The formula for the volume of cylinder with base area B and height H is V = B × H.
What is the volume of the cylinder?A cylinder is a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Area of a circle which is the base of a cylinder = πr²
Given that;
Base area = BHeight = HPlug the given values into the above formula.
V = π × r² × h
V = πr² × h
V = Base area × Height
V = B × H
Therefore, formula for the volume is V = B × H.
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Which is a factor of the polynomial f x 6x 4 21x 3 4x 2 24x 35?
One of the factor of the given polynomial 6x^4 - 21x^3 - 4x^2 + 24x - 35 is (2x-7).
According to Rational Root Theorem,
Leading coefficient = 6
Trailing constant = 35
Factors of leading coefficient = 1, 2, 3, 6
Factors of trailing constant = 1, 5, 7, 35
Check for the rational roots
Let P = 7, Q = 2, then
P/Q = 3.5
F(P/Q) = 0
Apply Factor theorem which means the given polynomial must be divisible by P/Q, that is (2x-7)
Divide the polynomial into two groups
Group 1 6x^4 - 21x^3
Take 3x^3 common, we get
3x^3(2x - 7)
Group 2 - 4x^2 + 24x - 35
When we divide it by (2x - 7) we get (-2x + 5)
⇒ - 4x^2 + 24x - 35 = (-2x + 5)(2x - 7)
⇒ 6x^4 - 21x^3 - 4x^2 + 24x - 35 = (2x - 7)(3x^3 - 2x + 5)
Hence the correct option is A.
-- The given question is incomplete, the complete question is
"Which is a factor of the polynomial f(x) = 6x^4 - 21x^3 - 4x^2 + 24x - 35? A) 2x - 7 B) 2x + 7 C) 3x - 7 D) 3x + 7" --
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How do you graph the function y =- 5x 3?
The required graph of the given function y = -5x + 3 which has been attached below.
What is a graph?A graph can be described as a visual representation or a diagram that represents data or values.
To graph the function y = -5x + 3, you can start by making a table of values.
Here's an example:
x y
-2 -11
-1 -6
0 3
1 -2
2 -7
To plot these points, start by graphing the point (0,3). This is the y-intercept, where the line crosses the y-axis.
Then, use the slope of the line (-5) to find the next point. For example, if you go one unit to the right on the x-axis (from 0 to 1), the y-value decreases by 5 (from 3 to -2).
Continue graphing points in this way until you have plotted enough points to see the shape of the line. You should see that the line has a negative slope, meaning it goes down from left to right.
The required graph of the given function y = -5x + 3 has been plotted.
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The graph of the given function is a straight line.
What is straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point and has no curve.
Equation of straight line ( slope-intercept form) is, y= mx+ c
Where, m= slope of the line & c= y-intercept.
Here, given function is, y=-5x+3 , which is an equation of straight line.
So, here, m= -5 & c=3
That is the line will passes through the point (0,3)
Now, if we put, y=0 then, x= 3/5=0.6
i.e., the line will also passes through the point (0.6,0)
So, we get, the required graph of the function ,
Hence, the graph of the function is a straight line.
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What is the area of a 10x10 square?
Answer: The answer is 100 :)
Step-by-step explanation:
you multiply L x W and that would be 10 x 10 and if you do the math right you should get an answer of 100
An archer performs 100 joules of work pulling back the string of a bow. What will be the distance traveled by a 0. 5 kg arrow when it is fired from the bow to the nearest tenth of a meter?.
The distance traveled by the arrow cannot be determined from the given information. The distance traveled by the arrow depends on the speed at which it is fired, which is determined by the amount of energy released when the bowstring is released.
Where are the asymptotes in a function?
The asymptotes in a given function is a line that the graph of a function approaches as either x or y go to positive or negative infinity.
What is an asymptote in a function?An asymptote in a function is defined as the a line that the graph of a function approaches as either x or y go to positive or negative infinity.
There are various types of asymptote which include the following:
vertical,horizontal and obliqueTo determine the asymptote of a function in a graph is a descending curve that approaches but does not reach the horizontal axis is said to be asymptotic to that axis, which is the asymptote of the curve.
