Which of the relationships below represents a function with the same rate of change (slope) as the the function y = -5x + 3?
Answers
Given the function:
\(y\text{ = -5x + 3}\)The rate of change (slope) is expressed as
\(\begin{gathered} \text{slope = }\frac{rise}{run} \\ =\frac{y_2-y_1}{x_2-x_1} \end{gathered}\)The slope is also evaluated from the general equation of the line function expressed as
\(\begin{gathered} y\text{ = mx + c} \\ \text{where} \\ m\Rightarrow slope \\ c\Rightarrow y-intercept \end{gathered}\)In the given function,
\(y\text{ = -5x + 3}\)This implies that in comparison with the general equation of the line function, the rate of change (slope) is evaluated to be -5.
In option A,
taking any two points for (x₁, y₁) and (x₂, y₂),
\(\begin{gathered} (x_1,y_1)\Rightarrow(4,\text{ -10)} \\ (x_2,y_2)\Rightarrow(8,\text{ -15)} \\ \end{gathered}\)the slope is evaluated to be
\(\begin{gathered} \text{slope = }\frac{-15--10}{8-4}=\frac{-15+10}{8-4} \\ =-\frac{5}{4} \\ \text{slope = -}\frac{5}{4} \end{gathered}\)In option B,
\(\begin{gathered} (x_{1,}y_1)\Rightarrow(-1,0) \\ (x_2,y_2)\Rightarrow(0,\text{ -5)} \end{gathered}\)the slope is evaluated to be
\(\begin{gathered} \text{slope = }\frac{-5-0}{0--1}=-\frac{5}{1} \\ \text{slope =-5} \end{gathered}\)In option C,
\(\begin{gathered} (x_{1,}y_1)\Rightarrow(0,4) \\ (x_2,y_2)\Rightarrow(3,22\text{)} \end{gathered}\)the slope is evaluated to be
\(\begin{gathered} \text{slope = }\frac{22-4}{3-0}=\frac{18}{3} \\ \text{slope = 6} \end{gathered}\)In option D,
\(\begin{gathered} (x_{1,}y_1)\Rightarrow(-1,0) \\ (x_2,y_2)\Rightarrow(0,4\text{)} \end{gathered}\)the slope is thus evaluated as
\(\begin{gathered} \text{slope =}\frac{4-0}{0--1}=\frac{4}{1} \\ \text{slope = 4} \end{gathered}\)Since the slope in option B is evaluated to be -5 which is equivalent to the slope of the function in question, the correct option is B.
Related Questions
How can X-2/3=5/6 be solved for x in one step?
O Add 2/3 to both sides.
O Add 5/6 to both sides.
O Subtract 2/3 from both sides.
O Subtract 5/6 from both sides.
Answers
This allows you to isolate c
A technology company is going to issue new ID codes to its employees. Each code will have two letters, followed by one digit, followed by one letter. The letters D, G, and Z and the digit 8 will not be used. So, there are 23 letters and 9 digits that will be used. Assume that the letters can be repeated. How many employee ID codes can be generated?
Answers
Using the concept of permutation, the company can generate 108,927 different employee ID codes.
How many employee ID codes can be generated?To know the number of employee ID codes that's generated, we can check the number of possibilities of each component and multiply them together.
Given:
- Two letters can be chosen from 23 letters (excluding D, G, and Z).
- One digit can be chosen from 9 digits.
- One letter can be chosen from 23 letters (excluding D, G, and Z).
Number of possibilities for the first letter = 23
Number of possibilities for the second letter = 23
Number of possibilities for the digit = 9
Number of possibilities for the third letter = 23
To calculate the total number of employee ID codes, we multiply these possibilities together:
By using the concept of permutation;
Total number of ID codes = 23 × 23 × 9 × 23
Total number of ID codes = 108,927
Therefore, the company can generate 108,927 different employee ID codes.
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Name all the chords ...
Answers
Answer:
option 3 is the answer.
The Two-Steppers numbered 10 more than 5 times the number of waltzers. Also there were 10 times as many Two-steppers as waltzers. How many of each were there?
