Answer:
g(x) = (x - 8)² - 64 will be the answer.
Step-by-step explanation:
The given function in the standard form is g(x) = -16x + x²
We have to write this function in the vertex form.
Since vertex form of a quadratic function is in the form of
f(x) = (x - h)² + k
Therefore, g(x) = x² - 16x may be written as
g(x) = x² - 16x + 64 - 64
= x² - 2(8x) + 64 - 64
= (x - 8)² - 64
Therefore, g(x) = (x - 8)² - 64 will be the answer.
Evaluate the function for
f(x) = x + 3 and g(x) = x2 − 2.
(f − g)(0)
(f − g)(0) =
To evaluate (f - g)(0), find f(0) and g(0) for the functions f(x) = x + 3 and g(x) = x^2 - 2, and then subtract the latter from the former. For f(0) we have 3, and for g(0) we have -2. Subtracting, we get (f - g)(0) = 5.
Explanation:To evaluate the expression (f - g)(0), it means we need to find the value of the function f at x = 0, subtract the value of the function g at x = 0, and combine them. Given the functions f(x) = x + 3 and g(x) = x^2 − 2, let's calculate their values at x = 0:
For f(x), we have f(0) = 0 + 3 = 3For g(x), we have g(0) = (0)^2 − 2 = 0 − 2 = −2Now, let's subtract g(0) from f(0):
(f - g)(0) = f(0) - g(0) = 3 - (-2) = 3 + 2 = 5
Therefore, the value of (f - g)(0) is 5.
The amount of interest earned on a savings account varies directly with the amount of money saved. If $208 in interest is earned on $6,500 of savings, how much interest will be earned on $8,000 of savings over the same time period? $224 $240 $256 $272
The width (l) of a sheet of plywood that is one half the length l
L=2+4W
W=L/2
f=3d
hope this is the right question????
The base and the height of sail b are x times greater than the base and the height of sail
a. how many times greater is the area of sail b? write your answer as a power.
When both the base and height of a shape are multiplied by x, the area increases by a factor of x^2. Therefore, the area of Sail B is x^2 times greater than that of Sail A.
Explanation:The area of a shape with a base and height is commonly found using the formula Area = 1/2 * Base * Height. If the base and the height of Sail B are x times greater than those of Sail A, then both the base and height of Sail B are multiplied by x, resulting in an area that is x^2 (x squared) times greater. This is because, in the formula, base and height are multiplied together, so if both are multiplied by x, the overall multiplication is by x*x, or x^2. Therefore, the area of Sail B is x^2 times greater than the area of Sail A.
Learn more about Area Multiplication here:https://brainly.com/question/29156658
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Find the dimensions of a rectangle whose area is 221 cm2 and whose perimeter is 60 cm. (enter your answers as a comma-separated list.)
The dimensions of a rectangle with an area of 221 cm² and a perimeter of 60 cm are found by solving a system of equations derived from the definitions of area and perimeter. The dimensions are 13 cm by 17 cm, or equivalently, 17 cm by 13 cm.
Explanation:To find the dimensions of a rectangle with an area of 221 cm2 and a perimeter of 60 cm, we will let the length be x and the width be y. The area of a rectangle is found by multiplying the length and width, so we have the equation x * y = 221. The perimeter is twice the sum of the length and width, so we have 2x + 2y = 60, which simplifies to x + y = 30.
To solve these equations, divide the perimeter equation by 2 to find y = 30 - x. Substituting this into the area equation gives x(30 - x) = 221. Expanding this and bringing all terms to one side provides a quadratic equation: x2 - 30x + 221 = 0. Solving this quadratic equation by factoring or using the quadratic formula gives the dimensions of the rectangle.
The solutions to the quadratic equation are x = 13 and x = 17. Since x and y are interchangeable as length and width, the two sets of possible dimensions for the rectangle are 13 cm by 17 cm and 17 cm by 13 cm.
