What system of linear inequalities is shown in the graph?
Enter your answers in the boxes.
(graph is in picture)
Answers
We know that, since it is a dotted line, it is an inequality (< or >, rather than ≤ or ≥). We also see that the area under this line is shaded, so it is a less-than inequality:
y < mx + b, where m is the slope and b is the y-intercept.
The slope is -3, since the line moves down 3 and over 1
The y-intercept is 1
y < -3x + 1
For the second graph, we apply the same steps:
y ≥ mx + b
m = 1/2 (up one, over 2), b = -1
y ≥ (1/2)x -1
System of inequalities:
y < -3x + 1
y ≥ (1/2)x -1
Related Questions
A line has a slope of between the points (10,5) and (16,n).
What is the value of n?
8
2
10
16
6
Answers
Any way, I can show you how to calculate the answer given a generic value of the slope.
Assuming that the slope values m, you can use the formula:
m = rise / run = change in y / change in x
=> m = (n - 5) / (16 - 10)
=> n - 5 = m (16 - 10)
=> n - 5 = 6m
=> n = 6m + 5
Now I am going to calculate the value of n for several values of the slope (m):
m n = 6m + 5 answer
1/2 n = 6(0.5) + 5 = 8 the first option
-1/2 n = 6(-0.5) + 5 = 2 the second option
5/6 n = 6(5/6) + 5 = 10 the third option
11/6 n=6(11/6) + 5 = 16 the fourth option
1/6 n = 6(1/6) + 5 = 6 the fifth option
Now you have the procedure and the answer for several values of the slope, so you do not have problems to answer this question.
x3-27i=0 solve for the root equation
Answers
Add 27i to both sides
x * 3 - 27i + 27i = 0 + 27i
Then simplify
The form x * 3 = 27i
Divide both sides by 3
x * 3 27i
____ = ____
3 3
And now simplify to get your final answer
x = 9i
What is the volume of a sugar cube that measure 1cm on each side? what is the cross-sectional area of the cube? the total surface area?
Answers
The volume of a cube of side length x is x^3.
The cross-sectional area is x^2.
The total surface area is A = 6x^2.
differentiate please..
y= √x +6 ÷ √x-6
Answers
[tex]\bf \cfrac{dy}{dx}=\cfrac{\frac{1}{2}x^{-\frac{1}{2}}~(\underline{\sqrt{x}}-6~-~\underline{\sqrt{x}}-6)}{(\sqrt{x}-6)^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{1}{2}x^{-\frac{1}{2}}(-12)}{(\sqrt{x}-6)^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{\frac{-12}{2\sqrt{x}}}{(\sqrt{x}-6)^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{-6}{\sqrt{x}}}{(\sqrt{x}-6)^2}\implies \cfrac{dy}{dx}=\cfrac{-6}{\sqrt{x}(\sqrt{x}-6)^2}[/tex]
Find the work done by the force field f(x, y, z) = y + z, x + z, x + y on a particle that moves along the line segment from (1, 0, 0) to (5, 3, 2).
Answers
[tex]\nabla\times\mathbf f(x,y,z)=\mathbf 0[/tex]
which means [tex]\mathbf f[/tex] is conservative. This means there is some scalar potential function [tex]f(x,y,z)[/tex] such that [tex]\nabla f(x,y,z)=\mathbf f(x,y,z)[/tex]. If we can find such a function, then we only need to evaluate the difference of [tex]f(5,3,2)[/tex] and [tex]f(1,0,0)[/tex] (because the gradient theorem holds in this case).
We're looking for a function [tex]f(x,y,z)[/tex] that satisfies
[tex]\dfrac{\partial f}{\partial x}=y+z[/tex]
[tex]\dfrac{\partial f}{\partial y}=x+z[/tex]
[tex]\dfrac{\partial f}{\partial z}=x+y[/tex]
Integrate the first equation with respect to [tex]x[/tex] to get
[tex]f(x,y,z)=xy+xz+g(y,z)[/tex]
Differentiate with respect to [tex]y[/tex], then we must have
[tex]\dfrac{\partial f}{\partial y}=x+z=x+\dfrac{\partial g}{\partial y}[/tex]
[tex]\implies\dfrac{\partial g}{\partial y}=z[/tex]
[tex]\implies g(y,z)=yz+h(z)[/tex]
[tex]\implies f(x,y,z)=xy+xz+yz+h(z)[/tex]
Differentiate with respect to [tex]z[/tex], and we have to have
[tex]\dfrac{\partial f}{\partial z}=x+y=x+y+\dfrac{\mathrm dh}{\mathrm dz}[/tex]
[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=0[/tex]
[tex]\implies h(z)=C[/tex]
[tex]\implies f(x,y,z)=xy+xz+yz+C[/tex]
Now, by the gradient theorem, we have
[tex]\text{work}=\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f(5,3,2)-f(1,0,0)=31[/tex]
where [tex]\mathcal C[/tex] is the line segment.
