what are the solutions to the quadratic equation of 2x^2-16x+32=0 show work?
Answer:
The Answer is 4
Step-by-step explanation:
2x² - 16x + 32 = 0
we would multiply 2x² and 32
= 64x²
then factorise 64x² such that the sum of the two nos = -16 AND the product of the nos = 64
the only value that satisfies this condition is -8 (-8 + -8 = -16, and -8 * -8 = 64)
so our equation becomes0 = 2x² - 8x -8x + 32
0 = (2x² - 8x) (-8x +32)
we bring out common terms i.e. factorise it2x(x - 4) -8(x - 4)
0 = (2x - 8) (x - 4)
0 = 2x - 8 or 0 = x - 4
8 = 2x or 4 = x
x = 8/2 or 4
x = 4 or 4
x = 4
hope it was clear
3^3 • 32 + 12 ÷ 4
a. 219
b. 291
c. 867
d. 437
using exponents, what is the simplified form of the expression 2^4*2^7?
To simplify 2^4\*2^7, you add the exponents because the bases are the same, resulting in 2^11 which equals 2048.
Explanation:When simplifying the expression 2^4\*2^7, we use the property of exponents that states when multiplying two exponential terms with the same base, you add the exponents. So, the simplified form of the expression would be 2^(4+7) which is 2^11. Since we are adding the exponents, this process is known as the sum of exponents and is a fundamental concept in the squaring of exponentials.
To calculate 2^11, you would multiply 2 by itself 11 times, but for the sake of simplicity, the answer is 2048.
a text book costs $108.00. if mathew paid a total of $113.94 for the book and sales tax, what rate of sales tax was he charged?
can you form an angle bisector hen the angle is a straight line?
The expression $1.25p + $3.50 can be used to calculate the total charge for printing p pages at a business service store. How much would it cost to print 8 pages
Anna is 4ft 9in tall. Express Anna's height in feet only by using a mixed number. If necessary, simplifyvthe fraction part of the mixed number
The line x - y = 5 passes through which set (-5, 0) (0, 5) (0, -5)
Represent real-world situations a rectangular piece of sheet metal is rolled and riveted to form a circular tube that is open at both ends, as shown. the sheet metal has a perimeter of 36 inches. each of the two sides of the rectangle that form the two ends of the tube has a length of x inches, and the tube has a circumference of x - 1 inches because an overlap of 1 inch is needed for the rivets. write a volume function for the tube in terms of x. then, to the nearest tenth, find the value of x that maximizes the volume of the tube. answer
Let f (x) = 2x - 1, g(x) = 3x, and h(x) = x2 + 1. Compute the following: f (h(x)) and. g (f (x))
Solve 9x-y=45, solve for y
a family went on a vacation and used 5.4 gallons of gasoline to travel 150 miles. how many total gallons of gasoline will they need to travel 200 more miles?
dakota runs a half marathon every 6 weeks. madison runs a half a marathon every 15 weeks. how many weeks untill they will run together?
To determine when Dakota and Madison will run a half marathon on the same week, we calculate the least common multiple of their running intervals, which is 60 weeks.
Explanation:The question is to find out how many weeks will pass until Dakota and Madison will run a half marathon on the same week.
We need to find the least common multiple (LCM) of their running intervals, which are 6 weeks for Dakota and 15 weeks for Madison.
To find the LCM, you can list the multiples of each number until you find the smallest number that appears in both lists.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...Multiples of 15: 15, 30, 45, 60, ...Here, we see that the smallest common multiple is 60 weeks.
Therefore, Dakota and Madison will run a half marathon together in 60 weeks.
How can you determine whether an equation is linear or non-linear?
The perimeter of the isosceles ΔABC with the base
BC is equal to 40 cm. Perimeter of the equilateral ΔBCD is 45 cm. Find BC and AB.
The length of BC is 15 cm and the length of AB is 12.5 cm.
The given parameters;
perimeter of isosceles ΔABC = 40 cmbase of the isosceles triangle = BCPerimeter of the equilateral ΔBCD = 45 cmAn equilateral triangle has three equal sides and the length of each side is calculated as;
[tex]|BC| = |BD| = |CD| = \frac{45}{3} = 15 \ cm[/tex]
Thus, the length of BC is 15 cm.
An isosceles triangle has two equal sides and a third side of different length. This third side is usually the base of the triangle.
