Answer: 4 feet.
Step-by-step explanation:
Their is one rectangular prison divided into two.
The volume of the first one is
V1= L X H X W=80.
Volume of the second one is
V2= L X H X W
V2= 6 X H X 5
V2 = 30H
Now from the question, the total volume is 200cubic feet which means V1 + V2 = 200, recall that V1=80 and V2=30H, so we say;
80+30H=200, collecting the like term we have, 30H=200-80.
30H=120, divide both side by 30
30H/30=120/30
H= 4feet.
Height is 4feet.
Final answer:
To find the height of Rectangular Prism B, subtract Rectangular Prism A's volume from the total volume to get Prism B's volume (120 cubic feet), then divide by the product of its length and width. The height is 4 feet.
Explanation:
The question is about finding the height of Rectangular Prism B given that the solid figure it's part of (when combined with Rectangular Prism A) has a total volume of 200 cubic feet, and that Rectangular Prism A has a volume of 80 cubic feet. Considering volume calculations for rectangular prisms are done using length × width × height, we can find the height of Prism B by isolating height in the formula. Since Prism B has a length of 6 feet and a width of 5 feet, and we know the combined volume of both prisms, we first subtract the volume of Prism A from the total volume to find the volume of Prism B, which is 120 cubic feet (200 cubic feet - 80 cubic feet).
Volume of Prism B = 120 cubic feet. The formula for volume is then applied as follows:
Volume = Length × Width × Height
120 cubic feet = 6 feet × 5 feet × Height
Height = 120 cubic feet / (6 feet × 5 feet)
Height = 120 cubic feet / 30 square feet
Height = 4 feet.
Therefore, the height of Rectangular Prism B is 4 feet.
A right rectangular prism's edge lengths are 2 1 2 inches, 2 inches, and 6 inches. How many unit cubes with edge lengths of 1 3 inch can fit inside the prism?
Answer:
810 cubes
Step-by-step explanation:
step 1
Find the volume of the rectangular prism
The volume of the rectangular prism is
[tex]V=LWH[/tex]
we have
[tex]L=2\frac{1}{2}\ in=2+\frac{1}{2}=\frac{5}{2}\ in[/tex]
[tex]W=2\ in\\H=6\ in[/tex]
substitute
[tex]V=(\frac{5}{2})(2)(6)[/tex]
[tex]V=30\ in^3[/tex]
step 2
Find the volume of the cube
The volume of the cube is
[tex]V=b^3[/tex]
where
b is the length side of the cube
we have
[tex]b=\frac{1}{3}\ in[/tex]
substitute
[tex]V=(\frac{1}{3})^3[/tex]
[tex]V=\frac{1}{27}\ in^3[/tex]
step 3
Find out how many unit cubes with edge lengths of 1/3 inch can fit inside the prism
Divide the volume of the prism by the volume of the cube
[tex]30:\frac{1}{27}=30(27)=810\ cubes[/tex]
Workers in an office of 60 staff were asked their favourite type of take-away.
The results are summarised in the table.
Take-away Frequency Angle
Pizza 7
a
Curry 19
b
Fish & chips 4
c
Kebab 5
d
Other 25
e
Work out the size of each angle to draw a pie chart.
Answer:
Angles: 42°, 114°, 24°, 30°, 150°.
Step-by-step explanation:
Pie Charts
They represent the comparative values of a given variable subject to study. The whole pie is cut in angular sections where all the angles must sum 360°. If the sum of all the values is S and one particular value is x, then the angle of its circular section is given by
[tex]\displaystyle angle=\frac{x}{S}\ 360^o[/tex]
We have the staff of an office is S=60. When asked about their favorite type of takeaway we get:
Pizza: 7. Its corresponding angle is
[tex]\displaystyle angle=\frac{7}{60}\ 360^o=42^o[/tex]
Curry 19.
[tex]\displaystyle angle=\frac{19}{60}\ 360^o=114^o[/tex]
Fish & chips 4
[tex]\displaystyle angle=\frac{4}{60}\ 360^o=24^o[/tex]
Kebab 5
[tex]\displaystyle angle=\frac{5}{60}\ 360^o=30^o[/tex]
Other 25
[tex]\displaystyle angle=\frac{25}{60}\ 360^o=150^o[/tex]
We can see the sum of all angles is 360°
The angles for the pie chart are as follows:
- Pizza: 42 degrees
- Curry: 114 degrees
- Fish & chips: 24 degrees
- Kebab: 30 degrees
- Other: 150 degrees
These angles can be used to create a pie chart that accurately represents the favorite take-away choices of the office staff.
