Step-by-step explanation:
The given equation:
[tex]28v^3+16v^2-21v-12[/tex]
To find, the factors of [tex]28v^3+16v^2-21v-12[/tex] = ?
∴ [tex]28v^3+16v^2-21v-12[/tex]
[tex]=(4\times 7)v^3+(4\times 4)v^2-(3\times 7)v-(3\times 4)[/tex]
= [tex]4v^2(7v+4)-3(7v+4)[/tex]
= [tex](7v+4)(4v^2-3)[/tex]
= [tex](7v+4)[(2v)^2-\sqrt{3}^2][/tex]
Using the algebraic identity,
[tex]a^{2}-b^{2}=(a+b)(a-b)[/tex]
= [tex](7v+4)(2v+\sqrt{3})(2v+\sqrt{3})[/tex]
∴ The factor of [tex]28v^3+16v^2-21v-12[/tex] = [tex](7v+4)(2v+\sqrt{3})(2v+\sqrt{3})[/tex] or [tex](7v+4)(4v^2-3)[/tex]
15. The volume of a rectangular pyramid
is 10,500 cubic centimeters. It has a
length of 15 centimeters and a width of
85 centimeters. What is its height?
Answer:
Its height is 24.71 centimeters.
Step-by-step explanation:
Given:
The volume of a rectangular pyramid is 10,500 cubic centimeters.
It has a length of 15 centimeters and a width of 85 centimeters.
Now, to find the height.
Let the height be [tex]h.[/tex]
Volume of rectangular pyramid = 10,500 cubic centimeters.
Length (l) = 15 centimeters.
Width (w) = 85 centimeters.
Now, to get the height by putting formula:
[tex]Volume=\frac{l\times w\times h}{3}[/tex]
[tex]10500=\frac{15\times 85\times h}{3}[/tex]
[tex]10500=\frac{1275h}{3}[/tex]
Multiplying both sides by 3 we get:
[tex]31500=1275h[/tex]
Dividing both sides by 1275 we get:
[tex]24.71 =h\\\\h=24.71\ centimeters.[/tex]
Therefore, its height is 24.71 centimeters.
Stacey buys 6 pounds of chicken for $39 days how much will she pay for 11 more pounds of chicken?
Answer:
$110,5
Step-by-step explanation:
If 6 pounds costs $39, then 17 pounds (11+6) will cost $110,5
The solution can be found using famous math rule called "Rule of three".
In this case we have an unknown quantity [tex]\left \{ {{6=39}\atop {17=?}} \right.[/tex] where ? can be found multiplying $39 x 17 (new quantity) and dividing by the first quantity, [tex]? = \frac{39x17}{6}[/tex]
help pls pls pls
4 x 10
plssss plz plz plzz so hard
Answer:
40
Step-by-step explanation:
4 x 10= 40
PlZ add brainliest.
Answer:
40 is the answer to this question
What is the sign of 3x y3xy3, x, y when x>0x>0x, is greater than, 0 and y<0y<0y, is less than, 0?
Answer: It's negative! Dude, could I please have brainiest!?!
Final answer:
The sign of the expression 3x * y^3 is negative when x is positive and y is negative because a negative number raised to an odd power remains negative.
Explanation:
The question asks about the sign of a mathematical expression where the variables have specified signs based on their values. Given that x is positive (x > 0) and y is negative (y < 0), the expression 3x * y^3 encompasses multiplying a positive number by a negative number raised to an odd power. Multiplying a positive number by a negative number results in a negative number, and raising a negative number to an odd power preserves the negative sign. Therefore, the product 3x * y^3 will be negative because y^3 maintains its negative sign while 3x is positive.
Decide whether the rates are equivalent.
$16 for 4 pounds
$1 for 4 ounces
Answer:
No i dont think so
Step-by-step explanation:
Because 16:4 isn't an equivilent ratio to 1:4
plz ans a,b,c and d.
