which of the following systems of linear inequalities is represented by the solution graphed below?

Answer:

x = sqrt(33)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

4^2 + x^2 = 7^2

16 + x^2 = 49

Subtract 16 from each side

x^2 = 49-16

x^2 = 33

Take the square root of each side

sqrt(x^2) = sqrt(33)

x = sqrt(33)

[tex]\quad\quad\quad \boxed{ \tt{\color{blue}{c}^{2} = {a}^{2} + {b}^{2} }}[/tex]

[tex]\quad\quad\quad \boxed{ \tt{\color{blue}{a} = \sqrt{ {c}^{2} - {b}^{2} \: \: } }}[/tex]

[tex]\quad\quad\quad \boxed{ \tt{\color{black}{a} = \sqrt{ {c}^{2} - {b}^{2} \: \: } }}[/tex]

[tex]\quad\quad\quad \boxed{ \tt{{x} = \sqrt{ {c}^{2} - {b}^{2} \: \: } }}[/tex]

[tex]\quad\quad\quad \boxed{ \tt{{x} = \sqrt{ {7}^{2} - {4}^{2} \: \: } }}[/tex]

[tex]\quad\quad\quad \boxed{ \tt{{x} = \sqrt{ {49} - {16} \: \: } }}[/tex]

[tex]\quad\quad\quad \boxed{ \tt \color{black}{{x} = \sqrt{ 33} }}[/tex]

[tex]\quad\quad\quad \boxed{ \tt \color{green}{{x} = \sqrt{ 33} }}[/tex]

_________

#LetsStudy

Answer:

9 < √97 < 10

Step-by-step explanation:

√97 is a little less than √100

Which is 10

9 < √97 < 10

=====================================================

Explanation:

Consider that 81 < 97 < 100 is a true statement. Note the 81 and 100 are perfect squares such that 81 = 9^2 and 100 = 10^2

We can apply the square root to all three sides to get the following

[tex]81 < 97 < 100\\\\\sqrt{81} < \sqrt{97} < \sqrt{100}\\\\\sqrt{9^2} < \sqrt{97} < \sqrt{10^2}\\\\9 < \sqrt{97} < 10\\\\\text{The number }\sqrt{97} \text{ is between 9 and 10}\\\\[/tex]

Using a calculator, we can help verify this

[tex]\sqrt{97} \approx 9.85[/tex]

Hope This Helps!!!

Hope This Helps!!!Have A Great Day!!!

Answer:

x = - 10

Step-by-step explanation:

Expand the equation first then simplify it

Answer:

Step-by-step explanation:

I'll show you how to do the first one; the other are exactly the same, so pay attention.

The formula for arc length is

[tex]AL=\frac{\theta}{360}*2\pi r[/tex] where θ is the central angle's measure. It just so happens that the measure of the central angle is the same as the measure of the arc it intercepts. Our arc shows a measure of 40°; this measure is NOT the same as the length. Measures are in degrees while length is in inches, or cm, or meters, etc. Going off that info, our central angle measures 40°. Filling in the formula and using 3.1415 for π:

[tex]AL=\frac{40}{360}*2(3.1415)(3)[/tex]. I'm going to reduce that fraction a bit (and I'll use the same reduction in the Area of a sector coming up next):

[tex]AL=\frac{1}{9}*2(3.1415)(3)[/tex] which makes

AL = 2.09 units. Now for Area of the Sector. The formula is almost identical, but instead uses the idea that the area of a circle is πr²:

[tex]A_s=\frac{\theta}{360}*\pi r^2[/tex] where θ is, again, the measure of the central angle (which is the same as the measure of the arc it intercepts). Filling in:

[tex]A_s=\frac{1}{9}*(3.1415)(3)^2[/tex] which simplifies a bit to

[tex]A_s=\frac{1}{9}*(3.1415)(9)[/tex]. As you can see, the 9's cancel each other out, leaving you with

[tex]A_s=3.14[/tex] units²

Answer:

Step-by-step explanation:

