The sequence below shows the number of trees that a nursery plants each year.2, 8, 32, 128 ...Let an represent the current term in the sequence and an-1 represent the previous term in thesequence. Which formula could be used to determine the number of trees the nursery will plantin year n?
Answers
According to the given sequence, the formula that could be used to determine the number of trees the nursery will plant in year n is [tex]a_{n}= 4a_{n-1}[/tex]. Thus, option (A) is correct.
The given sequence of the number of trees that a nursery plants each year is -
2, 8, 32, 128, .....
[tex]a_{n}[/tex] = The current term in the sequence
[tex]a_{n-1}[/tex] = The previous term in the sequence
We have to find out the formula that could be used to determine the number of trees that the nursery will plant in the year n.
From the sequence we can see that -
8 = 2*4
32 = 8*4
128 = 32*4
So, this can be said that the current term in the sequence ([tex]a_{n}[/tex]) is 4 times the previous term in the sequence ([tex]a_{n-1}[/tex]).
=> [tex]a_{n}= 4a_{n-1}[/tex]
Thus, according to the given sequence, the formula that could be used to determine the number of trees the nursery will plant in year n is
[tex]a_{n}= 4a_{n-1}[/tex]
Thus, option (A) is correct.
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Related Questions
2. The line plot shows the results of a survey about kitchen sinks. Kitchen Sink Survey + 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Capacity (gallons) Write a paragraph summarizing the data set. In your summary include the following A description of the data, including the unit of measure The number of data values The shape of the distribution The value of an appropriate measure of center The value of an appropriate measure of spread
Answers
Given: The information and line plot showing
..
From the plot we can write a table of values for the data
From the table we can get the mean
[tex]\begin{gathered} M_{\text{ean}}=\frac{\Sigma fx}{\Sigma f} \\ M_{\text{ean}}=\frac{(12\times0+13\times1+\ldots+24\times1+25\times0)}{1+2+4+5+...+1+0} \\ M_{\text{ean}}=\frac{354}{21} \\ M_{\text{ean}}=16.86 \\ M_{\text{ean}}\approx17 \end{gathered}[/tex]The standard deviation
[tex]\begin{gathered} S_{\text{tandard deviation}}=\sqrt[]{\frac{\Sigma f(x-\mu)^2}{\Sigma f}} \\ S_{\text{tandard deviation}}=\sqrt[]{\frac{0(12-17)^2+1(13-17)^2+\cdots+1(24-17)^2}{21}} \\ S_{\text{tandard deviation}}=\sqrt[]{\frac{150.571}{21}} \\ S_{\text{tandard deviation}}=2.68 \end{gathered}[/tex]ANSWER SUMMARY
It can be observed that the capacity of the kitchen sink ranges from 12 gallons to 25 gallons. There are 21 kitchen sink with different capacity in gallons. The shape of the distribution is skewed right with an appropriate measure of centre (that is the mean) as 17 gallons. The measure of spread including the range (between 13 gallons to 24 gallons) is 11 gallons, the median is 16 gallons sink and the standard deviation is 2.68 gallons
Answer:
poopsicle
Step-by-step explanation:
A triangle has side lengths of 6, 8, and 10Is it a right triangle?
Answers
To be a right triangle it must comply with the following:
[tex]a^2+b^2=c^2[/tex]Where:
a = 6
b = 8
c = 10
So:
[tex]\begin{gathered} 6^2+8^2=10^2 \\ 36+64=100 \\ 100=100 \end{gathered}[/tex]This means that it is a right triangle.
Answer: Yes, It is a right triangle
Find the measure of chord EF. Enter your numerical answer.
