Applying the commutative law to our question, we have; 14 + ab = ab + 14
How to use the commutative law?The commutative law in algebra states that the change in position of two numbers while adding or multiplying them does not change the result. For example;
ab + cd = cd + ab
similarly, fg * jk = jk * fg
Applying the above commutative law to our question, we have;
14 + ab = ab + 14
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The sixth grade band students are selling magazines to raise money for new instruments. As a reward for selling, the students earn points to spend on prizes. Each student gets 25 points to start with, and then they earn an additional 5 points for each magazine they sell. If m represents the number of magazines a student sells, write an expression to represent the total number of points the student has.
WRITER
Answer:
okay he's saying that each student gets 25 points to start with and then they get five more like 25 / 25 * 5 or like 25 + 5 or 25 - 5 like represent those numbers and like get the number or something like that
Two poles of different heights are used for a climbing event and need to be secured to the ground using wires. The shorter pole is 6.0 m tall and the wire is secured 8.0 m from the base of the pole. If wire of the taller pole is 16.0 m long. Determine the height of the taller pole .
Using similar triangles, it is found that the height of the taller pole is of 9.6m.
What are similar triangles?Similar triangles are triangles that have the same angles, and whose side lengths are proportional.
The hypotenuse of the smaller triangle is given as follows:
h² = 6² + 8² -> h = 10.
Hence the proportional relationship is:
[tex]\frac{10}{16} = \frac{6}{h}[/tex]
Applying cross multiplication:
10h = 96
h = 9.6m.
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Explain how you can find the constant of proportionality from a graph representing a proportional relationship when it shows a point with an x-value of 1 and if it doesn’t show an x-value of 1.
For a proportional relationship, the constant is found dividing all values of y by each respective value of x.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
The constant can be represented as follows:
[tex]k = \frac{y}{x}[/tex]
Hence the constant is found dividing all values of y by each respective value of x.
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g(x) = (x ^ 3 - 9x)/(x ^ 2 - 6x + 9)
The expression is simplified to x
How to simplify the expressiong(x) = (x ^ 3 - 9x)/(x ^ 2 - 6x + 9)
First, we simplify the numerator
= [tex]\frac{x (x^2 - 3^2)}{x^2 - 6x + 9}[/tex]
Now, let's solve the quadratic equation in the denominator
= [tex]\frac{x(x^2 - 3^2)}{x^2 - 3x - 3x + 9}[/tex]
= [tex]\frac{x(x^2 - 3^2)}{x(x-3) - 3(x - 3)}[/tex]
= [tex]\frac{x(x - 3) (x -3)}{(x -3) ( x-3)}[/tex]
Divide the like factors
= x
The answer is x
Thus, the expression is simplified to x
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Which equation can be simplified to find the inverse of y = 2x²?
0-2x²
O
y-1x²
O -y = 2x²
O x = 2y²
O
Answer:
D.) x = 2y²
Step-by-step explanation:
You can find the inverse of an equation by swapping the positions of the "x" and "y" variables. Then, you would need to rearrange the equation to re-isolate the "y" variable.
As such, D.) is the correct option because it is identical to the original equation except that the variables are swapped.
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]y = 2x^2\hspace{5em}\stackrel{\textit{quick switcheroo}}{\boxed{x = 2y^2}}\implies \cfrac{x}{2}=y^2\implies \sqrt{\cfrac{x}{2}}=\stackrel{f^{-1}(x)}{y}[/tex]
Elias and niko are polishing the silver at the heritage museum. elias could polish all the silver himself in 40 minutes. that task would take niko 50 minutes to complete alone. which table is filled in correctly and could be used to determine how long it would take if elias and niko polished the silver together? a table showing rate in part per minute, time in minutes, and part of silver polished. the first row shows elias, and has startfraction 1 over 40 endfraction, t, and startfraction 1 over 40 endfraction t. the second row shows niko and has, startfraction 1 over 50 endfraction, t, and startfraction 1 over 50 endfraction t. a table showing rate in part per minute, time in minutes, and part of silver polished. the first row shows elias, and has r, startfraction 1 over 40 endfraction, and startfraction 1 over 40 endfraction r. the second row shows niko and has, r, startfraction 1 over 50 endfraction, and startfraction 1 over 50 endfraction r. a table showing rate in part per minute, time in minutes, and part of silver polished. the first row shows elias, and has 40, t, and 40 t. the second row shows niko and has, 50, t, and 50 t . a table showing rate in part per minute, time in minutes, and part of silver polished. the first row shows elias, and has r, 40, and 40 r. the second row shows niko and has, r 50, and 50 r .
