Answers
The slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
The first point = (-5,6)
The second point = (-9,-6)
The slope of the line defined as the change in y coordinates with respect to the change in x coordinates.
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line m = [tex]\frac{-6-6}{-9-(-5)}[/tex]
= -12/-4
= 3
Hence, the slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
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Related Questions
A 90% confidence interval for a proportion is found to be (0.52, 0.58). What isthe sample proportion?
Answers
A 90% confidence interval for a proportion is given as (0.52,0.58).
It is required to find the sample proportion.
Recall that for confidence interval (x,y), the sample proportion is the midpoint:
[tex]c=\frac{x+y}{2}[/tex]Substitute x=0.52 and y=0.58 into the equation:
[tex]c=\frac{0.52+0.58}{2}=\frac{1.1}{2}=0.55[/tex]The answer is C.
Set up the equation for the following word problem and solve the equation. Let y be the unknown number.18 times a number minus 97 is equal to 9 less than the number.Step 1 of 2: Write out the equation.
Answers
Hello there. To solve this question, we'll have to remember some properties about set up an equation and solving them.
"Let y be an unknown number. 18 times a number minus 97 is equal to 9 less than the number."
We need to find this number.
Starting with the equation:
[tex]18y-97=y-9[/tex]On the left hand side, we have 18y as 18 times the number, then subtracted 97 for the minus 97 part. On the right hand side, 9 less than the number is represented as the number minus 9.
So, subtract y - 97 on both sides of the equation
[tex]\begin{gathered} 18y-97-(y-97)=y-9-(y-97) \\ 18y-97-y+97=y-9-y+97 \\ 17y=88 \end{gathered}[/tex]Divide both sides of the equation by a factor of 17
[tex]\begin{gathered} \frac{17y}{17}=\frac{88}{17} \\ \\ y=\frac{88}{17} \end{gathered}[/tex]This is the number we've been looking for.
How to find the area of a regular hexagon with a radius of 12 inches? Please help
Answers
Garret is removing a hem from a skirt. It takes
Garret 5 min to remove 4 in. of the hem. He wants to
know how long it will take to remove 5 ft of the hem if
he continues to work at the same rate.
Lavar
How can Garret determine how long it will take to remove 5 ft of the hem?
Choose one option from each drop-down menu to answer the question.
It takes Garret Choose... min to remove 1 ft of hem.
He should multiply the number of minutes by Choose... to determine the number of minutes it will take to
remove 5 ft of hem.
It will take Choose.... min to remove 5 ft of hem.
Answers
It takes Garret Choose min to remove 1 ft of hem. He should multiply the number of minutes by Choose... to determine the number of minutes it will take to remove 5 ft of hem.
What is the unitary method?The unitary method is a technique used to determine the value of a single unit from the value of many units and the value of multiple units from the value of a single unit. We typically utilize it for math calculations. This approach will come in handy for topics involving ratio and proportion, algebra, geometry, etc. In the unitary technique, we always count the value of a unit or one quantity first before figuring out the values of more or fewer quantities. This method is referred to as the "unitary method" for this purpose.
There are two types of unitary methods because they result in two types of variations and those are given below:
Direct VariationIndirect VariationTo know more about the unitary method ,visit:
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You have been tracking an adult female Australian flatback sea turtle who weighs 25 kg. How many kilocalories must she consume each day to maintain her body weight?
Answers
The kilocalories that she must consume each day to maintain her body weight is 6250 kilocalories.
How to calculate the value?From the information, the person has been been tracking an adult female Australian flatback sea turtle who weighs 25 kg.
It should be noted that the requirements is 250kcal per kilograms.
Therefore, the calories will be:
= Weight × Required calories
= 250 × 25
= 6250 kcaloriies
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I need some help. Could someone explain it to me?
