The maximum value of the quadratic function f(x)=-[tex]x^2+8x-20[/tex] is -4, which occurs at x=4. This value can be found by using the vertex formula for parabolas.
The function in question is f(x)=-[tex]x^2[/tex]+8x-20. This is a quadratic function, and since the coefficient of [tex]x^2[/tex] is negative, the graph of the function will be a downward-opening parabola. To find the maximum value of this function, we need to determine the vertex of the parabola.
The vertex of a parabola in the form of f(x)=[tex]ax^2[/tex]+bx+c is given by the formula h=-b/(2a). Plugging in our coefficients a=-1 and b=8, we find the x-coordinate of the vertex to be h=-8/(2(-1))=4. To find the corresponding y-coordinate, which is the maximum value, we substitute x=4 into the original function [tex]ax^2[/tex]+bx+c:
f(4)=[tex]-4^2+8\times4-20[/tex]
f(4)=-16+32-20
f(4)=-4
Therefore, the maximum value of the function f(x)=-[tex]x^2+8x-20[/tex] is -4, which occurs at x=4.
shari’s class is making team pennants for an upcoming field day.they cut the pennants out of a large sheet of paper in the pattern shown below. the area of the whole pattern is 1600 cm2. they need to know the length of the pennant base how long is the base of each pennant
Answer:
10cm Base
Step-by-step explanation:
Actually the answer is 10 cm for the base.
First step is take 1600cm2 and divide it by 4 (or how many pendents you have) so it'll look like this
1600/4 =400cm2
Then you need to find the area of the Triangles.
Area of the Triangle=1/2xbase xheight
400=1/2xbx80
400=40xb
10=b
Answer: 10cm Base
Step-by-step explanation:
A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $10 million after 4 years while profits increased $7.5 million per year. Select the correct graph of this function.
The sum of three integers is 74. The first integer is twice the second and the third is six more than the second. What are the three integers
What is 7700 divided by 623
if an obtuse angle is split in half, how can the two new angles be classified? give an example.
Splitting an obtuse angle in half will either result in two acute angles or right angles, depending on the original angle's measure.
When an obtuse angle is split in half, each of the two new angles will be either acute or right angles, depending on the measure of the original obtuse angle. An obtuse angle is one that is greater than 90 degrees but less than 180 degrees.
By splitting an obtuse angle exactly in half, both resulting angles will have a measure less than 90 degrees, making them acute, unless the original angle was exactly 180 degrees, in which case the split would result in two angles of 90 degrees each, making them right angles.
Consider the obtuse angle, ABC, which measures 120 degrees. When we bisect angle ABC to create two new angles, namely ABD and DBC, each of these angles will measure 60 degrees, classifying them as acute angles.
whats the exact value of tan (300°)
Answer:
[tex]Tan(300^{\circ})= - \sqrt{3}[/tex]
Step-by-step explanation:
Tan (300°) can be written as Tan (360°-60°) ---1
Using identity :
[tex]Tan(360^{\circ}-\theta)=- Tan\theta[/tex]
Using 1
So, [tex]Tan(360^{\circ}-60^{\circ})= - Tan60^{\circ}[/tex]
The value [tex] Tan60^{\circ}=\sqrt{3}[/tex]
So, [tex]Tan(300^{\circ})= - \sqrt{3}[/tex]
Thus the exact value of [tex]Tan(300^{\circ})= - \sqrt{3}[/tex]
Answer:
[tex]-\sqrt{3}[/tex] or Option A on E2020 Quiz
Step-by-step explanation:
what is 118/13 = 59/z?
THIS IS MY LAST ONE BROS.
Mrs. Lamb is going to make a 3 question true false test. She wants to see how many different answer keys would be possible. What could she do to simulate this quiz? What would the sample space be?
How do you solve this math problem-2(x+3y)=18
how many 6 ounce cups can be filled from 4 gallons of juice?
Lia gets paid $45 an hour plus $150 each week. She hopes to earn at least $690 this week.
Answer: Hi, if the question is "how many hours she needs to work this week in order to win at least $690"
then, per week Lia wins:
$150 + $45*x,
where x is the amount of hours that she worked in the week.
then the equation we need to solve is:
$150 + $45*x = $690
$45*x = $690 - $150 = $540
x = 540/45 = 12
then she needs to work at least 12 hours this week in order to win at least $690.
The cost y (in dollars) to rent a camping tent is proportional to the number x of days that the tent is rented. It costs $56 to rent a tent for 7 days. Write an equation that represents the cost to rent a camping tent for x days.
Answer:
[tex]y=8x[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In this problem the linear equation represent a proportional variation
Let
x------> the number of days
y-----> the cost to rent a camping tent
The linear equation is equal to
[tex]y=kx[/tex]
we know that
It costs [tex]\$56[/tex] to rent a tent for [tex]7[/tex] days
Find the value of k
[tex]56=7k\\ \\k=56/7\\ \\k=8\frac{\$}{day}[/tex]
substitute
The linear equation is equal to
[tex]y=8x[/tex]
Walmart is advertising a sale where all Lego sets are 15% off. Mrs. Snyder decides to purchase a Lego set that originally cost $39. What will Mrs. Snyder pay for the Lego set on sale?
Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a total of $48. Which of the following are true? Select all that apply.
A. One pound of pistachios plus 1 pound of almonds cost $20.
B. The pistachios cost twice as much per pound as the almonds.
C. Reducing the number of pounds of almonds by one results in a total cost of $40. D. The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48. E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.
We want to find a system of equations, and by solving that system we will be able to see which statements are true.
We will see that options A, C, and E are true.
We know that:
Venetta buys 2lb of pistachios
Venetta buys 3 lb of almonds.
Let's define the variables:
x = price per pound of pistachios
y = price per pound of almonds.
Now we also know that:
"The pistachios cost $4 more per pound than the almonds."
This can be written as:
[tex]x = y + \$4[/tex]
"She pays a total of $48"
This can be written as:
[tex]2*x + 3*y = \$48.[/tex]
So a system of equations:
[tex]x = y + \$4[/tex]
[tex]2*x + 3*y = \$48.[/tex]
To solve this system, the first thing we need to do is isolate one of the variables in one of the equations, particularly we can see that x is already isolated in the first equation, so we can skip that step.
Now we can replace the isolated variable in the other equation to get:
[tex]2*(y + \$4) + 3*y = \$48[/tex]
now we can solve this for y:
[tex]2*y + \$8 + 3*y = \$48[/tex]
[tex]5*y + \$8 = \$48[/tex]
[tex]5*y = \$48 - \$8 = \$40[/tex]
[tex]y = \$40/5 = \$8[/tex]
now that we know this, we can use:
[tex]x = y + \$4 = \$8 + \$4 = \$12[/tex]
now that we know:
y = $8
x = $12
Let's see which statements are true:
A) One pound of pistachios plus 1 pound of almonds cost $20.
True, $8 + $12 = $20.
B) The pistachios cost twice as much per pound as the almonds.
False, $12 is not the double of $8.
C) Reducing the number of pounds of almonds by one results in a total cost of $40.
True, one pound less of almonds means $8 less in the price.
D) The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48
Simplifying the expression we get:
2*(a - 4) + 3a = -8 + a = 48
a = 48 + 8 = 52
This clearly does not model the price of one pound of almonds, this statement is false.
E) The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.
Solving the equation we get:
2*p + 3*p - 12 = 48
5*p = 48 + 12 = 60
p = 60/5 = 12
This is true.
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15(−22.38−10.12) HELP PLEASE!!!
lots of points
Compare and contrast the different battles that took place at: Ticonderoga, Necessity, William Henry, Quebec, Montreal, and Duquesne.
the product of 2 consecutive natural numbers is greater than their sum by 109. find the numbers
Write two ratios that are equivalent to 5/7
What is the solution to this equation? 3(d+2)−12=d−2 A)d = 2 B)d = 4 C)d = 8 D)d = 10
Answer: d = 2
Step-by-step explanation:
3(d+2)−12=d−2
Do you think it is okay to make friends over the internet or is it too dangerous to trust what people over the internet are saying. What should you do if you make a internet friend and they ask to meet. Should you agree or tell an adult. USE COMPLETE SENTENCES.
Making friends on the Internet can be beneficial, especially for those who struggle with face-to-face interactions, but it is vital to remain cautious and maintain online safety by keeping personal information private and consulting adults about meetings.
Explanation:Making friends over the Internet has become increasingly common and can be a positive experience; however, it comes with its risks. Understanding the nature of online relationships and knowing how to navigate them safely is crucial. When interacting online, remember that not everything shared may be private, and it's essential to be cautious about what personal information you disclose. If an Internet friend asks to meet in person, it is vital not to agree to it without consulting an adult. Adults can provide guidance, help assess the situation, and ensure that if a meeting is to occur, it takes place in a safe, public environment under the right supervision.
The Internet indeed offers opportunities to form meaningful connections, especially for those who may find face-to-face interactions challenging. Research has highlighted that virtual relationships could be as intimate as in-person ones. Yet, it is critical to stay vigilant about the risks associated with forming friendships online, such as privacy concerns, the potential for misinformation, or encountering online predators. Keeping personal information private, being careful about accepting friend requests from strangers, and paying attention to privacy settings are essential steps to maintaining online safety.
In summary, while making friends over the Internet can have its advantages, one must exercise caution and involve an adult when decisions about meeting such friends arise.
The area of the parallelogram is 45 square miles. Find its base and height
Final answer:
The student's question involves finding the base and height of a parallelogram given its area. Without additional information, there are infinite base-height combinations possible. The formula used is base multiplied by height equals the area of the parallelogram.
