Which of the following equations is used to find the value of c?

Answer:

3

Step-by-step explanation:

a tangent to a circle makes right angle with the radius at that point ( here the point is B)

thus,

ABC is a right angled triangle

By Pythagoras theorem :-

By Pythagoras theorem :-AC² = AB² + BC²

(r + 2)² = 4² + r²

r² + 4 + 4r = 16 + r²

subtracting r² from both sides and taking 4 common

4(1 + r) = 16

diving both sides by 4

1 + r = 4

r = 3 units

The value of r is,

⇒ r = 3 units

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

AB is tangent to circle C.

Now,

By Pythagoras theorem, we get:-

AC² = AB² + BC²

(r + 2)² = 4² + r²

r² + 4 + 4r = 16 + r²

subtracting r² from both sides and taking 4 common

4(1 + r) = 16

diving both sides by 4

1 + r = 4

r = 3 units

Thus, The value of r is,

⇒ r = 3 units

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Answer:

Tomas

Step-by-step explanation:

Divide Distance by Time

[tex]\frac{distance}{time}[/tex] = speed

Answer:

Tomas is the fastest

Step-by-step explanation:

To find out who is the fastest, divide the distance by the time to get the unit rate. (The amount they drove each hour.)

Maren: 60 / 1 = 60

Safiya: 120 / 3 = 40

Tomas: 84 / 1.2 = 70

Cam: 75 / 1.5 = 50

Tomas has the largest unit rate therefore he is  the fastest.

Answer:  30 cans (buy them by the six-pack; so you'd buy 5 six-packs)

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

Explanation:

Let's say you buy six-packs only. Divide the amount of money you have over the cost per six-pack.

15/(2.59) = 5.7915 which rounds down to 5.

If you buy six-packs only, then you can buy a max of 5 of them. That gets you 5*6 = 30 cans of soda.

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

Now let's say you buy individual cans only. We'll use the same idea mentioned earlier but this time divide over 0.80

15/(0.80) = 18.75 which rounds down to 18

We round down because we can't buy that 19th can of soda (note how 19*0.80 = 15.2 which is larger than 15).

So if you buy individual cans only, then you can get a max of 18 cans.

We see that it's better to go with the six-pack option (in the first section) since we can get 30 cans compared to 18 cans.

Answer:

8.42

Step-by-step explanation:

* means multiply

31.65/5.45 = x/1.45

5.45x = 31.65 * 1.45

5.45x = 45.8925

x = 45.8925/5.45

x = 8.42064220183

Answer:

30 if that is an [tex]x^{2}[/tex] in g(x)

Step-by-step explanation:

f(2) = 2x + 1

      = 2(2) + 1

      = 4 + 1

f(2) = 5      

g(5) = [tex]x^{2}[/tex] + 5

      = [tex]5^{2}[/tex] + 5

      = 25 + 5

g(5) = 30

Answer: 30

Step-by-step explanation:

First find f(2)

f(2) = 2(2) + 1 = 4 + 1 = 5

Therefore g(f(2)) = g(5)

Now solve for g(5)

g(5) = (5)² + 5 = 25 + 5 = 30

Answer: The b-value is the middle number, the number next to the X

Hello,

Answer A

Indeed:

[tex]c^2=c^2+b^2-2ab*cos(\theta) < a^2+b^2\\\\-cos(\theta)<0\\\\cos(\theta)>0\ \Longrightarrow \theta < 90^o[/tex]

True statements are:

A.  [tex]\theta[/tex] is an acute angle.

C. The triangle is a right triangle.

D. The triangle is not a right triangle.

An angle is a combination of two rays (half-lines) with a common endpoint.

Given:

a² + b² > c²

as, the triangle with sides a, b and c.

If this is a right triangle, then the condition a² + b² > c² apply.

Using cosine law.

angle> 90 degrees which is an obtuse angle.

Also, cos [tex]\theta[/tex] is negative.

Hence, the conditions that are true are A, C and D.

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Answer:

ayan po answer nasa picture

Answer:

3

Step-by-step explanation:

9½=√9=3

ie. a number to the power of ½ is the same as the square root of the number

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]\huge x=-6[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\-8x-4(x-4)=88\\-------------\\\rightarrow -8x-4x+16=88\\\\\rightarrow -12x + 16 = 88\\\\\rightarrow -12x + 16 - 16 = 88 - 16\\\\\rightarrow -12x = 72\\\\\rightarrow \frac{-12x=72}{12}\\\\\rightarrow \boxed{x=-6}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer: x = -6

Step-by-step explanation: Start by changing the - 4 to plus a negative 4 so that you know you're distributing a -4 through the parentheses.

