Based on corresponding angles and vertical angles, which angles must always be congruent to the angles given? Complete the table.

Answer:

30 mm.

Step-by-step explanation:

The longest side = sqrt(5^2 + 12^2)

= sqrt169

= 13.     (Using Pythagoras).

So the perimeter = 5+12+13

= 30 mm.

Perimeter of the piece of jewelry = 30mm

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides".

Given,

Shape of jewelry is right angle triangle ABC

length of shorter sides,

AB = 5mm

BC = 12mm

By Pythagoras theorem,

AC² = AB²+BC²

AC = √(5² + 12²)

AC = √169

AC = 13 mm

Perimeter of Triangle = AB + BC + AC

                                    = 5 + 12 + 13

Perimeter of Triangle = 30

Hence, 30 mm is the perimeter of jewelry.

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Answer:$247

Step-by-step explanation

The third ordered pair that satisfy the given equation is (123, 369).

The given parameters;

The third ordered pair of the equation can be determined by using general equation of a circle;

[tex]a^2 + b^2 = r^2\\\\a^2 + b^2 = (123\sqrt{10} )^2\\\\a^2 + b^2 = (\sqrt{151290} )^2\\\\a^2 + b^2 = 151290\\\\a^2 = 151290- b^2\\\\ a= \sqrt{151290 - b^2}[/tex]

The radius of the circle is calculated as;

[tex]r^2 = 151290\\\\r = \sqrt{151290} \\\\r = 388.96[/tex]

The value of a can be obtained by randomly choosing numbers less than the radius as values of b.

[tex]b < r\\\\b < 388.96[/tex]

[tex]a = \sqrt{151290 \ - \ (387)^2} \\\\a = 39\\\\(39, \ 387)\\\\a = \sqrt{151290 \ - \ (333)^2}\\\\a = 201\\\\(201, \ 333)\\\\a = \sqrt{151290 \ - \ (369)^2}\\\\a = 123\\\\(123, \ 369)[/tex]

Thus, the third ordered pair that satisfy the given equation is (123, 369).

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Answer:

Joel can do 20 math problems in 90 seconds

He can do 1 math problem in 90/20 = 4.5 seconds

Now, Joel can do 32 math problems in

4.5×32

= 144 seconds

= 2 minutes 24 seconds

Step-by-step explanation:

Here I used the unitary method to sovle the question

Answer:

f(-18) = -5

Step-by-step explanation:

Substitute−18forxiny=

1/3 x+1:

y= 1/3x+1

y= 1/3(−18)+1

y=−5(Simplify both sides of the equation)

Answer:

It takes 30 minutes to get to the front of the line, and 15 minutes to walk, so 45 minutes. 45 is less than 60, so you will make it.

Step-by-step explanation:

To calculate unit rate, 75/5 = 15/1 120*15=1800/60=30 minutes

(divide by 60 to convert to minutes)

Answer:

x + y = - 1.2

Step-by-step explanation:

7x - 7y = 5 ; y = x - [tex]\frac{5}{7}[/tex] ; the slope is 1 , and slope of ⊥ line is ( - 1 )

x + 5y = - 6 ; y = - [tex]\frac{1}{5}[/tex] x - [tex]\frac{6}{5}[/tex] ; y-intercept is ( - 1.2 )

Equation is y + [tex]\frac{6}{5}[/tex] = - ( x - 0 ) ; y = - x - 1.2 ; x + y = - 1.2

Answer:

true i think

Step-by-step explanation:

Answer:

3 hours

Step-by-step explanation:

7hours - 4hours

hope it helped

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Answer:

Vertical asymptote is at [tex]x=-3[/tex]

Step-by-step explanation:

Let us plot the function

Here

[tex]\frac{x-5}{x^{2}-2x-15}=\frac{x-5}{(x-5)(x+3)}\\\\=\frac{1}{x+3}[/tex]

Function does not exits at [tex]x=-3[/tex]

Vertical asymptote is at [tex]x=-3[/tex]

Answer:

1000 = 450 + 50w

Step-by-step explanation:

She starts with $450 so that is why you add it. The amount she started with will not change.

