What is the exact surface area of the right rectangular pyramid below? Leave your answer in simplified radical form.
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Usually, to calculate the area of a solid we need to calculate the area of every face. Here we have a rectangle down, and four triangles. Our desired area (TA) will be the sum of those areas. Let's calculate those areas:
Area of the rectangle) The area of the rectangle (R) is
[tex]R=(leng\ldots)(wid\ldots)=(10cm)\cdot(4cm)=40\operatorname{cm}^2[/tex]Area of the front triangle and the back tringle) Note that the front triangle and the back triangle are the "same". So the area of each of them is equal (this simplifies our work...). The area of each of them (FB) is
[tex]FB=\frac{(base)\cdot(high)}{2}[/tex]What is their high?
The triangle with red, blue, and green edges is a right triangle... Its hypotenuse is the blue edge. We know the red edge, its length is 6cm, but what is the length of the green edge? Because our solid is a rectangular pyramid, we can say that the green edge is half of the length of the rectangle. that is, 5cm (10cm/2). Now, we know the red and green edges; so we can apply The Pythagoras theorem to get
[tex](blue)^2=(red)^2+(green)^2[/tex][tex](blue)^2=(6cm)^2+(5cm)2=36\operatorname{cm}+25\operatorname{cm}=61\operatorname{cm}^2[/tex][tex]undefined[/tex]
Related Questions
I need help with this practice problem If you can, show your work step by step so I can take helpful notes
Answers
The given geometric series is
[tex]120-80+\frac{160}{3}-\frac{320}{9}+\cdots[/tex]In a geometric series, there is a common ratio between consecutive terms defined as
[tex]r=\frac{-80_{}}{120_{}}=-\frac{2}{3}[/tex]The sum of the first n terms of a geometric series is given by
[tex]S_n=\frac{a(1-r^n)}{1-r},r<1[/tex]Where a is the first term.
From the given series
a = 120
Hence, the sum of the first 8 terms is
[tex]S_8=\frac{120(1-(-\frac{2}{3})^8)}{1-(-\frac{2}{3})}[/tex]Simplify the brackets
[tex]S_8=\frac{120(1-\frac{2^8}{3^8}^{})}{1+\frac{2}{3}}[/tex]Simplify further
[tex]\begin{gathered} S_8=\frac{120(1-\frac{256}{6561})}{\frac{3+2}{3}} \\ S_8=\frac{120(\frac{6561-256}{6561})}{\frac{5}{3}} \\ S_8=\frac{120(\frac{6305}{6561})}{\frac{5}{3}} \\ S_8=\frac{120\times6305}{6561}\div\frac{5}{3} \\ S_8=\frac{120\times6305}{6561}\times\frac{3}{5} \\ S_8=\frac{120\times6305}{6561}\times\frac{3}{5} \\ S_8=\frac{8\times6305}{729} \\ S_8=\frac{50440}{729} \end{gathered}[/tex]Therefore, the sum of the first 8 terms is
[tex]\frac{50440}{729}[/tex]Find the area to the right of x=71 under a normal distribution curve with the mean=53 and standard deviation=9
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Answer:
[tex]Area=0.0228\text{ or 2.28\%}[/tex]Explanation:
We were given the following information:
This is a normal distribution curve
Mean = 53
Standard deviation = 9
We are to find the area right of x = 71
This is calculated as shown below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ x=71 \\ \mu=53 \\ \sigma=9 \\ \text{Substitute these into the formula, we have:} \\ z=\frac{71-53}{9} \\ z=\frac{18}{9} \\ z=2 \end{gathered}[/tex]We will proceed to plot this on a graph as sown below:
The area to the right of x = 71 (highlighted in red above) is given by using a Standard z-score table:
[tex]\begin{gathered} =1-0.9772 \\ =0.0228 \\ =2.28\text{\%} \end{gathered}[/tex]Therefore, the area that lies to the right of x = 71 is 0.0228 or 2.28%
A trail mix brand guarantees a peanut to raisin ratio of 5:2. If a bag of that trail mix contains 30 peanuts, how many raisins are in the bag?