So we have -8x - 4x + 16 = 88.

Simplifying the left side further gives us -12x + 16 = 88.

Now subtract 16 from both sides to get -12x = 72.

From here it should be easy to find the x = -6.

Hello,

A=(1,2) ==> A'=(1,2)+(1,1)=(2,3)

B=(6,2) ==> B'=(6,2)+(1,1)=(7,3)

C=(4,4) ==> C'=(4,4)+(1,1)=(5,5)

D=(1,4) ==> D'=(1,4)+(1,1)=(2,5)

Answer:

Step-by-step explanation:

Second hand on a clock rotates at rate 360 degrees per 60 seconds.

360 degrees - 60 sec

x degrees - 15 sec

90 clockwise rotation (none hand of a clock rotates counter-clockwise :))

Answer:

90 degrees clockwise rotation

Step-by-step explanation:

Answer:

Option 3 is correct

tex]\frac{1yd}{36 in}=\frac{7yd}{252 in}[/tex]

Step-by-step explanation:

1.[tex]\frac{1 in}{2.54 cm}=\frac{7 in}{17.68 cm}[/tex]

1 in=2.54 cm

[tex]7 in=2.54\times 7=17.78 cm[/tex]

[tex]\frac{1 in}{2.54 cm}=\frac{1 in}{1 in}=1[/tex]

[tex]\frac{1 in}{2.54 cm}\neq \frac{7 in}{17.68 cm}[/tex]

Hence, it is not correct.

2.[tex]\frac{1 ft}{12 in}=\frac{7ft}{74 in}[/tex]

1 foot=1 2in

[tex] 7ft=7\times 12=84 foot[/tex]

[tex]\frac{1 ft}{12 in}=1[/tex]

[tex]\frac{7ft}{74 in}\neq 1[/tex]

[tex]\implies \frac{1 ft}{12 in}\neq \frac{7ft}{74 in}[/tex]

Hence, it is not correct.

3.[tex]\frac{1yd}{36 in}=\frac{7yd}{252 in}[/tex]

1 yd=36 in

[tex]\frac{1yd}{36 in}=\frac{36}{36}=1[/tex]

[tex]7yd=7\times 36=252 in[/tex]

[tex]\frac{7yd}{252 in}=\frac{252 in}{252 in}=1[/tex]

[tex]\implies \frac{1yd}{36 in}=\frac{7yd}{252 in}[/tex]

Hence, it is correct.

4.[tex]\frac{1 m}{3.28ft}=\frac{7m}{22.86ft}[/tex]

1 m=3.28 ft

[tex]\frac{1 m}{3.28ft}=\frac{3.28}{3.28}=1[/tex]

[tex]7m=7\times 3.28=22.96 ft[/tex]

[tex]\frac{7m}{22.86ft}\neq 1[/tex]

[tex]\frac{1 m}{3.28ft}\neq \frac{7m}{22.86ft}[/tex]

Hence, option is not correct.

Answer:

1506meters

Step-by-step explanation:

1hour-60minutes

which means half an hour is 30minutes,so it's more like they are asking you to find how far the swimmer can swim in 30minutes

50.2-1min

x -30min

x=50.2×30

x=1506meters

Answer:

Cylinder H has the greater volume.

Step-by-step explanation:

Recall that the volume of a cylinder is given by:

[tex]\displaystyle V=\pi r^2h[/tex]

Where r is the radius and h is the height.

Cylinder H has a radius of 4.5 meters and a height of 3 meters. Thus, its volume is:

[tex]\displaystyle \begin{aligned} V&=\pi(4.5)^2(3)\\&=60.75\pi \\&\approx190.8518\text{ m}^3\end{aligned}[/tex]

Cylinder J has a diameter of 7 meters and a height of 4.5 meters. The radius is half the diameter, so Cylinder J's radius is 3.5 meters. Thus, its volume is:

[tex]\displaystyle \begin{aligned}V&=\pi(3.5)^2(4.5)\\&=55.125\pi \\&\approx 173.1803\text{ m}^3\end{aligned}[/tex]

Thus, Cylinder H has the greater volume.

five I think I am not sure

Given equation of the Circle is ,

[tex]\sf\implies x^2 + y^2 = 25 [/tex]

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]

Here we can see that the distance of point from centre is less than the radius.

Hence the point lies within the circle .

