The value of the expression -x³ + 3x² - x + 20 when x = -1 is 23.
What is the value of the given expression when x = -1?Given the expression in the question;
-x³ + 3x² - x + 20
x = -1To determine the value of the expression,
First, we substitute -1 for x in the expression:
-( -1 )³ + 3( -1 )² − ( -1 )) + 20
Next, we simplify each term using the order of operations (also known as PEMDAS):
-( -1 )³ = -( -1 ) = 1
(recall that the exponent is evaluated first, then the negative sign is applied)
3( -1 )² = 3(1) = 3
(recall that the exponent is evaluated first)
-( -1 ) = 1
(recall that subtracting a negative is the same as adding a positive)
Now, putting these simplified terms back into the original expression, we get:
1 + 3 + 1 + 20
Finally, we add these terms together to get the final answer:
23
Therefore, the value of the expression is 23.
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Anna is buying a house selling for $ 245,000. To obtain the mortgage, Anna is required to make a 15% down payment. Anna obtains a 30-year mortgage with an interest rate of 5%.
a) Determine the amount of the required down payment.
b) Determine the amount of the mortgage.
c) Determine the monthly payment for principal and interest.
Anna's monthly payment for principal and interest is $1,117.78.
How to solve the mortgage problem?a) The amount of the required down payment can be calculated as follows:
Down payment = 15% of $245,000
Down payment = 0.15 x $245,000
Down payment = $36,750
Therefore, Anna is required to make a down payment of $36,750.
b) The amount of the mortgage can be calculated as follows:
Mortgage = Total price of the house - Down payment
Mortgage = $245,000 - $36,750
Mortgage = $208,250
Therefore, Anna's mortgage amount is $208,250.
c) The monthly payment for principal and interest can be calculated using the formula for a fixed-rate mortgage:
[tex]$M = P\left[\frac{i(1+i)^n}{(1+i)^n-1}\right][/tex]
Where:
M = Monthly Mortgage
P = Principal (amount of the loan)
i = Monthly interest rate (5% / 12 = 0.0041667)
n = Total number of payments (30 years x 12 months = 360)
Plugging in the values, we get:
[tex]$M = \frac{\$208,250 \left[0.0041667(1+0.0041667)^{360}\right]}{\left[(1+0.0041667)^{360}-1\right]}[/tex]
M = $1,117.78
Therefore, Anna's monthly payment for principal and interest is $1,117.78.
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Please help on this fast
Answer:the top one
Step-by-step explanation:
2. Blake interviewed 24 students to see whether they collected sports cards and whether they participated in sports. The table below shows his data Sports-Card Collecting and Sports Participation Collects Sports Cards Does Not Collect Sports Cards Participates in Sports 6 Does Not Participate in Sports 3 7 How many total students Blake interviewed, participate in sports?
Therefore, out of the 24 students that Blake interviewed, 9 of them participate in sports.
What is equation?An equation is a mathematical statement that indicates that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign "=" which means that the two expressions have the same value.
Here,
According to the table, Blake interviewed a total of 24 students. To find out how many of these students participate in sports, we need to add up the number of students who collect sports cards and participate in sports, as well as the number of students who do not collect sports cards and participate in sports. So:
Total students who participate in sports = Number of students who collect sports cards and participate in sports + Number of students who do not collect sports cards and participate in sports
Total students who participate in sports = 6 + 3
Total students who participate in sports = 9
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order the angles from least to greatest 21m 24m 17m
The order of the angles is 43.8°, 63.2, and 75.02 (Here the values are approximate values).
Ordering the angles of the triangle:To order the angles of a triangle from least to greatest, we need to first determine the angles of the triangle, and then order the remaining two angles in increasing order.
The formulas we used are
Cosine formula: Cos C = (a² + b² - c²)/2ab
Law of sine: a/ sin(A) = b / sin(B) = c / sin(C)
Here we have
The sides of the triangle are 21m 24m and 17m
Use the Law of Cosines to find one of the angles
=> Cos C = (a² + b² - c²)/2ab
Where a, b, and c are the lengths of the sides of the triangle, and C is the angle opposite the side of length c.
