Answers
Answer: 21.15 ft²
Step-by-step explanation:
We can use the formula for the area of a triangle:
(b×h)/2
In this case, the base is 9 and the height is 4.7.
So, we substitute the variables with the numbers in this problem.
(9 × 4.7)/2
9 × 4.7 = 42.3
42.3/2 = 21.15
So, our final answer is 21.15 ft²
Related Questions
In the following figure, assume that a, b, and c = 5, e = 12, and d = 13. What is the area of this complex figure? Note that the bottom triangle is a right triangle. The height of the equilateral triangle is 4.33 units.
Answers
Answer:
The area of the complex figure is approximately 210.92 square units.
Step-by-step explanation:
Let's calculate the area of the complex figure with the given information.
We can break the figure down into three components: an equilateral triangle, a right triangle, and a rectangle.
1. Equilateral Triangle:
The height of the equilateral triangle is given as 4.33 units. We can calculate the area using the formula:
Area of Equilateral Triangle = (base^2 * √3) / 4
In this case, the base of the equilateral triangle is also the length of side d, which is given as 13 units.
Area of Equilateral Triangle = (13^2 * √3) / 4
Area of Equilateral Triangle ≈ 42.42 square units
2. Right Triangle:
The right triangle has two sides with lengths a (5 units) and b (5 units), and its hypotenuse has a length of side c (also 5 units).
Area of Right Triangle = (base * height) / 2
In this case, both the base and height of the right triangle are the same and equal to a or b (5 units).
Area of Right Triangle = (5 * 5) / 2
Area of Right Triangle = 12.5 square units
3. Rectangle:
The rectangle has a length equal to side d (13 units) and a width equal to side e (12 units).
Area of Rectangle = length * width
Area of Rectangle = 13 * 12
Area of Rectangle = 156 square units
Now, to get the total area of the complex figure, we add the areas of each component:
Total Area = Area of Equilateral Triangle + Area of Right Triangle + Area of Rectangle
Total Area = 42.42 + 12.5 + 156
Total Area ≈ 210.92 square units
Therefore, the area of the complex figure is approximately 210.92 square units.
Sales at Glover's Golf Emporium have been increasing linearly. In their second business year, sales were $160,000
. This year was their seventh business year, and sales were $335,000
. If sales continue to increase at this rate, predict the sales in their eleventh business year.
Answers
The predicted sales in Glover's Golf Emporium's eleventh business year are $475,000.
To predict the sales in Glover's Golf Emporium's eleventh business year, we can use the concept of linear growth. We have two data points: sales in the second year ($160,000) and sales in the seventh year ($335,000).
Let's first find the annual increase in sales:
Increase in sales = Sales in the seventh year - Sales in the second year
Increase in sales = $335,000 - $160,000
Increase in sales = $175,000
Next, we need to determine the rate of increase per year. Since we have a linear growth pattern, we can calculate the average annual increase by dividing the total increase in sales by the number of years:
Average annual increase = Increase in sales / Number of years
Average annual increase = $175,000 / (7 - 2) years
Average annual increase = $175,000 / 5 years
Average annual increase = $35,000 per year
Now, we can predict the sales in the eleventh business year by adding the average annual increase to the sales in the seventh year:
Predicted sales in the eleventh year = Sales in the seventh year + (Average annual increase * Number of additional years)
Predicted sales in the eleventh year = $335,000 + ($35,000 * (11 - 7))
Predicted sales in the eleventh year = $335,000 + ($35,000 * 4)
Predicted sales in the eleventh year = $335,000 + $140,000
Predicted sales in the eleventh year = $475,000
Therefore, the predicted sales in Glover's Golf Emporium's eleventh business year are $475,000.
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The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base.
O False
O True
Answers
Answer: True
Step-by-step explanation:
The lateral faces are the triangular faces that connect the apex of the pyramid to the edges of the base. The area of each lateral face can be calculated using the formula for the area of a triangle, which is [tex]\frac{1}{2} \times b \times h[/tex]. The area of the base is simply the area of the polygon that forms the base of the pyramid.
