Answers
7 x 4 = 28
than you need to do y + 5x
than you get you answer 6
Related Questions
Which lists all the real zeros of the polynomial p(x)=(2x-7)(x^2-49) ?
Answers
The real zeros of the polynomial p(x) are 7/2, -7, and 7. Option D is the correct answer.
What in algebra is the Factor Theorem?According to the algebraic principle known as the Factor Theorem, if a polynomial f(x) has a factor of (x - a), then f(a) = 0. To put it another way, if (x - a) is a factor of f(x), then the polynomial f(x) is equal to zero when x equals a. By finding the components of the polynomial and computing the values of x that make each factor equal to zero, this theorem may be used to locate the roots or zeros of a polynomial. The effective factorization and solution of polynomial problems are made possible by the Factor Theorem, a potent algebraic tool.
The given polynomial can be written as follows:
p(x) = (2x - 7)(x + 7)(x - 7)
The real zeros are the values of x that make the polynomial equal to zero. Therefore, the real zeros are:
x = 7/2, -7, 7
Therefore, the real zeros of the polynomial p(x) are 7/2, -7, and 7.
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Find the average rate of change of f(x)=x^2+3x+1 from x=−5 to x=−3. Simplify your answer as much as possible.
Answers
The average rate of change of f(x)=x^2+3x+1 from x=−5 to x=−3 is −5.
The average rate of change of a function f(x) over an interval [a,b] is given by the formula:
average rate of change = (f(b) - f(a)) / (b - a)
In this case, we are given the function f(x)=x^2+3x+1 and the interval [−5,−3], so we can plug in the values into the formula:
average rate of change = (f(−3) - f(−5)) / (−3 - (−5))
First, we need to find the values of f(−3) and f(−5):
f(−3) = (−3)^2 + 3(−3) + 1 = 9 − 9 + 1 = 1
f(−5) = (−5)^2 + 3(−5) + 1 = 25 − 15 + 1 = 11
Now, we can plug these values back into the formula:
average rate of change = (1 - 11) / (−3 - (−5)) = (−10) / 2 = −5
Therefore, the average rate of change of f(x)=x^2+3x+1 from x=−5 to x=−3 is −5.
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Find the equation for the line that passes through the point
(3,−2) , and that is perpendicular to the line with the equation
x=2 .
Answers
The equation for the line that passes through the point (3,−2) , and that is perpendicular to the line with the equation x=2, is given by y = -2
How do we find the equation?To find the equation for the line that passes through the point (3, -2) and is perpendicular to the line x = 2, we need to find the slope of the perpendicular line and use the point-slope form of an equation.
The slope of the line x = 2 is undefined, since it is a vertical line. A line that is perpendicular to a vertical line is a horizontal line, and the slope of a horizontal line is 0.
Using the point-slope form of an equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can plug in the values for the slope and the point:
y - (-2) = 0(x - 3)
Simplifying the equation, we get:
y + 2 = 0
y = -2
So the equation for the line that passes through the point (3, -2) and is perpendicular to the line x = 2 is y = -2. This is a horizontal line that passes through the y-axis at -2.
Answer: y = -2
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 9 above 80 to 89, at 9 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Flower Town.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Desert Landing is skewed
IQR, because Desert Landing is symmetric
Range, because Flower Town is skewed
Range, because Flower Town is symmetric
Answers
Using IQR would be the appropriate measure of variability to compare the consistency of temperatures between Desert Landing and Flower Town.
What is Graph ?
A graph is a visual representation of data that displays the relationship between variables or sets of data. Graphs are commonly used in various fields such as mathematics, statistics, economics, and science to help people understand and analyze data.
IQR, because it is a measure of variability that is resistant to outliers and is appropriate for both symmetric and skewed distributions. It measures the spread of the middle 50% of the data, which gives a good indication of how consistent the temperatures are around the median.
Therefore, using IQR would be the appropriate measure of variability to compare the consistency of temperatures between Desert Landing and Flower Town.
