In the diagram shown, points B and D lie on sides AC and AE such that BD is parallel to CE. If AB=10, AD=16, and De=22 then find the length of AC
Answers
In triangle ACE, with BD parallel to CE, using similar triangles and ratios, we get a quadratic equation with two possible solutions. Only the positive one is chosen, so AC is approximately 30.96 units long.
Since BD is parallel to CE, we can use the property of similar triangles to find the length of AC.
Triangles ABD and ACE are similar because they have the same corresponding angles. This means that the ratios of their corresponding side lengths are equal.
We know that AB = 10, AD = 16, and DE = 22.
Let x be the length of AC. Then, we have
AB/AD = CE/EA (by similarity of triangles ABD and ACE)
10/16 = CE/(x-16+22) (substituting CE = EA - DE and simplifying)
5/8 = CE/(x-6)
CE = (5/8)(x-6)
We also know that
BD/DE = AB/AE (by similarity of triangles ABD and ADE)
BD/22 = 10/(x-22) (substituting BD = CE and AE = AC - CE - DE, and simplifying)
CE = (220 - 10x)/(x-22)
Since CE is equal in both expressions, we can equate them and solve for x
(5/8)(x-6) = (220 - 10x)/(x-22)
5x² - 196x + 1320 = 0
x² - 39.2x + 264 = 0
Using the quadratic formula, we get
x = 30.96 or x = 8.54
The length of AC must be positive, so we choose x = 30.96.
Therefore, the length of AC is approximately 30.96 units.
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--The given question is incomplete, the complete question is given
" In the diagram shown, points B and D lie on sides AC and AE such that BD is parallel to CE. If AB=10, AD=16, and De=22 then find the length of AC "--
Related Questions
Which sequence below would best model the description? 50 points!
Answers
Therefore, the correct sequence to model the description is:
a) f(n) = 1.12f (n - 1) if f(n-1) < 6000
where:
- f(n) is the amount of oxygen released in pounds in year n
- f(n-1) is the amount of oxygen released in pounds in year n-1
The initial value is f(1) = 250 pounds, which is the amount of oxygen released by the tree in its first year.
Option (a) represents this sequence correctly. It says that the amount of oxygen released in year n is 1.12 times the amount released in year n-1, but only if the amount released in year n-1 is less than 6000 pounds.
A patient weighs 160 pounds and needs medication with dosage instructions of 15 mg/kg/day. It is to be given in 3 doses each day. How much medication should they receive per dose? Remember, 2.2 pounds is equal to 1 kilogram. Round to the nearest whole number.
Answers
The amount of medication should they receive per dose is,
⇒ 363.6 mg
Given that;
A patient weighs 160 pounds and needs medication with dosage instructions of 15 mg/kg/day.
And, It is to be given in 3 doses each day.
Hence, We get;
1 pounds = 1/2.2 kg
160 pounds = 160 x 1/2.2 kg
= 72.72 kg
Since, It is to be given in 3 doses each day.
Hence, The amount of medication should they receive per dose is,
⇒ 72.72 x 15 / 3
⇒ 363.6 mg
Thus, The amount of medication should they receive per dose is,
⇒ 363.6 mg
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The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 73.6% of their carbon-14. How old were the bones at the time they were discovered?
The bones were about how many years old?
Answers
The age of the radioactive element of half-life 5750 years is 11047.8 years.
What is a radioactive element?Radioactive elements are atoms that are unstable in normal conditions and are converted in another different atoms.
To calculate how old is the bone at the time it was discovered, we use the formula below.
Formula:
R/R' = [tex]2^{t/n}[/tex]...................... Equation 1Where:
R = Original percentage of the boneR' = Percentage of the bone after decayt = Years of the bonen = Half-lifeFrom the question,
Given:
R = 100%R' = 100-73.6 = 26.4%n = 5750 yearsSubstitute these values into equation 1 and solve for t
100/26.4 = [tex]2^{t/5750}[/tex][tex]2^{t/5750}[/tex] = 3.7878 t/5750 = log[tex]2^{3.7878}[/tex][tex]{t/5750}[/tex] = t/5750 = 1.921t = 1.921×5750t = 11047.8 yearsLearn more about radioactive element here: https://brainly.com/question/23759636
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(7x^9)^2*3x^11
^ is the exponent sign
Answers
The answer in exponent form is 147x^29.
What is a scientific notation?A scientific notation is a method of expressing very large numbers in the form of exponent.