The base of the isosceles triangle = BC = 15 cmThe two remaining sides = AB and AC[tex]|AB| = |AC| =\frac{Perimeter \ - \ |BC|}{2} = \frac{40 - 15}{2} = 12.5 \ cm[/tex]
Thus, the length of AB is 12.5 cm.
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In a country where prices are rising quickly, bread that now costs $1.39 will cost 2.4 times as much next year. How much will the bread cost next year
multiply the current price by the increase
1.39 * 2.4 = $3.34 ( price next year)
PLEASE PLEASE HELP!!!!
Given the system of equations, what is the value of the system determinant?
x + y = 8
x - y = 10
A. 0
B. -1
C. -2
Given the system of equations, what is the value of the y-determinant?
3x + y - 10 = 0
4x - y - 4 = 0
A. -28
B. -14
C. 28
Answer:
Given the system of equations, what is the value of the system determinant? x + y = 8
x - y = 10
C. -2
Given the system of equations, what is the value of the y-determinant?
3x + y - 10 = 0
4x - y - 4 = 0
A. -28
Step-by-step explanation:
The determinant of the system is the determinant of the matrix formed with the coefficients of the system, usually, this matrix is called A.
[tex]A=\left[\begin{array}{cc}1&1\\1&-1\end{array}\right][/tex]
In the 2x2 matrix, the determinant is calculated by obtaining the difference between the diagonally down product and the diagonally up product.
[tex]det(A)=\left|\begin{array}{cc}1&1\\1&-1\end{array}\right|=(1)(-1)-(1)(1)=-1-1=-2[/tex]
The y-determinant is the determinant of the matrix [tex]A_y[/tex], this matrix is formed substituting in the matrix A the coefficients of y with the constant terms.
[tex]A_y=\left[\begin{array}{cc}3&10\\4&4\end{array}\right][/tex]
[tex]det(A_y)=\left|\begin{array}{cc}3&10\\4&4\end{array}\right|=(3)(4)-(4)(10)=12-40=-28[/tex]
A line passes through the two given points. (1,0) (0,0) Is it vertical , horizontal , or neither ?
Answer: its horizontal
order :5/6,1/8,5/16,7/12 on the number line
Numberline: 0 ------------------------1
May I acquire some help on this homework as it is due tomorrow.
Jose is three times as old as his cousin Robert. The sum of their ages is more than 40. What are the smallest possible ages for each of them?
To find the smallest possible ages for Jose and Robert, set up a system of equations based on the given information. Robert's age is X, and Jose's age is 3X. The sum of their ages is more than 40, so the smallest possible age for Robert is 11, and Jose would be three times that, which is 33.
Explanation:To find the smallest possible ages for Jose and Robert, we need to set up a system of equations based on the given information.
Let's assume Robert's age is x. Since Jose is three times as old as Robert, his age would be 3x.
The sum of their ages is more than 40, so we can write the equation: x + 3x > 40.
Simplifying the equation: 4x > 40.
Dividing both sides of the equation by 4, we get x > 10.
Therefore, the smallest possible age for Robert is 11, and Jose would be three times that, which is 33.
which of the following is the equation of a line perpendicular to the line y= -3/2x+4 and passes through the points (3,9)
Answer:
[tex]2x-3y+21=0[/tex]
Step-by-step explanation:
We are given that an equation
[tex]y=-\frac{3}{2}x+4[/tex]
We have to find an equation of line which is perpendicular to given line and passing through the point (3,9).
We know that when two lines of slope [tex]m_1\;and\;m_2[/tex] are perpendicular then
[tex]m_1=-\frac{1}{m_2}[/tex]
By comparing with
[tex]y=mx+b[/tex]
Where m=Slope of line
Slope of given line=[tex]=m_1=\frac{-3}{2}[/tex]
Slope of the line=[tex]-\frac{1}{m_1}=-\frac{1}{\frac{-3}{2}}=\frac{2}{3}[/tex]
Slope of the line=[tex]\frac{2}{3}[/tex]
The equation of line passing through the point (3,9) is given by
[tex]y-y_0=m(x-x_0)[/tex]
Substitute the values
The equation of line which passing through the point (3,9) is given by
[tex]y-9=\frac{2}{3}(x-3)[/tex]
[tex]3y-27=2(x-3)[/tex]
[tex]3y-27=2x-6[/tex]
[tex]3y=2x-6+27[/tex]
[tex]2x-3y+21=0[/tex]
Talia gave her hairdresser a 20 percent tip, which amounted to $7. What was the price of the service before the tip?
