Plot and connect the points A(2,3), B(2,-5), C(-4,-3), and find the area of the triangle it forms.
Answers
so we can simply split the triangular area into two smaller triangles, notice their base and height.
so, simply, get the area of each triangle, sum them up, and that's the area of the triangular section.
[tex]\bf \stackrel{\textit{yellow triangle}}{\cfrac{1}{2}(6)(6)}~~~~+~~~~\stackrel{\textit{blue triangle}}{\cfrac{1}{2}(6)(2)}[/tex]
The area of the triangle is 24 square unit.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.
If we plot the points A(2,3), B(2,-5), C(-4,-3) on the graph we get a triangle which can be divided into two right Triangles.
So, Area of Triangle 1
= 1/2 x base x height
= 1/2 x 6 x 6
= 18 sq units
Now, area of Triangle 2
= 1/2 x base x height
= 1/2 x 6 x 2
= 6 sq units
Thus ,the Area of required triangle
= 18 + 6
= 24 sq units
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Related Questions
When scholastic achievement test scores (sats) are sent to test-takers, the percentiles associated with scores are also given. suppose a test-taker scored at the 59th percentile on the verbal part of the test and at the 36th percentile on the quantitative part. interpret these results?
Answers
A salesperson has to drive 500 miles. For the first three hours she drove at 65 mi/h. For the next two hours she drove at 55 miles per hour. How many more miles does she have to drive?
Answers
First, you do 65 times 3 and that gives you 195 miles.
Then you do 55 times 2 and that gives you 110 miles.
You add both answers and get 305.
Do 500-305 and you get =195.
Rewrite the equation below in standard form 2/3x=-5/2y+2
Answers
Answer:
4x + 15y = 12
Step-by-step explanation:
The standard form of a linear equation is Ax + By = C where A and B cannot be fractions and A is not negative. To write in standard form, move -5/2y to the other side of the equal sign. Then clear the denominators by multiplying the equation by 6.
2/3x=-5/2y+2
2/3x + 5/2y = 2
6(2/3x + 5/2y = 2)
4x + 15y = 12
8% of what is 2.8??
Answers
8% × what = 2.8
0.08 × what = 2.8
what = 2.8/0.08
what = 35
8% of 35 is 2.8.
what is 231 scaled down by a factor of 1/10
Answers
231
We have the following scale factor:
1/10
Applying the scale factor we have:
(number) * (scale factor)
(231) * (1/10) = 23.1
Answer:
The new number is given by:
23.1
If it takes 2 nurses 2 minutes to measure the blood pressure of 2 patients, how long would it take 200 nurses to measure the blood pressure of 200 patients (in minutes)?
Answers
Answer:
it will take 2 minutes for 200 nurses to measure the blood pressure of 200 patients .
Step-by-step explanation:
We know that the work-time and number of labor and efficiency formula is given by:
[tex]Efficiency=\dfrac{Number\ of\ labor\times Time}{Work\ done}[/tex]formula is given by:
Here Number of labor=Number of nurses.
Work=Number of patients whose blood pressure were noted.
As the efficiency will be same this means that:
[tex]\dfrac{2\times 2}{2}=\dfrac{200\times x}{200}[/tex]
where x denotes the number of time taken by 200 nurses.
Hence,
[tex]x=2[/tex]
Hence, the answer is:
2 minutes.
Based in the graph, what is the initial value of the linear relationship
A)-4
B)-3
C)5/3
D)5
Answers
Answer:
D)5
Step-by-step explanation:
The initial value of the linear relationship is the value that exists in the "Y" axis when the "x" value is 0, as you can see in the graph, when the X value is 0, the Y value is 5, so the inital value of the linear relationship is 5.
If you wish to calculate this on an inequality, you just have to insert in the inequality 0 as the value for x, and you will get as a result the initial value.
Cameron used 1 3/4 ounces of hydrochloric acid in one experiment. She used 2 1/8 ounces of the acid in a second experiment. How much more acid did Cameron use in the second experiment?
Answers
2 1/8 -1 3/4 =
17/8 - 14/8 = 3/8ths
Answer:
Amount required is [tex]x=\frac{3}{8}[/tex]
Step-by-step explanation:
Given : Cameron used [tex]1\frac{3}{4}[/tex] ounces of hydrochloric acid in one experiment. She used [tex]2\frac{1}{8}[/tex] ounces of the acid in a second experiment.
To find : How much more acid did Cameron use in the second experiment?
