Answer:
y = -2x
Step-by-step explanation:
It passes through -5, 10 and 5, -10
gradient = Δy/Δx
gradient = -10 - 10 / 5 -- 5
gradient = -20 / 10
gradient = -2
let's use -5, 10 for y = mx + b
10 = -2(-5) + b
10 = 10 + b
b = 10 - 10
b = 0.
the equation of the line is just y = -2x
p + (-q) - 2 = ? When p = -3 and q = 5
Answer:
= -10
Step-by-step explanation:
p + (-q) - 2 = x
if:
p = -3
q = 5
then:
-3 + (-5) - 2 = x
we know that:
+(-) = -
then:
-3 +(-5) - 2 = -3 - 5 - 2 = x
x = -10
The value of the expression p + (-q) - 2 is -10 if the p = -3 and q = 5 the answer is -10.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have given an expression:
= P + (-q) - 2
Plug p = -3
q = 5
= -3 + (-5) - 2
= -3 - 5 - 2
= -10
Thus, the value of the expression p + (-q) - 2 is -10 if the p = -3 and q = 5 the answer is -10.
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PLEASE HELP
Question 3 Alexa wants to use an indirect proof to prove that all rectangles are not squares. She first assumes that all rectangles are squares. Alexa then provides the following counterexample to disprove her assumption. She concludes that all rectangles must not be squares. Which statement best describes Alexa's indirect proof? Alexa's proof is incorrect. She followed the steps of an indirect proof in the wrong order. O Alexa's proof is incorrect. She made an error in her assumption. O Alexa's proof is correct and contains no errors. Alexa's proof is incorrect. She made an error in her counterexample. #
Alexa's proof is incorrect. She made an error in her counterexample.
What is rectangle?"It is a quadrilateral whose all angles measure 90°, opposite sides are parallel and equal in length."
What is square?"It is a parallelogram whose all sides are equal in length and all angles measure 90° "
What is parallelogram?"It is quadrilateral whose opposite sides are parallel and equal in length."
What is counterexample?"It is a special kind of example that disproves a statement. "
For given question,
Alexa wants to use an indirect proof to prove that all rectangles are not squares.
We know that, to prove a theorem indirectly, we assume the hypothesis is false, and then arrive at a contradiction. It follows the that the hypothesis must be true.
Alexa first assumes that all rectangles are squares.
Then she provides counterexample as shown in the given diagram.
The diagram represents the parallelogram not a rectangle.
This means she made an error in her counterexample.
Therefore, Alexa's proof is incorrect. She made an error in her counterexample.
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Help please! Geometry word problem!
By applying reflection theory and constructing a geometric system of two proportional right triangles, the height of the stainless steel globe is approximately 140 ft.
How to estimate the height of the stainless steel globe
By physics we know that both the angle of incidence and the angle of reflection are same. Thus, we have a geometric system formed by two proportional right triangles:
5.6 ft / 4 ft = h / 100 ft
h = (5.6 ft × 100 ft) / 4ft
h = 140 ft
By applying reflection theory and constructing a geometric system of two proportional right triangles, the height of the stainless steel globe is approximately 140 ft.
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Let’s say you bought a car for $16,500. The car is expected to last 8 years and then it can be sold for scrap for $500. The value at the end of the life of the car is sometimes called the “salvage value” or “residual value.” Part A: If we assume that the relationship between the value of the car and the year is linear, how much will the value of the car depreciate each year? Explain your strategy. Part B: Complete the table of values. Years of Ownership Value of the Car 0 1 2 Part C: Create a sketch of the data points on your paper. Be sure to label the graph thoroughly. Would it make sense to connect the points? 3) Consider all of the information you have collected in Question 2. Part A: Write an equation for the value of the car in terms of the year. Part B: What is the slope of the line? Explain what the slope means in this context. 4) Are the value of the car and the number of years since the car was purchased proportional? Justify your response. 5) Look at the changes in the value of the car and the corresponding changes in the years of ownership. Are the changes proportional? How do you know? 6) Examine the proportionality of these two equations: � = 2� + 3 � = 2� Which is an example of a linear equation that is also proportional? Justify your
Answer:
value of car depreciate each year = $2000
y + 2000x = 16,500
slope of line = -2000
No, not proportional
Step-by-step explanation:
Value of depreciation of an object is given by :-
Depreciation = [tex]\frac{ total Cost-scrap value}{estimated life}[/tex]
according to question ;
total cost = $16500
scrap value = $500
estimated life = 8 years
therefore,
depreciation = [tex]\frac{16500 - 500}{8}[/tex] = [tex]\frac{16000}{8}[/tex] = $2000
now,
let the value of car after 'x' years be 'y'
therefore linear equation showing the relation of x and y is
y + 2000x = 16500
The graph of a linear equation is a line.