The price of the service that was charged before the tip was:
$ 35
Step-by-step explanation:Let the price of the service be $ x.
Now it is given that:
Talia gave her hairdresser a 20 percent tip, which amounted to $7.
This means that the 20% of total service charge=7
i.e. 20% ×x =7
i.e. 0.20×x=7
i.e. x=7/0.20
i.e. x=35
Hence, the price of the service that was paid before the tip is: $ 35
Suppose that the time it takes to do a job is inversely proportional to the number of workers. that is, the more workers on the job the less time required to complete the job. if it takes 2 workers 8 days to finish a job, how long will it take 8 workers?
Joel is walking down a street and sees a 115 ft tall building in front of him. he stops 190 feet from the base of the building at the tip of the building's shadow. round answers to three decimal places.
a. if there was a piece of rope from the top of the building to joel, how long would it be?
b. what is the angle of elevation from joel to the top of the building?
c. margaret says that she could find the angle of depression from the top of the building to joel by subtracting the angle of elevation from 90°. is she correct? explain.
If there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet. The angle of elevation from Joel to the top of the building is approx [tex]31.18 ^ \circ[/tex]
What is angle of elevation and angle of depression?You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.
Similarly, there is angle of depression, when you look horizontal, then down, the angle between both positions is the angle of depression.
How to use right triangles to find the length of the rope?Remember that we assume that buildings are usually vertical to the ground. This means, there is 90° formation. The length of the rope can be taken as length of hypotenuse.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Referring to the figure attached below, we get:
Length of the rope = Length of the line segment AC = |AC|
Using the fact that the triangle ABC is right angled triangle, we can use Pythagoras theorem.
We get the length of AC as:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\|AC| = \sqrt{|AB|^2 + |BC|^2} \\\text{positive square root since length is non-negative quantity}\\\\|AC| = \sqrt{115^2 + 190^2} = \sqrt{51325} \approx 222.01 \: \rm ft[/tex]
Thus, if there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet.
The angle of elevation is calculated as:
[tex]\tan(\angle ABC) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}} = \dfrac{|AB|}{|BC|}\\\theta = tan^{-1}(\dfrac{115}{190}) \approx 31.18^\circ[/tex]
The angle of depression is actually equal to angle of depression because they are pair of alternate interior angles (made by traversing line AC between two parallel lines).
Thus, Margaret statement is false.
Therefore, we get the answers as:
If there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet.The angle of elevation from Joel to the top of the building is approx [tex]31.18 ^ \circ[/tex]Margaret's statement is false.Learn more about Pythagoras theorem here:
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Factor completely 2x2 − 2x − 40.
2(x − 5)(x + 4)
(2x − 10)(x + 4)
(x − 5)(2x + 8)
2(x − 4)(x + 5)
The factor of quadratic function 2x²-2x-40 is 2 (x-5) (x+4).
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
Given:
The quadratic function 2x²-2x-40.
To find the factors;
Take common term out,
2(x²-x-20)
= 2 (x²-5x + 4x -20)
= 2 {x (x-5) + 4(x -5)}
= 2 (x-5) (x+4)
Therefore, the factors are 2 (x-5) (x+4).
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the table shows the volume of gasoline in a gas tank at different times. Find th e rate of change for each time interval. During which time interval did the volume decrease at the greatest rate?
To find the rate of change for each time interval, calculate the difference in volume for each interval and divide it by the difference in time. Compare the rates of change to determine the time interval with the lowest rate of change.
Explanation:To find the rate of change for each time interval, we need to calculate the difference in volume for each interval and divide it by the difference in time. Let's assume the time intervals are 12-18 hours, 18-24 hours, and 12-24 hours. The rate of change for each interval can be calculated as follows:
Rate of change for 12-18 hours = (Volume at 18 hours - Volume at 12 hours) / (18 hours - 12 hours)
Rate of change for 18-24 hours = (Volume at 24 hours - Volume at 18 hours) / (24 hours - 18 hours)
Rate of change for 12-24 hours = (Volume at 24 hours - Volume at 12 hours) / (24 hours - 12 hours)
The time interval during which the volume decreased at the greatest rate will be the interval with the lowest rate of change. Compare the rates of change calculated for each interval to find the time interval with the lowest rate of change.
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Match the expression with its name. 9x4 – 3x + 4
Answer:
fourth degree trinomial
Step-by-step explanation:
What number produces a rational number when added 1/5
What is the best metric unit to measure the distance from ohio to texas?