Solution :
In one experiment,
Cameron used [tex]1\frac{3}{4}[/tex] ounces of hydrochloric acid
i.e [tex]1\frac{3}{4}=\frac{7}{4}[/tex]
In second experiment,
She used [tex]2\frac{1}{8}[/tex] ounces of the acid.
i.e. [tex]2\frac{1}{8}=\frac{17}{8}[/tex]
Let x amount more she used then experiment 1 in experiment 2.
So, the equation became
[tex]\frac{7}{4}+x=\frac{17}{8}[/tex]
[tex]x=\frac{17}{8}-\frac{7}{4}[/tex]
[tex]x=\frac{17-14}{8}[/tex]
[tex]x=\frac{3}{8}[/tex]
Therefore, Amount required is [tex]x=\frac{3}{8}[/tex]
Find the directional derivative of f(x, y, z) = xy + yz + zx at p(1, −1, 7) in the direction from p to q(2, 4, 5). duf(1, −1, 7)
Answers
[tex]\implies\nabla f(x,y,z)=(y+z,x+z,y+x)[/tex]
[tex]\vec{pq}=\mathbf q-\mathbf p=(2-1,4-(-1),5-7)=(1,5,-2)[/tex]
[tex]\|\vec{pq}\|=\sqrt{30}[/tex]
[tex]D_{\vec{pq}}f(1,-1,7)=\nabla f(1,-1,7)\cdot\dfrac{(1,5,-2)}{\sqrt{30}}=\dfrac{(6,8,0)\cdot(1,5,-2)}{\sqrt{30}}=\dfrac{46}{\sqrt{30}}[/tex]
The directional derivative of f(x, y, z) = xy + yz + zx at p(1, -1, 7) towards q(2, 4, 5) is found by first calculating the unit vector in the direction from p to q, then the gradient of f at p, and calculating the dot product of the two vectors. The directional derivative comes out to be 16/ √30.
Explanation:The directional derivative of the function f(x, y, z) = xy + yz + zx at a point p(1, -1, 7) towards the point q(2, 4, 5) can be found by first getting the unit vector in the direction from p to q, then calculating the gradient of the function at p, and finally calculating the dot product of these two vectors (the unit vector and the gradient of the function).
First, calculate the unit vector u = (q - p) / |q - p|. That gives u = (1, 5, -2), and normalize it to get u = 1/ √30 (1, 5, -2).
Next, get the gradient of the function at p(1, -1, 7), which is the vector of first order derivatives. The partial derivatives of f(x, y, z) with respect to x, y, z are y+z, x+z, and x+y respectively. This gives the gradient vector at p as (-8, 8, 0).
Finally, the directional derivative is the dot product of the unit vector and the gradient, which comes out to be 1/ √30 * ((1*-8) + (5*8) + ((-2)*0)) = 16/ √30.
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Four sizes of scaled text are shown. What is the unknown scale size?
Answers
Answer:
font size of top line will be 1.067
Step-by-step explanation:
Scale factor between 4th line text size to the 3rd line text will be
= [tex]\frac{0.937}{0.878}=1.067[/tex]
Scale factor between 3rd line and second line will be = [tex]\frac{1}{0.937}=1.067[/tex]
Therefore, scale factor between 2nd and 1st text size will be = [tex]\frac{x}{1}=1.067[/tex]
x = 1.067
It reveals that the font size of top line will be 1.067
What is the following sum? 4(5 sqrt x^2y)+3(5 sqrt x^2y)
Answers
[tex]4(5 \sqrt{ {x}^{2}y } ) + 3(5 \sqrt{ {x}^{2} y} ) = 35x\sqrt{y}[/tex]
EXPLANATION
The given expression is
[tex]4(5 \sqrt{ {x}^{2}y } ) + 3(5 \sqrt{ {x}^{2} y} )[/tex]
We need to simplify the above expression first before, we add them.
