The equation that represents the volume of the storage container(rectangular prism) in terms of its width is 12w + 6w²
How to find the volume of a rectangular prism?volume of a rectangular prism = lwh
where
l = lengthw = widthh = heightTherefore,
h = 6 ft
l = 2 + w
Hence,
volume of the rectangular prism = (2 + w) × w × 6
volume of the rectangular prism = (2w + w²)6
volume of the rectangular prism = 12w + 6w²
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A ′ B ′ C ′ triangle, A, prime, B, prime, C, prime is the image of △ A B C △ABCtriangle, A, B, C under a rotation about the origin, ( 0 , 0 ) (0,0)left parenthesis, 0, comma, 0, right parenthesis.
The angle of rotation of triangle ABC to A'B'C is 105°
How to illustrate the information?It should be noted that the rotation from ABC to A'B'C is in a clockwise direction.
Point B is also on the x axis and point B' is in the second quadrant.
In this case, the angle that depicts the second quadrant is 105°.
In conclusion, the correct option is D.
The complete question is:
Triangle A’ B’ C’ is the image of A B C under a rotation about the origin, (0,0)
Determine the angle of rotation
A. -105 degrees
B. -75 degrees
C. 75 degrees
D. 105 degrees
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Write a polynomial function of least degree with integral coefficients that has the given zeros. -1/3, 2/3, -1/4
Step-by-step explanation:
"integral" means here that the factors in the polynomial are integers.
we have 3 zeros.
the least degree of a polynomial with 3 zeros is 3.
and yes, that works also for 2 zeros (the degree must be at least 2, it must be at least a quadratic equation).
or 4 zeros (at least 4th degree).
it in general n zeros (at least nth degree).
constructing this out of the given zeros is easy.
what happens, when I multiply something by 0 ? the total result will be 0.
and so, we simply multiply 3 short terms with each other, where each term turns 0 for one of the given zeros.
what expression in x turns 0, when x = -1/3 ?
well : x + 1/3 or with integers 3x + 1 (multiplied by 3)
and for x = 2/3 ?
x - 2/3 or with integers 3x - 2
and for x = -1/4 ?
x + 1/4 or with integers 4x + 1
so, our polynomial function (of at least 3rd degree) is then
(3x + 1)(3x - 2)(4x + 1)
basically this could be already the result, depending on what your teacher wants.
for the fully extended form we need to do the multiplications :
(3x + 1)(3x - 2) = 9x² - 6x + 3x - 2 = 9x²- 3x - 2
(9x²- 3x - 2)(4x + 1) = 36x³ + 9x² - 12x² - 3x - 8x - 2 =
= 36x³ - 3x² - 11x - 2
the requested polynomial function is
f(x) = 36x³ - 3x² - 11x - 2
According to the rational root theorem, the numbers below are some of the potential roots of f(x) = 10x3 29x2 – 66x 27. select all that are actual roots.
The actual roots of the function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex] are -9/2, 3/5 and 1.
Given function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex].
Function is a relationship between two or more variables expressed in equal to form.
The roots of a polynomial function are the zeroes of the polynomial function. A polynomial function is a function that involves only non negative integer powers in an equation.
The polynomial function is given as:
[tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex]
factorize the above function
[tex]f(x)=(2x+9)(5x-3)(x-1)[/tex]
Now put the function f(x) equal to zero.
f(x)=(2x+9)(5x-3)(x-1)
split the function means put all the expressions equal to zero as under:
(2x+9)(5x-3)(x-1)=0
solve each for the value of x
x=-9/2,x=3/5,x=1
Hence the roots of the function [tex]f(x)=10x^{3} +29x^{2} -66x+27[/tex] are which are also the values of x are -9/2,3/5,1.
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Answer:
Step-by-step explanation:
To estimate the number of bass in a lake, a biologist catches and tags 32 bass. several weeks later, the biologist catches a new sample of 55 bass and finds that 5 are tagged. how many bass are in the lake?
