Answer:
Inequality: 5 + 20p ≤ 225
p ≤ 11
Explanation:
The total cost can be calculated as the sum of the parking and ticket costs. So, we can calculate the total cost as:
5 + 20p
Because 20p represents the total ticket cost for p people.
Then, this total cost should be less than or equal to 225. It means that the inequality that represents the situation is:
5 + 20p ≤ 225
Finally, we can solve the inequality by subtracting 5 from both sides as:
5 + 20p - 5 ≤ 225 - 5
20p ≤ 220
Then, divide both sides by 20, to get:
20p/20 ≤ 220/20
p ≤ 11
So, the number of people who can go to the amusement park is less than or equal to 11.
Therefore, the answers are:
Inequality: 5 + 20p ≤ 225
p ≤ 11
5. List all of the factors of 24.O1, 2, 4, 6, 8, 121,2,3,4,61, 2, 3, 4, 6, 8, 12, 2424, 48, 72, 96, 192I need to learn this.
To find the factors of a number we must find all the numbers that divide 24, two numbers are always easy, 1 and the number itself! But how do we find the others? We start at 1 and divide the number (here it's 24) by all the possible numbers until we reach the number we are finding the factor, it the division is an integer number, then it's a factor!
Another thing may help us! if we divide a number, for example, 24 by 2, the result is 12. Then 2 is a factor of 24 but 12 is also a factor of 24! Then when we find one factor, in fact, we have 2 factors. Now let's apply it to our problem:
As we can see, just by 3 divisors we found all the factors of 24! They are 1, 2, 3, 4, 6, 8, 12, 24
Final answers: 1, 2, 3, 4, 6, 8, 12, 24
a parking lot is distracted in the shape of a parallelogram if the base is 200 feet the height is 120 ft and the Dialganal with is 140 feet what is the area of the parking lot?
a parking lot is distracted in the shape of a parallelogram if the base is 200 feet the height is 120 ft and the Dialganal with is 140 feet what is the area of the parking lot?
we know that
the area of parallelogram is equal to
A=b*h
where
b is the base
h is the height
substitute the given values
A=200*(120)
A=24,000 ft^2
the area is 24,000 square feetneed help with example #4 Find all missing angles and sides.
We will use the law of sines and law of cosines shown below
[tex]\begin{gathered} c=\sqrt{a^2+b^2-2ab\cos C}\rightarrow\text{ law of cosines} \\ and \\ \frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}\rightarrow\text{ law of sines} \end{gathered}[/tex]Therefore, in our case, finding side c.,
[tex]\begin{gathered} a=28,b=13,C=49\degree \\ \Rightarrow c=\sqrt{784+169-2*28*13cos(49\degree)} \\ \Rightarrow c\approx21.8 \end{gathered}[/tex]Thus, side c is approximately 21.8km.
Finding the missing angles using the law of sines,
[tex]\begin{gathered} A=\cos^{-1}(\frac{c^2+b^2-a^2}{2bc}) \\ \Rightarrow A=\cos^{-1}(\frac{21.8^2+13^2-28^2}{2*13*21.8}) \\ \Rightarrow A\approx104.3 \\ \end{gathered}[/tex]Similarly, in the case of angle B,
[tex]sinB=\frac{13}{21.8}sin(49\degree)\approx26.7\degree[/tex]Therefore, the answers are
c=21.8km,
Solve: Tom is building a barn 36 feet wide and 60 feet long. How many feet long will the diagonal be across the footer if the footer is square?
Solution
For this case we can do the following:
Then we can use the Pythagoras theorem and we can solve for d and we got:
[tex]d=\sqrt[]{60^2+36^2}=\sqrt[]{4896}=69.97[/tex]Then the answer would be:
69.97 ft
-ExerciseActivity 1Please see the image above & use table NOTE: HELP ME ASAP
Given:
Required:
To complete the table.
Explanation:
[tex]\begin{gathered} 1\text{ pinch = }\frac{1}{16}\text{ teaspoon} \\ 2pinch\text{ = }\frac{2}{16\text{ }}tps \\ 2p\imaginaryI nch=\frac{1}{8}\text{ tps} \end{gathered}[/tex][tex]\begin{gathered} 1\text{ teaspoon = 76.0012} \\ 3\text{ teaspoons = 1 tablespoon} \end{gathered}[/tex]Since
[tex]\begin{gathered} 16\text{ tablespoon = 1 cup} \\ \end{gathered}[/tex]Divide by 8 into both sides.
