Answers
The variables for this problem are given as follows:
a = 16, [tex]b = 16\sqrt{2}[/tex] , c = 16, d = 16.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:
Sine of angle = opposite side/hypotenuse.Cosine of angle = adjacent side/hypotenuse.Tangent of angle = opposite side/adjacent side = sine/cosine.For side lengths a and c, we have a right triangle with angles of 45º, hence using the 45-45-90 Triangle Rule, with the hypotenuse of [tex]16\sqrt{2}[/tex], the lengths a and c are given as follows:
a = c = 16.
The length a is also the geometric mean of the lengths c and d, hence:
16² = 16d
d = 16.
Then the length b is obtained applying the Pythagorean Theorem as follows:
b² = 16² + 16²
[tex]b = \sqrt{2 \times 16^2}[/tex]
[tex]b = 16\sqrt{2}[/tex]
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Related Questions
William throws a football in the air from a height of 4 feet with an initial upward velocity of 96 feet per second.
Write a rule in the form of h=at^2+bt+c that models the height h of the football after t seconds.
Answers
Answer:
Step-by-step explanation:
its 123 jd
8) John wishes to make a line
plot of the heights in inches for a soccer team. The heights are
listed below. How many dots
would be above the greatest
height recorded?
Answer options
1
2
3
4
Answers
There are three dots in the greatest height recorded.
We have,
From the table,
We see that,
The greatest height is 75 inches.
The lowest height is 62 inches.
Now,
If we make a line plot with dots above the height as:
* *
* * * * *
* * * * *
62 66 68 72 75
Thus,
There are three dots in the greatest height recorded.
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4) Students in Ms. Udon
science class planted 13
conifers in different places
around the school yard. They
measured the heights (in inches)
of the conifers one month after
planting them. How many
conifers are greater than 6 1/4
inches tall but less than 8 1/2
inches tall?
Answers
Considering the dot plot, the tallest conifer is 3.25 inches taller than the shortest conifer.
This shows, with dots, the number of times that each of the measures appears in a data set.
For finding the dot plot, we have that:
The shortest conifer measures 6 and 1/4
= 6.25 inches.
The tallest conifer measures 9.5 inches.
The difference is:
9.5 - 6.25 = 3.25 inches.
Therefore the tallest conifer is 3.25 inches taller than the shortest conifer.
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Find the variance and standard deviation of each of the following scores.
x
1-3
4-6
7-9
10-12
13-15
16-18
19-21
f
1
9
25
35
17
10
3
Answers
The variance and standard deviation of the frequency distribution data are;
The variance, s² = 14
The standard deviation, s ≈ 3.742
What is a frequency distribution?A frequency distribution displays the number of data within a specified interval.
The steps to find the variance and the standard deviation of the grouped data are as follows;
The midpoints of the class intervals are found as follows;
Class interval [tex]{}[/tex] Midpoint
1 - 3 [tex]{}[/tex] 2
4 - 6 [tex]{}[/tex] 5
7 - 9 [tex]{}[/tex] 8
10 - 12 11
13 - 15 [tex]{}[/tex] 14
19 - 21 [tex]{}[/tex] 20
The mean is then found as follows;
(2×1 + 5×9 + 8×25 + 11×35 + 14×17 + 17×10 + 20×3)/(1+9+25+35+17+10+3)
The variance can then be found as follows;
s² = (2-11)²×1 + (5-11)²×9 + (8-11)²×25 + (11-11)²×35 + (14-11)²×17 + (17-11)²×10 + (20-11)²×3)/(1+9+25+35+17+10+3 - 1) = 14The standard deviation is therefore; s = √(14) ≈ 3.742Learn more on the standard deviation of a dataset here: https://brainly.com/question/11340286
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Write the number 6,600,000 in scientific notation.
Answers
Answer:
6.6 x 10^6
Step-by-step explanation:
Sheila was setting up a room with tables for an event. The room had
12 plastic tables and 3 composite tables. Each table can seat 8
people.
