Answers
To finde the equation of the line troughh the points (0;0) and (-8;-5) first you must find the slope of the line. You have to use the next formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Replacing the points in the previous formula
[tex]m=\frac{-5-0}{-8-0}=\frac{5}{8}[/tex]As the line passes trough the origin of coordinates (point (0;0)) the equation is:
[tex]y=\frac{5}{8}x[/tex]So the answer is y= 5/8 x (option B)
Related Questions
Describe in words where cube root of 30 would be plotted on a number line.
Between 3 and 4, but closer to 3
Between 3 and 4, but closer to 4
Between 2 and 3, but closer to 2
Between 2 and 3, but closer to 3
Answers
Cube root of 30 is 3.107.
How to find cube root of a number?
Cube root is the number that needs to be multiplied three times to get the original number.
The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:
Step 1: Start with the prime factorization of the given number.
Step 2: Then, divide the factors obtained into groups containing three same factors.
Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number is not a perfect cube and we cannot find the cube root of that number.
We have to find the cube root of 30.
Prime factorization of 30 = 2*3*5.
Therefore the cube root of 30 = ∛(2*3*5)= ∛30 .
As ∛30 cannot be reduced further, then the result for the cube root of 30 is an irrational number as well.
So here we will use approximation method to find the cube root of 30 using Halley's approach:
Halley’s Cube Root Formula: ∛a = x[(x³ + 2a)/(2x³ + a)]
The letter “a” stands in for the required cube root computation.
Take the cube root of the nearest perfect cube, “x” to obtain the estimated value.
Here we have a = 30
and we will substitute x = 3 because 3³ = 27< 30 is the nearest perfect cube.
Substituting a and x in Halley's formula,
∛30 = 3[(3³ + 2*30)/(2*3³ + 30)]
= 3[(27+60)/(54+30)]
= 3(87/84)
= 3*1.0357
∛30 = 3.107.
Therefore the cube root of 30 is 3.107.
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in the figure above
Answers
Since AB is tangent to the circle, the angle BAO equals π/2.
The same happens to BC, so the angle BCO also equals π/2.
Now, for any quadrilateral, the sum of the internal angles is 2π. Therefore:
ABC + AOC + BAO + BCO = 2π
ABC + 3π/7 + π/2 + π/2 = 2π
ABC = 2π - 3π/7 - π/2 - π/2 = π - 3π/7 = (7π - 3π)/7
ABC = 4π/7
What is the approximate probability thata point chosen inside the rectangle is inthe shaded region?
Answers
In order to determine the required probability, calculate the total area of the shaded regions frist:
Consider that there is a rectangle and a triangle with shaded area, then, you have:
A1 = (1 ft)(2 ft) = 2 ft² rectangle area
A2 = (2 ft)(2 ft)/2 = 2ft² triangle area
Then, the total shaded area is:
A = A1 + A2
A = 2 ft² + 2 ft²
A = 4 ft²
Next, calculate the total area of the given figure:
A' = (3 ft + 1 ft)(2 ft) = 8 ft²
Next, the probability is the quotient in between the area of th shaded regions over the area of the total figure:
p = A/A'
p = (2 ft²)/(4 ft²)
p = 0.50
Hence, the probability that a point chosen is inside a shaded region is 0.50
in the diagram of JEA below, JEA = 90° and EAJ = 48°. Line segment MS connects points M and S on the triangle, such that EMS = 59°. Find the measure of JSM.
Answers
The value of m∠JSM is 17 degrees.
Given data;
The measure of the ∠JAE = 48 degrees.
The measure of the ∠AEJ = 90 degrees.
The measure of the ∠EMS = 59 degrees.
In triangle JEA;
By angle sum property, we know that;
∠JAE + ∠AEJ + ∠EJA = 180 degree
Substitute the given values in the above expression.
48 degree + 90 degree + ∠EJA = 180 degree
∠EJA = 42 degrees
The angle JMS is,
∠JMS = 180 - ∠EMS (Linear pair)
∠JMS = 180 degrees - 59 degrees = 121 degrees.
In triangle JMS,
By angle sum property, we know that;
∠JMS + ∠JSM + ∠EJA = 180 degree
121 degree + ∠JSM + 42 degree = 180 degree
∠JSM = 17 degree
Thus, the measure of ∠JSM is 17 degrees.
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Hello! I need some assistance with this homework question, pleaseQ13
Answers
we have the new function
[tex]f(x)=\frac{2}{3}\mleft|x\mright|+3[/tex]The vertex of this function is the ordered pair (0,3)
The coordinates of the second point
(2,2) ------------> (2,f(2))
Find the value of f(2)
[tex]\begin{gathered} f(2)=\frac{2}{3}|2|+3 \\ f(2)=\frac{2}{3}\cdot(2)+3 \\ f(2)=\frac{4}{3}+3=\frac{13}{3} \end{gathered}[/tex]the new coordinates of point (2,2) are (2,13/3)
see the attached figure
use the display of data to find the mean, median, mode, and midrange 10,3, 11,3, 12,4, 13,5, 14,2, 15,3
Answers
The mean, median, mode and midrange of the given data is 7.92, 7.5, 3 and 8.2 respectively.
What is median and midrange?The mid-way between the least value and the greatest value of the data set is called the midrange, and the median is the middle number in a sorted list of numbers.
Given a data 10,3, 11,3, 12,4, 13,5, 14,2, 15,3
Mean = (2+3+3+3+4+5+10+11+12+13+14+15)/12 = 7.92
Median = 15/2 = 7.5
Mode = 3
Midrange = (2+15)/2 = 8.2
Hence, The mean, median, mode and midrange of the given data is 7.92, 7.5, 3 and 8.2 respectively.
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By which Theorem or postulate is Change ABC congruent Change BAD?
Answers
Solution
we are given that
[tex]\begin{gathered} |AB|=|BC| \\ We draw the diagram as followsNotice the lettering on each triangle, they both represent the triangle we are given in the question
The postulate here is Sides, Angle, Sides (SAS)
Option C
4)Erica and Megan each improved theiryards by planting daylilies and shrubs.They bought their supplies from thesame store. Erica spent $200 on 9daylilies and 10 shrubs. Megan spent$185 on 13 daylilies and 5 shrubs. Whatis the cost of one daylily and the cost ofone shrub?Type text here
Answers
One daylily $10 and 1 shrub $11
1) Gathering the data from the question
Erica spent $200 on 9 daylillies and 10 shrubs
Megan spent $185 on 13 daylilies and 5 shrubs
9d+10s=200
13d+5s=185
2) Let's solve this system of linear equations now
9d+10s=200
13d+5s=185 Multiply by (-2)
9d +10s=200
-26d-10=-370
----------------------
-17d =-170
17d=170
d=10
9(10) +10s=200
90+10s-90=200-90
10s=200-90
10s=110
s=11
So the cost of one daylily is$10 and 1 shrub is $11
How can i calculate the number of students that graduated from the university faculty of natural sciences in 2002? how can i determine the sector angle that will represent the number of graduates in each subject? how can i hence construct a pie chart of radius 4cm to represent the information given in the table?
Answers
A table showing the number of graduates by subject from a university's faculty of natural science in 2002.
1) To calculate the number of students that graduated, find the sum of the number of graduates from each subject.
[tex]9+15+19+12+5=60[/tex]The number of students that graduated is 60.
2) To determine the sector angle that will represent the number of graduates in each subject, divide the number of graduates in each subject by the total number of students and then multiply by 360º.
3) To construct a pie chart with radius, 4cm to represent the information, draw a circle of radius 4cm and partition it into sectors with central angles as calculated in (2) above.
Two angles are complementary to each other. One angle measures 32°, and the other angle measures (12x − 20)°. Determine the value of x. 64 6.5 32.5 6
Answers
Answer:
B) 6.5
Step-by-step explanation:
Complementary angles are angles that are put together to equal 90 degrees.
Angle one is 32 degrees.
90-32= 58
So we need to get the number 58 for it to be complementary. The reason for this is because 32+58=90. Which would make it complementary.
When we plug in 6.5 we get 58, which is what we want.
12(6.5)- 20= 90
78-20=58
Hope this helps!!!
The value of x is 6.5.
Complimentary angles are known as angles which makes the sum of 90°.
The angles sum up to form a right angle. When two angles complement each other they sum up to be 90°.
According to question one angle - 32° and other angle [12x - 20].
⇒ 32 + [12x - 20] = 90
⇒ 12x - 20 = 58
⇒ 12x = 78
⇒ x = 6.5
Hence, the value of x is 6.5.
