Answer:
Step-by-step explanation:
4 then add 5 + 1 which would = 4
An investor invested a total of $3,300 in two mutual funds. One fund earned a 4% profit while the other earned 2% profit. If the investors total profit was $94, how much was invested in each mutual fund
Answer:
.04x + .02($3,300 - x) = $94
.04x + $66 - .02x = $94
.02x = $28
x = $1,400 in 4% fund
$3,300 - $1,400 = $1,900 invested in 2% fund
are these functions. {(2, 3), (1, 3), (5, 3), (2, 6)}
Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of four fifths to create polygon A′B′C′D′. If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′.
A′(−3.2, 4.8), B′(−1.6, 1.6), C′(3.2, −1.6), D′(3.2, 3.2)
A′(−16, 24), B′(−8, 8), C′(16, −24), D′(16, 16)
A′(3.2, −4.8), B′(1.6, −1.6), C′(−3.2, 1.6), D′(−3.2, −3.2)
A′(4.5, −3), B′(1.5, −1.5), C′(−1.5, 3), D′(3, 3)
Answer:
A.
Step-by-step explanation:
New x-coordinate = (-4) * (4/5) = -16/5 = -3.2
New y-coordinate = 6 * (4/5) = 24/5 = 4.8
that's the only option with a -3.2 for A
Kayla can see that the measure of Angle I and Angle J
form a straight line. Since Kayla knows that a straight line has
an angle measure of 180°, what is the measure (in degrees) of
Angle J? please answer as quickly as you can
Angle J is equal to 90°.Hence, the measure of Angle J is 90°.
Kayla can see that the measure of Angle I and Angle J form a straight line. Since Kayla knows that a straight line has an angle measure of 180°, what is the measure (in degrees) of Angle J
Given,The angle formed by angle I and J is a straight line which measures 180°.We need to find the measure of angle J.To find the measure of angle J, we need to find out the angle measure of angle I.
From the above information, we know that the angle formed by angle I and J is a straight line that measures 180°.So,Angle I + Angle J = 180°Substitute Angle I in terms of Angle J. We know that the angles are supplementary and they add up to 180 degrees.
If we know the measure of one of the angles, we can find the measure of the other angle as well.So ,Angle I = 180° - Angle JNow, substitute the value of Angle I in the above equation.Angle I + Angle J = 180°(180° - Angle J) + Angle J = 180°180° - Angle J + Angle J = 180°
Thus, Angle J is equal to 90°.Hence, the measure of Angle J is 90°.
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Two number in ratio 4:1 sum is 60 find largest number
Answer:
48
Step-by-step explanation:
4 : 1
4 + 1 = 5
60/5 = 12
12 × 4 = 48
12 × 1 = 12
48 : 12 are numbers in a 4:1 ratio and add to 60.
Answer: 48
Answer:
larger # is 48
look at attachment
Step-by-step explanation:
4x+1x=60
1. Solve for x.
(4x + 1)º
47°
Answer:
x = 33
Step-by-step explanation:
(4x + 1)° and 47° lie on a straight line and sum to 180° , that is
4x + 1 + 47 = 180
4x + 48 = 180 ( subtract 48 from both sides )
4x = 132 ( divide both sides by 4 )
x = 33
The value of x is:
x = 33Work/explanation:
The two angles form a linear pair, which means they add to [tex]\sf{180^o}[/tex].
Because they add up to 180, we can set up an equation to find x.
