what are the zeros of the quadratic function f(x)=8x2-16x-15
Answer: The zeroes of the given polynomial f(x) are
[tex]x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Step-by-step explanation: We are given to find the zeroes of the quadratic function below:
[tex]f(x)=8x^2-16x-15.[/tex]
To find the zeroes, we must find the roots of the following equation
[tex]f(x)=0\\\\\Rightarrow 8x^2-16x-15=0~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex].
We know that the roots of the quadratic equation of the form [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]
In the given quadratic equation , a = 8, b = -16 and c = - 15.
Therefore, the roots of the equation are
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\\Rightarrow x=\dfrac{-(-16)\pm\sqrt{(-16)^2-4\times 8\times (-15)}}{2\times 8}\\\\\\\Rightarrow x=\dfrac{16\pm\sqrt{256+480}}{16}\\\\\\\Rightarrow x=\dfrac{16\pm\sqrt{786}}{16}\\\\\\\Rightarrow x=\dfrac{16\pm4\sqrt{46}}{16}\\\\\\\Rightarrow x=\dfrac{4\pm\sqrt{46}}{4}\\\\\\\Rightarrow x=1\pm\sqrt{\dfrac{46}{16}}\\\\\\\Rightarrow x=1\pm\sqrt{\dfrac{23}{8}}\\\\\\\Rightarrow x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Thus, the zeroes of the given polynomial f(x) are
[tex]x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Option (C) is correct.
The zeroes of the given polynomial f(x) = 8x^2-16x-15 are x = 1 + [tex]\sqrt{23}[/tex] / 8 and x = 1 -[tex]\sqrt{23}[/tex] / 8 Thus, Option C is correct.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We are given to find the zeroes of the quadratic function f(x) = 8x^2 - 16x-15
f(x) = [tex]8x^2-16x-15[/tex] = 0
We know that the roots of the quadratic equation ax² + bx + c = 0 is
x = -b ± [tex]\sqrt{b^2 - 4ac}[/tex] / 2a
In the given quadratic equation , a = 8, b = -16 and c = - 15.
So,
x = -b ± [tex]\sqrt{b^2 - 4ac}[/tex] / 2a
x = -(-16) ± [tex]\sqrt{(-16)^2 - 4(8)(-15)}[/tex] / 2(8)
x = 16 ± [tex]\sqrt{256+ 480}[/tex] / 16
x = 16 ± [tex]\sqrt{786}[/tex] / 16
x = 4 ± [tex]\sqrt{46}[/tex] / 4
x = 1 ± [tex]\sqrt{23}[/tex] / 8
Thus, the zeroes of the given polynomial f(x) are
x = 1 + [tex]\sqrt{23}[/tex] / 8 and x = 1 -[tex]\sqrt{23}[/tex] / 8. Option C is correct.
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TEXASCHIC! :)
1. Sam is observing the velocity of a car at different times. After three hours, the velocity of the car is 51 km/h. After five hours, the velocity of the car is 59 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equation obtained in Part A for the first six hours? (5 points)
My answer:
Part A:
y - 51 = 59 - 51 / 5 - 3 (x-3)
y - 51 = 4 (x-3)
y = 4x -12 + 51
y= 4x + 39
where x is the time and y is the velocity of car at any time x.
Part B:
y =4 * 6 + 39 = 24 + 39 = 63 ~km/h
The velocity of the car is represented by the equation y = 4x + 39, where 'x' is time and 'y' is the velocity. You can graph this for the first six hours by substituting x=6 to find: y=63 km/h. Thus, the car's velocity after six hours would be 63 km/h.
Explanation:In order to solve this problem, we first find the equation representing the change in the car's velocity. The point (3, 51) represents the condition that after three hours, the car is moving at 51 km/h. Similarly, the point (5, 59) stands for the velocity being 59 km/h after five hours. We derive the slope of the line connecting these two points by subtracting the y-coordinates and dividing by the difference of the x-coordinates, (59-51)/(5-3) = 4.
This slope represents an increase of 4 km/h for every hour that passes. Our equation then becomes y - 51 = 4(x - 3) which simplifies to y = 4x + 39. In this equation, 'x' represents time in hours and 'y' is the car's velocity at any given time 'x'.
