1. what is the area of the board shown on the scale drawing? explain how you found the area.2. how can Adam use the scale factor to find the area of the actual electronics board? remember, he uses a different method than Jason.3. what is the area of the actual electronics board?
Answers
Answer:
1. 1800 square cm.
2. See below
3. 45000 square cm.
Explanation:
Part 1
The dimensions of the drawing are 36cm by 50cm.
[tex]\begin{gathered} \text{The area of the board}=36\times50 \\ =1800\operatorname{cm}^2 \end{gathered}[/tex]Part 2
Given a scale factor, k
If the area of the scale drawing is A; then we can find the area of the actual board by multiplying the area of the scale drawing by the square of k.
Part 3
[tex]\begin{gathered} \text{Area of the scale drawing}=1800\operatorname{cm}^2 \\ \text{Scale Factor,k=5} \end{gathered}[/tex]Therefore, the area of the actual drawing will be:
[tex]\begin{gathered} 1800\times5^2 \\ =45,000\operatorname{cm}^2 \end{gathered}[/tex]Related Questions
X 즈 - + 3 = 15 -4someone help me confused
Answers
First we have to transfer the number 3 the other side of equal sign as follows,
[tex]\begin{gathered} \frac{x}{-4}=15-3 \\ \frac{x}{-4}=12 \end{gathered}[/tex]Now, we need to transfer (-4) to the other side of the equal side by multiplying with the number 12.
[tex]\begin{gathered} \frac{x}{-4}=12 \\ x=12\ast(-4) \\ x=-48 \end{gathered}[/tex]Thus, the answer of the x is (-48).
Colton’s gym charges an initiation fee of $40 plus a monthly fee of $50 . Which of the following he equations below shows the cost c of joining the gym for m months ? A . C = 50 + 40mB . C = 40 + 50mC. C = 40 - 50 m
Answers
given that Colton gym charges initial fee of $40
there is an addiontional fee of $50
C is the cost of joining the gym
m is the number of months
so the equation that can show the cost of joining the gym in m month is:
$40 which is the initial feel been added to $50 the additional charge multiply by m the number of months.
therefore the equation is:
C = 40 + 50m
so the correct option is B
4. A bookstore owner ordered 4032 books. The books were sent in 9 boxes. Each box hadthe same number of books. How many books were in each box?
Answers
448 books in each box
Number of books: 4032
Number of boxes: 9
Since each box had the same number of books, divide the number of books by the number of boxes.
4032/9 = 448
A circle has a circumference of 43.96 inches. What is the area?
Answers
Solution:
Given that the circumference of the circle is
[tex]C=43.96in[/tex]Step 1:
Calculate the radius of the circle
To calculate the radius of the circle, we will use the formula below
[tex]\begin{gathered} C=2\pi r \\ \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} C=2\pi r \\ 43.96=2\times\pi\times r \\ 43.96=6.28r \\ \text{divide both sides by 6.28} \\ \frac{6.28r}{6.28}=\frac{43.96}{6.28} \\ r=7in \end{gathered}[/tex]Step 2:
Calculate the area of the circle using the formula below
[tex]\begin{gathered} A=\pi r^2 \\ \text{Where,} \\ \pi \\ r=7in \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A=\pi r^2 \\ A=\pi\times7^2 \\ A=\pi\times49 \\ A=153.94in^2 \end{gathered}[/tex]Hence,
The Area of the circle is = 153.94 in²
Explain why (-1)^n = 1 for any even number n.How is this possible? I thought it would equal -1. Does that mean the answer is "not possible"?
Answers
The expression (-1)^n means the number -1 multiplies itself n times.
So for example if n = 2, we have that:
[tex](-1)^2=(-1)\cdot(-1)=1[/tex]For n = 3, we have:
[tex](-1)^3=(-1)\cdot(-1)\cdot(-1)=1\cdot(-1)=-1[/tex]For n = 4:
[tex](-1)^4=(-1)^2\cdot(-1)^2=1\cdot1=1[/tex]We can see that the result alternates from -1 and 1, and when n is odd, the result is -1, and when n is even, the result is 1.
So for any even number n, the result will be 1.
A triangle has angle measurements of 15°, 90°, and 75°. What kind of triangle is it?
Answers
The triangle has one angle of 90 degrees, so it is a rigth triangle.
As the other two angles are different between them, the triangle is also scalene (all sides are different)
.
f(t) = 2t-3g(t) = t^3 + tFind (f •g)(0)
Answers
1) Given those functions, f(t) and g(t) let's find the composite function, for (f(g(0)) or (f •g)(0)
2) Let's pick the function f(t)
f(t) = 2t-3
And plug into that g(t), like this
f(g(t))= 2(t³ +t) -3
3) Finally, let's plug the value 0 into that composite function:
f(g(t))= 2(t³ +t) -3
f(g(0))= 2(0³ +0) -3 ⇒f(g(0))= 2(0) +3
f(g(0))= 3
(f •g)(0)=3
what is the least common denominator for the two fractions 2 / 5 3 / 2
Answers
The multiples of the denominator of 2/5 is,
5,10,15,20,25....
