The hypotenuse of a right triangle measures 9 cm and one of its legs measures 4 cm. Find the measure of the other leg.

[tex]\text{Width} ~= w ~ cm \\\\ \text{Length}~,l = (20+ w) ~ cm \\\\\text{Area of rectangle} = 1000 cm^2\\\\\\\text{Now,}\\\\l \cdot w = 1000\\\\\implies (20 + w) w= 1000\\\\\implies w^2 +20w -1000=0\\\\\\\implies w = \dfrac{-20 \pm \sqrt{20^2 - 4 \cdot 1 \cdot (-1000)}}{2 \cdot 1}\\\\\\\implies w = \dfrac{-20 \pm \sqrt{4400}}{2}= \dfrac{-20\pm 20\sqrt{11}}2 = -10 \pm 10\sqrt{11}\\\\\text{Width cannot be negative so,} \\\\w= -10+10\sqrt{11}=10\left(\sqrt{11} - 1 \right) ~ cm\\\\[/tex]

[tex]\text{And length,}[/tex]

[tex]l= 20+ 10\left(\sqrt{11} - 1} \right) = 20 + 10\sqrt{11} - 10 = 10 + 10\sqrt{11} = 10 \left(1+ \sqrt{11} \right)~ cm[/tex]

Answer:

Step-by-step explanation:

We can write the equation for such a line using the point-slope form [(y - y₁) = m (x - x₁)] where m = - 4 & (x₁ , y₁) = ( 3, 5 ). We can then find the x and y-intercept. The line we draw through these three points will be the line we are trying to find.

Equation of the Line

y - 5 = - 4 (x - 3)

Finding x and y-intercepts

y-intercept is 'c' when the line is in the slope-intercept form (y = mx + c)

since y - 5 = - 4 (x - 3)

         y - 5 = -4 x + 12

              y = -4 x + 17    

            ∴ point of the y-intercept is (0, 17)

x-intercept occurs when y = 0

 y = -4 x + 17  

 0 = -4 x + 17

-17 = -4x

   x = ¹⁷/₄

            ∴ point of the x-intercept is (¹⁷/₄, 0)

Graph the line

We can now plug in the points and draw the line.

See the example below.

Note: You only need two points to graph the line. I just did a third as a check.

Answer:

28/4

Step-by-step explanation:

the slash is also a division sign.

Answer:

B: 28/4 should be the correct answer, correct me if I'm wrong.

Answer:

=34

Step-by-step explanation:

4x+12x-6=4(4x+7) ur question

using BODMAS

4x+12x-6=16x+28

16x-6=16x+28

16x-16x=28+6

0=34

but make sure your question is right, can you go through it again

Answer:

\(x = 1\)

Step-by-step explanation:

Based on the given conditions, formulate: \(x = 12 \div 12\)

Cross out the common factor:\(x = 1\)

Answer: \(x = 1\)

Answer:

Step-by-step explanation:

1. ∠WVX , ∠YZX are right angled triangles       1.Given

2. WV ≅ YZ                                                          2. Given

3. X is the midpoint of WY                                  3. Given

4. WX ≅ YX                                                          4. definition of midpoint

5. ΔWVX ≅ ΔYZX                                               5. RH congruent

Answer:

Step-by-step explanation:

Value of x= `

4x+5y-6z =2

x= (2-5y+6z) divided by 4

For example : if x is 2.5

2.5 = 2 - 5x2 + 6x3

Answer:

b = 39

Step-by-step explanation:

To complete the full circle would need 360°

So, the equation is:

b + 28 + 293 = 360

b + 321 = 360

b = 360 - 321

b = 39

Answer:

225

Step-by-step explanation:

25:75=75:?

25*3 is 75, so 75*3 is ?

75*3 is 225

Hope this helps!

Let me know if it does

Answer: 225 cats

Step-by-step explanation:

25 dogs x 3: 75 cats x 3

75 dogs: 225 cats

Answer:

c (I think it is c, but I am not a 100% sure)

Step-by-step explanation:

x and y have to be same

Have a nice day! :-)

Answer:

  a.  ∞, -∞

Step-by-step explanation:

The line has negative slope, so the sign of the end value of y will be the opposite of the sign of the end value of x.

  x → -∞,  y → ∞ . . . . . off the top of the graph as x goes to the left

  x → ∞, y → -∞ . . . . . . off the bottom of the graph as x goes to the right

The end behavior is summarized as ...

  ∞, -∞ . . . . . matches choice A

Answer: Montresor struggles with anger, and grudges. Montresor feels remorse at the end but excuses it as the dampness of the catacombs.

He sees the world without justice and sees to make justice for himself. In the story he talks about the misgivings and insults he receives from fortunato. He takes vengeance against him.

(haven´t read book based off summary) Princess Irene  shares a friendship that is strong. I infer this based off the trust and bonding they share in the book. She struggles against goblins.  

