Given the equation of the straight line AB is 3x+KY=8 where k is a constant. the straight line AB is parallel to the straight line connecting the point P(-1, 6) with the point Q(5, -3). Find the value of k then calculate the x-intercept of the straight line AB
Answers
If we have two parallel lines, than their slopes must be the same.
One way of comparing slopes of linear equations is to write them in the slope-intercept form:
[tex]y=mx+b[/tex]In this form, m is the slope and b is the y-intercept.
So, let's write the first equation in this form:
[tex]\begin{gathered} 3x+ky=8 \\ ky=-3x+8 \\ y=-\frac{3}{k}x+\frac{8}{k} \end{gathered}[/tex]To find the value of k, we can find the slope of the parallel line and compair it to the slope in this equation.
The slope of a line given two points on it can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}_{}[/tex]Since we have points (-1, 6) and (5, -3), we can calculate the slope of the parallel line:
[tex]m=\frac{-3-6}{5-(-1)}=\frac{-9}{5+1}=-\frac{9}{6}=-\frac{3}{2}[/tex]Since both lines are parallel, their slopes are the same.
We know that the slope of the first line is -3/k and the second line is -3/2, so, since they are parallel:
[tex]\begin{gathered} -\frac{3}{k}=-\frac{3}{2} \\ -3\cdot2=-3\cdot k \\ 2=k \\ k=2 \end{gathered}[/tex]Since we have the value for k, we can substitute it into the equation for AB:
[tex]\begin{gathered} y=-\frac{3}{k}x+\frac{8}{k} \\ y=-\frac{3}{2}x+\frac{8}{2} \\ y=-\frac{3}{2}x+4 \end{gathered}[/tex]To find the x-intercept, we can see that it happens when the value of y is equal to 0, so we can plug in y = 0 and find the value of x:
[tex]\begin{gathered} y=0 \\ 0=-\frac{3}{2}x+4 \\ \frac{3}{2}x=4 \\ x=\frac{2}{3}\cdot4 \\ x=\frac{8}{3} \end{gathered}[/tex]So, the value of k is 2 and the x-intercept is 8/3.
Related Questions
6. An odometer shows that a car has traveled 56,000 miles by January 1, 2020. The car travels 14,000 miles each year. Write an equation that represents the number y of miles on the car's odometer x years after 2020.
Answers
Answer:
y=14000x
Step-by-step explanation:
x represents years after 2020 and y is the number of miles
The required equation for the distance travelled versus number of years after 2020 is given as y = 14000x + 56000.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The given problem can be solved as follows,
Suppose the year 2020 represents x = 0.
The distance travelled per year can be taken as the slope of the linear equation.
This implies that slope = 14000.
And, the distance travelled by January 1, 2020 is 56000.
It implies that for x = 0, y = 56000.
The slope-point form of a linear equation is given as y = mx + c.
Substitute the corresponding values in the above equation to obtain,
y = 14000x + c
At x = 0, y = 56000
=> 56000 = 14000 × 0 + c
=> c = 56000
Now, the equation can be written as,
y = 14000x + 56000
Hence, the required equation for number of miles and years for the car is given as y = 14000x + 56000.
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What is the solution to the equation below? 3x = x + 10 O A. x = 10 B. x = 0 C. X = 5 D. No Solutions
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Hence, the correct option is C: x=5
using the box and whisper plot shown, find the quartile values Q1 and Q3
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
box-and-whisker plot
Step 02:
quartile values:
We must analyze the plot to find the solution.
box-and-whisker plot:
q1 = - 4
q3 = 6
The answer is:
q1 = - 4
q3 = 6
Question 31 of 50 2 Points An assumption about a population parameter that is verified based on the results of sample data is a/an OA. statistical hypothesis OB. assumption OC. presumptive statement OD. prediction
Answers
From the question, it is:
An assumption about a population parameter that is verified based on the real results of sample data is a/an Statistical Hypothesis.
Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution.
Therefore, the correct options is A, which is Statistical Hypothesis.
The relation described in the following diagram is function. A. True B. False
Answers
Answer:
False
Explanation:
A relation is a function each term of the first set is related to only one term of the second set. In this case, 1 is related to 5 and to 10, so it is not a function.
Therefore, the answer is
False
Suppose that our section of MAT 012 has 23 students, and the other two sections of MAT 012 have a total of 44 students. What percent of all the students taking MAT012 are in our section of MAT 012?
