The y-intercept of the graph of y = x2 is shifted up 3 units.
Exponential equationThe standard exponential equation is expressed as y = ab^x. Exponential equation is inverse of logarithmic equation.
Translation of coordinatesTranslations is a transformation technique that changes the position of an object from one point on the plane to another.
Given the parent function f(x) = x^2
If the function is shifted 3 units up, the function g(x) is derived by adding 3 to the function f(x). The resulting function is given as;
g(x) = f(x) + 3
g(x) = x^2 + 3
Hence the equation of the new graph g(x) is expressed as g(x) = x^2 + 3
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Please help, need for math hw and cant figure it out
The standard form of the quadratic function f(x) = -3x^2 + 6x - 2 is f(x) = -3x^2 + 6x - 2
How to represent the quadratic function in standard form?The quadratic function is given as
f(x) = -3x^2 + 6x - 2
The standard form of a quadratic function is represented as:
f(x) = ax^2 + bx + c
When both equations are compared, we can see that the function f(x) = -3x^2 + 6x - 2 is already in standard form
Where
a = -3
b = 6
c = -2
Hence, the standard form of the quadratic function f(x) = -3x^2 + 6x - 2 is f(x) = -3x^2 + 6x - 2
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A farmer finds there is a linear relationship between the number of bean stalks, n , she plants and the yield, y , each plant produces. When she plants 30 stalks, each plant yields 25 oz of beans. When she plants 32 stalks, each plant produces 24 oz of beans. Find a linear relationship in the form y=mn+b that gives the yield when n stalks are planted.
Answer:
y = -1/2n +40
Step-by-step explanation:
We are given two ordered pairs (stalks, ounces) and asked for the slope-intercept form equation of the line through them.
SlopeThe slope of the desired line can be found from the formula ...
m = (y2 -y1)/(x2 -x1)
For the given points (30, 25) and (32, 24), the slope is ...
m = (24 -25)/(32 -30) = -1/2
Y-interceptThe y-intercept of the desired line can be found from the formula ...
b = y -mn
b = 25 -(-1/2)(30) = 25 +15 = 40
Slope-intercept equationThe slope-intercept equation of a line is ...
y = mn +b . . . . . line with slope m and y-intercept b
y = -1/2n +40 . . . . . . line with slope -1/2 and y-intercept 40
The linear relationship between stalks (n) and yield (y) is ...
y = -1/2n +40
Which of the LCM (40,120,150)?
Answer:
2400
Step-by-step explanation:
40 = 2^3 * 5
120 = 2^5 * 5
150 = 2 * 3 * 5^2
LCM = 2^5 * 3 * 5^2
Which of the following represents a quadratic function?
a. y = 3x - 2
b. y=6+5x + x²
c. x³10x = 21
d. y= 2² +4
Answer:
○ [tex]y = 6 + 5x + x^2[/tex]
Explanation:
What is a quadratic equation?A quadratic equation is an algebraic equation where the highest power of [tex]x[/tex] is 2. The general form of a quadratic equation is as follows:
[tex]\boxed{ax^2 + bx + c = 0}[/tex],
where a, b, and c represent known constants, and [tex]x[/tex] is the unknown.
In this question, if you take a look at the second option, you will see that it is possible to rearrange the equation to make it look the general form:
[tex]y = 6 + 5x + x^2[/tex]
⇒ [tex]y = x^2 + 5x + 6[/tex]
Therefore, this equation is quadratic.
The other three options are not quadratic equations because none of them have an [tex]x^2[/tex] term in them.