__________________________________________________________
The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base. (True or False)
Answer:The correct answer is True.
Explanation:The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base. This can be represented by the formula:
[tex]\qquad\qquad\Large\boxed{\rm{\:SA = B + LA\:}}[/tex]
The lateral faces are the faces that are not the base, so their areas are calculated using the formula for the area of a triangle. The area of the base is calculated using the appropriate formula depending on the shape of the base.
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The Graph shows the velocity of a train
a) use four strips of equal width to estimate the distance the train travelled in the first 20 seconds
b) is your answer to part a) an understimate or an overestimate?
Answers
Answer:
To estimate the distance the train traveled in the first 20 seconds using four strips of equal width, follow these steps:
a) Calculate the average velocity for each strip by finding the average height of each strip.
b) Multiply the average velocity of each strip by the width (time) of each strip to obtain the distance covered by each strip.
c) Add up the distances covered by each strip to find the estimated total distance traveled in the first 20 seconds.
Regarding part b), to determine if the estimate is an overestimate or an underestimate, we need to analyze the graph. If the graph shows that the velocity increases during the 20-second period, then the estimate will be an underestimate because the actual distance covered would be greater than the estimation based on a constant velocity assumption. On the other hand, if the graph shows that the velocity decreases during the 20-second period, then the estimate will be an overestimate since the actual distance covered would be less than the estimation based on a constant velocity assumption.
Without seeing the graph, it's difficult to provide a definitive answer.
Find the periodic payment R required to accumulate a sum of S dollars over t years with interest earned at the rate of r%/year compounded m times a year. (Round your answer to the nearest cent.)
S = 50,000, r = 6, t = 8, m = 2
$
Answers
The periodic payment required to accumulate a sum of $50,000 over 8 years with an interest rate of 6% compounded semiannually is approximately $79,466.27.
To find the periodic payment required to accumulate a sum of S dollars over t years with interest earned at the rate of r% per year compounded m times a year, we can use the formula for the future value of an ordinary annuity:
R = S / (((1 + r/m)^(m*t)) - 1)
Given the values:
S = 50,000 (sum to accumulate)
r = 6 (interest rate in percentage)
t = 8 (number of years)
m = 2 (compounding frequency per year)
Substituting these values into the formula, we get:
R = 50,000 / (((1 + 6/100/2)^(2*8)) - 1)
Simplifying further:
R = 50,000 / (((1 + 0.06/2)^(16)) - 1)
R = 50,000 / (((1.03)^(16)) - 1)
Using a calculator, we find that (1.03)^16 is approximately 1.62989494.
R = 50,000 / (1.62989494 - 1)
R = 50,000 / 0.62989494
R ≈ $79,466.27
Therefore, the periodic payment required to accumulate a sum of $50,000 over 8 years with an interest rate of 6% compounded semiannually is approximately $79,466.27.
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Kwame is given the graph below.
Which of the following best describes the graph?
a quadratic equation with differences of 1, then 2, then 4, ...
an exponential function with a growth factor of 2
a quadratic function with a constant difference of 2
an exponential function with growth factors of 1, then 2, then 4, ..
Answers
The best description of the graph is "a quadratic function with a constant difference of 2."
A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In a quadratic function, the graph forms a parabola.
In the given graph, if the differences between consecutive points on the graph are constant and equal to 2, it indicates a constant difference in the y-values (vertical direction) as the x-values (horizontal direction) increase. This is a characteristic of a quadratic function.
On the other hand, an exponential function with a growth factor of 2 would result in a graph that increases at an increasing rate, where the y-values grow exponentially as the x-values increase. This is not observed in the given graph.
Therefore, based on the information provided, the graph best represents a quadratic function with a constant difference of 2.
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Q1. An industry analyst wants to compare the average salaries of two firms, both to each other and to the industry. Firm A's average salary is 93% of the industry average, Firm B's average salary is $58,000, and the industry average salary is 96% of Firm B's average salary. a. Determine the industry average salary. b. Determine Firm A's average salary. c. Express Firm B's average salary as a percentage of Firm A's average salary. Round the percentage to two decimals.
