The line PQ has equation 3x - 2y = 12 Pis the point with coordinates (6, 3) and Q is the point with coordinates (- 2, k)
a) Find the value of k.
Answers
Answer:
k = - 9
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given equation of PQ is
3x - 2y = 12 ( subtract 3x from both sides )
- 2y = - 3x + 12 ( divide through by - 2 )
y = \(\frac{3}{2}\) x - 6 ← in slope- intercept form
with slope m = \(\frac{3}{2}\)
now calculate the slope of PQ using the slope formula and equate to \(\frac{3}{2}\)
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = P (6, 3 ) and (x₂, y₂ ) = Q (- 2, k )
m = \(\frac{k-3}{-2-6}\) = \(\frac{k-3}{-8}\)
equating the slopes of PQ
\(\frac{k-3}{-8}\) = \(\frac{3}{2}\) ( cross- multiply )
2(k - 3) = - 8 × 3 = - 24 ( divide both sides by 2 )
k - 3 = - 12 ( add 3 to both sides )
k = - 9
Related Questions
Robyn invests $1500 at 4.85% compounded quarterly. Write an equation to represent the amount of money A she will have in tyears.
Answers
The amount of money A after t years, with a rate r, an initial investment P and a number of times n that the interest is compounded per year, is:
\(A=P(1+\frac{r}{n})^{nt}\)If the initial investment is $1500, the rate is 4.85% anually compounded quarterly (n=4), then:
\(\begin{gathered} A=1500(1+\frac{4.85/100}{4})^{4t} \\ =1500(1+\frac{4.85}{400})^{4t} \end{gathered}\)Therefore, the amount of money that she will have after t years, is:
\(A=1500(1+\frac{4.85}{400})^{4t}\)There is a bag filled with 5 blue, 2 red and 3 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 the same colour?
Answers
The probability of getting 2 the same colour will be 39/100.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
The probability of getting 2 blue will be:
= 5/10 × 5/10
= 1/4.
The probability of getting 2 red will be:
= 2/10 × 2/10
= 1/25
The probability of getting 2 green will be:
= 3/10 × 3/10.
= 9 / 100
The probability of getting 2 the same colour is:
= 1/4 + 2/25 + 9 / 100
= 39/100
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Determine the length of x in the triangle. Give your answer to two decimal places. Show the steps, please.
Answers
Answer:
35.09 units
Step-by-step explanation:
This is a right-angled triangle where:
Hypotenuse = x units
With respect to angle 20°:
Opposite = 12 units
Use trigonometric function sinФ to solve for x:
sinФ = \(\frac{Opposite}{Hypotenuse}\)
∴sin20° = \(\frac{12}{x}\)
Cross-multiplication is applied:
\((x)(sin20) = 12\)
x has to be isolated and made the subject of the equation:
∴\(x = \frac{12}{sin20}\)
x = 35.09 units (Rounded to 2 decimal places)
Answer:
The length of x is 35.09 units to two decimal places.
Step-by-step explanation:
In the given right triangle, we have been given the length of the side opposite the angle and need to find the length of the hypotenuse.
To find the value of x, use the sine trigonometric ratio.
\(\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)
Substitute θ = 20°, O = 12 and H = x into the ratio and solve for x:
\(\implies \sin 20^{\circ}=\dfrac{12}{x}\)
\(\implies x=\dfrac{12}{\sin 20^{\circ}}\)
\(\implies x=35.085652...\)
\(\implies x=35.09\; \sf (2\;d.p.)\)
Therefore, the length of x is 35.09 units to two decimal places.
(b) What is the probability that a random sample of n = 35 oil changes results in a sample mean time less than 15 minutes?
The probability is approximately
(Round to four decimal places as needed.)
Answers
Answer:.8056
Step-by-step explanation:
Given the following function, find f(-5), f(0), and f(3).
f(x) = x^2+5
Answers
Answer:
f(-5) = 30
f(0) = 5
f(3) = 14
Step-by-step explanation:
=> f(x) = x²+5
for , f(-5) = (-5)² +5
=> 25 +5
=> 30
for , f(0) = (0)² +5
=> 5
for , f(3) = (3)² + 5
=> 9 + 5
=> 14
Veronica has two offers for a $65,000 student loan. The first loan has a 6.3% interest rate for 15 years, and the second loan has a 4.8% interest rate for 20 years. Both loans have interest compounded every month. Veronica is interested in finding the loan that minimizes the amount of interest that she will pay over the life of the loan. Which loan has a lower amount of interest paid?
Answers
The second option has a lower amount of interest paid.
In order to determine the loan option that minimizes loan payment, the future value of both loan options has to be determined.
