Find the remaining sides of a 45°-45°-90° triangle if the longest side is 20.

Answers

Answer 1

45°-45°-90° is an isosceles right triangle. The longest side is hypotenuse.
All 45°-45°-90° triangles have sides that are in a unique ratio. The two legs are the exact same length, and the hypotenuse is that length times the √2.

Let a be the leg then hypotenuse = a√2.

[tex]a \sqrt{2}=20 \ \to a= \frac{20}{ \sqrt{2} } \approx 14.14 \ \text{units}[/tex]

Related Questions

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Line A passes through points (-1, 5) and (3, -1). Line B passes through points (7, 2) and (6, -1). At what point does line A intersect line B?

Answers

Line A
slope = (-1 - 5)/(3+1) = -6/4 = -3/2
y = mx + b
5 = -3/2(-1) + b
b = 5 - 3/2
b = 7/2
equation of line A: y = -3/2x + 7/2

Line B
slope = (-1 - 2)/(6-7) = -3/-1 = 3
y = mx + b
2 = 3(7) + b
b = 2- 21
b = - 19
equation of line B: y = 3x -19

line A intersect line B when -3/2x + 7/2 = 3x -19
so
-3/2x + 7/2 = 3x -19
3x + 3/2x = 19 + 7/2
9/2x = 45/2
x = (45/2) * (2/9)
x = 5

y = 3x - 19 = 3(5) -19 = 15 -19 = -4

(5 , -4)

answer
line A intersect line B at (5, -4)

Complete the statement f(3) is

Answers

f(3) is asking us "What output do I get with 3 as the input?". Looking at the Domain (all possible inputs) we see that 3 is indeed a possible input so that part is ok. Checking the Range (all possible outputs) we see that an input of 3 gives one and only one output (incidentally since this is true of all inputs, this is a function in 'x'). The only output that we get with an input of 3 is -1.

The corresponding output for an input value of 3 is -1. Hence f(3) is -1

from the mapping function given, the domain values are the input values of the function while the range is the output.

To get the value of f(3), we need to check the corresponding output when the input variable is 3.

From the given one-on-one mapping, we can see that the corresponding output for an input value of 3 is -1. Hence f(3) is -1

Learn more here; https://brainly.com/question/3373678

Identify the terms and coefficients for4p+5-3g

Answers

Terms are numerals and variables separated by + and - signs.

Terms:
4p
5
-3g

Coefficients are numbers multiplied by variables.

Coefficients:
4
-3

What is the graph of the function?

f(x) = 2x 2

Answers

The function given is f(x)=2x²

Check the coordinate of y when x=0 ⇒ f(0)=0
Check the coordinate of x when y=0 ⇒ x=0

We have two pairs of coordinate, (0, 0) and (0, 0)

The first two graphs have these coordinates so we need to do further checking

take x=1 ⇒ f(1) = 2(1)² = 2
take x=2 ⇒ f(2) = 2(2)² = 8

we have two pairs of coordinates; (1, 2) and (2, 8)

The correct answer is OPTION A

Answer:

For f(x)=2x² graph, the answer is A.

Step-by-step explanation:

For x = -2; y = 8For x = -1; y = 2For x = 0; y = 0For x = 1; y = 2For x = 2; y = 8

Create a set of numbers where the mode is equal to 10 the median is equal to 12 and the average is 12.

Please I really need help!

Answers

10,10,10,12,13,14,15

MEDIAN: 12
MODE: 10
MEAN: 12

mean 12 because it's the average so you have to add the data set all up and divided by the numbers that are in the data set like 84 divided 7 which is 12, your answer.

