The equation that have same solution to 3x-12=24 is 4x - 30 = 18.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The equation given is illustrated as:
3x - 12 = 24
Collect like terms
3x = 24 + 12
3x = 36
Divide through by 3.
3x / 3 = 36 / 3
x = 12
In this case, 4x - 30 = 18 will be:
4x - 30 = 18.
Collect like terms
4x = 18 + 30.
4x = 48
Divide
x = 48/4
x = 12
Therefore, 4x - 30 = 18 has same solution.
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Hey! Could anybody help me out with this? I would like a very brief explanation leading to the answer as I already kinda understand the topic. Thanks!
Domain and Range of a Function
The domain of a function f is the set of values of the input (or independent) variable, often called x. The range is the set of values of the output (or dependent) variable, often called y, or f(x).
The function shown in the image has a shape that opens up to infinity (marked with the two arrows). This means that x can have any real value from minus infinity to plus infinity, that is, all real numbers.
Now for the range, we can see not every value of y belongs to the function. The graph decreases down to the vertex of the parabola that is located at (3,-12). This means that from y=-12 and up, the function exists, but not below this value.
Summarizing:
Domain: All real numbers
Range: y ≥ -12
21 = -3/4y solve for y and simplify your answer as much as possible
Answer:
y = -28
Step-by-step explanation:
21 = -3/4y
so:
-3/4y = 21
divide both sides by -3/4:
(-3/4y)/(-3/4) = 21/(-3/4)
y = -28
The price of an item has risen to $300 today. Yesterday it was $125. Find the percentage increase.
Answer:
140
Step-by-step explanation:
if 1 cm is equivlent to 10km what is 50 cm equivlant to
Answer:
50cm is equivalent to 500km
Have a good one!
ALTAThe graph shown compares the rent Andrew and Dave pay for renting bikes from different stores,Andrew's and Dave'sBike Rentalsу13DaveAndrew11Rent Paid (dollars)2319117HoursAfter how many hours would the amount Andrew and Dave pay for the rentals be equal?
We have the following:
The first thing is to calculate the equation by means of the graph.
For Andrew, we can see that he starts at $ 3 and every hour that passes, he charges $ 2, therefore the equation is:
[tex]y=3+2x[/tex]where x is the number of hours.
For Dave, we can see that he starts at $ 6 and every hour that passes, he charges $ 1.5, therefore the equation is:
[tex]y=6+1.5x[/tex]where x is the number of hours.
to calculate the number of hours when the value is equal, we must match the equations like this
[tex]\begin{gathered} 3+2x=6+1.5x \\ 2x-1.5x=6-3 \\ 0.5x=3 \\ x=\frac{3}{0.5}=6 \end{gathered}[/tex]Which means that at 6 hours they have the same price
Write the sentence as an equation.
279 is the same as 157 more than the quantity m times 398
Answer:
279=157+398m
Step-by-step explanation:
hope its right?
A function is shown. What is the value of f(–8)?
f(x) = 12 – 3x
*Type in your answer.
f(–8) =
Answer:36
Step-by-step explanation:
f(x)=12-3*(-8)
=36
Given m||n, find the value of x.
(6x-20)°
(6x-4)°
Answer:
x = 7
Step-by-step explanation:
19) f(x) = -x +3
g(x)= x - 4
Find f(x) · g(x)
Answer:
-8x + (3x - 12)
Step-by-step explanation:
f(x) · g(x)
(-x + 3) · (x - 4)
(-2x · 4x) + (3x - 12)
-8x + (3x - 12)
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do blood-building drugs help brain development in babies born prematurely? researchers randomly assigned 53 babies, born more than a month premature and weighing less than 3 pounds, to one of three groups. babies either received injections of erythropoietin (epo) three times a week, darbepoetin once a week for several weeks, or no treatment. results? babies who got the medicines scored much better by age 4 on measures of intelligence, language, and memory than the babies who received no treatment.how many different treatments were there and what principle of experimental design does that address?
There were three different treatments: erythropoietin, darbepoetin, and no treatment. This selection exemplifies the principle of randomization principle.
What is a treatment?In experiments, the word treatment refers to the use of a specific medicine, therapy, or condition that is controlled by the research to test the effect of the treatment on subjects. For example, if the researcher wants to find out the ideal amount of water for a plant to grow, the treatment would be the amount of water.