Answers
Notice that each chord (CD and EF) defines a segment in the circle whose arc length has the same value. Thus, the length of both chords has to be the same; then,
[tex]\begin{gathered} CD=EF \\ \Rightarrow9x-1=41-5x \\ \Rightarrow14x=42 \\ \Rightarrow x=3 \end{gathered}[/tex]Finding the length of EF,
[tex]\begin{gathered} x=3 \\ \Rightarrow EF=41-5*3=26 \end{gathered}[/tex]Therefore, the answer is 26
Hello, I need help on how to read attached graph based on the questions.Thank you
Answers
As can be seen in the above graph:
(a) g(x) > 0 in the interval: (-4, -2) U (0, 2)
(b) g(x) < 0 in the interval: (-2, 0)
(c) g(x) = 0 at the next x-values: -4, -2, 0, 2
Graphically, the derivative of a function evaluated at a point is seen as the slope of the tangent line that passes through that point of the function.
Then, if the slope is positive, the derivative is positive, if the slope is zero (a horizontal line), the derivative is zero, and if the slope is negative, the derivative is negative.
In the next graph, we can see some of these slopes:
Therefore, the intervals where g'(x) is positive, negative or zero are:
(d) g'(x) > 0 in the interval: (-4, -3) U (-1, 1)
(e) g'(x) < 0 in the interval: (-3, -1) U (1, 2)
(f) g'(x) = 0 at the next x-values: -3, -1, 1
Find the lowest multiple of each group.show the factors you used.1. 5,20,28
Answers
Given the following question:
1, 5, 20, 28
1 = 1
5 = 5
20 = 2 × 2 × 5
28 = 2 × 2 × 7
2 × 2 × 5 × 7
2 × 2 = 4
4 × 5 = 20
20 × 7 = 140
LmM = 140
what's false 16 / 10 equal 25 / 40
Answers
10/16 = 25/40
Divide each
0.625 = 0.625
Second option:
15/60= 35/140
0.25 = 0.25
Third option
24/36=50/75
0.6666= 0.6666
Fourth option
14/35=35/70
0.4=0.5
FALSE
special right triangle find the value of the variables answer must be in simplest radical form
Answers
Here, we have a special right triangle.
Let's solve for the variables, x and y.
Given:
common side = x
Hypotenuse of the larger triangle = 8
Let's find x using trigonometric ratio.
We have:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \\ \sin 30=\frac{x}{8} \\ \\ x=8\sin 30 \\ \\ x=8(0.5) \\ \\ x=4 \end{gathered}[/tex]To solve for y, we have:
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \\ \tan 60=\frac{x}{y} \\ \\ \tan 60=\frac{4}{y} \\ \\ \text{Multiply both sid}es\text{ by y:} \\ y\tan 60=\frac{4}{y}\ast y \\ \\ y\tan 60=4 \\ \\ \text{Divide both sides by tan60} \\ \\ \frac{y\tan 60}{\tan 60}=\frac{4}{\tan60} \\ \\ \\ y=\frac{4}{\tan 60} \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} y=\frac{4}{\sqrt[]{3}} \\ \\ \end{gathered}[/tex]Multiply both numerator and denominator by √3:
[tex]\begin{gathered} y=\frac{4}{\sqrt[]{3}}\ast\frac{\sqrt[]{3}}{\sqrt[]{3}} \\ \\ y=\frac{4\sqrt[]{3}}{3} \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} x=4 \\ \\ y=\frac{4\sqrt[]{3}}{3} \end{gathered}[/tex]Disprove each statement , and then find all values of a and b for which the statement happens to be true . Explain your results If f(x) = x ^ (1/3) does f(a + b) = f(a) + f(b) ?
Answers
We are given the following function:
[tex]f(x)=x^{\frac{1}{3}}[/tex]To determine the value of f(a) we will replace the value of "x" for "a" in the function:
[tex]f(a)=a^{\frac{1}{3}}[/tex]Using the same procedure we determine the value of f(b):
[tex]f(b)=b^{\frac{1}{3}}[/tex]Now we determine the value of f(a+b):
[tex]f(a+b)=(a+b)^{\frac{1}{3}}[/tex]We are asked about the equatity:
[tex]f\mleft(a+b\mright)=f\mleft(a\mright)+f\mleft(b\mright)[/tex]replacing the values we get:
[tex](a+b)^{\frac{1}{3}}=a^{\frac{1}{3}}+b^{\frac{1}{3}}[/tex]We get an equality that is not true for any value of "a" and "b" since the left expression can't be converted into the right expression for any "a" or "b". The statement is false.