FV = P (1 + r)^nm
FV = Future value
P = Present value
R = interest rate
m = number of compounding
N = number of years
First loan option
65000( 1 + 0.063/12)^300 = 312,707.21
Second loan option
65000( 1 + 0.048/12)^240 = 169,435.51
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Suppose 50% of the people in a particular population have high blood pressure. Of the people with high blood pressure, suppose 75% smoke; whereas, only 50% of the people without high blood pressure actually smoke. What percent of people who smoke have high blood pressure
Answers
Answer:
37.50%
Step-by-step explanation:
The computation of the percentage of people who smoke have high blood pressure is shown below:
Given that
There is 50% of the people who has the high blood pressure
And, out of which 75% would smoke
So, the percent of the people who smoke have high high blood pressure is
= 50% × 0.75
= 37.50%
When writing a proof, how do you construct the first statement?
A) By writing the justification for the first statement in the right column.
B) By copying the “prove” statement(s) from the original problem.
C) By writing the next logical statement from the current one.
D) By copying the “given” statement(s) from the original problem.
Answers
When writing a proof , by copying the “given” statement(s) from the original problem
Given data ,
A true assertion that is provided in the problem or is known to be true should be the first statement in a proof. The subsequent logical argument has this as its foundation.
We can provide the groundwork for the proof and proceed to the desired conclusion by duplicating the "given" statement(s) from the original problem.
Once the first statement is established, we can move on to writing additional statements that are each logically supported by the first statement.
The logical evolution of the preceding assertions demonstrates that the last statement should be the intended conclusion.
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PLEASE HELP !! Select all the correct answers.
Janine needs to calculate the value of log12 81
Which expressions could she input into her calculator to find this value?
Answers
Answer: In 81/ In 12 AND log 81/log 12
Step-by-step explanation: PLATO ANSWER I got 100%
To solve the problem we must know about the change of base rule for Logarithm.
What is the change of base rule for Logarithm?The change of base rule for Logarithm helps us to change the base of any logarithmic expression to any other logarithmic expression.
\(log_ab = \dfrac{log_x b}{log_x a}\)
where x is any base.
The expression can be expressed as \(\dfrac{log\ 81}{log\ 12}\).
Given to us
\(log_{12}81\)Change of base rule\(log_{12}81\\\)
use the change of base rule, \(log_ab = \dfrac{log\ b}{log\ a}\),
\(log_{12}81=\dfrac{log\ 81}{log\ 12}\)
Hence, the expression can be expressed as \(\dfrac{log\ 81}{log\ 12}\).
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solve that please
show all work
Answers
Answer:
There is not enough information to find a solution. The work to find it if more variable are filled is below. You can also solve the problem by inputting these equations as solutions.
Step-by-step explanation:
(x^(2)+a)(x^(2)-b)=0
You can find x by taking the square root of both sides
√(-a), -√(-a), √b, -√b
You can find a by -x^(2)
You can find b by x^(2)
fv=100000, pmt=4000, i/y=5%, n=10, what is pv?
Answers
The Present value is $6,139.132.
We have,
FV=100000, pmt = 4000, I =5%, n=10
So, The present value formula is
PV=FV / (1 + \(i)^n\)
So, PV = 100, 000 / (1+ 5/100\()^{10\\\)
PV = 100,000 / (1+ 0.05\()^{10\\\)
PV = 100, 000/ (1.05\()^{10\\\)
PV = 100,000 / 1.6288946
PV= $6,139.132
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The difference of -10 and the product of p and q
Answers
The expression of "The difference of -10 and the product of p and q" in algebraic notation is pq + 10
Writing the algebraic expression in algebraic notationFrom the question, we have the following parameters that can be used in our computation:
The difference of -10 and the product of p and q
The numbers are given as
p and q
The product of p and q means pq
So, we have the following
The difference of -10 and pq
The difference of -10 and pq means
pq + 10
Hence, the expression is pq + 10
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The length of the field is 3 yards less than triple the width. What are the dimensions of the playing field
Answers
Answer:
45=w answer
Step-by-step explanation:
Here's what we know:
P = 2L + 2w
L = 3w + 3 (length is 3 yards more than 3 times the length)
P = 366
We have a value for length and perimeter, so plug them in:
366 = 2(3w + 3) + 2w
366 = 6w + 6 + 2w
366 = 8w + 6
360 = 8w
45 = w
Explain why there is no solution to the simultaneous equations x + y = 5 and x + y = 7
Answers
The same quantity, x+y, cannot be equal to 2 different values, in this case 5 and 7.
please help i am struggling
Answers
By using the equations of sides and angles and congruence properties, the values of x and y are equal to 34 and 8, respectively. (Correct choice: A)
How to find the values of the variables associated with two congruent trianglesHerein we find two triangles that are congruent when the share the same sides and angles in magnitudes and distribution. As triangle CDE and triangle LMN are congruent, then we have following relationships:
DE = LN (1)
CE = MN (2)
m ∠ D = m ∠ L (3)
m ∠ C = m ∠ M (4)
By (1):
2 · y + 1 = 17
2 · y = 16
y = 8
By (2):
MN = 4 · 8 - 3
MN = 29
By (3):
x + 17 = 51
x = 34
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an = r·(an-1)
determine the recrusive function to model the geometric sequence.
