. [tex]y = -5(x-5 ) ^2+ 1125[/tex]
In Mathematics and Euclidean Geometry, the vertex form of a quadratic function is represented by the following mathematical equation:
[tex]y = a(x - h)^2 + k[/tex]
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.In order to determine an equation for the line of best fit or quadratic regression line that models the data points contained in the table of values, we would have to use a graphing calculator (Microsoft Excel).
Based on the scatter plot (see attachment) which models the relationship between the number of $2 increase in price (in dollars), x and revenue, y, the quadratic regression is given by:
[tex]y =-5x^2 + 50x + 1000\\\\y = -5(x^2 - 10x) + 1000\\\\y = -5(x^2 - 10x + (\frac{10}{2})^2 ) + 1000+ (\frac{10}{2})^2\\\\y = -5(x^2 - 10x + 25 ) + 1000+25\\\\y = -5(x-5 ) ^2+ 1125[/tex]
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
The coefficient of the x term is -32.
A parallelogram has vertices E(−8, 3), F(2, −2), G(−1, 3), and H(−5, −2). What are the coordinates of the midpoint of each diagonal?
(3, −0.5)
(−4.5, 3)
(−3, 0.5)
(0.5, −1.5)
Answers
Then, join the points to find the parallelogram sought.
We observe that the half point of both diagonals is the same.
Therefore, it is enough to calculate the half point of only one of the diagonals.
The half point is calculated according to the expression:
(((x1 + x2) / 2), ((y1 + y2) / 2))
Substituting values of one of the diagonals:
(((-1-5) / 2), ((3-2) / 2))
(-3, 0.5)
Answer:
(-3, 0.5)
Which answer describes the transformation of f (x) = x^2 −1 to g(x)=(x+2)^2−1 ?
a horizontal compression by a factor 2
a vertical stretch by a factor of 2
a horizontal translation 2 units to the left
a vertical translation 2 units down
Answers
In this case, we are changing the variable x before it is being squared. This will have the effect of changing the input of the function. Imagine input 2 into the equation. Your first step would be to add 2. Therefore, you would need to start with a negative 2 to get us back to 0, or the beginning.
Since -2 is to the left of 0, the graph is moving 2 units to the left.
6. Angle ABC is congruent to which angle?
1. Angle CAB
2. Angle XYZ
3. Angle XZY
4. Angle YZX
~
7.
Side CA is congruent to which side?
1. ZX
2.YX
3.XY
4.YZ
Answers
7. ZX
Answer:
[tex]\angle ABC \cong \angle XYZ[/tex]
[tex]CA \cong ZX[/tex]
Step-by-step explanation:
According to the given figures:
[tex]\angle ABC \cong \angle XYZ[/tex]
Also,
[tex]CA \cong ZX[/tex]
Therefore, the answer to the first question is Angle XYZ, and the answer to the second question is ZX.
You can deduct these answers by observing the number of line that match each pair of congruent elements.
Translate shapes , pls help me with this
Answers
B. (-3,-4)
C. (0,2)
D. (-2,-1)
Try this
Answer:
A: (-4,-2)
B: (-3,-4)
C: (0,2)
D: (-2,-1)
Hope this helps! I'm not the best at math though, so it could be incorrect.
Name the Property of Equality that justifies the statement: If m<A + M<B = M<C. Then, M<A = M<C - M<B
Transitive Property
Symmetric Property
Reflexive Property
Subtraction Property
Answers
Answer:
subtraction property
Step-by-step explanation: