Solve the problem.
Four students used different methods to approximate the diagonal distance across the middle school gym. The students and their measurements are shown in the following table. Calculate the decimal equivalent for each measurement rounded to the nearest hundredth yard. Write the decimal next to each worker’s name in the tableStudent
Measurement (yards) Decimal Calculation
Arturo
6
√
28
Bonnie
8
√
17
Courtney
10
π
Dawson
3.1
√
100
The measurements of the diagonal distance across the middle school gym is given by the following persons and is rounded to the nearest hundredths
The calculation of Arturo = 31.75 yards
The calculation of Bonnie = 32.98 yards
The calculation of Courtney = 31.42 yards
The calculation of Dawson = 31 yards
What is rounding up numbers?There are basically two rules while rounding up numbers
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Non-zero digits are always significant
Zeros between non-zero digits are always significant
Leading zeros are never significant
Trailing zeros are only significant if the number contains a decimal point
Given data ,
Let the measurements of the diagonal distance across the middle school gym be represented as A
Now , the measured values are
a)
The measurement of Arturo = 6√28 yards
The measurement of Arturo = 6 x 5.2915
On rounding , we get
The measurement of Arturo = 31.75 yards
b)
The measurement of Bonnie = 8√17 yards
The measurement of Bonnie = 8 x 4.123
On rounding , we get
The measurement of Bonnie = 32.98 yards
c)
The measurement of Courtney = 10π yards
The measurement of Courtney = 10 x 3.142
On rounding , we get
The measurement of Courtney = 31.42 yards
d)
The measurement of Dawson = 3.1√100 yards
The measurement of Dawson = 3.1 x 10
On rounding , we get
The measurement of Dawson = 31 yards
Hence , the measurements are rounded
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If a seed is planted, it has a 95% chance of growing into a healthy plant.
If 8 seeds are planted, what is the probability that exactly 3 don't grow?
The probability that exactly three plants don't grow is given as follows:
0.0054 = 0.54%.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
n = 8, as there are 8 plants.p = 0.05, as 95% of the plants grow, hence 5% don't grow.The probability that exactly three don't grow is P(X = 3), hence:
P(X = 3) = C(8,3) x (0.05)^3 x (0.95)^5 = 0.0054.
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A new car is purchased for 27,200 dollars. The value of the car depreciates at a rate of
5% per year. Which equation represents the value of the car after 7 years?
The value of the car after 7 years is approximately $18,994.7.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
Let V be the value of the car after 7 years.
In the first year, the value of the car depreciates by 5%, so the value after the first year is:
V1 = 0.95 × 27,200
In the second year, the value of the car depreciates again by 5%, so the value after the second year is:
V2 = 0.95 × V1
Similarly, the value of the car after the third year is:
V3 = 0.95 × V2
We can continue this process for each of the 7 years:
V4 = 0.95 × V3
V5 = 0.95 × V4
V6 = 0.95 × V5
V7 = 0.95 × V6
So, the equation that represents the value of the car after 7 years is:
V = 0.95⁷ × 27,200
Simplifying this expression, we get:
V ≈ 18,994.7
Therefore, the value of the car after 7 years is approximately $18,994.7.
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Evaluate the expression 10a - 2b when
a = 2 and b = - 3?
Answer:
26
Step-by-step explanation:
10(2) -2(-3)=20+6=26
Answer:
[tex]\bf 26[/tex]Step-by-step explanation:
[tex]\tt 10a-2b[/tex]
[tex]\tt a=2[/tex]
[tex]\tt b=-3[/tex]
______
[tex]\tt 10\times \:2-2\left(-3\right)[/tex]Simplify: 10×2 = 20
[tex]\tt 20-2x-3[/tex]Simplify: 2×-3= -6
[tex]\tt 20-(-6)[/tex][tex]\tt 20+6[/tex]Simplify:-
[tex]\tt 26[/tex]_____________________
Hope this helps! :)
Volume of 5in, 9in , 10in Triangular Prism
Answer:
[tex]\mathrm{225\:in\:\right)^3}[/tex]
Step-by-step explanation:
Given:
base = b = 10 in
height = h = 9 in
length = l = 5 in
[tex]\mathrm{Use\:formula}\:\mathrm{V= \dfrac{1}{2}\times\:b\times\:h\times\:l:}[/tex]
[tex]\mathrm{V= \dfrac{1}{2}\times\:10\times\:9\times\:5}[/tex]
[tex]\mathrm{= 225\:in\:\right)^3}[/tex]
Final answer is rounded to 3 decimal places.
