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?
Answers
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
Related Questions
Find the value of a.
Answers
In the given triangle, the measure of ∠a is 18°.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.Triangles can be divided into three sorts based on the lengths of their sides, and they are Scalene, Isosceles, and Equilateral.So, we know that the sum of all 3 angles of a triangle is 180°.
Then, calculate for ∠a as follows:
63 + 99 + a = 180162 + a = 180a = 180 - 162a = 18°Therefore, in the given triangle, the measure of ∠a is 18°.
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Determine whether the system of equations below has one solution, infinitely many solutions, or no solution. 10x +9y = 25 20x + 6y = - 10 [classify]show work too please and will give brainliest for the right answer with work shown
Answers
Let's try to solve the system:
Taking the first equation and solving for x, we get:
[tex]\begin{gathered} 10x+9y=25 \\ 10x=25-9y \\ x=\frac{25-9y}{10} \\ x=2.5-0.9y \end{gathered}[/tex]Replacing it on the second and solving for y, we get:
[tex]\begin{gathered} 20x+6y=-10 \\ 20(2.5-0.9y)+6y=-10 \\ 50-18y+6y=-10 \\ 50-12y=-10 \\ -12y=-10-50 \\ -12y=-60 \\ y=\frac{-60}{-12} \\ y=5 \end{gathered}[/tex]Now, we can calculate x, replacing y by 5 as follows:
[tex]\begin{gathered} x=2.5-0.9y \\ x=2.5-0.9(5) \\ x=2.5-4.5 \\ x=-2 \end{gathered}[/tex]It means that x = -2 and y = 5 is the solution for the system.
Answer: The system has one solution and it is x = -2 and y = 5
The recursive formula, an = an-1 - 12 with a0 = 84 describes the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled. Find a5, he amount of water left in the tub after 5 minutes.
Answers
After 5 minute, the water left in the bath tub is 24 gallons.
What is recursive relation?A recurrence relation is an equation that applies a rule to the previous phrase or terms in the series to produce the next term in the sequence.
The given recursive formula for amount of water,
aₙ = aₙ₋₁ - 12
Also given that,
a₀ = 84,
To find a₅, the amount of water left in bath tub after 5 minutes,
Follow the steps,
a₁ = a₀ - 12 ⇒ a₁ = 84 - 12 ⇒ a₁ = 72
a₂ = a₁ - 12 ⇒ a₂ = 72 - 12 ⇒ a₂ = 60
a₃ = a₂ - 12 ⇒ a₃ = 60 - 12 ⇒ a₃ = 48
a₄ = a₃ - 12 ⇒ a₄ = 48 - 12 ⇒ a₄ = 36
a₅ = a₄ - 12 ⇒ a₅ = 36 - 12 ⇒ a₅ = 24
Therefore, after 5 minute, the water left in the bath tub is 24 gallons.
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if a flock of ducks is growing by 6 percent per year and starts with a population of 68 about how many ducks will be there in 10 years
Answers
We know that the next year the flock of ducks will have 6% more than the current year. If the current year the number of ducks is x, then
0.06 · x = the increase number
Then, the population of ducks next year will be
x + 0.06x = number of ducks next year
we can simplify the equation:
1.06x = number of ducks next year
Two years after, then number of ducks will be:
1.06 · number of ducks next year = number of ducks two years after
using the equation we found:
1.06 · (1.6x) = number of ducks two years after
1.06²x = number of ducks two years after
Similarly, three years after will be
1.06³x = number of ducks three years after
If we keep writing equations for every year, we will find a relation between the number of years that pass and the exponent...
n years after will be:
1.06ⁿx = number of ducks n years after
Since the current year the population is 68, then
1.06ⁿ · 68 = number of ducks n years after
We want to find the number of ducks after 10 years. This is n = 10:
[tex]1.06^{10}\cdot68=\text{ number of ducks 10 years after}[/tex]Since
[tex]\begin{gathered} 1.06^{10}=1.79 \\ 1.79\cdot68\approx121.78 \end{gathered}[/tex]Then, the equation we found says that:
number of ducks 10 years after = 121.78
But it is not possible because we cannor have 121.78 ducks, we always have an integer. Then we round it to the nearest integer: 122
Then
answer - the number of ducks 10 years after will be 122
2+32 + 3 + 5 + 5 + 5
Answers
Solution
We have the following expression:
2+32+3+5+5+5
And we can do this:
34 +3+5+5+5
37 + 5 +5 +5
42 +5+5
42+10 =52
Finala answer : 52
6. In deciding whether to set up a new manufacturing plant, company analysts have established that a reasonable function for the total cost to produce x items is C(x) = 500,000 + 4.75x. (a) Find the total cost to produce 100,000 items. (b) Find the marginal cost of the items to be produced in this plant.