In the case presented, there are three treatments:
Erythropoietin (epo) three times a week.Darbepoetin once a week for several weeks.No treatment.What principle of experimental design does that address?Randomization is the principle applied because the subjects are selected randomly for each of the groups and this reduces bias.
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When Luke left his house in the morning, his cell phone battery was partia
charged. Let B represent the charge remaining in Luke's battery, as a perc
hours since Luke left his house. The table below has select values showing t
relationship between t and B. Determine the number of hours until Luke's
dies.
Step-by-step explanation:
Solution:
From the graph, the coordinates of the points A, B and C are (- 1, 0) (0, - 2) and (2, 0) respectively.
Let the equation representing the graph be y = a * x ^ 2 + bx + c
(1)
The curve represented by (i) passes through A(- 1, 0) B(0, - 2) and C(0, 2) So,
- 2 = 0 + 0 + c
c = - 2
Also 0 = a - b - 2
and 0 = a * (0.4 + 2b - 2)
⇒a a - b = 2 2a + b = 1 (ii) ..(iii)
Adding (ii) and (iii)
3a = 3
a = 1
Substituting the value of a in (ii), we have
1 - b = 2
b = - 1
The equation of the curve is y = a * x ^ 2 + bx + c i.e. y = x ^ 2 - x - 2
3.5 gallons to liters
It is known that 1 gallon is 3.78541 litres.
So it follows:
[tex]\begin{gathered} 1\text{ gal= 3.78541 litres} \\ 3.5\text{ gal=3.78541x3.5 litres} \\ 3.5\text{gal}=13.2489litres \end{gathered}[/tex]Hence the value of 3.5 gallons is 13.2489 litres.
last question of the day :)
Answer:
0.5
Step-by-step explanation:
0.5 x 0.5 = 0.25
Answer:
x=0.5
Step-by-step explanation:
x=±√0.25
x=±0.5
x=0.5,−0.5
find mean propertion between 5 and 125
charlyn walks completely around the boundary of a square whose sides are each 55 km long. from any point on her path she can see exactly 11 km horizontally in all directions. what is the area of the region consisting of all points charlyn can see during her walk, expressed in square kilometers and rounded to the nearest whole number?
The area of the region consisting of all the points Charlyn can see during her walk is equal to, A = 4840 km.
Charlyn is walking around the boundary of square A, which is 55 km long, and she has a horizontal vision of 11 km.
So as she walks around the square of 55 km, let there be another square B which lies outside square A, which is created due to her 11 km field of vision.
length of sides of square B = 55+(2×11) which is equal to 77 km.
And as she walks around the square of 55 km, let there be yet another square C which lies inside square A, which is created due to her 11 km field of vision.
length of sides of square C = 55-(2×11) which is equal to 33 km.
The area that Charlyn can see throughout her walk is equal to,
A = Area of square B - Area of square C.
The area of square B = Side² = 77² = 5929.
The area of square C = Side² = 33² = 1089.
A = 5929 - 1089.
A = 4840 km.
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A pack of paper costs $1.75, including tax. Mr. Valentino wants to purchase packs of paper for his class and has a $25 budget. Write and solve an inequality to solve for the number of packs of paper Mr. Valentino can purchase, and describe the graph of the solution.
The inequality according to the the cost of pack of paper can be written as x ≤ 14.28 and Mr. Valentino can purchase a maximum of 14 packs of paper.
What is inequality?
A connection that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics. The majority of the time, size comparisons between two numbers on the number line are made. The two most common notations for representing various forms of inequalities are as follows:
The symbol a < b indicates that a is smaller than b.
The symbol a > b indicates that a is bigger than b.
Let's assume he can buy x pack of paper.
Cost of x pack of paper will be equal to the x times cost of 1 pack of paper
i.e. Total cost = 1.75x
Now, Mr. Valentino has $25
Therefore,
1.75x ≤ 25
Inequality is ⇒ x ≤ 14.28
It tells us that Mr. Valentino can purchase only 14 packs of paper.