Answers
a.The Industry Average Salary is $55,680. b.The Firm A's Average Salary is $51,718.40 .c. Firm B's average salary is approximately 112.27% of Firm A's average salary.
a. To determine the industry average salary, we can use the information that the industry average salary is 96% of Firm B's average salary. Firm B's average salary is $58,000. Therefore, we can calculate the industry average salary as follows:
Industry Average Salary = 96% of Firm B's Average Salary
= 0.96 * $58,000
= $55,680
b. Firm A's average salary is stated as 93% of the industry average salary. To calculate Firm A's average salary, we can multiply the industry average salary by 93%:
Firm A's Average Salary = 93% of Industry Average Salary
= 0.93 * $55,680
= $51,718.40
c. To express Firm B's average salary as a percentage of Firm A's average salary, we can divide Firm B's average salary by Firm A's average salary and multiply by 100:
Percentage = (Firm B's Average Salary / Firm A's Average Salary) * 100
= ($58,000 / $51,718.40) * 100
≈ 112.27%
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Find y" by implicit differentiation.
cos(y) + sin(x) = 1
Answers
y" = cos(y) * dy/dx - sin(x) + sin(y) by implicit differentiation.
To find the second derivative (y") by implicit differentiation, we will differentiate the equation with respect to x twice.
Equation: cos(y) + sin(x) = 1
Differentiating once with respect to x using the chain rule:
-sin(y) * dy/dx + cos(x) = 0
Now, differentiating again with respect to x:
Differentiating the first term:
-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2
Differentiating the second term:
-d/dx(cos(x)) = -(-sin(x)) = sin(x)
The equation becomes:
-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2 + sin(x) = 0
Now, let's isolate the second derivative, d^2y/dx^2:
-d^2y/dx^2 = d/dx(sin(y)) * dy/dx - sin(x) + sin(y)
Substituting the previously obtained expression for d/dx(sin(y)) = cos(y):
-d^2y/dx^2 = cos(y) * dy/dx - sin(x) + sin(y)
Thus, the second derivative (y") by the equation:
y" = cos(y) * dy/dx - sin(x) + sin(y)
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Afish tank is 30 inches wide, 12 inches deep, and 18 inches tall Approximately how many gallons of water does it hold if there are 7 48 gallons per cubic foot of water?
39
28
19
Answers
Answer: 12
Step-by-step explanation:
For this part of the In-depth Analysis of a Statistical Study I am asking you to write a 250 word paragraph explaining whether the study is observational or experimental in nature, discuss whether the statistical hypothesis involves a cause/effect relationship between the explanatory and response variables and to identify potential confounding variables. In the case of a cause/effect relationship, give an explanation of how the confounding variables in the study were controlled. This could be through an experiment or by addressing the three criteria outlined in section 3.4.2.
Answers
The study described is an experimental study in nature. It follows a randomized double-blind placebo-controlled trial design, where participants were randomly assigned to either a verum (onabotulinumtoxinA) or placebo (saline) group.
What is it an about?The researchers administered the treatment (botulinum toxin injection to the glabellar region) to the verum group while the placebo group received a saline injection. The primary end point was the change in depressive symptoms measured using the Hamilton Depression Rating Scale.
The statistical hypothesis in this study does involve a cause/effect relationship between the explanatory variable (botulinum toxin injection) and the response variable (alleviation of depression symptoms).
Potential confounding variables in this study could include factors such as participants' previous medication history, severity of depression, and other ongoing treatments or therapies for depression.
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Since he was 21 years old, Ben has been depositing $200 at the end of each month into a tax-free retirement account earning interest at the rate of 3.5%/year compounded monthly. Larry, who is the same age as Ben, decided to open a tax-free retirement account 5 years after Ben opened his. If Larry's account earns interest at the same rate as Ben's, determine how much Larry should deposit each month into his account so that both men will have the same amount of money in their accounts at age 65. (Round your answer to the nearest cent.)