[tex]\begin{gathered} 2\text{ tablespoon = }\frac{1}{8}\text{ cup} \\ 4\text{ tablespoon=}\frac{\text{1}}{4}\text{{\text{cup}}} \end{gathered}[/tex][tex]\begin{gathered} 16\text{ tablespoon = 1 cup} \\ 8\text{ tablespoon=}\frac{1}{2}\text{cup} \end{gathered}[/tex][tex]\begin{gathered} 2\text{ cups = 1 pint} \\ 4\text{ cups = 2 pint} \end{gathered}[/tex][tex]4\text{ quarts = 1 gallon}[/tex]Final Answer:
Explain in explanation parts.
a store advertises a 20% markdown on a dishwasher that normally sells for $952. what is the price on sale
The price on sale of the dishwasher is $201.6
How to determine the price on sale?From the question, we have the following parameters that can be used in our computation:
Mardown = 20%
Selling price = $252
The price on sale of the dishwasher is calculated using the following equation
Price on sale = Selling price * (1 - Mardown)
Substitute the known values in the above equation, so, we have the following representation
Price on sale = 252 * (1 - 20%)
Evaluate
Price on sale = 201.6
Hence, the price is $201.6
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The length of a side of a square is (2x + 1) km. Find the area of thesquare in terms of the variable x
The area of the square is given by:
[tex]A=s^2[/tex]Where s is the length of the side. Then s=(2x+1) km.
By replacing this into the formula we have:
[tex]A=(2x+1)^2[/tex]Also, the square of a sum is given by:
[tex](a+b)^2=a^2+2ab+b^2[/tex]If a=2x and b=1, then:
[tex]\begin{gathered} (2x+1)^2=(2x)^2+2(2x)(1)+(1)^2 \\ (2x+1)^2=4x^2+4x+1 \end{gathered}[/tex]Thus, the area of the square in terms of the variable x is:
[tex]A=4x^2+4x+1[/tex]Don’t know how to solve with the -1 before the x
ANSWER and EXPLANATION
We are given a function and its inverse function:
[tex]\begin{gathered} f(x)=\frac{1}{2}x \\ f^{-1}(x)=2x \end{gathered}[/tex]To solve the problems, we have to substitute the values of x in the brackets into the appropriate function (or inverse function).
Therefore, we have that the value of the function for x = 2:
[tex]\begin{gathered} f(2)=\frac{1}{2}\cdot2 \\ f(2)=1 \end{gathered}[/tex]For x = 1, we have that the value of the inverse function is:
[tex]\begin{gathered} f^{-1}(1)=2(1) \\ f^{-1}(1)=2 \end{gathered}[/tex]For x = -2, we have that the value of the inverse function is:
[tex]\begin{gathered} f^{-1}(-2)=2\cdot-2 \\ f^{-1}(-2)=-4 \end{gathered}[/tex]For x = -4, we have that the value of the function is:
[tex]\begin{gathered} f(-4)=\frac{1}{2}\cdot-4 \\ f(-4)=-2 \end{gathered}[/tex]For the fifth option, substitute the value of the function at x = 2 into the inverse function.
That is:
[tex]\begin{gathered} f^{-1}(f(2))=f^{-1}(1)=2\cdot1 \\ f^{-1}(f(2))=2 \end{gathered}[/tex]For the sixth option, substitute the value of the inverse function at x = -2 into the function.
That is:
[tex]\begin{gathered} f(f^{-1}(-2))=f(-4)=\frac{1}{2}\cdot-4 \\ f(f^{-1}(-2))=-2 \end{gathered}[/tex]To find the general form of the function:
[tex]f^{-1}(f(x))=f(f^{-1}(x))[/tex]either substitute the function for x in the inverse function or substitute the inverse function for x in the function.
Therefore:
[tex]\begin{gathered} f^{-1}(f(x))=2(\frac{1}{2}x)) \\ f^{-1}(f(x))=x \end{gathered}[/tex]That is the answer.
Triangle ACD is dilated about the origin.10D'984DC'с-7-8-5-4-3-234-1-2Which is most likely the scale factor?O3O223
ACD has a base (AC) with a length of 3 units.
A'C'D' has a base (A'C') with a length of 9 units.
Therefore, the scale factor is 9/3 = 3.
lebron walked 4 1/2 miles to library in 2 1/4 hours. he walked the return trip at the same average rate , but a different route, taking my 2 1/2 hours. How many miles did lebron walk on the return trip?
