In the right triangle shown, DF=EF=3DF=EF=3D, F, equals, E, F, equals, 3.

How long is DEDED, E?
Choose 1 answer:

Answer:

Number of pieces of candy in the bowl=64

Step-by-step explanation:

Let

x=number of pieces of candy in a bowl

Shirley took=1/2 of x

=1/2x

Remaining

x-1/2x

= 2x-x/2

=1/2x

Rose took half of the pieces left in the bowl=1/2 of 1/2x

=1/2*1/2x

=1/4x

Remaining

1/2x-1/4x

=2x-x/4

=1/4x

Susan took 1/2 of the remaining pieces of candy=1/2 of 1/4x

=1/2*1/4x

=1/8x

Remaining 8

1/8x=8

x=8÷1/8

=8*8/1

=64

x=64

Answer:

x-1

Step-by-step explanation:

| x-1|  x> 1

Since x is greater than x, the absolute value will be positive so we can remove it

x-1

Lets use a number to check

Let x = 4

| 4-1|    4>1

3  which is positive

Answer:

x - 1

Step-by-step explanation:

| x - 1 |

x > 1

x is greater than 1. The absolute value is not needed, since the value inside will only be for positive integers.

x - 1

We can check by plugging x as 2.

2 - 1 = 1 (positive)

2 > 1

Answer:

60

Step-by-step explanation:

8640/60 is 144. 144 is a perfect square. 12*12 is 144

Hey there! I'm happy to help!

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INTRO TO PERFECT CUBES

A perfect cube is any number whose cube root is an integer. In English, that means that if you take any number without a fraction (this is called an integer, such as -7, 8, 100, none have fractions) and multiply it by itself three times, you get a perfect cube.

If you cube the number 4, you get 64, which is (4×4×4). 64 is an example of a perfect cube.

You can use the cube root button on your calculator to see if a number is a perfect cube. If you do the cube root of 64, you get 4, telling you that 64 is a perfect cube. The cube root of 10 is 2.154434...... so 10 is not a perfect square because it does not give you an integer (number that does not have a fraction) as the answer.

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SOLVING THE PROBLEM

So, we want to find the smallest numbers we can divide 8640 to equal a perfect cube.

I will assume that we will not be dividing by fractions but only whole numbers (positive integers).

We could try dividing by 1, but we see that 8640 is not a perfect cube because it's cube root is 20.519711....

Let's just keep counting up! The first divisor we run into that gives a quotient that it is a perfect cube is the smallest whole number possible that will give us that result.

8640÷2=4320

∛4320≈16.2865....... Not a perfect cube

8640÷3=2880

∛2880≈14.22757..... Not a perfect cube

8640÷4=2160

∛2160≈12.92660..... Not a perfect cube

8640÷5=1728

∛1728=12, a perfect cube!

Since 12 cubed is equal to 1728, this means that 1728 is a perfect square, so 5 is the smallest number we can divide 8640 by to get a perfect square.

The answer is 5.

I hope that this helps! Have a wonderful day! :D

Answer:

55°

Step-by-step explanation:

The corresponding image, which I will attach, is missing in order to solve the exercise.

We know that the flat angle is 180 °, which we know to be the one that is formed with the horizontal, therefore the following equation remains:

55 ° + (70 ° + x °) = 180 °

we solve x °

x ° = 180 ° - 55 ° - 70 °

x ° = 55 °

So the value of x is 55 °

Answer:

Amount of solution = 15 liter

Step-by-step explanation:

Given:

One third of solution is acid

Amount of acid = 5 Liter

Find:

Amount of solution

Computation:

Amount of solution = Amount of acid (1 / One third of solution is acid)

Amount of solution = Amount of acid (3)

Amount of solution = (5)(3)

Amount of solution = 15 liter

Answer:

39 investors contributed $6,000, and 21 investors contributed $12,000.

Step-by-step explanation:

Let's say that x investors contributed $6,000, and y investors contributed $12,000.

x + y = 60

6,000x + 12,000y = 486,000

x + 2y = 81

x + y = 60

y = 21

x + 21 = 60

x = 39

So, 39 investors contributed $6,000, and 21 investors contributed $12,000.

Hope this helps!

Answer:

8 inches

Step-by-step explanation:

3/4+(3/4*2)=3/4+6/4=9/4=2 1/4

2 1/4+6=8 1/4=8.25

Answer: 8.25 inches

Step-by-step explanation:

Answer:

2400months

Step-by-step explanation:

6/100*40,000

maybe

Answer:

The answer is C.

Step-by-step explanation:

The formula to find equation is y - y1 = m(x - x1).