What is the probability that the first person to enter the room will be
randomly seated at a plastic table?
Answers
The probability that the first person will be seated at a plastic table is 0.8
The probability that the first person will be seated at a plastic table?From the question, we have the following parameters that can be used in our computation:
Plastic tables = 12
Composite tables = 3
Using the above as a guide, we have the following:
Total tables = 12 + 3
Evaluate the sum
Total tables = 15
So, we have the probability to be
P = Plastic tables/Total tables
Substitute the known values in the above equation, so, we have the following representation
P = 12/15
Evaluate
P = 0.8
Hence, the probability that the first person will be seated at a plastic table is 0.8
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Which of the following function pairs are inverses?
Question 3 options:
A)
B)
C)
f (x) = x2 – 16 and g(x) = x – 4
D)
Answers
The function pairs that are inverses are:
C) f(x) = 5x - 3 and g(x) = (x + 3)/5
To determine if two functions are inverses, we need to check if applying one function and then the other function will return the original input.
Let's go through each option:
A) f(x) = -2x and g(x) = (1/2)x
To check if they are inverses, we can apply function f(g(x)) and see if it returns x:
f(g(x)) = f((1/2)x) = -2(1/2)x = -x
Since f(g(x)) = -x ≠ x, these functions are not inverses.
B) f(x) = 4x² and g(x) = √x
To check if they are inverses, we can apply function f(g(x)) and see if it returns x:
f(g(x)) = f(√x) = 4(√x)² = 4x
Since f(g(x)) = 4x = x, these functions are not inverses.
C) f(x) = 5x - 3 and g(x) = (x + 3)/5
To check if they are inverses, we can apply function f(g(x)) and see if it returns x:
f(g(x)) = f((x + 3)/5) = 5((x + 3)/5) - 3 = x + 3 - 3 = x
Since f(g(x)) = x, these functions are inverses.
D) f(x) = x² - 16 and g(x) = x - 4
To check if they are inverses, we can apply function f(g(x)) and see if it returns x:
f(g(x)) = f(x - 4) = (x - 4)² - 16 = x² - 8x + 16 - 16 = x² - 8x
Since f(g(x)) = x² - 8x ≠ x, these functions are not inverses.
Based on the analysis above, the function pairs that are inverses are:
C) f(x) = 5x - 3 and g(x) = (x + 3)/5
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The complete question:
Which of the following function pairs are inverses?
A) f(r) = -2x and g(x) = (1/2)x
B) f() = 4x² and g(x) = √x.
C) f(x) = 5x - 3 and g(x) = (x + 3)/5
D) f(x) =x² - 16 and g(x) = x - 4
THE ONE-EYED JACK MINE INVESTIGATION
The abandoned One-Eyed Jack Mine is about 31 miles off the main road adjacent to the Salmon River Wilderness area. There is only a rutted dirt track left where the access road used to run. It is so steep that when we hiked up it we had to pause every fifty feet or so to catch our breath. It seemed impossible but 3- 5 miles further we found remnants of the old wagons, the mineshaft, and the mill. The gold ore found in this mine was embedded in quartz and prospectors used the mill to grind up the quartz and rinse it with acid in huge shallow vats that were agitated so that the gold would sink to the bottom and the quartz could be washed away.
One arrangement of equipment we noticed included a circular vat about 18 feet in diameter which must have been connected by a huge belt to a smaller circular drive wheel 10 feet in diameter. The distance between the wheel and the vat was 8 feet. The equipment had been partially pre-fabricated then carried up the hill piece by piece to be re-assembled on the spot. Just the belt to connect the vat to the drive wheel would have been a major burden. We wondered how many times they had to carry new ones up to replace it. Calculate the length of belt needed to go around the drive wheel and the vat.
