Answers
----------------------------------------------------------
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Explanation:
There are two basic ways to find the slope.
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The first way is where we use the slope formula
m = (y2-y1)/(x2-x1)
The two points are (x1,y1) = (-1,8) and (x2,y2) = (2,-4)
Plug the coordinate of those points into the slope formula, then simplify
m = (y2-y1)/(x2-x1)
m = (-4-8)/(2-(-1))
m = (-4-8)/(2+1)
m = (-12)/(3)
m = -4
The slope is -4
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The second way is to use a more visually oriented approach.
Start at (-1,8).
Draw a straight vertical line through this point. Then move to the point (2,-4) and draw a completely flat horizontal line through this point.
Mark the intersection between these two lines (vertical and horizontal) as point A
Now go back to (-1,8). Count the number of spaces you must move down to go from (-1,8) to point A. You should count out 12 spaces. This is the run, which in this case is negative since we're going downhill as we move from left to right
Then count 3 spaces to go from point A to (2,-4). This is the run
Rise = -12
Run = 3
Slope = Rise/Run = -12/3 = -4
As you can probably see, this effectively mirrors some parts of the slope formula above
No matter which method you use, the slope is -4
-4 is the same as -4/1
A slope of -4/1 means we go down 4 units and then move to the right 1 unit
So that means rise/run = -12/3 is the same as saying rise/run = -4/1
Related Questions
To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.
At approximately what angle does the wire meet the ground?
Answers
12 feet would be the hypotenuse...
56.4 degrees my friend. That is ur answer.
Which is the next number in this pattern. What is the rule ? 0,1,1.5,1.75
A.2
B.1.875
C.1.85
D.1.8
Answers
A circle with radius 5 and a center at (2, 3) was transformed to a circle with radius 10 and a center of (‒1, 4).
Show that the two circles are similar by describing the transformations that would have to be performed.
Answers
Answer:
First of all, remember that all circles are similar to each other regardless of how to twist the cartesian plane.
Let the origin in first case(radius 5) be at (0,0) , so if we shift the origin to (2-(-1),3-(4)) = (3,-1) {shifting origin to shift the first circle to second's place}. So, we arrive at a circle of radius 5 and center (-1,4).
Since similarly has no constraints on size comparison increase the radius to 10 units. Thus we arrive at the circle of radius 10 and center (-1,4).
Step-by-step explanation:
First of all, remember that all circles are similar to each other regardless of how to twist the cartesian plane.
A small airplane used 5 2/3 gallons of fuel to fly 2 hour trip. How many gallons were used each hour
Answers
Solve for x.
5(x - 3) + 4(x + 3) = 3(x - 1)
x = 0
x = 1/4
x = 1/2
x = 1
Answers
5x−15+(4x+12)=3(x−1)
Simplify by adding terms.
Remove unnecessary parentheses.5x−15+4x+12=3(x−1)
Add 5x and 4x to get 9x.9x−15+12=3(x−1)
Add −15 and 12 to get −3.9x−3=3(x−1)
Simplify the right side.
Apply the distributive property.9x−3=3x+3⋅−1
Multiply 3 by −1 to get −3.9x−3=3x−3
Move all terms containing x to the left side of the equation.
Since 3x contains the variable to solve for, move it to the left side of the equation by subtracting 3x from both sides.9x−3−3x=−3
Subtract 3x from 9x to get 6x.6x−3=−3Move all terms not containing x to the right side of the equation.
Since −3 does not contain the variable to solve for, move it to the right side of the equation by adding 3 to both sides.6x=3−3Subtract 3 from 3 to get 0.6x=0Divide each term by 6 and simplify.x=0
9x - 3 = 3x - 3
9x = 3x
3x = x
3x - x = 0
2x = 0
x = 0
What is the significance of the mean of a probability distribution? choose the correct answer below.
a. it gives information about how the outcomes vary.
b. it represents the most likely possible outcome.
c. it is the expected value of a discrete random variable.
d. it can never be negative?