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The diagrams show the position of a tap when off and fully on. When fully on, water flows out of the tap at 15 litres per minute. The rate at which water flows out is in direct proportion to the angle of turn. The tap is turned 123° 123 The water flows into a tank with a capacity of 90.2 litres. How long, in minutes, will it take to fill the tank?
Answer:
8.8 mins
Step-by-step explanation:
to find how long in mins it would take to fill the tank
at 180 degrees the speed of water is 15 liters/min at 123 degrees
so [tex]\frac{15}{180} *123[/tex] = 10.25 liters/min
the capacity of the tank is 90.2 liters
[tex]\frac{90.2}{10.25} \\[/tex] = 8.8 mins
Which among the options is one of the factors of x2 x6 − 16?
The sum of two or more numbers that results in a third number is called a factor.
The factor of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex] exists 2x + 1.
What is meant by factors?The definition of a factor is a number that divides another number by itself with no remainder. In other words, if multiplying two whole numbers results in a product, the numbers we are multiplying are factors of the product since the product is divisible by them.
What can split a number exactly are factors. So there is no residual after division. Factors are the sums of two or more numbers that produce a third number. Consequently, a factor is a number that divides another.
The use of more variable factors—those whose values do fluctuate with output—occurs as production rises and falls. Workforce, energy, and directly used raw materials are examples of typical variable components.
Let the given equation be [tex]$& x^2+\frac{x}{6}-\frac{1}{6} \\[/tex]
[tex]$& =\frac{6 x^2+x-1}{6} \\[/tex]
simplifying the above equation, we get
[tex]$& =\frac{1}{6}\left(6 x^2+x-1\right)[/tex]
We will factorize the polynomial by splitting its middle term.
[tex]$& \frac{1}{6}\left(6 x^2+x-1\right) \\[/tex]
[tex]$& =\frac{1}{6}\left(6 x^2+3 x-2 x-1\right) \\[/tex]
simplifying the above equation, we get
[tex]$& =\frac{1}{6}(3 x(2 x+1)-1(2 x+1)) \\[/tex]
[tex]$& =\frac{1}{6}(3 x-1)(2 x+1)[/tex]
[tex]$\frac{1}{6^{}}(3 x-1)$[/tex] and (2x + 1) are factors of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex]
Therefore, the correct answer is option B. 2x + 1
The complete question is:
Which among the following is a factor of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex] ?
A. 3x + 1
B. 2x + 1
C. [tex]$x-\frac{1}{5}$[/tex]
D. [tex]$x-\frac{1}{2}$[/tex]
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B, D, E and F are points on a circle, centre O. ABC is a tangent to the circle. ODC is a straight line. BOE is a diameter of the circle. Angle BCD = 48° Find the size of angle DFE.
Answer:
m∠DFE = 69°
Step-by-step explanation:
The tangent of a circle is always perpendicular to the radius.
Therefore, as ABC is the tangent to the circle, and OB is the radius of the circle:
⇒ m∠CBO = 90°
Interior angles of a triangle sum to 180°. Therefore:
⇒ m∠COB + m∠CBO + m∠BCO = 180°
⇒ m∠COB = 180° - m∠CBO - m∠BCO
⇒ m∠COB = 180° - 90° - 48°
⇒ m∠COB = 42°
Angles on a straight line sum to 180°. Therefore:
⇒ m∠DOE + m∠COB = 180°
⇒ m∠DOE = 180° - m∠COB
⇒ m∠DOE = 180° - 42°
⇒ m∠DOE = 138°
The angle at the center is twice the angle at the circumference.
Therefore:
⇒ m∠DOE = 2 × m∠DFE
⇒ m∠DFE = m∠DOE ÷ 2
⇒ m∠DFE = 138° ÷ 2
⇒ m∠DFE = 69°
Find the inverse of the following functions. Show all work
f(x) = 2√x+7
Answer:
the inverse of f(x)=2x−7 f ( x ) = 2 x - 7 .
