What is the solution of the equation 6x - 8 = 4x? X=
Hans the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 6 clients who did Plan A and 5 who did Plan B. On Tuesday there were 2 clients who did Plan A and 3 who did Plan B. Hans trained his Monday clients for a total of 7 hours and his Tuesday clients for a total of 3 hours. How long does each of the workout plans last?
A = hours for plan A
B = hours for plan B
Monday: 6A + 5B = 7
Tuesday: 2A + 3B = 3
use elimination by multiplying the 2nd equation by 3.
Doing that we get 3(2A + 3B = 3) = 6A + 9B = 9
So the two equations are now:
6A + 9B = 9
6A + 5B = 7
Subtract and we have 4B = 2
B = 2/4 = 1/2 of an hour
Now put 1/2 back into either equation to solve for A
6A + 5(1/2) = 7
6A + 5/2 = 7
6A = 14/2 -5/2
6A = 9/2
divide by 6 to get A = 9/12 = ¾ hours
Plan A = 3/4 hour
Plan B = 1/2 hour
Final answer:
By setting up and solving a system of equations, we find that Plan A lasts for 45 minutes per session and Plan B lasts for 30 minutes per session.
Explanation:
Solving for the Duration of Workout Plans
We have information regarding the total duration of workouts and the number of clients for two consecutive days. To find the duration of each workout plan, we use a system of equations. Let A represent the duration of Plan A and B represent the duration of Plan B. The equations based on the given information are:
6A + 5B = 420 minutes (7 hours on Monday)
2A + 3B = 180 minutes (3 hours on Tuesday)
Multiplying the second equation by 3 gives us:
6A + 9B = 540
Subtracting the first equation from this result gives us:
4B = 120 minutes, therefore, B = 30 minutes
Now we substitute B = 30 in the first equation:
6A + 150 = 420, which simplifies to 6A = 270, hence A = 45 minutes
Thus, Plan A lasts for 45 minutes and Plan B lasts for 30 minutes.
How do I solve this? (Geometry)
7x4 = 28
5 x z = 28
z = 28/5 = 5.6
How do you graph y^2=x^3?
A party rental company has chairs and tables for rent. The total cost to rent 3 chars and 2 tables is $20. The total cost to rent 8 chairs and 4 tables is $45. What is the cost to rent each chair and each table?
Equations:
8c + 4t = 45
3c + 2t = 20
Modify for elimination: ( multiply 2nd eq by -2)
8c + 4t = 45
-6c + -4t = -40
Subtract and solve for "c":
2c = 5
c = $2.50 (cost of one chair)
Solve for "t":
3c + 2t = 20
3(2.50) + 2t = 20
7.50 + 2t =20
2t=12.50
T= 12.50/2 =6.25
t = $ 6.25 (cost of one table)
Table = 6.25 each
Chair = 2.50 each
Check:
3(2.50) + 2(6.25) =
7.50 +12.50 = 20
8(2.50) + 4(6.25) =
20.00 + 25.00 = 45.00
Write | √3 - 2i | in a + bi form.
Find the value of x. If necessary, round your answer to the nearest tenth. O is the center of the circle. The figure is not drawn to scale.
A. 13
B. 26
C. 77
D. 38.5
When $n$ is divided by 10, the remainder is $a$. when $n$ is divided by 13, the remainder is $b$. what is $n$ modulo 130, in terms of $a$ and $b$?
If
N = a (mod 10)
N = b (mod 13)
gcd(10,13) = 1
then
N = 10 bx + 13 ay (mod 130)
Where
10x + 13y = 1
-> (10x + 13) (mod 2) = 1 (mod 2)
-> y (mod 2) = 1
y = -3, x = 4
-> N = 40b – 39a (mod 130)
It is given that ra + sb should be non-negative:
N = 40b – 39a (mod 130)
N = 40b + (130 – 39)a (mod 130)
N = 40b + 91a (mod 130)
Therefore, N modulo 130, in terms of a and b is: N = 40b + 91a (mod 130).
Final answer:
To find the value of n modulo 130 in terms of a and b, one must solve two congruences using the Chinese Remainder Theorem. The solution would require computations beyond the scope of this response and would result in n expressed as a linear combination of a and b modulo 130.
Explanation:
To solve for the values of n modulo 130, given that when n is divided by 10, the remainder is a, and when n is divided by 13, the remainder is b, we can express n in the following forms:
n = 10k + a, where k is some integer
n = 13l + b, where l is some integer
Since 10 and 13 are coprime, Chinese Remainder Theorem tells us that there is a unique solution for n modulo 130 that satisfies both of these congruences. To find n in terms of a and b, we must find k and l such that these two equations give the same n for a particular value of n between 0 and 129 inclusive. This can be done through careful calculations or using a method designed for solving simultaneous congruences.
Once the suitable k and l values are found, the value of n modulo 130 can be stated. Since the exact solution requires more context or computational techniques, we can't provide the specific number in this case, but the final answer will be in the form: n ≡ (something involving a and b) (mod 130).
Which expression is equivalent to r^9/r^3
Answer:
The correct option is B.
Step-by-step explanation:
The given expression is
[tex]\frac{r^9}{r^3}[/tex]
According to the property of exponent,
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
Using this property of exponent, we get
[tex]\frac{r^9}{r^3}=r^{9-3}[/tex]
[tex]\frac{r^9}{r^3}=r^{6}[/tex]
The expression [tex]r^{6}[/tex] is equivalent to the given expression.
