the legs of a right triangle are 75 and 100. what is the length of the hypotenuse

Hi! I'm happy to help!

For our equation, we need to find out what our two smaller equations are.

We can see that angle HGF is our largest angle, and it is composed of EGF, and HGE. We can insert our values into an equation to solve:

16x+4=110+3x+11

We can then combine like terms:

16x+4=121+3x

To solve for x, we need to put it by itself on one side of the equation. So, let's subtract 4 from both sides:

16x=117+3x

Now, let's subtract 3x from both sides:

13x=117

Now, let's divide both sides by 13 to solve for x:

x=9

Now, we know that x=9.

I hope this was helpful, keep learning! :D

9514 1404 393

Answer:

  "complete the square" to put in vertex form

Step-by-step explanation:

It may be helpful to consider the square of a binomial:

  (x +a)² = x² +2ax +a²

The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...

  2a = 1

  a = 1/2

That means we can write ...

  (x +1/2)² = x² +x +1/4

But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:

  [tex]x^2+x+1\\\\=(x^2+x+\frac{1}{4})+\frac{3}{4}\\\\=(x+\frac{1}{2})^2+\frac{3}{4}[/tex]

_____

Another way to consider this is ...

  x² +bx +c

  = x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*

  = (x +b/2)² +(c -(b/2)²)

for b=1, c=1, this becomes ...

  x² +x +1 = (x +1/2)² +(1 -(1/2)²)

  = (x +1/2)² +3/4

_____

* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).

Taking into account the original image that appears in the attached document and verifying the correct solution in each case:

1. The figures that are scaled copies of the original are:

2. I'm not agree with Tyler's affirmation.

SCALING FIGURES.

When you must scale figures, you must remind the scale must be applied in all dimensions of the figure, when a figure is in two dimensions, I mean, the figure has height and length, the scale must be applied to this two dimensions, and the figure must the same form of the original to be a scaled copy.

In the first exercise, the original A is a figure with two squares of height and two squares of length 2x2, by this reason, each scaled copy must be the same height as length (1x1, 3x3, 4x4, 5x5, 6x6 and others).

As you can see, the figure 2 has 4 units of height and 4 units of length 4x4, it's a scaled copy, the figure 4 has 1 unit of height and 1 units of length 1x1, it's a scaled copy, but the figure 1 has 3 units of height and 2 units of length 3x2, it's not a scaled copy, and the figure 3 hasn't the same form of the original A, by this, it's not a scaled copy.

In the second exercise, you can´t agree with Tyler because the figure B is the half of the figure A, but just in the height, remember this must be the same in the length to obtain a correct scaled copy, you can see in the exercise, the figure B has the same length as the figure A, by this reason, the affirmation of Tyler is wrong, for that to be true, the height and the length should be half in the figure B.

You can see other exercises with scales in the next links:

https://brainly.com/question/22384038?referrer=searchResults

https://brainly.com/question/21605248?referrer=searchResults

Answer: 0.5(43,560)/ 40(128)

Step-by-step explanation:

Answer:

i hope it helped U

stay safe stay happy

Step-by-step explanation:

Hey there!

The given points are: (-3,-6) and (3,-6).

x 1 = -3 y1 = -6

x 2 = 3 y2 = -6

Use distance formula;

[tex]d = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]

Keep all the values;

[tex]d = \sqrt{( {3 - ( - 3))}^{2} + ( { - 6 - ( - 6))}^{2} } [/tex]

Simplify:

[tex]d = \sqrt{ {(6)}^{2} + {( - 6 + 6)}^{2} } [/tex]

[tex]d = \sqrt{ {(6)}^{2} } [/tex]

Therefore, the distance is 6 units.

Hope it helps!

Answer:

-0.450 as a fraction is -9/20

Step-by-step explanation:

Since there 3 decimal places, divide it by 1000

-450/1000 and simplify it

Answer:

Cheena has 6 pieces of fabric.

Step-by-step explanation:

3/4 yard of fabric also means 6/8 yard of fabric.

(6/8) / (1/8) = 6

Or

6/8 yard = 6  1/8 yard pieces

a.yes

Step-by-step explanation:

a.angle BCD =b because angle BCD is alternate angle of angle ABC

b.the two angles angle BAC and angle ACD is co-interior angle because they are inside a parallel line

Answer:

[tex]\displaystyle f(b+2) = 2b^2 + 11b +6[/tex]

Step-by-step explanation:

We are given the function:

[tex]\displaystyle f(x) = 2x^2 + 3x - 8[/tex]

And we want to find:

[tex]\displaystyle f(b + 2)[/tex]

Substitute:

[tex]\displaystyle f(b+2) = 2(b+2)^2 + 3(b+2) - 8[/tex]

Expand and simplify:

[tex]\displaystyle \begin{aligned}f(b+2)&= 2(b^2+4b+4)+(3b+6)-8 \\ &= (2b^2+8b+8)+(3b+6)-8 \\ &= (2b^2) + (8b+3b)+ (8+6-8) \\ &= 2b^2 + 11b + 6 \end{aligned}[/tex]

In conclusion:

[tex]\displaystyle f(b+2) = 2b^2 + 11b +6[/tex]

Answer:

[tex]y=3x+6[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x=0)

We're given that the slope of the line is 3. Plug this into [tex]y=mx+b[/tex] as m:

[tex]y=3x+b[/tex]

We're also given the point (0,6). Since the y-intercept occurs when x=0, the y-intercept is therefore 6. Plug this into [tex]y=3x+b[/tex] as b:

[tex]y=3x+6[/tex]

I hope this helps!