Answer:
5 miles
Explanation:
First, we need to transform the mixed number into decimal numbers using as follows:
[tex]\begin{gathered} 4\frac{1}{2}=4+\frac{1}{2}=4+0.5=4.5\text{ miles} \\ 2\frac{1}{4}=2+\frac{1}{4}=2+0.25=2.25\text{ hours} \\ 2\frac{1}{2}=2+\frac{1}{2}=2+0.5=2.5\text{ hours} \end{gathered}[/tex]Now, the average rate was the same, so the ratio of the miles to the hours is always the same. Therefore, we can write the following equation:
[tex]\frac{\text{Miles}}{\text{Hours}}=\frac{4.5\text{ Miles}}{2.25\text{ Hours}}=\frac{x}{2.5\text{ Hours}}[/tex]Where x is the number of miles that Lebron walked on the return trip. So, solving for x, we get:
[tex]\begin{gathered} \frac{4.5}{2.25}=\frac{x}{2.5} \\ \frac{4.5}{2.25}\times2.5=\frac{x}{2.5}\times2.5 \\ 5=x \end{gathered}[/tex]Therefore, Lebron walked 5 miles on the return trip.
What is the meaning of the x-intercept? A) Olivia's maximum distance from the pool was about 10.5 meters. B) It takes Olivia about 3.2 seconds to enter the pool. C) Olivia's dive was from a 10-meter platform. D) Olivia's speed was not constant.
Explanation:
X- intercept is the value of x when y is equal to zero.
On the graph, we have distance(meters) over time (secs).
The time is in the x axis. The value of x when y is equal to zero is a bit above 3.
This means when Olivia's distance is at point 0 meters, the seconds it takes to enter to pool is a bit over 3 secs (around 3,
From the options, the correct answer is It takes Olivia about 3.2 seconds to enter the pool (option B)
A city counsel has a square lot to place a playground. They plan to place a diagonal of treesto create two distinct play areas. To determine if there is enough money in the budget, theyneeds to know the distance. If the length of each side of the lot is 32√7 m, how long is thediagonal?
Answer: 13.01m
Explanation
A right triangle is a triangle with a 90º angle. If the square lot is divided by a diagonal, then two right triangles are formed:
The right triangle satisfies the Pythagorean Theorem:
[tex]c^2=a^2+b^2[/tex]
where c is the diagonal (hypotenuse), and a and b are the sides. In our case, as it is a square, a = b, meaning:
[tex]c^2=32\sqrt{7}+32\sqrt{7}[/tex]Thus, simplifying and solving for c we can find the diagonal:
[tex]c^2=2(32\sqrt{7})[/tex][tex]\sqrt{c^2}=\sqrt{64\sqrt{7}}[/tex][tex]c\approx13.01m[/tex]Use the sum and difference identities to rewrite the following expression as a trigonometric function of asingle number.sin(15°)cos(135) + cos(159) sin(135)
The value of the given trigonometric function is [tex]\sqrt{3} +1[/tex]
The given trigonometric function is sin(15°)cos(135) + cos(15) sin(135).
Evaluating the expression with the sum and difference identities.
We know, SinACosB + CosASinB = Sin(A +B)
Now, We have :
sin(15°)cos(135) + cos(15) sin(135) = Sin ( 15 +135 ) = Sin150
Now, Sin 150 = Sin(120 +30) = Sin120Cos30 + Cos120Sin30
Sin 150 =
[tex]=\frac{\sqrt{3} }{2} * \frac{\sqrt{3} }{2} + \frac{1}{2}*\frac{1}{2} = \frac{2\sqrt{3} }{2} +\frac{2}{2} \\\\= \sqrt{3} +1[/tex]
Hence, the value of the given trigonometric function is [tex]\sqrt{3} +1[/tex]
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14. Consider the function / graphed below. For whatvalues of Xo does lim /(x) exist?Sorry if u were last tutor, the app crashed
The limit exists at all values of x₀ where the function is continuous, i.e. where there is no break in the graph.
So only consider the points where there is a vertical asymptote (x₀=-6), where there are holes and jump discontinuity (x₀=-3,3).
The vertical asymptote is a place where the function is undefined and the limit of the function does not exist.
Hence, the limit does not exist at x₀=-6.
For the point where there is a hole, x₀=-3, notice that the graph approaches the same y-value both from the left and right, hence the limit exists at this point, as this is a removable discontinuity.
For the point, x₀=3 where there is a jump discontinuity, notice that the graph approaches different values from the left and right, respectively. Hence, the left and right limits are not equal and thus the limit does not exist.
