Find the length of the third side. If necessary, round to the nearest tenth

Pythagorean Theorem (Rounding)

Expansion : [tex](x+1)(x+9) = x(x+9) + 1(x+9) = x^{2} +9x + x + 9[/tex]
Simplify : [tex]x^{2} +10x + 9[/tex]

Answer:

[tex]\huge\boxed{ \bf\:x^{2} + 10x + 9}[/tex]

Step-by-step explanation:

[tex](x + 1)(x+9)[/tex]

Let's expand it at first.

[tex](x + 1)(x + 9)\\= x (x + 9) + 1 (x + 9)\\= x^{2} + 9x + x + 9[/tex]

Now, simplify it.

[tex]x^{2} + x + x + 9\\= \boxed{ x^{2} + 10x + 9}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

Using the slope concept, it is found that the distance the plane traveled from point A to point B was of 18052.4 ft.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

At point A, the vertical change is of 7475 ft, with an angle of 16º, hence the equation below can be solved to find the position:

[tex]\tan{16^\circ} = \frac{7475}{x_A}[/tex]

[tex]x_A = \frac{7475}{\tan{16^\circ}}[/tex]

[tex]x_A = 26068.4[/tex]

At point B, the angle is of 43º, hence:

[tex]\tan{43^\circ} = \frac{7475}{x_B}[/tex]

[tex]x_B = \frac{7475}{\tan{43^\circ}}[/tex]

[tex]x_B = 8016[/tex]

Hence, the distance in feet is given by:

[tex]d = x_A - x_B = 26068.4 - 8016 = 18052.4[/tex]

More can be learned about the slope concept at https://brainly.com/question/18090623

Answer:

68

Given:

Substitute equation 1 into 2

Find y:

y = x - 5

y = 1 - 5     (when x is 1)

y = -4

========

y = x - 5

y = 4 - 5        (when x is 4)

y = -1

Then 4x² + 4y²:

Answer:

68

Step-by-step explanation:

[tex]\textsf{Equation 1}:\:x-5=y[/tex]

[tex]\textsf{Equation 2}:\:xy+4=0[/tex]

Substitute Equation 1 into Equation 2:

[tex]\implies x(x-5)+4=0[/tex]

[tex]\implies x^2-5x+4=0[/tex]

Factorize:

[tex]\implies (x-1)(x-4)=0[/tex]

Therefore:

[tex]x=1, x=4[/tex]

Substitute found values of [tex]x[/tex] into Equation 1 and solve for [tex]y[/tex]:

[tex]x=1\implies 1-5=-4[/tex]

[tex]x=4\implies 4-5=-1[/tex]

Substitute found values into [tex]4x^2+4y^2[/tex] and solve:

[tex]\textsf{For}\:(1,-4)\implies 4(1)^2+4(-4)^2=68[/tex]

[tex]\textsf{For}\:(4,-1)\implies 4(4)^2+4(-1)^2=68[/tex]

Note:  As [tex]4x^2+4y^2[/tex], the values of x and y can be interchanged, so no need to input both sets of ordered pairs into the equation to solve.

Answer:

22 in.

Step-by-step explanation:

total volume= big thingy + long thingy

=>x=2.2.3+5.2=12+10=22

Answer:

x = -1

x = 3

Step-by-step explanation:

[tex]\sf x^2 - 2x = 3[/tex]

Add 1 to both sides:

[tex]\sf \implies x^2 - 2x+1 = 3+1[/tex]

Factor the left side:

[tex]\sf \implies (x-1)^2 = 4[/tex]

Square root both sides:

[tex]\sf \implies x-1 = \pm2[/tex]

Therefore:

[tex]\sf \implies x-1=-2 \implies x=-1[/tex]

[tex]\sf \implies x-1=2 \implies x=3[/tex]

Using an exponential function, it is found that the mass of the radioactive sample at the beginning of the 13th day of the experiment was of 169.1 mg.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

At the beginning of the first day of the experiment the mass of the substance was 500 grams and mass was decreasing by 8% per day, hence A(0) = 500, r = 0.08, and the equation is given by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 500(1 - 0.08)^t[/tex]

[tex]A(t) = 500(0.92)^t[/tex]

At the 13th day, the mass is given by:

[tex]A(13) = 500(0.92)^{13} = 169.1[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

Answer:

6.3 :)

Step-by-step explanation:

Pythagorean theorem: a^2 + b^2 = c^2

Now lets solve!!!

3^2 + b^2 = 7^2

9 + b^2 = 49

Now we subtract!!

49 - 9 = b^2

40 = b^2

Now we need to find the square root!!

[tex]\sqrt{40}[/tex] = 6.3

Have an amazing day!!

Please rate and mark brainliest!!!

finish the question..............

Answer:

Part 1- Lydia

Step-by-step explanation:

The full question should be

Four friends each took a different path walking from the lunchroom to the gymnasium. The table shows the distance that each of them walked. Who walked the farthest?

Answer:

39364.

Step-by-step explanation:

I guess its an = 4*(3)^(n-1)

r = 3, a1 = 4 and n = 9

Sum of n terms = a1 * (r^n - 1) / (r - 1)

so S9 = 4 *(3^9 - 1) / (3 - 1)

= 4 * (19683  - 1) / 2

= 78728/2

= 39364.

Answer:

70.