Final Answer:
Word done = 31 units
Explanation:
To find the work done by a force field [tex]$\mathbf{F}(x, y, z)$[/tex] on a particle moving along a path, we can use the line integral of the force field along that path.
First, we need to define the force field [tex]$\mathbf{F}(x, y, z)$[/tex] and the parametric equations for the line segment.
Given the force field
[tex]$$\mathbf{F}(x, y, z) = \langle y + z, x + z, x + y \rangle,$$[/tex]
we have the following components:
[tex]F_x &= y + z, \\\\F_y &= x + z, \\\\F_z &= x + y.[/tex]
Now, let's find the parametrization of the line segment from the point (1,0,0) to the point (5,3,2). We can define a vector [tex]$\mathbf{r}(t)$[/tex] that describes this line segment by
[tex]$$\mathbf{r}(t) = \mathbf{r_0} + t(\mathbf{r_1} - \mathbf{r_0}),$$[/tex]
where [tex]$\mathbf{r_0} = \langle 1, 0, 0 \rangle$[/tex] is the starting point, [tex]$\mathbf{r_1} = \langle 5, 3, 2 \rangle$[/tex] is the ending point, and t is a parameter that goes from 0 to 1.
So we have
[tex]\mathbf{r}(t) &= \langle 1, 0, 0 \rangle + t(\langle 5, 3, 2 \rangle - \langle 1, 0, 0 \rangle) \\\\ &= \langle 1, 0, 0 \rangle + t\langle 4, 3, 2 \rangle \\\\ &= \langle 1 + 4t, 3t, 2t \rangle.[/tex]
From the parametric equation, we have the components:
[tex]x(t) &= 1 + 4t, \\\\y(t) &= 3t, \\\\z(t) &= 2t.[/tex]
The line integral of the force field along the path can be computed by
[tex]$$W = \int_C \mathbf{F} \cdot d\mathbf{r},$$[/tex]
where [tex]$d\mathbf{r}$[/tex] is the differential element along the path C, and the dot product represents the scalar product of the force field and the differential path element.
We can express [tex]$d\mathbf{r}$[/tex] in terms of t as
[tex]$$d\mathbf{r} = \mathbf{r}'(t) dt = \langle \frac{dx}{dt}, \frac{dy}{dt}, \frac{dz}{dt} \rangle dt = \langle 4, 3, 2 \rangle dt.$$[/tex]
Then the work done is
[tex]W &= \int_{t=0}^{t=1} \mathbf{F}(x(t), y(t), z(t)) \cdot \mathbf{r}'(t) dt \\\\ &= \int_{0}^{1} \langle 3t + 2t, 1 + 4t + 2t, 1 + 4t + 3t \rangle \cdot \langle 4, 3, 2 \rangle dt \\\\ &= \int_{0}^{1} [(5t)(4) + (6t + 1)(3) + (7t + 1)(2)] dt \\\\ &= \int_{0}^{1} [20t + 18t + 3 + 14t + 2] dt \\\\ &= \int_{0}^{1} [52t + 5] dt \\\\ &= [26t^2 + 5t]_{0}^{1} \\\\ &= 26(1)^2 + 5(1) - (26(0)^2 + 5(0)) \\\\ &= 26 + 5 \\\\ &= 31.[/tex]
So, the work done by the force field [tex]$\mathbf{F}(x, y, z)$[/tex] on the particle as it moves along the line segment from (1, 0, 0) to (5, 3, 2) is 31 units of work.
A seafood company sold 9,125 pounds of fish last month. If 6 seafood companies sold the same amount of fish, how much fish did the 6 companies sell last month in all ?
Answers
Jane has a 5 × 7-inch photograph that she wants enlarged to a 10 × 14-inch photograph.
What is the scale factor from the original photograph to the enlarged photograph?
