Answer:
(7x + 27) units
Step-by-step explanation:
A rectangle is a quadrilateral (has four sides) in which opposite sides are equal and parallel, also all the angles are equal. The area of a rectangle is given as:
Area = Length × Width
Given that the area of the rectangle is 21x + 81 and the width is 3 unit, to find the length of the rectangle, we have to use the formula of the area and then get the length. Therefore:
Area = Length × Width
21x + 81 = Length × 3
Length = (21x + 81) /3
Length = 7x + 27
The length of the rectangle is 7x + 27 units
Which of the following functions is neither even nor odd? A. f(x)=x6−3x4−4x2 B. f(x)=2x3−3x2−4x+4 C. f(x)=x5−2x3−3x D. f(x)=6x5−x3
even function : [tex] f(x)=f(-x)[/tex] , odd function: $f(x)=-f(-x)$
it is neither odd nor event when both condition don't hold.
See option B.
$f(x)=2x^3-3x^2-4x+4$
$f(-x)=-2x^3-3x^2+4x+4=-(2x^3+3x^2-4x-4)$
clearly, it is neither odd nor even.
Farmer Green sent his two children out to count the hens and sheep. His daughter counted 40 hens, and his son counted 100 legs. How many of each animal is on the farm?
Answer:
40 hens, 5 sheep
Step-by-step explanation:
40 x 2 = 80 (hens have 2 legs)
100 - 80 = 20 ----> 20 legs left for sheep,, sheep have 4 legs
20/4 = 5 so there are 5 sheep
Answer:
40 hens, 5 sheep
Step-by-step explanation:
40 x 2 = 80 (hens have 2 legs)
100 - 80 = 20 ----> 20 legs left for sheep,, sheep have 4 legs
20/4 = 5 so there are 5 sheep
Ivana wants to give books from her store to the local library. She needs to place 8 books in each box. If she has 1,125 books to give away, how many boxes will she need
Answer:
140.625
Step-by-step explanation:
1125 books, placed into 8 per boxes, 1125/8=140.625
Draw a line for the axis of symmetry of function f. Also mark the x-intercept(s), y-Intercept, and vertex of the function.
f(x)= x^2- 4x-5
+
10-
Line
8
6
4
2-
-10
-8
Answer:
1) Please find attached the graph sowing the line of symmetry
The symmetry line is a vertical line passing through (2, -9)
2) The x-intercept are (5, 0) and (-1, 0)
The y-intercept is (0, -5)
The vertex is (2, -9)
Step-by-step explanation:
The given function is;
f(x) = x² - 4·x - 5
The data values are generated as follows;
x, f(x)
-1, 0
-0.8, -1.16
-0.6, -2.24
-0.4, -3.24
-0.2, -4.16
0, -5
0.2, -5.76
0.4, -6.44
0.6, -7.04
0.8, -7.56
1, -8
1.2, -8.36
1.4, -8.64
1.6, -8.84
1.8, -8.96
2, -9
2.2, -8.96
2.4, -8.84
2.6, -8.64
2.8, -8.36
3, -8
3.2, -7.56
3.4, -7.04
3.6, 6.44
3.8, -5.76
4, -5
4.2, -4.16
4.4, -3.24
4.6, -2.24
4.8, -1.16
5, 0
The minimum is found from differentiating the function, f(x), with respect to x and looking for the zeros of the result as follows;
f'(x) = 2·x -4
f'(x) = 0 = 2·x -4
x = 2
The y-coordinate gives; f(2) = 2² - 4×2 - 5 = -9
Therefore, the symmetry line is a vertical line passing through (2, -9)
The x-intercept is the point at which y = 0, therefore, from f(x) = x² - 4·x - 5, we have;
0 = x² - 4·x - 5 = (x - 5)·(x + 1)
Therefore, the x-intercept are x = 5 or -1
The x-intercept are (5, 0) and (-1, 0)
The y-intercept occur at the point where the x value = 0, therefore, we have;
The y-intercept occur at y = f(0) = 0² - 4·0 - 5 = -5
The y-intercept is (0, -5)
Re-writing the equation in vertex form y = a(x - h)² + k gives;
f(x) = x² - 4·x - 5 = 1·(x - 2)² - 9
Therefore, the vertex is (2, -9)
Answer:
see attached graph
The x-intercept are (5, 0) and (-1, 0)
The y-intercept is (0, -5)
The vertex is (2, -9)
Step-by-step explanation:
If you randomly choose a number from 1 to 10 and multiply them together, what is the probability that the number ends in a 0?
