Answer:
[tex]L + 2K = 200[/tex]
Step-by-step explanation:
Given
[tex]E=1000[/tex] --- Expenditure
[tex]L=200[/tex] --- Labor
[tex]K = 100[/tex] --- Capital
Required
Determine the budget line
First, we calculate the units of labor
[tex]U_1 = \frac{E}{L}[/tex]
[tex]U_1 = \frac{1000}{200}[/tex]
[tex]U_1 = 5[/tex]
Next, the units of capital
[tex]U_2 = \frac{E}{K}[/tex]
[tex]U_2 = \frac{1000}{100}[/tex]
[tex]U_2 = 10[/tex]
The budget line equation is:
[tex]U_1 * L + U_2 * K = E[/tex]
At this point, we take L and K as variables.
So, the equation becomes
[tex]5* L + 10* K = 1000[/tex]
[tex]5 L + 10K = 1000[/tex]
Divide through by 5
[tex]L + 2K = 200[/tex] -- Budget line equation
What is the equation of the line that passes through the point (-1,-7)(−1,−7) and has a slope of 2
Answer:
y = 2x - 5
Step-by-step explanation:
Put it in point-slope form:
y + 7 = 2(x + 1)
y + 7 = 2x + 2
y = 2x - 5
You want to buy 7 tickets at that same rate. Explain the mathematical process you used to determine the cost of 7 tickets. (Include the unit rate in your explanation)
Answer:
7x
Step-by-step explanation:
To purchase 7 tickets at the same rate ;
Mathematically, Total Cost of an item is :
Cost = unit price * quantity
Here,
quantity = 7 tickets
Since price per ticket(rate) is the same ; then we can take rate as x
Hence, the cost of the 7 tickets is :
Quantity * rate
7 * x = 7x
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Answer:
Step-by-step explanation:
f(x) = |x - 3| + 2
g(x) = |x + 1| - 5
Please help will give you brainliest
Answer:
14 ft squared
Step-by-step explanation:
Area is length x width so 7 x 2 = 14.
Hope this helps :D
someone please do this for me... i will mark brainliest. all work needs to be shown. (picture shown above)
Step-by-step explanation:
just use step by step process so dum
please help thank you :)
Answer:
∠7 = 85°
Step-by-step explanation:
∠1 = 180 - 115 = 65° Because they are supplementary angles
∠2 = 180 - 65 - 85 = 30° Because the sum of all interior angles in a triangle
equals 180°
∠3 = 90° given
∠6 = 180 - 90 - 30 = 60° Because they are supplementary angles
∠4 = 180 - 155 = 25° Because they are supplementary angles
∠5 = 180 - 25 - 60 = 95° Because the sum of all interior angles in a
triangle equals 180°
∠7 = 180 - 95 = 85° Because they are supplementary angles
4x + 7 = ? (I'm not so good in math so please help)
Answer:
4(x+ 1.75)
Step-by-step explanation:
Answer: 4
i wish that helped
A shark is swimming 25 feet below the surface of the water. It goes down another 12 feet. What is the new depth the shark is swimming at?
Answer:
37 feet below the surface or -37 ft
Step-by-step explanation:
The isotope Herodium-100 decreases by half every minute, Herodium-100 is there
isotope that gives a super hero their strength. Once the amount depletes to 4 ml, a
superhero becomes tired and need to leave the fight. If Mathman has 2000mL in his
body, when will he have to rest and replenish, rounded to the nearest minute?
Answer:
After about 9 minutes.
Step-by-step explanation:
We can write an exponential function to model the decay of Herodium-100.
We are given that it decreases by half every minute.
The standard exponential function is given by:
[tex]f(m)=A(r)^m[/tex]
Where A is the initial amount, r is the rate, and m is the rate (in this case, in minutes).
Mathman initially has 2000 mL of Herodium-100. Therefore, A = 2000.
And since it decreases by half every minute, r = 1/2. Thus:
[tex]\displaystyle f(m)=2000\Big(\frac{1}{2}\Big)^m[/tex]
Mathman needs to rest when the Herodium-100 levels drop to 4 mL. Therefore, we can substitute 4 for f(m) and solve for m:
[tex]\displaystyle 4=2000\Big(\frac{1}{2}\Big)^m[/tex]
Solve for m. Divide both sides by 2000:
[tex]\displaystyle \frac{4}{2000}=\frac{1}{500}=\Big(\frac{1}{2}\Big)^m[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln\Big(\frac{1}{500}\Big)=\ln\Big(\frac{1}{2}^m\Big)[/tex]
By logarithm properties:
[tex]\displaystyle \ln\Big(\frac{1}{500}\Big)=m\ln\Big(\frac{1}{2}\Big)[/tex]
Therefore:
[tex]\displaystyle m=\frac{\ln(1/500)}{\ln(1/2)}\approx 8.9657\approx 9\text{ minutes}[/tex]
Mathman will have to rest and replenish after 9 minutes.
