Line p is the perpendicular bisector of MN. Write the equation of line p in slope-intercept form.
Answers
Line p is perpendicular bisector of line MN. This means that it divides line MN equally. Thus, point B is the midpoint of line MN. Thus, we would find the midpoint of line MN by applying the midpoint formula which is expressed as
(x1 + x2)/2, (y1 + y2)/2
Looking at the given points of line MN,
x1 = - 5, y1 = 2
x2 = 7, y2 = - 1
Midpoint = (- 5 + 7)/2, (2 + - 1)/2
Midpoint = 2/2, 1/2
Midpoint = 1, 1/2
We would find the slope of line MN. The formula for finding slope is expressed as
m = (y2 - y1)/(x2 - x1)
Looking at the given points of line MN,
x1 = - 5, y1 = 2
x2 = 7, y2 = - 1
m = (- 1 - 2)/(7 - - 5) = - 3/(7 + 5) = - 3/12 = - 1/4
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. This means that the slope of line p is 4/1 = 4
Thus, line p is passing through point (1, 1/2) and has a slope of 4
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
To determine the equation of line p, we would substitute m = 4, x = 1 and y = 1/2 into the slope intercept equation. It becomes
1/2 = 4 * 1 + c
1/2 = 4 + c
c = 1/2 - 4
c = - 7/2
Substituting m = 4 and c = - 7/2 into the slope intercept equation, the equation of line p would be
y = 4x - 7/2
Related Questions
Jackson purchased a pack of game cards that was on sale for 22% off. The sales tax in his county is 6%. Let y represent the oeiginal price of the card.. Wrote an expression that can be used to determine the final cost of the cards.
Answers
Given:
Discount - 22% = 0.22
Sales Tax - 6% = 0.06
Required:
Expression for the final cost of the cards, x
Solution:
Let: y represent the original price of the card.
x represent the final cost of the cards
D represent the discounted cost of the cards
Assume that the the sales tax is applied to the price after the discount.
D= Original Price ( 1 - Discount) = y ( 1 - 0.22) = 0.78y
To compute for the final cost,
Final Cost = D + Tax
Tax = 0.06 D
x = D + 0.6(D)
x = 1.06D
x = 1.06 ( 0.78 y)
x = 0.827y
Answer:
The final cost of the card can be describe by the expression:
x = 0.827y
Write an expression to determine the surface area of a cube-shaped box, S A , in terms of its side length, s (in inches).
Answers
The cube consists of 6 equal faces thus the surface area of the cube in terms of its side length s is 6s².
What is a cube?A three-dimensional object with six equal square faces is called a cube. The cube's six square faces all have the same dimensions.
A cube is become by joining 6 squares such that the angle between any two adjacent lines should be 90 degrees.
A cube is a symmetric 3 dimension figure in which all sides must be the same.
The cube has six equal squares.
It is known that the surface area of a square = side²
Therefore, the surface area of the given cube is 6 side².
Given cube has side length = s
So,
Surface area = 6s²
Hence the cube consists of 6 equal faces thus the surface area of the cube in terms of its side length s is 6s².
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Can someone do it for me please
Answers
Step-by-step explanation:
13.
a/7 + 5/7 = 2/7
a/7 = 2/7 - 5/7 = -3/7
a = -3
14.
6v - 5/8 = 7/8
6v = 7/8 + 5/8 = 12/8
v = 12/8 / 6 = 2/8 = 1/4
15.
j/6 - 9 = 5/6
j - 54 = 5
j = 5 + 54 = 59
16.
0.52y + 2.5 = 5.1
0.52y = 5.1 - 2.5 = 2.6
y = 2.6/0.52 = 5
17.
4n + 0.24 = 15.76
4n = 15.76 - 0.24 = 15.52
n = 15.52/4 = 3.88
18.
2.45 - 3.1t = 21.05
-3.1t = 21.05 - 2.45 = 18.6
t = 18.6/-3.1 = -6
I’m confused on this question. I just have to choose which one
Answers
SOLUTION:
Case: Circle theorems
Method:
From the given circle
Theorem: The angle at the center of the circle is twice the angle at the circumference formed by the same segment.