The dimensions of the rectangle are [tex]17\ cm , 13\ cm[/tex]
To find the dimensions [tex]\( l \)[/tex] (length) and [tex]\( w \)[/tex] (width) of the rectangle given its area and perimeter, we start with the following equations:
1. Area equation:
[tex]\[l \times w = 221\][/tex]
2. Perimeter equation:
[tex]\[ 2l + 2w = 60 \][/tex]
Step-by-Step Solution:
The dimensions of the rectangle are [tex]{{17, 13} \) cm.[/tex]
From the perimeter equation, divide everything by [tex]2[/tex] to simplify:
[tex]\[l + w = 30\][/tex]
Now we have a system of equations:
[tex]\[\begincases}l \times w = 221 \\l + w = 30\end{cases}\][/tex]
Let's solve this system using substitution or elimination:
From [tex]\( l + w = 30 \)[/tex], we can express [tex]\( w \)[/tex] in terms of [tex]\( l \)[/tex]
[tex]\[w = 30 - l\][/tex]
Substitute [tex]\( w = 30 - l \)[/tex] into the area equation:
[tex]\[l \times (30 - l) = 221\][/tex]
[tex]\[30l - l^2 = 221\][/tex]
Rearrange this equation to form a quadratic equation:
[tex]\[l^2 - 30l + 221 = 0\][/tex]
Now, solve this quadratic equation using the quadratic formula [tex]\( l = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = -30 \), and \( c = 221 \)[/tex]
[tex]\[l = \frac{-(-30) \pm \sqrt{(-30)^2 - 4 \times 1 \times 221}}{2 \times 1}\][/tex]
[tex]\[l = \frac{30 \pm \sqrt{900 - 884}}{2}\][/tex]
[tex]\[l = \frac{30 \pm \sqrt{16}}{2}\][/tex]
[tex]\[l = \frac{30 \pm 4}{2}\][/tex]
Calculate both possible values of [tex]\( l \)[/tex]
[tex]\[l = \frac{30 + 4}{2} = 17 \quad \text{or} \quad l = \frac{30 - 4}{2} = 13\][/tex]
Corresponding values of \( w \)
[tex]If\ \( l = 17 \), then \( w = 30 - 17 = 13 \)[/tex]
[tex]If\ \( l = 13 \), then \( w = 30 - 13 = 17 \)[/tex]
Therefore, the dimensions of the rectangle are [tex]\( 17 \) cm[/tex] by [tex]\( 13 \) cm.[/tex]
Verification:
[tex]Area: \( 17 \times 13 = 221 \) cm\(^2\)[/tex]
[tex]Perimeter: \( 2 \times (17 + 13) = 2 \times 30 = 60 \) cm[/tex]
Both conditions match the given area and perimeter, confirming that the dimensions are correct.
Find the exact volume of the cylinder.
Julia bought name tags for a party. Each name tag is 334 inches wide and 213 inches high. The formula for the area of a rectangle is A=bh. What is the area of one name tag?
Answer:the correct answer is 71142 just multiply 334 and 213
Step-by-step explanation:
**Giving away 20 points**. I need to know the arc length for EF and the area of sector EOF please:) (also plz show work thanks!!)
(Economics) Select all that apply.
Select the items that apply to calculating the Gross Domestic Product.
a. final goods and services
b. intermediate goods and services
c. last year's products
d. new products
GDP calculations should include 'final goods and services' and 'new products' to reflect a nation's current economic activity accurately while preventing double counting.
Explanation:The question pertains to what should be included when calculating the Gross Domestic Product (GDP). The options given were a. final goods and services, b. intermediate goods and services, c. last year's products, and d. new products. According to the principles of economics, GDP is the market value of all final goods and services produced within a country in a given period of time.
It is crucial to understand that GDP calculations include only new products that are produced within the current year to reflect the nation's current economic activity. This method helps statisticians avoid the mistake of double counting, which would inflate GDP figures inaccurately. Consequently, the correct selections are a. final goods and services and d. new products.
Find, to the nearest tenth, the area of the region that is inside the square and outside the circle. The diameter of the circle is 14 in
Answer:
Option [tex]42.1\ in^{2}[/tex]
Step-by-step explanation:
we know that
The area of the region that is inside the square and outside the circle is equal to the area of the square minus the area of the circle
see the attached figure to better understand the problem
Step 1
Find the area of the square
Remember that
The area of the square is
[tex]A=b^{2}[/tex]
where
b is the length side of the square
we have
[tex]b=14\ in[/tex]
substitute
[tex]A=14^{2}=196\ in^{2}[/tex]
Step 2
Find the area of the circle
Remember that
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=14/2=7\ in[/tex]
substitute
[tex]A=\pi(7^{2})=153.9\ in^{2}[/tex]
Step 3
Find the area of the region
[tex]196\ in^{2}-153.9\ in^{2}=42.1\ in^{2}[/tex]
Given the inequality below: x + 2y ≥ 10
helpppppppppppppppppppppppppppppppppppppppppp
How many points determine a unique line?
A.
1 point
B.
2 points
C.
any 3 points
D.
3 noncollinear points
I say 2 points!
Answer:
B. 2 points
Step-by-step explanation:
1 point is a dot in space, 2 can make a line
) how many ways are there to divide a group of 10 kids into two groups of 5 to play soccer?