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Ramu bought 12 metre long ribbon. He cut it into 2and 3 by 4 m and 1 and 1 by 2 meter long. Find the length of remaining ribbon
Answers
Ramu bought 12 metre long ribbon, and he cut it into different pieces then the length of remaining ribbon is equals to the 10 metre.
Ramu bought a long ribbon with lengths in meters. We have to calculate the length of remaining ribbon.
Total length of ribbon, L = 12 meters
After that he cut it into 2 and 3 by 4 m and 1 and 1 by 2 meter long. Two pieces of ribbon has length of 3/4 metre in each piece. So, total length of two pieces
= 2×3/4 = 3/2 meters
Also, he cut one piece of ribbon
length of this piece = 1/2 meter
Thus, total length of cutting pieces of ribbon = 3/2 metre + 1/2 metre
= 4/2 = 2 metre
The length of remaining ribbon = total length of ribbon - cutting pieces length
= 12 metre - 2 metre
= 10 metre
Hence, the required length is 10 metre.
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Score: 8 Penalty: None Singleton tic Operations on Functions 11:58:12 PM hat f(x)=x^(2)+5x-36 and g(x)=x-4, find f(x)+g(x) an the result as a polynomial in simplest form.
Answers
The final answer sum of f(x) and g(x) is [tex]x^2 + 6x - 40[/tex], which is a polynomial in simplest form.
To find the sum of two functions, we simply need to add their respective terms together.
In this case, we have:
f(x) = [tex]x^2 + 5x - 36[/tex]
g(x) = x - 4
So, f(x) + g(x) = [tex](x^2 + 5x - 36)[/tex] +[tex](x - 4) = x^2 + 6x - 40[/tex]
Therefore, the sum of f(x) and g(x) is [tex]x^2 + 6x - 40[/tex], which is a polynomial in simplest form.
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Solve the following equation exactly. Use an inverse function when appropriate.
√x³ - 100 = 5
Answers
Answer:
Starting with the given equation:
√x³ - 100 = 5
Adding 100 to both sides:
√x³ = 105
Squaring both sides:
x³ = 11025
Taking the cube root of both sides:
x = 15
Therefore, the exact solution to the given equation is x = 15.
Note that no inverse functions were needed to solve this equation
Step-by-step explanation:
What is the ratio of perimeters for two regular pentagons with areas of 18 cm² and 50 cm²?
18:50
09:25
15:25
O 3:5
Answers
Answer:
Step-by-step explanation:its 18.50
Use substitution to solve
Answers
Answer:
x=4, y=-2
Step-by-step explanation:
[tex]2y=x-8\\2y-x=-8\\2(2x-10)-x=-8\\4x-20-x=-8\\3x-20=-8\\3x=-8+20\\x=12/3\\x=4\\\\\\y=2x-10\\y=2(4)-10\\y=8-10\\y=-2[/tex]
Molly is verifying if the two functions are inverses of each other? Her answer is as follows:
f(g(x))=x+5 g(f(x))=x+5
She stated that they are not inverses of each other. Is she correct and why? Explain.
Answers
Answer:
Molly is correct in stating that the two functions are not inverses of each other.
To be inverses of each other, two functions must satisfy the property that when they are composed in either order, they result in the identity function, which is represented by f(x) = x.
In this case, we have:
f(g(x)) = (x + 5) + 5 = x + 10
g(f(x)) = (x + 5) + 5 = x + 10
Since both compositions of the functions result in x + 10, which is not equal to x, the two functions are not inverses of each other.
Step-by-step explanation:
Answer:
Molly is correct. The fact that $f(g(x)) = g(f(x)) = x+5$ indicates that the two functions, $f$ and $g$, are symmetric about the line $y=x$, which means that they are not inverses of each other.
To determine whether two functions are inverses of each other, we need to show that their composition results in the identity function. That is, if $f(x)$ and $g(x)$ are two functions, then $f(g(x)) = g(f(x)) = x$ for all $x$ in the domain of $f$ and $g$.
