what is the length of arc S? angle in radians ​

Answer:

5 cm

Step-by-step explanation:

As we can see in the attached figure that G is the point at which the three medians of the triangle meet  i.e we called the centroid

And, according to the property of the centroid, it divides the medians in ratio i.e 2:1

DG: CG = 2 : 1

Since the DG is 10 cm

So, the CG would be half of DG i.e 5 cm

Hence, the CG is 5 cm

Therefore the first option is correct

Answer:

the answer is 5 cm

Step-by-step explanation:

Answer:

The fence must have:

220 meters

Step-by-step explanation:

The perimeter of the field is equal to the long of the fence round the field.

then:

perimeter = 2(long + wide)

perimeter = 2(85 + 25)

perimeter = 2*110

perimeter = 220m

Answer:

The axis of symmetry of parabola is the equation where it cuts the middle of the graph.

So the axis of symmetry is x = 2 .

Answer:

Hey there!

Circumference: [tex]2\pi r+95+95[/tex]

Area: [tex]\pi r^2+70(95)[/tex]

r=35

Circumference: 410

Area: 10498.

Hope this helps :)

Answer:

Area=  10498.5 cm²

Step-by-step explanation:

Area of rectangle= l x w

= 95 x 70 = 6650

Area of circle = πr²

= π x 35²

= 1225π

=3838.5 cm²

Area of shape: 6650 + 3848.5 = 10498.5 cm²

Answer: 5.0693 ounces

Step-by-step explanation:

For a 6 ounce cup to overflow, then the cup content is beyond 6 ounce, at 2%

P(x > 6) = 2% = 0.02; similarly

P(x<6) = 1 - P(x > 6)'.

P(x<6) = 1 - 0.02 = 0.98

The z-score for 0.98 = 2.326

The z - formular for a normally distributed goes thus :

Zscore =(observed score - mean) / standard deviation

Substituting the vamus :

2.326 = (6 - mean) / 0.4

2.326 × 0 4 = 6 - mean

0.9304 = 6 - mean

Mean = 6 - 0.9304

Mean = 5.0693

Answer:

Step-by-step explanation:

In an isosceles trapezoid, two pairs of adjacent angles are supplementary. It means that the sum of the adjacent angles is 180°

Looking at the diagram, angle X and angle W are adjacent angles. It means that

X + W = 180

Since X = 105, then

105 + W = 180

W = 180 - 105 = 75°

Since W = b + 25°, then

b + 25° = 75

b = 75 - 25 = 50°

Answer: In an isosceles trapezoid, two pairs of adjacent angles are supplementary. It means that the sum of the adjacent angles is 180°Looking at the diagram, angle X and angle W are adjacent angles. It means that X + W = 180Since X = 105, then105 + W = 180W = 180 - 105 = 75°Since W = b + 25°, thenb + 25° = 75b = 75 - 25 = 50°

Step-by-step explanation:

Answer:

36°

Step-by-step explanation:

<U + < V + <W = 180° (sum of angles in a triangle)

<W = 54°

The tangent is always perpendicular to the radius drawn to the point of tangency...

therefore,

<U = 90°

90° + <V + 54° = 180°

144° + <V = 180°

<V = 180° - 144°

<V = 36°

Answer:

V=36

Step-by-step explanation:

tangent makes rigt angle with radius angle U=90

W+V+U=180

V=180-90-54

V=36

Answer:

541.4 m²

Step-by-step Explanation:

Step 1: find m < V

V = 180 - (50+63) (sum of the angles in ∆)

V = 67

Step 2: find side length of XW using the law of sines

[tex] \frac{XW}{sin(V)} = \frac{XV}{sin(W)} [/tex]

Where,

V = 67°

W = 63°

XV = 37 m

XW

[tex] \frac{XW}{sin(67)} = \frac{37}{sin(63)} [/tex]

Multiply both sides by sin(67) to solve for XW

[tex] \frac{XW}{sin(67)}*sin(67) = \frac{37}{sin(63)}*sin(67) [/tex]

[tex] XW = \frac{37*sin(67)}{sin(63)} [/tex]

[tex] XW = 38.2 m [/tex] (to nearest tenth)

Step 3: find the area using the formula, ½*XW*XV*sin(X)

area = ½*38.2*37*sin(50)

Area = 541.4 m² (rounded to the nearest tenth.

