The area of the rectangle is 0.75 of the square of the length. When the length is doubled, the width is 37.5 % of the length.
Explanation:The area of a rectangle is calculated by multiplying its length and width. In this case, the width is 75% of the length. So if we denote the length as 'L', then the width would be 0.75 * L. Therefore, area would be L * 0.75L = 0.75 * L^2.
Now, if the length of the rectangle is doubled, the width remains the same, so it becomes 0.75 * 2L. So the width becomes a smaller fraction of the length. We can work out this out as follows: (0.75L / 2L) * 100 = 37.5%.
So, when the length of the rectangle is doubled, the width is 37.5 % of the length.
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1. The area of the rectangle is 0.75 times the square of the length.
2. The width is now 75% of the length.
Part 1:
What is the area of the rectangle?
If the width of the rectangle is 75% of its length, then we can express the width as 0.75 * length.
The area of a rectangle is calculated by multiplying the length and width, so the area of the rectangle in this case is:
Area = length * width = length * 0.75 * length = 0.75 * length^2
Therefore, the area of the rectangle is 0.75 times the square of the length.
Part 2:
The length of the rectangle is doubled. What percent of the length is the width now? Explain your reasoning.
If the length of the rectangle is doubled, then the width is now half of 75% of the new length.
To calculate this, we can use the following steps:
Calculate the new length of the rectangle: old_length * 2 = new_length
Calculate 75% of the new length: 0.75 * new_length
Divide the width by the new length to get the percentage: width / new_length
For example, if the old length of the rectangle was 10 cm, then the new length would be 20 cm. 75% of 20 cm is 15 cm. Therefore, the width is now 75% of the length.
Answer: The width is now 75% of the length.
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Determine the answer to (−3) + (−5) and explain the steps using a number line. (5 points)
Answer: -8
Step-by-step explanation: In this problem we're asked to add -3 + -5 so let's use a number line. A negative represents a move the left on the number line and a positive represents a move to the right on the number line.
So starting at 0, -3 tells us to move 3 units to the left along the number line. From there, -5 tells us to move 5 units further to left so you can see from the picture that we end up at -8.
This means that -3 + -5 is -8.
Answer:
-8
Step-by-step explanation:
you go 5 to the left of negitive 3 in the numberline
The base of a 40-foot ladder is 8 feet from the wall. How high is the ladder on the wall (round to the nearest foot)?
Answer:
Around 39.2
Step-by-step explanation:
To do this question, you use the pythag theorem, a^2 + b^2 = c^2. You have the hypotenuse of the triangle, 40 feet in length, and you have a because it's 8 feet from the wall. You now have b^2 = 1600-64. b^2 = 1536. Take the square root, and you have the height of the latter on the wall is equal to 39.1918 or 39.2 rounded
What is the solution to 2x2+x+2 = 0?
Answer:
Step-by-step explanation:
Plug this into the quadratic formula. It's the easiest and surest way to solve a quadratic.
a = 2
b = 1
c = 2
Filling in the quadratic formula:
[tex]x=\frac{-1+/-\sqrt{1^2-4(2)(2)} }{2*2}[/tex]
which simplifies to
[tex]x=\frac{-1+/-\sqrt{-15} }{4}[/tex]
You can't have a negative under the square root sign (or ay even index radical, for that matter), so we will rewrite it as
[tex]x=\frac{-1+/-\sqrt{(-1)(15)} }{4}[/tex]
and since i-squared is equal to -1:
[tex]x=\frac{-1+/-\sqrt{15i^2} }{4}[/tex]
The only perfect square we can pull out of that square root is the i from the i-squared, so when we do that we get:
[tex]x=-\frac{1+/-\sqrt{15}i }{4}[/tex]
or you could put the i out front; it doesn't change the answer at all. The third choice down is the one you want.
A, B, C are circular regions as shown below. There are 7 items in C and there are 20 items in A but 10 of those items are not in B. How many items are in B that are not in C
Answer:
3 items are in B that are not in C
Step-by-step explanation:
a: only in a, not count those in b or c
b: only in b, not count those in a or c
c: only in c, not count those in a or b
A = a + b + c = 20
c = 7
a + b = 20 - 7 = 13
10 not in b, of course not in c ∴ a = 10
b = 13 -10 = 3
is 3.456 a rational number
Answer:
Yes
Step-by-step explanation:
Answer:
yes it is
Step-by-step explanation:
3.456 could be written as a fraction, that means it is a rational number because rational number is any number that could be written as a fraction.
3.456=3456/1000
FIND RATIOS
4. A string that is 75 inches long will be cut into two pieces in the ration of 4:11. Find the lengths
of the two pieces of string.