In this case, we see that $f(g(x)) = g(f(x)) = x+5$, which is not the identity function. Therefore, the two functions are not inverses of each other.
In the following figure, AE and BD are segments.
1. ABC and CDE are similar. How do we know this?
2. What is the scale factor of the similarity transformation that takes
ABC to CDE?
3. What is the value of the ratio of the area of ABC to the area of CDE? Explain how you
know.
4. If the area of ABC is 40 cm² What is the area of CDE?
Answers
According to the image we can infer that both figures are similar. Their ratio is 11:4; their scale factor is 1:2 and their areas are: 40cm² and 14.54cm²
How do we know that the two figures are similar?We know that the two figures are similar because they have the same angles. Therefore they are similar. In this case it can be inferred that they have a scale factor close to half because the small triangle represents more or less half of the large triangle.
The value of the ratio can be found taking as reference the measurements of the base of the triangles. Then it would be a ratio of 11:4, that is to say that for every 11cm of large triangle, the small one has a 4cm base.
Finally, if the area of the large triangle is 40cm², the area of the small triangle would be the following:
11cm base = 40cm²
4 cm base = cm²
4 * 40 / 11 = 14.54cm²
1. ABC and CDE are similar. How do we know this?Yes they are similar because they have the same angle values.
2. What is the scale factor of the similarity transformation that takes ABC to CDE?According to the graph we can infer that the scale factor of the similarity transformation that takes ABC to CDE is 1:2.
3. What is the value of the ratio of the area of ABC to the area of CDE? Explain how you know.According to the information, we can infer that the ratio of the area of both triangles is 11:4 because those values correspond to their base length.
4. If the area of ABC is 40 cm² What is the area of CDE?if the area of the large triangle is 40cm², the area of the small triangle would be the following:
11cm base = 40cm²
4 cm base = cm²
4 * 40 / 11 = 14.54cm²
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7y-7=0
Help pls I need it asap.
Answers
Answer:
y=1
Step-by-step explanation:
Answer:1
Step-by-step explanation: 7y = 7
divide both sides by 7 to isolate y
y = 1
Complete the following sentence. The division (4+3i)/(5-7i) is performed by multi
Answers
The division (4+3i)/(5-7i) is performed and the result is (-1/74)+(43/74)i.
The division (4+3i)/(5-7i) is performed by multiplying the numerator and denominator by the complex conjugate of the denominator. In this case, the complex conjugate of (5-7i) is (5+7i).
So, the division can be performed as follows:
(4+3i)/(5-7i) * (5+7i)/(5+7i) = (4+3i)(5+7i)/(5-7i)(5+7i)
Multiplying the numerator and denominator gives:
(20+28i+15i+21i^2)/(25+35i-35i-49i^2)
Simplifying the numerator and denominator gives:
(20+43i-21)/(25+49)
Combining like terms gives:
(-1+43i)/(74)
Finally, dividing the numerator and denominator by 74 gives:
(-1/74)+(43/74)i
So, the division (4+3i)/(5-7i) is performed and the result is (-1/74)+(43/74)i.
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Please help!
Answers
Answer:
Step-by-step explanation:
So first you have to divide the monkey by the + sign then when you did that you take the exponent and turn it into a ratio. When you are done doing that you have to multiply and divide and then you have your answer.
4C. Construct orthonormal basis using Gram-Schmidt orthogonalization process from the set of linearly independent vectors {v1 = (1, 0, 1), v2 = (1, 0, -1), V3 = (0,3,4)}. =
Answers
The orthonormal basis constructed using the Gram-Schmidt orthogonalization process from the set of linearly independent vectors {v1 = (1, 0, 1), v2 = (1, 0, -1), V3 = (0,3,4)} is {u1 = (1/√2, 0, 1/√2), u2 = (0, 0, -1), u3 = (0, 1, 0)}.
