lines AD and BE intersect at point C, as shown. create an expression that represents the measure of the angle DCE in terms if X

part 2 of question: using your expression, solve for the missing value of X if DCE was 120 degrees.

To simplify the expression 54, divide it by 2 and 3 to get the simplified result of 9.

To simplify the expression 54, you need to consider the properties of the number 54. First, note that 54 is divisible by 2. Next, check if it is also divisible by 3. If it is, continue dividing by 3 until you can no longer do so. In this case, 54 is divisible by both 2 and 3, so you can simplify it as follows:

Therefore, the simplified expression 54 is equal to 9. So, the correct answer is A. 20.

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Answer:

12 (-0.25)ⁿ

Step-by-step explanation:

recall that the general form for each term in the geometric progression is

arⁿ

such that the geometric progression looks something like.

ar⁰, ar¹, ar², ar³, ....., arⁿ, ......

also note that r⁰ = 1, hence ar⁰ is simply a

hence the G.P can be written

a, ar, ar², ar³, ....., arⁿ, ......  

also note that r can be obtained by simply dividing the 2nd term with the 1stterm. i.e

r = ar ÷ a

now we are given the first 3 terms in the GP as

12, -3, 3/4, ....

comparing with the GP in the previous paragraph, we can see that ,

a = first term = 12

also

r = 2nd term ÷ 1st term

= -3 ÷ 12

= -0.25

hence the nth term

= arⁿ

= 12 (-0.25)ⁿ

The unit rate is calculated by dividing the total quantity by the total number of units. In this case, it takes 4 minutes to fill the aquarium to a depth of 2/5 meters. So, the unit rate for filling the aquarium is 10 minutes per meter.

To calculate the unit rate, you divide the total quantity by the total number of units. In this case, it takes 4 minutes to fill the aquarium to a depth of 2/5 meters. So, for the unit rate in minutes per meter, you would set up the division as follows:

4 minutes / (2/5) meters

When you divide 4 by 2/5, you actually multiply 4 by the reciprocal of 2/5, which is 5/2.

So, 4 * (5/2) = 10

Therefore, the unit rate for filling the aquarium is 10 minutes per meter.

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Step-by-step explanation:

[tex] (\frac{3}{2} ) \frac{9}{7} = \frac{3}{2} \times \frac{9}{7} = \frac{27}{14} \\ [/tex]

Answer:

it means 3/2 of 9/7

Step-by-step explanation:

those are fractions

Answer: 135cm

Step-by-step explanation

Volume of a cylinder = πr²h

Volume of a cone. = 1/3πr²h

The two shapes are both solid shapes.

Since the have same volume, we can then equate the two together and solve for the height of the cone.

Now make H the height and R the radius of the cylinder and h the height and r the radius of the cylinder.

Now equating the two

πR²H = 1/3πr²h

Now substitute for the values now

Multiply through by 3

3πR²H = πr²h

But π is common so it could be obliterated from the equation

3R²H = r²h

3 x 12² x 20 = 8² x h

3 x 144 x 20 = 64 x h

60 x 144 = 64h

8640. = 64h

Therefore

h = 8640/64

= 135cm

Answer:

1.29 minutes

Step-by-step explanation:

The scientist has a record of the amount of rainfall during the afternoon as around 0.43 minutes in each hours.

Now, we have to calculate the total amount of rainfall in three hours.

As the each hour rainfall is of 0.43 minutes, so the total rainfall in three hours will be (0.43 × 3) = 1.29 minutes. (Answer)

Answer:

y=2/15x-3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-5-(-3))/(-15-0)

m=(-5+3)/-15

m=-2/-15

m=2/15

y-y1=m(x-x1)

y-(-3)=2/15(x-0)

y+3=2/15(x)

y+3=2/15x

y=2/15x-3

Answer:

Step-by-step explanation:

y−intercept=  

−7

1

​  

=−0.14286

Answer:

Step-by-step explanation:

let x represent the leg length

if we use the Pythagorean theorem we get:

x² + x² = 12²

then

2x² = 12²

Then

x² = 144/2 = 72

then

x = √(72)

 =8,485281374239

Answer: 35 F

Step-by-step explanation:

night time

The correct answer is y=3/2x+4

Answer:

Step-by-step explanation:

programs can be written in multiply languages. for this solution I'll be writing in C++.

