Answer:
The function translated 4 units right and 9 units down
The third answer
Step-by-step explanation:
* To solve the problem you must know how to find the vertex
of the quadratic function
- In the quadratic function f(x) = ax² + bx + c, the vertex will
be (h , k)
- h = -b/2a and k = f(-b/2a)
* in our problem
∵ f(x) = x²
∴ a = 1 , b = 0 , c = 0
∵ h = -b/2a
∴ h = 0/2(1) = 0
∵ k = f(h)
∴ k = f(0) = (0)² = 0
* The vertex of f(x) is (0 , 0)
∵ g(x) = -8x + x² + 7 ⇒ arrange the terms
∴ g(x) = x² - 8x + 7
∵ a = 1 , b = -8 , c = 7
∴ h = -(-8)/2(1) = 8/2 = 4
∵ k = g(h)
∴ k = g(4) = (4²) - 8(4) + 7 = 16 - 32 + 7 = -9
∴ The vertex of g(x) = (4 , -9)
* the x-coordinate moves from 0 to 4
∴ The function translated 4 units to the right
* The y-coordinate moves from 0 to -9
∴ The function translated 9 units down
* The function translated 4 units right and 9 units down
Final answer:
The question seeks the translation moving the vertex of f(x) = x^2 to match the vertex of g(x) = -8x + x² + 7. To achieve this, the function f(x) needs to be translated right by 4 units and down by 9 units, resulting in the translation (x, y) -> (x+4, y-9).
Explanation:
The student's question is asking for the translation that would move the vertex of a quadratic function f(x) to match the vertex of another quadratic function g(x). We are given two functions: f(x) = x2 and g(x) = -8x + x² + 7. To find the translation, we need to determine the vertices of both parabolas.
In the standard form of a quadratic function, y = a x² + bx + c, the vertex can be found using the formula h = -b/2a for the x-coordinate of the vertex. For f(x), the vertex is at (0, 0) since there is no b or c value, and it's just x² . For g(x), we can calculate the vertex by finding the x-coordinate: h = -(-8)/2(1) = 4. The y-coordinate can be found by substituting x = 4 into g(x) to get g(4) = -8(4) + 4² + 7 = -32 + 16 + 7 = -9. Therefore, the vertex of g(x) is at (4, -9).
To translate the vertex of f(x) to the vertex of g(x), we need to shift it right by 4 units and down by 9 units. The translation that does this is (x, y) -> (x+4, y-9).
an equation in slope-intercept form for the line that passes through (4,-4) and is parallel to 3+4x=2y-9
Answer:
[tex]\large\boxed{y=-\dfrac{1}{2}x-2}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\======================[/tex]
[tex]\text{If}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2\ \text{are\ parallel, then}\ m_2=-\dfrac{1}{m_1}\\===========================[/tex]
[tex]\text{We have the equation of a line:}\ 3+4x=2y-9.\\\text{Convert it to the slope-intercept form:}\\\\2y-9=3+4x\qquad\text{add 9 to both sides}\\\\2y=12+4x\qquad\text{divide both sides by 2}\\\\y=6+2x\\\\y=2x+6\to m_1=2\\\\\text{therefore}\ m_2=-\dfrac{1}{2}\\\\\text{We have the equation:}\ y=-\dfrac{1}{2}x+b\\\\\text{Put the coordinates of the given point (4, -4) to the equation:}\\\\-4=-\dfrac{1}{2}(4)+b\\\\-4=-2+b\qquad\text{add 2 to both sides}\\\\-2=b\to b=-2\\\\\text{Finally we have the equation:}\ y=-\dfrac{1}{2}x-2[/tex]
Ollie has $400 balance on her credit card.She pays $60 a month on the card.Does this situation have a positive or negative rate of change?explain
Answer:
It has a negative rate of change.
Step-by-step explanation:
She is losing money so the rate of change is negative
The local weather report states that there is more than a 2/3 chance of rain for Saturday.
What is the likelihood that it will rain on Saturday?
The likelihood is 66.67% or about 67%. Hope this helped!
Answer: B. It is likely to rain on Saturday.
Step-by-step explanation:
how many triangles can be made if two sides are 4 inches and the angle between them is 90
Answer:
it's either two or three. Sorry for the short answer.
Step-by-step explanation:
The sum of an integer n and four is equal to the difference of ten and two.What is the value of n?
Answer:
n=4
Step-by-step explanation:
Attachment has my work.
At a garden center, grass seed sells for $8 per pound. Kalil spent $10 on grass seed. What amount of seed did he buy?
