Answer:
The answer is 1800
Step-by-step explanation
9% of 20,000 = 1800
Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?
y = 2x – 2
y = 2x + 2
y = x + 2
y = x – 2
Answer:
C
Step-by-step explanation:
We know that line CD passes through the two points (0, 2) and (4, 6).
First and foremost, let’s find the slope of the line. We can use the slope formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where (x₁, y₁) and (x₂, y₂) are our two points.
So, let’s let (0, 2) be (x₁, y₁) and (4, 6) be (x₂, y₂). Substitute appropriately:
[tex]\displaystyle m=\frac{6-2}{4-0}[/tex]
Evaluate:
[tex]\displaystyle m=\frac{4}{4}=1[/tex]
Hence, our slope is 1.
Now, we can use the slope-intercept form:
[tex]\displaystyle y=mx+b[/tex]
Where m is our slope and b is our y-intercept.
Notice from our given points that we are given (0, 2).
So, our y-intercept is 2.
Therefore, we will substitute 1 for m and 2 for b. This yields:
[tex]\displaystyle y=(1)x+(2)[/tex]
Simplify:
[tex]\displaystyle y=x+2[/tex]
Hence, our answer is C.
Square PQRS is transformed as shown on the graph.
Which rule describes the transformation?
Ra 90°
Ro, 180°
O RO, 270
O Ro 360
S
The rule that describes this transformation is R₀ 270°
TransformationTransformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
If a point A(x, y) is rotated clockwise by 270 degrees, the new point is at A'(-y, x)
Quadrilateral PQRS is at P(-3, 5), Q(-1, 3), R(-3, 1) and S(-5, 3). If PQRS is rotated 270 degrees clockwise, the new point is at P'(-5, -3), Q'(-3, -1), R'(-1, -3) and S'(-3, 5)
Find out more on transformation at: https://brainly.com/question/1548871
5)
2x + 8+ = 32
Solve the question
Answer:
x = 12
General Formulas and Concepts:
Order of Operations: BPEMDAS
Step-by-step explanation:
Step 1: Define equation
2x + 8 = 32
Step 2: Solve for x
Subtract 8 on both sides: 2x = 24Divide 2 on both sides: x = 12Step 3: Check
Plug in x to verify it's a solution.
Substitute: 2(12) + 8 = 32Multiply: 24 + 8 = 32Add: 32 = 32A rectangular fence with a positive area has length represented by the expression 3x2+5x-8 and width by 2x2+6x
1. Write expressions in terms of x for the perimeter.
2. Write expressions in terms of x for the area. Give your answers in standard polynomial form and show your work.
3. If the perimeter of the rectangular fence is 16 units, prove, using the quadratic formula, that the solutions to the equation are x=1 and x=-3.2.
4. Using the first solution as x, show work and give the dimensions of the rectangular fence.
5. Using the second solution as x, show work and give the dimensions of the rectangular fence.
6. Explain which dimensions of the fence make sense in the context of the problem.
7. Using the dimensions from #6, what is the area of the rectangular fence?
Answer:
1. [tex]Perimeter = 10x^2+ 22x - 16[/tex]
2. [tex]Area = 6x^4 +28x^3 + 14x^2 - 48x[/tex]
3. [tex]x = 1[/tex] or [tex]x = -3.2[/tex]
4. [tex]Length = 0[/tex] and [tex]Width = 8[/tex]
5. [tex]Length = 6.72[/tex] and [tex]Width = 1.28[/tex]
6. Second Solution
7. [tex]Area = 8.6016[/tex]
Step-by-step explanation:
Given
[tex]Length = 3x^2 + 5x - 8[/tex]
[tex]Width = 2x^2 + 6x[/tex]
Solving (1): The perimeter
Perimeter is calculated as thus:
[tex]Perimeter = 2 * (Length + Width)[/tex]