Answer:

f(x) =  3x⁴ - [tex]\frac{2X^{3} }{3}[/tex] - 17x +  [tex]\frac{68}{3}[/tex]

Step-by-step explanation:

To find f'(x), we will follow the steps below:

We will start by integrating both-side of the equation

∫f'(x) = ∫(12x^3 - 2x^2 - 17)dx

f(x)  = 3x⁴ - [tex]\frac{2X^{3} }{3}[/tex] - 17x + C

Then we go ahead and find C

f(1) = 8

so we will replace x by 1 in the above equation and solve for c

f(1)  = 3(1)⁴ - [tex]\frac{2(1)^{3} }{3}[/tex] - 17(1) + C

8 = 3 - [tex]\frac{2}{3}[/tex] - 17 + C

C =8 - 3 + 17 + [tex]\frac{2}{3}[/tex]

C = 22 +  [tex]\frac{2}{3}[/tex]

C =[tex]\frac{66 + 2}{3}[/tex]

C = [tex]\frac{68}{3}[/tex]

f(x) =  3x⁴ - [tex]\frac{2X^{3} }{3}[/tex] - 17x +  [tex]\frac{68}{3}[/tex]

Answer:

3√6

Step-by-step explanation:

tan60=opp/adj

opp(d)=tan60*3√2=√3*3√2=3√6

Answer: the answer is 151

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos ? = adj / hyp

cos ? = 30/48

Taking the inverse cos of each side

cos ^ -1 cos ? = cos ^ -1 ( 30/48)

? = 51.31781255

To the nearest degree

? = 51

Since this is a right triangle, we can use trig functions

cos ? = adj / hyp

cos ? = 40/53

Taking the inverse cos of each side

cos ^ -1 cos ? = cos ^ -1 ( 40/53)

? = 40.99935365

To the nearest degree

? = 41

Since this is a right triangle, we can use trig functions

tan ? = opp/adj

tan ? = 1/2

Taking the inverse tan of each side

tan ^ -1 tan ? = tan ^ -1 ( 1/2)

? = 26.56505118

To the nearest degree

? = 27

Since this is a right triangle, we can use trig functions

sin ? = opp / hyp

sin ? = 29/35

Taking the inverse sin of each side

sin ^ -1 sin ? = sin ^ -1 ( 29/35)

? = 55.95226763

To the nearest degree

? = 56

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

All the triangles are right triangles, we can use trigonometric functions.

5) cos θ  = adj / hyp

cos x = 30/48

cos⁻¹ cos x = cos⁻¹ (30/48)

x = 51.31781...

x ≈ 51

6) cos θ = adj / hyp

cos x = 40/53

cos⁻¹ cos x = cos⁻¹ (40/53)

x = 40.99935...

x ≈ 41

7) tan θ = opp/adj

tan x = 1/2

tan⁻¹ tan x = tan⁻¹ (1/2)

x = 26.56505...

x ≈ 27

8) sin θ = opp / hyp

sin x = 29/35

sin⁻¹ sin x = sin⁻¹ (29/35)

x = 55.95227...

x ≈ 56

Answer: A. 51%

Step-by-step explanation:

Area of circle = [tex]\pi r^2[/tex] , where r = radius of the circle.

In the figure below, we have the complete question.

