Answer:
slope = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
given f(4) = 6 and f(- 2) = 8 , then 2 points on the line are
(4, 6 ) and (- 2, 8 )
calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 6 ) and (x₂, y₂ ) = (- 2, 8 )
m = [tex]\frac{8-6}{-2-4}[/tex] = [tex]\frac{2}{-6}[/tex] = - [tex]\frac{1}{3}[/tex]
If f(x) and f¹(x) are inverse functions of each other and f(x) = 2x+ 5, what is ƒ˜¹ (8) ?
If f(x) and f¹(x) are inverse functions of each other then value of ƒ˜¹ (8) = 3/2.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
We have,
f(x) = 2x + 5
Let us consider f(x) as y
So, y= 2x + 5
Now replace x to y and y to x
x= 2y+ 5
Solving for y we get
2y = x - 5
y = (x - 5)/2
[tex]f^{-1[/tex](x) = (x - 5)/2
Now, [tex]f^{-1[/tex](8) = (8 - 5)/2
[tex]f^{-1[/tex](x) = 3/2
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A grain silo can be modeled as a right cylinder topped with a hemisphere. Find the volume of the silo if it has a height of 41 m and a diameter of 12 m. Round your answer to the nearest tenth if necessary. (Note: diagram is not drawn to scale.)
The volume of the silo = volume of the hemisphere + volume of the cylinder ≈ 4,410.8 m³.
What is the Volume of a Hemisphere and Cylinder?Volume of a hemisphere = 2/3πr³
Volume of cylinder = πr²h
The volume of the silo = 2/3πr³ + πr²h
r = 12/2 = 6 mh = 41 - 6 = 35 mPlug in the values
The volume of the silo = 2/3π(6³) + π(6²)(35) ≈ 4,410.8 m³
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Answer:
989.6 m^3
Step-by-step explanation:
refer to images hope this helps x
Find the value of x. (4x-101) (2x+3)
A. 31
B.107
C.52
D.46
(4x−101)(2x+3)
Apply the distributive property by multiplying each term of 4x−101 by each term of 2x+3.
8x²+12x−202x−303
Combine 12x and −202x.
8x²−190x−303
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the value of x in [tex]\mathrm{(4x-101)(2x+3)}[/tex].
◈ Note:
⇛ We can't find the value of x, but we can simplify this expression.
This is how we'll simplify it:
◆ Multiply 4x times 2x and 3 first:
[tex]\large\pmb{4x\times2x=8x^2}[/tex]
[tex]\large\pmb{4x\times3=12x}[/tex]
Add the terms:
[tex]\large\pmb{8x^2+12x}[/tex]
Now, do the same thing with -101 - multiply that times 2x and 3:
[tex]\large\pmb{-101\times2x=-202x}[/tex]
[tex]\large\pmb{-101\times3=-303}[/tex]
Add the terms:
[tex]\large\pmb{-202x-303}[/tex]
Put all 4 of the terms together:
[tex]\large\pmb{8x^2+12x-202x-303}[/tex]
Combine like terms (12x and -202x):
[tex]\large\pmb{8x^2-190x-303}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
In the fall of 2003, a magazine article reported that about 87% of adults drink milk. A local dairy farmers' association is planning a new marketing campaign for the tri-county area they represent. They randomly polled 800 people in the area. In this sample, 654 people said that they drink milk. If 87% is the correct percentage of adults who drink milk, what is the probability that the association would observe 654 or less people who drink milk in the sample
Using the normal distribution, it is found that the probability that the association would observe 654 or less people who drink milk in the sample is of 0%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].For the binomial distribution, the parameters are given as follows:
n = 800, p = 0.87.
Hence, the mean and the standard deviation of the approximation are given by:
[tex]\mu = np = 800 \times 0.87 = 696[/tex][tex]\sigma = \sqrt{np(1-p)} = \sqrt{80 \times 0.87 \times 0.13} = 9.5121[/tex].The probability that the association would observe 654 or less people who drink milk in the sample, using continuity correction, is [tex]P(X \leq 654.5)[/tex], which is the p-value of Z when X = 654.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{654.5 - 696}{9.5121}[/tex]
Z = -4.36
Z = -4.36 has a p-value of 0.
0% probability that the association would observe 654 or less people who drink milk in the sample.
