Area = 19.63cm²
Step-by-step explanation:A=πr2=π·2.52≈19.63495cm²
graph both lines. first graph line 1 then graph line 2 following the guidelines. line 1: y=-2/3x+5 line 2: Parallel to line 1 with a y-intercept of 0
The equation of line 1 is y = (-2/3)x + 5.
The equation of line 2 is y = (-2/3)x.
The graph is shown below.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Line 1:
y = (-2/3)x + 5 ____(1)
m = -2/3
y-intercept = 5
Line 2:
It is parallel to line 1 so,
m = -2/3
y-intercept = 0
The equation of line 2 is
y = -2/3x ______(2)
We will make the graph for equations (1) and (2) as shown below.
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-2 ≤4-3a ≤ 13 solve the inequality
The inequality is 2 ≤ a ≤ 3.
What is inequality ?
The mathematical expressions with inequalities are those with unequal sides on both sides. Unlike equations, we compare two values when we work with inequality. The equal sign is substituted between by the less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign. It's not always necessary to balance an equation in mathematics by using the "equal to" symbol on both sides. When something is more than or less than another, it can sometimes be said that the two are not equal.
-2 ≤4-3a ≤ 13
-2 -4≤-3a ≤ 13-4
-6 ≤-3a ≤ 9
-6/3 ≤-a ≤ 9/3
2 ≤ a ≤ 3
Hence the inequality will be 2 ≤ a ≤ 3.
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bert can weed the garden in 3 hours. if bert and ernie work together, they can finish the job in 2 hours. how long would it take ernie to do the job by himself? letting x equal the number of hours it takes ernie to do the job by himself, write and solve an equation.
Answer:
It will take Ernie 6 hours to do the job by himself
Step-by-step explanation:
Rate x time = job
Burt's rate x time + Ernie's rate x time = 1 job getting completed.
[tex]\frac{1}{3}[/tex](2) + x(2) = 1 To clear the fraction multiply everything by 3
2 + 6x = 3 Subtract 2 from both sides
6x = 1 Divide both sides by 6
x = [tex]\frac{1}6}[/tex] This is Ernie's rate
The rate is the number of jobs 1 over the number of hours 6, so it will take Ernie 6 hours to do this job by himself
Breakdown of clearing the fraction:
([tex]\frac{1}{3}[/tex])(2) + x2 = 1 Multiply everything by 3 to clear the fraction.
([tex]\frac{3}{1}[/tex])([tex]\frac{1}{3}[/tex](([tex]\frac{2}{1}[/tex]) + (3)(x2) = (3) (1)
[tex]\frac{6}{3}[/tex] + 6x = 6
2 + 6x = 6
pls help
How to express 5 x 5 x 5 using exponent?
(A) 103 (B) 53 (C) 23
The expression 5 × 5 × 5 is expressed using the exponent [tex]5^3[/tex]
The given expression is
5 × 5 × 5
The expression is the mathematical statement that consist of different variables, numbers and mathematical operator.
The power of a number that consider of base number and the exponent.
Therefore the power of a number is the a base number raised to the exponent.
The exponent of the number is defined as the number of times a number is multiplied by itself.
Here the given expression is
5 × 5 × 5 = [tex]5^3[/tex]
Where 5 is the base number and 3 is the exponent
Hence, the expression 5 × 5 × 5 is expressed using the exponent [tex]5^3[/tex]
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pls give answer ASAP
Answer:
B
Step-by-step explanation:
D is the father of J, who is the brother to R and A happens to be his sister.
Therefore, D is the father of J,R and A
Find the equation of the straight line passing through each of the following pairs of points.
(16 , 13) and (4, -5)
Answer:
y = [tex]\frac{3}{2}[/tex] x - 11
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (16, 13 ) and (x₂, y₂ ) = (4, - 5 )
m = [tex]\frac{-5-13}{4-16}[/tex] = [tex]\frac{-18}{-12}[/tex] = [tex]\frac{3}{2}[/tex] , then
y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (12, 13 ) , then
13 = 24 + c ⇒ c = 13 - 24 = - 11
y = [tex]\frac{3}{2}[/tex] x - 11 ← equation of line
E=5s^2. If s is doubled, what happens to E?
I assume it stays the same
Luke was given a gift card for coffee shop. Each morning, Luke uses the card to buy one cup of coffee. The original amount of money on the gift card was $30 and after buying 6 cups of coffee, the card had a $12 remaining balance. Write an equation for A, in terms of x, representing the amount of money remaining on the card after buying X cups coffee.