Step-by-step explanation:
check if f−1(f(x))=x f - 1 ( f ( x ) ) = x and f(f−1(x))=x f ( f - 1 ( x ) )
Answer:
f(x) = 1/4 x² - 7
Step-by-step explanation:
x + 7 ≥ 0
x ≥ -7
y/2 = 2 /2 √(x+7)
y/2 = √(x+7)
y ≥ 0
(y/2)² = √(x+7)²
y²/4 = x +7
x = y²/4 - 7
f(x) = x²/4 - 7
-9(z-8)
write an equivalent expression
Answer:
-9z + 72
Step-by-step explanation:
1>-1=-3>-5 this property is called?
Answer:
linear inequation with 1 variable
Is this right?
I dont know whether the 3 or the y should be negative
Answer:
You are correct
This is my answer: -3x^a y^f+b z^g+c
Step-by-step explanation:
(3x^a y^b z^c) (-y^f z^g)
-3x^a y^f+b z^g+c
Because both have the same base is y, so we add both f and b
Same with z, both have the same base is z, so we have z^g+c
My answer is different in order, but both are correct!
How should I solve this problem? I need steps..
Refer to the photos taken.
Reasoning 54.8 x 7.29 = 399.492
A) Write down three more calculations that have the same answer.
B)Write down a division that has an answer of 54.8.
C)Write down a division that has an answer of 0.729.
D)Charlie says that 54.8 x 72.9 = 3989.44. Explain why Charlie must be wrong.
Answer:
B)Write down a division that has an answer of 54.8.
Now answer the following question: compute the area of an ellipse using green's theorem if the vertex is 2 and co-vertex is 3
Answer:
2+3=5
Step-by-step explanation:
2+
3=
5
answer 2+3=5
A shop charges `\$4. 95` for a large `9`-ounce frozen yogurt. What is the cost per ounce of the frozen yogurt?.
Answer:
$0.55/ounce
Step-by-step explanation:
The problem gives us the ratio of cost to ounce. We need to create a proportion (when you set two ratios equal to each other) to solve for one variable of the second ratio.
⭐ The first ratio is [tex]$4.95/9 ounces[/tex], which means that it costs $4.95 for 9 ounces.
⭐ The second ratio is [tex]x/1 ounce[/tex], where x is the cost for 1 ounce of frozen yogurt.
. . . . . . . "per ounce" means "for every 1 ounce"
⭐ We need to set these two ratios equal to each other and solve for x.
. . . . . . . In proportions, keep the units of the numerators and denominators the same. In this case, we'll keep the cost as the numerators and the ounces as the denominators.
. . . . . . . [tex]\frac{4.95}{9} = \frac{x}{1}[/tex]
. . . . . . . [tex]\frac{4.95}{9}(1) = x[/tex]
. . . . . . . ∴ x = $0.55/ounce
If f(x)=root 4x+9+2 which inequality can be used to find the domain of f(x )
Answer:
x>=-11/4
Step-by-step explanation:
f(x)=[tex]\sqrt{4x+9+2}[/tex]
The number which has a square root has to be greater than or equal to 0.
Hence, 4x+9+2>=0
Solve the inequality:
4x+9+2>=0
4x+11>=0
4x>=-11 ==> subtract 11 on both sides to isolate x
x>=-11/4 ==> divide both sides by 4
What graph is best for comparing change over time?
Bar graph is best for comparing change over time.
What is a Bar Graph ?Using rectangular bars with heights or lengths proportionate to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.
The visual display of data (often grouped) in the shape of vertical or horizontal rectangular bars, with the length of the bars corresponding to the measure of the data, is called a bar graph. Bar charts are another name for them. One tool used in statistics for processing data is the bar graph.
Bar graph components
Title: The graph's topic is covered in the title.Scale: The numbers that represent the units used in the bar graph's scale.Labels: The bottom and side of the bar graph each include a label indicating the type of data displayed.The data number is measured by the bar.To learn more about Bar Graph refer to :
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When comparing data between groups or monitoring changes over time, bar graphs are utilized.
