It would take Brian 20 hours to build the model car on his own.
To determine the time it would take Brian to build the model car on his own, we can follow these steps:
1. Let's denote the time it takes John to build the model car as J hours.
2. Since it takes Brian 15 hours longer than John, we can express the time it takes Brian as J +15 hours.
3. If they work together, they can build the model car in 4 hours. This means that in 1 hour, they complete [tex]\(\frac{1}{4}\)[/tex] of the job together.
4. In 1 hour, John completes [tex]\(\frac{1}{J}\)[/tex] of the job, and Brian completes [tex]\(\frac{1}{J + 15}\)[/tex] of the job.
5. So, the equation representing the rate at which they work together is:
[tex]\[ \frac{1}{J} + \frac{1}{J + 15} = \frac{1}{4} \][/tex]
6. Now, we solve this equation to find J, the time it takes John to build the model car on his own.
7. Once we find J, we can find J+15 which represents the time it takes Brian to build the model car on his own.
So, the equation representing the rate at which they work together is:
[tex]\[ \frac{1}{J} + \frac{1}{J + 15} = \frac{1}{4} \][/tex]
To solve this equation, we can multiply both sides by the least common denominator, which is [tex]\( 4J(J + 15) \)[/tex], to clear the fractions:
[tex]\[ 4(J + 15) + 4J = J(J + 15) \][/tex]
Expanding and simplifying:
[tex]\[ 4J + 60 + 4J = J^2 + 15J \]\[ 8J + 60 = J^2 + 15J \]\[ J^2 + 15J - 8J - 60 = 0 \]\[ J^2 + 7J - 60 = 0 \][/tex]
Now, we have a quadratic equation. We can solve this equation using factoring, completing the square, or the quadratic formula. Let's use factoring:
[tex]\[ (J - 5)(J + 12) = 0 \][/tex]
Setting each factor equal to zero:
[tex]\[ J - 5 = 0 \] or \( J + 12 = 0 \)[/tex]
Solving each equation:
[tex]For \( J - 5 = 0 \), we get \( J = 5 \).For \( J + 12 = 0 \), we get \( J = -12 \).[/tex]
Since time cannot be negative, we discard the negative solution.
Now that we have found J=5 hours, which represents the time it takes John to build the model car on his own, we can find [tex]\( J + 15 = 5 + 15 = 20 \)[/tex] hours.
Use the Remainder Theorem to determine which of the following is a factor of p(x) = x 3 - 2x 2 - 5x 6.
Answer:
x-3
Step-by-step explanation:
The slope of a line running through points (2, 3) and (1, 7) is:
4.
-4.
2.
-2.
How many ways are there to select 7 countries in the united nations to serve on a council if 1 is selected from a block of 56, 3 are selected from a block of 63 and 3 are selected from the remaining 70 countries?
If a circle has a diameter of 30 meters, which expression gives its area in square meters?
A.15^2 x π
B. 30 x π
C. 30^2 x π
D. 15 x π
Answer:
A.15^2 x π (APEX)
Step-by-step explanation:
You pick 3 digits (0-9) at random without replacement, and write them in the order picked. what is the probability that you have written the first 3 digits of your phone number? assume there are no repeats of digits in your phone number.
The required probability of the numbers picked of the first three digits of the mobile number is 0.037.
Given that,
Pick 3 digits (0-9) at random without replacement, and write them in the order picked. what is the probability that you have written the first 3 digits of your phone number? assume there are no repeats of digits in your phone number is to be evaluated.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
From 0 to 9 we have 10 numbers,
For the number to be picked,
There must be no repetition,
So the number of ways to 1 pick 1st number is 10,
The number of ways to pick 2nd number is 9
The number of ways to pick 3rd number is 8
Total number of ways = 10 + 9 + 8 = 27
Now probability, that this three-digit would be a mobile number,
= 1 / 27
= 0.037
Thus, the required probability of the numbers picked of the first three digits of the mobile number is 0.037.
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What is the approximate difference in the amount of wax needed to make a candle from each of these molds? use π = 3.14. 16.75 cubic inches 20.93 cubic inches 24.25 cubic inches 33.49 cubic inches?
what is the question ?????
What is the approximate difference in the amount of wax needed to make a candle from each of these molds? use π = 3.14. 16.75 cubic inches 20.93 cubic inches 24.25 cubic inches 33.49 cubic inches? what are we taking the diffference from
Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim t → −2 t4 − 3 2t2 − 3t + 3
Final answer:
To evaluate the limit of the given function, substitute the value that t is approaching into the expression. In this case, t is approaching -2. Plugging -2 into the function, we get 0.7647.
