Is the relation a function

Yes
No

Answer:

[tex]\angle ADE =[/tex] [tex]69^\circ[/tex]

Step-by-step explanation:

Given:

[tex]\angle ABD = 32^\circ[/tex]

BA = BD

CB = CD

In [tex]\triangle ABD:[/tex]

BA = BD

We know that in a triangle, angles opposite to equal sides will also be equal.

[tex]\Rightarrow \angle BAD = \angle BDA[/tex]

We know that sum of internal angles of a triangle is equal to [tex]180^\circ[/tex]

[tex]\angle BAD + \angle BDA +\angle ABD=180^\circ\\\Rightarrow \angle BAD + \angle BDA +32=180\\\Rightarrow \angle BAD + \angle BDA = 180 -32\\\Rightarrow \angle BAD + \angle BDA = 148\\\Rightarrow \angle BAD = \angle BDA = \dfrac{148}{2} = 74^\circ[/tex]

Quadrilateral ABCD is cyclic so, sum of opposite angles is equal to [tex]180^\circ[/tex].

[tex]\angle BAD + \angle BCD = 180^\circ\\\Rightarrow 74 + \angle BCD = 180\\\Rightarrow \angle BCD = 180-74 = 106^\circ[/tex]

In [tex]\triangle BCD:[/tex]

BC = CD

We know that in a triangle, angles opposite to equal sides will also be equal.

[tex]\Rightarrow \angle DBC = \angle CDB[/tex]

We know that sum of internal angles of a triangle is equal to [tex]180^\circ[/tex]

[tex]\angle DBC + \angle BCD +\angle CDB=180^\circ\\\Rightarrow \angle DBC + 106 +\angle CDB=180\\\Rightarrow \angle DBC +\angle CDB=180 - 106\\\Rightarrow \angle DBC =\angle CDB=\dfrac{74}{2} = 37^\circ[/tex]

It is given that the line CDE is a straight line, so the sum of angles on one side of point D is [tex]180^\circ[/tex].

[tex]\angle CDB + \angle BDA +\angle ADE = 180^\circ\\\text{Putting values of } \angle CDB \text{ and }\angle BDA:\\\Rightarrow 37 + 74 + \angle ADE = 180\\\Rightarrow \angle ADE = 180 -111\\\Rightarrow \angle ADE = 69^\circ[/tex]

So, the answer is [tex]\angle ADE =[/tex] [tex]69^\circ[/tex]

The size of ∠ADE of the cyclic quadrilateral is;

∠ADE = 53°

We are given;

BA = BD

CB = CD

∠ABD = 32°

Now, ΔABD is an isosceles triangle and since sum of angles in a triangle is 180°, then;

∠ABD + ∠BAD + ∠BDA = 180°

∠BAD + ∠BDA = 180 - 32

∠BAD + ∠BDA = 148°

Since isosceles, then;

∠BAD = ∠BDA = 148/2

∠BAD = ∠BDA = 74°

Now, in cyclic quadrilaterals, opposite angles are supplementary and as such add up to 180°. Quadrilateral ABCD is cyclic and Thus;

∠BAD + ∠BCD = 180°

74 + ∠BCD = 180°

∠BCD = 180 - 74

∠BCD = 106°

ΔBCD is an isosceles triangle and as such;

∠CBD = ∠CDB = 106/2

∠CBD = ∠CDB = 53°

Now, sum of angles on a straight line add up to 180°. Thus;

∠CBD + ∠BDA + ∠ADE = 180°

Plugging in the relevant values gives;

53° + 74° + ∠ADE = 180°

∠ADE = 180 - (53 + 74)

∠ADE = 53°

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[tex](a + b) {}^{3} = a {}^{3} + 3a {}^{2} b + 3ab {}^{2} + b {}^{3} \\ \\ x {}^{6} + 6x {}^{4} y + 12x {}^{2} y {}^{2} + 8y {}^{3} [/tex]

Answer:

x^6 + 6x^4 y + 12x^2 y^2 + 8y^3.

Step-by-step explanation:

Using the Binomial Theorem:

(x^2 + 2y)^3 = (x^2)^3 + 3C1 (x^2)^2 (2y) + 3C2 x^2 (2y)^2 + (2y)^3

= x^6 + 3*x^4*2y + 3*x^2*4y^2 + 8y^3

= x^6 + 6x^4 y + 12x^2 y^2 + 8y^3.

