Given a 45-45-90 triangle with the hypotenuse measuring 5√7 feet. Which is the exact measure of each leg?

Given A 45-45-90 Triangle With The Hypotenuse Measuring 57 Feet. Which Is The Exact Measure Of Each Leg?

Answers

Answer 1

Answer:

Step-by-step explanation:

First, we know a 45-45-90 triangle has two legs that are the same because two angles are the same, so we can say that:

[tex]$a^2+b^2=c^2=a^2+a^2=c^2$[/tex]

Remember that [tex]a^2[/tex] and [tex]a^2[/tex] are the legs, which are the same length, so we can do this. Now, we solve the equation.

[tex]a^2+a^2=c^2\\2a^2=5\sqrt{7}\\2a=(5\sqrt{7})^2\\2a=5\\a=\frac{5}{2}[/tex]

HOPE THIS HELPS :D

Answer 2

The Pythagoras is the sum of the square of two sides equal to the square of the longest side. Then the exact measure of each leg is 9.4 ft.

What is a right-angle triangle?

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

A right-angle 45-45-90 triangle with the hypotenuse measuring 5√7 feet.

We know that if two angles of any triangle are the same then their opposite sides are also the same.

Let each side length of x ft. Then by the Pythagoras theorem. we have

[tex]\begin{aligned} x^2 + x^2 &= (5\sqrt7)^2\\\\2x^2 &= 25 \times 7\\\\x^2 &= \dfrac{175}{2}\\\\x^2 &= 87.5\\\\x &= 9.354 \approx 9.4 \ \rm ft \end{aligned}[/tex]

More about the right-angle triangle link is given below.

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Related Questions

Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 of an inch, it is 4 3/4 inches.

What is the largest the actual height of the plant could be?
4 7/10
inches

Answers

Answer:

Step-by-step explanation:

Given that the height(h) of the plant to the nearest 1/4 of an inch is 3/4 inches = 0.75 inches.

It is obvious that the height will lie within the range

2.5/4<h<3.5/4

which corresponds to the range

5/8<h<7/8 OR 0.625<h<0.875

Thus,

a. The largest actual height could be 0.875 inches, while

b. The smallest actual height could be 0.625 inches

c. The percentage error is given by the formula:

[(approx.-exact)/exact]*100%

If we take the lowest value, for instance, as the exact, i.e. 0.625 inches,

then % error = [(0.75-0.625)/0.75]*100% = 16.7%

Obviously, the same value is expected if we take the upper limit of 0.875, i.e. % error = [(0.75-0.875)/0.75]*100% = -16.7%, only that the absolute value will be taken.

An Apple Watch was marked down 1/9 of the original price. If the sales price was $224 what is the original price?

Answers

Answer:

ok so that means that the new price is 8/9th of the original one so we divide 224 by 8/9=252

Hope This Helps!!!

Marked down 1/9 means it sold for 8/9 of the original price.

Divide the sale price by 8/9:

224 / 8/9 = 224 x 9/8 = (224 x 9)/8 = 2016/8 = 252

The original price was $252

help me please

Explain what you would do first to simplify the expression below. Justify why, and then state the result of performing this step.

Answers

First clear the bracket of the inner fraction's numerator. This would allow you to reduce the inner fraction to lowest terms.

Given the expression

[tex](\frac{(2r^2t)^3}{4t^2})^2[/tex]

In order to simplify, note that the numerator and denominator of the fraction

[tex]\frac{(2r^2t)^3}{4t^2}[/tex]

have common factors. So, we would first remove the bracket in the numerator. This would allow us to reduce the fraction to lowest terms.

To clear the numerator's bracket, note that

[tex](2r^2t)^3=(2r^2t)\times(2r^2t)\times(2r^2t)\\=(2\times2\times2)\times(r^2\times r^2\times r^2)\times(t\times t\times t)\\=8\times r^6 \times t^3=8r^6 t^3[/tex]

that was long. The shorter way was to do the following

[tex](2r^2t)^3=2^3\times r^{2\times3}\times t^3=8r^6t^3[/tex]

so back to the original question, to simplify

[tex](\frac{(2r^2t)^3}{4t^2})^2[/tex]

we would do

[tex](\frac{(2r^2t)^3}{4t^2})^2=(\frac{2^3r^{2\times3}t^3}{4t^2})^2\\\\=(\frac{8r^6t^3}{4t^2})^2[/tex]

Now that we have removed the bracket from the numerator, we can now accomplish the step of reducing the fraction to lowest terms

[tex](\frac{8r^6t^3}{4t^2})^2=(\frac{8}{4}\times r^6\times \frac{t^3}{t^2})^2\\=(2\times r^6\times t^{3-2})^2\\=(2\times r^6\times t^1)^2\\=(2r^6t)^2[/tex]

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Can I get some help with these questions?​

Answers

Answer:

For the first question its X=110 For the second question angle AEF is 75 degrees and for angle ADF  is 105 degrees

Step-by-step explanation:

the total angle is 150 so take 4+22 and you get 26 then add 6+8 and you get 14 add 26+14 and you get 40 do 150-40 and you get 110 therefore x=110

Identify the slope!!

