a+b = 65
b - 2a = 5
Solve one variable in terms of another:
b = 5 + 2a
Substitute in this variable:
a + 5 + 2a = 65
3a = 70
a = 23.3
Use this to find the other variable:
23.3 + b = 65
b = 41.7
Check the answer:
23.3 + 41.7 = 65
65 = 65
ANSWERS:
a = 23.3
b = 41.7
Miguel rode his bike 20 miles in 2.5 hours
Miguel rode his bike 20 miles in 2.5 hours
(1)Starting information is , In 2,5 hours Miguel traveled 20 miles
(2)Now we complete the table
In 2,5 hours distance traveled = 20 miles
So in 1 hour distance traveled = [tex]\frac{20}{2.5} =8 miles per hour[/tex]
Time 0 0.5 1 1.5 2 2.5
Distance 0 4 8 12 16 20
(3) The graph is attached below
(4) Equation y = kx
y is the distance
x is the time
Distance = k (time)
We know speed is 8 miles per hour
So k is 8
y = 8k is the final equation
(5) k is the constant of proportionality
the value of k= 8
so 8 is the constant of proportionality.
Answer:
Step-by-step explanation:
1). Miguel rode his bike 20 miles in 2.5 hours.
2). Since Miguel rode his bike with the speed = [tex]\frac{20}{2.5}=8[/tex] miles per hour
So the table will be
Time 0 0.5 1 1.5 2 2.5
Distance 0 4 8 12 16 20
3). Graph for the given equation is attached.
4). Since y = kx represents the situation then for Distance y = 4 miles in time x = 0.5 hours
4 = k(0.5)
k = [tex]\frac{4}{0.5}=8[/tex]
Therefore, equation will be y = 8x.
5). Since y = kx
⇒ k = [tex]\frac{y}{x}[/tex]
Proportionality constant k represents the speed of Migual.
Solve these equations:
1. 2(n+1)+1=(n-5)+(n-2)
2. 3(n-1)-2=4(n-4)-(n-1)
Hey there!!
First equation :
Given equation :
... 2 ( n + 1 ) + 1 = ( n - 5 ) + ( n - 2 )
Excluding the parenthesis and using the distributive property :
... 2n + 2 + 1 = n - 5 + n - 2
Combining all the like terms on each side :
... 2n + 3 = 2n - 7
Subtracting 2n and subtracting 3 on both sides :
... 0 = -10
Hence, the first equation has "zero" values.
Second equation :
Given equation :
... 3 ( n - 1 ) - 2 = 4 ( n - 4 ) - ( n - 1 )
Using the distributive property :
... 3n - 3 - 2 = 4n - 16 - n + 1
Combining all the like terms :
... 3n - 5 = 3n - 15
Adding 5 and subtracting 3n on both sides :
... 0 = -10
Hence, the second equation has "zero" values.
Hope my answer helps!!
2/3=1.2/x solve for x
First isolate x by multiplying by x on both sides. It will look like this:
(2/3)x=1.2
Then devise by (2/3) on both sides to get:
x= 1.2/(2/3)
The easiest way to get this is plug that into a calculator and get the answer:
x=1.8
Final answer:
To solve the proportion 2/3 = 1.2/x, we use cross multiplication resulting in the equation 2x = 3.6. Dividing both sides by 2 gives us x = 1.8.
Explanation:
To solve for x in the proportion 2/3 = 1.2/x, we can set up a cross multiplication. This will give us the equation 2x = 3.6 (since 2 multiplied by x equals 1.2 times 3). To find the value of x, we then divide both sides of the equation by 2, leading to x = 3.6 / 2.
Therefore, we get x = 1.8 after simplifying the division.
51 is the product of diego’s score and 3
Translate into an equation
Answer:
3d = 51 is the desired equation; its solution is d = 17.
Step-by-step explanation:
Let d represent Diego's score. Then 3d = 51, or d = 17.
"51 is the product of Diego's score and 3" is written as 51=3x. We know this because "is" means "=", and "the product of" means multiplication. Since "Diego's score" is unknown, it would be a number x (multiplied by 3 would make it 3x). The answer to this is 17, because 51/3=17. :)
5j+s=t-2 solve for t
The answer is
T= 5j+s+2
t=5j+s+2. Your answer should be: t=5j+s+2.
Let's solve for t.
5j+s=t−2
Step 1: Flip the equation.
t−2=5j+s
Step 2: Add 2 to both sides.
t−2+2=5j+s+2
t=5j+s+2
Myra multiplies 5 integers. The product is negative. AT LEAST, how many of the integers must be negative?
1, If 0 are negative the product is positive, but if 2 are negative then answer is still positive. At least 1 but could also be 1,3,5.
1, If 0 are negative the product is positive
I need help please!!
the first answer is correct
Find all whole values for y for which the double inequality is true:
-5
28
5 and 28 if wrong let me know
Help! Geometry question.