In the given question, we have;
(7x^9)^2*3x^11
applying the law of indices,
(7x^9)^2*3x^11 = (7^2)*x^(9*2)*3x^11
= 49x^18*3x^11
= (49*3)*x^(18+11)
= 147x^29
Thus, the expression can be simplified as: 147x^29.
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Lin has 9 plates she puts 1/4 of a sandwich on each plate which expression represents the sandwiches in the situation
A. 9x4
B. 9x1/4
C. 4x9
D. 4x1/9
Answers
Explanation:
It says there are 9 PLATES
she puts 1/4 of a sandwhich on EACH!
meaning that each plate of the 9 plates have 1/4.
You are trying to determine if a router you’re thinking of purchasing will give off a strong enough wifi signal to cover the area in your house. The router you have selected will cover an area of 850 ft^2
HELP ME PLEASE AND SHOW WORK THANK YOU WILL MARK BRAINLIEST.
Answers
Based on the image, we can infer that the router cannot cover the kitchen area.
How to calculate if the router covers the living room and kitchen area?To calculate if the router covers the living room and kitchen area, we must identify the area that the router can cover. In this case, the router covers an area of 850 square feet. However, we must take into account that this area is counted around the router.
From the above, we can infer that the router has signal coverage of 14 meters around it, so it would only cover the living room area.
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The sum of two numbers is 998
The difference between them is 10
What are the two numbers?
Answers
Answer:
The two numbers are 494 and 504
Step-by-step explanation:
Let x = one of the numbers
Let y = the other number
x + y = 998
x - y = 10 or x = y + 10
Substitute y + 10 for x in the first equation and solve for y
x + y = 998
y + 10 + y = 998 Subtract 10 from both sides
y + y = 988 Combine like terms
2y = 988 Divide both sides by 2
y = 494
One of the numbers is 494.
x = y + 10 Substitute 494 for y
x = 494 + 10
x = 504
The other number is 504.
Check:
x + y = 998
504 + 494 = 998
998 = 998 checks
x - y = 10
504 - 494 = 10
10 = 10 checks
Helping in the name of Jesus.
The diagonal of a square is 32 cm. What is the length of one side of the square rounded to the nearest tenth?
Answers
The length of the square with a diagonal of 32 cm is 22.6 cm.
What is a square?A square is a plane shape with all sides and angles equal.
To calculate the length of the square from its diagonal, we use Pythagoras formula
Formula:
d² = l²+l².................... Equation 1Where:
d = Diagonal of the squarel = length of the squareFrom the question,
Given:
d = 32 cmSubstitute these values into equation 1 and solve for l
32² = l²+l²1024 = 2l²l² = 1024/2l² = 512l = √512l = 22.6 cmLearn more about square here: https://brainly.com/question/27307830
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What is the midpoint of the line segment with the given endpoints (4,6) (3,-3)
Help it’s urgent
Answers
The coordinates of the midpoints of the given line segment is:
(3.5, 1.5)
How to find the midpoints of a line segment?The midpoint of a line segment is simply referred to as the center of that specific line segment.
Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.
The coordinates of the endpoints of the line are:
(4,6) and (3,-3)
The formula to find the coordinates of the midpoint of the line is:
(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2
Thus, we have:
(x, y) = (4 + 3)/2, (6 - 3)/2
= (3.5, 1.5)
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PLEASE HELP ITS DUE TOMORROW!!!
Answers
Answer:
Step-by-step explanation:
House
B) Down Payment: $151,800
C) $607,200
D) $819,720
E) $1,426,920
F) $47,564
Car:
B) $2,902.50
C) $16,447.50
D) $3,700.6875 = $3,700.69
E) $20,148.1875 = $20,148.19
F) $335.803125 = $335.80
DONE !!! :)
Write the coordinates of the vertices after a reflection over the x-axis.
y
x
-10
10
-10
10
0
T
U
V
T(-1, 7)
→
T′(
,
)
U(-1, 8)
→
U′(
,
)
V(9, 6)
→
V′(
,
)
Answers
T(-1, 7)
→
T′(-1, -7)
U(-1, 8)
→
U′(-1, -8)
V(9, 6)
→
V′(9, -6)
The approximate number of zombies in a certain city over time is given in the table below. Answer the questions below to determine what kind of function would best fit the data, linear or exponential.
Number of Hours Since Zombies First Spotted, x
1
2
3
4
Approximate Number of Zombies, f(x)
24
56
88
122
function would best fit the data because as x increases, the y values change
. Rounded to the nearest .5, the
of this function is approximately
Answers
A linear function would be the best fit for the given data because as x increase the y-values change linearly.
Rounded to the .5 the slope of the function is approximately 32.5
Which type of function models the population?A linear relation means that any increase of 1 unit in the independent variable (x) has always the same impact in the other variable (y).