If the biologist catches and tags 32 bass and from sample of 55 he found only 5 tagged then there are 352 bas in the lake.
Given Biologist catches and tags 32 bass, when sample of 55 bass is taken then 5 are found tagged.
Population is basically number of living thing exists in a particular area.
Number of bass which are tagged in lake=32
Sample size=55
Number of bass found tagged=5
means percentage of tagged bas found is 5/32*100=1.6%
We have to calculate number of times 5 is multiplied to get 32 which is 6.4.
Number of bass in the lake=55*6.4
=352 basses.
Hence there are 352 basses in the lake if 5 are found tagged in a sample of 55.
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I'm not very good at solving these problems
1 atom of C has a mass of 12 amu (atomic mass unit).
1 atom of O has a mass of 16 amu.
1 molecule of CO₂ thus has a mass of 12 + 2×16 = 44 amu.
C thus makes up 12/44 ≈ 0.27 of the total mass of CO₂, while O makes up the remaining 32/44 ≈ 0.73.
Then in a 2 kg = 2000 g block of CO₂, carbon makes up about 12/44 × 2000 ≈ 545 g.
6) Stacie was solving the triangle below. Can you find her mistake?
Stacie did the mistake that he put the value of base in place of perpendicular and vice versa.
The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°
Solution is supposed to be
[tex]tan_ (-1) (28/21) = 53.33[/tex]
Thus,Stacie did the mistake that he put the value of base in place of perpendicular and vice versa.
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f(x) = 4^ x / 8
can you Graph this ?
Answer:
Graph is below
Brainliest, please :)
Harry decided to buy some candy bars that
cost $2.19 each. He also bought a drink for
$3.55. Harry paid a total of $10.12. Write an
equation to find how many candy bars Harry
purchased.
A diagonal of a cube measures StartRoot 150 EndRoot cm. The diagonal of a face measures 10 cm.
What is the length, in centimeters, of an edge of the cube? Round the answer to the nearest tenth.
The side of the edge of the cube is 7. 07cm
How to determine the lengthGiven that a diagonal of a cube measures the square root of 150 cm and the diagonal of a face measures 10 cm.
Let's find the edge of the face
Note that the face of the cube is in the shape of square .
The diagonal of the face is 10 cm.
The formula for diagonal of square = [tex]\sqrt{2a}[/tex]
a is the side of the square face
We have that,
[tex]\sqrt{2a} = 10[/tex]
Make 'a' subject of formula
a = [tex]\frac{10}{\sqrt{2} }[/tex]
Find the surd of the equation, we have
a = [tex]\frac{10}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]
a = [tex]\frac{10\sqrt{2} }{2}[/tex]
a = [tex]5\sqrt{2}[/tex]
a = [tex]7. 07cm[/tex]
Thus, the side of the edge of the cube is 7. 07cm
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4. A juice bottling company makes a variety pack
with 24 orange juices, 12 apple juices, and 8
grape juices. Describe the ratio of the juices to
one another (orange: apple: grape).
(A) 2:1:1
(B) 3:1:2
(C) 4:2:2
(D) 6:3:2
The ratio of orange juice to apple juice to grape juice is 6: 3 : 2
What is ratio?A ratio says how much of one thing there is compared to another thing.
Therefore, we are comparing the numbers of juice produce by a bottling company.
Hence,
number of orange juice = 24
number of apple juice = 12
number of grape juice = 8
Therefore, the ratio of orange juice to apple juice to grape juice is as follows:
ratio = 24 : 12 : 8
divide through by 4
ratio = 6: 3 : 2
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At what meter mark will Ario be when Miguel starts the race? Round to the nearest tenth.
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
A number line goes from 0 to 25. A line is drawn from 3 to 25. The point at 3 is labeled Start and the point at 25 is labeled End.
Miguel and his brother Ario are both standing 3 meters from one side of a 25-meter pool when they decide to race. Miguel offers Ario a head start. Miguel says he will start when the ratio of Ario’s completed meters to Ario’s remaining meters is 1:4.