Hey!!

Solution,

3x^2+6x

take the common,

3x(X+2)

hope it helps

Good luck on your assignment

the 11 units from 0 is c only

Answer:

17 dominoes

Step-by-step explanation:

21 and 1/4 in divided by how far they need to be spaced apart, 1 and 1/4 in, is equal to 17 dominoes.

Answer:

y = 16x +8

Step-by-step explanation:

Per means for every so and so, and a fee is one-time thing, so 16 would be with x and 8 as the y (intercept)

Answer:

EF = 34, FG = 25

Step-by-step explanation:

EG is the total of the two smaller segments, EF and FG.

Therefore:

8x-14 + 4x+1 = EG

8x-14 + 4x+1 = 59

Now we can solve this equation.

8x-14 + 4x+1 = 59

12x-13 = 59

12x = 72

x = 6

Now, we can plug in the values of x into the expressions for the lengths of EF and FG:

EF

8x-14

8(6)-14

48-14

= 34

FG

4x+1

4(6)+1

24+1

= 25

[tex]\text{Solve:}\\\\2x+3=2(x+3)\\\\\text{Use the distributive property:}\\\\2x+3=2x+6\\\\\text{Subtract 2x from both sides}\\\\3=6\\\\\text{Since 3 doesn't equal 6, this equation is not true}\\\text{Therefore, there are no solutions}\\\\\boxed{\text{No solutions}}[/tex]

Answer:

The number of different combinations of three students that are possible is 35.

Step-by-step explanation:

Given that three out of seven students in the cafeteria line are chosen to answer a survey question.

The number of different combinations of three students that are possible is given as:

7C3 (read as 7 Combination 3)

xCy (x Combination y) is defines as

x!/(x-y)!y!

Where x! is read as x - factorial or factorial-x, and is defined as

x(x-1)(x-2)(x-3)...2×1.

Now,

7C3 = 7!/(7 - 3)!3!

= 7!/4!3!

= (7×6×5×4×3×2×1)/(4×3×2×1)(3×2×1)

= (7×6×5)/(3×2×1)

= 7×5

= 35

Therefore, the number of different combinations of three students that are possible is 35.

There are 35 different combinations to chose 3 students from the 7 students

The given parameters are:

Students, n = 7

Selected , r = 3

The number of different combinations is calculated using:

Combination = nCr

This gives

Combination = 7C3

Using the combination formula, we have:

Combination = 35

Hence, there are 35 different combinations to chose 3 students from the 7 students

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Answer:

y= x/4 - 3

Step-by-step explanation:

Answer:

Factored Form:        x = y/2 + 7

Standard Form: 2x - y = 14

Step-by-step explanation:

Answer:

3^2 = 9

8^2 = 64

10^2 = 100

Step-by-step explanation:

4x - 13 = 3x + 7

4x - 3x = 7 + 13

x = 20

Therefore x = 20

Answer:

42

Step-by-step explanation:

Answer:42.5%

Step-by-step explanation:

Answer:

the answer is 42.5%

Step-by-step explanation:

you multiply both 40 and 17 by 2.5 to get 42.5/100 which is the percent in fraction form

Answer:

C. Inverse

Step-by-step explanation:

The second statement is the inverse, because in an inverse, the hypothesis and the conclusion are both negated. In this case, the sun doesnt shine and the people wont be in a good mood, as opposed to the sun will shine, and the people will  be in a good mood.

Answer:

Inverse

Step-by-step explanation:

Answer:

GCF= 16

Step-by-step explanation:

factors of 32= 32, 16, 8, 4, 2, 1

factors of 16= 16, 8, 4, 2, 1

16 is the largest factor both numbers have in common

Answer: 16

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

There are 46 children attending the field trip.

Each van needs to transport 8 children.

To find the number of vans they need, we will divide the number of children by the number of children per van:

46 / 8 = 5.75 ≅ 6 vans

They need 6 vans.

Answer:

The ball will hit the ground at 0.968 seconds.

Step-by-step explanation:

Please refer to the attached graph in the answer area.

The given equation of height according to input variable time 't' is:

[tex]h = - 16 t^{2} + 15 ...... (1)[/tex]

h is in feet

t is in seconds

Both the values 't' and 'h' will be positive. (Time and height can never be negative)

To determine the time, at which the ball hits the ground, i.e. the height becomes 0.

