Answer:
Length = 14m
Width = 12m
Step-by-step explanation:
The length of a rectangle is 2m greater than the width.
The area of the rectangle = 168m²
Let's say the width is x meters.
The length will be (x + 2) meters.
Area of a rectangle = length × width
x(x + 2) = 168
x² + 2x - 168 = 0
Solving x by applying the quadratic formula we get;
x = 12 or -14
Since the width cannot be negative, we take 12 meters to be the dimensions of the width.
The length = 12 + 2 = 14 meters.
To find the length and width of the rectangle, we formulate an equation based on the known relationship between the dimensions and the given area. Solving the equation, we get the width as 12 m and length as 14 m.
Explanation:The question is about finding the length and width of a rectangle given the area and a relationship between the two dimensions. We can set up an equation based on the information given and the formula for the area of a rectangle. Namely, the area of a rectangle is equal to its length multiplied by its width (A = lw).
According to the problem, the length of the rectangle is 2 m more than the width. We can express this relationship as L = W + 2. We also know that the area of the rectangle is 168 m2, which results in the equation (W + 2)W = 168.
Solving this quadratic equation, we find that the width (W) is 12 m and the length (L) is 14 m. These are the dimensions of the rectangle.
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A store charges $6.96 for a case of mineral water. Each case contains 2 boxes of mineral water. Each box contains 4 bottles of minerals water. What is the cost of each bottle of mineral water?
The cost of each bottle of mineral water is $0.87.
Explanation:To find the cost of each bottle of mineral water, we need to divide the total cost of the case by the number of bottles in the case. A case contains 2 boxes and each box contains 4 bottles, so there are 2 x 4 = 8 bottles in a case. The cost of a case is $6.96, so the cost of each bottle is $6.96 divided by 8, which equals $0.87.
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The cost of each bottle of mineral water is $0.87.
Explanation:To find the cost of each bottle of mineral water, we need to divide the total cost of the case by the number of bottles.
The case of mineral water contains 2 boxes, and each box contains 4 bottles.
So, the total number of bottles in the case is 2 x 4 = 8.
Since the cost of the case is $6.96,
we can divide it by the number of bottles to find the cost of each bottle: $6.96 / 8 = $0.87.
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32.
Simplify the expression.
-(10)^-2
10^2 -1/10^2
Answer:
Step-by-step explanation:
-(10)^-2 = -1/ 10² = -1/ 100
10² - 1/10² =100 - (-1/100 ) = 100+ 1 /100 = 9999/100
Which values are in the solution set of |x| -8 < 12?
xm=x+z ,solve for x, Algebra 1
Answer: x = z/(m-1).
Step-by-step explanation: xm - x = z
x (m - 1) = z ; x = z/(m-1).
Janice caught three trout when she went fishing .one trout weighted 1.38 pounds ,and the second trout weighted 2.01 pounds,and the third trout weighted 1.2 pounds. How much is the total weight of the fish
Answer:
4.59
Explanation:
1.38 + 2.01 = 3.39
1.2 = 1.20
3.39 + 1.20 = 4.59
4*3-(24divided6)+8=?
Answer:
16
Step-by-step explanation:
Follow the correct order of operations.
4 * 3 - (24 divided 6) + 8 =
Parentheses first.
= 4 * 3 - 4 + 8
Now, the multiplication.
= 12 - 4 + 8
Now additions and subtractions in the order they appear from left to right.
= 8 + 8
= 16
If i^2 = −1 and x = i + 9, which is the result of squaring x?
Answer:
80 + 18i
Step-by-step explanation:
i² = -1
x = i + 9
x² = (i + 9)²
Applying; (a + b)² = a² + 2ab + b² concept,
x² = i² + 18i + 81
We know that i² = -1
So x² = -1 + 18i + 81
x² = 81 - 1 + 18i = 80 + 18i
The square of the complex number x = i + 9 is computed by squaring each term and combining the results, giving us 80 + 18i as the final squared value.
To square the complex number x = i + 9, we use the formula for squaring a binomial:
Square the first term: i² = -1.
Square the second term: 9² = 81.
Multiply the first term by the second term and by 2 for the middle term: 2 times i times 9 = 18i.
Sum all the terms together -1 + 81 + 18i = 80 + 18i.
So, the result of squaring x is 80 + 18i.
how do I show my work for this 50.04- 1.103
To show your work for the subtraction [tex]\(50.04 - 1.103\)[/tex], follow these steps:
1. Line up the Decimals:
Align the decimal points of both numbers, ensuring they are in the same vertical position.
[tex]\[ &50.040 \\ - &1.103 \end{align*} \][/tex]
2. Subtraction:
Begin subtracting from the rightmost column. Subtract 3 from 0, borrow 1 from 4, subtract 0 from 10, subtract 1 from 4, and subtract 1 from 5.