Answers
Answer: I think it is 1,200
Step-by-step explanation: search it up
Without multiplying, how can you tell which product will be greater, 3 x 4 or 6 x 2?
Answers
Answer:
we can compare 4 x 3 and 2 x 6, equal to 12. So, we can see that both products are similar and neither is greater.
Step-by-step explanation:
We can use the commutative property of multiplication to see that 3 x 4 is the same as 4 x 3 and 6 x 2 is the same as 2 x 6. When multiplying two numbers, the order of the numbers does not affect the product. Therefore, we can compare 4 x 3 and 2 x 6, equal to 12. So, we can see that both products are similar and neither is greater.
NEED MORE EXPLANATION?
The commutative property of multiplication states that when multiplying two numbers, the order of the numbers does not affect the product. This means that 3 x 4 is the same as 4 x 3, and 6 x 2 is the same as 2 x 6. We can use this property to compare 4 x 3 and 2 x 6, equal to 12. Therefore, we can see that both products are identical and neither is greater.
What is the unit rate of a line that goes through the points (3,1)?
Answers
Answer:
3.
Step-by-step explanation:
3 divided by 1 equals 3.
Please mark me brainliest I need it!!!
pls help me this my my second assignment help me!!!
Answers
Answer:
Step-by-step explanation:
F/4 = 18
Multiply both sides by 4
F = 72 N
answer is A
Answer:
72N
Step-by-step explanation:
pressure=force/Area
MAKE FORCE SUBJECT OF THE FORMULA
:. FORCE=PRESSURE ×AREA
Force=18Nm² × 4m²
Force= 18N ×4
:. Force=72N
PLEASE MARK AS BRILLIANT ANSWER
rewrite the expression without absolute value bars
Answers
The expression without absolute value bars is 3.84.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
|√10 - 7 |
= | 3.16 - 7 |
= | -3.84 |
= 3.84
Thus,
The value of the expression is 3.84.
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Atlanta and Cincinnati 440 miles apart. John leaves Cincinnati; driving
toward Atlanta at an average rate of 60 mph. Pat leaves Atlanta at the same time, driving toward Cincinnati in her antique auto, averaging 28 mph. How long will it take them to meet?
Answers
Answer:
5 hours
Step-by-step explanation:
28x = 60(440-x)
28x = 60*440 - 60x
88x = 60*440
x = 60*440/88
x = 300mi, distance Jon travels
300mi/60mph = 5hrs, the time it took them to meet
CHECKING OUR ANSWER
60MPH*5HR + 28MPH*5HR = 300MI + 140MI = 440MI
Find the area of the composite figure below (help pls)
Answers
Answer:
189.25
Step-by-step explanation:
multiply 15 by 10 to find area of rectangle.
The area of rectangle is 150.
To find area of semicircle 1/2(pi r^2)
divide 10 by 2 to find radius, which is 5
area of semicircle would be 39.27
add 150 to 39.27
the answer is 189.27
189.25 is close enough so that is answer
What is the image point of (3,3)(3,3) after the transformation D_{5}\circ T_{0,-1}D
5
∘T
0,−1
?
Answers
The coordinates of image point is (15, 20)
How to determine the image pointA dilation is a transformation that changes the size of a figure but not its shape.
In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.
The transformation is given as
T<0, 1>D5
Mathematically, this
(x, y) = 5(x, y + 1)
So the image point is
(x, y) = 5(3, 3 + 1)
(x, y) = (15, 20)
So the image point of is (15, 20)
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Suppose there is a simple index of two stocks, stock A and stock B. Stock A opens on Monday with 5000 shares at $2.75 per share. Stock B opens on Monday with 3000 shares at $4.30 per share. Stock A opens on Tuesday at $3.10 per share, and stock B opens on Tuesday at $4.85 per share. Both stocks have the same number of shares that they opened with on Monday. What is the rate of change of this simple index over 1 day?
Answers
The rate of change of the simple index over one day is approximately 12.78%.
To calculate the rate of change of the simple index over one day, we need to determine the percent change in the total value of the index between Monday's opening and Tuesday's opening.