Let us deal with the expressions within the parenthesis first,
[tex]4(5 \sqrt{ {x}^{2}y } ) + 3(5 \sqrt{ {x}^{2} y} ) = 4(5 \sqrt{ {x}^{2}}\times \sqrt{y} ) + 3(5 \sqrt{ {x}^{2} } \times \sqrt{y} )[/tex]
This will simplify to,
[tex]4(5 \sqrt{ {x}^{2}y } ) + 3(5 \sqrt{ {x}^{2} y} ) = 4(5 x\times \sqrt{y} ) + 3(5 x \times \sqrt{y} )[/tex]
We now multiply out the brackets to obtain,
[tex]4(5 \sqrt{ {x}^{2}y } ) + 3(5 \sqrt{ {x}^{2} y} ) = 20 x\times \sqrt{y} + 15 x \times \sqrt{y} )[/tex]
This implies that,
[tex]4(5 \sqrt{ {x}^{2}y } ) + 3(5 \sqrt{ {x}^{2} y} ) = 20 x\sqrt{y} + 15 x \sqrt{y} )[/tex]
This will give us,
[tex]4(5 \sqrt{ {x}^{2}y } ) + 3(5 \sqrt{ {x}^{2} y} ) = 35x\sqrt{y}[/tex]
Answer:
7(5 sqrt x^2y) or C
Step-by-step explanation:
From a basket of mangoes, the king took 1/6, the queen took 1/5 of the remainder, the three chief princes to ¼, 1/3, and ½ of the successive remainders, respectively. the youngest child took the remaining 3 mangoes. how many mangoes were in the basket originally
Answers
x---------> quantity of mangoes that were in the basket originally
we know that
the king took 1/6
(1/6)*x-------> remainder is (5/6)*x
the queen took 1/5 of the remainder
(1/5)*(5/6)*x---> (1/6)*x----> remainder is (5/6-1/6)*x----> (4/6)*x
one chief princes to ¼ of the remainder
(1/4)*(4/6)*x-----> (1/6)*x------> remainder is (4/6-1/6)*x----> (3/6)*x
second chief princes to 1/3 of the remainder
(1/3)*(3/6)*x-----> (1/6)*x-------> remainder is (3/6-1/6)*x----> (2/6)*x
third chief princes to 1/2 of the remainder
(1/2)*(2/6)*x-----> (1/6)*x--------> remainder is (2/6-1/6)*x----> (1/6)*x
we know
the remaining is 3 mangoes
so
(1/6)*x=3-------> x=6*3------> x=18 mangoes
the answer is
18 mangoes
Final answer:
The original basket contained 72 mangoes, determined by working backward from the known remainder of 3 after the sequential distribution between the king, queen, and princes.
Explanation:
From a basket of mangoes, the distribution among the royal family leads to a classic fractional subtraction problem. The solution involves working backward from the known remainder. The youngest child took the remaining 3 mangoes, which indicates that this was what was left after the king, the queen, and the three chief princes took their respective shares.
Let's denote the original number of mangoes as x. The king took 1/6 of x, leaving 5/6x. The queen then took 1/5 of the remainder (5/6x), leaving 4/5 * 5/6x = 4/6x or 2/3x. Successively, the three chief princes took 1/4, 1/3, and 1/2 of their respective remainders, each action further reducing the quantity of mangoes. The problem states that after these distributions, 3 mangoes were left, which were taken by the youngest child.
To find the original number of mangoes, we begin by denoting the final 3 mangoes as the remaining half after the last prince's share, work through the inverse operations for each prior transaction, and solve for x. Through this back calculation, we find that the original number of mangoes was 72.
what are the zeroes of 2x squared plus 6x minus 8
Answers
The results of a survey are shown below.in the survey,12 students said that they would like to learn French.
Answers
Which equation could have been used to create this function table? 1 2,3 6,4 8,5 10, 10 20 A. y = 5x B. y = x + 1 C. y = x + 2 D. y = 2x
Answers
The correct equation used to create the function table provided is Option D: y = 2x, which indicates a linear relationship where y is twice the value of x.
The function table given in the question indicates the relationship between values of x and their corresponding y values. To determine which equation was used to create this table, you can compare the differences between these values. In the given pairs (1, 2), (3, 6), (4, 8), (5, 10), and (10, 20), it is observed that the y values are exactly twice the x values. Therefore, the equation representing this relationship must be y = 2x, which is a linear function with a slope of 2.
Looking at the options provided, Option D: y = 2x is the correct one, as it fits the pattern shown in the function table: for every unit increase in x, y increases by 2 units, implying a line with a slope of 2.
What is the value of 1*2+ 3 / 6*5 - 4? Express as a fraction.
Answers
Helpp me graph thesse on a scatter plot sooo confused eee!! @musiclover helpp plzz lol
Answers
1. The scatter plot does not show a linear model.
2. Since the plotted data are all around the temperature of 10, the slope would be a horizontal line at 10. A horizontal line does not have any slope, this tell me that the average temperature stays an average of 10 no matter what the humidity level is.
3. There is no vertical intercept shown.
2nd page:
1. yes, because there were 2 small clusters separated by a little bit of space.