Answers
Problem
We have the following table given:
x y
0 2
1 6
4 -9
8 8
Solution
We know that the domain correspond to the value of x in the relationship and then the correct answer for this case would be:
2
0
Jusrt 2,9 are the values in the domain of the function
In the figure, ∆ABD ≅ ∆CBD by Angle-Side-Angle (ASA). Which segments are congruent by CPCTC? BC ≅ AD CB ≅ AB AB ≅ CD DB ≅ DC
Answers
By CPCTC this is the only valid answer:
CB ≅ AB
Another statement should be AD≅ CD
A pool is built in the shape of an ellipse, centered at the origin. The maximum vertical length is 40 feet, and the maximum horizontal width is 18 feet. Which of the following equations represents the pool?
Answers
If the maximum vertical length of pool is 40 feet, and the maximum horizontal width of pool is 18 feet , then the equation that represent the pool is x/81 + y/400 = 1 , the correct is option is (B) .
In the question ,
it is given that
the shape of the pool is ellipse .
the maximum vertical length is 40 feet
the maximum horizontal length is 18 feet .
the general equation of the ellipse , is given by x/a + y/b = 1 ,
where a is the length of horizontal axis from origin
and b is the length of the vertical axis from the origin ,
So , the equation that represents the pool is x/81 + y/400 = 1
Therefore , if the pool is in the shape of ellipse , then the equation of the pool is x/81 + y/400 = 1 .
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Can you explain this math to me please I’ve never seen it before and don’t understand
Answers
For a quadratic function in standard form,
[tex]\begin{gathered} \text{a = coefficient of x}^2 \\ b\text{ = coeffcient of x} \\ c=\text{ the constant term} \end{gathered}[/tex]For the polynomial f(x),
a = 2, b = -3 and c = 4
For the polynomial g(x)
a = 4, b = -6, c = 10
For the polunomial h(x),
a = 7, b = 0, c = 8
For the polynomia p(x),
a = 1, b = -10, c = 0
Metric area unit conversion with decimal valuesTammy has a rectangular poster. The poster is 1.2 meters long and 0.9 meters wide. What is the area of the poster in square centimeters? Do not round youranswer.cmcm²cm³
Answers
We are asked to find the final area in square centimeters.
We must first convert the measurements of the poster into centimeters:
1.2m = 120cm
0.9m = 90cm
Area = length * width
= 120*90
= 10800 square centimeters.
The convex polygon below has 8 sides. Find the value of x.140°11801270153013401561170
Answers
Explanation
The formula for calculating the sum of interior angles in a polygon is ( n − 2 ) × 180 ∘ where is the number of sides.
[tex](n-2)\cdot180=\text{ Sum of internal angles}[/tex]Step 1
find the sum of the internal angles in the given polygon
Let
number of sides = 8
Now, replace
[tex]\begin{gathered} (n-2)\cdot180=\text{ Sum of internal angles} \\ (8-2)\cdot180=\text{ Sum of internal angles} \\ 6\cdot180=\text{Sum of internal angles} \\ 1080=\text{Sum of internal angles}\rightarrow equation(1) \end{gathered}[/tex]Step 2
now, we have the other angles, so
sum of internal angles is:
[tex]\text{angle}1+\text{angle}2+\text{angle}3+\text{angle}4+\text{angle}5+\text{angle}6+\text{angle}7+\text{angle}8=\text{ sum of the internal angles}[/tex]replace
[tex]\begin{gathered} 127+140+118+153+156+117+x+132=\text{ Sum of internal angles} \\ x+943=\text{Sum of internal angles}\rightarrow equation\text{ (2)} \end{gathered}[/tex]hence
[tex]x+945=1080[/tex]subtract 945 in both sides to solve for x
[tex]\begin{gathered} x+945=1080 \\ x+945-945=1080-945 \\ x=135 \end{gathered}[/tex]i hope this helps you
In an office building, 54 office are currently being rented, this represent 30% of the total units. how many offices are in the building
Answers
given that,
54 offices are currently rented
and it represent 30% of the total unit
to get the total offices in the building
let the total offices be x
30% of x = 54
30/100 X x = 54
cross multiply
30x = 5400
dividing both sides by 30
30x/30 = 5400/30
x = 5400/30
x = 180
therefore the total offices in the building is 180
Paulina bought a used car as she was entering college and planned to trade it in when she graduated four years later. She had learned in her high school financial algebra class that the average used car depreciated at an annual rate of 15%. If she had paid $13,900 for her car, how much can she expect to get when it is time for her to trade it in for a new car?