If c = 0 in a linear equation (so y = mx), then the equation is a proportional linear relationship between y and x.
If c ≠ 0, then y = mx + c is a non-proportional linear relationship between y and x.
here equation is of type,
y = mx +c, thus it is not linear.
also in the equation y = mx +c,
'm' is the slope of line
therefore by comparing the equation,
y +2000x = 16500
y = -2000x + 16500
slope is - 2000
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Generalize A system of linear equations has exactly one solution. What can you say about the slopes of the lines when the equations are graphed? How do you know? Generalize A system of linear equations has exactly one solution . What can you say about the slopes of the lines when the equations are graphed ? How do you know ?
If a system of linear equations has exactly one solution then the slopes of both the lines should be different.
Given A system of linear equations has exactly one solution.
Linear equation is a type of equation when when plotted on the graph gives a straight line. The slope is the ratio of the vertical change to the horizontal change between two distinct points on a line.
let two equations be who have one solution
2x+3y=7
5x+6y=1
solving them
x=7-3y/2
put the value of x in second equation
5(7-3y)/2+6y=1
35-15y/2+6y=1
35-15y+12y=2
-3y=-33
y=11
put the value of y in x=7-3y/2
x=7-3*11/2
x=7-33/2
x=-26/2
x=-13.
There is only one solution which is (-13,11)
Taking equations and convert them into standard form
first
y=7/3-2/3x
second
y=1/6-5/6x
The standard form is y=a+bx where b is slope
from the above equations we can find that the slope of first equation is -2/3 and the slope of second equation is -5/6. In this way we are able to conclude that slopes should be different for one solution.
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help me pleaseeeeeeeeeeee i need the answer fast because it is limited
i will mark as brainiest
Answer:
D
Step-by-step explanation:
Original area = x * x = x^2
New area = x ( x +3.5) = x^2 + 3.5x <====the underlined is the increase in area
A random sample is selected from a population with mean = 100 and standard deviation = 10. Determine the mean and standard deviation of the x sampling distribution for each of the following sample sizes. (Round the answers to three decimal places.)
If N=41
If N=130
The mean and standard deviation of the x sampling distribution for each of the following sample sizes will be [tex]N(100,10/\sqrt{41} ), N(100,10/\sqrt{130} )[/tex].
What is the distribution of the sample mean for large samples?Suppose X has a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma,[/tex]then,
the distribution of the mean of samples of size n, drawn from the values of X, is normally distributed with a mean equal to the mean of X, and a standard deviation equal to [tex]\sigma/\sqrt{n}[/tex]
Symbolically, we write it as:
[tex]X \sim N(\mu, \sigma) \implies \overline{X} \sim N(\mu,\sigma/\sqrt{n} )[/tex]
A random sample is selected from a population with a mean = of 100 and a standard deviation = of 10.
The mean and standard deviation of the x sampling distribution for each of the following sample sizes.
If N=41
[tex]X \sim N(100, 10) \implies \overline{X} \sim N(100,10/\sqrt{41} )[/tex]
If N=130
[tex]X \sim N(100, 10) \implies \overline{X} \sim N(100,10/\sqrt{130} )[/tex]
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What is the solution to the equation shown below?
-1/3(6x+6)+21=3y
Answer:
A or 19/5
Step-by-step explanation:
To solve first we isolate are variables so we distubte to get -2y-2+21=3y then we add 2y to the opposite side to get -2+21=5y. Then we add -2+21 to get 19 so are equation is 19=5y. Next we just divide 19 by 5 to get y=(19/5) or option A
please help. Show with steps please.
Solve the compound inequality.
0 < 5-2x/3 <5
Answer: The answer is x < 5/2 and x > -5.
Step-by-step explanation:
First you need to separate the inequality and keep x on one side to maintain consistency. For instance the problem-
[tex]\frac{5-2x}{3} > 0\\\frac{5-2x}{3} < 5\\[/tex]
Now solve as normal.