2. I think the location of the area the data came from may change the relationship between the variables.
3. I think by switching the axis's the data may be grouped closer together since most of the data points are along a vertical line.
Answer:
1. The scatter plot does not show a linear model.2. Since the plotted data are all around the temperature of 10, the slope would be a horizontal line at 10. A horizontal line does not have any slope, this tell me that the average temperature stays an average of 10 no matter what the humidity level is.3. There is no vertical intercept shown.2nd page:1. yes, because there were 2 small clusters separated by a little bit of space.2. I think the location of the area the data came from may change the relationship between the variables.3. I think by switching the axis's the data may be grouped closer together since most of the data points are along a vertical line.
Step-by-step explanation:
Factor the expression. 40z – 20
a) 2z - 1
b) 2(20z-10)
c) 20(2z-1)
d) 20(2Z-20)
Answers
20 is the greatest common factor. Then divide.
Answer:
[tex]\bf\pink{20(2z-1)}[/tex]Step-by-step explanation:
Given Expression :-[tex]\rm\gray{40z-20}[/tex]Steps to factorise :-[tex]\\\to\:\:\to\:\:\rm\red{40z - 20}[/tex]
Factor out [tex]\bf\blue{20}[/tex] from the expression[tex]\\\to\:\:\to\:\:\rm\green{20(2z-1)} \\ [/tex]
(Refer the attachment for graph representation)
Graph Details :-[tex]\bigstar\:\:\bf\purple{y = 40z-20} \\ [/tex]
[tex]\rm{Root \: \bigg( \dfrac{1}{2}, \:0\bigg) }[/tex][tex]\rm{ Domain \: \:z \: \in\:{\mathbb{R}}}[/tex][tex]\rm{Range \: \:y \: \in\:{\mathbb{R}}}[/tex][tex]\rm{Vertical \: intercept\:\:(0,\:-20)}[/tex]Landry is opening two savings accounts. He is opening the first account with an initial deposit of $500. The account will compound continuously each year at a rate of 3%.
He is opening the second account with an initial deposit of $300. The account will compound continuously each year at a rate of 5%.
Landry would like to know how long it will take for the balance of the two accounts to be equal.
Create a system of equations to model the situation above, and use it to determine if there are any solutions. If there are any solutions, determine if they are viable or not.
There are two solutions and both are viable.
There is only one solution and it is viable.
There is only one solution and it is not viable.
There are no solutions.
Answers
Answer:
B. there is only one solution, and it is viable
Step-by-step explanation:
The coordinates of an ordered pair have opposite signs. In which quadrant(s) must the ordered pair lie? Explain.
Answers
Final answer:
Ordered pairs with opposite signs for their coordinates are located in the second or fourth quadrants of a Cartesian plane, depending on the signs of the x and y-coordinates.
Explanation:
The coordinates of an ordered pair with opposite signs indicate its position in the coordinate plane. When the x-coordinate and y-coordinate have opposite signs, the ordered pair lies either in the second or fourth quadrant. This is because the sign of the x-coordinate is positive on the right side of the y-axis (first and fourth quadrants) and negative on the left side (second and third quadrants), and similarly, the sign of the y-coordinate is positive above the x-axis (first and second quadrants) and negative below it (third and fourth quadrants). Thus, if an ordered pair has coordinates with opposite signs, it lies in the quadrant where one axis is positive and the other is negative. For example, if the x-coordinate is positive and the y-coordinate is negative, the ordered pair will be in the fourth quadrant. Conversely, if the x-coordinate is negative and the y-coordinate is positive, it will lie in the second quadrant.
Lena made 32 ounces of a fruit drink mix using pineapple juice and grapefruit juice. The number of ounces of pineapple juice in the fruit drink mix is 5 more than 2 times the number of ounces of grapefruit juice in the fruit drink mix. Which graph shows the number of ounces of pineapple juice, x, and the number of ounces of grapefruit juice, y, in the fruit drink mix?
Answers
let
x-------> the number of ounces of pineapple juice
y------> the number of ounces of grapefruit juice
we know that
x+y=32
x=2y+5-----> x-5=2y
using a graph tool
see the attached figure N 2
the solution is
x=23 ounces (pineapple juice)
y=9 ounces (grapefruit juice)
therefore
the answer is the option a
Use common sense to determine whether the given event is impossible; possible, but very unlikely; or possible and likely.
An accountant was struck by lightening three times in his lifetime.
Possible and likely
Possible, but very unlikely
Impossible
Answers
Option B is the right answer.