#include<iostream> // this is called the preprocessor definition

using namespace std;

int main()                      //the main function

{

   int num, product;      //declaration of the variables

    cout << "enter the whole number";  

    cin >> num;

    product = num * 12;

     cout << product; // displaying the final results

     return 0;

}

Answer:

i think its 11,700

Step-by-step explanation:

Answer:

11,700

Step-by-step explanation:

When trying to find the new area, you take you 2 numbers, 52 and 15, square the 15,  then multiply them

52 x 15^2 = 11,700

80

The question implies that you're counting by tens & the number comes after 70 and before 90. This is the only number that fits this description.

Using logical concept, the value of the number in question will be 80.

Let the number be n ;

Hence, we have ;

70, n, 90

n - 70 = 10 - - (1)

90 - n = 10 - - - (2)

Using either of the two expressions, we can obtain the value of n :

n - 70 = 10

n = 10 + 70

n = 80

Hence, the number is 80

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Answer:

23/100

Step-by-step explanation:

Any percent is out of 100, so you can just say 23/100. This works for any percentage but you can still simplify it. 23/100 is already in its simplest form so you can not simplify it any more. 23% in decimal form is 0.23.

Answer:

study more that should help you out

Step-by-step explanation:

study more

Answer:

try to study

Step-by-step explanation:

Answer:

128 yards

Step-by-step explanation:

Final answer:

By applying the Pythagorean theorem to the right-angled triangle sail, with the longest edge being the hypotenuse (16 yards) and the bottom edge as one side (8 yards), the height of the sail is calculated to be approximately 13.856 yards.

Explanation:

To determine how tall the sail is, we can use the Pythagorean theorem if we assume that the sail is a right-angled triangle, which is common in sailboat sails. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. If we let the longest edge (16 yards) be the hypotenuse (c) and the bottom edge (8 yards) be one of the other sides (a), we can find the height (b) of the sail using the equation:

c² = a² + b²

So,

16² = 8² + b²

256 = 64 + b²

b² = 256 - 64

b² = 192

b = √192

b ≈ 13.856 yards (rounding to three decimal places)

Therefore, the sail is approximately 13.856 yards tall.

Answer:

its A :)

Step-by-step explanation:

Answer:

  100°

Step-by-step explanation:

The larger one is 5/(5+4) = 5/9 of the total, so is ...

  5/9 × 180° = 100°

The measure of the larger angle is 100°.

Answer:

Therefore the new coordinate of the point is (2,-4)

Step-by-step explanation:

A point (2,4) is rotated [tex]90^\circ[/tex] clockwise .

The point (2,4) lies on the first coordinate.If the point rotated [tex]90^\circ[/tex]clockwise direction It will be go fourth coordinate.

Therefore the new coordinate of the point is (2,-4)

There are 56 different combinations of 5 friends that can be selected from the group of 8 friends (option C)

To determine the number of different combinations of 5 friends that can be selected from a group of 8 friends, we use the concept of combinations in combinatorial mathematics.

The number of ways to choose [tex]\( k \)[/tex] elements from a set of [tex]\( n \)[/tex] elements is given by the binomial coefficient [tex]\(\binom{n}{k}\)[/tex], which is calculated as:

[tex]\[\binom{n}{k} = \frac{n!}{k!(n-k)!}\][/tex]

In this scenario:

[tex]\( n = 8 \)[/tex] (total number of friends)

[tex]\( k = 5 \)[/tex] (number of tickets available, hence number of friends to be chosen)

We need to calculate [tex]\(\binom{8}{5}\)[/tex]:

[tex]\[\binom{8}{5} = \frac{8!}{5!(8-5)!} = \frac{8!}{5! \cdot 3!}\][/tex]

First, we calculate the factorials involved:

[tex]\( 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320 \)[/tex]

[tex]\( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \)[/tex]

[tex]\( 3! = 3 \times 2 \times 1 = 6 \)[/tex]

Now, substitute these values into the binomial coefficient formula:

[tex]\[\binom{8}{5} = \frac{40320}{120 \times 6} = \frac{40320}{720} = 56\][/tex]

Therefore, there are [tex]\( 56 \)[/tex] different combinations of 5 friends that can be selected from the group of 8 friends.