[tex]\sf{4x+1+47=180}[/tex]
Combine like terms on the left side
[tex]\sf{4x+48=180}[/tex]
Subtract 48 on each side
[tex]\sf{4x=132}[/tex]
Divide each side by 4
[tex]\sf{x=33}[/tex]
Hence, x = 33.Alex opened a savings account with an intial deposit of $50. Each month, he deposits the same amount of money. He uses the equation t = 50 + 25m to determine t, the total amount of money in his savings account in m months. What is the unit rate and what is the meaning of the unit rate
Answer:
The unit rate is 25$
Step-by-step explanation:
The unit rate gives the amount by which the money in the his account increases per month. It measures the rate of increase in the account.Which in this case the unit rate is 25$
Fill in the table using this function rule y = 5+5x
Using the function rule y = 5 + 5x, we can fill in the table as follows:
x | y
0 | 5
1 | 10
2 | 15
3 | 20
4 | 25
To fill in the table using the function rule y = 5 + 5x, we can substitute different values of x into the equation and calculate the corresponding values of y.
Let's create a table:
x | y
0 | 5 + 5(0) = 5 + 0 = 5
1 | 5 + 5(1) = 5 + 5 = 10
2 | 5 + 5(2) = 5 + 10 = 15
3 | 5 + 5(3) = 5 + 15 = 20
4 | 5 + 5(4) = 5 + 20 = 25
Using the function rule y = 5 + 5x, we can substitute each value of x into the equation to find the corresponding value of y. For example, when x = 0, y = 5. When x = 1, y = 10, and so on.
Therefore, the completed table is:
x | y
0 | 5
1 | 10
2 | 15
3 | 20
4 | 25
These values satisfy the given function rule y = 5 + 5x.
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You have a 12 inch by 14 inch picture that you framed. When you hung the picture, you found that the entire area is 261.44 inches squared. What is the width of the frame?
The width of the frame is 1 inch.
To determine the width of the frame, we must subtract the area of the picture from the total area.
Therefore: total area - picture area = frame area
261.44 - 168 = 93.44 square inches
The frame area can also be calculated by multiplying the frame width by 2 (since there are two sides of the frame) and adding it to the picture dimensions.
Thus:2w + 12 = length2w + 14 = width where w is the width of the frame.
Using the above equations, we can solve for w: 2w + 12 = 14, 2w = 2, and w = 1
Therefore, the width of the frame is 1 inch.
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2. A company owns two flourmills (A and B) which have different production capacities for HIGH, MEDIUM and LOW grade flour. This company has entered contract supply flour to a firm every week with 12, 8, and 24 quintals of HIGH, MEDIUM and LOW grade respectively. It costs the Co. $1000 and $800 per day to run mill A and mill B respectively. On a day, mill A produces 6, 2, and 4 quintals of HIGH, MEDIUM and Low grade flour respectively. Mill B produces 2, 2 and 12 quintals of HIGH, MEDIUM and LOW grade flour respectively. How many days per week should each mill be operated in order to meet the contract order most economically. Solve the problem graphically.
Mill A and Mill B should be operated for 6 days each in order to meet the contract order most economically
Understanding Economic Production of FlourLet's define the variables:
- Let 'x' represent the number of days mill A is operated per week.
- Let 'y' represent the number of days mill B is operated per week.
We need to minimize the cost function, which is the sum of the operating costs for both mills:
Cost = 1000x + 800y
Now, let's consider the production constraints:
For the HIGH grade flour:
Mill A produces 6 quintals per day, so the total weekly production is 6x.
Mill B produces 2 quintals per day, so the total weekly production is 2y.
To meet the contract requirement of 12 quintals per week, we have the constraint:
6x + 2y ≥ 12
For the MEDIUM grade flour:
Mill A produces 2 quintals per day, so the total weekly production is 2x.
Mill B produces 2 quintals per day, so the total weekly production is 2y.
To meet the contract requirement of 8 quintals per week, we have the constraint:
2x + 2y ≥ 8
For the LOW grade flour:
Mill A produces 4 quintals per day, so the total weekly production is 4x.
Mill B produces 12 quintals per day, so the total weekly production is 12y.
To meet the contract requirement of 24 quintals per week, we have the constraint:
4x + 12y ≥ 24
The graph will have the axes 'x' and 'y' representing the number of days mill A and mill B are operated, respectively.