*Note: When dividing a side or multiplying a side by a negative number, the sign of the inequality switches (this will be shown when I do the equation if it doesn't make since how I word it).
[tex]5-2x > 0*3\\5-2x < 5*3[/tex]
[tex]-2x > 0-5\\-2x < 15-5[/tex]
[tex]x < \frac{-5}{-2} =x < \frac{5}{2} \\x > \frac{10}{-2} =x > -5[/tex]
So, x < 5/2 and x > -5.
If anything is confusing about the procedure just leave a comment, and I'll try to explain further.
he table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.
The height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have given a table:
Time height
2 8
4 12
6 16
8 20
10 24
The slope of the line = (12-8)/(4-2) = 4/2 = 2
The value of the slope is positive we can say, the height of water increases as time passes.
Thus, the height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.
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the answer is A: The height of the water increases 2 inches per minute.
hope this helped :)
Which is the equation of the line with slope 0 passing through the point (-3, -1)?
Which pair of equations below represents two lines that are not parallel?
Select one:
a.
y = 2x + 8 and y = 2x + 8
b.
y = ( 1 / 6 ) x + 1 /2 and y = (1 / 6 ) x + 2
c.
y = ( 1 / 6 ) x + 8 and y = 6x + 4
d.
y = ( 1 / 2 ) x + 9 and y = ( 1 / 2) x + 4
The pair of equations (c) y = (1 / 6) x + 8 and y = 6x + 4 are not parallel
How to determine the pair of equations?A linear equation is represented as:
y = mx + b
Where m is the slope of the line
Two lines are said to be parallel if their slopes are the same
i.e. y = mx + b and y = mx + c
Using the above as a guide, the option (c) represents lines that are not parallel, because they do not have the same slope
Hence, y = (1 / 6) x + 8 and y = 6x + 4 are not parallel
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The radius of a circle is 3ft. What is the circumference of the circle? Use 3.14 for pie.
A class of students consists of 9 men and 51 women. Write a proper fraction to represent the part of the class that is women. Reduce the fraction. Change the fraction to a percent.
Answer:
85%
Step-by-step explanation:
9+51 = 60
(51/3) ÷ (60/3) = 17/20
(17/20)% = 85%
Find f(g(x)) for the functions f(x)=5sqrt(x+1)-2 and g(x)=x^2-1
The value of the composite function f(g(x)) is 5x + 2
Composite functionsComposite functions are functions inside another function. Given the following functions:
f(x) = 5√x+1 - 2
g(x) = x² - 1
Determine the composite function f(g(x))
f(g(x)) = f(x² - 1)
f(x² - 1) = 5√x² - 1+1 - 2
f(x² - 1) = 5√x² + 2
f(x² - 1) = 5x + 2
Hence the value of the composite function f(g(x)) is 5x + 2
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Find the reciprocal of the sum of the reciprocals of 1/-5 and -1/6
Answer:
-1/11
Step-by-step explanation:
A reciprocal means the reverse of a number. So the numerator becomes a one and the number goes in the denominator (for example 2 becomes 1/2). Or vice versa: the one becomes the denominator and the denominator becomes the numerator (for example 1/2 becomes 2/1 which is 2).
The reciprocal of -1/5 is -5.
The reciprocal of -1/6 is -6.
The sum of both reciprocals: -5 + -6 = -11
The reciprocal of the sum -11 is -1/11.
Which ordered pair is on the graph of the equation 4x + 3y = 13?
(1, 6)
(0, –3)
(1, –3)
(4, –1)
15 In the figure, O is the centre of the circle. The diameter of the circle, AB, is 14 cm, and
is the same as the length of each side of the square PQRS. Find
Answer:
56cmsquared
Step-by-step explanation:
if you look clearly at that question that diagram which has the coloured part out of that small square comes a quarter circle.
now take that quarter circle and get its area .
then put a dotted line such that they'll be formation of a triangle in that quarter circle.
then get the area of that quarter triangle in minus it from the area of the quarter circle.
and you'll get the area of 1 shaded part because you had subdivided those shaded parts by the dotted line you had kept earlier in order to emerge with a triangles
after that what multiply what you got by two to get the whole shaded part then finalize by multiplying by two because two shapes were shaded.
good day
Need help with this please!! :)
The following are scores for students in Ms. Kennedy's math class.What is the range of the scores?
