find the equation of the line that contains the point (6,4) and is perpendicular to the line y=3x-5
The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .
What is a equation of line?The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.
Given that,
equation of given line with a slope of m = 3
y=3x-5
A line perpendicular to that line will have a slope that is the negative reciprocal of 3.
The reciprocal of 3 is 1/3. So the negative reciprocal of 3 is -1/3.
Therefore, we want to write the equation of a line with slope, m = -1/3, and passes through the point (6, 4) = (x, y).
y = mx + b
4 = (-1/3)(6) + b
(we've set up the equation with only one unknown, b, that we can now solve for)
4 = -2 + b
b = 6
With a slope, m = -1/3, and a y-intercept, b = 6, the equation of our line relating x and y is:
y = (-1/3)x + 6
Hence, The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .
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Solve Step by step
8 = x/7 + 9
Answer:
[tex]x=\frac{-1}{7}[/tex]
Step-by-step explanation:
[tex]8=x/7+9\\[/tex]
Subtract 9 from both sides
[tex]-1=x/7[/tex]
Multiply both sides by 7
[tex]\frac{-1}{7} =x[/tex]
Swap the order because you're a smart person
[tex]x=\frac{-1}{7}[/tex]
Find the length of the hypotenuse if the length of the legs are 6 inches and 9 inches. Round to two decimal places.The length of the hypotenuse is ___ inches.
The hypotenuse (longest side) of a right angled triangle can be derived using the Pythagoras' theorem as shown;
[tex]\begin{gathered} AC^2=AB^2+BC^2 \\ \text{Where AC is the hypotenuse, you now have;} \\ AC^2=6^2+9^2 \\ AC^2=36+81 \\ AC^2=117 \\ \text{Add the square root sign to both sides} \\ AC=\sqrt[]{117} \\ AC=10.8166 \\ AC=10.82\text{ (To 2 decimal places)} \end{gathered}[/tex]The answer is 10.82 inches, to 2 decimal places
Solve the system of equations below to find it's solution. List the x-coordinate and y-coordinate.y = 2x - 56x - 2y= 20
y = 2x - 5 Eq(1)
6x - 2y= 20 Eq(2)
We are going to use the elimination method to solve the system.
y-2x = -5 Transpose x to the othe side in Eq(1)
2y - 4x = -10 Multiply all terms of Eq(1) by 2. Then add Eq(1) to Eq(2)
2y - 4x = -10
+ -2y +6x= 20
----------------------
2x = 10 Operating like terms
x= 10/2 Isolating x
x = 5
Replacing x in Eq(1)
y = 2*(5) -5
y= 10 - 5 = 5
The answer is the point with coordinates ( 5 (x-coordinate) , 5(y-coordinate)).
Give the name (monomial,binomial, trinomial etc.) anddegree of the polynomial.
12x^3
Name: Monomial , because it has only 1 term
Degree: 3, exponent of the monomial
Write a formula for the function of tamed when the graph is shifted as described below
Given the function
[tex]f(x)=|x|[/tex]Then, the function is shifted down 3 units means you subtract 3 to f(x).
[tex]f(x)=|x|-3[/tex]And the function is shifted to the right 1 unit means you subtract 1 from the argument of f(x), this is "x". Therefore, the new function is:
[tex]f(x)=|x-1|-3[/tex]Answer:
[tex]f(x)=|x-1|-3[/tex]Which equation represents a line that has a slope of 1/3 and passes through point (-2, 1)? O y=1/3x-1 Oy=1/3x+5/3 O y=1/3 x-5/3 O y=3x+1
Explanation:
The equation of a line in the slope-intercept form is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
We have that the line has a slope of 1/3:
[tex]y=\frac{1}{3}x+b[/tex]To find the y-intercept b we have to use the point. Replace x = -2 and y=1 and solve for b:
[tex]\begin{gathered} 1=\frac{1}{3}(-2)+b \\ 1=-\frac{2}{3}+b \\ b=1+\frac{2}{3}=\frac{5}{3} \end{gathered}[/tex]Answer:
The equation is:
[tex]y=\frac{1}{3}x+\frac{5}{3}[/tex]Measure the angle in degrees.0806100-110120130140150160170-1800The measure of this angle is
The measure of this angle is 65°
The measure of this angle is 60°
Explanation:
1) From the diagram the angle is between 10° and 75°
One of the arrows is on 10°
the other arrow is on 75°
the measure of the angle is between the two angles, so we subtract the smaller one from the bigger one
The angle in degrees is the difference between the 75° and 10°
= 75 - 10
= 65°
The measure of this angle is 65°
2) The second diagram is from 0° to 60°
Difference between them = 60° - 0°= 60°
The measure of this angle is 60°
A phone company offers two monthly plans. Plan A costs $19 plus an additional $0.07 Tor each minute of calls. Plan B costs $12 plus an additional $0.11 for each minute of calls. For what amount of calling do the two plans cost the same? minutes What is the cost when the two plans cost the same? Х Submit AS
Explanation
Step 1
let x represents the number of minutes.
