Answer:
Elliot = 16 years old
Miya = 10 years old
Cara = 25 years old
Step-by-step explanation:
Define the variables:
x = Elliot's agey = Miya's agez = Cara's ageThe average age of Elliot, Miya and Cara is 4 years more than the average age of Elliot and Miya:
[tex]\implies \dfrac{x+y+z}{3}=\dfrac{x+y}{2}+4[/tex]
[tex]\implies \dfrac{x+y+z}{3}=\dfrac{x+y+8}{2}[/tex]
[tex]\implies 2(x+y+z)=3(x+y+8)[/tex]
[tex]\implies 2x+2y+2z=3x+3y+24[/tex]
[tex]\implies 2z=x+y+24[/tex]
[tex]\implies x=2z-y-24[/tex]
Cara is 9 years older than Elliot:
[tex]\implies z = x + 9[/tex]
Four years ago, Elliot was double the age of Miya:
[tex]\implies (x - 4) = 2(y - 4)[/tex]
[tex]\implies x - 4 = 2y-8[/tex]
[tex]\implies x +4 = 2y[/tex]
[tex]\implies y=\dfrac{1}{2}x +2[/tex]
Substitute the equations for z and y into the equation for x and solve for x:
[tex]\implies x=2z-y-24[/tex]
[tex]\implies x=2(x+9)-\left(\dfrac{1}{2}x +2\right)-24[/tex]
[tex]\implies x=\dfrac{3}{2}x-8[/tex]
[tex]\implies \dfrac{1}{2}x=8[/tex]
[tex]\implies x=16[/tex]
Substitute the found value of x into the equation for z and solve for z:
[tex]\implies z = 16 + 9[/tex]
[tex]\implies z = 25[/tex]
Substitute the found value of x into the equation for y and solve for y:
[tex]\implies y=\dfrac{1}{2}(16) +2[/tex]
[tex]\implies y=8+2[/tex]
[tex]\implies y=10[/tex]
Therefore, the ages of Elliot, Miya and Cara are:
Elliot = 16 years oldMiya = 10 years oldCara = 25 years oldIn Exercises 13-15, use f(x) = x² and g(x) = 4x - 6 to find h(x).
13. h(x) = f(x) - g(x)
14. h(x) = f(g(x))
15. h(x) is the inverse of g(x)
The value of the function h(x) is x² - 4x +6 and 4-6 x².
What is a formula for a function?Any function's x-intercept, y-intercept, and slope can be calculated using function formulas. You could also determine a quadratic function's vertex. Additionally, the function can be graphed for various x values.
Simply adding the values of the functions f(x) and g will yield the value of the function f(x) and g(x).
Therefore, we get
f(x) = x² and we have g(x) = 4x - 6
h(x) = f(x) - g(x)
h(x) = x² - 4x +6
h(x) = f(g(x))
= x²( 4x - 6)
= 4-6 x²
h(x) is the inverse of g(x)
= inverse of 4x - 6
= 1/ 4x - 6
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The first equation in the second system is a multiple of second equation
is the first equation and the second equation in the second system is a multiple of both equation in the first system
What is simultaneous equations? Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. Each of these equations on their own could have infinite possible solutions.In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are soughtSimultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables satisfies all such equations. This implies that the simultaneous equations have a common solution. Some of the examples of simultaneous equations are: 2x - 4y = 4, 5x + 8y = 3On occasions you will come across two or more unknown quantities, and two or more equations relating them. These are called simultaneous equations and when asked to solve them you must find values of the unknowns which satisfy all the given equations at the same time.To learn more about simultaneous equations refers to:
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Anthony's brother was 0.45
meters tall last year. He grew
another 0.5 meters this past
year. How tall is he now?
Answer:
0.95meters
Step-by-step explanation:
last year her was 0.45m tall
this past year he is 0.5m
Total = 0.45 + 0.5 = 0.95
Answer: 0.95
Step-by-step explanation: add 0.45+0.5=0.95
If g(x) = x³ - 2x, find the value of g(2+h)-g(2)dividebyh answer is h square plus six h plus ten
Answer: To find the value of g(2+h)-g(2) divided by h, we can use the definition of the derivative. The derivative of a function at a point is a measure of the slope of the function at that point, and it can be calculated by taking the limit of the difference quotient as h approaches 0.