Answers
1st year
depreciable value: $13900
annual depreciation: $13900*15% = $2085
2nd year
depreciable value: $13900 - $2085 = $11815
annual depreciation: $11815*15% = $1772.25
3rd year
depreciable value: $11815 - $1772.25 = $10042.75
annual depreciation: $10042.75*15% = $1506.41
4th year
depreciable value: $10042.75 - $1506.41 = $8536.34
annual depreciation: $8536.34*15% = $1280.45
Final value: $8536.34 - $1280.45 = $7255.89
I need help the right side box are the answer choices
Answers
Statement: JKLM is a parallelogram
Reason - Give
Statement:
[tex]JK\parallel LM,\text{ }KL\parallel MJ[/tex]Reasons:
Definition of a parallelogram.
Statement:
[tex]\angle1\cong\angle2,\angle3\cong\angle4[/tex]Reasons:
Alternate interior angle theorem.
Statement:
[tex]Jl\cong Jl[/tex]Reasons:
Reflexive Propert
Statement:
[tex]\Delta JKL\cong\Delta LMJ[/tex]Reasons:
ASA
Statement:
[tex]JK=LM,KL=MJ[/tex]Reasons:
CPCTC
The radius of a circle is 8 inches. What is the area?Give the exact answer in simplest form. _____ square inches. (pi, fraction)
Answers
Given:
Radius of circle is 8 inches.
The objective is to find the area of the circle.
The formula to find the area of the circle is,
[tex]\begin{gathered} A=\pi r^2 \\ =\pi\times8\times8 \\ =64\pi \\ =201in^2 \end{gathered}[/tex]Hence, the area of the circle is 201 square inches.
If a square has a perimeter of 28 inches, what is its area in square inches?
Answers
Remember that
The formula to calculate the perimeter of a square is
[tex]P=4*b[/tex]where
b is the length side of the square
we have
P=28 in
substitute in the formula
[tex]\begin{gathered} 28=4*b \\ sol\text{ve for b} \\ b=\frac{28}{4}=7\text{ in} \end{gathered}[/tex]The area of a square is
[tex]A=b^2[/tex]substitute the value of b
[tex]\begin{gathered} A=7^2 \\ A=49\text{ in}^2 \end{gathered}[/tex]The area is 49 square inchesoption CCorky writes four equations to show each of the properties of equality. Which of Corky's equation is incorrect? Explainwill send image.
Answers
6 + m = 12
A. This IS equivalent
6 + m - m = 12 - m ==> 6 = 12 - m ==> 6 + m = 12
B. This IS NOT equivalent
6 + m - 6 = 12 - 12 ==> m = 0
C. This IS equivalent
6 + m + 2 = 12 + 2 ==> 6 + m = 12
D. This IS equivalent
6 + m - 6 = 12 - 6 ==> m = 6 ==> 6 + m = 12
Answer:
B is not equivalent
In ABC, B = 51°, b = 35, and a = 36. What are the two possible values for angle A to the nearest tenth of a degree?Select both correct answers.
Answers
Using the law of sines:
[tex]\frac{a}{\sin(A)}=\frac{b}{\sin (B)}[/tex]Solve for A using the data provided:
[tex]\begin{gathered} \sin (A)=\frac{\sin (B)\cdot a}{b} \\ A=\sin ^{-1}(\frac{\sin (51)36}{35}) \\ A\approx53.1 \\ or \\ A\approx126.9 \end{gathered}[/tex]what is the mean of 36,38,39,28,34
Answers
We are to find the mean of
[tex]36,\text{ 38, 39, 28, 34}[/tex]Finding mean
[tex]\begin{gathered} M\text{ean = }\frac{36\text{ + 38 + 39 + 28 + 34 }}{5} \\ Mean\text{ = }\frac{175}{5} \\ M\text{ean = 35} \end{gathered}[/tex]Therefore,
mean = 35
5. Use a number line to find the product: 5 x (-3)=
Answers
First, we solve the expression.