For Part B, we graph the equation over the first six hours by inputting x=6 into the equation, giving us y = 4*6 + 39 = 63 km/h. Therefore, after six hours, the car would be moving at a velocity of 63 km/h.
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What is 2.828427125 to the nearest thousandth?
what is the slope of the line given by the equation y=2.3x
How to do this ?? How
Change the column heading for the row sum column which represents the total of each type of session, to total number of sessions
You can change a column heading by clicking it, then right-clicking to select 'Rename Column' and inputting 'Total Number of Sessions'.
Explanation:To change the column heading for the row sum which represents the total of each type of session to 'Total Number of Sessions', you need to follow these steps:
Firstly, click on the column heading which you want to change. This will usually highlight the entire column.Right-click on the highlighted column heading, and select 'Rename Column' from the drop-down menu.In the text box that appears, type 'Total Number of Sessions' and hit 'Enter'.This will effectively rename your column heading to represent the total number of sessions accurately.
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∠A and ∠B are vertical angles with m∠A=x and m∠B=4x−30 . What is m∠A ? Enter your answer in the box.
Answer:
[tex] x = 4x -30[/tex]
We can solve for x subtracting x on both sides:
[tex] x-x= 4x-x-30[/tex]
And then we can add 30 in both sides:
[tex] 30= 3x[/tex]
And dividing both sides by 3 we got:
[tex] x = 10[/tex]
Step-by-step explanation:
For this case we know the measure of two angles:
[tex]m <A = x[/tex]
[tex] m<B = 4x-30[/tex]
And we know that both angles are vertical and by definition vertical angles are the angles opposite each other when two lines cross.
For this case since both angles are vertical we have the property that:
[tex] m<A = m<B [/tex]
And replacing what we got we have:
[tex] x = 4x -30[/tex]
We can solve for x subtracting x on both sides:
[tex] x-x= 4x-x-30[/tex]
And then we can add 30 in both sides:
[tex] 30= 3x[/tex]
And dividing both sides by 3 we got:
[tex] x = 10[/tex]
I feel really stupid but how do you solve: v+9/3+8
Soda is sold in aluminum cans that measure 6 inches in height and 2 inches in diameter. how many cubic inches of soda are contained in a full can?
A cylinder is a three-dimensional figure that has a radius and a height.
The volume of a cylinder is given as:
Volume = π r²h
The amount of soda in a full can is 18.84 cubic inches.
What is a cylinder?A cylinder is a three-dimensional figure that has a radius and a height.
The volume of a cylinder is given as:
Volume = π r²h
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm
We have,
Aluminum cans:
Height = 6 inches
Diameter = 2 inches
Radius = diameter/2 = 2 / 2 = 1 inches
The aluminum can is in the shape of a cylinder.
The volume of the aluminum can:
= πr²h
= 22/7 x 1 x 1 x 6
= 18.84 cubic inches
The amount of soda in a full can is 18.84 cubic inches.
Thus,
The amount of soda in a full can is 18.84 cubic inches.
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Please help with this equation!!! 30 points!
The following equation is shown.
[tex] x^{2} - \sqrt{2.5} -l + ( -\pi + z ) = A[/tex]
Solve for the variable z.
How does the volume of a cone compare to the volume of a cylinder with the same radius and height?
Given that ΔJKL ≅ ΔUVW and ΔUVW ≅ ΔABC, complete the following statements. Triangle JKL is congruent to triangle ABCBCACBA. Side LK corresponds to sides UV and ABVU and BCWV and CB. Angle JLK corresponds to angles UVW and ABCUWV and ACBWUV and CAB
For ΔJKL ≅ ΔUVW and ΔUVW ≅ ΔABC, we conclude congruence JKL ≅ ABC, LK corresponds to UV and AB, and JLK corresponds to UVW and ABC.
The given information implies that triangle JKL is congruent to triangle ABC, and side LK corresponds to sides UV and AB. Angle JLK corresponds to angles UVW and ABC.
Therefore, the statements can be completed as follows:
Triangle JKL is congruent to triangle ABC.
Side LK corresponds to sides UV and AB.
Angle JLK corresponds to angles UVW and ABC.
Therefore, these statements reflect the congruence relationships established through the given information.