In this case, we have:
a = 21 m, b = 24 m and c = 17 m
Cos(C) = (21² + 24² - 17²) / (2 × 21 × 24)
Cos (C) = 728/1008 = 0.722
C = cos⁻¹(0.722) = 43.8°
So angle C is 43.8°, which is the smallest angle in the triangle.
To order the remaining two angles in increasing order use the Law of Sines to do this:
a / sin(A) = b / sin(B) = c / sin(C)=> 21/sin(A) = 24 / sin(B) = 17 / sin(43.78)
=> 21/sin(A) = 24 / sin(B) = 17 /0.69
=> 21/sin(A) = 17/0.69
=> Sin A = (21 × 0.69)/17
=> Sin A = 0.85
=> A = Sin⁻¹(0.85)
=> A = 63.2
=> 24 / sin(B) = 17 /0.69
=> Sin B = (24 × 0.69)/17
=> Sin B = 0.97
=> B = Sin⁻¹(0.97)
=> B = 75.02
Hence, the order of the angles is 43.8°, 63.2, and 75.02
Therefore,
The order of the angles is 43.8°, 63.2, and 75.02 (Here the values are approximate values).
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Complete Question:
Order the angles from least to greatest 21m 24m 17m
a pyramid has a height of 5 inches and a volume of 60 cubic inches ?
Answer:
36 square inches.
Step-by-step explanation:
volume is given by 1 by 3, into base into height is based. His height and volume and area of the base is given by area of the ashe area of the base is given by 3 into 60 by 5. As given in the question on solving it, we get it equals to 36 square inches.
A diy superstore sold 10 ride-on lawnmowers in a week and earned €23,380. what was the cost per lawnmower?
Answer:
Cost per lawnmower = total earnings / number of lawnmowers sold
Cost per lawnmower = €23,380 / 10
Cost per lawnmower = €2,338
Therefore, the cost per lawnmower was €2,338.
Miles per gallon of a vehicle is a random variable with a uniform distribution from 23
to 47. The probability that a random vehicle gets between 28 and 36 miles per gallon
is: Answer: (Round to four decimal places)
Answer:
Step-by-step explanation:
The range of the uniform distribution is from 23 to 47, so the minimum value (a) is 23 and the maximum value (b) is 47.
The probability density function for a uniform distribution is:
f(x) = 1 / (b - a) if a ≤ x ≤ b
= 0 otherwise
We want to find the probability that a random vehicle gets between 28 and 36 miles per gallon. This is the same as finding the area under the probability density function between x = 28 and x = 36.
Since the distribution is uniform, the probability density function is a horizontal line between x = 23 and x = 47, with height equal to 1 / (47 - 23) = 1/24.
The area under the probability density function between x = 28 and x = 36 is:
P(28 ≤ x ≤ 36) = (36 - 28) * 1/24 = 8/24 = 1/3
Therefore, the probability that a random vehicle gets between 28 and 36 miles per gallon is 1/3, or 0.3333 rounded to four decimal places.
(a)Draw a tree diagram to display all the possible outcomes that can occur when you flip a coin and then toss a six-sided die.
(b) How many outcomes contain a head and a number greater than 2?
(c) Assuming the outcomes displayed in the tree diagram are all equally likely, what is the probability that you will get a head and a number greater than 2 when you flip a coin and toss a six-sided die? (Round your answer to three decimal places.)