Answers
Explanation
We can deduce from the information that MAT 012 has 3 sections, namely:
Our section, and two other sections
Then, we can also infer that MAT012 has a total of:
[tex]23+44=67\text{ students}[/tex]Our task will be to get the percentage of our section taking MAT 102
Since our section has 23
Then we can calculate the answer as
[tex]\frac{23}{67}\times100=34.33\text{ \%}[/tex]Thus, the answer is 34.33%
4/3x+2/3=1 can someone help me
Answers
Given the expression 4/3x+2/3=1, we are to find the value of x from the expression. This is as shown below;
4/3x+2/3=1
subtract 2/3 from both sides
4/3x+2/3-1/3=1-1/3
4/3x = (3-1)/3
4/3x = 2/3
cross multiply
2(3x) = 4(3)
6x = 12
Divide both sides by 6
6x/6 - 12/6
x = 2
Hence the value of x is 2
there are 64 hamburgers and 52 hot dogs at the picnic. what is the ratio of the number of hamburgers to the total number of lunch items?
Answers
Answer: The ratio of hamburgers to the total lunch items is 16 : 29
Number of hamburgers = 64
Number of hot dogs = 52
Total number of items for lunch = number of hamburgers + number of hot dogs
Total number of items for lunch = 64 + 52
Total number of items for lunch = 116
The ratio of number of hamburgers to the total number of lunch items
64/116
16 : 29
Therefore, the ratio of hamburgers to the total lunch items is 16 : 29
suppose each cube in this right rectangular prism is a 1/2-in unit cube
Answers
Answer:
The length of each cube is given below as
[tex]l=\frac{1}{2}in[/tex]Concept:
To figure out the dimension of the prism, we will calculate the number of cubes to make the length,width and height and multiply by 1/2
To figure out the length of the prism,
we will multiply 1/2in by 5
[tex]\begin{gathered} l=\frac{1}{2}in\times5 \\ l=2.5in \end{gathered}[/tex]To figure out the width of the prism,
we will multiply 1/2in by 4
[tex]\begin{gathered} w=\frac{1}{2}in\times4 \\ w=2in \end{gathered}[/tex]To figure out the height of the prism,
we will multiply 1/2 in by 3
[tex]\begin{gathered} h=\frac{1}{2}in\times3 \\ h=\frac{3}{2}in=1.5in \end{gathered}[/tex]Hence,
The dimensions of the prism are
Length = 2.5in
Width = 2in
Height = 1.5 in
2.5in by 2in by 1.5in
Part B:
To figure out the volume of the prism, we will use the formula below
[tex]\begin{gathered} V_{prism}=base\text{ area}\times height \\ V_{prism}=l\times w\times h \\ l=2.5in,w=2in,h=1.5in \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} V_{pr\imaginaryI sm}=l\times w\times h \\ V_{pr\mathrm{i}sm}=2.5in\times2in\times1.5in \\ V_{pr\mathrm{i}sm}=7.5in^3 \end{gathered}[/tex]Alternatively, we will calculate below by calculate the volume of each cube and then multiply by the total number of cubes
[tex]\begin{gathered} volume\text{ of each cube=} \\ =l^3=(\frac{1}{2})^3=\frac{1}{8}in^3 \\ The\text{ total number of cubes =} \\ =5\times4\times3 \\ =60cubes \\ Volume\text{ of the prism } \\ =\frac{1}{8}in^3\times60 \\ =7.5in^3 \end{gathered}[/tex]Hence,
The volume of the prism is = 7.5in³
2. The length of Sally's garden is 4 meters greater than 3 times the width. Theperimeter of her garden is 72 meters. Find the dimensions of Sally's garden.The garden has a width of 8 and a length of 28.
Answers
L = length
W = width
L = 4 + 3*W
The perimeter of a rectangle is the sum of its sides: 2L + 2W. Since it's 72, we have:
2L + 2W = 72
Now, to solve for L and W, the dimensions of the garden, we can use the first equation (L = 4 + 3*W) into the second one (2L + 2W = 72):
2L + 2W = 72
2 * (4 + 3*W) + 2W = 72
2 * 4 + 2 * 3W + 2W = 72
8 + 6W + 2W = 72
8W = 72 - 8
8W = 64
W = 64/8 = 8
Then we can use this result to find L:
L = 4 + 3W = 4 + 3 * 8 = 4 + 24 = 28
Therefore, the garden has a width of 8 and a length of 28.
Kwan had 16 3/4 inches of wire. He cut of 4 2/4 inches of wire to use in a craft project how much wire does kwan have left
Answers
We know that the total is 40 students, and 24 of them are girls, then the fraction that represents it is
[tex]\frac{24}{40}[/tex]But we must simplify the fraction, let's divide the denominator and numerator by 4
[tex]\frac{24}{40}=\frac{6}{10}[/tex]Now we can do it again by 2
[tex]\frac{24}{40}=\frac{6}{10}=\frac{3}{5}[/tex]Therefore the correct answer is the letter B.
[tex]\frac{3}{5}[/tex]Answer: 12 1/4
Step-by-step explanation: 16 =4 is 12, and 3/4 - 2/4 is 1/4
hope this helps :)
2. When we are in a situation where we have a proportional relationship between two quantities, what information do we need to find an equation?
Answers
Answer:
If two quantites have a proportional relatio
Which of the following is equivalent to –(–5.25) ? 5 5.25 –5 –5.25please answer fast
Answers
the given expression is,
= - ( - 5.25)
= 5.25
thus, the answer is 5.25
△GHI~△WVU.51010IHG122UVWWhat is the similarity ratio of △GHI to △WVU?Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
Answers
Answer: 5
To get the similarity ratio, we must know that for the given triangles:
[tex]\frac{IG}{UW}=\frac{GH}{WV}=\frac{HI}{VU}[/tex]From the given, we know that:
UW = 2
WV = 2
VU = 1
IG = 10
GH = 10
HI = 5
Substitute these to the given equation and we will get:
[tex]\begin{gathered} \frac{IG}{UW}=\frac{GH}{WV}=\frac{HI}{VU} \\ \frac{10}{2}=\frac{10}{2}=\frac{5}{1} \\ 5=5=5 \end{gathered}[/tex]With this, we have the similarity ratio of ΔGHI to ΔWVU is 5
-3.9-3.99-3.999-4-4.001-4.01-4.10.420.4020.4002-41.5039991.53991.89try valueclear tableDNEundefinedlim f(2)=lim f(2)=2-)-4+lim f (30)f(-4)-4
Answers
In order to determine the limit of f(x) when x tends to -4 from the right (4^+), we need to look in the table the value that f(x) is approaching when x goes from -3.9 to -3.99 to -3.999.
From the table we can see that this value is 0.4.
Then, to determine the limit of f(x) when x tends to -4 from the left (4^-), we need to look in the table the value that f(x) is approaching when x goes from -4.1 to -4.01 to -4.001.
From the table we can see that this value is 1.5.
Since the limit from the left is different from the limit from the right, the limit when x tends to -4 is undefined.
Finally, the value of f(-4) is the value of f(x) when x = -4. From the table, we can see that this value is -4.
what is the ratio of sin b
Answers
we have that
sin(B)=56/65 -----> by opposite side angle B divided by the hypotenuse
thank you for viewing my question I seem to be stuck on this and need help thank you
Answers
ANSWER
[tex]\begin{gathered} A=\frac{1}{4} \\ B=\frac{1}{2} \\ C=\frac{1}{4} \end{gathered}[/tex]EXPLANATION
From the given data;
Event A; Alternating even and odd numbers means;
EOE and OEO
Number of favourable outcome is 2 while number of possible outcome is 8
Hence, the probability of Event A IS;
[tex]\begin{gathered} Prob(A)=\frac{2}{8} \\ =\frac{1}{4} \end{gathered}[/tex]In Event B; More even numbers than odd means having;
EEE,OEE,EEO and EOE
[tex]\begin{gathered} EEE,OEE,EEOandEOE \\ Prob(B)=\frac{4}{8} \\ =\frac{1}{2} \end{gathered}[/tex]For Event C; an even number on both the first and the last rolls;
EEE and EOE
[tex]\begin{gathered} EEEandEOE \\ Prob(C)=\frac{2}{8} \\ =\frac{1}{4} \end{gathered}[/tex]A tepee in the shape of a right cone has a slant height of 18.5 feet and a diameter of 20 feet. Approximately how much canvas would be needed to cover the tepee?
Answers
To find:
The area of canvas needed to cover the tepee.
Solution:
Given that the tepee is in the shape of a right cone, with slant height 18.5 feet and diameter of 20 feet then the radius is 10 feet.
The area of canvas is equal to the curved surface area of the tepee. It is known that the curve surface area of the cone is given by:
[tex]CSA=\pi rl[/tex]Where, r is the radius of the cone and l is the slant height of the cone. So,
[tex]\begin{gathered} CSA=3.14\times10\times18.5 \\ =580.9ft^2 \end{gathered}[/tex]Thus, the approximate canvas that would be needed to cover the tepee is 580.9 ft^2.
581Answer:
Step-by-step explanation:
What value of x would make lines land m parallel?5050°t55°75xº55m105
Answers
If l and m are parallel, then ∠1 must measure 55°.
The addition of the angles of a triangle is equal to 180°, in consequence,
I need to simplify this equation 7b + 3x − 5b + 21x
Answers
Answer:
2b + 24x
Step-by-step explanation:
The equation is,
→ 7b + 3x − 5b + 21x
Simplifying the given equation,
→ 7b + 3x − 5b + 21x
→ (7b - 5b) + (3x + 21x)
→ 2b + 24x
Hence, the answer is 2b + 24x.
Write a word problem that the bar model in problem 2 could represent.
Answers
An example of a problem for the given diagram:
You go to a store to buy the school supplies you will need for the next term. There are boxes of 7 pencils each, and you decide to buy 5 of those boxes. How many pencils do you end up buying?
Given the following data: {3, 7, 8, 2, 4, 11, 7, 5, 9, 6),a. What is the median? (remember to put the data in order first)
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please help me solve. The answer I have is in yellow. They are wrong.
Answers
Let's simplify the radicals:
[tex]\begin{gathered} \sqrt[]{30}\cdot\sqrt[]{5}=\sqrt[]{30\cdot5} \\ =\sqrt[]{150} \\ =\sqrt[]{25\cdot6} \\ =\sqrt[]{25}\sqrt[]{6} \\ =5\sqrt[]{6} \end{gathered}[/tex]I’m circle P with m ∠NRQ=42, find the angle measure of minor arc NQ
Answers
Here we must apply the following rule:
[tex]arc\text{ }NQ=2\cdot m\angle NRQ[/tex]Since m ∠NRQ = 42°, we have:
[tex]arc\text{ }NQ=2\cdot42=84\degree[/tex]x^2-18x-57=6 solve each equation by completing the square
Answers
x=-3
x=21
If Mason made 20 free throws, how many free throws did he attempt in all?
Answers
Answer:
what is the shooting percentage?
Write an equation of the line perpendicular to the line –4x + 3y = –15 and passes through the point (–8, –13)
Answers
4y = -3x - 76
Explanations:The given equation is:
-4x + 3y = -15
Make y the subject of the formula to express the equation in the form
y = mx + c
[tex]\begin{gathered} -4x\text{ + 3y = -15} \\ 3y\text{ = 4x - 15} \\ y\text{ = }\frac{4}{3}x\text{ - }\frac{15}{3} \\ y\text{ = }\frac{4}{3}x\text{ - 5} \end{gathered}[/tex]Comparing the equation with y = mx + c
the slope, m = 4/3
the y-intercept, c = -5
The equation perpendicular to the equation y = mx + c is:
[tex]y-y_1\text{ = }\frac{-1}{m}(x-x_1)[/tex]The line passes through the point (-8, -13). That is, x₁ = -8, y₁ = -13
Substitute m = 4/3, x₁ = -8, y₁ = -13 into the equation above
[tex]\begin{gathered} y\text{ - (-13) = }\frac{-1}{\frac{4}{3}}(x\text{ - (-8))} \\ y\text{ + 13 = }\frac{-3}{4}(x\text{ + 8)} \\ y\text{ + 13 = }\frac{-3}{4}x\text{ - 6} \\ y\text{ = }\frac{-3}{4}x\text{ - 6 - 13} \\ y\text{ = }\frac{-3}{4}x\text{ - 19} \\ 4y\text{ = -3x - }76 \end{gathered}[/tex]Find the distance from P to l. Line l contains points (2, 4) and (5, 1). Point P has coordinates (1, 1).
Answers
First we need to find the equation of the line l passing through the points (2, 4) and (5, 1).
The equation of a line is expressed as y = mx+c
m is the slope
c is the intercept
m = y2-y1/x2-x1
m = 1-4/5-2
m = -3/3
m = -1
Get the intercept
Substitute any point (2, 4) and the slope m = -3 into the expression y = mx + c
4 = -3(2)+c
4 = -6 + c
c = 4+6
c = 10
The equation of line l is y = -3x+10
Next is to find the equation of the line w perpendicular to the line l, through P(1, 1).
Since the line w is perpendicular to lin
Can you pls help me with this question thank you
Answers
To solve this question, follow the steps below.
Step 01: Substitute j and k by its corresponding values.
j = 6
k = 0.5
Then,
[tex]\begin{gathered} 3.6j-2k \\ 3.6\cdot6-2\cdot0.5 \\ \end{gathered}[/tex]Step 02: Solve the multiplications.
[tex]21.6-1[/tex]Step 03: Solve the subtraction.
[tex]20.6[/tex]Answer: b. 20.6.
I need help on this. and there's two answers that's right but I don't know
Answers
Answer
Options B and C are correct.
(5⁸/5⁴) = 625
(5²)² = 625
Explanation
We need to first know that
625 = 5⁴
So, the options that the laws of indices allow us to reduce to 5⁴
Option A
(5⁻²/5²) = 5⁻²⁻² = 5⁻⁴ = (1/5⁴) = (1/625)
This option is not correct.
Option B
(5⁸/5⁴) = 5⁸⁻⁴ = 5⁴ = 625
This option is correct.
Option C
(5²)² = 5⁴ = 625
This option is correct.
Option D
(5⁴) (5⁻²) = 5⁴⁻² = 5² = 25
This option is not correct.
Hope this Helps!!!