the hypotonuse of a right triangle measures 15cm and one of its legs meauseres 8cm find the measure of the other leg

Answer:

<DEF = 107

Step-by-step explanation:

The way to best solve this problem is by starting with angle F. Remember that all angles in a straight line must add up to 180. So by subtracting 135 from 180 we get 45 for angle F.

180 - 135 = 45

After that, we can figure out the measure of <DEF. All the angles of a triangle must add up to 180. So:

180 - 28 - 45 = 107

Making the answer 107 for the measure of <DEF

Answer:

height = 4.8 cm

area = 120 cm²

perimeter = 62 cm

Step-by-step explanation:

**Please refer to the attached diagram when following the step-by-step**

First, find m∠C (green angle on diagram) by using the cosine rule:

[tex]c^2=a^2+b^2-2abcos(C)[/tex]

[tex]\implies 29^2=6^2+25^2-2(6)(25)cos(C)[/tex]

[tex]\implies cos(C)= \frac{29^2-6^2-25^2}{-2(6)(25)}[/tex]

[tex]\implies cos(C)= \frac{180}{-300}=-\frac{3}{5}[/tex]

[tex]\implies cos(C)=126.8698976... \textdegree[/tex]

Therefore, the interior angle of the right triangle at point C (blue angle on diagram) is:

[tex]180-cos^{-1}(-\frac{3}{5})=53.13010235... \textdegree[/tex]

Now use the Sine Rule (for finding sides) to determine height (h):

[tex]\frac{6}{sin(90)}=\frac{h}{sin(53.13..)}[/tex]

[tex]\implies \frac{6}{1}=\frac{h}{\frac{4}{5}}[/tex]

[tex]\implies 6 \times \frac{4}{5}=h[/tex]

[tex]\implies h=\frac{24}{5}=4.8[/tex]

So the height = 4.8 cm

Now we have determined the height, we can calculate the area by using the area of a parallelogram formula:

Area of a parallelogram = base x perpendicular height

⇒ area = 25 x 4.8 = 120 cm²

Parallelogram is a four-sided shape made up of two pairs of straight parallel lines that are equal in length.

Perimeter = sum of the sides

⇒ perimeter = 6 + 6 + 25 + 25 = 62 cm

Answer:

My best recommendation is to find the median.

Step-by-step explanation:

To find a median, find the averaging number and divide by 2. Round them up for odd numbers. For even numbers, leave them and if it's a decimal, find a remainder. If the median method does not work, put the numbers on a ratio comparison and see if that gives you the next patterns.

I tried my best so I really do hope this helps you.

Answer:

3 degrees and 87 degrees

Step-by-step explanation:

If the angle is x, its complement is (90-x).

This means that x+84=90-x.

2x=6

x=3.

So the measures are 3 degrees and 90-3=87 degrees

The percentage by which it is less than the other is 10%

From the question we are asked to find the percentage of which the difference of the two numbers are. To do this, we take the subtraction of both

110 - 100 = 10

Then we find the percentage of this number.

10/100 * 100 = 10%

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Answer:

1 foot is 12 inch so the tail of boeing will be 63 2/3 x 12

Step-by-step explanation:

https://brainly.com/question/3663351

Hoped this helped and have a nice day

Answer: y=2/(x-1)

Step-by-step explanation:

We can tell this is a rational function that looks somewhat like y=1/x, execpt that the asymptote is at x=1, not x=0. This means we have y=k/(x-1), where k is a constant.

Substituting in the coordinates of a point on the graph, say (0, -2), we get that -2=k/-1, meaning k=2.

So y=2/(x-1).

Answer:

8 science fiction movies

Step-by-step explanation:

2+s=10

-2   -2

s=8

Travis streamed 8 science fiction movies

Hi!

I can help you with joy!

Remember that

* Zeros in the beginning of decimals are not significant figures.

For example, 0.021 has only 2 significant figures: 2 and 1.

* Zeros in the end of decimals are significant.

For example, 2.100 has 4 significant digits.

Now, let's round 0.02852 to 3 significant digits.

Right now it has 4.

Recall the Rounding Rules:

[tex]\text{5 is followed by a number less than 5, so we round down.}[/tex]

[tex]\text{0.02852 Round down: 0.0285 (Answer)}[/tex]

Hope it helps!

Enjoy your day!

Answered by

~Silent~

to get the slope of any straight line we only need two points off of it, hmmm let's use the points in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{2}}}\implies \cfrac{4}{2}\implies 2[/tex]

Answer:

She will need to buy 3 more boxes of candies.

Step-by-step explanation:

72-45=27

27/9= 3

Answer:

[tex]\huge\boxed{\sd -9, \ 1}[/tex]

Step-by-step explanation:

Given quadratic equation is:

x² + 8x - 9 = 0

Using mid-term break formula

x² + 9x - x - 9 = 0 (When we multiply middle terms, we get side terms as answer which is mid term break formula.)