Answer:
shape?Draw a tree diagram to display all the possible outcomes that can occur when you flip a coin and then toss a six-sided die.(b) How many outcomes contain a head and a number greater than 2?(c) Assuming the outcomes displayed in the tree diagram are all equally likely, what is the probability that you will get a head and a number greater than 2 when Sure, I can help you with that! Here's a tree diagram showing all the possible outcomes of flipping a coin and rolling a six-sided die: ``` H T / \ / \ 1 2 3 4 / \ / \ / \ / \ 1 2 3 4 5 6 1 2 ``` Each branch represents a possible outcome, with the first letter indicating the outcome of the coin flip (H for heads, T for tails), and the second number indicating the outcome of the die roll. (b) To find the number of outcomes that contain a head and a number greater than 2, we can look at the branches that start with H and have a 3, 4, 5, or 6 on the second level. There are four of
Answer: There are 3 outcomes that contain greater than 2
PLEASE RATE THIS BRAINLIEST
A quadrilateral in the coordinate plane has vertices ( -3, 1), ( 2, 1), ( 2, -2) and (-3, -2). What is the perimeter, in units, of the quadrilateral
Answer:
To find the perimeter of the quadrilateral, we need to find the distance between its vertices and then add them up. We can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the distance between each pair of adjacent vertices:
Distance between (-3, 1) and (2, 1):
d = sqrt((2 - (-3))^2 + (1 - 1)^2) = sqrt(25) = 5
Distance between (2, 1) and (2, -2):
d = sqrt((2 - 2)^2 + (-2 - 1)^2) = sqrt(9) = 3
Distance between (2, -2) and (-3, -2):
d = sqrt((-3 - 2)^2 + (-2 - (-2))^2) = sqrt(25) = 5
Distance between (-3, -2) and (-3, 1):
d = sqrt((-3 - (-3))^2 + (1 - (-2))^2) = sqrt(9) = 3
Now we can add up these distances to get the perimeter:
perimeter = 5 + 3 + 5 + 3 = 16
Therefore, the perimeter of the quadrilateral is 16 units.
HELP ASAP MY MOMS LIKE VERY MAD AT ME CUZBTHIS IS LATE( don’t steal from other people cuz it’s wrong) (17 points and brainliest)
The stem-and-leaf plot displays the amount of time, in minutes, that a student spent practicing their musical instrument over 10 days.
1 5
2 0, 2, 5
3 2, 4
4 5
5 3, 6
6 0
Key: 2|0 means 20
Part A: Calculate the mean and median for the data given. (2 points)
Part B: A student would like to show their teacher that they have practiced long enough for the day. Which measure of center should the student give to their teacher? Explain your answer. (2 points)
The mean is 27.3. and the median is 24.5.
What is a mean median and mοde?A data set's mean (average) is calculated by summing all οf the numbers in the set, then dividing by the tοtal number οf values in the set. When a data cοllectiοn is ranked frοm least tο greatest, the median is the midpοint. The number that appears mοst frequently in a data set is called the mοde.
Part A:
Tο calculate the mean, we need tο add up all the values and divide by the tοtal number οf values:
15 + 20 + 22 + 24 + 25 + 26 + 30 + 35 + 36 + 60 = 273
273 / 10 = 27.3
Therefοre, the mean is 27.3.
Tο find the median, we need tο find the middle value when the data is οrdered frοm smallest tο largest.
Median = (24 + 25) / 2 = 24.5
Therefοre, the median is 24.5.
Part B:
The measure οf centre that the student shοuld give tο their teacher depends οn the teacher's preference. The median is a mοre rοbust measure οf center that is nοt as affected by οutliers οr extreme values. The median alsο gives a better sense οf the typical value in the data.
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Use the angle relationship in the figure below to solve for x. Assume that line A and line B are parallel, line C is a transversal and the given angles are given in degrees.
Step-by-step explanation:
the 2 angles are supplementary. that means together they have 180°
4x + 29 = 180 - (12x + 55) = 180 - 12x - 55 = 125 - 12x
16x = 96
x = 96/16 = 6
Solve the equation without using a calculator
[tex](x^3-1000)^{1/2}=(x^2+100)^{1/3}[/tex]
Without using a calculator, the only solution to the equation [tex](x^3 - 1000)^{1/2} = (x^2 + 100)^{1/3}[/tex] is 10.1136.
What is the solution of the equation?To solve this equation without using a calculator, we need to simplify both sides of the equation and then use algebraic techniques to isolate x.
