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1 year ago

Which of the following expressions is equivalent to 13^(2)-3^(2)

Mathematics

1 answer:

Amiraneli [1.4K]1 year ago

8 0

Answer:

160

Step-by-step explanation:

13² - 3² = 13 × 13 - 3 × 3 = 169 - 9 = 160

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If the second number is subtracted from the sum of the first number and 2 times the third number, the result is 1. The thrid num

weeeeeb [17]

Answer:

Step-by-step explanation:

$x,\ y,\ z-\text{three numbers}\\\\\left\{\begin{array}{ccc}(x+2z)-y=1&(1)\\z+2x=3&(2)\\x+3y+z=18&(3)\end{array}\right\\\\(2)\\z+2x=3\qquad\text{subtract}\ 2x\ \text{from both sides}\\z=3-2x\qquad(*)\\\\\text{Substitute}\ (*)\ \text{to (1) and (3)}\\\\\left\{\begin{array}{ccc}x+2(3-2x)-y=1&\text{use the distributive property}\\x+3y+(3-2x)=18\end{array}\right$

$\left\{\begin{array}{ccc}x+(2)(3)+(2)(-2x)-y=1\\x+3y+3-2x=18&\text{subtract 3 from both sides}\end{array}\right\\\left\{\begin{array}{ccc}x+6-4x-y=1&\text{subtract 6 from both sides}\\(x-2x)+3y=15\end{array}\right\\\left\{\begin{array}{ccc}(x-4x)-y=-5\\-x+3y=15\end{array}\right\\\left\{\begin{array}{ccc}-3x-y=-5&\text{multiply both sides by 3}\\-x+3y=15\end{array}\right$

$\underline{+\left\{\begin{array}{ccc}-9x-3y=-15\\-x+3y=15\end{array}\right}\qquad\text{add all sides of the equations}\\.\qquad-10x=0\qquad\text{divide both sides by (-10)}\\.\qquad\boxed{x=0}\\\\\text{Put it to the second equation:}\\-0+3y=15\\3y=15\qquad\text{divide both sides by 3}\\\boxed{y=5}\\\\\text{Put the value of}\ x\ \text{to}\ (*):\\\\z=3-2(0)\\\boxed{z=3}$

7 0

2 years ago

What is the equation of the line that passes through (5, 3) and (4, 5)

lara31 [8.8K]

Answer:

y = - 2x + 13

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (5, 3) and (x₂, y₂ ) = (4, 5)

m = $\frac{5-3}{4-5}$ = $\frac{2}{-1}$ = - 2, thus

y = - 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 5), then

5 = - 8 + c ⇒ c = 5 + 8 = 13

y = - 2x + 13 ← equation of line

7 0

2 years ago

A 1414-ft ladder leans against a wall at a point 55 feet above the ground. how far is the bottom of the ladder from the wall?

viva [34]

Assume ladder length is 14 ft and that the top end of the ladder is 5 feet above the ground.

Find the distance the bottom of the ladder is from the base of the wall.

Picture a right triangle with hypotenuse 14 feet and that the side opposite the angle is h. Then sin theta = h / 14, or theta = arcsin 5/14. theta is

0.365 radian. Then the dist. of the bot. of the lad. from the base of the wall is

14cos theta = 14cos 0.365 rad = 13.08 feet. This does not seem reasonable; the ladder would fall if it were already that close to the ground.

Ensure that y ou have copied this problem accurately from the original.

7 0

3 years ago

Which is equivalent to 4 square root 9^1/2^?

zzz [600]

I think this is it,please try and looking it up also for a better explanation

3 0

3 years ago

Scarlett Squirrel teaches a hula dancing class to young squirrels. 141414 squirrels showed up to class on Monday, 101010 squirre

Temka [501]

Answer:

93107

Step-by-step explanation:

add all of the numbers together

divide by 5 since there are 5 numbers

you would get 92106.8

so round that up since you cannot have 1/8 of a squirrel

Hope this helps!!

3 0

3 years ago