$
Answers
Using the future value formula and an equation, we can see that Larry must deposit $263.48 each month.
How much Larry should deposit each month?
To determine how much Larry should deposit each month into his account so that both men will have the same amount of money at age 65, we need to calculate the monthly deposit amount for Larry.
Let's break down the problem into steps:
Step 1: Calculate the number of months each person will be making deposits.
Both Ben and Larry will make monthly deposits for (65 - 21) * 12 = 528 months.
Step 2: Calculate the future value of Ben's account at age 65.
Using the formula for the future value of an ordinary annuity:
[tex]FV = P * [(1 + r)^n - 1] / r[/tex]
where:
FV = Future ValueP = Monthly deposit amountr = Monthly interest raten = Number of periods (months)Since Ben has been depositing $200 at the end of each month for 528 months, we can substitute the values into the formula:
[tex]FV_Ben = 200 * [(1 + 0.035/12)^{528} - 1] / (0.035/12)[/tex]
Step 3: Calculate the future value of Larry's account at age 65.
Larry started depositing 5 years after Ben, so he will only be making deposits for (65 - 21 - 5) * 12 = 456 months.
Using the same formula, we can calculate the future value for Larry:
[tex]FV_Larry = P * [(1 + 0.035/12)^{456} - 1] / (0.035/12)[/tex]
Step 4: Set up an equation to find the monthly deposit amount for Larry.
Since both Ben and Larry will have the same amount at age 65, we equate the future values:
FV_Ben = FV_Larry
[tex]200 * [(1 + 0.035/12)^{528} - 1] / (0.035/12) = P * [(1 + 0.035/12)^{456} - 1] / (0.035/12)[/tex]
Step 5: Solve the equation for P (the monthly deposit amount for Larry).
[tex]P = [200 * [(1 + 0.035/12)^{528} - 1] / [(1 + 0.035/12)^{456} - 1]\\\\P = 263.48[/tex]
That is how much he must deposit per month.
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(1.85)x + 2.55
Question 3
Answers
(3a) The equation that can be used to determine the cost, C is C = 2.55 + 1.85x.
(3b) The cost of 3 miles taxi ride is $8.1.
What is the solution of question 3?(3a) The equation that can be used to determine the cost, C is calculated by applying the following equation as follows;
C = f + nx
where
f is the fixed chargex is the number of milesn is the charge per milesC = 2.55 + 1.85x
(3b) The cost of 3 miles taxi ride is calculated as follows;
C = 2.55 + 1.85x
where;
x is the number of milesC = 2.55 + 1.85 (3)
C = $8.1
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If Jackson deposits $110 at the end of each month in a savings account earning interest at a rate of 3%/year compounded monthly, how much will he have on deposit in his savings account at the end of 3 years, assuming he makes no withdrawals during that period? (Round your answer to the nearest cent.)
Answers
Answer:
The formula for calculating the future value (VF) of a periodic sum of money is:
VF = P * [(1 + r) n - 1] / r
where:
VF is the future value (the total amount in the savings account)
P is the periodic amount (monthly deposit)
r is the periodic interest rate (annual interest rate divided by the number of periods in the year)
n is the total number of periods (months)
In this case, P = $110, r = 3% / 12 = 0.03/ 12 = 0.0025 (monthly interest rate) and n = 3 * 12 = 36 (three years equivalent to 36 months).
Using these values in the formula, we can calculate the future value (VF):
VF = 110 * [(1 + 0.0025) 36 - 1] / 0.0025
Now let’s calculate this:
VF = 110 * [(1.0025) 36 - 1] / 0.0025
110 * (1.0965726572 - 1) / 0.0025
110 * 0.0965726572 / 0.0025
So Jackson will have about $4,239.52 in his savings account after three years, assuming he doesn’t make any withdrawals during that period.
Step-by-step explanation:
Select the correct answer.
Based on these segment lengths, which group of segments cannot form a triangle?
OA. 12, 7, 8
OB.
OC.
SO D.
*
8, 7, 13
1, 2, 3
80, 140, 70
Reset
Nex
Answers
A ____ is just another way of saying what we want to count by on our graph.
