Which expressions are equivalent to g16? Check all that apply.

The length of the side CD of the triangle is 12.686 cm up to 3 significant figures.

We know from the information that

AB = 6cm AC = 12cm

Now we have to calculate the length of DC

From given figure, we have,

In Δ ACB,

CA² = BA² + BC² (By using Pythagoras theorem)

12² = CB²+ 6²

CB² = 12² - 6²

CB² = 144 - 36

CB² = 108

∴ BC = √( 108) cm.

Now consider, in Δ CBD,

as, we know that from trigonometric ratios , sin x = opposite side / hypotenuse

sin 55° = BC / DC

0.81915 = √108 / DC

DC = 10.392 / 0.81915

⇒ DC = 12.68632...

∴ DC ≈ 12.686 cm

Therefore the length of the side DC is approximately 12.686 cm up to 3 significant figures.

Disclaimer: The missing image of the triangle is attached below.

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Using the subtraction, the number of member who only like caava is 12.

In the given question we have to find how many member like caava.

Total member of family = 48

Member who like caava=24

Member who like potato=36

Member who like both caava and potato=12

In the given number of member who like caava having a member who also like potato and some are who only like caava.

So the number of member who only like caava = Total number of member who like caava−Total number of member who like both caava and potato

The number of member who only like caava =24−12

The number of member who only like caava =12

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Answer:

h(x) = -1/3 x - 1

Step-by-step explanation:

Solution

h(x) = - f(x)                               This is a given

f(x) = (1/3) x + 1                         Put h(x) on the left. Use a minus sign for f(x)

h(x) =-1((1/3)x + 1)                      Remove the outside brackets.

h(x) = -(1/3) x - 1

The outside brackets make 1/3 x and 1 = to a minus when a minus is put in front of f(x)

Answer:

Albert drove further.

He drove 5 miles further.

Step-by-step explanation:

The formula d = r x t is used to determine distance.

D is distance. R is rate ( in this case miles per hour). T is time.

Tom: D= 50 x 2.5

50 multiplied by 2.5 hours = 125

Tom drove 125 miles.

Albert: D= 65 multiplied by 2 hours = 130

Albert drove 130 miles.

Answer:  i think its a=52

and b=8 srry if its wrong tell me and ill try to fix it thx:)

Step-by-step explanation:

Answer:

~201.1[tex]u^2[/tex]

Step-by-step explanation:

Formula for area of a circle:

[tex]\pi r^2[/tex]

The diameter is any straight line that passes through the circle and endpoints lie on the perimeter of the circle.

We are given the diameter: 16. The diameter is twice the radius (for all circles) Divide the diameter, 16 by 2 to get the radius. If the problem gives you the radius, which is a line from the center of the circle, do not divide by 2 and directly plug into formula.

16/2 = 8

Plug into formula.

[tex]\pi r^2[/tex]

[tex]\pi 8^2[/tex]

Using PEMDAS, the standard order of operations order for math, we firsty do 8^2 before multiplying by pi.

8^2 = 8 x 8 = 64

[tex]64*\pi[/tex] = ~201.1

Answer:

x=1

Step-by-step explanation:

in photo

Answer:

Y= 2x+3

Step-by-step explanation:

Slope = (y-y1)/(x-x1)

2= (y-5)/(x-1)

Cross multiply

Y-5= 2x-2

Collect like terms

Y= 2x+3

The value of x in the given figure is x = 71° , the correct option is (c) .

In the question ,

a triangle ABC is given ,

the measure of angle A = 38°

we can see that length of the sides AB and AC is 21 , and we know when the length of two sides of the triangle is equal , it is called as isosceles triangle .

In isosceles triangle , the two angles corresponding to the two equal sides are equal , that means

angle B = angle C = x

In triangle ABC ,

By Angle Sum Property , we get

angle A + angle B + angle C = 180°

38 + x + x = 180

38 + 2x = 180

subtracting 38 from both the sides , we get

2x = 180 - 38

2x = 142

Dividing both sides by 2 , we get

x = 142/2

x = 71

Therefore , The value of x in the given figure is x = 71° .

The given question is incomplete , the complete question is

What is the value of x  ,in the figure given below ? Drawing not to scale

(a) 21°

(b) 42°

(c) 71°

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If Mario will use all the rope as instructed right the number of 8 1/4 inch sections of  Mario that can come from the rope is: 6.