hence:
Plan A costs $19 plus an additional $0.07 for each minute of calls
[tex]A=19+0.07x[/tex]Plan B costs $12 plus an additional $0.11 for each minute of calls
[tex]B=12+0.11x[/tex]Step 2
there is a number of minutes x, such both plnas cost the same,so
[tex]undefined[/tex]The mean height of women in a certain country ( ages 20 29) is 64.1 inches .A random sample of 70 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches if the standard deviation is 2.52
The mean height is given as 64.1 . We want to obtain the probability that he mean height for the sample is greater than 65 inches if the standard deviation is 2.52.
To proceed we, find the z-score of 65 in the distribution, we make use of the formula;
[tex]z=\frac{x-\mu}{(\frac{\sigma}{\sqrt[]{n}})}[/tex]x = 65, mu = population mean = 64.1, sigma = standard deviation = 2.52, n = sample size = 70.
inserting these values, we have;
[tex]\begin{gathered} z=\frac{65-64.1}{\frac{2.52}{\sqrt[]{70}}} \\ z=0.043 \end{gathered}[/tex]The problem now boils down to finding the probability of the z-score greater than 0.043
From z-score tables. the probability of the z-score greater than 0.043;
[tex]Pr(z>0.043)=0.48285[/tex]Therefore, the probability that the mean height for the sample is greater than 65 inches is 0.48285
Assessment
Time Remaining: 2:33:21 | Question 16
Charmaine spent $21 on fruit at the grocery store. She spent a total of $70 at the store. What percentage of the total did she spend on fruit?
%
which expression would be easier to simplify if used the associative property to change the group.A.4+(1.2 +(-0.2)b. 85+(120+80)c. (2+3/7)+4/7d. [-40+(60)] +52
The easiest expression to simplify by using the associative property is expression "b", since there is an addition already set (120 + 80 =200) to be performed.
'The other expressions involve more steps.
Ai Mi was out at a restaurant for dinner when the bill came. Her dinner came to $9. After adding in a tip, before tax, she paid $11.79. Find the percent tip.
Answer:
I don't know if it is the answer
Find the missing value.Hint: Use the number line to find the missing value.-(-5) = -7A-15-10-5051015
Given:
The expression is ___-(-5) = -7.
The objective is to find the missing value using number line.
Consider the missing value as x.
Now, the expression can be rearranged as,
[tex]\begin{gathered} x-(-5)=-7 \\ x+5=-7 \\ x=-7-5 \end{gathered}[/tex]So, we have to solve -7-5 on number line, which means starting from -7 subtract 5 in the number line.
Hence, the missing value is -12.
24. Write the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5
The slope of two perpendicular lines is the negative reciprocal of each other.
Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.
Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.
[tex]y-y_1=m(x-x_1)[/tex]where m = slope.
[tex]\begin{gathered} y-(-13)=\frac{1}{2}(x-0) \\ y+13=\frac{1}{2}(x) \\ y=\frac{1}{2}x-13 \end{gathered}[/tex]Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.
Step-by-step explanation:
The slope of two perpendicular lines is the negative reciprocal of each other.
Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.
Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.
y-y_1=m(x-x_1)y−y
1
=m(x−x
1
)
where m = slope.
\begin{gathered}\begin{gathered} y-(-13)=\frac{1}{2}(x-0) \\ y+13=\frac{1}{2}(x) \\ y=\frac{1}{2}x-13 \end{gathered}\end{gathered}
y−(−13)=
2
1
(x−0)
y+13=
2
1
(x)
y=
2
1
x−13
Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.