The Gram-Schmidt orthogonalization process is a method for constructing an orthonormal basis from a set of linearly independent vectors. In this case, we are given the set of linearly independent vectors {v1 = (1, 0, 1), v2 = (1, 0, -1), V3 = (0,3,4)}. We will use the Gram-Schmidt orthogonalization process to construct an orthonormal basis from this set.
Step 1: The first vector in the orthonormal basis is simply the normalized version of the first vector in the original set. So, we have u1 = v1/||v1|| = (1, 0, 1)/√2 = (1/√2, 0, 1/√2).
Step 2: The second vector in the orthonormal basis is the normalized version of the projection of the second vector in the original set onto the orthogonal complement of the first vector in the orthonormal basis. So, we have u2 = (v2 - (v2·u1)u1)/||(v2 - (v2·u1)u1)|| = ((1, 0, -1) - ((1, 0, -1)·(1/√2, 0, 1/√2))(1/√2, 0, 1/√2))/||((1, 0, -1) - ((1, 0, -1)·(1/√2, 0, 1/√2))(1/√2, 0, 1/√2))|| = (0, 0, -√2)/√2 = (0, 0, -1).
Step 3: The third vector in the orthonormal basis is the normalized version of the projection of the third vector in the original set onto the orthogonal complement of the first two vectors in the orthonormal basis. So, we have u3 = (v3 - (v3·u1)u1 - (v3·u2)u2)/||(v3 - (v3·u1)u1 - (v3·u2)u2)|| = ((0, 3, 4) - ((0, 3, 4)·(1/√2, 0, 1/√2))(1/√2, 0, 1/√2) - ((0, 3, 4)·(0, 0, -1))(0, 0, -1))/||((0, 3, 4) - ((0, 3, 4)·(1/√2, 0, 1/√2))(1/√2, 0, 1/√2) - ((0, 3, 4)·(0, 0, -1))(0, 0, -1))|| = (0, 3, 0)/3 = (0, 1, 0).
Therefore, the orthonormal basis constructed using the Gram-Schmidt orthogonalization process from the set of linearly independent vectors {v1 = (1, 0, 1), v2 = (1, 0, -1), V3 = (0,3,4)} is {u1 = (1/√2, 0, 1/√2), u2 = (0, 0, -1), u3 = (0, 1, 0)}.
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Solve for w. -(7)/((w+1)(w-7))=4+(3)/(w-7) If there is more than one solution, separate the
Answers
The two possible solutions for w are 6 and -3/4.
To solve for w, we need to use algebraic manipulation to isolate w on one side of the equation. Here are the steps:
1. Multiply both sides of the equation by (w+1)(w-7) to clear the fractions: -(7) = 4(w+1)(w-7) + 3(w+1)
2. Distribute the 4 and 3 on the right side of the equation: -(7) = 4w^2 - 24w - 28 + 3w + 3
3. Combine like terms on the right side of the equation: -(7) = 4w^2 - 21w - 25
4. Move all terms to one side of the equation: 4w^2 - 21w - 18 = 0
5. Use the quadratic formula to solve for w: w = (-(-21) ± √((-21)^2 - 4(4)(-18)))/(2(4))
6. Simplify the equation: w = (21 ± √(441 + 288))/(8)
7. Simplify the equation further: w = (21 ± √729)/(8)
8. Solve for the two possible values of w: w = (21 + 27)/(8) or w = (21 - 27)/(8)
9. Simplify the two possible values of w: w = 48/8 or w = -6/8
10. Simplify the two possible values of w further: w = 6 or w = -3/4
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Choose the answer to complete each statement.
The slope of the line is ___.
The y-intercept is at ___.
The graph represents the function ___.
Answers
Answer:
Step-by-step explanation:
slope of line = 7/3
y-intercept is = 7
Amanda is the manager of Gladrags. She just got a new shipment of jeans and is pricing them for the store to make money. Her invoice fo states that the jeans cost her store $20 per pair. Amanda marks the jeans up to sell for $55 per pair. Three weeks later, Amanda sees that selling and puts them on sell for 50% off. Will her store still earn a profit on the jeans, break even, or will the store lose money?