So the limit exists over the set of real numbers except {-6,3}.
Find the inverse of 1/4x^3+2x-1=y
In industrial art class. Elizabeth created a figure from sheet metal. She created a right circular cylinder that has a radius of 6 inches.And hieght of 12 inches.What is the volume in cubic inches of the figure she created OPTIONS1,356.48 inches3648 inches3339.12 inches3226.08 inches3
In industrial art class. Elizabeth created a figure from sheet metal. She created a right circular cylinder that has a radius of 6 inches, and a height of 12 inches.
What is the volume in cubic inches of the figure she created
OPTIONS
1,356.48 inches3
648 inches3
339.12 inches3
226.08 inches3
_________________________
Can you see the updates?
____________________________
Cylinder volume = A(circle) * height
Cylinder volume = π r^2 * h
Cylinder volume = π (6 in)^2 * 12 in
Cylinder volume = π (6 in)^2 * 12 in
Cylinder volume = π 432 in^3
Cylinder volume = 1357. 17
______________
Answer
π= 3.14
1,356.48 inches3
need help asappppppp
Here, we want to get the length of the ladder
The kind of triangle we have is a right triangle for which obeys the Pythagoras' theorem
According to the theorem, the square of the hypotenuse equals the sum of the squares of the two other sides
The length of the ladder marked as h is the hypotenuse
Thus, we have it that;
[tex]\begin{gathered} h^2=9^2+7^2 \\ h^2\text{ = 81 + 49} \\ h^2\text{ = 130} \\ h\text{ = }\sqrt[]{130} \\ h\text{ = 11.40 meters} \end{gathered}[/tex]Is a tutor availible?
this is a conversion problem
First you must understand that 1 foot = 12inches
Given a ribbon that is 5 1/2 feet long
To convert to inches, you will simply multiply 5 1/2 by 12 as shown;
= 5 1/2 * 12
convert the mixed fraction to improper fraction
= 11/2 * 12
= 11 * 12/2
= 11 * 6
= 66 inches
Hence the ribbon is 66 inches long
n a 45 minute basketball game, 30 girls want to play. Only 10 can play at once. If each player is to play the same length of time, how many minutes should each play?
A 45 minute basketball game, 30 girls want to play. Only 10 can play at once. If each player is to play the same length of time. 15 minutes should each play
10/30=1/3
[tex]\frac{1}{3} \times 45$$[/tex]
Convert element to fraction: [tex]$\quad 45=\frac{45}{1}$[/tex]
[tex]=\frac{1}{3} \times \frac{45}{1}$$[/tex]
Apply the fraction rule:[tex]$\frac{a}{b} \times \frac{c}{d}=\frac{a \times c}{b \times d}$[/tex]
[tex]=\frac{1 \times 45}{3 \times 1}$$[/tex]
[tex]$\frac{1 \times 45}{3 \times 1}=\frac{45}{3}$[/tex]
[tex]=\frac{45}{3}[/tex]
Divide the numbers: [tex]$\frac{45}{3}=15$[/tex]
=15
15 minutes for 3 groups of 10 each to play basketball.
To add or subtract fractions, the denominator must be the same (the bottom value). Subtraction and addition with the same denominators If the denominators are already the same, all that remains is to add or subtract the numerators (the top value).
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need help answering the question step by step explanation please
Given that:
- Lucy must have the construction job done within 30 days.
- The bid of the first engineer is $2050 per hour, 8 hours per day.
- The bid of the second engineer is 1¢ per day which will double each day.
Let be "x" the number of days of work and "y" the total cost (in dollars)
• Using the data given, you can set up this equation to represent the bid of the first engineer:
[tex]\begin{gathered} y=(2050)(8)x \\ \\ y=16400x \end{gathered}[/tex]And you can set up this equation to represent the bid of the second engineer:
[tex]y=0.01(2)^{x-1}[/tex]• In order to graph them, you can give values to the variable "x" and evaluate, in order to get the corresponding y-values.
By substituting this value into the first equation:
[tex]\begin{gathered} \\ x=5 \\ \\ x=10 \end{gathered}[/tex]You get:
[tex]y=16400(5)=82000[/tex][tex]y=16400(10)=164000[/tex]- For the second equation, substitute this value:
[tex]x=20[/tex]And evaluate:
[tex]y=0.01(2)^{20-1}=5242.88[/tex]Now you can graph them:
You can identify in the graph that the total cost is greater in the first line than the cost in the second line. Therefore, the cost of the bid given for the first engineer will be greater.