A ladder is leaning up against a 17 foot Wall at an angle of elevation of 37°. How far is the foot of the latter from the wall? Round your answer to the nearest 10th of a foot

Answers

This is the concept of trigonometry, the distance from the foot of the ladder will be given by:
tan theta=[opposite]/[adjacent]
opposite=17 ft
adjacent=x ft
theta=37°
thus
tan 37=17/x
x=17/tan 37
x=22.56 ft
=22.6 ft (to the nearest 10th of a foot)

How to find the midpoint formula

Answers

[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 6}}\quad ,&{{ -1}})\quad % (c,d) &({{ -3}}\quad ,&{{ -13}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left(\cfrac{-3+6}{2}~,~\cfrac{-13-1}{2} \right)[/tex]

and fairly sure you know how much that is.

The perimeter of a rectangle is 120 feet. The ratio of the width to the length is 2:3. Find the length and width.

Answers

Since the ratio of width to length is 2:3, that is a total of 5 parts.
Multiply this by 2 (P = 2L + 2W) = 10 parts.
120/10 = 12
Each part = 12
W:L

12*2:12*3 = 24:36

CHECK

2(24) + 2(36) ??=?? 120

48 + 72 ??=?? 120

120 = 120 checks

Length = 36 ft
Width = 24 ft

g(a) = 3^3a-2 . Find g(1)

Answers

sub 1 for a

[tex]G(1)=3^{3(1)-2}[/tex]
[tex]G(1)=3^{3-2}[/tex]
[tex]G(1)=3^{1}[/tex]
[tex]G(1)=3[/tex]

It takes Brian 15 hours longer to build a model car than it takes John. If they work together, they can build the model car in 4 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Brian to build the car on his own

Answers

It would take Brian 20 hours to build the model car on his own.

To determine the time it would take Brian to build the model car on his own, we can follow these steps:

1. Let's denote the time it takes John to build the model car as J hours.

2. Since it takes Brian 15 hours longer than John, we can express the time it takes Brian as J +15 hours.

3. If they work together, they can build the model car in 4 hours. This means that in 1 hour, they complete [tex]$\frac{1}{4}$[/tex] of the job together.

4. In 1 hour, John completes [tex]$\frac{1}{J}$[/tex] of the job, and Brian completes [tex]$\frac{1}{J + 15}$[/tex] of the job.

5. So, the equation representing the rate at which they work together is:

[tex]\[ \frac{1}{J} + \frac{1}{J + 15} = \frac{1}{4} \][/tex]

6. Now, we solve this equation to find J, the time it takes John to build the model car on his own.

7. Once we find J, we can find J+15 which represents the time it takes Brian to build the model car on his own.

So, the equation representing the rate at which they work together is:

[tex]\[ \frac{1}{J} + \frac{1}{J + 15} = \frac{1}{4} \][/tex]

To solve this equation, we can multiply both sides by the least common denominator, which is [tex]$ 4J(J + 15) $[/tex], to clear the fractions:

[tex]\[ 4(J + 15) + 4J = J(J + 15) \][/tex]

Expanding and simplifying:

[tex]\[ 4J + 60 + 4J = J^2 + 15J \]\[ 8J + 60 = J^2 + 15J \]\[ J^2 + 15J - 8J - 60 = 0 \]\[ J^2 + 7J - 60 = 0 \][/tex]

Now, we have a quadratic equation. We can solve this equation using factoring, completing the square, or the quadratic formula. Let's use factoring:

[tex]\[ (J - 5)(J + 12) = 0 \][/tex]

Setting each factor equal to zero:

[tex]\[ J - 5 = 0 \] or $ J + 12 = 0 $[/tex]

Solving each equation:

[tex]For $ J - 5 = 0 $, we get $ J = 5 $.For $ J + 12 = 0 $, we get $ J = -12 $.[/tex]

Since time cannot be negative, we discard the negative solution.

Now that we have found J=5 hours, which represents the time it takes John to build the model car on his own, we can find [tex]$ J + 15 = 5 + 15 = 20 $[/tex] hours.

At the Atkins County Fair, the crowd for a concert by The Cooper Band cannot exceed a certain number. The limit for the number of people who can attend the concert is 0.04 people per square foot of space in the arena. If the arena is shaped as a rectangle with sides 220 feet by 200 feet, how many people can attend the concert?