On Monday, Stock A has 5000 shares at $2.75 per share, so its total value is:
Total value of Stock A on Monday = 5000 * $2.75 = $13,750
Similarly, on Monday, Stock B has 3000 shares at $4.30 per share, so its total value is:
Total value of Stock B on Monday = 3000 * $4.30 = $12,900
The total value of the index on Monday is the sum of the values of Stock A and Stock B:
Total value of the index on Monday = $13,750 + $12,900 = $26,650
On Tuesday, Stock A opens at $3.10 per share, and Stock B opens at $4.85 per share. Both stocks still have the same number of shares as on Monday.
The total value of Stock A on Tuesday is:
Total value of Stock A on Tuesday = 5000 * $3.10 = $15,500
The total value of Stock B on Tuesday is:
Total value of Stock B on Tuesday = 3000 * $4.85 = $14,550
The total value of the index on Tuesday is the sum of the values of Stock A and Stock B:
Total value of the index on Tuesday = $15,500 + $14,550 = $30,050
To calculate the percent change in the index, we use the formula:
Percent Change = ((New Value - Old Value) / Old Value) * 100
Percent Change = (($30,050 - $26,650) / $26,650) * 100 ≈ 12.78%
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10 POINTS!!!!which polynomial represents the sum below?
Answers
Answer:
The right answer to the question is A
Find the exterior of a rectangle in a polygon
Answers
The measure of each exterior angles of rectangle is 90°
Finding the exterior of a rectangle in a polygonFrom the question, we have the following parameters that can be used in our computation:
A rectangle
A rectangle is a polygon with 4 sides
So, the measure of the exterior angle can be calculated using the formula for the exterior angles in a polygon
The exterior angles in a polygon are found by using:
Exterior of a rectangle in a polygon = 360°/Number of sides of the polygon
In this case,
The number of sides of the rectangle = 4
So, we have
Exterior of a rectangle = 360°/4
Evaluate
Exterior of a rectangle = 90°
Hence, the value of the measure of each exterior angles of rectangle is 90°
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Complete question
Find the measure of each exterior angles of rectangle?
Step by step
no links please
Evaluate 10v for v = -8.
A.
2
B.
-90
C.
80
D.
-80
Answers
Step-by-step explanation:
10(-8) substitute (-8) for V
10 • -8 = -80 Then solve by multiplying
An
Write the fraction as a mixed number 10/20
Answers
One positive number is 8 times another number. Their difference is 70.
Which of the following equations could be used to find the numbers?
Answers
Answer:
X equals 10.
8x - x = 70
Step-by-step explanation:
8 x 10 = 80
80 - 10 = 70
suppose y varies directly as x, and y=48 when x=6. find x when y=72.
Answers
Using the constant of proportionality the value of x when y is 72 is 9.
What is a COP?
The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.
If y varies directly as x, it means that y can be expressed as a constant multiple of x, i.e., y = kx, where k is the constant of proportionality.
To find k, we can use the given information that y = 48 when x = 6 -
y = kx
48 = k(6)
k = 8
Now that we know k, we can use it to find x when y = 72 -
y = kx
72 = 8x
x = 9
Therefore, when x = 72, the value of x = 9.
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Which of the following relations is not a function?
{(-1, 3), (4, 2), (-1, 5)}
{(1, 2), (3, -5), (-1, 7)}
{(0, 0), (1, 0), (2, 0)}
{(7, -1), (3, -2), (5, -2)}
Answers
keeping in mind that a function has no X-Repeats, namely the 1st coordinate in every pair is never repeated, Check the picture below.
Greetings to everyone! Can anyone be willing to help me in the word problems on Normal Distributions? I will forever be thankful and grateful to you!