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
[tex]\leadsto[/tex] A quadratic equation is an algebraic equation of the second degree. The formula is:
▪ [tex]\longrightarrow \sf{y = ax^2 + bx + c}[/tex]
This can also be written as:
▪ [tex]\longrightarrow \sf{y = c + bx+ax^2}[/tex]
Comparing the equation above with each of the options, the equation that represents a quadratic function is:
[tex]\longrightarrow \sf{y=6+5 + x^2}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex] \large\bm{b. \: y=6+5x + x^2}[/tex]
The dialogue of a square is X units what is the area of the square in terms of X
The area of the square in terms of x unit is x²/ 2
Diagonal of a square
The expression for the diagonal of a square is written as'
d^2=s^2+s^2
Where
s² is the area of the squared² is the diagonal of the same squareBut from the given question we have that the diagonal of the said square is 'x'
Now, let's substitute the values into the expression of the diagonal given above,
d^2=s^2+s^2
d² = s² + s²
We have,
x² = s² + s²
Collect and add like terms
x² = 2s²
But we know that s² represents the area of the square
So,
x² = 2 × area
Make 'area' subject of formula
Area = x²/ 2
Now, we can say that the area of the square in terms of x units is x²/2
Therefore, the area of the square in terms of x unit is x²/ 2
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Donna has a $300 loan through the bank she is charged a simple rate The total interest she paid on the loan was $63 As a percentage what was the annual interest rate on her loan
The annual interest rate is 21%
How to determine the annual interest rate?The given parameters are
Loan Amount, P = $300
Interest, I = $63
Number of years, T = 1
The annual interest rate is calculated as
I = PRT
Substitute the known values in the above equation
63 = 300 * R * 1
Evaluate the product
300R = 63
Divide through by 300
R = 21%
Hence, the annual interest rate is 21%
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832 x156 show your work
Answer:
129792
Step-by-step explanation:
156
× 832
----------
312
468
+ 1248
---------------
129792
At the beach, Nardia collected triple the number of seashells that Pierre did. Together, they collected 52 seashells. Which equations represents p, the number of seashells that Pierre collected.
3 p + p = 52
3 + p = 52
52 + p = 3 p
52 + p = 3
Answer:
A
Step-by-step explanation:
p = Pierre shells
Nardia shells = 3p
3p + p = 52
Answer:
a
Step-by-step explanation:
Solve for x
A. 4
B. 7
C. 1
D. 9
The value of x when the secants intersect is 4
How to find side when two secant intersect?A secant of a circle is a line that connects two distinct points on a curve.
The secant touches two sides of the circumference of a circle.
Therefore, using secant rule,
4(x + 2 + 4) = 5(x - 1 + 5)
Hence,
4(x + 6) = 5(x + 4)
Hence, open the brackets
4x + 24 = 5x + 20
Therefore, subtract 4x from both sides
4x - 4x + 24 = 5x - 4x + 20
24 = x + 20
subtract 20 from both sides
24 - 20 = x + 20 - 20
x = 4
Therefore, the value of x is 4.
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find the domain of the function expressed by the formula:
y=1/x-7
The domain of the function is x ≠ 7
How to determine the domain?The function is given as:
y = 1/x - 7
Set the denominator not equal to 0
x - 7 ≠ 0
Add 7 to both sides
x ≠ 7
Hence, the domain of the function is x ≠ 7
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What is the equation of the circle that has its center at -26,120 and passed through the origin
well, first off let's check those two points, we know it's centerd at (-26 , 120) and we also know it passes through (0 , 0), so the distance between those two points is its radius
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{-26}~,~\stackrel{y_2}{120})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{(~~-26 - 0~~)^2 + (~~120 - 0~~)^2} \implies r=\sqrt{(-26)^2 + (120 )^2} \\\\\\ r=\sqrt{( -26 )^2 + ( 120 )^2} \implies r=\sqrt{ 676 + 14400 } \implies r=\sqrt{ 15076 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-26}{h}~~,~~\underset{120}{k})}\qquad \stackrel{radius}{\underset{\sqrt{15076}}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-26) ~~ )^2 ~~ + ~~ ( ~~ y-120 ~~ )^2~~ = ~~(\sqrt{15076})^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (x+26)^2+(y-120)^2 = 15076~\hfill[/tex]
y+6=5(x-4)
wtirte the formula for f(x) in terms of x
The formula for f(x) in y + 6 = 5(x - 4) in terms of x is f(x) = 5(x - 4)- 6
What is a linear equation?A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to rewrite the formula?A system of linear equations is a collection of at least two linear equations.
In this case, the linear function in the question is given as:
y + 6 = 5(x - 4)
Subtract 6 from both sides of the equation
y + 6 - 6 = 5(x - 4) - 6
Evaluate the difference in the above equation
y = 5(x - 4) - 6
Express the above equation as a function f(x) i.e. we express y as a function of x
f(x) = 5(x - 4) - 6
Hence, the formula for f(x) in y + 6 = 5(x - 4) in terms of x is f(x) = 5(x - 4) - 6
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After descending 8.25 feet, a bird is now
at a height of 16.5 feet. What was the initial
height of the bird?