In this particular case, the increases in the y-value are:
56 - 24 = 32
88 - 56 = 32
122 - 88 = 34
The mean of that, rounded to .5, is (32 + 32 + 34)/3 = 32.5
So the change is almost the same one, then this seems to be a linear relation.
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Pls help
Me i have alot and this is due tomorrow
Answers
8,8,8,8, 9 ,10,12,12,14
9. Which statements contradict each other? I. triangle ABC is a right triangle. II. m angle A = 41° III. m angle B = 103° A. I and II B. I and III C. II and III D. None of the statements are contradictory. 1
Answers
The contradicting statement is
B. I and III
How to know the contradictory statementThe contradictory statement is that of I and III since the sum of angles in a triangle is always 180 degrees.
Given that
I. triangle ABC is a right triangle. say angle C = 90 degrees and
angle B = 103 degrees,
So the sum of the angles in the triangle would be:
= angle B + m angle C
= 103 + 91
= 194
This is against the law of angles of a triangle
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whats the answer to this
Answers
The calculated length of XY in the right triangle XYZ is 6
Calculating the length of XY in the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The value of XY in the right triangle can be calculated using the following sine ratio
sin(30) = XY/XZ
So, we have
sin(30) = XY/12
Cross multiply the equation
So, we have
XY = 12 * sin(30)
Evaluate the products
XY = 6
Hence, the length of XY in the right triangle is 6
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Lou is 1,200 feet from the base of a building that stands 500 feet tall. Assuming Lou's height is negligible, determine the angle of elevation from him to the top of the building. First, choose which angle represents the angle of elevation and then select the measure of that angle from the choices provided.
Select TWO correct answers.
Answers
We can see from the calculation that the angle of elevation of the building is 22.6 degrees.
Explain angle of elevation
The angle of elevation is the angle between the horizontal plane and the line of sight from an observer to an object that is above the observer's level. It is the upward angle from the observer's eye to the object being observed.
We have that;
Tan θ = 500/1200
θ = tan-1 (500/1200)
θ = 22.6 degrees
Thus the angle of elevation is obtained as 22.6 degrees as we can see here.
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1. A biologist hypothesizes that the mean life expectancy of a cockroach is 17 days. Researchers believe the true mean is less than 17 days and they plan a hypothesis test at the 10% significance level on a random sample of 80 of these cockroaches. If the alternative hypothesis is correct, for which of the following values of μ is the power of the test greatest?
A. μ = 9
B. μ = 10
C. μ = 17
D. μ = 20
E. μ = 21
2.Automobile tires can have a symmetric tread or an asymmetric tread. An experiment is to be conducted to determine whether the stopping distance is the same for both types of tire treads. In previous studies, it was determined that automobile size (small, medium, large) is associated with stopping distance, but automobile type (van, truck, SUV, and so on) is not associated with stopping distance. How could the experiment BEST be conducted?
A. By blocking on stopping distance
B. By blocking on tire tread type
C. By blocking on automobile type
D. By blocking on automobile size
E. Without blocking
3. A popular podcast wants to know the proportion of listeners that think assault weapons should be banned for civilians. Listeners are asked to text "Y" for yes or "N" for no to a provided number. Sixty-five percent of the 1,500 people that responded texted "Y." Which condition for inference has NOT been met?
A. All conditions appear to be met.
B. The sample is an SRS of the population.
C. N > 10n
D. np ≥ 10 and n(1 - p) ≥ 10
E. Inference about a proportion is the objective.
4.Fifteen pairs of measurements were taken at random to estimate the relation between variables X and Y. A least-squares line was fitted to the collected data. The resulting residual plot is shown.
Which of the following conclusions is appropriate?
A. A line is an appropriate model to describe the relation between X and Y.
B. A line is not an appropriate model to describe the relation between X and Y.
C. The assumption of the Law of Averages has been violated.
D. The variables X and Y are not related at all.
E. There is not enough information about the variables X and Y to form a conclusion.
Answers
The average height of young adult males has a normal distribution with standard deviation of 2.7 inches. You want to estimate the mean height of students at your college or university to within one inch with 93% confidence. How many male students must you measure?
Answers
You must measure 24 male students to estimate the mean height within one inch with 93% confidence.
