ABCD is a square. Square A B C D is shown. A diagonal is drawn from point A to point C. The measure of angle B A C is question mark. What is the measure of angle BAC? 30° 45° 60° 90

Answer:

22.8

Step-by-step explanation:

Step-by-step explanation:

[tex]6x - 30 = 5(x - 4)[/tex]

[tex]6x - 30 = 5x - 20[/tex]

[tex]6x - 30 - 5x = - 20[/tex]

[tex]x - 30 = - 20[/tex]

[tex]x = - 20 + 30[/tex]

[tex]x = 10[/tex]

Hope this is correct and helpful

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Answer:

A. - 4

Step-by-step explanation:

f(4) = 4(4) - 20 = 16 - 20 = - 4

Answer:

283 cm^2

Step-by-step explanation:

Solution:-

We have a cone with a circular base of radius r = 5 cm

The height of the cone is h = 12 cm

The slant height of the cone is L = 13 cm

We are to determine the surface area of the cone. The surface area of the cone is comprised of two parts:

         Base Area : Circle

               [tex]A_1 = \pi r^2\\\\A_1 = \pi 5^2\\\\A_1 = 25\pi[/tex]

        Curved Surface: conical

                [tex]A_2 = \pi * r*L\\\\A_2 = \pi * 5*13\\\\A_2 = 65\pi[/tex]

The total surface area of the cone can be written as ( A ):

               [tex]A = A_1 + A_2\\\\A = (25 + 65 )*\pi \\\\A = 90*(3.14) \\\\A = 282.7433 cm^2[/tex]

Answer: The surface area of the cone to nearest whole number would be 283 cm^2

Answer:

The most helpful function in an attempt to determine the time it takes for the dolphin to re-enter is h(x) = 2·(x - 1)·(x - 4)·(x - 6)

Step-by-step explanation:

For 2·x²·(x - 11) + 4·(17·x - 12)

h(5) = 2×5^2×(5 - 11) + 4×(17×5 - 12) = -8

For the function h(x) = 2·x·(x² - 11·x + 34) -48 we have;

h(5) = 2×5×(5^2 - 11×5 + 34) -48 = -8

For the function h(x) = 2·(x - 1)·(x - 4)·(x - 6) we have;

h(5) = 2×(5 - 1)×(5 - 4)×(5 - 6) = -8

For the function h(x) = 2·x³ - 22·x² + 68·x -48 we have;

h(5) = 2×5^3 - 22×5^2 + 68× 5  - 48 = -8

Given that the values of the function are all equal at x = 5, the function that will be most helpful in determining the time it takes for the dolphin to re-enter the sea after leaping out of the water is the function that is already factorized

Thereby where the value of the function h(x) at which the dolphin re-enters the the sea is h(x) = 0, we have the function h(x) = 2·(x - 1)·(x - 4)·(x - 6), readily gives the time values, x, as x = 1 second or 4 second or 6 second, therefore, the most helpful function is h(x) = 2·(x - 1)·(x - 4)·(x - 6).

Answer:

6 to the north

Step-by-step explanation:

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Answer:

42 ducks remain in the pond

Step-by-step explanation:

First, find the number of white ducks

28*2=56

Add them to the brown ducks

56+28= 84

Then divide by 2 because half flew away

84/2=42

So 42 ducks remain in the pond. Hope this helps :)

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Work Shown:

Let x = 0.363636...

The "36" pattern goes on forever as indicated by the three dots.

Multiply both sides by 100 to get 100x = 36.363636...

Effectively, multiplying by 100 moves the decimal point over 2 spots to the right. The "36" goes on forever here too. The key is to match up the infinite sequences of "36"s and cancel them out through subtraction

36.363636... - 0.363636... = 36

while

100x - x = 99x

So after subtracting the equations, we end up with 99x = 36

From here we solve for x by dividing both sides by 99 and reducing the fraction

99x = 36

x = 36/99

x = (9*4)/(9*11)

x = 4/11

As a check, use your calculator to find that

4/11 = 0.36363636...

so the answer is confirmed

Note: your calculator may display something like 0.3636363636364, that 4 should not be there. It's a result of rounding (due to the next digit being a 6). Keep in mind that rounding error is often a possibility when it comes to approximate calculations. The calculator only has so much memory and display space.

Answer:

The equation, when graphed together with the line y=-3x +6, which will form a system of equations with no solution is y=-3(x +6), meaning the second option on the picture.

Step-by-step explanation:

hope this helps!

Answer: 2 or B

Step-by-step explanation:

Answer:

Kevin is 6 years old and Daniel is 3 years old

Step-by-step explanation:

They are now 3 years apart but two years ago, they were 4 and 1 years old, so Kevin was 4 times older than.