Step-by-step explanation:
All you have to do is divide 8 into 10 which equals, 0.8 seeds
Solace this pleasehdbfbfbf
A=bh and since the garden is 2 1/2 by 2 and the trench+garden= 3 1/2 by 3 the trench would be 1 by 1. So A=1x1 = 1
Answer:11/2 m sq
Step-by-step explanation:
Area of the garden =L•W
2 1/2•2=
5/2•2= 5 m sq
Area of the garden & trench =L•W
3 1/2•3 =
7/2•3 =
7•3/2=
21/2 m sq
21/2-5 =
21/2-10/2=
21-10/2=
11/2
The area of the trench is 11/2 m sq
Which model represents 140%
Answer: The answer is H
Write the product as a power 15×15×15×15
Hopefully this helps
Answer:
15^4
Step-by-step explanation:
42 is 15% of what number here is to help you people on this question
is/of=%/100
280
42 times 100 divided 15 equals 280.
Can you conclude that this parallelogram is a rectangle? Explain.
To conclude if a parallelogram is a rectangle, we need to check if its opposite sides are congruent and if its angles are right angles.
Explanation:To determine if a parallelogram is a rectangle, we need to check if its opposite sides are congruent and if its angles are right angles.
In a rectangle, opposite sides are congruent and all angles are right angles (90 degrees).
So, if we can prove that the given parallelogram has congruent opposite sides and right angles, then we can conclude that it is a rectangle.
Alternatively, we can also look for other properties of rectangles such as diagonals being congruent or the presence of perpendicular bisectors.
A conclusion that be drawn based on the parallelogram include the following: C. No; the diagonals may not be congruent.
In Mathematics and Euclidean Geometry, a rectangle is a type of quadrilateral or polygon in which its opposite sides are equal and all the angles that are formed are right angles.
Generally speaking, the diagonals of a rectangle divide it into two equal parts and this implies that, the two diagonals of any rectangle are congruent.
In this scenario, we can logically deduce that this parallelogram is not a rectangle because its diagonals may not be congruent, as no congruence symbols were shown.
Brian works 24 hours this week. His earns 9.25 per hour. He pays $37.50 in payroll tax. He deposits half of his pay after taxes in his savings account. He deposits the other half of his pay after taxes in his checking account. How much money is deposited into each account?
Answer:
$92.25
Step-by-step explanation:
Begin with 24 hours times $9.25 an hour.
Get $222.
Subtract $37.50.
Get $184.5.
Divide this by 2.
Get $92.25 as your final answer
Brian will deposit $92.25 into both his savings account and his checking account after calculating his net pay by subtracting payroll taxes from his gross earnings and dividing the remainder by two.
To calculate how much money is deposited into Brian's savings and checking accounts, we need to follow these steps:
First, calculate Brian's gross pay by multiplying his hourly wage by the number of hours he worked.Deduct the payroll taxes from the gross pay to find out the net pay.Divide the net pay by two to determine how much goes into each account.Let's do the math:
Brian's gross pay = 24 hours x $9.25/hour = $222Brian's net pay after taxes = $222 - $37.50 = $184.50Money deposited into each account = $184.50 / 2 = $92.25So, Brian will deposit $92.25 into his savings account and another $92.25 into his checking account.
Which measurement correctly completes the statement 627 L=? mL A. 6.27 B. 627,000 C. 62,700 627,000,000? Pls help I’ll give you brainliest!
Final answer:
To convert liters to milliliters, multiply the number of liters by 1000. Therefore, 627 liters is equal to 627,000 milliliters.
Explanation:
To correctly complete the statement 627 L = ? mL, we need to convert liters to milliliters. Since there are 1000 milliliters (mL) in 1 liter, we multiply the number of liters by 1000 to find the number in milliliters.
Thus, the conversion is:
627 L × 1000 = 627,000 mL
Therefore, the statement 627 L = 627,000 mL is correct.
Carlos bought 6 1/2 pounds of bananas for 5.20. What quantity of bananas would one dollar buy? You answer should be in the form _ _._ bananas Write your answer as a mixed number in decimal form. _ _ ._
Answer:
$1 would buy 1.25lbs of bananas
Step-by-step explanation:
In order to find the amount $1 will buy, we need to create a proportion. One the left side we can use the unit rate. On the right we use the unknown quantity.
6.5lbs/$5.20 = xlbs/$1.00
Now we cross multiply
6.5 * 1.00 = 5.20 * x
6.5 = 5.20x
1.25 = x
Carlos can buy approximately 4.17 bananas with one dollar.
Explanation:To find out how many bananas one dollar can buy, we need to divide the total cost of the 6 1/2 pounds of bananas by the total cost of the bananas Carlos bought. $5.20 / 6 1/2 = $0.80 per pound. To find the quantity of bananas one dollar can buy, we divide $1.00 by $0.80 per pound. $1.00 / $0.80 = 1.25 pounds. Since there are 2 pounds in 1 kilogram and 0.5 kilograms is equal to 1 pound, we can convert the 1.25 pounds to kilograms. 1.25 pounds * 0.5 kilograms/pound = 0.625 kilograms. Finally, assuming each banana weighs approximately 0.15 kilograms, we can calculate how many bananas one dollar can buy. 0.625 kilograms / 0.15 kilograms/banana = 4.167 bananas.