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8) can u answer this question pls
Answer: 346.19cm²
Step-by-step explanation:
π= 3.14
Divide 21 (the diameter) by 2 to get the radius( it 's half of the diameter). so the radius is 10.5
Area= πr²
= 3.14x10.5x10.5
= 346.185
So next round up the value you got to the nearest tenth, so when u round up to the nearest tenth you get 346.19
Cecilia made an envelope to mail a letter. She colored the regular trapezoid flap on the bottom of the envelope blue,
shown.
5 in.
2 in
9 in.
What is the area of the blue flap of the envelope?
O 14 in 2
O 18 in 2 45in2. 90in2
Answer:
14 inch ^2
Step-by-step explanation:
Area of a trapezium= (a+b) 2 times h
so side a= 5 inches
side b= 9 inches
then times by 2 times the height (2)
you can rearrange the formula to this- a + b/ 2 times height.
5+9/2 times 2= 14
I hope this helps, have a lovely day.
What is the distance between the points located at (5, 1) and (10, 11) ?
[tex]\large{\underline{\underline{\pmb{\frak {\color {red}{Question:}}}}}}[/tex]
[tex] \sf \red{What \: is \: the \: distance \: between \: the \: points \: located \: at \: (5, 1) \: and \: (10, 11) ?}[/tex]
[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}[/tex]
Let, the points be A(5,1) and B(10,11) on the number line.
Here,
[tex]x_{1}[/tex] = 5. [tex]x_{2}[/tex] = 10
[tex]y_{1}[/tex] = 1. [tex]y_{2}[/tex] = 11
We,know that to find distance between two points, the formula is:
[tex] \sqrt{( {x}_{2} - {x}_{1})^{2} + ( {y}_{2} - {y}_{1} )^{2} } \\ \\ = \sqrt{(10 - 5) ^{2} + (11 - 1)^{2} } \\ \\ = \sqrt{ ({5)}^{2} + ( {10})^{2} } \\ \\ = \sqrt{25 + 100} \\ \\ = \sqrt{125} \\ \\ = 11.18[/tex]
Therefore, the distance between the two points (A) and (B) is 11.18
[tex] \boxed{ \frak \red{Hope \: it \: helps \: you}}[/tex]
represent , the set of numbers between 10 to 50 when they are divided by 5 then the remainder is 2 by description method listing method and set builder method
The numbers between 10 and 50 when they are divided by 5 then the remainder is 2 is shown in the form of description method and in set-builder form is {12, 17, 22, 27, 32, 37, 42, 47}.
What is set?A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.
We have:
The set of numbers between 10 and 50 when they are divided by 5 then the remainder is 2
The numbers are:
12, 17, 22, 27, 32, 37, 42, 47
By description method:
1 2 3 4 5 6 7 8
12 17 22 27 32 37 42 47
By set builder form:
s = {12, 17, 22, 27, 32, 37, 42, 47}
Thus, the numbers between 10 and 50 when they are divided by 5 then the remainder is 2 is shown in the form of description method and in set-builder form is {12, 17, 22, 27, 32, 37, 42, 47}.
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During a sale, a store offered a 10% discount on a camera that originally sold
for $430. After the sale, the discounted price of the camera was marked up by
10%. To the nearest whole number, what percent of the original price was the
price after markup?
Answer:
$4,30 that is the answer I'd my working on paper
Answer:
425.70
Step-by-step explanation:
Marc is trying to determine how many blue marbles are in a bag of `100` marbles. he can only fit `10` marbles in his hand at a time. he takes `11` samples of `10` marbles, returning the marbles to the bag each time. based on these results, how many of the `100` marbles do you expect are blue
Based on the result from the box plot, the number of blue marbles is equal to the median of the data set and this is equal to 40.
What is a boxplot?A boxplot is a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread. Also, the five-number summary include the following:
MinimumFirst quartileMedianThird quartileMaximumFor this exercise, we would create a box plot (see attachment) for the marbles in a bag of 100 marbles. By critically observing the box plot, we can logically deduce that the number of blue marbles is equal to the median of the data set and this is given by:
Median = 4 × 10
Median = 40.
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there are 100 students in the 5th grade. of those 43 of them are in the school band.what percent of 5th grade are in the band
Answer:
43 percent
Step-by-step explanation:
When you divide 43 by 100 you get .43 which is 43%
Answer:
43%
Step-by-step explanation:
Because if you divide 43 by 100 you get, .43 and so there you have it, 43% Hope you understand <3
Find an angle with a positive measure and an angle with a negative measure that are coterminal with each angle. 175
Answer:
185 anle with the postive measure and a negative measure
(0.6.01) The probability that an event will occur is 2/3. Which of these best describes the likelihood of the event occurring?