5a + 3b = 13
7a + 6b = 20
Answer:
5a + 3b = 13
7a + 6b = 20
And solve for the values of "a" and "b" using algebraic methods like substitution or elimination.
Step-by-step explanation:
Solving for a and b in the system of equations:
5a + 3b = 13
7a + 6b = 20
We can multiply the first equation by 2 to get:
10a + 6b = 26
Then, we can subtract the second equation from this to eliminate b:
(10a + 6b) - (7a + 6b) = 26 - 20
3a = 6
Solving for a, we get:
a = 2
Substituting this value into the first equation, we can solve for b:
5a + 3b = 13
5(2) + 3b = 13
10 + 3b = 13
3b = 3
b = 1
Therefore, the solution to the system of equations is:
a = 2
b = 1.
Hector is playing a new video game. To get to the next level, he must capture the golden brick and then choose the correct door chance that he chooses the correct door is 40%. The probability that he dos the probability thatHector is playing a new video game. To get to the next level, he must capture the golden brick and then choose the correct door. The chance that he captures the golden brick is 70%. The chance that he chooses the correct door is 40%. The probability that he does both is 20%. Create a Venn Diagram and determine the probability that:
He captures the golden brick and chooses the correct door:
He only captures the golden brick:
He only chooses the correct door:
He doesn’t complete either task:
The probability that Hector captures the golden brick and chooses the correct door is approximately 0.2, or 20%.
What is probability ?
Probability can be defined as ratio number of favourable outcomes, total number of outcomes.
A represents the event that Hector captures the golden brick (with a probability of 0.7), B represents the event that Hector chooses the correct door (with a probability of 0.4), and C represents the intersection of A and B (the event that Hector captures the golden brick and chooses the correct door, with a probability of 0.2).
The probability of event C can be calculated using the formula:
P(C) = P(A and B) = P(A) * P(B|A)
where P(A) is the probability of event A (capturing the golden brick), and P(B|A) is the conditional probability of event B (choosing the correct door) given that event A has occurred (i.e., Hector has captured the golden brick). We are given that P(A) = 0.7, P(B) = 0.4, and P(A and B) = 0.2, so we can calculate:
P(B|A) = P(A and B) / P(A) = 0.2 / 0.7 ≈ 0.286
Therefore, the probability of event C (capturing the golden brick and choosing the correct door) is:
P(C) = P(A and B) = P(A) * P(B|A) = 0.7 * 0.286 ≈ 0.2
Therefore, the probability that Hector captures the golden brick and chooses the correct door is approximately 0.2, or 20%.
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A self-serve car wash charges $5.25 to use its facilities, plus an additional $0.69 for each minute the customer is at the self-serve car wash. If Tiffany was at the car wash for 8 minutes, how much was she charged?
Using linear equations, Tiffany was charged $10.77 for 8 minutes at the self-serve car wash.
What Does It Mean to Solve Linear Equations?Solving a linear equation involves determining the answer to a linear equation with one, two, three, or more variables. The answer to a linear equation is the value or values of the variable(s) that are part of the equation. In the elimination procedure, any coefficient is first made equal, then deleted. After elimination, the equations are solved to provide the other equation.
Given that, the car wash charges $5.25 to use its facilities, plus an additional $0.69 for each minute.
C = 5.25 + 0.69x
For 8 minutes:
C = 5.25 + 0.69(8)
C = $10.77
Hence, Tiffany was charged $10.77 for 8 minutes at the self-serve car wash.
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[tex]-3\sqrt{x} +2\ \textless \ 15[/tex]
Answer:
12
Step-by-step explanation:
'what are the equivalence classes of the equivalence relations in exercise 1?