[tex](x^3 - 1000)^{1/2} = (x^2 + 100)^{1/3}[/tex]
square both sides of the equation and cube both sides of the equation, we will have;
(x³ - 1000)³ = (x² + 100)²
We can simplify the left-hand side of the equation by applying the cube of a binomial formula, which states that:
(a + b)³ = a³ + 3a²b + 3ab² + b³
Let's apply this formula with a = x³ and b = -1000:
(x³ - 1000)³ = x⁹ - 3x⁶(1000) + 3x³(1000)² - 1000³
Next, let's simplify the right-hand side of the equation:
(x² + 100)² = x⁴ + 200x² + 10000
Now we can substitute these expressions back into the original equation:
x⁹ - 3x⁶(1000) + 3x³(1000)² - 1000³ = x⁴ + 200x² + 10000
We can then rearrange the terms to get a polynomial equation in x:
x⁹ - 3x⁶(1000) + 3x³(1000)² - x⁴ - 200x² - 10000 - 1000³ = 0
This equation is difficult to solve exactly, but we can make an educated guess that x is close to 10. If we substitute x = 10, we get:
(10³ - 1000)³ ≠ (10² + 100)²
Increase the value of x a little, say 10.1136
(10.1136³ - 1000)³ ≈ (10.1136² + 100)²
This is true, so x = 10.1136 is a solution to the equation. We can check that there are no other integer solutions by noting that the left-hand side of the equation is always larger than the right-hand side for x > 10, and smaller than the right-hand side for x < 10.
Therefore, the only solution to the equation is x = 10.1136.
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Which describes the graph of y = −(x − 3)2 − 8?
A.Opens up with a vertex at (−3, −8)
B.Opens up with a vertex at (3, −8)
C.Opens down with a vertex at (−3, −8)
D.Opens down with a vertex at (3, −8)
Opens down with a vertex at (3, −8)
WILL GIVE BRAINLIEST PLEASR HELP ASAP
A set of 3 cards, spelling the word ADD, are placed face down on the table. Determine P(A, D) if two cards are randomly selected with replacement.
-In
Note that in the above Theoretical Probability prompt, the P(A, D) if two cards are randomly selected with replacement is 2/9. (Option C)
What is Theoretical Probability?
Theoretical probability is a branch of mathematics that deals with predicting the likelihood of events based on mathematical reasoning and assumptions, rather than empirical evidence or observations.
Where it is required to determine the P(A, D) if two cards are randomly selected from cards (A,D,D) with replacement:
P (A) = 1/3
P (D) = 2/3
Thus, P (A, D) = 1/3 * 2/3
= 1/3 × 2/3
= (1×2) / (3×3)
= 2/9
Thus, it is correct to state that the probability, if two cards A, and D are randomly selected with replacement is 2/9. (Option C)
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11. A rectangular room measures 16 feet by 18 feet. The ceiling is 9 feet high.
a. Find the total area of the four walls in the room.
b. If a gallon of paint costs $37.99 and it covers 400 square feet on average, what is the cost of
painting the room, including the ceiling, with two coats of paint? Explain your answer.
c. This room is well insulated and is on the north side of the house. How large of an air
conditioner would this room require? Round to the next highest thousand BTUs.
d. A scale drawing is made of this room using the scale 1 sq ft = sq in. What are the
dimensions of this room on the drawing?
Therefore , the solution of the given problem of area comes out to be a.720 sq. ft, b.$227.94 , c.64,800 BTUs. and d.2,592 sq in.
What does an area actually mean?Calculating how much space would be needed to fully enclose its exterior will reveal its overall size. The neighboring area is considered when selecting a comparable good for the rectangular design. The surface area of something determines its overall measurements. The number of sides between a cuboid's four trapezoidal shapes determines how much water it can hold.
Here,
A.
=> 2(144 sq. ft.) + 2(162 sq. ft.) = 720 sq. ft.
b.
16 * 18 = 288 square feet
The entire region that needs painting is:
=> 720 square feet + 288 square feet = 1008 square feet.
We need to apply two layers of paint to the following surface area:
=> 2 * 1008 square feet = 2016 square feet.
5.04 gallons are obtained by multiplying 2016 square feet by 400 square feet per gallon.
=> $6 liters* $37.99/gallon = $227.94
c. 16 feet by 18 feet by 9 feet equals 2,592 cubic feet
As a result, the room's necessary cooling capacity is:
=> 2,592 cubic feet*25 BTUs per cubic foot = 64,800 BTUs.
Rounding up to the next greatest thousand BTUs, we need an air conditioner with a capacity of 65,000 BTUs.
d.
