If we shift the origin without changing the direction and point P(x, y) is changed to P(X, Y) then the new coordinates will be x = X + h and y = Y + k.
Shifting of origin is the phenomenon of changing the coordinates of the origin which is generally (0, 0) to another point which has coordinated (h, k). This phenomenon is usually carried out graphically. This is done when there is difficulty to solve the problems in coordinate geometry when we take the origin at (0, 0).
If we shift the origin which is at P(x, y) to another point (h, k) then the coordinates of new point P(X, Y) will be
x = X + h and y = Y + k
If h is positive, then coordinates will be x = X + h and if h is negative then coordinates will be x = X - h. If k is positive, then coordinates will be y = Y + k and if k is negative then coordinates will be y = Y - k.
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Jovani has 144 feet of fencing to make a rectangular garden in his backyard. he wants the length to be 32 feet more than the width. find the width.
The width of rectangular garden comes out to be 20 feet .
Let the width be x feet .
Therefore , length is ( x + 32 ) feet .
Formula for perimeter of a rectangle :
perimeter = 2 ( length + breadth )
By substituting the values in the formula above , the equation becomes ,
2 ( x + x + 32 ) = 144
2 x + 32 = 144 / 2
2 x = 40
x = 20
Hence , width = 20 feet , length = 52 feet .
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Aiden surveyed 300 of the students in his school about their favorite color. 85% said their favorite color was red. How many students favorite color was red?
The number of people who like red color is 255 students when 85% said their favorite color was red.
What is percentage?Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. percentage.
Given:
Total students =300
85% said their favorite color was red.
So, students whose favorite color was red
=85/100 *300
=85*3
= 255 students.
Hence, 255 students whose favorite color was red
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Elliot uses 3/8
pound of clay to make a charm for a necklace. How much clay does he use to make
Answer:
five thousand clay to school
Glen rolls a biased dice 400 times.
The results are shown below in the table.
Score Frequency
1 95
2 134
3 45
4 26
5 75
6 25
Jake rolls the same dice 720 times.
Estimate how many 5's he can expect to get. Answer
When Jake rolls the same dice 720 times, the number of 5s will be 135.
How to illustrate the information?It should be noted that the frequency for 5 is 75 out of 400. This will be:
= 75 / 400
= 3/ 16
Therefore, when Jake rolls the same dice 720 times, the number of 5s will be:
= 3/16 × 720
= 135
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A company designs a new water pitcher. They take a picture of the pitcher for their promotional materials. What is the approximate area filled by the water in the picture on the flyers? The picture shows the outline of a pitcher. The height of a pitcher's body is 12 in, and the height from neck to top is 4 in. The width of the bottom is 8 in, the neck is 3 in, and the top open is 5 in.
Answer:
32in2
Step-by-step explanation:
Find the least common denominator for these fractions. Enter your answer in the space provided. 1/2 and 2/9
Answer:
18.
Step-by-step explanation:
2 = 2
9 = 3*3
So, the LCD = 2*3*3 (no duplicates in the 2 lists).
= 18.
3x - 4+1 = -2x - 5 + 5x
Answer:
No solution
Step-by-step explanation:
Simplify and combine like terms
3x - 3 = 3x - 5
Subtract 3x on both sides.
-3=-5
No solution
Answer:
-2
Step-by-step explanation:
Please help! And show your work for each answer so I can understand, ty
Answer:
a=17, R=101
Step-by-step explanation:
10:
We know that if all angles of a triangle are congruent, the angles must be as well. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
We also know that all interior angles of a triangle add up to 180 degrees. If they are all equal this only leaves us with the possibility of every angle equaling 60 degrees, otherwise they wouldn't add up to 180 AND be equal simultaneously.
To find the value of a set the equation equal to 60.
[tex]4a-8=60[/tex]
Solve for a:
[tex]4a-8=60\\4a=68\\a=17[/tex]
19:
We know in a parallelogram all interior angles sum to 360 degrees.
Remember the sum of angle pairs between parallel lines is 180 degrees. Meaning if we add angles T and S and set them equal to 180 degrees we can then find the value of angle S as we would have the value of variable x.
