We can use the formula:
[tex]m = (y2 - y1) / (x2 - x1) = (5 - 3) / (-4 - 1) = 2/5[/tex]
Describe a slope.In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
20) The point-slope form of a line is[tex]y - y1 = m(x - x1)[/tex], where [tex](x1, y1)[/tex] is a point on the line and m is the slope. The slope of the line can be found by using the coordinates of two points on the line. To find the slope between the points [tex](1, 3)[/tex] and [tex](-4, 5)[/tex], we can use the formula:
[tex]m = (y2 - y1) / (x2 - x1) = (5 - 3) / (-4 - 1) = 2/5[/tex]
The point-slope form of the line is then:
[tex]y - 3 = (2/5)(x - 1)[/tex]
To convert this to slope-intercept form (y = mx + b), we can solve for y:
[tex]y = (2/5)x + (3 - (2/5)) = (2/5)x + (12/5)[/tex]
21) The line is parallel to [tex]y = -2x - 5[/tex], so we know that the slope of the line is -2. We can use the point [tex](4, -7)[/tex]and the slope -2 to write the equation in point-slope form:
[tex]y - (-7) = -2(x - 4)[/tex]
or
[tex]y + 7 = -2x + 8[/tex]
To convert this to slope-intercept form [tex](y = mx + b)[/tex], we can solve for y:
[tex]y = -2x + 1[/tex]
22) The line is perpendicular to [tex]y = -3/2x + 1[/tex], so we know that the slope of the line is the negative reciprocal of [tex]-3/2[/tex]. The slope of the line is [tex]2/3[/tex]. We can use the point [tex](3, 5)[/tex] and the slope [tex]2/3[/tex] to write the equation in point-slope form:
[tex]y - 5 = (2/3)(x - 3)[/tex]
or
[tex]y = (2/3)x + (5 - (2/3)3) = (2/3)x + (5 - 2) = (2/3)x + 3[/tex]
To convert this to slope-intercept form [tex](y = mx + b)[/tex], we can solve for y:
[tex]y = (2/3)x + 3[/tex]
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Select the symbol = (equal to) or ≠ (not equal to) to make the expression true.
{0} ? { }
Answer:
=
Step-by-step explanation:
{0}={} because 0 means that there is nothing and in null set too, there is no elements.
Graph the image of the polygon after a reflection in the line y = t.
Answer:
see the attached
Step-by-step explanation:
Reflection over a line moves each point so that the segment between it and its image has the reflection line as its perpendicular bisector.
Reflection over y=xThe line of reflection y=x has the effect of swapping the x- and y-coordinates:
(x, y) ⇒ (y, x) . . . . . reflection in y=x
For example, point C(2, 3) moves to point C'(3, 2).
The attachment shows the reflected figure.
The box plot below shows the total amount of time, in minutes, the students of a class surf the Internet every day: Part A: List two pieces of information that are provided by the graph and one piece of information that is not provided by the graph. (4 points)
Part B: Calculate the interquartile range of the data, and explain in a sentence or two what it represents. (4 points)
Part C: Explain what affect, if any, there will be if an outlier is present. (2 points)
The pieces of information that is provided by the box plots are the median and first quartile.
The piece of information that is not provided by the box plots is the mean.
The interquartile range is 22.50.
An outlier would distort the values of the median and the quartiles.
What is a box plot?
A box plot is used to study the distribution and level of a set of scores. The end of the first line represents the minimum number and the end of the second line represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. The difference between the quartiles is the interquartile range.
Interquartile range = 60 - 37.50 = 22.50
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Which of the following equations represents F(x)= x4 reflected across the line
y = x?
OA. F(x)=√x
OB. F(x)=√x
OC. F(x)=-4x
OD. F(x) = ±**
The reflection of F(x) = x⁴, across the line y = x, results in the function [tex]y = F(x) = \pm \sqrt[4]x[/tex], making option A the right choice.
For any function f(x), the reflection across the line y = x, gives the inverse of the function f(x).
