The standard form of the function is f(x) = -x² +4x, The vertex form isf(x) = -(x-2)² + 4
What is a function?
A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.
Given table is
x f(x)
-1 -5
0 0
1 3
2 4
3 3
4 0
Find the difference to find the degree of the given function
f(x) -5 0 3 4 3 0
1st difference 5 3 1 -1 -3
2nd difference -2 -2 -2 -2
The degree of the function is 2.
The general form of a second-degree function is
f(x) = ax²+bx+c
Putting x = 0 and f(0) =0 in f(x) = ax²+bx+c:
f(0) = a×0²+b×0+c
0 = c
Now putting x = 1 and f(1) =3 in f(x) = ax²+bx+c:
f(1) = a×1²+b×1+0 [since c=0]
3 = a + b ....(i)
Now putting x = 2 and f(2) =4 in f(x) = ax²+bx+c:
f(2) = a×2²+b×2+0 [since c=0]
4 = 4a + 2b ....(ii)
Solve equations (i) and (ii) by using the elimination method:
Multiply equation (i) by 2 and subtract it from (ii)
4a + 2b = 4
2a + 2b = 6
(-) (-) (-)
__________
2a = -2
a = -1
Putting a = -1 in equation (i):
-1 + b = 3
b = 3+1
b = 4
The function is f(x) = -x² +4x
Rewrite the given function in vertex form:
f(x) = -(x² - 4x +4-4)
f(x) = -(x-2)² + 4
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if two lines in a plane intersect then they are not parallel true or false
Answer:
true because parallel means lines that doesnt meet
Answer:true, parallel line never intersect, I hope this helps!!
Cute cat btw<3
What is the solution to 3(1-3x)=2(-4x+7)?
Answer:
x = -11
Step-by-step explanation:
3(1 - 3x) = 2(-4x + 7)
Distribute the 3.
(3 - 9x) = 2(-4x + 7)
Distribute the 2.
3 - 9x = -8x + 14
Add 8x to both sides.
3 - x = 14
Subtract 3 from both sides.
-x = 11
Multiply by -1.
x = -11.
Proof:
3(1 - 3x) = 2(-4x + 7)
3(1 - 3(-11)) = 2(-4(-11) + 7)
3(1 + 33) = 2(44 + 7)
3(34) = 2(51)
102 = 102
The Paulsens ordered $75.41 worth of Chinese food. They paid 11.5% sales tax and left a
15% tip on $75.41. What was the total cost?
Answer:
$95.39
Step-by-step explanation:
First, find sales tax
75.41×(11.5/100)=8.67
Then, tip
75.41×(15/100)=11.31
Therefore,
75.41+8.67+11.31
is the total cost
Answer:
95.39
Step-by-step explanation:
1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9
2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)
3. -2 \leq -2 Subtract 6 from both sides, then 8, and then 2
4. -4 < 8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given few inequalities and some operations are performed on them
For first inequality:
=> 4 < 7
Multiply both sides by 3, then by 2, then by 4, then by 9
=> 4 *3 * 2 * 4 * 9 < 7 *3 * 2 * 4 * 9
=> 864 < 1512
there is no change in the inequality sign and it is still true.
For the second inequality:
=>11 > -2
Add 3 to both sides, then add 3, then add (-4)
=> 11 +3 + 3 + (-4) > -2 + 3+3 + (-4)
=> 13 > 0
there is no change in the inequality sign and it is still true.
For the third inequality:
=> -2 ≤ -2
Subtract 6 from both sides, then 8, and then 2
=> -2 -6 -8 -2 ≤ -2 -6 -8 -2
=> -18 ≤ -18
there is no change in the inequality sign and it is still true.
For the fourth inequality:
=> -4 < 8
Divide both sides by -4
=> -4 / -4 < 8 / -4
Since, after dividing or multiplying on both sides by a negative sign, inequality changes its sign
=> 1 > -2
Divide both sides by -2
=> -1/2 < 1
there are two times a change in the inequality sign and it is still true.
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Ans the question...... very urgent
Answer:
The solution should be log7^3(49)-1/3log7(49)=1/3*2
B-2/3
The point A (1,1) and the point B(5,-1) lie on the line L. Find the equation of the line L
9. Which equation is represented by the table?
X
0
1
2.
3
у
40
20
10
5
a. 40(2)^x
b. 40(1/2)^x
What is the measure of ZB?
Answer:
m<B=60°
Step-by-step explanation:
an exterior angles equals the sum of its two remote interior angles, so:
m<A+m<B=m<BCG:
3x+4x=10x-45
7x=10x-45
-3x=-45
x=15
to find the measure of <B:
since m<B=4x:
4(15)=60°
so, m<B=60°
Answer:
Step-by-step explanation:
The value of πPhone stock has increased 9% each year for the past several years. In 2020, the stock was worth $75. What will the stock be worth in 7 years? What was the stock worth in 2016?