The first table is filled correctly and can be used to determine how long it takes for Elias and Niko to polish the silver.
How to interpret Mathematical Tables?The first table is filled correctly and can be used to determine how long it takes for Elias and Niko to polish the silver.
The rate is the unit rate.
Now, since Elias polishes all of the silver himself in 40 minutes, his rate is 1/40.
Similarly, Niko’s rate would be 1/50.
Their time is the same because they are working at the same time, and as such we can write that as t. Then, the part of the silver polished would be the rate * time, or:
Thus;
Part polished by Elias: ¹/₄₀ * t
Part Polished by Niko: ¹/₅₀ * t
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The function f is defined by f(x)=2-x. If 2f(p)=8, what is f(2p)?
If function 'f' is defined by f(x)=2-x and 2f(p)=8 then the value of f(2p) is 6.
Given, f(x) = 2-x
Solve this problem by making a series of substitutions.
First, find the value of p.
Then use the definition of the function f to find the value of f(2p).
We are given
f(x) = 2 - x
Multiply both sides by 2, and simplify.
2f(x) = 2(-x +2)
2f(x) = -2x + 4
Let x = p.
2f(p) = -2(p) + 4
We are given that 2f(p) = 8.
Substitute 20 for 2f(p).
8 = -2p + 4
2p = -4
p = -2
Now we know that p = -2, so we can find f(2p).
f(x) = -x + 2
f(2p) = -2p + 2
Substitute -2 for p.
f(2p) = -2(-2) + 2
f(2p) = 4 +2
f(2p) = 6
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simplify: 2y(y2-4y+1)-2(4y²+5y-2) +5y-8
please tell me fast with full solution
Answer:
look the answer is in the picture and don't forget to like and brainlest
From the top of a 16 m tall building, the angle of depression to a car on the road is 35°. To the nearest metre, how far is the car from the base of the building?
The distance of the car to the base of the building is 23 metres.
How to find the distance of the car from the building using angle of depression?The situation will form a right angle triangle.
Therefore, the distance of the car to the base of the building is the adjacent side of the right angle triangle formed.
Therefore,
tan 35 = opposite / adjacent
tan 35 = 16 / x
x tan 35 = 16
x = 16 / tan 35
Therefore,
x = 16 / 0.70020753821
x = 22.8506141103
x = 23 meters
Therefore, the distance of the car to the base of the building is 23 metres.
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A roller coaster’s height is given by the equation h = –.025t2 + 4t + 50, where t represents the time in seconds. How long will it take riders to pass over the hill and reach ground level? Hint: Set h = 0.
Answer Options:
A.11.65
B.50.00
C.171.65
D.210.00
The time it took the rider to reach the ground level is 171.651seconds
Quadratic functionsQuadratic functions are functions that has a leading degree of 2.
Given the equation that represents roller coaster’s height as shown
h = –0.025t^2 + 4t + 50
The coaster will reach the ground when h = 0
Substitute
0 = –0.025t^2 + 4t + 50
Factorize
On factorizing, the time it took the rider to reach the ground level is 171.651seconds
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Answer:
171.65 seconds
Step-by-step explanation:
did the test and got it right
Find the value of z.
A. 100
B. 82
OC. 118
OD. 75
o'
105°
120°
68⁰
Answer:
B. 82
Step-by-step explanation:
I hope it helps you :)
The value of z in the given figure of circle with two lines dividing it into segments is 100.
We are given that the measures of angles ∠1 and ∠2 are 105° and 120°, respectively.
Step 1: Since the interior angles of a triangle add up to 180°, we know that the measure of ∠3 is 180° - 105° - 120° = 55°.
Step 2: Since ∠3 and ∠z are supplementary angles, we know that m∠3 + m∠z = 180°.
Step 3: Substituting the measures of ∠3 from step 1 into step 2, we get 55° + m∠z = 180°.
Step 4: Subtracting 55° from both sides of the equation in step 3, we get m∠z = 180° - 55° = 125°.
Step 5: Since m∠z = 125°, then z = 125°.
Therefore, the value of z is 100.
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There are 15 players on a volleyball team. Only 6 players can be on the court for a game. How many different groups of players of 6 players can the coach make, if the position does not matter?
There are 5005 different groups
How to determine the number of groups?The given parameters are:
Players, n = 15
Selected, r = 6
The number of groups is then calculated as:
[tex]Group = ^{n}C_r[/tex]
This gives
[tex]Group = ^{15}C_6[/tex]
Apply the combination formula
[tex]Group = \frac{15!}{9!6!}[/tex]
Evaluate the expression
Group = 5005
Hence, there are 5005 different groups
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Warm-Up
Consider the graph of function f.
Determine which equation matches each described transformation of function f.
Drag the tiles to the correct boxes to complete the pairs.
If this is the one you are talking about then:
horizontal translation of 3 units is: y= f(x-3)
vertical stretch by a scale factor of 3 is: y= 3f(x)
reflection over the x-axis is: y= -f(x)
vertical translation of 3 units is: y= f(x)+3
Step-by-step explanation:
Adding a value to f(x) translates the graph of f vertically. So, the equation that shows a vertical translation of 3 units is y = f(x) + 3.
Adding a value to the input, x, of f(x) translates the graph of f horizontally. So, the equation that shows a horizontal translation of 3 units is y = f(x − 3).
Multiplying f(x) by a negative value reflects the graph of f over the x-axis. So, the equation that shows a reflection over the x-axis is y = -f(x).
Multiplying f(x) by a constant, k, vertically stretches the graph of f by a scale factor of k. So, the equation that shows a vertical stretch by a scale factor of 3 is y = 3f(x).
Find the zeros of: [tex]f(x)=-\frac{1}{1500} (x^3+10x^2-275x-1500)[/tex], and the use them to find all of the linear factors of the polynomial function
The function f(x) = -(1/1500)(x³ + 10x² - 275x - 1500) the zeros are at (-20, 0), (-15, 0) and (15, 0). Hence the factors of the function are x + 20, x + 15 and x - 15.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the graph of the function f(x) = -(1/1500)(x³ + 10x² - 275x - 1500) the zeros are at (-20, 0), (-15, 0) and (15, 0). Hence the factors of the function are x + 20, x + 15 and x - 15.
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F(x)= x(x+3)(x+1)(x-4) has zeros at x=-3
Answer: C) Sometimes positive; sometimes negative
============================================================
Explanation:
Pick a value between x = -1 and x = 0. Let's say we go for x = -0.5
Plug this into f(x)
f(x) = x(x+3)(x+1)(x-4)
f(-0.5) = -0.5(-0.5+3)(-0.5+1)(-0.5-4)
f(-0.5) = -0.5(2.5)(0.5)(-4.5)
f(-0.5) = 2.8125
We get a positive value.
This shows that f(x) is positive on the region of -1 < x < 0
----------------
Now pick a value between x = 0 and x = 4. I'll use x = 1
f(x) = x(x+3)(x+1)(x-4)
f(1) = 1(1+3)(1+1)(1-4)
f(1) = 1(4)(2)(-3)
f(1) = -24
Therefore, f(x) is negative on the interval 0 < x < 4
----------------
In short, f(x) is both positive and negative on the interval -1 < x < 4
It's positive when -1 < x < 0
And it's negative when 0 < x < 4
Answer:
sometimes positive sometimes negative
Step-by-step explanation:
I did it on Khan Academy
[tex]\sqrt15-x +\sqrt3-x=6[/tex]
As currently written, solving for [tex]x[/tex], we have
[tex]\sqrt{15} - x + \sqrt3 - x = 6[/tex]
[tex]2x = \sqrt{15} + \sqrt3 - 6[/tex]
[tex]x = \dfrac{\sqrt{15} +\sqrt3 - 6}2[/tex]
I suspect you meant to write
[tex]\sqrt{15 - x} + \sqrt{3 - x} = 6[/tex]
Move one of the roots to the other side, then take squares on both sides.
[tex]\sqrt{15 - x} = 6 - \sqrt{3 - x}[/tex]
[tex]\left(\sqrt{15 - x}\right)^2 = \left(6 - \sqrt{3 - x}\right)^2[/tex]
[tex]15 - x = 36 - 12 \sqrt{3 - x} + (3 - x)[/tex]
[tex]12 \sqrt{3 - x} = 24[/tex]
Take squares again
[tex]\left(12\sqrt{3-x}\right)^2 = 24^2[/tex]
[tex]144 (3 - x) = 576[/tex]
[tex]432 - 144x = 576[/tex]
[tex]144x = -144[/tex]
[tex]\boxed{x = -1}[/tex]
Please help me!! due today. Find the volume of the right triangular prism !:)
Answer: 115.5 cubic m
Step-by-step explanation:
[tex]V=\frac{1}{2}(7)(11)(3)=115.5[/tex]
The area of the base of the cone is 8 pi mm^2. what is the volume of the cone in terms of pi?
The volume of cone whose area of base is 8π[tex]mm^{2}[/tex] is 32π/3 [tex]mm^{3}[/tex].
Given area of base of the cone 8π[tex]mm^{2}[/tex].
We are required to find the volume of the cone.
We know that base of a cone used to be in circle so the area of base of cone is equal to π[tex]r^{2}[/tex].
Area=8π (given)
π[tex]r^{2}[/tex]=8π
[tex]r^{2}[/tex]=8
r=[tex]\sqrt{8}[/tex]
r=2[tex]\sqrt{2}[/tex]
Volume of cone=1/3*π[tex]r^{2} h[/tex]
=1/3*π[tex](2\sqrt{2} )^{2}[/tex]*4
=1/3*8*4π
=32π/3
(We are not required to put value of π so our answer will be 32π/3.)
Hence the volume of cone whose area of base is 8π is 32π/3.
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Question is incomplete as it should also include height of cone be 4 mm.
To calculate accurate ____________________ (vital/hospital) statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.
To calculate accurate vital statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.
What are vital statistics?The term "vital statistics" refers to the collection of data on live births, deaths, migration, fetal deaths, marriages, and divorces. Civil registration, an administrative system used by governments to record vital events that occur in their populations, is the most prevalent method of gathering information on these events. Efforts to increase the quality of vital statistics will thus be inextricably linked to the growth of countries' civil registration systems. Since the nineteenth century, civil registration has followed the practice of churches keeping such records. To compute accurate vital statistics rates for the full United States, multiply the quotient by a suitable factor, such as 1,000 or 100,000 to represent the greater population.As it is given in the description itself, to compute accurate vital statistics rates for the full United States, multiply the quotient by a suitable factor, such as 1,000 or 100,000 to represent the greater population.
Therefore, to calculate accurate vital statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.
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Plss help...
Write down the rule in the form y=
Answer:
yxthgggggyhfffghgggggvggvvggvv
can someone please help me
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{3\pi }{4}[/tex] is an angle in the second quadrant where sin > 0 and cos < 0
cos([tex]\frac{3\pi }{4}[/tex] )
= cos (π - [tex]\frac{3\pi }{4}[/tex] )
= - cos ([tex]\frac{\pi }{4}[/tex] )
= - [tex]\frac{\sqrt{2} }{2}[/tex]
and similarly
sin ([tex]\frac{3\pi }{4}[/tex] )
= sin ([tex]\frac{\pi }{4}[/tex] )
= [tex]\frac{\sqrt{2} }{2}[/tex]
A wall is in the shape of a trapezoid. The lengths of the parallel bases are 8 feet and 20 feet. The height of the room is 8 feet. How much paint is needed to cover the wall? 80 ft2 112 ft2 160 ft2 224 ft2
The amount of paint needed to cover the wall is 112 square feet
How to determine the amount of paint?The given parameters are:
Parallel bases = 8 feet and 20 feet
Height = 8 feet
The area is calculated as:
Area = 0.5 * (Sum of parallel bases) * Height
So, we have;
Area = 0.5 * (8 + 20) * 8
Evaluate
Area = 112
Hence, the amount of paint needed to cover the wall is 112 square feet
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Solve to find the value for x in the linear equation: 3(−4x 5) = 12. 1. use the distributive property: 2. use the subtraction property of equality: 3. division property of equality: 3(−4x) 3(5) = 12 −12x 15 = 12 −12x 15 − 15 = 12 − 15 −12x = −3 x =
Answer:
1/4
Step-by-step explanation:
I think that you forgot the addition or the subtraction sign between -4x and 5. I will assume that it was an addition sign
3(-4x+5) = 12 Multiply everything in the parentheses by 3
-12x + 15 = 12 Subtract 15 from both sides
-12x = -3 Divide both sides by -12
x = -3/-12 = 3/12 =1/4
Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below. In this function, Po is the air pressure at the surface of the Earth, and h is the height above the surface of the Earth, measured in meters. Which expression best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth
The expression that best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth is 3,000ρg.
Air pressure at an altitude above the surface of the EarthThe air pressure at an altitude of 3,000 meters above the surface of the Earth is calculated as follows;
Po = ρgh
where;
ρ is density of airg is acceleration due to gravityh is the altitudeSubstitute the value of altitude into the equation;
Po = 3,000ρg
Thus, the expression that best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth is 3,000ρg.