Answers
Answer:
Step-by-step explanation:
ANSWER C : It is the expected value of a discrete random variable
There are 180 pages in the book Diana is reading. Diana has read 90 pages. What percent of the book has she read?
Answers
=90/180×100%
=1/2×100%
=50%
Thus the percentage is 50%
1. In ΔPQR, PQ = PR and M is the midpoint of QR . Prove that PM bisects ∠QPR.
ANSWER FORMAT: ΔPQM = Δ (?) because... (reason)
2. In ΔABC, m∠B = m∠C. The angle bisector of ∠B meets
AC
at point H and the angle bisector of ∠C meets
AB
at point K. Prove that BH = CK.
ANSWER FORMAT: ΔBCK = Δ (?) because... (reason)
3. In ∆ABC the median
AM
is extended to ray
AM
and point P on
AM
is taken so that
PM = AM. What is the distance from point P to vertices C and B if AB = c and AC = b?
Answers
You forget the last two digits of your password for a website. What is the probability that you randomly choose the correct digits?
Answers
Which of the following has the ability to turn light energy into chemical energy? A. a generator B. an automobile C. a tree D. water
Answers
Rewrite and simplify ln(4500) in terms of ln5 and ln6
Answers
Simplified form of the given logarithmic expression ln(4500) will be ln(4500) = 3ln(5) + 2ln(6)
Given logarithmic expression in the question is,
ln(4500)We have to convert this expression in terms of ln(5) and ln(6).
Since, Factored form of 4500 = 5×5×5×6×6
= 5³×6²
Therefore, ln(4500) = ln(5³×6²)
= ln(5³) + ln(6²) [Since, ln(a × b) = ln(a) + ln(b)]
= 3ln(5) + 2ln(6) [Since, ln(a³) = 3ln(a)]
Hence, ln(4500) = 3ln(5) + 2ln(6) will be the answer.
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Determine the ordered pair that lies on the unit circle corresponding to startfraction 5 pi over 4 endfraction .
Answers
the table shows the sales of admission tickets to a science museum. A table labeled Science Museum Admission Revenue. It contains a row for Tickets Sold with the amounts 128, 264, 308, 514, 520, 650, 722, and a row for Sales with the amounts 1088, 2244, 2618, 4369, 5525, and 6137. The equation y = 9.75x represents the number of dollars, y, earned by an art museum for selling x tickets. Which statements about the costs of the admission tickets at the museums are true? Select each correct answer. It costs $9.75 per ticket for admission to the art museum. It costs $8.75 per ticket for admission to the science museum. Art museum tickets are more expensive than science museum tickets. Given the same number of ticket sales, the science museum earns more revenue. 1 2 3 4 5
Answers
Answer: It costs $9.75 per ticket for admission to the art museum.
Art museum tickets are more expensive than science museum tickets.
Step-by-step explanation:
From the given table of Science Museum Admission Revenue, we can see that the sales amount by selling 128 tickets = $1088
Therefore, the cost of each ticket for science museum =[tex]\frac{1088}{128}=\$8.5[/tex]
∴ It costs $8.5 (not 8.75) per ticket for admission to the science museum.
Also,The equation [tex]y = 9.75x[/tex] represents the number of dollars, y, earned by an art museum for selling x tickets.
At x=1, y=9.75
∴ It costs $9.75 per ticket for admission to the art museum.
Clearly, 9.75>8.5
∴ Art museum tickets are more expensive than science museum tickets.
If the number of ticket sales will be same then art museum will earn more revenue.
Since the price of one ticket to an art museum ($9.75) is higher than the price per ticket for science museum ($8.5), therefore the following statements about the cost at both museums would be true:
Price per ticket for admission to the art museum cost $9.75 (Option A)
Art Museum tickets cost more than that of science (Option C).
Price per ticket to a science museum:
Given the table showing the sales of admission tickets to a science museum:
Thus,
The unit rate/price per ticket sold at the science museum using a pair of values from the table, say, (128, 1088) is: y/x
Thus:
unit rate/price per ticket = [tex]\frac{1088}{128} = 8.5[/tex]That is, a ticket to a science museum costs $8.5.