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A cylinder has a radius of 10 cm and a height of 9 cm. A cone has a radius of 10 cm and a height of 9 cm. Show that the volume of a cylinder is three times the volume of the cone. someone help me out
Step-by-step explanation:
We start with the formulas for the volumes of a cylinder and a cone.
Cylinder:
[tex] V_{cylinder} = \pi r^2 h [/tex]
Cone:
[tex] V_{cone} = \dfrac{1}{3} \pi r^2 h [/tex]
Now we calculate the two volumes.
Cylinder:
[tex] V_{cylinder} = \pi r^2 h [/tex]
[tex] V_{cylinder} = \pi \times (10~cm)^2 \times 9~cm [/tex]
[tex] V_{cylinder} = \pi \times 100~cm^2 \times 9~cm [/tex]
[tex] V_{cylinder} = 900 \pi~cm^3 [/tex]
Cone:
[tex] V_{cone} = \dfrac{1}{3} \pi \times (10~cm)^2 \times 9~cm [/tex]
[tex] V_{cone} = \dfrac{1}{3} \pi \times 100~cm^2 \times 9~cm [/tex]
[tex] V_{cone} = 300 \pi~cm^3 [/tex]
The volume of the cylinder is 900pi cm^3, and the volume of the cone is 300pi cm^3.
Now we divide the volume of the cylinder by the volume of the cone.
[tex] \dfrac{900 \pi~cm^3}{300 \pi~cm^3} = 3 [/tex]
Dividing the volume of the cylinder by the volume of the cone gives us 3, showing that the volume of the cylinder is 3 times the volume of the cone.
The volume of a cylinder is three times the volume of a cone.
Explanation:To show that the volume of a cylinder is three times the volume of a cone, we need to compare their formulas. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height.
Let's calculate the volume of the cylinder first. Given that the radius (r) is 10 cm and the height (h) is 9 cm, we can substitute these values into the formula: V = π(10 cm)²(9 cm) = 900π cm³.
Now let's calculate the volume of the cone. Again, substituting the values for r and h, we have V = (1/3)π(10 cm)²(9 cm) = 300π cm³.
Comparing the volumes, we have 900π cm³ for the cylinder and 300π cm³ for the cone. Dividing the volume of the cylinder by the volume of the cone, we get (900π cm³) / (300π cm³) = 3. This shows that the volume of the cylinder is three times the volume of the cone
name the polynomial based on degree and number of terms. 7x^2+2x+5
2nd degree trinomial
Help me solve please
Answer:
0.10822510822
Step-by-step explanation:
use a calculator
a tree is 8ft tall and grows 8 inches each year. In how many years will the tree reach a height of 30 feet?
A.27
B.33
C.45
D.52
Answer:
B
Step-by-step explanation:
30 ft = 360 in
8 ft = 64 in
360 in - 64 in = 296 in
296 / 8 = 33
It will take approximately 32.84 years for the tree to reach a height of 30 feet.
To determine the number of years it will take for the tree to reach a height of 30 feet, let's break down the growth process step by step.
Initially, the tree is 8 feet tall.
The tree grows 8 inches (0.67 feet) each year.
Let's assume it takes "x" years for the tree to reach a height of 30 feet.
So, the height of the tree after "x" years can be represented by the following equation:
Height after x years = Initial height + (Growth rate * x)
In this case, the initial height is 8 feet, and the growth rate is 0.67 feet (8 inches).
Height after x years = 8 + (0.67 * x)
Now, we need to solve for "x" when the height reaches 30 feet:
30 = 8 + (0.67 * x)
Subtract 8 from both sides of the equation:
22 = 0.67 * x
To isolate "x," divide both sides by 0.67:
x = 22 / 0.67
Now, calculate "x":
x ≈ 32.84 years
So, the Answer: B. 33 years
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Which of the following is equal to the expression below?
(8*320)1/3
The answer is 853.33333-
Answer:
for plato users its 8 [tex]\sqrt[3]{5}[/tex]
Step-by-step explanation
please mark as Brainliest
In part, this lesson will look at the process of buying a house. True False
Answer:
True
Step-by-step explanation:
Ya just yeet it on your paper
Answer:
true
Step-by-step explanation:
odyssey ware
please help me the photo is my queston
Answer:
i think it would be 30
Step-by-step explanation:
I don’t know these property’s!
1) 3rd down.
2) 2nd down.
3) 1st down.
4) 6th down.