Answers
Answer:
if some does this than this would happen
Step-by-step explanation:
help help help help help help help help help help help help help help help help help help help help help help help help help help help help
Answers
Eltel uie diswer the space provided.The two triangles shown have the same perimeters.6x + 32x + 15x
Answers
We have the following:
\(6x+3+2x+1+4x=5x+5x+3x+2\)solving for x:
\(\begin{gathered} 6x+3+2x+1+4x=5x+5x+3x+2 \\ 12x+4=13x+2 \\ 13x-12x=4-2 \\ x=2 \end{gathered}\)Therefore, the answer is x is equal 2
38. Which of the following describes a median of a triangle? (1 point)
a segment drawn from a vertex to the midpoint of the opposite side
a segment drawn from the vertex perpendicular to the line containing the opposite side
a segment drawn through the midpoint of a side and at a right angle to the side.
segment drawn from the center of an angle to the side opposite.
Answers
A statement that describes the median of a triangle include the following: A. a segment drawn from a vertex to the midpoint of the opposite side.
What is a triangle?In Mathematics and Geometry, a triangle is a two-dimensional geometric shape that comprises three sides, three vertices and three angles only.
In Mathematics and Geometry, the median of a triangle can be defined as a line segment with end points that is typically drawn from a vertex to the midpoint of the opposite side of the triangle.
In this context, we can logically deduce that a line segment with end points at the vertex and the midpoint of the triangle's opposite side simply refers to the median of a triangle.
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ASAPP PLEAASSEE!!!
Nathan deposits $940 every 2 months into his daughter's RESP. If the account earns 3.99% / annual, compound quarterly, how much will be in the account after 25 years?
Answers
There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.
To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (amount in the account after 25 years)
P = Principal amount (amount deposited every 2 months)
r = Annual interest rate (in decimal form)
n = Number of times the interest is compounded per year
t = Number of years
In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.
Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.
Now, we can substitute these values into the formula:
A = 940(1 + 0.0399/4)^(4*25)
Calculating the exponent first:
(1 + 0.0399/4)^(4*25) ≈ 2.703236
Now, substituting the calculated exponent and the number of deposits into the formula:
A = 940 * 2.703236 * 150 ≈ $594,311.34
Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.
It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.
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Solve the system.
2x + y + 3z = 20
X + 2y - z = -11
3x - 2z = -3
Enter your answer as an ordered triple.
Answers
The solution to the system, as an ordered triple is: (3, -4, 6).
How to Solve a System of Equations?To solve the following given system of equations:
2x + y + 3z = 20 --> eqn. 1
x + 2y - z = -11 --> eqn. 2
3x - 2z = -3 --> eqn. 3
Multiply equation 1 by 2 to get eqn. 4:
4x + 2y + 6z = 40 --> eqn. 4
Subtract eqn. 4 from eqn. 2:
x + 2y - z = -11 --> eqn. 2
4x + 2y + 6z = 40 --> eqn. 4
-3x - 7z = -51 --> eqn. 5
Add equations 3 and 5 together:
3x - 2z = -3 --> eqn. 3
-3x - 7z = -51 --> eqn. 5
-9z = -54
z = -54/-9
z = 6
Substitute the value of z into equation 5:
-3x - 7(6) = -51 --> eqn. 5
-3x - 42 = -51
-3x = -51 + 42
-3x = -9
-3x/-3 = -9/-3
x = 3
Find the value of y by substituting the values of x and z into equation 1:
2(3) + y + 3(6) = 20 --> eqn. 1
6 + y + 18 = 20
24 + y = 20
y = 20 - 24
y = -4
The solution as an ordered triple is: (3, -4, 6).
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Drag each tile to its equivalent measure, rounded to the nearest tenth.
Options: 19.8, 10.2, 22.7, 15.4
Measure Equivalent
4 in. _____ Cm
7 kg _____lb
6 gal _____L
65 ft _____ m
Answers
The correct matches are: 4 in. → 10.2 cm , 7 kg → 15.4 lb
6 gal → 22.7 L and 65 ft → 19.8 m.
What are conversions?Conversions refer to the process of changing a measurement from one unit to another unit that measures the same quantity.
For example, converting distance from miles to kilometers, or converting weight from pounds to kilograms.
Here are the conversions:
1 inch = 2.54 cm (approx.)
1 kg = 2.205 lb (approx.)
1 gal = 3.785 L (approx.)