In the question, we are asked for the equation, representing the reflection of f(x) = x⁴, across the line y = x.
The function can be shown as:
y = f(x) = x⁴,
or, x⁴ = y,
or, [tex]x = \pm\sqrt[4]{y}[/tex]
Changing the variables to general form, that is, y as the dependent variable and x as the independent variable, we get the inverse function as, [tex]y = F(x) = \pm \sqrt[4]x[/tex].
Thus, the reflection of F(x) = x⁴, across the line y = x, results in the function [tex]y = F(x) = \pm \sqrt[4]x[/tex], making option A the right choice.
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The complete question is:
"Which of the following equations represents F(x) = x⁴ reflected across the line y = x?
A. [tex]F(x)= \pm\sqrt[4]{x}[/tex]
B. [tex]F(x)= \sqrt[4]{x}[/tex]
C. [tex]F(x)= \pm x^4[/tex]
D. [tex]F(x)=- \sqrt[4]{x}[/tex] "
The acute angle between the lines x – 3y – 6 = 0 and y = 2x + 5 is
Answer:
Step-by-step explanation:
eq. of line x-3y-6=0
3y=x-6
y=1/3 x-6/3
or
y=1/3 x-2
its slope m1=1/3
y=2x+5
slope m2=2
if α is the angle between the lines then
[tex]tan~\alpha =|\frac{m1-m2}{1+m1m2} |=|\frac{\frac{1}{3} -2}{1+1/3\times 2}| =|\frac{1-3\times2}{3+2}| =5/5=1=tan 45\\\alpha =45^\circ\\[/tex]
f(x) = [(9,11),(-11,4),(7,-6),(11,-1), (-6,-15),(-13,-5)].
f^-1(f(93)) = m
(f(7)) = n
Find m and n
Using the inverse functions property:
f⁻¹(f(93)) = m = 93f(7) = n = -6How to find the values of m and n?
Two functions f(x) and f⁻¹(x) are inverses if:
f( f⁻¹(x) ) = x
f⁻¹(f(x)) = x
We want to get:
f⁻¹(f(93)) = m
By using the above definition we get:
f⁻¹(f(93)) = m = 93
Now for the second one we want:
f(7) = n
If you look at the table, you can see that f(x) contains the point (7, -6), then:
f(7) = n = -6
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An athlete has 75% of winning the race if he is not injured. If he is injured, his probability of winning the race is only 15%. If the total chances of winning is 51%, what is the probability that he gets injured?
Answer:
X = 'is the athlete injured' (X in {0,1})
Y = 'the athlete wins' (Y in {0,1})
P(Y=1|X=0) = 0.75
P(Y=1|X=1) = 0.15
P(Y=1) = 0.51
We are looking for P(X=1) - P(Y=1) = P(Y=1|X=0)*(1-P(X=1)) + P(Y=1|X=1)*P(X=1)
The above equation should provide you with the answer 0.4!
Step-by-step explanation:
This is the photo for the last question
All the angles required to complete each sentence are:
m ∠ 4 = 60, m ∠ 2 = 120m ∠ 3 = 110, m ∠ 4 = 70m ∠ 2 = x, m ∠ 1 = 180 - xHow to find measures of missing angles by Euclidean geometry
In this question we must take advantage of definitions and theorems of Euclidean geometry to complete the three sentences seen in the figure. Now we proceed to present each sentence completed in detail:
If m ∠ 5 = 60, then m ∠ 4 = 60 by alternal internal angles between parallel lines and m ∠ 2 = 120 by supplementary angles.If m ∠ 7 = 110, then m ∠ 3 = 110 by corresponding angles between parallel lines and m ∠ 4 = 70 by supplementary angles. If m ∠ 6 = x, then m ∠ 2 = x by corresponding angles and m ∠ 1 = 180 - x by supplementary angles.To learn more on angles: https://brainly.com/question/7116550
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19. Solve each equation by graphing. Round to the nearest tenth.