Explanation:
To evaluate the limit of the given function, we can substitute the value that t is approaching into the expression. In this case, t is approaching -2. Plugging -2 into the function, we get:
lim t → -2 t^4 - 3 / 2t^2 - 3t + 3 = (-2)^4 - 3 / 2(-2)^2 - 3(-2) + 3 = 16 - 3 / 8 + 6 + 3 = 13 / 17 = 0.7647
Therefore, the limit is approximately 0.7647.
The coordinates of quadrilateral FGHJ are F(-5, -3), G(-3, 3), H(3, 5), and J(7, -1).
Find the midpoint of FJ
A) (0,4)
B) (1, -2)
C) (-4, 0)
D) (5, 2)
This is a question from my math chapter 20: Figures in the Coordinate Plane
i think that is C i had that one but i forget
hope that help
BMK
Answer:
B. [tex](1,-2)[/tex]
Step-by-step explanation:
We have been given that coordinates of quadrilateral FGHJ are F(-5, -3), G(-3, 3), H(3, 5), and J(7, -1). We are asked to find the coordinates of mid-point of segment FJ.
We will use mid-point formula to solve our given problem.
[tex]\text{Mid-point}=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}[/tex]
Upon substituting the coordinates of points F and J in mid-point formula we will get,
[tex]\text{Mid-point}=\frac{-5+7}{2},\frac{-3+-1}{2}[/tex]
[tex]\text{Mid-point}=\frac{2}{2},\frac{-4}{2}[/tex]
[tex]\text{Mid-point}=1,-2[/tex]
Therefore, the coordinates of mid-point of segment FJ are [tex](1,-2)[/tex] and option B is the correct choice.
You need to buy 5 notebooks for your classes at school. Each notebook costs $2.79. What is the total costs of 5 notebooks Before tax?
multiply 2.79 x 5
2.79*5 = 13.95 before tax
Jordan is cutting a 2 meter by 1 1/4 meter piece of rectangular paper into two pieces along its diagonal. what is the area of each of the pieces?
area = 1/2 * b * h=
1/2 * 2 * 1 1/4 = 1 1/4 square meters each
Answer: area = 1/2 * b * h=
1/2 * 2 * 1 1/4 = 1 1/4 square meters each
use any method to solve the equation. If necessary, round to the nearest hundredth. 11x^2=8
Answer:
x = + 0.85 , -0.85
Step-by-step explanation:
Given : 11x² = 8.
To find : use any method to solve the equation. If necessary, round to the nearest hundredth.
Solution : We have given that : 11x² = 8.
First we divide both sides by 11,
x² = [tex]\frac{8}{11}[/tex].
Now taking square root both sides .
x = [tex]\sqrt{\frac{8}{11}}[/tex].
x =± 0.8528.
Therefore, x = + 0.85 , -0.85
Simplify the expression
Which is the equation of the trend line that can be generated by using the data from year 1 and 5?
For those looking for the letter the answer is C
Your welcome :)
What is the point-slope equation of a line with slope -4 that contains the point (-2, 7)?
A. y + 7 = -4(x + 2)
B. y + 7 = -4(x - 2)
C. y - 7 = -4(x - 2)
D. y - 7 = -4(x + 2)
Two pools are being filled with water. To start, the first pool contains 922 liters of water and the second pool contains 1300 liters of water. Water is being added to the first pool at a rate of 33.75 liters per minute. Water is being added to the second pool at a rate of 20.25 liters per minute.
After how many minutes will the two pools have the same amount of water?
How much water will be in each pool when they have the same amount?
After 28 minutes, both pools will have the same amount of water, which will be 1653 liters in each pool.
Explanation:To find out after how many minutes the two pools will have the same amount of water, we can set up an equation where the volume of water in the first pool plus the water added over time equals the volume of water in the second pool plus the water added to it over the same period.
Let x represent the number of minutes after which both pools will have the same amount of water. The equation can be expressed as:
922 + 33.75x = 1300 + 20.25x
To solve for x, we subtract 20.25x from both sides:
922 + 13.5x = 1300
Now, subtract 922 from both sides to isolate the term with x:
13.5x = 378
Divide both sides by 13.5 to solve for x:
x = 28
So, it will take 28 minutes for both pools to have the same amount of water.
To calculate how much water will be in each pool at that time, we can multiply the rate by the number of minutes and add the initial amount of water for either pool:
For the first pool: 922 + (33.75 * 28) = 1653 liters
For the second pool: 1300 + (20.25 * 28) = 1653 liters
Therefore, after 28 minutes, each pool will contain 1653 liters of water.
what is x
3x = 0.5x2
At the movie theatre, child admission is $6.20 and adult admission is $9.80 . On Monday, twice as many adult tickets as child tickets were sold, for a total sales of $593.40 . How many child tickets were sold that day?