Set the two sets of parentheses in the denominator equal to zero and solve for the x’s. These would be the vertical asymptotes

(X+2) = 0

X = -2

(X-1)=0

X =1

The vertical asymptotes are -2 and 1

Answer:

slope = - 1

Step-by-step explanation:

The slope of the curve m is measured by

m = [tex]\frac{dy}{dx}[/tex] at x = a

Differentiate using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

Given

y = - 3x - x², then

[tex]\frac{dy}{dx}[/tex] = - 3 - 2x

x = - 1 → [tex]\frac{dy}{dx}[/tex] = - 3 - 2(- 1) = - 3 + 2 = - 1 ← slope at (- 1, 2 )

Answer:

No, the expressions are NOT equivalent.

Step-by-step explanation:

Solve each:

11t - 4t

(11 × 2) - (4 × 2)

22 - 8

= 14

4t - 11t

(4 × 2) - (11 × 2)

8 - 22

= -14

14 is NOT equivalent to -14

Answer:

5

Step-by-step explanation:

The median is 5. Cross off the dots on both sides one by one until you reach the center.

The value of [tex]\sec\theta =\pm\sqrt{\frac{11}{8}}[/tex].

Solution:

Given data:

[tex]$\tan^2\theta=\frac{3}{8}[/tex]

To find the value of [tex]\sec\theta:[/tex]

Using trigonometric identity,

[tex]\sec^2\theta=1+\tan^2\theta[/tex]

Substitute [tex]\tan^2\theta=\frac{3}{8}[/tex] in the identity, we get

[tex]$\Rightarrow \sec^2\theta=1+\frac{3}{8}[/tex]

1 can be written as [tex]\frac{1}{1}[/tex].

             [tex]$ =\frac{1}{1} +\frac{3}{8}[/tex]

Do cross multiplication.

            [tex]$ =\frac{8}{8} +\frac{3}{8}[/tex]

Denominators are same, so you can add the fractions.

            [tex]$ =\frac{8+3}{8}[/tex]

[tex]$\Rightarrow \sec^2\theta =\frac{11}{8}[/tex]

Taking square root on both sides, we get

[tex]$\Rightarrow \sec\theta =\pm\sqrt{\frac{11}{8}}[/tex]

Option B is the correct answer.

Hence the value of [tex]\sec\theta =\pm\sqrt{\frac{11}{8}}[/tex].

Answer:

Step-by-step explanation:

Let g = amount of general admission tickets

Let s = amount of student tickets

Since seventy people attended the concert, this includes the people who bought general admission tickets and the people who bought the student tickets. As a result, g + s = 70. A student ticket is $3.25, so it would be 3.25s and a general admission ticket is $4.75, so it would be 4.75g. Since there was $272.50 collected in all, the second equation would be 3.25s + 4.75g = 272. 50.

g + s = 70

4.75g + 3.25s = 272.50

Multiply the first equation by 3.25 (or 4.75) so that you can use elimination to get rid of one variable.

3.25g + 3.25s = 227.50

4.75g + 3.25s = 272.50

Now, you subtract so that you can eliminate s.

-1.50g = -45

g = 30

This means that there are 30 general admission tickets. Now, you substitute 30 in for g to find s.

30 + s = 75

Subtract 30 from both sides.

s = 45

This means that there are 30 general admission tickets and 45 student tickets.

let's say the original number is "a".

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of "a"}}{\left( \cfrac{5}{100} \right)a}\implies \cfrac{5a}{100} \\\\\\ \stackrel{\textit{"a" increased by 5\%}}{a + \cfrac{5a}{100}\implies \cfrac{105a}{100}}~\hfill \stackrel{\textit{5\% of }\frac{105a}{100}}{\left( \cfrac{5}{100} \right)\cfrac{105a}{100}}\implies \cfrac{525a}{10000}\implies \cfrac{21a}{400}[/tex]

[tex]\bf \stackrel{\frac{105a}{100}\textit{ increased by 5\%}}{\cfrac{105a}{100}+\cfrac{21a}{400}}\implies \cfrac{21a}{20}+\cfrac{21a}{400}\implies \cfrac{420a+21a}{400}\implies \cfrac{441a}{400} \\\\\\ 1.1025a\implies 1a+0.1025a\implies \stackrel{\textit{original}}{a} + \stackrel{\textit{10.25\% added}}{\cfrac{10.25}{100}a}[/tex]