Answers
Answer:
12
Explanation:
In the bag, the guaranteed ratio of peanut to raisin = 5:2
Number of peanuts = 30
Let the number of raisins =x
We therefore have that:
[tex]\begin{gathered} 5\colon2=30\colon x \\ \frac{5}{2}=\frac{30}{x} \\ 5x=30\times2 \\ x=\frac{30\times2}{5} \\ x=12 \end{gathered}[/tex]The number of raisins in the bag is 12.
When 6 is subtracted from the 5 times of a number the sum becomes 9 find the number
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Let that unknown number be x
⇒Mathematically this is written as
[tex]5(x)-6=9\\5x-6=9\\5x=9+6\\5x=15\\\frac{5x}{5} =\frac{15}{5} \\x=3[/tex]
This just means that the unknown number is 3
GOODLUCK!!
Answer:
nine plus six
= 15 ÷ five
answer Three
Clark and Lindsay Banks have agreed to purchase a home for $225,000. They made a down payment of 15%. They have obtained a mortgage loan at a 6.5% annual interest rate for 25 years. What is the mortgage total if they finance the closing costs?
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SOLUTION
We will be using the annual compound interest formula to solve this question.
[tex]\begin{gathered} A=P(1+\frac{R}{100})^{mn} \\ \text{where m=1, n=25years, R=6.5,} \end{gathered}[/tex]After a down payment of 0.15 x $225,000 = $33750
The principal value will be $225,000 - $33750 = $191250
Put all these values into the compound interest formula above,
we will have:
[tex]\begin{gathered} A=191250(1+\frac{6.5}{100})^{1\times25} \\ A=191250(1+0.065)^{25} \end{gathered}[/tex][tex]\begin{gathered} A=191250(1.065)^{25} \\ \text{ = 191250}\times4.8277 \\ \text{ =923,297.63} \end{gathered}[/tex]The mortgage total if they finance the closing costs will be:
$923,297.63
Is y-x+wz=5 linear? And not, why and if so, can you put it in slope intercept form?
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A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of this kind of equation is given by:
[tex]Ax+By=C[/tex]For the equation:
[tex]y-x+wz=5[/tex]We can conclude is not a linear equation since there is a product between two variables.
Omar has $84 and maryam has $12. how much money must Omar give to maryam so that maryam will have three times as much as omar? let x be the amount of dollars Omar will give maryam. which equation best represents the situation described above? A.) 84 - x = 3(12) + xB.) 3(84 - x) = 12 - xC.) 3(84 - x ) = 12 + xD.) 3x = 84 - (12 + x)
Answers
Given data:
The given money Omar has $84.
The given money maryam has $12.
The expression for the money Omar give to maryam so that maryam will have three times as much as omar.
[tex]3(84-x)=12+x[/tex]Thus, the final expression is 3(84-x)=12+x.
