Triangle ABC is shown below.
What is the length of line segment AC?
7
DS
9
2x
3x - 7
O 14
18
B
4x - 10
с
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Answer: 196πcm²

Given

Diameter = 14

Radius = d/2

= 14/2

= 7

Surface area = 4πr²

Take π = 22/7

= 4×22/7×7×7

= 616 cm²

Must click thanks and mark brainliest

[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\purple{Formula \: \: Using \: = \: 4 \: \pi \: {r}^{2} }}}}}\end{gathered}[/tex]

[tex]\bf \ \implies \: \: r \: = \: \frac{Diameter}{2} \\ [/tex]

[tex]\bf \ \implies \: \: r \: = \: \frac{14}{2} \\ [/tex]

[tex]\bf \ \implies \: \: r \: = \: \cancel\frac{14}{2} \: \: \large ^{7} \: \\ [/tex]

[tex]\bf \ \implies \: \: r \: = \: 7 \: cm[/tex]

[tex]\bf \large \longrightarrow \: \: 4 \: \pi \: {r}^{2} [/tex]

[tex]\bf \large \longrightarrow \: \: 4 \: \times \: \pi \: \times {7} \: ^{2} [/tex]

[tex]\bf \large \longrightarrow \: \: 4 \: \times \: \pi \: \times 49[/tex]

[tex]\bf \large \longrightarrow \: \: 196 \: \pi \: {cm}^{2} [/tex]

Hence , the surface area of sphere is 196 π cm²

Answer:

34

Step-by-step explanation:

Angle XYZ is an inscribed angle and arc XZ is the arc it intercepts

An inscribed angle is equal to half the measure of its intercepted arc

Hence Angle XYZ = half of arc XZ

If arc XZ = 68 then angle XYZ = half of 68

68/2=34

XYZ = 34

Answer:

No.B is correct statement

Answer:

soln:

(5.5 × 107)

(3.2 × 10')

+ 2 × 105

_______________

8.8. ×.1011

Answer:

We want to find a solution of the system:

x^2 + y^2 > 49

y ≤ –x^2 – 4

Here we do not have any options, so let's try to find a general solution.

First, we can remember that the equation of a circle centered in the point (a, b) and of radius R is:

(x - a)^2 + (y - b)^2 = R^2

If we look at our first inequality, we can write it as:

x^2 + y^2 > 7^2

So the solutions of the first inequality are all the points that are outside (because the symbol used is >) of the circle of radius R = 7 centered in the origin.

From the other equation, we would get:

y ≤ –x^2 – 4

This is parabola, anything that is in the graph of the parabola or below will be a solution for this inequality.

Then the solutions of the system, are the ones that are in the region of solutions for both inequalities.

You can see the graph below, where both regions are graphed. The intersection of these regions is the region of the solutions for the system of inequalities:

by looking at the graph, we can see a lot of points that are solutions, like:

(0, -10)

(0, -15)

(2, -10)

etc.

Answer:

C on Edge or (1,-9)

Step-by-step explanation:

Answer:

x = 2 ±sqrt( 97)

Step-by-step explanation:

log10(x^2 -4x+7) =2

Raise each side to the base 10

10 ^ log10(x^2 -4x+7) =10^2

x^2 -4x +7 = 100

Subtract 7 from each side

x^2 -4x+7-7 = 100-7

x^2 -4x = 93

Complete the square

-4/2 = -2  (-2)^2 = 4

Add 4 to each side

x^2 -4x+4 = 93+4

(x-2)^2 = 97

Take the square root of each side

sqrt((x-2)^2 )=±sqrt( 97)

x-2 = ±sqrt( 97)

Add 2 to each side

x = 2 ±sqrt( 97)

Answer:

a)sin153°=0.454

cos153°=   -0.891

tan153°=   -0.510

b)sin 204°=  -0.407

cos204°=    -0.914

tan204° =   0.445

c)sin320°=   -0.643

cos320° =  0.766

tan320°=  -0.839

Step-by-step explanation:

Answer:

156

Step-by-step explanation:

f(x)= 4^(2x) -100

Let x =2

f(2)= 4^(2*2) -100

   = 4^4 - 100

   = 256 -100

   = 156

Given that the vertex is at (50, 1000), the max profit is $1000 when 50 items are produced

Answer: Second week

Step-by-step explanation:

Given

In first week, campers choose programmes in the ratio of [tex]7:5:8[/tex]

In second week, this ratio becomes [tex]7:6:4[/tex]

Suppose 100 campers Joined the camp

Number of hikers who choose camp craft in first week are

[tex]\Rightarrow \dfrac{7}{7+5+8}\times 100=\dfrac{7}{20}\times 100\\\\\Rightarrow 35[/tex]

Number of hikers who choose camp craft in second week are

[tex]\Rightarrow \dfrac{7}{7+6+4}\times 100=\dfrac{7}{17}\times 100\\\\\Rightarrow 41.17\approx 41[/tex]

Therefore, in second week more campers take part in camp craft.

If 100 campers take part then, 6 more campers takes part in camp craft.

[tex] \frac{9}{41} [/tex]

Step-by-step explanation:

The ratio cosine tell us that

In other words,

[tex] \cos(x) = \frac{adj}{hyp} [/tex]

The side adjacent to angle a is 9. The hypotenuse is 41.

So

[tex] \cos(a) = \frac{9}{41} [/tex]

Answer:

Hence the greatest number of books that could be on the shelf is 30.

Step-by-step explanation:

Step 1:-

Here the given number of books is m,  

m < 45.  

