Given the following points that pass through the line:
Point A : 12,4
Point B : 22,9
Step 1: Let's determine the slope of the line (m).
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{9\text{ - 4}}{22\text{ - 12}}[/tex][tex]\text{ m = }\frac{5}{10}\text{ = }\frac{1}{2}[/tex]Step 2: Let's determine the y-intercept (b). Substitute m = 1/2 and x,y = 12,4 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ 4 = (}\frac{1}{2})(12)\text{ + b }\rightarrow\text{ 4 = }\frac{12}{2}\text{ + b}[/tex][tex]\text{ 4 = 6 + b}[/tex][tex]4\text{ - 6 = b}[/tex][tex]\text{ -2 = b}[/tex]Step 3: Let's complete the equation. Substitute m = 1/2 and b = -2 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (}\frac{1}{2})x\text{ + (-2)}[/tex][tex]\text{ y = }\frac{1}{2}x\text{ - 2}[/tex]Therefore, the equation of the line is y = 1/2x - 2.
in a recent year the annual salary of the governor of New York was 1790000 during the same year the annual salary of the governor of Tennessee was 940000 less write and solve an equation to find the annual salary of the government of Tennessee in that year
Step 1 : Let's review the information given to us to answer the problem correctly:
• Annual salary of the governor of New York = $ 1,790,000
,• Annual salary of the governor of Tennessee = $ 940,000
Step 2: Let x to represent the annual salary of the governor of New York
and let's find the ratio of the salary of the governor of Tennessee, as follows:
940,000/1,790,000 = 0.525
Step 3: Now, let's write the equation for calculating the salary of the governor of Tennessee for any given year, this way:
• 0.525x = Annual salary of the governor of Tennessee
,•
Step 4: If the salary of the governor of New York for the next year is 2,000,000, then we can calculate the salary of the governor of Tennessee, this way:
0.525x = 0.525 * 2,000,000 = 1,050,000
The annual salary of the governor of Tennessee woudl be 1,050,000
I need the slope the y intercept is -2 and the x intercept is -1
The x intercept is the value of x when y = 0
Given that x intercept = - 1, the coordinate is (- 1, - 0)
The y intercept is the value of y when x = 0
Given that y intercept = - 2, the coordinate is (0, - 2)
Slope = (y2 - y1)/(x2 - x1)
x1 = - 1, y1 = 0
x2 = 0, y2 = - 2
Slope = (- 2 - 0)/(0 - - 1)
slope = - 2/1
slope = - 2
Use the table to find the slope of the line.Round your answer out to two decimal places
Given:
The points are (8, -3) and (-5, 1).
To find the slope of the line:
The slope formula is,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{1-(-3)}{-5-8} \\ =\frac{1+3}{-13} \\ =-\frac{4}{13} \\ =-0.30769 \\ \approx-0.31 \end{gathered}[/tex]Hence, the slope of the line is -0.31 (rounded to the nearest two decimal places).
Here are the exam scores for the 15 students in Mr. Kirk's statistics class:
72 75 75 78 81 83 85 89 90 90 90 91 95 95 98
Karen was at the 20th percentile of the distribution. What score did Karen earn on the exam?
(A) 75
(B) 78
(C) 81
(D) 83
Pls help with my hw pls
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
the rriangle is 3 4 5 triangle so 5×5 is 25
find the value of x
For supplementary angles, we can do the following equality
[tex]3x+4=x+70[/tex]What we have to do, is to clear "x" to find its value.
[tex]\begin{gathered} 3x-x=70-4 \\ 2x=66 \\ x=\frac{66}{2} \\ x=33 \end{gathered}[/tex]In conclusion, the value of x is 33
A radio tower is located 250 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 31∘ and that the angle of depression to the bottom of the tower is 29∘
How tall is the tower? ____________ feet.
Given a radio tower of 250 feet and angles of 31 and 29 degrees, the height of the tower is given as 308.58 ft
What is angle of depression?This is the term that is used to refer to the angle that lies between the horizontal line and the object that would be observed from the horizontal line.
In the question we have the following data
b = 250 feet
angles = 31 degrees, 29 degrees
for the top α = 31 degrees, β = 59
For the bottom α = 29 degrees, β = 61 degrees
We have the formula as
a /sin α = b / sin β = c
tan ∅ = opp / adj
for ΔOCA
h1 = 250 x tan 39 degrees
= 250 x 0.8098
= 202.45
h2 = OCB
= 250 x tan 23
= 250 x 0.4245
= 106.125
The height h = h1 + h2
= 202.45 + 106.125
= 308.58
The height of the tower is 308.58 ft
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Figure 2 is a scaled copy of Figure 1.B.Figure 1AsADMYColJFigure 2MYHKProIdentify the side in Figure 2 that corresponds to side BC in Figure 1.