6x² +18x=0
3,6
0, -3
-3, -6
-1,6
Math 2
Answer:
0, -3
Step-by-step explanation:
Attachment.
In short, it is way easier to not graph it, however, if you really need to graph it, change it to the correct form, then do some plug and chug if the equation is not so friendly.
For which interval is the function constant? (−4,0) begin ordered pair negative 4 comma 0 end ordered pair (4,∞) left parenthesis 4 comma infinity right parenthesis (0,4) begin ordered pair 0 comma 4 end ordered pair (−∞,−4)
Answer: (-4, 0)
Step-by-step explanation: I just took the quiz and got it correct!
The function is constant on the intervals: (-4, 0), (4, ∞), and (0, 4). Within these intervals, the function's output remains the same for all values of x in each interval.
To determine the interval in which the function is constant, we need to examine the given ordered pairs (x, y) and check if the function's output (y-values) remains the same within that interval.
Let's analyze each interval:
1. (-4, 0): This interval represents all x-values greater than -4 and less than 0. In this interval, the function takes the value 0 for all x-values in the interval. Therefore, the function is constant (equal to 0) within this interval.
2. (4, ∞): This interval represents all x-values greater than 4. In this interval, the function's output is given as "∞" (infinity) for all x-values in the interval. The function is constant (equal to infinity) within this interval.
3. (0, 4): This interval represents all x-values greater than 0 and less than 4. In this interval, the function takes the value 4 for all x-values in the interval. Therefore, the function is constant (equal to 4) within this interval.
4. (-∞, -4): This interval represents all x-values less than -4. In this interval, the function's output is not specified or may not be constant. The information provided does not give us the exact function to determine the output for all x-values in this interval.
The function is constant on the intervals: (-4, 0), (4, ∞), and (0, 4). Within these intervals, the function's output remains the same for all values of x in each interval. However, we don't have enough information to determine if the function is constant on the interval (-∞, -4).
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someone please help me find the value of x
Hello,
5x² = 90/2
5x² = 45
x² = 45/5
x² = 9
x = √9 or x = -√9
x = 3 or x = -3
Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?
A function which could represent the graph is: C. f(x) = x⁴(x - a)(x - b)².
How to interpret the graph?The nature of the intercept on a polynomial graph highlights the nature of its multiplicity. Also, the polynomial graph has no single zero (factor) but bounced off the x-axis at three (3) different locations.
This ultimately implies that the polynomial graph has an even multiplicity at these three (3) points:
x⁴
x - a
(x - b)²
In conclusion, a function which could represent the graph is f(x) = x⁴(x - a)(x - b)².
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Case Study:
ABC factory produces 24,000 units. The cost sheet gives the following information:
Direct Materials Rs. 1,20,000
Direct Labour Rs. 84,000
Variable overheads Rs. 48,000
Semi variable overheads Rs. 28,000
Fixed overheads Rs. 80,000
Total Cost
Rs. 3,60,000
Presently the product is sold at Rs. 20 per unit.
The management proposes to increase production by 3,000 units for sales in the foreign market. It is estimated that semi-variable overheads wil
1,000. But the product will be sold at Rs. 14 per unit in the foreign market. However, no additional capital expenditure will be incurred.
O
Answer:
Current Cost = Rs 360000
24000 units sold at rs 20 per unit
Turnover = 24000 * 20 = Rs 480000
Present Profit = 480000 - 360000 = Rs 120000
Profit per unit = 120000/24000 = 5 rs per unit
cost increased for increasing 3000 Production
Direct Material cost increase = (120000/24000) * 3000 = Rs 15000
Direct Labour cost increase = (84000/24000) * 3000 = Rs 10500
Variable overhead increase = (48000/24000) * 3000 = Rs 6000
Semi variable cost increased = Rs 1000
Cost Increased = 15000 + 10500 + 6000 + 1000 = 32500
Price per unit = Rs 14
Turnover from 3000 units = 14 * 3000 = Rs 42000
Proposed Profit from 3000 units = 42000 -32500 = Rs 9500
Proposed Profit per unit = 9500/3000 = Rs 3.17
Decision Depends upon management as Profit is there in a new market but per unit profit is lesser than current profit
Step-by-step explanation:
Got the answer from amitnrw
Find AC if EC = 9, ED = 12, and BD = 20. Round to the nearest tenth.