The local appliance store is advertising a 17% off sale on a new flat-screen TV. If the saleprice is $664, what was the original price of the flat-screen TV? Use X in the equation
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Let's assume X is the original price of the flat-screen TV
The store is advertising a 17% off sale in that price, so the real sale price should be less than the original price
To calculate a % discount, we proceed as follows:
Compute the discount:
discount = 17% of X
Recall a percentage can be expressed as the number divided by 100, that is:
discount = 17 / 100 * X = 0.17X
Now we have the discount, we calculate the actual or sale price, which is the original price minus the discount:
sale price = original price - discount
sale price = X - 0.17X
We apply simple algebra to simplify the expression, just subtracting 1-0.17=0.83
sale price = 0.83X
We know the sale price is $664, thus:
0.83X = 664
Finally, we solve for X
[tex]X=\frac{664}{0.83}=800[/tex]This means that the original price of the TV was $800. Let's verify our result
Consider the following quadratic function Part 3 of 6: Find the x-intercepts. Express it in ordered pairs.Part 4 of 6: Find the y-intercept. Express it in ordered pair.Part 5 of 6: Determine 2 points of the parabola other than the vertex and x, y intercepts.Part 6 of 6: Graph the function
Answers
Answer:
The line of symmetry is x = -3
Explanation:
Given a quadratic function, we know that the graph is a parabola. The general form of a parabola is:
[tex]y=ax^2+bx+c[/tex]The line of symmetry coincides with the x-axis of the vertex. To find the x-coordinate of the vertex, we can use the formula:
[tex]x_v=-\frac{b}{2a}[/tex]In this problem, we have:
[tex]y=-x^2-6x-13[/tex]Then:
a = -1
b = -6
We write now:
[tex]x_v=-\frac{-6}{2(-1)}=-\frac{-6}{-2}=-\frac{6}{2}=-3[/tex]Part 3:For this part, we need to find the x-intercepts. This is, when y = 0:
[tex]-x^2-6x-13=0[/tex]To solve this, we can use the quadratic formula:
[tex]x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4\cdot(-1)\cdot(-13)}}{2(-1)}[/tex]And solve:
[tex]x_{1,2}=\frac{6\pm\sqrt{36-52}}{-2}[/tex][tex]x_{1,2}=\frac{-6\pm\sqrt{-16}}{2}[/tex]Since there is no solution to the square root of a negative number, the function does not have any x-intercept. The correct option is ZERO x-intercepts.
Part 4:
To find the y intercept, we need to find the value of y when x = 0:
[tex]y=-0^2-6\cdot0-13=-13[/tex]The y-intercept is at (0, -13)
Part 5:
Now we need to find two points in the parabola. Let-s evaluate the function when x = 1 and x = -1:
[tex]x=1\Rightarrow y=-1^2-6\cdot1-13=-1-6-13=-20[/tex][tex]x=-1\Rightarrow y=-(-1)^2-6\cdot(-1)-13=-1+6-13=-8[/tex]The two points are:
(1, -20)
(-1, -8)
Part 6:
Now, we can use 3 points to find the graph of the parabola.
We can locate (1, -20) and (-1, -8)
The third could be the vertex. We need to find the y-coordinate of the vertex. We know that the x-coordinate of the vertex is x = -3
Then, y-coordinate of the vertex is:
[tex]y=-(-3)^2-6(-3)-13=-9+18-13=-4[/tex]The third point we can use is (-3, -4)
Now we can locate them in the cartesian plane:
And that's enough to get the full graph:
lily ordered a set of green and brown pin.she received 35 pins, and 80% of them were green.How many green pins did lily receive?
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In total there are 35 pins so that correspound to the 100%, so we can use a rule of 3 to solve it so:
[tex]\begin{gathered} 35\to100 \\ x\to80 \end{gathered}[/tex]So the equation is:
[tex]x=\frac{35\cdot80}{100}=28[/tex]So there are 28 green pins
I need help with the entire problem. The question is about a sketchy hotel.
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Let d and s be the cost of a double and single- occupancy room, respectively. Since a double-occupancy room cost $20 more than a single room, we can write
[tex]d=s+20\ldots(A)[/tex]On the other hand, we know that 15 double-rooms and 26 single-rooms give $3088, then, we can write
[tex]15d+26s=3088\ldots(B)[/tex]Solving by substitution method.
In order to solve the above system, we can substitute equation (A) into equation (B) and get
[tex]15(s+20)+26s=3088[/tex]By distributing the number 15 into the parentheses, we have
[tex]15s+300+26s=3088[/tex]By collecting similar terms, it yields,
[tex]41s+300=3088[/tex]Now, by substracting 300 to both sides, we obtain
[tex]41s=2788[/tex]then, s is given by
[tex]s=\frac{2788}{41}=68[/tex]In order to find d, we can substitute the above result into equation (A) and get
[tex]\begin{gathered} d=68+20 \\ d=88 \end{gathered}[/tex]Therefore, the answer is:
[tex]\begin{gathered} \text{ double occupancy room costs: \$88} \\ \text{ single occupancy room costs: \$68} \end{gathered}[/tex]The table represents a linear function.What is the slope of the function?y08-2.04х-4-2-112-10-14-22-26O 2O 5
Answers
Answer
Option B is correct.