[tex]\[50.040 \\ - &1.103 \\ \underline{-} \end{align*} \][/tex]
[tex]\[ 48.937 \][/tex]
3. **Final Result:**
The result of [tex]\(50.04 - 1.103\)[/tex] is [tex]\(48.937\).[/tex]
By displaying each step of the subtraction process, you provide a clear and organized representation of your work.
What is the value of x
What is the value of x?
Applying the triangle sum theorem, the value of x is: A. 28°.
The Triangle Sum TheoremThe triangle sum theorem states that, if all three interior angles in a triangle are added together, it will sum up to 180 degrees.Thus:
x = 180 - 95 - 57
x = 28°
Therefore, applying the triangle sum theorem, the value of x is: A. 28°.
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Answer:
28° or A
Step-by-step explanation:
Let's find x:
What information do we have to help us?
Information:
- Angle 1 = 95°
-Angle 2 = 57°
- Triangle
Using this information, we can solve for x.
A triangles sides all add up to 180°.
That is because it is half of a square and a squares sides all add up to 360°.
Let's make an algebraic equation.
95 + 57 + x = 180
Simplify.
152 + x = 180
Cancel out 152 by subtracting 152 from each number.
152 - 152 = 0
180 - 152 = 28
Plug into the equation.
x = 28°
The value of x is 28°.
That matches choice A.
Desiree and her mother went to the movies two times in the month of April. Each time she was charged the student rate of $7.50 while her mother was charged $9.00. How much money did Desiree and her mother spend on movie tickets in April?
Answer:
They spend $33.
Step-by-step explanation:
multiply 7.50x2=15 and multiply 9.00x2=18. Then add 15+18=33.
The number line shows the graph of an inequality: A number line is shown from negative 5 to positive 5 with increments of 0.5. All the whole numbers are labeled on the number line. An empty circle is shown on the first mark to the left of 0. The region to the left of the empty circle is shaded. Which statement explains whether −1.5 can be a value in the shaded region? Yes it can, because −1.5 lies to the left of −0.5 Yes it can, because −1.5 lies to the right of −0.5 No it cannot, because −1.5 lies to the left of −0.5 No it cannot, because −1.5 lies to the right of −0.5
Answer:
Option A.
Step-by-step explanation:
Draw a number line from negative 5 to positive 5 with increments of 0.5. Make an empty circle on the first mark to the left of 0. It means mark an open circle at -0.5.
The region to the left of the empty circle is shaded. It means all the points lie on the left side of -0.5 at in the shaded region.
We need to find a statement that explains whether −1.5 can be a value in the shaded region.
Since −1.5 lies to the left of −0.5 , therefore -1.5 is in the shaded region.
Therefore, the correct option is A.
Answer:
C.)
Step-by-step explanation:
You have to use the line graph!
Please try to resist cheating and do the work!
Make sure the fraction is fully reduced:
3y/13 + 7y/26
Answer:
[tex] \dfrac{y}{2} [/tex]
Step-by-step explanation:
The LCD of 13 and 26 is 26.
[tex] \dfrac{3y}{13} + \dfrac{7y}{26} = [/tex]
[tex] = \dfrac{2 \times 3y}{2 \times 13} + \dfrac{7y}{26} [/tex]
[tex] = \dfrac{6y}{26} + \dfrac{7y}{26} [/tex]
[tex] = \dfrac{13y}{26} [/tex]
[tex] = \dfrac{y}{2} [/tex]
Joe gets paid $20 per hour for his work as a human billboard and this week with the elections so near he plans to work 10 hours overtime by weeks end the government will have taken out $240 in taxes from his check leaving him a total of $760 how many hours does joe normally work per week
Answer:
100 i think im not sure but i think its 100
Step-by-step explanation:
im not dat good at math either
Evaluate the expression -5-3+1
Answer:
The answer is -7
Step-by-step explanation:
-5 - 3 = -8
-8 + 1 = -7
Hope I helped :)
Answer:
-7
Step-by-step explanation:
The rule for subtraction, in this case it is -5-3, you change the subtraction sign to addition and use the opposite of the second number, making it -5+(-3) which is -8. Then, you add 1 to -8, and the rule for this specific expression is to take the absolute value of both -8 and 1, then subtract the two, making the expression as of now 8-1. Subtract them, and get 7, but you take the sign of whichever number had the greatest absolute value, which was -8, so now the answer is -7. That's how you get your answer
-5-3+1= -5+(-3)+1
-8+1= |-8|-|1|
8-1= -7 (because you take the sign with the greatest absolute value, which is -8.)
is 19 2/9 a integer
Answer:No
Step-by-step explanation: Integers are whole numbers that can be positive or negatives no decimals or fractions.
a submarine dives 462 feet beneath the surface. it then climes up 250 feet. what is the depth of the submarine now?