The statement could be right if "a" or "b" equal zero, for example, let's take a = 0, we get:
[tex](0+b)^{\frac{1}{3}}=(0)^{\frac{1}{3}}+b^{\frac{1}{3}}[/tex]Simplifying:
[tex]b^{\frac{1}{3}}=b^{\frac{1}{3}}[/tex]Which is a true statement. .
A city is built on the banks of a river and some islands in the river. The map below shows the bridges connecting the various land masses. Draw a graph that models the connecting relationships in the map below. The vertices represent the land masses and the edges represent bridges connecting them. Is it possible to find a circuit through the city that uses each bridge once? If so, enter the sequence of land masses(vertices) visited, for example ABDEA. If it is not possible, enter DNE. Use Fleury's algorithm and show all work and the graph as demonstrated in class.
Answers
We can graph the model as:
The Fleury's algorithm start with any vertex, and then select an edge that start from this vertex and go to another vertex. Then we pick another edge that starts from the last vertex, and so on. The condition is that all the vertices in the graph are always connected to each other: that is, there is always a path to conect any two vertices.
We start with A.
We can go to C, then B, then D, then E, then A.
After this part, we are left with these edges:
As the last vertex was A, we start from there.
We go to D, then to B, then to C, then to A again and we end in E.
We are never able to go back to the vertex we start (A), so there is no possible sequence.
Answer: DNE
Please help me on my hw I need help on #2
Answers
Given:
The number is,
[tex]5.232323\ldots\text{.}[/tex]To express the given number into fraction . it means in the form,
[tex]\frac{a}{b}[/tex]We can express the given number into geometric series as,
[tex]\begin{gathered} 5.232323\ldots=5+\frac{23}{100}+\frac{23}{10000}+\frac{23}{100000}+\text{.}\ldots\ldots \\ =5+\frac{23}{100}+23(\frac{1}{100})^2+23(\frac{1}{100})^3+\text{.}\ldots\ldots\text{.}\mathrm{}(1) \\ \frac{23}{100}+23(\frac{1}{100})^2+23(\frac{1}{100})^3+\text{.}\ldots=-23+\sum ^{\infty}_{n\mathop=1}23(\frac{1}{100})^{n-1} \\ =-23+\frac{23}{1-\frac{1}{100}} \\ =-23+\frac{23(100)}{99} \\ =-23+\frac{2300}{99} \\ =\frac{-2277+2300}{99} \\ =\frac{23}{99} \end{gathered}[/tex]Now, equation (1) becomes,
[tex]5+\frac{23}{99}=\frac{518}{99}[/tex]Answer:
[tex]\frac{518}{99}[/tex]Sophie put $3330 in a savings account at a simple interest rate of 7.4% per year.
Adam put $2795 in a savings account at a simple interest rate of 8.1% per year.
Who will have earned more interest after 5 years? How much more?
Answers
Sophie earned more simple interest of $100.
Simple interest is a short and easy technique for calculating the interest price on a mortgage. simple interest is decided with the aid of multiplying each day's interest charge via the most important by the variety of days that elapse among bills.
To calculate Simple interest, multiply the main quantity by using the interest charge and the time. The method written out is Simple interest = principle x interest price x Time." This equation is the most effective way of calculating interest.
Calculation:-
For Sophie
SI = PRT/100
= ($3330 × 7.4 × 5 ) /100
= $1232
For Adam
SI = PRT/100
= ($2795 × 8.1 × 5 ) /100
= $1132
Therefore, Sophie earned more interest of $1232 - $1132 = $100
simple interest is based on the most important amount of a loan or the primary deposit in a financial savings account. simple interest doesn't compound, and because of this a creditor will most effectively pay interest on the foremost amount, and a borrower might in no way have to pay extra interest at the previously amassed interest.