To calculate the size of each angle for the pie chart representing the favorite take-away choices of the 60 office staff, we need to determine the percentage each category represents in the total.
First, add up the frequencies:
Pizza + Curry + Fish & chips + Kebab + Other = 7 + 19 + 4 + 5 + 25 = 60
Now, calculate the percentage for each category:
- Pizza: (7/60) * 100% = 11.67%
- Curry: (19/60) * 100% = 31.67%
- Fish & chips: (4/60) * 100% = 6.67%
- Kebab: (5/60) * 100% = 8.33%
- Other: (25/60) * 100% = 41.67%
Now that we have the percentages, we can calculate the corresponding angles for the pie chart.
Each percentage corresponds to a fraction of the total 360 degrees in a circle.
So, for example, Pizza would be (11.67/100) * 360 = 42 degrees, Curry would be (31.67/100) * 360 = 114 degrees, and so on.
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what is 17½ divided by ⅚
Answer:
Step-by-step explanation:
(17 1/2) / (5/6) =
(35/2) / (5/6) =
35/2 * 6/5 =
105/5 =
21 <===
Find the area of a square Park whose perimeter is 320m.
Answer:
Step-by-step explanation:
A square is equal on each side. There are a total of 4 sides so we would take 320 and divide it by four to find the size of one side.
320/4
80
A = lw
A = 80 x 80
A = 6400 m^2
What is the value of the expression below?
7 divided by 2 minus 4.5 x times 3 + 8
Answer:
-2
Step-by-step explanation:
What is the slope intercept form of this equation? 8x +6y=12
Answer:
y=-4/3x+2
Step-by-step explanation:
If it is 12:50, what will the time be 5 hours and 20 minutes later?
Lets first make it easier.
If you add the 20 minutes to 12:50 it will turn to 1:10.
After this you add the 5 hours.
This will turn 1:10 into 6:10.
Hope this helps :)
What is the LCM (least common multiple) of 2 and 7?
Answer:
14
Explanation:
2 l 7
4 l 14
6 l 21
8 l 28
10 l 35
12 l 42
14 l 49
If you noticed the italized, bold, and underlined number fourteen, you would notice that 2 and 7 both have number fourteen as a multiple and it is also the least common multiple.
What is the product? [4 2] x [-2 5 7 -1]
Answer:
The answer is [6 18}
Step-by-step explanation:
I just took the test :)
The product of the matrices [4 2] and [-2 5 7 -1] is a 1x4 matrix. The resulting matrix is [-8 -4 20 10].
In order to find the product of two matrices, we need to ensure that the number of columns in the first matrix matches the number of rows in the second matrix. The first matrix, [4 2], has 1 row and 2 columns (1x2), while the second matrix, [-2 5 7 -1], has 2 rows and 4 columns (2x4). Since the number of columns in the first matrix matches the number of rows in the second matrix, we can proceed with matrix multiplication.
To compute the product, we perform the following steps:
Step 1: Take the first row of the first matrix and multiply each element by the corresponding element in the first column of the second matrix.
- First element: 4 * (-2) = -8
- Second element: 2 * (-2) = -4
Step 2: Take the first row of the first matrix and multiply each element by the corresponding element in the second column of the second matrix.
- Third element: 4 * 5 = 20
- Fourth element: 2 * 5 = 10
Step 3: Now, we have the elements for the first row of the resulting matrix: [-8 -4 20 10].
Step 4: Repeat the above steps for the second row of the first matrix.
Step 5: Combine the results to form the final product matrix: [-8 -4 20 10].
So, the product of the matrices [4 2] and [-2 5 7 -1] is the 1x4 matrix
[-8 -4 20 10].
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Find the missing number:
QUICKLY PLEASE
Missing value is Decreased by 20%
Step-by-step explanation:
We need to find the missing term.
As we can see from the figure we go from Decreased 10% and then decreased 10% to reach the final goal.
If we directly go from starting point to end point the total will be decreased by 20% as (10%+10%= 20%)
So, Missing value is Decreased by 20%
In x-5=9 the correct way to isolate the variable is to The number On both sides.