[tex](4x+1)+(3x+4)=180\\7x+5=180\\7x=175\\x=25[/tex]
Now substitute in the known value of x to find angle S:
[tex]3(25)+4\\75+4\\79[/tex]
Angle S measures 79 degrees.
Using our previous knowledge of two angles on a parallel line summing to 180 degrees, we can find the measure of angle R by subtracting 79 from 180.
[tex]180-79=x\\101=x[/tex]
R=101
HELP!!
What is the volume of this solid?
A. 39
B. 108
C. 27
D. 63
Answer: B
Step-by-step explanation:
4 times 3 times 3 times 3 times 3=108
Answer:
A. 39
Step-by-step explanation:
Given:
Length of a pyramid (lpy ) = 4 cm
Width of a pyramid (wpy ) = 3 cm
Height of a pyramid (hpy ) = 3 cm
It is given that the rectangular pyramid fits exactly on top of the prism, the length and width of the prism are the same for the base of the pyramid.
So, Length of a prism (lpr) =3 cm, width of a prism (wpr) = 3cm and height of a prism (hpr) = 3 cm
Volume of Prism (Vpr) = lpr × wpr × hpr
⇒ Vpr = 3 cm × 3 cm × 3 cm
⇒ Vpr = 27 cm³ ....(eq 1)
Volume of Rectangular Pyramid Vpy
= (lpy × wpy × hpy ) / 3
⇒ Vpy = (4 × 3 × 3) ÷ 3
⇒ Vpy = 12 cm³ ....(eq 2)
From 1 and 2, Volume of composite space,
Volume of composite space = Volume of prism + Volume of Pyramid
⇒ V = 27 cm³ + 12 cm³ = 39 cm³
⇒ V = 39cm³
Singing star bitsy carlyle isnt as popular as she used to be at her latest concert she was only able to sell 910 tickets for a total of 15620 barely enough to pay her agent if regular seats cost 18.50 and mezzanine seats the only other option cost 16.25 how many mezzanine tickest were sold
The number of mezzanine tickets sold = 540
Total number of tickets sold = 910
Total number of tickets sold is the sum of the number of regular seats and the number of the mezzanine seats sold.
Let 'x' be the number of regular seats and 'y' be the number of mezzanine seats.
Then x + y = 910 ----------(1)
Cost of a regular seat = $ 18.50
So cost of x regular seats = 18.50x dollars
Cost of a mezzanine seat = $ 16.25
So cost of y mezzanine seats = 16.25y
Total amount of money she got by selling tickets = $ 15620
Therefore, 18.5x + 16.25y = 15620 ----------------(2)
Solve equations (1) and (2) for x and y.
Multiplying (1) with 18.5 throughout,
18.5x + 18.5y = 16835 ---------------(3)
Subtracting (2) from above equation (3), we get,
(18.5 - 16.25)y = 16835 - 15620
⇒ 2.25y = 1215
⇒ y = 1215/2.25
⇒ y = 540
Hence 540 mezzanine tickets were sold.
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A snack recipe calls for 1 1/4 cups of dip and 1/5 cup of chips. charlie wants to make the same recipe using 1 cup of chips. how many cups of dip will charlie need?
Using the concept of ratio the number of cups of chips Charlie needs can be found out.
What is ratio?A ratio in mathematics shows how many times one number is contained in another. The ratio symbol is represented by a colon (:).A ratio is still valid if all of the quantities are multiplied by the same number. By dividing each quantity by the sum of all the numbers' common factors, ratios can be lowered (much like fractions are). The simplest version of a fraction is one in which the ratio's numbers are the smallest feasible integers.
Amount of dip required by the recipe be 'a' =[tex]1\frac{1}{4}[/tex] cups=[tex]\frac{5}{4}[/tex]cups
Amount of chips required by the recipe be 'b'= [tex]\frac{1}{5}[/tex]cups
Amount of chips to be used be 'c'= 1 cup
Number of cups of chips Charlie needs
=[tex]\frac{c*a}{b}[/tex]
=[tex]\frac{1*\frac{5}{4} }{\frac{1}{5} }[/tex]
=[tex]\frac{5*5}{4}[/tex]
=[tex]\frac{25}{4}[/tex] cups
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Dendra's boat uses 3 gallons of gas in 4 hours. How many gallons of gas will she use in 15 hours?