Start with congruencies of 130°:
∠1 and 130° are vertical angles
∠2 and 130° are corresponding angles
∠5 and 130° are alternate exterior angles
m∠1 = m∠2 = m∠5 = 130°
∠7 and 130° are supplementary angles (which means their sum is 180°). So, ∠7 = 50°
Next, find congruencies of ∠7:
∠3 and ∠7 are vertical angles
∠4 and ∠7 are corresponding angles
∠6 and ∠7 are alternate exterior angles
m∠3 = m∠4 = m∠6 = m∠7 = 50°
Answer: B
The graph shows the amount of money Miguel earns after working x hours
Answer:
13
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
trust
What is the justification for each step in the solution of the equation?
23x−13=2(x+2)
Select from the drop-down menus to correctly justify each step.
HEEEEELLLPPP!!!!!!
23x-13=2(x+2)
First you would distribute the 2 into the parenthesis
It will look like this after: 23x-13=2x+4
Then you would subtract 2x on both sides because u have to get the x's on one side
It will look like this after:21x-13=4
Then you would add 13 to both sides
It will look like this after: 21x=17
Then you would divide 21 on both sides
Your final product is 21/17
The solution to the equation 23x - 13 = 2(x + 2) is found by distributing, subtracting 2x, adding 13, dividing by 21, and then checking the solution.
To solve the algebraic equation 23x - 13 = 2(x + 2), let's apply algebraic methods and justify each step:
Distribute the 2 into the parentheses on the right side of the equation: 23x - 13 = 2x + 4. This step applies the distributive property a(b + c) = ab + ac.
Subtract 2x from both sides to start isolating x: 21x - 13 = 4. This maintains the balance of the equation, following the subtraction property of equality.
Add 13 to both sides in order to get terms with x on one side and constants on the other: 21x = 17. This action uses the addition property of equality.
Divide both sides by 21 to solve for x: x = 17/21. This is done using the division property of equality to isolate the variable x.
Check the solution by substituting x back into the original equation to ensure that both sides are equal.
By following these steps, we arrive at the correct solution for x and justify the use of algebraic properties that ensure the balance and equivalence of the equation throughout the process.
Timmy writes the equation f(x) = 1/4x – 1. He then doubles both of the terms on the right side to create the equation g(x) = 1/2x – 2. How does the graph of g(x) compare to the graph of f(x)? The line of g(x) is steeper and has a higher y-intercept. The line of g(x) is less steep and has a lower y-intercept. The line of g(x) is steeper and has a lower y-intercept. The line of g(x) is less steep and has a higher y-intercept.
Remark
The best way to answer something like this is to actually graph both equations. I have done that for you below.
Red Line: f(x) = 1/4x - 1
Blue Line: g(x) = 1/2x - 2
Now look at the answers.
A: The first one is incorrect. You don't need the graph to tell you that. The larger the number in front of the x, the steeper the line. Put another way, the larger the slope, the steeper the line. The y intercept is lower however.
B is wrong. g(x) is steeper, but the y intercept is lower not higher than f(x) [Negatives do strange things].
C:The g(x) is steeper (we've said that a couple of times), and it has a lower y intercept.
D is correct.
E is just wrong. Both parts are incorrect.
if (x) = 7 -x , find f(3)
f(3) means you replace x with 3.
f(x) = 7-x
f(3) = 7-3
f(3) = 4
Hey there!!
Given :
f( x ) = 7 - x
What is f(x)?
f(x) is basically the y.
The question states :
y = 7 - x
Now, find ( 3 )
This states that, I have given the value for x and find y.
y = 7 - x
y = 7 - 3
y = 4
Hence, f(3) = 4
Hope helps!
The table shows the rates at which Ajay and Tory are biking along the same trail.
Person: Rate:
Ajay: 200
Tory: 250
a. Suppose Ajay began the trail 325 meters ahead of Tory. Write a system of equations to represent the distance y each person will travel after any number of mimutes x.
Answer:
For Ajay , [tex]y=200x+325[/tex]
For Tory, [tex]y=250x[/tex]
Step-by-step explanation:
Formula to find distance = rate × time
Rate of Ajay = 200
Rate of Tory = 250
In x minutes
Distance travelled by Ajay = 200 ×x = 200x
Distance travelled by Tory = 250 ×x = 250x
But Ajay was already ahead by 350 meters.
So for Ajay, the distance y traveled in x minutes
[tex]y=200x+375[/tex]
For Tory
[tex]y=250x[/tex]
Answer:
The rates are:
Ajay : 200
Tory : 250
I assume those are in meters per minute.
Now, we suppose that Ajay began the trail 325 meters ahead, so if we put the zero in Tory position, we got:
Ajay position = 325 meters + 200*x meters
Tory position = 250*x meters
Where x is the number of minutes after they started to bike.