Answer:
x=14
Step-by-step explanation:
not sure what your asking for???
x-5=9
x=14
a cheetah runs at a rate of 75 miles per hour about how many leaders can it run in 5 seconds
Answer:
Distance in meters D = 167.75 meters
Step-by-step explanation:
Distance covered in 5 seconds is given by:
Distance, D = Speed (S) X Time (T)
Where,
Distance = ?
Speed = 75mph
Time = 5s
Since we are calculating distance in meters, we have to convert 75miles per hour to meters per second
75mph = 75miles/1hr X 1km/0.621miles X 1000m/1km X 1hr/60mins X 1min/60s
= (75X1000) / (0.621X60X60) meter per second
= 75000/2235.6 meter per second
= 33.55 meter per second
∴ Distance D = 33.55 meter per second X 5 seconds
= 167.75 meters
A building is 3 ft from an 8-ft fence that surrounds the property. A worker wants to wash a window in the building 13 ft from the ground. He plans to place a ladder over the fence so it rests against the building. (See the figure.) He decides he should place the ladder 8 ft from the fence for stability. To the nearest tenth of a foot, how long a ladder will he need?
Answer:
Length of the ladder used by worker = 17 feet
Step-by-step explanation:
Given:
Height of the window from the ground = 13 ft
Distance of fence from the building = 3 ft
Distance of ladder from the building = (3+8) = 11 ft
We have to find the length of the ladder.
Let the length of the ladder be 'x'
From the diagram we can also say that 'x' is the hypotenuse of the right angled triangle.
Using Pythagoras formula:
⇒ [tex]hypotenuse\ 'x' =\sqrt{(perpendicular)^2+(base)^2}[/tex]
Here base length = 11 ft
Perpendicular = 13 ft
Plugging the values:
⇒ [tex]x=\sqrt{(13)^2+(11)^2}[/tex]
⇒ [tex]x=\sqrt{(169+121)}[/tex]
⇒ [tex]x= \sqrt{290}[/tex]
⇒ [tex]x=17.02[/tex] feet
The length of the ladder = 17 feet to its nearest tenth.
The worker will need a ladder that is approximately 8.5 feet long. This calculation is based on the Pythagorean theorem, considering the ladder's placement 8 feet from the fence and the need to reach a window 13 feet above the ground.
To find the length of the ladder the worker needs, we can use the Pythagorean theorem, as the ladder, the distance from the building, and the distance from the fence form a right triangle.
Let:
L be the length of the ladder.
D be the distance from the building to where the ladder rests (8 ft).
F be the distance from the fence to where the ladder rests (3 ft).
According to the Pythagorean theorem, we have:
[tex]L^2 = D^2 + F^2[/tex]
Substitute the known values:
[tex]L^2 = 8^2 + 3^2[/tex]
[tex]L^2 = 64 + 9[/tex]
[tex]L^2 = 73[/tex]
Now, take the square root of both sides:
L ≈ √73 ≈ 8.54 ft (rounded to the nearest tenth)
So, the worker will need a ladder that is approximately 8.5 feet long to safely reach the window 13 feet above the ground when placed 8 feet from the fence for stability.
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4/5 divided by 3/4 which equals something
Answer:
1.067
Step-by-step explanation:
What is the answer to -8(-8x-6)=-6x-22
Answer:
THE ANSWER IS 1.2068965517
Step-by-step explanation:
729.46 what digit is in the tenths place ?
Answer:
4
Step-by-step explanation:
The first digit after the decimal point is the tenths place. in this case, it would be 4
Answer:
4 Is in the tenths place
Step-by-step explanation:
7 in the hundreds
2 in the tens
9 in the ones
4 in the tenths
6 in the hundredths
Kate wants to build a fence around her garden to prevent her rabbits from eating her vegetables. The rabbit fencing costs $7.50 per metre. How much will it cost to enclose a square garden with an area of 144m^?