Answers

The first thing to do was to find the area of the space to do that we would need to do:
220*200= 44000
the area is [tex]44000ft^{2} [/tex]
next you would do:
44000/.4 to find how many people can fit
this equals 11000
11,000 people can attend the concert

2x-3y=8 solve for (y)?

Answers

2x-3y=8

Subtract 2x from both sides

-3y=-2x+8

Divide both sides by -3

y=2/3x-8/3

remember, you can do anything to an equation as long as you do it to both sides

so

2x-3y=8
minus 2x both sides
-3y=-2x+8
divide both sides by -3
y=(-2/-3)x+(8/-3)
y=2/3 x-8/3

what is the simplified form of (6^2+4)-15

Answers

First solve the parentheses and you get 36+4 which is 40 and then subtract 15 so you get 25

A vehicle travels on a highway at a rate of 65 mi/h. How long does it take the vehicle to travel 25 mi?

Answers

[tex]\bf \begin{array}{ccll} miles&hour\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 65&1\\ 25&h \end{array}\implies \cfrac{65}{25}=\cfrac{1}{h}\implies h=\cfrac{25\cdot 1}{65}[/tex]

The solutions to the inequalities 0≤x≤2,0≤y≤1, and y≤−12x+32 form a polygonal region in the plane. How many sides does this polygon have?

Answers

In order to know the shape of the polygon you plot first the last inequality because it form a line in the graph. In plotting this equation, disregard the inequality sign first. Then, set arbitrary points of x, determine y and plot them. The line is shown in the picture. Next, we test the inequality. Suppose we choose the point of origin, then,

y≤−12x+32
0 ≤ -12(0)+32
0 ≤ 32

This is true. Thus, the shaded region must include (0,0) which is located to the left of line (blue-shaded region). Next, use the two remaining boundaries. The inequality 0≤x≤2 is denoted as the black horizontal line from x=0 to x=2. Moreover, the inequality 0≤y≤1 is denotes as the black vertical line. The resulting figure is a rectangle. Therefore, the polygon has 4 sides.

To which subset of real numbers does -18 not belong?

Answers

The subsets of the real numbers are the irrational numbers, rational numbers, integers, whole numbers, and the natural numbers. First, figure out where does -18 belong? Well, -18 is a rational number because it can be expressed as a fraction of two integers. It's also an integer.

So, it doesn't belong in the sets of irrational numbers, whole numbers, and the natural numbers.

We have that the -18 is a rational quantity due to the fact it can be expressed as a fraction of two integers. It's additionally an integer.

Rational number & Integer

Real numbers

Generally

The subsets of the actual numbers are as follows

Irrational numbersRational numbersWhole numbersNatural numbers etc

-18 is a rational quantity due to the fact it can be expressed as a fraction of two integers. It's additionally an integer.

For more information on Numbers visit

https://brainly.com/question/21094767

All right triangles with the same acute angle θ are

Answers

All right triangles with the same acute angle θ are SIMILAR

If a sphere has a radius of 2 cm what is the approximate surface area of the sphere

Answers

The formula for the surface area of a sphere is [tex]SA=4 \pi r^{2} [/tex]
If your radius is 2, then filling in that formula looks like this:
[tex]SA=4 \pi ( 2^{2} )[/tex] or [tex]16 \pi [/tex]. If you leave your answer in terms of pi, which is the exact answer, you're done. But if you multiply pi in, your surface area is SA = 50.264 square cm.

The mapping diagram shows a relation.

What is the domain of the relation?

{x| x = –4 , 0, 1, 2}.

{x| x = –7, –6, 2, 11, 3}.

{y| y = –4, 0, 1, 2}.

{y| y = –7, –6, 2, 11, 3}.

Answers

i can't see the diagram but when you talk about domain you mean x values so the answers are the first or second options.

Answer:B. {x| x = –7, –6, 2, 11, 3}.