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The Young family has collected movies. They have 18 action movies. 16 comedies. 8 mysteries, and 12 dramas. How many movies do they have in total?
Answers
The family has 54 movies in total
Explanation:The movies the family have in total is the addition of the number of movies in each category:
18 + 16 + 8 + 12
= 54
Which of the following is an arithmetic sequence? A. 1, 0, 1, 0, 1, 0, ...B. 800, 200, 50, ...C. 10, 7, 4, 1, -2, ...D. 1, 3, 9, 27,...
Answers
Given:
The sequences in options.
Required:
Which of the sequence is an arithmetic sequence.
Explanation:
The arithmetic sequence has a common ration, that is equal for every pair of number
[tex]d=a_2-a_1,d=a_3-a_2[/tex]Now, in option c
[tex]\begin{gathered} d=7-10=-3 \\ d=4-7=-3 \\ d=1-4=-3 \end{gathered}[/tex]So, common ratio is -3 and hence sequence is arithmetic sequence.
Answer:
So, option c is correct.
jamial walked 210 miles he has walked 70%of the way how many more miles does he have left
Answers
Given that: jamial walked 210 miles he has walked 70%of the way
So 70% of the total walked he covered
[tex]210\times\frac{70}{100}=147\text{ miles}[/tex]He covered 147 miles
The remaining distance he have to be cover :
[tex]210-147=63\text{ miles}[/tex]> Next question Get a similar question You can retry this a 8.1 ft 9.7 10.6 Name the Shape: • triangle trapezoid kite parallelogram
Answers
The given figure is has three sides and three vertices : Triangle
In the given triangle, height = 9.7 ft, base = 8.1 ft,
Area of triangle = 1/2 x Base x Height
Area of traingle = 1/2 x 8.1 x 9.7
Area of traingle = 39.28 ft²
Area of the given figure = 39.28 ft²
Every week a company provides fruit for its office employees. They canchoose from among five kinds of fruit. What is the probability distribution forthe 30 pieces of fruit, in the order listed?FruitNumber ofpiecesProbabiltyApples Bananas62
Answers
Answer:
D.
Explanation:
We were given that:
A company provides fruit for its employees
The employees can pick among five kinds of fruit
The fruits obtained this week is:
Apples = 6 pieces
Bananas =2 pieces
Lemons = 10 pieces
Oranges = 8 pieces
Pears = 4 pieces
Total = 30 pieces
The probability distribution for this is given by:
[tex]\begin{gathered} P(apples)=\frac{Number\text{ of apples}}{Total}=\frac{6}{30}=\frac{1}{5} \\ P(apples)=\frac{1}{5} \\ \\ P(bananas)=\frac{Number\text{ of bananas}}{Total}=\frac{2}{30}=\frac{1}{15} \\ P(bananas)=\frac{1}{15} \\ \\ P(lemons)=\frac{Number\text{ of lemons}}{Total}=\frac{10}{30}=\frac{1}{3} \\ P(lemons)=\frac{1}{3} \\ \\ P(oranges)=\frac{Number\text{ of oranges}}{Total}=\frac{8}{30}=\frac{4}{15} \\ \\ P(pears)=\frac{Number\text{ of pears}}{Total}=\frac{4}{30}=\frac{2}{15} \\ P(pears)=\frac{2}{15} \\ \\ \therefore P=\frac{1}{5},\frac{1}{15},\frac{1}{3},\frac{4}{15},\frac{2}{15} \end{gathered}[/tex]Therefore, the answer is D
if f(x) = 13 when f(x)=5x -√8, find x.
