impossible, the maximum value of either cos(t) or sin(t) is 1; look to the unit circle for proof
The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is the number of photos printed, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem?
Part B: Determine the x-intercepts. What do these values mean in the context of the problem?
The base of the parallelogram, b, can be found by dividing the area by the height. If the area of the parallelogram is represented by 6x2 + x + 3 and the height is 3x, which represents b, the length of the base
Answer:
[tex]2x+\frac{1}{3}+\frac{1}{x}=Base[/tex]
Step-by-step explanation:
Given: The area of the parallelogram is [tex]6x^2+x+3[/tex] and the height is 3x.
To find: The base of the given parallelogram.
Solution: It is given that The area of the parallelogram is [tex]6x^2+x+3[/tex] and the height is 3x.
Now, area of parallelogram is given as:
[tex]A=b{\times}h[/tex] where b is the base and h is the height of teh gievn parallelogram.
Substituting the given values, we have
[tex]6x^2+x+3=b{\times}3x[/tex]
⇒[tex]\frac{6x^2+x+3}{3x}=Base[/tex]
⇒[tex]\frac{6x^2}{3x}+\frac{x}{3x}+\frac{3}{3x}=Base[/tex]
⇒[tex]2x+\frac{1}{3}+\frac{1}{x}=Base[/tex]
which is the required expression for the base of the given parallelogram.
The length l of a rectangle is 4 inches greater than its width w. The area of the rectangle is 252 square inches.Using the method of completing the square, what are the length and width of the rectangle? Show your work.
PLEASE HELP ASAP ILL GIVE BRAINLIEST IF YOURE RIGHT!!
Find the greatest possible error for each measurement.
9 g
a.
1/2 g
b.
1/4 g
c.
1/6 g
d.
1/8 g
gpe = 1/2 of the unit measures
since 9 is a whole number the gpe would be 1/2 g
how many solutions does this system have -3x+6y=10 -3x+6y= -4
Table to estimate how many pounds of dog food his dog eat in one year which of the following would be the best strategy
Rewrite the formula to find the radius of a sphere. The volume (V) of a sphere is given by the formula V=4/3 pi r^2
Two pools are being filled with water. To start, the first pool contains 2200
liters of water and the second pool contains 1840
liters of water. Water is being added to the first pool at a rate of 21.25
liters per minute. Water is being added to the second pool at a rate of 32.5
liters per minute.
(PLEASE ANSWER QUICK)
2200 + 21.25X = 1840 +32.50X
subtract 1840 from each side
360+ 21.25X= 32.50X
subtract 21.25x from each side
360=11.25X
x= 360/11.25 = 32 minutes pool will have the same amount
21.25*32 = 680+2200 = 2880 liters
32.5*32 = 1040 + 1840=2880 liters
it will take 32 minutes and they will have 2880 liters each
Mike wants to make meatloaf. His recipe uses a total of 6 pounds of meat. If he uses a 3 to 1 ratio of beef to pork how much pork will he use? Enter your answer as a mixed number in simplest terms
Mike will use 1 1/2 pounds of pork for his meatloaf recipe, which calls for a 3 to 1 ratio of beef to pork and a total of 6 pounds of meat.
Mike's meatloaf recipe has a total of 6 pounds of meat and uses a 3 to 1 ratio of beef to pork. To find out how much pork he will use, we can express the total amount of meat as the sum of beef and pork parts.
First, we know that there are 3 + 1 = 4 parts in total because of the given ratio. Since the ratio is 3 to 1, for every 4 parts of meat, 1 part is pork. Therefore, we calculate the weight of each part by dividing the total weight by the number of parts:
6 pounds ÷ 4 parts = 1.5 pounds per part
Since one part is pork, Mike will use 1.5 pounds of pork for his meatloaf. Expressed as a mixed number, that's 1 1/2 pounds of pork in simplest terms.