Answers
Answer:
The length of the belt needed to go around the drive wheel and the vat is approximately 79.6 feet. This is calculated by using the circumference formula C = 2πr where r is the radius of the wheel (5 feet) and the radius of the vat (9 feet). The total circumference is then 2 x 3.14 x (5 + 9) = 79.6 feet.
Answer:
79.6 feet.
Step-by-step exp
2 x 3.14 x (5 + 9) = 79.6 feet.
Write two numbers that multiply to the value on top and add to the value on bottom. 24 + - 25
Answers
The two numbers that multiply to the number 24 and add up to the number -25 as required to be determined are; -24 and -1.
What are the two numbers as described?It follows from the task content that the two numbers which multiply to give 24 and add up to give -25 are to be determined.
By observation, the two numbers in discuss are; -24 and -1. This follows from the fact that: -24 × -1 = 24 and also, -24 + -1 = -25.
Consequently the two numbers as required to be determined are; -24 and -1.
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A cylinder has the height of 12 inches and radius of 7 inches what is the volume
Answers
Answer:
588π
Step-by-step explanation:
Volume of cylinder = π r ² h
= π (7)² (12)
= 588π
19
A
Straight line A passes through the points (-1, 2) and (1,6)
Straight line B has equation y-x
Work out the coordinates of the point where line A crosses line B
You may use the grid to help you.
40
10
+
7
-2
14
T
6
5-
4-
3
2
O
-1-
-2-
-3
-5-
-6-
Answer (
2
3
5
6
[4 marks]
Answers
First, let's find the equation of line A using the two given points:
Calculate the slope (m) of line A:
m = (y2 - y1) / (x2 - x1)
m = (6 - 2) / (1 - (-1))
m = 4 / 2
m = 2
Use the point-slope form of a line to write the equation of line A:
y - y1 = m(x - x1)
Taking (-1, 2) as a point on line A:
y - 2 = 2(x - (-1))
y - 2 = 2(x + 1)
y - 2 = 2x + 2
y = 2x + 4
Now we need to find the point where line A (y = 2x + 4) crosses line B (y - x).
Substitute y = 2x + 4 into the equation y - x:
2x + 4 - x = 0
x + 4 = 0
x = -4
Substitute the value of x into the equation of line A to find the corresponding y-coordinate:
y = 2x + 4
y = 2(-4) + 4
y = -8 + 4
y = -4
Therefore, the coordinates of the point where line A crosses line B are (-4, -4).
Gillians net worth is 90,500 based on the information in the table what is the amount of money gillans owens student loans
Answers
The amount of money Gillians owes for student loans is $12,250
How to determine this
When Gillians net worth = $90,500
House(Current value) = $87,900
Checking account = $950
Credit- card = -$2,650
Automobile(current value) = $10,300
Student loans = ?
Investment = $5,000
Personal loans = 1,200
Savings account = $2,450
To calculate the money Gillians Owen owes student loans
Let x represent the student loans
$90,500 = $87,900 + $950 - $2,650 + $10,300 + x + $5,000 - $1,200 + $2,450
$90,500 = $102,750 + x
Collect like terms
x = $90,500 - $102,750
x = 12,250
Therefore, the money Gillians owes student loans is $12,250
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what is the surface area of 10 in 10 in 10in
Answers
The surface area of a three dimensional shape is the total area of all of the faces. To find the surface area of a shape, we find the area of each face and add them together. E.g. The measurements here are in centimetres so the surface area is measured in square centimetres ( c m 2 ) (cm^2) (cm2).
Suppose that the common shares of Oceanic Luxury Vessels , Inc. , is trading for $ 38 a share and that 5 million shares are outstanding . The company also has 75,000 bonds outstanding , which are selling at 102 percent of par . If Oceanic Luxury Vessels , Inc. , was considering an active change to its capital structure so that the firm would have a D/E ratio of 1.6 , which type of security ( stocks or bonds ) would it need to sell to accomplish this , and how much would it have to sell ? A. Debt ; $ 349.9 million B. Stock : $ 445.2 million C. Debt ; $ 248.5 million D. Stock ; $ 289.4 million
Answers
Answer:
To have a D/E ratio of 1.6, Oceanic Luxury Vessels, Inc. would need to sell debt securities.
