Given linear equations in algebra: -3y >-3-4x
The above is an inequality.
To solve linear equation with two variables we need two equations.
Only one equation is given. The only other explanation is to solve for any of the variables by making it the subject of formula.
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Therefore, when daily output is 106300 units, the cost will be at its lowest.
Define costs.The average cost, or how much it generally costs to produce a unit, can be discovered using the cost function. The average cost function is defined as A(x)=C(x)x, where x > 0. The average cost per unit is calculated by dividing the total cost by the number of units produced. Costing is necessary to make sure that all costs are met and that the group decides on a price that will result in a profit. Finding ALL of a company's costs, including manufacturing, sales, administration, overhead, etc., is the first and most crucial stage. Costs are then divided into fixed and variable costs.
Given,
C=0.04x2 - 8.504x + 25302....... (1), where x is the number of units produced in thousands, gives the cost of generating x thousands of units of lemon-scented widgets in a day.
We must determine the daily production rate that will reduce costs.
dC/dx = 0
The current prerequisite for minimum cost is
0.08x - 8.504 = 0
0.08x = 8.504
x = 106.3
In light of equation (1),
x =106.3
Therefore, when daily output is 106300 units, the cost will be at its lowest.
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Original price of a camera: $799.95Discount: 17%What's the selling price
Answer:
$663.95
Explanation:
Given the following:
Original price of a camera: $799.95
Discount: 17%
Discounted price = 17% of original price of the camera
Discounted price = 0.17*$799.95
Discounted price = $135.99
Selling price = Original Price - Discounted price
Selling Price = $799.95 - $135.99
Selling price = $663.96
Hence the selling price is $663.95
5x + 12 - 9x - 4 - 16
This problem is about a simple algebraic expression which we need to reduce in its simplest form. To do that, we need to reduce like terms, that is, terms that are similar, for example, terms 5x and 9x are similar because they have the same variable; also terms 12, 4, and 16 are also similar because they are single numbers.
Now, we reduce them using the algebraic sum properties, that is, numbers with the same sign will sum, and numbers with different signs will subtract:-
[tex]5x+12-9x-4-16[/tex]Then, we have
[tex]-4x-8[/tex]Therefore, the simplest expression is -4x-8.8Σ-(-2): -1-i=1Evaluate each geometric series described. (Find the total sum)
The given expression is
[tex]\sum ^8_{i\mathop=1}-(-2)^{i-1}[/tex]To solve this, we just have to replace each value of the sum in the expression, then we sum. Let's do it
[tex]\begin{gathered} -(-2)^{1-1}=-1 \\ -(-2)^{2-1}=-(-2)^1=2 \\ -(-2)^{3-1}=-(-2)^2=-4 \\ -(-2)^{4-1}=-(-2)^3=8 \\ -(-2)^{5-1}=-(-2)^4=-16 \\ -(-2)^{6-1}=-(-2)^5=-(-32)=32 \\ -(-2)^{7-1}=-(-2)^6=-64 \\ -(-2)^{8-1}=-(-2)^7=-(-128)=128 \end{gathered}[/tex]Now, we sum all these items
[tex]-1+2-4+8-16+32-64+128=85[/tex]Therefore, the total sum is 85.Need help with this question please!
Answer: the picture
Step-by-step explanation:
Ty hiked up a mountain to 2523 meters above sea level. Pete is a scuba diver and dove 319 meters below sea level. If Ty and Pete started at the same elevation, how much higher was Ty than Pete when they were the farthest apart?
Ty hiked up a mountain to 2523 meters above sea level.
Height of the TY above the sea level = 2523meter
. Pete is a scuba diver and dove 319 meters below sea level
Depth of the Pete = 319 meter
To find the how much higher was Ty than Pete,
Find the differecne between thier disatnce from sea level
[tex]\begin{gathered} Ty\text{ was higher than Pete=2523-319} \\ Ty\text{ was higher than pete by }2204\text{ meter} \end{gathered}[/tex]Answer: Ty was 2204 meter higher than Pete
Diego bought a new car for 26,525 he was surprised at the dealer than attitude thousand $387.25 what was the sales tax rate for this purchase do not include the percentage sign in your answer
2387.25 is the amount of tax
Take the original price and multiply by x to get the tax added
26525 * x = 2387.25
Divide each side by 26525
x = 2387.25/26525
x =.09
Change this to a percent form
.09 * 100%
x = 9 %
The sales tax percent 9 %
5) Solve for x:X - 7.5 = 186) Solve for x:45x = 14.5
We have the following:
5)
[tex]x-7.5=18[/tex]solving for x:
[tex]\begin{gathered} \text{let's add 7.5 on each side} \\ x-7.5+7.5=18+7.5 \\ x=25.5 \end{gathered}[/tex]6)
[tex]\begin{gathered} 45x=14.5 \\ \\ \end{gathered}[/tex]solving for x:
[tex]\begin{gathered} \text{ divide on each side by 45} \\ x=\frac{14.5}{45} \\ x=0.32 \end{gathered}[/tex]need help with this problem
First option describes line e: Each point is less than 4 units from the y-axis.