The slope of this function = -4
Explanation
For a linear function, the slope of the line can be obtained when the coordinates of two points on the line or the values of the linear function (y) at different values of x are known. If the two points are described as (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the two extreme points, (x₁, y₁) and (x₂, y₂) are (-4, -2) and (2, -26).
x₁ = -4
y₁ = -2
x₂ = 2
y₂ = -26
[tex]\text{Slope = }\frac{-26-(-2)}{2-(-4)}=\frac{-26+2}{2+4}=\frac{-24}{6}=-4[/tex]Hope this Helps!!!
What number is 75% of 96?
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The number 96 is equivalent to the 100%. So we can state the following rule of three:
[tex]\begin{gathered} 96\text{ ------ 100 \%} \\ x\text{ -------- 75 \%} \end{gathered}[/tex]By cross-multiplying these numbers, we have
[tex]\text{ (100\%)}\times x=(96)\times\text{ (75 \%)}[/tex]So, x is given by
[tex]\begin{gathered} x=\frac{(96)\times\text{ (75 \%)}}{\text{ 100\%}} \\ x=72 \end{gathered}[/tex]Therefore, the answer is 72
the red line equation is y=0.5*2^xthe blue line equation is y=2x+25Compare and contrast this graph
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In this question, we are given two lines.
1) y = 0.5*2^x
2) y = 2x + 25
The standard equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
The positive slope moves the line upwards and the negative slope moves the line downwards.
If we compare both the equations, we see the 2nd equation maps with the standard line form. Hence, the second equation is a line with the slope equals to 2 and y-intercept equals 25. As the slope is positive, the line is moving upwards.
The standard equation of an exponential function is y = a*b^x, where b is the base, x is the exponent and a is the y-intercept.
The positive value of the base moves the function upwards and the negative value moves it downwards.
If we compare both the equations, we see the 1st equation maps with the standard exponential form. Hence, the 1st equation is an exponent form with the base to 2 and y-intercept equals 0.5. As the base is positive, the line is moving upwards.
Find the set A n Φ.U = {1, 2, 3, 4, 5, 6, 7, 8, 9)A = 2, 3, 8, 9)Selectthe correct choice below and, if necessary, fill in the
Answers
Answer
Option B is the correct answer.
A n Φ = {}
A n Φ is the empty set.
Explanation
We are told to find the intersection between set A and the empty set Φ.
The intersection of two sets refers to the elements that belong to the two sets, that is, the elements that they both have in common.
Set A = (2, 3, 8, 9)
Set Φ = {}
What the elements of set A and set Φ (an empty set) have in common is nothing.
Hence, the intersection of set A and set Φ is an empty set.
A n Φ = {}
Hope this Helps!!!
The sum of two numbers is ten. One number is
twenty less than four times the other. Find the
numbers.
Note: List numbers with a comma separating
them, e.g. 5, 12.
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By solving the equations, we can conclude that the two numbers are 4 and 6.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, the two numbers are:
Let the 2nd number be 'x'.Then, the 1st number will be '4x - 20'.The equation will be:
4x - 20 + x = 10Now, solve this equation for 'x' as follows:
4x - 20 + x = 105x = 10 + 205x = 30x = 6Now, 4x - 20:
4(6) - 2024 - 204Therefore, by solving the equations, we can conclude that the two numbers are 4 and 6.
Know more about equations here:
https://brainly.com/question/28937794
#SPJ13
Identify the type of polar graph for the equation: r = 3-5cos θ aLimacon with inner loop bCardioid cDimpled limacon dConvex limacon eRose Curve fCircle gLemniscate
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Given the equation:
[tex]r=3-5\cos \theta[/tex]Let's identify the type of polar graph for the equation.
To identify the type of polar graph, use the formula below to get the Cartesian form:
[tex](x^2_{}+y^2)=r(\cos \theta,\sin \theta)[/tex]Thus, we have:
[tex](x^2+y^2)=3\sqrt[]{x^2+y^2}-5x[/tex]We have the graph of the equation below:
We can see the graph forms a Limacon with an inner loop.