Figure 1 was enlarged to figure 2
Hence the side |AB| is corresspounding to the side |PQ|
Determine the functions value when x= -1?a. g(-1) = -3b. g(-1) = 0c. g(-1) = 1d. g(-1) = 27
Problem
Determine the functions value when x= -1?
a. g(-1) = -3
b. g(-1) = 0
c. g(-1) = 1
d. g(-1) = 27
Solution
For this case we just need to find the value of g when x= -1 and if we look at the table we got:
g(-1)= (-1)^3 + 6(-1)^2 +12(-1) +8
g(-1)= -1 +6 -12+8 = 5-12+8= 1
And then the solution for this case would be:
c. g(-1) = 1
In how many ways can 3 students from a class of 23 be chosen for a field trip?aYour answer is:
SOLUTION:
This is a combination problem.
The number of ways 3 students from a class of 23 be chosen for a field trip is;
[tex]23C_3=\frac{23!}{(23-3)!3!}=1771\text{ }ways[/tex]Looking to receive assistance on the following problem, thank you!
Given:
[tex]\begin{gathered} v=3i-4j \\ u=-2i-7i \\ w=5j \end{gathered}[/tex]So the value is:
(a)
[tex]\begin{gathered} u=-2i-7j \\ 2u=2(-2i-7j) \\ 2u=-4i-14j \end{gathered}[/tex][tex]\begin{gathered} 2u-v=-4i-14j-(3i-4j) \\ =-4i-14j-3i+4j \\ =-7i-10j \end{gathered}[/tex](b)
[tex]\begin{gathered} w=5j \\ 3w=3\times5j \\ 3w=15j \end{gathered}[/tex][tex]\begin{gathered} u=-2i-7i \\ 4u=4(-2i-7j) \\ 4u=-8i-28j \end{gathered}[/tex][tex]\begin{gathered} 3w+4u=15j+(-8i-28j) \\ =15j-8i-28j \\ =-8i-13j \end{gathered}[/tex](c)
The dot product of v and u.
[tex]\begin{gathered} v=3i-4j \\ u=-2i-7i \end{gathered}[/tex]dot product is:
[tex]\begin{gathered} vu=(3i-4j)\cdot(-2i-7j) \\ =-6(i\cdot i)-21(i\cdot j)+8(j\cdot i)+28(j\cdot j) \end{gathered}[/tex]The doat product (i.i = 1) and ( j.j=1) and ( i.j=0) and ( j.i = 0)
[tex]\begin{gathered} =-6(1)-21(0)+8(0)+28(1) \\ =-6+28 \\ =22 \end{gathered}[/tex]could someone please help :(
Given from the number line:
D = -2 and F = 13
So, the distance DF = 13 - (-2) = 13 + 2 = 15
1) find E such that, DE : EF = 2 : 1
so,
so, x : (15 - x) = 2 : 1
x = 30 - 2x
3x = 30
x = 10
So, E = -2 + 10 = 8
=========================================================================
2) E is 4/5 of the distance from F to D
So, the distance from F = 4/5 * 15 = 12
So, E = 13 - 12 = 1
=====================================================================
3) the ratio of DE : EF = 2 : 3
So,
3x = 2 ( 15 - x)
3x = 30 - 2x
5x = 30
x = 30/5 = 6
E = -2 + 6 = 4
=================================================
4) E is 1/3 of the distance from D to F
So, the distance DE = 1/3 * 15 = 5
So, E = -2 + 5 = 3
=====================================================
As a summery:
1) E = 8
2) E = 1
3) E = 4
4) E = 3
The stock price for dgy was $38.21. In June. In July the stocked had in by 7 percent, but in August the price fell by 7 percent. What was the price of dgy stock in august . Round your answer to nearest cent , if necessary
The initial price is $38.21, and it got an increase of 7%, so the new price is the old one multiplied by 1.07:
[tex]38.21\cdot1.07=40.88[/tex]Then, the new price decreased by 7%, so let's multiply it by 0.93 (that is, 1 minus 0.07):
[tex]40.88\cdot0.93=38.02[/tex]So the price in August is $38.02.