4.4 meters
7.4 meters
17.6 meters
20.6 meters
The meter mark at which Ario wil be when Miguel starts the race is; 7.4 meters
How to calculate the distance?A ratio such as the ratio 1:4 shows the proportion of two factors. In this case, it shows the ratio between the completed meters vs the remaining meters.
To find the distance, we will have to determine how much 1:4 represents in the total distance.
Total distance = 25 meters - 3 metes = 22 meters
Thus; 22 * 1/ 5 = 22/5 = 4.4
However, we also know they are three meters behind the start.
Thus, the meter mark at which Ario will be when Miguel starts the race
4.4 + 3 =7.4 meters
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Which type of parent function is f(x) = 1/x
Since it has a variable in the denominator, the function f(x) is a parent function classified as rational.
What are rational functions?Rational functions are functions that have the input variable, be it x, t, or any other, in the denominator.
The most simple example is given by:
[tex]f(x) = \frac{1}{x}[/tex].
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Answer: Reciprocal
Step-by-step explanation:
Reciprocal functions are functions that contain a constant numerator and x as its denominator. Its parent function is y = 1/x.
Kelly has 2 liters of milk in the refrigerator. she used 12 liters of milk in the morning with breakfast. she then used the same quantities of milk at both lunch and dinner, such that she used up all the milk. what quantity of milk did she use at dinner?
Kelly used a volume of [tex]\frac{3}{4}[/tex] liters of milk at dinner.
What is Volume?Each thing in 3-D takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity. Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank. The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.Given we have, Initial amount of milk is [tex]2[/tex] liters.
The amount of milk used in the morning is [tex]\frac{1}{2}[/tex] Liters.
Now, Milk left = [tex]2[/tex] liters- [tex]\frac{1}{2}[/tex] liter= [tex]\frac{3}{2}[/tex] liters
[tex]\frac{3}{2}[/tex] liters used in half:
[tex]\frac{1}{2} \frac{3}{2}[/tex] = [tex]\frac{3}{4}[/tex] liters.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
Considering the given equation of the circle, the true statements are given as follows:
The radius of the circle is of 3 units.The center of the circle lies on the x-axis.The circle has the same radius as the circle with equation x² + y² = 9.What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The equation given is:
x2 + y² - 2x - 8 = 0.
Completing the squares, the equation is given as follows:
(x - 1)² + y² = 8 + 1
(x - 1)² + y² = 9.
Researching the problem on the internet, the true statements are:
The radius of the circle is of 3 units.The center of the circle lies on the x-axis([tex]y_0 = 0[/tex]).The circle has the same radius as the circle with equation x² + y² = 9.More can be learned about the equation of a circle at https://brainly.com/question/24307696
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find the value of x
A. √30
B. 16
C. 2√2
D. 20
Answer:
A. √30
=================
Use the intersecting chords theorem, according to which, the products of the lengths of the line segments on each chord are equal,
or
TW × WU = CW × WVSubstitute the lengths and solve for x:
x*2x = 6*102x² = 60x² = 30x = √30The matching answer choice is A.
20 points. The length of a rectangular room is 4.5 m and it’s width is 9.6 m. Find the area of the room
Answer:
43.2 m square is ur answer .
Answer:
43.2 m^2
Step-by-step explanation:
The area of a rectangle is the width times the length.
Area = (9.6 m)*(4.5 m)
Area = 43.2 m^2
Find a cubic polynomial whose zeros are 1/2,1 and -3.
Answer:
2x³+3x²-8x+3
Step-by-step explanation:
So we know x=½,x=1 and x=-3
Then (2x-1)(x-1)(x+3) are the factors
(2x-1)[(x²+3x-x-3)]
(2x-1)[(x²+2x-3)]
2x³+4x²-6x-x²-2x+3
2x³+3x²-8x+3
P l e a s e h e l p~!!!!!!~!!~~~!