Let (x1,y1) be (6,2) and m is -5/7.

So the equation is,

y - 2 = -5/7(x - 6)

Answer:

4 + 3+3+3+3

Step-by-step explanation:

We add up all the areas to find the surface area

The bottom is

2*2 = 4

The sides are all the same

The area of one side is

A = 1/2 bh =  1/2 (2*3) = 3

There are 4 triangular side

SA = 4 + 3+3+3+3

Answer:

4 + 3 + 3 + 3 + 3

Step-by-step explanation:

The base is a square.

Find area of a square.

2² = 4

Find the area of one triangle.

2 × 3 × 1/2 = 3

There are 4 triangles.

3 + 3 + 3 + 3

Add all the areas:

4 + 3 + 3 + 3 + 3

Answer:

15√3

Step-by-step explanation:

This is a 30-60-90 triangle, so in order to solve for v, we can multiply the short leg by √3, which we will get 15√3.

Answer:

v = 25.98

Step-by-step explanation:

You could do this a number of ways. Some are much longer than others. The shortest way is to use the tangent.

Formula

Tan(theta) = opposite / adjacent

Givens

Theta = 30o

Opposite = 15 km

Adjacent = x

Solution

tan(30) = 15 / v                       Multiply both sides by v

v*tan(30) = 15                         Divide by tan(30)

v = 15/tan(30)

tan(30) = 0.5774

v = 15 / 0.5774

v = 25.98

Answer:

£289.20

Step-by-step explanation:

13:2 = x:16 or 13/2 = x/16

cross multiply: 208 = 2x

simplify: x = 104

16 blue tiles x £2.80 each = £44.80

104 white tiles x £2.35 each = £244.40

44.80 + 244.40 = £289.20

Answer:

[tex]x=y-22[/tex]

Step 1:

In order to solve this equation, we must subtract the y on both sides so the y could be cancelled out on the left and could move to the right side of the equation.

[tex]y=3x+22-2x\\=-y+3x+22-2x[/tex]

Step 2:

Then, we add 2x on the right side of the equation to cancel out the -2x and bring it to the left of the equation, where the y was before.

[tex]=-y+3x+22-2x\\2x=-y+3x+22[/tex]

Step 3:

Then, we do the same thing with 3x: subtract it from the right side and add it to the 2x, which becomes -x.  

[tex]2x=-y+3x+22\\2x-3x=-y+22\\-x=-y+22[/tex]

Step 4:

Finally, we divide all the numbers by -1 to get our final answer! Reminder: we are doing all this because we have to isolate the x, since we are solving for x.

[tex]-x=-y+22\\\frac{-x}{-1} =\frac{-y}{-1}+\frac{22}{-1} \\x=y-22[/tex]

Our answer is x = y - 22. Hope this helps!

Answer:

answer: x=y-22

Step-by-step explanation:

first subtract y from both sides. then, add -2x on both sides and subtract 3x from the right so the 2x will be -x. divide everything by a - and the answers x=y-22

Answer:

a) CD = 41 m

b) 77.32°

c) 1380 square metres

Step-by-step explanation:

We can divide the trapezium as shown in the diagram below.

a) To find CD, we use Pythagoras Rule:

[tex]CD^2 = 9^2 + 40^2[/tex]

[tex]CD^2 = 81 + 1600\\\\CD^2 = 1681\\\\=> CD = 41 m[/tex]

b) To find <BCD, we use trigonometric function SOHCAHTOA:

sin(BCD) = opp / hyp

sin(BCD) = 40 / 41

sin(BCD) = 0.9756

=> <BCD = 77.32°

c) The area of a trapezium is given as:

A = 1/2 (a + b) * h

where h = height = 40 m

a = top length = 30 m

b = bottom length = 39 m

A = 1/2 * (30 + 39) * 40

A = 1/2 * 69 * 40

A = 1380 square metres

Answer:

20

Step-by-step explanation:

30(0)

= 0

50 + 0 - 30

= 50 - 30

= 20

Answer:

20

Step-by-step explanation:

We know that 30 × 0 = 0. Next, we can take 50 and add 0 which is still 50. Now, we take 50 - 30 which equals to 20.

If the first term is [tex]a[/tex], then the second term is [tex]ar[/tex], the third is [tex]ar^2[/tex], the fourth is [tex]ar^3[/tex], and the fifth is [tex]ar^4[/tex].

We're given

[tex]\begin{cases}ar=6\\ar^4=48\end{cases}\implies\dfrac{ar^4}{ar}=r^3=8\implies r=2\implies a=3[/tex]

So the first five terms in the GP are

3, 6, 12, 24, 48

Adding up the first four gives a sum of 45.