Answers

Answer:

Step-by-step explanation:Method 2 of 2: Solving for Slope Get a line of which you want to know the slope. Make sure that the line is straight. ... Pick any two coordinates that the line goes through. Coordinates are the x and y points written as ( x, y ). Pick which point's coordinates are dominant in your equation. ... Set up the equation using the y-coordinates on top and the x-coordinates on bottom. More items.

Graph the functions to find The solution.

f(x)=x^2 - 2
g(x)= 2x + 1

Answers

Answer: Look at the picture ⬇️

Find the equation of the line that has a slope of 1 and passes through the point (−10,−6).

Answers

Answer:

See below.

Step-by-step explanation:

Hi there!

We want to find the equation of the line that has a slope (m) of 1 and that passes through the point (-10, -6)

There are 3 ways to write the equation of the line:

Slope-intercept form, which is y=mx+b, where m is the slope and b is the y interceptPoint-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a pointStandard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be equal to zero, and a cannot be negative

Since we are given both a point and a slope in this situation, it makes sense to write the equation in point-slope form.

Let's label the values of everything we were given to avoid confusion and mistakes:

m=1

[tex]x_1=-10\\y_1=-6[/tex]

Now substitute these values into the equation (note: we have NEGATIVE numbers, while the formula gives SUBTRACTION, which is why we're subtracting a negative)

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y--6=1(x--10)[/tex]

Simplify:

y+6=1(x+10)

The equation can be left as this, or it can be converted into slope-intercept form if you wish.

In that case, we would distribute 1 to each number on the right side.

y+6=x+10

Then, we'll isolate y on one side. Subtract 6 from both sides.

y=x+4

You can also convert it into standard form if you would prefer it that way. To do that, start with slope-intercept form, which we earlier found as y=x+4

In standard form, x and y are on the same side. So subtract x from both sides to move it

-x+y=4

Remember we don't want a (the coefficient in front of x) to be negative. In order to flip the sign, multiply both sides by -1

x-y=-4

Therefore, the answer can be written as y+6=1(x+10), y=x+4, or x-y=4.

Hope this helps!

What is the value of the 9 in the number 567.09?

Answers

Answer:

After the decimal point (left to right) are the tenths, hundredths, thousandths, ten-thousandths, and so on. The value of the 9 would be 9 hundredths.

:)

The value of 9 is 9 hundredths

Sandy worked extremely hard at her job and earned a large bonus at the end of the year. She decided to give her children 2/5 of the money and her grandchildren 1/4 of her bonus. How much of her bonus did she keep for herself?

Answers

Answer:

7/20 of her bonus

Step-by-step explanation:

Solution:

She gives her children 2/5 of her bonus and grandchildren 1/4 of her bonus.

= 1 - 2/5 - 1/4

= 1 - 8/20 - 5/20

= 1 -13/20

= 7/20

I hope it helps.

I need help im horrible at math and who ever does this for me please i will give you 100 pts and brainliest

Answers

Answer:

1/4 > 1/9

Step-by-step explanation:

Answer:

Step-by-step explanation:

mhmh idek man

79 percent of 67 miles is what

Answers

Answer:

52.93

Step-by-step explanation:

What is the greatest common factor of 15, 35, and 10?

Answers

Answer: The GCF of 10, 15, and 35 is 5.

Would appreciate brainliest <3

Answer:

5.

Step-by-step explanation:

First, we write them in prime factor form, then pick out the common factors.