Nina has 19.50 to ride the subway around New York it will cost her 0.75 every time she rides identify the dependent variable and independent variable in this scenario
The independent variable is the cost of riding the subway.
The dependent variable is the number of times she can ride the subway.
What is independent variable and independent variable?The independent variable is the variable whose value is given. It is the value of the independent variable that determines the dependent variable. The dependent variable is the variable whose value is determined by changes in the independent variable.
In this question, the cost of each ride is given. There is little or nothing Nina can do to change the price of the subway ride. Thus, it is the independent variable. The total amount of rides Nina can go on is dependent on the cost per ride and the total amount she has. Thus, it is the dependent variable.
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What mathematical symbol goes between the two parentheses to show that you will be using the distributive property?
8 x 57 = (8 x 50) _______ (8 x 7)
Answer: The Answer is the addition symbol
Step-by-step explanation:
8 x 50 = 400
8 x 7 = 56
400 + 56 = 456
8 x 57 = 456
6) Write an equation of the line parallel to: y = -1/4x + 8 with a y-intercept of -10.
The given equation is
[tex]y=-\frac{1}{4}x+8[/tex]The y-intercept of the new line is -10.
We have to find a new parallel line to the given equation, which means they must have the same slope.
Remember that the coefficient of x is the slope, so the slope of the given line is -1/4. This means the new line has a slope fo -1/4 because it's parallel.
So, we know that the new line has a slope of -1/4 and its y-intercept is -10. We use the slope-intercept form to write the equation.
[tex]\begin{gathered} y=mx+b \\ y=-\frac{1}{4}x-10 \end{gathered}[/tex]Therefore, the equation is[tex]y=-\frac{1}{4}x-10[/tex]At the toy store you could get 4 board games for $22.96. Online the price for6board games is $34.74. Which place has the Highest price for a board game?
To determine the price for each board game on the stores, we need to divide the total price by the number of board games bought.
[tex]\begin{gathered} \text{board 1}=\frac{22.96}{4}=5.74 \\ \text{board 2}=\frac{33.74}{6}=5.79 \end{gathered}[/tex]The price online is higher, because it is $5.79 per board game.
There are 175 students enrolled in Blue Bear High School. Twenty-five students train in Karate (T) and 35 students compete with other schools in Karate (C). One hundred students practice martial arts, but not Karate. How many students qualify for a Karate tournament if they train and compete at Blue Bear High School? A. 0 B. 15 C. 60 D. 115
Number of students qualify for a karate tournament if they train and compete at Blue Bear High School is equal to 60.
As given in the question,
Total number of students enrolled in Blue Bear High School =175
Number of students train in karate = 25
Number of students compete with other school in karate =35
Number of students practice martial arts but not karate=100
Number of students qualify for a karate tournament if they train and compete at Blue Bear High School
= 25 + 35
= 60
Therefore, number of students qualify for a karate tournament if they train and compete at Blue Bear High School is equal to 60.
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In null hypothesis significance testing, if a result is unlikely under the hypothesis, then we infer
support for the _______ hypothesis.
Answer:
Step-by-step explanation:
A crucial step in null hypothesis testing is finding the likelihood of the sample result if the null hypothesis were true. This probability is called the p value. A low p value means that the sample result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis.
what is the median value?if another 5 is added, which statement must be true the mean would increase the mean would decrease the median would increaseboth the median and mean will stay the samehow many people made 3 or less trips to the movie
Solution
We have the following data:
0, 0, 0, 0, 1, 1, 1, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5
And the mean would be:
Mean = 2.958
And the median
Median = 4
Then if we add a 5 then the median would be the same 4
And the mean = 3.04
then the solution is:
The mean would increase
And for the other part of the question
we have:´
4+3+1+2 = 10 people made 3 or less trips to the movie
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
The three equations that have the same value of x as 3/5(30 x minus 15) = 72 are:
C) 18x - 9 = 72D) x = 4.5E) 18x = 81.What are equations?Equations are mathematical statements that show the equality of mathematical expressions.
These statements claim that two or more expressions are equal or equivalent.
To show this equality, the expressions are joined with the equal sign (=).
3/5(30x - 15) = 72
= 18x - 9 = 72
18x = 81
x = 4.5 (81/18)
Thus, the three correct equations, sharing the same value of x as 3/5(30 x minus 15) = 72 are Options C, D, and E.