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Use Composition of FunctionsBOX OFFICE A movle theater charges $8.50 for each of the xtickets sold. The manager wants to determine how much the movietheater gets to keep of the ticket sales If they have to glve thestudlos 75% of the money earned on ticket sales t(x). If the amountthey keep of each ticket sale is k(x), which composition representsthe total amount of money the theater gets to keep?
Answers
Given: The amout charged per ticket is $8.50
If x tickets are sold
Then the total revenue (amount made) will be =>
[tex]8.5\text{ x }x\text{ = \$8.50x}[/tex]If t(x) represents how much the studio collects
and k(x) represents how much is kept
Given: t(x) = 75% then
k(x)= (100 -75)%= 25 %
So that
The total amount that will be kept will be
25% of $8.50x
=>
[tex]\frac{25}{100}\text{ x (\$8.50x) }[/tex][tex]\frac{25\text{ x \$8.50x}}{100}\text{ = }\frac{212.5x}{100}=\text{ \$2.125x}[/tex]The amount that will be kept will be
= > $2.125x
Where x is the number of tickets
10. Quadrilateral PQRS with P(-5,1). Q(-2,6), R(3,7), and S(6,4); dilate by a factor of 1/2 12 a. Is this an enlargement or reduction? How do you know? 14 b. What are the vertices of the image after the transformation?
Answers
a.
The dilation is a reduction, this comes from the fact that the dilation factor is less than 1.
b.
A point after a dilation is given as:
[tex](x,y)\rightarrow(kx,ky)[/tex]where k is the dilation factor.
In this case we need to divide all the coordinates by two, then we have that:
[tex]\begin{gathered} P^{\prime}(-\frac{5}{2},\frac{1}{2}) \\ Q^{\prime}(-1,3) \\ R^{\prime}(\frac{3}{2},\frac{7}{2}) \\ S^{\prime}(3,2) \end{gathered}[/tex]The line with a slope of -1 and that contains the point (1, 3).Find the equation of the line in standard form.
Answers
ANSWER
x + y = 4
EXPLANATION
The standard form of a linear equation is given as:
ax + by = c
To do this, we have to find the equation of the line using point-slope method:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through
m = slope
The given slope is -1 ad the point the line passes through is (1, 3).
Therefore, we have:
y - 3 = -1(x - 1)
y - 3 = -x + 1
=> x + y = 1 + 3
x + y = 4
That is the equation of the line in standard form.
Can you pls help me with number 6 my treacher said that it was d but I got b is me correct or my treacher
Answers
Given the algebraic expression below
[tex]6a+4y+a+2a[/tex]Collect like terms
[tex]6a+2a+a+4y[/tex]Add possible like terms using the distributive property of algebra
[tex]\begin{gathered} (6+2+1)a+4y \\ 9a+4y \end{gathered}[/tex]Hence, the final answer is 9a + 4y
Option D is correct
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?-5-4-3-2 -1 01+4123on++at-5-2+ o+1-1234501-5-4-3+o-2-1+1N+W+A+5++-5-4-3-2+o-1NT1345
Answers
To find the solution, lets first simplify the inequality:
[tex]undefined[/tex]Determine the area of the figure: 1.5 cm 5 cm 5.5 cm Your answer
Answers
We can add the are of the 3 rectangle, so we get that the area is:
[tex]A=1.5\cdot5+1.5\cdot5+1.5\cdot0.5=15.75\operatorname{cm}[/tex]The vertices of a figure are A(1, -1), B(5.-6), and C(1, - 6). Rotate the figure 90 counterclockwise about the origin. Find the coordinates of the image. Polygon Undo Redo x Reset 7A 6. 5 4 3 2. 1 --7-6-5--4 -3 -2 -1 1 1 2 a 4 - 2 -3 -5 -6 -7 The coordinates of the image are:
Answers
The vertices of the given figure are
A(1, -1), B(5.-6), and C(1, - 6).