Answers
compare the 5 and 10 dimension then the 7 and 14 dimensions
10/5 =2
14/7 =2
they both are the same ratio/factor
the factor is 2
Answer:
2:1
Step-by-step explanation:
it asks for the scale since 5 x 2 = 10 and 7 x 2 = 14
the scale is 2 : 1
Alice leaves her house and walks to school. She walks 45 meters south and 336 meters east. How far is Alice from her house?
Answers
-20,480 , -5,120 , -1280 , -320 what goes next
Answers
- 1280/4 = -320
- 320/4 = - 80
Find the volume of a sphere with a diameter 40 cm in length. Approximate pi as 3.14 and round your answer to the nearest tenth.
Answers
now lets sub
V = 4/3 * 3.14 * 20^3
V = 4/3 * 3.14 * 8000
V = 32,000/3 * 3.14
V = 100480/3
V = 33493.3 cm^3 <===
Delta airlines quotes a flight time of 2 hours, 5 minutes for its flights from cincinnati to tampa. suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.what is the probability that the flight will be no more than 5 minutes late (to 2 decimals)?
Answers
The likelihood that the flight will be no more than 5 minutes late would be equal to a flight that arrives between 2 hours and 2 hours and 10 minutes.
So the answer would be:
P (5 late or less) = 10 * 1/20 = 0.5
The answer is 0.5
But if we are looking for the probability of the flight that would be 10 minutes late, the likelihood of that event would be 0.25.
Final answer:
The probability that a Delta airlines flight from Cincinnati to Tampa will be no more than 5 minutes late, given that the actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes, is 0.50.
Explanation:
The question deals with the uniform distribution of flight times and calculating the probability that a flight will be no more than 5 minutes late. Assuming flight times are uniformly distributed between 2 hours (120 minutes) and 2 hours, 20 minutes (140 minutes), the total range of flight times is 20 minutes (140 minutes - 120 minutes).
Delta airlines quotes a flight time of 2 hours, 5 minutes, which is 125 minutes. Therefore, a flight being no more than 5 minutes late means the flight time would be at most 130 minutes. To find the probability that the flight time is 130 minutes or less, we calculate the proportion of the distribution that falls within this range.
The probability that the flight will be no more than 5 minutes late is the length of the interval from 120 minutes to 130 minutes divided by the total range (20 minutes), which is (130 - 120) / 20 = 10 / 20 = 0.5. Thus, the probability is 0.50 to two decimal places.
write the equation of the line MN, which is formed by the points M(-3,5) and N(2,0)
Answers
Step 1
Find the slope of the given line
Let
[tex]M(-3,5)\ N(2,0)[/tex]
we know that
the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{0-5}{2+3}[/tex]
[tex]m=\frac{-5}{5}[/tex]
[tex]m=-1[/tex]
Step 2
Find the equation of the line
we know that
the equation of the line into point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-1[/tex]
point N [tex](2,0)[/tex]
substitute the values
[tex]y-0=-1(x-2)[/tex]
[tex]y=-x+2[/tex]
therefore
the answer is
[tex]y=-x+2[/tex]
What are 2 ways three people can share fifths?
Answers
Final answer:
Three people can share fifths by dividing one pie into five slices and each taking three, or dividing three pies into fifteen slices and each person getting one slice from each pie. Both methods ensure each person receives three-fifths of a pie.
Explanation:
Two ways that three people can share fifths involve division and allocation of pie (or any other divisible whole). One way is to take a single pie, divide it into five equal slices, and each person takes three slices. However, since we need to divide these among three people and a pie has only five slices, we'll end up with a fraction of a slice per person. The second way is to start with three pies, divide them so that there are a total of fifteen slices (five slices per pie), and then each person gets one slice from each pie, totaling three slices per person.
Here are two arithmetic representations of the scenarios:
First method: (3 slices/person) / 5 slices = 3/5 per personSecond method: 1 slice from each of 3 pies / 5 slices per pie = 3/5 per personWhether we are dealing with one pie or three, each person ends up with the same fraction of the total available pie: three-fifths.
Mark earns $135 for selling a $1500 refrigerator. Which sale listed has the same commission rate? $36 commission on a $400 dryer or B) $40 commission on a $500 dryer sale C) $210 commission on $1400 oven sale d) $30 commission on a $600 freezer sale?
salelisted has the same commssion rate. ?
Answers
36/400 * 3.8 = 136.6/1520
40/500 * 3 = 120/1500
210/1400 (not even close)
30/600 * 3 = 90/1800 (not even close)
so the two answer choices that are close are A and B, A has the closest numbers to the original commission rate.