Answer:
a.i) 1 piece = 20 days
1 day= 1/20 piece =0.05 of a piece
a.ii) 0.05*5 =0.25
a.iii) 0.05*10 =0.5 done.
so if the total is 1, 0.5 is half, so he has 0.5 work left
b.i)1 piece=12 days
4 days = 1/3 = 0.3333333333 of his work
b.ii)1/4=0.25
so 12*0.25 = 3 days
c.i)1/3 = 6 days
1 (work)= 6*3 = 18 days
c.ii) 1/18 = 1 day = 0.05555555555
c.iii) 0.5 since 9/18 = 1/2 = 0.5
d.i) 1 hour= 60 mins
whole tank = 60 mins
20 mins = 60/20 = 1/3 of a tank
if capacity = 1500L
1500 = 60 mins
1500/3 = 20 mins
=500 Liters
Please help. I’ll mark you as brainliest if correct
Answer:
527, no mistakes this time
Step-by-step explanation:
what toolkit function are discontinuous
The functions that are discontinuous are:
Step Function
Absolute Value Function
Dirichlet Function
Piecewise-defined Functions
We have,
Several functions are known to be discontinuous at certain points or intervals.
Here are a few common examples of functions that exhibit discontinuity:
- Step Function:
A step function is a piecewise-defined function that "jumps" from one constant value to another at specific points.
- Absolute Value Function:
The absolute value function, denoted as |x|, is discontinuous at x = 0, where it changes its slope abruptly.
- Dirichlet Function:
The Dirichlet function is defined as follows: D(x) = {1 for rational x, 0 for irrational x}.
This function is discontinuous at all rational numbers and irrational numbers.
- Piecewise-defined Functions:
Functions that are defined using different formulas or rules for different intervals can exhibit discontinuities at the points where the rules change.
Thus,
The functions that are discontinuous are:
Step Function
Absolute Value Function
Dirichlet Function
Piecewise-defined Functions
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Find the volume of the pet carrier shown at the right
Answer:
Volume of the pet carrier [tex]=2702.5[/tex] cubic inches
Step-by-step explanation:
The Pet carrier in the image is in the shape of a cuboid
The volume of a cuboid can be found by the formula
volume of cuboid= [tex]Length*Breadth*Height[/tex]
Given:
Length = 20 inches, Breadth=[tex]11\frac{3}{4} =\frac{(11*4)+3}{4}=\frac{47}{4}[/tex] inches,
Height=[tex]11\frac{1}{2}=\frac{23}{2}[/tex] inches
Volume of the pet carrier:
[tex]=20*\frac{47}{4}* \frac{23}{2}\\\\= 5*47*\frac{23}{2} \\\\=5*47*11.5\\[/tex]
[tex]=2702.5[/tex] cubic inches
Volume of the pet carrier [tex]=2702.5[/tex] cubic inches
Jacob earns $8 per hour babysitting. The table below shows the amount of money he earns for hours worked. Which of the following is the independent variable
Answer:
What table below
Step-by-step explanation:
The independent variable is what you change
The dependent variable is what you measure
So the money he earns per hour seems like a constant, and it won't change. Therefore the dependent variable would be the amount of money he earns.
The number of hours he works can be changed, so the independent variable would the number of hours he works/babysits
Use the table at the right.
a. What is the approximate volume of the small truck?
Volume of the small truck = 554.54 cubic ft
Solution:
Given data:
Length of the small truck = [tex]11\frac{1}{13}[/tex] ft
Width of the small truck = [tex]7\frac{5}{12}[/tex] ft
Height of the small truck = [tex]6\frac{3}{4}[/tex] ft
Volume of the small truck = length × width × height
[tex]$=11\frac{1}{13}\times7\frac{5}{12}\times 6\frac{3}{4}[/tex]
Let us change the mixed fraction into improper fraction.
[tex]$=\frac{11\times 13 + 1}{13}\times\frac{7 \times 12 + 5}{12}\times \frac{6 \times 4 + 3}{4}[/tex]
[tex]$=\frac{144}{13}\times\frac{89}{12}\times \frac{27}{4}[/tex]
[tex]$=\frac{7209}{13}[/tex]
= 554. 54 cubic ft
Volume of the small truck = 554.54 cubic ft
You start at (6, 7). You move up 2 units. Where do you end?