15 = 3*5

35 = 5*7

10 = 2*5

So the GCF is 5.

the Greatest Common Factor of 24, 36 and 50

Answers

Answer:

2

Step-by-step explanation:

they all share a factor of 2

I put a picture

—PLEASE HELP

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Base of a cube is a square, and in the given figure it's stated that the measure of each side is " x " ft

Therefore it's Area is equal to : -

[tex]side \times side[/tex]

[tex]x \times x[/tex]

[tex] {x}^{2} [/tex]

Now, since it's Area is given as 1/4 ft², let's equate the Areas to find the measure of each side ~

that is ~

[tex] {x}^{2} = \dfrac{1}{4} [/tex]

[tex]x = \sqrt{ \dfrac{1}{2} \times \dfrac{1}{2} } [/tex]

[tex]x = \dfrac{1}{2} \: \: feet[/tex]

It's time to find the volume of cube that is ~

[tex](side) {}^{3} [/tex]

So, let's plug the value of side length (1/2 ft)

Volume is equal to ~

[tex] { \bigg(\dfrac{1}{2} \bigg) }^{3} [/tex]

[tex] \dfrac{1}{8} \: \: ft {}^{3} [/tex]

Hence, the required 1/8 or 0.125 ft³

I hope it helped ~

[tex]\mathrm{✌TeeNForeveR✌}[/tex]

Answer:

Step-by-step explanation:

side=Base=x

Area=side * side

Area=[tex]\frac{1}{4}[/tex] [tex]ft^{2}[/tex]

Substitute values in the above formula:

[tex]\frac{1}{4}[/tex] [tex]ft^{2}[/tex]=x * x

[tex]x^{2}[/tex]=[tex]\frac{1}{4}[/tex] [tex]ft^{2}[/tex]

x=[tex]\frac{1}{2}[/tex]ft

Now,

The formula of volume of Cube:

Volume=x*x*x

Substitute the values of x=[tex]\frac{1}{2}[/tex]ft in the formula of Volume:

Volume=[tex]\frac{1}{2}[/tex]ft * [tex]\frac{1}{2}[/tex]ft * [tex]\frac{1}{2}[/tex]ft

Volume=[tex]\frac{1}{8}[/tex] [tex]ft^{3}[/tex]

If you need to ask any questions, please let me know.

Solve for g.

19 = 3g + 4

g =

Answers

19 = 3g + 4

Subtract 4 from both sides.
19 - 4 = 3g

You get:
15 = 3g
Divide both sides by 3.

5 = g

Answer:

ANS is g=5

step 1: 3g=19-4

step2: or,3g=15

step 3: or,g=15%3

step 4: or,g=5

Hope it helps.

Can you give me BRAINLIEST ANSWER

THANK YOU

40 cans of food. 30% of cans damaged. how many cans were damaged?

Answers

12 were cans were damaged

Answer:

12 cans were damaged

EXPLANATION:

Cause When You Divide 4 To Divide 40, It Gives You 100% Calculation, And Subtract 30% from 100% it gives you 70%, which is 28 cans of food

Simplify the following expression. (0.5x – 3)(0.5x + 3)​

Answers

Answer:

0.25x^2-9

Step-by-step explanation:

Difference of squares converse:

0.25x^2-9

Answer:

0.25x^2-9

Step-by-step explanation:

multiply 0.5x with 0.5x which is 0.25x^2. then multiply 0.5x with 3 which is 1.5x. then multiply -3 with 0.5x which is -1.5x. then multiply -3 with 3 which is 9. so you will have 0.25x^2+1.5x-1.5x-9.

1.5x and -1.5x is 0. so you are left with 0.25x^2-9

right now michael earns an annual salary of $46,023 he is Considering a job offer with an annual salary of $51,145 what is the difference in the monthly pay for these two jobs rounded to the nearest cent

Answers

Answer:  The job pays $32,400 per year, and the agency fee is equal to 45% of one month's pay.


if p(x)=x^2+x+1 and q(x)=3x^2-1, find p(7)

Answers

Answer:

p(7) = 57

Step-by-step explanation:

Because this is a function, all you have to do is input 7 for x like so:

p(x)=x^2+x+1 --------------->     p(7)=7^2+7+1

                                            so 49 + 8

                                                = 57

What is the slope of this line?
A - 1/5
B 5
C -5
D 1/5

Answers

Answer:

It is 1/5

Step-by-step explanation:

rise/run and it rises by one and runs by 5.

Point A is located at (2, 6) and point B is located at (18, 12). What point partitions the directed line segment ​AB¯¯¯¯¯​ into a 2:3 ratio?
A. (8 2/5, 8 2/5)
B. (10 1/2, 10 1/2)
C. (11 3/9, 9 3/5)
D. (14 1/2, 12)

Answers

Answer:

  A. (8 2/5, 8 2/5)

Step-by-step explanation:

You want to find point P such that ...