5. The ratio of two supplementary angles is 4:1. Find the measures of the two angles.
6. The ratio of the measures of the angles in a triangle is 3:5-7. Find the measure of each angle.
7. The ratio of the measure of the sides of a triangle is 5;7:8 and its perimeter is 40 inches. Find
the measure of each side.
Step-by-step explanation:
4. 4+11=15
to find the length of The first piece
4/15*75=20
to find the length of the second one
11/15*75=55
5. 4+1=5
to find the length of the first one
4/5*180=144
to find the length of the second one
1/5*180=36
7. 5+7+8=20
to find the length of the first one
5/20*40=10
to find the length of the second one
7/20*40=14
to find the length of the third one
8/20*40=16
4. The lengths of the two pieces are 20 inches and 55 inches.
5. The measures of the two angles are 144 degrees and 36 degrees.
6. The measures of the angles are 36 degrees, 60 degrees, and 84 degrees.
7. The lengths of the sides are 10 inches, 14 inches, and 16 inches.
4: A string that is 75 inches long will be cut into two pieces in the ratio of 4:11. Find the lengths of the two pieces of string.
The total length of the string is 75 inches.
The ratio given is 4:11.
First, find the total parts in the ratio by adding the two numbers: [tex]4 + 11 = 15[/tex].
Now, to find the length of each piece:
For the first piece: [tex](4/15) \times 75 = 20[/tex] inches.For the second piece: [tex](11/15) \times 75 = 55[/tex] inches.5: The ratio of two supplementary angles is 4:1. Find the measures of the two angles.
Supplementary angles add up to 180 degrees.
The given ratio is 4:1.
Find the total parts in the ratio: [tex]4 + 1 = 5[/tex].
Now, calculate the measures of the angles:
For the first angle: [tex](4/5) \times 180 = 144[/tex] degrees.For the second angle: [tex](1/5) \times 180 = 36[/tex] degrees.6: The ratio of the measures of the angles in a triangle is 3:5:7. Find the measure of each angle.
The sum of the angles in a triangle is 180 degrees.
The given ratio is 3:5:7.
Total parts in the ratio: [tex]3 + 5 + 7 = 15[/tex].
Now, calculate each angle's measure:
For the first angle: [tex](3/15) \times 180 = 36[/tex] degrees.For the second angle: [tex](5/15) \times 180 = 60[/tex] degrees.For the third angle: [tex](7/15) \times 180 = 84[/tex] degrees.7: The ratio of the measure of the sides of a triangle is 5:7:8 and its perimeter is 40 inches. Find the measure of each side.
The perimeter of the triangle is 40 inches.
The given ratio is 5:7:8.
Total parts in the ratio: [tex]5 + 7 + 8 = 20[/tex].
Now, calculate the length of each side:
For the first side: [tex](5/20) \times 40 = 10[/tex] inches.For the second side: [tex](7/20) \times 40 = 14[/tex] inches.For the third side: [tex](8/20) \times 40 = 16[/tex] inches.I need help please and thanks
How do you wire 0.52 in words
Answer: fifty-two hundredths
Step-by-step explanation:
given the 5th term is 103 and the come differences is -6 2/3 what is the 6th term?
Answer:
102 1/3
Step-by-step explanation:
To find the 6th term, add the common difference to the 5th term:
103 + (-6 2/3) = 102 1/3
what property is -2x - 2 + 5x
Answer:
3x-2
Step-by-step explanation:
-2x-2+5x=-2x+5x-2=3x-2
Which value of x would make NO || KJ?
1
6
8
10
Answer:
x = 8
Step-by-step explanation:
If NO is parallel to KJ then the sides LK and LJ are in proportion, that is
[tex]\frac{KN}{NL}[/tex] = [tex]\frac{JO}{OL}[/tex], substitute values
[tex]\frac{x+2}{x-3}[/tex] = [tex]\frac{x}{x-4}[/tex] (cross- multiply )
x(x - 3) = (x + 2)(x - 4) ← expand factors on both sides
x² - 3x = x² - 2x - 8 ( subtract x² - 2x from both sides )
- x = - 8 ( multiply both sides by - 1 )
x = 8
Answer:
8
Step-by-step explanation:
Romi opened a gift shop in 1995 and closed it in 2000. In 1995, her inventory of stuffed animals was 350. In 2000 her inventory of stuffed animals was 0. Let x represent the number of years since 1995. Write an equation, in slope-intercept form, that represents that data
Answer:
y=-70x+350
Step-by-step explanation:
Since x is the number of years since 1995, this means that at 1995, x=0. This also means that in 2000, x=5. The values of the stuffed animals were 350 in 1995 and 0 in 2000. The formula for slope is rise over run, so we can find the answer using this mathematical expression: y2-y1/x2-x1. Plugging in our values, we get 0-350/5-0 which simplifies into -350/5. This further simplifies into -70. Our slope is -70. The definition of y-intercept is the value of y when x=0. We know that x=0 at 1995 and the value for the stuffed animals was 350 at that time. This tells us that the y-intercept is 350. Slope-intercept form is y=mx+b, so plugging in our information, we get y=-70x+350.
