solve the equation for x.
ax+bx=c
Answers
abx = c
abx/ab = c/ab
x = c/ab
Answer: x = c/a + b
Step-by-step explanation: I have put the variable x in purple in the image that I have made so you can see it better.
Notice that the variable we are solving for in
this problem appears in 2 separate terms.
In this situation, we must factor the x out
of both terms to get x(a + b) = c.
Think about it as the reverse of the distributive property.
In other words, if we take our second step and distribute the x
through the parentheses, we end up back at our first step.
The beauty of factoring is that the two x's in this problem
have now been combined into one x and we can get x
by itself by dividing both sides by a + b.
This gives us x = c/a + b.
Related Questions
Miranda buys 6 pounds of nuts. if she puts 3/4 pound in each bag, how many bags can she make?
Answers
B = 6 ÷ 3/4
B = 6 • 4/3
B = 24/3
B = 8
Answer:
Number of bags Miranda makes equals:
8
Step-by-step explanation:
Miranda buys 6 pounds of nuts.
She puts 3/4 pound in each bag
Let she makes x bags
then total nuts in x bags=[tex]\dfrac{3}{4}x[/tex]
also total nuts must be equal to 6
i.e. [tex]\dfrac{3}{4}x=6[/tex]
Multiplying both sides by 4, we get
3x=24
Dividing both sides by 3, we get
x=8
Hence, number of bags Miranda makes equals:
8
When using a multiplicative power function (y = a x1b1 x2b2 x3b3) to represent an economic relationship, estimates of the parameters (a, and the b's) using linear regression analysis can be obtained by first applying a ____ transformation to convert the function to a linear relationship?
Answers
Alex has 48 stickers. This is 6 times the number of stickers max has. How many many stickers does max have?
Answers
48÷6=8
You can check yourself to make sure you're correct by multiplying 6•8 which equals 48.
What is the equation of this line in standard form? −6x+11y=13 −6x+7y=−17 −6x+11y=−13 −11x+6y=−13 Number graph that ranges from negative five to five on the x and y axes. A line passes through the labeled points begin ordered pair negative four comma negative one end ordered pair and begin ordered pair one and begin fraction one-half end fraction comma, two end ordered pair
Answers
A ( - 4. - 1 )
B ( 1 1/2, 2 )
The point-slope form:
y = m x + b
m = ( 2-(-1)) / (3/2-(- 4)) = ( 2 + 1 ) / 3/2 + 4 ) = 3 / 11/2 = 6 / 11
2 = 6/11 * 3/2 + b
2 = 9/11 + b
b = 2 - 9/11 = 22/11 - 9/11 = 13/11
The equation in the slope-intercept form is:
y = 6/11 x + 13/11 / * 11 ( we will multiply both sides by 11 )
11 y = 6 x + 13
Answer :
A ) - 6 x + 11 y = 13
6 x - 1 1 y = - 1 3
Identify the slope and y-intercept of the graph of the equation. y = 1/4x + 3
A slope: 1/4 ; y-intercept: 3
B slope: 1/4; y-intercept: –3
C slope: 4; y-intercept: 3
D slope: 4 ; y-intercept: –3
Answers
Fun.
So the equation: y = 1/4x = 3 is in slope-intercept form where, y = mx + b.
'm' is the slope and 'b' is the y-intercept.
Knowing this, we can easily conclude that Choice A is the correct answer.
Why?
Well, just look below.
y=1/4x + 3
y = mx + b
We simply match up the values with the slope-intercept formula and see that 3 falls under the y-intercept category, and m, which always equals slope is replaced by 1/4.
Thus, A is the correct choice.
Final answer:
The slope of the equation y = 1/4x + 3 is 1/4 and the y-intercept is 3, corresponding to option A: slope: 1/4 ; y-intercept: 3.
Explanation:
To identify the slope and y-intercept of the equation y = 1/4x + 3, we can compare it to the general form of the slope-intercept equation for a line, which is y = mx + b. In this form, m represents the slope of the line, and b represents the y-intercept of the line. Thus, looking at the given equation, the coefficient of x (which is 1/4) is the slope, and the constant term (which is 3) is the y-intercept.
The correct answer is:
Slope: 1/4Y-intercept: 3Therefore, the answer is option A: slope: 1/4 ; y-intercept: 3
Cheryl Falkowski has a collection of silver spoons from all over the world. She finds that she can arrange her spoons in sets of 7 with 1 left over, sets of 8 with 7 left over, or sets of 15 with 3 left over. If Cheryl has fewer than 200 spoons, how many are there?