Answer:
Option A is the correct choice.
Step-by-step explanation:
We have been given that Mark earns $135 for selling a $1500 refrigerator.
Since proportions states that two fractions are equal , so we will use proportions to find the same commission rate with the listed price from our given choices.
We can set proportion for commission and listed price as:
[tex]\frac{\text{Commission}}{\text{Listed price}}=\frac{135}{1500}[/tex]
Let us compare our given choices one by one.
A. $36 commission on a $400 dryer.
[tex]\frac{36}{400}=\frac{135}{1500}[/tex]
Upon simplifying our proportion we will get,
[tex]\frac{9}{100}=\frac{9}{100}[/tex]
[tex]0.09=0.09[/tex]
We can see that commission rates for both items are equal, therefore, option A is the correct choice.
B. $40 commission on a $500 dryer sale.
[tex]\frac{40}{500}=\frac{135}{1500}[/tex]
Upon simplifying our proportion we will get,
[tex]\frac{2}{25}=\frac{9}{100}[/tex]
[tex]0.08\neq 0.09[/tex]
We can see that both commission rates are different, therefore, option B is not a correct choice.
C. $210 commission on $1400 oven sale.
[tex]\frac{210}{1400}=\frac{135}{1500}[/tex]
Upon simplifying our proportion we will get,
[tex]\frac{3}{20}=\frac{9}{100}[/tex]
[tex]0.15\neq 0.09[/tex]
Since the commission rates are different, therefore, option C is not a correct choice.
D. $30 commission on a $600 freezer sale.
[tex]\frac{30}{1400}=\frac{135}{1500}[/tex]
Upon simplifying our proportion we will get,
[tex]\frac{3}{140}=\frac{9}{100}[/tex]
[tex]0.0214\neq 0.09[/tex]
Since the commission rates are different, therefore, option D is not a correct choice.
6 tractors take 10 days to collect the harvest. How long would it take 15 tractors to do the same amount of work
Answers
bc 6/10 equals .375, then 15/ .375 is 40, divided by 10 is 4?
Which of the following statements must be true about a rectangle? Choose all answers that apply: Choose all answers that apply: A It has four sides of equal length. B It has four right angles. C It has two pairs of parallel opposite sides.
Answers
because a rectangle has not the same exact side lengths like a square
Answer:
The correct answers are options B and C.
Step-by-step explanation:
B It has four right angles.
C It has two pairs of parallel opposite sides.
All angles are right angles by definition of a rectangle. The rectangle has 2 pairs of parallel opposite sides.
Option A is wrong as its a square whose all 4 sides have equal length.
Find the point on the plane 2x+5y+z=8 that is nearest to (2,0,1).
Answers
Answer:
(2.2, 0.5, 1.1)
Step-by-step explanation:
The parametric equation of the line normal to the plane and through point (2, 0, 1) can be written ...
... L = (2, 0, 1) + t(2, 5, 1)
We want to find the value of t (and the corresponding point) that makes L satisfy the equation of the plane.
... 2(2+2t) +5(0 +5t) +1(1+t) = 8 . . . . . put values from L in for x, y, z in plane
... 5 + 30t = 8 . . . . . simplify
... t = (8 -5)/30 = 0.1 . . . . solve for t (subtract 5, divide by 30)
For this value of t, L is ...
... (2, 0, 1) + 0.1(2, 5, 1) = (2.2, 0.5, 1.1)
What is the 250th term of this sequence. Please explain. 4, 9,14,19,24
Answers
a2 = second term = a1+5 = 4+5 = 0
a3 = third term a1 + 5 + 5 = a1 + 5(n-1), where n is the subscript that represents which term we're discussing.
an=4+5(n-1).
Is this correct? Let's check it and find out.
What is your prediction for a2? Here, n = 2. Then a2 = 4+5(2-1), or 4+5, or 9. That agrees with the given sequence rule.
Thus, the 250th term would be 4+5(250-1). Evaluate this, please.
Julianna works 32 hours each week. She earns $14.15 an hour. Which is closest to the amount of money Julianna will earn if she works for 46 weeks.(Please show work?)
A) $16,800
B) $18,000
C) $21,000
D) $22,500
Answers
1,472 * $14.15 = 20,828.8
Answer C is your answer
Julianna will earn $22,579.20 if she works for 46 weeks, which is closest to the option D) $22,500.
