The equation of the parabola in vertex form is y=-2(x-4)²+4.
Given that the vertex point is (4,4), (3,2).
The equation of a parabola in vertex form is y=a(x-h)²+k where a is called stretch coefficient and the point (h,k) is the vertex of the parabola.
A parabola with its vertex at the point (4,4), therefore h=4,k=4 and we can write
y=a(x-4)²+4
To find the value of a we use the point (3,2). Substituting on the equation we get:
y=a(x-4)²+4
2=a(3-2)²+4
2=a(1)²+4
2=a+4
2-4=a
-2=a
Then the equation of the parabola in vertex form is y=-2(x-4)²+4.
Hence, the equation of the parabola in vertex form from the given point (4,4), (3,2) is y=-2(x-4)²+4.
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according to the rational root theorem, which function has the same set of potential rational roots as the function g(x)
Option (A)'s f(x) = 3x⁵ -2x⁴ - 9x³ + x² -12 has the same set of potential rational roots as the given function g(x).
What are roots of an equation?Roots of an equation refer to the values that when put into the variable of the equation, satisfy the equation and give the required value as 0.
Given:
g(x) = 3x⁵ - 2x⁴ + 9x³ - x² + 12 = 0
To find: Function having same set of potential rational roots as g(x).
Finding:
Finding the rational roots of g(x):Let 'm' denote the rational roots of 12.=> Then, m = ±1, ±2, ±3, ±4, ±6
2. Let 'n' denote the rational roots of 3.
=> Then n = ±1, ±3
Hence, the rational roots [tex]\frac{m}{n}[/tex] will be given by: ±1, ±2, ±3, ±4, ±6, ±[tex]\frac{1}{3}[/tex], ±[tex]\frac{2}{3}[/tex], ±[tex]\frac{4}{3}[/tex].
Now, in the Option A's equation: f(x) = 3x⁵ -2x⁴ - 9x³ + x² -12,The rational roots will be taken of 12 and 3 in the same position as in g(x).
Hence, the rational roots of f(x) will also be given by: ±1, ±2, ±3, ±4, ±6, ±[tex]\frac{1}{3}[/tex], ±[tex]\frac{2}{3}[/tex], ±[tex]\frac{4}{3}[/tex].
Thus, Option (A)'s f(x) = 3x⁵ -2x⁴ - 9x³ + x² -12 has the same set of potential rational roots as the given function g(x).
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(COMPLETE QUESTION:
According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?
A).f(x) = 3x5 – 2x4 – 9x3 + x2 – 12
B).f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x
C).f(x) = 12x5 – 2x4 + 9x3 – x2 + 3
D).f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48)
driver delight has 3 circluar go cart tracks. track 1 has a radius of 60 feet. track 2 has a radius of 85 feet. track 3 has a radius of 110 feet.
Compute the circumference of track 3.
The circumference of track 3 is 691.43 feet
What is the circumference of track 3 ?The circumference of a circle is the distance round the circle. It is the perimeter of the circle. The radius of a circle is a straight line that goes from the center of the circle to its circumference.
The circumference of a circle = 2πr
Where:
r = radius π = 22/72 x (22/7) x 110 = 691.43 feet
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Samir can rent a moving truck from Company A for $135 plus $0.50 per mile or from Company B for $125 plus $0.70 per mile. Which statement is true?
Renting from Company B will be cheaper if Samir drives the truck 100 miles. Then the correct option is D.
What is a linear equation?
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let y be the total amount and x be the number of miles.
Samir can rent a moving truck from Company A for $35 plus $0.50 per mile. Then the equation will be
y = 0.5x + 35 ....1
Company B for $25 plus $0.70 per mile. then the equation will be
y = 0.7x + 25 ....2
For the same rent, the number of miles will be
0.7x + 25 = 0.5x + 35
0.2x = 10
x = 50 miles
Renting from Company B will be cheaper if Samir drives the truck 100 miles. Then the correct option is D.
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Samir can rent a moving truck from Company A for $35 plus $0.50 per mile or from
Which statement is true?
Company B for $25 plus $0.70 per mile .
A. Renting from Company A will always be cheaper.
B. Renting from Company B will always be cheaper.
C. Renting from both companies will cost the same if Samir drives the truck 50 miles.
D. Renting from Company B will be cheaper if Samir drives the truck 100 miles.
Обчислив площу поверхні Куба ребро якого дорівнює 4,2 м
Answer: I calculated the surface area of a cube whose edge is 4.2 m
Step-by-step explanation: hope this helps
A research study variable that is believed to be related to the study's variable of interest is accurately described by each of the following terms except ___________.