I need help question
Solution
- The first integral is bounded by the x-values of [6, 22]
- The second integral is bounded by the x-values of [6, 14]
- When we are asked to find the difference between the two integrals, since, they both begin at 6, it implies that, when the second integral is taken away from the first integral, there must be some extra x-values.
- The extra values are from 14 to 22.
- Thus, we have:
[tex]\int_6^{22}f(x)-\int_6^{14}f(x)=\int_{14}^{22}f(x)[/tex]Final Answer
[tex]\begin{gathered} b=22 \\ a=14 \end{gathered}[/tex]Original cost $21.99 Markup 5%. What's the new price?
Explanation:
We have to find 5% of the original cost first:
[tex]21.99\times\frac{5}{100}=21.99\times0.05=1.0995[/tex]And then add it to the original price:
[tex]21.99+1.0995=23.0895[/tex]Since it's a price, we have to round this result to the nearest hundredth
Answer:
The new price is $23.09
I'm trying to simplify negative 5/8 divided by negative 3/4 how do I do that?
In triangle XYZ, | XZ | = | YZ | ∆YXZ = 40⁰ and ∆XZY = (13x - 20)⁰. Find the value of x.
Given the triangle XYZ with the following parameters
[tex]\begin{gathered} |XZ|=|YZ| \\ \measuredangle YXZ=40^0 \\ \measuredangle XZY=(13x-20)^0 \\ \text{Therefore} \\ \measuredangle ZYX=40^0 \end{gathered}[/tex]The diagram of the triangle is shown below
To find the value of x, we will apply sum of interior angle of triangle theorem
[tex]\begin{gathered} 40^0+40^0+(13x-20)^0=180^0(\text{ sum of angles in a triangle)} \\ 80^0+13x-20^0=180^0 \\ 13x+60^0=180^0 \\ 13x=180^0-60^0 \\ 13x=120^0 \\ x=\frac{120^0}{13} \\ x=9.2308^0 \end{gathered}[/tex]Hence, the value of x is 9.2308°
The points (-6, -10) and (23, 6) form a line segment.
Write down the midpoint of the line segment.
A line segment has the endpoints at (-6, -10) and (23, 6) then the midpoints of the line segment will be (17, -2).
What is meant by line segment?An area or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be estimated by utilizing either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.
A line segment has the endpoints at (-6, -10) and (23, 6).
Mid point of the line segment is given by [tex]$\left(\frac{x_1+x_2}{2}\right),\left(\frac{y_1+y_2}{2}\right)$[/tex]
The midpoints of the line segment will be
= [tex]$\frac{23+-6}{2}[/tex], [tex]$\frac{-10+6}{2}}[/tex]
= 17, -2
Therefore midpoints of the line segment will be (17, -2).
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Which transformations of quadrilateral PQRS would result in the imageof the quadrilateral being located only in the first quadrant of thecoordinate plane?
Given:
The quadrilateral PQRS is given.
The aim is to locate the given quadrilateral into first quadrant only.
The graph will be reflected across x=4 then the graph will not be located to the first quadrant.
An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an airplane located at that point. Express the bearing using both methods.(-8,0)
Given,
The coordinates of the point is (-8, 0).
There are two methods of bearing is:
Compass bearing
True bearing.
The figure of the point is,
The bearing of the point with respect to anticlockwise from north is,
[tex]\begin{gathered} \tan \theta=\frac{y}{x} \\ \tan \theta=\frac{0}{-8} \\ \theta=\tan ^{-1}0 \\ \theta=0^{\circ} \\ \text{Bearing from north=(90}^{\circ}-0^{\circ})=90^{\circ} \end{gathered}[/tex]The bearing of point from west is 0 degree and from anticlockwise north is 90 degree.