24, 6, 1.5
show work
Answers
On solving the provided question, we got to know that - recursive function to model the geometric sequence is 0.25
What is recursive function?In order to create a sequence of terms, a recursive function either repeats itself or uses a previous term to compute a new term. An arithmetic-geometric series with terms that differ from each other frequently is used to explain this function.
Given, geometric sequence
24, 6, 1.5
First term of this sequence = 6
a1 = 6
Recursive formula geometric sequence
\(a_{n} = a_{(n-1)}r\)
\(Here r = common. ratio .of .successive. and previous term\\From .the given .sequence\\\)
r = a2/a1
r = 6/24
r = 0.25
\(Recursive formula of the given sequence will be,\)
\(a_{n} = a_{(n-1)}(0.25)\)
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Hudson and his children went into a bakery where they sell cupcakes for $4.75 each
and brownies for $2 each. Hudson has $30 to spend and must buy at least 7 cupcakes
and brownies altogether. If x represents the number of cupcakes purchased and y
represents the number of brownies purchased, write and solve a system of
inequalities graphically and determine one possible solution.
Answers
An electronics store advertised a television as $17 a day for 30 days rather than the full price of $510. Why did the store choose to advertise the television this way?
A.Because it looks like a deal
B. Because they accept partial payments
C.To help customers pay for it
D.To show the daily consumption cost
Answers
Answer:
A.Because it looks like a deal
Step-by-step explanation:
17$ a day for 30 days is just multiplication which ends up with 510$ which is the full price they only put the ad up to make it seem like a deal. Understand well il break it down for you take the seventeen and 30. multiply the 7 and the 30 then 10 and the 30. add both of the products together to get 510 or 510$.
Describe the location of point (−7, 6, −4) in three-dimensional coordinate space.
Answers
The description of the location of the point, (−7, 6, −4) in three-dimensional coordinate space is this: A. From the origin, move 7 units back, 6 units right, and 4 units down.
What is a three-dimensional coordinate space?The meaning of a three-dimensional coordinate space is a requirement for three units to come together to form a point. In the location of the point above, we are given three units namely, -7, 6, and -4.
The indication of signs in front of them are as follows; -7, means moving 7 units back, 6 means moving 6 units right, ad -4 means moving 4 units down.
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In class of 35 students, 19 take Spanish, 18 take French and 3 Take neither. Calculate
how many takes:
A) Both French and Spanish
B) Just Spanish
C) Just French
Answers
40 - 35 = 5
so 5 take both
14 take just spanish
13 take just french
Students takes both French and Spanish is 5 members
Student takes just Spanish = 14 members
Student takes just French = 13 members
Given :
Total numbers of students in class = 35
how many members take spanish = 19
how many members take french = 18
students take neither = 3
To find :
A) Both French and Spanish
B) Just Spanish
C) Just French
Solution :
from venn diagram
a+b+c+d = 35 → 1
b+c = 19 → 2
c+d = 18 → 3
a = 3 → 4
Substract equation 1 and equation 2
a+b+c+d-b-c=35-19
a+d=16 → 5
substract a=3 in the eqution 5
3+d=16
d=13
put d=13 in equation 3
c+d=18
c+13=18
c=5
Students takes both French and Spanish is 5 members
Student takes just Spanish = 14 members
Student takes just French = 13 members
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Can some help with the answer please it’s very much needed and apprIeciated
Answers
Answer:
A
Step-by-step explanation:
The degree of the Polynomial is 3
A circle has a circumference of 452.16. What is the radius of the circle
Answers
Formula: r = C/2π
Solve with the given values.
r = 452.16/2(3.14)
r = 452.16/6.28
r = 72
Therefore, the radius is approximately 72 units.
Best of Luck!
Is this a linear function?
Answers
Answer:
Yes
Step-by-step explanation:
a+bx is the formula so the slope is negative 8 and the y intercept is -21.
−4 1/2÷(−2 2/3) i need help
Answers
Answer:
\(1\frac{11}{16}\)
Step-by-step explanation:
Convert mixed numbers into improper fractions.