2.) A shop sells oranges at 6 for N100. A trader sells the same kind of oranges at 8 for N120.
Which price is cheaper, by how much per orange?
The cheaper price among this set of orange sales is the one done by trader B, who sells 8 for N120.
How is the cheaper price determined?The cheaper price can be computed by finding out the price per unit.
Data and Calculations:Price of Set Unit Price
Sale of 6 oranges N100 N16.67 (N100/6)
Sale of 8 oranges N120 N15.00 (N120/8)
Thus, selling 8 oranges for N120 is cheaper than selling 6 oranges for N100, and N1.67.
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X is 30% of Y and Y is 45% of 600. What is the value of X?
Answer:
X = 81
Step-by-step explanation:
600 × 0.45 = 270
270 × 0.3 = 81
X = 81
A. What are the coordinates of R’ if R (-2, 7) is dilated around the origin with k=3?
B. What are the coordinates of T’ if T (4,-1) is dilated by a scale factor of ½ with R as the center of the dilation?
A: The coordinates of the point R' are (- 6, 21).
B: The coordinates of the point T' are (1, 3).
How to generate new points by definition of dilation
In this question we must make use of rigid transformations to find the location of new points, rigid transformations are transformations used in geometric loci such that Euclidean distance is conserved. In this case, we need to use a kind of rigid transformation known as dilation, which is defined below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)] (1)
Where:
O(x, y) - Center of dilationk - Dilation factorP(x, y) - Original pointP'(x, y) - Resulting pointPart A - If we know that O(x, y) = (0, 0), R(x, y) = (- 2, 7) and k = 3, then the coordinates of point R' are:
R'(x, y) = (0, 0) + 3 · [(- 2, 7) - (0, 0)]
R'(x, y) = (- 6, 21)
Part B - If we know that O(x, y) = (- 2, 7), T(x, y) = (4, - 1) and k = 1/2, then the coordinates of point T' are:
T'(x, y) = (- 2, 7) + (1 / 2) · [(4, - 1) - (- 2, 7)]
T'(x, y) = (- 2, 7) + (1 / 2) · (6, - 8)
T'(x, y) = (- 2, 7) + (3, - 4)
T'(x, y) = (1, 3)
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kerri said that the quotient of 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths /5 do you agree with Kerris reasoning?
Kerris reasoning that 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths/5 is correct
How to interpret Kerris reasoning?The quotient is given as:
4.2/5
Kerris reasoning is that
4.2/5 is approximately 0.8
We start by calculating the actual value of the quotient 4.2/5
Using a calculator, we have:
4.2/5 = 0.84
Approximate to the nearest tenth
4.2/5 = 0.8
This means that Kerris reasoning that 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths/5 is correct
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How many workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days?
Considering the simple inverse rule of three, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.
Inversely proportional relationshipTwo variables are related when a change in one of them causes a change in the other.
Two variables have an inversely proportional relationship when an increase in one variable causes the other to decrease or, analogously, a decrease in one causes the other to increase.
In other words, two magnitudes are inversely proportional when as one increases, the other decreases in the same proportion, and as the first decreases, the second increases in the same proportion.
Simple inverse rule of threeThe simple inverse rule of three is used when the problem deals with two inversely proportional magnitudes where the amount of one of a magnitude corresponding to a given amount of the other magnitude must be calculated.
To carry out an inverse rule of three, it must be taken into account that if for a value A of one magnitude, there is a value B of the other magnitude, while for a value of C of the first magnitude, the second magnitude is will correspond a value of X:
A → B
C → X
So: [tex]X=\frac{AxB}{C}[/tex]
Amount of workers neededThe number of people who perform a task is inversely proportional to the time it takes: a greater number of workers corresponds to less time to perform the task. Then:
9 days → 8 workers
6 days → amount of workers
So:[tex]amount of workers=\frac{9 daysx8 workers}{6 days}[/tex]
amount of workers= 12 workers
Finally, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.
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25(0.3x-4)-5(1.5x-6)+100·13/4
Answer:
255 (assuming x is the variable x)
340 (assuming x is the multiplication sign)
See explanation below.