Step-by-step explanation:
An accountant was struck by lightening three times in his lifetime. This event is Possible, but very unlikely.
We know that a probability near 0 means an unlikely event. Probability around 1/2 indicates an event that is neither unlikely nor likely. Similarly, probability near 1 indicates a likely event.
Here, in a lifetime the accountant was struck 3 times. If the average lifetime is 70 years, so probability becomes [tex]\frac{3}{70}= 0.04[/tex]. This is close to zero, indicating that the event is very unlikely.
And people are struck by lightening so it is a possible event.
Combining both, we get option B as the final answer.
A group would like to estimate the percentage of town residents who would support a teen curfew.
Which statement describes a method that will help the group accurately estimate this percentage?
Take a random sample of towns in the state. Ask an administrator in the city office whether the town has a teen curfew, and then calculate the percentage of the total who say "yes."
Identify all nearby towns that have a teen curfew. Contact the mayor of each of those towns and ask whether he or she thinks the curfew is a good policy. Calculate the percentage of the total who say "yes."
Contact every parent who lives in the town and ask whether they support a teen curfew. Calculate the percentage of the total who say "yes."
Take a random sample of residents in the town, and ask each resident in the sample whether or not they support a teen curfew. Then calculate the percentage of the total who say "yes."
Answers
Your best answer here would be:
Take a random sample of residents in the town, and ask each resident in the sample whether or not they support a teen curfew. Then calculate the percentage of the total who say "yes."
This is because you are taking a sample of votes from residents.
Hope this helps!
The correct statement that describes a method that will help the group accurately estimate this percentage is;
⇒ Take a random sample of residents in the town, and ask each resident in the sample whether or not they support a teen curfew. Then calculate the percentage of the total who say "yes."
What is Random Sampling?Random sampling is defined as a sampling method that utilizes randomization of sample selection.
In random sampling, each sample has the same probability of being selected as that of other samples to be selected to serve as a representation of an entire population.
Now, in this question, since the group would like to estimate the percentage of town residents who would support a teen curfew, then the sampling method they should use is random sampling which is in option C.
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the weight of an object on mars varies directly with its weight on earth. an object that weighs 50 pounds on mars weighs 150 pounds on earth. if an object weighs 120 pounds on earth, write and solve a direct variation equation to find how much an object would weigh on mars.
Answers
Wm α We => Wm = kWe, Where Wm = Weight on mars, We = Weight on earth, k = constant of proportionality.
For Wm = 50 pounds, We = 150 pounds;
k = Wm/We = 50/150 = 1/3
Now, for 120 pounds on earth;
Wm = k*We
Substituting;
Wm = 1/3 * 120 = 40 pounds
To find the weight of an object on Mars, we can use a direct variation equation. By finding the constant ratio from the given values, we can then solve for the weight on Mars when the weight on Earth is known. In this case, the object would weigh 40 pounds on Mars if it weighs 120 pounds on Earth.
Explanation:To solve this problem, we will use the concept of direct variation. The weight of an object on Mars varies directly with its weight on Earth. This means that the weight on Mars can be found by multiplying the weight on Earth by a constant ratio. Let's represent the weight on Mars as WM and the weight on Earth as WE. According to the problem, an object that weighs 50 pounds on Mars weighs 150 pounds on Earth. This gives us the following direct variation equation:
WM = k * WE
where k is the constant ratio.
We can now substitute the given values: 50 pounds for WM and 150 pounds for WE.
50 = k * 150
To solve for k, divide both sides of the equation by 150:
k = 50 / 150
k = 1 / 3
Now that we have the value of the constant ratio, we can find the weight of an object on Mars when it weighs 120 pounds on Earth. Let's represent the weight on Mars as x and the weight on Earth as 120:
x = (1 / 3) * 120
x = 40
Therefore, the object would weigh 40 pounds on Mars.
Graph The Parabola. y=3x^2+18x+20
Answers
[tex]y = 3x {}^{2} + 18x + 20[/tex]
The final solution for y is
[tex]y = 3x {}^{2} + 18x + 20,x \:e \: r [/tex]
where e = ∈
Graph details as follows
Domain: x ∈ ℝ
Minimum : ( - 3, - 7)
y-intercept : (0, 20)
you roll a standard number cube. Find P(number greater than 5)
Answers
On a standard number cube there are 6 numbers and only one of them is greater than 5.
The probability of getting the one number out of 6 total numbers is 1/6
P( number greater than 5) = 1/6
Use the euclidean algorithm to find
a.gcd(12, 18).
b.gcd(111, 201).
c.gcd(1001, 1331).
d.gcd(12345, 54321).
e.gcd(1000, 5040). f ) gcd(9888, 6060).