Equivalence class of {x} is the set of all elements of the set {A} which are related to {x} i.e. → [x]R={y ∈ A ∣ xRy}.
What are equivalence relations?A binary relation which is symmetric, transitive and reflexive is called a equivalence relation.
Given is to find the equivalence classes of the equivalence relations.
If it is given that {R} is an equivalence relation on {A} and {x} ∈ A, then we can write the equivalence class of {x} is the set of all elements of the set {A} which are related to {x} i.e. →
[x]R={y ∈ A ∣ xRy}.
Therefore, equivalence class of {x} is the set of all elements of the set {A} which are related to {x} i.e. → [x]R={y ∈ A ∣ xRy}.
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Jessica is running for class president and to raise money she is selling candy bars and drinks. Here are her
profits.
. 50 candy bars and 40 drinks for $65
100 candy bars and 50 drinks for $100
How much did she sell the drinks for?
Jessica sold the drinks for $1 each to raise money as she is running for class president.
What is elimination method?The elimination method is a technique used to solve a system of linear equations in two variables. In this method, we multiply one or both equations by appropriate constants to obtain equivalent equations in which one of the variables has the same coefficient but with opposite signs. Then we add the equations to eliminate one of the variables, and solve for the remaining variable.
According to question:Let the price of one candy bar be represented by x, and the price of one drink be represented by y.
From the first equation, we know that:
50x + 40y = 65
From the second equation, we know that:
100x + 50y = 100
We want to find the value of y, so we can solve for y using either substitution or elimination method. Here, we will use elimination method.
Multiplying the first equation by 2, we get:
100x + 80y = 130
Subtracting the above equation from the second equation, we get:
100x + 50y - (100x + 80y) = 100 - 130
Simplifying the left side and right side of the equation, we get:
-30y = -30
Dividing both sides by -30, we get:
y = 1
Therefore, Jessica sold the drinks for $1 each.
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What is the area of the figure?
A line passes through the points (-1, 3) and (1, -5). Which points lie on the same line?
Select all that apply.
(0, -2)
(-3, 12)
(-5, 1)
(-2,7)
(4, 15)
(2, -9)
( 2,-9) points lie on the same line.
Line point intercept is defined.
Quantifying soil cover, including vegetation, litter, rocks, and biotic crusts, quickly and accurately can be done using the line-point intercept approach.
These metrics deal with the erosion caused by wind and water, water infiltration, and the site's capacity to withstand damage and recover from it.
k = -5 - 3/1 - (-1) = -8/2 = -4
the formula of the line is
y - 3 = -4(x+ 1)
when x = -3 , y = 11 ≠ 12 the points aren't on line.
when x = -5, y = 19 ≠ 1
when x = 4, y = -7 ≠ 15
when x = 2, y = -9 ≠ 7
when x = 0, y = -1 ≠ -2
( 2,-9) are on the same line.
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Need help fast 24 pts and the brainliest
Answer:
65
Step-by-step explanation:
All 4 sides of a polygon equals 360 degrees. We are given the equation of 2 sides to find the degree.
12x + 19 + 8x + 1 = 180
(We put it equal to 180 instead of 360 since we are only given 2 sides)
Subtract 19 from both sides
12x + 8x + 1 = 161
Subtract 1 from both sides
12x + 8x = 160
Add 12x + 8x
20x = 160
Divide 20x by 160
x = 8
Plug in x value to (8x + 1)
(8(8) + 1)
= 65
There are 1 3/4 cookies. If there is 1/8 of a cookie in each bag, how many bags are there
Answer: 8
Step-by-step explanation:
Since 1 batch uses 1/8 of a bag of flour, I would use equivalent fractions to find how many 8ths are in 3/4. 3/4=?/8
4 times 2 equals 8, so I would multiply 3 by 2 also. 3/4=6/8. If 1 batch takes 1/8, then 6 batches would use 6/8 or 3/4 of a bag of flour.
The probability of a passenger missing a flight is 0.0993. Airlines sometimes overbook their flights so that they can be sure that there are no empty seats. Suppose that a particular plane has the capacity for 250 passengers. If 270 tickets are sold, what is the probability that there are not enough seats on the flight?