The implication to the circle in the question is:
[tex]\begin{gathered} \hat{mST}=2m\angle2 \\ OR \\ m\angle2=\frac{1}{2}(\hat{mST}) \end{gathered}[/tex]Final answer
[tex]m\operatorname{\angle}2=\frac{1}{2}(\hat{mST})[/tex]I need help with this question can you please help me
Answers
Given the following question:
[tex]\begin{gathered} x^2+3x-5=0 \\ \text{ Convert using the quadratic formula:} \\ x^2+3x-5=0=x_{1,\:2}=\frac{-3\pm\sqrt{3^2-4\cdot\:1\cdot\left(-5\right)}}{2\cdot\:1} \\ x_{1,\:2}=\frac{-3\pm \sqrt{3^2-4\cdot \:1\cdot \left(-5\right)}}{2\cdot \:1} \\ \text{ Solve} \\ 3^{2}-4\times1(-5) \\ 1\times-5=-5 \\ 3^2-4\times-5 \\ 3^2=3\times3=9 \\ =29 \\ =\sqrt{29} \\ x_{1,\:2}=\frac{-3\pm \sqrt{29}}{2\cdot \:1} \\ \text{ Seperate the solutions:} \\ x_1=\frac{-3+\sqrt{29}}{2\cdot \:1} \\ x_2=\frac{-3-\sqrt{29}}{2\cdot\:1} \\ \text{ Simplify} \\ 2\times1=2 \\ x=\frac{-3+\sqrt{29}}{2} \\ x=\frac{-3-\sqrt{29}}{2} \end{gathered}[/tex]Your answers are the first and second options.
he two-way frequency table given shows the results from a survey of students who attend the afterschool program.
Takes Art Class Doesn't Take Art Class Total
Plays a Sport 45 120
Doesn't Play a Sport 45
Total 225
Does the data show an association between taking an art class and playing a sport?
There is a strong, positive association.
There is a strong, negative association.
There is a weak, positive association.
There is a weak, negative association.
Answers
The association between the variables art class and playing a sport is classified as follows:
There is a strong, negative association.
What is the association between the two variables?The association between variables can be classified either as positive or as negative, as follows:
Positive: both variables behave similarly, either both increases or both decreasing.Negative: the variables behave in an inversely manner, with one increasing and the other decreasing, or vice-versa.In the context of this problem, it is found that of the students that take art class, the majority do not play a sport, while among those who do not take art class, the majority play a sport, hence there is a strong and negative association between the two variables.
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Question
Mrs. Hanson has a potato salad recipe that calls for 238 pounds of potatoes, but she wants to make 112 times as much as the recipe calls for.
The diagram represents the number of pounds of potatoes that Mrs. Hanson needs.
How many pounds of potatoes does Mrs. Hanson need?
Answers
Answer:
3 9/16 lbs
Step-by-step explanation:
69=2g-24 I NEED TO FIND G
Answers
Add 24 to 69 to get 93. Then divide 93 by 2 to get G
13 nickels to 43 dimes in a reduced ratio form
Answers
The reduced ratio form of 13 nickels to 43 dimes is 13/86.
What is a ratio?
a ratio let us know that how many times one number contains another number.
We are given 13 nickels and 43 dimes.
We know that 1 dime equal to 2 nickels.
Hence 43 dimes equals 86 nickels.
Now we find the ratio of the 2.
Which will be [tex]\frac{13}{86}[/tex]
Hence the reduced ratio form is 13/86.
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Explain when you can cancel a number that is in both the numerator and denominator and when you cannot cancel out numbers that appear in both the numerator and the denominator.
Answers
Let me write here an example of a common number/term in both numerator and denominator that we can cancel.
[tex]\frac{4xy}{4}=xy[/tex]In the above example, we are able to cancel out the common number 4 because they are stand alone numbers. We can divide 4 by 4 and that is 1. Hence, the answer is just xy.
Another example:
[tex]\frac{(x+2)(x-1)}{(x+2)(2x-1)}=\frac{(x-1)}{(2x-1)}[/tex]In the above example, we are able to cancel out (x + 2) because this term is a common factor to both numerator and denominator.
In the example, we can also see that -1 is a common number however, we cannot cancel it out because the number -1 is not a standalone factor. It is paired with other number/variable. (x - 1) and (2x - 1) are both factors but are not the same, that is why, we are not able to cancel that.
Another example:
[tex]\frac{(x+2)+(x-1)}{(x+2)+(2x-1)}=\frac{(x+2)+(x-1)}{(x+2)+(2x-1)}[/tex]As we can see above, (x + 2) is a common term however, we cannot cancel it. We can only cancel common terms if they are common factors of both numerator and denominator. (Notice the plus sign in the middle. )
The term (x + 2) above is not a factor of the numerator and denominator, hence, we cannot cancel it.
[tex] f(x) = 3x^{2} - 2x + 3[/tex]if (-3,n) is an element of the function what is the value of n?