The equation representing the data of Romi's stuffed animal inventory is y = -70x + 350
The given problem involves finding an equation in slope-intercept form to represent the data of Romi's stuffed animal inventory from 1995 to 2000. Let's first find the slope and y-intercept of the equation using the given data. We know that the inventory in 1995 was 350 and in 2000 was 0. We can use these two points to find the slope and y-intercept.
Slope (m) = (change in y)/(change in x) = (0 - 350)/(2000 - 1995) = -350/5 = -70
Using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values
y = -70x + b
To find the value of b, we can substitute one of the given points into the equation. Let's use the point (0, 350).
350 = -70(0) + b
350 = b
Substituting the value of b back into the equation, we have the final equation:
y = -70x + 350
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Which ordered pair is a solution of system 2x-y<5 and x +2y > 2
A) (1,-1)
B) (4,1)
C) (2,0)
D) (3,2)
Answer:
D
Step-by-step explanation: When you plug 3 into where x in the first equation and plug 2 in for y. When you do that you get 6-2<5, 6-2 is 4 and 4 is less than 5, so this makes this equation true. For the second equation you do the same. 3 goes into the x spot and 2 into the y, after doing this you get 3+2(2)>2, 3 times 4 is 12 and that is greater than 2, hich also means that equation is ture. So there you have both equations are ture and that is how you get your answer.
ABCD IS A PARALLELOGRAM. IF SIDE AB=6X-10, SIDE BC=4X-5, AND SIDE CD= 3X+5, FIND THE VALUE OF X
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
we know that
In a parallelogram opposite sides are parallel and congruent
In this problem
AB and CD are opposite sides
so
AB=CD
substitute the given values
[tex]6x-10=3x+5[/tex]
solve for x
[tex]6x-3x=10+5[/tex]
[tex]3x=15[/tex]
[tex]x=5[/tex]
21. What method can be used to prove the
triangles below are congruent?
A. SSS
B. SAS
C. HL
D. Not Possible
Answer:
there is not a triangle
Step-by-step explanation:
but if is has all 3 sides the same it is sss, if there is two sides and an angle in between them it is sas, and if there is a hypotenuse and then a leg then it is hl, or if it is none it is d
The method that can be used to prove the triangles below are congruent is the SAS (Side-Angle-Side) criterion. To prove that two triangles are congruent using the SAS criterion, you need to show that two pairs of corresponding sides are congruent and the included angles between them are congruent. In the given options, B. SAS is the correct answer.
Explanation:The method that can be used to prove the triangles below are congruent is the SAS (Side-Angle-Side) criterion.
To prove that two triangles are congruent using the SAS criterion, you need to show that two pairs of corresponding sides are congruent and the included angles between them are congruent.
In the given options, B. SAS is the correct answer.
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An experienced tinter can tint a car in 3 hours. A beginning tinter needs 6 hours to complete the same job. Find how long it takes for the two to do the job together.
Answer:
2.5 hours/3 hours
Step-by-step explanation:
If it takes the beginner 6 hours and experienced tinter 3 hours working together it should take roughly 2.5 hours to 3 hours because the time would be cut in half.
It will take them 2 hours to do the job together .
The tinter can tint a car in 3 hours . He does it at the rate of 1 / 3 per hour
A beginner needs 6 hours to do the same job. He does it at the rate of 1 / 6 per hour
For both of them to do the same job , the rate can be calculated below.
1 / 3 + 1 / 6 = 1 / 2 per hour
If they do the job at the rate of 1 / 2 per hour, how long will it take to complete 2 / 2 ?
2 / 1 = 2 hours
The time it will take them to do the job is 2 hours.
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You have an above ground pool that is 20 feet in diameter. One bag of sand does three square feet. How many bags of sand do you need?
Answer: Number of sand bags are 105
Step-by-step explanation:
Alright, lets get started.