For a 90 counterclockwise about the origin, a coordinate, (x, y) would be (- y, x)
This means that after the 90 degrees rotation,
coordinate A would be (- - 1, 1) = (1, 1)
Coordinate B would be (- - 6, 5) = (6, 5)
Coordinate C would be (- - 6, 1) = (6, 1)
solve 10 + 15x - 30 = 40
Answers
We have the next equation
[tex]10+15x-30=40[/tex]We sum similar terms
[tex]15x-20=40[/tex]then we clear x
[tex]\begin{gathered} 15x=40+20 \\ 15x=60 \\ x=\frac{60}{15} \\ x=4 \end{gathered}[/tex]the value of x=4
if 5 guys are putting yogurt in a girl's mouth and each liter is 5 liters how much is the girl carrying in her mouth ️️
Answers
5 guys are putting yogurt in a girl's mouth
Each of the yogurt is 5 liters
The total yogurt the girl is carrying = 5 x 5
= 25
The answer is 25 liters of yogurt
Determine the concavity of the graph of f(x) = 4 - x^2 between x= -1 and x = 5 by calculating average rates of change over intervals of length 2. 1. The average rate of change over the interval 3 ≤ 2 < 5 =
Answers
Given the function:
[tex]f(x)=4-x^2[/tex]For the given function, we will determine the concavity between x = -1 and x = 5
By the average rate of change over the interval 3 ≤ x < 5
We will use the following formula:
[tex]\frac{f(5)-f(3)}{(5)-(3)}[/tex]First, we will find the value of f(5) and f(3)
[tex]\begin{gathered} x=5\rightarrow f(5)=4-5^2=-21 \\ x=3\rightarrow f(3)=4-3^2=-5 \end{gathered}[/tex]Substitute into the formula:
So, the average rate of change will be as follows:
[tex]\frac{f(5)-f(3)}{(5)-(3)}=\frac{(-21)-(-5)}{5-3}=\frac{-16}{2}=-8[/tex]As the average rate of change is negative, the concavity of the graph will be concave down
Name the relationship between the pair of angles and find the value of x.
Answers
Consecutive interior angles (Same side)
x = -8
Explanations:The two angles are 136 + x and x + 56
The two angles are consecutive-interior angles because they are on the same side of the transversal.
Note that consecutive -interior angles are supplementary and they add up to 180 degrees.
Applying this rule to the diagram shown:
(136 + x) + (x + 56) = 180
136 + 56 + x + x = 180
192 + 2x = 180
2x = 180 - 196
2x = -16
x = -16 / 2
x = -8
Write the equation of a sine or cosine function to describe the graph. Please help I’ve tried but I keep missing something like finding the c/b. Thanks in advance!!!
Answers
Since the function starts at it maximum value, let's use a cosine function to represent it:
[tex]f(x)=A+B\cos(C(x+D))[/tex]Since the midline of the periodic function is y = 2, we have A = 2.
The period of the function is 4pi/3, so we have:
[tex]\begin{gathered} T=\frac{2\pi}{C}\\ \\ \frac{4\pi}{3}=\frac{2\pi}{C}\\ \\ \frac{2}{3}=\frac{1}{C}\\ \\ C=\frac{3}{2} \end{gathered}[/tex]Since the function already starts at its maximum value, there is no horizontal phase shift, so D = 0.
The amplitude is 1 (it goes up and down 1 unit from the midline), so we have B = 1.
Therefore the function is:
[tex]f(x)=2+\cos(\frac{3}{2}x)[/tex]What would be the correct way to solve this?[tex] {x}^{2} - 5x - 84[/tex]
Answers
Answer:
(x + 7 ) ( x - 12 )
Explanation:
We know that if we multiply any two expressions x + a and x + b then we have
[tex](x+a)(x+b)=x^2+(a+b)x+ab[/tex]Now similarly,
[tex]x^2+(a+b)x+ab=x^2-5x-84[/tex]meaning
[tex]\begin{gathered} a+b=-5 \\ ab=-84 \end{gathered}[/tex]In other words, what are the two numbers that if I add them together I get -5 and If I multiply them I get -84. The answer comes from educated guesses. We guess that if we add 7 and -12 we get 5 and if we multiply then we get -84; therefore,
[tex]\begin{gathered} a=7 \\ b=-12 \end{gathered}[/tex]Hence, the expression can be factored as
[tex]=x^2-5x-84=(x-12)(x+7)[/tex]which is our answer!
A bank pays 3% per annum compound interest, calculate how much interest would you get if you invested £45 for 3 years
Answers
Answer:
405
Step-by-step explanation:
don't forget to follow rate like
Can some one help me with 7 , 8 and 9 please?