Answer:
A. 100
Step-by-step explanation:
Angle 1 = 40
Angles 1 and 2 are equal. Add the angles 1 and 2 together.
40+40=80
The last step is to subtract 80 from 180.
180-80=100.
∠3=100
Hope this helps!
If not, I am sorry.
The price of an emergency light is $375 and it decreased by
2% each year. Find the exponential model representing
this situation.
The price of the light as a function of x is given by the exponential function:
[tex]p(x) = \$375*(0.98)^x[/tex]
Which exponential model represents this situation?
We know that the original price of the light is $375.
This value decreases a 2% each year, so each year we need to multiply the above price by (1 - 2%/100%) = (1 - 0.02) = 0.98
Then, if x represents the number of years, the price of the light as a function of x is given by the exponential function:
[tex]p(x) = \$375*(0.98)^x[/tex]
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D
Distance
ST
Speed
Time
A bus is moving at an average speed of 70 mph on the
motorway.
The journey takes 3 hours 30 minutes.
How far did the bus travel?
miles
The distance would be 231 miles.
What is speed?Speed can be calculated as the ratio of distance traveled to the time taken
Given information;
Time taken = 3 hours 30 minutes
Speed = 70 mph
We know that,
Distance = speed x time
Distance = 70 x 3.30
Distance = 231 miles
Thus, the distance would be 231 miles.
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How do the areas of the parallelograms compare? the area of parallelogram abcd is 4 square units greater than the area of parallelogram efgh. the area of parallelogram abcd is 2 square units greater than the area of parallelogram efgh. the area of parallelogram abcd is equal to the area of parallelogram efgh. the area of parallelogram abcd is 2 square units less than the area of parallelogram efgh.
option third "The area of parallelogram ABCD is equal to the area of parallelogram EFGH" is correct.
What is parallelogram?In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
The area of the parallelogram is:
A = b×h
Here b is the base length and h is the height
In ABCD parallelogram:
A = (3)×(3)
A = 9 square units
EFGH parallelogram:
a = (3)×(3)
A = 9 square units
The area of parallelogram ABCD is equal to the area of parallelogram EFGH.
Thus, option third "The area of parallelogram ABCD is equal to the area of parallelogram EFGH" is correct.
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look at the pic below and please help.
Answer:
1) Equation's:
y = 500 + 15x y = 350 + 18x2) Number of guest and the charge:
Cost is same for both at 50 meals. The cost is $1250.Part 1
Turn sentences into equation's (Let 'y' be total cost and x per meal) :
(i) charges $500 and $15 per meal
y = 500 + 15x(ii) charges $350 and $18 per meal
y = 350 + 18xPart 2
y = y
500 + 15x = 350 + 18x
18x - 15x = 500 - 350
3x = 150
x = 150/3
x = 50
Charge at guest's 50 meal:
y = 500 + 15(50)
y = $1250
Point : (50, 1250)
Write a polynomial function with the real
zeros -3, 0, and 3.
[tex]f(x)=x(x-3)(x+3)[/tex]
Create a list of steps, in order, that will solve the following equation. (x-5)^2=25(x−5) 2 =25left parenthesis, x, minus, 5, right parenthesis, squared, equals, 25 Solution steps:
The value of x in the equation (x - 5)² = 25 is 10.
How to solve an equation?(x - 5)² = 25
Take the square root of both sides
Therefore,
√(x - 5)² = √25
x - 5 = 5
add 5 to both sides
x - 5 + 5 = 5 + 5
x = 10
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A ratio is...
O where two numbers are written as a fraction in lowest terms.
O where two or more values are compared in lowest terms.
O when two numbers are written as a division problem.
O all of these.
Answer:
All of these definitions are correct.
helppp!!!
Lynn is putting tiles on her bathroom floor. Each tile measures 1 square foot each. The floor measures 4 1/2 ft by 3 3/4 ft. How many tiles will she need to cover the floor?