The surface would be 0.
First it dives 462:
0 - 462 = -462 feet,
It then climbs 250:
-462 + 250 = -212
The submarine is at -212 feet. ( 212 feet below the surface.)
Four more than five times a number is
two less than the number.
Answer:
4 + 5x = x - 2
Answer:
4 + 5x = x - 2
x=-1.5
Step-by-step explanation:
4 + 5x = x - 2
subtract 4 from both sides (or add negative whichever you prefer)
5x=x-6
now subtract x from both sides
4x=-6
now divide by 4
x=-1.5
Jennie is training for a race. On Tuesday She finished her sprint 0.305 second faster than on Monday. be How can you explain the meaning of 0.305 Solve this problem anyway you choose
Answer: Hello there!
we know that on Tuesday, Jennie finished her sprint 0.305 seconds faster than on Monday, and we want to model this with math.
If we define x as the time in which she finished ger sprint on Monday, we can write the time for Tuesday as x - 0.305s
this is because she finished her sprint 0.305 seconds "faster", this means that she finished it in less time, so you need to subtract this number to the previous time.
Then the meaning of 0.305 is the amount of time that you need to subtract from the previous time, in order to get the actual time that she needs to finish the sprint.
Which expressions represent a perfect square monomial and its square root? Check all that apply.
121: 11
4x2, 2x
9x2 – 1; 3x - 1
25x, 5x
49x4; 7,22
Answer: A,B,E
Step-by-step explanation:
Answer:
Option 1,2 and 5 represent a perfect square monomial and its square root.
Step-by-step explanation:
To find : Which expressions represent a perfect square monomial and its square root? Check all that apply.
Solution :
1) 121, 11
As [tex](11)^2=121[/tex]
This expression represents a perfect square monomial and it’s square root.
2) [tex]4x^2,2x[/tex]
As [tex](2x)^2=4x^2[/tex]
This expression represents a perfect square monomial and it’s square root.
3) [tex]9x^2-1,3x-1[/tex]
As [tex](3x-1)^2=9x^2+1-6x[/tex]
This expression does not represents a perfect square monomial and it’s square root.
4) [tex]25x,5x[/tex]
As [tex](5x)^2=25x^2[/tex]
This expression does not represents a perfect square monomial and it’s square root.
5) [tex]49x^4,7x^2[/tex]
As [tex](7x^2)^2=49x^4[/tex]
This expression represents a perfect square monomial and it’s square root.
Therefore, Option 1,2 and 5 represent a perfect square monomial and its square root.
A hot tub pump circulates 4 cubic feet of water per minute. How many cubic inches of water does it circulate per minute
12 inches= 1 foot
We have 4 feet
12*4=48
Therefore 48 cubic inches is the answer
Hope this helps!!!
A hot tub pump that circulates 4 cubic feet of water per minute circulates 6912 cubic inches of water per minute, as 1 cubic foot equals 1728 cubic inches.
Explanation:This question involves a conversion from cubic feet to cubic inches. 1 cubic foot is equivalent to 1728 cubic inches. Therefore, if the hot tub pump circulates 4 cubic feet of water per minute, we need to multiply 4 by 1728 to find out how many cubic inches that would be.
Using the multiplication rule for units, we get:
4 cubic feet x 1728 cubic inches/cubic foot = 6912 cubic inches
Therefore, the hot tub pump circulates 6912 cubic inches of water per minute>.
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Simplify each expression. ( 5 v − 4 v 2 − 2 v 4 ) − ( 3 v 3 + 8 v + v 4 )
Answer:
the answer is 0
Step-by-step explanation:
i only have the answer
-32v I did the expression and I got -32v. This is a better answer than the other guy.
Point M begins at (5,-2). Write the coordinates of Ry= 1 (M). Is this correctly illustrated
below?
Answer:
No
Step-by-step explanation:
The reflection (R) around the line y = 1 is not the point illustrated.
Notice that the original point M (5,-2) is THREE (3) units below the line y=1, therefore when doing the reflection, it should end up THREE units above the y=1 line.
That is, it should end up at the point (5,4 ) and not at (5,3) as is shown in the picture.
Help help me I need help my mom don’t wanna help me
Answer: 32÷4+3=11
Step-by-step explanation:
24÷3=8
The total cost f(x), in dollars, for renting a car for a day and driving it x miles is shown:
f(x) = 90 + 0.11x
What does f(30) represent?
The number of dollars spent to rent the car for 30 days
The number of miles driven on the car in 30 days
The number of dollars it costs to drive the car 30 miles
The number of miles driven for a cost of $30
The total cost f(x), in dollars, for renting a car for a day and driving it x miles is shown:
f(x) = 90 + 0.11x
What does f(30) represent?