Answers
SOLUTION
[tex]\begin{gathered} f(x)=3x^2\text{ - 2x + 3 } \\ \text{Here, (-3, n) can be written as (x, y), where x = -3 and y = n} \\ \text{Also y is also = f(x). } \\ \text{That is y = }3x^2\text{ - 2x + 3 } \end{gathered}[/tex]Now putting x = -3 into f(x) or y, we have that
[tex]\begin{gathered} y=3(-3)^2\text{ -2(-3) + 3} \\ y\text{ = 3(9) + 6 + 3} \\ y\text{ = 27 + 6 + 3} \\ y\text{ = 36. } \\ \text{Since y = n, therefore, n = 36. } \end{gathered}[/tex]The value of n is 36
Based on the experimental probability, predict the number of times that you will roll a 5 if you roll the number cube 300 timesExperiment result on previews question: The number 5 was rolled 9 times out of 20 on a previous question
Answers
Explanation: To understand this problem we need to know that there are two different types of probability. The experimental probability and the theoretical probability.
- The experimental probability occurs once you conduct the experiment and after the experiment, you calculate the probability using the result of the experiment.
- The theoretical probability occurs before the experiment. Once you have information about the situation so you calculate the probability the get a specific result before trying.
Step 1: For this question, once we have a number cube with faces 1,2,3,4,5 and 6 and we want to know the experimental probability to get a 5 once you roll the cube 300 times you would need to get in real life a number cube and to roll it 300 times. After this experiment we would get all the results of each time we roll it and we would know how many times (from 300 times) we got a number 5. After that, we would use the following formula
[tex]Experimental_{probability}=\frac{number\text{ of times we got a number 5}}{300}[/tex]Once the get this result we finish the question.
A local real estate company has 5 real estate agents. The number of houses that each agent sold last year is shown in the bar graph below. Use this bar graph to answer the questions.
Answers
Given:
Rachel sold 4 houses.
Heather sold 4 houses.
Kaitlin sold 12 houses.
Lena sold 11 houses.
Deshaun sold 3 houses.
Required:
a) We need to find which agent sold the most houses.
b) We need to find the number of houses Lna soldemore than Heather.
c) We need to find the number of agents who sold fewer than 4 houses.
Explanation:
a)
The greatest number of houses sold =12 houses.
Kaitlin sold 12 houses.
Answer:
The agent Kaitlin sold the most houses.
The agent sold 12 houses.
b)
Lena sold 11 houses.
Heather sold 4 houses.
The difference between 11 and 4 is 11-4 =7.
Answer:
Lena sold 7 housmore than Heather
2. What is the greatestcommon factor of12. 18, and 36?
Answers
The Solution:
Given the numbers below:
12, 18 and 36.
We are asked to find the greatest common factor of the above numbers.
Note:
Greatest Common Factor means Highest Common Factor (HCF).
Recall:
The Greatest common factor of 12, 18 and 36 is the highest number that can divide 12, 18 and 36 without any remainder.
Thus, the correct answer is 6.
ten B В 15 cm А 20 cm С C
Answers
Tangent segment, of a circle
Apply formulas
20^2 - 15^ 2 = AB^2
Also
15^2 = 20•( 20 - AB)
225 = 400 - 20AB
Then
20AB = 400-225= 175
AB = √ 175= 13 + 6/25 =13.24
(Algebra 1 Equivalent equations)
In a family, the middle child is 5 years older than the youngest child.
Tyler thinks the relationship between the ages of the ages of the children can be described with 2m-2y=10, where m is the age of the middle child and y is the age of the youngest.
Explain why Tyler is right.
Answers
Let the middle child is m and youngest is y.
The middle child is 5 years older than the youngest child, it can be shown as:
m - y = 5Tyler's equation is equivalent to ours since it can be obtained by multiplying both sides of our equation by 2:
2(m - y) = 2*52m - 2y = 10 ⇔ m - y = 5So Tyler is right.
Finding an output of a function from its graphThe graph of a function fis shown below.Find f (0).543-2f(0) =I need help with this math problem.
Answers
Given:
Given a graph of the function.
Required:
To find the value of f(0), by using graph.
Explanation:
From the given graph
[tex]f(0)=-4[/tex]Final Answer:
[tex]f(0)=-4[/tex]Factor the quadratic expression2x²+x-62x+ +x-6= (Factor completely.)
Answers
2x² + x - 6
The coefficient of x² is 2 and the constant term is -6. The product of 2 and -6 is -12. The factors of -12 which sum 1 are -3 and 4 so:
2(2x - 3) + x(2x - 3)
Factor 2x - 3 from 2(2x - 3) + x(2x - 3):
(2x - 3)(x + 2)
Shaun deposits $3,000 into an account that has an rate of 2.9% compounded continuously. How much is in the account after 2 years and 9 months?
Answers
The formula for finding amount in an investment that involves compound interest is
[tex]A=Pe^{it}[/tex]Where
A is the future value
P is the present value
i is the interest rate
t is the time in years
e is a constant for natural value
From the question, it can be found that
[tex]\begin{gathered} P=\text{ \$3000} \\ i=2\frac{9}{12}years=2\frac{3}{4}years=2.75years \end{gathered}[/tex][tex]\begin{gathered} e=2.7183 \\ i=2.9\text{ \%=}\frac{2.9}{100}=0.029 \end{gathered}[/tex]Let us substitute all the given into the formula as below
[tex]A=3000\times e^{0.29\times2.75}[/tex][tex]\begin{gathered} A=3000\times2.21999586 \\ A=6659.987581 \end{gathered}[/tex]Hence, the amount in the account after 2 years and 9 months is $6659.99
A stock is worth $28,775 and drops 33% in one day. What percent does the stock have to grow the next day to get back to $28,775
Answers
ANSWER:
49.254%
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the value after it has drops by 33%, like this:
[tex]\begin{gathered} 28775-28775\cdot33\% \\ \\ 28775-28775\cdot0.33 \\ \\ 28775-9495.75=19279.25 \end{gathered}[/tex]Now, we calculate what should grow by the following equation:
[tex]\begin{gathered} 19279.25+19279.25\cdot \:x=28775\: \\ \\ x=\frac{28775\:-19279.25}{19279.25} \\ \\ x=\frac{9495.75}{19279.25} \\ \\ x=0.49254\cong49.254\% \end{gathered}[/tex]The percent that should grow is 49.254%
Solve the equation.k²=47ks.(Round to the nearest tenth as needed. Use a comma to separate answers as needed.
Answers
The initial equation is:
[tex]k^2=47[/tex]Then, we can solve it calculating the square root on both sides:
[tex]\begin{gathered} \sqrt[]{k^2}=\sqrt[]{47} \\ k=6.9 \\ or \\ k=-6.9 \end{gathered}[/tex]Therefore, k is equal to 6.9 or equal to -6.9
Answer: k = 6.9 or k = -6.9
if [tex] \sqrt{ \times } [/tex]is equal to the coordinate of point D in the diagram above, then X is equal to:
Answers
11)
The number line is divided into 5 equal intervals. if the fourth segment is 7, then we would find the distance between each segment
The distance between the fourth segment and the first segment is 7 - - 1 = 8
Since we are considering the distance between segment 1 and segment 4, the distance between each segment would be
8/4 = 2
Thus,
point D = 7 + 2 = 9
If
[tex]\begin{gathered} \sqrt[]{x\text{ }}\text{ = D, then} \\ \sqrt[]{x}\text{ = 9} \\ \text{Squaring both sides of the equation, we have} \\ x=9^2 \\ x\text{ = 81} \end{gathered}[/tex]Option E is correct
The table below shows possible outcomes when two spinners that are divided into equal sections are spun. The first spinner is labeled with five colors, and the second spinner is labeled with numbers 1 through 5. Green Blue Pink Yellow Red 1 Gi B1 P1 Y1 R1 1 2 . G2 B2 P2 Y2 R2 3 G3 B3 P3 Y3 R3 4 G4 B4 P4 Y4 R4 5 G5 B5 P5 Y5 R5 According to the table, what is the probability of the first spinner landing on the color pink and the second spinner landing on the number 5?
Answers
Answer:
P = 0.04
Explanation:
The probability is equal to the number of options where the first spinner is landing on the color pink and the second spinner is landing on the number 5 divided by the total number of options.
Since there is only one option that satisfies the condition P5 and there are 25 possible outcomes, the probability is:
[tex]P=\frac{1}{25}=0.04[/tex]So, the answer is P = 0.04
3. The data in the table gives the number of barbeque sauce bottles (y) that are sold with orders of chicken wings (x) for each hour on a given day at Vonn's Grill. Use technology to write an equation for the line of best fit from the data in the table below. Round all values to two decimal places.
Answers
1) Let's visualize the points
2) To find the equation for the line of best fit we'll need to follow some steps.
2.1 Let's find the mean of the x values and the mean of the Y values
2.2 Now It's time to find the slope, with the summation of the difference between each value and the mean of x times each value minus the mean over the square of the difference of the mean of x and x.