Explanation:To calculate the amount of money Julianna will earn if she works for 46 weeks, we need to multiply the number of work hours per week (32) by the hourly wage ($14.15), and then multiply that result by the number of weeks worked (46). This can be calculated as follows:
Total earnings = (32 hours/week) × ($14.15/hour) × (46 weeks)
Total earnings = $22,579.20
Therefore, the closest amount of money Julianna will earn if she works for 46 weeks is $22,579.20, which is closest to option D) $22,500.
Learn more about Calculating Earnings here:https://brainly.com/question/11921889
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At an automobile factory, 1849 parts are made in 4 hours. What is the average rate at which parts are made per hour?
Answers
or 1849 parts/ 4 hours, or 462.25 parts/hour, or (rounded off) 462 parts/hour.
Answer:
462.25
Step-by-step explanation:
At an automobile factory, the number of parts are made in 4 hours = 1849.
We have to calculate the average rate of production per hour.
We will divide the production of parts in 4 hours by 4 to get the number of parts made per hour.
The average rate of production in one hour = [tex]\frac{1849}{4}[/tex]
= 462.25/hour
462.25 parts are made per hour.
what is the sum of (1-5q)+2(2.5q+8)
Answers
Answer:
17
Step-by-step explanation:
Eliminating parentheses, we have ...
... 1 - 5q +2·2.5q +2·8
... = 1 -5q +5q +16 . . . . . carry out the multiplication
... = q(-5+5) +(1 +16) . . . . group like terms
... = q·0 +17 . . . . . . . . . . . combine like terms
... = 17
Emma uses 5 ounces of milk to make a shake.she want to buy enough milk to make 7 shake and she want to buy the smallest size container ok milk that she can.should she buy a pint a quart or gallon of milk?justify your answer Help
Answers
Daniel dives into a swimming pool. The height of his head is represented by the function h(t) = -8t(squared) - 28t + 60, where t is the time in seconds and h(t) is the height of his head, in inches. How many seconds will it take for Daniel's head to reach the surface of the pool?
Answers
Therefore:
-8t² - 28t + 60 = 0 To simplify, divide both sides by -4
2t² + 7t - 15 = 0
Consider the trinomial ax² + bx + c
To factor by grouping, we must find two numbers that multiply to equal AC (-30) and add up to B (7)
Two numbers that satisfy this are 10 and -3:
2t² + 10t - 3t - 15 = 0 Rewrite the equation using 10t and -3t
2t (t + 5) -3 (t +5) = 0 Regroup, then rewrite
(2t -3) (t+5) = 0
2t-3 = 0
2t = 3
t = 3/2
OR
t + 5 = 0
t = -5
We know t cannot be a negative number, so the answer is:
t = 3/2, or 1 and a half seconds
Which ordered pairs are solutions to the inequality y−4x≥−5 ?
Select each correct answer.
(−2, 1)
(−4, 2)
(4, 0)
(5, −2)
(1, −1)
Answers
y - 4x ≥ - 5
To find the correct answer, we should test each answer as shown below.
Test (-2. 1):
y - 4x = 1 - 4(-2) = 9
It is ≥ -5.
CORRECT
Test (-4, 2)
y - 4x = 2 - 4(-4) = 18
It is ≥ -5
CORRECT
Test (4,0)
y - 4x = 0 - 4(4) = -16
It is < -5
INCORRECT
Test (5,-2)
y - 4x = -2 - 4(5) = -22
It is < -5
INCORRECT
Test (1,-1)
y - 4x = -1 - 4(1) = -5
It is ≥ -5.
CORRECT
Answer: The correct answers are
(-2,1)
(-4,2)
(1,-1)
Answer:
The correct answers are
(-2,1)
(-4,2)
(1,-1)
Step-by-step explanation:
hope dis help u guys, habe a good rest of ya day!
. Hot dogs come in packs of 8. Hot dog rolls come in packs of 12. What is the least number of packs of each Shawn should buy to have enough to serve 24 people and have none left over?