The probability that there are not enough seats on the flight is approximately 0.9735 or 97.35%.
The probability of a passenger missing a flight is 0.0993. Therefore, the probability that a passenger does not miss the flight is:
P(not missing the flight) = 1 - 0.0993 = 0.9007
The plane has a capacity for 250 passengers, but 270 tickets are sold. Assuming that the probability of a passenger missing a flight is independent of other passengers, we can model the number of passengers who show up for the flight as a binomial distribution with n = 270 and p = 0.9007.
Let X be the number of passengers who show up for the flight. We want to find the probability that there are not enough seats on the flight, which means that X > 250. We can use the complement rule to find this probability:
P(X > 250) = 1 - P(X ≤ 250)
To find P(X ≤ 250), we can use a binomial probability table or a calculator with a binomial probability function. Using a calculator, we get:
P(X ≤ 250) = binomcdf(270, 0.9007, 250) ≈ 0.0265
Substituting this into the complement rule formula, we get:
P(X > 250) = 1 - 0.0265 ≈ 0.9735
Therefore, the probability that there are not enough seats on the flight is approximately 0.9735 or 97.35%.
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Fancy Flowers Florist has just received a shipment of 250 red roses. They use 200 of the roses
to decorate for the grand opening of the Historical Museum. What percentage of the red roses
did Fancy Flowers Florist use to decorate for the grand opening at the museum?
A. 60%
B. 70%
C. 80%
D. 90%
The percentage of the red roses did Fancy Flowers Florist use to decorate for the grand opening at the museum is 80%
What is percentage?A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
Given that, a flower shop received a shipment of 250 red roses, they will use 200 out of this for decorating for the grand opening of the Historical Museum,
We need to find the percentage of the red roses used there,
So, the percentage of the red roses used in decoration =
200 / 250 x 100
= 0.8 x 100
= 80%
Hence. the percentage of the red roses did Fancy Flowers Florist use to decorate for the grand opening at the museum is 80%
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Question content area top
Part 1
To the right are the outcomes that are possible when a couple has three children. Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the probability that when a couple has three children, there are exactly 0 girls.
1st
2nd
3rd
boy
−
boy
−
boy
boy
−
boy
−
girl
boy
−
girl
−
boy
boy
−
girl
−
girl
girl
−
boy
−
boy
girl
−
boy
−
girl
girl
−
girl
−
boy
girl
−
girl
−
girl
Question content area bottom
Part 1
What is the probability of exactly 0 girls out of three children?
enter your response here (Type an integer or a simplified fraction.)
The probability that when a couple has three children, there are exactly 0 girls is 12.5%
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Calculation of the probability:
Here we assume b for boy, g for girl
Now, the probability conditions are;
g - g - g
g - g - b
g - b - g
g - b - b
b - g - g
b - g - b
b - b - g
b - b - b
Thus, There are 8 outcomes, one of which (b - b - b) with exactly 0 girls.
So, We get;
⇒ 1 ÷ 8
= 0.125
= 12.5%
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the muscular muscle is 75kg and the muscle is pulling on the bone at an angle of 15 degrees. what are the vertical and horizontal components of this muscular force?
a. which of these forces would be responsible for the rotation of this bone around the joint
b. which of these forces would cause a compressive force at the joint?
please show work and draw a diagram and label
Answer:
Step-by-step explanation:
To find the vertical and horizontal components of the muscular force, we can use trigonometry. Let F be the force exerted by the muscle, and θ be the angle it makes with the horizontal.
Horizontal component of the force Fx = F cos θ
Vertical component of the force Fy = F sin θ
Given that the muscular force is 75kg and the angle of pull is 15 degrees, we have:
Fx = 75kg x cos(15) = 72.62 kg (approx.)
Fy = 75kg x sin(15) = 19.34 kg (approx.)
To determine which force would be responsible for the rotation of the bone around the joint, we need to consider the torque or moment created by the force. The torque is given by the force times the lever arm, which is the perpendicular distance from the line of action of the force to the axis of rotation. In this case, the axis of rotation is the joint, and the lever arm is the distance from the joint to the point where the muscle attaches to the bone.