The sum of three consecutive even integers is 30 more than the largest
Answer:
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can someone plsss help me
Answer:
The equation for charge is = current x times
What is the coefficient of q in the sum of these two expressions?
(23q – 34) and (–16q – r)
2/3
3/4
1/2
1
Answer:
23 and - 16 are the coefficients
Step-by-step explanation:
Is r<23 true or false
Answer:
Step-by-step explanation:
True
I'm confused, I'm used to doing these problems with both coordinates :/
Answer:
{0, 1, 16, 81}
Step-by-step explanation:
If the domain of this function is the set {0, 1, 4, 9}, we find the set representing the range by evaluating the function at each of the four values in the domain.
f(0) = 0
f(1) = 1
f(4) = 16
f(9) = 81
and so the range is the set {0, 1, 16, 81}.
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Answer:
The slope represents the number of cookies sold for each dollar.
Answer: it is C
Step-by-step explanation: each point is a number boxes sold and some profit
which statement is true about the extreme value the given quadratic equation? y = -3x^2 + 12x - 33 Oa. The equation has a maximum value with a y coordinate of -27 Ob. The equation has a minimum value with a y coordinate of -21 Oc. the equation has a minimum value with a y coordinate of -27 Od. The equation has a maximum value with a y coordinate of -21
Answer:
D. The equation has a maximum value with a y coordinate of -21Step-by-step explanation:
The quadratic equation has the extreme value at vertex with x-coordinate of
x = -b/2aFor the given equation the vertex is:
x = -12/2(-3) = 2The value of y at x = 2 is:
y = -3(2²) + 12(2) - 33 = -12 + 24 - 33 = -21Since the leading coefficient is negative, the extreme is the maximum for the given equation.
Correct choice is D
What is 7/2 divided by 5/4?
HURRY UP PLZ!!
Answer:
[tex] \frac{14}{5} [/tex]
Step-by-step explanation:
1) Use this rule : a ÷ b/c = a × c/b.
[tex] \frac{7}{2} \times \frac{4}{5} [/tex]
2) Use this rule: a/b × c/d = ac/bd.
[tex] \frac{7 \times 4}{2 \times 5} [/tex]
3) Simplify 7 × 4 to 28.
[tex] \frac{28}{2 \times 5} [/tex]
4) Simplify 2 × 5 to 10.
[tex] \frac{28}{10} [/tex]
5) Simplify.
[tex] \frac{14}{5} [/tex]
Therefor, the answer is 14/5. And is decimal form it would be, 2.8.
Hi I need help please
Answer:
x = 9
Step-by-step explanation:
8x - 10 = 62
8x = 72
x = 9
In ΔSTU, the measure of ∠U=90°, ST = 67 feet, and TU = 14 feet. Find the measure of ∠T to the nearest degree.
Answer:
78
Step-by-step explanation:
Answer:
78
Step-by-step explanation:
18. State the slope and y-intercept of each linear equations.
a. 6(x + y) = 3(x - y)
b. 2(x + y) = 5(y + 1)
c. 5x + 10y - 20 = 0
Answer:
a. The slope is [tex]\frac{-1}{3}[/tex] and the y-intercept is 0
b. The slope is [tex]\frac{2}{3}[/tex] and the y-intercept is [tex]-\frac{5}{3}[/tex]
c. The slope is [tex]\frac{-1}{2}[/tex] and the y-intercept is 2
Step-by-step explanation:
The easiest way to find the slope and y-intercept is to put each equation in the slope-intercept form
That is:
y = mx = c
where m is the slope and c is the y-intercept
Part a:
6(x+y) = 3(x-y)
2(x+y) = x-y
2x + 2y = x - y
3y = -x
[tex]y = \frac{-1}{3}x[/tex]
Comparing this with the general formula, we can conclude that:
The slope is [tex]\frac{-1}{3}[/tex] and the y-intercept is 0
Part b:
2(x+y) = 5(y+1)
2x + 2y = 5y + 5
3y = 2x - 5
[tex]y = \frac{2}{3}x - \frac{5}{3}[/tex]
Comparing this with general formula, we can conclude that:
The slope is [tex]\frac{2}{3}[/tex] and the y-intercept is [tex]-\frac{5}{3}[/tex]
Part c:
5x + 10y -20 = 0
10y = -5x + 20
[tex]y = \frac{-1}{2} x+2[/tex]
Comparing this with the general formula, we can conclude that:
The slope is [tex]\frac{-1}{2}[/tex] and the y-intercept is 2
Hope this helps :)
What is the definition of a tangent in math
Answer:
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. ... The word "tangent" comes from the Latin tangere, "to touch".