Answers
basically it simplifies down to 12x=24 and 8x=24
which means he should buy 2 packs of hot dog rolls and 3 packs of hot dogs
Billy wants to live in the area defined by y < 3x − 6. Explain how you can identify the houses in which Billy is interested in living. (2 points)
Answers
to graph an inequality, you pretty much first off, need to graph the "equality" or equation, so for y < 3x − 6, first off, graph the line y = 3x − 6.
and then you do a "true" or "false" check.
now, if you look at the line below, it splits the grid in two sections, so, let's check a point in either section, if one is false, the other is true and the other way around.
so, let's check the region on the left-hand-side, hmmmm say point 0,0, the origin.
y < 3x - 6
y = 0, x = 0 thus
0 < 3(0) - 6
0 < -6 <--- now, is that really true? is 0 lesser than -6? not quite, is false.
recall that on the negative side, the closer to 0, the larger the value, so -1 is much larger than -1,000,000.
because the point 0,0 yielded a false inequality, that region is the "false region" and thus not shaded, therefore, the other side must be the "true region", and thus we shade that then.
we can run a quick check on that btw, say on point 4,4
y =4, x = 4 thus
4 < 3(4) - 6
4 < 12 - 6
4 < 8 <---- yeap, is true, 4 is lesser/smaller than 8.
hmm ohh yes, the line needs to be dashed for a < or >, because it "has that boundary but it does not include it", unlike ⩽ and ⩾, which is a solid line, because it has that boundary and it includes it too.
Sam opened a savings account with an initial deposit of $2,000. Since then, he has never made any other deposits or withdrawals. His savings account earns 0.4% interest monthly and an annual bonus of 1.5% interest. Which equation gives the approximate amount, A(x), he has in his savings account as a function of x, the number of years since his initial deposit?
A(x) ≈ 2,000 + (1.059)x3
A(x) ≈ 2,000(1.019)x2
A(x) ≈ 2,000(1.065)x
A(x) ≈ 2,000(1.059)x2
Answers
Answer:
Third option:
[tex]A(x)\approx 2,000(1.065)^x[/tex]
Step-by-step explanation:
Notice if we invest 2,000 then the first month then after the first 0.4% interest is earned we will have in the account:
2,000(1+0.004) = 2,000(1.004)
I just applied the simple interest formula.
Then after the second month we will have:
[tex]2,000(1.004)(1.004) = 2,000(1.004)^2[/tex]
And so on each month.
So at the end of the first year (12 months) we have:
[tex]2,000(1.004)^{12}[/tex]
But we also earn an additional 1.5% in the year, so we will have:
[tex]2,000(1.004)^{12}(1.015)[/tex]
At the end of the second year we will have:
[tex]2,000[(1.004)^{12}(1.015)]^2[/tex]
At the end of the third year:
[tex]2,000[(1.004)^{12}(1.015)]^2[/tex]
And so on,
So if the number of years is denoted with x, at the end of x years we will have the following amount in the savings:
[tex]2,000[(1.004)^{12}(1.015)]^x[/tex]
We use our calculator to simplify that inside the brackets:
[tex](1.004)^{12}(1.015)=1.06481[/tex]
Rounding to the third decimal place we get: 1.065
So notice the amount in the savings after x years will be:
[tex]2,000(1.065)^x[/tex]
Since they want it in function notation we just write the A(x) that denotes the amount in the savings:
[tex]A(x)\approx 2,000(1.065)^x[/tex]
A person made an estimate for a three–minute interval. the estimate was 241.5 seconds. what was the error of this estimate?
Answers
One canned juice drink is 25% orange juice; another is 10% orange juice. How many liters of each should be mixed together in order to get 15L that is 17% orange juice
Answers
likewise, we'll use "y" of the 10% OJ, and it will end up with (10/100) *y or 0.10y of juice in it.
whatever "x" and "y" are, they must add up to 15 Liters, and the juice concentration on that mixture, must also be the sum of their sum concentration.
[tex]\bf \begin{array}{lccclll} &\stackrel{liters}{amount}&\stackrel{juice~\%}{quantity}&\stackrel{juice}{quantity}\\ &------&------&------\\ \textit{25\% juice}&x&0.25&0.25x\\ \textit{10\% juice}&y&0.10&0.10y\\ ------&------&------&------\\ mixture&15&0.17&2.55 \end{array} \\\\\\ \begin{cases} x+y=15\implies \boxed{y}=15-x\\ 0.25x+0.10y=2.55\\ ----------\\ 0.25x+0.10\left(\boxed{15-x} \right)=2.55 \end{cases} \\\\\\ 0.25x-0.10x+1.5=2.55\implies 0.15x=1.05\implies x=\cfrac{1.05}{0.15} \\\\\\ x=7[/tex]
how much will be it of the 10% juice? well, y = 15 - x.
kalen's truck has a 60 gallon fuel tank The fuel gauge points to 1/4 how much fuel does he need to buy to fill the tank show Your work