Taking common

x(x + 9) - 1(x + 9) = 0

Take (x + 9) common

(x + 9)(x - 1) = 0

According to zero's method:

Either:

x + 9 = 0      OR    x - 1 = 0

x = -9           OR       x = 1

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

10.99

Step-by-step explanation:

I JUST HAD THAT AND GOT IT RIGHT TRUST ME NOW GIVE ME BRAINLY I SWEARRR

Answer: 12 and 8

Step-by-step explanation:

there not

The integer m whose factors are 15,12,10 and 6 is 60 and 8 is not, therefore, for integer 60, 8 will be not the factor so option (D) is correct.

An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.

Integer ; ....-2 , -1 , 0 , 1 , 2 , .....

Integers are non-decimal numbers and all integers are rational numbers.

The factors of 10 ⇒ 2 × 5

The factors of 12 ⇒  2 × 2 × 3

The factors of 10 × 12  ⇒  2 × 5 × 2 × 2 × 3

We can make all factors by 2 × 5 × 2 × 2 × 3 like 5 × 3 = 15 , 2 × 2 × 2 = 8.

So find a number whose all will be a factor except one.

The factor of 60 ⇒ 2 × 2 × 3 × 5

We cannot make 8 by this factor but can make 15,12,10,6.

Example 15 = 3 × 5 , 12 = 2 × 2 × 3

Hence "The integer m whose factors are 15,12,10 and 6 is 60 and 8 is not, therefore, for integer 60, 8 will be not the factor".

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Answer:

on the third column it should be tens and not ones.good job so far tho!

Answer:

here may be more than one correct answer.  

Cubic, f(x)=x^3

Quadratic, f(x)=x^2

Square root, f(x)=√x

Constant, f(x)=c

Linear, f(x)=x

Step-by-step explanation:

The domain of the square root parent function is x ≥ 0 as the square root of only non-negative values exists and that of negative values does not exist, while the domain of the cube root parent function is the set of all real numbers as the cube root of all numbers exists.

A function is a relation between a dependent variable f(x) and an independent variable x, where for every value of x in its domain, there is one and only one value of f(x).

The domain of a function is the set of values of x, for which f(x) exists.

The range of a function is the set of values of f(x), in a given domain of x.

We are asked why is the domain of the square root parent function x ≥ 0 and the domain of the cube root parent function all real numbers.

We know that the domain of a function is the set of values of x, for which f(x) exists.

Let the square root parent function be f(x) = √x.

The domain of this function is x ≥ 0, as the square root of negative values does not exist in the real number system.

Let the cube root parent function be g(x) = ∛x.

The domain of this function is all real numbers, as the cube root of all values does exist in the real number system.

∴ The domain of the square root parent function is x ≥ 0 as the square root of only non-negative values exists and that of negative values does not exist, while the domain of the cube root parent function is the set of all real numbers as the cube root of all numbers exists.

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Let number be x

[tex] \leadsto \sf {x}^{2} + 2 = 227[/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto \sf {x}^{2} = 227 - 2[/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto \sf {x}^{2} = 225[/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto \sf {x} = \sqrt{225} [/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto \sf {x} = \sqrt{15 \times 15} [/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto \sf {x} = 15[/tex]

Number = 15

Answer:

5

Step-by-step explanation:

tan(0) = sin(0)/cos(0) = 5sqrt(26)/(26)/sqrt(26)/26

Cancel the common factor which is sqrt(26)

tan(0) = sin(0)/cos(0) = 5/26 * 26

Cancel common factor again which is 26 here

tan(0) = sin(0)/cos(0) = 5

Considering the definition of probability, the probability that the next customer will pay with a debit card is [tex]\frac{12}{139}[/tex].

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases.

[tex]P(A)=\frac{number of favorable events}{ total number of possible events}[/tex]

The probability of event A can only be a number between 0 and 1; although it can also be written as a percentage.

In this case, you know:

Replacing in the definition of probability:

[tex]P(A)=\frac{12}{ 139}[/tex]

Finally, the probability that the next customer will pay with a debit card is [tex]\frac{12}{139}[/tex].

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Answer:

22

Step-by-step explanation:

Answer:

399.77 yd³

Step-by-step explanation:

Circumference: 2πr

Solve for r:

Solve for volume: 4/3(πr³)

-Chetan K

Answer:

4 cm

Step-by-step explanation:

1/8·n = 1/2

multiply each side by 8/1

n = 8/2 or 4

The length on the map that represents 1 meter in real is 4 centimeters.

A ratio shows us the number of times a number contains another number.

Given that Each 1/2 centimeter on a map represents an actual length of 1/8 of a meter. Therefore, the ratio can be written as,

Length on Map / Actual Length = (1/2) centimeters / (1/8) meters

Length on Map / Actual Length = 4 centimeters per meters

Now, the length on the map that represents 1 meter in real is,

Length on Map / Actual Length = 4 centimeters per meters

Length on Map / 1 meter = 4 centimeters / 1 meters

Length on Map = 4 centimeters

Hence, the length on the map that represents 1 meter in real is 4 centimeters.