The true bearing is,
[tex]\begin{gathered} \theta=0^{\circ} \\ B=(360^{\circ}-90^{\circ}) \\ B=270^{\circ} \end{gathered}[/tex]HelppppppFunction f is a(n)functionThe graph is a reflection in thewith a verticaland atranslationunits:The domain of f isThe domain of the parent function is;The range of f isThe range of the parent function is
Answer:
In order of appearance of boxes
quadraticx-axisstretch3 (units)upall real numbersall real numbersy ≤ 3y ≥ 0Step-by-step explanation:
The given function f(x) = -2x² + 3 belongs to the quadratic family of equations. A quadratic equation has a degree of 2. The degree is the highest power of the x variable in the function f(x)
The parent f(x) = x²
Going step by step:
2x² ==> graph x² is vertically stretched by 2. For any value of x in x², the new y value is twice that the old value. For example, in the original parent function x², for x = 2, y = 4. In the transformed function 2x², for x = 2, y = 2 x 4 = 8 so it has been stretched vertically. It becomes skinnier compared to the original
-2x² => graph is reflected over the x-axis. It is the mirror image of the original graph when viewed from the x-axis perspective
-2x² + 3 ==> graph is shifted vertically up by 3 units
Domain is the set of all x-input values for which the function is defined. For both x² and -2x² + 3 there are no restrictions on the values of x. So the domain for both is the set of all real numbers usually indicated by
-∞ < x < ∞
The range is the set of all possible y values for a function y = f(x) for x values in domain.
The range of f(x) = x² is x≥ 0 since x² can never be negative
Range of -2x² + 3 is x ≤ 3 : Range of -2x² is y ≤ 0 since y cannot be negative and therefore range of -2x² + 3 is y ≤ 3
Garret is removing a hem from a skirt. It takes
Garret 5 min to remove 4 in. of the hem. He wants to
know how long it will take to remove 5 ft of the hem if
he continues to work at the same rate.
Lavar
How can Garret determine how long it will take to remove 5 ft of the hem?
Choose one option from each drop-down menu to answer the question.
It takes Garret Choose... min to remove 1 ft of hem.
He should multiply the number of minutes by Choose... to determine the number of minutes it will take to
remove 5 ft of hem.
It will take Choose.... min to remove 5 ft of hem.
It takes Garret Choose min to remove 1 ft of hem. He should multiply the number of minutes by Choose... to determine the number of minutes it will take to remove 5 ft of hem.
What is the unitary method?The unitary method is a technique used to determine the value of a single unit from the value of many units and the value of multiple units from the value of a single unit. We typically utilize it for math calculations. This approach will come in handy for topics involving ratio and proportion, algebra, geometry, etc. In the unitary technique, we always count the value of a unit or one quantity first before figuring out the values of more or fewer quantities. This method is referred to as the "unitary method" for this purpose.
There are two types of unitary methods because they result in two types of variations and those are given below:
Direct VariationIndirect VariationTo know more about the unitary method ,visit:
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find the area of the composite figures by either adding and subtracting regions
Explanation:
This figure is a rectangle and a quarter of a circle. We can find their areas and add them to find the total area of the figure.
The area of the rectangle is:
[tex]A_{\text{rectangle}}=17cm\times10\operatorname{cm}=170\operatorname{cm}^2[/tex]The area of a circle is:
[tex]A_{\text{circle}}=\pi\cdot r^2[/tex]Where r is the radius of the circle. In this case we have a quarter of a circle, so its area is a quarter of the area of the circle:
[tex]A_{1/4\text{circle}}=\frac{A_{\text{circle}}}{4}=\frac{\pi\cdot r^2}{4}[/tex]The radius of this circle is 8cm:
[tex]A_{1/4\text{circle}}=\frac{\pi\cdot8^2}{4}=\frac{\pi\cdot64}{4}=\pi\cdot16\approx50.27\operatorname{cm}^2[/tex]The total area of the figure is:
[tex]A_{\text{figure}}=A_{\text{rectangle}}+A_{1/4\text{circle}}=170\operatorname{cm}+50.27\operatorname{cm}=220.27\operatorname{cm}^2[/tex]Answer:
The area is 220.27 cm²
Given the graph of f (x), determine the domain of f –1(x).
Radical function f of x that increases from the point negative 3 comma negative 2 and passes through the points 1 comma 0 and 6 comma 1
The domain of the function f(x) that has a range of [-2, ∞) is [-2, ∞)
What is the inverse of a function?The inverse of a function that maps x into y, maps y into x.