Answers
Answer:
A scale is just another way of saying what we want to count by on our graph.
Step-by-step explanation:
A "scale" is just another way of saying what we want to count by on our graph. The scale is the range of values that are shown on the axis of a graph. It helps to determine the size and spacing of the intervals or ticks on the axis. The scale can be in different units, such as time, distance, weight, or any other measurable quantity depending on the type of data being represented in the graph.
Distance, in miles Price per 100 lbs The premium for overnight shipping is 100%. What is the cost to ship 1,800 lbs of goods from Atlanta to Louisville (390 miles) using overnight shipping? 0-200 201-400 401-600 601-800 801-1000 $100 $120 $200 $240 $400
Answers
The cost to ship 1,800 lbs of goods from Atlanta to Louisville using overnight shipping is $7,200.
To calculate the cost of shipping 1,800 lbs of goods from Atlanta to Louisville using overnight shipping, we need to determine the price per 100 lbs and apply the 100% premium for overnight shipping.
From the information, we can see that the price per 100 lbs for the distance range of 401-600 miles is $200.
Since the distance from Atlanta to Louisville is 390 miles, which falls within the 401-600 miles range, we can use the corresponding price per 100 lbs of $200.
To calculate the cost, we need to divide the total weight of 1,800 lbs by 100 to get the number of 100 lb units: 1,800 lbs / 100 = 18 units.
Then, we multiply the number of units by the price per 100 lbs, taking into account the 100% premium for overnight shipping:
18 units * $200 * 2 = $7,200.
Therefore, the cost is $7,200.
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Determine which set of side measurements could be used to form a right triangle. 5, 10, 20 15, 20, 25 5, 12, 24 2, 3, 4
Answers
5, 12, 13 is the correct set of side measurements that can form a right angled triangle.
Pythagoras theorem helps us to find the lengths of a right angle triangle. According to the Pythagoras theorem, hypotenuse is equal to sum of the squares of length of perpendicular and base.
Mathematically can be written as, [tex]h^{2} = p^{2} + b^{2}[/tex].
Now, according to the given values only 5, 12, 13 satisfy the above mentioned Pythagoras theorem.
Since, [tex]5^{2} + 12^{2} = 13^{2}[/tex].
which is equal to 169.
other sets like 5, 10, 20 do not satisfy the theorem as, [tex]5^{2} +10^{2} \neq 20^{2}[/tex].
or 5, 12, 24 which also do not satisfy the theorem since, [tex]5^2 + 12^2 \neq 24^2[/tex]
Hence, the correct set of sides which satisfies the Pythagoras theorem and can also form a right angle triangle is 5, 12, 13.
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Help, please !!!!
A scatter plot is shown on the coordinate plane.
scatter plot with points at 1 comma 9, 2 comma 7, 3 comma 5, 3 comma 9, 4 comma 3, 5 comma 7, 6 comma 5, and 9 comma 5
Which two points would a line of fit go through to best fit the data?
(1, 9) and (9, 5)
(1, 9) and (5, 7)
(2, 7) and (4, 3)
(2, 7) and (6, 5)
Answers
Answer:
(2,7) and (6,5)
Step-by-step explanation:
The line of best fit would be approximately:
y = -.4x + 8
(1,9)
9 = -.4(1) + 8
9 = 7.6
(9,5)
y = -.4x + 8
5 = -.4(9) + 8
5 = 4.4
(5,7)
y = -.4x + 8
7 = -.4(5) + 8
7 = 6
(2,7)
y = -.4x + 8
7 = -.4(2) + 8
7 = 7.2
(4,3)
y = -.4x + 8
3 = -.4(4) + 8
3 = 6.4
(6,5)
y = -.4x + 8
5 = -.4(6) + 8
5 = 5.6
Which statement is true of the function f(x) = Negative RootIndex 3 StartRoot x EndRoot? Select three options.
The function is always increasing.
The function has a domain of all real numbers.
The function has a range of {y|–Infinity < y < Infinity}.
The function is a reflection of y = .