Substitute values for Length and Width
[tex]Perimeter = 2 * (3x^2 + 5x - 8 + 2x^2 + 6x)[/tex]
Collect Like Terms
[tex]Perimeter = 2 * (3x^2+ 2x^2 + 6x + 5x - 8 )[/tex]
[tex]Perimeter = 2 * (5x^2+ 11x - 8 )[/tex]
Open Bracket
[tex]Perimeter = 10x^2+ 22x - 16[/tex]
Solving (2): The Area:
Area is calculated as thus:
[tex]Area = Length * Width[/tex]
Substitute values for Length and Width
[tex]Area = (3x^2 + 5x - 8) * (2x^2 + 6x)[/tex]
Expand Bracket
[tex]Area = 2x^2(3x^2 + 5x - 8) + 6x(3x^2 + 5x - 8)[/tex]
Open Bracket
[tex]Area = 6x^4 + 10x^3 - 16x^2 + 18x^3 + 30x^2 - 48x[/tex]
Collect Like Terms
[tex]Area = 6x^4 + 10x^3 + 18x^3 - 16x^2 + 30x^2 - 48x[/tex]
[tex]Area = 6x^4 +28x^3 + 14x^2 - 48x[/tex]
Solving (3): If perimeter is 16, show that x = 1 and x = -3.2
In (a) [tex]Perimeter = 10x^2+ 22x - 16[/tex]
Substitute 16 for Perimeter
[tex]16 = 10x^2+ 22x - 16[/tex]
Equate to 0
[tex]10x^2+ 22x - 16 -16=0[/tex]
[tex]10x^2+ 22x - 32=0[/tex]
Expand
[tex]10x^2+ 32x -10x- 32=0[/tex]
Factorize
[tex]x(10x + 32) - 1(10x + 32) = 0[/tex]
[tex](x - 1)(10x + 32) = 0[/tex]
Split
[tex]x - 1 =0[/tex] or [tex]10x + 32 = 0[/tex]
[tex]x = 1[/tex] or [tex]10x = -32[/tex]
[tex]x = 1[/tex] or [tex]x = -32/10[/tex]
[tex]x = 1[/tex] or [tex]x = -3.2[/tex]
Solving (4): Using x = 1; Solve the dimension of the rectangle
We have that:
[tex]Length = 3x^2 + 5x - 8[/tex]
[tex]Width = 2x^2 + 6x[/tex]
Substitute 1 for x in the given parameters
[tex]Length = 3(1)^2 + 5(1) - 8[/tex]
[tex]Length = 3*1 + 5*1 - 8[/tex]
[tex]Length = 3 + 5 - 8[/tex]
[tex]Length = 0[/tex]
[tex]Width = 2(1)^2 + 6(1)[/tex]
[tex]Width = 2*1 + 6*1[/tex]
[tex]Width = 2 + 6[/tex]
[tex]Width = 8[/tex]
Solving (5): Using x = -3.2; Solve the dimension of the rectangle
We have that:
[tex]Length = 3x^2 + 5x - 8[/tex]
[tex]Width = 2x^2 + 6x[/tex]
Substitute -3.2 for x in the given parameters
[tex]Length = 3(-3.2)^2 + 5(-3.2) - 8[/tex]
[tex]Length = 3*10.24 + 5(-3.2) - 8[/tex]
[tex]Length = 30.72 -16 - 8[/tex]
[tex]Length = 6.72[/tex]
[tex]Width = 2(-3.2)^2 + 6(-3.2)[/tex]
[tex]Width = 2*10.24 + 6(-3.2)[/tex]
[tex]Width = 20.48 -19.2[/tex]
[tex]Width = 1.28[/tex]
[tex]Length = 6.72[/tex] and [tex]Width = 1.28[/tex]
Solving (6):
In the first solution of the dimensions in number 4, we have that
[tex]Length = 0[/tex] and [tex]Width = 8[/tex]
This dimension can not be considered because the length of a rectangle can not be 0
In the second solution of the dimensions in number 5, we have that
[tex]Length = 6.72[/tex] and [tex]Width = 1.28[/tex]
This dimension makes more sense because both dimensions are greater than 0
Solving (7): Using (6), determine the Area
In (6), we conclude that
[tex]Length = 6.72[/tex] and [tex]Width = 1.28[/tex]
So, Area is calculated as thus:
[tex]Area = Length * Width[/tex]
[tex]Area = 6.72 * 1.28[/tex]
[tex]Area = 8.6016[/tex]
express 182 as a product of its prime factors
Answer:
2x7x13
Step-by-step explanation:
182 = 91 x 2
91 = 13 x 7
PLEASE URGENT (ALGEBRA)
Find the number of calories in a honeydew and a cantaloupe
(1.) A honeydew has 20 more calories than a cantaloupe
(2.) Six honeydew and 3 cantaloupes have 750 calories
Answer:
1) A honeydew has 20 more calories than a cantaloupe
If f(x) = 3x2 - 2 and g(x) = 2x + 4, find (f - g)(x).