What is a bar graph?A bar chart, often known as a bar graph, is a diagram that displays categorical data as rectangular bars with heights or lengths proportional to the values they stand for. You can plot the bars either vertically or horizontally. A vertical bar chart may also be referred to as a column chart.Comparing different discrete categories is displayed in a bar graph. The chart's other axis depicts a measured value, while the first axis displays the specific categories under comparison. Some bar graphs show clusters of more than one bars, displaying the values of multiple measured variables.Bar charts have clear categories within their domain and are often scaled to accommodate all the data. Bars on the chart may be placed in any order if there is no obvious hierarchy among the categories being compared. Pareto charts are bar graphs that display incidence in order from highest to lowest.Hence, When comparing data between groups or monitoring changes over time, bar graphs are utilized.
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A stock lost 8 3/8 points on Monday and then another 1 5/8 points on Tuesday. On Wednesday, it gained 13 points. What was the
net gain or loss of the stock for these three days?
a. a gain of 6 1/2 points
b. a loss of 1 points
c. a gain of 17 1/2 points
d. a gain of 23 points
Answer:
A gain of 3 points
Step-by-step explanation:
I'm not sure the options are correct. But normally, you add up the lost points on the both days. Then you compare it to the gained point on Wednesday.
What does changing the base of a log function do to the graph?
The larger the base of a log function, the closer the graph approaches the asymptote of x = 0.
We know that for a exponential function b^x = y, b is the base, y is the exponent to which the base b is raised and x is the result obtained.
We can write this in logarithmic form as:
log_b(x) = y
A logarithm base is the subscript of the logarithm that carries or raises the exponent.
For example in case of log_(3) 9 = 2, the base here is 3.
The change of base formula is:
log_b(x) = log_c(x) / log_c(b)
Also as we know the bigger the logarithm base, the smaller the curve on the graph. This means, the larger the base of a log function, the closer the graph approaches the asymptote of x = 0.
The log function may increase at a slower rate if the base increases.
Therefore, if the base of a log function is large, the graph approaches the asymptote of x = 0.
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What is the coefficient of x² in 3x² 5 )( 4 4x²?
The Coefficient of x² in the equation (3x²-5)(4+4x²) after simplification is -8 .
The Equation is given as : (3x²-5)(4+4x²)
To simplify , we first multiply the terms inside the bracket ;
So , given equation can be written as (3x²-5)×(4+4x²)
⇒ 12x² + 12x⁴ - 20 - 20x²
Adding the like terms of the equation ,
we get ;
⇒ (12 - 20)x² + 12x⁴ - 20
Simplifying further , we get
⇒ 12x⁴ - 8x² - 20 .
In the equation above we see that the numerical term with the x² is (-8) .
Therefore , the required coefficient is -8 .
The given question is incomplete , the complete question is
What is the coefficient of x² in the equation after simplification ; (3x²-5)(4+4x²) ?
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What are the 5 types of expression?
The 5 types of expression include:
monomial, polynomial, binomial, trinomial, multinomialWhat is an expression?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.
Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it. They include monomial, polynomial, binomial, trinomial, multinomial.
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Julie wanted to match Lisa's obstacle course record of 74.6 seconds. She has already spent forty and one-fourth seconds on wall climbing and 10.56 seconds on the ropes. How much time did she have left to match the record?
23.79 seconds
29.69 seconds
34.35 seconds
64.04 seconds
Julie has only 23.79 seconds left to match the record.
How to calculate time left?
We know that times deals with a continued sequence of existence and events that occurs in an apparently irreversible succession from the past
From the question, the given times are:
Time to match Lisa's record = 74.6 seconds
Time to clin the wall = 10.56 seconds
Time already spent on climbing wall = 4.025 seconds
Time left is calculated thus
74.600 seconds =(40.025+10.56) seconds
=74.600-50.585
=23.79 seconds
Therefore time left is 23.79 seconds
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Someone pls help me answer this question and give a thorough explanation!!!!!