The equation A, in terms of x, will be (30-6x=12) where x represents the price of one coffee cup.
According to the question,
We have the following information:
The original amount of money on the gift card was $30 and after buying 6 cups of coffee, the card had a $12 remaining balance.
Now, let's take the cost of 1 cup of coffee to be $x.
So, the total cost of 6 coffee cups will be 6x.
Now, the remaining balance will be equal to the amount spent in buying 6 cups of coffee subtracted from the original balance.
So, we have the following expression:
30-6x = 12
Hence, the equation A, in terms of x, will be (30-6x=12) where x represents the price of one coffee cup.
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me function.
f(x)=x²-2x+3
Find f(1)
The function f(x)=[tex]x^2[/tex]-2x+3 after putting x=1 then f(1)=2.
What is function?
An association between each element of a non-empty set A and at least one element of a different non-empty set B is called a function. In mathematics, a function is defined as a relation f between a set A (the function's domain) and a set B (its co-domain). f = (a,b)| for all values of a A and b B. Every element of set A must have exactly one image in set B for a relation to be considered a function. A relation from a non-empty set B is called a function if it has the property that no two separate ordered pairs in f have the same first element.
Here the given function is ,
=> f(x)=[tex]x^2[/tex]-2x+3
Now put x= 1 then
=> f(1) = [tex]1^2[/tex]-2(1)+3
=>f(1) = 1-2+3
=> f(1) = 2
Hence the value of f(1)=2.
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Solve for x. x/6-3=2
The solution of linear equation x/6-3 = 2 is given by x=30.
Given the linear equation is,
x/6 - 3 = 2
Solving the linear equation we get,
x/6-3 = 2
x/6-3+3 = 2+3, adding 3 to both sides
x/6 = 5
x = 5*6, multiplying 5 to both sides
x = 30
Hence the solution for the given linear equation is x=30.
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|-2| o -4
Is least greatest or equal
Answer: |-2| is greater
Step-by-step explanation:
I hope it's right(Which i'm like 99.9 percent sure it is)
Answer:
|-2| < -4
Step-by-step explanation:
Take the absolute value of -2.
Which is 2.
2 is larger than -4.
how do you factor the expression 51xy − 34xy2
The simplified expression is 17xy( 3 - 2y).
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
51xy − 34xy²
Now, factorizing
51xy= 3 x 17 × x × y
34xy² = 2 ×17 × x × y ×y
So, the simplification can be
51xy − 34xy²
= 3 x 17 × x × y- 2 ×17 × x × y ×y
= 17xy( 3 - 2y)
Hence, the simplified expression is 17xy( 3 - 2y).
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(1,-5) and (-2,-17) in intercept form
Answer:
y = 4x - 9
Step-by-step explanation:
y = mx + b
m = (y_2 - y_1)/(x_2 - x_1) = (-17 - (-5))/(-2 - 1) = -12/(-3) = 4
y = 4x + b
-5 = 4(1) + b
-9 = b
y = 4x - 9
Elsie bought a video game for $85.00. if the store charges 170% of its cost for the game, how much is the store's profit? SHOW YOUR WORK PLEASE AND THANK YOU!!!! <3
The store's profit on the video game is $35.
According to the question,
We have the following information:
Elsie bought a video game for $85.00. And the store charges 170% of its cost for the game.
Now, let's take the original price of the video game to be $x.
So, we have the following expression:
170% of x = 85
170x/100 = 85
Using the cross multiplication method:
170x = 85*100
x = 8500/170
x = 50
So, we have the cost of the video game.
Now, we know that the formula to find the profit is as follows:
Profit = Selling price - cost of the product
Profit = $(85-50)
Profit = $35
Hence, the store's profit on the video game is $35.
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Solve the equation 4x + 5y = 9 for x.
x equals negative 5 times y plus 9 over 4
x equals negative 5 over 4 times y plus 9
x equals the quantity 5 times y plus 9 end quantity over 4
x equals the quantity negative 5 times y plus 9 end quantity over 4
Answer:
(d) x equals the quantity negative 5 times y plus 9 end quantity over 4
Step-by-step explanation:
You want to solve for x: 4x +5y = 9.
SolutionThis can be treated like any other 2-step equation. First isolate the variable term of interest. Then divide by its coefficient.