Therefore the correct option is B.
can someone pls help me
The following is an incomplete paragraph proving that ∠WRS ≅ ∠VQT, given the information in the figure where segment UV is parallel to segment WZ.:
Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively
According to the given information, segment UV is parallel to segment WZ while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem. Because angles SQU and WRS are corresponding angles, they are congruent according to the Corresponding Angles Postulate. Finally, angle VQT is congruent to angle WRS by the _____________________.
Which Property of Equality accurately completes the proof?
Reflexive
Substitution
Subtraction
Transitive
Answer:
Transitive
Step-by-step explanation:
Just took the test
Hope it helps :)
Write an equation that can be used to find the area A of a rectangular rug whose sides are 5 feet long and x feet long
What is the measure of RST?
Answer:
∠TSR = 93°
Step-by-step explanation:
In the figure attached as we know ∠S = [tex]\frac{mQR+mPT}{2}[/tex] [ By the theorem of angles of the intersecting secants in a circle]
∠S = [tex]\frac{131+43}{2}[/tex]
= [tex]\frac{174}{2}[/tex]
= 87°
Now we have to find the measure of ∠RST
Since ∠QSR + ∠TSR = 180° [ supplementary angles]
87° + ∠TSR = 180°
∠TSR = 180 - 87 = 93°
Therefore, m∠TSR = 93° is the answer.
A baby wriggled so much that weighing him at the clinic was a problem. So the doctor held the baby and stood on a scale. Then the nurse held the baby and stood on the scale. Then the doctor held the nurse who held the baby and stood on the scale. the three results were 78 kg, 69 kg and 142 kg respectively. What was the weight of the baby.
Long question but help me out ( it was 69 kg I mean)
What is the initial value of the function represented by this graph?
A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 2 with the ordered pair 7, 5.
0
1
2
5
The initial value of a function is the value of the function when x = 0
o when x = 0, y = 2 so the initial value is 2
Answer:
2
Step-by-step explanation:
The initial value is what you start off with, so it is 2! :)
Mika wrote the table of points below. x y 0 2 3 5 6 8 Which explains whether or not Mika has described a proportional relationship, and why?
Answer:
B
Step-by-step explanation:
Edg 2020
Answer:
Step-by-step explanation: Answer B
Your job pays $8 per hour. (a) Write an algebraic expression for your pay in dollars for working h hours. (b) What is your pay if you work 36 hours?
How many cookies will Tanya have if she bakes 6batches more than the maximum number of batches in the table
Answer:
325 cookies
Step-by-step explanation: I just took the test and got it right.
Find the limit of the function algebraically. limit as x approaches negative nine of quantity x squared minus eighty one divided by quantity x plus nine.
What is the range of this set of heights in centimeters?
{140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178}
38
41
46
50
(If you can help me with this maybe you can help me with my last posted question? It hasn't been answered and I need help!)
Final answer:
The range of the given set of heights is 50 cm, which is determined by subtracting the smallest height (132 cm) from the largest height (182 cm) in the set.
Explanation:
The range of a set of numbers is the difference between the largest and the smallest numbers in the set. To find the range of the given heights in centimeters, you first identify the largest and smallest numbers in the set {140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178}. The smallest height is 132 cm, and the largest is 182 cm.
Now, subtract the smallest value from the largest value to determine the range:
Range = Largest value – Smallest value
Range = 182 cm – 132 cm
Range = 50 cm
Therefore, the range of the given set of heights is 50 cm.
Need help with this question! Will attach pic! A satellite is to be put into an elliptical orbit around a moon as shown below.The moon is a sphere with radius of 1000 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 953 km to 466 km
1 + 4 + 7 + 10 ... what is last number that makes sum go over 1 million.
the questionnnnnnnn issssssssss
Find x 58 degrees and adjacent 4.0
Evaluate the following expression using the values given:
Find 3x2 − y3 − y3 − z if x = 3, y = −2, and z = −5.
Sam picked a card from a standard deck. What is the probability that Sam picked a heart or a king?
A. 1/13
B. 16/52
C. 17/52
D. 16/53
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
Number of cards in a deck = 52
Number of heart = 13
Number of king = 4
But we know that heart contains one king too.
So, to avoid double counting we have to subtract 1 from it.
so, Number of king = 3
So, Probability that Sam picked a heart or a king is given by
[tex]\frac{13}{52}+\frac{3}{52}\\\\=\frac{16}{52}\\\\[/tex]
Hence, Option 'B' is correct.
what can 4 and 22 divided into equally the answer is smaller than 88
Plato-Match each set of conditions with the corresponding relationship between ∆ABC and ∆XYZ and the criterion (if any) that proves the relationship.
Jessica plans to purchase a car in one year at a cost of $30,000. how much should be invested in an account paying 10% compounded semiannually to have the funds needed?
Solve for z: 3z -5 +2z=25 -5z
To answer this question you will have to combine like terms.
3z-5+2z=25-5z
Combine 3z and 2z first because they have z in common and are on the same side: 3z+2z=5z
Now you have -5+5z=25-5z
Now you will go ahead and distribute since you can't combine anymore on certain sides.
You can add 5 to 25 on the other side: 25+5=30
Then add 5z to 5z on the other side: 5z+5z=10z
So now your equation should look like this: 10z=30
From here you will have to divide both sides by 10: 10/10=1(since it came to 1 it will just stay as z instead of 1z) 30/10=3
So your solution should come to: z=3