Let's solve the problem graphically:
To plot each constraint, we can convert them into linear equations:
1) 6x + 2y ≥ 12
Rewrite as: 3x + y ≥ 6
Plot the line: 3x + y = 6
From the graph, Mill A should be operated for 2 days per week while Mill B should be operated for 6 days per week.
2) 2x + 2y ≥ 8
Rewrite as: x + y ≥ 4
Plot the line: x + y = 4
From the graph, Mill A should be operated for 4 days per week while Mill B should be operated for 4 days per week.
3) 4x + 12y ≥ 24
Rewrite as: x + 3y ≥ 6
Plot the line: x + 3y = 6
From the graph, Mill A should be operated for 6 days per week while Mill B should be operated for 2 days per week.
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please help find g(12)
Answer:
g(12) = 10
Step-by-step explanation:
To find g(12)
here t = 12 and lies in the range 6 ≤ t ≤ 12
so we use g(t) = [tex]\frac{5t}{6}[/tex]
⇒ g(12) = [tex]\frac{5*12}{6}[/tex]
= 5*2
= 10
g(12) = 10
Use the equation of the line to identify a point the line passes through and the slope of the line. Then, graph the line.
y+3=1/3(x+3)
The point is (3, 2 1/3).
Given the equation of the line,y + 3 = 1/3(x + 3)
To identify a point the line passes through and the slope of the line, we first need to convert the equation of the line into slope-intercept form.y + 3 = 1/3(x + 3) y = 1/3x + 1
As we can see from the slope-intercept form of the equation, the slope of the line is 1/3.
To graph the line, we need to choose two points on the line and connect them with a straight line.
Let's choose the y-intercept and another point on the line.
The y-intercept is (0,1). To find another point, we can choose x = 3.y = 1/3x + 1y = 1/3(3) + 1y = 2(1/3)
Thus, the point is (3, 2 1/3).
We can now plot these points and connect them with a straight line to get the graph of the line. Graph of the line y + 3 = 1/3(x + 3)
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2. Find x if the mZFED= 1190, mZIED= x+61, and m/FEI= x + 66, is
Answer:
x = - 4
Step-by-step explanation:
∠ FEI and ∠ IED form ∠ FED , that is
∠ FEI + ∠ IED = ∠ FED ( substitute values )
x + 66 + x + 61 = 119
2x + 127 = 119 ( subtract 127 from both sides )
2x = - 8 ( divide both sides by 2 )
x = - 4
Suppose f is a one-to-one function with the following values. f(−7)f(−2)=−8=5 Which of the following must be true? Select all correct answers. Select all that apply: f−1(−8)=5 f−1(−7)=8 f−1(5)=−2 f−1(−2)=−5 f−1(−8)=−7 f−1(5)=−7
Based on the analysis, the only statement that must be true is: -[tex]f^{(-1)(-8)} = -7[/tex]
How to determine the statement that must be trueGiven that f is a one-to-one function, it implies that it has an inverse function denoted as [tex]f^{(-1)}.[/tex] The inverse function undoes the operation of the original function, such that [tex]f(f^{(-1)(x))} = x[/tex] for any x in the domain.
Now let's analyze the given options:
1. [tex]f^{(-1)(-8)} = 5[/tex]: We cannot determine the truth of this statement based on the given information. It depends on the behavior of the function f and its inverse.
2.[tex]f^{(-1)(-7)} = 8:[/tex] This option contradicts the given information. The value of f(-7) is -8, so the inverse function evaluated at -8 should yield -7, not 8.
3. [tex]f^{(-1)(5)} = -2[/tex]: We cannot determine the truth of this statement based on the given information. It depends on the behavior of the function f and its inverse.
4.[tex]f^{(-1)(-2)} = -5:[/tex]We cannot determine the truth of this statement based on the given information. It depends on the behavior of the function f and its inverse.