Yolanda paid for her movie ticket using 28 coins, all nickels and quarters. The ticket cost $4. Which system of linear equations can be used to find the numberof nickels, n, and the number of quarters, q, Yolanda used?
Answer:
[tex]\left \{ {{n+q=28} \atop {n(0.05)+q(0.25)=4}} \right.[/tex]
And the pair [tex](n,q)=(15,13)[/tex] is the solution.
Step-by-step explanation:
We know that Yolanda paid for her movie ticket using 28 coins. She only paid with nickels and quarters.
We also know that the ticket cost $4.
We need to form a linear equation system that solves this problem.
We have the following variables :
n : number of nickels
q : number of quarters
We know that she used 28 coins ⇒ the number of nickels plus the number of quarters must be equal to 28.
We have our first equation :
[tex]n+q=28[/tex] (I)
For the second equation we need to use the ticket price information.
We know that the ticket cost $4 and she only paid with nickels and quarters.
Therefore we can write the following equation that relates the variable ''n'' and the variable ''q'' :
[tex]n(0.05)+q(0.25)=4[/tex] (II)
This equation represents that the number of nickels ''n'' per its value plus the number of quarters ''q'' per its value is equal to $4 that it is the value of the movie ticket.
With (I) and (II) we form the linear equation system :
[tex]\left \{ {{n+q=28} \atop {n(0.05)+q(0.25)=4}} \right.[/tex]
This linear equation system can be used to find the value of ''n'' and ''q''.
For example, in equation (I)
[tex]n+q=28[/tex]
we can solve it in terms of ''n'' :
[tex]n=28-q[/tex] (III)
If we use (III) in (II) :
[tex](28-q)(0.05)+q(0.25)=4[/tex]
[tex]1.4-(0.05)q+(0.25)q=4[/tex]
[tex]q(0.2)=2.6[/tex]
[tex]q=\frac{2.6}{0.2}=13[/tex]
[tex]q=13[/tex]
Now replacing this value of q in (III) :
[tex]n=28-13=15[/tex]
[tex]n=15[/tex]
We find that Yoland used 15 nickels and 13 quarters to paid the movie ticket .
x+2/x+8 divided by 2x/3
What is the square root of -1
PLEASE SOMEONE HELP ME ON THIS
you leave your house and walk for half an hour at a speed of 3 miles per hour. Then you run for 15 minuets at a speed of 7 miles per hour. You are now halfway to town. Write and solve an equation to find the distance from your house to town
Final answer:
To find the total distance to town, the distance walked (1.5 miles) and run (1.75 miles) were calculated, and it was found that the student is 3.25 miles away from home. This is halfway to town, so the total distance to town is 6.5 miles.
Explanation:
To solve the problem, we will calculate the distance traveled by walking and running and then use these to find the total distance to town.
Step 1: Calculate the distance walked
First, we convert the walking time into hours since the speed is given in miles per hour. Half an hour of walking at 3 miles per hour will cover:
Distance walked = Speed × Time = 3 mph × 0.5 hours = 1.5 miles
Step 2: Calculate the distance run
Since 15 minutes is a quarter of an hour, we can calculate the distance run at 7 miles per hour as:
Distance run = Speed × Time = 7 mph × 0.25 hours = 1.75 miles
Step 3: Determine the total half distance
Now, we combine the distances to find the halfway point to town:
Total half distance = Distance walked + Distance run = 1.5 miles + 1.75 miles = 3.25 miles
Step 4: Find the full distance to town
Since this is half the distance, the full distance to town is:
Full distance = Total half distance × 2 = 3.25 miles × 2 = 6.5 miles
Conclusion
Therefore, the total distance from the student's house to town is 6.5 miles.
Final answer:
The total distance from the house to town is found by doubling the sum of the distances walked and run, which were 1.5 miles and 1.75 miles, respectively. The full distance to town is 6.5 miles.
Explanation:
To solve for the distance from your house to town, we will use the information provided about your walking and running times and speeds. Since you walked for half an hour (0.5 hours) at a speed of 3 miles per hour and ran for 15 minutes (0.25 hours) at a speed of 7 miles per hour, and this brought you halfway to town, we can set up the following equation:
Distance walked = Speed walked × Time walked
= 3 mph × 0.5 hours
= 1.5 miles
Distance run = Speed run × Time run
= 7 mph × 0.25 hours
= 1.75 miles
The total distance you traveled to get halfway to town is the sum of the distance walked and the distance run:
Total distance halfway = Distance walked + Distance run
= 1.5 miles + 1.75 miles
= 3.25 miles
Since 3.25 miles is only halfway to town, the full distance to town is twice that amount:
Full distance to town = 2 × Total distance halfway
= 2 × 3.25 miles
= 6.5 miles
Therefore, the total distance from your house to town is 6.5 miles.