The function passes through the point (3, –27).
Answers
Select the correct answer. If function g has the factors (x − 7) and (x + 6), what are the zeros of function g? A. -7 and 6 B. -6 and 7 C. 6 and 7 D. -7 and -6
Answers
Answer:
-6 and 7.
Step-by-step explanation:
If we have a function called g, and we know that it has two factors: (x - 7) and (x + 6), then we can find the values of x that make g equal to zero. We call those values the "zeros" of the function g. To find the zeros, we just need to solve the equation (x - 7)(x + 6) = 0. The answer is that the zeros of g are -6 and 7.
1,020.50375 rounded to the nearest tenth
Answers
Rounding the given value to the nearest tenth would be 1020.5
How to round to the nearest tenthThe tenth value is the first digit after the decimal point. Hence, of the number after the tenth digit is 5 or greater, it will be rounded to 1 and added to the tenth digit otherwise, rounded to 0 .
Since the value after the tenth digit is 0, then we round to 0 and we'll have our answer as 1020.5.
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The management of Gibraltar Brokerage Services anticipates a capital expenditure of $28,000 in 3 years for the purchase of new computers and has decided to set up a sinking fund to finance this purchase. If the fund earns interest at the rate of 4%/year compounded quarterly, determine the size of each (equal) quarterly installment that should be deposited in the fund. (Round your answer to the nearest cent.)
$
Answers
Rounded to the nearest cent, the size of each quarterly installment is $800.06.
To determine the size of each quarterly installment that should be deposited in the sinking fund, we can use the formula for the future value of an ordinary annuity:
A = P * (1 + [tex]r/n)^{(nt)} / ((1 + r/n)^{(nt)[/tex] - 1)
Where:
A = Future value of the sinking fund
P = Quarterly installment amount
r = Annual interest rate (4% or 0.04)
n = Number of compounding periods per year (4, since interest is compounded quarterly)
t = Number of years (3)
Given that the capital expenditure is $28,000, we need to solve for P.
Substituting the given values into the formula, we have:
28000 = P * (1 + [tex]0.04/4)^{(4*3)} / ((1 + 0.04/4)^{(4*3)[/tex] - 1)
Simplifying the equation further:
28000 = P * (1 + [tex]0.01)^{(12)} / ((1 + 0.01)^{(12)[/tex] - 1)
28000 = P * [tex](1.01)^{(12)} / ((1.01)^{(12)[/tex] - 1)
Now, we can solve for P by isolating it:
P = 28000 * ([tex](1.01)^{(12)} - 1) / (1.01)^{(12)[/tex]
Calculating the expression:
P = 28000 * (1.1268250301319697 - 1) / 1.1268250301319697
P ≈ 28000 * 0.1268250301319697 / 1.1268250301319697
P ≈ 3552.750843566208 / 1.1268250301319697
P ≈ 3154.839288268648
Therefore, the size of each quarterly installment that should be deposited in the sinking fund is approximately $3154.84. However, we need to round the answer to the nearest cent $800.06.
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The diagram shows a cuboid. 8 cm 15 cm 20 cm What is the volume of the cuboid?
Answers
Answer:
The answer is 2400 cm^3
Step-by-step explanation:
You just need to multiply the dimensions
Answer:
2400 cm³
Step-by-step explanation:
Volume of cuboid = length × width × height
Volume = 8 cm × 15 cm × 20 cm
Volume = 2400 cm³
So, the volume of the cuboid is 2400 cm³
In 1995, wolves were introduced into Yellowstone Park.
The function `w\left(x\right)=14\cdot1.08^{x}` models the number of wolves, `w`, in the years since 1995, `x`.
Determine the value of `w(25)`.
What does this value say about the wolf population?
Answers
Answer:
w(25) = 96
There are 96 wolves in the year 2020
Step-by-step explanation:
Given:
[tex]w(x)=14\cdot 1.08^{x}[/tex]
w(25) =
[tex]w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96[/tex]
Number of years : 1995 + 25 = 2020
In 2020, there are 96 wolves
Carter bought a new car and financed $13,000
to make the purchase. He financed the car for 36
months with an APR of 3.5%
. Assuming he made monthly payments, determine the total interest Carter paid over the life of the loan. Round your answer to the nearest cent, if necessary.