Which has a greater area, a square with sides that are x - 1 units long or a rectangle with a length of x units and a width of x - 2 units?
The amount of an ordinary $7,500.00 annuity for 3 years at 12 percent compounded quarterly is
Answer:
$180,997.50.
Step-by-step explanation:
1. On TABLE 14-1 Future Value of $1.00 Ordinary Annuity, select the periods row corresponding to the number of interest periods.
2. Select the rate-per-period column corresponding to the period interest rate.
3. Locate the value in the cell where the periods row intersects the rate-per-period column.
4. Multiply the annuity payment by the table value from step 3.
Future value = annuity payment × table value
FV = $7500.00 * 24.133 = $180,997.50
a 23 gram sample of a substance thats a by-product of fireworks has a K-value of .13. whats the substances half life in days
Answer:
5.3 is the right answer.
Step-by-step explanation:
Shyla used a probability simulator to pull 3 colored marbles from a bag and flip a coin 50 times. The results are shown in the tables below:
16 blue
20 green
14 yellow
heads 18
tails 32
Using Shyla's simulation, what is the probability of pulling a blue marble and the coin landing tails up?
Answer:
512/2500
Step-by-step explanation:
1/2(6x-4)=2/3x How do i solve this?
Solve 2x2 + 5x + 5 = 0. Round solutions to the nearest hundredth.
Rounded to the nearest hundredth, they are:
[tex]\[x_1 \approx -0.63 + 1.35i\][/tex]
[tex]\[x_2 \approx -0.63 - 1.35i\][/tex]
To solve the quadratic equation [tex]\(2x^2 + 5x + 5 = 0\)[/tex], we can use the quadratic formula:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
where [tex]\(a = 2\), \(b = 5\)[/tex], and [tex]\(c = 5\)[/tex].
Substituting the values into the quadratic formula:
[tex]\[x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 2 \cdot 5}}}}{{2 \cdot 2}}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{{25 - 40}}}}{{4}}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{{-15}}}}{{4}}\][/tex]
Since the discriminant [tex](\(b^2 - 4ac\))[/tex] is negative, the solutions will involve imaginary numbers.
Using the imaginary unit [tex]\(i\)[/tex], where [tex]\(i^2 = -1\),[/tex] we can rewrite [tex]\(\sqrt{{-15}}\)[/tex] as [tex]\(i\sqrt{{15}}\):[/tex]
[tex]\[x = \frac{{-5 \pm i\sqrt{{15}}}}{{4}}\][/tex]
So, the solutions to the equation [tex]\(2x^2 + 5x + 5 = 0\)[/tex] are complex numbers. Rounded to the nearest hundredth, they are:
[tex]\[x_1 \approx -0.63 + 1.35i\][/tex]
[tex]\[x_2 \approx -0.63 - 1.35i\][/tex]
These solutions represent the points where the graph of the quadratic equation intersects the x-axis. They lie on the complex plane.
An equilateral triangle and a square have the same perimeter of 12 inches. what is the ratio of the side length of the triangle to the side length of the square? express your answer as a common fraction.
HELP PLEASE! Which of these shows the following expression factored completely? 6x^2-13x=5
a (3x-1)(2x+5)
b (3x-5)(2x-1)
c (3x-1)(2x-5)
d (3x-5)(2x+1)
The solution is: the following expression factored completely,
6x^2-13x=5 is: c (3x-1)(2x-5)
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Here, we have,
we have,
6x² - 13x = +5
6x² - 13x - 5 = 0
6x² - 15x + 2x - 5 =0
so, we get,
(3x-1)(2x-5) = 0
The sign of the constant term is the product of the signs of the constants in the binomial factors: (+1)·(+5). We want a positive sign for the constant, so both binomial factor constants must have the same sign.
When the signs of the binomial factor constants are the same, the x-term constant will match them. Thus, for a positive x-term constant, both binomial factor constants must be positive.
