Answer:
The length of rectangle is 14.25 inches and the width of rectangle is 8.25 inches
Step-by-step explanation:
we know that
The perimeter of rectangle is equal to
[tex]P=2(L+W)[/tex]
[tex]P=45\ in[/tex]
so
[tex]45=2(L+W)[/tex]
simplify
[tex]22.5=L+W[/tex] -----> equation A
The length of a rectangle is 6 inches more than its width
so
[tex]L=W+6[/tex] ----> equation B
Solve the system by substitution
substitute equation B in equation a
[tex]22.5=(W+6)+W[/tex]
solve for W
[tex]22.5=2W+6\\2W=22.5-6\\2W=16.5\\W=8.25\ in[/tex]
Find the value of L
[tex]L=W+6[/tex]
substitute the value of W
[tex]L=8.25+6=14.25\ in[/tex]
therefore
The length of rectangle is 14.25 inches and the width of rectangle is 8.25 inches
HELP I WILL PAY YOU WITH TONS OF POINTS
options: (choose 3)
4.5
2
1/2
6
10
Answer:
I believe 4.5, 2 and 1/2
Answer:
4.5 , 2 , 1/2
Step-by-step explanation:
Because if you multiply 5 by 0.9, which is less than 1, you will get 4.5
If you multiply 5 by 0.4, which is less than 1, you will get 2
And finally if you multiply 5 by 0.1, which is less than 1, you will get 1/2
simplify the expression.
2k^8 • 3k^3
A. 6k^24
B. 6k^11
C. 5k^11
D. 5k^24
Answer:
B. 6k^11
Step-by-step explanation:
2k^8 • 3k^3
The • sign means
multiplication
So 2k^8 x 3k^3
6k^8+3
6k^11
I need an accurate answer please
x = –6
Solution:
Given expression is [tex]\sqrt[3]{x-2}+5=3[/tex].
Step 1: Isolate the radical by subtracting 5 from both sides of the equation.
[tex]\Rightarrow\sqrt[3]{x-2}+5-5=3-5[/tex]
[tex]\Rightarrow\sqrt[3]{x-2}=-2[/tex]
Step 2: Cube both sides of the equation to remove the cube root.
[tex]\Rightarrow(\sqrt[3]{x-2})^3=(-2)^3[/tex]
Cube and cube root get canceled in left side of the equation.
[tex]\Rightarrow\ x-2=-8[/tex]
Step 3: To solve for x.
Add 2 on both sides of the equation.
[tex]\Rightarrow\ x-2+2=-8+2[/tex]
[tex]\Rightarrow\ x=-6[/tex]
Hence the solution is x = –6.
A librarian receives two boxes of books for the library. The first box has 136 books.
The second box has 58 fewer books than the first box. What is the total number of books the
ibrarian receives?
Final answer:
The librarian receives a total of 214 books, with the first box containing 136 books and the second box containing 78 books (58 fewer than the first).
Explanation:
To find the total number of books the librarian receives, we first need to determine how many books are in the second box. We are told that the second box has 58 fewer books than the first box, which contains 136 books. Therefore, we can calculate the number of books in the second box by subtracting 58 from 136.
The calculation for the second box will be: 136 books - 58 books = 78 books.
To find the total number of books, we then add the number of books in the first box to the number of books in the second box:
Total books = 136 books + 78 books = 214 books.
Thus, the librarian receives a total of 214 books.
Final answer:
Subtract 58 from 136 to find the number of books in the second box (78 books), then add the number of books from both the first and the second box to get the total (214 books).
Explanation:
The student has asked how to calculate the total number of books a librarian receives if the first box contains 136 books and the second box contains 58 fewer books than the first. To find the number of books in the second box, we subtract 58 from 136, which gives us 78 books. To find the total number of books received, we then add the number of books in both boxes together: 136 books from the first box plus 78 books from the second box equals 214 books in total.
If 4(a+3)=2a+12, then a= [blank] −−−−−−
Answer:
a=0
Step-by-step explanation:
Solve for a
4a + 12 = 2a +12
4a-2a=12-12
2a=0
a=0/2
a=0
Determine if the three given side lengths would form a right triangle
9 ft, 12 ft, 16 ft
Answer:
Yes.
Step-by-step explanation:
You can use the triangle inequality theorem: the sum of any two sides must be greater than the third side. You can also just check the two smallest sides.
9+12=21
21>16 --> yes it is a triangle.
hope this helped!
If the sum of the lengths of any two sides of a triangle is less than or equal to the length of the third side, then the triangle is not possible.
If a triangle has sides with lengths of 9, 12, and 16, notice that 9 + 12 or 21 is greater than 16. So the sum of the lengths of two sides of the triangle is greater than the length of the third side.