5.[tex]f^{(-1)(-8)} = -7:[/tex] This option aligns with the given information. The value of f(-7) is -8, so the inverse function evaluated at -8 should yield -7.
6. [tex]f^{(-1)(5)} = -7:[/tex] We cannot determine the truth of this statement based on the given information. It depends on the behavior of the function f and its inverse.
Based on the analysis, the only statement that must be true is:
[tex]f^{(-1)(-8)} = -7[/tex]
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Find y' by (a) applying the Product Rule and (b) multiplying the factors to produce a sum of simpler terms to differentiate.
y=(3-x^2)(x^3-5x+5)
a. Apply the Product Rule. Let u=(3-x^2) and v=(x^3-5x+5).
b. Multiply the factors of the original expression, u and v to produce a sum of simpler terms.
Find y'.
The factors of the original expression, u and v to produce a sum of simpler terms, the derivative of y with respect to x is: y' = -2x⁴ - x² - 10x + 15
Given the expression y = (3 - x²) (x³ - 5x + 5),
We need to find the derivative of y with respect to x.
We can find y' using two methods:
Method 1: Applying the Product RuleIf y = uv, then we know that y' = u'v + uv'Applying this formula to the given expression, We get:
y = (3 - x²) (x³ - 5x + 5)u = (3 - x²) and v = (x³ - 5x + 5)
Differentiating u and v, we get:u' = -2x and v' = 3x² - 5
Substituting these values into the formula for y', we get:
y' = u'v + uv' = (-2x) (x³ - 5x + 5) + (3 - x²) (3x² - 5)
Simplifying this expression, we get:
y' = -2x⁴ + 10x² - 10x - 3x² + 15 = -2x⁴ - x² - 10x + 15
Method 2: Multiplying the Factors to Produce a Sum of Simpler Terms to Differentiate
Expanding the given expression, we get:
y = 3x³ - 15x + 15 - x⁵ + 5x³ - 5x - 3x² + 15x² - 15x
Differentiating this expression, we get: y' = 9x² - 15 + 0 - 5x⁴ + 15x² - 5 - 6x + 30x - 15
Simplifying this expression, we get:
y' = -2x⁴ - x² - 10x + 15
Therefore, the derivative of y with respect to x is:y' = -2x⁴ - x² - 10x + 15
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Question for experts !
Recommend books for partial differential equations from beginner to advanced
Answer:
Here are some recommended books on partial differential equations (PDEs) from beginner to advanced level:
1. "Partial Differential Equations: An Introduction" by Walter A. Strauss: This is a great introductory book on PDEs that covers the basics of first-order equations, second-order equations, and higher-order equations.
2. "Partial Differential Equations" by Lawrence C. Evans: This is a more advanced textbook that covers a wide range of topics in PDEs, including elliptic equations, parabolic equations, hyperbolic equations, and conservation laws.
3. "Nonlinear Partial Differential Equations" by Peter J. Olver: This is an advanced book that covers the theory and applications of nonlinear PDEs, including Hamiltonian systems, solitons, and integrable systems.
4. "Introduction to the Theory of Nonlinear Elliptic Equations" by V. G. Maz'ya and S. Poborchi: This is an advanced book that provides a comprehensive introduction to the theory of nonlinear elliptic equations.
5. "Geometric Partial Differential Equations and Image Analysis" by Guillermo Sapiro: This is an advanced book that covers the application of PDEs to image analysis, including topics such as denoising, segmentation, and registration.
These books provide a good foundation for understanding PDEs and their applications, and can be useful for students and researchers at various levels of expertise.
Geometry
Answer fast
Answer:
Your correct
Step-by-step explanation:
The transversal,a, creates right angles for line b, c, and d. This they are parallel
HELP FIND TRIANGLE GRAPH TRANSFORMATION
The triangle after the reflection over the line y = x has image points: (x'k), (5,-2), and (-6,-1). The corresponding preimage points are: (3,4), (4,3), and (-2,5).
