What is the length of BD?
Round to one decimal place.

[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

   Find the gradient of the line joining (-1,9) and (3,5)

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

Use the slope formula:-

[tex]\boxed{\frac{y_2-y_1}{x_2-x_1}}[/tex]

Replace the letters with the numbers:-

[tex]\boxed{\frac{5-9}{3-(-1)}}[/tex]

[tex]\circ[/tex] On simplification,

[tex]\boxed{\frac{-4}{3+1}}[/tex]

[tex]\circ[/tex] On further simplification,

[tex]\boxed{\frac{-4}{4}}[/tex]

[tex]\circ\sf{SLOPE=-1}[/tex]

[tex]\rule{300}{1}[/tex]

Answer:

Step-by-step explanation:

Area of sector :

Answer:

x= -2 y= 36 (-2. 36)

x = -1 y = 6 (-1, 6)

x = 1 y = [tex]\frac{1}{6}[/tex] (1, [tex]\frac{1}{6}[/tex])

Step-by-step explanation:

Our function is [tex]y = (\frac{1}{6})^x[/tex]

all we need to do is fill in our x (given in the table) to solve for y

[tex]y = (\frac{1}{6})^{-2}[/tex]

[tex]y = 36[/tex]

[tex]y = (\frac{1}{6})^{-1}[/tex]

[tex]y = 6[/tex]

[tex]y = (\frac{1}{6})^1 = \frac{1}{6}[/tex]

Step-by-step explanation:

x = 4

y = -2

z = 3

= 6x + 4y - z

= 6.4 + 4.-2 - 3

= 24 - 8 - 3

= 13

Answer:

14 gm

Step-by-step explanation:

34 minutes is TWO half lives   1/2 * 1/2 = 1/4   will be left

   1/4 * 56 = 14 gm

Answer:

14

Step-by-step explanation:

If Bob has 22 pints, and one glass is one pint, the 22-8 = 14

Answer:

14

Step-by-step explanation:

you would subtract 8 pints of soda left from the total pints which is 22 to get 14 pints used during the party

22-8=14

Step-by-step explanation:

it shows that all the small triangles that together make the complete square (c²) under the Hypotenuse consist of exactly all the composing triangles of the squares above the legs (a² and b²).

we find the 2 purple, the 2 orange, the 2 yellow and the 2 blue triangles there.

so, the area of c² must be the same as the sum of the areas of a² and b².

Answer:

50%

half of the numbers are even

Step-by-step explanation:

Answer:  Angle Y is 90 degrees, angle X is 35.  

Answer:x=35 and y=35

Step-by-step explanation:

Angle on straight line =180

so 180/2=90

90-55=35

and x and y opposite angle so are eqaul

Answer: -4 and 9

Step-by-step explanation:

Ok so firstly, you need to remember that when a radius is touching a tangent, the angle is always equal to 90°. So x + 57° = 90°. That means your angle is 33°. You have drawn a right angle which is correct so the left triangle's angle is 90° - 33° = 57°. Now because both sides of the triangle is radius, that means c and 57° are equal. That means c = 57°.

Answer:

c = 57 degrees.

Step-by-step explanation:

This is the Alternate Segment theorem:

The angle between a chord of a circle and a tangent to the circle = the angle subtended by the chord in the alternate segment.

So c = 57 degrees.

Answer:

34,220

Step-by-step explanation:

Because order doesn't matter, but the numbers can't be repeated, we need to find the number of combinations where 3 individual numbers can be chosen out of 60 possible numbers using the binomial coefficient:

[tex]\binom{n}{k}=\frac{n!}{k!(n-k)!}\\ \\\binom{60}{3}=\frac{60!}{3!(60-3)!}\\\\\binom{60}{3}=\frac{60!}{3!(57)!}\\\\\binom{60}{3}=\frac{60*59*58}{3*2*1}\\ \\\binom{60}{3}=34220[/tex]

Thus, Elias can make 34,220 unique 3-number codes given 60 different numbers.

Answer:

32

Step-by-step explanation:

Multiply both sides by 8.

y/8 = 4

y/8 × 8 = 4 × 8

y = 32

Answer:

-81/-9

both minus will be cut so

81/9

9

Step-by-step explanation:

the answer is 9

Answer:

2q + 94

Step-by-step explanation:

2q + 2 + 92 ← collect like terms

= 2q + (2 + 92)

= 2q + 94

Answer:

Step-by-step explanation:

2q + 2 + 92

Reorder and group

2q + (2 + 92)

Caculate

2q + 94

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Answer:

Step-by-step explanation:

Sum of all angles of triangle = 180

     5x - 11 + 3x - 3 + 3x + 18 = 180

      5x + 3x + 3x  -11 - 3 + 18 = 180

Combine like terms

                             11x  + 4 = 180

                                   11x = 180 - 4

                                   11x = 176

                                      x = 176/11

                                       x = 16

∠R = 5x - 11

   = 5*16 - 11

   = 80 - 11

    = 69

Apply angle sum property

m<R

The approximate area of each half of ​△ACB is 28 square feet

The formula for calculating the area of a triangle is expressed as:

A = 0.5absintheta

Given the following

PB =11ft

<PCB = 65degrees

Using the SOH CAH TOA identity

tan<PCB = 11/CP
CP = 11/tan65
CP = 5.13 ft

Determine the required area

Area = 0.5(11)(5.13)sin90

Area = 5.5 * 5.13

Area . = 28 square ft

Hence the approximate area of each half of ​△ACB is 28 square feet

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Using the combination formula, and supposing that you have n parts, it is found that the number of trains you can make is of:

[tex]N = C_{n,3} = \frac{n!}{3!(n - 3)!} = \frac{n!}{6(n-3)!}[/tex]

The order in which the parts are taken is not important, hence the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 3 parts are taken from a set of n, hence the total number of trains is given by:

[tex]N = C_{n,3} = \frac{n!}{3!(n - 3)!} = \frac{n!}{6(n-3)!}[/tex]

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Answer:

(x+y)(z+1)

Step-by-step explanation:

trust me .......