Hope this helped :)

Answer:

23

Step-by-step explanation:

Raise 3 to the power of 3

27 - 4

Subtract 4 from 27

23

Hope this was correct

Answer:

23

Explanation:

step 1 - rewrite the expression with the value of x

[tex]x^3 - 4[/tex]

[tex](3)^3 - 4[/tex]

step 2 - solve the exponent

[tex](3)^3 - 4[/tex]

[tex]27 - 4[/tex]

step 3 - subtract

[tex]27 - 4[/tex]

[tex]23[/tex]

therefore, the value of the expression is 23.

Answer:

  1

Step-by-step explanation:

Use the form for the factoring of the sum of cubes.

To make this easier to write, we'll use the substitutions ...

  a = sin(θ), b = cos(θ)

It looks like you may want to simplify ...

  (a³ +b³)/(a +b) +ab

  = ((a +b)(a² -ab +b²))/(a +b) +ab

The factors of (a+b) cancel. In this case, we know that a² +b² = 1, so this becomes ...

  = (1 -ab) +ab

  = 1

  [tex]\boxed{\dfrac{\sin^3{\theta}+\cos^3{\theta}}{\sin{\theta}+\cos{\theta}}+\sin{\theta}\cos{\theta}=1}[/tex]

Answer:

2x -5

Step-by-step explanation:

-3 + 2(x - 1)

Distribute

-3 +2x -2

Combine like terms

2x -5

Answer:

5x -2

Step-by-step explanation:

Answer: -6y= -3x-9

Since the slope is -6

y will be -6y

and the rest is -9, -3x

The length of the arc s is 6.283 inches.

The length of an arc is given by the formula,

[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360}[/tex]

where

θ is the angle, which arc creates at the center of the circle in degrees.

Radius, r = 8 in.

Angle, θ = 45°,

[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360}[/tex]

[tex]\rm{ Length\ of\ the\ Arc\ s = 2\times \pi \times(8)\times\dfrac{45}{360}[/tex]

[tex]\rm{ Length\ of\ the\ Arc\ s =6.283\ inches.[/tex]

Hence, the length of the arc s is 6.283 inches.

Learn more about Length of an Arc:

https://brainly.com/question/1577784

The approximate length of arc s on the given circle is; 6.28inches

The length of an arc is given by the formula;

Therefore,

Length, L = (45/360) × 2 × 3.14 × 8

Read more on length of an arc;

https://brainly.com/question/2005046

Answer:

x = 1

Step-by-step explanation:

Given

8 - 5(x - 3) = 18 ( subtract 8 from both sides )

- 5(x - 3) = 10 ( divide both sides by - 5 )

x - 3 = - 2 ( add 3 to both sides )

x = 1

Answer:

Side LM is congruent to side RQ

Angle MNO is congruent to angle RST

Side ON is congruent to side ST

Angle LMN is congruent to angle QRS

Step-by-step explanation:

A way to solve this is to use parchment paper or draw the same shape next to each other, as you will get these:

Side LM is congruent to side RQ

Angle MNO is congruent to angle RST

Side ON is congruent to side ST

Angle LMN is congruent to angle QRS

Answer:

3. 7/12.

4. 7/5.

5. 1.

Step-by-step explanation:

The slope of a line can be obtained by taking the ratio of change in y-coordinate to that of x-coordinate. Mathematically, it is expressed as:

Slope = Δy /Δx

Δy = y2 – y1

Δx = x2 – x1

With the above formula in mind, let us answer the questions given above.

3. Point => (–8, –2) (4, 5)

x1 = –8

x2 = 4

Δx = x2 – x1

Δx = 4 – –8

Δx = 4 + 8

Δx = 12

y1 = –2

y2 = 5

Δy = y2 – y1

Δy = 5 – – 2

Δy = 5 + 2

Δy = 7

Slope = Δy /Δx

Slope = 7/12

4. Point => (3, –5) (8, 2)

x1 = 3

x2 = 8

Δx = 8 – 3

Δx = 5

y1 = –5

y2 = 2

Δy = y2 – y1

Δy = 2 – – 5

Δy = 2 + 5

Δy = 7

Slope = Δy /Δx

Slope = 7/5

5. Point => (–4, –5) (4, 3)

x1 = –4

x2 = 4

Δx = x2 – x1

Δx = 4 – –4

Δx = 4 + 4

Δx = 8

y1 = –5

y2 = 3

Δy = y2 – y1

Δy = 3 – – 5

Δy = 3 + 5

Δy = 8

Slope = Δy /Δx

Slope = 8/8

Slope = 1

Answer:

20

Step-by-step explanation:

Since 30 and 3x are complementary we can write:

30 + 3x = 90

3x = 60 so x = 20°.

Answer:

20

Step-by-step explanation:

30 + 3x = 90

=> 3x = 90 - 30

=> 3x = 60

=> x = 60/3

=> x = 20

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Answer:

69

Step-by-step explanation:

A triangle has a 180 degree angle so you do 180-111=69

Answer: x=24

Step-by-step explanation:

lets say 94 is ∠ a

41 is ∠ b

___ ∠  c

111∠ d

x ∠ e

so with that you will figure out that ∠  c is to find X

108-94-41= 45

so ∠ c is 45

now you can ∠a ∠ b∠ c

with that yo take

108-111-45=24

So X=24

Answer:

8677

Notice that all the numbers in the sequence are divisible by 3 except 8677.