First, we need to calculate the market value of the company's equity.
Market value of equity = Number of shares outstanding × Market price per share
Market value of equity = 5,000,000 × $38
Market value of equity = $190,000,000
Next, we can calculate the current debt-to-equity (D/E) ratio of the company:
Current D/E ratio = Total debt / Total equity
Total debt = Number of bonds outstanding × Bond price per bond × Par value
Total debt = 75,000 × 1.02 × $1,000
Total debt = $76,500,000
Current D/E ratio = $76,500,000 / $190,000,000
Current D/E ratio = 0.403
To achieve a D/E ratio of 1.6, the company would need to increase its total debt by a factor of 1.6/0.403 = 3.97.
New total debt = 3.97 × $76,500,000
New total debt = $304,305,000
To calculate the amount of debt securities the company would need to sell, we can subtract the current total debt from the new total debt:
Amount of debt to be sold = $304,305,000 - $76,500,000
Amount of debt to be sold = $227,805,000
Therefore, the company would need to sell debt securities worth $227.8 million to achieve a D/E ratio of 1.6.
The correct answer is C. Debt; $248.5 million.
PLEASE HELP MEEE RIGHT NOWWWW
Tell whether volume applies to the situation ( please tell a , b , c , d , and e)
A. Wrapping paper used to wrap a gift
B. Milk poured into a glass
C. Air needed to blow up a ball
D. Fabric for making a quilt
E. How much will fit in a suitcase
Last one
Describe another situation in which volume would apply.
THANKS
Answers
B. Milk poured into a glass - Volume does apply to this situation as the amount of milk poured into a glass can be measured in volume.
C. Air needed to blow up a ball - Volume does apply to this situation as the amount of air needed to inflate a ball can be measured in volume.
D. Fabric for making a quilt - Volume does not apply to this situation as fabric is measured in terms of area and not volume.
E. How much will fit in a suitcase - Volume does apply to this situation as the amount of stuff that can fit in a suitcase can be measured in volume.
Another situation in which volume would apply is:
F. Determining the amount of water required to fill a swimming pool.
Which number is equivalent to 7/11
?
Answers
The equivalent fractions of 7/11 are 14/22, 21/33, 28/44 and 35/55
There are infinitely many numbers equivalent to 7/11
since 7/11 is a fraction that can be simplified in different ways.
We can multiply the numerator and denominator with the same number to get the equivalent fractions
7/11×2/2 = 14/22
7/11×3/3= 21/33
7/11×4/4 =28/44
7/11×5/5 =35/55
Hence, the equivalent fractions of 7/11 are 14/22, 21/33, 28/44 and 35/55
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Which graph represents the PARENT function of y = x^2- 5?
Answers
Answer:
Graph A--------------------
The function y = x² - 5 is the translation of the parent function y = x² down by 5 units.
Since the parent function is y = x², it is a parabola that has its vertex at the origin and opens up as its coefficient is positive.
Looking at the answer choices, we see option A is the correct one.
Other options are incorrect:
Option B is reflection of parent function in the x-axis, Option C is translated down, Option D is translated to the right.When we write four thousand two hundred that is what form?
Answers
The equivalent value of the expression is A = four thousand two hundred and A = 4,200
Given data ,
Let the expression be represented as A
Now , the value of A is
A = four thousand two hundred
On simplifying the equation , we get
A = 4,200
And , when we write "four thousand two hundred," it is written in word form
Hence , the equation is A = 4,200
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What do you know about the graphs of polynomials with positive end behavior compared to the graphs of polynomials with negative end behavior?