The difference quotient is defined as:
[g(2+h) - g(2)] / h
So, to find the derivative of g at x=2, we can substitute the value of x in the function g(x) and take the limit as h approaches 0:
lim h→0 [g(2+h) - g(2)] / h
Substituting the value of x in the function g(x), we get:
lim h→0 [(2+h)³ - 2(2+h) - (2² - 2*2)] / h
This simplifies to:
lim h→0 [8+6h+h²-2h - 4] / h
Which simplifies to:
lim h→0 [h²+6h+4] / h
And, finally:
lim h→0 [h(h+6)] / h
The limit of a quotient is equal to the quotient of the limits, as long as the limit of the denominator is not 0. In this case, the limit of the denominator (h) is 0, but the limit of the numerator (h(h+6)) is not. Therefore, we can safely take the limit:
h+6
So, the derivative of g at x=2 is h+6. When h=0, the derivative is equal to the function's value at that point, so the value of g(2) is 6.
Therefore, the value of g(2+h)-g(2) divided by h is:
(h+6) - 6 / h
Which simplifies to:
h / h
Which is equal to:
1
So, the final answer is 1.
Step-by-step explanation:
Trace triangle JKL and point P.
Draw the dilation of AJKL
using scale factor 3 and P
as the center of dilation,
The dilation of triangle JKL, with point P at the origin and scale factor of 3, is graphed on the image shown at the end of the answer.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The coordinates of the vertices of the original triangle JKL for this problem are attributed as follows:
J(1,1).K(1,5).L(4,1).The scale factor of the dilation is given as follows:
k = 3.
Meaning that each coordinate of each vertex of the triangle will be multiplied by 3, thus obtaining the coordinates of the vertices of the image of triangle JKL after the dilation, as follows:
J'(3,3).K'(3,15).L'(12,3).More can be learned about dilation at brainly.com/question/3457976
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13 People fit comfortably in a 5 feet by 5 feet area. Use this value to estimate the size of a crowd that is
5 feet deep on both sides of the street along a 2.7-mile section of a parade route.
The size of the crowd that is 5 feet deep on both sides of the street along a 2.7 -mile section of a parade route is 74,131 people.
How to calculate the crowd?The number of people that can fit comfortably in a 5 feet by 5 feet area = 13.
Therefore;
The ratio of the number of people per unit area = 13/(5 × 5) = 13/25
The area A occupied by the crowd = 5 feet × 2.7 mile × 2
2.7 miles = 14,256 feet
∴ A = 5 feet × 14,256 feet × 2 = 1,42,560ft²
We then have:
[tex]\frac{number\ of\ people}{1,42,560} = \frac{13}{25}[/tex]
∴Number of people = 13/25 × 1,42,560 = 74,131.2 ≈ 74,131 people
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Determine which two numbers come next in the sequence 5,5,10,15,25, __, __
The two numbers that come next in the sequence 5,5,10,15,25, are 40 and 65.
How can the two numbers that come next in the sequence be calculated?To calculate this , You can figure it out by taking the first number, which is 5. However, since the previous number is 0, the sum is 5, and you proceed in the same manner.
5 + 5 = 10
(5 + 10) = 15
(10 + 15) = 25
(15 + 25) = 40
(25 + 40) = 65
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If Nayesha pumps 9.4 gallons of gas in her gas tank and each gallon costs $2.98, how much money will she spend? QUCIKLY
Answer:
28.012
Step-by-step explanation:
9.4*2.98 = 28.012
A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad.
The probability of drawing a bag with bad potatoes is less than 1.
True or False
The probability of drawing a bag with good potatoes is greater than 0.
True or False
What is the probability of drawing a bag with bad potatoes?
What is the expected probability of the complement of the event?
Answer:
The probability of drawing a bag with bad potatoes is less than 1. True
The probability of drawing a bag with good potatoes is greater than 0. True
What is the probability of drawing a bag with bad potatoes?
The probability of drawing a bag with bad potatoes is (2 bad bags) / (20 total bags) = 0.1 or 10%.
What is the expected probability of the complement of the event?
The complement of the event of drawing a bag with bad potatoes is drawing a bag with good potatoes. The probability of drawing a bag with good potatoes is (18 good bags) / (20 total bags) = 0.9 or 90%.
Uday Tahlan
Which of the following best describes X on the scatter plot below?
The option that best describes X on the scatterplot is;
C: Outlier
How to Interpret a scatterplot?Let us first define the terms in the given options before we analyze the scatterplot.
1) Negative correlation is defined as a relationship between two variables whereby one variable increases while the other decreases, and vice versa.
2) A nonlinear relationship is also referred to as nonlinear association, and it exists when a constant change in the independent variable does not result in a constant change in the dependent variable.
3) An outlier is defined as a data point that differs significantly from other observations.
4) Clusters are small populations that a wider population is divided into.
Now, from the scatter plot, we see that X is isolated from the plotted points which tells us that it differs greatly from the other points and as such it fits the definition of an outlier.
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The missing options are;
A. negative correlation
B. nonlinear association
C. outlier
D. cluster
Simplify the following rational expression. Be sure to state the condition.
The simplified form of the rational expression (x²+5x+6)/(3x+6) is (x+3)/2.
And we used factorization to find the simplified form.
What is factorization?Factorization is a process to simplify the expression by finding the factors of that expression.
And to find the same expression from factors, you have to reverse the process.
Given:
The rational expression,
(x²+5x+6)/(3x+6).
Simplifying,
the expression using factorization method.
First, (x²+5x+6),
= x²+2x+3x+6
= x(x+2)+3(x+2)
= (x+2) (x+3)
And 3x+6 = 3(x+2)
Substituting the simplified values to the given expression,
(x²+5x+6)/(3x+6),
= (x+2) (x+3) / {3(x+2)}
Factor out the common factor,
= (x+3)/2
Therefore, the simplified form is (x+3)/2.
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Write the following expression in expanded form:9 to power of 3× 7to the power of 4
Exponential Expressions into Expanded Form into Answer:
[tex]9^{3}[/tex] = 9⋅9⋅9 = 729
[tex]7^{4}[/tex] = 7⋅7⋅7⋅7 = 2401
I hope this helps, have a good day!
Answer:
= 9⋅9⋅9 = 729
= 7⋅7⋅7⋅7 = 2401
Step-by-step explanation:
Ian is taking a true/false quiz that has four questions on it. The correct sequence of answers
is T, T, F, T. Ian has not studied and yet guesses all answers correctly- He decides he wants
to determine how likely this is to happen using a simulation. He decides to use a fair coin to
do the simulation.
Describe the design of a simulation that would allow Ian to determine how likely it would
be to guess all answers correctly on this quiz.
The design of a simulation that would allow Ian to determine how likely it would
be to guess all answers correctly on this quiz can be Illustrated through a coin.
How to design the simulation?Ian can design a simulation to determine the likelihood of guessing all answers correctly on the quiz by using a fair coin. He can flip the coin four times, with each flip representing a guess on the quiz. If the coin lands heads up, he marks it as a true answer, and if it lands tails up, he marks it as a false answer.
He can repeat this process a large number of times (e.g. 1000) and count the number of times that the sequence T, T, F, T is generated. The proportion of times that this sequence is generated out of the total number of simulations will be an estimate of the probability of guessing all answers correctly on the quiz by chance.
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can you simplify 2/6?
Answer:
1/3
Step-by-step explanation:
2÷2=1
6÷2=3
Solution: 1/3
name all the terms realted to subtraction
Answer:
Other words for subtraction:
taking away
withdrawal
abstraction
removal
discounting
Step-by-step explanation:
A traffic radar records the speed of cars driving through an intersection. It records these statistics:
Mean=36.2 mph
Median=28.5 mph
Mode=30.0 mph
What is the most common speed of a car driving through the intersection?
a. 31.6
b. 36.2
c. 30.0
d. 28.5
The most common speed of a car driving through the intersection is 30.0 mph which is indicated by the Mode.
What is the mode of data?A mode of data is defined as an observation with the highest frequency among the values that appear most frequently in the given data.
In the case of ungrouped data, all that is required is to find the observation that happens most frequently.
A traffic radar records the speed of cars driving through an intersection. It records these statistics:
Mean = 36.2 mph
Median = 28.5 mph
Mode = 30.0 mph
As per the question, a car driving through the intersection at 30.0 mph is the most common speed.
This is indicated by the Mode which is the value that appears most frequently in a data set.
Hence, the correct answer would be an option (C).
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Solve for x
Select the correct response:
A: 14
B: 19.25
C: 10
D: 6.5
The value of the x is 10.
What is the exterior angle theorem?
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle.
We have given,
angles of the triangle:
Interior angles :
∠D = 2x + 7,
∠E = 26°,
Exterior angle:
∠C = 6x - 7
To find x = ?
few common properties about the angles of a triangle:
A triangle has 3 internal angles which always sum up to 180 degrees.
It has 6 exterior angles and this theorem gets applied to each of the exterior angles.
Note that an exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles.
Exterior angles are defined as the angles formed between the side of the polygon and the extended adjacent side of the polygon.
So,
∠C = ∠D + ∠E
6x - 7 = 2x + 7 + 26,
6x - 7 - 2x - 7 = 26,
4x - 14 = 26,
4x = 40
x = 40/4
x = 10,
Hence, the value of the x is 10.
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The water depth in a harbor rises and falls over time. The function f(t) = 4.1 sine (StartFraction pi Over 6 EndFraction t minus StartFraction pi over 3 EndFraction) + 19.7 models the water depth, in feet, after t hours.
During the first 24 hours, at what times does the water depth reach a maximum?
Answer:
Below
Step-by-step explanation:
f(t) = 4.1 (sin pi/6 t - pi/3) + 19.7 <===will be a maximum when the sin portion is equal to 1
so sin ( pi/6 t - pi/3) = 1 given that sin is equal to one at 0 and pi and 2 pi and 3 pi and 4 pi etc
pi/6 t - pi/3 = 0 or pi , 2 pi, 3 pi , 4 pi
then t = 2 and 8 and 14 and 20 hrs ( every 6 hrs starting with t = 2)
The volume of
a refrigerator, in cubic centimeters, is given
by the function V(x) = (x)(x + 1)(x – 2). Write a
new function for the volume of the refrigerator
in cubic millimeters if x is in centimeters.
The newly rewritten function expression of V(x) is V(x) = (x)(x + 1)(x – 2)/1000
How to rewrite the function expression?From the question, we have the following parameters that can be used in our computation:
A function expression
The function expression is given as
V(x) = (x)(x + 1)(x – 2)
Where if x is in centimeters and V(x) is in cubic centimeters
The new function for the volume of the refrigerator is stated to be in cubic millimeters
Using the above as a guide, we have the following:
1 cubic centimeters = 1000 cubic millimeters
So, we have
V(x) = (x)(x + 1)(x – 2)
1 cubic centimeters = 1000 cubic millimeters
Cross multiply
V(x) * 1000 = 1* (x)(x + 1)(x – 2)
Divide both sides by 1000
V(x) = (x)(x + 1)(x – 2)/1000
Hence, the function is V(x) = (x)(x + 1)(x – 2)/1000
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Read the situations in the table below. Then drag a graph and equation to represent each situation. Indicate whether each of the relationships is proportional or non-proportional.
The equation for situation 1 is y=4x and is directly proportional and the situation two will have equation y=x+4 and is not proportional.
What are linear equations?
Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here, graph 1 varies 4 times the x value every time there is an increase of 1 in the x-axis and in graph 2 it is a linear equation with intercept at 4 and thus the graph increases with +4 and A proportional relationship exists between two values x and y when they can be expressed in the general form y = kx,
Hence, The equation for situation 1 is y=4x and is directly proportional and the situation two will have equation y=x+4 and is not proportional.