According to that,

Radius of outer circle = 7ft

Radius of inner circle = 5ft

The probability that the thumbtack will be placed on the inner circle

[tex]=\dfrac{\text{Area of inner circle}}{\text{Area of outer circle}}\\\\=\dfrac{\pi (5)^2}{\pi (7)^2}\\\\=\dfrac{25}{49}[/tex][π is canceled from numerator and denominator

in percent, [tex]\dfrac{25}{49}\times100=51.0204081633\%\approx51\%[/tex]

So, the probability that the thumbtack will be placed on the inner circle = 51%

Hence, the correct option is A. 51%.

Answer:

y = -8

Step-by-step explanation:

Start by filling 8 in place of x

y = 8 - 2(8)

Multiply -2(8)

y = 8 - 16

Subtract 16 from 8

y = -8

the answer would end up rounding to 31. :)

9.77 in

Step-by-step explanation:

arc length is 80/360 × 2 × pi × radius

2/9 × 2 × 22/7 × 7

88/9

9.77in

Answer:

arc length = 9,76(8) inches

Step-by-step explanation:

Formula

2π·r(x°/360°)

= 2·3,14·7in·80°/360°

= 3516,8in/360

= 9,76(8) inches

Answer:

A. [tex]\frac{3}{5}[/tex]

B. [tex]\frac{7}{10}[/tex]

C. B (you already got that right)

Step-by-step explanation:

To find the probability of something, we have to see how many times it happened over the total amount of attempts.

On Tuesday the target was hit 18 times in 30 attempts. So our probability fraction is [tex]\frac{18}{30}[/tex] which simplifies to [tex]\frac{3}{5}[/tex].

Looking at the total results, we can see Ben hit the target 84 times out of 120, so the fraction is [tex]\frac{84}{120}[/tex] which simplifies to [tex]\frac{7}{10}[/tex].

There’s always one rule of statistics/probability - the more data the better. If we want to create a more reliable probability, we’d want more data, and the total data gives us more than just Tuesday’s Data.

Hope this helped!

Answer:

6.93 cm

Step-by-step explanation:

You have a right triangle (90°), so you do as follow:

If I understand correctly, you are looking for the hypotenuse so

[tex]cos(30) = \frac{PQ}{QR} = \frac{8 cm}{QR}[/tex]

That is equal to [tex]QR = cos(30)*8 cm = 6.928 cm[/tex]

Answer:

12

Step-by-step explanation:

Correct question :

There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 7 9 . There are 28 red marbles in the bag and each is equally likely to be chosen. Work out how many marbles in total there must be.

Answer:

Total number of marbles = 36

Step-by-step explanation:

Marbles in bag: Red and Blue only

Probability of randomly choosing a red marble = 7/9

Number of red marbles = 28

Total number of marbles in the bag =?

Probability = required outcome / Total possible outcomes

P(red marble) = required outcome (number of red marbles) / Total possible outcomes(total number of marbles

7/9 = 28 / total number of marbles

Total number of marbles * 7/9 = 28

Total number of marbles = 28 ÷ 7/9

Total number of marbles = 28 * (9/7)

= 252 / 7

Total number of marbles = 36

Answer:

The coordinates of point B are (-2, 2).

Step-by-step explanation:

Given:

Point A (2,−8)

Point C (−4,7)

Point B divides the line AB such that the ratio AB:BC is 2:1.

To find: The coordinates of point B.

Solution:

We can use the segment formula here to find the coordinates of point B which divides line AC in ratio 2:1

[tex]x = \dfrac{mx_{2}+nx_{1}}{m+n}\\y = \dfrac{my_{2}+ny_{1}}{m+n}[/tex]

Where [tex](x,y)[/tex] is the co-ordinate of the point which  

divides the line segment joining the points [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] in the ratio [tex]m:n[/tex].

m = 2

n = 1

As per the given values  

[tex]x_{1} = 2\\x_{2} = -4\\y_{1} = 8\\y_{2} = 7[/tex]

Putting the values in the formula:

[tex]x = \dfrac{2 \times (-4)+1\times 2}{2+1}=\dfrac{-8+2}{3} =-2\\y = \dfrac{2\times 7+1 \times (-8)}{2+1} = \dfrac{6}{3} =2[/tex]

So, the coordinates of point B are (-2, 2).