A) The store will break even on the jeans by selling them for the same amount that they bought them for.
B) The store will lose money by selling the jeans for less than they bought them for.
C) The store will still earn a profit on the jeans by selling them for more than they bought them for.
Answers
Answer:
Step-by-step explanation: B) The store will lose money by selling the jeans for less than they bought them for.
The answer
Evaluate h(x)=−2x+9
when x=−2,0,
and 5
.
h(−2)=
h(0)=
h(5)=
Answers
Answer:
h(-2) = 13, h(0) = 9, and h(5) = -1.
Step-by-step explanation:
To evaluate h(x) = -2x + 9 for the given values of x, we can substitute each value of x into the expression and simplify:
h(-2) = -2(-2) + 9 = 13
h(0) = -2(0) + 9 = 9
h(5) = -2(5) + 9 = -1
Therefore, h(-2) = 13, h(0) = 9, and h(5) = -1.
At a restaurant, 600 customers were served during a 10-hour period of time. Which graph has a slope that best represents the number of customers that were served per hour at this restaurant?
Answers
Answer: The correct answer would be Graph H.
Step-by-step explanation:
Answer:
top right
Step-by-step explanation:
600 per 10 hours is a rate of 60/hour.
You need a graph that has a slope of 60 and includes the point (1, 60).
Answer: top right
Mr Khumalo has a budget of R30000 to fence off the garden
Determine if he will have sufficient funds to fence off the garden if it is further giveb that a gate of 1. 2m width, thats cost R500, will be fitted on one side of the garden
Answers
Answer:
No R30000 will be enough as the gate of 1.2m width cost R500
If we know the length of the garden and the cost per meter of fencing, we can determine if Mr. Khumalo has sufficient funds to fence off the garden, taking into account the cost of the gate.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To determine if Mr. Khumalo will have sufficient funds to fence off the garden,
We need to calculate the total cost of the fence excluding the cost of the gate.
Let's assume the length of the garden is L meters.
The perimeter of the garden is then 2L + 1.2 meters (due to the gate on one side).
If the cost of fencing per meter is R, then the total cost of the fence will be:
Cost of the fence.
= (2L + 1.2) × R
Since Mr. Khumalo has a budget of R30000, we can set up an inequality to determine if the cost of the fence is within his budget:
(2L + 1.2) × R + 500 ≤ 30000
Simplifying the inequality, we get:
(2L + 1.2) × R ≤ 29500
Therefore,
If we know the length of the garden and the cost per meter of fencing, we can determine if Mr. Khumalo has sufficient funds to fence off the garden, taking into account the cost of the gate.
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9. An arts and crafts store has a crate that contains glass,
wood, and brass beads. Friends take turns choosing a bead without
looking, recording the bead type, and returning the bead to the
crate. The table shows the results of 300 selections.
a. Write a probability model for choosing a bead.
b. Based on the frequencies in the table, estimate the number of
each type of bead that will be chosen if the friends select a total
of 450 beads from the crate.
Choosing Beads
Glass 60
Wood 96
Brass 144
Answers
In regards to question A:
P(G) = 0.2
P(W) = 0.32
P(B) = 0.48
B: we can estimate that the friends will choose approximately 90 glass beads, 144 wood beads, and 216 brass beads if they select a total of 450 beads from the crate.