Answers
1)
a) Let's find out the total Cost to Produce 100,00 items considering x to stand for "items", so we can write out:
[tex]\begin{gathered} C(x)=500,000+4.75x \\ C(100,000)=500,000+4.75(100,000) \\ C(100,000)=\$975,000 \end{gathered}[/tex]Note that we just had to plug into x, the number of items.
b) The Marginal Cost
On the other hand, the Marginal Cost can be found by taking the first derivative of the Total Cost function, so we can write out:
[tex]\begin{gathered} C(x)=500,000+4.75x \\ C^{\prime}(x)=4.75 \end{gathered}[/tex]The basic idea of the marginal cost is the cost per unit $4.75
3) Hence, the answer is:
a) $975,000
b) $4.75 per unit
How much money do they make by selling the house ?
Answers
ANSWER
$16,200
EXPLANATION
First, they bought the house for $186,700, and then, they sold it for $202,900, which is a greater amount than what they paid for the house. The amount of money they made by selling the house is the difference between the selling prince and the price they paid for,
[tex]202,900-186,700=16,200[/tex]Hence, they made $16,200 selling the house.
A number decreased by 7 is less than -6. Find the number.
Answers
Answer:
The number is less than 1.
[tex]x<1[/tex]Explanation:
Let x represent the number.
When the number is decresed by 7, it becomes;
[tex]x-7[/tex]From the question, When the number is decresed by 7 it is less than -6.
So;
[tex]x-7<-6[/tex]Solving the inequality by adding 7 to both sides of the equation. we have;
[tex]\begin{gathered} x-7+7<-6+7 \\ x<1 \end{gathered}[/tex]Therefore, the number is less than 1.
[tex]x<1[/tex]what is the maximum profit
Answers
Total Profit=Total Revenue - Total Cost
P(x) = R(x)-C(x)
where x is the number of unit sold
From the question,
R(x) = 20x - 0.1x² and c(x) =4x + 2
P(x) = R(x) - c(x) = 20x - 0.1x² - 4x - 2
= -0.1x² + 16x - 2
Profit = -0.1x² + 16x - 2
We have a quadratic equation;
a=-0.1 b= 16
Maximum occurs when x = -b/2a
substitute the values of a and b in the above
x = -16/2(-0.1) = -16/-0.2 = 80
To find the maximum profit, we will substitute x=80 in our profit function
Profit = -0.1(80)² + 16(80) - 2
= -640 + 1280 - 2
= 638
Hence, the maximum profit is $638
A home improvement store advertises 60 square feet of flooring for $305.00 including an $80.00 installation fee. How much does each square foot of flooring cost? The variable s represents: Equation: Each square foot of floring costs $
Answers
Each square foot of flooring costs $ 6.41
What is algebraic expressions?Algebraic expressions contain numbers, operations, and variables. Suppose you have at least $4 in your piggy bank, but an unknown amount of more in your bank. We can use the algebraic expression 4+x to represent the total amount in the piggy bank. where x is an unknown amount. If you find that the unknown amount is $6, you can evaluate the expression 4+x and replace x with 6. The result is 4 + 6 = 10, so you have $10 in your piggy bank.
Each square foot of flooring costs $6.41
The total cost of flooring is $305.00 + $80.00 = $385.00
Now, since the total are to be floored in the mentioned cost is 60 ft²
So, for the cost of flooring each square which we are assuming as (s); we have the following equation:
Total cost of flooring = Area of floor × cost of flooring each square
$385.00 = 60 ft² × s
s = [tex]\frac{385}{60}[/tex]
s = $ 6.41
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which expression is equivalent to ^3 square root 54x + 3^3 square root 2x if x does not equal 0?
