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3 years ago

6

These two triangles are congruent by the hypotenuse leg theorem.

1 answer:

Blababa [14]3 years ago

5 0

X-y=x+2
2x-y=4x+2y (same as we would write 2x+3y=0)

-y=2+x-x
y=-2

so 2x+3y=0 is
2x+3×(-2)=0
2x=6
x=6/2=3

x=3

answer: x=3

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How many persons are in the line? Ashley is in the line to buy a ticket. There are twice as many people in front of Ashley as th

Klio2033 [76]

Answer:

I am pretty sure there are 10 people in line.

Since Ashley is the seventh person in line, we can deduce that <u><em>there are 6 people in front of her</em></u>.

Since the amount of people in front of her is "twice as many people as there are behind her," we can divide the value of the people in front of her in half to get the value of people behind her.

6/2 is 3, so <em>there are </em><u><em>3 people behind Ashley</em></u><em>. </em>

Now, lets add the amount of people in front of Ashley to the amount of people behind her. 3 + 6 = 9, and since Ashley is also in the line, we should add 1 to the sum.

9 + 1 = 10, so <u><em>there are 10 people in the line</em></u>.

4 0

3 years ago

Solve 5x^2-2=-12 by taking the square root

k0ka [10]

Answer:

x = ±i√2

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality

Division Property of Equality

Addition Property of Equality

Subtraction Property of Equality<u> </u>

<u>Algebra II</u>

Imaginary root <em>i</em>

<em>i</em> = √-1

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

5x² - 2 = -12

<u>Step 2: Solve for </u><em><u>x</u></em>

[Addition Property of Equality] Add 2 on both sides: 5x² = -10
[Division Property of Equality] Divide 5 on both sides: x² = -2
[Equality Property] Square root both sides: x = ±√-2
Rewrite: x = ±√-1 · √2
Simplify: x = ±i√2

7 0

3 years ago

Help me solve this problem please

lara31 [8.8K]

Answer:

CD = 45

Step-by-step explanation:

CE = 180

( x + 6 ) + ( 4x - 21 ) = 180

5x - 15 = 180

5x = 195

x = 39

substitute x in CD

CD = x + 6

CD = 39 + 6

CD = 45

5 0

3 years ago

Eduardo spent $34 on a magazine and some candy bars if the magazine cost $6 and each candy bar cost $4 then how many candy bars

tatiyna

Answer: 7 candy bars

Step-by-step explanation:

First we need to subtract the cost of the magazine from the total cost

$34-$6=$28

Now the $28 that remains is the cost of all the candy bars, so if we divide by the price, we will get the amount.

$28/$4=7 candy bars

7 0

3 years ago

Unsure how to do this calculus, the book isn't explaining it well. Thanks

krok68 [10]

One way to capture the domain of integration is with the set

$D = \left\{(x,y) \mid 0 \le x \le 1 \text{ and } -x \le y \le 0\right\}$

Then we can write the double integral as the iterated integral

$\displaystyle \iint_D \cos(y+x) \, dA = \int_0^1 \int_{-x}^0 \cos(y+x) \, dy \, dx$

Compute the integral with respect to $y$ .

$\displaystyle \int_{-x}^0 \cos(y+x) \, dy = \sin(y+x)\bigg|_{y=-x}^{y=0} = \sin(0+x) - \sin(-x+x) = \sin(x)$

Compute the remaining integral.

$\displaystyle \int_0^1 \sin(x) \, dx = -\cos(x) \bigg|_{x=0}^{x=1} = -\cos(1) + \cos(0) = \boxed{1 - \cos(1)}$

We could also swap the order of integration variables by writing

$D = \left\{(x,y) \mid -1 \le y \le 0 \text{ and } -y \le x \le 1\right\}$

and

$\displaystyle \iint_D \cos(y+x) \, dA = \int_{-1}^0 \int_{-y}^1 \cos(y+x) \, dx\, dy$

and this would have led to the same result.

$\displaystyle \int_{-y}^1 \cos(y+x) \, dx = \sin(y+x)\bigg|_{x=-y}^{x=1} = \sin(y+1) - \sin(y-y) = \sin(y+1)$

$\displaystyle \int_{-1}^0 \sin(y+1) \, dy = -\cos(y+1)\bigg|_{y=-1}^{y=0} = -\cos(0+1) + \cos(-1+1) = 1 - \cos(1)$

7 0

1 year ago