The value of AC = 23
According to the statement
Here we have given the values of tangent from the diagram
EC = 9, ED = 12, and BD = 20.
and we have to find the value of AC.
We know that the according to the given diagram the tangent
BE is always equal to the Tangent AE.
So, we generate a equation to find the AC then
BE = AE
Convert this into parts like
BD +DE = AC+CE
Substitute the values in it which are given in the statement
20+12 = AC + 9
32 = AC + 9
32 -9 = AC
AC = 23
So, The value of AC = 23
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In the diagram above, angle 1=40. Find the measure of angle 4
Answer:
40
Step-by-step explanation:
angle 1 and 4 are vertical angles therefore they have the same measure of 40 degrees
Select the correct answer. What are the solutions to this equation? 16x2 + 9 = 25
The solutions to the given quadratic equations are x = -25/16 and x = 1
Quadratic equationsFrom the question, we are to determine the solutions to the given quadratic equation
The given quadratic equation is
16x² + 9 = 25
The equation can be solved as follows
16x² + 9 = 25
16x² + 9 - 25 = 0
16x² -16x +25x -25 = 0
16x(x -1) +25(x -1) = 0
(16x +25)(x -1) = 0
16x + 25 = 0 OR x - 1 = 0
16x = -25 OR x = 1
x = -25/16 OR x = 1
Hence, the solutions to the given quadratic equations are x = -25/16 and x = 1
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Determine which equation is belongs to the graph of the limacon curve below.
[-5,5] by [-5,5]
a.
r = 1 + 3 sin theta
c.
r = 1 + 3 cos theta
b.
r = 2 + 2 sin theta
d.
r = 3 + sin theta
Option a. The equation that is used to show the graph of the limacon is given as r = 1 + 3 sin theta.
How to solve for the equationWe have these ppoints [-5,5] by [-5,5]
The limacoin is used to represent a shape that may appear like that of a snail.
This is written in the form of
r = a ± b sin θ
and
r = a ± b cos θ
Given that we have the ± sign, the curve that is at the top of the horizontal; line is the + sign and the one below is the -
If a/b < 1 then a circle is within the circle that was formed as a graph.
Hence from the description that we have given here, the graph has the forms of
r = a + b sin θ
This is the equation that can be used to suit the form r = 1 + 3 sin theta
Hence option a is right.
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Evaluate the expression. 2+6+ – 4 4 /5 ÷ – 3 Write your answer as a fraction or as a whole or mixed number.
Answer:
9 3/5
Step-by-step explanation:
2+6+-4 4/5 ÷ -3
PEMDAS! First is multiplicationSo, solve the bold
2+6+ -4 4/5 ÷ -3
So,
2+6+ 1 3/5
Next is Addition(IN ORDER OF THE EQUATION), So solve the bold,
2+6+ 1 3/5
So, the answer is
9 3/5
One week, Tanisha earned $255.00 at her job when she worked for 17 hours. If she is paid the same hourly wage, how much would she make the next week if she worked 11 hours?
Answer:
67
Step-by-step explanation:
Suppose y varies inversely with x, and y = 36 when x=112
What inverse variation equation relates x and y ?
The inverse variation equation that relates x and y is x = 4032 / y.
What is the equation that relates x and y?if two variables vary inversely, there is a negative relationship between both variables. the increase in one variable leads to a decrease in the other variable
The equation that represents inverse proportion : x = b/y
where b = constant of proportionality
112 = b /36
b = 36 x 112 = 4032
The equation : x = 4032 / y
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a infant grew 2/4 inches in the first month 7/4 inches in the third month . first find the total inches the infant grew over the three months . then find the difference in the infants from the second month to the third month
The fraction computed shows that the total inches the infant grew over the three months is 3 3/4 inches.