Which of the following would be appropriate to measure in centimeters?
the length of a paperclip
the yearly increase in a child's height
the width of a swimming pool
the distance between Philadelphia and New York City
the height of a standard ceiling
Answer:
Centimeter is a small measuring unit, usually used to measure small things like the length of a pencil.
Let us check all the options:
1. the length of a paperclip - yes it can be measured in cm. Like a standard paperclip is 3.5 cm long.
2. the yearly increase in a child's height - Yes it can be measured in cm.
3. the width of a swimming pool - No, it can be measured in feet or meters.
4. the distance between Philadelphia and New York City - No, it can be measured in km or miles.
5. the height of a standard ceiling - No, it can be measured in feet.
Solve the system of equations y=8x+15 and y=x+57
Answer:
x=6, y=63
Step-by-step explanation:
since both equal y, they equal each other-
8x+15=x+57
7x=42
x=6
then to solve for y-
y=(6)+57
y=63
The solution to the system of equations y = 8x + 15 and y = x + 57 is found via substitution, yielding x = 6 and y = 63 as the answer.
To solve the system of equations y = 8x + 15 and y = x + 57, we can use the method of substitution or elimination. However, since both equations are already solved for y ,, the most straightforward approach is substitution, implying that 8x + 15 = x + 57. To find the value of x, we subtract x from both sides and subtract 15 from both sides, yielding 7x = 42. Dividing both sides by 7, we find that x = 6. Substituting x = 6 into either of the original equations, for instance, y = 8(6) + 15, gives us y = 63. Therefore, the solution to the system of equations is x = 6 and y = 63.
The $120 repair bill included $36 for parts and rest for labor. What percent of the bill was for labor?
Answer:
30%
Step-by-step explanation:
70% of the $120 repair bill was for labor, calculated by subtracting the cost of parts from the total bill and then finding the percentage of the remaining labor cost.
Explanation:The question is asking what percent of a $120 repair bill was for labor if $36 was for parts. Since the total bill is $120, the cost for labor is the total bill minus the cost for parts, which is $120 - $36 = $84 for labor. Now, to find the percentage of the bill that was for labor, you use the formula (part/whole) × 100, which in this case is ($84/$120) × 100 = 70%. Therefore, 70 percent of the bill was for labor.
Will mark BRAINLIEST!!! Need answer ASAP!!!
Graph the solution for the following linear inequality system. Click on the graph until the final result is displayed.
y > 5
y ≥ x
Answer:
The fourth graph with the long dotted line shows the system.
Step-by-step explanation:
By graphing both inequalities and shading, you'll find that the overlap shows the fourth graph. Also, there was no need to ask here, you really could have just used desmos.com, it's a great online graphing tool.
Answer:
4th graph : )
Step-by-step explanation:
HELP ASAP :
A movie theater calculates its revenue using the equation R=4.85t, where R is revenue in dollars and t is the number of tickets sold. What is the revenue if 88 tickets are sold?
1) $426.80
2) $88.00
3) $426.08
4) $18.14
4.85×88=$426.80.
1) $426.80 is the answer
what is x, the length of the diagonal, to the nearest whole number
Answer:
It’s (A) 16
Step-by-step explanation:
It just is
The length of the diagonal x= 5 units( nearest whole number) in the given parallelogram.
What is diagonal?" Diagonal is defined as the length between the opposite vertices of the given polygon."
Formula used
Cosine law
[tex]a^{2} =b^{2} +c^{2} -2bc Cos A[/tex]
According to the question,
In the given parallelogram PQRS
In ΔPQS
PQ = 6units
PS = 4 units
QS = x units
∠QPS = 55°
Apply cosine law to get the length of the diagonal we have,
[tex]x^{2} = 6^{2} +4^{2} -2(6)(4)Cos 55\°[/tex]
⇒ [tex]x^{2} = 36 +16 -48( 0.5736)[/tex]
⇒[tex]x^{2} = 24.4672[/tex]
⇒[tex]x= 4.946[/tex]
⇒ x≈5 ( nearest whole number)
Hence, the length of the diagonal x= 5 units( nearest whole number) in the given parallelogram.
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When the following quadratic equation is written in standard form, what is the value of c?-3/4 x^2+2=0
When the quadratic equation is written in standard form the value of c is 8
To find the value of c when the quadratic equation -3/4 x² + 2 = 0 is written in standard form (ax² + bx + c = 0), follow these steps:
Move the constant term to the right side:
-3/4 x² = -2
Multiply both sides by -4/3 to get the standard form:
4x² = 8
Identify the coefficient of x² (a) and the constant term (c):
In this case, a = 4 and c = 8.
Therefore, when the equation is written in standard form, c = 8.
Calculate the slope:
rise: 37
run: 63
Answer:
.587
Step-by-step explanation:
Slope is rise over run.
rise/run=37/63=.587