The second option describes line f:
Graph the line with the slope -3/4 passing through the point (5,2)
We need to first determine the expression of the line, for that we will use the point slope form, which is given below:
[tex]y-y_1=m\cdot(x-x_1)[/tex]Where m is the slope and (x1, y1) are the coordinates of a known point on the line.
[tex]\begin{gathered} y-2=-\frac{3}{4}(x-5) \\ y=-\frac{3}{4}(x-5)+2 \\ y=-\frac{3}{4}x+\frac{15}{4}+2 \\ y=-\frac{3}{4}x+\frac{15+8}{4} \\ y=-\frac{3}{4}x+\frac{23}{4} \end{gathered}[/tex]Now we need to graph it, for that we need two points. We already know the coordinates of one of them (5,2), now we need another, we can use the point for which x is equal to 0.
[tex]\begin{gathered} y=-\frac{3}{4}\cdot0+\frac{23}{4} \\ y=\frac{23}{4} \end{gathered}[/tex]Now we have (0, 23/4). We need to draw a line that passes
Kimberly and Clay leaves a concert hall at the same time, traveling in buses going opposite directions, Kimberly's bus tra els at 40mph and Clay's bus travels at 60mph. In how many hours will Kimberly and Clay be 350 miles apart?
let s1 and s2 be the distance covered by the two buses
s1 + s2 = 350 ................................eqn I
velocity (v) = distance (s)/time (t) .........................eqn II
from eqn II the velocity of the first bus, v1 = s1/t1
s1 = v1t1 .................................eqn III
velocity of the second bus, v2 = s2/t2
s2 = v2t2 ...........................eqn IV
substitute eqn III and eqn IV into eqn I
v1t1 + v2t2 = 350
the time taken for any two moving objects to simultaneously cover any distance is equal. Thus,
t1 = t2 = t
eqn V becomes
v1t + v2t = 350
t(v1 + v2) = 350
v1 = 40
v2 = 60
t(40 + 60) = 350
100t = 350
divide both sides by 100
100t/100 = 350/100
t = 3.5 hours
A printer prints 5 photos each minute. Let P be the number of photos printed in M minutes. Write an equation relating P to M. Then graph your equation using the axes below.
The equation is:
P = 5M
The graph is shown in the explanation
Explanation:Given that a printer prints 5 photos per minute.
Since P represents the number of photos printed in M minutes, we have:
[tex]P=5M[/tex]The graph of this is shown below:
One-sixth of the fourth graders and one-third of the fifth graders miss school on Friday. The absentee sheet for Friday shows the names of 9 fourth graders and 16 fifth graders. How many fourth and fifth graders are enrolled in the school?
Answer:
There are 54 4th graders.
There are 48 5th graders.
Step-by-step explanation:
1/6 of the 4th graders is 9 students.
1/6 x = 9
x = 9 × 6
x = 54
There are 54 4th graders.
1/3 of the 5th graders is 16 students.
1/3 x = 16
x = 3 × 16
x = 48
There are 48 5th graders.
There are 54 Fourth grader and 48 Fifth graders were enrolled in the school.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the number of fourth graders be x.
and, let the number of fifth graders be y.
As, One-sixth of the fourth graders is 9.
and, one-third of the fifth graders is 16.
Then, 1/6 x = 9
x= 54
and, 1/3 y= 16
y= 48
Hence, there are 54 Fourth grader and 48 Fifth graders were enrolled in the school.
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Telephone numbers are in the form NYZ-ABC-XXXX. the following restrictions were placed; N can only be numbers: 2-9; Y can only be numbers 0-7 and A&C cannot be 2. how many phone numbers are there?
Answer
The answer = 5,184,000,000
There are 5,184,000,000 possible phone numbers.
Explanation
The question told us that telephone numbers are in the form NYZ-ABC-XXXX, then proceeds to give us the restrictions on some of the positions available.
- N can only be numbers: 2-9;
- Y can only be numbers 0-7
- and A&C cannot be 2
We are then told to calculate the number of phone numbers possible.
This question is a special type of permutation and combination.
To solve it, it will be a multiplication of the possible numbers that can take up each position.