A research study variable that is believed to be related to the study's variable of interest is accurately described by each of the following terms except dependent.
What is a research variable?
Any variable employed in research that has a cause and effect relationship is referred to as a research variable (also known as a study variable) informally. An array of variables, including independent factors, dependent variables, and intervening variables, can be employed in a study, including research/study variables.
Independent and dependent variables are crucial in research since they provide the framework for a study to be carried out. Confounding factors, controlled variables, superfluous variables, and moderator variables are some other sorts of variables that could be used in a research.
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(Please Help) The vertex of a parabola is (−2,8) and its y-intercept is (0,4). The parabola is the boundary of a quadratic inequality. The boundary is drawn with a solid line, and the exterior of the parabola is shaded.
What is the inequality represented?
(i got it graphed like what i have already but I don't know if its right even thought i gotten it)
Using the equation of the parabola, the inequality represented is:
y ≥ -(x + 2)² + 8.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For this problem, the vertex is at (-2,8), hence:
h = -2, k = 8.
y = a(x + 2)² + 8.
The y-intercept is of (0,4), when when x = 0, y = 4, which we use to find a as follows:
4 = 4a + 8
4a = -4
a = -1.
Hence the parabola is:
y = -(x + 2)² + 8.
The exterior of the parabola is shaded, that is, the part that is above the concave down parabola, hence the inequality is:
y ≥ -(x + 2)² + 8.
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Ted works as a travel guide for a mountain resort, earning
$15.72 per hour. Ted is paid weekly, and works 40 hours in
one week. His current federal withholding per week is $69.
He works in a state with a flat-rate income tax of 4.63%. He
will receive a raise of 5% of his hourly rate. Determine the
change in Ted's net pay per paycheck, after taxes, if his new
federal withholding per week is $75.
Ted's net pay per week after the taxes is $559.09
Net Pay:
Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.
Given,
Ted works as a travel guide for a mountain resort, earning $15.72 per hour. Ted is paid weekly, and works 40 hours in one week. His current federal withholding per week is $69. He works in a state with a flat-rate income tax of 4.63%. He will receive a raise of 5% of his hourly rate.
Here we need to find the Ted's net pay per paycheck, after taxes, if his new federal withholding per week is $75.
Through the given details we know that,
Per hour pay = $15.72
Total work per week = 40
So, the total amount for a week is
=> 15.72 x 40
=> $628.8
After federal withholding tax, then the amount is
=> $628.8 - 69
=> $559.8
Now the tax is 4.63%, then
=> $559.8 x 4.63%
=> $559.8 x (4.63/100)
=> $25.91
So, the remaining amount is
=> $559.8 - $25.91
=> $533.88
Now, he will receive 5% for his hourly rate,
Then,
=> $15.72 x (5%)
=> $15.72 x (5/100)
=> 0.78
So, the increased amount is
=> $16.5
Now, the net pay is,
=> (16.5 * 40) - (75 + 25.91)
=> 660 - 100.91
=> 599.09
So, Ted's net pay per paycheck, after taxes is $559.09.
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Natalie's fifth grade classroom is 900 square feet. The length is 30 feet. What is the width of her classroom?