1) 8k-(6k-4)=10 show work please

2) -12x+8+5x=36 show work please

3) -2y+4=8y-6

Answers

1) 8k - (6k - 4) = 10

[tex]\mathsf{8k-6k+4=10}\\\\ \mathsf{2k=10-4}\\\\ \mathsf{2k=6}\\\\ \underline\mathsf{k=\dfrac{6}{2}=3}}[/tex]

2) -12x + 8 + 5x = 36

[tex]\mathsf{-12x+8+5x=36}\\\\ \mathsf{-12x+5x=36-8}\\\\ \mathsf{-7x=28}\\\\ \mathsf{x={28}{-7}}\\\\ \underline{\mathsf{x=-4}}[/tex]

3) -2y + 4 = 8y - 6

[tex]\mathsf{-2y+4=8y-6}\\\\ \mathsf{-2y-8y=-6-4}\\\\ \mathsf{-10y=-10}\\\\ \mathsf{y=\dfrac{-10}{-10}}\\\\ \underline{\mathsf{y=1}}[/tex]

A ramp 24 ft long rises to a platform that is 20 ft off the ground. find x , the angle of elevation of the ramp. round your answer to the nearest tenth of a degree.

Answers

[tex]sin(x)= \frac{BC}{AC}= \frac{20}{24} \approx 0.8333 \ \ \to \ \ x\approx56.4^o[/tex]

Final answer:

To determine the angle of elevation x, we use the sine function with the opposite side (20 ft) and the hypotenuse (24 ft) to get sin(x) = 20/24, and by taking the arcsin of the result, we find that x ≈ 56.4° when rounded to the nearest tenth of a degree.

Explanation:

To find x, the angle of elevation of the ramp, we can use trigonometric functions. Since we have the length of the ramp (hypotenuse) and the height of the platform (opposite side) in a right-angled triangle, we can use the sine function, which is defined as the ratio of the opposite side to the hypotenuse.

Using the sine function: sin(x) = opposite/hypotenuse = 20/24.

We first calculate the ratio: sin(x) = 20/24 = 0.8333.

To find the angle x, we take the inverse sine (also known as arcsine) of the ratio: x = arcsin(0.8333).

Using a calculator set to degree mode, we find that x ≈ 56.4° when we round to the nearest tenth of a degree.

A student has some 1 and 5 bills in his wallet. he has a total of 14 bills that are worth 50 how many of each type of bill does he hae

Answers

x = ones

y = fives

x+y = 14 total bills

rewrite as x = 14-y

1x +5y = 50

1(14-y) +5y = 50

14-1y +5y = 50

14 +4y = 50

4y = 36

y = 36/4 = 9

x = 14-y = 14-9 = 5

9+5 = 14

9x5 = 45 +5x1 = 50

he had 9 fives and 5 ones

Answer:

There were 5 bills of '1' and 9 bills of '5'.

Step-by-step explanation:

let the number of '1' bill be x

let the number of '5' bill be y.

Total number of bills = 14

x + y = 14 ..[1]

Worth of 14 bills = 50

So,[tex]x\times 1+y\times 5=\$50[/tex]

[tex]x+5y=50[/tex]..[2]

x + y = 14

x = 14 - y

Putting value of x in [2]:

[tex]14- y +5y=50[/tex]

[tex]y=\frac{50-14}{4}=9[/tex]

y = 9

x = 14-y = 14 - 9 = 5

There were 5 bills of '1' and 9 bills of '5'.

which description matches the transformations y=cosx undergoes to produce y= -2cos3x

A. Horizontal compression by factor 1/3, vertical stretch by factor 2, then a reflection through the x-axis
B. reflection through the y-axis, vertical shift of 2 units, horizontal shift right by 3 units
C.Horizontal shift 2 units, then vertical shift up by 3 units
D.Horizontal stretch by factor 2, reflection through the x-axis, then the vertical stretch by factor 3

Answers

the 3 before the x causes a horizontal compression , the -2 causes a vertical stretch followed by reflection in x axis. Its A

Answer: A. Horizontal compression by factor 1/3, vertical stretch by factor 2, then a reflection through the x-axis

Step-by-step explanation:

Since, If there is a function, y= a cos bx

Then a shows vertical stretch while b shows horizontal compression.