4x = -5y +9 . . . . . . subtract 5y
x = (-5y +9)/4 . . . . . divide by 4
an empty rectangular tank 1.5m by 1.8m is left outaide, uncovered in the rain. during a storm the deoth of water rises to 1.4cm. How many litres of water is this?
Answer:
37.8 litres
Step-by-step explanation:
V=a*b*c
a=1.5m=150cm
b=1.8m=180cm
c=1.4cm
1l=1000cm³
V=150cm*180cm*1.4cm=37800cm³
(37800cm³:1000cm³)*l=37,8l
a group of 234 students are going to see a thanksgiving parade, traveling in 4 busses and 3 vans. Each bus holds 6 more than 3 times a number a van can hold. How many students can fit in one bus?
48 students can fit in one bus.
Given, a group of 234 students are going to see a thanksgiving parade, traveling in 4 busses and 3 vans.
Each bus holds 6 more than 3 times a number a van can hold.
Let the van holds 'x' students
then, bus holds 6 + 3x students
Now, according to the question
4(6 + 3x) + 3x = 234
24 + 12x + 3x = 234
24 + 15x = 234
15x = 234 - 24
15x = 210
x = 210/15
x = 14
So, bus holds 6 + 3x students
= 6 + 3(14)
= 6 + 42
= 48
Hence, 48 students can fit in one bus.
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Solve each equation by taking square roots
3b² +5=-25
Answer:
b = -3.16
Step-by-step explanation:
3b² + 5 = -25
3b² = -30
b² = -10
b = -3.1623 (5 significant figures)
= -3. 16
A bowl has 15 apples, and 10 of the apples are red. To the nearest whole percent, what percent of the apples are red?.
Answer:
66%
Hope this helps! :)
Minstrel manufacturing uses a job order costing system. During one month, minstrel purchased $198,000 of raw materials on credit; issued materials to production of $195,000 of which $30,000 were indirect. Minstrel incurred a factory payroll of $150,000, of which $40,000 was indirect labor. Minstrel uses a predetermined overhead application rate of 150% of direct labor cost. If minstrel incurred total overhead costs of $167,800 during the month, compute the amount of under- or overapplied overhead:.
If Minstrel Manufacturing incurred total overhead costs of $167,800 during the month, the underapplied overhead was $2,800.
What is underapplied overhead?Underapplied overhead arises when the applied overhead is less than the actual overhead incurred.
On the other hand, overapplied overhead suggests that the applied overhead is more than the actual overhead incurred.
Overhead application is the allocation of overhead costs to units of products or jobs using a predetermined application rate.
Predetermined overhead application rate = 150% of direct labor cost
Direct labor cost = $110,000 ($150,000 - $40,000)
Applied overhead = $165,000 ($110,000 x 150%)
Actual overhead = $167,800
Underapplied overhead = $2,800 ($165,000 - $167,800)
Thus, during the month, the company underapplied overhead by $2,800.
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Question 1(Multiple Choice Worth 2 points)
(Angle Relationships MC)
Angles A and B are complementary to each other. If mZA = 41° and mZB = (2x + 19), find the value of x.
Ox= 15
Ox=11
Ox= 58
Ox= 30
If A and B are complementary angles, m∠A = 41° and m∠B = (2x + 19)° then the value of x is 15°
What are complementary angles?
When the sum of two angles is 90°, then the angles are known as complementary angles.
According to the given question:
Angles A and B are complementary to each other.
Measure of angle A is 41°
Measure of angle B is 2x + 19
Since the angles are complementary to each other, sum of angles is 90°
∴ 41° + 2x + 19 = 90°
2x = 30
x = 15°
Hence the value of x is 15°
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need asap
What is the slope-intercept form of the line represented in the table of values?
Answer: I think its y = x - 2
Step-by-step explanation:
-8 to -2 is a positive increase of 6
-10 to -4 is a positive increase of 6
rise/run
6/6 = 1/1
so the slope is x
then the y-intercept is given
Answer:
C: Y=x-2
Step-by-step explanation:
Slope intercept form is y=Mx+b
M is slope and b is y intercept
To find slope we use y2-y1/x2-x1
5-1/7-3
4/4
1 is the slope
To find the y intercept we look at when x is zero on the table and y is -2 so now we can make an equation
y=x-2
Hopes this helps please mark brainliest
A bank is offering 3. 5% simple interest on a savings account. If you deposit $7,500, how much interest will you earn in two years?.