Since it is a negative number we have to place it 15 places to the left ( from zero)
Ary is writing thank you cards to everyone who came to her wedding. It takes her of an hour to write one thank you card. If it took her 8 hours to finish writing all of the cards, how many thank you cards did she write? 48 thank you cards 36 thank you cards 46 thank you cards 40 thank you cards
Answers
The question doesn't specify which fraction of an hour it takes Ary to write a thank you card.
Let's imagine that it takes her 1/4 of an hour to write a thank you card.
In such case, in one hour she will be able to write 4 thank you cards.
and therefore in 8 hours, ishe will be able to write 32 thank you cards (8 times 4 cards).
If it takes her 1/6 of an hour to write a thank you card, then in hone hour she will write a total of 6 thank you cards, and therefore, in 8 hours she will be able to write 8 times 6 thank you cards: 8 x 6 = 48 thank you cards.
If it takes her 1/5 of an hour to write a thank you card, then in hone hour she will write a total of 5 thank you cards, and therefore, in 8 hours she will be able to write 8 times 5 thank you cards: 8 x 5 = 40 thank you cards.
You just use this type of criteria to solve the problem whatever the fraction of the hour it takes to write one card as they specify in the question.
Please step-by-step help me how much of a circle is shaded
Answers
The given data is ratio from the the total are of circle is 1 .
let the shaded area is x then:
All area is equal to one.
[tex]\begin{gathered} \frac{1}{2}+\frac{2}{9}+x=1 \\ \frac{9+4}{18}+x=1 \\ \frac{13}{18}+x=1 \\ x=1-\frac{13}{18} \\ x=\frac{18-13}{18} \\ x=\frac{5}{18} \end{gathered}[/tex]So area of shaded region is
[tex]\frac{5}{18}[/tex]A local company employs a varying number of employees each year, based on its needs. The labor costs for the company include a fixed cost of $47,312.00 each year, and $28,431.00 for each person employed for the year. For the next year, the company projects that labor costs will total $2,492,378.00. How many people does the company intend to employ next year?
Answers
Plot the point given by the following polar coordinates on the graph below. Each circular grid line is 0.5 units apart.230(2.5. -,
Answers
Solution:
Given:
[tex](2.5,-\frac{2\pi}{3})[/tex]identify whether each phrase is an expression equation or quantity
Answers
the last one of the right column is a inequality, because it has the sign "<"
the second one of the right column in an expression because it doen't have the sign "="
the first one of the right column is a equation because it has the sign "=".
True or false the surface area of a sphere with a radius of 10 units is larger than the surface area of a cube with edge lengths of 10 units
Answers
The surface area of a sphere is given by
[tex]S_s=4\pi r^2[/tex]in our case r=10 units ( the radius). By substituting this value into the last formula, we have
[tex]S_s=4(3.1416)(10^2)[/tex]which gives
[tex]S_s=1256.64u^2[/tex]On the other hand, the surface area of a cube is given by
[tex]S_c=6L^2[/tex]where L is the length of one side, that is, L=10. Then, we have
[tex]\begin{gathered} S_c=6\cdot(10^2) \\ S_c=6\cdot100=600u^2 \\ S_c=600u^2 \end{gathered}[/tex]By comparing both results, we can see that the surface area of our sphere is larger than the surface area of the given cube. So the answer is TRUE.
Andrea invites 12 cousins 6 aunts 4 brothers 2 sisters what fraction of her party guests are cousins?
Answers
To determine the fraction of cousins, you have to divide the number of cousins she invited by the total number of guests.