Step-by-step explanation: I really hope this helps havent read the books in a long time.!!

Step-by-step explanation:

the sum of the interior angles of a polygon (a closed object with n edges) is always (n-2)×180°.

we have here 5 edges, so the sum of all 5 angles is

(5-2)×180 = 3×180 = 540°.

now, let's simply calculate

5x + 2 + 7x - 11 + 13x - 31 + 8x - 19 + 10x - 3 = 540

43x - 62 = 540

43x = 602

x = 14

therefore,

angle S = 13x - 31 = 13×14 - 31 = 182 - 31= 151°

Answer:

Obtuse Angle

Step-by-step explanation:

Answer:

Acute

Step-by-step explanation:

Answer:

125

Step-by-step explanation:

75 + 50

Answer:

  A) $3100

  B) $6700

Step-by-step explanation:

The first table entry is the value of the opening balance of Caroline's account.

$3100 was in Caroline's account when it was opened.

__

After 1 month, the balance in Caroline's account increased by $3250 -3100 = $150. There are 12 months in a year, so after 2 years, Caroline will have made 12×2 = 24 additional deposits of $150. Her account value will be ...

  24 × monthly deposit + initial balance

  = 24 × $150 + $3100 = $3600 +3100 = $6700

Caroline would have saved $6700 after 2 years.

Answer:

Step-by-step explanation:

The numbers are in the form of:

When a = 16, b = 10 the number is:

Correct choice is A

Answer:

See picture

Step-by-step explanation:

Hope this helps!

Answer:

number 3

Step-by-step explanation:

angleNGL=~angleHGF

Answer:

NG≅GF

Step-by-step explanation:

Since the side has to be in between the two angles so it from a ASA

The angles ∠N is the same as ∠F and ∠NGL is the same as ∠HGF

Answer:

n = 8.

Step-by-step explanation:

The interior angle of a regular hexagon = 120 degrees.

So m < GAB = 360 - 120 - 105

= 135 degrees so the regular polygon has a total of 135n degrees.

Using the formula for the sum of interior angles of a polygon,

For the polygon with n sides:

Sum of interior angles = 180(n - 2)

135n = 180(n - 2)

135n = 180n - 360

45n = 360

n = 360/45 = 8.

Answer:

r = ± [tex]\sqrt{q^2-p^4[/tex]

Step-by-step explanation:

p² = [tex]\sqrt{q^2-r^2}[/tex] ( square both sides )

(p² )² = q² - r²

[tex]p^{4}[/tex] = q² - r² ( subtract q² from both sides )

[tex]p^{4}[/tex] - q² = - r² ( multiply through by - 1 )

q² - [tex]p^{4}[/tex] = r² ( take square root of both sides )

± [tex]\sqrt{q^2-p^4}[/tex] = r

Answer:

c. -19

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Given a polynomial in standard form

The leading coefficient is the coefficient of the variable with the largest exponent.

The term with the largest exponent of the variable is

[tex]\frac{1}{4}[/tex] [tex]x^{5}[/tex]

Then the leading coefficient is [tex]\frac{1}{4}[/tex] → A

Answer:

110000

Step-by-step explanation:

first, expand 10^5, which is 100000

use a calculator (or long multiplication) to multiply 1.1*100000, which is 110000

Answer:

The fraction is 13/21.

Step-by-step explanation:

The denominator of a fraction is 8 more than its numerator.

Let x be the numerator: x

So the denominator is: x + 8

[tex]\frac{x}{x + 8}[/tex]

If 1 is subtracted from the numerator and 3 is added to the denominator, the fraction becomes 1/2.

It will become:

[tex]\frac{x - 1}{x + 8 + 3} = \frac{1}{2}[/tex]

[tex]\frac{x - 1}{x + 11} = \frac{1}{2}[/tex]

Now, by using cross multiplication, multiply (x - 1) by 2 and (x+11) by 1.

It will become:

2x - 2 = x + 11

Now transpose and combine the same values. Make sure to change the integer sign. If the integer is positive, change it to negative when you transpose it.

2x - x = 11 + 2

x = 13

So the value of x is 13. Now to check if it is correct. Go back to the equation([tex]\frac{x - 1}{x + 11} = \frac{1}{2}[/tex])

Put the value of x in it.

[tex]\frac{13-1}{13+11} = \frac{1}{2}[/tex]

[tex]\frac{12}{24} = \frac{1}{2}[/tex]

12/24 is equivalent to 1/2 so that is correct.

Now, to find the main fraction. Go back to the original equation which is;

([tex]\frac{x}{x + 8}[/tex])

Put the value of x.

[tex]\frac{13}{8 + 13}[/tex]

= 13/21

Not a verified expert but I put much effort to answer your question. Hope it helps:)