Step-by-step explanation:
A straight line touching a curve at a single point without crossing it there is tangent.
Determine the approximate average rate of change in the number of tickets sold between the 3rd and 10th days after the release.
OA.
OB.
The number of tickets sold changed at an average rate of approximately -20 tickets per day.
The number of tickets sold changed at an average rate of approximately – 7 tickets per day.
The number of tickets sold changed at an average rate of approximately –10 tickets per day.
The number of tickets sold changed at an average rate of approximately –3 tickets per day.
Ос.
D.
Answer:
-3 Is the average rate
Step-by-step explanation:
The number of tickets sold changed at an average rate of approximately -20 tickets per day. The correct answer is option A.
What is the average rate of change?The average rate of change is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
The rate of change is calculated by the formula below:-
Rate of change = Final value - initial value.
From the given graph the value of tickets on the 3rd day is 100 and on the 10th day is 80. The final value of tickets is 80 and the initial value is 100.
The average rate of change in the number of tickets sold between the 3rd and 10th days after the release will be calculated as below:-
Rate of change = Final value - initial value.
Rate of change = 80 - 100
Rate of change = -20
Therefore, the number of tickets sold changed at an average rate of approximately -20 tickets per day. The correct answer is option A.
To know more about the average rate of change follow
https://brainly.com/question/8728504
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State whether or not each equation or situation represents direct variation.
give me time will think and say
Answer:
The new Yorker is a very different kind than the word
Pleaseee help! HELP NEEDED ASAP!
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Answer:
1.(that looks like letter L) Yes for congruent and no for similar 2.(circles) Yes congruent and no for similar 3. (triangles) yes similar and no for congruent 4. ( square & rectangle) yes it is similar no for congruent
Step-by-step explanation:
congruent is are the same size and shape, similar have different sizes.
Ms lebea, is a grade 10 mathematical literacy teacher at nkami high school gave learners a test out of 70 marks. She has 60 learners in her class and 35 are girls..
1.1 determine the number of boys in the classroom.
1.2 calculate the number of girls as a percentage of total learners in the classroom
1.3 what will be the ratio of girls to boys in the classroom.
1.4 calculate the actual pass mark of the test, if the pass percentage is 30% for the test
Answer:
1.2)60-35=25
therefore there are 25 boys in the class
1.2)35/60×100=58.333%
1.3)35:25
7 : 5
The sum of the two numbers is 121. The difference between the numbers is 15. What are the two numbers?
Answer:
First number = 75.5
Second number = 45.5
2) Solve the system of equations using substitution.
2x – 9y = 14
x= -6y +7
Answer:
(7,0) ---> (x = 7) and (y = 0)
Step-by-step explanation:
2x – 9y = 14
x= -6y +7 <-- (Substitute for x to above equation)
---------------------------------------------------------------------------------------------------------
2(-6y +7)– 9y = 14
-12y + 14 - 9y = 14 <-- combine like terms
-21y + 14 = 14
-14 = -14 <-- inverse operation on both sides
-21y = 0 <-- Divide
y = 0 <--- Substitute for y to get x ↓
-------------------------------------------------------------------------------------------------------
2x – 9y = 14
2x – 9(0) = 14 <-- Substituted y from above
2x = 14 <-- Divide
x = 7
ANSWER FAST ITS DUE IN AN HOURRRRRR
A family charges a trip to the zoo on a credit card. The simple interest rate is 12%. The charges are paid after 3 months. What is the total amount paid for the trip? Round your answer to the nearest hundredth.
Answer:
$180.806
Step-by-step explanation:
The computation of the total amount paid for the trip is shown below;
As we know that
Simple interest = Principal × rate of interest × time period
= (67.70 + 62.34 + 45.50) × 12% × 3 months ÷ 12 months
= 5.2662
Now the amount is
= Principal + simple interest
= 175.54 + 5.2662
= $180.806