N, can only be numbers 2 to 9. Number of possible digits = 8
Y, can only be numbers 0 to 7. Number of possible digits = 8
Z, no restriction, can have numbers 0 to 9. Number of possible digits = 10
A, number cannot be 2. Number of possible digits = 9
B, no restriction, can have numbers 0 to 9. Number of possible digits = 10
C, number cannot be 2. Number of possible digits = 9
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
Total number of possible phone numbers
= 8 × 8 × 10 × 9 × 10 × 9 × 10 × 10 × 10 × 10
= 5,184,000,000
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Which describes a bar diagram showing the percent of students who participated in dances?1 shaded square out of 10 squares2 shaded squares out of 10 squares3 shaded squares out of 10 squares4 shaded squares out of 10 squares
From the information on the pie chart, the proportion of students that participated in dances is 20 out of 100.
Then, if we represent this in a bar chart where 100% is 10 squares, the proportion of students that participated in dances should be represented by:
[tex]\begin{gathered} 100\%\longrightarrow10\text{ squares} \\ \frac{20}{100}\cdot100\%=20\%\longrightarrow\frac{20\%}{100\%}\cdot10=2\text{ squares} \end{gathered}[/tex]Answer: 2 shaded squares out of 10 squares
Maria invested her savings in two investment funds. The amount she invested in Fund A was $7000 less than the amount she invested in Fund B. Fund Areturned a 7% profit and Fund B returned a 3% profit. How much did she invest in Fund B, if the total profit from the two funds together was $1610?
It is given that,
The amount she invested in Fund A was $7000 less than the amount she invested in Fund B.
So, A=B-7000
And it is given that, Fund A returned a 7% profit and Fund B returned a 3% profit.
The total profit from the two funds together was $1610.
It can be written as,
7% of A +3% of B=1610
Substitute A=B-7000, we get
7% of (B-7000) +3% of B=1610
On solving we get,
[tex]\begin{gathered} \frac{7}{100}(B-7000)+\frac{3}{100}B=1610 \\ \frac{7}{100}B-490+\frac{3}{100}B=1610 \\ \frac{10}{100}B-490=1610 \\ \frac{1}{10}B=1610+490 \\ \frac{1}{10}B=2100 \\ B=21000 \end{gathered}[/tex]Hence, the investment in fund B is $21,000.
Enter the digit that can replace (blank box) 526 < 5 _ 5 < 541 The digit that fits in the gray box is ?
3
1) The number to be found, is a multiple of 5 and also greater than 526 but also lesser than 541.
2) So we have, the next number whose last digit is 5 immediately greater than 526 and lesser than 541 is 535
3) So 3 is the missing digit
Kaylee has a bag of candy full of 15 strawberry chews and 5 cherry chews that she eatsone at a time. Which word or phrase describes the probability that she reaches inwithout looking and pulls out an orange chew?impossiblelikelySubmit Answeran equal chance or 50-50O unlikely
Given that:
- There are 15 strawberry chews in the bag.
- There are 5 cherry chews in the bag.
You know that there is no orange chew in Kaylee's bag. Therefore, knowing this, you can determine that the probability that Kaylee reaches in without looking and pulls out an orange chew is:
[tex]P=0[/tex]By definition, the probability is zero when it is impossible for the events to happen.
Since there is no orange chew in her bag, it is impossible that she reaches in
without looking and pulls out an orange chew.
Hence, the answer is: Impossible.
Long divide 4x^4-3x^3+1 / x-5
We have the following division:
for this, we have to divide each remainder by x, and use the law of signs in reverse order. The division will look like this:
Therefore, the result of the division is:
[tex]\frac{4x^4-3x+1}{x-5}=4x^3+17x^2+85x+425+\frac{2126}{x-5}[/tex]A firm uses trend projection and seasonal factors to simulate sales for a given time period.
It assigns "0" if sales fall, "1" if sales are steady, "2" if sales rise moderately, and "3" if sales
rise a lot. The simulator generates the following output.
0102200123202022123122203002121
Estimate the probability that sales will rise at least moderately.
Answer:
3
Step-by-step explanation:
0+1=1-1+0+2=3-3+1+2+0-1=4
Transform 12 + 3y = 9 into an equivalent equation that is in slope-intercept form.A. y=3/4x - 1/4B. y=-4x+3C. y=4x-3D. y=-1/4x+3/4
Given:
[tex]12x+3y=9[/tex]Find: Slope - intercept form.