  AP : PB = 2 : 3

  3AP = 2PB . . . . . . . . cross multiply

  3(P -A) = 2(B -P) . . . recognize length XY = Y - X

  5P = 3A +2B . . . . .  collect P terms

  P = (3A +2B)/5 = (3(2, 6) +2(18, 12))/5 = (6+36, 18+24)/5= (42, 42)/5

  P = (8 2/5, 8 2/5) . . . . matches choice A

6x + 13 = 12x - 20 solutions

Answers

Answer:

6x + 13 = 12x - 20

Step-by-step explanation:

6x + 13 = 12x - 20

No links No Files Need help ASAP

Answers

Answer: 6

Step-by-step explanation: I think think the answer is 6 because if you cut 6 in half you get 3 and if cut 4 in half u get 2 the mutiply them...dont get mad if it wrong

Answer: A = 24 units^2

Step-by-step explanation: If you cut the shaded region in half it's two rectangles so you have to find the area of it using the formula to find the area of a rectangle.

A = (w)(l)                                                                                                                   A = (6)(4)                                                                                                               A = 24 units^2

Complete the square to rewrite y=x^2+6x+3 in vertex form. Then state whether the vertex is a maximum or a minimum and give its coordinates

Answers

Answer:

Step-by-step explanation:

take b, divide it by 2 and then square it

(6/2)²=9 so add then subtract 9

(x²+6x+9)+3-9

x²+6x+9=(x+3)²

3-9= -6

(x+3)²-6

The vertex is a minimum and the coordinates are (-3,-6)

How many factors of 2 are there in 2³? answers> 1 2 3 5​

Answers

Answer:

2

Step-by-step explanation:

2^3= 2*2*2

factors of 8= 1,2,4,8

factors of 2= 1,2

What are 2 multiplication expressions that have the product of 28.34 ?!?!?!? NEED HELP ASAP!!!!

Answers

Answer:

28.34  x 1 = 28.34

14.17 x 2 = 28.34

There are required two multiplication expressions that might generate the result 28.34. Here are a number of such examples:

28.34 × 1

14.17 × 2

What is the Multiplication operation?

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

We have to determine two multiplication expressions that have the product of 28.34

As per the given question, the required solution would be as:

There are many possible multiplication expressions that could result in the product of 28.34. Here are two examples:

28.34 × 1

14.17 × 2

In the first example, the product is 28.34 because any number multiplied by 1 is equal to itself.

In the second example, the product is 28.34 because 14.17 multiplied by 2 is equal to 28.34.

Hence, the required answers are 28.34 × 1 and 14.17 × 2

Learn more about Multiplication operations here:

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please help, please and ty.

Answers

Answer:

l.y=4

m.y=-2x+4

n.1x-1

p.x=-4

Step-by-step explanation:

The equations of the lines given in the graph will be,

y = x - 1

y = -2x +4

y = 4

What is an equation of the line?

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

For line one the points are:-

( 3,2 ) and ( 1,0)

Slope = ( 0 -2 ) / ( 0 - 3 )

Slope = 1

The equation will be,

y = x + c

0 = 1 + c

c = -1

For line two the points are:-

(0,4) and (2,0),

Slope = ( 0 - 4 ) / ( 2 - 0 )

Slope = -2

The y-intercept will be,

y = mx +c

y = -2x + c

c= 4

The equation can be written as:-

y = -2x +4

The equation of the line parallel to x-axis is,

y = 4

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Write a system of linear inequalities represented by the graph?
Inequality 1:
Inequality 2:

Answers

Answer:

y > x - 2

y >= 5x + 1

Step-by-step explanation:

Linear inequalities represented by the graph are y>5x+1 and  y>x-2

What is Inequality?

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The first line passes through the points

(0, 1) and (-1, -4)

The slope of line is m=-4-1/-1=5

Let us find the y intercept

1=5(0)+b

b=1

So the equation of line is y=5x+1

As the shading is outside so y>5x+1

Now let us find for 2nd line

(2, 0) and (-2, -4)

m=-4/-4=1

Now y intercept is 0=2+b

b=-2

So equation is y=x-2

As shading is outside so  y>x-2

Hence,  linear inequalities represented by the graph are y>5x+1 and  y>x-2

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Write the phrase as an equation /
inequality
Four is twenty more than the number.
Help pls

Answers

Answer:

4 = 20 + n, where n is the number

Step-by-step explanation:

Here are a few key words to use when converting words to an equation

"is": =

"more": +

"less": -

"more than", "greater than": >

"less than": <

N is the variable we are using here so four and twenty are the coefficients here

So the answer would be

4=20+N

Do not round your answer. Type in just the number. 0.48 is what percent of 1.6

Answers

Answer:

30 percent

Step-by-step explanation:

That is not rounded. Just straight, plain, 30 percent.

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