Answer:
The number of dollars it costs to drive the car 30 miles
option C. The number of dollars it costs to drive the car is 30 miles.
The total cost f(x), in dollars, for renting a car for a day and driving it x miles is shown:
f(x) = 90 + 0.11x.
What does f(30) represent?
It represents the number of dollars it costs to drive the car 30 miles.
How much gas will it take to drive 30 miles?1.5 gallons
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30. 3 x (5 + 6) = 33
33. 14 - (8 - 2) - 1 =
36. (3 + 2) × (4 + 6) =
39. 6 x 4 + 5) =
Answer:
39. 29
36. 50
33. 7
30. 33
Step-by-step explanation:
39. According to the Order of Operations, in this case, Subtraction & Addition are evaluated after Division & Multiplication:
[tex]6 \times 4 + 5 = 24 + 5 = 29[/tex]
36. Evaluate everything since everything is wrapped in parentheses:
[tex](3 + 2) \times (4 + 6) = 5 \times 10 = 50[/tex]
33. Evaluate everything inside of parentheses FIRST:
[tex]14 - (8 - 2) - 1 = 14 - 6 - 1 = 7[/tex]
I am joyous to assist you anytime.
60 is 5 times as great as k.
Answer:
k=12
Step-by-step explanation:
60÷5=12
OR5+5+5+5+5+5+5+5+5+5+5+5=60
↑=12 5's
Hope this helps!!!
Brady
Answer:
It's 12
Step-by-step explanation:
60 = 5k
or, 60/5 =k
or, k=12
Hence, 60 is 5 times great as 12
Was it useful?
This circle is centered at the origin, and the length of its radius is 4. What is
the equation of the circle?
Answer:
D. x² + y² = 4²
Step-by-step explanation:
The general equation of a circle is given in the attached graphic.
In this case, we can see that the center of the circle is at the origin i.e (0,0) and that the radius is 4 units.
the values for h, k and r in the general equation are as follows:
h = 0, k=0, r = 4
putting this into the general equation:
(x-h)² + (y-k)² = r²
(x-0)² + (y-0)² = 4²
x² + y² = 4²
The equation of the circle centered at the origin with a radius of 4 is:
x² + y² = 4².
Option D is the correct answer.
We have,
The equation of a circle centered at the origin (0, 0) with a radius of 4 can be written in the form:
[tex]x^2 + y^2 = r^2[/tex]
where (x, y) represents any point on the circle and r is the radius.
Substituting the given radius of 4 into the equation, we have:
x² + y² = 4²
x² + y² = 16
Therefore,
The equation of the circle centered at the origin with a radius of 4 is:
x² + y² = 4².
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Andre is helping his father build a toy box for his little brother. The amount of space inside the toy box can be found by multiplying its width, length, and height. Write the amount of space, using an exponent. Then evaluate. The width is 3 ft. The length is 3 ft. The height is 3 ft.
Answer:3^3 (3 to the 3rd power) which is equal to 27 cubic ft.
Step-by-step explanation:
3x3x3=3^3
3^3=27
How do I do the algebra problem 5(b-1)?
Answer:
5b-5
Step-by-step explanation:
When doing these kinds of problems you want to do dributive property which means you multiply whatever number is outside of the (), which is 5, and multiply that by b and 1.
when numbers are outside the () and right next to them without anything like +,-, or a division sign, it means to multiply.
In order to find the answer to this question you will have to simplify using the distributive property.
[tex]5(b-1)[/tex]
Applying the distributive property:
[tex]5b+5\times-1[/tex]
[tex]5\times-1=-5[/tex]
[tex]5b-5[/tex]
Therefore the answer is "5b-5."
Hope this helps.
A plumber charges $80 per hour to complete a job. She also charges an
additional fiat fee of $50 for each job. The total charge for one particular job
was $490. This situation is represented by the equation 80x-50 = 490.
How long did the job take?
Answer:
5.5! Now, you need to know why. The total cost was $490, there is a fee of $50, so subtract the fee from the total cost and you should then divide that by $80 because thats how much it is an hour.
The actual equation should be 80x + 50 = 490, not 80x - 50 = 490. By solving it, we find out that the job took 5.5 hours to complete.
Explanation:The given equation in the problem is incorrect. It should be 80x + 50 = 490, where x represents the number of hours the plumber worked. This equation accounts for the hourly charge (80x) and the upfront flat fee ($50). To solve for x, we begin by isolating it on one side of the equation. We subtract 50 from both sides to get 80x = 440. Then we divide both sides by 80, resulting in x = 5.5. Therefore, the plumber worked for 5.5 hours on this particular job.
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