Sol:
Slope - intercept form:
[tex]y=mx+c[/tex][tex]\begin{gathered} 12x+3y=9 \\ 3y=-12x+9 \\ y=\frac{-12}{3}x+\frac{9}{3} \\ y=-4x+3 \end{gathered}[/tex]Slope intercept form of equation is:
[tex]y=-4x+3[/tex]6. The budget for a new house can only afford 1/4 of the floor area to be done inceramic tile. The rest of the floor area will be carpeted. The size of the kitchen areahas not yet been determined. Not including the kitchen, the architect has alreadydesigned 2200 square feet of floor area, 15% of which has tile floors specified.What area, in square feet, can be planned for the kitchen if its entire floor area is tohave ceramic tile? Assume all values are ex
The budget of a new house can only afford 1/4 of the floor area
the total area of the floor is designed to be 2200 square feet
15% of the floor is tiled
let the budget be x
area to be done in ceramic tile is 1/4 x the total budget
1/4 * 2200 = 550
550 square feet area of the floor will be use for ceramic tiles alone
What Values of x make two expressions below equal?(X+3)(x+8) = x+3————— —— 5(x+8) 5
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
CONCLUSION:
The final answer is:
( OPTION C )
Write an expression to represent:The sum of one and the product of one and a number I.Stuck? Watch a video or use a hint.Written in expression to represent the sum of one and a product of one and a number x
In this case, we'll have to carry out several steps to find the solution.
Step 01:
We must analyze the problem to write the expression.
Step 02:
The expression is:
x = number
1 + 1 * x
The solution is:
1 + 1 * x
If g(x) = 2x-10 what is g(7)?
Answer:
4
Explanation:
Given the below function;
[tex]g(x)=2x-10[/tex]To find g(7), all we need to do is substitute the x for 7 in the below and solve;
[tex]g(7)=2(7)-10=14-10=4[/tex]01018Annual SalaryANNUAL SALARY VERSUSYEARS OF SERVICE$60,000$50,000$40,000$30,000$20,0005 10 15 20Years of ServiceIn the scatterplot above, each dot represents the annual salary and corresponding years of service for each ofthe 19 employees at Company X. How many of the employees have more than 10 years of service but anannual salary of less than $40,000 ?
To determine how many employees have more than 10 years of service we need to look for dots that are to the right of the "10" position on the horizontal axis. There are a total of 11 employees that fit that criterion. We now need to look for which of these 11 employees earn less than 40,000 per year, for that we have to find the number of dots below the line of 40,000 and to the right of 10 years of service. There are a total of 5 dots.
There are 5 employees with more than 10 years of service which earn less than $40,000.
____+3/10=3/15 option 3/5
First we can simplify the result
[tex]\frac{3}{15}=\frac{1}{5}[/tex]in order to know the missing fraction, we will call x
[tex]\begin{gathered} x=\frac{1}{5}-\frac{3}{10} \\ x=-\frac{1}{10} \end{gathered}[/tex]we can check it
[tex]-\frac{1}{10}+\frac{3}{10}=\frac{2}{10}=\frac{1}{5}=\frac{3}{15}[/tex]- Consider the function represented by this table of values.Xу6385324263 202 14Which function could have produced the values in the table?Ay = 6x + 2By = -6x + 2C) y = (x - 116y = -x - 44
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First you need to find the slope using the formula
Slope = (y2 - y1) / (x2 - x1)
Choose two points from the table
P1 = (6, 38)
P2 = (5, 32)
Identify x1, y1, x2, y2
x1 = 6 y1 = 38 x2 = 5 y2 = 32
Substitute the values to find the slope
slope = m = (32 - 38) / (5 - 6)
= -6/-1
= 6
Find the equation of the line using the formula
y - y1 = m(x - x1)
x1 = 6 y1 = 38
Substitution
y - 38 = 6(x - 6)
Simplify
y - 38 = 6x - 36
Solve for y
y = 6x - 36 + 38
y = 6x + 2
Two observation posts A and B are 12 km apart. A third observation post C is located 15 km from A such that CBA is 67º. Find the measure of CÂB
Using the law of sines:
[tex]\begin{gathered} \frac{AB}{\sin(C)}=\frac{AC}{\sin (B)} \\ so\colon \\ \sin (C)=\frac{AB\cdot\sin (B)}{AC} \\ \sin (C)=\frac{12\cdot\sin (67)}{15} \\ C=\sin ^{-1}(\frac{12\cdot\sin(67)}{15}) \\ C\approx47.43^{\circ} \end{gathered}[/tex]Using the triangle sum theorem:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C=180 \\ so\colon \\ x+47.43+67=180 \\ x=180-67-47.43 \\ x=m\angle C=m\angle CAB=65.57^{\circ} \end{gathered}[/tex]The parent function of the function g(x) = (x-h)² + k is f(x) = x2. The vertex of the function g(x) is located at (9,-8).
What are the values of h and k?
g(x) = (x-
².
Answer:
The values of h and k are 9 and -8, respectively
Step-by-step explanation:
This is how to determine the values of h and k
The vertex of the function g(x) is located at (9, –8)
The vertex of a function is represented as:
Vertex = (h,k)
This means that:
(h,k) = (9,-8)
By comparison, we have:
h = 9 and k = -8
So, the values of h and k are 9 and -8, respectively