What is the probability about?a. The probability model for choosing a bead can be represented by a discrete probability distribution, where the sample space consists of the three types of beads - glass, wood, and brass - and the probabilities of selecting each type are proportional to their respective frequencies. Let P(G) denote the probability of selecting a glass bead, P(W) denote the probability of selecting a wood bead, and P(B) denote the probability of selecting a brass bead. Then:
P(G) = [tex]\frac{60}{300}[/tex] = 1 ÷ 5 = 0.2
P(W) = [tex]\frac{96}{300}[/tex] = 8 ÷ 25 = 0.32
P(B) = [tex]\frac{144}{300}[/tex] = 12÷ 25 = 0.48
b. To estimate the number of each type of bead that will be chosen if the friends select a total of 450 beads from the crate, we can use the probabilities calculated above to find the expected number of beads of each type. Let X_G, X_W, and X_B denote the random variables representing the number of glass, wood, and brass beads, respectively, that are selected out of the 450 total selections. Then:
E(X_G) = P(G) × 450 = (1 ÷ 5) × 450 = 90
E(X_W) = P(W) × 450 = (8 ÷ 25) × 450 = 144
E(X_B) = P(B) × 450 = (12 ÷ 25) × 450 = 216
Therefore, based on the frequencies in the table, we would expect approximately 90 glass beads, 144 wood beads, and 216 brass beads to be chosen if the friends select a total of 450 beads from the crate.
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PLEASE HELP QUICK!!
Timmy and Susie both work at the Monster Burger. Timmy works for 40 hours and makes 720 dollars. He has been working there longer than Susie who makes only 600 dollars in the same amount of time. Monster Burger employees are given a 50 cent raise a year. How much higher is Timmy's pay rate than Susie's? How much longer had Timmy worked at Monster Burger than Susie?
Answers
Answer:
A. Tim's pay rate is $3/hr than Susie's
B. Tim worked 6 years longer than Susie
Step-by-step explanation:
Timmy makes $720 in 40 hrs
=> he makes 720/40 = $18.00/hr
Susie makes $600 in 40 hrs
=> she makes 600/40 = $15.00/hr
So Tim makes 18 - 15 = $3/hr than Susie
50 cent = $0.5
If pay raise is $0.5/yr
=> 3/0.5 = 6 yr
Tim worked 6 years longer than Susie
Suppose that y varies directly as the cube root of x, and that y=100 when x=6859. What is y when x=1331? Round your answer to two decimal places if necessary.
Answers
The value of y = 57.86 when x = 1331.
We are given that y varies directly as the cube root of x. This means that the equation relating y and x is of the form:
y = k * cube_root(x)
Where k is the constant of proportionality. We are also given that y = 100 when x = 6859. We can use this information to find the value of k:
100 = k * cube_root(6859)
k = 100 / cube_root(6859)
k = 100 / 19
k = 5.26
Now we can use the value of k to find y when x = 1331:
y = 5.26 * cube_root(1331)
y = 5.26 * 11
y = 57.86
Therefore, y is approximately 57.86 when x is 1331. We can round this answer to two decimal places to get:
y = 57.86
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Given the cost formula Y= $15,000 + $5X, what is the total cost at an activity level of 8,000 units? (2 marks) $23,000. $40,000 $15,000 $55,000
Answers
The total cost at an activity level of 8,000 units is $55,000.
The total cost at an activity level of 8,000 units can be found by plugging in the value of X into the cost formula Y= $15,000 + $5X.
Step 1: Plug in the value of X into the cost formula:
Y= $15,000 + $5(8,000)
Step 2: Simplify the equation by multiplying $5 and 8,000:
Y= $15,000 + $40,000
Step 3: Add $15,000 and $40,000 to get the total cost:
Y= $55,000
Therefore, the total cost at an activity level of 8,000 units is $55,000. The correct answer is $55,000.
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Find the size of angle x. 65° X 35°
Answers
The value of 'x' using the Triangle sum theorem is found as: x = 80°.