How to compute the fraction?First month = 2/4 inches
Second month = 1 inch
Third month = 7/4 inches.
The total inches the infant grew over the three months will be;
= 2/4 + 1 + 7/4
= 3 1/4 inches.
The difference in the infants from the second month to the third month will be:
= 7/4 - 1
= 3/4 inches.
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how many pairs of each type of angles do two lines and a transversal form? vertical angles
The number of pairs of angles formed are about 7 types.
What are the Pairs of Angles Formed by a Transversal and Two Lines?In the image given, when transversal t crosses the two lines, a and b, 8 angles are formed.
The pairs of angles formed are:
Vertical angles, for example, angles 2 and 4.Linear pair angle, for example angles 1 and 2.Corresponding angles, for example angles 1 and 5.Alternate interior angles, for example angles 4 and 5.Alternate exterior angles, for example angles 1 and 8.Same-side interior angles, for example angles 3 and 5.Same-side exterior angles, for example angles 2 and 8.Therefore, there are about 7 types of pairs of each type of angles formed.
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Solve the inequality. -3x + 2x - 34 Enter the exact answer in interval notation.
Answer:
x = -34
Step-by-step explanation:
-3x + 2x -34 = 0
sum the x
-3x + 2x = -x
replace -x in the equation
-x -34 = 0
move -34 to other side
-x = 34
divide the two sides by -1 to get x value
x = -34
now replace x value in the equation:
-3(-34) + 2(-34) -34 =
102 -68 -34 =
102 -102 = 0
f(x)=2^x. What is g(x)?
The function g(x) is g(x)= (3x)^2
How to solve for g(x)?The complete question is in the image
From the graph in the image, we have:
f(x) = x^2
The function f(x) is stretched by a factor of 3 to form g(x).
This means that:
g(x) = f(3x)
So, we have:
g(x)= (3x)^2
Hence, the function g(x) is g(x)= (3x)^2
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Part II: Use the formula from Part I to find the midpoint of the
segment with endpoints at (-2,-1) and (0, 9). Show your work.
PLS
Answer: (-1, 4)
Step-by-step explanation:
[tex]\left(\frac{-2+0}{2}, \frac{-1+9}{2} \right)=\boxed{(-1, 4)}[/tex]
(-1, 4) is the midpoint of the segment with endpoints at (-2,-1) and (0, 9). This can be obtained by using the formula for finding the midpoint of a line segment.
Find the midpoint of the line segment:When the end points of a line segment are known, the mid point of the line segment is calculated using the midpoint formula,
Midpoint formula,
[tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex]
(x₁, y₁) and (x₂, y₂) are the endpoints of the line segment.
⇒ This means that, the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is [tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex].
From the question it is given that,
(x₁, y₁) = (-2,-1) (x₂, y₂) = (0, 9)are the endpoints of the line segment.
By using the Midpoint formula we get,
[tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex] = [tex](\frac{-2+0 }{2},\frac{-1+9}{2})[/tex]
[tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex] = [tex](-1, 4)[/tex]
Hence (-1, 4) is the midpoint of the segment with endpoints at (-2,-1) and (0, 9).
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Name the following polynomial: 4x^2 +8+16 cubic polynomial quartic trinomial quadratic trinomial cubic trinomial
The polynomial is quadratic trinomial
How to name the polynomial?The polynomial function is given as:
4x^2+ 8x +16
The highest power in the above polynomial is 2.
This represents quadratic
The number of terms in the above polynomial is 3
This represents trinomial
Hence, the polynomial is quadratic trinomial
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f(x)
X
(b)
Use the graph to determine the limit visually (if it exists). (If an answer does not exist, enter DNE.)