NW u ovo
0
1
2
3
4
5
6
7
8
9 10
If you start at (6, 7) and you move up 2 units, you will end at point (6, 9) as shown in the image attached below.
In Mathematics and Euclidean Geometry, the translation a geometric figure upward means adding a digit to the value on the positive y-axis of the pre-image;
g(x) = f(x) + k
In this exercise, we would apply a translation of 2 units up to the point (6, 7), in order to determine the coordinates of its image as follows;
(x, y) → (x, y + 2)
A (6, 7) → (6, 7 + 2) = (6, 9).
So, if you start at (6, 7) and you move up 2 units, you will end at point (6, 9) as shown in the image attached below.
Norachai traveled to the recycling plant and back. The trip back took 5 hours. He averaged 9mph faster on the trip there than on the return trip. What was norachai average speed on the outbound trip?
Answer:
[tex]His\ average\ speed\ to\ trip\ there\ =45\ mph\\\\His\ average\ speed\ in\ return\ trip=45-9=36\ mph\\\\His\ average\ speed\ during\ whole\ trip=40\ mph[/tex]
Step-by-step explanation:
[tex]Let\ distance\ from\ one\ side=d[/tex]
Trip:
[tex]Let\ speed\ when\ he\ was\ going=x\ mph\\\\Time\ taken=4\ hours\\\\distance=d\\\\distance=speed\times time\\\\d=x\times 4\\\\d=4x\ ...................................eq(1)[/tex]
Return Trip:
[tex]Speed=x-9\ \ \ \ \ (as\ it\ is\ 9\ mph\ slower)\\\\Time\ taken=5\ hours\\\\Distance=d\\\\Distance=speed\times time\\\\Distance=5\times (x-9)\\\\d=5x-45\ ........................................eq(2)[/tex]
[tex]from\ eq(1)\ and\ eq(2)\\\\5x-45=4x\\\\5x-4x=45\\\\x=45\ mph\\\\from\ eq(1)\\\\d=4\times 45=180\ miles[/tex]
[tex]Average\ speed\ during\ whole\ trip=\frac{total\ distance}{total\ time}=\frac{2\times 180}{5+4}=\frac{360}{9}=40\ mph[/tex]
[tex]His\ average\ speed\ to\ trip\ there\ =45\ mph\\\\His\ average\ speed\ in\ return\ trip=45-9=36\ mph\\\\His\ average\ speed\ during\ whole\ trip=40\ mph[/tex]
Each side of a suspension bridge has a cable that is secured at either end of the span by two supporting towers. The cable is attached to the tops of the two towers. In the section between the two towers, the cable forms a parabolic curve. At its lowest point, the cable is 40 feet above the surface of the bridge. The towers are 450 feet apart, and the vertical distance from the surface of the bridge to the top of each tower is 500 feet. Use the left tower as the y-axis. Hint y=a(x-h)2+ k
Answer: y= 40
Step-by-step explanation:
1. The lowest point of the cable is 40 feet above the surface of the bridge.
2. The towers are 450 feet apart.
3. The vertical distance from the surface of the bridge to the top of each tower is 500 feet.
We’ll use the general form of a parabolic equation:
[ y = a(x - h)^2 + k ]
Where:
(y) represents the vertical position (height) of the cable.
(x) represents the horizontal position along the bridge.
(h) represents the horizontal position of the vertex (lowest point) of the parabola.
(k) represents the vertical position of the vertex.
Given that the lowest point of the cable is at (y = 40) feet, we have:
[ k = 40 ]
Now let’s find the vertex position ((h)). Since the towers are 450 feet apart, the midpoint between the towers corresponds to the vertex. Therefore:
[ h = \frac{{450}}{2} = 225 ]
Now we can express the equation as:
[ y = a(x - h)^2 + k ]
Next, let’s find the value of (a). At the top of each tower, the cable is at a height of 500 feet. So, when (x = 0) (left tower) or (x = 450) (right tower), we have:
At the left tower (left end of the span): [ y = 500 = a(0 - 225)^2 + 40 ] Solving for (a): [ a = \frac{{500 - 40}}{{225^2}} = \frac{{460}}{{50625}} ]
At the right tower (right end of the span): [ y = 500 = a(450 - 225)^2 + 40 ] Solving for (a): [ a = \frac{{500 - 40}}{{225^2}} = \frac{{460}}{{50625}} ]
Since the value of (a) is the same at both ends, we can use either tower to find the equation of the parabolic curve:
[ y = \frac{{460}}{{50625}}(x - 225)^2 + 40 ]
v(t)=659,500(0.91)
find the initial value of the house
Answer: 659,500 is the initial value
Step-by-step explanation:
A sphere intersects a plane that is 6 units away from its center; the intersection is a circle of radius 8. What is the radius of the sphere?