Explain about the Triangle sum theorem?According to the triangle sum theorem, all of a triangle's inner angles add up to 180 degrees. It is also known as the triangle's angle sum property.The triangle sum principle states that the sum of another three angles of any triangle is 180 degrees. According to their sides and angles, triangles can be classified into various mathematical kinds. These triangles are all three-sided and adhere to the triangle sum concept.Given that the triangle in the image is a triangle and that two of its angles is 65° and 35°.180° = 65°+35°+x
180° = 100°+x
180° - 100° = x
x=80° (value of x)
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Question 2 Consider the following set of vectors, where c is a parameter: A = {(2, 2, 0),(1, 2, c),(0, 0, c),(1, 0, 0)}. a) (1pt) Explain why A is linearly dependent for all values of c. b) (2pts) For c = 0, give a complete geometric description of Span(A). c) (2pts) Find all value(s) of c for which (4, 1, 3) is in Span(A).
Answers
We have to, A is linearly dependent for all values of c, the set of all vectors of the form (2a + b + c, 2a + 2b, 0) and the only value of c for which (4, 1, 3) is in Span(A) is c = 1.
a) A is linearly dependent for all values of c because there are more vectors than there are dimensions in the vector space. This means that one of the vectors can be expressed as a linear combination of the other vectors. Specifically, the vector (0, 0, c) can be expressed as a linear combination of the other vectors: (0, 0, c) = c*(2, 2, 0) + 0*(1, 2, c) + 0*(1, 0, 0).
b) For c = 0, the set of vectors A becomes {(2, 2, 0),(1, 2, 0),(0, 0, 0),(1, 0, 0)}. The span of this set of vectors is the set of all linear combinations of these vectors. Since the third vector is the zero vector, it does not contribute to the span. The span of the remaining vectors is the set of all linear combinations of the form a*(2, 2, 0) + b*(1, 2, 0) + c*(1, 0, 0). This is the set of all vectors of the form (2a + b + c, 2a + 2b, 0), which is a plane in R3 that contains the origin and is parallel to the xy-plane.
c) To find all values of c for which (4, 1, 3) is in Span(A), we need to find all values of c for which there exist scalars a, b, and d such that (4, 1, 3) = a*(2, 2, 0) + b*(1, 2, c) + d*(1, 0, 0). This gives us the following system of equations:2a + b + d = 42a + 2b = 1bc = 3We can solve this system of equations to find the values of a, b, and c. From the first equation, we can express d in terms of a and b: d = 4 - 2a - b. Substituting this into the second equation gives us 2a + 2b = 1 - 4 + 2a + b, which simplifies to b = 3. Substituting this value of b back into the third equation gives us 3c = 3, which gives us c = 1. Therefore, the only value of c for which (4, 1, 3) is in Span(A) is c = 1.
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if three times a number is increased by 4 the result is -8
Answers
Answer:
-4
Step-by-step explanation:
3x + 4 = -8
3x = -8 -4
3x = -12 /3
x = -4
Please help a brother out!!!
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Answer:
Just help your mother to wash your dise
Find the equation of the line passing through the point P
(2,1,-1) and orthogonal to the plane 2x-y+3z=10? [use X=P+TD
vector, X=x,y,z]
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This is the equation of the line passing through the point P (2,1,-1) and orthogonal to the plane 2x-y+3z=10.
The equation of the line passing through the point P (2,1,-1) and orthogonal to the plane 2x-y+3z=10 can be found using the X=P+TD vector equation. In this equation, X represents the point on the line, P represents the point through which the line passes, T represents a scalar parameter, and D represents the direction vector of the line.
To find the direction vector of the line, we can use the normal vector of the plane, which is given by the coefficients of the x, y, and z terms in the equation of the plane. The normal vector of the plane is (2,-1,3).
Since the line is orthogonal to the plane, the direction vector of the line will be parallel to the normal vector of the plane. Therefore, the direction vector of the line is also (2,-1,3).
Now, we can plug in the values of P and D into the X=P+TD equation to find the equation of the line:
X = (2,1,-1) + T(2,-1,3)
X = (2+2T, 1-T, -1+3T)
The equation of the line in parametric form is:
x = 2+2T
y = 1-T
z = -1+3T
This is the equation of the line passing through the point P (2,1,-1) and orthogonal to the plane 2x-y+3z=10.
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