This means that the triangle with sides of lengths
9, 12, and 16 is possible.
Can you guys please answer this question 20 ASAP
Answer:
a the answer is a
Step-by-step explanation:
how many packs of pencils can you get if there is 1,440 pencils and 6 in each pack
Divide 1440 by 6 to get 240 packs.
You mix 2 1/2 quarts of juice with 6 2/3 quarts of ginger ale to make fruit punch. What is the ratio of the amount of juice to the amount of ginger ale in simplest form
The ratio of the amount of juice to the amount of ginger ale is 3 : 8
Step-by-step explanation:
Fruit punch = amount of juice + amount of gingle ale
(convert the mixed fraction into proper fraction)
amount of juice = 2 1/2 = 5/2 amount of ginger ale = 6 2/3 = 20/3Ratio of the amount of juice to the amount of ginger ale = (5/2) / (20/3)
⇒ (5/2)[tex]\times[/tex](3/20)
⇒ (1/2)[tex]\times[/tex](3/4)
⇒(3/8)
∴ The ratio of juice to ginger ale is 3 : 8
If you were to describe a translation of triangle ABC, what information would you
need to include in your description?
Answer:
The information you'll include is the amount of spaces moved from ABC to form A'B'C' which will be based on the opposite side.
To describe a translation of triangle ABC, you need to identify the direction and distance of the translation. The triangle's shape, size, and orientation remain the same after translation.
Explanation:In describing a translation of triangle ABC, you would include the direction and distance of the translation. The direction could be up, down, left, or right. The distance would determine how far the triangle moves from its original position.
For instance, you may describe a translation as moving the triangle ABC 3 units to the right and 2 units down. It's important to note that under a translation, the shape of the triangle does not change. The size, shape, and orientation of triangle ABC remain consistent in the translated image.
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State your first and last name. Use the letters in your first name and last name to write an equation of a line in slope-intercept form, y=mx + b as follows:
1. Let x = the number of letters in your first name. Write down the coordinates of the x-intercept using this value for x (If your first name is hyphenated, you may use only the first or last part).
2. Let y = the number of letters in your last name. Write down the coordinates of the y-intercept using this value of y (If your last name is hyphenated, you may use only the first or last part).
3. Find the slope of your line using the x and y intercepts from #1 & #2.
Part Two (3 points): Write the equation of the line using y = mx + b. Replace the m with the slope from #3 and the b with the y value from #2. Use the equation generated to complete a table of at least four ordered pairs. You already have two ordered pairs from #1 and #2.
Part Three (5 points): Use graph paper to sketch a graph of the line in part two. Please be sure to write the coordinates of all points on the graph, label the x and y axes, place arrows on your graph.
My name has 6 letters and my last name 9
Answer:
i) b = 9
ii) m = -3/2
iii) another two ordered pairs on the graph can be (2, 6) and (8, -3).
Step-by-step explanation:
i.) equation of the line is y = mx + b
ii) x = number of letters in my first name = 6 is the x-intercept
iii) y = number of letters in my last name = 9 is the y-intercept
iv) if x = 0 then y-intercept is b. then 9 = (0 [tex]\times[/tex] m) + b. Therefore b = 9
v) if y = 0 then x -intercept is given by 0 = (6 [tex]\times[/tex] m) + 9.
Therefore 0 = 6m + 9 [tex]\Rightarrow[/tex] 6m = -9, m = -3/2
vi) another two ordered pairs on the graph can be (2, 6) and (8, -3).
how to multiply and divide algebraic fractions
Answer:
Step-by-step explanation:
Multiplying two algebraic fractions produces a new algebraic fraction. Multiply the two numerators to get the new numerator and multiply the two denominators to get the new denominator. Then simplify by reducing the new fraction to lowest terms.
for example:
[tex]\frac{x}{y} \\[/tex]×[tex]\frac{a}{b}[/tex] = [tex]\frac{xa}{yb}[/tex]
Division of algebraic fractions
The procedure for dividing algebraic fractions is the same as the procedure for dividing common fractions. Replace the division by a fraction by the multiplication by the reciprocal of that fraction, like this. Then carry out the multiplication of the two fractions as described above.
for example:
[tex]\frac{\frac{a}{b} }{\frac{x}{y} }[/tex]
can be written as
[tex]\frac{a}{b}[/tex]×[tex]\frac{x}{y}[/tex]= [tex]\frac{ax}{by}[/tex]
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Simplify (x^2y)(xy^4)
Answer:
y^4x^1+2y
Step-by-step explanation:
Answer:
8xsquareysquare (square=2 on right hand corner)
Step-by-step explanation:
2yx4xy
3) 4x -8y=-24
4x - 10y=-12
Why might you need to use the addition or subtraction property of equality more than once after you have used the distributive property and combined like terms? Explain.
