There were 35 children and 10 adults in a picnic. What is the ratio of children to the total number of people in the picnic?

See below for the verification of ∠ACD =  ∠ABC + ∠BAC

The following proof works for both triangles.

The sum of angles in a triangle is 180 degrees.

So, we have:

∠ABC + ∠BAC + ∠ACB = 180

Make ∠ACB the subject

∠ACB = 180 - ∠ABC - ∠BAC

The sum of angles on a straight line is 180 degrees.

So, we have:

∠ACD + ∠ACB = 180

Make ∠ACB the subject

∠ACB = 180 - ∠ACD

Substitute ∠ACB = 180 - ∠ACD in ∠ACB = 180 - ∠ABC - ∠BAC

180 - ∠ACD = 180 - ∠ABC - ∠BAC

Subtract 180 from both sides

- ∠ACD = - ∠ABC - ∠BAC

Multiply both sides by -1

∠ACD =  ∠ABC + ∠BAC

Hence, ∠ACD =  ∠ABC + ∠BAC has been verified

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Answer:

59

Step-by-step explanation:

[tex] \sqrt{ {6}^{2} + {5}^{2} } = \sqrt{36 + 25} = \sqrt{61} [/tex]

[tex] \cos(p) = \frac{4}{ \sqrt{61} } [/tex]

[tex]p = {cos}^{ - 1} \frac{4}{ \sqrt{61} } = 59[/tex]

Make sure your calculator is in degree mode.

The largest angle of the pentagon with the given ratio of angles is: 180°.

A pentagon is a 5-sided polygon with 5 interior angles that have a sum of 540 degrees.

If the ratio of the angles are: 1:2:2:3:4, then the largest angle would be calculated as shown below:

4/(1+2+2+3+4) × 540

4/12 × 540 = 180°

The largest angle is: 180°.

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Answer:

-14/15

Step-by-step explanation:

"of" means multiply, thus:

-8/15 * 21/12

-8 * 21 / 15 * 12

-2 * 7 / 15

-14/15

Answer:

-14/15

Step-by-step explanation:

So first you need to get rid of the negative sign. Don't worry you will add it back later!

So, you will do

-8/15×21/12

Once you cross cancel, you will have

-2/5x7/3

That would be equivalent to

-14/15

That's your answer!

Hope this helped :)

Answer:

Each pizza was $12.55.

Step-by-step explanation:

et's take it piece by piece.

Salad and the tip together is 4.95 + 5 = 9.95, right?

47.60 - 9.95 = 37.65 spent on pizza

37.65/3 = 12.55

Answer:

113 degrees

Step-by-step explanation:

Two angles are called supplementary when they add up to 180 degrees

[tex]180 = x + y \\ 180 = 67 + y \\ y = 180 - 67 \\ y = 113 \\ therefore \: mB \: = 113[/tex]

The tomb are worth preserving as they are important to the legacy of the people.

It should be noted that a tomb simply means a repository of the remains of the dead. The Tombs of Buganda Kings can be found in Uganda.

It's a royal tomb and represents the heart of the Baganda people.

In this case, the tomb are worth preserving as they are important to the legacy of the people.

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Answer:

62/235 +95/383

Step-by-step explanation:

P(satisfied or junior)= P(satisfied participant that are junior) + P(junior participant)

P(satisfied or junior)= 62/235 + 95/383

P(satisfied or junior)= 46071/90005

Answer:

What is the slope of the line represented by the equation y = y equals StartFraction 4 Over 5 EndFraction x minus 3.x – 3?

Step-by-step explanation:

The equation of line that is parallel to the given line having slope m = -1 and passes through the point ( -3 , 1 ) is y = -x - 2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -3 , 1 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

The slope of the line m = -1

Now , the line is parallel to the line passing through P

So , the slopes of the lines are equal

And , the equation of line is y - y₁ = m ( x - x₁ )

On simplifying , we get

y - 1 = -1 ( x - ( -3 ) )

y - 1 = -1 ( x + 3 )

Adding 1 on both sides , we get

y = -x - 3 + 1

y = -x - 2

Hence , the equation of line is y - 1 = -1 ( x + 3 )

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The volume of 10% solution will be 6 l and 9 litre of the 30 % solution will be taken.

Volume is the space occupied by a three dimensional object .