Step-by-step explanation:
I assume that x is the variable x.
25(0.3x-4)-5(1.5x-6)+100·13/4 =
= 7.5x - 100 - 7.5x + 30 + 25 × 13
= -70 + 325
= 255
If my assumption above is incorrect, and x really means the multiplication sign, then we have this:
25(0.3×-4)-5(1.5×-6)+100·13/4 =
= 25(-1.2) - 5(-9) + 100(3.25)
= -30 + 45 + 325
= 340
if im taking a 32 hour course and ive completed 73% of it how much time do i have left
Answer:
8.64 hours, so
8 hours, 38 mins, 24 seconds
Just find that 27% you have left, then find how much that 27% is in terms of time.
It might be wrong so double check it please.
Answer:
8.64 hours
which is 8hrs 38mins and 24secs
Step-by-step explanation:
If you've completed 73% then you have 27% left to go still. (100-73 = 27)
27% of 32
= .27×32
= 8.64 hours left
That is 8hrs and .64 of an hour .64×60=38.4 mins
which is 38 mins and .4 of a minute.
.4×60 = 24secs
Probably you will just round this answer.
i need help pls.............
Answer:
P = 6750n +7800rn ≤ 19r ≤ 31160n +620r ≤ 8110n = 19r = 8190,650 peopleStep-by-step explanation:
This linear programming problem is described by an objective function and constraints on the variables. A graphical solution works well.
Objective functionThe goal is to maximize the number of people exposed to the company's ad(s). The number of people reached is the sum of the products of the number of ads and the number reached per ad.
For n newspaper ads, we are told that 6750n people are reached.
For r radio ads, we are told that 7800r people are reached.
The total number of people reached is ...
P = 6750n +7800r . . . . . . . the function we wish to maximize
Newspaper adsWe can run at most 19 newpaper ads:
n ≤ 19
Radio adsWe can run at most 31 radio ads:
r ≤ 31
BudgetThe cost of n newspaper ads will be $160n.
The cost of r radio ads will be $620r.
We must stay within a budget for the ads, $8100:
160n +620r ≤ 8110
SolutionThe white area in the first quadrant of the attached graph represents the feasible solution space. (We reversed the inequality symbol in each inequality so the solution space would be white, not triple-shaded.) The corners of the solution space represent possible (n, r) pairs where the objective function might be maximized.
The solid red line on the graph shows the maximum value the objective function might have, and the (n, r) pairs that would give that maximum value. The value of the objective function increases the farther the line is from the origin. Drawing the line on the graph lets us readily identify the (n, r) coordinate pair that will place this line as far as possible from the origin, maximizing P. We find that to be (n, r) = (19, 8).
the number of newspaper ads to run is 19the number of radio ads to run is 8the group exposure is (6750)(19) +(7800)(8) = 190,650cual es el valor x-3=11
Pls need help 100 points and crown if right!!!
Marlene only has enough ingredients to make a 1/3
batch of cookies. For the smaller batch, she only needs 3/4
cup of sugar. How much sugar does the recipe for a full batch of cookies call for? Include all your work in your answer.
Answer:
[tex]\sf 2\dfrac{1}{4}\ cups \ of \ sugar[/tex]
Explanation:
Let the full batch be x
Here given:
3/4 cup of sugar required to make 1/3 batch of cookies
Build equation:
[tex]\sf \rightarrow \dfrac{1}{3}x = \dfrac{3}{4} \ cup \ of \ sugar[/tex]
Solve:
[tex]\sf \rightarrow x = \dfrac{3(3)}{1(4)}[/tex]
[tex]\sf \rightarrow x = \dfrac{9}{4}[/tex]
[tex]\rightarrow \sf x = 2\dfrac{1}{4}[/tex]
Answer:
2 2\3 cups of sugar.
Step-by-step explanation:
Find the value of x.
Answer:
x = 106 degrees
Step-by-step explanation:
x + 104 + 40 + 110 = 360
x + 254 (No more 254)
- 254 (Again no more 254)
x = 106
A car traveled at an average speed of 80 km/h for 5 hours. What was
the distance traveled?
Answer:
400 km
Step-by-step explanation:
Distance = rate times time
Distance = 80(5)
Distance = 400
The function f(x) is shown in the graph
f(a)
Which type of function describes ((x)?