Answer:
(f - g)(x) = 3x² - 2x - 6
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra
Combining like termsStandard Form: ax² + bx + c = 0Step-by-step explanation:
Step 1: Define
f(x) = 3x² - 2
g(x) = 2x + 4
(f - g)(x) is f(x) - g(x)
Step 2: Find
Substitute: (f - g)(x) = 3x² - 2 - (2x + 4)Distribute -1: (f - g)(x) = 3x² - 2 - 2x - 4Combine like terms: (f - g)(x) = 3x² - 2x - 6factorise 2x^2 - 9x -5
Answer:
(x-5)(2x+1)
Step-by-step explanation:
Its called google XD
learning task 1 identify if the if the given equation is a polynomial equation or not
Answer:
In particular, for an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions.
Step-by-step explanation:
A lollipop costs $0.90. A candy necklace costs $0.31. How much more does a lollipop cost
than a candy necklace?
I really need help !!!!!! Gibing 89 points
Answer:
$0.59 more than the candy necklace
Step-by-step explanation:
you subtract .90 from .31
x-4y=8 in slope-intercept form
Answer:
y= 1 over 4 x -2
Step-by-step explanation:
hope you understand that
Answer:
y = [tex]\frac{1}{4}[/tex] x - 2
Step-by-step explanation:
y = mx + b is slope-intercept form of linear equation.
Solve x - 4y = 8 for "y"
- 4y = - x + 8
y = [tex]\frac{1}{4}[/tex] x - 2
K
KL = 7, JL = 24, and JK = 25. Find tan J.
Answer:
Tan J = 0.2917
Step-by-step explanation:
Here, we want to find the value of tan J
Firstly, we need to understand that the numbers 24, 25 and 7 are a Pythagorean triple and as such the three measures represent the values of length of the sides of a right angled triangle
The tangent of an angle= measure of the opposite/measure of the adjacent
In the question, the opposite to point J measures 7 while the adjacent measures 24
So ;
tan J = 7/24
= 0.2917
HELP 30 Points ANy wrong/bad answers will be deleted by one of my moderator friends.
Hope this helps?
Please mark my answer as brainliest?
When angles are complementary, the sum of their measures is 90 degrees. Two complementary angles have the measures of 2x - 10 degrees and 3x - 10 degrees. Find the measures of each angle
Answer:
2x - 10 = 34 degrees
3x - 10 = 56 degrees
Step-by-step explanation:
Since they're complementary, they'd equal 90-degrees.
Solve for x:
2x - 10 + 3x - 10 = 90
5x -20 = 90
5x = 110
x = 22
2(22)-10 = 34
3(22)-10 = 56
Jina and her husband are each starting a saving plan. Jina will initially set aside $650 and then add $135 every month to the savings. The amount A (in dollars) saved this way is given by the function =A+135N650, where N is the number of months she has been saving. Her husband will not set an initial amount aside but will add $585 to the savings every month. The amount B (in dollars) saved using this plan is given by the function =B585N. Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible.
Step-by-step explanation:
If A=650+135N; and B=585N,
then A+B= 650+135N+585N=650+620N
T=720N+650
A function assigns values to each element. An equation relating T to N can be represented by T=650+720N.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function which tells the amount that is been saved by Jina is given by the function A=650+135N, while the function which tells the amount that will be saved by her husband is B=585N.
Since the total saving amount is represented by T which is the sum of the two functions A and B. Therefore, the function of T can be written as,
[tex]\rm T=A+B\\\\T = (650+135N)+585N\\\\T = 650+135N+585N\\\\T = 650+720N[/tex]
Thus, an equation relating T to N can be represented by T=650+720N.
Learn more about Function:
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What is the value of Negative 5 Superscript 6? –15,625 –30 30 15,625
Answer:
D
Step-by-step explanation:
The value of the expression (-5)⁶ is, 15,625. So option D is correct
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
The expression (-5)⁶
In mathematical terms, this means that the expression
⇒ (-5) x (-5) x (-5) x (-5) x (-5) x (-5)
⇒ 15625
So, the value of the expression (-5)⁶ is 15625.
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10. Reka Rahim is employed at a restaurant. She has family medical coverage through the company's group
medical plan. The annual cost of Reka's family coverage is $3,700.00. The company pays 35% of the cost. How
much does Reka pay annually for medical insurance?
$3,700.00
$1,295.00
$2,405.00
$4,050.00
When x = 1/2, what is the value of 8x-3/x ?
During his vacation, Dalyn rents a small boat from a rental service that charges a flat fee of $40 plus $20 per hour (including taxes).
The total charge comes to $120. Which equation can be used to calculate the number of hours, a, that Dalyn rents the boat?