The torque due to the horizontal component of the force is zero, since it acts perpendicular to the lever arm. The torque due to the vertical component of the force is:
Torque = Fy x d
where d is the lever arm. If we assume that the lever arm is 5 cm, we have:
Torque = 19.34 kg x 0.05 m = 0.967 Nm
Therefore, the vertical component of the force would be responsible for the rotation of the bone around the joint.
To determine which force would cause a compressive force at the joint, we need to consider the direction of the force. A force that acts perpendicular to the bone would cause compression at the joint. In this case, the vertical component of the force is perpendicular to the bone, while the horizontal component is parallel to it. Therefore, the vertical component of the force would cause a compressive force at the joint.
Here is a diagram of the situation:
|\
Fy | \ /|
| \ / |
| \ / |
| \ / |
| \ / |
| \/ |
| /\ |
| / \ |
| / \ |
| / \ |
| / \ |
| / \|
|/______\
Fx
In the diagram, Fx is the horizontal component of the force, Fy is the vertical component of the force, and the bone is represented by the vertical line. The angle θ is the angle between the force and the horizontal. The lever arm d is the distance between the joint and the point where the muscle attaches to the bone.
The length of Trevor’s pool is 5feet more than 3 times it’s width. The deck surrounding the pool is 2 feet in width. The area of the deck is 196 feet squared. What is the width of the pool.
Answer:
Let's start by defining some variables to represent the width and length of the pool:
Let w be the width of the pool (in feet).
Let l be the length of the pool (in feet).
We know from the problem statement that the length of the pool is 5 feet more than 3 times its width:
l = 3w + 5
We also know that the deck surrounding the pool is 2 feet wide. This means that the overall width of the pool and the deck combined is:
w_total = w + 2 + 2 = w + 4
Similarly, the overall length of the pool and the deck combined is:
l_total = l + 2 + 2 = l + 4
We are given that the area of the deck is 196 square feet. The area of the deck can be calculated by subtracting the area of the pool from the area of the pool and deck combined:
Area of deck = Area of pool and deck - Area of pool
196 = w_total * l_total - w * l
We can substitute the expressions for w_total and l_total in terms of w and l:
196 = (w + 4) * (l + 4) - w * l
Simplifying this expression gives:
196 = wl + 4w + 4l + 16
We can substitute the expression for l in terms of w:
196 = w(3w + 5) + 4w + 4(3w + 5) + 16
Simplifying this expression gives:
196 = 13w + 36
Solving for w, we get:
w = 14
Therefore, the width of the pool is 14 feet.
Figure ABC has vertices A(-3,3), B (1,-1), and C (0,5). Sketch ABC and draw its image after the translation (x,y) (x+4, y + 2).
Sketch of ABC and drawn image after the translation (x,y) (x+4, y + 2) is mentioned below.
Describe Translation?In mathematics, translation refers to the process of moving a geometric shape or object from one location to another without changing its size, shape, or orientation. This movement is typically described in terms of the distance and direction of the translation.
For example, a point on a coordinate plane can be translated by adding or subtracting a constant value to its x and y coordinates. Similarly, a line segment or polygon can be translated by moving each of its vertices by the same distance and in the same direction.
Mathematical translations can be represented using transformation matrices or vectors. A translation matrix is a square matrix that describes the movement of a point or object in a specific direction and distance. A translation vector is a one-dimensional vector that describes the direction and distance of the translation.
To sketch the triangle ABC, we first plot the three given points on a coordinate plane:
We connect the three points to form triangle ABC:
|
6 | C(0,5)
| /\
3 | / \
| / \
| / \
| / \
| /__________\
|A(-3,3) B(1,-1)
|
|
|
|
|
|
-3 -1 1 3
To find the image of the triangle under the translation (x,y) → (x+4, y+2), we add 4 to the x-coordinates and 2 to the y-coordinates of each point. This gives us the following new coordinates:
A(-3,3) → A'(-3+4, 3+2) = A'(1,5)
B(1,-1) → B'(1+4, -1+2) = B'(5,1)
C(0,5) → C'(0+4, 5+2) = C'(4,7)
We can now plot these new points and connect them to form the image of triangle ABC under the given translation:
|
9 | C'(4,7)
| / \
7 | / \
| / \
5 | / \
| / \
| /__________\
3 |A'(1,5) B'(5,1)
|
|
|
1 |
|
|
-3 -1 1 3 5
This is the final image of triangle ABC after the translation.