The diameter of pool is given as : [tex]20 \ \text{feet}[/tex]
The radius of pool will be : [tex]r=\frac{20}{2}=10[/tex]
So the area of the pool will be:
Area = [tex]\pi r^2[/tex]
Area = [tex]\pi *10^2[/tex]
Area = [tex]100 \pi[/tex]
Area = [tex]314.16[/tex]
3 square feet is covered by 1 sand bag, so
314.16 square feet will be covered by : [tex]\frac{314.16}{3}[/tex]
So, no of sand bag = [tex]104.7[/tex]
Rounding off to nearest number
Number of sand bags are 105 : Answer
Hope it will help :)
The student will need 105 bags of sand.
The student asked about the necessary quantity of sand bags required to cover an area for an above ground pool. First, we need to calculate the area of the pool's base. Since the pool is circular with a diameter of 20 feet, we can use the formula for the area of a circle, which is A = [tex](\pi d^2)/4,[/tex] where d is the diameter.
The area A works out to [tex]\(A = \pi \times (20 feet)^2 / 4 = \pi \times 400 / 4 = \pi \times 100)[/tex] square feet. Assuming [tex]\pi[/tex] is approximately 3.14, the area is about 314 square feet.
Since one bag of sand covers 3 square feet, we divide the total area by the coverage area per bag: 314 square feet / 3 square feet per bag. This calculation gives us approximately 104.67 bags. Since we can't have a fraction of a bag, we need to round up to the nearest whole number. The student would therefore need 105 bags of sand to cover the area of the pool evenly.
A teacher handed out 10 notebooks in packs with 5 notebooks in each pack. How many packs were there?
Answer:
2 packs
Step-by-step explanation:
Since there is 10 packs just divided it by how many notebooks were in the pack.
Each story in Will's apartment building is 9 feet tall. There are 10 stories in the building. How tall is the apartment building?
Answer:
the building is 90 feet tall
Step-by-step explanation:
each floor is 9 feet, there are 10 floors,
9 x 10 = 90 feet
What is the slope of the line parallel to the line y = -5/3x + 5?
A) -5/3
B) -3/5
C) 3/5
D) 5/3
Answer:
C
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 )
y = - [tex]\frac{5}{3}[/tex] x + 5 ← is in slope- intercept form
with slope m = - [tex]\frac{5}{3}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular }[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{5}{3} }[/tex] = [tex]\frac{3}{5}[/tex]
Answer:
5/3
Step-by-step explanation:
Consider the formula S = sf/F
where
S represents sweetness of a cake,
• s represents the amount of sugar in a cake,
f represents the amount of frosting and
• F represents the amount of flour.
Select an appropriate measurement unit for sweetness of a cake,
SAY LETTER OR ANSWER
Answer:
D
Step-by-step explanation:
Answer:
D. (sugar * frosting)/Flour
Step-by-step explanation:
Given that
The formula for sweetness of a cake is represented by S = sf/F
where the
sweetness of a cake is denoted with S
amount of sugar in a cake, with A
amount of frosting, with f
amount of flour with F.
To get the appropriate unit, all we need to do is to substitute the letter representation of each unit with the original word.
So,
S = sf/F becomes
S = (sugar * frosting)/Flour
We arrive at this by replacing s with sugar; f with frosting and F with Flour
Translate
Your grade must be at least 60 to pass this class
Answer:in Spanish: su calificación debe ser 60 para aprobar esta clase
Step-by-step explanation:
Answer:
That mean you must have 60 and above to pass and anything below that is failure
Step-by-step explanation:
Please help!
(will mark brainliest)
What is the solution to the system of linear equations graphed below?
Answer:
The answer is d (-21/2 , 2)
Step-by-step explanation:
That's where the lines meet up
What’s the pattern 788,778,768
Answer:
the tens place is going down one number each time
Step-by-step explanation:
To find the pattern of the data set we can subtract the 1st term to the 2nd term.
788 - 778 = 10
Now, multiply the 2nd term to the 3rd term to check.
778 - 768 = 10
Thus, the rule of the pattern is 10.
Best of Luck!
Solve the equation:
5*4 / 10 + 4 =
Answer:
6
Step-by-step explanation:
5 times 4 is 20
20 divided by 10 is 2
2 plus 4 is 6
5 * 4 / 10 + 4
20 / 10 + 4
2 + 4
6
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Solve -5 = x - 3y
Solve 11 = -3x + 7y
Answer:
x=1, y=2. (1, 2).
Step-by-step explanation:
x-3y=-5
-3x+7y=11
----------------
x=3y+(-5)
x=3y-5
-3(3y-5)+7y=11
-9y+15+7y=11
-2y=11-15
-2y=-4
2y=4
y=4/2
y=2
x-3(2)=-5
x-6=-5
x=-5+6
x=1
Emily's family loves to work together
in the garden. They have a.
preference for flowers as 80% of
their plants are flowers and the rest
are vegetables. They have 90 plants
in the garden. How many vegetable
plants do they have?