Answer:

1/4

Step-by-step explanation:

HT represent the probability of tossing a head then Tail.

There is 4 possible results and only 1 give us HT.

We call this theoretical probability. which is

[tex] \frac{x}{y} [/tex]

where x is favorable outcomes and y is total number of outcomes.

So there is a 1/4 probability of getting a head followed by a tail.

7/11 , 0.636, and 0.63

Hope this helps

Answer:

Least to Greatest

7/11 ,  0.636,  0.63

Step-by-step explanation:

7/11 = 0.6363636363636364

so this number is least

Answer:

It doesn't say what to do with that 0.1 of a gallon. I would buy another gallon or dilute what I had so it came to exactly 9.1 gallons. In math, I suppose the answer is 9.

In reality it would be 10.

You have to choose.  What has been done with other questions like this.

Step-by-step explanation:

1 can covers 55 square feet.

h = 10

w1 = 10 feet

w2 = 10 feet

w3 = 15 feet

w4 = 15 feet

Total area = Area of wall 1 + wall 2 + wall 3 + wall 4

Total area = 10*10 + 10*10 + 10*15 + 10* 15

Total area = 100  + 100 + 150 + 150

Total area = 500  feet^2

1 gallon / 55 ft^2 = x / 500 ft^2          Cross multiply

55 * x = 500                                       Divide by 55

x = 500/55

x = 9.1 gallons.

In real life you would buy another gallon.

Hi

Answer:

3bc

Step-by-step explanation:

3×b=3b

3b×c=3bc

Answer:  The guage block height is 4.98 m

The base of the right triangle that is formed is 7.3784 m

The last angle in the triangle is 56 degrees

Step-by-step explanation:

Redraw the triangle formed in the picture and use H for the hypotenuse, O for the block height, and A for the base.  Now we can use trig (SOHCAHTOA) to find the answaers.

Using sine, we can first find the gauge block height, O (Opposite).  Given the Hypotenuse (H) is 8.9 m, we can use the definition of the sine of an angle to find the height, O.

Sine(34) = Opposite/Hypotenuse (O/H), or O = H*Sine(34)

O = (8.9)*(0.5592)

O = 4.98 m, the height of the gauge block,

The base of the triangle, A, can be determined with cosine.

Cosine(34) = A/O, or A = Cosine(34)*O

A = (0.82904)*(8.9)

A = 7.3784 m

The sum of all angles in a triangle is 180 degrees.  

180 = X + 34 + 90

X = 56 degrees

Answer:

288m^3

Step-by-step explanation:

the volume is base* height

to find the second side, use the Pythagorean theorem : [tex]\sqrt{10^2-8^2} = \sqrt{100-64}= \sqrt{36} = 6[/tex],

now find the area of the triangle: 6*8/2=24

now multiply it by the height and you get the volume: 24*12=288

Explanation:

The like terms k and -5k combine to -4k

The like terms -5 and 1 combine to -4

So overall, that's how we end up with -4k-4

Answer:

Step-by-step explanation:

1). (k - 5k) + (-5 + 1) {Collect like terms}

2). -4k - 4 {Simplify}

Answer:

10

Step-by-step explanation:

Subtracting a negative is like adding

3 +7

10

Answer:

0.4141 rounded to the nearest thousandth is 0.414.

Step-by-step explanation:

Since the number is 0.4141, and the number following the thousandths place is under 5, the thousandth place stays the same. If it were 5 or over, it would round up making it 0.415, but it's not so it is 0.414.

Answer:  5.6g - 2h + 9

Explanation:

Flip the sign of each term inside the parenthesis.

These sign flips occur because of the negative out front the parenthesis. It's the same as having -1 outside, and we distribute the -1 through.

Answer:

Solution given

-2u+(-1)=-13

open bracket

-2u-1=-13

add 1 on both side

-2u-1+1=-13+1

-2u=-12

divide both side by -2

-2u/-2=-12/-2

u=6

[tex]\huge\text{Hey there!}[/tex]

[tex]\textsf{-2u + (-1) = -13}\\\textsf{-2u - 1 = -13}\\\large\text{ADD 1 to BOTH SIDES}\\\textsf{-2u - 1 + 1 = -13 + 1}\\\large\text{CANCEL out: -1 + 1}\\\large\text{KEEP: -13 + 1}\\\rightarrow\textsf{-2u = -12}\\\large\text{DIVIDE -2 to BOTH SIDES}\\\mathsf{\dfrac{-2u}{-2}= \dfrac{-12}{-2}}\\\textsf{CANCEL out: }\mathsf{\dfrac{-2}{-2}}\\\textsf{KEEP: }\mathsf{\dfrac{-12}{-2}}\\\mathsf{u = \dfrac{-12}{-2}}\\\mathsf{u = \bf 6}\\\huge\boxed{\mathsf{Answer: u = 6}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}\\\\\frak{Amphitrite1040:)}[/tex]