Answers
let N=total number of spoons so
N mod7 1 ---->7a+1=n where a is a natural num
N mod 8 7---->8b+7=n where b is a natural num
N mod 15 3----->15c+3=n where c is a natural n
for the first set {8,15,22,29,36,43,50,57,65,71....}
for the second set {15,23,31,39,47,55,63,71,79..}
for the third set {18,33,48,63,78,....}
and find them manually but what is easier is to solve them using algebra and logic (college level)
N=840m+183 where m is zero or a postive integer
so the only N below 200 is 183
let us check
183/7=26 R 1
183/8=22 R 7
183/15=12 R 3
which means our soultion is correct
63 satisfies all three congruences and is less than 200, Cheryl has 63 silver spoons.
The number of spoons Cheryl has can be represented by the following system of congruences:
1. [tex]\( n \equiv 1 \mod 7 \)[/tex]
2. [tex]\( n \equiv 7 \mod 8 \)[/tex]
3. [tex]\( n \equiv 3 \mod 15 \)[/tex]
Additionally, we know that [tex]\( n < 200 \).[/tex]
To solve this system, we can start by examining each congruence:
1. For the first congruence, [tex]\( n \equiv 1 \mod 7 \)[/tex], the possible values of ( n ) are [tex]\( 1, 8, 15, 22, \ldots \)[/tex]
2. For the second congruence, [tex]\( n \equiv 7 \mod 8 \)[/tex], the possible values of ( n ) are [tex]\( 7, 15, 23, 31, \ldots \)[/tex]
3. For the third congruence, [tex]\( n \equiv 3 \mod 15 \)[/tex], the possible values of ( n ) are [tex]\( 3, 18, 33, 48, \ldots \)[/tex]
Now, we need to find a number ( n ) that satisfies all three congruences and is less than 200.
[tex]\( 63 \equiv 1 \mod 7 \)[/tex] (satisfies the first congruence)
[tex]\( 63 \equiv 7 \mod 8 \)[/tex] (satisfies the second congruence)
Since 63 satisfies all three congruences and is less than 200, Cheryl has 63 silver spoons.
Therefore, the final answer is [tex]\(\boxed{63}\).[/tex]"
According to modern science, Earth is about 4.5 billion years old and written human history extends back about 10,000 years. Suppose the entire history of Earth is represented with a 100-meter-long timeline, with the birth of Earth on one end and today at the other end. a. What distance represents 11 billion years? b. How far from the end of the timeline does written human history begin?
Answers
Answer:
A- The distance that represents 11 billion years is 244.4 meters.
B- Written human history begins 0.2 milimeters far from the end of the timeline.
Step-by-step explanation:
A- We can solve this problem by using crossed multiplication.
4,5 billion years --- 100 meters
11 billion years --- X
11 x 100 / 4,5 = X
X= 244.4
B- Once again, this can be solved using crossed multiplication.
If 4,500,000,000 years are represented in 100 meters, that would be:
4,500,000,000 --- 100 meters
10,000 --- X
10,000 x 100 / 4,500,000,000 = X
X= 0.0002 meters
0.0002 meters are 0.2 milimeters
Write v as a linear combination of u and w, if possible, where u = (2, 2) and
w = (2, −3).
(Enter your answer in terms of u and w. If not possible, enter IMPOSSIBLE.)
v = (4, −1)
Answers
The vector v = (4, -1) can be written as a linear combination of the vectors u = (2, 2) and w = (2, -3). The coefficients are both 1, which means that v = u + w.
Explanation:In this problem, we are trying to express the vector v = (4, -1) as a linear combination of the vectors u = (2, 2) and w = (2, -3). A linear combination means that we want to find coefficients a and b such that a*u + b*w = v.
Setting that equation up, we have:
a(2, 2) + b(2, -3) = (4, -1).
This leads to two equations:
2a + 2b = 4 and 2a - 3b = -1.
After solving this system of equations, we find that a = 1 and b = 1. Therefore, the vector v can be written as a linear combination of u and w as v = u + w.
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V can be written as v=u+w.