Answer:
10
Step-by-step explanation:
Consider the triangle consisting of the segment from the center of the sphere to the center of the circle, a radius of the circle, and the radius of the sphere to the other end of the radius of the circle. The given leg dimensions of that right triangle are 6 and 8, so the Pythagorean theorem tells you the hypotenuse (radius of the sphere) is ...
√(6²+8²) = √(36+64) = √100 = 10
The radius of the sphere is 10 units.
_____
You may recognize this as a 3-4-5 right triangle scaled by a factor of 2.
In this case, the radius of the sphere is 10 units.
The distance from the center of the sphere to the plane is given as 6 units.
According to the Pythagorean theorem, we have:
[tex]\[ r^2 = d^2 + r'^2 \][/tex]
[tex]\[ r^2 = 6^2 + 8^2 \][/tex]
[tex]\[ r^2 = 100 \][/tex]
Taking the square root
[tex]\[ r = \sqrt{100} \][/tex]
r = 10
The radius of the sphere is 10 units.
Choose the solution(s) of the following system of equations:
x² + y² = 6
x² - y=6
Answer:
see attachment
Step-by-step explanation:
Answer:
2nd 4th 6th 8th or B D F H
Step-by-step explanation:
I did it on edge
50 apple's cost $25. How much would 75 apples cost?
Answer:
$37.5
Step-by-step explanation:
(25/50) x 75 = 37.5
$25/50 .... each apple cost $0.5
0.5 x 75 = 37.5
The correct answer is 75 apples would cost $37.50.
To solve this problem, we first need to determine the cost per apple when 50 apples cost $25. We can calculate this by dividing the total cost by the number of apples:
Cost per apple = Total cost / Number of apples
Cost per apple = $25 / 50 apples
Cost per apple = $0.50 per apple
Now that we know the cost per apple is $0.50, we can calculate the cost for 75 apples by multiplying the cost per apple by the number of apples:
Cost for 75 apples = Cost per apple * Number of apples
Cost for 75 apples = $0.50 * 75
Cost for 75 apples = $37.50
Therefore, 75 apples would cost $37.50.
Which one of these graphs matches the function below?
Answer:
The lower right graph.
Step-by-step explanation:
If the mean of the following distribution is 91 and sum of frequencies is 150 find x and y
Answer:
Step-by-step explanation:
Mean = ∑x/ N
91 = ∑x / 150
∑x = 150 * 91 = 13650
x= 6825 and y = 6825
1) The table shows the height in centimeters, that a weight bouncing from a spring would achieve if there were no friction, for a given number of seconds.
From it's resting position, how long does it take the weight to bounce one direction, then the other, and then back to it's resting position?
Answer:
The graph shows that a consistent time to go from resting position to point A, then back to resting, then to point B, then back to resting, and so on is 0.75 seconds.
To bounce from resting to point A then point B and back to resting is 3 seconds.
The question pertains to the period of oscillation in a simple harmonic motion scenario involving a weight and a spring. The period is calculated using the formula T = 2π√(m/k). The student asks how long it takes for the weight to complete one full oscillation cycle, which can be calculated using mass and spring constant.
Explanation:The students asked about the period of oscillation for a weight attached to a spring. In physics, especially concerning simple harmonic motion (SHM), the period is the time it takes for one full cycle of motion: moving in one direction, reversing, and returning to the starting point. To find the period of a mass-spring system, we use the formula T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant. This formula is derived from the motion equations that describe SHM.
