Train A's speed = x
Train B's speed = x + 10
4.5(x + x + 10) = 432
Distribute both sides by 4.5
x + x + 10 = 96
Combine like terms.
2x + 10 = 96
Subtract 10 from both sides.
2x = 86
Divide both sides by 2
x = 43
Train A = x = 43 mph
Train B = x + 10 = 43 + 10 = 53 mph
Speed is the ratio of distance and time.
Speed = Distance /Time
Distance = Speed x Time
If Train B travels 10 mph faster than Train A.
The speed of train A is 48 mph.
The speed of train B is 58 mph.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
Example:
The speed of a car moving 4km in 2 hours is 2km per hour.
We have,
Train A:
Speed = x
Train B:
Speed = x + 10
Speed = Distance / Time
Distance = Speed x Time
At time = 4.5 hours, the train is 432 miles apart.
This can be written as,
Distance = (Speed of train A + Speed of train B) x Time
432 = (x + x + 10) x 4.5
Divide both sides by 4.5.
432 / 4.5 = 2x + 10
96 = 2x + 10
Subtract 10 on both sides.
96 - 10 = 2x
86 = 2x
Divide both sides by 2.
2x = 96
x = 96/2
x = 48
Now,
x + 10 = 48 + 10 = 58
Thus,
If Train B travels 10 mph faster than Train A.
The speed of train A is 48 mph.
The speed of train B is 58 mph.
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Find the length of each line segment or object
Answer:
1 ⁷/₈ in
Step-by-step explanation:
that is exactly 1 ⁷/₈ in
Write 10 × 10 × 10 × 10 × 10 × 10 as a power of 10 using exponents.
Answer:
10⁶
Step-by-step explanation:
B
Because there is 6 10s so... yeah hope this helps
Answer:
6
10
Step-by-step explanation:
Identify the domain and range of the function. Enter your answers as numbers in the boxes; do not include units. Enter the range values in ascending order separated by commas inside the curly brackets. Age Admission Price under 5 free 5-17 $25 18-64 $40 65 and over $35 What is the range?
Answer:
When we have a function y = f(x)
The set of the possible values of x is called the domain, and the set of the possible values of y is called the range.
In this case, we have:
x = age, and y = price.
x y
< 5 $0
5 - 17 $25
18 - 64 $40
≥ 65 $35
Then the range is the possible age of the customer, and it goes for all the possible ages (as whole numbers)
So the domain will be the set of all the positive integers:
D = {1, 2, 3, 4, 5, ...}
(of course, we can not have an age equal to 1300 or infinity, but we really can not cap the domain)
The range is the possible values of y, in this case is discrete, because we have only 4 possible prices, so the range is:
R = {$0, $25, $40, $35}
Help quickly please hurry i am almost done
Answer:
Might be wrong but i got c( NOPE NOT C ITS A
Step-by-step explanation:
What is the simplified value of the expression below?
8(9.75-3.25)+ 12x4
100
O 152
256
O 347
Answer:
100
Step-by-step explanation:
=(8)(6.5)+(12)(4)
=52+(12)(4)
=52+48
=100
31-X + (2 x + 1)] = x - 1.
X =
Answer:
answer is X= 2/1 ×5+2 ok
Plz hellppp -4(x-2) +5 = -10
Answer:
The answer is 5.75
Step-by-step explanation:
I used desmos
Steps to solve:
-4(x - 2) + 5 = -10
~Distribute left side
-4x + 8 + 5 = -10
~Combine like terms
-4x + 13 = -10
~Subtract 13 to both sides
-4x = -23
~Divide -4 to both sides
x = 23/4
Best of Luck!
what is an equivalent expression to 6(x-5)?
Answer:
6x-30
Step-by-step explanation:
you use distribution
Answer: 6x -30
Step-by-step explanation: Distribute the 6 to x and -5 to get 6x -30.
what value of x the given expression is undefined x+4/x-4
Answer:
At x= 4 the given expression is undefined.
Step-by-step explanation:
In a given function , if the denominator becomes zero then the function is undefined.