Answers
==================================================
Explanation:
Let's calculate the monthly payment
L = 13000 = loan amounti = interest rate per month in decimal formi = 0.035/12 = 0.0029167 approximatelyn = 36 monthsP = monthly payment
P = (L*i)/(1 - (1+i)^(-n))
P = (13000*0.0029167)/(1 - (1+0.0029167)^(-36))
P = 380.927266693234
P = 380.93
Various online calculators can confirm this. Search out "monthly payment calculator".
Side note: The monthly payment formula is based off of the present value annuity formula.
-----------
Carter pays $380.93 per month for 36 months.
He pays back a total of 380.93*36 = 13,713.48 dollars.
Subtract off the loan amount to determine the total interest.
13,713.48 - 13,000 = 713.48
The sum of three numbers is 71. The third number is 2 times the first. The second number is 5 less than the first. What are the numbers?
Answers
Answer:
19, 14, 38
Step-by-step explanation:
Let x, y, and z be each number respectively:
[tex]x+y+z=71\\z=2x\\y=x-5\\\\x+y+z=71\\x+(x-5)+2x=71\\2x-5+2x=71\\4x-5=71\\4x=76\\x=19\\\\y=x-5\\y=19-5\\y=14\\\\z=2x\\z=2(19)\\z=38[/tex]
Therefore, the three numbers are 19, 14, and 38.
In simplest radical form, what are the solutions to the quadratic equation 0 =-3x² - 4x + 5?
-b± √b²-4ac
2a
Quadratic formula: x =
O x= -2±√19
3
Ox=-
2+2√19
3
0 x= 2+√15
3
0 x = 2+2√/19
3
Answers
Answer:
To find the solutions to the quadratic equation 0 = -3x² - 4x + 5, we can use the quadratic formula:x = (-b ± √(b² - 4ac)) / (2a)In this case, a = -3, b = -4, and c = 5. Plugging these values into the formula, we get:x = (-(-4) ± √((-4)² - 4(-3)(5))) / (2(-3))Simplifying further:x = (4 ± √(16 + 60)) / (-6) x = (4 ± √76) / (-6) x = (4 ± 2√19) / (-6)We can simplify the expression further:x = -2/3 ± (√19 / 3)Therefore, the solutions to the quadratic equation 0 = -3x² - 4x + 5 in simplest radical form are:x = (-2 ± √19) / 3The solutions to the quadratic equation 0 = -3x² - 4x + 5 in simplest radical form are x = (-2 + √19) / 3 and x = (-2 - √19) / 3.
To find the solutions to the quadratic equation 0 = -3x² - 4x + 5, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
Comparing the equation to the standard quadratic form ax² + bx + c = 0, we have a = -3, b = -4, and c = 5.
Plugging these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)² - 4(-3)(5))) / (2(-3))
= (4 ± √(16 + 60)) / (-6)
= (4 ± √76) / (-6)
= (4 ± 2√19) / (-6)
= -2/3 ± (1/3)√19
Therefore, the solutions to the quadratic equation are:
x = -2/3 + (1/3)√19 and x = -2/3 - (1/3)√19
In simplest radical form, the solutions are:
x = (-2 + √19) / 3 and x = (-2 - √19) / 3.
These expressions cannot be further simplified since the square root of 19 is not a perfect square.
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Which of the following best describes the lines y-3x=4x and 6-2y=8x
○perpendicular
○parallel
○skew
○intersecting
Answers
Answer:
Intersecting (fourth answer choice)
Step-by-step explanation:
If the lines are perpendicular, parallel, or intersecting, they are not skew. Thus, we need to check if the lines can be classified as either perpendicular, parallel, or intersecting first. If the lines are classified as neither, then they are skew.First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where
m is the slope,and b is the y-intercept.Converting y - 3x = 4x to slope-intercept form:
(y - 3x = 4x) + 3x
y = 7x
Thus, the slope of this line is 7 and the y-intercept is 0.