If "positive" end behavior:
1. The graph hits the x-axis
2. The arrows point in opposite directions
3. The arrows point in the same direction
4. The right arrow is up
5. The graph hits the y-axis
6. The right arrow is down
If "negative" end behavior:
1. The graph hits the x-axis
2. The right arrow is down
3. The graph hits the y-axis
4. The right arrow is up
5. The arrows point in the same direction
6. The arrows point in opposite directions
Answers
The end behavior of a polynomial with positive leading coefficient is either "up-up" or "down-down" depending on the degree of the polynomial the end behavior of a polynomial with negative leading coefficient is either "up-down" or "down-up" depending on the degree of the polynomial.
Actually, the end behavior of a polynomial refers to the behavior of the function as the input variable (usually x) approaches positive or negative infinity.
The end behavior of a polynomial is determined by the degree and leading coefficient of the polynomial.
If the degree of the polynomial is even and the leading coefficient is positive, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial approaches the x-axis from above (the arrows point in opposite directions).
As x approaches positive infinity, the graph of the polynomial approaches the x-axis from below (the arrows point in opposite directions).
If the degree of the polynomial is even and the leading coefficient is negative, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial approaches the x-axis from below (the arrows point in opposite directions).
As x approaches positive infinity, the graph of the polynomial approaches the x-axis from above (the arrows point in opposite directions).
If the degree of the polynomial is odd and the leading coefficient is positive, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial goes down to negative infinity (the arrows point in the same direction).
As x approaches positive infinity, the graph of the polynomial goes up to positive infinity (the arrows point in the same direction).
If the degree of the polynomial is odd and the leading coefficient is negative, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial goes up to positive infinity (the arrows point in the same direction).
As x approaches positive infinity, the graph of the polynomial goes down to negative infinity (the arrows point in the same direction).
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30 POINTS HELP! To analyze the change in the number of dog walks over time, draw a line to model the data. Use the connect line to draw the line.
Answers
The line of the best fit that models the data is added as an attachment
Drawing a line to model the data.
From the question, we have the following parameters that can be used in our computation:
The graph
To draw a line to model the data is to draw the line of best fit
A good line of best fit would have equal number of points on either sides
To plot the graph, we draw a line that divides the points on the graph evenly
This line when drawn on the scattered points divided the points approximately evenly
Hence, the line of the model is attached
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I need help with number three.
Answers
Answer:
1761 ft²
Step-by-step explanation:
The shape of the attic is a triangular prism.
It has 5 faces: The bases are 2 faces that are congruent triangles. The other 3 faces are rectangles, 2 of which are congruent.
surface area = area of the bases + area of 3 rectangles
surface area = 2 × area of triangle + 2 × area of rectangle + area of other rectangle
surface area = 2 × (1/2)bh + 2 × length × width + LENGTH × WIDTH
surface area = 2 × (1/2)(15 ft)(15 ft) + 2(15 ft)(30 ft) + (21.2 ft)(30 ft)
surface area = 225 ft² + 900 ft² + 636 ft²
surface area = 1761 ft²
coordinate plane with segment AB located at A 0 comma 2 and B 2 comma 3 segment AB is dilated from the origin to create segment A prime B prime at A′ (0, 8) and B′ (8, 12). What scale factor was segment AB dilated by? one half 2 3 4
Answers
The required scale factor for the dilation of segment AB to create segment A'B' is 2.
If the length of the original segment AB is 5 units and the length of the dilated segment A'B' is 10 units, the scale factor can be calculated as follows:
Scale factor = Length of A'B' / Length of AB
Scale factor = 10 / 5
Scale factor = 2
Therefore, the correct scale factor for the dilation of segment AB to create segment A'B' is 2.
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The ratio 5x +2 : y - 2 is equal to 6:5. Express y in terms of x .
Answers
Answer:
y = [tex]\frac{25x+22}{6}[/tex]
Step-by-step explanation:
express the ratios in fractional form
[tex]\frac{5x+2}{y-2}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )
6(y - 2) = 5(5x + 2) ← distribute parenthesis on both sides
6y - 12 = 25x + 10 ( add 12 to both sides )
6y = 25x + 22 ( divide both sides by 6 )
y = [tex]\frac{25x+22}{6}[/tex]
A set contains 13 elements.
a) How many subsets does it have?
b) How many proper subsets does it have?