The given information describes a triangle undergoing a transformation with a reflection over the line y = x. Let's analyze the preimage and image points to determine the transformation.
Preimage points: (3,4), (4,3), and (-2,5)
Image points: (x'k), (5,-2), and (-6,-1)
Since we know the reflection is over the line y = x, we can determine the image points by swapping the x and y coordinates of the preimage points. Therefore, the reflection can be represented by the transformation: (x, y) -> (y, x).
Applying this transformation to the preimage points, we get the image points as follows:
(3,4) -> (4,3)
(4,3) -> (3,4)
(-2,5) -> (5,-2)
Now we can check if the image points match the given image points:
(4,3) matches (x'k)
(3,4) matches (5,-2)
(5,-2) matches (-6,-1)
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The inequality 5m − 7 > 16 holds true for all numbers
than
in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
The inequality 5m - 7 > 16 holds true for the values m = 6, 7, 8, 9, and 10, in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
To determine the values for which the inequality 5m - 7 > 16 holds true, we can solve it algebraically and then check if each value in the given set satisfies the inequality.
Let's solve the inequality:
5m - 7 > 16
Adding 7 to both sides, we have:
5m > 23
Dividing both sides by 5, we get:
m > 23/5
Now we need to check if each number in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} satisfies the inequality m > 23/5.
For m = 1:
1 is not greater than 23/5, so the inequality does not hold true.
For m = 2:
2 is not greater than 23/5, so the inequality does not hold true.
For m = 3:
3 is not greater than 23/5, so the inequality does not hold true.
For m = 4:
4 is not greater than 23/5, so the inequality does not hold true.
For m = 5:
5 is not greater than 23/5, so the inequality does not hold true.
For m = 6:
6 is greater than 23/5, so the inequality holds true.
For m = 7, 8, 9, and 10:
All these values are also greater than 23/5, so the inequality holds true for them as well.visit
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Help me with 8 pls
-5 10
-3 6
-1 2
Answer:
12
Step-by-step explanation:
Select any two random points on the graph of the line (preferably with integer coordinates).
Label them as A and B (in any order).
Calculate the "rise" from A to B. While going vertically from A to B, if we have to go. ...
Calculate the "run" from A to B. ...
Now, use the formula: slope = rise/run.
Answer:
a) -2
b) 1/2
Step-by-step explanation:
To find the slope given 2 points use the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Use the 2 points:
(-5,10)
(-3,6)
[tex]\frac{6-10}{-3+5}\\ \frac{-4}{2} \\-2[/tex]
So, a has a slope of -2.
Given the 2 points on the graph:
(-1,4)
(-5,2)
use the same formula:
[tex]\frac{2-4}{-5+1}\\ \frac{-2}{-4}\\ 1/2[/tex]
so b has a slope of 1/2
Hope this helps! :)
graph the line with slope of 4 and y-intercept 1
The graph of the line y = 4x + 1 is on the graph at the end.
How to graph the line?A linear equation in the slope-intercept form is written as:
y = ax + b
Where a is the slope and b is the intercept of the y-axis.
Here we know that:
slope = 4 ---> a = 4
y-intercept = 1 ---> b = 1
Then our line is:
y = 4x + 1
To graph this we just need two points on the linear equation, that then we can graph and connect with a line.
when x = 0
y = 4*0 + 1 = 1
So we have (0, 1)
when x = 1
y = 4*1 + 1 = 5
So we have (1,5)
With these two points we will get the graph of the line that you can see below.
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The graph below shows the percentages of ingredients in a salad mix.
A pie chart titled Percentages in salad mix. 40 percent is iceberg, 27 percent is romaine, 15 percent is spinach, 12 percent is arugula, 6 percent is carrots.
Dominic buys a 64-ounce container of salad mix. About how many ounces of romaine lettuce does the container have?