Solution:
Given that,
Kate wants to build a fence around her garden to prevent her rabbits from eating her vegetables
Given is a square garden
Area = 144 square meter
The area of square is given as:[tex]Area = (side)^2\\\\144 = (side)^2\\\\Take\ square\ root\ on\ both\ sides\\\\side = 12[/tex]
Thus length of side of square is 12 meter
Find the perimeter of square garden:Perimeter = 4(side)
Perimeter = 4(12)
Perimeter = 48 meter
The rabbit fencing costs $7.50 per meter[tex]Cost = perimeter \times 7.50\\\\Cost = 48 \times 7.50\\\\Cost = 360[/tex]
Thus it costs $ 360 to enclose a square garden with an area of 144 square meter
Calculate for pressure (P=F/A)
Force = 2,000 N
Area = 80 cm2
Answer:
25Ncm^2
Step-by-step explanation:
Pressure = force/area
Force = 2000N
Area = 80cm^2
Therefore,
Pressure = 2000/80
= 25Ncm^2
What is the first step when solving the equation below for x 4x - 0.2 = 1.9
A. Add 1.9 to both sides of the equation
B. Subtract 0.3 from both sides of the equation
C. Divide each side of the equation by 4
D. Add 0.3 to both sides of the equation
Answer:
First add 0.2 to both sides
x = 0.53
Step-by-step explanation:
4x - 0.2 = 1.9
4x - 0.2 + 0.2 = 1.9 + 0.2
4x = 2.1
Divide both sides by 4
4x/4 = 2.1/4
x =0.53
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Find the area of the shaded region.
540 sq km
113.1 sq km
426.9 sq km
320 sq km
Answer:
426.9 Km²
Step-by-step explanation:
The shaded area is the area of the triangle subtract the area of the circle.
Area of triangle = 0.5 bh ( b is the base and h the perpendicular height )
Here b = 40 and h = 27, thus
Area = 0.5 × 40 × 27 = 20 × 27 = 540 Km²
Area of circle = πr² ← r is the radius
Here the diameter is 12, thus radius = 12 ÷ 2 = 6
Area = π × 6² = 36π ≈ 113.1 Km²
Shaded area = 540 - 113.1 = 426.9 Km²
Which statement correctly compares the constants of variation for the graph and the equation below?
On a coordinate plane, a line goes through points (0, 0) and (1, 3).
StartFraction 10 x Over 3 y EndFraction = 1
The graph has a greater constant of variation.
The equation has a greater constant of variation.
The constant of variation is the same for the graph and the equation.
The constant of variation cannot be compared because the equation is nonproportional.
Answer:
The equation has a greater constant of variation
Step-by-step explanation:
The graph is of a line through point (0, 0) can be represented by the equation ...
y = kx
Using the given values for x and y, we see that ...
3 = k·1
k = 3 . . . . . the constant of variation for the graph
__
The given fraction can be rewritten as ...
y = (10/3)x = (3 1/3)x
In this form, the constant of variation is 3 1/3, greater than that of the graph.
Answer:
The equation has a greater constant of variation
Step-by-step explanation:The equation has a greater constant of variation
1/2x-1/3y=5
X=2/3y+10
What is the y and the x
Answer:
The system has infinite solutions
Is a consistent dependent system
Step-by-step explanation:
we have
First equation
[tex]\frac{1}{2}x-\frac{1}{3}y=5[/tex]
Isolate the variable y
[tex]\frac{1}{3}y=\frac{1}{2}x-5[/tex]
Multiply by 3 both sides
[tex]y=\frac{3}{2}x-15[/tex] ----> equation A
Second equation
[tex]x=\frac{2}{3}y+10[/tex] -
Isolate the variable y
[tex]\frac{2}{3}y=x-10[/tex]
Multiply by 3/2 both sides
[tex]y=\frac{3}{2}x-15[/tex] ---> equation B
Compare equation A and equation B
The equations are identical
therefore
The system has infinite solutions
Is a consistent dependent system
Jack has a square garden in front of his house. The garden has an area of 66 square yards. Find the length of each side of the garden. Round your answer to the nearest tenth of a yard.
1. 8.2 yards
2. 8.1 yards
3. 8.3 yards
4. 8.4 yards
What are the coordinates of the image of vertex R after a reflection across the y-axis? (–4, 3) (4, –3) (–3, –4) (3, 4)
(–4, 3) (4, –3) (–3, –4) (3, 4)
this is a rather simple yet complex concept the easiest way to solve these is to do the exact opposite.
so in this instance it is refrcted across the y-axiss so we swap ONLY the x value NOT the Y ie (-4,3) would switch to (4,3)
same thing would apply if it reflected across x-axis ex (-4,-3)
If it reflect across orgin you change both signs. ex (4,-3)
ie.
(–4, 3) (4, –3) (–3, –4) (3, 4)
changes to
(4, 3) (-4, –3) (3, –4) (-3, 4)
hope it helps
The coordinates of the image of vertex R after a reflection across the y-axis is (3, 4).
What is reflection?A reflection is an involution: when applied twice in succession, every point returns to its original location, and every geometrical object is restored to its original state.
