Evaluate each expression

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:

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

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:

The  inverse of the function of f(x) = 4x is h(x) = x/4

Since f(x) = 4x, to obtain its inverse, we write f(x) = y

So, y = 4x.

We now divide both sides by 4. so, we have

y/4 = 4x/4

y/4 = x

Next, we replace x with y. So,

y/4 = x

x/4 = y

Next, we now replace y with f⁻¹(x) which is the inverse of f(x).

So, y = x/4

f⁻¹(x) = x/4

Since  f⁻¹(x) = h(x), replacing these, we have

h(x) = x/4

So, the  inverse of the function of f(x) = 4x is h(x) = x/4

Learn more about inverse of a function here:

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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:

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]

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).

Learn more about equation of circle here: https://brainly.com/question/1506955

Answer:

7.8

Step-by-step explanation:

subtract 85 - 77.2

Answer:

x=61

Step-by-step explanation:

2x-6+x+3=180

3x-3=180

3x=183

x= 61

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.

Answer:

The answer is 13,200 feet.

Step-by-step explanation:

1 mile equals 5,280 feet, So all we have to do is multiply 5,280 by 2.5 miles.

5,280 * 2.5 = 13,200.

If you don't have a calculator you can multiply be splitting the parts.

5,280 * 2 = 10,560

+ 2,640 = 13,200

You get the 2,640 feet by dividing 5,280 by 2 because the 0.5 in 2.5 is half of a mile and 5,280 feet is a whole mile. Meaning that we have to cut the 5,280 in half to find the 0.5 in 2.5

Hope this helps! :)

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Answer:

13200 feet. Guaranteed

Step-by-step explanation:

Answer:$247

Step-by-step explanation

Answer:

There are a couple different solutions to your equation:

[tex]x=0[/tex]

[tex]x=\sqrt[22]{\frac{13}{n}}[/tex]

[tex]x=-\sqrt[22]{\frac{13}{n}}[/tex]

[tex]\:n\ne \:0[/tex]

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:

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:

c(1) = -15

c(n) = c(n - 1) + 4

Step-by-step explanation:

Given arithmetic sequence is,

-15, -11, -7, -3...........

Common difference between each successive and previous term is,

d = -11 - (-15)

 = -11 + 15

 = 4

Since recursive formula of the arithmetic sequence is represented by,

a₁ = First term of the sequence

a(n) = a(n - 1) + d

where a(n) is the nth term and a(n-1) is the previous term of the nth term.

Form the given sequence,

c₁ = -15

c(n) = c(n - 1) + 4

Step-by-step explanation:

Answer:

Here is my answer I have solved hope this helps

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:

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:

Step-by-step explanation:

Answer:

3/50

Step-by-step explanation:

Answer:

0.06 is equal to 3/50.

Hope that helps. x

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

Answer:

Hope it will help you...

Answer:   i have never did a math problem like this before because i'm only in the 2nd semester of 7th grade but i will try, i think it is 2090

Step-by-step explanation: 5000 divided by 2 = 2500. then you do 2500-410. 2500-410= 2090.  (i hope this will help you and sorry if i did it wrong) :)

[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:

Step-by-step explanation:

Answer:

7a + 6

Step-by-step explanation:

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

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.

Learn more about Pythagoras theorem here:

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Answer:

[tex]-2\frac{1}{2}[/tex]

Step-by-step explanation:

→ Minus the 2 numbers from each other

[tex]-1\frac{1}{5} -1\frac{3}{10}[/tex]

→ Find the LCM

[tex]-1\frac{2}{10} -1\frac{3}{10}[/tex]

→ Simplify

[tex]-2\frac{5}{10} =-2\frac{1}{2}[/tex]

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