To express v as a linear combination of u and w, we need to find scalars a and b such that:
v = a * u + b * w
Given: u = (2, 2), w = (2, -3), and v = (4, -1)
We can set up the following system of equations based on the components:
2a + 2b = 4 (Equation 1 from x-components)
2a - 3b = -1 (Equation 2 from y-components)
Solving Equation 1 for 'a':
2a + 2b = 4
a + b = 2
a = 2 - b
Substituting 'a' in Equation 2:
2(2 - b) - 3b = -1
4 - 2b - 3b = -1
4 - 5b = -1
-5b = -5
b = 1
Substituting 'b' back into a = 2 - b:
a = 2 - 1
a = 1
Thus, v can be written as:
v = 1 * u + 1 * w
So, v = u + w
Paula completely covered a square wall using 87.5 ft2. Which is the side length of the wall?
Answers
Area is 87.5 ft^2.
Take the square root of 87.5; each wall side is going to be the same length since it's a square. Since each side is the same length, it means one wall x another wall will give you the area.
This is the answer you get: 9.35414346693.
Round the number to make it look a little prettier: 9.354.
When you multiply 9.354 x 9.354, you get 87.497316.
Round the number again to make it look a little prettier: 87.5
Hope this helps. :)
Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2 h, and Car B traveled the distance in 1.5 h. Car B traveled 15 mph faster than Car A. How fast did Car B travel? (The formula R⋅T=D , where R is the rate of speed, T is the time, and D is the distance can be used.) Enter your answer for the box.
Answers
notice, the distance are the same, say it was "d" miles.
and if car A is travelling at a speed of say "r" mph, then B is going at "r+15" mph.
[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{Car A}&d&r&2\\ \textit{Car B}&d&r+15&1.5 \end{array} \\\\\\ \begin{cases} \boxed{d}=2r\\ d=1.5(r+15)\\ ----------\\ \boxed{2r}=1.5(r+15) \end{cases} \\\\\\ 2r=1.5r+22.5\implies 0.5r=22.5\implies r=\cfrac{22.5}{0.5}\implies \boxed{r=\stackrel{mph}{45}}[/tex]
how far is B going? well, r + 15.
A newspaper writers compensation package includes the total cost of a $150 per month health insurance plan the total cost of a $55 per month life insurance plan and a salary of 45,000 per year what would the yearly value of the compensation package be
Answers
55 x 12 = 660
1800 + 660 + 45000 = 47,460
Answer:
The answer is: $ 47,460.
Step-by-step explanation:
$ 150 x 12 month health insurance plan = 1800 $
$ 55 x 12 month life insurance plan = $ 660
With an annual salary of $ 45,000 + Health Insurance $ 1800 + Life insurance $ 660 = $ 47460
The answer is: $ 47,460.
Geometry.
What is the equation of the circle with the given graph?
A) (x - 3)² + (y + 2)² = 3
B) (x + 3)² + (y - 2)² = 9
C) (x - 3)² + (y + 2)² = 9
D) (x +3)² + (y - 2)² = 3
Answers
[tex] (x - h)^{2} + (y - k)^{2} = r^{2} [/tex]
In this case, the center of the circle is (-3, 2), and the radius is 3.
You have h = -3, k = 2, r = 3
[tex] (x- (-3))^{2} + (y - 2)^{2} = 3^{2} [/tex]
Simplifying, you get
[tex] (x + 3)^{2} + (y - 2)^{2} = 9 [/tex]
Which property should be used next in this solution process?
3x+2+3=7(x−1)−4
3x+5=7(x−1)−4
Answers
What is the slope of a line that is parallel to the line shown on the graph?
A.–3
B.-1/3
C.1/3
D. 3
Answers
The slope of a line that is parallel to the line shown on the graph is -3.
What is slope of a line?
The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.
For the given situation,
The slope of a line from its graph by looking at the rise and run.
The vertical change between two points is called the rise, and the horizontal change is called the run.
One characteristic of a line is that its slope is constant all the way along it. So, you can choose any 2 points along the graph of the line to figure out the slope.
Now take points (0,2) and (1,-1)
[tex]Slope = \frac{rise}{run}[/tex]
Line slants down from left to right. So line has a negative slope.
⇒ [tex]Slope =\frac{y2-y1}{x2-x1}[/tex]
⇒ [tex]Slope =\frac{-1-2}{1-0}[/tex]
⇒ [tex]Slope = -3[/tex]
The slope of the line that is parallel to the given line is same as that of the line.
Hence we can conclude that the slope of a line that is parallel to the line shown on the graph is -3.