Considering the area of the rectangle, it is found that she will need 17 tiles to cover the floor.
What is the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of dimensions, that is:
A = lw
The dimensions in feet are given as follows:
l = 4 1/2 ft = 4.5 ft.w = 3 3/4 ft = 3.75 ft.Hence the area in square feet is given by:
A = 4.5 x 3.75 = 16.875 ft².
Each tile has 1 square foot, hence, rounding, she will need 17 tiles to cover the floor.
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In the diagram, the circle will be dilated by a scale factor of 3 about the origin. The points C, A, and B map to C', A', and B' after the dilation. What is the length of ? Use the distance formula to help you decide: . The graph shows a circle with three points, A is equal to (8, 15), B is equal to (12, 13), and C is equal to (8, 10). C is the center of the circle. A line is joining AC and BC A. 24 units B. 45 units C. 21 units D. 15 units E. 5 units Reset Next
The length of C'B' after dilation using a scale factor of 3 is: D. 15 units.
What is Dilation?Dilation is the reduction or enlargement of an image by a scale factor, whereby the original and new images are similar.
Applying the distance formula, we have:
BC = √[(8−12)² + (10−13)²]
BC = √(−4)² + (−3)²]
BC = √(16+9)
BC = √25
BC = 5 units
Applying the scale factor:
Length of C'B' = 3(5) = 15 units.
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help me with the fonction please im stuck U_U
Answer:
It is NOT a function
Step-by-step explanation:
No it is NOT a function.....each value of x can only have one y value....
this has two y values for x = 2 : y = 2 and 4 therefore not a function
Consider the line y=3x-3.
Find the equation of the line that is perpendicular to this line and passes through the point (4, 5)
Find the equation of the line that is parallel to this line and passes through the point (4, 5).
Answer:
Perpendicular: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]
Parallel: [tex]y=3x-7[/tex]
Step-by-step explanation:
So when two lines are perpendicular, that means the the slope is the reciprocal with the opposite sign so: [tex]\frac{a}{b} \text{ has a slope perpendicular to } -\frac{b}{a}[/tex]. In this case we have the equation in slope-intercept form, so it's easy to determine the slope, it's 3. So that means the perpendicular line will have a slope of: [tex]-\frac{1}{3}[/tex]. Since you have a slope of 3/1 which becomes 1/3 and also an opposite sign. This gives you the equation: [tex]y=-\frac{1}{3}x+b[/tex]. We can solve for b, by plugging in a coordinate it passes through. This is given in the problem, with it being (4, 5) = (x, y). So plugging these values in as (x, y) gives you the equation: [tex]5=-\frac{1}{3}(4)+b\implies\frac{15}{3}=-\frac{4}{3}+b\implies\frac{19}{3}=b[/tex]. This gives you the complete equation: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]
So when two lines are parallel, that means they have the slope, and a different y-intercept. This is because if they had the same y-intercept, then the two lines would be the same exact line. We already know the slope, it's 3. So we have the general equation: [tex]y=3x+b\text{ where b}\ne-3[/tex]. The restriction on b, was explained on the previous sentence, if b=-3, then we have the same equation, which is not parallel, they would be the same line, meaning they would intersect at infinite points, which is completely different than two lines that never intersect. So now we can plug in the given point (4, 5) to solve for b. Plugging these coordinates in gives you: [tex]5=3(4)+b\implies5=12+b\implies-7=b[/tex]. This gives you the complete equation: [tex]y=3x-7[/tex]
Write and simplify an expression to represent the area. Then determine the area when x = 3
Answer:
5*8 = 40
Step-by-step explanation:
2(3) -1 = 5
3 +5 = 8
area = 5*8 = 40
Answer:
formula-Area=l×b
Step-by-step explanation:
Length (l)=2x-1
Breadth(b)=x+5
We know that,
Area(A)=l×b
=(2x-1)×(x+1)
=(2×3-1)×(3+1)
=5×4
=20cm*2*