Therefore, the type of polar graph for the given equation is a limacon with inner loop.
ANSWER:
the coordinates of two points on a line are (-4,8) and (2,2). Find the slope of the line.
Answers
the coordinates of two points on a line are (-4,8) and (2,2). Find the slope of the line.
Applying the formula to calculate the slope
we have
m=(2-8)/(2+4)
m=-6/6
m=-1
slope is -1What’s the correct answer asap for brainlist
Answers
Answer:
Step-by-step explanation:its a 69420 dum as
You play a game where you toss a die. If the die lands on a 6, you win $6. It costs $2 toplay. Construct a probability distribution for your earnings. Find your expected earnings.
Answers
SOLUTION
Now from the question, if the die lands on 6, I win $6. So probability of landing on 6 is
[tex]\frac{1}{6}\text{ since a die has 6 faces }[/tex]Since I will pay $2 to play, we subtract this from $6 that we will win.
And probability of losing becomes
[tex]\frac{5}{6}\text{ }[/tex]The table becomes
From the table the expected earnings is calculated as
[tex]\begin{gathered} E=\sum_^xP(x) \\ =4(\frac{1}{6})-2(\frac{5}{6}) \\ =\frac{4}{6}-\frac{10}{6} \\ =-\frac{6}{6} \\ =-1 \end{gathered}[/tex]Hence expected earnings is -$1
the client is to receive cimetidine 300mg by mouth every 6 hours. The medication is available as cimetidine 300mg/5ml. How many teaspoons should the nurse instruct the client to take?
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Step 1
Given; The client is to receive cimetidine 300mg by mouth every 6 hours. The medication is available as cimetidine 300mg/5ml.
Required; How many teaspoons should the nurse instruct the client to take?
Step 2
[tex]\begin{gathered} 1\text{ teaspoon =5ml } \\ Patient\text{ takes 300mg/5ml or 300mg/teaspoon} \\ \frac{Required\text{ dosage in mg}}{Dosage\text{ in 1 teaspoon}}\times5ml \\ Required\text{ dosage in mg=300mg} \\ Dosage\text{ in 1 teaspoon=300mg} \\ \frac{300mg}{300mg}\times5ml=5ml \\ From\text{ the table 5ml is the equivalent of 1 teaspoon .} \end{gathered}[/tex]Thus, the client takes 300mg every six hours. This means that the nurse will instruct the client to take 1 teaspoon every 6 hours.
Answer;
[tex]1\text{ teaspoon every 6 hours}[/tex]5.) y = -5/4 x + 10 (Use Slope Int. Method Make apparent your Int. Point AND the point from your slope = RISE/RUN)
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65+ (blank) =180
11x + (blank)=180
11x =
x =
Answers
Answer:
sorry if this is wrong
I just answered it according to the question you gave not the pic
Step-by-step explanation:
x = 65
11x + x = 180
12x = 180
x = 180 ÷ 12
= 15
I got 4089 for the answer but it was incorrect
Answers
Let A be the event "person under 18" and B be the event "employed part-time". So, we need to find the following probability
[tex]P(A\text{ or B) =P(A}\cup B)[/tex]which is given by
[tex]P(A\text{ or B) =P(A}\cup B)=P(A)+P(B)-P(A\cap B)[/tex]Since the total number od people in the table is equal to n=4089, we have that
[tex]P(A)=\frac{28+174+395}{4089}=\frac{597}{4089}[/tex]and
[tex]P(B)=\frac{174+194+71+179+173}{4089}=\frac{791}{{4089}}[/tex]and
[tex]P(A\cap B)=\frac{174}{4089}[/tex]we have that
[tex]P(A\text{ or B) =}\frac{597}{4089}+\frac{791}{{4089}}-\frac{174}{4089}[/tex]which gives
[tex]P(A\text{ or B) =}\frac{597+791-174}{4089}=\frac{1214}{4089}=0.29689[/tex]Therefore, the answer the searched probability is: 0.296