If you were asked to find the sum of many, many more terms, having a formula for the n-th partial sum would convenient. Let [tex]S_n[/tex] denote the sum of the first n terms in the GP:

[tex]S_n=3+3\cdot2+3\cdot2^2+\cdots+3\cdot2^{n-2}+3\cdot2^{n-1}[/tex]

Multiply both sides by 2:

[tex]2S_n=3\cdot2+3\cdot2^2+3\cdot2^3+\cdots+3\cdot2^{n-1}+3\cdot2^n[/tex]

Subtract this from [tex]S_n[/tex], which eliminates all the middle terms:

[tex]S_n-2S_n=3-3\cdot2^n\implies -S_n=3(1-2^n)\implies S_n=3(2^n-1)[/tex]

Then the sum of the first four terms is again [tex]S_4=3(2^4-1)=45[/tex].

Answer:

Step-by-step explanation:

Given the total number of games played by the softball team = 18 games

Total games won = 15 games

Ratio of the softball team's wins to its total number of games played can be gotten by simply dividing the total games won by the total games played

Ratio = [tex]\frac{total \ teams's win}{total\ number\ of \ games\ played}[/tex]

[tex]Ratio = \frac{15}{18}[/tex]

Expressing the ratio in its lowest term

[tex]Ratio = \frac{3*5}{3*6} \\\\Ratio = \frac{5}{6}[/tex]

Hence, the ratio of the softball team's wins to its total number of games played is 5:6

Answer:

Step-by-step explanation:

i cant see answers help my insta is 813.caden

Answer:

y+1=4(x-2)

y=4x+11

8x-2y+6

Step-by-step explanation:

Answer: √3

Step-by-step explanation:

Hi, since the situation forms a right triangle we have to apply the next trigonometric function.  

Sin α = opposite side / hypotenuse  

Where α is the angle (30°), the hypotenuse is the longest side of the triangle (in this case 2), and the opposite side is x. (not t or 2)

Replacing with the values given:  

Sin 30 = x /2

Sin 30 (2) = x

x=1

Applying the Pythagorean theorem:

c^2 = a^2 + b^2  

Where c is the hypotenuse of the triangle (2) and a and b are the other sides.  

2^2 = t^2 + 1^2

4= t^2 +1

4-1 = t^2

3 = t^2

√3 = t

Feel free to ask for more if needed or if you did not understand something.  

Answer:

[tex]n = 65m[/tex]

Number of minutes is 80 minutes

Step-by-step explanation:

Given

The attached table

Calculating the number of copies the machine can make in a minute

Represent number of minutes with m and number of copies with n

First, we need to calculate the ratio of m to n

[tex]Ratio = \frac{n}{m}[/tex]

When m = 5; n = 325

[tex]Ratio = \frac{325}{5}[/tex]

[tex]Ratio = 65[/tex]

When m = 10; n = 650

[tex]Ratio = \frac{650}{10}[/tex]

[tex]Ratio = 65[/tex]

When m = 15; n = 975

[tex]Ratio = \frac{975}{15}[/tex]

[tex]Ratio = 65[/tex]

When we continue for other values of m and n, the ratio remains the same;

So; we make use of [tex]Ratio = \frac{n}{m}[/tex] to determine the relationship between m and n

Substitute 65 for Ratio

[tex]65 = \frac{n}{m}[/tex]

Multiply both sides by m

[tex]m * 65 = \frac{n}{m} * m[/tex]

[tex]65m = n[/tex]

[tex]n = 65m[/tex]

This implies that, you have to multiply the number of minutes by 65 to get the number of copies

Calculating the number of minutes to print 5200 copies;

In this case;

Ratio = 65 and n = 5200

So;

[tex]Ratio = \frac{n}{m}[/tex] becomes

[tex]65 = \frac{5200}{m}[/tex]

Multiply both sides by m

[tex]65 * m = \frac{5200}{m} * m[/tex]

[tex]65 * m = 5200[/tex]

Divide both sides by 65

[tex]\frac{65 * m}{65} = \frac{5200}{65}[/tex]

[tex]m = \frac{5200}{65}[/tex]

[tex]m = 80[/tex]

Hence; number of minutes is 80 minutes

Answer:

Monthly fee that will yield the maximum monthly revenue is  $12.5

Then the value of the maximum monthly revenue is $156 250

Step-by-step explanation:

x   - value of decrease

1000x   - number of new subscribers for $x decrease

10000+1000x  - number of subscribers after $x decrease in the monthly fee

15-1x      the monthly fee after $x decrease

f(x) = (10000 + 1000x)(15 - x)           ← quadratic function

For quadratic function given in standard form:  f(x) =a(x-h)²+k  where a<0 the f(x)=k is the maximum value of function, and occurs for x=h

[tex]h=\frac{-b}{2a}\ ,\quad k=f(h)[/tex]

Expressing given function to standard form:

f(x) = 1000(10 + x)(15 - x)

f(x) = 1000(150 - 10x + 15x - x²)

f(x) = 1000(-x² + 5x + 150)

f(x) = -1000x² + 5000x + 150000                          {a=-1000<0}

[tex]h=\dfrac{-5000}{2\cdot(-1000)}=\dfrac{5000}{2000}=\dfrac52=2.5\\\\k=f(2.5)=1000(10+2.5)(15-2.5)=1000\cdot12.5\cdot12.5=156\,250[/tex]

15-2.5 = 12.5

Answer:

Monthly fee is $12.5

Value of revenue is $156,250

Answer: Graph is shown in the attached image below

This is a V shaped graph with the vertex at (3,0). The V opens upward

Explanation:

The equation y = |x-3| is the result of shifting the parent function y = |x| three units to the right. The vertex moves from (0,0) to (3,0). The "x-3" portion moves the xy axis three units to the left. If we held the V shape in place while the xy axis moved like this, then it gives the illusion the V shape moved 3 spots to the right.

Side note: the equation y = |x-3| is composed of two linear functions y = x-3 and y = -x+3. The value of x will determine which gets graphed. When x < 3, then we'll graph y = -x+3; otherwise we graph y = x-3. This is known as a piecewise function.

If Amir is not courageous, then he will not join the indian army.

Answer:

The value of t that will satisfy the equation is π/6 (which is 30 degrees)

Step-by-step explanation:

The function that models the movement of the particle is given as;

S(t) = 2 sin(t) + 3 cos (t)

Now we want to the value of t between 0 and pi/2 that satisfies the equation;

s(t) = (2+ 3√3)/2 = 1 + 3√3/2

What we do here is simply find that value of t that would ensure that;

2sin(t) + 3cos(t) = 1 + 3√3/2

Without any need for rigorous calculations, this value of t can be gotten by inspection.

From our regular trigonometry, we know that the sin of angle 30 is 1/2 and its cos value is √3/2

We can make a substitution for it in this equation.

We obtain the following;

2 sin(30) + 3cos (30) and that is exactly equal to 1 + 3√3/2

Do not forget however that we have a range. And the range in question is between 0 and π/2

Kindly that π/2 in degrees is 90 degrees

So our range of values here is between 0 and 90 degrees.

So to follow the notation in the question, the value within the range that will satisfy the equation is π/6

Step-by-step explanation:

I answered the first three in your next question :)

4) 2x + 15 = 37

Subtract 15

2x = 12

Divide by 2

x = 6

Ryan is 6 years old

5) A = 2/5(10)

A = 4

Andy is 4 years old

Hope it helps <3

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = expected outcome of event/total outcome of event

Given the total amount of chocolate in a box = 39chocolates

Amount of nuts = 16

Mount of caramel = 13

Amount of solid chocolate = 10

If he randomly selects a nut chocolate and eat, the probability of selecting a nut chocolate = Amount of nuts/total chocolate in the box = 16/39

IF he selects a seconnd piece (caramel chocolate) and eat, the probability of selecting a caramel chocolate = Amount of caramel/total chocolate in the box = 13/39 = 1/3

The probability of selecting a nut chocolate followed by a caramel chocolate will be 16/39*1/3 = 16/117

Answer:

All numbers greater than 5, i.e., [tex]x>5[/tex] .

Step-by-step explanation:

The given inequality is  

[tex]80x>150+50x[/tex]

Isolate variable terms on one side to find the solution.

Subtract  50x from both sides.

[tex]80x-50x>150+50x-50x[/tex]

[tex]30x>150[/tex]

Divide both sides by 30.

[tex]\dfrac{30x}{30}>\dfrac{150}{30}[/tex]

[tex]x>5[/tex]

It means, all the numbers which are greater than 5, are the solutions of the given inequality and 5 is not included in the solution set.

Answer:

241 mm^2.

Step-by-step explanation:

There are 10 mm in a cm so there are 10*10 = 100 mm^2 in  a cm^2.

So the answer is 2.41 * 100 = 241 mm^2.

Answer:

241mm²

Step-by-step explanation:

If 10mm = 1cm,

then 100mm² = 1cm²

2.41 × 100 = 241mm²