The multiples of the denominator of 3/2 is,
2,4,6,8,10.....
Thus, the required least common denominator is 10.
the perimeter of the rectangle belowis 112 units. Find the value of y
Answers
Question:
Solution:
The perimeter of a rectangle is the sum of the lengths of its sides. According to this, we get the following equation:
[tex]P\text{ = 2(4y+2)+2(5y)}[/tex]since P = 112, we obtain:
[tex]112\text{ = 2(4y+2)+2(5y)}[/tex]Applying the distributive property, we obtain:
[tex]112\text{ = 8y+4+10y}[/tex]this is equivalent to:
[tex]18y\text{ = 112-4}[/tex]that is:
[tex]18\text{ y = 108}[/tex]solving for y, we get:
[tex]y\text{ = }\frac{108}{18}=6[/tex]that is:
[tex]y\text{ = 6}[/tex]so that, we can conclude that the correct answer is:
[tex]6[/tex]Isabella earns interest at an annual rate of 10% compounded annually on her savings account. She deposits $2,000 into her account. What is the total amount of money Isabella will have in her account after 2 years? (Use the formula to calculate compound interest: A = P(1 + r)')
Answers
As it indicates on the text, compound interest is represented by the following expression:
[tex]\begin{gathered} A=P(1+r)^t \\ \text{where,} \\ A=\text{ Amount} \\ P=\text{ Principal} \\ r=\text{ interest rate in decimal form} \\ t=\text{ time} \end{gathered}[/tex]Then, substituing the information given:
[tex]\begin{gathered} A=2,000(1+0.1)^2 \\ A=2,420 \end{gathered}[/tex]Isabella will have $2,420 after 2 years.
Debra the trainer has two solo workout plans that she offers her clients: plan A and plan B. Each client does either one or the other (not both). On Wednesday there were 5 clients who did plan A and 3 who did plan B. On Thursday there were 7 clients who did plan A and 9 who did plan B. Debra trained her Wednesday clients for a total of 6 hours and her Thursday clients for a total of 12 hours. How long does each of the workout plans last?
Answers
The solo plans Debra offers her clients are plan A and plan B. Each client can only do one plan .
According to the question the plan only ran on wednesday and thursday.
Wednesday = plan A has 5 client and plan B has 3 clients.
Thursday = plan A has 7 client and plan B has 9 clients.
On wednesday she trained her client for 6 hours.
On thursday she trained her client for 12 hours.
let
x = hour of plan A workout for each client
y = hour of plan B workout for each client
[tex]\begin{gathered} 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}\mathrm{}(i) \\ 7x\text{ + 9y = 12}\ldots\ldots\ldots\text{.(2)} \\ 3y\text{ = 6 - 5x} \\ y\text{ = }\frac{6}{3}\text{ - }\frac{5}{3}x \\ y\text{ = 2 - }\frac{5}{3}x \\ 7x\text{ + 9(2 - }\frac{5}{3}x\text{) = 12} \\ 7x\text{ + 18 - }\frac{45}{3}x\text{ = 12} \\ 7x\text{ + 18 - }15x\text{ = 12} \\ -8x\text{ = 12 - 18} \\ -8x\text{ = - 6} \\ x\text{ = }\frac{6}{8} \\ x\text{ = }\frac{3}{4} \\ 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}(i) \\ 5(\frac{3}{4})\text{ + 3y = 6} \\ \frac{15}{4}\text{ + 3y = 6} \\ 3y\text{ = 6 - }\frac{15}{4} \\ 3y\text{ = }\frac{24-15}{4} \\ 3y\text{ = }\frac{9}{4} \\ y\text{ = }\frac{9}{4}\text{ }\times\text{ }\frac{1}{3} \\ y\text{ = }\frac{9}{12} \\ y\text{ = }\frac{3}{4} \end{gathered}[/tex]on wednesday plan A lasted for 5 * 3/4 = 15/4 hrs and plan B lasted for 3 * 3/4 = 9/4 hrs
On thursday plan A lasted for 7* 3/4 = 21/4 hrs and plan B lasted for 9 * 3/4 = 27/4 hrs
Each of the work out lasted for 3/4 hrs = 0.75 hrs
1) Circle the tables that represent y as a function of x.хХ-31X-10у-5515-3y3608-2-4- 1-2-2-5- 1290у-1-1- 1-11-2-52-5
Answers
The answer is the last table
The answer is the last table
Complete the sentence. The amount of time it takes to complete a puzzle is most likely to be a function of the .