Answer:

57%

Step-by-step explanation:

200+245+125 = 570

570/1000 = .57

Answer:

57%

Step-by-step explanation:

First find the total number of families in the sample.

Total = 350 + 200 + 245 + 125 + 66 + 10 + 4

Total = 1000

Next find the number of families that have 3, 4 or 5 people.

Total(3,4 or 5) = 200 + 245 + 125

Total(3,4 or 5) = 570

Now the % = (Total 3,4 or 5) / Total ) * 100

% = 570 / 1000 * 100

% = 57%

Answer:i dont know

Step-by-step explanation:

Answer:

x = - 7, x = - 1

Step-by-step explanation:

Given

x² + 8x + 7 = 0

Consider the factors of the constant term (+ 7) which sum to give the coefficient of the x- term (+ 8)

The factors are + 7 and + 1 , since

7 × 1 = 7 and 7 + 1 = 8 , then

(x + 7)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x + 1 = 0 ⇒ x = - 1

Answer:

[tex]x=-1,-7[/tex]

Step-by-step explanation:

[tex]x^2+8x+7=0[/tex] where a [tex]\neq[/tex] 0 so a = 1 b = 8 c = 7

Quadratic Formula: [tex]x=-b\frac{\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=-8\frac{\sqrt{8^2-4(1)(7)} }{2(1)}[/tex]

[tex]x=-8\frac{\sqrt{64-28} }{2}[/tex]     Evaluate the exponent and multiply 4ac

[tex]x=-8\frac{\sqrt{36} }{2}[/tex]          Subtract b^2 - 4ac and multiply 2a

[tex]x=-8\frac{\sqrt{6} }{2}[/tex]           Solve for the sqrt root of 35

x = - 8 ± 6/2 =

x = - 8 + 6/2 = -1

x = - 8 - 6/2 = -7

Given:

The function is:

[tex]F(x)=x^3[/tex]

To find:

The function G(x) if the graph of F(x) can be compressed vertically and shifted to the right to produce the graph of G(x).

Solution:

The transformation is defined as

[tex]g(x)=kf(x+a)+b[/tex]                .... (i)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

It is given that F(x) can be compressed vertically and shifted to the right to produce the graph of G(x). So, the value of k must be lies between 0 and 1, and a<0.

In option A, [tex]0<k<1[/tex] and [tex]a<0[/tex]. So, this option is correct.

In option B, [tex]0<k<1[/tex] and [tex]a>0[/tex]. So, this option is incorrect.

In option C, [tex]k>1[/tex] and [tex]a>0[/tex]. So, this option is incorrect.

In option D, [tex]k>1[/tex] and [tex]a<0[/tex]. So, this option is incorrect.

Therefore, the correct option is A.

Answer:

The speed of the plane with no wind is 378 miles per hour.

Step-by-step explanation:

Since at maximum speed, an airplane travels 1680 miles against the wind in 5 hours, and flying with the wind. the plane can travel the same distance in 4 hours, to determine what is the speed of the plane with no wind, the following calculation must be performed:

Against the wind = 1680/5 = 336

With the wind = 1680/4 = 420

420 - ((420 - 336) / 2) = X

420 - 42 = X

378 = X

Therefore, the speed of the plane with no wind is 378 miles per hour.

Answer:

Domain: {-3, -1, 1}

Range: {-1, 2, 4, 5}

Step-by-step explanation:

The domain is all the x-values, and the range is all the y-values. When listing values, repeated values are only written down once.

Answer:

Step-by-step explanation:

1,

-10,20,-40,80,...

common ratio=20/-10=-2

it is a geometric sequence.

2.

15,-5,-25,-45

common difference=-5-15=-20

it is an arithmetic sequence.

Answer:

possibility of yellow÷ total possibilities

1÷8

1/8

Step-by-step explanation:

hope this is helpful

Answer:

Center (h, k) = 2 and -3

Radius = 4

Step-by-step explanation:

Given the mathematical expression;

(x - 2)² + (y + 3)² = 16  ......equation 1.

The general equation for a circle is given by the formula;

x² + y² + 2hx + 2ky + c = 0 ......equation 2.

Where the center is C(-h, -k)

Similarly, the standard form of the equation of a circle is;

(x - h)² + (y - k)² = r² ......equation 3.

Where;

Comparing equation 1 and equation 3, we have;

The center of the circle, C(h, k) are 2 and -3

Radius = √16 = 4

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3:8

The ratio of small circle

12:32

If we divide both of them by 4 we get 3:8