Answers
Given that we have the function f(x) = 5x-√8, it is equal to 13 at some value of x. This relation can be written in equation as
[tex]5x-\sqrt[]{8}=13[/tex]Move √8 to the other side of the equation so that only the term with x will be left on the left-hand side. We have
[tex]5x=13+\sqrt[]{8}[/tex]Divide both sides by 5, we get
[tex]\begin{gathered} \frac{5x}{5}=\frac{13+\sqrt[]{8}}{5} \\ x=\frac{13+\sqrt[]{8}}{5} \end{gathered}[/tex]The square root of 8 can be further simplified as
[tex]\sqrt[]{8}=\sqrt[]{4\cdot2}=2\sqrt[]{2}[/tex]Hence, the value of x can also be rewritten as
[tex]x=\frac{13+2\sqrt[]{2}}{5}[/tex]Thus, the value of x to satisfy f(x) = 13 when f(x)=5x -√8 is
[tex]x=\frac{13+\sqrt[]{8}}{5}=\frac{13+2\sqrt[]{2}}{5}=\frac{13}{5}+\frac{2\sqrt[]{2}}{5}[/tex]Find 3 ratios that are equivalent to the given ratio 6:13
Answers
In order to find equivalent ratios, we can multiply the numerator and denominator by the same value.
For example, let's multiply by 2, by 3 and by 4:
[tex]\begin{gathered} 6:13\\ \\ =6\cdot2:13\cdot2\\ \\ =12:26\\ \\ \\ \\ 6:13\\ \\ =6\cdot3:13\cdot3\\ \\ =18:39\\ \\ \\ \\ 6:13\\ \\ =6\cdot4:13\cdot4\\ \\ =24:52 \end{gathered}[/tex]Therefore the equivalent ratios are 12:26, 18:39 and 24:52..
What is the volume of a sphere with a diameter of 7.5 cm, rounded to the nearesttenth of a cubic centimeter?
Answers
Find the value of x and the value of y.A. x = 15, y = 10sqrt3B. r = 20, y = 10sqrt3C. r = 20sqrt3, y = 5sqrt3D. x=15, y = 5sqrt3
Answers
To find the values of x and y it is necessary to use trigonometric ratios.
To find x it is necessary to use sine. Sine is the ratio between the opposite side to a given angle and the hypotenuse. In this case, the given angle is 60°, the opposite side is x and the hypotenuse is 10 sqrt 3. Use this information to find x:
[tex]\begin{gathered} \sin 60=\frac{x}{10\sqrt[]{3}} \\ 10\sqrt[]{3}\cdot\sin 60=x \\ x=15 \end{gathered}[/tex]To find y it is necessary to use cosine. It is the ratio between the adjacent side to a given angle and the hypotenuse. The given angle is 60°, the adjacent side is y and the hypotenuse is 10 sqrt 3. Follow the same procedure as with sine:
[tex]\begin{gathered} \cos 60=\frac{y}{10\sqrt[]{3}} \\ 10\sqrt[]{3}\cdot\cos 60=y \\ y=5\sqrt[]{3} \end{gathered}[/tex]The correct answer is D. x=15, y=5sqrt3.
In the figure below, AB is an angle bisector. What is the value of x? Show and explain work
Answers
Since AB is the angle bisector:
[tex]\begin{gathered} m\angle CAB=m\angle DAB \\ so\colon \\ 33=4x+1 \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 4x=33-1 \\ 4x=32 \\ x=\frac{32}{4} \\ x=8 \end{gathered}[/tex]Answer:
x = 8
Given the parent graph f(x)=e^x, which of the following functions has a graph that has been translated 3 to the left and reflected over the x-axis?following functions given to pick from are g(x)=−e^x+3g of x is equal to negative e raised to the x plus 3 powerg(x)=e^−(x+3)g of x is equal to e raised to the negative open paren x plus 3 close paren powerg(x)=e^3−xg of x is equal to e raised to the 3 minus x powerg(x)=−e^3−x
Answers
Given the parent function:
[tex]f(x)=e^x[/tex]Let's determine the function that has a graph which has been translated 3 units to the left and reflected over the x-axis.