From this, we can compare their positions, and see in which minute x Tory position and Ajay position are the same.
325 + 200x = 250x
325 = 250x - 200x = 50x
x = 325/50 = 6.5 minutes.
So before of x = 6.5 minutes, Ajay is ahead. After x =6,5 minutes, Tory is ahead.
Mr. James deposits $450,000 at the end of each year for 10 years. What will be the value of his money at the end of 10 years at (a) 9%, (b) 10% and (c) 12%?
A. 405,000
B. 450,000
C. 540,000
What are the solutions to the equation? x2(x+2)(x+6)=0 Enter your answers in the boxes. x = or x = or x =
[tex]x^2(x+2)(x+6)=0\\\\x^2=0 \vee x+2=0 \vee x+6=0\\\\x=0 \vee x=-2 \vee x=-6[/tex]
Here we need to find the 3 solutions of the equation x^2*(x + 2)*(x + 6) = 0.
The solutions are:
x = 0, x = -2, and x = -6
Let's see how to get the solutions:
First, notice that for an equation like:
A*B*C = 0
We must have:
A = 0, or B = 0, or C = 0.
Notice that our equation x^2*(x + 2)*(x + 6) = 0 has 3 coefficients, we will get one solution by making each one of these equal to zero.
x^2 = 0
x = √0 = 0.
(x + 2) = 0
x = 0 - 2 = -2
(x + 6) = 0
x = 0 - 6 = -6
Then the 3 solutions are:
x = 0, x = -2, and x = -6
If you want to learn more, you can read:
https://brainly.com/question/14400360
The rectangle below has a total perimeter of 190 in:
rectangle with width of 4
Which of the following equations can be used to determine the length of the longer side of the rectangle?
x + 4 = 190
4x = 190
2x + 8 = 190
16x = 190
Let
x-------> the length of the rectangle
y------> the width of the rectangle
we know that
the perimeter of the rectangle is equal to
[tex]P=2x+2y[/tex]
[tex]P=190\ in[/tex]
so
[tex]2x+2y=190[/tex]------> equation A
[tex]y=4\ in[/tex] ------> equation B
substitute equation B in equation A
[tex]2x+2*4=190[/tex]
[tex]2x+8=190[/tex]
therefore
the answer is
[tex]2x+8=190[/tex]
An angle is formed by:
A. any ray and any line
B. parallel lines
C. any two rays
D. two rays that share the same endpoint
The answer is choice D) Two rays that share the same endpoint
======================================
Here's a full breakdown of the four choices
A. False. If the ray and line aren't touching, then an angle can't be formed.
B. False. Parallel lines never cross. The same issue as before (in part A) comes up.
C. False. Again the rays need to meet up somehow.
D. True. If you have two rays that share the same endpoint, then they form an angle. Think of it like a pair of scissors. Each blade is a ray. The blades are joined at a common node to allow the blades to swing open or closed. You could have an angle formed by line segments or lines, but they would have to intersect in some way.
Option D. two rays that share the same endpoint, is correct.
An angle is formed by:
A. any ray and any line
B. parallel lines
C. any two rays
D. two rays that share the same endpoint
The angle can be defined as the one line inclined over other line.
When the line as same end points and
one of the line is inclined over other by some measure called as angle.
Thus the option D two rays that share the same endpoint is correct
Learn more about Angles here:
https://brainly.com/question/13954458
#SPJ2
Combine the like terms to create an equivalent expression:
−2x − x + 8
Will Mark Brainliest!
Answer:
-3x+8
Step-by-step explanation:
-x is the same as -1x
-2x plus -x is 3x
8 stays the same
A 6.7 kg object moves with a velocity of 8 m/s . What it’s kinetic energy ?
Answer:
The Correct answer to this question for Penn Foster Students is: 214.4 J
Step-by-step explanation:
two cousin one is five years older. the sum of there age is 37. how old are they
Subtract the difference from the total, then divide by 2, that would be the age of the youngest, then add the difference to that for the age of the oldest.
37 - 5 = 32
32 / 2 = 16
The youngest is 16.
16 + 5 = 21
The oldest is 21.
The ages are 16 and 21.
7.5x+20y=900 models how many hours (x) and how many lawns mowed (y) Jon has to work in order to save $900. Give 3 combinations of hours worked and lawns mowed that result in $900.
Final answer:
The equation 7.5x + 20y = 900 can be solved for y by substituting different values for x to find three combinations that satisfy the equation: (0 hours, 45 lawns), (40 hours, 30 lawns), and (80 hours, 15 lawns).
Explanation:
The equation 7.5x + 20y = 900 models the relationship between the hours worked (x) and lawns mowed (y) for Jon to save up $900. To find combinations that result in $900, we can select different values for x or y and solve for the other variable.