Hence, the answer is:
• Equation 1st:
[tex]y=16400x[/tex]• Equation 2nd:
[tex]y=0.01(2)^{x-1}[/tex]• Graph:
• Better deal: The bid of the second engineer (the graph shows that the total cost using this deal will be less than the total cost using the first deal).
if I need 1/2 cup of oil but I only have 1/3 cup of oil how much oil do I need
We need 1/2 cup of oil and we are told that we already have 1/3 cup of oil, to find out how much we need we subtract this and the result will be the amount of oil we need.
[tex]\frac{1}{2}-\frac{1}{3}=\frac{3-2}{6}=\frac{1}{6}[/tex]In conclusion, the answer is 1/3 cup of oil
If pp is inversely proportional to the square of qq, and pp is 22 when qq is 8, determine pp when qq is equal to 4.
Given that p is inversely proportional to the square of q that implies:
[tex]p\propto\frac{1}{q^2}[/tex]Remove the sign of proportionality and put a proportionality constant k such that:
[tex]p=\frac{k}{q^2}[/tex]Given that when q is 8 then p is 22. So,
[tex]22=\frac{k}{8^2}\Rightarrow k=22\times64=1408[/tex]Put k = 1408 and q = 4 in the equation to find the value of p:
[tex]p=\frac{1408}{4^2}=\frac{1408}{16}=88[/tex]Thus, the answer is 88.
Solve the following system of linear equations.x + 3y + z = - 42x – 4y – 3z = 73x – 3y + 4z = 13AnswerBH」KeyboardX =y =z =
Given
Solve the following system of linear equations.
x + 3y + z = - 4
2x – 4y – 3z = 7
3x – 3y + 4z = 13
Solution
[tex]\begin{bmatrix}x+3y+z=-4 \\ 2x-4y-3z=7 \\ 3x-3y+4z=13\end{bmatrix}[/tex]Substitute x= -4-3y-z
[tex]\begin{bmatrix}2\mleft(-4-3y-z\mright)-4y-3z=7 \\ 3\mleft(-4-3y-z\mright)-3y+4z=13\end{bmatrix}[/tex]Simplify
[tex]\begin{bmatrix}-10y-5z-8=7 \\ -12y+z-12=13\end{bmatrix}[/tex]Make y the subject
[tex]\begin{gathered} -10y-5z-8=7 \\ -10y\text{ -5z=7+8} \\ -10y-5z=15 \\ \text{divide all through by 5} \\ -2y-z=3 \\ y=-\frac{z+3}{2} \end{gathered}[/tex]Now substitute
[tex]\begin{bmatrix}-12\mleft(-\frac{z+3}{2}\mright)+z-12=13\end{bmatrix}[/tex]Simplify
[tex]\begin{gathered} \\ \begin{bmatrix}7z+6=13\end{bmatrix} \\ \text{Make z the subject} \\ 7z=13-6 \\ 7z=7 \\ \text{divide both sides by 7} \\ \frac{7z}{7}=\frac{7}{7} \\ z=1 \end{gathered}[/tex]Now substitute z=1
[tex]\begin{gathered} y=-\frac{z+3}{2} \\ y=-\frac{1+3}{2}=-\frac{4}{2}=-2 \end{gathered}[/tex]Finally, to find x
when z =1 and y =-2
[tex]\begin{gathered} x+3y+z=-4 \\ x+3(-2)+1=-4 \\ x-6+1=-4 \\ \text{collect the like terms} \\ x-5=-4 \\ x=-4+5 \\ x=1 \end{gathered}[/tex]The final answer
[tex]\begin{gathered} x=1 \\ y=-2 \\ z=1 \end{gathered}[/tex]The product of a number and 5 is always greater than 15.Which of the following shows this inequality?
Let x be the unkown number.
