Answer:
the possible length and width b:
1 and 20
10 and 2
5 and 4
120 = 1*20*6
120 = 10*2*6
120 = 5*4*6
The possible length and width for Derek's rectangular prism with a volume of 120 cubic inches and a height of 6 inches is 6 inches and 20 inches, respectively.
To find the possible length and width of Derek's rectangular prism, we can use the formula for the volume of a rectangular prism:
Volume = Length x Width x Height
Given that the volume is 120 cubic inches and the height is 6 inches, we can substitute these values into the formula:
120 = Length x Width x 6
To find the possible values for length and width, we need to factorize 120 and check the combinations that satisfy the equation. Let's find the factors of 120:
1 x 120
2 x 60
3 x 40
4 x 30
5 x 24
6 x 20
8 x 15
10 x 12
Now let's substitute these factors into the equation and solve for the missing dimension:
For the combination 1 x 120:
120 = 1 x 120 x 6
This does not work because the width would be 120 inches, which is not feasible.
For the combination 2 x 60:
120 = 2 x 60 x 6
This does not work because the width would be 60 inches, which is not feasible.
For the combination 3 x 40:
120 = 3 x 40 x 6
This does not work because the width would be 40 inches, which is not feasible.
For the combination 4 x 30:
120 = 4 x 30 x 6
This does not work because the width would be 30 inches, which is not feasible.
For the combination 5 x 24:
120 = 5 x 24 x 6
This does not work because the width would be 24 inches, which is not feasible.
For the combination 6 x 20:
120 = 6 x 20 x 6
This works because the width would be 20 inches:
120 = 6 x 20 x 6
120 = 720
This combination satisfies the equation.
For the combination 8 x 15:
120 = 8 x 15 x 6
This does not work because the width would be 15 inches, which is not feasible.
For the combination 10 x 12:
120 = 10 x 12 x 6
This does not work because the width would be 12 inches, which is not feasible.
Therefore, the possible length and width for Derek's rectangular prism with a volume of 120 cubic inches and a height of 6 inches is 6 inches and 20 inches, respectively.
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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.
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.
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
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.
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.)
$
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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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?
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
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.)
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:
(1.85)x + 2.55
Question 3
(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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Shawn wants to paint all the surfaces of the table shown below.
A. the volume of 3 rectangular prisms
B. the surface area of 1 triangle and 4 cylinders
C. the volume of 1 rectangular prism and 3 cylinders
D. the surface area of 2 triangles and 1 rectangular prism
What's the answer? How do I solve for this?!
the answer is D
The figure can be divided into a rectangle and 2 triangles
Given f(x)=5x and g(x) = 1/x-5 which value is in the domain of f g? (5x in the problem has that one symbol) (this is platoweb)
Answer:
f(x)=5x
g(x)=1/x-5
f(g)=5(1/x-5)
f(x)=5/x- 25
therefore domain is x=0
The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 68 minutes and a standard deviation of 14 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(
68
Correct,
14
Correct)
b. Find the probability that a randomly selected person at the hot springs stays longer then 81 minutes.
c. The park service is considering offering a discount for the 8% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount?
minutes.
d. Find the Inter Quartile Range (IQR) for time spent at the hot springs.
Q1:
minutes
Q3:
minutes
IQR:
minutes
a. The distribution of X is X ~ N(68, 14).
b. The corresponding area to the right of 0.9286, which is approximately 0.1772.
c. The longest amount of time a patron can spend and still receive the discount is approximately 48.5654 minutes.
d. The Inter Quartile Range (IQR) for time spent at the hot springs is approximately 21.373 minutes.
a. The distribution of X is X ~ N(68, 14), where X represents the amount of time a person spends at Grover Hot Springs, 68 is the mean, and 14 is the standard deviation.
b. To find the probability that a randomly selected person stays longer than 81 minutes, we need to calculate the area under the normal curve to the right of 81.
Using the z-score formula: z = (x - μ) / σ, where x is the value (81), μ is the mean (68), and σ is the standard deviation (14).
Plugging in the values, we have z = (81 - 68) / 14 = 0.9286.
Using a standard normal distribution table or a calculator, we can find the corresponding area to the right of 0.9286, which is approximately 0.1772.
c. To find the longest amount of time a patron can spend at the hot springs and still receive the discount, we need to find the value that corresponds to the lowest 8% of the distribution.
Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to the 8th percentile, which is approximately -1.4051.
Using the z-score formula, we can calculate the longest amount of time: x = μ + z [tex]\times[/tex] σ = 68 + (-1.4051) [tex]\times[/tex] 14 = 48.5654 minutes.
Therefore, the longest amount of time a patron can spend and still receive the discount is approximately 48.5654 minutes.
d. The Inter Quartile Range (IQR) is a measure of the spread of the data and represents the range between the first quartile (Q1) and the third quartile (Q3).
To find Q1 and Q3, we can use the z-score formula and the standard normal distribution table.
For Q1, we find the z-score corresponding to the 25th percentile, which is approximately -0.6745.
Using the formula Q1 = μ + z [tex]\times[/tex] σ, we have Q1 = 68 + (-0.6745) [tex]\times[/tex] 14 = 57.053.
Therefore, Q1 is approximately 57.053 minutes.
For Q3, we find the z-score corresponding to the 75th percentile, which is approximately 0.6745.
Using the formula Q3 = μ + z [tex]\times[/tex] σ, we have Q3 = 68 + (0.6745) [tex]\times[/tex] 14 = 78.426.
Therefore, Q3 is approximately 78.426 minutes.
Finally, we can calculate the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 78.426 - 57.053 = 21.373 minutes.