A. Likely
B. Certain
C. Unlikely
D. Impossible
the right answer of this question is
C. unlikely
(TR)546 - (TR)540
pls help!
The computation of (TR)546 - (TR)540 will give a value of 3261.
How to compute the value?
TR(546) = 546(546 + 1)/2 = 273 * 547
TR (540) = 540(540 + 1)/2 = 270 * 541
273 * 547 = (270 + 3)(541 + 6)
= 270*541 + 270*6 + 541 *3 + 18
= 270*541 + 1620 + 1623 + 18
= 270*541 + 3261
TR(546) -TR (540) = 270*541 + 3261 - 270 * 541
= 3261
TR(546) -TR (540) = 3261
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Julian has partially filled the prism below with 16 unit cubes.
A rectangular prism with a length of 4, height of 3, and width of 3.
How many more unit cubes will he need to completely fill the prism?
11
20
25
36
He needs 20 more unit cubes to completely fill the prism
How to determine the number of unit cubes?The dimension of the prism is given as;
4 by 3 by 3
The volume is calculated as:
Volume = 4 * 3 * 3
Volume = 36
He has already filled 16 units.
So, the units remaining is
Remaining = 36 - 16
Evaluate
Remaining = 20
Hence, he needs 20 more unit cubes to completely fill the prism
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given that y= 6 cm and θ= 32 °, work out x rounded to 1 dp.
(not drawn to scale)
X=7.1cm
The solution is in the attached file
math sos help please.
[tex](\frac{4m^5n^2}{m^2n})^3 = (\frac{4m^5n^2}{m^2n})(\frac{4m^5n^2}{m^2n})(\frac{4m^5n^2}{m^2n})[/tex]
---Essentially, we're taking the given expression and multiplying it by itself three times. So, we can solve the problem by multiplying fractions or simply distributing the 3 to each term. Remember, we will be multiplying the existing exponents by the 3, not adding 3.
[4^3 m^15 n^6] / [m^6 n^3]
---Now, we need to simplify the expression. Since there are 15 m's on the top, and 6 m's on the bottom, we can take 15 - 6 to now have only 9 m's on the top.
64 m^9 n^3
Answer: A
Hope this helps!
and final part sorry brainly
Answer:
15 2/3
Step-by-step explanation:
4 2/3 = 14/3
11 = 33/3
14/3 + 33/3 = 47/3
47/3 = 15 2/3
Carson is organizing textbooks on his bookshelf. he has a spanish textbook, a math textbook, a history textbook, and a writing textbook. how many different ways can he line the textbooks up on his bookshelf?
Answer:
16
Step-by-step explanation:
Answer:24
Step-by-step explanation:
PLEASE HELP ME WHOEVER HELPS I WILL MARK BRAINLEST :)
Remember the shortcut way for graphing quadratic equations
A quadratic function has graph as parabolaHence on both sides of vertex the parabola is symmetric and axis of symmetry is vertex x values .y on both sides for -x and +x is same#1
y=2(x-3)²-1Vertex
(h,k)=(3,-1)As a is positive parabola facing upwards
Find y for same x distance from vertex
I took 3-1=2 and 3+1=4
f(2)=2(2-3)²-1=2(-1)²-1=2-1=1f(4)=2(4-3)²-1=1Now plot vertex and these two points (2,1) and (4,1) on graph then draw a parabola by freehand
#2
y=(x-2)(x+4)y=x²+4x-2x-8y=x²+2x-8Convert to vertex form
y=x²+2x+1-9y=(x+1)²-9Vertex at (-1,-9)
Same take two equidistant x values
Let's take -1-1=-2 and -1+1 =0
f(-2)=(-2+1)²-9=1-9=-8f(0)=(1)²-9=-8Put (-1,-9),(-2,-8),(0,-8) on graph and draw a freehand parabola
#3.
Yes it can be verified by finding the coordinate theoretically on putting them on function then can be verified through putting them on graph whether they matches or not
Which of the following statements about the triangle shown above is true? . The triangle is scalene. The triangle is an equilateral triangle in which the length of all three sides is 10. . The triangle is an isosceles triangle in which two sides are of length square root 61. The triangle is an isosceles triangle in which two sides are of length 5.