To make it simpler, let's use this table:
The slope then is the summation of the 5th column over the 6th column, we're using the least square method
[tex]m=\frac{939.625}{1270.875}=0.7393\cong0.74[/tex]The Linear coefficient
[tex]\begin{gathered} b=Y\text{ -m}X \\ b=14.625-0.73(19.875) \\ b=0.11625\cong0.12 \end{gathered}[/tex]3) Finally the equation of the line that best fit is
[tex]y=0.73x+0.12[/tex]12/13+-1/13 equals what ?
Answers
Given:
[tex]\frac{12}{13}+(-\frac{1}{13})[/tex]Adding a negativen number is the same as subtracting that number, so:
[tex]\frac{12}{13}-\frac{1}{13}[/tex]Since both denominators (bottom number ) are equal we can subtract the numerators ( top numbers)
[tex]\frac{(12-1)}{13}=\frac{11}{13}[/tex]Answer:
[tex]\frac{11}{13}[/tex]Use the graph below to determine the equation of the circle in (a) center-radius form and (b) general form.10-(-3,6)(-6,3(0,3)-10(-3,0)1010
Answers
Question:
Solution:
An equation of the circle with center (h,k) and radius r is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]This is called the center-radius form of the circle equation.
Now, in this case, notice that the center of the circle is (h,k) = (-3,3) and its radius is r = 3 so that the center-radius form of the circle would be:
[tex](x+3)^2+(y-3)^2=3^2[/tex]To obtain the general form, we must solve the squares of the previous equation:
[tex](x+3)^2+(y-3)^2-3^2\text{ = 0}[/tex]this is equivalent to:
[tex](x^2+6x+3^2)+(y^2-6y+3^2)\text{ - 9 = 0}[/tex]this is equivalent to
[tex]x^2+6x+9+y^2-6y\text{ = 0}[/tex]this is equivalent to:
[tex]x^2+y^2+6x-6y\text{ +9= 0}[/tex]so that, the general form equation of the circle would be:
[tex]x^2+y^2+6x-6y\text{ +9= 0}[/tex]thus, the correct answer is:
CENTER - RADIUS FORM:
[tex](x+3)^2+(y-3)^2=3^2[/tex]GENERAL FORM:
[tex]x^2+y^2+6x-6y\text{ +9= 0}[/tex]I need help on doing this finding the slope of a line
Answers
Given:
[tex](x_1,y_1)=(1,6)and(x_2,y_2)=(6,1)[/tex][tex]\text{Slope(m)=}\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{Slope(m)=}\frac{1-6}{6-1}[/tex][tex]\text{Slope(m)}=-\frac{5}{5}[/tex][tex]\text{Slope (m)=-1}[/tex]Find the expression for the possible width of the rectangle.
Answers
Given the area of the rectangle is given by the following expression:
[tex]A=x^2+5x+6[/tex]The area of the rectangle is the product of the length by the width
So, we will factor the given expression
To factor the expression, we need two numbers the product of them = 6
and the sum of them = 5
So, we will factor the number 6 to find the suitable numbers
6 = 1 x 6 ⇒ 1 + 6 = 7
6 = 2 x 3 ⇒ 2 + 3 = 5
So, the numbers are 2 and 3
The factorization will be as follows:
[tex]A=(x+3)(x+2)[/tex]So, the answer will be the possible dimensions are:
[tex]\begin{gathered} \text{Length}=x+3 \\ \text{Width}=x+2 \end{gathered}[/tex]find the equation of the axis of symmetry of the following parabola algebraically. y=x²-14x+45
Answers
Answer:
x = 7, y = -4
(7, -4)
Explanation:
Given the below quadratic equation;
[tex]y=x^2-14x+45[/tex]To find the equation of the axis of symmetry, we'll use the below formula;
[tex]x=\frac{-b}{2a}[/tex]If we compare the given equation with the standard form of a quadratic equation, y = ax^2 + bx + c, we can see that a = 1, b = -14, and c = 45.
So let's go ahead and substitute the above values into our equation of the axis of symmetry;
[tex]\begin{gathered} x=\frac{-(-14)}{2(1)} \\ =\frac{14}{2} \\ \therefore x=7 \end{gathered}[/tex]To find the y-coordinate, we have to substitute the value of x into our given equation;
[tex]\begin{gathered} y=7^2-14(7)+45 \\ =49-98+45 \\ \therefore y=-4 \end{gathered}[/tex]Which inequality is equivalent to this one?y-83-2O y-8+82-2-8O y 8+82-248o y 8+22-248o Y8+ 25-242
Answers
Given the inequality:
[tex]y-8\le-2[/tex]If we add 2 on both sides, the inequality remains the same and we get:
[tex]y-8+2\le-2+2[/tex]