Consider an election with 681 votes a) If there are 5 candidates, what is the smallest number of first-place votes a candidate could win with under the Plurality method?
Answer:
137 votes
Step-by-step explanation:
considering an election with 681 votes and 5 candidates up for the election
dividing the votes among'st 5 candidates
= 681 / 5 = 136.2 hence the least number of first-place votes needed by a candidate using the plurality method would be = 137 votes
136.2 + 136.2 + 136.2 + 136.2 + 136.2 = 681 ( dividing the votes equally )
136 + 136 + 136 + 136+136 = 680
hence the remaining vote = 681 - 680 = 1
least first-place vote = 136 + 1 = 137 votes
For 4 hours Sam traveled at 40 miles per hour. Then he increased his speed to 60 miles per
hour and drove for another 3 hours. How far did he go in the 7 hours he traveled?
Quadrilateral ABCD has coordinates A (3, 1), B (4, 4), C (7, 5), D (6, 2). Quadrilateral ABCD is a (4 points)
Answer:
Quadrilateral ABCD is a SQUARE
Step-by-step explanation:
When we are given coordinates (x1, x2) and (y1 , y2) for a Quadrilateral, we solve for the sides using this formula.
√(x2 - x1)² + (y2 - y1)²
A (3, 1), B (4, 4), C (7, 5), D (6, 2)
Side AB = A (3, 1), B (4, 4)
√(x2 - x1)² + (y2 - y1)²
= √(4 - 3)² + (4 - 1)²
= √1² + 3²
= √1 + 9
= √10
Side BC = B (4, 4), C (7, 5)
√(x2 - x1)² + (y2 - y1)²
= √(7 - 4)² + (5 - 4)²
= √3² + 1²
= √9 + 1
= √10
Side CD = C (7, 5), D (6, 2)
√(x2 - x1)² + (y2 - y1)²
= √(6 - 7)² + (2 - 5)²
= √(-1) ² + (-3)²
= √1 + 9
= √10
Side AD = A (3, 1), D (6, 2)
√(x2 - x1)² + (y2 - y1)²
= √(6 - 3)² + (2 - 1)²
= √3² + 1²
= √9 + 1
= √10
From the above calculation,
Side AB = √10
Side BC = √10
Side CD = √10
Side AD = √10
Hence, AB = BC = CD = AD
When all the side of a Quadrilateral are the same or equal to each other, it means the Quadrilateral is a square.
Therefore, Quadrilateral ABCD is a SQUARE
Azila is a salesgirl for a cosmetic product. Her salary is RM375 per week with 5% commission of her weekly sales. What is the least value of a product that Aliza must sell if she targets a minimum salary of RM550 for a particular week?
Answer:
RM3,500
Step-by-step explanation:
Salary=RM375 per week
5% commission per week
If she target a minimum of RM 550.
Let x=minimum Sales
RM550=RM375 + 5% of x
RM550=RM375 + 0.05x
RM550 - RM375=0.05x
RM175=0.05x
Divide both sides by 0.05
RM175/0.05=0.05x/0.05
RM3,500=x
For Azila to earn a minimum of RM550 in a week, her salary will be RM375 plus 5% commission on the sales of RM3,500 value of product.
Check:
5% of RM3,500
=0.05*3,500
=RM175
Plus
Salary of RM375
RM175 + RM375=RM550
Work out the circumference of a circle with diameter 1.8 cm.
Take a to be 3.142 and give your answer to 1 decimal place.
Answer:
The answer is
5.6 cmStep-by-step explanation:
Circumference of a circle( C) = πd
where d is the diameter
π = 3.142
From the question
d = 1.8cm
Substitute d = 1.8 into the above formula
Circumference of the circle is
3.142 × 1.8
= 5.6556
We have the final answer as
C = 5.6 cm to one decimal placeHope this helps you
A quadrilateral ABCD has the area 10 square feet. After a dilation with a scale factor of 3, find the area of quadrilateral A'B'C'D'.
10 x 3^2
= 10 x 9
= 90
help me asap you guys i need help
Hi there! :)
Answer:
[tex]\huge\boxed{C}[/tex]
To simplify the process, convert each given weight into standard notation:
Lion:
[tex]1 * 10^{5} = 1 * 100000 = 100,000 g[/tex]
Ant:
[tex]2 * 10^{-3} = 2* 0.001 = 0.002[/tex]
Divide the ant's weight from the lion's weight:
[tex]100000 / 0.002 = 50,000,000[/tex]
Convert to scientific notation: (use # of zeros to determine exponent)
[tex]50,000,000 = 5 * 10^{7}[/tex]
Therefore, the correct answer is C.