=> 16 ft x 144 sq in/ft = 2,304 sq in by
=> 18 ft x 144 sq in/ft = 2,592 sq in
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Which of the following are considered variable costs? (Check all that apply.)
Answer:
??
Step-by-step explanation:
is there an image or something?
SECTION III - Show all your working 37. Mr. Morrie shared $1050 among his three children Daniel, Eva and Francis. Eva received $185.00 more than Daniel who received $175.00 less than Francis. How much money did each child receive?
Answer:
Daniel received $230.00, Eva received $415.00, and Francis received $405.00.
Step-by-step explanation:
Let's assume that Daniel received x dollars.
Then, according to the problem, Eva received $185.00 more than Daniel, which means she received (x + 185) dollars.
Similarly, we know that Daniel received $175.00 less than Francis, which means Francis received (x + 175) dollars.
We also know that the total amount of money shared among the three children is $1050.00. Therefore, we can write the following equation:
x + (x + 185) + (x + 175) = 1050
Simplifying the equation:
3x + 360 = 1050
3x = 690
x = 230
Therefore, Daniel received $230.00, Eva received (x + 185) = $415.00, and Francis received (x + 175) = $405.00.
To check that these values are correct, we can verify that they add up to the total amount of money shared:
$230.00 + $415.00 + $405.00 = $1050.00
Therefore, Daniel received $230.00, Eva received $415.00, and Francis received $405.00.
find the slope of the line that that passes through each pair of points (-7,5) (1,1)
Answer:[tex]-\frac{1}{2}[/tex]
Step-by-step explanation:The line is diagonal to the left(\) , so the slope is negative.
[tex]\frac{rise}{run}[/tex]
Rise one(up), Run two(left)
So the CORRECT answer is [tex]-\frac{1}{2}[/tex]
A triangle has sides with lengths 15, 23, and x. What is the range of possible values of x?
Answer:
8 < x < 38
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , that is
23 - 15 < x < 23 + 15 , then
8 < x < 38
Kofo saved N30.00 with the post office savings bank for 2 years. At the end of this period he received N2.40 as simple interest on his money. At what rate per annum was the interest paid?
Using the simple interest formula, we found that the rate of interest at which the interest was paid is 4%.
What is meant by simple interest?
The financial fee for borrowing money is called interest, and it is typically stated as a percentage, such as an annual percentage rate (APR). For the use of their money, lenders may earn interest, and borrowers may pay interest.
A way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time is by using simple interest. Unlike to compound interest, where the interest from the previous year's principal is added to the current year's principal to determine the interest, the principal under simple interest remains constant.
Given,
The principal amount P = 30 naira
The time period t = 2 years
Interest amount received I = 2.40 naira
We are asked to find the rate of the interest r.
the simple interest formula is:
I = ( P *r * t )/ 100
2.4 = (30*r*2)/100
240 = 60r
r = 240/60 = 4%
Therefore using the simple interest formula, we found that the rate of interest at which the interest was paid is 4%.
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please help
The table of values represents a quadratic function f(x).
x f(x)
−8 7
−7 2
−6 −1
−5 −2
−4 −1
−3 2
−2 7
−1 14
0 23
What is the equation of f(x)?
f(x) = (x − 5)2 − 2
f(x) = (x − 4)2 − 1
f(x) = (x + 4)2 − 1
f(x) = (x + 5)2 − 2
Answer:
Step-by-step explanation:
From the symmetry in the table, we can see that the vertex of the parabola is located at (-5, -2). We will pick another point from the table to use in our model to solve for the a value, just in case there is one. I picked (-4, -1). Any point from the table will work.
Our model is
[tex]y=a(x-h)^2+k[/tex] where h and k are the coordinates of the vertex and x and y are the coordinates from the other point chosen from the table. Filling in to solve for a:
[tex]-1=a(-4+5)^2-2[/tex] and
[tex]-1=a(1)^2-2[/tex] and
-1 = a - 2 so
a = 1.
Now we can fill in the equation with the coordinates of the vertex and the value found for a to get
[tex]y=(x+5)^2-2[/tex] You don't need to put the 1 out in front; it's unnecessary. Your choice is the last one there in the list.