The signs of the x-term and the constant term are both positive, so the signs of the constants in the binomial factors must be the same and must both be positive. The only offering that meets that requirement is
... C (3x-1)(2x-5)
Hence, The solution is: the following expression factored completely, 6x^2-13x=5 is: c (3x-1)(2x-5)
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Thank you very much for your help!
A triangle has measurements of 39, 52, and 65 units. Is it a right triangle?
Yes
No
Not enough information to tell
Solve the following equation by transforming it into a perfect square trinomial. x2 – 4x = 5 will mark as brilliant
The solution of the given equation is -1 or 5
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example, 3x + 5 = 15.
Given is an equation, x²-4x = 5,
we need to transform it into a perfect square,
The equation is =
x²-4x = 5
Add 4 to each side,
x²-4x+4 = 5+4
x²-4x+4 = 9
(x-2)² = 9
Solving for x,
x-2 = √9
x-2 = ±3
x = -1 or x = 5
Hence, the solution of the given equation is -1 or 5
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What is the length of diagonal ac in parallelogram ABCD if the diagonal BD = 10cm which is twice the diagonal AC?
The length of the diagonal AC in parallelogram ABCD is 5 cm.
Explanation:Given that the diagonal BD is twice the length of diagonal AC, we can represent the length of diagonal AC as x. So, the length of diagonal BD would be 2x. From the given information, we know that BD = 10 cm. Therefore, we can write the equation 2x = 10 to solve for x. Dividing both sides of the equation by 2 gives x = 5. So, the length of diagonal AC is 5 cm.
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In the given parallelogram, the length of the diagonal AC is 5 cm, given that the length of the diagonal BD is twice that of AC.
Explanation:The question pertains to the properties of a parallelogram. In this case, it has been provided that diagonal BD (10 cm) is twice the length of the other diagonal AC. This implies that the length of diagonal AC is half the length of BD. Therefore, to find the length of AC, take the length of BD and divide by 2:
AC = BD / 2 = 10 cm / 2 = 5 cm
So, the length of diagonal AC is 5 cm.
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ROUND 3.05947821031 TO THE NEAREST WHOLE NUMBER HELP
. The total cost of gasoline varies directly with the number of gallons purchased. Gas costs $1.77 per gallon. Write a direct variation to model the total cost c for g gallons of gas.
A . c=g/1.77
B. c=1.77g
C. g=1.77c
D. c=g+1.77
Y varies jointly as x and z, and y = 32 m, x = 6 m, and z = 8 m. what is the value of y when x = 5 m and z = 12 m?
a. 90 m
b. 4 m
c. 40 m
d. 9 m
Which side has an equal measure to BC?
A.DE
B.AB
C.EF
D.DF
PLEASE HELP
In the given diagram, we are given two triangles, triangle ABC and triangle DEF.
And we are given a line or reflection l.
Triangle DEF is the mirror image of triangle ABC.
Therefore, all sides of the triangle ABC would be congruent to sides of triangle DEF.
AB = DF
AC = DE and
BC = EF.
We can see than BC is the smallest side of triangle ABC and EF is the smallest side of triangle DEF.
Therefore, correct option is C option.C.EFUe can wash a car in 1 hour. steve can wash a car twice as fast as sue. how long will it take them to wash a car if they work together, but sue starts 30 minutes before steve?
A quadratic equation is shown below:
25x2 + 10x + 1 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 4x2 − 4x + 1 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
hello :
help :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 ) Δ > 0 the equation has two reals solutions : x = (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ < 0 : no reals solutions
Half of the population of cool town owns a bicycle, and 25% of the population owns a car. if 10% of the population owns both a car and a bicycle, what is the probability that a person chosen at random from cool town owns either a car or a bicycle or both?
.help me with this please thanks
at right is graph of this situation predict how the line would change to present the average cost of gas in dicember of 2005 when gas cost $2.20 per gallon on average