First step is to convert the 7 feet rope to inches

7 feet robes = 84 inches

Second step is to find the inches of rope left

Inches of rope left =84 inches - 34.5 inches

Inches of rope left = 49.5 inches

Now let find the number of 8 1/4 inch sections

Number of 8 1/4 inch sections =49.5 / 8.25

Number of 8 1/4 inch sections =6

Therefore 6 is the number of 8 1/4 inch sections .

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Using the theories of prezygotic, we got that in my words prezygotic mechanisms of Reproductive isolation is defined as the mechanism that keeps species from mating with others. Prezygotic isolation actually prevents the fertilization of eggs while the postzygotic isolation prevents the formation of fertile offspring.

Reproductive isolation keeps species from mating with others. Prezygotic mechanisms include the habitat isolation, mating seasons, "mechanical" isolation, gamete isolation and the behavioral isolation.

Hence, in my words, prezygotic mechanisms of reproductive isolation is defined as  the mechanism that keeps species from mating with others. Prezygotic isolation actually prevents the fertilization of eggs while the postzygotic isolation prevents the formation of fertile offspring.

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The solid has an estimated volume of 1510.8 cubic yards

The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. Cylinder’s volume is given by the formula, πr²h , where r is the radius of the circular base and h is the height of the cylinder.

The volume of the cylinder can be calculated as

v = πr²h

v = π* 10² * 5

v = 500π yd³

Let's calculate the volume of the rectangular figure

v = l * w * h

v = 3 * 4 * 5

v = 60 yd³

We should subtract the volume of the rectangular figure from the volume of cylinder to determine the volume of the solid.

V = 500π - 60

v = 1510.8 yd³

The volume of the solid is calculated as 1510.8 yd³

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Answer:

1,510

Step-by-step explanation:

Answer:

58 miles

Step-by-step explanation:

              One truck                           second truck

rate               85                                          60

time                t                                              t

Distance      d + 10                                     d -10

d + 10 = 85t                                                d - 10 = 60t

d = 85= -10                                                  d = 60t +10

Set the two equations equal to each other and solve

85t -10 = 60t + 10  Subtract 60t from each side

25t - 10 = 10  Add 10 to each side

25 t = 20  Divide both sides by 25

t = [tex]\frac{4}{5}[/tex]

Each were driving 4/5 of an hour.  Plug into the one of the equaions

d + 10 = 85t

d + 10 = 85([tex]\frac{4}{5}[/tex])

d +10 = 68  Subtract 10 from both sides

d = 58

Answer:

Step-by-step explanation:

Givens

Truck = 85 km/hr

Van = 65 km/hr

t is the time they meet

Note

Truck A is travelling faster, so the place where they meet is closest to Town B.

Solution

Let the distance travelled by the truck be

d/2 + 10

Let the distance travelled by the van be

-d/2 + 10

Let t be the time they meet

85* (d/2 + 10) /t = -60*(d/2 + 10)/t            multiply both sides by t

85*(d/2 + 10)*t/t = -60*(d/2 + 10)*t/t         Combine

85*(d/2 + 10) = -60(d/2 + 10)                    Remove the brackets.

42.5 d + 850 = -30d - 600                      Add 30 d to both sides

72.5d+ 850 = - 600                                 Subtract 850 from both sides.

72.5d = - 600 - 850                                 Combine

72.5d = -1450                                           Divide by 72.5  

d = -1450 / 72.5

d = -20

The minus means that you are looking at it from the van's point of view.

The percent markup is 11.11%.

There is a department store. The total number of shirts bought by the department store is 400. The total cost of the shirts bought by the department store is $10,800. The department store sells all the shirts for $30 each. We need to find the percent markup.

We first need to find out the cost of each shirt. The cost price of each shirt is the total cost of all the shirts divided by the total number of shirts bought by the department store.

C = $10,800/400

C = $27

Hence, each shirt was purchased for a price equal to $27. To find the markup percentage, we need to find the percentage difference between the cost price and the selling price of the shirt.

M = [(30 - 27)/27]*100%

M = (3/27)*100%

M = 100/9%

M = 11.11%

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Answer:

16

Step-by-step explanation:

=6(4)-(8)

=24-8

=16

Answer:

y = mx + b

-2 = ½(-4) + 6

Step-by-step explanation:

formula ; y = mx + b

where y = y co-ordinate

m = slope

x = x co-ordinate

b = y intercept

Therefore; y = mx + b

-2 = ½(-4) + 6

The equation for straight line can be used to plot it on the graph. The amount of discount is 4.