Here, denominator is x-4 so at x = 4 it will become zero. So we can say that at x=4 , the function is undefined
Solve the equation for the specified variable
S=gr-5gk*3, for g
Answer:
[tex]g = \sqrt{\frac{S}{3kr^{-5}}}[/tex]
Step-by-step explanation:
Given
[tex]S=gr^{-5}gk*3[/tex]
Required
Solve for g
[tex]S=gr^{-5}gk*3[/tex]
Split into different entities
[tex]S=g * r^{-5}*g*k*3[/tex]
Reorder in terms of like terms
[tex]S=g*g * r^{-5}*k*3[/tex]
[tex]S=g^2 * r^{-5}*k*3[/tex]
[tex]S=g^2 * 3kr^{-5}[/tex]
Solve for [tex]g^2[/tex]
[tex]g^2 = \frac{S}{3kr^{-5}}[/tex]
Take square root of both sides
[tex]g = \sqrt{\frac{S}{3kr^{-5}}}[/tex]
Which is a solution for 4x+8 = 3x + 14?
O A. 2
OB.
c. 14/3
OD. 6
O E. 7
Answer: 6
Step-by-step explanation:
4x+8=3x+14
x+8=14
x=6
The solution of the given equation will be; X = 6
We know that the equation can be defined as an expression that shows the relationship between two or more numbers and variables.
WE are given the equation as;
4x+8 = 3x + 14
Now solving for x;
4x+8 = 3x + 14
Combine the like terms here;
x+8=14
Subtract 8 from right side
x=6
The value of x will be; x = 6
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Subtract 10 from Thanh's age and double the result, and you get Xuyen's age. Xuyen is 22. How old is Thanh?
Answer:
let thanh age be x
Step-by-step explanation:
xuyen age= 22
therefore= (X-10)2=22
=2x-20=22
=2x=44
x=22
thanh age is 22
What is the value of the expression below?
x/3+6=12
Answer:
x=108
Step-by-step explanation:
x/3+6=12 [tex]\frac{x}{3+6}=12[/tex]
1) 3+6=9
2) multiply both sides by 9
9x/9=12*9 [tex]\frac{9x}{9}=12*9[/tex]
3) Simplify
9x/9=x [tex]\frac{9x}{9}=x[/tex] (9 cancels out)
12*9=108
x=108
Using this linear inequality: 10C + 4 > 2C
Explain how to solve the inequality use both English and Math Sentences in your explanation, and how complete your explanation is.
Answer:
C > –½
Step-by-step explanation:
10C + 4 > 2C
The above inequality can be solved as follow:
10C + 4 > 2C
Collect like terms
4 > 2C – 10C
4 > – 8C
Divide both side by –8
Note: the inequality sign will change since we are dividing by a negative value.
4/ –8 < –8C/ –8
– ½ < C
Thus,
C > –½
I NEED HELP ASAP. PLEASE HELP MEE!
Answer:
9,6
Step-by-step explanation:
Hopefully this helps you :)
pls mark brainlest ;)
11. You have $200 and wish to buy a computer. You find an investment that increases
by 0.6% each month, and you put your $200 into the account. When will the
account enable you to purchase a computer costing $500?
Answer:
I’m not a hundred percent it’s correct
Step-by-step explanation:
I used the online book to get the answer.
Hope this helps
Using an exponential equation, it is found that the account will enable the person to purchase the computer after 153 months.
An exponential equation of increase is modeled by:
[tex]A(n) = A(0)(1 + r)^n[/tex]
In which
A(0) is the initial value.r is the rate of increase, as a decimal.In this problem:
$200 put into the account, thus [tex]A(0) = 200[/tex].Increases 0.6% each month, thus [tex]r = 0.006[/tex].Then:
[tex]A(n) = A(0)(1 + r)^n[/tex]
[tex]A(n) = 200(1 + 0.006)^n[/tex]
[tex]A(n) = 200(1.006)^n[/tex]
You need $500 to purchase the computer, then:
[tex]A(n) = 200(1.006)^n[/tex]
[tex]500 = 200(1.006)^n[/tex]
[tex](1.006)^n = \frac{500}{200}[/tex]
[tex](1.006)^n = 2.5[/tex]
[tex]\log{(1.006)^n} = \log{2.5}[/tex]
[tex]n\log{1.006} = \log{2.5}[/tex]
[tex]n = \frac{\log{2.5}}{\log{1.006}}[/tex]
[tex]n = 153[/tex]
The account will enable you to purchase a computer after 153 months.
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1. What percent of 29 is 3?