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The vertices of the translated figure are A'(1, 5), B'(5, 1), and C'(4, 7).
What is translation?
A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.
To translate the figure by (x+4, y+2), we add 4 to the x-coordinate and 2 to the y-coordinate of each vertex.
So the new coordinates of A' would be -
x-coordinate: -3 + 4 = 1
y-coordinate: 3 + 2 = 5
Therefore, A' has coordinates (1, 5).
The new coordinates of B' would be -
x-coordinate: 1 + 4 = 5
y-coordinate: -1 + 2 = 1
Therefore, B' has coordinates (5, 1).
The new coordinates of C' would be -
x-coordinate: 0 + 4 = 4
y-coordinate: 5 + 2 = 7
Therefore, C' has coordinates (4, 7).
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What are the domain and range of the function shown below? write the answers as a list using commas. Enter values in order from least to greatest.
The domine of function = {0, 1, 2, 3}
The range of function = {-3, -1, 1, 3}
Domain:The domain of a function is the set of all possible input values for which the function is defined. It can be restricted by certain conditions, such as division by zero, square roots of negative numbers, or logarithms of non-positive numbers.
Range:The range of a function is the set of all possible output values that the function can produce. It depends on the nature of the function and the restrictions on the domain.
Here we have a table
x - 0 1 2 3
f(x) -3 -1 1 3
Here x values are indicates input values for the function f(x)
Hence, the domine of function = {0, 1, 2, 3}
The values of f(x) represent the output values for each input value of 'x'
Hence, the range of function = {-3, -1, 1, 3}
Therefore,
The domine of function = {0, 1, 2, 3}
The range of function = {-3, -1, 1, 3}
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The distance between points A and B is 35 feet, the distance between points B and C is 35 feet, and the distance between points C and D is 80 feet. How wide is the
canyon? Explain your reasoning.
The answer of the question based on distance and width of the canyon is width of the trapezoid is approximately 67.43 feet.
What is Trapezoid?A trapezoid is quadrilateral ( four-sided polygon) that has two parallel sides and two non-parallel sides. The parallel sides are referred to as bases of the trapezoid, while the non-parallel sides are called legs. The distance between two parallel sides is called height or altitude of trapezoid.
The figure in the provided link is a trapezoid with parallel sides AB and CD, and non-parallel sides BC and AD.
Since AB and CD are parallel, we know that the length of the altitude is the same as the distance between them.
Let's call the width of the trapezoid "x". Then, we can use the following equation using the Pythagorean Theorem:
(AC)^2 = (BC)^2 + (AB - CD + 2x)^2
where AC is the diagonal connecting points A and C.
Substituting the given values, we get:
(AC)^2 = (35)^2 + (35 - 80 + 2x)^2
(AC)^2 = 1225 + (2x - 45)^2
(AC)^2 = 1225 + 4x^2 - 180x + 2025
(AC)^2 = 4x^2 - 180x + 3250
Now, we can use the distance formula to find the length of AC:
AC = sqrt[(A - C)^2 + (B - D)^2]
AC = sqrt[(35 + 35)^2 + 80^2]
AC = sqrt[4900 + 6400]
AC = sqrt(11300)
AC = 106.23 feet (rounded to two decimal places)
Substituting the value in equation above, we will get:
(106.23)^2 = 4x^2 - 180x + 3250
11299.77 = 4x^2 - 180x + 3250
4x^2 - 180x + 8049.77 = 0
Solving the quadratic equation using quadratic formula, we will get:
x = [180 ± sqrt(180^2 - 4(4)(8049.77))] / (2(4))
x = [180 ± sqrt(129322.08)] / 8
x = [180 ± 359.44] / 8
We take the positive root, since x represents a length, and we get:
x = (180 + 359.44) / 8
x = 67.43 feet (rounded to two decimal places)
Therefore, the width of the trapezoid is approximately 67.43 feet.