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

The given equation is as follows,

5x + (–2y) = 8

Here, x is the number of picture frames purchased after discount.

And, y is the total amount spent.

In order to find the discount, write the equation in terms of y as,

5x + (–2y) = 8

=> 2y = 5x - 8

=> y = 5 / 2 x - 4

The above equation can be plotted as a graph which is shown below,

It is found from the graph that slope is 5 / 2 which is the rate of per picture.

Since the frames are being purchased after the discount, from the above graph  discount can be obtained as 4.

Hence, the discount on the picture frames is given by 4.

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Applying the triangle sum theorem and the angle-side relationship, the longest side of triangle ABC is: side AC.

The triangle sum theorem states that if we add all three interior angles of a triangle, the sum we get would be equal to 180 degrees.

The angle-side relationship of a triangle explains that the longest side of a triangle is always opposite to its largest angle, the medium side is opposite to the medium angle, and the shortest side is to the smallest angle of the triangle.

Given that triangle ABC has the following angle measures:

m∠A = 60°

m∠B = (3x - 2)°

m∠C = (2x + 7)°

Therefore:

m∠A + m∠B + m∠C = 180

Substitute:

60° + (3x - 2)° + (2x + 7)° = 180

60 + 3x - 2 + 2x + 7 = 180

Combine like terms:

65 + 5x = 180

5x = 180 - 65

5x = 115

x = 23

Find the measure of each of the angles by plugging in the value of x:

m∠B = (3x - 2)° = 3(23) - 2 = 67°

m∠C = (2x + 7)° = 2(23) + 7 = 53°

The largest angle is m∠B = 67°.

AC is opposite to angle B, therefore, AC is the longest side of the triangle.

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The p-value is found to be 0.0006 by using the f-ratio.

Given that ,

SST = 10, 800 , SSTR = 4560

Sum of Square error SSE = SST- SSTR = 10800- 4560

SSE = 6240

df for treatment K= 1, where K are the level of treatment and given that K=3.

df treatment = k-1 = 3 - 1 = 2.

df error = n-k = 30- 3=27.

df total = n- 1 = 30 - 1= 29 .

Mean Square for treatment = SSTR / If treatment

=4560/ 2 = 2280

MSTR = 2280

MSE = SSE/ df error = 6240/27 = 231.11

F-ratio = MSTR/ MSE = 2280 / 231.11

= 9.8654 -=9.87 ( rounded to 2 decimal )

F ratio = 9.87

By using F-table the value of P-value in

F = 9.87 , and df1 = 2, df2=27 , with Significance level =0.05 , then the value is

P-value = 0.0006 .

Therefore, The p-value is 0.0006

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y= -3(-1)+3[slope intercept form]

Answer:

36/5

Step-by-step explanation:

32.55

Step-by-step explanation:

21/4×31/5

651/20

The equation be which has the solution x = 9 are:

x/3 + 7 = 8

substract 7 from both sides

x/3 = 8 - 7

x/3 = 1

cross product

x = 3

4 + 5x = 18

Subtract 4 from both sides

5x = 18 - 4

5x = 14

divide both sides by 5

x = 14/5

x = 2.8

81/x - 3 = 6

Add 3 to both sides

81/x = 6 + 3

81/x = 9

cross product

81 = 9x

divide both sides by 9

x = 81/9

x = 9

24 - 2x = 13

Subtract 24 from both sides

-2x = 13 - 24

-2x = -11

divide both sides by -2

x = -11/-2

x = 5.6

2x - 3 = 15

Add 3 to both sides

2x = 15 + 3

2x = 18

divide both sides by 2

x = 18/2

x = 9

3x + 2 = 25

Subtract 2 from both sides

3x = 25 - 2

3x = 23

divide both sides by 3

x = 23/3

x = 7.67

So therefore, the equations 81/x - 3 = 6, 2x - 3 = 15 has x = 9 as the solution.

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The value of the expression -13+√70 to the nearest tenth is -4.6

Arithmetic operations involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

The expression -13+√70 comprises of addition of -13 and √70

The value of √70 is 8.4(to the nearest tenth).

Therefore the value of -13+√70

=-13+8.4

= -4.6( nearest tenth)

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Answer:

x > - 4

Step-by-step explanation:

5x + 7 > - 13 ( subtract 7 from both sides )

5x > - 20 ( divide both sides by 5 )

x > - 4

Answer:

x is undefined

Step-by-step explanation: