The domain of the composite function is - x - 3 ≥ 0 , x ≤ -3 .
The correct answer is (B).
Given,
In the question:
Over the set of real numbers.
F(x) = -x-3, G(v) = √y
G(F(x)) = √√-3-x
To find the domain of the composite function.
Now, According to the question:
Based on the given conditions:
The domain of F(x) = -x -3 is all real numbers.
The domain of
G(v) = √y is y ≥ 0
{The relationship of the domain of a composite function and the original functions}
So, - x - 3 ≥ 0 , x ≤ -3
Hence, The domain of the composite function is - x - 3 ≥ 0 , x ≤ -3 .
The correct answer is (B).
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Ruben wants to shade some of the squares below. He wants to have a ratio of shaded to unshaded of 3 to 4. How many squares should be shade?
Answer: He should shade 3 and leave 4 unshaded.
Step-by-step explanation:
Find the slope between these two points. *
(17,8), (17, 24)
O 0
undefined
1
1/2
c
The slope between points (17,8) and (17,24) is (B) undefined.
We know that the slope of a line passing through two points (a,b) and (c,d) is given by,
m = (d-b)/(c-a)
So here given points are (17,8) and (17,24)
Then, a=17, b=8, c=17, d=24
Now the slope between these two points is given by,
m = (24-8)/(17-17) = 16/0
So the slope value does not exist or infinity.
Hence the slope between the points (17,8) and (17,24) is Infinity or undefined.
Thus, the correct option is (B).
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Solve this problem using estimation and rounding each amount to the nearest ten
dollars.
Over a two-month period, Mr. Bryant's sixth grade class donated their spare change
to help another student. The class raised $58.23 the first month and $66.57 the
second month. About how much money did Mr. Bryant's class raise for their
classmate?
Answer:
$124.80
Step-by-step explanation:
$58.23 + $66.57 = $124.80
Evaluate z + 3x
when X= –6 and Z= 4
Answer:
-14
Step-by-step explanation:
Hello!
You can evaluate the value of z + 3x by substituting the given values of z and x into the equation.
Evaluatez + 3x; x = -6, z=4(4) + 3(-6)4 - 18-14The evaluated value is -14.
Answer:
-14
Step-by-step explanation:
4+3(-6)
4-18
-14
Callie ha a rope that i 14. 7 inche long. She cut the rope into 3 piece. If each piece i the ame length, how long i each piece of rope?
the length of each rope would be 4.9 inches.
One of the four fundamental operations in mathematics is division; the other three are addition, subtraction, and multiplication. Simply put, division is the process of dividing a large group into smaller ones so that each group has the same number of items. In mathematics, it is a procedure for equal sharing and grouping.
Callies has a rope of length = 14.7 inches,
she cut the rope into pieces = 3
let 'x' be the length of each rope,
if each piece is of the same length, the length of the original rope would be 3x.
this implies, 3x = 14.7 inches,
x = 4.9 inches.
therefore, the length of each rope would be 4.9 inches.
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(complete question)
Callie has a rope that is 14.7 inches long. She cut the rope into 3 pieces. If each piece is the same length, how long is each piece of rope?
Makayla rents a kayak. She pays a rental fee of $12.99 plus $3.75 for each hour that he spends in the water. How much did Makayla spend if he was on the river for 4 1/2 hours? Round to the nearest hundredth.
Makayla spend $29.87 if he was in the river for 4(1/2) hours.
Given, Makayla rents a kayak.
She pays a rental fee of $12.99 plus $3.75 for each hour that he spends in the water.
Now, we have to find that how much did she pay if she was in the river for 4(1/2) hours.
Let the no. of hours in the water be, x
So, Rental fee = 12.99 + 3.75x
As, she was in the water for 4(1/2) hours i.e. 9/2 hours
the rent will be = 12.99 + 3.75(9/2)
Rent = 12.99 + 1.875(9)
Rent = $29.865
Hence, Makayla spend $29.87 if he was in the river for 4(1/2) hours.
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A volunteer knits a 5-foot long scarf at a constant rate. After 4 hours, the volunteer still has to knit 3 feet of the scarf. How much time does it take to knit the scarf from start to finish?
The time that it take to knit the scarf from start to finish is 10 hours.
How to calculate the time?From the information, the volunteer knits a 5-foot long scarf at a constant rate and after 4 hours, the volunteer still has to knit 3 feet of the scarf.
Therefore, the volunteer used 4 hours to knit 2 scarf. The time used per scarf is 4/2 = 2 hours.
In this case, the time taken to finish the scarf will be:
= Time per feet × Total feet
= 2 × 5
= 10 hours.
It'll take 10 hours.
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PLEASE HELP ME! I WILL NAME YOU THE BRAINLIEST IF YOU ANSWER! WORK DOES NOT NEED TO BE SHOWN PLEASE HURRY! THE THING IS IN THE PHOTO! PLEASE HELP AND PLEASE HURRY! THIS IS DUE TONIGHT!
Answer: Y+5= 2/9(X+2)
Answer: (x + 2) = 2/9 (y + 5)
Step-by-step explanation:
y – y₁ = m(x – x₁)
view picture please!!!
Answer:
90 degrees
Step-by-step explanation:
The question asks for the temp after an hour and a half. This is the same as 90 minutes. With this, you plug 90 in for t.
This is what it looks like:
T(t)=69e^-0.0174(90) + 76
Then you solve for T(t)
T(t)=69e^-1.566 +76
T(t)=69(0.2088) +76
T(t)=14.41265 +76
T(t)=90.41265
Then round to 90 degrees
Solve this system of equations using the SUBSTITUTION method, then answer the questions below.
x + 2y = 4
3x + 6y = 18
What did you get for the (x, y) solution to this system? (2 points)
If you were to graph these equations, would their lines cross? Explain why or why not. (2 points)
The system of equations does not have any solutions since the values on both sides of the final expression are different and the lines will not cross.
Solving system of equationsA system of equations, usually referred to as an equation system, is a collection of finite equations for which common solutions are sought.
Given the system of equations below;
x + 2y = 4............ 1
3x + 6y = 18 ........... 2
From equation 1:
x = 4 - 2y .........3
Substitute equation 3 into 2 to have:
3(4 - 2y) + 6y = 18
3(4) - 3(2y) + 6y = 18
12 - 6y + 6y = 18
12= 18
Since the values on both sides of the resulting expression is different, hence the given system of equation has NO solutions showing the lines will not cross on the graph.
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Help me find terms and like terms please
The like terms in the expression are -8x^2,-10x,14 and -6. The like terms are 14 and -6
What are terms in algebraic expression?A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms. For example, in the expression 5x + y, the two terms are 5x and y.
In the expression 14-8x^2-6-10x, there are 4 terms in it: 14, -8x^2, - 6, - 10x.
out of the four terms only two are alike because of they are both constant. This like terms are -6 and 14.
10x and -8x^2 are unlike terms because x^2 is a different term from 10x.
Therefore the like terms are -6 and 14
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when the lengths of two opposite sides of a square garden were increased by x meters each and the lengths of the other two sides were decreased by x meters each, the area of the new garden was 64 square meters. what was the area of the original square garden?
the area of the original square garden is 80 square meters.
Let the side of the original square be a. We are given that the area of the new garden was (a - x)(a + x) = a² - x² = 64.
We want to find the area of the original square, so the value of a².
(1) The area of the new garden was 80 percent of the area of the original square garden --> 64 = 0.8a² --> a² = 80. Sufficient.
(2) x = 4 --> a² - 4² = 64 --> a² = 80. Sufficient.
the area is the quantity that expresses the quantity of a location on the aircraft or on a curved surface. The place of an aircraft region or plane vicinity refers back to the location of a form or planar lamina, at the same time as floor area refers to the place of an open surface or the boundary of a 3-dimensional object. location may be understood as the quantity of fabric with a given thickness that might be vital to style a model of the form, or the amount of paint necessary to cowl the surface with an unmarried coat. it's by far the two-dimensional analog of the duration of a curve (a one-dimensional idea) or the volume of a strong (a three-dimensional concept).
place plays a vital position in current mathematics. further to its apparent importance in geometry and calculus, the place is associated with the definition of determinants in linear algebra and is a simple asset of surfaces in differential geometry. In analysis, the vicinity of a subset of the plane has defined the use of the Lebesgue measure, though no longer every subset is measurable. In the trendy, region in better mathematics is visible as a unique case of quantity for two-dimensional regions.
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• 3 pages are edited every 5 minutes.
• 5 pages are edited every 3 minutes.
• 6/10 of a page is edited per minute.
• 1 2/3 of a page is edited per minute.
a) 1 and 2
b) 1 and 3
c) 3 and 4
d) None of the above
Answer:
1 and 3
Step-by-step explanation:
where the dots on the graph are, you can read that in 5 minutes, 3 pages are edited. in 10 minutes, 6 pages.
so statement 1 is correct.
when every 10 minutes 6 pages are edited, divide both by 10 to get what is edited per minute. -> 6/10 pages are edited per minute.
Which is an equivalent expression for ((5/7)2 x (1/3)-3)-1
(5/7)2 x (1/3)-3
(5/7) x (1/3)-4
(7/5)-2 x (1/3)-3
(7/5)2 x (1/3)3
The equivalent expression for the expression given; (( 5/7 )² × (1/3)-³)-¹ is; (7/5)² • (1/3)³.
What is the equivalent expression for the given expression?It follows from the task content that the expression which is equivalent to that which is given is to be determined.
Hence, since the given expression is; (( 5/7 )² × (1/3)-³)-¹;
It follows from the power of powers law of indices that we have;
( 5/7 )-² • (1/3)³
Also, according to the negative exponent law of indices; we have;
(7/5)² • (1/3)³.
On this note, the required equivalent expression is; (7/5)² • (1/3)³.
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How to solve and find derivative of y at 1
After differentiation of function with respect to y, the value of y'(1) is 0.225.
In the given question we have to find the value of derivative of y at 1.
The given function is [tex]\frac{x^2}{36}+\frac{y^2}{64}=1[/tex]
To find the derivative of y at 1 we have to firstly derivate the given function with respect to y.
Now writing the given function in the y form
[tex]\frac{x^2}{36}+\frac{y^2}{64}=1[/tex]
Subtract x^2/36 on both side, we get
[tex]\frac{y^2}{64}=1-\frac{x^2}{36}[/tex]
Multiply by 64 on both side, we get
[tex]y^2=64-64\times\frac{x^2}{36}[/tex]
[tex]y^2=64-\frac{16x^2}{9}[/tex]
Differentiating with respect to y on both side
[tex]2y\frac{dy}{dx}=0-\frac{16\times2x}{9}[/tex]
[tex]2y\frac{dy}{dx}=\frac{32x}{9}[/tex]
Simplifying
dy/dx = 16x/9y
We can write dy/dx as y' so
y' = 16x/9y
We have to find the value of y'(1).
Since the y is the function of x so we put x=1 and we know y(1)=7.89, so
y'(1) = 16*1/9*7.89
y'(1) = 16/71.01
y'(1) = 0.225
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The parent function f(x) = log4x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of two and shifting it up five units. Which function is representative of this transformation?
a. g(x) = log4(2x) + 5
b. g(x) = 2log4(x) - 5
c. g(x) = -2log4(x) + 5
d. g(x) = log4(-2x) - 5
The function which is representative of the transformation of the parent function f(x) = log4x by reflecting it over the x-axis, stretching it vertically by a factor of two, and shifting it up five units is g(x) = -2log4(x) + 5. Option C is correct.
The reflection over the x-axis is given by the transformation:
f₁(x) = - f(x)
Therefore, the first step we get is:
f₁(x) = - log(4x)
Stretching by a factor n along the y-axis is given by the transformation:
f₂(x) = n · f₁(x)
Therefore, we will get:
f₂(x) = -2 · log(4x)
Shifting a function up of a quantity n is given by:
f₃(x) = f₂(x) + n
Therefore, we will get:
f₃(x) = -2 · log(4x) + 5
So,
g(x) = -2 log4(x) + 5
Thus, the function which is representative of the transformation of the parent function f(x) = log4x by reflecting it over the x-axis, stretching it vertically by a factor of two, and shifting it up five units is g(x) = -2log4(x) + 5. Option C is correct.
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Matt's bus ride to school is 3 minutes more than 1/4 the time of Rick's bus ride. Write an equation to model this situation and graph it
An equation that models the relationship between the amount of time taken by Rick's bus ride and Matt's bus ride is M = t/3 + 3, which is shown in the graph attached below.
How to write an equation to model this situation?In order to write this equation, we would assign variables to the amount of time taken by Matt's bus ride and Rick's bus ride to school respectively, and then translate the word problem into algebraic equation as follows:
Let the M indicate the amount of time taken by Matt's bus ride.Let the t indicate the amount of time taken by Rick's bus ride.Next, we would translate the word problem into an algebraic equation as follows;
Matt's bus ride Time = 3 minutes more than 1/4 the time of Rick's bus ride
M = (1/4 × t) + 3
M = t/3 + 3
Based on the graph shown in the image attached below that models the relationship between the amount of time taken by Rick's bus ride and Matt's bus ride, we can reasonably and logically deduce that the y-intercept is equal to 3 and the slope of the graph is equal to 1/4.
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*CHECK IMAGE FOR ACCURATE QUESTION 13. Body surface area (BSA) is used to determine doses of medications. The H.M., where H is the height in centimeters and M is the V 3,600' mass in kilograms. A doctor calculates that a particular dose of medicine is appropriate for an individual whose BSA is less than 1.6. If the mass of the individual is 68 kilograms, how many centimeters tall can she be for the dose to be appropriate?
135.53 centimeters the height of a patient in cm if he weighs 68kg and has a BSA of 1.6m².
Given that,
Some medical professionals determine a patient's medicine dosage based on the patient's body surface area (BSA). The BSA calculation method that is most frequently employed is BSA = [tex]\sqrt{\frac{wh}{3600} }[/tex].
where BSA is expressed in square meters, w is the patient's weight (in kg), h is their height (in cm),
We have to determine the height of a patient in centimeter if he weighs 68kg and has a BSA of 1.6m².
1.6= [tex]\sqrt{\frac{wh}{3600} }[/tex]
1.6= [tex]\sqrt{\frac{68h}{3600} }[/tex]
Squaring on both sides.
1.6²= 68h/3600
2.56 × 3600 =68h
9216 = 68h
h= 9216/68
h = 135.53.
Therefore, 135.53 meters the height of a patient in cm if he weighs 68kg and has a BSA of 1.6m².
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Change the subject of the formula y = g√x + h to x.
Answer:
[tex]x=\frac{(y-h)^{2} }{g^{2} }[/tex]
Step-by-step explanation:
[tex]y=g\sqrt{x} +h\\\\[/tex]
[tex]-g\sqrt{x} =h-y[/tex]
[tex]\sqrt{x} = -\frac{h-y}{g}[/tex]
[tex]\sqrt{x} =\frac{y-h}{g}[/tex]
∴ [tex]x=\frac{(y-h)^{2} }{g^{2} }[/tex]
HELP and please explain it
Answer:
SAS, ASA, SSS, ASA, Yes
Step-by-step explanation:
Find all values that are NOT in the domain of h/g.
The results of the division between the two functions are listed below:
a) (h / g) (- 1) = - 1 / 15
b) x = 7 / 8 is not in the domain of (h / g) (x).
How to evaluate a division between two functions and determine its domain
Herein we have two functions h(x) and g(x), the former is a quadratic equation and the latter is a linear equation and the division between the two functions is described below:
(h / g) (x) = h(x) / g(x), for all x such that g(x) ≠ 0
If we know that h(x) = 2 · x² - 3 and g(x) = - 8 · x + 7, then the division between the two functions is:
(h / g) (x) = (2 · x² - 3) / (- 8 · x + 7)
Now we evaluate the function at x = - 1:
(h / g) (- 1) = [2 · (- 1)² - 3] / [- 8 · (- 1) + 7]
(h / g) (- 1) = (- 1) / 15
(h / g) (- 1) = - 1 / 15
To determine the value of x such that does not belong to g(x), we need to solve the following expression:
g(x) = 0
- 8 · x + 7 = 0
8 · x = 7
x = 7 / 8
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Greg and Max left Ottawa for Toronto in their old jalopy to see the Grey Cup football game
The mileage gauge on the car was not working but the speedometer was. Their jalopy
averaged 40 mph from Ottawa to Toronto and 35 mph on the return trip. The total
traveling time for the round trip was 15 hours. Being good mathematics students, Greg and
Max were able to determine the distance between the two cities. What is this distance?
The distance between the two cities, Ottawa and Toronto, as determined by Greg and Max is 280.37 miles.
What is a Speedometer?
The instrument on a car that measures and shows speed is called a speedometer, and it is crucial for safety on roads and highways all over the world.By instantly sensing the speed on the ground, the speedometer on a car, truck, or motorbike can instantly notify the driver how fast the vehicle is travelling at any given moment.The instrument currently appears in many forms as a motorcycle speedometer or a bike speedometer and is digital in many modern automobiles.What is Distance?
The measurement of the distance between two objects or locations can be quantitative or occasionally qualitative.Distance in physics or common language can refer to a physical length or an assumption based on other factors. The term is also frequently used metaphorically to denote a measurement of the degree of separation or difference between two related objects.A metric space is a mathematical concept that is used to define the majority of these conceptions of distance, both literal and figurative.How is Distance Calculated?
The distance between two locations can be calculated using the formula,
d = s x t,------ (1)
where [tex]d[/tex] is the distance travelled, [tex]s[/tex] is the average speed, and [tex]t[/tex] is the total time.
In the given question, it is given that Greg and Max travel from Ottawa to Toronto with an average speed of 40 mph and 30 mph for the return trip.
So, [tex]s_{1}=40 mph[/tex] and [tex]s_{2}=35mph[/tex].
The total travelling time for the round trip, T = 15h ------(2)
Let the distance from Ottawa to Toronto be x.
From (1), we get that, the formula for the time taken is,
[tex]t=\frac{d}{s}[/tex]
So, the time taken to travel from Ottawa to Toronto,
[tex]t_{1} =\frac{d}{s_{1} } \\\implies t_{1} =\frac{x}{40}[/tex] ------- (3)
And, the time taken for the return trip (back from Toronto to Ottawa),
[tex]t_{2} =\frac{d}{s_{2} } \\\implies t_{2} =\frac{x}{35}[/tex] --------(4)
Here, the total time travelled from the round trip is equal to the sum of the time taken to travel from Ottawa to Toronto and back from Toronto to Ottawa.
T = t_1 + t_2------(5)
Substituting the values of (2), (3), and (4) in (5), we get
15 = x/40 + x/35
--> 15 = 0.0535x
Simplifying,
x = 15/0.0535
--> x = 280.37 miles
Therefore, the distance between the two cities as determined by Greg and Max is equal to 280.37 miles.
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ASAP! exponent rules
The answer is [tex]a^{-3}=\frac{1}{x^{3} }[/tex]
Exponent
An exponent is a number that has a power. In numbers with exponents, there are several rules. This rule is used to calculate the exponents operation.
The rules are, including:
[tex]a^{m}a^{n}=a^{m+n} \\\frac{a^{m} }{a^{n} }=a^{m-n}\\( a^{m}) ^{n}=a^{mn}\\ (ab)^{m}= a^{m}b^{m} \\\frac{a}{b} ^{m}=\frac{a^{m} }{b^{m} } \\a^{-m}=\frac{1}{a^{m} }\\ \sqrt[n]{a^{m} } =a^{\frac{m}{n} }[/tex]
From the properties rules, the rules that can be used in the problem are
[tex]a^{-m}=\frac{1}{a^{m} }[/tex]
From the properties above, it can be concluded that negative exponents mean one per number to that power. Do not reverse with the cube root, where the cube root the one per is the power, not the base number.
If the question is asked [tex]a^{-3}[/tex]
then it can be directly substituted in the rule above.
With that rule, let's find the number that equivalent with [tex]4^{-3}[/tex].
[tex]a^{-3}=\frac{1}{x^{3} }[/tex]
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I WILL MARK BRAINLIEST IT WAS DUE LAST WEEK PLS HELP
Answer:
[tex]y=\frac{3}{2}x-6[/tex]
Step-by-step explanation:
y=Mx+b is slope intercept form
M- slope
b- y intercept
We know b because when x is zero y is -6 so that is the y intercept
b=-6
Now to fin the slope we use y2-y1/x2-x1
0-(-3)/4-2
3/2
m=3/2
So we just put it all into the equation to get
y=3/2x-6
Hopes this helps
Answer: i'm writeing this so you can mark the other person brainliest
Step-by-step explanation:
If you travel from the United States to Spain, then you must have a passport. Can this be written as a biconditional? If so, what is the biconditional.
O If you have a passport, then you travel from the United States to Spain.
O You travel from the United States to Spain if and only if you have a passport.
O You have a passport if and only if you travel from the United States to Spain.
O This cannot be written as a biconditional.
You travel from the United States to Spain if and only if you have a passport. When both sides of a biconditional statement have the same truth value, the statement is said to be true.
What does a biconditional mean?
When both sides of a biconditional statement have the same truth value, the statement is said to be true. A double-headed arrow indicates the biconditional operator.If both the initial conditional assertion and the opposite statement are true, a statement is said to be biconditional."An A is guaranteed if you receive a perfect score on the final." ... Last but not least, it is a widely recognized principle that the conditional and biconditional operators have...A statement is logically true if it cannot logically be wrong. If a sentence can be expressed in the form "P if and only if Q," it is a biconditional assertion.To learn more about Biconditional statement refer to:
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You travel from the United States to Spain if and only if you have a passport. When both sides of a biconditional statement have the same truth value, the statement is said to be true.
What does a biconditional mean?When both sides of a biconditional statement have the same truth value, the statement is said to be true. A double-headed arrow indicates the biconditional operator. If both the initial conditional assertion and the opposite statement are true, a statement is said to be biconditional.
"An A is guaranteed if you receive a perfect score on the final." ... Last but not least, it is a widely recognized principle that the conditional and biconditional operators have. A statement is logically true if it cannot logically be wrong. If a sentence can be expressed in the form "P if and only if Q," it is a biconditional assertion.
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Rewrite the expression 12x + 8 to find an equivalent expression
. Show three possible expressions what do the rewritten expression tell you about the relesginship among the quantities
Three Expression equivalent to 12x + 8 are,
4 ( 3x+2 ) , 12 (x + 2/3) , 8 (2x/3 + 1)
Equivalent expressions:
Equivalent expressions are expressions that work the same even though they look different.
If two or more algebraic expressions are equivalent, then all expressions will give the same value if we put different value of variable.
Here,
given expression is " 12x + 8 "
we have to write three equivalent expression to 12x + 8
a.
If we take 4 common we will get,
12x + 8 = 4 ( 3x+2 )
so,
one of the expression equivalent to 12x + 8 is 4 ( 3x+2 )
b.
If we take 12 common then,
12x + 8 = 12 (x + 8/12)
= 12 (x + 2/3)
one of the expression equivalent to 12x + 8 is 12 (x + 2/3)
c.
If we take 8 common then,
12x + 8 = 8 ( 12x/8 + 1)
= 8 (2x/3 + 1)
one of the expression equivalent to 12x + 8 is 8 (2x/3 + 1)
Hence,
Three Expression equivalent to 12x + 8 are,
4 ( 3x+2 ) , 12 (x + 2/3) , 8 (2x/3 + 1)
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Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60 percent of their plants are flowers and 40 percent are vegetables. They have 50 plants growing in the garden.
How many vegetable plants do they have?
If they have 50 plants growing in the garden. The number of vegetable plants they have is :20.
How to determine the number of vegetable plants?Using this formula to find the number of vegetable plants
Number of vegetable plants = Percentage of vegetable plants × Number of plants in the garden
Let plug in the formula
Number of vegetable plants = 40% × 50
Number of vegetable plants = 20
Therefore the number of vegetable plants is 20.
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Find the range of the functio
h(x) = -x^2; {-2,-1,3}
Answer:
in the picture
Step-by-step explanation:
hope it helped
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The data in the table describes the preferred type of exercise of student athletes.
Cycling. Running Row Totals
Male 0.22 0.32 0.54
Female. 0.15 0.31 0.46
Column Totals 0.37 0.63. 1.00
What is the conditional relative frequency that a male prefers cycling? Round your answer to two decimal places.
0.41
0.58
0.59
0.62
Step-by-step explanation:
you take the specific number (males prefer cycling = 0.22) and the fitting total.
note there are 2 possibilities for that total :
all males
all people preferring cycling
the way it was phrased I would say the reference is all males.
the conditional relative frequency is then
0.22 / 0.54 = 0.407407407... ≈ 0.41
but if the meaning would be rather about how many of all people preferring cycling are male, then we would have
0.22 / 0.37 = 0.594594595... ≈ 0.59
both results are in your answer options.
I think the intended result is 0.41, because I understand the problem that way :
find the conditional relative frequency that a student athlete surveyed prefers cycling, given that the student is male.
the other should be phrased like
find the conditional relative frequency that a student athlete surveyed is male, given that the student prefers cycling.
Find the measures of the exterior angles of the polygon. 75°
x°
90°
90°
The measure of the exterior angle x of the polygon is x = 105° .
In the question ,
it is given that ,
in the figure, the measure of external angles are 75° , 90° , 90° and x .
we know that By Polygon Exterior Angle Sum Theorem states that the sum of measure of all exterior angle of a polygon is 360° ,
So , 75° + 90° + 90° + x = 360°
75° + 180° + x = 360°
255° + x = 360°
Subtracting 255 from both the sides , we get
x = 360° - 255°
x = 105°
Therefore , The measure of the exterior angle x of the polygon is x = 105° .
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