Answer:
30
Step-by-step explanation:
30*30 is 900
Answer:
30
Step-by-step explanation:
let x =width
900=(×)(30)
900=30×
900/30=30×/30
30=×
= 30 width
8.2 - 4.3 i really need help-
Answer:
3.9
Step-by-step explanation:
8.2-4.3=3.9
3.9+4.3=8.2
1/2 log25/4base10-2log4/5base10+log320/125base10
Answer: 1
Step-by-step explanation:
[tex]\displaystyle\\\frac{1}{2}lg\frac{25}{4} -2lg\frac{4}{5} +lg\frac{320}{125}=\\\\lg\sqrt{\frac{5^2}{2^2} } -lg(\frac{4}{5})^2+lg\frac{5*64}{5*25}=\\\\lg\sqrt{(\frac{5}{2})^2 } -lg\frac{4^2}{5^2} +lg\frac{64}{25}=\\\\[/tex]
[tex]lg\frac{5}{2} -lg\frac{16}{25}+lg\frac{64}{25} =\\\\ lg\frac{5}{2}+lg\frac{64}{25} -lg\frac{16}{25} =\\\\lg\frac{5*64}{2*25} -lg\frac{16}{25}=\\\\ lg\frac{5*2*32}{2*5*5}-lg\frac{16}{25}= \\\\lg\frac{32}{5}-lg\frac{16}{25}=\\\\lg\frac{32*25}{5*16}=\\\\lg\frac{16*2*5*5}{5*16} =\\\\lg(2*5)=\\\\lg10 =\\\\1[/tex]
Find the value of the variable and YZ if Y is between X and Z. XY= 11d, YZ=9d-2, XZ=5d+28
Answer:
d = 2
YZ = 16
Step-by-step explanation:
X-Y-Z
so XY + YZ = XZ
11d + (9d -2) = 5d + 28
11d + 9d - 5d = 28 + 2
15d = 30
d = 30/15 = 2
YZ = 9d - 2 = 9(2) - 2 = 18 - 2 = 16
joe bought a condo for $200,000. he put down 20%, which was $40,000. how much does he owe on the condo?
By taking the difference between the total cost of the condo and the amount that he already paid, we conclude that Joe owes a total of $160,000 for the condo.
How much does he owe on the condo?To find how much he owes on the condo, we need to find the difference between the total cost of the condo, which is $200,000, and the amount that he already paid, which is $40,000.
(Remember that difference means a subtraction)
It gives.
$200,000 - $40,000 = $160,000
In this way, we conclude that Joe owes a total of $160,000 for the condo.
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Find the point of intersection between the plane that contains the axis intercepts p(4, 0, 0)
The equation is 7x+11y+14z=33.
What is an equation?A mathematical statement made up of two gestures joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value for the variable x as x = 7 after solving this equation.So,
The family of planes equation passing through the intersection of the planes x+2y+3z4=0 and 2x+yz+5=0 is:
(x + 2y + 3z − 4) + k(2x + y − z + 5)=0(2k+1)x+(k+2)y+(3−k)z=4−5k ......(1)[tex]\frac{\mathrm{x}}{\left(\frac{4-5 \mathrm{k}}{2 \mathrm{k}+1}\right)}+\frac{\mathrm{y}}{\left(\frac{4-5 \mathrm{k}}{\mathrm{k}+2}\right)}+\frac{\mathrm{z}}{\left(\frac{4-5 \mathrm{k}}{3-\mathrm{k}}\right)}=1[/tex]It is assumed that the required plane's x-intercept is twice its z-intercept.
[tex]\left(\frac{4-5 \mathrm{k}}{2 \mathrm{k}+1}\right)=2\left(\frac{4-5 \mathrm{k}}{3-\mathrm{k}}\right)[/tex](4−5k) (3−k) = (4k+2) (4−5k)(4 − 5k) (3 − k − 4k −2) = 0(4 − 5k) (1 − 5k) = 04 − 5k = 0 or 1−5k = 0k = 4/5 or k = 1/5Substitute k = 4/5 in equation (1) as follows:
[tex]\left(2 \times \frac{4}{5}+1\right) x+\left(\frac{4}{5}+2\right) y+\left(3-\frac{4}{5}\right) z=4-5 \times \frac{4}{5}[/tex]7x + 11y + 14z = 15As a result, the required plane's equation is 7x+11y+14z=15.
Also,
7x+11y+14z=15 is the equation of the plane passing through the point (2,3,1) and parallel to the plane.
7(x−2) + 11(y−3) + 14(z+1) = 07x + 11y + 14z = 33Therefore, the equation is 7x+11y+14z=33.
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the complete question is given below;
Find the equation of the plane which contains the line of intersection of the planes x+2y+3z−4=0 and 2x+y−z+5=0 and whose x−intercept is twice its z−intercept. Hence, write the equation of the plane passing through the point (2,3,−1) and parallel to the plane obtained above.
Is -2.5 greater than or less than 2.1?
Answer: less
Step-by-step explanation:
Answer: The answer is less than
because negative are always less than positives
Step-by-step explanation:
I hope this helps
what would be the value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 25.32 and the sum of squares due to error (sse) is 6.89? a. 19.32 b. 15.32 c. 18.43 d. 31.89
The value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 25.32 and the sum of squares due to error (sse) is 31.89
What is regression?Regression is a statistical technique used in the fields of finance, investing, and other disciplines that aims to establish the nature and strength of the connection between a single dependent variable (often represented by Y) and a number of independent variables (known as independent variables).