How to solve for the sample sizeSince we want to estimate the mean height within one inch, the margin of error (E) is 1 inch:
E = Z * (Standard deviation / √Sample size)
Now, we can rearrange the formula to solve for the Sample size (n):
1 = 1.81 * (2.7 / √n)
Solving for n:
n = (1.81 * 2.7 / 1)²
n ≈ (4.887)²
n ≈ 23.88
Since we cannot have a fraction of a person, we round up to the nearest whole number:
n ≈ 24
So, you must measure 24 male students to estimate the mean height within one inch with 93% confidence.
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Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 14 gallons of fuel, the airplane weighs 2091 pounds. When carrying 48 gallons of fuel, it weighs 2312 pounds. How much does the airplane weigh if it is carrying 52 gallons of fuel?
Answers
The airplane weigh if it is carrying 52 gallons of fuel will be, 2338 pounds
Let,
Weight of airplane = y
Amount of fuel = x
The general linear equation can be written as, y=mx + c, where, (m) is slope, and (c) is a constant.
It is given,
2091 = 14m + c ..... (1)
2312 = 48m + c ..... (2)
On subtracting, (1) with (2), we get
221 = 34m
m= (221/34)= 6.5
Now, on putting the value of (m) in (1), we get,
2091 = 14(6.5) + c
So,
c = 2000
Therefore, the linear equation can be written as,
y = (6.5)mx + 2000
Now to find the airplane weight at 52 gallons of fuel, we put x = 52, to find y.
That is,
y = (6.5)(52) + 2000
y = 2338
So, the airplane weigh if it is carrying 52 gallons of fuel will be, 2338 pounds.
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A triangle is translated by using the rule (x,y) → (x-4.y+1). Which describes how the figure is moved?
O four units left and one unit down
O four units left and one unit up
O one unit right and four units down
O one unit right and four units up
Mark this and return
Save and Exit
Next
Submit
Answers
Answer:
Four units left and one unit up
Step-by-step explanation:
Since we're subtracting from x, the figure is going to go toward the left side of the coordinate plane, and since we're adding to y, the figure is going to go up.
8 is less than or equal to -3x +26
Answers
The solution is: x ≥ 6.
What is linear inequalities?
Linear inequality is an equation or expression that do not have a definite solution. Thus it consist of either of greater than, less than, greater than or equal to, less than or equal to etc.
In the given inequality question, we have;
8 is less than or equal to -3x +26
This can be expressed as;
8 ≤ -3x +26
so that collecting like terms,
8 - 26 ≤ -3x
-18 ≤ -3x
-18/ -3 ≤ x
6 ≤ x
Therefore, x ≥ 6.
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Find the length of the shortest path from vertex A to vertex L.
Answers
The shortest path from vertex A to vertex L in the given diagram is ABDGJLKFI, with a total length of 89.
We can find the length of the shortest path from vertex A to vertex L by calculating the sum of the shortest paths from A to C to F to I to L.
Using Dijkstra's algorithm, we can find the shortest path from A to C, then from C to F, then from F to I, and finally from I to L.
The shortest path from A to C is AB + BC = 3 + 16 = 19. The shortest path from C to F is CF = 25. The shortest path from F to I is FI = 21. The shortest path from I to L is IL = 24.
Therefore, the length of the shortest path from A to L is 19 + 25 + 21 + 24 = 89.
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if you are standing 350 feet away from a "1000" foot tall skyscraper, what angle of elevation is needed for you to look up and see the top of the building? when your angle of elevation is at 25 degrees you see your friend waving at the window. exactly how far apart are you?
Answers
Answer:
70.7°
350 feet
Im not too sure about the last one
Need this answer please and show work
Answers
The value of the "trigonometric-expressions' are :
(a) tan(5π/2) is undefined,
(b) sec(315°) is √2.
Part(a) : The expression "tan(5π/2)" is undefined because the tangent function is undefined at odd multiples of π/2, which includes 5π/2.
Part(b) : To find the value of sec(315°), we use the identity: sec(θ) = 1/cos(θ),
First, we convert 315° to radians:
Which is : 315° = (7π/4) radians;
Next, we find the value of cos(7π/4):
⇒ cos(7π/4) = cos(π/4) = (√2)/2;
Finally, we substitute in the identity for sec(θ);
So, Sec(7π/4) = 1/cos(7π/4) = 1/[(√2)/2] = √2.
Therefore, value of sec(315°) is √2.
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The given question is incomplete, the complete question is
Find the value of the trigonometric expressions :
(a) tan(5π/2)
(b) sec(315°)
Write an equation that can be used to determine the angle measure, in degrees, of angle DBC. Let n represent the measure of angle DBC. Then determine the measure of n
Answers
An equation that can be used to determine the angle measure, in degrees, of angle DBC is 67 + n = 90.
The measure of n is equal to 23 degrees.