(a)
lim f(x)
X--1
-2
lim f(x)
x 0
Write a simpler function that agrees with the given function at all but one point.
q(x) =
a) Since both limits are distinct and do not exist, we conclude that x = - 1 is not part of the domain of the rational function.
b) The function [tex]f(x) = \frac{x}{x^{2}+ x}[/tex] is equivalent to the function [tex]g(x) = \frac{1}{x + 1}[/tex].
How to determine whether a limit exists or not
According to theory of limits, a function f(x) exists for x = a if and only if [tex]\lim_{x\to a^{-}} f(x) = \lim_{x \to a^{+}} f(x)[/tex]. This criterion is commonly used to prove continuity of functions.
Rational functions are not continuous for all value of x, as there are x-values that make denominator equal to 0. Based on the figure given below, we have the following lateral limits:
[tex]\lim_{x \to -1^{-}} \frac{x}{x^{2}+x} = - \infty[/tex]
[tex]\lim_{x \to -1^{+}} \frac{x}{x^{2}+x} = + \infty[/tex]
Since both limits are distinct and do not exist, we conclude that x = - 1 is not part of the domain of the rational function.
In addition, we can simplify the function by algebra properties:
[tex]\frac{x}{x^{2}+ x} = \frac{x}{x\cdot (x + 1)} = \frac{1}{x + 1}[/tex]
[tex]g(x) = \frac{1}{x + 1}[/tex]
The function [tex]f(x) = \frac{x}{x^{2}+ x}[/tex] is equivalent to the function [tex]g(x) = \frac{1}{x + 1}[/tex].
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PLS HELPPPPP ASAPPP OR IMAAA FAIL HELPPPPPPPPPPPPPPPPPPPPPPPPPPPp
Answer:
Step-by-step explanation:
(a). A = 5x( 7x - 2 ) - 3x( 2x + 4 )
(b). A = 35x² - 10x - 6x² - 12x = 29x² - 22x
A = 29x² - 22x
a ship with a bearing of 33 degrees first light a lighthouse at a bearing of north 65 degrees east.after travelling 8.5 miles, the ship observed the lighthouse at bearing of south 50 degrees east. find the distance from the ship to the lighthouse when the first sighting was made?
Applying the law of sines, when the first lighting was made, the distance from the ship to the lighthouse was: 3.2 miles.
What is the Law of Sines?The law of sines is expressed by the equation, sin A/a = sin B/b = sin C/c.
Using the information we are provided with, the diagram that shows the ship and other information is drawn and shown in the image attached below, where:
m∠CAB = 65 + 30 = 95°
m∠BCA = 50 - 30 = 20°
m∠B = 180 - 95 - 20 = 65°
c = the distance from the ship to the lighthouse
Considering triangle ABC, use the Law of Sines to find c:
sin B/b = sin C/c
B = 65°
b = 8.5 miles
C = 20°
Plug in the values
sin 65/8.5 = sin 20/c
Cross multiply
c(sin 65) = (8.5 × sin 200)
Divide both sides by sin 65
c(sin 65)/sin 65 = (8.5 × sin 200)/sin 65
c = (8.5 × sin 200)/sin 65
c ≈ 3.2 miles
Thus, when the first lighting was made, the distance from the ship to the lighthouse was: 3.2 miles.
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Using the following accounts and balances, prepare the “Stockholders’ Equity” section of the balance sheet. 60,000 shares of common stock authorized, and 4,000 shares have been reacquired.
Common Stock, $50 par $2,400,000
Paid-In Capital from Sale of Treasury Stock 48,000
Paid-In Capital in Excess of Par—Common Stock 576,000
Retained Earnings 1,368,000
Treasury Stock 25,000
The total Stockholders’ Equity is $4,367,000
Total Stockholders’ EquityCommon Stock, $50 par $2,400,000
Paid-In Capital in Excess of Par—Common Stock $576,000
Paid-In Capital from Sale of Treasury Stock $48,000
Total paid in capital $3,024,000
Retained Earnings $1,368,000
Less Treasury stock $25,000
Total Stockholders’ Equity $4,367,000
Therefore the total Stockholders’ Equity is $4,367,000.
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