The given coordinates of the points on the radical function, f(x) are; (-3, -2), (1, 0), (6, 1)
To determine the domain of
[tex] {f}^{ - 1}( x)[/tex]
The graph of the inverse of a function is given by the reflection of the graph of the function across the line y = x
The reflection of the point (x, y) across the line y = x, gives the point (y, x)
The points on the graph of the inverse of the function, f(x), [tex] {f}^{ - 1} (x)[/tex] are therefore;
[tex]( - 3, \: - 2) \: \underrightarrow{R_{(y=x)}} \: ( - 2, \: - 3)[/tex]
[tex]( 1, \: 0) \: \underrightarrow{R_{(y=x)}} \: ( 0, \: 1)[/tex]
( 6, \: 1) \: \underrightarrow{R_{(y=x)}} \: ( 1, \: 6)
The coordinates of the points on the graph of the inverse of the function, f(x) are; (-2, -3), (1, 0), (1, 6)
Given that the coordinate of point (x, y) on the image of the inverse function is (y, x), and that the graph of the function, f(x) starts at the point (-3, -2) and is increasing to infinity, (∞, ∞), such that the range of y–values is [-2, ∞) the inverse function, [tex] {f}^{ - 1}( x)[/tex], which starts at the point (-2, -3) continues to infinity, has a domain that is the same as the range of f(x), which gives;
The domain of the inverse of the function, [tex] {f}^{ - 1}( x)[/tex], using interval notation is; [-2, ∞)
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I have a practice problem that I need help on.These are included in the problem as well Where did Arjun make errors?Explain his errors and the properties of logarithms that leads to the answer. State the correct answer.
Arjun applied the wrong laws of logarithms.
The question can be solved as shown below:
[tex]\log _7x+\log _7y+\log _7z[/tex]Step 1: Apply the addition rule of logarithm given as
[tex]\log _am+\log _an=\log _a(m\cdot n)[/tex]Thus, we have:
[tex](\log _7x+\log _7y)+\log _7z=\log _7(x\cdot y)+\log _7z[/tex]Step 2: Apply the subtraction rule of logarithm given as
[tex]\log _am-\log _an=\log _a(\frac{m}{n})[/tex]Thus, we have:
[tex]\log _7(x\cdot y)+\log _7z=\log _7(\frac{x\cdot y}{z})[/tex]Therefore, the correct answer is:
[tex]\log _7x+\log _7y+\log _7z=\log _7(\frac{xy}{z})[/tex]Which equation shows a proportional relationship? options: O y = x O y + 1 = 7x O y - 2 = x + 8 O x = y + 5
A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:
y = kx
for some constant k , called the constant of proportionality . This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.
From the given options, the baove property is satisfied by,
[tex]y=\frac{2}{3}x[/tex]Thus, the correct option is A.
A lighthouse beacon will illuminate to a distance of 12 km. If the lighthouse is located at (-5,2) on a grid, find the equation of the location of the furthest points lit the beacon.
Light house is located at (-5,2)
Lighthouese beacon will illuminate a distnce =12 km
Use the distance formula to find the equation :
Distance formula is expressed as :
[tex]\begin{gathered} (x-a)^2+(y-b)^2=c^2 \\ \text{where (a,b) \& (x,y) are the coordinates and c is the distance} \end{gathered}[/tex]Substitute the given values :
[tex]undefined[/tex]Write the slope-intercept form of the equation of the line with the given characteristics. Perpendicular to y = -5x + 2 and passing through (3,-1).
The slope intercept form of a line can be expressed as,
[tex]y=mx+c[/tex]Here, m is the slope of the line and c is the y intercept.
Comparing the above equation with the given equation of a line y=-5x+2, we get
m=-5.
The slope of a line perpendicular to line with slope m is -1/m.
Hence, the slope of line perpendicular to y=-5x+2 is,
[tex]m_1=\frac{-1}{m}=\frac{-1}{-5}=\frac{1}{5}[/tex]The new line is given to be passing through point with coordinates (x1, y1)=(3, -1).
The point slope form of a line passing through point with coordinates (x1, y1)=(3, -1) and having slope m1 is,
[tex]\begin{gathered} y-y_1=m_1(x-x_1) \\ y-(-1)=\frac{1}{5}(x-3) \\ y+1=\frac{1}{5}x-\frac{3}{5} \\ y=\frac{1}{5}x-\frac{3}{5}-1 \\ y=\frac{1}{5}x-\frac{3-5}{5} \\ y=\frac{1}{5}x-\frac{8}{5} \end{gathered}[/tex]Therefore, the slope-intercept form of the equation of the line perpendicular to y = -5x + 2 and passing through (3,-1) is,
[tex]y=\frac{1}{5}x-\frac{8}{5}[/tex]The table shows the cost for a clothing store to buy jeans and khakis. The total cost for Saturday's shipment, $1,800, is represented by the equation 15x + 20y = 1,800. Use the x- and y-intercepts to graph the equation. Then interpret the x- and y-intercepts.