The most popular variation of this method is linear regression, which is also known as simple regression or ordinary least squares (OLS).
Linear regression determines the actual linear relationship between two variables based on a line of best fit. As a result, the slope of a straight line was used to depict linear regression indicating how altering one variable impacts modifying another. In a linear regression connection, the value of one variable when the value of the other is zero is represented by the y-intercept.
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the rainfall this year was 18.6 cm this is 3.2 cm less than half of the rainfall last year what was the rainfall
Answer: 43.6 cm
Step-by-step explanation:
18.6+3.2= 21.8
21.8*2= 43.6
Helpppppp 20 pointssss mathhh
I don’t really understand I think it’s distance formula but I got it wrong pls help
Perimeter of rectangular garden = 34 ft
Area of rectangular garden = 60 ft²
What is the Perimeter and Area of a Rectangle?Perimeter = 2(length + width)
Area = (length)(width)
The rectangular garden has the following vertices:
Q(-5, 3)R(7, 3)S(7, -2)T(-5, -2)Length of the rectangular garden = QR = |-5 - 7| = |-12| = 12 units
Width of the rectangular garden = RS = |3 -(-2)| = |3 + 2| = 5 units
Perimeter = 2(length + width) = 2(12 + 5) = 34 units = 34 ft
Area = (length)(width) = (12)(5) = 60 units = 60 ft²
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5x - 2y. Could you please help me
3.5+2=2x-10help me HELP ME JIGGABOOS
What is the volume of a rectangular prism with a base area of 32 cm and a height 7cm
Answer:
224 cm³
Step-by-step explanation:
Volume = Area of base x height
V = 32 x 7
V = 224 cm³
In this question, all the required information is given so we'll simply have to solve.
[tex]\large\boxed{\bold{V= \ base \ area× \ height}}[/tex]
Now, substitute the values according to the formula.
[tex]V= \ 32 × 7[/tex]
[tex]\large\boxed{\bold{ V= \ 224 \ {cm}^{3}}}[/tex]
The answer is a whole number so we won't have to round off.
Hence, the volume of the given rectangular prism is 224 cubic centimeters.
a ball is dropped from rest. after $t$ seconds, the ball has fallen a distance $d$. relative to this location, how much farther does it fall after another 5$t$ seconds?
The ball will fall 35d after 5t seconds.
Equation Of Motion is used to define the basic concept of motion of object at various interval of times.
There are three equation of motion
[tex](i) v=u+at\\ \\ (ii) s=ut+\frac{1}{2} at^{2} \\ \\ (iii)v^{2}=u^{2} +2as[/tex] (where s=distance, v=final velocity, u=initial velocity ,t=time, a=acceleration)
According to the given question
Given distance = d
time=t
Acceleration a=g( gravity)
Using second equation of motion
[tex]d=ut+\frac{1}{2} at^{2}[/tex] ( given u=0 as the ball was at rest, a=g , s=d)
[tex]d=\frac{1}{2} gt^{2}[/tex]........(1)
Using first equation of motion
Speed after t sec
[tex]v=u+at\\ \\ v=0+gt\\ \\ v=gt[/tex] ....... (2)
Using second equation of motion distance after 5t seconds
since ball is moving with velocity "v", t=5t.
[tex]s=ut+\frac{1}{2} at^{2}\\ \\ d=v(5t)+\frac{1}{2} g(5t)^{2}[/tex]
Substituting the value v=gt from equation (2)
[tex]d=(gt)(5t)+\frac{1}{2} g(5t)^{2}\\ \\ =5gt^{2} +\frac{1}{2} g(5t)^{2}[/tex]taking LCM as 2 and solving further we get
[tex]=35(\frac{1}{2}gt^{2} )[/tex]
using equation (1) we get
=35d
Therefore , The ball will fall 35d after 5t seconds.
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PLS HELP
NOW IF POSSIBLE
Answer:
i think it is 4
Step-by-step explanation:
Ms. Hartman buys 4 pounds of potatoes for $12.76. How many pounds of potatoes could she get for $44.66?
Answer:
14
Step-by-step explanation:
44.66 / (12.76 / 4) = 14
Solve for x. 4x + 6 = 2(2x + 3)
Answer:
True for all x/infinite solutions.