Answers
7) The angle asked is ajacent to the leg given and we also have the hypotenuse. So we can use cossine:
[tex]\begin{gathered} \cos x=\frac{8}{18}=\frac{4}{9} \\ x=\arccos (\frac{4}{9})=64\degree \end{gathered}[/tex]8) Here we want the hypotenus given an angle an its opposite leg. So we can use sine:
[tex]\begin{gathered} \sin (65\degree)=\frac{10}{x} \\ x=\frac{10}{\sin (65\degree)}=11.0 \end{gathered}[/tex]9) We want the leg which is opposite of a given angle and we have the hypotenuse. So we can use sine again:
[tex]\begin{gathered} \sin (28\degree)=\frac{x}{15} \\ x=15\cdot\sin (28\degree)=7.0 \end{gathered}[/tex]using this input output machine,f(x)=?input. 2,3,5,7output. 9,15,33,59x^2+x+3x^2-x+3x^2+x-3x*2-5
Answers
We have values of x and f(x) and choices for the expression of f(x).
We can easily found the correct option just evaluating the expressions in the x values and see which have the correct value of f(x):
For x=2 the outpur=f(x)=9:
[tex]\begin{gathered} x^2+x+3\Rightarrow2^2+2+3=4+5=9,\text{ Correct!!!} \\ x^2-x+3\Rightarrow2^2-2+3=4+1=5 \\ x^2+x-3\Rightarrow2^2+2-3=4-1=3 \\ x\cdot2-5\Rightarrow2\cdot2-5=4-5=-1 \end{gathered}[/tex]You can evaluate in the other values of x and proof that the corretc option is the first.
6. Solve by any method:3x - 2y = 6x + y = 2
Answers
we can take any equation and solve for any variable, for example y will solve x from the second equation
[tex]\begin{gathered} x+y=2 \\ x=2-y \end{gathered}[/tex]now replace the value of x on the first equation
[tex]\begin{gathered} 3x-2y=6 \\ 3(2-y)-2y=6 \\ \end{gathered}[/tex]simplify
[tex]\begin{gathered} 6-3y-2y=6 \\ 6-5y=6 \end{gathered}[/tex]and solve for y
[tex]\begin{gathered} -5y=6-6 \\ -5y=0 \\ y=\frac{0}{-5} \\ \\ y=0 \end{gathered}[/tex]Value of y is 0 now we can replace y=0 on any equation and solve for x
for example I will replace y=0 on the second equation to find x
[tex]\begin{gathered} x+y=2 \\ x+(0)=2 \\ x=2 \end{gathered}[/tex]Value of x is 2
If we want to represent the solution as a point, the solution is
[tex](2,0)[/tex]which of the following reflective symmetries apply to the hexagon?
Answers
The line y = -7x/3 is a line of symmetry to the given hexagon while the line y=x is not a line of symmetry to it
This makes the answer to the first statement Yes and the second statement No. That is
Reflective symmetry over the line y=-7x/3 -------------------Yes
Reflective symmetry over the x-axis ------------------------------------No
A batter averaged 11 hits in 30 times at bat during the first half of the baseball season. He averaged 5 hits in 7 times at bat for the second half of the season. What was his average batting rate for the season?
*Find the answer to the nearest thousandth.
*(Compare total hits to total times at bat; the average of the two halves gives a wrong answer.)
Answers
Average batting rate for the season is 0.432.
Given,
Number of hits in first half of the season =11
Number of hits in second half of the season = 5
Number of times at bat during first half of the season = 30
Number of times at bat during second half of the season = 7
then,
Total number of hits in the season = 11+5 = 16
Total number of times at bat during the season = 30+7 =37
To find average batting rate use formula,
[tex]Average batting rate of season =\frac{Total number of hits in season}{Total number of at bat during season} \\\\=\frac{16}{37}\\\\ =0.432[/tex]
Hence, the batter's average batting rate for the season is 0.432.
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8. Determine the most precise name for quadrilateral PQRS.-8 -6P(-1, 1)-4 -28642-2-4-6-8Q(0, 2)R(1, 1)2S(0, -2)468
Answers
Answer:
[tex]Kite[/tex]Explanation:
Here, we want to determine the most precise name for the quadrilateral
At first sight, the image plot looks like a kite. We will have to confirm this using the properties of a kite
One of the important properties is to check that the diagonals intersect at right angles
Looking at the plot, QS and PR must be perpendicular
This is correct as they meet at right angles at the line through the origin
Also, for us to have a kite, PQ and QR must be equal
This is also correct as PQ and QR are equal in length
Furthermore, PS and RS must be equal in length
This is alo correct as the two are equal in length
We thus conclude that the quadrilateral is a kitecohis is als
plot looks like a kite. We will have to confirm this using the properties of a kite
plot looks like a kite. We will have to confirm this using the properties of a kite