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solve the value of n 20 = 2 (n - 3)
Answer:
13
Step-by-step explanation:
1. 20/2 = n - 3
2. 10 = n - 3
3. 10 + 3 = n
4. 13 = n
Write the equation of the circle in standard form
X^2+y^2-8x-6y+16=0
Show work
The equation of the circle x² + y² - 8x - 6y + 16 = 0 in standard form is (x - 4)² + (y - 3)² = 3².
What is the equation of the circle in standard form?Given the equation of the circle ;
x² + y² - 8x - 6y + 16 = 0
To write the equation of a circle in standard form, we need to express it as:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
To do this, we need to complete the square for both x and y terms in the given equation.
Starting with the x terms:
x² - 8x = x² - 8x + 16 - 16
= (x - 4)² - 16
Similarly, for the y terms:
y² - 6y = y² - 6y + 9 - 9
= (y - 3)² - 9
Substituting these results into the original equation, we get:
x² + y² - 8x - 6y + 16 = 0
(x - 4)² - 16 + (y - 3)² - 9 + 16 = 0
Simplifying, we get:
(x - 4)² + (y - 3)² - 9 = 0
(x - 4)² + (y - 3)² = 9
So the equation of the circle in standard form is:
(x - 4)² + (y - 3)² = 3²
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solve for x: (-x+18)(x+4)
(-x+18)(x+4)
-x(x+4) + 18 (x+4)
-(x^2+4x) + 18(x+4)
-x^2-4x+18x+72
−x^2+14x+72
I hope this helps! :)
Please help this too
the length of a rectangle poster is nine more inches than half it’s with. The area of the poster is 140 square inches. Solve for the dimensions of the poster.
The dimensions of the poster are 10 inches by 14 inches.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that length of a rectangle poster is nine more inches than half it’s width.
Length = 1/2 width +9
The area of the poster is 140 square inches.
Area=Length×Width
140=(W/2+9)W
140=W²/2 +9W
W²+18W-240=0
(w + 28)(w - 10) = 0
W=-28 and w=10
We take only positive value so width is 10
Length=10/2+9
=5+9=14 inches
Hence, the dimensions of the poster are 10 inches by 14 inches.
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it is 4/10 of a mile to john's house from frank's house. How much less than a mile is the distance from frank's house to john's house and then back to frank's house
The distance from frank's house to john's house and then back to frank's house is less than a mile by 1/5 units.
How do you figure out the overall distance?While travelling from one location to another and back again just multiplying the distance between the two places will give you the total distance travelled when travelling from one spot to another and returning to the beginning position.
The distance from frank's house to john's house = 4/10.
The distance back to Frank's house = 4/10.
Total distance = 4/10 + 4/10
Total distance = 8/10
The distance is thus,
1 - 8/10
Take the LCM:
(10 - 8) / 10
2/10 = 1/5
Hence, the distance from frank's house to john's house and then back to frank's house is less than a mile by 1/5 units.
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Roberto has a tool box that is shaped like a rectangular prism with a volume of 4,500 cubic inches what is the width of the toolbox
The width of the rectangular prism shaped toolbox is 10 inches.
What exactly is a prism?A prism is a three-dimensional geometric shape that has two parallel and congruent bases that are connected by a set of parallelograms or rectangles. A prism is named according to the shape of its base, such as triangular prism, rectangular prism, or hexagonal prism.
A prism is characterized by its length, width, and height, and it has a volume equal to the product of its base area and its height. The lateral faces of a prism are parallelograms or rectangles, and the edges of a prism where the lateral faces meet the bases are perpendicular to the bases.
Now,
To find the width of the toolbox, we can use the formula for the volume of a rectangular prism, which is:
Volume = length x width x height
We are given that the volume of the toolbox is 4,500 cubic inches, the length is 30 inches, and the height is 15 inches.
Then
4,500 = 30 x width x 15
Simplifying the right side, we get:
4,500 = 450 * width
Dividing both sides by 450, we get:
width = 10 inches
Therefore, the width of the toolbox is 10 inches.
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