The concentration of solution required is 22% acid

The concentration of solution available is 10% and 30%

The total volume required is 15 liters

The formula for making a mixture is

Concentration = ( m₁x₁ +m₂x₂) / (x₁+x₂)

22 = (10 * x + 30 *(15 -x))/( 15)

10 x + 450 - 30x =330

-20x = -120

x = 6

The volume of 10% solution will be 6 l

and 9 litre of the 30 % solution will be taken.

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The frequency distribution has been illustrated based on the information given.

It should be noted that frequency distribution is the representation that displays the number of observations that are in a given interval.

From the data distribution, the frequency distribution will be:

Class. Frequency

0 - 14.         5

15 - 29.      15

30 - 44.     13

45 - 59.      6

60 - 74.      5

75 - 89.       1

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Answer:

374795-57770

Step-by-step explanation:

Abby uses

-1000000 that is the answer

hope this helps!

From the given mappings, we have

[tex]f(1) = 5, f(4) = 1, f(2) = 7[/tex]

and

[tex]g(3) = 1, g(5) = 4, g(-6) = 2[/tex]

Then the composition of [tex]f[/tex] with [tex]g[/tex], or [tex]f\circ g[/tex], is

[tex]\boxed{f\circ g = \{(3,5), (5,1), (-6, 7)\}}[/tex]

since

[tex]g(3) = 1 \implies (f\circ g)(3) = f(g(3)) = f(1) = 5[/tex]

[tex]g(5) = 4 \implies (f\circ g)(5) = f(4) = 1[/tex]

[tex]g(-6) = 2 \implies (f\circ g)(-6) = f(2) = 7[/tex]

To find the equation of a parabola given the vertex and the zeroes, we can use the intercept form equation to help us:

[tex]y=a(x-r)(x-s)[/tex]

We're given:

[tex]y=a(x-r)(x-s)[/tex]

⇒ Plug in the given information:

[tex]y=a(x-(-8))(x-4)\\18=a(-2-(-8))(-2-4)\\18=a(-2+8)(-2-4)\\18=a(6)(-6)\\18=a(-36)\\1=-2a\\\\a=-\dfrac{1}{2}[/tex]

[tex]a=-\dfrac{1}{2}[/tex]

If the distance on the map is 5.5​ cm. Then the actual distance between two town will be 11 miles.

The complete question is given below.

The scale on a map is 1 cm to 2 miles. What is the actual distance between two town if the distance on the map is 5.5​ cm.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The scale on a map is 1 cm to 2 miles.

If the distance on the map is 5.5​ cm.

Then the actual distance between two town will be

⇒ 5.5 cm = 5.5 × 2 miles

⇒ 5.5 cm = 11 miles

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A will have a value of 2. The value of A is found by the substitutional equation system.

A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.

The given equation in the problem is;

Equation 1: [tex]\rm \frac{3}{8} + \frac{1}{3} y= \frac{17}{24}[/tex]

Equation 2: [tex]x+7y=8[/tex]

Rearrange equation 2 as;

x=8-7y

Substitute the value of x;

[tex]\rm \frac{3}{8} + \frac{1}{3} y= \frac{17}{24} \\\\ \frac{3}{8}(8-7y)+\frac{1}{3}y=\frac{17}{24} \\\\ \frac{-21}{8} y+\frac{1}{3} = \frac{17}{24}-3 \\\\ \frac{-63y+8y}{24}=\frac{17-72}{24}\\\\ \frac{-55 \ y}{24} = - \frac{55}{24}\\\\ y= 1[/tex]

Substitute the value of y in equation 2 as;

x+7y=8

x+7(1)+8

x=8-7

x=1

The system of equations by substitution obtained the value of A is;

x + y = A

1+1=A

A=2

Hence the value of A will be 2.

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The area of the kite ABCD will be 60 square millimeters.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

In the Kite ABCD, AB = 5√2mm = 7.07 mm, AP= 5mm, PD = 7mm

Then the area of the kite ABCD will be

Area = 2(area of triangle APB and area of triangle APD)

The side length of PB will be

AB² = AP² + PB²

PB² = AB² – AP²

PB² = 7.07² – 5²

PB² = 50 – 25

PB² = 25

 PB = 5 mm

Then the area will be

Area = 2[(1/2 × 7 × 5) + (1/2 × 5 × 5)]

Area = 60 square mm

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Answer:

which class of this exam

Answer:

2. All reals

Step-by-step explanation:

It covers everything as absolute value (distance from 0)

If you graph it you will see

Reason:

Absolute value represents distance on a number line. Specifically it's the distance from x to 0.