Answer:
0.34%
Step-by-step explanation:
1. Start by representing the percentage with the variable, x %. Using x%, create an algebraic expression.
29% X x = 3
2. Solve for x by dividing both sides by 29.
29x divided by 29 =3 divided by 29.
x=0.1034
3.Convert 0.1034 into a percentage by multiplying the decimal by 100%
X =0.1034 x 100%
x=10.34%
Ms. bell has a 256 ounce bag of potting soil. what is the greatest number of 6 ounce pots she can completly fill with soil
Answer:
41 bags
Step-by-step explanation:
256 divided by 6 equals 42.6666667 but that is not a whole pot
if t(x)=-x+3, then what is f(x)=(t*t)(x)
Answer:
[tex]f(x) = {x}^{2} - 6x + 9[/tex]
Step-by-step explanation:
If f(x) = (tt)(x), that's essentially squaring t(x) so
[tex]f(x) = {t(x)}^2 \\ f(x) = (-x +3)^2 \\ f(x) = (-x +3)(-x +3) \\ f(x) = -x(-x +3) +3(-x +3)\\ f(x) = x^2 -3x -3x +9 \\ f(x) = x^2 -6x +9[/tex]
Solve inequalities 5x>2x+6
Answer:
x>2
Step-by-step explanation:
5x>2x+6 Subtract 2x from 5x
3x>6 Divide 3 by 6
x>2
Answer:
B. April
Step-by-step explanation:
In a triangle, the sum of the measures of the first two angles is 12 less than the measure of the third angle. In addition, the measure of the first angle is twice as big as the measure of the second angle. Create and solve a system of linear equations to represent this situation. Then select the true statement.
А. The solution to this system is nonviable because it results in a negative angle measure.
B. The solution to this system is nonviable because it results in too large of an angle measure.
C. The solution to this system is viable.
D. The solution to this system is nonviable because it results in fractical values for the angle measures.
the sum of the internal angles of a triangle are equal to 180 degrees.
once i remembered that the problem became a lot easier.
let a, b, and c be the angles of the triangle.
-----
let a = 2*b
-----
let c = a+b-12
-----
the above two statements are given.
since the sum of the internal angles of a triangle are equal to 180, then we have a third equation to work with which is
-----
a + b + c = 180
-----
we now have 3 equations for 3 unknowns and we should be able to solve for each of the unknowns.
-----
it looks like the easiest thing is to solve for b. once we find b, the rest should fall into place very nicely.
-----
since a = 2*b, we can substitute 2*b for a in the equation a + b + c = 180.
that equation then becomes 2*b + b + c = 180 which becomes 3*b + c = 180.
looking at the equation c = a + b - 12, we solve for b as follows:
since we know that a = 2 * b, we can substitute 2*b for a and the equation becomes c = 2*b + b - 12 which becomes c = 3*b - 12.
-----
the equation we are working with is 3*b + c = 180 which originally started as a + b + c = 180.
we can substitute 3*b - 12 for c and the equation becomes
3*b + 3*b - 12 = 180 which becomes 6*b = 192 after adding 12 to both sides and combining like terms.
dividing both sides of the equation by 6 and we get b = 32 degrees.
-----
we have b = 32 degrees.
we have a = 2 * b so a = 64 degrees.
we have c = a + b - 12 which becomes c = 32 + 64 - 12 which becomes c = 96 - 12 which becomes c = 84 degrees.
-----
substituting in the equation a + b + c = 180, we get 32 + 64 + 84 = 180 which becomes 96 + 84 = 180 which becomes 180 = 180.
-----
answer is:
a
The rule (x, y) → (-X, -y) maps A RST to A R'S'T',
Which statement correctly describes the relationship between ARST and A R'S'T'?
The triangles are congruent because AR'S'T' is a rotation of ARST, and a rotation is a rigid motion.
The triangles are congruent because AR'S'T' is a translation of ARST and a translation is a rigid
motion
The triangles are not congruent because AR'S'T' is a translation of ARST, and a translation is not a
rigid motion
The triangles are not congruent because AR'S'T' is a rotation of A RST, and a rotation is not a rigid
motion
Answer:
A
Step-by-step explanation:
These triangles are first off congruent, because the only value that is changing, is the negative sign in front.
This negative sign means that the triangle is being rotated to a different quadrant of the graph, so the answer is A.
You're making dessert, but your recipe needs adjustment. Your peanut butter cookie recipe makes 2 dozen cookies, but you need 3 dozen cookies. If the recipe requires 134 cups of sugar, 14 teaspoon of salt, and 113 cups of peanuts, how much of each of these ingredients are necessary for 3 dozen cookies? Simplify your answer.