Answer:

The 1st selection is appropriate.

_____

2nd: the rotation would need to be 90° CCW

3rd, 4th: rotation or double reflection will give the original orientation. This figure is reflected an odd number of times, so has its orientation reversed.

Hope it helps.. Mark brainliest

The sequence of transformations are reflection over the y-axis and then a rotation 90 clockwise about the origin.

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

Given that, figure G is rotated 90° clockwise about the origin and then reflected over the x-axis, forming figure H.

Vertices of triangle G are (-3, 1), (-1, 2) and (-2, 5).

The reflection of point (x, y) across the y-axis is (-x, y).

On reflection over x-axis, we get coordinates as (3, 1), (1, 2) and (2, 5)

90° clockwise rotation: (x, y) becomes (y, -x)

On 90° clockwise rotation, we get coordinates as (1, -3), (2, -1) and (5, -2)

Triangle H has points (2, -1), (1, -3), (5, -2).

Hence, the sequence of transformations are reflection over the y-axis and then a rotation 90° clockwise about the origin.

Learn more about the rotation of 90° counterclockwise here:

brainly.com/question/1571997.

#SPJ6

Answer:

Step-by-step explanation:

Hello!

To compare different prices of several brands of a product the best is to express the price for the same quantities of product.

Since the three options are original in 300g, 450g and 600g, I'll express all prices on a base of 100g of product. You can use simple rule of three for this:

Option 1

300g cost $3.89

100g cost [tex]\frac{100*3.89}{300} = $1.296[/tex]

Option 2

450g cost $ 4.77

100g cost [tex]\frac{100*4.77}{450}= $1.06[/tex]

Option 3

600g cost $ 6.59

100g cost [tex]\frac{100*6.59}{600}= 1.098[/tex]

So:

Option 1: $1.296/ 100g

Option 2: $1.06/100g

Option 3: $1.098/100g

The cheapest option is number 2

I hope this helps!

Answer:

Option D is correct.

In Deductive reasoning you start from a 'Given' set of rules and conditions to determine what must be true.

Step-by-step explanation:

Deductive reasoning is a top-to-down reasoning method that makes its conclusion on the basis of given premise(s) which is/are commonly assumed to be true.

It uses given rules, theorems, conditions, methods etc. to prove that other statements are true or not.

Hence, in Deductive reasoning you start from a 'Given' set of rules and conditions to determine what must be true.

Hope this Helps!!!

Answer:

36 : 6 and -6

12 = [tex]2\sqrt{3} , -2\sqrt{3}[/tex]

1.96 =1.4 and -1.4

0.64 : 0.8 and -0.8

400 : 20 and -20

25/36 = 5/6 and -5/6

Step-by-step explanation:

we know that

(-x)^2 = x^2

ALSO

(x)^2 = x^2

thus, square of both negative and positive number is same positive number.

_________________________________________________

36 = 6*6

36 = -6*-6

hence

square roots of 36 is both -6 and 6

12 = 4*3 = [tex]2^2*\sqrt{3} *\sqrt{3}[/tex]

[tex]\sqrt{12} = 2\sqrt{3}[/tex]

also

12 = [tex]-2\sqrt{3} *-2\sqrt{3}[/tex]

[tex]\sqrt{12} = -2\sqrt{3}[/tex]

___________________________________

1.96 = 196/100 = (14/10)^2

1.96 = 196/100 = (-14/10)^2

hence

[tex]\sqrt{1.96} = 14/10 \ or -14/10[/tex]

_______________________________

0.64 = 64/100 = (8/10)^2 = 0.8^2

0.64 = 64/100 = (-8/10)^2 = (-0.8)^2

Thus, square root of  0.64 = 0.8 and -0.8

_________________________________

400 = 20^2

400 = (-20)^2

[tex]\sqrt{400} = 20\\\sqrt{400} = -20\\[/tex]

__________________________________

25/36 = (5/6)^2

25/36 = (-5/6)^2

[tex]\sqrt{ 25/36} = 5/6 \\\sqrt{ 25/36} = (-5/6[/tex]

Answer:

26.25 cm²

Step-by-step explanation:

The area of the shaded part is the area of the shaded triangle subtract the area of the white triangle.