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Is the trend line linear? If so, write a linear equation that represents the trend line. Show your work. PLSSSSSSS HELPPPP SHOW UR WORK TO ON HOW YOU FIGURED IT OUT THE EQUATION FOR IT USE SLOPE TOO ILL INCLUDE AN IMAGE TOO
The trend line is linear and the trend line has an equation of y = 500/9x + 100
The type of the trendFrom the graph, we can see that:
The points appear to be on a straight line and it increases along the x-axis
This means that the points can appear on an approximate straight line
So, we can conclude that the trend is a linear trend
The equation of the lineOn the line, we have the following points
(x, y) = (0, 100) and (9, 600)
We start by calculating the slope of the points using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where x and y are defined above
So, we have
Slope = (600 - 100)/(9 - 0)
Evaluate
Slope = 500/9
The equation is then calculated as
y = Slope(x - x₁) + y₁
Where
(x₁, y₁) = (0, 100) and Slope = 500/9
So, we have
y = 500/9 * (x - 0) + 100
Evaluate
y = 500/9x + 100
Hence, the equation is y = 500/9x + 100
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Please solve the following. 12 divided by 3 . 5 - 4 to the power of 2
Answer:
44
:)
Step-by-step explanation:
y =40x^2 find X when y =10,360,1000,4000
1. The public primary/secondary school dropout rate in Washington State is 6%. Suppose 35
individuals of primary/secondary school age are interviewed at random on a city street. What is
the probability that:
a. (5 points) Exactly 7 of them are dropouts?
The probability that exactly 7 individuals are dropouts out of 35 is 0.0033288.
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.
Given,
Probability of dropouts=p= 6%= 0.06
Probability of not dropouts=q=1-p=1-0.06=0.94
n=35
We use the probability mass function of binomial distribution, as there are only two possible outcomes for the given situation. If the individual is dropout or not a dropout.
P(X=x)= nCr x p^r x q^(n-r)
P(X=7)= 35C7x(0.06)^7x(0.94)^28
P(X=7)=6724520x(0.06)^7x(0.94)^28
P(X=7)=0.00332889
Therefore, the probability of exactly 7 of them are dropouts is 0.00332889.
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How can this expression be written another way? 60x−24 Factor using the distributive property and the greatest common factor to write an equivalent expression.
The equivalent expression of the given expression 60x - 24 using distributive property and greatest common factor is 12(5x-2).
Distributive property is a property with which we multiply the sum or difference of two numbers with a number. For example:
a×(b+c) = a×b + a×c
a×(b-c) = a×b - a×c
The greatest common factor is a number which is common multiple of all the given numbers.
Now, solve the given expression 60x - 24
The factors of terms
60x = 12 × 5x
24 = 12 × 2
The greatest common factor is 12, so we take 12 common and the given expression can be written as
60x - 24
= 12 × 5x - 12 × 2
= 12(5x - 2)
Hence, the equivalent expression is 12(5x-24)
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Adi is 5 inches short than Sunee. Sunee is n inches tall. What is an expression that represents Adi's height in inches?
The expression that represents the Adi's height in inches is n - 5.
Expression:
An expression is the mathematical statement which consists of numbers, variables and an arithmetic operation like addition, subtraction and division etc. between them.
Given,
Adi is 5 inches short than Sunee. Sunee is n inches tall.
Here we need to find the expression for Adi's height in inches.
Through the given question we know that,
Sunee is n inches tall.
And Adi is 5 inches lesser than Sunee.
Here we have the word short or less, that represents that we have to reduce that amount from the total.
Therefore, the expression for Adi's height in inches is,
=> n - 5.
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Write the sentence as an equation.
d is equal to y minus 300
Answer:
d=y-300
Step-by-step explanation:
The vertices of a figure are W(-6,-2), X(-2,-2), Y(-2,-6), and Z(-5, -6).. Rotate the figure 270°
counterclockwise about the origin.
W'(-2 , 6), X'(-2 , 2), Y'(-6 , 2), Z'(-6 , 5).
This is the vertices after the 270° counterclockwise rotation.
What does counterclockwise rotation mean ?Counterclockwise is a turn to the left, opposite the direction of the hands on a clock.Given vertices,
W(-6,-2), X(-2,-2), Y(-2,-6), and Z(-5, -6).
Here we have to rotate 270°.
We know that,
Rotating a point 90° counterclockwise: (x, y) → (-y, x).
Rotating a point 180° counterclockwise: (x, y) → (-x, -y).