[tex]Arc \ Length = 2 \pi r \frac{ \theta}{360}[/tex]

[tex]Sector \ Area = \pi r^2 \frac{ \theta }{360}[/tex]

[tex]1) Arc \ Length = 2 \pi \times 3 \times \frac{40}{360} = 2\pi \times 3 \times \frac{1}{9} = \frac{2}{3} \pi = 2.09[/tex]

  [tex]Sector \ Area = \pi \times 9 \times \frac{40}{360} = 9\pi \times \frac{1}{9} = \pi = 3.14[/tex]

[tex]2) Arc \ Length = 2 \pi \times 5 \times \frac{88}{360}= 7.68[/tex]

  [tex]Sector \ Area = \pi \times 25 \times \frac{88}{360} = 19.2[/tex]

[tex]3) Arc \ Length = 2 \pi \times 6 \times \frac{260}{360} = 27.22[/tex]

  [tex]Sector \ Area = \pi \times 36 \times \frac{260}{360} = 81.68[/tex]

Answer:

Step-by-step explanation:

radius of circle is 12

also there is 2 right angles in the triangle if you wanted to solve this problem yourself

but here's the answer:

arc angle of the triangle inside the sircle is double the angle closest to x.

(the pointy area of the triangle is half the angle length of the arc)

i can add more though:

Answer:

95

Step-by-step explanation:

14 + (42 + 7) + 32

14 + 49 + 32

63 + 32

95

Answer:

95

Step-by-step explanation:

Let's use BEDMAS to solve this (Brackets, Exponents, Division, Multiplication, Addition, Subtraction)

1. Calculate the brackets.

42 + 7 = 49

2. Add 14 + 49 + 32

14 + 49 + 32 = 95

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Have a great summer :)

Answer:

3/25

Step-by-step explanation:

Answer:

=325

Showing Work:

12%=12100

=0.12

=0.121×100100

=12100

=325

goodStep-by-step explanation:

Answer:

x = ±3 sqrt(2)

Step-by-step explanation:

x^2 = 18

Take the square root of each side

sqrt(x^2) = sqrt(18)

x = ± sqrt(18)

x =±sqrt(9*2)

x = ±sqrt(9) sqrt(2)

x = ±3 sqrt(2)

Answer: Should be (3, 1) :)

Step-by-step explanation:

Answer: (4,-8)

Step-by-step explanation:

you look at the point it is and flip it to a negative

Step-by-step explanation:

[tex]\frac{120+30}{\frac{66}{1126}-8*3+17-4*4 }[/tex]

[tex]\frac{-42225}{6458}[/tex]

Answer:

The base of the ladder is 3.2 meters far from the wall.

Step-by-step explanation:

We need to calculate the base of a right triangle. The given information is:

h: hypotenuse = length of the ladder = 6 m      

b: is the base =?

θ: is the angle between the hypotenuse and the base = 58°

To find the base we can use the following trigonometric equation:

[tex]cos(\theta) = \frac{b}{h}[/tex]

[tex] b = cos(\theta)*h = cos(58)*6 = 3.2 m [/tex]

Therefore, the base of the ladder is 3.2 meters far from the wall.

I hope it helps you!

Answer:

Max

Step-by-step explanation:

the function given that h = -16t³+64t+10

the general function Equation:

h = at²+bt+c

=> t at the highest point is defined by t = -b/2a

= -64/2(-16) = -64/-32 = 2 second

the total times that the ball hits the ground

= 2× 2 seconds = 4 seconds.

so, Max is right

Answer:

Solution given:

Let h=0=when the ball hit the ground,the height=0.

h= -16t^2 + 64t + 10.

0=16t²-64t-10

8t²-32t-5=0

∆=[tex] \frac{32±\sqrt{32²+4*5*8}}{2*8}=\frac{8±\sqrt{74}}{4}[/tex]

taking positive

t1=[tex] \frac{8+\sqrt{74}}{4}=4.15seconds[/tex]

t2=[tex] \frac{8-\sqrt{74}}{4}(t2<O)(neglected)[/tex]

So

t=4.15seconds closer to 4seconds.So

Max is closer.