Answers
[tex]18=1\cdot12+6[/tex]
[tex]12=2\cdot6+0[/tex]
[tex]\implies\mathrm{gcd}(12,18)=6[/tex]
b)
[tex]201=1\cdot111+90[/tex]
[tex]111=1\cdot90+21[/tex]
[tex]90=4\cdot21+6[/tex]
[tex]21=3\cdot6+3[/tex]
[tex]6=2\cdot3+0[/tex]
[tex]\implies\mathrm{gcd}(111,201)=3[/tex]
c)
[tex]1331=1\cdot1001+330[/tex]
[tex]1001=3\cdot330+11[/tex]
[tex]330=30\cdot11+0[/tex]
[tex]\implies\mathrm{gcd}(1001,1331)=11[/tex]
d)
[tex]54321=4\cdot12345+4941[/tex]
[tex]12345=2\cdot4941+2463[/tex]
[tex]4941=2\cdot2463+15[/tex]
[tex]2463=164\cdot15+3[/tex]
[tex]15=5\cdot3+0[/tex]
[tex]\implies\mathrm{gcd}(12345,54321)=3[/tex]
e)
[tex]5040=5\cdot1000+40[/tex]
[tex]1000=25\cdot40+0[/tex]
[tex]\implies\mathrm{gcd}(1000,5040)=40[/tex]
f)
[tex]9888=1\cdot6060+3828[/tex]
[tex]6060=1\cdot3828+2232[/tex]
[tex]3828=1\cdot2232+1596[/tex]
[tex]2232=1\cdot1596+636[/tex]
[tex]1596=2\cdot636+324[/tex]
[tex]636=1\cdot324+312[/tex]
[tex]324=1\cdot312+12[/tex]
[tex]312=26\cdot12+0[/tex]
[tex]\implies\mathrm{gcd}(9888,6060)=12[/tex]
The Euclidean Algorithm is used to find the greatest common divisor (GCD) of two numbers, this method has been applied to find the GCDs of multiple pairs of numbers.
Explanation:The Euclidean Algorithm is basically a method to find the greatest common divisor (GCD) of two numbers. It is based on the principle that the GCD of two numbers is the same as the GCD of the remainder when the larger number is divided by the smaller one.
gcd(12, 18): Using the Euclidean algorithm, 18 = 12*1 + 6. Now replace 18 with 12 and 12 with the remainder 6. So, 12 = 6*2 + 0. As we reached 0, our GCD is 6. gcd(111, 201): Apply the Euclidean algorithm, the GCD is 3. gcd(1001, 1331): The GCD is 11. gcd(12345, 54321): The GCD is 3. gcd(1000, 5040): The GCD is 40. gcd(9888, 6060): The GCD is 68. Learn more about Euclidean Algorithm here:
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find the surface area of a triangular prism that is 16 inches long 12 inches wide and 5 inches high
A. 714in2
B. 644 in2
C. 960 in2
D. 689 in2
Answers
hey can you please help me posted picture of question
Answers
One way to check if a function is inverse of the other is to take their composition. The composition of two inverse functions will always result in x.
[tex]F(x) = x-2 \\ \\ F^{-1}(x)=x+2 \\ \\ F(F^{-1}(x)) = F(x+2) \\ \\ F(F^{-1}(x)) = (x+2) -2 = x [/tex]
Thus x - 2 and x + 2 are the inverse of each other.
Mrs. Wilton is planning a rectangular flower box for her front window. She wants the flower box to hold exactly 16 cubic feet of soil. How many different flower boxes, all with the whole-number dimensions and a different-size base, will hold exactly 16 cubic feet of soil.
Answers
There are 3 different sizes of flower boxes that have different dimensions. Then the dimensions will be 2 by 1, 2by 3, and 2 by 4.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Mrs. Wilton is planning a rectangular flower box for her front window.
She wants the flower box to hold exactly 16 cubic feet of soil.
Let the height of the flower boxes will be 1 foot.
Then the number of the flower boxes with the whole dimensions and different-size base will be
Volume = Area × 1
Area = 16 square ft.
There are 3 different sizes of flower boxes that have different dimensions. Then the dimensions will be
Area = 16
Area = 2 + 6 + 8
Area = 2 × 1 + 3 × 2 + 2 × 4
Then the dimensions are 2 by 1, 2by 3, and 2 by 4.
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