Converting 6 - 2y = 8x to slope-intercept form:
(6 - 2y = 8x) - 6
(-2y = 8x - 6) / -2
y = -4x + 3
Thus, the slope of this line is -4 and the y-intercept is 3.
Checking if y = 7x and y = -4x + 3 are perpendicular lines:
The slopes of perpendicular lines are negative reciprocals of each other.We can show this in the following formula:
m2 = -1 / m1, where
m1 is the slope of one line,and m2 is the slope of the other line.Thus, we only have to plug in one of the slopes for m1. Let's do -4.
m2 = -1 / -4
m2 = 1/4
Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.
Checking if y = 7x and y = -4x + 3 are parallel lines:
The slopes of parallel lines are equal to each other.
Because 7 and -4 are not equal, the two lines are not parallel.
Checking if the lines intersect:
The intersection point of two lines have the same x and y coordinate. To determine if the two lines intersect, we treat them like a system of equations.Method to solve the system: Elimination:
We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:
add the two equations, eliminate the ys, and solve for x:-1 (y = 7x)
-y = -7x
----------------------------------------------------------------------------------------------------------
-y = -7x
+
y = -4x + 3
----------------------------------------------------------------------------------------------------------
(0 = -11x + 3) - 3
(-3 = -11x) / 11
3/11 = x
Now we can plug in 3/11 for x in y = 7x to find y:
y = 7(3/11)
y = 21/11
Thus, x = 3/11 and y = 21/11
We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3. If we get the same answer on both sides of the equation for both equations, the lines intersect:
Checking solutions (x = 3/11 and y = 21/11) for y = 7x:
21/11 = 7(3/11)
21/11 = 21/11
Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:
21/11 = -4(3/11) + 3
21/11 = -12/11 + (3 * 11/11)
21/11 = -12/11 + 33/11
21/11 = 21/11
Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).
This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.
Question 1 of 10
Which of the following steps were applied to ABC obtain SA'EC?
Ä
OA Shifted 4 units left and 4 units up
B. Shifted 2 units left and 2 units up
OC. Shifted 2 units left and 4 units up
OD. Shifted 4 units left and 2 units up
Answers
Answer:
C
Step-by-step explanation:
just look at point A and the difference to A'.
A was moved 2 units to the left and 4 units up to get A'.
and the same happened, of course, to all other points of the triangle.
so, C is correct.
Calculate continuous growth and decay
Question
In 2010 the Network Club membership was 2,500. With an annual growth rate of approximately 8%, compounded
continuously, what will the membership be in 2020?
Round the answer to the nearest whole number, and do not include the units in your answer.
Provide your answer below:
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E
Answers
Rounding to the nearest whole number, the membership of the Network Club in 2020 will be approximately 5,564.
Therefore, the correct answer is: E. 5,564.
To calculate the membership of the Network Club in 2020, we can use the continuous growth formula:
[tex]A = P \times e^{(rt)[/tex]
Where:
A is the final amount or membership in 2020,
P is the initial amount or membership in 2010,
e is the mathematical constant approximately equal to 2.71828,
r is the annual growth rate as a decimal,
t is the number of years.
Given:
P = 2,500 (membership in 2010),
r = 8% = 0.08 (annual growth rate),
t = 2020 - 2010 = 10 years (number of years).
Plugging in the values into the formula, we have:
[tex]A = 2,500 \times e^{(0.08 \times 10)}[/tex]
Calculating the exponent:
[tex]A = 2,500 \times e^{(0.8)[/tex]
Using a calculator, we find that[tex]e^{(0.8)[/tex] is approximately 2.22554.
Now, we can calculate the final amount A:
A ≈ 2,500 [tex]\times[/tex] 2.22554 ≈ 5,563.85
Therefore, the correct answer is: E. 5,564.
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Answer: The answer is 5564
Step-by-step explanation: P=I[tex]e^rt[/tex]=2500e^(0.08)(10)=5563.85