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A rocket on a computer screen has a path modeled by the equation h=-t2+3t+10 where t is time in seconds and h is the height above a platform and is in computer units. Find how long the rocket takes to reach the platform.
Answers
what is the value of (2³)²
Answers
8 x 8 = 64. The answer would be 64
solve for g: 4gh+3=-8
Answers
Final answer:
To solve for g in the equation 4gh+3=-8 with H=-1, we substitute H and solve for g, resulting in g=11/4.
Explanation:
The question asks to solve for g in the equation 4gh + 3 = -8. To do this, we need to isolate g on one side of the equation. Given that H = -1, we can substitute this value into the equation, which simplifies to 4g(-1) + 3 = -8. This further simplifies to -4g + 3 = -8. Solving for g, we subtract 3 from both sides to get -4g = -11, and then divide both sides by -4 to get g = 11/4. Therefore, the solution is g = 11/4.
Banks and other financial institutions sometimes calculate simple interest based on
Answers
stan, a local delivery, is paid 3.50 per mile driven plus a daily amount of $75. on Monday, he is a signed a route that is 30 miles long. how much is he being paid for that day.
Answers
when he drives 30 miles.....so sub in 30 for m
y = 3.5(30) + 75
y = 105 + 75
y = 180 <== Stan is getting paid $ 180 for the day
How many ways can a person with five nickels, three dimes, and two quarters make a 75-cent purchase from the machine?
Answers
Amy runs 6 miles in 45 minutes. At the same rate, how many minutes would she take to run 4 miles?
Answers
You could also find her rate: 6 miles / 45 minutes, or 8 miles / 60 minutes.
Write an equation of ratios:
8 mi 4 mi
---------- = ------------
60 min x
Solving for x: 8x = 240; x = 30 minutes
When the consumer price index decreases from 200 to 150, prices decrease by 50%.
A. True
B. False
Answers
Answer:
Apex answer: FALSE
Step-by-step explanation:
Final answer:
The consumer price index decreasing from 200 to 150 represents a 25% decrease, not 50% as incorrectly stated.
Explanation:
The statement that prices decrease by 50% when the consumer price index (CPI) decreases from 200 to 150 is false. To calculate the percentage decrease in CPI, we use the formula for percentage change: ((new value - original value) / original value) × 100. In this case, ((150 - 200) / 200) × 100 = (-50 / 200) × 100 = -25%. This shows that there is a 25% decrease in the CPI, not 50%.
The correct calculation reveals that the decrease in the Consumer Price Index (CPI) is 25%, not 50%.
Understanding the accurate interpretation of percentage changes is crucial for assessing economic indicators and making informed decisions.
WILL GIVE BRAINEST
These tables of value represent continuous functions. In which table do the values represent an exponential function?
Answers
Answer:
The correct option is B.
Step-by-step explanation:
In table A, the function has constant rate of change. For each value of x, the value of y increased by 8.
Since the rate of change of a linear function is constant, therefore table A represents a linear function.
In table B, for each value of x, the value of y is twice of its previous value. In other words we can say that the value of y increases in the same proportion.
[tex]\frac{y_2}{y_1}=\frac{8}{2}=2[/tex]
[tex]\frac{y_3}{y_2}=\frac{16}{8}=2[/tex]
[tex]\frac{y_4}{y_3}=\frac{32}{16}=2[/tex]
[tex]\frac{y_5}{y_4}=\frac{64}{32}=2[/tex]
Therefore it is an exponential function with growth factor 2.
[tex]f(x)=a(2)^x[/tex]
The function passing through the point (1,4).
[tex]4=a(2)^1[/tex]
[tex]2=a[/tex]
The exponential function is
[tex]f(x)=2(2)^x[/tex]
Thus, option B is correct.
In table C, the function has constant rate of change. For each value of x, the value of y increased by 5.
Since the rate of change of a linear function is constant, therefore table C represents a linear function.
In table D, the function has constant rate of change. For each value of x, the value of y increased by 1.
Since the rate of change of a linear function is constant, therefore table D represents a linear function.
In 33,294 how is the value of the 3 in the ten thousands place related to the value of the 3 in the thousands place ?
Answers
Answer:
The value of the 3 in the ten thousands place is 10 times the value of the 3 in the thousands place.
Step-by-step explanation:
Let's see the value of each algarism in this number.
33294.