What is a complementary angle?In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).
By substituting the given parameters into the complementary angle formula, the sum of the angles is given by the following mathematical equation;
∠ABD + ∠DBC = 90
∠ABD + n = 90
67 + n = 90.
n = 90 - 67
n = 23°
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Find the volume of the cylinder. Use π = 3.14.
(If answered correctly with an explanation giving brainlyest)
A. 321.54 ft3
B. 10,048 ft3
C. 8,038.4 ft3
D. 100.48 ft3
Answers
The volume of a cylinder whose diameter measures 32 feet and has a height of 10 feet is equal to: C. 8,038.4 ft³.
How to calculate the volume of a cylinder?In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.Note: Radius = diameter/2 = 32/2 = 16 ft.
By substituting the parameters, we have:
Volume of cylinder, V = 3.14 × 16² × 10
Volume of cylinder, V = 8,038.4 cubic feet.
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If x=3t+t^2 and y=7−2t, find an equation y=mx+b of the tangent to the curve at t=2.
m=
b=
Answers
The values of m and b after evaluation is -2 and 23 under the condition that If x=3t+t² and y=7−2t, and tangent to the curve at t=2.
In orde to evaluate the equation of the tangent to the curve at t=2, we have to calculate the slope of the curve at t=2.
The slope of the curve at t=2 is presented by the derivative of y with respect to x at t=2.
y = 7 - 2t
x = 3t + t²
dy/dx = -2
Then, the slope of the tangent to the curve at t=2 is -2.
Now we have to evaluate the point on the curve at t=2.
x = 3(2) + (2)² = 10
y = 7 - 2(2) = 3
So, the point on the curve at t=2 is (10,3).
Applying point-slope form of equation of line:
y - y₁ = m(x -x₁)
Here,
m = slope and (x₁,y1) is a point on the line.
Staging m=-2 and (x₁,y₁)=(10,3),
y - 3 = -2(x - 10)
Applying simplification
y = -2x + 23
Then, the equation of the tangent to the curve at t=2 is y=-2x+23.
So, m=-2 and b=23.
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Christian earned a grade of 67% on his multiple choice science final that had a total of 200 problems. How many problems on the final exam did Christian answer correctly?
Answers
Answer: 134.
Step-by-step explanation:
First revert 67% into it's decimal form. You get 0.67. Then, multiply 0.67 by 200 because there were 200 problems.
0.67 x 200
67 x 2
134
So, christian got 134 out of 200 problems correct.
Evaluate (11/16−(3/4)2)×1
Answers
Answer:
-166/, -0.82,
Step-by-step explanation:
The above fraction, decimal are all evaluated answer for (11/16−(3/4)2)×1
The table shows the home state of the 175 high school students who attended a tri-state debate tournament. The ratio of Illinois students to Michigan students was 6:5. How many students were from Indiana?
Answers
Let's start by setting up a proportion to represent the ratio of Illinois students to Michigan students:
Illinois students / Michigan students = 6/5
We can simplify this proportion by multiplying both sides by 5:
Illinois students = 6/5 * Michigan students
Next, we can use the information in the table to set up an equation that relates the number of Illinois students, Michigan students, and Indiana students:
Illinois students + Michigan students + Indiana students = 175
We can substitute the expression we obtained for the number of Illinois students into this equation:
6/5 * Michigan students + Michigan students + Indiana students = 175
Multiplying both sides by 5 to eliminate the fraction, we get:
6 * Michigan students + 5 * Michigan students + 5 * Indiana students = 875
Combining like terms, we get:
11 * Michigan students + 5 * Indiana students = 875
Now we can use the fact that the ratio of Illinois students to Michigan students is 6:5 to set up another equation:
Illinois students / Michigan students = 6/5
Substituting the values from the table, we get:
Illinois students / Michigan students = 24/20
Cross-multiplying, we get:
Illinois students * 20 = Michigan students * 24
Simplifying, we get:
Illinois students = 6/5 * Michigan students = 24/20 * Michigan students = 6/5 * 24 Michigan students = 28.8 Michigan students
Since the number of students must be a whole number, we can round 28.8 up to 29. This means that there were 29 Michigan students.
Substituting this into the equation we obtained earlier, we get:
11 * 29 + 5 * Indiana students = 875
Solving for Indiana students, we get:
5 * Indiana students = 875 - 11 * 29 = 546
Dividing both sides by 5, we get:
Indiana students = 546/5 = 109.2
Since the number of students must be a whole number, we can round 109.2 up to 110. This means that there were 110 Indiana students.
Therefore, the answer is 110 students from Indiana.