Therefore, the Inter Quartile Range (IQR) for time spent at the hot springs is approximately 21.373 minutes.
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Which of the following best describes the lines y-3x=4x and 6-2y=8x
○perpendicular
○parallel
○skew
○intersecting
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.
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.
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 the slope of the line graphed below.
Answer:
m = 3
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-1,-1) (0,2)
We see the y increase by 3 and the x increase by 1, so the slope is
m = 3
Answer:
slope = 3
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (0, 2) ← 2 points on the line
m = [tex]\frac{2-(-1)}{0-(-1)}[/tex] = [tex]\frac{2+1}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3
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
Answer: 12
Step-by-step explanation:
Sadie is going to see a movie and is taking her 4 kids. Each movie ticket costs $15 and there are an assortment of snacks available to purchase for $4.50 each. How much total money would Sadie have to pay for her family if she were to buy 6 snacks for everybody to share? How much would Sadie have to pay if she bought x x snacks for everybody to share?
Answer: 102 dollars/4.5x+75
Step-by-step explanation: Your question isn't really straightforward, x x snacks for everybody to share? Please elaborate, and are they talking about the total cost, or just the cost of 6 snacks?
First, we have to take into account that if SADIE is taking her FOUR kids, there will be 5 people.
Cost of tickets is equal to $15 per one, and
5x (where x=15, per 5)
5(15)=75, and now onto the snacks
4.5x2=9, and 6/2=3, so 9x3=27, or 4.5x6=27
75+27=102
then for x snacks, if 1 snack costs 4.5 dollars than it'd be 4.5x (x number of snacks)+75 to find the total cost with tickets and all.
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
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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Find y" by implicit differentiation.
cos(y) + sin(x) = 1
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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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?
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.
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).
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The three true statements are:
1. The radius of the circle is 3 units.
2. The center of the circle lies on the x-axis.
3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
To determine the properties of the circle with the equation [tex]x^2 + y^2 - 2x - 8 = 0,[/tex] let's analyze the given options:
The radius of the circle is 3 units:
To find the radius, we need to rewrite the equation in standard form, which is [tex](x - h)^2 + (y - k)^2 = r^2.[/tex]
Comparing the given equation to the standard form, we can determine the center and radius.
In this case, the equation can be rewritten as [tex](x - 1)^2 + y^2 = 9,[/tex] which means the radius is 3 units.
Therefore, this statement is true.
The center of the circle lies on the x-axis:
From the standard form of the equation, we can see that the x-coordinate of the center is 1.
Since the y-coordinate is 0 in the equation, the center lies on the x-axis. Thus, this statement is true.
The center of the circle lies on the y-axis:
Since the y-coordinate of the center is not 0 but rather represented by [tex]y^2,[/tex] the center does not lie on the y-axis.
Therefore, this statement is false.
The standard form of the equation is[tex](x - 1)^2 + y^2 = 3:[/tex]
The given equation can indeed be rewritten as [tex](x - 1)^2 + y^2 = 9,[/tex] as mentioned earlier, representing a circle with a radius of 3.
However, the statement incorrectly specifies a radius of 3 instead of 9. Thus, this statement is false.
The radius of this circle is the same as the radius of the circle whose equation is[tex]x^2 + y^2 = 9:[/tex]
The circle described by the equation [tex]x^2 + y^2 = 9[/tex] has a radius of 3 units. Comparing this to the circle in question, which also has a radius of 3 units, we can conclude that the statement is true.
Therefore, the three true statements are:
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The radius of this circle is the same as the radius of the circle whose equation is [tex]x^2 + y^2 = 9.[/tex]
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Find the equation of the line in slope-intercept form, parallel to a line joining the points (1,-2) and (-4,3) and passing through (-4,-5).
I
The equation of the line parallel to a line joining points (1,-2) and (-4,3) and passing through (-4,-5) is
(Simplify your answer. Type your answer in slope-intercept form.)
The equation of the line parallel to the line passing through (1, -2) and (-4, 3) and passing through the point (-4, -5) is y = -x - 9 in slope-intercept form.
To find the equation of a line parallel to a given line, we need to determine the slope of the given line and then use it to construct the equation of the parallel line.
First, let's calculate the slope of the given line passing through points (1, -2) and (-4, 3). The slope, denoted as m, can be found using the slope formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates, we have:
m = (3 - (-2)) / (-4 - 1) = 5 / (-5) = -1
Now that we have the slope, we can use it to construct the equation of the parallel line.
We'll use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
where (x1, y1) represents the coordinates of a point on the line.
We'll use the point (-4, -5) on the parallel line:
y - (-5) = -1(x - (-4))
y + 5 = -1(x + 4)
Simplifying further:
y + 5 = -x - 4
y = -x - 9
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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?
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.
1,020.50375 rounded to the nearest tenth
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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A ____ is just another way of saying what we want to count by on our graph.
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.
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
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.
The diagram shows a cuboid. 8 cm 15 cm 20 cm What is the volume of the cuboid?
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
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
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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what is the volume of the cylinder below height 15 radius 11
Answer:
πr^2 h
π(11)^2 (15)
= 1815π or = 5701
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
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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Find the linear function
The linear function for this case is:
f(x) = 5,000*x + 7,000
How to find the linear function?The general linear function is written as:
f(x) = a*x + b
Where a is the slope and b is the y-intercept.
Here we want a linear function for the given scenario, we know that the initial population is 7,000, then we can write:
f(x)= a*x + 7,000
Then we know that the population increases by 5,000 per year for 5 years, so the slope is 5,000, then we can write the function as:
f(x) = 5,000*x + 7,000
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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
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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