Answer:
2027 = $122.25
2016 = $48
Step-by-step explanation:
Find 1% of 75
75 / 100 = 0.75
multiply by 9
0.75 * 9 = 6.75
So that's $6.75 each year
Now, lets find our answers for 7 years.
6.75 * 7 = $47.25
75 + 47.25 = $122.25
The stock will be $122.25 in 2027
Now for 2016.
$6.75 * 4 = $27
$75 - $27 = $48
The stock was $48 in 2016
When working modulo m, the notation a^-1 is used to denote the residue b for whichab = 1 (mod m), if any exists. For how many integers a satisfying 0 < a < 100 is it true thata(a − 1)−¹ = 4a-¹ (mod 20)?Please hurry up guys!!
There are 10 integers that satisfy 0 < a < 100.
What are integers?
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
Here, we have
Given: When working modulo m, the notation a⁻¹ is used to denote the residue b for which ab = 1 (mod m), if any exists.
We have to find integers that satisfy 0 < a < 100.
a(a − 1)⁻¹ ≡ 4a⁻¹ (mod 20)
a ≡ 4a⁻¹(a − 1)(mod 20)
a² ≡ 4(a-1)(mod 20)
a² - 4a + 4 ≡ 0(mod 20)
(a - 2)² ≡ 0(mod 20)
a = 2 + 10n | for n = (0, 1, 2, 3.....9)
Hence, there are 10 integers that satisfy 0 < a < 100.
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ILL BRAINLIEST YOU PLEASE HELP ME
Answer:
x = 71/5 (as an improper fraction)
x = 14 1/5 (as a proper fraction
x = 14.2 (as a decimal)
Step-by-step explanation:
It's a rectangle so the diagonals are equal
7x - 9 = 2x + 62
Subtract 2x from both sides
5x - 9 = 62
Add 9 to both sides
5x = 71
Divide both sides by 5
x = 71/5 (as an improper fraction)
x = 14 1/5 (as a proper fraction
x = 14.2 (as a decimal)
Answer:
x= 14.2
Step-by-step explanation:
BD and and AC are equal so
7x-9 = 2x+62
isolate the variable means x = 14.2
first time I had to take out pencil and paper so I hope it's right
please help due next hour this is one of my answer I'm struggling with Show WORK please. No links
x/2 = -1
please help I need it
x/2 = -1
=> x = -1 × 2
=> x = -2
Determine the value of c for each figure
Answer:
can you tell me a little bit more?
36-x=-36 what's the answer to It
Answer:
x = 72
Step-by-step explanation:
36 - x = -36
*subtract 36 from both sides*
-x = -72
*divide by -1*
x = 72
Answer:
0 is the answer of the equation
The following dotplot shows the centuries during which the 111111 castles whose ruins remain in Somerset, England were constructed. Each dot represents a different castle. According to the 1.5.IQR rule for outliers, how many high outliers are there in the data set?
The conclusion which we get after analyzing the data given is that there aren't outliers in the displayed data set.
We will calculate the interquartile range and us the rule 1.5 .
The formula to calculate interquartile range is to subtract the value of first quartile by the value of second quartile.
IQR = Q3 - Q1
Therefore, interquartile range becomes,
IQR = 17 - 13
IQR = 4
Now , we will apply rule 1.5 and for that we will multiply 4 by 1.5 first
4 * 1.5 = 6
and then,
17 + 6 = 23
on applying the rue we will get ,
13 - 6 = 7 .
This value means that there is no outlier in the displayed data set.
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test form 1a answers 6th grade three times Geoff's age plus 3 is myrkas age. myrka is 48. what is Geoff's age
Geoff is therefore 15 years old.Rearranging terms in an equation to get the solution is known as "solving by rearranging.
What does a math reshuffle mean?Rearranging terms in an equation to get the solution is known as "solving by rearranging." Keep these guidelines in mind when solving by rearranging: To shift terms from one side to the other, do the reverse operation.Rearranging terms in an equation to get the solution is known as "solving by rearranging." Keep these guidelines in mind when solving by rearranging: To shift terms from one side to the other, do the reverse operation.Geoff is therefore 15 years old.Rearranging terms in an equation to get the solution is known as "solving by rearranging.Age of Myrka = 3x + Age of Geoff
3x + 3 = 48
3x = 48 - 3
3x = 45 x = 15
Geoff is therefore 15 years old.