Answer:
534.1875
Step-by-step explanation:
7500 ⋅ (1+3.5%)²-7500
534.1875
find the dimensions of the rectangular dog park split into two pens (sharing a fence) of the same size producing the greatest enclosed area given 240 ft of fencing
the dimensions of each pen will be _____ feet by _____ feet
According to the area of the rectangle, the dimensions of each pen will be 15.5 feet by 15.5 feet
Area of rectangle:
Basically, the area of the rectangle refers the region occupied by a rectangle within its four sides or boundaries.
Given,
Here we need to find the dimensions of the rectangular dog park split into two pens (sharing a fence) of the same size producing the greatest enclosed area given 240 ft of fencing
Let us consider the length of the rectangle is l and the width of the rectangle is w.
Here in the given question, the length and width of the will be same.
Then the it can be calculated as,
=> 240 = s²
=> s = √240
=> s = 15.5
Therefore, the dimension is 15.5 feet by 15.5 feet.
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the sum of 6 times a number and 7
Answer:
The sum of 6 times a number and 7 turned into an equation would be:
6n + 7
Step-by-step explanation:
I found this out because the term "sum" means addition, and if you are multiplying 6 by a number, you are supposed to simplify the "number" into n. So, that's what I did:
6n + 7
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
a+3b/5 = a-2b/2 Find the ratio a:b! Please help!!!
Answer:
16 : 3
Step-by-step explanation:
(a+3b)/5=(a-b)/2 or 2 (a+3b) = 5 (a-2b) or 2a + 6b = 5a-10b or 3a. or a/b = 16/3 so a.b = 16:3
Danny wants to buy the new sci-fi book for $15.75. Some of the books were signed by the author, and those cost an additional 60%. What will be the new selling price for a signed sci-fi book?
If Danny wants to buy the new sci-fi book for $15.75. Some of the books were signed by the author, and those cost an additional 60%. Then new selling price for a signed sci-fi book is $25.52
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given,
Danny wants to buy the new sci-fi book for $15.75.
Some of the books were signed by the author, and those cost an additional 60%
We need to calculate 60% of 15.75
Change 60% to decimal value by dividing with 100
60/100=0.6
Now multiply 0.6 with 15.75 to find 60% of 15.75
0.6×15.75
9.45
So 9.45 is the cost of books.
Add 15.75 with 60% amount
$15.75+$9.45
$25.52
Hence the new selling price for a signed sci-fi book is $25.52
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What is the value of x ?
NEED HELP URGENTLY! 40 POINTS FOR ANSWER, HIGH SCHOOL GEOMETRY DILATIONS
explain how to graph the points.
The graph of the polygon with given vertices and its image after a dilation with a scale factor k = 0.25 is as shown below.
In this question, we have been given the coordinates of the vertices of polygon.
We need to graph the polygon with given vertices and its image after a dilation with a scale factor k = 0.25
The coordinates of the polygon are:
J = (4, 0 ), K = (-8, 4), L = (0, -4), M = (12, -8)
The coordinates of the polygon after a dilation with a scale factor k = 0.25 would be:
J' = (1, 0), K' = (-2, 1), L' = (0, -1), M' = (3, -2)
Therefore, the graph of the polygon with given vertices and its image after a dilation with a scale factor k = 0.25 is as shown below.
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find the volume of a frustum of a right circular cone with height 25, lower base radius 13 and top radius 5.
Volume of the frustum of right circular cone = 271.22 [tex]units^{3}[/tex]
Volume of frustum of right circular cone:
Formula for the Volume of Frustum of Cone (V)= 1/3 πH ([tex]R^{2}[/tex]+Rr+[tex]r^{2}[/tex] )
where,
H = Height of frustum
R = Radius of lower base
r = Radius of top base
According to given question,
Height of frustum(H) = 25 units
Radius of lower base(R) = 13 units
Radius of top base (r) = 5 units
Substituting all the given values in the formula of volume of frustum of cone we will get,
Volume of frustum of right circular cone(V) = 1/3 πH ([tex]R^{2}[/tex] + Rr + [tex]r^{2}[/tex] )
= 1/3 π ( 13x13 + 13x5 + 5x5)
= 1/3 π ( 169 + 65 +25)
= 1/3 π (259)
= 86.33 π
= 271.22 [tex]units^{3}[/tex]
Volume of the frustum of right circular cone = 271.22 [tex]units^{3}[/tex]
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