1 ft = 0.3048 m (approx.)
Using these conversions, we can find the equivalent measures:
4 in. → 4 × 2.54 = 10.16 ≈ 10.2 cm
7 kg → 7 × 2.205 = 15.435 ≈ 15.4 lb
6 gal → 6 × 3.785 = 22.71 ≈ 22.7 L
65 ft → 65 × 0.3048 = 19.812 ≈ 19.8 m
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Each of 5 friends has x action figures in
his or her collection. Each friend buys 11 more action figures. Now
the 5 friends have a total of 120 action figures.
a. Write an equation that models the problem.
b. Solve the equation to find the number of action figures, x, that each friend had originally.
Answers
Answer:
13
Step-by-step explanation:
Here, each of the 5 friends has an x action figure. When they buy 11 more we have 5(x+11). Now they have a total of 120 action collections and here we have 5(x+11)=120
→\(5(x+11)=120\\\\\)
→\(5x+55=120\\\)
→\(5x=120-55\)
→\(5x=65\)
→\(x=65/5\\\)
→\(x=13\)
Hence, each of the friends has 13 action collections originally.
\(→5(x +11) = 120\)
\(→5x + 55 = 120\)
\(→5x = 120 - 55\)
\(→ 5x = 65\)
\(→x = \frac{65}{5}\)
\(→x = 13 \)
So, each of the friends has 13 action collections originally.
use the photo shown to solve for inequalities in two triangles
Answers
Solutions
\(ComparingI can infer that:\(\begin{gathered} 5x-35<90 \\ adding\text{ }35\text{ }to\text{ }both\text{ }sides; \\ 5x<90+35 \\ 5x<125 \end{gathered}\)Divide through with the coefficient of x;
\(\begin{gathered} x=\frac{125}{5} \\ x=25^o \end{gathered}\)Similarly;
I can Infer that;
\(\begin{gathered} 5x-35>0 \\ 5x>0+35 \\ 5x>35 \\ x>\frac{35}{5} \\ x>7 \end{gathered}\)Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations.
(a) The process standard deviation is 0.25, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.75 or greater than 10.25 ounces will be classified as defects. If required, round your answer for the probability of a defect to four decimal places and for the number of defects to the nearest whole number.
Probability of a defect:
Number of defects:
Answers
The probability of a defect is 5.7330 x \(10^{-5}\) and the number of defects is 5.73.
To calculate the probability of a defect, we need to find the area under the standard normal curve that lies outside of the process control limits of 9.75 ounces and 10.25 ounces. We can use the standard normal distribution table to find this area.
First, we need to standardize the weight limits as follows -
\(Z_{lower}\) = (9.75 - 10) / 0.25 = -4
\(Z_{upper}\) = (10.25 - 10) / 0.25 = 4
Next, we will find the area under the standard normal curve that lies outside of these limits as follows -
P(Defect) = P(Z < -4) + P(Z > 4)
Using a standard normal distribution table, we can find that P(Z < -4) = 2.8665 x \(10^{-5}\) and P(Z > 4) = 2.8665 x \(10^{-5}\) .
So, the total probability of a defect is -
P(Defect) = 2.8665 x \(10^{-5}\) + 2.8665 x \(10^{-5}\) = 5.7330 x \(10^{-5}\)
Finally, we will find the number of defects for a 1,000-unit production run as follows -
The number of defects = 1000 * 5.7330 x \(10^{-5}\) = 5.73 (rounded to the nearest whole number).
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Kyle sold an antique through an online auction website. The website host charges kyle $15, plus 2.5% of the final selling price of the antique. After selling the antique, kyle had to pay the website host $32. What was the selling price?
Answers
The selling price of the antique through an online auction website is $680.
Given that,
Kyle sold an antique through an online auction website.
The website host charges Kyle $15, plus 2.5% of the final selling price of the antique.
After selling the antique, Kyle had to pay the website host $32.
Let x be the selling price of the antique.
We get an equation,
15 + (2.5% × x) = 32
15 + 0.025x = 32
0.025x = 17
x = $680
Hence the selling price is $680.
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