Answer:Use the properties of equality and the distributive property to solve equations ... Although multi-step equations take more time and more operations, they can still be ... First “undo” the addition and subtraction, and then “undo” the multiplication and ... We need to “move” one of the variable terms in order to solve the equation.
Step-by-step explanation:
Answer:
If there is a variable term and a constant on each side of the equation, then you will need to use the addition or subtraction property of equality once to isolate the variable term and once to isolate the constant.
Step-by-step explanation:
Express 18 hours as a percent of 3 days
Answer:
25%
Step-by-step explanation:
Convert days into hours
3 days = 3×24 = 72 hours
18/72 × 100 = 25%
What is 9+10?
A) 910
B) 21
C) 19
D) 90
Answer:
C) 19
Step-by-step explanation:
9+10 = 19
Answer:
B) 21
Step-by-step explanation:
Because 3×3=9 and 2×5=10
If you switch it, 3×2 and 3×5, that is equal to 6 and 15.
6+15=21
A group of marine biologists are scuba diving. For safety, they dive in pairs. The two divers in a pair must be at most 35 feet away from each other at all times. One diver is 122 feet below sea level. The other driver is at 159 feet below sea level. How far apart are the divers?
Answer: They are 37 feet apart each other
Step-by-step explanation:
We are told that two divers are at a certain distance between them. The first diver is at a depth of 122 ft and the second diver is at a depth of 159 feet.
Note we are talking about depth, since both divers are below sea level.
Now, if we want to know the distance that separates them, we only have to take the difference between both depths:
[tex]159 ft-122 ft=37 ft[/tex] This is the distance beweent both divers.
This means they have to reduce their distance by 2 feet in order to accomplish the safety rules.
The store offers a 20% discount. The regular price of a T-shirt is $18. What is the discount price?
Answer:
$16.40
Step-by-step explanation:
First we find the how much the discount takes off
$20 × .18 = $3.60
So, the discount takes off $3.60, we then subtract that from $20
$20 - $3.60 = $16.40
Which then gives the price of the shirt as $16.40
How many centimeters equal 39.4 meters?
Answer:
Step-by-step explanation:
100CM equal 1m
Therefore
39.4*100=3940cm
Write a word phrase for the expression 10+(6-4)
Answer:
Ten added to the difference of six and four. Or, the difference of six and four added to ten.
Step-by-step explanation:
The word phrase for the mathematical expression 10+(6-4) is 'Ten plus the difference of six and four'. It is the representation of the arithmetic operation in a sentence format.
Explanation:The word phrase for the mathematical expression 10+(6-4) is 'Ten plus the difference of six and four'. In this phrase, 'Ten plus' corresponds to the 10+ part of the expression. 'The difference of six and four' means you subtract 4 from 6, which corresponds to the (6-4) part of the expression.
The expression 10+(6-4) can be simplified using the order of operations. First, we need to subtract 4 from 6, which equals 2. Then, we add the result 2 to 10, which equals 12. Therefore, the word phrase for the expression 10+(6-4) is "Ten plus the difference of six and four."
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975,462 were downloaded in one day. Round this number to the nearest hundred thousand to estimate how many songs were downloaded in one day
Answer:
975,462.00000
Step-by-step explanation:
975,462 rounded to hundred thousand
The number 975,462 rounded to the nearest hundred thousand is 1,000,000 because the ten thousand digit (7) is more than 5.
Explanation:To round the number 975,462 to the nearest hundred thousand, you have to look at the ten thousand digit. In this case, that's 7. If this digit is 5 or more, you round up the hundred thousand digits. If it is less than 5, you leave the hundred thousand digits as it is. In our number, the ten thousand digit is 7, so we round up the hundred thousand digit which is 9 to 10. Since there is no '10' in the digit system, it overflows to the next digit, making it 1,000,000. So, 975,462 rounded to the nearest hundred thousand is 1,000,000.
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given a sphere with a radius of 2 cm find the volume of the nearest whole number
Answer:
34cm3
Step-by-step explanation:
Volume of sphere = 4/3 pi x cube of radius
Radius =2cm , pi = 3.142
Volume = 4/3 x 3.142 x 2 x 2 x 2
Volume = 1.3333 x 3.142 x 8
Volume = 33.5cm3
Volume = 34cm3 to the nearest whole number
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A dog is standing 5 feet from the base of a tree, looking up at a cat that has climbed 16 feet up the tree. What is the angle of elevation from the point the dog is standing on the ground to the cat?