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The surface area of this regular pyramid is 1040 cm2. The base is a regular pentagon with side b = 16 cm and slant height l =15 cm. Find its apothem (a).
show work please. i will give brainliest ! :)
Answer:
(a) = 11 cm
Step-by-step explanation:
The formula for finding the surface area of a regular pyramid is B + (1/2*P*l), with B being the area of the base, p being the perimeter of the base, and l being the slant of the pyramid.
The area of a pentagon can be solved using the formula 1/2*a*p, with a being the apothem and p being the perimeter of the pentagon.
B + (1/2*80*15) = 1040B + 600 = 10401040 - 600 = 440 (440 is the area of pentagon)1/2*a*(16*5) = 44040*a = 440440/40 = 11The apothem is 11 cm. Hope this helps!
look at the screenshot.....
Answer:
the total surface area is 360 cm
Step-by-step explanation:
Lois is saving $11.00 out of her $32.00 allowance each week for a
scooter. She must divide the rest between her savings account, a
charity of her choice, and her college fund. Lois gives $10.00 per week
to a local charity. She puts the same amount in her saings account as
her college fund. How much does Lois put in her college fund each
week?
Answer:
the answer is $5.50
Step-by-step explanation:
32 total
10+11=21
32-21=11
so 11 left for college and saving account
now divide it with 2 so both gets same amount
11/2=5.50
Is 8 15 17 a right triangle?
No, the sides of a right triangle do not include 8, 15, and 17. The sides of a right triangle must follow the Pythagorean theorem, so the sum of the squares of the two shorter sides must equal the square of the longest side. 8² + 15² does not equal 1
8² + 15² = 64 + 225 = 289
17² = 289
Therefore, 8, 15, and 17 are not the sides of a right triangle.
The Pythagorean theorem is an important mathematical concept used to determine if three numbers form the sides of a right triangle. This theorem states that the sum of the squares of the two shorter sides must equal the square of the longest side. In the case of 8, 15, and 17, 8² + 15² does not equal 17², so it is not a right triangle. To test this, we can calculate 8² + 15² = 289, and then 17² = 289. Since the two values are not equal, we can conclude that 8, 15, and 17 are not the sides of a right triangle.
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im not sure how to answer thank you
The value of x in the triangle WXY is 27°
What is an equation?An equation shows how two or more numbers and variables are related to each other.
∠VWY + ∠XWY = 180° (sum of angle in straight line)
6x + ∠XWY = 180°
∠XWY = 180 - 6x
∠XYW + ∠ZYW = 180° (sum of angle in straight line)
∠XYW + 4x = 180°
∠XYW = 180 - 4x
∠XWY + ∠XYW + ∠YXW = 180° (angle in a triangle)
(180 - 6x) + (180 - 4x) + 90 = 180
450 - 10x = 180
10x = 270
x = 27°
The value of x is 27°
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An aerospace engineer is designing a model of a portion of a new telescope, a cylinder with a cone cut-out as shown below. What is the total volume of the materials used to make the new telescope piece?
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the required figure is not attached to the question.
From the question, we can deduce that the telescope is a composite figure made from a cone and a cylinder.
To get the volume of the materials used, you have to calculate the volume of the cone and that of the cylinder.
The sum of these volumes, is your answer.
Assume the following dimensions:
Cone
[tex]r = 5\\[/tex] --- radius
[tex]h = 7[/tex] --- height
Cylinder
[tex]r = 5\\[/tex] --- radius
[tex]h = 20[/tex] --- height
The volume of the cone is:
[tex]Volume = \frac{1}{3} \pi r^2h[/tex]
[tex]V_1= \frac{1}{3} \pi *5^2*7[/tex]
[tex]V_1= \frac{1}{3} \pi *25*7[/tex]
[tex]V_1= \frac{175}{3} \pi[/tex]
The volume of the cylinder is:
[tex]Volume = \pi r^2h[/tex]
[tex]V_2 = \pi * 5^2 * 20[/tex]
[tex]V_2 = \pi * 25* 20[/tex]
[tex]V_2 = 500\pi[/tex]
The total is:
[tex]Volume = V_1 + V_2[/tex]
[tex]Volume = \frac{175\pi}{3} + 500\pi[/tex]
Take LCM
[tex]Volume = \frac{175\pi+1500\pi}{3}[/tex]
[tex]Volume = \frac{1675\pi}{3}[/tex]
How many square feet of outdoor carpet will
we need for this hole?
Answer:
8
Step-by-step explanation:
Find the area of this parallelogram. Be sure to include the correct unit in your answer.
Answer:
The area of this parallelogram is 140 square feet.
Step-by-step explanation:
A = bh
A = 14 * 10
A = 140
Hope this helps; have a wonderful day!
Question 2 of 5
Simplify.
(m3)6 +m18
A. m4
B. 1
C. m
D. m-9
SUBMIT
Using the first index law, the solution provided indicates that this has a value of 1.