4 is the unit. So the value of the 4 in this number is [tex]4 \times 10^{0}[/tex]
9 is the tenth. So the value of the 9 in this number is [tex]9 \times 10^{1} = 90[/tex]
2 is the centh. So the value of the 2 in this number is [tex]2 \times 10^{2} = 200[/tex]
3 is the thousanth. So the value of the second 3(from the start to the end) in this number is [tex]3 \times 10^{3} = 3000[/tex]
3 is also the ten thousanths. So the value of the first 3 is this number is [tex]3 \times 10^{4} = 30000[/tex]
So
[tex]33294 = 30000 + 3000 + 200 + 90 + 4[/tex]
how is the value of the 3 in the ten thousands place related to the value of the 3 in the thousands place ?
[tex]\frac{3 \times 10^{4}}{3 \times 10^{3}} = 10[/tex]
The value of the 3 in the ten thousands place is 10 times the value of the 3 in the thousands place.
Katie earned $1200 in 8 years on an investment at a 6% annual simple interest rate. How much was Katie’s investment?
$945
$2500
$4500
$9000
Answers
Time = 8 yer a
Rate = 6% = 0.06
Interest earned = $1200
Simple Interest
Let P = the principal (the investment)
Then
P*8*0.06 = 1200
0.48P = 1200
P = 1200/0.48 = $2500
Answer: $2500
The container that holds the water for the football team is 1/3 full. After pouring out 6 gallons of water it is 1/9 full. How many gallons can the container hold?
Answers
The container cannot hold a specific number of gallons.
Explanation:To solve this problem, we can use a proportion. Let's assume that the number of gallons the container can hold is According to the problem, the container is initially 1/3 full, so we can write this as 1/3 of After pouring out 6 gallons of water, it becomes 1/9 full, which we can write as 1/9 of Setting up the proportion, we have:
1/3 of = 1/9 of
To solve for we can cross multiply:
9 * (1/3) * = 1 * (1/9) *
Canceling out the variables and multiplying, we have:
3= /9
Multiplying both sides by 9, we get:
27=
Dividing both sides by , we have:
27 = 1
Since the equation is not true, we have a contradiction. This means there is no solution, or the container cannot hold a specific number of gallons.
Final answer:
The total capacity of the football team's water container is 27 gallons. We determine this by comparing the change in water level from being 1/3 full to 1/9 full after removing 6 gallons and calculating proportionally.
Explanation:
To solve the problem regarding the water container for the football team, we need to find out the total capacity of the container. When 6 gallons of water is poured out, it results in the container being 1/9 full rather than 1/3, which means the removal of 6 gallons of water equates to 1/3 - 1/9 of the container's capacity.
First, let's find the common denominator for 1/3 and 1/9 which is 9. So the difference in the water level when the 6 gallons were removed is (3/9 - 1/9) or 2/9 of the container's capacity. This tells us that 2/9 of the container's capacity is equal to 6 gallons.
Step-by-Step Calculation
Set up the proportion: 2/9 = 6 gallons.
To find the full capacity, we solve for 9/9 (which is the whole): (9/9) / (2/9) = X / 6 gallons.
Cross multiply to solve for X: 2X = 54.
Divide both sides by 2: X = 27.
Therefore, the total capacity of the water container is 27 gallons.
Curtis is packing to move. He finds 23 photo albums in the attic and 45 albums in a closet. If he divides them equally among 4 boxes, how many albums will he put in each box?
Answers
Answer:
68 divide by 4
Step-by-step explanation:
John is running in a race.The race is 25 miles long. After two hours,John has run 7 miles.How many miles does John have left to run?
Answers
25 - 7 = 18
So he needs to run 18 more miles.
What is cultural imperialism?
the impact of a nation’s culture on its trade policies
the imposition of a foreign culture on a nation’s population
the impact of culture on people’s buying and spending habits
the spread of foreign culture through immigrants from various nations
Answers
Answer:
The correct answer is : B) the imposition of a foreign culture on a nation's population.
Step-by-step explanation:
Cultural imperialism shows the cultural aspects of imperialism that is a culture being imposed on other countries.
And imperialism can be defined as maintaining the unequal relationships between civilizations.
So, the correct answer is : B) the imposition of a foreign culture on a nation's population.
Planet Strusenope travels one full rotation around its sun in approximately 365.25 days. How many minutes does it take for Strusenope to travel one full rotation around the sun?
Answers
The time is equal to
[tex](365.25 \, days)*(1440 \, \frac{min}{day} ) = 525960 \, min[/tex]
Answer: 525,960 minutes