Answer:
B isosceles with sides sqrt (61)
Step-by-step explanation:
Find the two sides' lengths via pythagorean theorem to be
sqrt ( 5^2 + 6^2) = sqrt (61)
Statement
4x = 7x - 21
Reason
?
Answer:
solution;
21=7x-4x
21=3x
21x/3x
Then finalay aneswer is 7x
Select the best method of finding an accurate solution to a system of linear equations.
Answer:
Substitution. Substitution is a good method to use when one of the variables is isolated in the equation or the coefficient of one of the variables is 1 or -1. When you isolate that variable to substitute into the other equation, you will not be introducing additional fractions into the problem.
What is the value of m in the equation m-n=16, when n = 8?
20
32
44
48
Answer: 24
Step-by-step explanation:
m - 8 = 16
m = 24
Answer:
24
Step-by-step explanation:
To find the value of "m", you need to plug n = 8 into the equation.
m - n = 16 <---- Original equation
m - 8 = 16 <----- Plug 8 in for "n"
+ 8 + 8 <---- Isolate "m" by adding 8 to both sides
m = 24 <----- Final answer
3. There are 1800 students in a school, out of which 950 are girls and the rest are
boys. If 40% of the girls and 30% of the boys come to school by public transport,
find the number of students who come to school through other modes of
transportation?
The number of students who come to school through other modes o transportation is 1,165.
How do we solve a percentage problem?The number of students who come to school through other modes o transportation can be calculated as follows:
A = Number of girls that uses other modes o transportation = (100% - 40%) * 950 = 570
B = Number of boys that uses other modes o transportation = (100% - 30%) * (1800 - 950) = 595
C = Total number of studens that uses other modes o transportation = A + B = 570 + 595 = 1,165
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Please Help I Don't Understand!
Answer:
The triangles are not similar.
Step-by-step explanation:
First, what's all the information we know?
We know we're trying to prove that triangle BAC is similar to triangle DEC.
We know AC=12 and EC =12 (proving 1 side equal).
We know angle BCA and angle DCE or equal.
However, we do not know any information further than this, and there is no postulate/theorem for AS. Therefore, the triangles are not similar.
Find the axis of symmetry of the graph of the function. (5 points) f(x) = 3x2 + 12x + 9
Considering the definition of axis of symmetry, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.
Axis of symmetryAn axis of symmetry is an imaginary reference line that, when dividing any shape into two parts, its opposite points are equidistant from each other, that is, they are symmetrical.
In other words, the axis of symmetry is a vertical line that divides the parabola into two congruent halves.
The axis of symmetry is the line perpendicular to the "x" axis that contains the vertex of the function, that is, it always passes through the vertex of the parabola. So the x-coordinate of the vertex is the equation of the axis of symmetry.
That is, in a quadratic function that has the form:
f(x)= ax² + bx + c
the axis of symmetry is a vertical line and it is defined as [tex]x=\frac{-b}{2a}[/tex].
Axis of symmetry of f(x) = 3x² + 12x + 9In this case, you know:
a= 3b=12c=9Replacing in the definition of axis of symmetry:
[tex]x=\frac{-12}{2x3}[/tex]
Solving:
[tex]x=\frac{-12}{6}[/tex]
x= -2
Finally, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.
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y=-2/5x
a. direct
b. inverse
c. neither
Answer:
a. direct
Step-by-step explanation:
direct variation is y = kx and y = -2/5x is written in direct variation.
Write the expression in repeated multiplication form. Then write the expression as a power.
(6^4)^2
The expression in repeated multiplication form is
The expression as a power is
Answer:
6^8
Step-by-step explanation:
(6^4)(6^4)
6^8
or something like that
There are two pieces of wires, each of length 66 cm. One wire is bent into a square and the other wire is bent into a circle. Find (a) the area of the square, (b) the area of the circle.
Answer:
Area of Circle = 346.5 cm².
Area of square = 272.25 cm ² .
Step-by-step explanation:
So , 2πR = 66
2 × 22 / 7 × R = 66
R comes out is 21/2 cm .
Area of Circle = 22/7 × 21/2 × 21/2 = 33×21/2
= 693 / 2 = 346.5 cm².
If bent into the shape of a square ;
4 a = 66
a = 33/2 . ( Side of a square )
Area of square = a ² = 33×33/4 = 1089/4
= 272.25 cm ² .