Find the value of the variable(s). (9x + 12) 3x (4y - 10)
Answer:
2.07648468018
Step-by-step explanation:
While Mary Corens was a student at the University of Tennessee, she borrowed $14,000 in student loans at an annual interest rate of 7%. If Mary repays $1,800 per year, then how long (to the nearest year) will it take her to repay the loan? Do not round intermediate calculations. Round your answer to the nearest whole number.
Answer:
The number of years needed to repay the loan is 11.47 years or 11 years.
Step-by-step explanation:
The loan amount, Present value = $14000
Annual repayment amount (annuity) = $1800
Interest rate = 7% per annum.
Now we have to find the number of years consumed to repay the loan amount. Below is the calculation.
Present value = (Annuity[1-(1+r)^-n] )/ r
14000 = (1800 × [1- (1+ 0.07 )^-n] )/ 0.07
14000 × 0.07 = 1800 × [1- (1+ 0.07 )^-n]
980 = 1800 × [1- (1+ 0.07 )^-n]
0.54 = [1- (1+ 0.07 )^-n]
n = 11.47 or 11 years.
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Please answer this question now
Answer:
1471.15
Step-by-step explanation:
10. RP3-M
Jeanette purchased a concert ticket on a web site. The original price of the ticket was $75.
She used a coupon code to receive a 20% discount. The website applied a 10% service fee
to the discounted price. Jeannette's ticket was less than the original price by what percent?
Answer:
Jeannette's ticket was less than the original pice by 30%
Step-by-step explanation:
original price = $75
percentage discount = 20% of original price = 20% of $75
discounted price = [tex]\frac{20}{100} \times\ 75\ =\ 15[/tex]
discounted price = $15
website service fee = 10% of original price
website service fee = [tex]\frac{10}{100}\times 75 = \$7.5[/tex]
New discounted price = discount price + website service fee
= 15 + 7.5 = $22.5
Next, let us calculate what percentage of the original price that will give the new discount price.
Let the percentage of the original price = x%
x% of 75 = $22.5
[tex]\frac{x}{100} \times\ 75\ = 22.5\\\\\frac{75x}{100} = 22.5\\\\75x = 2250\\\\x = \frac{2250}{75} \\\\x = 30[/tex]
Therefore, Jeannette's ticket was less than the original pice by 30%
When a shape is dilated, the _________ of the lengths in the image to the corresponding lengths in the pre-image are equal to the scale factor.
A. ratios
B. lengths
C. scale factors
D. proportions
What is the correct answer to this multiple choice question? Please help!!!
Answer:
By translating the function cos(x) 90 degrees to the right.
Step-by-step explanation:
The sine function is just the cosine function translated 90 degrees to the right. You can see the visualization below. They overlap.
If you're wondering why the diagram shows a shift in
[tex]\pi / 2[/tex]
That's just the equivalent to 90 degrees in radians.
The shape of the sign outside Bob's Burger Barn is a regular octagon. How many degrees are in the measure of an interior angle of this sign?
Answer:
An octagon has eight interior angles.
Interior angle total sum = (n-2) x 180, where n = number of sides.
Since an octagon has 8 sides, we have:
6 x 180 / 8, which is 135.
The answer is 135.
Let me know if this helps!
PLEASE HELP!!!!
The degree of x y 3 + 5 x 2 y − 3 x xy 3 +5x 2 y−3xis 8. True False
Answer:
it's true
Step-by-step explanation:
Based on the data, which of the following statements must be true?
Answer:
hope this help
Step-by-step explanation:
here is the answer
can i help please??? :) Is 3.22×10 to the 4 power equal to 32,200?
Answer:
Yes
Step-by-step explanation:
we move the decimal point 4 times to the right
1st time
32.2
2nd time
322
3rd time
3220
4th time
32,200
Answer:
No
Step-by-step explanation:
3.22 x 10 = 32.2
32.3 to the fourth power = 107.50
107.50 < 32,200
Therefore it is not equal to 32,200
The circle shown above has a radius of 5 units, and the central angle of the sector that is shaded is 25π radians. Determine the area of the shaded sector, in terms of π. Enter the area of the sector.