Answer:
They have 18 vegetable plants.
Step-by-step explanation:
Given:
Emily's family loves to work together in the garden.
They have a. preference for flowers as 80% of their plants are flowers and the rest are vegetables.
They have 90 plants in the garden.
Now, to find the number of vegetable plants.
Total plants in the garden = 90.
80% of the plants are flowers.
So, number of plants which are flowers = 80% of 90.
[tex]=\frac{80}{100} \times 90[/tex]
[tex]=\frac{7200}{100}[/tex]
[tex]=72\ plants.[/tex]
The number of flower plants = 72.
Total plants = 90 (given)
So, to get the number of vegetable plants we subtract:
[tex]90-72=18\ plants.[/tex]
Thus, vegetable plants = 18.
Therefore, they have 18 vegetable plants.
24. A bag contains 6 red marbles, 5 yellow marbles, and
7 green marbles. How many additional red marbles
must be added to the 18 marbles already in the bag so
that the probability of randomly drawing a red marble
is
?
F. 12
G. 16
A. 18
J. 24
K. 36
Answer:
the answer is a 18 because that would mean there are more red than any color in the bag
To make the probability of drawing a red marble 1/2 with the current bag of marbles, you would need to add 12 more red marbles.
Explanation:To answer the question about how many additional red marbles must be added to the 18 marbles already in the bag so that the probability of randomly drawing a red marble is 1/2, we first need to understand how the probability of an event is calculated. Probability is calculated by dividing the number of ways an event can occur by the total number of outcomes. In this case, the event is drawing a red marble and the total number of outcomes is the total number of marbles in the bag.
Currently, there are 6 red marbles and 18 total marbles in the bag, so the probability of drawing a red marble is 6/18 = 1/3. We want this probability to increase to 1/2, so we need to add more red marbles. Let's represent the number of red marbles we need to add as x. To find x, we need to solve the following equation: (6 + x) / (18 + x) = 1/2.
Solving for x, we get x = 12. Therefore, you need to add 12 more red marbles to the bag to make the probability of drawing a red marble 1/2.
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A group was selling tickets for their fundraising event. For the first day of the event, they sold 30 pre-sale tickets and 45 tickets at the door. For the second day, they sold 40 pre-sale tickets and 20 at the door. They made $180 more on the tickets for the first day than they did for the second day. All tickets were the same price. How much did they charge for each ticket? Write and solve an equation.
Answer:
4
Step-by-step explanation:
£360 is shared between Abby, ben, chloe and denesh. the ratio of the amount abby gets to the amount that ben gets is 2:7. chloe and denesh get 1.5 times the amount abby gets. work out the amount of money that ben gets.
Answer:
[tex]210[/tex] £
Step-by-step explanation:
Let amount that abby gets[tex]=x[/tex]
Given that [tex]\frac{Amount\ of\ abby}{Amount\ of\ Ben} =\frac{2}{7}[/tex]
[tex]Amount\ of\ ben=\frac{7}{2}\times Amount\ of\ abby\\ =\frac{7}{2}\ x[/tex]
Amount of chole + amount of Danesh [tex]=1.5\times[/tex]of abby
[tex]=1.5 \ x[/tex]
[tex]x +\frac{7}{2} \ x + 1.5 \ x =360\\\\6x=360\\\\x=\frac{360}{6}\\\\x=60[/tex]
[tex]Amount\ of\ Ben =\frac{7}{2}\ x = \frac{7}{2} \times 60\\\\=7\times 30\\\\=210[/tex]
The amount got by Ben = £210
£360 is shared between Abby, Ben, Chloe and Denesh.
The ratio of the amount Abby gets to the amount that Ben gets is 2:7.
Chloe and Denesh get 1.5 times the amount Abby gets.
We have to work out the amount of money that Ben gets.
Let the amount Abby gets = x ...........(1)
According to the given situation
[tex]\rm \dfrac{Amount\; got\; by\; Abby }{Amount \; got \; by \; Ben }= \dfrac{2}{7}[/tex]
[tex]\rm Amount \; got \; by \; Ben = (7/2) x......(2)[/tex]
[tex]\rm Amouut\; goy \; by\; Chole + Amount\; got \; by \; Denesh = 1.5 x........(3)[/tex]
The total amount = £360
From equation (1) (2) and (3) we get
[tex]\rm x + (7/2)x + 1.5x = 360\\x(1+3.5 +1.5) = 360\\x (6) = 360 \\x = 360/6= 60[/tex]
The amount got by Abby = £60
So the amount got by Ben = 3.5 (60) = £210
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