The drawing below is an example of what kind of perspective?
One-point
Two-point
Three-point
Four-point
Five-point
Answer:
Two-point
Step-by-step explanation:
"Orthogonal" lines intersect the horizon at two points. This is an example of 2-point perspective.
Melinda has 1 seashell, and Jun has 9 seashells. If Melinda and Jun put their seashells together and then divide them up equally, how many will each one of them have? 3 5 8 10
Answer:
B.) 5
Step-by-step explanation:
Just did this :3
The formula F=9/5(K−273.15)+32
converts a temperature from kelvin K to degrees Fahrenheit F
a. Solve the formula for K
The formula for K in terms of F is [tex]K = \frac{5}{9} (F - 32) + 273.15[/tex]
The given expression:
[tex]F = \frac{9}{5} (K - 273.15) + 32[/tex]
To find:
the formula for KThe formula for K is obtained by making K the subject of the formula as shown below;
[tex]F = \frac{9}{5} (K - 273.15) + 32\\\\subtract \ 32 \ from \ both \ sides \ of \ the \ equation\\\\F - 32 = \frac{9}{5} (K - 273.15)\\\\multiply \ both\ sides \ by \ 5\\\\5(F - 32) = 9(K - 273.15)\\\\divide \ both\ sides \ by \ 9\\\\\frac{5}{9} (F - 32) = K - 273.15\\\\add \ 273.15 \ to \ both\ sides \ of \ the \ equation\\\\\frac{5}{9} (F - 32) + 273.15 = K\\\\[/tex]
Thus, the formula for K in terms of F is [tex]K = \frac{5}{9} (F - 32) + 273.15[/tex]
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If 3 consecutive integers sum to 63, the largest of the 3 = ?
This problem states that the sum of 3 consecutive integers is 63 and it asks us to find the largest integer.
Three consecutive integers can be represented as followed.
X → first integer
X + 1 → second integer
X + 2 → third integer
Since the sum of our three consecutive integers is 24, we can write an equation.
X + X + 1 + X + 2 = 63
We can simplify our equation on the left and it will read...
3x + 3 = 63 -3 -33x = 60 ÷3 ÷3 ← divide both sides by 3X = 20Largest integer = X + 220 + 2 = 22Largest integer = 22Simplify 1/x-10 divided by 9x/x^2-9x-10
Answer:(x+1)/9x
Step-by-step explanation: Hope this helps
Lou has 3 over 4 of an hour to do his math homework, play video games and help with dinner. If he splits his time equally between the three activities, how much time will he spend on each?
_____ of an hour
3/4 divided by 3
3/4 *1/3 = 3/12 = 1/4
NEED ASAP
Which linear inequality is represented by the graph?
y ≤ 1/3x − 1
y ≥ 1/3x − 1
y < 3x − 1
y > 3x − 1
Answer:
[tex]y\geq \frac{1}{3}x -1[/tex]
Step-by-step explanation:
To find linear inequality, first we find the equation of the line.
LEts pick two points (3,0) and (0,-1)
To get equation of a line [tex]y=mx+b[/tex], use slope formula to find slope m
[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{0+1}{3-0} =\frac{1}{3}[/tex]
y intercept is (0,-1) . so b=-1
The equation of the line becomes
[tex]y=\frac{1}{3}x -1[/tex]
now we look at the shaded region.
the graph is shaded at the top and also we have solid line . so we use >= symbol
[tex]y\geq \frac{1}{3}x -1[/tex]
If tan theta = -4/3 in quadrant II, what is cos theta?
A. -4/5
B. 3/5
C. 4/5
D. -3/5
Answer:
The answer is:
D. -3/5
He measures of the angles of a triangle are in the extended ratio 4 : 5 : 6. what is the measure of the smallest angle?
How do you do this problem?
What are the roots of the equation y=x^2 -5x-24
If i want to be a real boy whats the equation?
Answer: 15²=225
225-(7.5²•3.14)=48.375 or to the nearest form 48.38.
Step-by-step explanation: In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equals sign "=".
Raina wants to paint the ceiling of her restaurant. The ceiling is in the shape of a square. Its side lengths are 55 feet. Suppose each can of paint will cover 275 square feet. How many cans will she need to paint the ceiling?
area of the ceiling = 55 x 55 = 3025 square feet
3025/275 = 11 cans