To find the function, apply the transformation rules for functions.
• After a translation 3 units to the left, we have:
[tex]g(x)=e^{x+3}[/tex]• Followed by a reflection over the x-axis:
[tex]g(x)=-e^{x+3}[/tex]Therefore, the function that has a graph which has been translated 3 units to the left and reflected over the x-axis is:
[tex]g(x)=-e^{x+3}[/tex]The grade a student makes on a test varies directly with the amount of time the student spends studying. Suppose a student spends 5 hours studying and makes a grade of 89 on the test. What is an equation that relates the grade earned on a test, g, with the amount of time spent studying, t. in hours?
Answers
It is given that,
A student spends 5 hours studying and makes a grade of 89 on the test.
To write an equation that relates the grade earned on a test in t hours.
Let us take,
For 5 hours, the grade is 89
For 1 hour, the grade will be,
[tex]\frac{89}{5}=17.8[/tex]Then for t hours, the general equation will be,
[tex]g=17.8t[/tex]Hence, the answer is g=17.8t.
write an equation to find the area of each figure. Then determine the area of the composite figure. When pi is used, the area will be an approximation.
Answers
ANSWER:
The area of the composite figure is 34 m^2
STEP-BY-STEP EXPLANATION:
To calculate the area of the complete figure, you have to separate the figure in two ways, just like this:
Figure A is a square and we calculate the area like this:
[tex]\begin{gathered} A_A=l^2 \\ A_A=4^2=16 \end{gathered}[/tex]Figure B is a trapezoid and we calculate the area like this:
[tex]\begin{gathered} A_B=\frac{b_1+b_2_{}}{2}\cdot h \\ A_B=\frac{4+8}{2}\cdot3 \\ A_B=18 \end{gathered}[/tex]Now the total area is the sum of both parts:
[tex]\begin{gathered} A_T=A_A+A_B \\ A_T=16+18 \\ A_T=34 \end{gathered}[/tex]Solve x2-12x + 11 = 0 by completing the square.
Answers
Given: A quadratic equation-
[tex]x^2-12x+11=0[/tex]Required: To solve the equation by completing the square method.
Explanation: The general form of a quadratic equation is-
[tex]ax^2+bx+c=0[/tex]The given equation can be solved by the method of completing the square by adding and subtracting the term-
[tex](\frac{b}{2})^2[/tex]Hence, the given equation can be written as-
[tex]x^2-12x+36-36+11=0[/tex]Now solving further as-
[tex]\begin{gathered} x^2-2\times6\times x+6^2-25=0 \\ (x-6)^2=25 \\ (x-6)=\sqrt{25} \\ (x-6)=\pm5 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} x-6=5\text{ or } \\ x-6=-5 \end{gathered}[/tex]This gives-
[tex]\begin{gathered} x=11\text{ or} \\ x=1 \end{gathered}[/tex]Final Answer: The solution to the equation is x=11 or x=1.
13. If a trapezoid has base lengths of 18and 40, what is the length of themedian?I●
Answers
The median of a trapezoid is a straight line that goes from the midpoint of one of the sides to the midpoint of the opposite side and is parallel to both bases.
Its length is the average of the lengths of both bases:
[tex]median=\frac{(upper.base+lower.base)}{2}[/tex]One of the bases of the trapezoid has a length of 18 units and the other base has a length of 40 units. Average both bases to determine the length of the median:
[tex]\begin{gathered} median=\frac{18+40}{2} \\ median=\frac{58}{2} \\ median=29 \end{gathered}[/tex]The length of the median is 29 units.
The number of protozoa in a biology laboratory experiment is given by the polynomial functionp(t) = 0.02t^4 + 0.3t^3 + 7t^2, where p is the number of protozoa after t hours.Step 2 of 2: How many protozoa are present after 2 days? Round your answer to the nearest wholenumber.