Here, Given function, y= cos x

After transformation, It is giving y = -2 cos 3x

therefore here is a horizontal compression occurs with factor 1/3.

Also Negative sign shows there also did reflection through x-axis.

And, It also, stretched vertically by factor 2. ( also shown in the below graph)

Thus, Option A) is correct.

A building manager installs sensors to see how often people turn off the lights when they leave a room. After a month, the manager has a sample size of 400, a sample mean of 47%, and a sample standard deviation of 4%. What is the confidence level for a confidence interval of 46.6% to 47.4%?

A. 68%
B. 85%
C. 99.7%
D. 95%

Answers

The answer is C.

The figures in your problem are inconsistent with the data.
The sample std deviation is not and cannot be .04 (4%).
the sample std dev is sqrt[(.47)(1-.47)/400]=.02495.
The margin of error from your CI is .474 -.47= .004 (very small).
This would represent .02495/.004= 6.24 std dev. from expected, which would have a very
high level of confidence (99.97.. %). Something is likely wrong with the figures in your problem.

Answer: 95%

Step-by-step explanation:

I'm having a bit of trouble, could you help?

Answers

Terms & Definitions:
-5-(3^2+2)=-16,
2^2-3*6=-14,
-2+4*3^2-6=28
5+4^2/2(3)=29

Evaluate: 12-6+(14-8)^2=42

not sure which youre having trosuble with so im gonna go with everything.

-5-(3^2 + 2)
= -5 - 9 -2
= -16
= D

2^2 - 3 × 6
= 4- (3 × 6) <==== principle of BODMAS
= -14
= C

-2 + (4×3^2) -6
= -2 + 36 - 6
= 28
= A

so the next answer is obviously B

Question 2.
12-6+(14-8)^2
= 6 + 6^2
= 6 + 36
= 42

A set of n = 15 pairs of X and Y scores has SSX = ...A set of n = 15 pairs of X and Y scores has SSX = 10,SSY = 40, and SP = 30. What is the slope for the regression equation for predicting Y from X?

Answers

This question is asking only for the slope of the regression equation. This slope can be easily calculated using the following rule:
slope = SP / SSx

Examining the givens, we will find that both parameters are given where:
SP = 30 and SSx = 10

Substituting with the givens in the above mentioned equations, we can calculate the slope as follows:
slope = 30 / 10 = 3

In two supplemantary angles, the measure of one angles is 6 more than the twice the measure of the other.the measure of these two angles are

Answers

Answer:
________________________________________________________
The measurements of the 2 (TWO) supplementary angles are:
________________________________________________________
           58° and 122° .
________________________________________________________
Explanation:
_________________________________________________
Two supplementary angles:
_________________________________________________
Angle 1: "x:
_________________________________________________
Angle 2: "(6 + 2x)"
_________________________________________________
        All supplementary angles, by definition, add up to 180 degrees, so given that the 2 (two) angles are supplementary:

(x) + (6 + 2x) = 180 ; Find "x" and "(6 + 2x)" .
__________________________________________________
   x + 6 + 2x = 180 ;

      3x + 6 = 180 ;

   Subtract "6" from each side of the equation ;
___________________________________________________
      3x + 6 − 6 = 180 − 6 ;

          3x = 174 ;
___________________________________________________
Divide each side of the equation by "3" ;
to isolate "x" on one side of the equation ; and to solve for "x" ;

          3x / 3 = 172 / 3 ;

               x = 58 ;
________________________________________________
So:
________________________________________________
Angle 1: "x" : x = 58 .
________________________________________________
Angle 2: "(6 + 2x)" =  " 6 + 2(58) = 122 .
________________________________________________
122 + 58 =? 180 ? Yes!
________________________________________________
So, the measurements of the 2 (TWO) supplementary angles are:
           58° and 122° .
________________________________________________

A board is 27 inches long. How long is the board in centimeters? Use the following conversion: 1 inch is 2.54 centimeters.