6 ounces
12 ounces
18 ounces
27 ounces
The correct Option is C. Dominic buys about 18 ounces of romaine lettuce in the 64-ounce container of salad mix.
From the pie chart, we can infer that the percentage of romaine lettuce in the salad mix is 27%.
We can find the number of ounces of romaine lettuce in a 64-ounce container of salad mix by multiplying 64 by 27/100.
This is because we want to find what fraction of the whole salad mix is romaine lettuce, and then multiply it by the total number of ounces in the container.
Using proportions, we can find that:Let x be the number of ounces of romaine lettuce in a 64-ounce container of salad mix.
27/100 = x/64
Solving for x, we get:x = (27/100) * 64 = 18.28
Therefore, there are about 18.28 ounces of romaine lettuce in a 64-ounce container of salad mix.
However, since we are asked to give an approximate answer, we can round this to the nearest whole number, which is 18.
So, Dominic buys about 18 ounces of romaine lettuce in the 64-ounce container of salad mix.
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This is the input-output table for the linear function y = 3x. Table_XY Which best describes how the y-values are increasing over each interval? Subtract 10 over each interval. Multiply by 2 over each interval. Add 3 over each interval..
Step-by-step explanation:
Can you provide an image please?
Answer:
C
Step-by-step explanation:
Use the graph to estimate the median cost of a home in 2014 (19 years after 1995).
Using the given graph, we can see that the median cost is 480 thousands of dollars.
How to estimate the cost in 2014?To find the cost in 2014, 19 years after 1995 which is the zero in the horizontal axis, first we need to locate the value x = 19 in the horizontal axis.
Once we do, we move vertically upwards until we meet the graph (in this case, the blue line).
Once we meet with the graph of the line, we move horizontally until we hit the vertical axis, and we record the correspondent value.
Doing that, we can see that the median cost of a home in 2014 is 480 thousands of dollars.
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Cant figure this out,not even for the life of me.
Find f(1) for the
piece-wise function.
f(x) =
2x
NIT
if x < 1
+/ ifx>1
x+
f(1) = [?]
well, f(1) is indicating that x = 1, hmmm for the piecewise, on what section is that?
well, x < 1 is just whenever "x" is less than 1, but not 1.
x ⩾ 1 is whenever "x" is either 1 or greater than 1, so that's our guy, so we use that subfunction to get it.
[tex]f(x)= \begin{cases} 2x&x < 1\\\\ \cfrac{1}{2}x+\cfrac{5}{2}&x\geqslant 1\hspace{3em}\textit{f(1) is in this section} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(1)=\cfrac{1}{2}(1)+\cfrac{5}{2}\implies f(1)=3[/tex]
you can approximate e by substituting large values for n into what expression
This method of approximation is derived from the mathematical concept of limits and the definition of the number e as the limit of (1 + 1/n)^n as n approaches infinity. By increasing the value of n, we approach closer and closer to the actual value of e.
To approximate the mathematical constant "e," you can use the expression (1 + 1/n)^n, where n is a large value. As n approaches infinity, this expression converges to the value of e. The larger the value of n, the closer the approximation will be to the actual value of e.
For example, let's substitute a large value, say n = 10,000, into the expression:
Approximation of e ≈ (1 + 1/10,000)^10,000
Calculating this expression, we get an approximation of e as approximately 2.7181459. Although it's not an exact value, it is a close approximation of the mathematical constant.
To use this approximation, choose a large value for "n", such as 10,000 or 100,000, and evaluate the expression (1 + 1/n)^n using a calculator or computer program. The result will be a close approximation of the value of "e". The larger the value of "n", the more accurate the approximation will be.
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Pls help it’s for my homework
Answer: I think it is 5
Therefore, The Volume of ORNAMENT ( B ) is 5^3 = 125 TIMES LARGER than the VOLUME of ORNAMENT ( A ).
Hence, The VOLUME of ORNAMENT (B) is 125 TIMES LARGER than the VOLUME of ORNAMENT (A).