Given is a point R = (-3, 4) we need to find the coordinates of the point R after it being reflected over y-axis,
So, we know that,
When dealing with reflection of a line or shape or a figure in the coordinate plane, especially if it is reflected across the y-axis, you just have to give the opposite of the given (original) x- coordinate in order to give a symmetric figure.
The rule of reflection over y-axis is =
(x, y) = (-x, y)
So,
R = (-3, 4), after it being reflected over y-axis =
R' = (3, 4)
Hence the coordinates of the image of vertex R after a reflection across the y-axis is (3, 4).
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pleaseeeee answer this questionnnn it would mean alot please show work and explain thanks☺
Answer:
Shown in the picture
Step-by-step explanation:
A:
Set the value of x to "5" and "30" to find the corresponding values of y (i.e. the altitudes of the plane at 5 or 30 minutes after beginning descent).
B:
Use the the same method to determine the set of coordinates (/ordered pairs) at each of the values for x given in part B of the question.
C:
The initial value is simply the starting value of y, or in other words, the altitude at which the plane begins to descend in this context;
So it will be 0 mins after the beginning of descent of the plane, i.e. when x = 0, therefore the answer is (0, 28000) as an ordered pair or simply 28000 ft.
D:
Rate of change is a fancy or more technical way of referring to the gradient of a function;
In this case of the context of a plane descending, it refers to the change in altitude over time;
This can be calculated using any two ordered pairs (or coordinates as I call them) using the formula of the difference in the y values divided by the difference in the x values.
Martin has a 7/23 balloon mortgage on his $195,000 home. He has been
making payments of $965 each month and will have a balloon payment due
for the amount of $170,143. If he decides to make the balloon payment, what
will be the total financed price he paid for his home?
Answer: 251,203
Step-by-step explanation:
Martin pays 965 every month for seven years. Therefore,
965×12×7= 81,060
Then, he has a balloon payment of 170,143 to make. Therefore, totaal financed price he paid for his home is 81,060+170,143= 251,203.
Answer: 251,203
Step-by-step explanation:
Martin pays 965 every month for seven years. Therefore,
965×12×7= 81,060
Then, he has a balloon payment of 170,143 to make. Therefore, totaal financed price he paid for his home is 81,060+170,143= 251,203.
Jane construct a four sided wall to wall to surround their castle . The wall has a perimeter of 100 feet. One side measures 16 feet. A different side side measures 22 feet. A third side measures 34 feet. What is the unknown side length
Answer:
34+22=56+16=72 100-72=28 feet
Step-by-step explanation:
What is x in this equation 2-3/4x=11
Answer:
x=-12
Step-by-step explanation:
2-3/4x=11
3/4x=2-11
3/4x=-9
x=-9/(3/4)
x=(-9/1)(4/3)
x=-36/3
x=-12
It takes 1 and 1 4th cups of milk to make 8 pancakes, how many cups of milk is needed to make 20
The length of a rectangle is five feet less than
its width. If the area of the rectangle is 84
square feet, find its dimensions.
Answer:
Length is w-5
Area = length x width
84 = (w-5)w
84 = w^2 - 5w
0 = w^2 - 5w - 84
0 = ( w - 12 )( w + 7 )
w + 7 = 0 leads to negative measures.
w-12=0 ---> w = 12
width is 12, length is 5 less, or 7
The dimensions of the rectangle are 12 feet by 7 feet, determined by solving the quadratic equation derived from the relationship between the length and width and the given area of the rectangle.
To find the dimensions of a rectangle where the length is five feet less than its width and the area is 84 square feet, we can set up an equation. Let's define the width of the rectangle as w feet. Then, the length would be w - 5 feet. Since the area of a rectangle is defined as the product of its length and width, we get the following equation:
w times (w - 5) = 84
Expanding the left side gives us:
w^2 - 5w = 84
To solve this quadratic equation, move all terms to one side to set the equation to zero:
w^2 - 5w - 84 = 0
Factoring the quadratic equation, we look for two numbers that multiply to give -84 and add to give -5. These numbers are -12 and +7. So the equation factors as follows:
(w - 12)(w + 7) = 0
The solutions to the equation are w = 12 and w = -7. However, width cannot be negative in this context, so we discard w = -7. Thus, the width is 12 feet and the length is 12 - 5 = 7 feet.
Therefore, the dimensions of the rectangle are 12 feet by 7 feet.