Step-by-step explanation:

1) to calculate the values of the 'x':

4x+15=x²-13x+85; ⇔ x²-17x+70=0; ⇔

x₁=7; x₂=10;

2) to calculate the required k:

k=x₁*x₂; k=7*10=70.

Hey there!

Option A.
23 + (4) - 4 * 2

= 23 + 4 - 4 * 2

= 27 - 4(2)

= 27 - 8

= 19

19 ≠ 32

Option B.
3 * 3 + (42) - 4

= 3 * 3 + 42 - 4

= 9 + 42 - 4

= 51 - 4

= 47

47 ≠ 32

Option C.
42 - 7 * 0

= 42 - 0

= 42

42 ≠ 32

Option D.
4 * 5 + 2 - 4 + 2

= 20 + 2 - 4 + 2

= 22 - 4 + 2

= 18 + 2

= 20

20 ≠ 32

None of them are equivalent to 32

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

A

Step-by-step explanation:

A) r = 8

B) r = 4

C) r = [tex]\sqrt{\frac{30}{\pi } }[/tex] ~ 3.09

D) r = [tex]\frac{30}{2\pi} = \frac{15}{\pi } ~ 4.77[/tex]

Circle A has the largest radius, and thus is the largest circle

Using arithmetic sequence concepts, it is found that the common difference is of 0.25.

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, we have that:

[tex]a_3 = 8, a_7 = 9[/tex]

Hence:

[tex]a_7 = a_3 + (7 - 3)d[/tex]

9 = 8 + 4d

4d = 1.

d = 0.25.

The common difference is of 0.25.

More can be learned about arithmetic sequence concepts at https://brainly.com/question/6561461

the image is formed of a rectangle and a square

perimeter of the cabin = perimeter of rectangle + perimeter of square

= 2(l+b) + 4×side

= 2(7+5) + 4×5

= 24 + 20

perimeter of the cabin = 44 cm

Answer:

g + a = 24. 2 g + a = 42.

Step-by-step explanation:

Each goal gets 2 points and each assist gets 1 point

If # of goals = g , and you get 2 points for each goal, then points acquired by goals can be represented by 2g

If # of assists = a, and you get 1 point for each assist, then points acquired by assists can be represented by a

The total # of points the player had was 42. This means that 2g + a = 42 (this is the first equation)

We are also told the player scored a total of 24 goals and assists. If g = # of goals and a = of assists, then g + a = 24 (this is the second equations)

So the two equations are g + a = 24. 2 g + a = 42.

Answer:

g + a = 24. 2 g + a = 42.

Step-by-step explanation

trust

(-2)-(-5)=0

bit 2 minuses= + so:

-2+5=0

3=0

Answer:

2 years

Step-by-step explanation:

If it is annunal I think it would be 2 years

5 x annual year (year) =2

Answer:

140

Step-by-step explanation:

5%/100 = 7/?

7 times 100 = 700

700 divided by 5 = 140 coins

1

Step-by-step explanation:

Seeing its an arithmetic sequence

T1=1......T2=2.....T3=3

To get your constant difference

T2=T1 is also equals to T3=T2

so 3-2=1 and 2-1=1

therefore the constant difference is 1

Mode is the number that is shown the most.

Answer: 1. Most

Answer:

12

Step-by-step explanation:

collect the like terms and divide

1) Water in a plastic container, p'= 10 - 3 p

2) Water in a glass container = 27 quarts

Water in a plastic container = 1 quarts

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A glass jug can hold (p + 6) quarts less water than a plastic container, 2 glass jugs and 2 plastic containers contain 6p quarts of water in all.

Now,

Let j represents water in one glass jag while p' represents the water in one plastic container,

Hence, According to the question,

⇒ j - p' = 6p+8 --------(1)

And, 2j+2p'=56p --------(2)

2 × equation (1)

⇒ 2 j - 2 p' = 12p + 16 ---------(3)

Equation (2) + equation (3)

We get, 4 j = 12 p + 72

⇒ j = 3 p + 18

Putting this value in equation (1),

We get, 3p+18-p'=6p+8

p' = -3p + 10 = 10 - 3p

Thus, water in a plastic container, p'= 10 - 3 p

b) If p=3

Water in a glass container = 3 × 3 + 18 = 27 quarts

Water in a plastic container = 10 - 3 × 3 = 1 quarts

Learn more about the mathematical expression visit:

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Answer:

"a linear function has the form y = mx + b. "

Answer:

3.  Object C.

Step-by-step explanation:

The inertia of an object is the measure of the force required to set it in motion.  For two objects to have the same motion, the one with the greater mass will require a proportionately greater force to achieve the same motion.

Object C, with a mass of 1,250,000 grams (1,250 kg) will have the greatest inertia.

Answer:324pie cm^2

Step-by-step explanation:

There are multiple possible solutions for x, two examples are x = 0° and x = 360°.

We need to solve the equation:

sin(2x) = sin(x)

Then we need to find a value x such that the sine of 2x is equal to the sine of x.

Now, because of the periodicity of the sine equation, there are a lot of possible values of x.

One example, trivial, is x = 0, this is because 2*0 = 0, then we would have:

sin(2*0) = sin(0)

sin(0) = sin(0).

Another case is if we take x = 360° (remember that 360° is the period of the sine function), then we can have:

sin(2*360°) = sin(360°)

sin(720°) = sin(360°) = 0

Then x = 360° is another solution.

If you want to learn more about the sine function, you can read:

https://brainly.com/question/9565966