Answer:
4 hours
Step-by-step explanation:
We can calculate this using the y=mx+c formula
y=total charge
m=per hour
x = (a) no. of hours
c= flat fee
y=20x+40
120=20x+40
We then solve like a normal equation
120-40=20x+40-40
80/20=20x/20
x=a
a=4
∴ Dalyn rents the boat for 4 hours
Write an equation for the line in the given form.
slope is -5 and (5, 4) is on the line; standard form
Answer:
5x+y=29
Step-by-step explanation:
You use the information that is given and convert it into point-slope form y-y1=m(x-x1) like so. y-4= -5(x-5). Then you solve for y and you get y= -5x+29 which is slope intercept form (y=mx+b). Then you transform it into Standard form (ax+by=c) so all you do is add 5 on both sides and you get 5x+y=29. Now you have found your solution.
If you can please make my answer the brainliest that would be much appreciated. Thanks!
1. So far, Marta has correctly predicted the winner of 6 out of 13 football games. She wants to know how many consecutive games she would have to predict correctly to raise the percent of correct predictions to 65%. (a) Write an equation to represent this situation. (3 points) (b) Solve the equation. Show all steps. (5 points) (c) Answer the question. How many consecutive games must she predict correctly to raise her percent to 65%? (1 point)
Answer:
[(6 + x) / 13+x] = 0.65
7
Step-by-step explanation:
Given that:
Total number of games = 13
Number of correct prediction = 6
Number of correct predictions needed to raise prediction % to 65%
(Number of correct predictions) / (total number of games) = 0.65
Let x = number of additional consecutive correct predictions
[(6 + x) / 13+x] = 0.65
Where x = number of consecutive predictions required
6 + x = (13 + x) * 0.65
6 + x = 8.45 + 0.65x
x - 0.65x = 8.45 - 6
0.35x = 2.45
x = 2.45 / 0.35
x = 7
7 consecutive correct predictions
a 2-liter bottle is filled completely with water from a faucet in 10 seconds. how much water is filled in to the bottles each second?
Answer:
[tex]\dfrac{1}{5}\ L[/tex]
Step-by-step explanation:
It is given that,
A 2-liter bottle is filled completely with water from a faucet in 10 seconds.
We need to find how much water us filled in to the bottles each seconds.
In 10 s = 2 L bottle is filled
In 1 s, [tex]\dfrac{2}{10}\ L=\dfrac{1}{5}\ L[/tex] of water is filled into the bottles.
Ann, Ben, and Cheryl share some money in the ratio 3:7:10. Ben received £650 more than Ann.
Calculate the total amount of money that they shared.
Answer:
Total amount = £ 3250
Step-by-step explanation:
Ann : Ben : Cheryl = 3 : 7 : 10
Money Ann received = 3x
Money Ben received = 7x
Money Cheryl received = 10x
Ben received £650 more than Ann.
7x - 3x = 650
4x = 650
x = 650/4
x = £ 162.50
Money Ann received = 3x = 3 *162.50 = £ 487.50
Money Ben received = 7x = 7 *162.50 = £ 1137.50
Money Cheryl received = 10x = 10* 162.50 = £ 1625
Total amount = 487.50 + 1137.50 + 1625 = £ 3250
Composite numbers have less than two factors. more than two factors. exactly two factors. greater than or equal to two factors.
Answer:
More than two factors
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
more than 2 answers
Stay safe,wear a mask,stay at home <3
You have 480 grams of radioactive kind of carbon. How much will be left after 60 minutes if it's half-life is 20 minutes?
Answer:
60 grams
Step-by-step explanation:
480/8 = 60
5x2 + 4x = 3(2 - x)
help me :p
Answer:
Step-by-step explanation:
5x^2+4x=3(2-x)
5x^2+4x=6-3x
5x^2+4x+3x-6=0
5x^2+7x-6
(5x^2-3x)+(10x-6)
x(5x-3)+2(5x-3)
(5x-3)(x+2)
x=3/5,-2
need help quick its my GCSE what is 1 +1 if you cant do it its okay LOL
THE ANSWER IS 2
PLS GIVE BRAINLIEST
Answer:
1 + 1 = 2
Step-by-step explanation:
I don't know why but I have been seeing a lot of questions like this lol
Mr. Peterson saves $55 each time he gets paid. If Mr. Peterson has saved $220, how many times has he gotten paid?
Answer:
4
Step-by-step explanation:
220 divided by 55 is 4
Answer:
He’s gotten paid 4 times.
Step-by-step explanation:
All you have to do is divide 220 by 55 and you get the answer! :)
Which is equivalent to 180x11 after it has been simplified completely?
O 3x10 /5x
O 3x55x
O 6x10,5x
O 6x5/5x
Answer:
O 6x5/5x
Step-by-step explanation:
Answer:
It should be D. I'm not 100% sure though. But D is what I chose.
Classify the following triangle. Check all that apply.