Answer:

(x+y) (z+1)

Step-by-step explanation:

xz + x + yz + y

- group the first two terms and the last two terms.

(xz + x ) + yz + y

- factor out the greatest common factor (GCF) from each group.

x (z + 1) + y (z + 1)

- factor the polynomial by factoring out the greatest common factor, z + 1.

(x+y) (z+1)

Answer;

10

Step-by-step explanation:

from the question we observed that the shape is a right angled triangle.

and according to Pythagoras theorem, In a right angled triangle the square of the hypothenus is equal to the square of the sum of the other two side

hypothenus = 10

10^2= 8^ + X^2

100= 64 +X^2

X^2 = 100-64

X^2 = 36

X = √36

X= 6

Solution, Diameter = 30[tex]radius = \frac{diameter}{2} = \frac{30}{2} = 15 \\ [/tex]

Now, []area = \pi {r}^{2} [/tex][tex] = 3.14 \times 15 \times 15[/tex][tex] = 706.5 [/tex]Hence the area is 706.5now........[tex]circumference = 2 \: \pi\: r[/tex][tex] = 2 \times 3.14 \times 15[/tex][tex] = 94.2[/tex]hence the answer is 94.2...

Solution,

Diameter = 30

[tex]radius = \frac{diameter}{2} = \frac{30}{2} = 15 \\ [/tex]

Now,

[tex]area = \pi {r}^{2} [/tex]

[tex] = 3.14 \times 15 \times 15[/tex]

[tex] = 706.5 [/tex]

Hence the area is 706.5

now........

[tex]=Circumference = 2 \: \pi\: r[/tex]

[tex] = 2 \times 3.14 \times 15[/tex]

[tex] = 94.2[/tex]

hence the answer is 94.2...

Answer:

- 95/18

Step-by-step explanation:

1st you have to convert the mixed number to an improper fraction so 2 ×6 = 12 +1 = 13 and that together equals 13/6 same goes for the next take away the parentheses 13/6 - 8/3 - 4 7/9

then you have to do the same thing with the 1st fraction convert it 4 × 9 = 36 + 7 = 43 that equals together 43/9

lastly you have to calculate the difference 13/6 - 8/3 - 43/9 and that equals negative 95/18

by the way the 95 isnt a negative the fraction itself is

See below for the proof of the trigonometry identity [tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex]

The trigonometry equation is given as:

[tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex]

Rewrite the equation as:

[tex]\frac{\tan^2(A) }{\tan(A) - 1} - \frac{\cot(A)}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]

Take LCM

[tex]\frac{\tan^2(A) - \cot(A)}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]

Express cot(A) as 1/tan(A)

[tex]\frac{\tan^2(A) - \frac{1}{\tan(A)}}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]

Take LCM

[tex]\frac{\tan^3(A) - 1}{\tan(A)(\tan(A) - 1)} =1 + \sec(A)\csc(A)[/tex]

Apply the difference of two cubes on the numerator

[tex]\frac{(\tan(A) - 1)(\tan^2(A) + \tan(A) + 1)}{\tan(A)(\tan(A) - 1)} =1 + \sec(A)\csc(A)[/tex]

Cancel out the common factors

[tex]\frac{\tan^2(A) + \tan(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]

Rewrite as:

[tex]\frac{\tan(A) + \tan^2(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]

Split the fraction

[tex]1 + \frac{\tan^2(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]

Express [tex]\tan^2(A) + 1[/tex] as [tex]\sec^2(A)[/tex]

[tex]1 + \frac{sec^2(A)}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]

Divide [tex]\sec^2(A)[/tex] by [tex]\tan(A)[/tex]

[tex]1 + \frac{1}{\sin(A)\cos(A)} = 1 + \sec(A)\csc(A)[/tex]

Take the inverse of sin and cosine

[tex]1 + \sec(A)\csc(A) = 1 + \sec(A)\csc(A)[/tex]

Both sides of the equation are the same.

Hence, the trigonometry identity [tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex] has been proved

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Answer:

May be the answer is 5 . I don't think it's the answer .

Explanation:

f(x) = (x-4)(x+2)

1) For x-intercept, y will be 0

x-intercept: (4, 0), (-2, 0)

2) For vertex: x = -b/2a where ax² + bx + c

Quadratic function:

vertex:

y: (x-4)(x+2) = (1-4)(1+2) = -9

ordered pair of vertex: (1, -9)

3) For y-intercept, x will be 0

y-intercept: (0, -8)

Answer:

Step-by-step explanation:

Q1 : Finding x-intercepts

Q2

Q3

Answer:

yes not function because 1 is repeated

Answer:

660 cubic cm

Step-by-step explanation:

Volume= bhl/2