© Exponential
O Logarithmic
O Rational
O Polynomial
Answer:
the function is an exponential funtion.
Step-by-step explanation:
learned it
4. Find the value of x & y from the following equation 4x+5y=90, x+y=20 a. 10, 15 b. 10, 5 c. 10, 8 d. 10, 10
Answer:
d. 10, 10
Step-by-step explanation:
4(10)+5(10) = 40 + 50 = 90
10 + 10 = 20
Hope this helps
An equation is formed of two equal expressions. In the two of the given equations, the value of x and y are 10 and 10, respectively. The correct option is D.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the two of the equation, which can be named as,
4x+5y=90 ...... equation 1
x+y=20 ............ equation 2
Solve the second equation for x,
x + y = 20
x = 20 - y ................ equation 3
In the first equation substitute the value of x from the third equation,
4x + 5y = 90
4(20 - y) + 5y = 90
Solving the equation for y,
80 - 4y + 5y = 90
y = 90 - 80
y = 10
Substitute the value of y in the second equation, to get the value of x,
x + y = 20
x + 10 = 20
x = 20 - 10
x = 10
Hence, In the two of the given equations, the value of x and y are 10 and 10, respectively.
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the sum of three numbers is 3068.Two of the numbers are 1266 and 1755,find the third number
Answer:
47
Step-by-step explanation:
3068 - 1266 - 1755 = 47
Answer:
The third number is 47.
Step-by-step explanation:
The sum of three numbers is 3068 - this can be expressed mathematically as:
[tex]\displaystyle{x + y + z = 3068}[/tex]
Given that two of the numbers are 1266 and 1755 (in order) then substitute x = 1266 and y = 1755:
[tex]\displaystyle{1266 + 1755 + z = 3068}[/tex]
Find the third number - solve for z-variable:
[tex]\displaystyle{3021 + z = 3068}\\\\\displaystyle{z = 3068-3021}\\\\\displaystyle{z = 47}[/tex]
Therefore, the third number is 47.
Twelve different video games showing drugs were observed. The duration times of drugs were recorded, with the times (seconds) listed below. Assume that these sample data are used with a 0.01 significance level in a test of the claim that the population mean is greater than 75 sec. If we want to construct a confidence interval to be used for testing that claim, what confidence level should be used for a confidence interval? If the confidence interval is found to be -34.1 sec < μ < 238.3 sec, what should we conclude about the claim?
88 15 537 53 0 52 197 40 182 0 2 59
1.) The confidence level should be _____%
2.) What should we conclude about the claim?
The given confidence interval __(contains / does not contain)___ the value of 75 sec, so there ___( is / is not )___ sufficient evidence to support the claim that the mean is greater than 75 sec.
_____________________________________________
NOTE: Please explain like I'm five. I'm not understanding why the confidence level should be anything but 90% and I don't know *why* we would conclude what we would conclude about this claim.
The answers to the questions are:
1. The confidence level is 99 percent.
2. We have to conclude that there is no sufficient evidence available to support this claim because the Confidence interval contains 75 sec.
How to solve for the confidence level1. The confidence level here should be
1- 0.01 = 0.99
= 99 percent
Given that, 99% confidence interval for population mean (μ) is (-34.1 sec u< u < 264.1 ) seconds.
We are to test the claim that the population mean is greater than 75 sec.
2.
The given confidence interval contains the value of 75 sec, so there is not sufficient evidence to support the claim that the mean is greater than 75 sec.
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Write a polynomial that has a GCF of 7m and another with a GCF of 2ab squared.
The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²
The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³
Writing PolynomialsFrom the question, we are to write a polynomial that has a GCF of 7m
That is,
We are to write a polynomial that has a greatest common factor of 7m
Writing the polynomial
14mn - 21m + 49m²n + 7mn²
The polynomial above has a greatest common factor of 7m. That is, 7m is the greatest factor that can divide each of the terms
We are to write a polynomial with a GCF of 2ab²
Writing the polynomial
6a²b² - 8ab³ + 4a³b² + 2a³b³
The polynomial above has a greatest common factor of 2ab². That is, 2ab² is the greatest factor that can divide each of the terms
Hence,
The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²
The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³
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