Explanation:
The student is asking about the relationship between the base, the height, and the area of a parallelogram. To find the base and height from the area, the formula for the area of a parallelogram is used, which is base x height = area. With an area of 45 square miles, if we have the measurement of either the base or the height, we can divide the area by that measurement to find the other dimension. However, with only the area given, the base and height can't be uniquely determined; there are infinitely many combinations of base and height that yield the same area. For instance, if the base is 9 miles, the height would be 5 miles, or if the base is 15 miles, the height would be 3 miles, and so on.
Write 2687 in expanded form
0.64 divided by 4 in standard algorithm
Answer:
Quotient = 0.16, Remainder = 0
Step-by-step explanation:
Standard algorithm of division is a step by step procedure to perform division.
In this question we have to divide 0.64 by 4, therefore, 0.64 is the dividend and 4 is the divisor.
Steps:
Zero times four is 0. Then we put decimal point in our quotient.
Continuing one times 4 is 4. We subtract 4 from 6 to have remaining value of 2. Then, we copy down 4. Thus, the remaining value now is 24.
Six times four is 24. Thus, the remaining value is zero.
Hence, we get the remainder of zero and quotient 0.16.
When 0.64 is divided by 4 using standard algorithm, we get 0.16.
What is Division?
Division in maths is the process of breaking a number up into equal parts, and finding out how many equal parts can be made.
Given is 0.64 divided by 4.
In order to divide 0.64 by 4, follow the given steps -
1 : 4 multiplied by 0 is equal to 0. Start writing the quotient as by writing 0 and decimal point after it.
2 : 4 multiplied by 1 is 4 and when 4 is subtracted from 6, we get 2. The quotient will now become 0.1 . Bring 4 down, next to 2.
3 : Now, 24 divided by 4 gives 6, this will leave remainder 0 and the final quotient will be 0.16
Therefore, 0.64 divided by 4 using standard algorithm, we get 0.16.
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Erik bought a savings bond. He could have invested in a mutual fund and earned 2 percent more. The 2 percent he could have earned is the _____.
Answer:
The 2 percent he could have earned is the opportunity cost.
Step-by-step explanation:
Erik bought a savings bond. He could have invested in a mutual fund and earned 2 percent more.
The 2 percent he could have earned is the opportunity cost.
The opportunity cost is defined as the loss of potential gain from other alternatives when one alternative is chosen.
A football team receives the ball on their own ten yard line. They make a gain of fifteen yards in the first play. What yard line is the ball on? What represents zero in this situation? Explain
The summation of 10 yds and fifteen yds is 25 yds thus the ball is the on 25 yd line and the zero represents the ball is in the net and goals.
What is summation?The summation is to add or subtract any two or more terms by doing that operation we will get a new result which could be big or small depending upon the number.
There could be only two terms, but there could be one hundred, a thousand, or a million.
As per the given question,
The initial position of the ball = 10 yd line
The team gained 15 yds in the first play.
Therefore, New position of the ball = 10 yds + 15yds = 25 yds
Hence "The summation of 10 yds and fifteen yds is 25 yds thus the ball is the on 25 yd line and the zero represents the ball is in the net and goals".
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A company employs 72 workers. It plans to increase the the number of employees by 6 per month until it has twice its current workforce. How many months will it take to double the number of employees
8 is 40 percent of what number
Answer:
20%
Step-by-step explanation: So 40 percent = 100 percent. If you divide 40 percent by 5 you get 8. 1/5 is equal to 20% and 8 is a fifth of 40. So the answer is 20%.
We have that the 8 is 40 percent of 20 and it is mathematically given as
x=20
Arithmetic
Question Parameters:
8 is 40 percent of what number
Generally the equation for the statement is mathematically given as
x*40%=8
Therefore
x*40%=8
x*0.4=8
x=20
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Divide.
8.64÷(−0.27)
A lab technician is diving a cell that has a diameter of 4.32 x 10^-4 millimeters. Each of the new cells has a diameter measuring exactly one half of the diameter of the original cell . Which is the diameter of the new cell ? A. 2.16 x 5^-2 B. 2.16 x 10-2 C.2.16 x 5-4 D.2.16x 10^-4
The diameter of the new cell, which is exactly half the diameter of the original cell (4.32 x 10^-4 millimeters), is 2.16 x 10^-4 millimeters.
Explanation:The lab technician is dividing a cell with an original diameter of 4.32 x 10^-4 millimeters. The new cells' diameter is stated to be exactly one half of the original diameter. Therefore, to find the diameter of the new cell, simply take half of the original cell's diameter. This can be accomplished by dividing the numerical value of the diameter by 2, which would be 4.32/2 = 2.16. The exponent remains the same because the size (magnitude) of cell diameter is only halved, not the order magnitude. So the diameter of the new cell is 2.16 x 10^-4 millimeters.
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I WILL GIVE BRAINIEST TO CORRECT ANSWER! All questions please.