How much greater will Jennifer’s January finance charge be if the finance charge is calculated using the previous balance method than if it is calculated using the adjusted balance method? a. $0.48 b. $1.15 c. $0.67 d. $0.85
Triangle HIJ has been reflected to create triangle H'I'J'. Segment HJ= H'J'= 4, segments IJ = I'J' = 7, and angles J and J' are both 32 degrees. Which postulate or theorem below would prove the two triangles are congruent?
A. SSS
B. SAS
C. ASA
D. HL
Kelly mixes the letters S E L E C T E and D thoroughly. Alex picks one letter. WHat is the probability that Alex will not select a consonant.
A. 3/8
B.3/5
C.5/8
D.1/2
Factor to find the zeros of the function defined by the quadratic expression.
7x2 + 14x − 105
Answer:
{-5, 3}
Step-by-step explanation:
7 is a factor common to all three terms of this polynomial function. Thus, after the first attempt to factor it, we have 7(x^2 + 2x - 15). The quadratic factors into (x + 5)(x - 3). Setting these = to zero individually, we get
x + 5 = 0, or x = -5, and
x - 3 + 0, or x = 3
Thus, the zeros of the given f(x) =7x2 + 14x − 105 are {-5, 3}.
Eli and Karl each throw a basketball straight up in the air at the same time. Eli is standing on a deck and the height of his ball, in meters, is given by the function f(x)=−4.9x2+12x+2.5 , where x is the number of seconds after the ball is released from his hands.
Karl is standing on the ground and the height of his ball, in meters, is given by the function g(x)=−4.9x2+14x , where x is the number of seconds after the ball is released from his hands.
There is a moment when the basketballs are at the same height.
What is this height?
Enter your answer, rounded to the nearest tenth of a meter, in the box.
Answer:
Just took the K12 quiz, and like killdrone said in the comments, the correct answer is 9.8 m
Step-by-step explanation:
The height at which both basketballs are at the same height is approximately 16.3 meters.
Explanation:To find the moment when the basketballs are at the same height, we need to find the common height value for both functions.
Setting the functions equal to each other, we get: -4.9x^2 + 12x + 2.5 = -4.9x^2 + 14x
Simplifying the equation, we get 2x = 2.5, which means x = 1.25.
Substituting this value back into the original function for Eli, we get f(1.25) = -4.9(1.25)^2 + 12(1.25) + 2.5 = 16.325
Therefore, the height at which both basketballs are at the same height is approximately 16.3 meters.
Help I'm taking a k12 quiz 2.04: composite figures but, I can't figure these out can anyone help me?
Question. 1 What is the area of this polygon? (Picture 1)
Question. 2 What is the area of this polygon? 42.5 Units? 41.5 Units? 35.5 Units? 29.5 Units? (Picture 2)
Question. 3 This figure is made up of a rectangle and parallelogram.
What is the area of this figure? (Picture 3)
Question. 4 What is the area of this composite shape? (Picture 4)
Thank you angels who help me with these
Given f(x)=3x^2+5 and g(x)=x−2 .
What is (fg)(x) ?
Which of the following pairs of numbers contains like fractions?
A. 6⁄7 and 1 5⁄7
B. 3⁄2 and 2⁄3
C. 3 1⁄2 and 4 4⁄4
D. 5⁄6 and 10⁄12
please help asap !! ill mark brainliest but be corrrecct
Answer:
k=4
Step-by-step explanation:
Given
A line x=7
The line has only y-intercept which means that it is a vertical line.
As the two points are
A(10,2) and B(k,2)
The y-intercepts of both the points are same i.e. y=2 which means that the line fomed by joining A and B is a horizontal line.
As x=7 is a vertical line and bisects the horizontal line, the mid-point of line AB will be the point where first line (x=7) bisects the second which is (7,2).
The x-coordinate of mid-point is 7 because the vertical line has 7 as x-intercept and y-intercept is two because the horizontal line has y-intercept 2.
So,
Mid-point=((10+k)/2 ,2)=(7,2)
Comparing the x-coordinate
(10+k)/2=7
10+k=7*2
10+k=14
k=14-10
k=4
△ABC∼△DEF , △ABC has a height of 20 inches, and △DEF has a height of 24 inches. What is the ratio of the area of △ABC to the area of △DEF ?
Dan has to carry 285 apples from a farm to the market. How many baskets will he need, given that each basket can hold 37 apples?
divide number of apples by how many fit I a basket:
285 / 37 = 7.70
so he will need 8 baskets