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Question Completion with Options:A) 18x - 5 = 72
B) 50x - 25 = 72
C) 18x - 9 = 72
D) x = 4.5
E) 18x = 81
What is the probability that a card drawn randomly from a standard deck of 52 cards is a red four? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
We have a deck of 52 cards.
We have to calculate the probability that when a card is randomly drawn from the deck, this cart is a red four.
There is only one red four in the deck. Then, if we calculate the probability of an event as the quotient between the number success events (getting a red four, in this case) and the total possible events (getting any card), we will get:
[tex]p=\frac{S}{N}=\frac{1}{52}[/tex]As there is only one card in the deck that gives a success event within the 52 cards, the probability is 1 in 52.
Answer: the probability is 1/52.
The table below represents the total weight, in pounds, of a set ofstone blocks.<
k=12
1) Gathering the data, and setting this table:
Blocks | Pounds
5 60
6 72
7 84
8 96
2) Since we have this table, and a proportional relationship means a linear function without linear coefficient, i.e. y =mx
Then we can write:
y =12x
3) So, as we can write it y=kx, then the constant of proportionality k =12 because the weight in pounds is 12 times the number of blocks.
5 x 12 = 60
6 x 12 =
A bag contains 1 gold marbles, 7 silver marbles, and 25 black marbles. Someone offers to play this game: You randomlyselect one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.What is your expected value if you play this game?
Okay, here we have this:
Considering the provided information, we are going to calculate the expected value for the game, so we obtain the following:
We will substitute in the following formula:
Expected Value=(Black Gain)*Black Chance (Gold Gain)*Gold Chance+(Silver Gain)*Silver Chance
Expected Value=(-1)*(25/33)+(3)*(1/33)+(2)*(7/33)
Expected Value≈-0.24
Finally we obtain that the expected value is approximately $-0.24.
Ahmad will rent a car for the weekend. he can choose one choose one of two plans. the first plan has an initial fee of $55 and cost an additional $0.13 per mile driven the second plan has an initial fee of $48 and cost am additional $0.17 per mile driven
SOLUTION
(a) The first plan cost $55 and an additional $0.13 per mile driven,
while the second plan cost $48 and an additional $0.17 per mile driven
Let the amount of driving be x
Then, this means that for the first plan we have
[tex]\begin{gathered} 55+(0.13\times x) \\ =55+0.13x \end{gathered}[/tex]And the second plan becomes
[tex]\begin{gathered} 48+(0.17\times x) \\ =48+0.17x \end{gathered}[/tex]So, for the plans to cost the same for a particular amount of driving x, it means that
[tex]55+0.13x=48+0.17x[/tex]Collecting like terms we have
[tex]\begin{gathered} 55-48=0.17x-0.13x \\ 7=0.04x \\ x=\frac{7}{0.04} \\ x=175 \end{gathered}[/tex]Hence the two plans cost the same at 175 miles
(b) The cost when the two plans cost the same is
[tex]\begin{gathered} 55+0.13x \\ 55+0.13(175) \\ =55+22.75=77.75 \\ Or\text{ } \\ 48+0.17x \\ =48+0.17(175) \\ =48+29.75=77.75 \end{gathered}[/tex]Hence the answer is $77.75
evaluate the following expression using exponential rules write the result in standard notation
this is
[tex]undefined[/tex]Write the equation of the quadratic with a directrix of y=-5 and vertex of (-2,-3).
answer step by step, please
The equation of the quadratic with a directrix of y= -5 and vertex of (-2, -3) is: y = 1/8 (x + 2)² - 3
How to write the equation of parabola with directrix of y = -5 and vertex of (-2,-3)Quadratic equation when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The vertex
v (h, k) = (-2,-3)
h = -2
k = -3
P in this problem, is the distance between the vertex and the directrix
P = -3 - -5 = -3 + 5 = 2
p = 2
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - -2)² = 4 * 2 (y - -3)
(x + 2)² = 8 (y + 3)
rearranging the equation
8 (y + 3) = (x + 2)²
y + 3 = 1/8 (x + 2)²
y = 1/8 (x + 2)² - 3 (standard vertex form)
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(｀・ω・´) thx for answering
Answer:
3nd one
Step-by-step explanation:
Hope I helped!
If I got it incorrect, please tell me, so I can at least try and see what I did wrong.