For example, if you have a mass of 0.750 kg attached to a spring with a spring constant of 150 N/m, you would calculate the period using the mass (m) and the spring constant (k) from Hooke's Law. Similarly, when a spring exerts an upward force of 2.00 mg at the lowest point, this is due to the spring force being equal to the gravitational force at that point (mg) and also providing the restoring force needed for SHM (another mg).
Understanding SHM and its principles such as spring constant, and force of gravity are critical in solving these types of physics problems. These concepts explain how an attached weight on a spring moves in the absence of friction and other forces, such as air resistance.
Explain how you found the volume of water in the fish tank if it was only 1/2 full with water.
You have a fish tank with the following dimensions:
Height: 3 feet
Width: 1.5 feet
Length: 2 feet
We found the volume of water by finding the volume of fish tank from given dimensions and dividing it by 2.
Step-by-step explanation:
Given,
Height of tank = 3 feet
Width of tank = 1.5 feet
Length of tank = 2 feet
We will first find the volume of tank;
Volume = Length * Width * Height
Volume = 3 * 1.5 * 2
Volume = 9 feet cubed
As we know the water is 1/2; therefore we will divide the volume of tank by 2.
Volume of water = [tex]\frac{9}{2} = 4.5\ ft^3[/tex]
We know that;
1 cubic feet = 7.481 gallons
4.5 cubic feet = 7.481*4.5 = 33.66 gallons
Keywords: volume, division
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h(x) = x2 + 1 k(x) = x – 2
(h + k)(2) =
(h – k)(3) =
Evaluate 3h(2) + 2k(3) =
Answer:
(h + k)(2) = h(2) + k(2) = [tex]2^{2}[/tex] + 1 + 2 - 2 = 4 + 1 = 5
(h - k)(3) = h(3) - k(3) = [tex]3^{2}[/tex] + 1 - (3 - 2) = 10 - 1 = 9
Step-by-step explanation:
h(x) = [tex]x^2 + 1[/tex]
k(x) = x - 2
(h + k)(2) = h(2) + k(2) = [tex]2^{2}[/tex] + 1 + 2 - 2 = 4 + 1 = 5
(h - k)(3) = h(3) - k(3) = [tex]3^{2}[/tex] + 1 -(3 - 2) = 10 - 1 = 9
Can someone help me with these and can give a explanation on how to do these thank you!
Answer:
x = 2 and x = 2
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
[tex]log_{x}[/tex] 8 = 3 ⇒ 8 = x³
Note 8 = 2³ = x³ ⇒ x = 2
Given
[tex]log_{5}[/tex] 25 = x ⇒ 25 = [tex]5^{x}[/tex]
25 = 5² = [tex]5^{x}[/tex] ⇒ x = 2
Can someone answer this question please answer it correctly and show work please
Answer:
40) D
41) -56.33
Step-by-step explanation:
40)
Equation #1) 1 centimeter = 2.5 meters on the drawing
Equation #2) Length of the cafeteria on the drawing = 12.25 cm
Actual length:
Multiply both sides of equation #1 by 12.25 to get the actual length of the cafeteria
1(12.25) = 2.5(12.25)
12.25 cm = 30.625 meters
D
41)
[tex]\frac{0.5\left(8\ +\ 3.2\right)}{-0.1}+\ \frac{3}{\left(-2.7\ -\ 6.3\right)}[/tex]
Start with multiplication inside the parenthesis
[tex]\frac{4\ +\ 1.6}{-0.1}+\ \frac{3}{\left(-2.7\ -\ 6.3\right)}[/tex]
Add/Subtract
[tex]\frac{5.6}{-0.1}+\ \frac{3}{-9}[/tex]
Simplify
[tex]-56+\left(-0.33\right)[/tex]
[tex]-56 - 0.33[/tex]
[tex]-56.33[/tex]Hope this helps ツ
0.599 as a percentage of 0.319
Answer: " 187. 774 % " .