Rotating a point 270° counterclockwise: (x, y) → (y, -x).
So here we are rotating the figure 270°,
W(-6,-2)→ W'(-2 , 6)
X(-2,-2)→ X'(-2 , 2)
Y(-2,-6)→ Y'(-6 , 2)
Z(-5, -6)→ Z'(-6 , 5)
The vertices after rotating 270° counterclockwise about origin is:
W'(-2 , 6), X'(-2 , 2), Y'(-6 , 2), Z'(-6 , 5).
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Cual es el producto de 3x^5 y de 2x^4
Opciones:
1)5x^9
2)5x^20
3)6x^9
4)6x^20
you spin two wheels with equal size wedges labeled with numbers 1 through 9. what is the probability that at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8?
The probability that at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8 is 53/99
The greatest number that can be formed by the two wheels is 99
Let event A be multiple of 4
Multiples of 4 between 1 to 9 is 4,8
Probability that at least one wheel land at a multiple of 4 is
[tex]\frac{2}{9} + \frac{2}{9}[/tex] = 4/9
Let event B be first value greater than 9
P(B) = 9/99 = 1/11
P(A∩B) = 0
Probability of at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8
P(A∪B) = P(A) + P(B) - P(A∩B)
= 4/9 + 1/11 - 0
= [tex]\frac{4(11)}{9 (11)} + \frac{1 (9)}{11(9)}\\\\ \frac{44 + 9}{99}\\\\ \frac{53}{99}[/tex]
Therefore, the probability that at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8 is 53/99
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An autonomous underwater vehicle (AUV) is at an elevation of -8.25 ft. It dives down 6 2/3 ft to collect a specimen. Then the AUV dives another 15 3/4 ft. What is the final elevation of the AUV? Show your work
The final elevation of the AUV is [tex]-31 \frac{5}{12}[/tex] feet.
Given that, AUV is at an elevation of -8.25 ft. It dives down [tex]6\frac{2}{3}[/tex] ft to collect a specimen. Then the AUV dives another [tex]15\frac{3}{4}[/tex] ft.
What is an elevation?The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".
Here, the mixed fraction can be written in improper fraction
[tex]6\frac{2}{3} = \frac{20}{3}[/tex] and [tex]15\frac{3}{4}=\frac{63}{4}[/tex]
Now, 8.25 = 825/100 = 33/4
The final elevation = -33/4-20/3-63/4
= -99/4 - 20/3
= -297/12 -80/12
= - 377/12
= [tex]-31 \frac{5}{12}[/tex]
Therefore, the final elevation of the AUV is [tex]-31 \frac{5}{12}[/tex] feet.
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cheesebugers and pizza are on todays menu. if the cafeteria serves cheeseburgers every 4th day and pizza every 6th day, how many more days until cheeseburgers and pizza are both on the menu again?
Answer:
12 more days
Step-by-step explanation:
Every time cheeseburger will be served: 4th day, 8th day, 12th day, 16th day
Every time pizza wil be served: 6th day, 12th day, 18th day
Since 12 is a common number, every 12 days both cheeseburgers and pizzas will be served
The table represents some points on the graph of a linear function. What is the rate of change of y with respect to x for this function?
A) 1/5
B) 1/2
C) 2
D) 5
Answer:
A
Step-by-step explanation:
the rate of change of y with respect to x.
that is the regular slope of the linear function, which is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
from (5, 2) to (10, 3)
x changes by +5 (from 5 to 10)
y changes by +1 (from 2 to 3)
the slope or rate of change is
+1/+5 = 1/5
2. Amy works at the local restaurant making $7.25 per hour in addition to tips. During her last shift, she earned $62 in tips and took home $112.75 for the day. How many hours did she work?
Answer:
She worked Seven (7) hours.
Step-by-step explanation:
$112.75 is the total
she earned $62 in tips which doesn't count because the questions asked for how long she worked.
Adding tips would make the equation unreliable because how long people work doesn't really affect how much tips you get. You maybe getting 50 bucks of tips in the first and 40 in the next.
solving steps: (where x = number of hours worked)
7.25x + 62 = 112.75 <<<the true equation based on the story
7.25x = 112.75 - 62
7.25x = 50.75
x = 50.75 ÷ 7.25
x = 7
Seven (7) hours worked.