Answers
"The ammount of time it takes to complete a puzzle is most likely to be a function of the number of pieces in the puzzle."
U.S. Customary unit conversion with mixed number values: One...Charlie bought 5 feet of fabric. How much is this in yards?Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.0OlaDOinftyd목x 5?Please help
Answers
Converting feet into yards.
Recall that one yard =3 feet
[tex]1\text{ yard=3 f}eet[/tex]Multiply by 5/3 on both sides, we get
[tex]1\times\frac{5}{3}\text{ yard=3 }\times\frac{5}{3}\text{f}eet[/tex][tex]\frac{5}{3}\text{ yard=}5\text{f}eet[/tex][tex]\text{Use }\frac{5}{3}=1\frac{2}{3}[/tex][tex]1\frac{2}{3}\text{ yard=}5\text{f}eet[/tex]The answer is
[tex]1\frac{2}{3}\text{ yards}[/tex]Which has quotient of 0.5
Answers
An example of a fraction that has a quotient of 0.5 is 2/4.
What is a quotient?A quotient is a quantity created by the division of two numbers in mathematics. The quotient is widely used in mathematics and is also known as the integer component of a division, a fraction, or a ratio.
In mathematics, the quotient is the number that is produced when two integers are divided. It is essentially the outcome of the division procedure. In arithmetic division, four primary terms are used: divisor, dividend, quotient, and remainder.
In this case, 2/4 = 0.5. This is the quotient.
Note that the information is incomplete and.an overview was given.
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64, 57, 50, 43, ... 50th term
Answers
For the next series, we will calculate its expression
[tex]v(n)=64-7(n-1)[/tex]For n = 1
v = 64
For n = 2
v = 57
For n = 3
v = 50
For n = 50
v = -279
University DataReceiving Not ReceivingFinancial Aid Financial AidTotalUndergraduates422238988120Graduates18797312610Total6101462910730If a student is selected at random, what is theprobability that the student receives aid and is agraduate (rounded to the nearest percent)? [? ]%
Answers
Pls. Help me ;( thx ur the best
Answers
Answer:
**NEED USEFUL ANSWER ASAP, H.W QUESTION**
Given that hotter blackbodies produce more energy than cooler blackbodies, why do cooler red giants have much higher luminosities than much hotter white dwarfs?
Step-by-step explanation:
46) The hundreds digit of the smallest six-digit number divisible by 12, 13,
14, 15 and 16 is
Answers
Answer: 2
Step-by-step explanation:
[tex]12=2^2 \times 3\\\\13=13\\\\14=2 \times 7\\\\15=3 \times 5\\\\16 =2^4\\\\\therefore \lcm(12, 13, 14, 15, 16)=2^4 \times 3 \times 5 \times 7 \times 13=21840[/tex]
Multiplying this by 5 to make it the smallest possible six-digit number, we get 109200, meaning the hundreds digit is 2.
Place the numbers in the table to show them in order from least to greatest
Answers
Given the following question:
[tex]\begin{gathered} -\frac{3}{8},\frac{1}{8},-\frac{1}{4},-\frac{3}{5},\frac{1}{5} \\ \text{ Negatives go first} \\ -\frac{3}{8}>-\frac{3}{5}>-\frac{1}{4} \\ \frac{1}{5}>\frac{1}{8} \\ -\frac{3}{5}<\frac{-3}{8}<\frac{-1}{4}<\frac{1}{8}<\frac{1}{5} \end{gathered}[/tex]What is the inverse of the given relation?y = 3x + 12I need to understand the step by step breakdown for how to solve this problem.
Answers
Given the function y, we want to find the inverse function y^-1.
Then, replace every x with a y and every y with an x. It yields,
[tex]x=3y+12[/tex]now, solve the equation for y. So, by subtracting 12 to both sides, we have
[tex]x-12=3y[/tex]or equivalently,
[tex]3y=x-12[/tex]and, by dividing both sides by 3, we obtain
[tex]y=\frac{x-12}{3}[/tex]Finally, replace y with y^-1. Then, the inverse function is given by:
[tex]y^{-1}=\frac{x-12}{3}[/tex]What is eight plus four minus three equal?