What is the first index law?X to the power of A multiplied by X to a power of B results in X to the power of A + B, according to the first law of indices. Keep in mind that adding the indices when multiplying terms with them means that the base must remain constant throughout.
What exactly is index theory?A topological invariant of a certain class of differential operations on a manifold is studied in index theory, as well as the invariant's local formula in terms of the manifold's geometry. inspirational cases. operator elliptic The index theorem by Atiyah-Singer.
According to the given information:(m³)⁶/m¹⁸ = m³ˣ⁸/m¹⁸
= m¹⁸/m¹⁸
= 1
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Remember, adjectives in Spanish agree with the gender of the noun they describe.
Por ejemplo: el chico ordenado / la chica artística
Answer:
1) A serious girl - Una chica seria/Una joven seria
2) The talented boy - El chico talentoso/El joven talentoso
3) An outgoing girl - Una chica extrovertida/Una joven extrovertida
4) The tasty ice cream - El helado delicioso/El helado sabroso
5) A funny book - Un libro divertido/Un libro entretenido
Step-by-step explanation:
Now, we present a possible set of solution, as there are solutions as many synonyms exist in Spanish. Then:
1) A serious girl - Una chica seria/Una joven seria
2) The talented boy - El chico talentoso/El joven talentoso
3) An outgoing girl - Una chica extrovertida/Una joven extrovertida
4) The tasty ice cream - El helado delicioso/El helado sabroso
5) A funny book - Un libro divertido/Un libro entretenido
1/4 - 7/1 (pls i nee answer)
Answer:3/4 is the answer
Step-by-step explanation:
Answer:(s)
1/4 - 7/1 = - 27/4
Decimal: - 6.75
Mixed number: - 6 3/4
Step-by-step explanation:
1/4 - 7/1 = - 27/4 or - 6.75 or - 6 3/4
LCM: 4, 1 = 4
Adjust Fraction Based On LCM:
1/4 - 28/4
Apply The Fraction Rule:
a/c - b/c = a - b/c
1 - 28/4
Subtract the numbers:
1 - 28 = - 27
= -27/4
Apply Fraction Rule:
- a/b = - a/b
Thus:
1/4 - 7/1 = - 27/4
Decimal: - 6.75
Mixed Number Form - 6 3/4
I hope that helps you!!!
What is the product of 2x 3y )( 2x 3y )? *?
The product of (2x-3y)(2x+3y) is 4x^2-9y^2
Product= (2x-3y)(2x+3y)
Let the product of (2x-3y)(2x+3y) be P
P=2x(2x+3y)-3y(2x+3y)
P= 2x(2x)+2x(3y)-3y(2x)-3y(3y) {using distributive property of multiplication}
This property states that multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. The multiplication of (a-b)(a+b) is equal to a^2 - b^2. This result is used as an identity.
P= 4x^2 +6xy - 6xy -9y^2
solving 6xy-6xy=0
P= 4x^2 - 9y^2
4x^2-9y^2 is the product of (2x-3y)(2x+3y).
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A small town surveyed 250 adults, 180 of whom were parents, about whether a park should be expanded. The results showed that 150 of the adults who were parents and 40 of the adults who err not parent’s thought the park should be expanded.
Answer: In this exercise we have to calculate the values of the people who voted to expand the parking lot, so we have to:
Yes: parents will be 150 and not parents 40
No; parents will be 40 and not parents 30
As it is about sets, we have to use the data that were:
total: 250 adults
180 of whom were parents a park should be expanded.
40 of the adults who were not parents thought the park should be expanded.
then calculate that:
Step-by-step explanation:
The surveyed parents favor park extension, and two way table is a way or representation of data. and The two-way table is completed as,
yes no
parents 150 | 30
|
not parents 40 | 30
The two-way table shown in the table is attached below.
What is two way table?
Two-way table is a way of representing of data to better understand it.
Given information-
The total number of adults took the survey is 250.
Total number of parents took the survey is 180.
150 of the adults with children and 40 of those without thought the park should be expanded.
Suppose the number of adults who are not the parents and took the survey is .
As the total number of adults took the survey is 250 in which the number of parents took the survey is 180. Thus the number of adults who are not the parents and took the survey is,
Suppose the parents who does not thing that the park should be expanded is .
There is total 180 parents. As 150 of the adults with children thought the park should be expanded. Thus, the parents who does not thing that the park should be expanded is,
Form the 70 adults who are not parents things that park should be expanded is 40, hence the adults who are not parents does not thing the park should be expanded is (70-40) which is 30.
Hence the two way table is completed as,
yes no
parents 150 | 30
|
not parents 40 | 30
the two way
YES NO
30
30
(parents 150
not parents_40
can someone pls help