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Rewrite the following expression using the Distributive Property. 5(2x -8)
A. -30x
B. 10x -40
C. 10x + 40
D. 10x -8
I think it is either B or C but I'm not sure.
Answer:
B. 10x -40
Step-by-step explanation:
To rewrite the expression 5(2x-8) using the distributive property, we need to separate the expression inside the parentheses and then multiply the two expressions by 5. The answer is: 10x-40.
Aftab pays £3.10 per concrete slab. (b) How much will it cost Aftab to buy enough concrete slabs to make the patio?
To determine how much it will cost Aftab to buy enough concrete slabs to make the patio, you will need to know the size of the patio and how many slabs are needed to cover it. Once you have this information, you can multiply the number of slabs by the cost per slab to find the total cost. For example, if the patio is 10 square meters and requires 20 concrete slabs to cover it, the total cost would be 3.10 * 20 = £62.
Given the example below, determine the property displayed.
7+3=3+7
Answer:
commutative property of addition
Step-by-step explanation:
commutative property of addition
The commutative property of addition allows you to change the order of the numbers in an addition.
For example, 1 + 2 = 2 + 1
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Consider the circumscribed angle. Determine the value of x.
1)
x = 12
2)
x = 29
3)
x = 4.75
4)
x = 17
Answer:
x = 12
Step-by-step explanation:
i. 29 = 2x + 5 [The length of two tangents to a circle at the point of contact from the same external point are equal]
ii. 29 - 5 = 2x
iii. 24 = 2x
iv. x = 24/2
v. x = 12
let there be 800 people at school. prove that 3 of them do share a birthday. how can we prove it according to the pigeonhole principle?
Compare.
2.2O 14/4
A. <
B. >
C. =
Answer:≤ sorry if it's wrong I'm not a fan of math
Step-by-step explanation:
PLEASE HURRY I WILL GIVE BRAINLY PLEASE HURRY
In triangle LMN, m∠L = (4c + 53)°. If the exterior angle to ∠L measures 87°, determine the value of c.
c = 87
c = 8.5
c = 35
c = 10
Answer:c=35
Step-by-step explanation:
i just did this
Question 5(Multiple Choice Worth 2 points)
(Sample Spaces LC)
A paper bag has seven colored marbles. The marbles are pink, red, green, blue, purple, yellow, and orange. List the sample space when choosing one marble.
A s= (1, 2, 3, 4, 5, 6
B s=(purple, pink, red, blue, green, orange, yellow}
C s=(g. r, b. y. o, p)
D s= (green, blue, yellow, orange, purple, red)
The sample space when choosing one marble will be B s=(purple, pink, red, blue, green, orange, yellow}
What is sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample space may contain a variety of outcomes.
A paper bag has seven colored marbles. The marbles are pink, red, green, blue, purple, yellow, and orange. The sample space when choosing one marble will be all the colors. The correct option is B.
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Math- algebra 1 - please help
For both pizzas A and B to cost the same, there must be 5 toppings. Equations can be categorized as identities or conditional equations.
what is equation ?The number is said to be in its simplest form when divided into its smallest equivalent fraction. What should be done to find the most basic form. Look for common factors in the numerator and denominator. Verify a fractional integer to verify if it qualifies as a prime number. A statement having two equilateral triangles and an equivalent sign in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The conventional form of a linear model is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables.
given
number of toppings be x
number of toppings for pizza A = $10 + x*$1.5
number of toppings for pizza B = $12.5 + x*$1
10 +1.5x = 12.5 + x
10 -12.5 = x- 1.5x
-2.5 = - 0.5x
x = 5
For both pizzas A and B to cost the same, there must be 5 toppings.
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Lena had 149 dollars to begin with. She just spent k dollars. Using k, write an expression for the number of dollars she has left.
Therefore , the solution to the given problem of expression comes out to be 149-k =x be used it as its expression.
Define Expression .A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Here,
Given : Lena has $149
she spends k amount of money
The money left be x
=> 149-k =x
Therefore , the solution to the given problem of expression comes out to be 149-k =x be used it as its expression.
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