She earns $50 per week so you add 50 multiplied by the number of weeks she works.

You do this until it equals 1000

Answer:

x=61

Step-by-step explanation:

2x-6+x+3=180

3x-3=180

3x=183

x= 61

Answer:

Step-by-step explanation:

Answer:

7.8

Step-by-step explanation:

subtract 85 - 77.2

Answer:

{},{a},{b},{c},{d},{a,b},{a,c},{a,d},{b,c},{b,d},{c,d},{a,b,c},{a,b,d},{a,c,d},{b,c,d},{a,b,c,d}

Step-by-step explanation:

Answer:

[tex]\blue{\rule{100pt}{999999pt}}[/tex] [tex]\blue{\rule{100pt}{999999pt}}[/tex]

Answer:

Integers

Step-by-step explanation:

Integers are the set of whole numbers and their opposites.

Answer:

11 mm, 21 mm, and 16 mm.

Step-by-step explanation:

since 11+21>16, 11+ 16>21>11, You can form a triangle with 11,21,16

Answer:

Step-by-step explanation:

Answer:

7a + 6

Step-by-step explanation:

Expand the brackets and then collect like terms. 4a + 3a = 7a

[tex]y = x + 4[/tex]

Step-by-step explanation:

Let [tex]P_1(-1, 3)[/tex] and [tex]P_2(0, 4)[/tex] and solve for the slope using the equation

[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{4 - 3}{0 - (-1)} = 1[/tex]

Therefore, the general slope-intercept form of the equation of the line is

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

where b is a constant. To solve for it, let's use one of the points. I'll use P2:

[tex]4 = (0) + b \Rightarrow b = 4[/tex]

Therefore, the slope-intercept form of the equation of the line is

[tex]y = x + 4[/tex]

Answer:

Here is my answer I have solved hope this helps

Answer:

Step-by-step explanation:

Let x be the adjacent side length in cm

opposite side is x + 2 cm

hypotenuse is x + 4 cm

x² + (x + 2)² = (x + 4)²

x² + (x² + 4x + 4) = (x² + 8x + 16)

x² - 4x - 12 = 0

(x - 6)(x + 2) = 0

so either

x - 6 = 0    x = 6

or

x + 2 = 0    x = -2

positive answer is x = 6 as negative length does not make sense

opposite side is 6 + 2 = 8

hypotenuse is 6 + 4 = 10

perimeter is 6 + 8 + 10 = 24 cm

Step-by-step explanation:

it is like a regular addition of numbers. you add the different positions.

3x + 7x = 10x

-y + y = 0

-5 + 15 = 10

so, D. is the right answer : 10x = 10

Answer:

A

D

B

C

Step-by-step explanation:

We can simplify the expressions for easier comprehension:

A. 60.7 x 10^-1 = 6.07

B. 6.07 x 10^3 = 6,070

C. 0.67 x 10^4 = 6,700

D. 6.7 x 10^2 = 670

Now, we can order them in ascending order (least to greatest):

A

D

B

C

Given that

log √x (x) + log c² (c)

⇛ log x^1/2 (x) + log c² (c)

We know that

log a^m (b^n) = m/n log a (b)

⇛ 1/2 log x (x) + 2 log c (c)

We know that

log a ( a) = 1

⇛ (1/2)(1) + 2(1)

⇛ (1/2)+2

⇛ (1+4)/2

⇛ 5/2

Answer:- log √x (x) + log c² (c) = 5/2

[(x) ,(c) , (a) represents the bases ]

Additional comment:

also read similar questions: if log^2(x)=log^2(a)+log^2(b)-log^2(c) then x is....

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simplify the following expression. log(x2) - log(x) A. log(x^2+x) B. log(x^3) C. log(x^2-x) D. log(x)....

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Answer:

No, It's false.

Step-by-step explanation:

In the long history of the United States, only one president, George Washington, did not represent a political party.

yo mama is so fat

when she saw you she died from diabetes

Answer:

$2,365

Step-by-step explanation:

Divide $61,490 by 26...

Answer:

the first one and the last one

Step-by-step explanation:

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