Step-by-step explanation:MAKE A PLAN:
We know that the Height of ORNAMENT ( B ) is FIVE (5) Times Larger than the Height of ORNAMENT ( A ). We need to Find the Ratio of their Volumes.
SOLVE THE PROBLEM:1) - Let the height of Ornament ( A ) be hA and the height of Ornament
( B ) be, hB
2) - We know the hB = 5 * hA
3) - Since the Ornaments are Mathematically Similar, Their Volumes are Proportional to the Cube of their heights.
4) - Calculate The Ratio of their Volumes:
(hB )^3 / (hA )^3 (5 * hA )^3 / (hA )^3
Draw the conclusion:Therefore, The Volume of ORNAMENT ( B ) is 5^3 = 125 TIMES LARGER than the VOLUME of ORNAMENT ( A ).
Hence, The VOLUME of ORNAMENT (B) is 125 TIMES LARGER than the VOLUME of ORNAMENT (A).
I hope this helps you!
What is the quotient of (x³ - 3x² + 5x - 3) + (x - 1)?
Ox²-2x-3
Ox²+2x+7
Ox²-3x+8
Ox²-2x+3
Answer:
(d) x² -2x +3
Step-by-step explanation:
You want the quotient (x³ - 3x² + 5x - 3) ÷ (x - 1).
Quick CheckThe constant in a product will be the product of the constants in the factors. That is if (x² +bx +c) is a factor of the cubic, we must have ...
-1·c = -3 . . . . . . . where the other factor is (x -1), having constant -1
c = 3
Only one answer choice matches: x²-2x+3.
Synthetic divisionUsing synthetic division to find the entire quotient can be almost as fast.
The tableau is shown in the attachment. It tells you the quotient is ...
x² -2x +3
__
Additional comment
"The entry in the left part of the table" is the zero of the binomial divisor. The divisor (x-1) is zero when x=1, so that entry is 1.
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which of the following situations has a straight line and passes through the origin? • Kevin gets $2 for each point he scores in a basketball match. • The area of district and its population. • The cost of a pie is $3.50 and the base charge is $2. • All of the choices.
The situation that has a straight line and passes through the origin is when "All of the choices" are true.
A straight line equation in slope-intercept form is given by; y = mx + b, where m is the slope and b is the y-intercept.However, when the straight line passes through the origin, then the value of b becomes zero, which means the equation becomes; y = mx.
Therefore, among the given situations, the one that has a straight line and passes through the origin is "All of the choices."
Since all the given situations have a proportional relationship, which means as one variable increases, the other variable increases, then they all form a straight line that passes through the origin.
Therefore, all the given situations have a straight line and passes through the origin.
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14 Find the distance between the two points. Imagine a right triangle connecting the two points. (-3,2) www (2,-2) Hint: Find the base of the triangle by calculating the distance between the x-values of each point. Jay |2 - (-3) = [?]
The distance between the points (-3, 2) and (2, -2) is approximately sqrt(41), which is an irrational number.
To find the distance between two points (-3, 2) and (2, -2), we can use the Pythagorean theorem and consider the points as the vertices of a right triangle.
The base of the triangle is the horizontal distance between the x-values of the two points.
In this case, it is given by:
Base = 2 - (-3) = 2 + 3 = 5
Next, we need to find the height of the triangle, which is the vertical distance between the y-values of the two points. It is given by:
Height = -2 - 2 = -4
Now, we have the base and the height of the triangle.
To find the distance between the two points, we can use the Pythagorean theorem, which states that the square of the hypotenuse (distance) is equal to the sum of the squares of the other two sides (base and height).
Using the Pythagorean theorem:
Distance^2 = Base^2 + Height^2
Distance^2 [tex]= 5^2 + (-4)^2[/tex]
Distance^2 = 25 + 16
Distance^2 = 41
To find the distance, we take the square root of both sides:
Distance = sqrt(41).
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