Answers
You have the following expression:
³√54x + 3(³√2x), x ≠ 0
In order to simplify the previous expression, write 54x as 27(2x). Moreover, take into account that 27 = 3³ and ³√27(2x) = ³√(3³(2x)) = 3(³√2x). Then, you have:
³√54x + 3(³√2x)
= 3(³√2x) + 3(³√2x)
= 6(³√2x)
Hence, the equivalent expression is
A. 6(³√2x)
what is the y- intercept when x =-1,0,1,2,3,4, and y= -4,-3.5,-3,-2.5,-2,-1.5
Answers
The y - intercept will be - 7/2.
What is Equation of line?
The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The values are,
x = -1, 0, 1, 2, 3, 4,
y = -4, -3.5, -3, -2.5, -2, -1.5
Now,
Take two points on the line as;
⇒ (x, y) = (- 1, - 4) , (1, - 3)
Hence, The slope of the line passing through the points (- 1, - 4) , (1, - 3) is;
⇒ m = (y₂ - y₁) / (x₂ - x₁)
⇒ m = (- 3 - (-4)) / (1 - (-1))
⇒ m = 1 / 2
So, The equation of line with slope 1/2 will be;
⇒ y - (-4) = 1/2 (x - (-1)
⇒ y + 4 = 1/2 (x + 1)
⇒ y + 4 = 1/2x + 1/2
⇒ y = 1/2x + 1/2 - 4
⇒ y = 1/2x - 7/2
Thus, The y - intercept will be - 7/2.
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Graph the solution set of the following linear inequality:2 - 4y > - 14 - 8xAnswerKeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. Theregions will be added once the line is drawn.AYChoose the type of boundary line:Dashed -O Solid (-) O--)SEnter two points on the boundary line:X10-5310-5Select the region you wish to be shaded:ОАOB10
Answers
The inequality is given
[tex]2-4y>-14-8x[/tex]ExplanationTo determine the graph of the inequality,
Solve the expression.
[tex]\begin{gathered} 2-4y>-14-8x \\ -4y+8x>-16 \end{gathered}[/tex]The inequality is given greater than -
That means
In △WXY, m∠W = (10x + 17), m∠X = (2x – 9), and m∠Y = (3x + 7)º. Find m∠Y.
Answers
Answer:
m∠Y = 40º
Explanation:
The sum of the angles in a triangle is 180 degrees. In △WXY:
[tex]m\angle W+m\angle X+m\angle Y=180\degree[/tex]Substitute the given values:
[tex](10x+17)\degree+(2x-9)\degree+(3x+7)\degree=180\degree[/tex]First, solve for x:
[tex]\begin{gathered} 10x+2x+3x+17-9+7=180\degree \\ 15x+15=180\degree \\ 15x=180-15 \\ 15x=165 \\ x=\frac{165}{15} \\ x=11 \end{gathered}[/tex]Next, solve for the measure of angle Y:
[tex]\begin{gathered} m\angle Y=(3x+7)º \\ =3(11)+7 \\ =33+7 \\ m\angle Y=40\degree \end{gathered}[/tex]Line A (y= 5x - 7) is transformed into Line B (y= 2x+3). which best describes the new slope and y-intercept? the slope is ___, and the line is shifted ____. a) steeper b) flatter ----a) upward b) downward
Answers
The graphs of both lines is shown below;
Note that the red line represents y = 5x - 7 and
The blue line represents y = 2x + 3
The slope changes from +5 to +2 and therefore is becoming flatter
The y-intercept has also chabged from -7 to +3 and therefore the line has shifted upward.
The a
1) A ferris wheel can accommodate 40 people in the 20 minutes. How many people could ride the ferris wheel in 3 hours? What was that rate per hour?