Since the triangles are similar then the ratios of corresponding sides are equal.

let the height of the white triangle be h, then

[tex]\frac{12}{9}[/tex] = [tex]\frac{10}{h}[/tex] ( cross- multiply )

12h = 90 ( divide both sides by 12 )

h = 7.5

shaded area = [tex]\frac{1}{2}[/tex] × 12 × 10 - [tex]\frac{1}{2}[/tex] × 9 × 7.5 = 60 - 33.75 = 26.25 cm²

Answer:

≈23.66

Step-by-step explanation:

Height ---> x

base ---> 5x

Formula for area of triangle: (base*height)/2

((5x)(x))/2 = 1400

[tex]5x^{2}[/tex]/2 = 1400

[tex]5x^{2}[/tex] = 1400 · 2 = 2800

[tex]x^2[/tex] = 2800/5 = 560

x= √560 ≈ 23.66

C). (3, 29) would be your answer.

Explanation?:

Rewrite the equation in vertex form.

y = -3(x - 3)^2 + 29

use the vertex form, y = a(x - h)^2 + k, to determine the values of a, h, and k.

a = -3

h = 3

k = 29

The vertex = (h, k)/(3, 29)

Hope this helps!

Answer:

It would be c

Step-by-step explanation:

Answer:

a = 7

b = 7

c = 14             [Correct option is B. 14]

Step-by-step explanation:

Since the shape is a parallelogram, to solve this problem, use some of the properties of a parallelogram:

(i) Opposite sides are parallel and congruent. Being congruent means the sides are identical. In other words, they have the same length.

From the diagram, this means that sides PQ and SR are identical. i.e

=> PQ = SR

=> 6a + 10 = 8a - 4          [collect like terms and solve]

=> 14 = 2a

=> a = 7

(ii) Opposite angles are congruent. Angles PQR and PSR are identical. i.e

<PQR = <PSR = (9b + 2)°

Also,

<SPQ = <SRQ = (18b - 11)°

(iii) Consecutive angles are supplementary. The sum of any two angles that are not opposite to each other is 180°. i.e.

<SPQ + <PQR = 180°

<PQR + <QRS = 180°

<QRS + <RSP = 180°

.

.

.

Also,

<PSR + <SPQ = 180°      

(9b + 2)° + (18b - 11)° = 180°        [expand bracket and solve for b]

9b  + 2 + 18b - 11 = 180

27b - 9 = 180

27b = 189

b = 7

Now, since a = 7 and b = 7;

c = a + b = 7 + 7 = 14

Therefore;

a = 7

b = 7

c = 14

Answer:

It has two solutions.

Step-by-step explanation:

Let as consider the given options are  

It has no solution.

It has one solution.

It has two solutions.

It has infinitely many solutions.

The given equation is

[tex]\dfrac{3}{4z}=\dfrac{1}{4z-3}+5[/tex]

Multiply both sides by 4z(4z-3).

[tex]3(4z-3)=4z+5(4z(4z-3))[/tex]

[tex]12x-9=4z+80z^2-60z[/tex]

[tex]0=-12x+9+80z^2-56z[/tex]

[tex]0=80z^2-68z+9[/tex]

It is a quadratic equation.

Therefore, it has two solutions.

Answer:

It has 1 solution

Step-by-step explanation:

I did the test I put the guys above me in and got it wrong