Price per ticket to an art museum:
The equation, y = 9.75x is given as the equation modelling the situation.
Where x = number of tickets soldy = amount in dollarsThus, this means that the price per ticket to the art museum is: $9.75.
Therefore, since the price of one ticket to an art museum ($9.75) is higher than the price per ticket for science museum ($8.5), therefore the following statements about the cost at both museums would be true:
Price per ticket for admission to the art museum cost $9.75 (Option A)
Art Museum tickets cost more than that of science (Option C).
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the top of a certain mountain in California has an altitude of 14,721 ft above sea level. The bottom Death Valley is 282 ft below sea level. using 0 as sea level, find the difference between these two elevations. what is the difference between these two elevations?
Answers
the scatter plot shows how many desks and computers were found in 12 different offices
how many offices had 11 computers
1
2
3
4
Answers
Answer:
It's three. Look at 11 on the Y axis (computers) and count how many dots are at 11. There's a total of three computers based on the dots at 11.
Step-by-step explanation:
A scatter plot is a set of points plotted on horizontal and vertical axes.
It shows the relationship between two sets of data.
The number of offices that have 11 computers is 3.
What is a scattered plot?A scatter plot is a set of points plotted on horizontal and vertical axes.
It shows the relationship between two sets of data.
We have,
Horizontal axes = number of desks
Vertical axes = number of computers
Each dot in the scatter plot indicates offices.
Number of offices = 12 dots = 12
We need to find the number of dots that is with 11 computers.
We see that there are 3 dots with 11 computes so there are 3 offices that have 11 computers.
Thus the number of offices that have 11 computers is 3.
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A painter uses 1.2 liters of the paint to cover 1m2 of the wall. How many square meters he can cover with (1)12 liters; (2)6.6 liters; (3)4.8 liters of paint?
Answers
Answer:
He can cover 10 sq. meters using 12 liters, 5.5 sq. meters using 6.6 liters, and 4 sq. meters using 4.8 liters of paint.
Step-by-step explanation:
1. 12 LITERS/ 1.2 LITERS = 10 SQ. METERS
2. 6.6 LITERS/ 1.2 LITERS = 5.5 SQ. METERS
3. 4.8 ITERS/ 1.2 LITERS = 4 SQ. METERS
How much in Federal taxes does Curtis annually pay?
Answers
he pays 29.59 a week
multiply that by 52 weeks in a year
29.59 * 52 = 1538.68 a year
Answer is A
Given: x - 5 > -2.
Choose the solution set.
{x | x R, x > -7}
{x | x R, x > -3}
{x | x R, x > 3}
{x | x R, x > 7
Answers
x-5>-2
x> -5+2
X>3
Answer is: {x | x R, x > 3}
Use the graph of f to estimate the local maximum and local minimum. (explain)
Answers
Answer:
The graph has local maximum at (0,0) and minimum at (-2,-4) and (2,-4).
Step-by-step explanation:
Consider the provided graph.
it is not always possible to find maximum or minimum for the whole function, but locally it is.
To find the local maximum and minimum we need to choose an interval first.
Local maximum: f(c) ≥ f(x) for all x in the interval
Local minimum: f(c) ≤ f(x) for all x in the interval
For better understanding refer the figure 1
Now consider the provided graph:
The graph of the function at (-2,-4) and (2,-4) shows the minimum value that is -4.
Because at x = -2 and 2 the value of function f(x)≥f(c) for every x in the domain.
Also the graph of the function has local maximum at (0,0) as at x = 0
The value of function f(x)≤f(c) for every x in the domain.
Hence, the graph has local maximum at (0,0) and minimum at (-2,-4) and (2,-4).
The height of a triangle is 7 ft more than its base. if the area of the triangle is 30 ft^ what is the lentgh of the base
Answers
area=0.5(base)(height)
height=base+7
let base=x
area=0.5(x)(7+x)
30=3.5x+0.5x^2
multiply the equation by 2
60=7x+x^2
subtract 60 from both sides
x^2+7x-60=0
(x-5)(x+12)=0
thus x=5 or x=-12 since we are only considering positive answers
x=-12 is rejected
so base=5 and height=5+7=12
For a normal distribution, the z value for an x value that is to the right of the mean is always:
Answers
In a normal distribution, the Z value for an X value that is to the right of the mean is always positive. It indicates how many standard deviations X is larger than the mean. Conversely, Z values are negative for X values to the left of the mean because they are smaller than the mean.