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Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the Mexican Shade Grown blend with the Rift Valley blend, but always in the same proportion. Yesterday, you mixed 80 pounds of the Mexican Shade Grown blend with 24 pounds of the Rift Valley blend. Today, there is 60 pounds of the Mexican Shade Grown coffee left in stock. How many pounds of the Rift Valley coffee should you mix with it to get your secret blend?
To get the secret blend, you should mix 18 pounds of the Rift Valley coffee with the 60 pounds of Mexican Shade Grown coffee.
Explanation:To find out how many pounds of the Rift Valley blend you should mix with the 60 pounds of Mexican Shade Grown coffee, we need to set up a proportion based on the ratio of the two blends. The ratio of the Mexican Shade Grown blend to the Rift Valley blend is 80:24, which can be simplified to 10:3. We can then set up the proportion: 10/3 = 60/x. By cross-multiplying, we get 10x = 180. Dividing both sides by 10, we find that x = 18. Therefore, you should mix 18 pounds of the Rift Valley coffee with the 60 pounds of Mexican Shade Grown coffee to get your secret blend.
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The clean up hitter on a baseball tean batted 1/3 of the runs the team scored. The hitter batted in 3 runs. Select the equation that represents the number of n of runs the team scored. Then solve the equation:
a.1/3n=3B.n/3=1/3C.3n=1/3D.3n=9
Evaluate the determinant for the following matrix [144] [522] [155]
Find the coordinates of the other endpoint of the segment with the given endpoint (6,2) and midpoint (2,0)
The 440 yard dash in track has been replaced by the 400 meter dash. which is the longer distance and by how many meters? hint: 1 yard = 3 feet
Final answer:
The 400 meter dash is the longer distance by 2.336 meters.
Explanation:
In order to determine which is the longer distance, we need to convert both the 440 yards and the 400 meters into the same unit of measurement. Since 1 yard is equal to 0.9144 meters, we can convert the 440 yards into meters by multiplying it by 0.9144:
440 yards * 0.9144 meters/yard = 402.336 meters
Therefore, the 400 meter dash is the longer distance by 2.336 meters.
Write the fraction 20/32 in simplest form.
The fraction given 20/32 can be written as 5/8 in its simplest form.
How to simplify fractions?The principle of simplifying fraction is to make both the numerator and the denominator smaller numbers but as proportional as the original fraction. This is convenient for mathematical operations and even for understanding proportions.
Now, to simplify fractions we need to divide the nominator and the denominator, the process is shown below:
20/32 divide both numbers by 420/ 4 = 532/ 4 = 8This means the new fraction is 5/8.
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Name 3 decimals between 16.4 and 16.5 draw a number line estmating the placement of all five decimals
Sarah has a collection of nickels, dimes, and quarters worth $13.80. she has 10 more dimes than nickels and twice as many quarters as dimes. how many coins of each kind does she have?
MATH HELP 20 POINTS!!!
A) Variable = x ( miles Tim walked )
B) Tim walked X miles, Molly walked 4+x miles ( 4 more than Tim)
Equation: x + x+4 = 10
C) x +x+4 = 10
2x+4 = 10
2x =6
x = 3
D)
Tim walked 3 miles, Molly walked 7 miles
Write a function rule: 7 more than the quotient of a number n and 4 is 9
pls help!!!
The average rate of change of the function between x = 15 to x = 29 is __________m/s2 and represents the car's acceleration.
Answer:
sorry guys that other question is absolutely no help at all. The answer is 1.266 m/s squared. I don't know what kind of IDIOT would try and take you to a completely other website.
Step-by-step explanation:
annie dome worked from 8:15 am to 11:45 am and from 12:30 pm to 4:15 pm. How many hours did she work? (include steps on how to do this problem)
Which statement best explains whether △PQR is congruent to △XYZ?
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a rotation of 180° about the origin.
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a translation 5 units down followed by a reflection across the y-axis.
△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a reflection across the y-axis followed by a reflection across the x-axis.
Help me please thanks
What is the standard form of the following equation?
y=−2/5x+4 Use integers for A, B, and C. Enter your answer in the box.
How do I solve this?
Is - √3 a real number, whole number, natural number, rational number, irrational number, an integer, or imaginary number?
REALLY NEED HELP PLEASE!!
The Smith family rented a recreational vehicle for a seven-day vacation. The cost to rent the recreational vehicle was $560 plus $0.50 per mile. How many miles were driven if the total cost was $1350?