Answers

1 inch = 2.54 cm

so multiply 27 by 2.54

27 x 2.54 = 68.58 cm long

To convert 27 inches to centimeters, multiply 27 by the conversion factor of 2.54 cm per inch, resulting in 68.58 centimeters.

The student has asked how long a board that is 27 inches long is in centimeters, given the conversion factor that 1 inch is equal to 2.54 centimeters. To convert inches to centimeters, you multiply the length in inches by the conversion factor. In this case, you would multiply 27 inches by 2.54 to find the length in centimeters.

Here is the calculation:
27 inches x 2.54 cm/inch = 68.58 centimeters.

Therefore, a board that is 27 inches long is 68.58 centimeters long.

what is the last line of proof

Answers

The answer to this question is the second choice
hope this helps:)

the third answer makes the most sense

How did Greek mathematician Pythagoras come up with the Pythagorean Theorem. Explain

Answers

The theorem was known to the Babylonians and Indians long before Pythagoras's time. However it is thought That the Greek Pythagoras was the first to construct a proof of the theorem, that,s why it was named after him.

Other Questions

If a product has 200 calories per serving and 100 calories from fat, then the percent of calories from fat would reveal that the product is:50% calories from fat and potentially an unhealthy choice50% calories from fat and a low-fat food item100% calories from fat and potentially an unhealthy choice50% calories from fat and potentially a healthy choice which type of political and social order is shown in this diagram ? What is the over-the-counter, lower-dose version of the fat-blocking prescription drug xenical (orlistat)? A diploid organism has 10 chromosomes; how many gene combinations can occur in the organisms gametes? Gabriella said a triangle with an angle of 98 degrees was an obtuse angle. Cynthia said a triangle with an angle of 98 degrees was an acute triangle. Who is right and why? Help me with this please!!! Your heart puffed and flowered like sheets drying on a line. Which poetic device does the word heart represent in these lines? personification figurative language imagery onomatopoeia Sociologists conduct research to understand society, groups of people and human behavior. For example, a sociologist may want to understand why there is a high divorce rate in America. Sociologists typically follow the scientific process when conducting research to ensure that the findings are reliable and valid. One important step to the scientific process is data-collection. List the four data-collection techniques and explain why a sociologist would choose to use each of them. write the ordered pair that represents yz. then find the magnitude of yz. Y(-5,7), Z(-1,2) . If ON = 4x 6, LM = 3x + 5, NM = x 4, and OL = 4y 3, find the values of x and y for which LMNO must be a parallelogram. three tables are placed side by side. one table is 6 feet 9 inches, another is 5 feet 11 inches wide, and the third is 2 feet 10 inches wide. how wide are they combined Leaving the scene of a crash resulting in property damage of more than $50 would result in the accumulation of _______ points. Verbal reasoning : Choose the most appropriate option to complete the statement . 'AC is to VJ as RO is to (??)' ________ el clima, es mejor mantener las ventanas abiertas.PorqueEs necesarioPorPara Read the following sentences and answer the question that follows: The cast and crew frantically made final adjustments to the scene even as the audience filed into the auditorium. Two actors moved the scenery into position. ____________, the entire company ensured the backdrop was firmly in place. I thought we wouldn't be ready in time! But at last the performance began. Which word or phrase best completes the passage above? Before Instead First Then Which of the following determines blood volume? -The strength of heart contraction -The amount of water in the blood -ABO blood type and Rh factor -Heart rate and respiratory rate A carton of juice shaped like a rectangular prism measures approximately 8 inches high and 4 inches along each edge. A cylindrical glass that is 3 inches in diameter is filled to a height of 3.5 inches. Approximately how many glasses of this juice can be poured from a full container? Use = 3.14. _____ are internal stakeholders in a company. Los profesores les (dar) la tarea a sus estudiantes. From 1801 to 1835, _____ served as chief justice of the supreme court and greatly increased the court's power. Steam Workshop Downloader