Let x = 0 (no hours worked), then 7.5(0) + 20y = 900, which simplifies to 20y = 900. Dividing both sides by 20 gives us y = 45. So, one combination is (0 hours, 45 lawns).Let x = 40 (hours worked), then 7.5(40) + 20y = 900, which simplifies to 300 + 20y = 900. Subtracting 300 from both sides gives us 20y = 600, and dividing by 20 results in y = 30. Thus, another combination is (40 hours, 30 lawns).Let x = 80 (hours worked), then 7.5(80) + 20y = 900, which simplifies to 600 + 20y = 900. Subtracting 600 from both sides gives us 20y = 300, and dividing by 20 results in y = 15. Therefore, a third combination is (80 hours, 15 lawns).These three combinations represent different ways Jon can work hours and mow lawns to reach his goal of saving $900.
What is 344 to the 8th power
Two triangular pyramids are similar. The volume of the larger pyramid is 729 cm3 , and the volume of the smaller pyramid is 64 cm3. If the perimeter of the base of the smaller pyramid is 8 cm, what is the perimeter of the base of the larger pyramid? 18 cm 18 cm2 27 cm 27 cm2
Answer:
It's the first option
Step-by-step explanation:
I just answered the question on edge
The perimeter of the base of the larger pyramid is 12 cm, determined through the ratio of the volumes of the pyramids.
Explanation:The volumes of similar figures are related by the cube of the ratio of their corresponding lengths. If the larger pyramid has a volume of 729 cm³ and the smaller pyramid has a volume of 64 cm³, then the ratio of their volumes is 729/64, which is the cube of the ratio of their corresponding lengths. Taking the cube root of this ratio gives 3/2, so the lengths in the larger pyramid are 3/2 times the lengths in the smaller pyramid. Thus, if the perimeter of the base of the smaller pyramid is 8 cm, the perimeter of the base of the larger pyramid is 3/2 times this, or 12 cm.
Learn more about Pyramids here:https://brainly.com/question/13057463
#SPJ12
Frances has piano lessons every fourth day.
She has ballet lessons every fifth day.
She has soccer every second day.
On which day will she first have all three activities?
Explain how you know.
Final answer:
Frances will first have piano lessons, ballet lessons, and soccer on the 20th day as it is the least common multiple of the days she has each activity (4, 5, and 2 days respectively).
Explanation:
The student is asking about the day Frances will first have piano, ballet, and soccer activities all on the same day. This calls for finding the least common multiple (LCM) of the numbers representing the days on which she has each activity (every fourth, fifth, and second day).
Frances has piano lessons every fourth day, ballet every fifth day, and soccer every second day. To find the day when all three activities coincide, we need to calculate the LCM of 4, 5, and 2:
The multiples of 4 are 4, 8, 12, 16, 20, 24,...The multiples of 5 are 5, 10, 15, 20, 25,...The multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20,...The first common multiple they all share is 20. Therefore, Frances will first have all three activities on the 20th day.
−4 4/5 ÷ 4 A. −1 1/5 B. −4/5 C. 4/5 D. 1 1/5
Answer:
A. -1 1/5
Step-by-step explanation:
−4 4/5 ÷ 4 = -1.2
-1.2 as a fraction would be, -1 1/5
Hope this helps :-)
200 = 16(6t - 13)
t = ?
Help!
Step 1. Divide both side by 16
100/16 = 6t - 13
Step 2. Dimplify 200/16 to 25/2
25/2 = 6t - 13
Step 3. Add 13 to both sides
25/2 + 13 = 6t
Step 4. Simplify 25/2 + 13 to 51/2
51/2 = 6t
Step 5. Divide both sides by 6
51/2/6 = t
Step 6. Simplify 51/2/6 to 51/2 * 6
51/2 * 6 = t
Step 7. Simplify 2 * 6 to 12
51/12 = t
Step 8. Simplify 51/12 to 17/4
17/4 = t
Step 9. Switch sides
t = 17/4
A veterinarian needs to know an animal's weight in kilograms if 20 lb is about 9 kg in a dog weighs 30 lb use a ratio table to find the dogs weigh in kilograms explain your reasoning
Answer:
13.5 kgs.
Step-by-step explanation:
Here we have to find conversion factor of lbs into kg.
For this we use the given information.
Given that the weight of a dog is 20 lbs and also 9 kg.
Hence we have conversion factor as
20 lbs = 9 kg
Or 1 lb =9/20 = 0.45 kg.
Using this, we find the 30 lb converted into kg.
For 1 lb, equivalent kg = 0.45
Hence for 30 lbs equivalent kg= 30(0.45) = 13.5 kg.
Find the measure of z.
A. 80°
B. 83 °
C. 70 °
D. 87 °
z and 100 are on the same line so the total is 180
180-100=z
80=z
Please give Brianest
Solve the equality, - (7c-18)-2c>0