[tex]\longrightarrow{\blue{ 2 \: ( \: 32 \: y + 3 \: x \: )}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]64 \: y + 6 \: x[/tex]

[tex] = 2 \: ( \: 32 \: y + 3 \: x \: )[/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer:

2 ( 32y + 3 x)

Step-by-step explanation:

64 y + 6x

factor out 2 from the equation

2 ( 32y + 3 x)

Answer:

At least 12

Step-by-step explanation:

I created 12 different number patterns greater than 540. I hope I was able to help you out :)

Answer:

$1,040

Step-by-step explanation:

First, turn your percent into a decimal

8% = 0.08

Next, multiply your decimal by 65.

0.08 × 65 = 5.2

Lastly, multiply your product by $200

5.2 x $200 = $1,040

Answer:

I am not completly sure, cause the answer might be a bit more complex but, for the spinner on the left 4/8 and the right 1/8 chances

Step-by-step explanation:

Answer: 5/8 is the correct answer.

Step-by-step explanation: The other dude is completely wrong.

Answer:

$213,200,000 or 2.132*10[tex]^{5\\}[/tex]

Step-by-step explanation:

82000*2600

Answer:

t=time

v=speed

t=k/v

8hr=k/36 mi/hr

k=288 mi

t=288 mi24 mi/hr =12 hours.

-------------------

The distance is 288 miles by multiplying 36 by 8.

divide that by 24 mph, and it is 12 hours.

Answer:

they are similar cuz it resembles a "z" pattern. The angles are so the same.

Answer:

Ummmm its just a black screen

Step-by-step explanation:

Answer:

First : Unbiased

Second : Biased

===================================================

Work Shown:

(5 oranges)/(2 dollars) = (20 oranges)/(x dollars)

5/2 = 20/x

5x = 2*20 .... cross multiply

5x = 40

x = 40/5 .... dividing both sides by 5

x = 8

20 oranges cost $8

--------------

Another way to approach the problem is to note that the jump from "5 oranges" to "20 oranges" is "times 4".

5*4 = 20

So we'll apply the "times 4" operation to the old cost of $2 to get the new cost being 2*4 = 8 dollars

Answer:

$8

Step-by-step explanation:

if 5 oranges cost $2 then 1 orange costs 2/5 of a dollar, or 40 cents

20 oranges multiplied by 40 cents is $8

or you can set up a proportion:

2/5 = x/20

cross-multiply to get:

5x = 40

x = 8

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{(x+2)(x+3)^2(x-3)}{(x-4)^2(x+4)}[/tex]

Step-by-step explanation:

i'm going to assume what you have looks like

[tex]\frac{x^2-9}{\frac{x^2-16}{\frac{x^2+5x+6}{x-4}}}[/tex]

Let's start by factoring everything

x²-9= (x+3)(x-3)

x²-16= (x+4)(x-4)

x²+5x+6=(x+3)(x+2)

x-4= x-4

which means what we have looks like

[tex]\frac{(x+3)(x-3)}{\frac{(x+4)(x-4)}{\frac{(x+3)(x+2)}{x-4}}}=\frac{(x+3)(x-3)}{(x+4)(x-4)}\div\frac{x-4}{(x+3)(x+2)}=\frac{(x+3)(x-3)}{(x+4)(x-4)}*\frac{(x+3)(x+2)}{x-4}=\frac{(x+3)^2(x-3)(x+2)}{(x+4)(x-4)^2}[/tex]

And I think that's as simplified as it can get

Answer:

y=1x+27

y=1(3)+27

Y=30

Step-by-step explanation:

X=DAYS

M=DOLLARS

Hope this helps brotha

Answer:

30-12=18

18-18=0

Step-by-step explanation:

2x + 12 = 30

X represents the snacks, 2 represents the $2 per snack, 12 represents the $12 entry fee, and 30 represents the $30 Olivia had.