Answer:
The answer is below
Step-by-step explanation:
Given that:
The radius of the circle (r) = 5 units
The central angle (θ) = 25π
A sector of a circle is the portion of a circle made up of two of its radii and an arc. The area of a sector that subtends with a central angle (θ) and a radius (r) is given by the formula:
[tex]Area\ of\ sector=\frac{\theta}{360} *\pi r^2[/tex]
Substituting the radius of the circle and the central angle:
[tex]Area\ of\ sector=\frac{\theta}{360} *\pi r^2\\\\Area\ of\ sector=\frac{25\pi}{360} *\pi (5)^2\\\\Area\ of\ sector=\frac{125\pi^2}{72}[/tex]
Positive numbers are not closed under subtraction. Give an example of this 1
below.
Answer:
5 -3 = 2
3-5 = -2
Step-by-step explanation:
In this question, we want to examine the validity of the statement by the use of an example.
Firstly, we need to understand the meaning of the fact that they are ‘closed’
By saying these numbers are closed under this arithmetic operation i.e subtraction, we directly mean that they obey the closure property.
Now, to obey the closure property means that if we move either way i.e by switching the numbers and performing the same arithmetic operation of subtraction, we are supposed to get same answer.
What this means in terms of examples is as follows;
Consider two positive numbers, 5 and 3
Now we know that 5-3 = 2
To check if the closure property is obeyed, switch the place of the numbers.
This means we would have;
3-5 = -2
We can see that both results are not the same. We can then conclude that the arithmetic operation of subtraction is not closed or does not obey the closure property for positive numbers.
f(x)=8−4x−x3 g(x)=x2+7x−9 Find f(x)+g(x). Select one: a. x3+x2+3x−1 b. −x3+x+3x−1 c. −x3+x2+11x−9 d. 8x2+3x−9x3
Answer:
B
Step-by-step explanation:
We are given the two functions:
[tex]f(x) = 8 - 4x - x^3\text{ and } g(x) = x^2 + 7x - 9[/tex]
And we want to find:
[tex]f(x) + g(x)[/tex]
Substitute:
[tex]= (8 - 4x - x^3) + (x^2 + 7x - 9)[/tex]
Rewrite:
[tex]= (-x^3) + (x^2) + (7x - 4x) + (8 - 9)[/tex]
Combine like terms:
[tex]= -x^3 + x^2 +3x -1[/tex]
In conclusion:
[tex]f(x) + g(x) = -x^3 + x^2 +3x -1[/tex]
Hence, our answer is B.
Joshua remembered he had a coupon in his pocket that would take and additional 30%off the price of the shirts. Calculate the new total cost of the shirts including a sales tax of 6.5%
Answer:
New cost of the shirt=$39.028416
Step-by-step explanation:
Target is having a Back to School sale where all polo shirts are discounted by 20%. Joshua wants to buy five shirts: two cost $10.98 each, one costs $11.50, and two others cost $15.99 each. Joshua remembered he had a coupon in his pocket that would take an additional 30% of the shirts. Which choice represents the new total cost of the shirts including the sales tax of 6.5%
Solution
Two shirts cost=$10.98 each
One shirt cost=$11.50
Two shirts cost=$15.99 each
Total cost of shirts=(2*$10.98 + $11.50 + 2*$15.99)
=$21.96 + $11.50 + $31.98
=$65.44
All polo shirts are discounted by 20%
It means he would pay 100%-20% of the total cost
100%-20%=80%
Discounted price=$65.44 * 80%
=$65.44 * 0.8
=$52.352
He has a coupon of 30% off the shirt
100% -30%=70%
=$52.352*70%
=$52.352 * 0.7
=$36.6464
Plus Sales tax of 6.5%
6.5% of $36.6464
=0.065* $36.6464
=$2.382016
New cost of the shirt=$36.6464 + $2.382016
=$39.028416
3.
Find the inverse of A if it has one, or state that the inverse does not exist.
I can only give you the answer
Answer:
Hello,
Answer A
Step-by-step explanation:
See jointed file: Methode du compagnon
96 is 30% of what number?
Step-by-step explanation:
If we substitue "what number" in the question "96 is 30 percent of what number?" with 320, we get this sentence: 96 is 30 percent of 320. Since this statement is true, we know that our answer is correct.
What does this mean? 20 points + brainleist! What other angle measures or side lengths can you determine using these added figures? List all the concepts and facts you use.
Step-by-step explanation:
The question has asked you to have another concepts or facts that can be used to find the other angles and measure of side length.
by looking the fig we can determine various sides and angles as all are joined together.