= \(\frac{-\frac{9}{2}}{\left(-2\frac{2}{3}\right)}\)
= \(\frac{-\frac{9}{2}}{\left(-\frac{8}{3}\right)}\)
= \(\frac{\frac{9}{2}}{\frac{8}{3}}\)
= \(\frac{9\cdot \:3}{2\cdot \:8}\)
= \(\frac{27}{2\cdot \:8}\)
= \(\frac{27}{16}\)
Convert improper fraction into mixed number.
= \(1\frac{11}{16}\)
-
16
Figure F is a scale image of figure E as shown. Enter the scale factor applied to figure E to produce figure F.
Answers
Step-by-step explanation:
that means that there is one scale factor for all sides of the triangles.
so,
2 × f = 14
f = 14/2 = 7
and to control, this has to work also for the other given side :
3 × 7 = 21
correct.
so, the scaling factor to get from E to F is 7.
How do you do this? Because I don’t get it
Answers
Answer:
5,-17
6,-21
Step-by-step explanation:
When the input goes up by 1 the output goes up by negative 4 each time
Note: If p(a) = 0 then (x - a) is a factor of p(x)
given that f(-1), f(-2) are zeros of f(x) find the missing values of these coefficients p, q
f(x) = x³ + px² - qx - 4
After finding the values of the coefficients factor and find the solutions of x1, x2 and x3.
Answers
Answer:
Since f(-1) = 0 and f(-2) = 0, we can set up two equations:
(-1)³ + p(-1)² - q(-1) - 4 = 0
(-2)³ + p(-2)² - q(-2) - 4 = 0
Simplifying each equation, we get:
-1 + p - q - 4 = 0
-8 + 4p - 2q - 4 = 0
Simplifying further, we get:
p - q = 5
2p - q = 6
Solving for p and q, we can add the two equations together to eliminate q:
p - q + 2p - q = 5 + 6
3p - 2q = 11
Then, we can substitute the value of q from the first equation into this equation to solve for p:
3p - 2(q + 5) = 11
3p - 2q - 10 = 11
3p - 2q = 21
3p - 2(5 + p) = 21
p - 10 = 7
p = 17
Substituting this value of p into either equation for q, we get:
q = p - 5 = 12
Therefore, the coefficients are p = 17 and q = 12. To factor the expression, we can use synthetic division or long division. Using synthetic division, we get:
-1 | 1 17 -12 -4
|__ -1 -16 28
1 1 12
This gives us the factorization:
f(x) = (x + 1)(x² + x + 12)
To find the solutions, we can use the quadratic formula on the quadratic factor:
x = (-1 ± sqrt(1 - 4(1)(12))) / 2(1)
x = (-1 ± sqrt(1 - 48)) / 2
x = (-1 ± sqrt(-47)) / 2
x1 = (-1 + i(sqrt(47))) / 2
x2 = (-1 - i(sqrt(47))) / 2
Therefore, the solutions are x1 = (-1 + i(sqrt(47))) / 2, x2 = (-1 - i(sqrt(47))) / 2, and x3 = -1.
Step-by-step explanation:
give me thanks for more! your welcome bud!
Collinear points are all points that are not on the same line.
False
True
Answers
Answer: False
Step-by-step explanation:
The definition of collinear points are they they are all on the same line. Therefore, the provided statement is false.
In the box below, describe the graph. 3x+4y
Answers
The graph of the equation 3x + 4y = 0 is a straight line with a negative slope passing through the origin.
The given equation, 3x + 4y = 0, represents a linear graph in the Cartesian coordinate system. Let's analyze its characteristics.
First, note that the equation is in the standard form for a linear equation, which is Ax + By = C, where A, B, and C are constants. In this case, A = 3, B = 4, and C = 0.
To graph this equation, we can rewrite it in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. By isolating y, we have y = (-3/4)x + 0. Since the y-intercept (b) is 0, the line intersects the y-axis at the origin (0,0).
Next, we can examine the slope. The coefficient of x, -3/4, represents the ratio of the change in y (vertical) to the change in x (horizontal) as we move along the line. In this case, the slope is negative, indicating that the line descends from left to right. The magnitude of the slope, 3/4, implies that for every 4 units moved horizontally to the right, the line goes 3 units down vertically.
Therefore, we can conclude that the graph of the equation 3x + 4y = 0 is a straight line passing through the origin (0,0) with a negative slope. It extends indefinitely in both directions, with the line getting steeper as we move to the right.
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Four friends shared 7 chocolate bars. Each of them was given an equal share of the chocolate bars. How many chocolate bars did each person get?
Answers
Answer:
19. 25 chocolate bars
Step-by-step explanation:
77 divided by 4=19. 25