451
560
600
422
603
514
A 109
B 149
C 178
D181
Answer:
The answer will be D. 181
Step-by-step explanation:
603 - 422 = 181
Please mark me as the brainliest.
Write a rule to describe each translation
Answer:
slide - translate
Step-by-step explanation:
you slided them both as neither of the figures changed
Divide.round to the nearest tenth .16÷.03220
Answer:
5.0
Step-by-step explanation:
0.16÷0.03220=4.9689
=5.0
If a = 7, b = 2 and c = 3, evaluate: a-bc.
Answer: 1
Step-by-step explanation:
[tex]a-bc=7-2(3)=7-6=\boxed{1}[/tex]
The graph shows that is translated horizontally and vertically to create the function .
On a coordinate plane, 2 exponential functions are shown. f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.5) and crosses the y-axis at (0, 1). g (x) approaches y = 2 in quadrant 2 and increases into quadrant 1. It goes through (0, 2) and (2, 3).
What is the value of h?
−2
−1
1
2
According to the function transformations, the value of h is -2
How to determine the value of h?The complete question is in the attachment
The functions are given as:
[tex]f(x) = (2.5)^x[/tex]
[tex]g(x) = (2.5)^{x-h[/tex]
From the question, we understand that the function f(x) is translated to the left to get g(x)
From the attached graph, we can see that the function h(x) is 2 units to the left of f(x).
This transformation is represented by:
(x, y) => (x + 2, y)
So, we have:
x - h = x + 2
Evaluate the like terms
h = -2
Hence, the value of h is -2
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Answer:H=-2
Step-by-step explanation:
What is the area of the triangle?
24 square units
32 square units
48 square units
96 square units
Answer:
24 square units
Step-by-step explanation:
1) the area can be calculated using the formula:
A=0.5*a*h, where a- base, h-height;
2) if a=8, h=6, then the required area is:
A=0.5*8*6=24 [units²].
Answer: 24 square units
Step-by-step explanation:
The base: 8
The height: 6
The area: 8 x 6 / 2 = 24
/ stands for divided by
A media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 degrees C. The difference from the previous year is less than the margin of error of about 0.13 degrees C, so that difference should be ignored. What is the best counterargument?
The difference is only 0.04, but that is still a significant change.
The margin of error is quite small compared to the change year over year, so it is a significant issue.
The change of 0.09 is not a lot and thus should be ignored.
The margin of error is larger than the increase, so we should consider it an issue of just extra information and thus can be ignored.
The best counterargument: the margin of error is quite small compared to the change year over year, so it is a significant issue.
What is Margin error?In statistics, the margin of error refers to half the confidence interval. It measures how much of a random sample does not fall within the confidence interval as the number of samples taken increases indefinitely.
As, the temperature rises by 0.09 degree.
So, the difference between margin error and increase is higher which is
= 0.13- 0.09
=0.04
Hence, The margin of error is quite small compared to the change year over year, so it is a significant issue.
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if the ratio of three angles of a triangle is 2:3:4 find the size of the largest angle
Question 5 of 50
Perpendicular lines are best defined as which of the following?
OA. Lines that intersect
O B. Lines that meet to form a right angle
OC. Lines that are not coplanar
O D. Lines that never intersect
A
A local high school has 1,203 students with 367 freshmen, 382 sophomores, 249 juniors, and 205 seniors. What is the relative frequency of students who are not
seniors at this high school?
The relative frequency is %.
(Type an integer or decimal rounded to the nearest tenth as needed.)
The relative frequency of students who are not seniors at this high school will be 82.96%.
How to find how much percent 'a' is of 'b'?Suppose a number is 'a'
Suppose another number is 'b'
We want to know how much percent of 'b' is 'a'.
Then, it is calculated as:
P = a/b × 100
A local high school has 1,203 students with 367 freshmen, 382 sophomores, 249 juniors, and 205 seniors.
Then the relative frequency of students who are not seniors at this high school will be
P = 998/1203 × 100
P = 0.82959 × 100
P = 82.959%
P ≈ 82.96%
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RATS is a parallelogram. M
Answer:
Answer:
x = 12
Step-by-step explanation:
m∠S + m∠T = 180
8x + 7x = 180
15x = 180
x = 12
does this help?