Explanation:In a normal distribution, the Z value corresponds to the number of standard deviations a value X is from the mean. Specifically, for an X value that is to the right of the mean, the Z score will always be positive. This is because values to the right of the mean are larger than the mean.
For example, if X = 10 and the mean is 5, and this corresponds to a Z score of 2.5, it means that X is 2.5 standard deviations to the right of the mean. In other words, X is larger than the mean by 2.5 times the standard deviation. The actual Z score, such as 2.5 in this example, indicates how far the score is from the mean, with greater Z scores indicating values further to the right of the mean.
In contrast, X values to the left of the mean have negative Z scores, indicating they are smaller than the mean. Finally, if X equals the mean, then X has a Z score of zero. This basic understanding of Z scores and their relation to the mean in a normal distribution is crucial in many statistical analyses.
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Rewrite the rational expression x^3+5x^2+3x-10/x+4 in the form q(x)+r(x)/b(x).
Answers
Hope I helped :)
Answer:
[tex]x^2+x-1-\frac{6}{x+4}[/tex]
Step-by-step explanation:
Rational expression form : [tex]\frac{a(x)}{b(x)}=q(x)+\frac{r(x)}{b(x)}[/tex]
a(x) = dividend
b(x) = divisor
q(x) = quotient
r(x) = remainder
Given expression : [tex]\frac{x^3+5x^2+3x-10}{x+4}[/tex]
We know that [tex]Dividend = Divisor \times Quotient+Remainder[/tex]
So, [tex]x^3+5x^2+3x-10 =x+4 \times (x^2+x-1)-6[/tex]
Thus a(x) = dividend = [tex]x^3+5x^2+3x-10 [/tex]
b(x) = divisor= [tex]x+4[/tex]
q(x) = quotient=[tex]x^2+x-1[/tex]
r(x) = remainder=-6
Substitute the value in the rational form.
[tex]\frac{x^3+5x^2+3x-10}{x+4}=x^2+x-1-\frac{6}{x+4}[/tex]
Hence the rational expression [tex]\frac{x^3+5x^2+3x-10}{x+4}[/tex] in the form of [tex]q(x)+\frac{r(x)}{b(x)}[/tex] is [tex]x^2+x-1-\frac{6}{x+4}[/tex]
In the diagram ABC = WRS. What is the perimeter of WRS?
Answers
Perimeter = 12 for both triangles.
Which graph models the equation 2x + 3y = 6?
Answers
graph according to y=mx + b
b is y intercept, so the graph crosses the point (0, 6)
m is the slope and slope is rise over run. So go down 2 and right 3 from (0,6) as many times as you need to fill up the graph.
Then go up 2 and left 3 from (0,6) as many times as you need to fill the graph.
Put arrows at each end of your line to show that it's a line.
Answer: i did the test and i got B and i was right so its B
Step-by-step explanation:
Luis ate three of the eight pizza slices. he paid $2.70 as his share of the cost. how much did the whole pizza cost?
Answers
21: stan bought a monster truck for $2,000 down and payments of $450 a month for five years. what's the total cost of the monster truck?
Answers
2000 + 450(60)
2000 + 27000 = 29,000
He spend $27,000 on the truck.
Hope this helps!
Answer:
The total cost of the monster truck = 29000 $
Step-by-step explanation:
Stan bought a monster truck for $2,000 down and payments of $450 a month for five years.
Initial payment = 2000 $
Monthly payment = 450 $
Number of years paid = 5
Number of months in 5 years = 12 x 5 = 60
Total amount paid = 2000 + 60 x 450 = 29000 $
The total cost of the monster truck = 29000 $
rewrite the expression as a multiple of a sum of two numbers with no common factor 15+24 _____
Answers
15 + 24 = 3(5 + 8)
To rewrite the expression as a multiple of a sum of two numbers with no common factor, find the prime factorizations of the given numbers and then multiply them together which brings the result as 39.