The sum of the digits must be divisible by 3.

8+6+7+7= 2+8 =10

10 isn't divisible by 3.

Answer:

Chocolate Chips cost $2.25 and Walnuts cost $3.25 per pound each

Step-by-step explanatChocion:

Let x = cost of pounds of chocolate chip cookies and y = cost of pounds of walnuts.

From the question, we get 5x+3y = 21 and 2x+6y = 24. To solve the equation, we use substitution. From the first equation, we get y = (21-5x)/3. We substitute the y into the second equation to get 2x + 6(21-5x)/3 = 24. This turns out to be 2x+(42-10x) = 24. Adding like terms you should get 42-8x = 24. Solving for x, x = $2.25 per pound. Plugging this into the first equation, we get 5(2.25)+3y = 21. Solving for y, we get $3.25 per pound of walnuts. If we plug in the numbers into the 2 equations, we will get the right total.

Answer:

112

Step-by-step explanation:

Define the variables:

x = number of French students sent by the school

Write the equation:

x / 21 = 1 / 3

Solve:

x = 7

The school sent 7 French students and 21 German students, for a total of 28 students.

The other 3 schools also sent 28 students.  So the total number of students sent is:

4 × 28 = 112

Answer:

Step-by-step explanation:

French students=F

[tex]\frac{F}{21} =\frac{1}{3} \\F=\frac{1}{3} \times 21 =7\\Total~ students~ of ~one~ school=21+7=28\\Total~language~students=28 \times 4=112[/tex]

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

- 3y + 4x = 9

3y = 4x - 9

Divide both sides by 3

y = 4/3x - 3

Comparing with the above formula

Slope / m = 4/3

Since the lines are parallel their slope are also the same

So slope of the parallel line l is also 4/3

Equation of the line using point (-12 , 6) is

y - 6 = 4/3(x + 12)

Multiply through by 3

That's

3y - 18 = 4(x + 12)

3y - 18 = 4x + 48

We have the final answer as

Hope this helps you

Answer:

fx/gx=10

Step-by-step explanation:

fx= (36x5)-(44x4)-(28x3)

fx=80

gx= 4x2

gx=8

To work out fx/gx:

fx/gx=80/8

fx/gx=10

Answer:

1.76m/s ; 1.76m/s ; 1.74m/s, 0.86m/s

Step-by-step explanation:

Given the following :

Distance jogged in first direction (A to B) = 300m

Time taken = 2 minutes 50s = (2*60) + 50 = 120 + 50 = 170s

Distance jogged in opposite direction (B to C) = 100m

Time taken = 1minute = 60s

Recall:

Speed = distance / time

Therefore Average speed from A to B

Average speed = 300m/ 170s = 1.764 = 1.76m/s

Average Velocity = Displacement / time

Displacement = 300m ; time = 170s

= 300m / 170s = 1.76m/s

Average speed (A to C)

Therefore, average speed = total distance / total time taken

Total distance = (300 + 100)m = 400m

Total time taken = (170 + 60)s = 230s

Average speed = 400m / 230s

= 1.739m/s = 1.74m/s

Average velocity:

Displacement = distance between initials position and final position.

Initial distance covered = 300m. Then 100m was jogged in the opposite direction.

Distance between starting and ending positions, becomes : (300 - 100)m = 200m

200 / 230 = 0.87m/s

Answer:

Step-by-step explanation:

First we must know that the sum of all the exterior angle of all polygons is 360°.

Measure of each angle of a polygon = 360°/total sides of the polygon

Since a regular nonagon has 9 sides, the measure of each angle of a polygon is expressed as thus;

Measure of each angle of a polygon  = 360°/9

Measure of each angle of a polygon  = 40°

Hence the measure of an exterior angle x of a nonagon is 40°

Answer:

B in Edg

Step-by-step explanation:

Answer:

B) This student performed better than 78% of the other test-takers in the verbal part and better than 34% in the quantitative part.

Step-by-step explanation:

In Statistics, Percentile refers to how specific variables can be divided according to the distribution of values in a population of 100 equal groups.

The data value of a given percentile can be determined  as 100 times the cumulative relative frequency of that value.

From the given question.

Suppose a test-taker scored at the 78th percentile for their verbal sent to test-takers, the percentiles associated grade and at the 34th percentile for their quantitative grade.  

This implies that ;

The student score shows the relation between a particular score of :

78% and the scores of the rest of a group for the verbal test takers   &

34% and the scores of the rest of a group for the quantitative test takers.

Therefore; we can conclude that ;

This student performed better than 78% of the other test-takers in the verbal part and better than 34% in the quantitative part.