Answer:
x=72.6
Step-by-step explanation:
use inverse trig because your finding a missing angle. use tan because you haved opp/adj
tan-1=(16/5)
x=tan-1(16/5)
*use a calculator
x=72.6
The the angle of elevation from the point the dog is standing on the ground to the cat is 72.6 degrees
We have given that a dog is standing 5 feet from the base of a tree, looking up at a cat that has climbed 16 feet up the tree
We have to find the angle of elevation
We can see in a figure.
What is the angle of elevation?The angle between the horizontal line of sight and the object.
use inverse trig because we are finding a missing angle.
use tan because we have given height of tree (one side) and a distance between dog and tree(second side)
[tex]tab(\theta)}= opp/adj[/tex]
Apply [tex]tan^-1[/tex] on both side we get,
[tex]\theta=tan-1(16/5)[/tex]
[tex]\theta=tan-1(16/5)[/tex]
[tex]\theta=72.6[/tex]
Therefore,the the angle of elevation from the point the dog is standing on the ground to the cat is 72.6 degrees
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In the figure above, square ABCD and triangle EFG have the same areas. If AB =6 and EG =8, what is the height o triangle EFG?
Answer:
The height of triangle EFG is 9 units
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the area of a square ABCD
The area of a square is equal to
[tex]A=b^2[/tex]
where
b is the length side of the square
we have
[tex]b=AB=6\ units[/tex]
substitute
[tex]A=6^2=36\ units^2[/tex]
step 2
Find the height of triangle EFG
The area of triangle EFG is equal to
[tex]A=\frac{1}{2}(b)(h)[/tex]
where
b is the base of triangle
h is the height of triangle
we have
[tex]b=EG=8\ units[/tex]
[tex]A=36\ units^2[/tex] ---> area of triangle EFG is the same that the area of square ABCD
substitute the given values in the formula
[tex]36=\frac{1}{2}(8)(h)[/tex]
solve for h
[tex]36=4h\\h=9\ units[/tex]
therefore
The height of triangle EFG is 9 units
Check 56 divided 16 using multiplication
Answer:
3.5
Step-by-step explanation:
3.5x16=56
Evaluate the expression 3.14(a2 + ab) when a = 3 and b = 4. (Input decimals only, such as 12.71, as the answer.)
Answer for Blank 1:
Replace a and b with the given values:
3.14(3^2 + 3x4)
Simplify:
3.14(9 +12)
3.14(21)
Multiply:
3.14 x 21 =65.94
Use the coordinate grid to determine the coordinates of point P:
A coordinate grid shown from negative 2 to positive 2 on x-axis and negative 2 to positive 2 on y-axis. There are 4 grid lines between a whole unit of the grid. A point labeled P is shown at the intersection of 8 grid lines to the left of the y-axis and 4 grid lines above the x-axis.
What are the coordinates of point P?
(0.8, −0.4)
(−0.8, 0.4)
(1.6, −0.8)
(−1.6, 0.8)
Option D: [tex](-1.6,0.8)[/tex] are the coordinates of the point P
Explanation:
It is given that "A coordinate grid shown from negative 2 to positive 2 on x-axis and negative 2 to positive 2 on y-axis. There are 4 grid lines between a whole unit of the grid".
Thus, the value of each grid is [tex]0.2[/tex]
It is also given that, "A point labeled P is shown at the intersection of 8 grid lines to the left of the y-axis and 4 grid lines above the x-axis".
Since the point P lies on the left of the y-axis and above the x-axis, the x-value will be negative and y-value will be positive.
Thus, the value of x-axis is given by
[tex]8\times0.2=-1.6[/tex]
And the value of y-axis is given by
[tex]4\times0.2=0.8[/tex]
Thus, the coordinates of the point P is [tex](-1.6,0.8)[/tex]
Hence, Option D is the correct answer.
If 6 workers can paint a house in 2 days; how
many days will it take for 3 workers to paint the same house?
Answer:
0, because the house is already painted. If this isn't a riddle then, it should take 4 days because that is half the people, two times the workload per person.
Answer:
4 days
Step-by-step explanation:
6 workers takes 2 days.
That means that each worker works 6*2 = 12 worker days.
To get the same amount it takes 3 workers 4 days to get 12 worker days.
To the nearest tenth, what is the population density of bacteria at the end of the third hour in petri dish A?
Answer:
The question is not complete or missing details. Here is a similar question ; Suppose the rate of growth of bacteria in a Petri dish is given by q(t)=2t, where t is given in hours and q(t) is given in thousands of bacteria per hour. If a culture starts with 3,000 bacteria, find a function Q(t) that gives the number of bacteria in the Petri dish at any time t. How many bacteria are in the dish after 4 hours? Round your answer to the nearest thousand and do not include units.
Step-by-step explanation:
The detailed steps are as shown in the attachment.
q(t)=2t
dq/dt = 2t
Integrating both sides as shown in the attachment.
Any other question can be approached the same way.