For example, |-2| = 2 means -2 is 2 units away from 0.

Since |x| represents a distance, we cannot have negative distance. So |x| is either 0 or positive. Furthermore, it means |x| is larger than any negative value you pick.

Therefore, |x| > -9 is true for any x value and it's why we go for "all reals" (aka "all real numbers")

The expression that has a value of 16 when n = 5 is  [tex]\rm 7+ \dfrac{45}{n}[/tex] , Option C is the correct answer.

An expression is mathematical statement consisting of variables , constant and mathematical operators.

The expression given in the question is

[tex]\rm \dfrac{ 25}{n} + 7 \\\\30-3n\\\\7+\dfrac{45}{n}\\\\n^3 -114[/tex]

On solving it can be seen that

The value of 16 when n= 5 is given by

7 +45/5 = 7+9 = 16

Therefore Option C is the right answer.

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Option C).

Answer ya so  1 is the answer

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Given expression:

[tex]\sf \left(\dfrac{3a^{-2}b^6}{2a^{-1}b^5} \right)^2[/tex]

To find the value of the expression when a = 3 and b = -2, substitute these values into the expression:

[tex]\implies \sf \left(\dfrac{3(3)^{-2}(-2)^6}{2(3)^{-1}(-2)^5} \right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}[/tex]

[tex]\sf \implies \left(\dfrac{3\left(\dfrac{1}{3^2}\right)(-2)^6}{2\left(\dfrac{1}{3^1} \right)(-2)^5} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{3\left(\dfrac{1}{9}\right)(-2)^6}{2\left(\dfrac{1}{3} \right)(-2)^5} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{3}{9}\right)(-2)^6}{\left(\dfrac{2}{3} \right)(-2)^5} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right)(-2)^6}{\left(\dfrac{2}{3} \right)(-2)^5} \right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad (-a)^n=a^n,\:\: \textsf{ if }n \textsf{ is even}[/tex]

[tex]\textsf{Apply exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right) (2^6)}{\left(\dfrac{2}{3} \right) (-(2^5))} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right) (64)}{\left(\dfrac{2}{3} \right) (-32)} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{1 \times 64}{3}\right)}{\left(\dfrac{2 \times -32}{3} \right)} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\dfrac{64}{3}}{\dfrac{-64}{3}} \right)^2[/tex]

When dividing fractions, flip the second fraction and multiply it by the first:

[tex]\implies \sf \left( \dfrac{64}{3} \times \dfrac {3}{-64} \right)^2[/tex]

[tex]\implies \sf \left( \dfrac{64 \times 3}{3 \times (-64)}\right)^2[/tex]

[tex]\implies \sf \left( \dfrac{192}{-192}\right)^2[/tex]

[tex]\implies \sf \left(-1\right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad (-a)^n=a^n,\:\: \textsf{ if }n \textsf{ is even}[/tex]

[tex]\sf \implies 1^2=1[/tex]

-5/7 x 1/5

-5 x 1 = -5

7 x 5 = 35

-5/35 = -1/7

Happy to help :P

Answer:

33.3333%

Step-by-step explanation:

Total number of kg- 2+3=5

Total money- (2×8)=16

(3×6)=18

16+18=34

$34=5000g

=250g

(250×$34)÷5000=$1.7

profit-2.55-1.7=0.85

(0.85/2.55)×100=33.333%

Answer:

P=70ft

Step-by-step explanation:

25^2-15^2=400
Sqrt400=20

2l+2w=P

40+30=70

The equivalent expression of square root of -64 is 8i

We have:

square root of -64

Rewrite as:

√-64

Expand

√64 * √-1

Take the square root of 64

8√-1

In complex numbers

√-1  = i

So, we have:

8i

Hence, the equivalent expression of square root of -64 is 8i

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The height of the tree is the man's height plus x.

[tex]\tan 26^{\circ}=\frac{x}{16}\\x = 16 \tan 26^{\circ}[/tex]

So, the height of the tree is [tex]\boxed{(16 \tan 26^{\circ}+1.8) \text{ m}}[/tex]