Answer:
The boats cross paths at the points (1,8) and (4,11)
Step-by-step explanation:
First, we want to find the points of intersection between the two paths. We are given two equations, both in the form y=(equation). Since we want to find the intersection points, we set the two equations equal to each other (since both equal y we can plug one of the equations in for y into the other equation) to get
-x^2+6x+3=x+7
From here, we solve this like a normal quadratic equation, move all variables to one side first
-x^2+5x-4=0
This factors to -(x-1)(x-4)=0, giving us x=1 and x=4
Now we plug these back into one of the original equations (in this case the linear equation is much more simple) to give us the points (1,8) and (4,11)
What is the relationship between the area and the volume of two similar solids?
If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.
Volume of A /Volume of B = ( a / b )^3
a is the radius of solid A and b is the radius of solid B.
solid figures
In Geometry, the shape or the figure that has three dimensions (length, breadth and height), are known as solids or three-dimensional shapes. Example:-Cube, Cuboid and Sphere. The major types of solid shapes are: cubes, cuboids, prisms, pyramids, platonic solids, torus, cone, cylinder, and sphere.
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Help me please on this IXL
Answer:
61
Step-by-step explanation:
Using the exterior angle theorem,
[tex]c-15+c-18=c+28 \\ \\ 2c-33=c+28 \\ \\ c-33=28 \\ \\ c=61[/tex]
What is the median of the data 78 56 22 34?
Median of the data 78 , 56 , 22 , 34 is 45.
The middle value of the observations in a data set , arranged in the order of size is known as the median.
It is calculated differently for odd and even number of observations.
1. For odd no. of observations, it is the middle value .
2. For even number of observations, it is calculated as the average of the middle two values.
In this problem , first we arrange the observations in the order of size i.e. 22 , 34, 56, 78.
Since, here the no. of observations is even , 4. So, the median is the average of middle two values.
The middle two values are 34 and 56 , and their mean is 45.
So, the median of the given data is 45.
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Arya knows that if they need to add antifreeze to their car's radiator the mixture used must contain 50% antifreeze. How many gallons of a mixture containing 70% antifreeze must be added to a 3-gallon mixture containing 20% antifreeze to obtain the mixture they need?
Arya needs to add 2 gallon of 70% antifreeze must be added to a 3-gallon mixture containing 20% antifreeze to obtain the mixture they need.
What is antifreeze?
Antifreeze is an additive that lowers a liquid's freezing point that is made of water. For cold environments, freezing-point depression is accomplished using an antifreeze mixture. Additionally, common antifreezes raise the liquid's boiling point, enabling higher coolant temperatures.
Let x be the amount of 70% antifreeze to be added, in gallons.
In terms of percentage of antifreeze, we write:
20% of 3 gallons + 70% of x gallons = 50% of (3 + x) gallons
0.2(3) + 0.7x = 0.5(3 + x)
0.6 + 0.7x = 1.5 + 0.5x
0.7x - 0.5x = 1.5 - 0.6
0.2x = 0.4
x = 2
Hence, Arya needs to add 2 gallon of 70% antifreeze must be added to a 3-gallon mixture containing 20% antifreeze to obtain the mixture they need.
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please help me and explain it
Answer:
Divide both sides by -3.
Step-by-step explanation:
This question is asking you how to get from step 1: [tex]-3(p-7) = -15[/tex] to step 2: [tex]p - 7 = 5[/tex].
We can see that the expression inside of the parentheses (p - 7) didn't go away from step 1 to step 2, and the term that was being multiplied by (p-7) had gone away. The only way you can "get rid" of a multiplied term is by doing the inverse of multiplication, which is division. Thus, you have to divide both sides by -3 to get to step 2.
A dodecahedral die has 12 sides numbered from 1 to 12. The die is rolled once. Find the probability that the upward face shows a number that is a multiple of 3.
The probability that the upward face shows a number that is a multiple of 3 is p = 1/3 .
Given :
When a dodecahedral die is rolled the possible outcomes are:
s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }
The total numbers of possible outcomes is 12.
The numbers of outcomes whose upward face is multiple of 3 .
= { 3 , 6 , 9 , 12 }
so Number of favorable outcomes = 4
What is probability ?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
Probability = number of favorable outcomes / number of possible outcomes
= 4 / 12
= 1 / 3
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