An 18-foot ribbon is attached to the top of a pole and is located on the ground 10 feet awayfrom the base of the pole. Suppose Mateo has a second ribbon that will be located anadditional 23 feet away past that point.Find the measure of the angle formed by Mateo's ribbon and the ground. Round the angle tothe nearest tenth of a degree.a10 ft18 ft23 ft8
Answers
To begin we need to find the value of a
We apply the Pythagorean theorem
[tex]\begin{gathered} 18^2=a^2+10^2 \\ a^2=18^2-10^2 \\ a=\sqrt{18^2-10^2} \\ a=4\sqrt{14} \end{gathered}[/tex]Now we find theta
Here we use the tangent that is the oppositive side over the adjacent side
[tex]\begin{gathered} \tan\theta=\frac{4\sqrt{14}}{33} \\ \\ \theta=\tan^{-1}(\frac{414}{33})=24.39\degree \end{gathered}[/tex]Read the following scenario and write two equations we could use to solve to find for the number of cars and trucks washed. Use the variables C for cars washed and T for trucks washed. (Hint: both equations should have T and C). SCENARIO: Western's eSports Team raised money for charity by organizing a car wash. They washed a total of 80 vehicles and raised a total of $486. They charged $5 to wash a car and $7 to wash a truck.
Answers
Let:
C = Number of cars washed
T = Number of trucks washed
They washed a total of 80 vehicles, so:
[tex]C+T=80[/tex]They raised a total of $486. They charged $5 to wash a car and $7 to wash a truck. so:
[tex]5C+7T=486[/tex]Let:
[tex]\begin{gathered} C+T=80_{\text{ }}(1) \\ 5C+7T=486_{\text{ }}(2) \end{gathered}[/tex]From (1) solve for T:
[tex]T=80-C_{\text{ }}(3)[/tex]Replace (3) into (2):
[tex]\begin{gathered} 5C+7(80-C)=486 \\ 5C+560-7C=486 \\ -2C=486-560 \\ -2C=-74 \\ C=\frac{-74}{-2} \\ C=37 \end{gathered}[/tex]Replace the value of C into (3):
[tex]\begin{gathered} T=80-37 \\ T=43 \end{gathered}[/tex]They washed 37 cars and 43 trucks
Can you please help me out with a question
Answers
Notice that the arc GH has the same measure as the angle GFH, which also has the same measure as the angle EFI since they are vertical angles.
On the other hand, EFI and IFS are adjacent angles, then:
[tex]m\angle EFI+m\angle IFS=m\angle EFS[/tex]Observe that the measure of the angle EFS is 90°. Since the measure of IFS is 20°, substitute those values into the equation to find the measure of EFI:
[tex]\begin{gathered} m\angle EFI+20=90 \\ \Rightarrow m\angle EFI=90-20 \\ \Rightarrow m\angle EFI=70 \end{gathered}[/tex]Thereore, the measure of GH is 70°.
A local road has a grade of 5%. The grade of a road is its slope expressed as a percent. What is the slope? What is the rise? What is the run?
Answers
a) Since the grade is given by the slope, and the grade has a 5%.
We can rewrite it as a fraction, like this:
[tex]\frac{5}{100}=\frac{1}{20}[/tex]Note that we have simplified this to 1/20 by dividing the numerator and the denominator (bottom number) by 5
So, the slope is:
[tex]\frac{1}{20}[/tex]b) The "rise" is the difference between two coordinates on the y-axis and the "run" is the subtraction between two coordinates on the x-axis. Let's remember the slope formula and the Cartesian plane:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{1}{20}[/tex]So the "rise" for this grade is 1 foot and the run is 20 feet.
3) Hence, the answers are:
[tex]\begin{gathered} a)\text{ }\frac{1}{20} \\ b)\text{ }Rise\colon\text{ }1\text{ Run: 20} \end{gathered}[/tex]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
In a recent poll, 13% of all respondents said that they were afraid of heights. Suppose this percentage is true for allAmericans. Assume responses from different individuals are independent.