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if the ordered pairs (x, -1) and (5, y) belong to the set {(a, b): b = 2a-3}, find x and y.
The following triangle is an isosceles triangle. What is the length of the missing side?
Considering that we have an isosceles triangle, the length of the missing side is of 11 inches.
What is an isosceles triangle?An isosceles triangle is a triangle that has two congruent sides.
Researching this problem on the internet, the triangle has two sides of 4 in and 11 in, and one missing side. The missing side is opposite to the side of 4 in, with the same scale, hence the length of the missing side is of 11 inches.
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The acts in a talent competition consist of 4 instrumentalists, 10 singers, and 6 dancers. If the acts are ordered randomly, what is the probability that a dancer performs first
Answer:
[tex] \frac{6}{20} = \frac{3}{10?} [/tex]
Step-by-step explanation:
total amount of acts = 4+10+6 = 20
amount of dancers = 6
probability of picking a dancer = number of dancers / total number of talents = 6/20 = 3/10
The probability that a dancer performs first is 3/10.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
The acts in a talent competition consist of 4 instrumentalists, 10 singers, and 6 dancers.
Total participants = 4+ 10 +6 = 20
So, the probability that a dancer performs first
= 6 /20
= 3/10
Hence, the probability that a dancer performs first is 3/10.
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Describe the sample variance using words rather than a formula. do the same with the population variance
A. The sample variance is the sum of the deviations from the mean divided by the number of measurements minus one. The population variance is the average of the distances of the measurements on all units in the population from the mean.B. The sample variance is the sum of the squared deviations from the mean divided by the number of measurements. The population variance is the sum of the squared deviations from the mean divided by the number of measurements minus one.C. The sample variance is the sum of the deviations from the mean divided by the number of measurements. The population variance is the sum of the deviations from the mean divided by the number of measurements minus one.D. The sample variance is the sum of the squared deviations from the mean divided by the number of measurements minus one. The population variance is the average of the squared distances of the measurements on all units in the population from the mean.
The option D is the correct option.
According to the statement
we have to define the sample variance in the words.
So,
The sample variance is the sum of the squared deviations from the mean divided by the number of measurements minus one.
and in the case of the population variance it becomes
The population variance is the average of the squared distances of the measurements on all units in the population from the mean.
This is the method by which we define the sample variance and population variance.
So, The option D is the correct option.
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Which is a solution for the following system of inequalities?
(7x+2y >3
(x-2y <2
The solution for the system of linear inequalities 7x+2y > 3 and x-2y < 2 are x = 5/8 and y = -11/16
What are linear inequalities?Linear inequalities are inequalities that have constant average rates of change, slope or gradient
How to determine the solution to the system of inequalities?A system of linear inequalities is a collection of at least two linear inequalities.
In this case, the system of linear inequalities is given as
7x+2y > 3
x-2y < 2
Rewrite the inequalities as equations
7x+2y = 3
x-2y = 2
Make x the subject in the second equation, by adding 2y to both sides of the equation
x - 2y +2y = 2 + 2y
This gives
x = 2 + 2y
Substitute x = 2 + 2y in 7x+2y = 3
7(2 + 2y) +2y = 3
Expand the brackets
14 + 14y + 2y = 3
Evaluate the like terms
16y = -11
Divide both sides by 16
y = -11/16
Substitute y = -11/16 in x = 2 + 2y
x = 2 - 2 * 11/16
Evaluate the product
x = 2 - 11/8
Evaluate the difference
x = 5/8
Hence, the solution for the system of linear inequalities 7x+2y > 3 and x-2y < 2 are x = 5/8 and y = -11/16
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On a coordinate plane, shapes show the size of swings, a slide, a merry-go-round, and a sandbox. The sandbox has points (0, 6), (8, 12), (12, 6), and (8, 0).
A sandbox is shaped like a kite. Each unit on the coordinate plane represents one foot. A planner would like to replace the wooden border around the sandbox. How many feet of wood does he need? Round up to the nearest whole number.
feet
The number of feet of wood that is needed is given as 35 feet of wood.
How to solve for the woodWe have to do this through the use of pythagoras theorem
a² = b² + c²
8² + 6²
a = √100
= 10
4² + 6²
= 52
a = √52
Then we would have
10 + 10 + √52 + √52
= 34.42
This is approximately 35 feet
The feet of wood that is needed is given as 35 feet
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Answer:
The number of feet of wood that is needed is given as 35 feet of wood
Step-by-step explanation:
I just did it on E2020 and got it right