Answers
Answer:
9
Step-by-step explanation:
8+4-3=9
im pretty sure 8+4-3=9
question 1 A new streaming company charges a rate of $5.99 per month. in order to generate some additional revenue upfront the company is offering a VIP rate of only $3.49 Per month to any subscriber who purchases a VIP pass for one time fee of $21 set up in solving any qualities to determine how many months it would take for subscriber to save money by purchasing the VIP pass
Answers
21 + 3.49x < 5.99x
x > 8.4
Explanations:The normal monthly rate = $5.99
The VIP monthly rate = $3.49
The one time VIP fee = $21
Let the number of months be x
At normal rate, the total charge for x months = 5.99x
For the VIP:
The total charge for x months = 21 + 3.49x
For a subscriber to save money by purchasing the VIP pass, it means the total charge for the VIP must be less than the total charge for the normal subscribers5.99x
Therefore, the inequality to determine how many months it will take for a subscriber to save money by purchasing the VIP pass is:
21 + 3.49x < 5.99x
Solve the inequality above:
21 < 5.99x - 3.49x
21 < 2.5x
2.5x > 21
x > 21/2.5
x > 8.4
Therefore, for a subscriber to save money by purchasing the VIP pass, it would take more than 8.4 months
Which ordered pair represent points on the graph of this exponential function?f(x) = 2^x+1A(1, 3)B(-4, -7)C(-2, -3)D(4, 9)
Answers
Answer:
[tex]A(1,3)[/tex]Step-by-step explanation:
To determine which of the given ordered pairs belongs to the given function, substitute each x-value and see if the y-value is correct.
[tex]\begin{gathered} f(1)=2^1+1 \\ f(1)=3 \\ \\ f(-4)=2^{-4}+1 \\ f(-4)=\frac{17}{16} \end{gathered}[/tex][tex]\begin{gathered} f(-2)=2^{-2}+1 \\ f(-2)=\frac{5}{4} \\ \\ f(4)=2^4+1 \\ f(4)=17 \end{gathered}[/tex]Therefore, the only point that represents points on the given function is A(1,3)
Frank uses 27/5 tablespoons of pista extract to make 9 servings of a recipe. How many tablespoons of pista extract does each serving need?
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Answer: 3/5 tablespoons.
Can you please help me to answer the question #46
Answers
Part A
S(0) = 1116 - 4.04(0) (Replacing h=0)
S(0)= 1116 (Multiplying)
The answer is 1116 ft/s
Part B
S(10) = 1116 - 4.04(10) (Replacing h=10)
S(10) = 1116 - 40.4 (Multiplying)
S(10)= 1075.06
The answer is 1075.06 ft/s
Part C
S(30) = 1116 - 4.04(30) (Replacing h=30)
S(30) = 1116 - 121.1 (Multiplying)
S(30)= 994.9 (Subtracting)
The answer is 994.9 ft/s.
Find all the zeros of the following function.
f(x)=x^4+8x²-9
The zeros of the function are
(Use a comma to separate answers as needed. Express complex numbers in terms of i.)
Answers
All the zeros of following function f(x)=x4−8x2−9 are 3, -3, i, -i
What do you mean by the roots of function?A number x that reduces the value of a function f to 0 is known as its root in mathematics: f(x) = 0.
Roots are actual objects since polynomials are functions as well.
Every polynomial with complex coefficients has at least one (complex) root, according to the fundamental theorem of algebra.
f(x)=x4−8x2−9
You should set (x4 - 8x2 - 9) to 0.
x4−8x2−9=0
Learn what x's value is.
Put u=x2 in the equation's place.
As a result, applying the quadratic formula will be straightforward.
u2−8u−9=0
Consider the equation x2+bx+c.
Write out the factored form (u-9)(u+1) = 0.
The answer is the set of all numbers that add up to (u9)(u+1)=0.
u=9,−1
If u=x2 has a genuine value, change it to x2=9, x2= -1
In the case of these equations, x = +3, -3, and -i, +i .
The whole solution is made of of the solution's positive and negative components.
x4- 8x2- 9 = 0 has a solution.
is x=3,−3, i,−i
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in a bag there are red and green balls in the ratio of 2:7. if there are 14 red balls,how many green balls are there
Answers
For the information given in the statement you have
[tex]\frac{\text{ number of red balls}}{\text{ number of green balls}}=\frac{2}{7}[/tex]Then
[tex]\frac{2}{7}=\frac{14\text{ red balls}}{x\text{ green balls}}[/tex]Solving for x
[tex]\begin{gathered} \frac{2}{7}=\frac{14}{x} \\ \text{ Apply cross multiplication} \\ 2\cdot x=14\cdot7 \\ 2x=98 \\ \text{ Divide by 2 into both sides of the equation} \\ 2x=\frac{98}{2} \\ x=49 \end{gathered}[/tex]Therefore, there are 49 green balls.
The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle? N O svē units O 4/3 units 10,5 units O 165 units M
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The all the sided of the equlatral triangle have the same lentgth. All the angles of the triangles are 60 degrees.
The expression for the hight of a equlatral triangle is,
[tex]\sin (60^0)=\frac{h}{l}_{}[/tex]Here, ''
helppppppppppppppppppppppppppppppp
Answers
Answer:
b=4
I believe this is correct.
Step-by-step explanation:
-(2)^3+7(2)^2-2(2)+12=
-8+28-16
-8+12
4