Suppose that 10 balls are put into 5 boxes, with each ball independently being put in
box with probability (), ∑(i = 1 to 5) () = 1
(a) Find the expected number of boxes that do not have any balls.
(b) Find the expected number of boxes that have exactly 1 balls.
Answer:
(a) Let X be the number of boxes that do not have any balls. We can calculate the probability that a particular box is empty, which is (1-p)^10, where p is the probability that a ball is put into that box. The expected number of boxes that are empty is then:
E(X) = 5(1-p)^10 (since each box has the same probability of being empty)
Substituting ∑(i = 1 to 5) p = 1, we get p = 1/5. Therefore,
E(X) = 5(1-1/5)^10 = 5(4/5)^10 ≈ 0.328
So, the expected number of boxes that do not have any balls is approximately 0.328.
(b) Let Y be the number of boxes that have exactly one ball. The probability that a particular box has exactly one ball is given by:
P(exactly one ball in a box) = 10p(1-p)^4
where p is the probability that a ball is put into that box. The expected number of boxes that have exactly one ball is then:
E(Y) = 5(10p(1-p)^4)
Substituting p = 1/5, we get:
E(Y) = 5(10/5^5) = 1/25
So, the expected number of boxes that have exactly one ball is 1/25.
What is the answer of this 7²(4)÷4
If your answer is correct thank you
Answer:
49
Step-by-step explanation:
WHAT DOES PEMDAS STAND FOR?P: Parenthesis
E: Exponent
M: Multiplication
D: Division
A: Addition
S: Subtraction
Start by solving what is inside the parenthesis first:
(4) which is equal to 4Next, solve for the exponent:
7² (which means 7 multiplied by itself twice)
7 x 7 = 49Now you can multiply 49 and 4:
49 × 4 = 196
Finally, divide 196 by 4:
196 ÷ 4 = 49
Therefore, the answer to the expression 7² (4) ÷ 4 is 49.
Juan bought 24 ounces of grapes grapes cost 2.90 per pound how much did he pay for the grapes
Juan paid Rs. 4.35 for the grapes. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
The four fundamental operations, frequently referred to as "arithmetic operations," are claimed to be able to explain all real numbers. The four mathematical operations that come after division, multiplication, addition, and subtraction are quotient, product, sum, and difference.
We are given that Juan bought 24 ounces of grapes and the grapes cost 2.90 per pound.
We know that 1 pound = 16 ounces.
So, 24 ounces = 1.5 pounds
Now, using multiplication operation, we get
⇒ 1.5 * 2.9 = Rs. 4.35
Hence, Juan paid Rs. 4.35 for the grapes.
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Find x, y and z. Round decimals to the nearest hundredth. 7.1 25 1 6 M
Answer:
x = 10.68y = 12.25z = 21.79Step-by-step explanation:
You want the side lengths in a right triangle geometry when the altitude to the hypotenuse of length 25 cuts off a segment of length 6.
Geometric mean relationsAll of the right triangles in this configuration are similar. The proportional relationships between the sides give rise to three geometric mean relations.
In effect each of the segments x, y, z is the geometric mean of the two segments of the hypotenuse it touches.
x = √(6·(25-6)) = √114 ≈ 10.68
y = √(6·25) = 5√6 ≈ 12.25
z = √((25 -6)·25) = 5√19 ≈ 21.79
__
Additional comment
To see how these arise, consider the ratio of long side to hypotenuse:
z/25 = 19/z
z² = 25·19
z = √(25·19) . . . . . the geometric mean of 25 and 19
The "geometric mean" of n numbers is the n-th root of their product. For two numbers, it is the square root of their product.
Which statement correctly defines the trigonometric ratio?
Responses
A). The cosine of an angle is defined as the length of the side opposite over the length of the hypotenuse.
B). The cosecant of an angle is defined as the length of the hypotenuse over the length of the side opposite.
C). The cotangent function is defined as the length of the side opposite over the length of the side adjacent.
D). The sine function is defined as the length of the hypotenuse over the length of the side adjacent.
The correct option is (b) i.e. The cosecant of an angle is defined as the length of the hypotenuse over the length of the side opposite.
What is Trigonometric ratio?