Answers
3 hours = 3 x 60 = 180 min, then
40 people ---> 20 min
x ----------------> 180 min
[tex]\begin{gathered} x\times20=40\times180 \\ 20x=7200 \\ \frac{20x}{20}=\frac{7200}{20} \\ x=360 \end{gathered}[/tex]answer 1: 360 people in 3 hours
[tex]\frac{360}{3}=120[/tex]answer 2: 120 people per hour
what is the inverseof f(x)=x/5+6
Answers
Let's begin by listing out the information given to us:
[tex]\begin{gathered} f\mleft(x\mright)=\frac{1}{5}x+6 \\ f(x)=y \\ y=\frac{1}{5}x+6 \end{gathered}[/tex]To find the inverse, of this equation, we have to interchange the two variables (x for y). We have:
[tex]\begin{gathered} y=\frac{1}{5}x+6\Rightarrow x=\frac{1}{5}y+6 \\ x=\frac{1}{5}y+6 \\ \text{Multiply through each element by 5, we have:} \\ 5\cdot x=\frac{1}{5}y\cdot5+6\cdot5 \\ 5x=y+30 \\ \text{Subtract 30 from both side, we have:} \\ 5x-30=y+30-30 \\ 5x-30=y\Rightarrow y=5x-30 \\ y=5x-30 \\ f(^{-1})=5x-30 \end{gathered}[/tex]On March 8, 2017, one South African rand was worth 0.08 U.S. dollars.(a) On that date, how many dollars was 168.18 rand worth?Round your answer to the nearest hundredth of a dollar.dollars(b) On that date, how many rand was 59.09 dollars worth?Round your answer to the nearest hundredth of a rand.I need help with these two problems.
Answers
Given: The conversion rate below
[tex]1(rand)=0.08(dollars)[/tex]To Deteremine: The worth of 168.18 rand in dollars
Solution
[tex]\begin{gathered} 1(rand)=0.08(dollars) \\ 168.18(rand)=x(dollars) \end{gathered}[/tex]Let us cross multiply
[tex]\begin{gathered} x\times1=0.08\times168.18 \\ x=13.4544 \\ x\approx13.45(nearest-hundredth) \end{gathered}[/tex]Hence, worth of 168.18 rand in dollars is approximately 13.45 U.S. dollars
(b) To Determine: How many rand was 59.09 dollars
[tex]\begin{gathered} Recollect \\ 1(rand)=0.08(dollars) \\ y(rand)=59.09(dollars) \end{gathered}[/tex]Let us cross-multiply
[tex]\begin{gathered} 0.08\times y=1\times59.09 \\ 0.08y=59.09 \\ y=\frac{59.09}{0.08} \\ y=738.625 \\ y\approx738.63(rand) \end{gathered}[/tex]Hence, 59.09 dollars is worth approximately 738.63 rands
Р(А) = 1/2 P(В) = 1/3 If A and B are independent, what is P(A n B)?1/6 5/61/21/3
Answers
Given that events A and B are independent.
It follows that the probability of the occurrence of both events is equal to the product of occurrence of each event independently,
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]According to the given problem,
[tex]\begin{gathered} P(A)=\frac{1}{2} \\ P(B)=\frac{1}{3} \end{gathered}[/tex]Substitute the values,
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]Find the measure of the arc.А1460EB.MABC = [ ? ]°
Answers
The measure of the arc m ABC is given by the central angles:
mBC = 360 - (146 + 90) (We have a right angle in the figure).
mBC = 360 - (236)
mBC = 124
The total length of the circle is the circumference:
C = 2*pi * r
If we use for pi = 22/7 (approximation)
Then the arc is given by the fraction that multiplies C:
(2 * pi * r) (mBC+m/360) =
Because 2/360 = 180, we have:
( pi * r) * (124/180)
(22/7) * r * (124/180)
Simplifying the fraction 124/180 by 4 (this is the greatest common divisor), we have:
22/7 * r * 31/45
Then, the measure for the arc is given by (a function of r):
m
22/7 * r * 31/45
For instance, if r = 3, then
The fox population in a certain region has an annual growth rate of 9% per year. In the year 2012 there were 23,900 fox counted in the area. What is the fox population predicted to be in year 2020?What calculations and thinking did you use to find the answer?
Answers
Given:
The initial population is P(i) = 23,900.
The annual growth rate is r = 9% = 0.09.
The number of year is t = 2020-2012 = 8 years.
The objective is to find the population in the year 2020.
Explanation:
The growth formula to find the final population is,
[tex]P=P(i)\times(1+r)^t\ldots\text{ . . . (1)}[/tex]On plugging the given values in equation (1),
[tex]P=23900(1+0.09)^8[/tex]On further solving the above equation,
[tex]\begin{gathered} P=23900(1.09)^8 \\ =47622.2471\ldots\text{.} \\ \approx47622 \end{gathered}[/tex]Hence, the final population using the exponential growth formula is 47622.