The product of a number and 5: multiplication of x and 5 (5x)
Is always greater than 15: >15
Inequality:
[tex]5x>15[/tex]Another form of write the inequality is soving x:
[tex]\begin{gathered} \frac{5}{5}x>\frac{15}{5} \\ \\ x>3 \end{gathered}[/tex]Posible Inequalities: 5x>15x>3Use the quadratic formula to solve for X. 3x^2 = -3x +7
The solutions are:
x = -2.11 or 1.11
Explanation:Given the equation:
[tex]3x^2=-3x+7[/tex]This can be written as:
[tex]3x^2+3x-7=0[/tex]Comparing this with the general equation;
[tex]ax^2+bx+c=0[/tex]We see that;
[tex]\begin{gathered} a=3 \\ b=3 \\ c=-7 \end{gathered}[/tex]The quadratic formula is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Substitute the values of a, b, and c
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^2-4\times3\times(-7)}_{}}{2\times3} \\ \\ =\frac{-3\pm\sqrt[]{9+84}}{6} \\ \\ =\frac{-3\pm\sqrt[]{93}}{6} \\ \\ =\frac{-3\pm9.64}{6} \\ \\ x=\frac{-3+9.64}{6}=1.11 \\ \\ OR \\ x=\frac{-3-9.64}{6}=-2.11 \end{gathered}[/tex]nQuestion 6Mutiple Choice Worth 1 points)(06.04 MC)The length of a rectangle is represented by the function L(x)= 2x. The width of that same rectangle is represented by the function W(x)=8x²-4x+1. Which of the following shows the area of the rectangle interms of x?(L+ W)(x)=8x²-2x+1(L + W)(x)=8x² - 6x +1(L• W)(x)=16x-4x+1(L • W)(x)=16x³-8x²+2x
Answer:
[tex]D\text{ :}(L\text{ }\circ\text{ W\rparen\lparen x\rparen= 16x}^3-8x^2+2x[/tex]Explanation:
Here, we want to select the option that best represents the area of the rectangle in terms of x
Mathematically, the area can be calculated by:
[tex]A(x)\text{ = L\lparen x\rparen }\times\text{ W\lparen x\rparen}[/tex]We have that as:
[tex]\begin{gathered} 2x\text{ }\times\text{ 8x}^2-4x+1 \\ =\text{ 2x\lparen8x}^2-4x+1) \\ =\text{ 16x}^3-8x^2+2x \end{gathered}[/tex]The sum of three numbers is 154. The first number is 10 more than the second. The third number is 4 times the second. What are the numbers?First number:х5?Second number:000Third number
Let's call those numbers a, b and c.
Since their sum is 154, we have:
a + b + c = 154
Also, since the first number is 10 more than the second, we have:
a = b + 10
And, since the third number is 4 times the second number, we have:
c = 4b
Now, we can use the expressions of a and c in terms of b in the first equation:
a + b + c = 154
b + 10 + b + 4b = 154
6b + 10 = 154
6b = 154 - 10
6b = 144
b = 144/6
b = 24
Then, we can use the value of b to find a and c:
a = b + 10
a = 24 + 10
a = 34
c = 4b
c = 4 * 24
c = 96
Therefore,
• First number: ,34
,• Second number: ,24
,• Third number: ,96
raina is jogging from her house to school her school is 4 3/4 miles from her house she has gone 1 1/3 miles so far how many miles does raina have left
Solution
For this case we have the following:
[tex]4\cdot\frac{3}{4}=\frac{19}{4}mi[/tex][tex]1\cdot\frac{1}{3}=\frac{4}{3}mi[/tex]then we can find the difference on this way:
[tex]\frac{19}{4}-\frac{4}{3}=\frac{41}{12}[/tex]Then she has 41/12 miles left
11. The volume of a pyramid is equal to1the product of the altitude and the area of the base. If the area of the base3remains the same and the altitude is doubled, the volume Please help
Answer:
Double
Explanation:
[tex]\text{Volume of a Pyramid=}\frac{1}{3}\times Base\text{ Area}\times Altitude[/tex]If the area of the base remains the same and the altitude is doubled, we have:
[tex]\begin{gathered} New\; Volume=\frac{1}{3}\times\text{Base Area}\times(2\times Altitude) \\ =2\times(\frac{1}{3}\times\text{Base Area}\times Altitude) \\ =2\times\text{Old Volume} \end{gathered}[/tex]Thus, if the area of the base remains the same and the altitude is doubled, the volume will double,
slope is -5 and (2, 1) is on the line; standard form
We have to find the equation of the line in standard form, knowing that the slope is m = -5 and it passes through the point (2, 1).
The standard form is:
[tex]Ax+By=C[/tex]When we know the slope and one point, we can write the equation in slope-point form. Then, we can rearrange the terms in order to find the standard form.
The slope-point form is:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-1=-5(x-2) \end{gathered}[/tex]We then can rearrange it as:
[tex]\begin{gathered} y-1=-5(x-2) \\ y=-5x-5\cdot(-2)+1 \\ y=-5x+10+1 \\ y+5x=11 \\ 5x+y=11 \end{gathered}[/tex]Answer: the standard form of the line is 5x + y = 11.