If they are arranged into piles of five books, each no books would remain.  

m is divisible by 5.  

The last digit of m would be 5 or 0.    

The same number of books, when arranged with piles of 7 books each, two books remain.  

m-2 is divisible by 7.  

Step 2:-  

The last digit of m is 5 or 0.  

m-2 will have the last digit 3 or 8.    

Multiples of 7 are 7,14,21,28,35, 42;  

among which only number 28 has the last digit 8 or 3.    

m - 2 = 28  

m = 30  

The greatest number of books that could be on the shelf is 30.

Answer:

15 lessons for $80.

Step-by-step explanation:

Answer:

7 sqrt(2) = c

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

7^2 + 7^2 = x^2

49+49 = c^2

98 = c^2

Taking the square root of each side

sqrt(98) = sqrt(c^2)

sqrt(49*2) = c

7 sqrt(2) = c

Answer:

Therefore, the value of x is 5.

Step-by-step explanation:

We can match each equation to find the solutions.

[tex]8x-40=x^{2}-2x-15[/tex]

[tex]0=x^{2}-2x-8x-15+40[/tex]

[tex]x^{2}-10x+25=0[/tex]

Now, we need solve this quadratic equation.

[tex](x-5)^{2}=0[/tex]

Therefore, the value of x is 5.

I hope it helps you!

Answer:

4 1/3 of her hair

Step-by-step explanation:

Just add 2 1/6 + 2 1/6 and there you go

There is the total amount of her hair she cut

Answer:

4

Step-by-step explanation:

(a,a),(a,b),(b,a),(b,b)

Answer:

5 trees per day

Step-by-step explanation:

Answer:

5 trees per day

Step-by-step explanation:

(1, 5)

(2,10)

the day increases by 1 and the trees increase by 5

Answer:

40

Step-by-step explanation:

here

3200/80

1600/40

800/20

400/10

40

Given:

The equation is:

[tex]2540=\dfrac{22}{7}r^2(20)[/tex]

To find:

The solution for the given equation.

Solution:

We have,

[tex]2540=\dfrac{22}{7}r^2(20)[/tex]

It can be written as:

[tex]\dfrac{2540\times 7}{22\times 20}=r^2[/tex]

[tex]\dfrac{17780}{440}=r^2[/tex]

[tex]\dfrac{889}{22}=r^2[/tex]

Taking square root on both sides, we get

[tex]\sqrt{\dfrac{889}{22}}=r[/tex]               [Radius cannot be negative]

[tex]r=6.3568145[/tex]

[tex]r\approx 6.36[/tex]

Therefore, the value of r is about 6.36 cm.

Answer:

sorry I don't know.....

Answer:

-3

Step-by-step explanation:

Input -3 for x.

2*-3 - 9

then simplify.

Answer:

x = 1, y = −1

x = 5/2, y = 1/2

Step-by-step explanation:

From the question given above, the following data were obtained:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

We can obtain the solutions to the equation as follow:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

Substitute the value of y in equation 2 into equation 1

y = 2x² − 6x + 3

y = x − 2

2x² − 6x + 3 = x − 2

Rearrange

2x² − 6x − x + 3 + 2 = 0

2x² − 7x + 5 = 0

Solve by factorization

Obtain the product of 2x² and 5. The result is 10x².

Find two factors of 10x² such that their sum will result to −7x.

The factors are −2x and −5x.

Replace −7x in the equation above with −2x and −5x as shown below:

2x² − 2x − 5x + 5 = 0

2x(x − 1) − 5(x − 1) = 0

(x − 1)(2x − 5) = 0

x − 1 = 0 or 2x − 5 = 0

x = 1 or 2x = 5

x = 1 or x = 5/2

Substitute the value of x into equation 2 to obtain y

y = x − 2

x = 1

y = 1 − 2

y = −1

x = 5/2

y = x − 2

y = 5/2 − 2

y = (5 − 4)/2

y = 1/2

SUMMARY:

x = 1, y = −1

x = 5/2, y = 1/2

Answer:

14.49 inches......I think this help you.....I am not dam sure this is right or not....

Answer:

-10ab

STEP BY STEP EXPLANATION

2a (3a + b) -3a(2a +4b)

6a² + 2ab - 6a²- 12ab

2ab-12ab 6a²-6a²

-10ab

Hope this will help you if not then sorry :)

Answer:

[tex]2a( 3a + b)- 3a(2a+4b)[/tex]

Expand by distributing terms.

[tex]6a ^{2} +2ab-3a(2a+4b)[/tex]

Expand by distributing terms.

[tex]6a 2+2ab-(6a^{2} +12ab)[/tex]

Remove parentheses

.[tex]6a ^{2} +2ab-6a^{2} -12ab[/tex]

Collect like terms.

[tex](6a^{2}-6a^{2})+(2ab-12ab)[/tex]

[tex]=-10ab[/tex]

OAmalOHopeO

Answer:

42

Step-by-step explanation:

prime factorisation of 1764 = 2^2 × 3^2 × 7^2

hence,

√1764 = √(2^2 × 3^2 × 7^2) =2 x 3 x 7 = 42

Answer:

42

Step-by-step explanation:

1764 = 2 * 882

        = 2 * 2 * 441

        = 2 * 2 *  3 * 147

        = 2 * 2 * 3 * 3 * 49

        = 2 * 2 * 3 * 3 * 7 * 7

[tex]\sqrt{1764} = \sqrt{2*2*3*3*7*7} = 2*3*7 = 42[/tex]

Answer:

[tex]( \frac{5}{9} ) ^{2} = \frac{25}{81} [/tex]