Dean has a table with a circular top. What isthe area, in square feet, of the table top?Use 3.14 for Pi. Round your answer to thenearest tenth.
Answers
Answer
124.7 ft²
Step-by-step explanation
The area of a circle is calculated as follows:
[tex]A=\frac{\pi D^2}{4}[/tex]where D is the diameter of the circle.
From the diagram, the diameter of the circular top is 12.6 ft, then its area is:
[tex]\begin{gathered} A=\frac{\pi(12.6)^2}{4} \\ A=124.7\text{ ft}^2 \end{gathered}[/tex]Greatest common factor 12,30,72
Answers
The first step is to write the prime factors of each number. We have
12 = 2 x 2 x 3
30 = 2 x 3 x 5
72 = 2 x 2 x 2 x 3 x 3
Looking at the factors, one 2 and one 3 are common to all three list of factors. Thus,
Greatest common factor = 2 x 3 = 6
Ben has a basket of 5 red socks, 3 yellow socks, and 2 green socks. What is the theoretical probability that if he randomly selects a sock from the basket it will be red?
Answers
the probability of pen being red is,
[tex]p=\frac{^5C_1}{10C_1}[/tex][tex]p=\frac{5}{10}=\frac{1}{2}=0.5[/tex]so the answer is 0.5
y-(-10) = 2/3 (x- (-12))what is y
Answers
We have the expression:
[tex]y-(-10)=\frac{2}{3}(x-(-12))\Rightarrow y=\frac{2}{3}x-2[/tex]From this we have that y equals to 2/3x-2 and therefore y represents a line with slope of 2/3 and with a y-intercept of -2.
Write a function that represents the sequences 7,14,21,28
Answers
Given:-
[tex]7,14,21,28,\ldots[/tex]To find the sequence inside the pattern.
Since the number are the numbers in 7th table the function can be,
[tex]f(n)=7n[/tex]So the required function is f(n)=7n
solve for x 8/9x +4=12
Answers
hello
to solve for x, we have to simplify this equation
step one
collect like terms
[tex]\begin{gathered} \frac{8}{9}x+4=12 \\ \frac{8}{9}x=12-4 \\ \frac{8}{9}x=8 \\ \end{gathered}[/tex]step two
cross multipy both sides
[tex]\begin{gathered} \frac{8}{9}x=8 \\ 8x=8\times9 \\ 8x=72 \end{gathered}[/tex]step three
divide both sides by the coefficient of x
[tex]\begin{gathered} 8x=72 \\ \frac{8x}{8}=\frac{72}{8} \\ x=9 \end{gathered}[/tex]from the calculation above, the value of x is equal to 9
15.A snack bar sells scoops of strawberry, chocolate, andvanilla ice cream. On Monday, the snack bar sold100 scoops in total of these flavors of ice cream. Thesnack bar sold 3 times as many scoops of chocolate asit did strawberry and 2 times as many scoops ofvanilla as it did chocolate. How many scoops ofchocolate ice cream did the snack bar sell onMonday?
Answers
54 scoops of chocolate.
1) Gathering the data from the question
Monday = 100 scoops in total
Snack bar sells 3x chocolate
x strawberry
1.5x Vanilla ( 3 : 1.5 = 2)
How many chocolate scoops?
2) Setting the expression:
3x+x+1.5x=100
4x +1.5x=100
5.5x=100
x=18.1 approximately then x = 18
Answer
3x = Chocolate
3*18 = 54 chocolate scoops
6v =792 how I do dat
Answers
In order to solve the equation 6v = 792 for v, we just need to divide both sides of the equation by the coefficient multiplying the variable v, that is, the number 6.
So we have that:
[tex]\begin{gathered} 6v=792 \\ \frac{6v}{6}=\frac{792}{6} \\ v=132 \end{gathered}[/tex]Therefore the value of v that is solution of this equation is v = 132.
Estimate the product. Round each factor to the nearest whole number, and then mult 4.6 x 4.1 The product is approximately Submit O
Answers
We need to multiply:
[tex]4.6\cdot4.1=\text{???}[/tex]But first, we will round each term to the nearest whole number
so,
4.6 will be rounded to 5 ( because 0.6 > 0.5 )
4.1 will be rounded to 4 ( because 0.1 < 0.5 )
so,
4.6 x 4.1 ( approximately ) = 5 * 4 = 20