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Answer:

Let x = salary of the architect, in thousands

Let 2x - 25 = salary of a lawyer, in thousands

2x + 2x - 25 = 206 (combined salaries, in thousands)

4x - 24 = 206

4x = 206 - 25 = 181

x = 45.25, in thousands.

The architect earns $45,250 yearly

The lawyer earns $65,500 yearly

If you want to set up a system of equations with 2 variables.

Let x = the salary of the architect, in thousands.

Let y = the salary of the lawyer, in thousands.

x + y = 206

y = 2x - 25

Solving by substitution will yield the same equation as above: x = 45.25 or $45,250

Then y = 2(45,250) - 25,000 = $66,500

Answer:

[tex]y=\frac{7}{2}x+11[/tex]

Step-by-step explanation:

To solve, we need to find the y-intercept (b). In order to find the y-intercept, we can plug in the slope and the (x,y) coordinate pair given to us into the equation to solve for the y-intercept:

y=mx+b

4=(-7/-2)*-2+b

4=14/-2+b

4=-7+b

Add 7 to both sides

b=11

Therefore the equation is:

[tex]y=\frac{7}{2}x+11[/tex] (note that the fraction is positive since the two negatives cancel out)

[tex] \\ [/tex]

What is the length and area of a rectangle whose perimeter is 24 cm and the breadth is 4 cm?

[tex] \\ [/tex]

[tex] \\ [/tex]

[tex] \\ [/tex]

[tex] \\ [/tex]

[tex] \\ [/tex]

[tex] \\ [/tex]

[tex] \\ [/tex]

[tex] \\ [/tex]

❁We know:-

Perimeter of rectangle =2 ( Length + Breadth )

[tex] \\ [/tex]

By using this formula we can find length of rectangle

[tex] \\ [/tex]

So:-

↣ Perimeter of rectangle =2 ( Length + Breadth )

[tex] \\ [/tex]

↣ 24 =2 ( Length + 4 )

[tex] \\ [/tex]

↣24 = 2(Length) + 2(4)

[tex] \\ [/tex]

↣24 = 2(Length) + 2 × 4

[tex] \\ [/tex]

↣24 = 2(Length) + 8

[tex] \\ [/tex]

↣24 - 8 = 2(Length)

[tex] \\ [/tex]

↣ 16 = 2(Length)

[tex] \\ [/tex]

↣2(Length) = 16

[tex] \\ [/tex]

↣ Length = 16/2

[tex] \\ [/tex]

↣ Length = 8 cm

[tex] \\ [/tex]

Now Finally Let's find area :-

[tex] \\ [/tex]

❁We know:-

Area of rectangle = Length × Breadth

[tex] \\ [/tex]

So:-

⇢Area of rectangle = Length × Breadth

[tex] \\ [/tex]

⇢Area of rectangle = 4 × 8

[tex] \\ [/tex]

⇢Area of rectangle = 32 cm²

Answers:

a = -2

b = -1

==========================================

Explanation:

The first piece 5 must match up with the ax+b when x = -2, or else the function wouldn't be continuous at this junction.

Plug in x = -2 and set the result equal to 5

We end up with -2a+b = 5

Solving for b gets us b = 5+2a

--------------

The middle piece ax+b must also equal the third piece -5 when x = 3 to ensure the second junction is continuous.

This leads us to the equation 3a+b = -5

Apply substitution and solve for 'a'

3a+b = -5

3a+5+2a = -5

5a+5 = -5

5a = -5-5

5a = -10

a = -10/5

a = -2 is one of the answers

Then use this to find b

b = 5+2a

b = 5+2(-2)

b = 5-4

b = -1 is the other answer

Step-by-step explanation:

let T be the top of the ladder

let F be the foot of the ladder

let B be the base of the wall

you need to find the distance between the foot of the ladder and the base of the wall, in other words the distance of the 'ground' ( refer to the diagram).

you are given that the hypotenuse - H is 3 m and that the opposite - O ( wall ) is 2.8 m.

i) find the angle

given

H, O → use SOH, sin.

sin x = opp. /hyp.

sin x = 2.8 / 3

x = sin-1 ( 2.8/ 3)

x = 68.960...

x = 70.0 ° ( 3 s.f)

ii) use either tan or cos to find the adjacent (wall)

using TOA, tan:

tan ( 68.96) = 2.8/ adj.

2.8 / adj. = tan (68.96)

adj. × tan (68.96) = 2.8

adj = 2.8/ tan (68.96)

adj = 1.0770...

adj. = 1.08 ( 3 sf)

base = 1.08 m

or you could rather simply work this out using Pythagoras Theorem:

where hyp. is c², the base is b² and height is a²;

c² = a² + b²

b² = c² - a²

b² = (3)² - (2.8)²

b² = 1.16

b = √1.16

b = 1.0770

b = 1. 08 m ( 3sf)

you can give your answer to 3 sf or 2 sf.

hope this helps you!

-s.