She invited 12 cousins, 6 aunts, 4 brothers, and 2 sisters, a total of 24 guests.
Then:
[tex]\frac{nº\text{cousins}}{\text{total guests}}=\frac{12}{24}[/tex]Both, 12 and 24 are divisible by 12, to simplify the fraction, divide the numerator and denominator by 12
[tex]\frac{12\div12}{24\div12}=\frac{1}{2}[/tex]The fraction
Use a trig equation to solve for x. Round to the nearest tenth.
Answers
Given a right angle triangle
We need to find the measure of the angle x
The opposite side to the angle x = 19
the adjacent side to the angle x = 15
We will find x using the tan function as follows:
[tex]\begin{gathered} \tan x=\frac{opposite}{adjacent} \\ \\ \tan x=\frac{19}{15} \\ \\ x=\tan ^{-1}\frac{19}{15}\approx51.7098^{} \end{gathered}[/tex]Round the answer to the nearest tenth
so, the answer will be x = 51.7
What is the equation for a line passing through (-2,5) perpendicular to y - 3x = 8
Answers
Consider that the equation of a line with slope 'm' and y-intercept 'c' is given by,
[tex]y=mx+c[/tex]Consider the given equation of line,
[tex]\begin{gathered} y-3x=8 \\ y=3x+8 \end{gathered}[/tex]Comparing the coefficient, it is found that the slope of the given line is 3,
[tex]m=3[/tex]Let 's' be the slope of the line which is perpendicular to this line.
Consider that two lines will be perpendicular if their product of slopes is -1,
[tex]\begin{gathered} m\times s=-1 \\ 3\times s=-1 \\ s=\frac{-1}{3} \end{gathered}[/tex]So the slope of the perpendicular line is given by,
[tex]y=\frac{-1}{3}x+c[/tex]Now, it is given that this line passes through the point (-2,5), so it must satisfy the equation of the line,
[tex]\begin{gathered} 5=\frac{-1}{3}(-2)+c_{} \\ 5=\frac{2}{3}+c \\ c=5-\frac{2}{3} \\ c=\frac{13}{3} \end{gathered}[/tex]Substitute the value of 'c' to get the final equation,
[tex]\begin{gathered} y=\frac{-1}{3}x+\frac{13}{3} \\ 3y=-x+13 \\ x+3y=13 \end{gathered}[/tex]Thus, the required equation of the perpendicular line is x + 3y = 13 .
A sample of size 39 will be drawn from a population with mean 47 and standard deviation 11. Use the TI-84 Plus calculator.
(a) Is it appropriate to use the normal distribution to find probabilities for x?
(b) Find the probability that x will be between 48 and 49. Round the answer to at least four decimal places.
(c) Find the 41st percentile of x. Round the answer to at least two decimal places.
O It is appropriate to use the normal distribution to find probabilities for x.
The probability that x will be between 48 and 49 is
The 41st percentile of x is
O It is not appropriate to use the normal distribution to find probabilities for x.
Answers
Utilizing a calculator First, STAT > EDIT, then enter all the x values in L1 and the probability for each x value in L2 to determine the mean and standard deviation of a probability distribution.
When the mean and standard deviation are known, how can you get the probability?If the data are normally distributed, you may calculate the likelihood of a specific event by knowing the mean and standard deviation. If you have them, you can use the formula z = (x - (mean)) / to determine the z-score (standard deviation).Utilizing a calculator First, STAT > EDIT, then enter all the x values in L1 and the probability for each x value in L2 to determine the mean and standard deviation of a probability distribution. In the second order, STAT > CALC > 1-Var Stats > 1-Var Stats L1, L2 ENTER.A population with a mean of 47 and a standard deviation of 11 will yield a sample size of 39. Calculate with the TI-84 Plus. A) Is the usage of the negative,Therefore,
An answer to the question is:
A) Yes
B) n = 39 = / n = 11 / 39 = 1.7614 P(48 49) = P[(48-4...
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