Putting value of h = 0 in equation (1)

[tex]0 = - 16 t^{2} + 15 \\\Rightarrow t^{2} = \dfrac{15}{16}\\\Rightarrow t = \sqrt{\dfrac{15}{16}}\\\Rightarrow t = 0.968\ sec[/tex]

Hence, the time at which the ball hits the ground is 0.968 seconds.

Answer:

three hundred and one

Step-by-step explanation:

This wasn't very clear..

Answer: the number 301 can be written as three hundred one.

Step-by-step explanation: the number 301 can be written as three hundred one. To find a, take the number and move a decimal place to the right one position. Now, to find b, count how many places to the right of the decimal. There are 2 places to the right of the decimal place.

Answer:

A = 100π units²

Step-by-step explanation:

To answer this we first find the circumference C = 2πr, and then multiply this C by the height:

C = 2πr, or C = πd.  Here, C = π(10 units).

Then the lateral area of the cylinder is A = C*(10 units), or

A = 10π(10) units², or

A = 100π units²

The lateral surface area of the given right cylinder is 314 square units.

The lateral surface area of a right cylinder is the product of the circumference of the base and the height of the cylinder.

Given, the base diameter(d) of the cylinder is 10 units.

Therefore, the base radius(r) of the cylinder is

[tex]= \frac{10}{2} units\\= 5 units[/tex]

The height(h) of the cylinder is 10 units.

Therefore, the lateral surface area of the cylinder is

= 2πrh square units

[tex]= 2(3.14)(5)(10)[/tex] square units

[tex]= 314[/tex] square units

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[tex]7:3[/tex]

The ratio of 7 to 3.

The ratio as a fraction would be:

[tex]\frac{7}{3}[/tex]

Answer:

(x+1) (x^2+3)

Step-by-step explanation:

x^3 + x^2 + 3x + 3

x^3 + x^2      + 3x + 3

Factor out x^2 from the first group and 3 from the second group

x^2(x+1)   +3(x+1)

Then factor out (x+1)

(x+1) (x^2+3)

Answer:

[tex](x + 1)( {x}^{2} +3 )[/tex]

Answer A is correct

Step-by-step explanation:

[tex] {x}^{3} + {x}^{2} + 3x + 3 \\ {x}^{2} (x + 1) + 3(x + 1) \\ = ( {x}^{2} + 3)(x + 1)[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Hey!Here is ur answer:

Danielle is wrong cause 'she has included a decimal'.

U might doubt that zero is might not be an integer but it is a neutral integer.

            HOPE IT MAKES UR DAY BETTER!!

Danielle says that her set of numbers are integers the statement is wrong as the set contain decimal number because decimal numbers are not integers, so option C is correct.

All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.

Given:

Danielle says that her set of numbers are integers. Left-brace negative 253, negative 45, negative 0.9, 0, 26 Right-brace,

Write the above phrase in the mathematical form as shown below,

(-253, -45, -0.9, 0, 26)

As we know that integers are whole numbers, they can't be a decimal numbers or a fraction,

Thus, the set of numbers are integers is wrong because it contains decimal numbers.

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Answer:

I THINK its the last one (8 root 10 to the power of 3x)

Step-by-step explanation:

A square root is the same thing as raising something to the 1/2. So the expression we have is (10^1/2)^3/4x.

Due to exponent rules we can multiply to get

10^3/8x which is the same thing as 10^3x/8

The 8 goes to the root and the 3x becomes the exponent

In this exercise we have to have knowledge about the properties of powers, so we have to:

Letter D

Recalling some properties of power, we find that:

Are returning to the exercise and using the properties informed, we find that:

[tex](10^{1/2})^{3/4x}\\10^{3/8x} = 10^{3x/8}[/tex]

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Answer:

b 2/7

Step-by-step explanation:

Because there is a 6/21 chance and 2/7=6/21

The probability that a number less than or equal to three is rolled is 1/2.

Given that, a number cube is rolled, we need to find that what is the probability that a number less than or equal to three is rolled,

So, the probability = favorable outcomes / total outcomes

Here, the favorable outcome = 1, 2, 3 = 3

The total outcomes = 1, 2, 3, 4, 5, 6 = 6

So, the probability = 3/6 = 1/2

Hence, the probability that a number less than or equal to three is rolled is 1/2.

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Answer:

2/3

Step-by-step explanation:

.that's the answer