_____________________________________
Step-by-step explanation:
_____________________________________
So, let's rewrite this statement as a question:
0.599 is "what percent" of: 0.319 ? ;
Set up an equation:
[tex]0.599 = (\frac{n}{100}) *0.319[/tex] ;
↔ [tex](\frac{n}{100}) * 0.319 = 0.599[/tex] ;
_____________________________________
Divide each side of the equation by: "(0.319)" ; as follows:
_____________________________________
[tex][ (\frac{n}{100}) * 0.319 ] / 0.319 = (0.599)/ (0.319)[/tex] ;
to get:
_____________________________________
[tex]\frac{n}{100} = 1.87774294671[/tex] ;
_____________________________________
Now, multiply each side of the equation by "100" ;
to isolate "n" on one side of the equation; & to solve for "n" ;
_____________________________________
[tex]100 * (\frac{n}{100)} = (1.87774294671) * 100[/tex] ;
_____________________________________
On the left-hand side of the equation; the "100's: cancel out to "1" ;
→ since: "[tex](\frac{100}{100} =1)[/tex]" ;
and we have:
→ n = 187.774294671 ;
round to three decimal places:
→ n = 187. 774 .
The answer is: 187.774 % .
_____________________________________
Dracula ate 70 fries in 14 minutes. Find his fry-eating rate in fries per
minute.
Answer
5 fries per minute
Step-by-step explanation:
To work out this question, you would need to divide 70 by 14. This would give you the rate of fries he eats per minute as 14 divided by 14 = 1.
Dracula's fry-eating rate is 5 fries per minute.
The subject of this question is Dracula's fry-eating rate. In mathematics, we often deal with rates, which are a measure of how something changes over time.
In this case, we are being asked to find how many fries Dracula eats per minute. This can be found by dividing the total number of fries he ate by the total time he took.
Given, Dracula ate 70 fries in 14 minutes.
To find the fry-eating rate, we need to divide the total fries by the total minutes. That is, fry-eating rate = total fries / total time.
So, the fry-eating rate = 70 fries / 14 minutes = 5 fries per minute. Therefore, Dracula's fry-eating rate is 5 fries per minute.
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The ratio of people to books in a classroom is 10:4 what is the unit ratio of people to per book ?
Answer:
[tex]2.5\ \frac{people}{book}[/tex]
Step-by-step explanation:
The correct question is
The ratio of people to books in a classroom is 10:4 what is the unit rate of people per book?
Let
x ----> the number of people
y ----> the number of books
we know that
To find out the unit rate of people per book , divide the total number of people by the total number of books
we have
[tex]x=10\ people\\y=4\ books[/tex]
so
[tex]\frac{x}{y}=\frac{10}{4}=2.5\ \frac{people}{book}[/tex]
Solve S= 2HW + 2HL + 2WL for L.
To solve for L, you need to isolate/get the variable "L" by itself in the equation:
S = 2HW + 2HL + 2WL Subtract 2HW on both sides
S - 2HW = 2HW - 2HW + 2HL + 2WL
S - 2HW = 2HL + 2WL Take out the "L" in 2HL and 2WL
S - 2HW = L(2H + 2W) Now divide (2H + 2W) to get "L" by itself
[tex]\frac{S-2HW}{2H +2W} =\frac{L(2H+2W)}{2H+2W}[/tex]
[tex]\frac{S-2HW}{2H+2W} =L[/tex]
I think you can stop here, but if you need or want to simplify:
[tex]\frac{S}{2H+2W} -\frac{HW}{H+W} =L[/tex] which looks longer so I don't know if you need to do this
To solve for 'L' in the given equation, we subtract 2HW and 2WL from each side, then divide each side by 2H. The solution is L = (S - 2HW - 2WL) / 2H.
Explanation:We are given the equation S= 2HW + 2HL + 2WL and we are asked to solve for L. To do this, we will need to isolate L on one side of the equation. Here are the steps:
Subtract 2HW and 2WL from both sides of the equation. We are left with: S - 2HW - 2WL = 2HL Divide each side of the equation by 2H to solve for L. Our final solution is: L = (S - 2HW - 2WL) / 2H
So the value of L in terms of the other variables in the equation is (S - 2HW - 2WL) / 2H.
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Find the value for the following determinant.
5
-5
-11