Answer:11.25
Step-by-step explanation:because we have to find out how many gallons we have in one hour so you divide both sides by 4
4/4 is 1 hour
3/4 is 0.75 gallons then you have to multiply both sides by 15
1 hour times 15 is 15 hours
the 0.75 x 15 is 11.25
so the answer is 11.25 gallons that she uses in 15 hours
hope this helps
The difference of 7 and the product of 2 and a number.
Pllss helppppppppppp
Answer: A. x=8
Step-by-step explanation:
0.4(5x-12)+0.5x=15.2
(0.4)(5x)-(0.4)(12)+0.5x=15.2
2x-4.8+0.5x=15.2
2.5x-4.8=15.2
2,5x-4.8+4.8=15.2+4.8
2,5x=20
(2.5)(x)=(2.5)(8)
Divide both parts of the equation by 2.5:
x=8
Express this number in scientific notation.
0.00067
A 1971 Indian Motorcycle is worth 30 times its original cost. Today it is worth $3000. How much did it originally cost in 1971?
Answer: $100
Step-by-step explanation:
3,000 divided by 30 is 100
Answer: 100
Step-by-step explanation: divide 3,000 by 30
Wayne placed an order for 1 2/3 sacks of brown lentils and 1/2 of a sack of green lentils. How much more brown lentils did Wayne order?
Answer:
1 1/6
Step-by-step explanation:
1 2/3 - 1/2 =
1 2/3 = 1 4/6
1/2 = 3/6
1 4/6 - 3/6 =
1 1/6
Emily purchased a pack of 6 shirts for $18. What was the cost per shirt? someone answer this please.
Answer:
$3
Step-by-step explanation:
Divide 6 from 18 to find the cost per shirt.
18/6=3
3 dollars per shirt.
Hope this helps!
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Amir has 2 checking accounts. The first has a balance of -$20 and the
second has a balance of $160. What is the sum of the two sum balances
Answer:
D. 140. ....,.....
Step-by-step explanation:
160-20=140
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The difference between the area of the square and the area of the circle is C. 9x²(4 - π).
How to calculate the area?The area of the square will be:
= Side ×Side
= 6x × 6x
= 36x²
The area of the circle will be:
= πr²
= 3.14 × (3x)²
= π × 9x²
= 9πx²
The difference will be:
= 36x² - 9πx²
= 9x²(4 - π)
Therefore, the correct option is C.
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23 + 10 ÷ 2 − (− 14 ÷ 2)
Please explain it.
Step-by-step explanation:
23 + 10 - 2 + 14 + 2
33 - 2 + 16
31 + 16 = 47
I cant find my answer help needed
Step-by-step explanation:
the domain is the interval or set of all valid x (input) values.
the range is the interval or set of all valid y (function result) values.
so, we see here, x goes from -2 to +2.
and y stays between -5 and -1.
the hole point at (-2, -1) means the point itself is not included. the full point (2, -1) means the point itself is included.
the domain is
-2 < x <= +2
"-2 < x" because (-2, -1) is not included.
"x <= +2" because (2, -1) is included.
the range is
-5 <= y <= -1
"y <= -1" because for the included point (2, -1) y can reach -1, even though (-2, -1) is excluded.
the numbers from $1$ to $150$, inclusive, are placed in a bag and a number is randomly selected from the bag. what is the probability it is neither a perfect square nor a perfect cube? express your answer as a common fraction.
The required probability is [tex]\frac{1}{10}[/tex].
This problem is related to probability.
First we have to calculate the number of outcomes and then the number of favorable outcomes.
In this case the numbers are from 1 to 150.
First we have to find the numbers which are perfect square between 1 to 150= {1,4,9,16,25,36,49,64,81,100,121,144}
Now we have to find the numbers which are perfect cube other than those which came in square={8,27,125}
Here the number of favorable outcome is 150 minus number of elements in set of perfect square and perfect cube.