Answers
In order to calculate the number of protozoa after 2 days (that is, 48 hours), let's use t = 48 in the function p(t) and calculate its value:
[tex]\begin{gathered} p(t)+0.02t^4+0.3t^3+7t^2 \\ p(48)=0.02\cdot48^4+0.3\cdot48^3+7\cdot48^2 \\ p(48)=0.02\cdot5308416+0.3\cdot110592+7\cdot2304 \\ p(48)=106168.32+33177.6+16128 \\ p(48)=155473.92 \end{gathered}[/tex]Rounding to the nearest whole number, the number of protozoa is 155474.
How many square feet of outdoor carpet are needed for this hole
Answers
The area of a rectangle is:
[tex]Ar=l\cdot h[/tex]Where:
Ar = area of the rectangle
l = lenght
w = width
And the area of a triangle is:
[tex]At=\frac{1}{2}\cdot b\cdot h[/tex]Where:
At = area of the triangle
b = base
h = height
To solve this problem divide the figure into triangles and rectangles, according to the figure below.
And the square feed (A) needed will be:
A = A1 - A2 + A3 + A4 + A5
Step 01: Calculate A1.
Figure 1 is a rectangle with sides 5 and 6 ft.
[tex]\begin{gathered} A1=5\cdot6 \\ A1=30ft^2 \end{gathered}[/tex]Step 02: Calculate A2.
Figure2 is a rectangle with sides 2 and 3 ft.
[tex]\begin{gathered} A2=2\cdot6 \\ A2=6ft^2 \end{gathered}[/tex]Step 03: Calculate A3.
Figure 3 is a triangle with base 4 (12 - 6 - 2 = 4) and height 3 ft.
[tex]\begin{gathered} A3=\frac{4\cdot3}{2} \\ A3=\frac{12}{2} \\ A3=6ft^2 \end{gathered}[/tex]Step 04: Calculate A4.
Figure 4 is a rectangle with sides 4 (12 - 6 - 2 = 4) and 2 (5 - 3 = 2) ft.
[tex]\begin{gathered} A4=4\cdot2 \\ A4=8ft^2 \end{gathered}[/tex]Step 05: Calculate A5.
Figure 5 is a rectangle with sides 2 and 5 ft.
[tex]\begin{gathered} A4=2\cdot5 \\ A4=10ft^2 \end{gathered}[/tex]Step 06: Find the area of the figure.
A = A1 - A2 + A3 + A4 + A5.
[tex]\begin{gathered} A=30-6+6+8+10 \\ A=48ft^2 \end{gathered}[/tex]Answer: 48 ft² is needed for this hole.
three points a b and c exist in space such that b is between a and C it is known that AB = 7 , BC= 4 and AC = 9 . Ar epoints a b and c Collinear? give a written explanation supported by mathematical evidence for your answer.
Answers
Points are collinear if they are in the same line.
So:
AB+BC = AC
Replacing with the values given:
7+4 = 9
11 =9 False
A,b, and c aren't collinear.
A straw is placed in a rectangular box that is 6 inches by 4 inches by 8 inches, as shown. If the straw fits exactly in the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
Answers
Explanation
you can solve this by using the distance between 2 points formula
[tex]D_{ab}=\sqrt[]{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2}[/tex]then
Step 1
Let
P1(0,0,0)
P2(6,4,8)
now , replace
[tex]\begin{gathered} D_{ab}=\sqrt[]{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2} \\ D_{ab}=\sqrt[]{(6-0)^2+(4-0)^2+(8-0)^2} \\ D_{ab}=\sqrt[]{(6)^2+(4)^2+(8)^2} \\ D_{ab}=\sqrt[]{36^{}+16+64} \\ D_{ab}=\sqrt[]{116} \\ D_{ab}=\sqrt[]{4\cdot29} \\ D_{ab}=2\sqrt[]{29} \end{gathered}[/tex]I hope this helps you