Step-by-step explanation:
[tex]4x+6=2\left(2x+3\right) < - Base Equation[/tex][tex]4x+6=4x+6 < - Expand-The-Equation-and-Simplify![/tex]
[tex]4x+6-6=4x+6-6 < - Subtract-Six-From-Both-Sides![/tex]
[tex]4x=4x[/tex]
[tex]4x-4x=4x-4x < - Subtract -4x- from- both -sides![/tex]
[tex]0=0[/tex]
________________________________________________________
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Help me help me help me please
Answer:
D. 24
Step-by-step explanation:
The area of a triangle is [tex]\frac{1}{2} (bh)[/tex].
The height is already given: 8
But we need to find the base and since the hypotenuse is given and it's a right triangle, we can use the pythagorean theorem. (Hypotenuse is longest, slanted side of a right triangle)
The pythagoren theorem is [tex]a^2+b^2=c^2[/tex] where a and b are the sides, and c is the hypotenuse.
Plugging in the given values => [tex]8^2+b^2=10^2[/tex]
We have to solve for b. So, squaring 8 and 10 we get [tex]64+b^2=100[/tex].
Next, subtract 64 from both sides to get b by itself: [tex]b^2=36[/tex]
Square root both sides to get [tex]b=6[/tex].
Now that we have our base we can plug it in to the area of triangle formula: [tex]1/2(6*8)[/tex].
Multiply inside the parenthesis: 1/2(48) => 24
A town has accumulated 4 inches of snow and the snow depth is increasing by 3 inches every hour . a nearby town has accumulated 1 inch and the depth is increasing by 5 inches every hour. how many hours will the snowfall of the towns be equal if the snow continues at the given rates?
answer as an equation and solve, please help!!
The equation which represents the given situation as described about snow depths in the task content is; 4 + 3x = 1 + 5x and the solution is; x = 1 and a half hours.
At what time will the snow fall of the towns in discuss have the same snow depth according to the given rates?It follows from the task content that the time at which the snowfall in the towns in discuss will be equal be determined.
According to.the word phrases given;
A town has accumulated 4 inches of snow and the snow depth is increasing by 3 inches every hour. Hence, we have;
4 + 3x.
Also, a nearby town has accumulated 1 inch and the depth is increasing by 5 inches every hour. Hence ,we have;
1 + 5x
Consequently, when the snowfalls are equal, we have;
4 + 3x = 1 + 5x
3 = 2x
x = 3/2.
x = 1 and a half hours.
Ultimately, the equation which represents the given situation as described about snow depths in the task content is; 4 + 3x = 1 + 5x and the solution is; x = 1 and a half hours.
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neve has 12 full box of jars of slime and 7 lose jars of slime if neve has a total of 187 jars of slime which equation can be used to find the number of jars in each box
Solving a linear equation, we can see that each box has 15 jars.
Which equation can be used to find the number of jars in each box?
We know that Neve has 12 full boxes of jars of slime, and 7 jars of slime, then if each box has N jars, the total number of jars that Neve has is given by the linear equation:
12*N + 7
Now we know that Neve has 187 jars in total, then we can write:
12*N + 7 = 187
We want to find the value of N, which is the number of jars in each box, so we need to solve the linear equation:
12*N + 7 = 187
12*N = 187 - 7
12*N = 180
N = 180/12 = 15
We conclude that there are 15 jars in each full box.
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B The table represents the location of QRST before and after a reflection. Use the table to
answer 3-5.
3. Give a verbal description of the transformation.
PRE-IMAGE
Q(-9,-8)
R(-9, -2)
S(-4,-2)
T(-4,-8)
IMAGE
Q'(9,-8)
R(9,-2)
S(4, -2)
?
4. Which best represents the transformation algebraically?
a. (x, y) b. (-x, y) c. (-x, -y)
d. (x + 18, y)
5. Find the location of T
3. The x-coordinate of the image is equal to the negative of that of the pre-image. The y-coordinate remains the same.
4. The transformation is best represented algebraically by (-x, y).
5. The location of the image of T is (4, -8).
3. The transformation makes the x-coordinate of the image equal to the negative of that of the pre-image. The y-coordinate remains the same.4. The transformation is best represented algebraically by (-x, y).5. The coordinates of the preimage of T are (-4, -8). On applying the transformation, the image of T becomes (-(-4), 8), i.e., (4, -8).To learn more about pre-image, visit :
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HELP 20 pointssss mathhhhh