Now the probability of the required problem is = [tex]\frac{15}{150}[/tex]
= [tex]\frac{1}{10}[/tex]
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There was a country concert held at the park. For every 5 men there were 7 women that went to the concert. If 40 more women attended the concert than men, how many men and how many women attended the concert? Use the following diagram to help solve the ratio problem.
Step-by-step explanation:
i think it is 35 but im probaly wrong
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
Answer:
Here SOLUTION: −5x + 4y = 20. 10x − 8y = −40.
Step-by-step explanation:
First, solve the first equation for y. Then, substitute for y in the second equation. This equation is an identity.
Jamal has a suitcase that contains only 10 white socks. he wants to add enough black socks so that the probability of randomly selecting a white sock is 1/5. how many black socks should jamal add to the suitcase? f. 30 g. 35 h. 40 j. 45 k. 50
40 black socks should be added to the suitcase( i.e., option h )
Let's take x = black socks added by Jamal
Based on the given condition, we have
[tex]\frac{10}{10 + x}[/tex] = 1/5
Here x ≠ -10
Because to define the fraction, the denominator should not be 0.
Now we need to find the value of x,
[tex]\frac{10}{10 + x}[/tex] = 1/5
50 = 10 + x
x = 40
Therefore 40 socks should Jamal add to the suitcase.
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HELP...................................! !
Answer:
Your answer would be 3.075.
Step-by-step explanation:
15 - 6.8 = 8.2
8.2 - 5 1/8 = 3.075
--------------------------------
Hope this helps!
Have a great day and God bless! :)
Factor. x^2-x=20
HUGE POINTS WOWZIE WOOZA
Answer:
(x-5)(x+4) = 0
Step-by-step explanation:
Pre-SolvingGivenWe are given the quadratic equation x²-x=20
And we want to factor it, meaning that we want to split it apart, usually to make it easier to solve.
SolvingFirst, let's subtract 20 from both sides, as when all 3 terms of a quadratic equation are on the same side, it makes it a lot easier to solve.
x² - x = 20
-20 -20
_______________
x² - x - 20 = 0
Now, we can get on to factoring.
In a quadratic equation, written as ax² + bx + c = 0 (like in here), b (the coefficient in front of just x, not x²) is equal to the sum of two numbers, while c is the product of the same two numbers.
The coefficient in front of x (b) is -1, and c is equal to -20.
Now think: which two numbers add up to -1, and multiply to equal -20?
Those numbers are -5 and 4.
Now, to factor a quadratic, we split it up into 2 binomials multiplied by each other, and each binomial is x + one of the numbers we found above. It looks like this: (x+1)(x+2). Remember that this only affects the left side; the right side stays the same.
In this case, we have -5 and 4, which will take the place of 1 and 2 in the example above.
Therefore, the factored form of x² - x - 20 = 0 is (x-5)(x+4) = 0.
Write a numerical expression for the verbal expression. eighteen divided by the sum of two and seven
The numerical expression for the verbal expression is 18 ÷ (2+7).
Given,
Verbal expression = Eighteen divide by the sum of two and seven
we know that ,
We can write any verbal expression to numerical expression by using playing with numbers.
Playing with numbers:
Playing with numbers involves activities like arranging the numbers, understanding , finding out whether a given number is a factor of another number or a multiple of another number, and understanding the properties of factors and multiples
Now, According to question
Eighteen divided by the sum of two and seven
18÷(2+7)
Therefore,
The numerical expression is 18÷(2+7).
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which of these expressions are equal?
I. 4.86x0.01
II.48. 6x 0.1
III. 0.0486x100
IV.48.6x10
Answer:
II. 48.6×0.1
III. 0.0486×100
Step-by-step explanation:
48.6×0.1 = 4.86
0.0486×100 = 4.86
Answer:
ll and lll are equal.
Step-by-step explanation:
4.86x0.01 = 0.0486
48.6 x 0.1 = 4.86
0.0485 x 100 = 4.86
48.6 x 10 = 486