Answers
Step-by-step explanation:
Answer and Explanation:
The set contains 13 elements here, so the total number of subsets can be calculated as 213=8192 2 13 = 8192 .
Sean says the value of a to the -3rd power is always less than 1 if a is positive.
Christine says the value of a to the -3rd power is always less than 1 when a is negative
Which one is correct, and for the one that is incorrect enter the number that proves in to be incorrect (if none say none).
Answers
Sean's statement is correct. Christine's statement is incorrect when a is negative.
The value of a to the -3rd power is always less than 1 if a is positive.
For example, if a = 2, then a to the -3rd power is 1/8, which is less than 1. Therefore, Sean's statement is correct.
The value of a to the -3rd power is always less than 1 if a is positive, but it is always greater than 1 if a is negative.
For example, if a = 2, then a to the -3rd power is 1/8, which is less than 1. But if a = -2, then a to the -3rd power is -1/8, which is greater than 1.
Therefore, Christine's statement is incorrect when a is negative.
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Find the measures of the acute angles.
29.67°
37°
168°
12°
Answers
Explanation:
Set them equal because of the Alternate Exterior Angles property. Solve:
2y + 13 = 4y - 11
24 = 2y
y= 12
Input the Y:
2(12) + 13 = 37
4(12) - 11 = 37
WILL GIVE BRAINLIEST PLEASE HELP
Answers
Explanation;
Corresponding Angles are on same side for both top group and bottom group. The pairs are: 1,5 2,6 3,7 4,8.
What is the range of the set of coordinates shown below?
(-10, 2), (-5, 3), (-7,4), (0, 0), (-10, 3), (3, 8)
Answers
Answer:
{0,2,3,4,8}
Step-by-step explanation:
Dakota measured a neighborhood park and made a scale drawing. The scale of the drawing was 1 inch : 5 yards. A soccer field in the park is 12 inches wide in the drawing. How wide is the actual field?
Answers
The actual width of the soccer field is 60 yards.
Given, the scale of the drawing is 1 inch : 5 yards.
The width of the soccer field in the drawing is 12 inches.
So, the actual width of the soccer field can be found by multiplying the width in the drawing by the scale factor:
Actual width = Width in drawing x Scale factor
The scale factor is 5 yards per inch, so we can write:
Actual width = 12 inches x 5 yards per inch
Actual width = 60 yards
Therefore, the actual width of the soccer field is 60 yards.
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Consider the equation -3 x e^5w = -88
Solve the equation for (W) Express the solution as a logarithm in base-e.
___
Approximate the value of (W). Round your answer to the nearest thousandth.
___
Answers
The solution for w is given by the natural logarithm of 88 divided by 3x, all raised to the power of 1/5.
Exponential functions are always increasing or decreasing, depending on the sign of the base "a".
The graph of an exponential function has a characteristic shape that depends on the base "a". When "a" is greater than 1, the graph is an increasing curve that becomes steeper as x increases; when "a" is between 0 and 1, the graph is a decreasing curve that approaches the x-axis as x increases.
Starting with the equation:
[tex]-3xe^{(5w)} = -88[/tex]
We can first isolate the exponential term by dividing both sides by -3x:
[tex]e^{(5w)} = \dfrac{88 }{ (3x)}[/tex]
Then, taking the natural logarithm of both sides, we get:
[tex]5w = ln(\dfrac{88} { 3x})[/tex]
Finally, dividing both sides by 5, we obtain the solution for w:
[tex]w = (\dfrac{1}{5}) ln(\dfrac{88} { 3x})[/tex]
Therefore, the solution for w is given by the natural logarithm of 88 divided by 3x, all raised to the power of 1/5.
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