Trigonometric ratios are mathematical functions used in trigonometry, which is the branch of mathematics that deals with the relationships between the sides and angles of triangles. The three main trigonometric ratios are sine, cosine, and tangent
All statements contain some sort of mistake except the statement (b).
The statements should be corrected as given below:
A). The cosine of an angle is defined as the length of the side adjacent over the length of the hypotenuse.
C). The cotangent function is defined as the length of the side adjacent over the length of the side opposite.
D). The sine function is defined as the length of the side opposite over the length of the hypotenuse.
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10. What is BD? Show work to support your answer.
Answer:
BD = 8
Step-by-step explanation:
To solve this, you need to use Pythagorean theorem which states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
For △ABC, AC (4+16) is the hypotenuse
=> AC^2 = AB^2 + BC^2
For △ABD, AB is the hypotenuse
=> AB^2 = AD^2 + BD^2
For △BCD, BC is the hypotenuse
=> BC^2 = BD^2 + CD^2
Therefore
AC^2 = AB^2 + BC^2
AC^2 = (AD^2 + BD^2) + (BD^2 + CD^2)
20^2 = 4^2 + BD^2 + BD^2 + 16^2
400 - 16 - 256 = 2BD^2
BD^2 = 128/2 = 64
BD = √64 = 8
Elena wonders how much water it would take to fill her cup. She drops her pencil in her cup and notices that it just fits diagonally. (See the diagram.) The pencil is 13 cm long and the cup is 12 cm tall. How much water can the cup hold? Explain or show your reasoning.
Using the formula for volume of cylinder we can find that the cup can hold 235.5cm³ volume of water.
Define volume?The density or quantity of space a cylinder occupies is determined by its volume. Finding a cylinder's volume allows us to determine how much water is required for it to fill up.
Volume of a cylinder equals circle's area times height.
Volume equals πr² h
V = πr²h cubic units, where h is the height and r is the radius, is the volume of a cylinder.
Let's assume the cup is a cylinder. The pencil length is simulating a diagonal (hypothenuse), which forms a right triangle with the height of the cylinder and the diameter at the bottom. So, we apply Pythagorean's Theorem.
13² = 12² + d²
⇒ d² = 169-144
⇒ d = √25
⇒ d =5cm.
Radius = d/2
= 5/2
=2.5cm.
Now,
Volume of the cup = π × r² × h
= 3.14 × 2.5² × 12
= 235.5cm³.
Therefore, the cup can hold 235.5cm³ volume of water.
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The complete question is:
Elena wonders how much water it would take to fill her cup. She drops her pencil in her cup and notices that it just fits diagonally. (See the diagram.) The pencil is 13 cm long and the cup is 12 cm tall. How much water can the cup hold? Explain or show your reasoning.
Select each pair of expressions that are equivalent O 3x+-x+1 4 and 4x + 1 2 +6x and 2(3x + 1) D 3(x + 1)–(1-X) and 2x+3 O 3xand 4(x + 1)-x-4 5.5 + 2.2x + 3.8x - 4.1 and 1.4 + 6X
convert 162.44 minutes to hours 2hours and 42 minutes show steps
Answer:
Step-by-step explanation: There are 60 minutes in each hour. You can do 162.44/60 and will get 2 with a remainder of 42.44 and the 42 goes towards minutes will the 0.42 left is for seconds. Your not converting to seconds so we can leave that as a decimal.
This will give you a total of 2 hours 42.44 minutes. If you want to check your work, you can do (2*60)+42.44=162.44.
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To convert 162.44 minutes to hours and minutes, we can follow these steps:
Divide the number of minutes by 60 to get the total number of hours:
162.44 ÷ 60 = 2.7073 hours (rounded to 4 decimal places)
The whole number part of the answer is the number of hours, and the decimal part represents the remaining minutes. In this case, we have:
2 hours and 0.7073 hours (or 42.438 minutes)
To convert the decimal part to minutes, we can multiply it by 60:
0.7073 × 60 = 42.438 minutes (rounded to 3 decimal places)
Finally, we can combine the whole number of hours with the remaining minutes:
2 hours and 42 minutes
Therefore, 162.44 minutes is equal to 2 hours and 42 minutes.