3 dozen cookies require 201 cups of sugar, 21 teaspoon of salt, and 169.5 cups of peanuts.
EquationAn equation is an expression that is used to show the relationship between two or more variables and numbers.
2 dozen cookies require 134 cups of sugar, 14 teaspoon of salt, and 113 cups of peanuts.
Hence for 3 dozen cookies:
Amount of sugar = (134)/2 * 3 = 201
Amount of salt = (14)/2 * 3 = 21
Amount of peanuts = (113)/2 * 3 = 169.5
3 dozen cookies require 201 cups of sugar, 21 teaspoon of salt, and 169.5 cups of peanuts.
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6multiplied by 3 to the -2nd power minus 3 to the fourth power multiplied by 9 plus 4 to the 0th power
Question 1
4 pts
Three researchers studying the behavior of moose at Isle Royale National Park in Lake Superior collect the
following information about 13 moose near their research station:
• Each moose's gender.
• Each moose's height measured in inches.
• How many hours each moose spends in the water each day.
An estimate of the average total weight of food eaten per day by each moose.
Which of the following best describes the individuals and variables that are being measured?
.
The three researchers are the individuals. There is one categorical variable and four quantitative variables,
The three researchers are the individuals. There are four categorical variables and one quantitative variable.
The 13 moose are the individuals. There is one categorical variable and four quantitative variables.
The 13 moose are the individuals. There are four categorical variables and one quantitative variable.
Next
The correct answer is C. The 13 moose are the individuals. There is one categorical variable and four quantitative variables.
Explanation:
In research, the individuals refer to the participants or population that is being analyzed. For example, if the purpose of the research is to know how many hours highschool students sleep, the individuals are high school students. In this context, the individual or population of this study ae the 13 moose.
Moreover, this research focuses on different variables such as gender, height, the number of hours each moose spends in the water, the weigh of the food eaten on average by each moose, and the average weight of food eaten every day. From these variables, the last four variables are quantitative because they can be measured using numbers, for example, the height is measured in inches. On the other hand, the first variable is categorical because each moose can be classified in only two categories: male or female.
Last week, Benjamin spent $82.80 on groceries and $132.48 on bills. The amount he spent on groceries
was 15% of his paycheck. What percent of his paycheck did Benjamin spend on bills?
Answer:
amount spend on groceries = 82.80
percent spend in groceries = 15%
let total paycheck be x
15%of x= 82.80
x=552
percent spend on bills = 132.48/552 = 24%
Step-by-step explanation:
Which is the best estimate of (Negative three-fifths) (17 and StartFraction 5 over 6 EndFraction)?
Answer:
-9
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
33. Find x
7 cm
15 cm
x
Answer:
(28√11 )
_______
15
Step-by-step explanation:
Answer:
x=13.2665 cm
Step-by-step explanation:
7²+x²=15²
49+x²=225
x²=225-49
x²=176
x=√176
x=13.2665
Here is the question 20 points and brainlest but I want a detailed answer
Answer:
18.75 sq.feet
Step-by-step explanation:
According to the question
1 card = 18 sq.in
150 cards = 150 * 18
= 2700 sq.in
= 18.75 sq.feet
Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the area of land mowed in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points? It takes Aaron about 1 hour to mow 2 acres. Aaron’s rate for mowing lawns is 0.5 acres per hour. The ratio of acres to time is 5 acres to 3 hours. The rate to mow a lawn is 0.6 hours per acre.
Answer: Aaron’s rate for mowing lawns is 0.5 acres per hour
Step-by-step explanation:
Hope this helps!!
The statement "The rate to mow a lawn is 0.5 acres per hour" correctly describes the slope of the line passing through the given points.
We have,
To determine the slope of the line passing through the points (3, 1.5) and (5, 2.5), we can use the slope formula:
Slope = (change in y) / (change in x)
Given the two points, we can calculate the change in y and the change in x:
Change in y = 2.5 - 1.5 = 1
Change in x = 5 - 3 = 2
Plugging these values into the slope formula:
Slope = 1 / 2 = 0.5
The slope represents the rate of change of the y-coordinate (area) with respect to the x-coordinate (time).
In this case, a slope of 0.5 means that for every hour it takes Aaron to mow a lawn (change in x), the area mowed (change in y) increases by 0.5 acres.
Therefore,
The statement "The rate to mow a lawn is 0.5 acres per hour" correctly describes the slope of the line passing through the given points.
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