Explanation:To rewrite the expression as a multiple of a sum of two numbers with no common factor, we need to find two numbers that have no common factors and multiply them together. Let's find the prime factorizations of 15 and 24:
15: 3 × 524: 2 × 2 × 2 × 3Now we can rewrite the expression as:
15 + 24 = (3 × 5) + (2 × 2 × 2 × 3) = 3 × (5 + 8) = 3 × 13 = 39
So, 15 + 24 can be written as a multiple of 3 × 13, which is 39.
Tiana's checking account charges a $7.75 monthly service fee and a $0.16 per-check fee. If Tiana writes 17 checks per month, should she switch to a checking account that charges a $10.50 monthly service fee and no per-check fee? A. No, because her monthly fees are currently greater than $10.50. B. No, because her monthly fees are currently less than $10.50. C. Yes, because her monthly fees are currently less than $10.50. D. Yes, because her monthly fees are currently greater than $10.50.
Answers
the answer to this question is B
Answer:
Option B. is correct.
Step-by-step explanation:
Tiana's checking account charges a $7.75 monthly service fee and $0.16 per check fee.
If Tiana writes 17 checks per month, her total charges =
0.16 × 17 = 2.72 + 7.75 = $10.47
Her total account charges $10.47 for 17 checks.
In the question it is asking that she should switch to a checking account that charges a $10.50 monthly service fee and no per check fee.
Answer : No, because her monthly fees are currently less than $10.50.
Which transformations are needed to change the parent cosine function to y=3cos(10(x-pi))
Answers
The parent cosine function is transformed [tex]y=3cos(10(x-\pi ))[/tex] by vertically stretching it by a factor of 3 (amplitude), horizontally compressing it by a factor of 10 (frequency), and shifting it to the right by [tex]\pi[/tex] units (horizontal shift or phase shift).
The question asks which transformations are required to alter the parent cosine function to [tex]y=3cos(10(x-\pi ))[/tex]. The transformations involved in this equation are:
Amplitude modification: The coefficient '3' indicates that the amplitude of the cosine function is scaled by a factor of 3.Frequency adjustment: The factor '10' inside the cosine function affects the function's frequency, indicating the function has 10 complete cycles within the interval of [tex]2\pi[/tex] radians. This is a horizontal scaling transformation.Horizontal shift (or phase shift): The subtraction of [tex]\pi[/tex] within the argument of the cosine function translates the function [tex]\pi[/tex] units to the right along the x-axis.No vertical shift is present because there is no addition or subtraction outside the cosine function.
To transform the parent cosine function [tex]\(y = \cos(x)\) to \(y = 3 \cos(10(x-\pi))\)[/tex], apply a vertical stretch by 3, horizontal compression by 1/10, and a right shift by [tex]\(\pi\)[/tex] units.
To transform the parent cosine function[tex]\(y = \cos(x)\)[/tex] to the function [tex]\(y = 3 \cos(10(x-\pi))\)[/tex], we need to apply the following transformations:
1. Amplitude change: Multiply the function by [tex]\(3\)[/tex], which increases the amplitude.
2. Horizontal compression: Multiply the input of the cosine function by [tex]\(10\),[/tex]which compresses the graph horizontally.
3. Phase shift: Shift the graph to the right by [tex]\(\pi\)[/tex]units, indicated by the term [tex]\(x - \pi\).[/tex]
So, the transformations needed are:
- Amplitude change: Vertical stretch by a factor of [tex]\(3\).[/tex]
- Horizontal compression: Compression by a factor of [tex]\(1/10\).[/tex]
- Phase shift: Right shift by [tex]\(\pi\)[/tex] units.
Solve. 5m+72=−2m+52 Drag and drop the answer into the box.
Answers
5m + 72 + 2m = -2m + 52 + 2m
7m + 72 = 52
7m + 72 - 72 = 52 - 72
7m = -20
7m/7 = -20/7
m = -20/7