Which angle is an acute angle?

The special angle pair relationship between the given angles are:

1. Corresponding angles

2. Alternate exterior angles

3. Consecutive

The following are some special angle pair relationships:

1. Angles 1 and 3 form a special angle pair relationship known as: corresponding angles.

2. Angles 8 and 4 form a special angle pair relationship known as: alternate exterior angles.

3. Angles 2 and 3 both lie on the same side of the given transversal, therefore, the special angle pair relationship between angle 2 and angle 3 is: consecutive interior angles.

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The obtained decimal number is 0.155.

To solve the question  [tex]\frac{3.1 * 10}{2.0 * 10^{2}}[/tex].

Canceling out 10 from the denominator and numerator

= [tex]\frac{3.1 }{2.0 * 10}[/tex]

= 3.1 / 20

Remove the decimal point from the numerator and add one zero in the denominator

= 31/ 200

As we divide the numbers using the long division method we get the decimal number as a result,

= 0.155

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Answer:

10.5:12:13.5

Step-by-step explanation:

The only two values you know and can compare are 8 and 12, so you have to find the relationship between them. 12/8 = 1.5. To get the two unknown values, you multiply 1.5 by the ones you do know.

7 * 1.5 = 10.5

9 * 1.5 = 13.5

So, you get 10.5:12:13.5

According to the Pythagorean theorem, "in a right-angled triangle, the squares of the hypotenuse side is equivalent to the sum of squares of the other two sides," the hypotenuse side is the longest side of the triangle.

This is further explained below.

Generally, The Pythagorean theorem is a well-known geometric theorem that states the number of squares just on the legs of a right triangle is equal to the square just on the hypotenuse (the side that is opposite the right angle).

This theorem can also be expressed in the familiar algebraic notation of a2 + b2 = c2, where a and b are the lengths of the legs of the triangle.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is an essential connection in Euclidean geometry that describes the relationships between the three sides of a right triangle.

It indicates that the total of the areas of the squares on the other two sides is equal to the area of the square whose side is the hypotenuse.

In conclusion, This means that the area of the square whose side is the hypotenuse is equal to that amount.

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CQ Not found: Answered Generally

expression :

[tex]\sqrt{5} \sqrt{5}[/tex] = [tex]\sqrt{5X5} = \sqrt{25} = 5[/tex].

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1) [tex]\angle A \cong \angle D, \angle C \cong \angle E, \overline{AB} \cong \overline{DF}[/tex] (given)

2) [tex]\triangle ABC \cong \triangle DFE[/tex] (AAS)

3) [tex]\angle ACB \cong \angle DEF[/tex] (CPCTC)

Write an algebraic expression to represent each statement.

the number, b, divided by thirty-six

b/36

Answer:

[tex]x=\boxed{13}\\\\y=\boxed{20}[/tex]

Step-by-step explanation:

Vertical Angle Theorem

When two straight lines intersect, they form two pairs of angles.  The vertically opposite (non-adjacent) angles are congruent.

Solving for x:

[tex]\boxed{\begin{aligned}(6x-26)^{\circ}&=4x^{\circ}\\6x-26&=4x\\6x-26+26&=4x+26\\6x&=4x+26\\6x-4x&=4x+26-4x\\2x&=26\\2x \div 2&=26 \div 2\\x&=13\\\end{aligned}}[/tex]

Solving for y:

[tex]\boxed{\begin{aligned}(7y-12)^{\circ}&=(6y+8)^{\circ}\\7y-12&=6y+8\\7y-12-6y&=6y+8-6y\\y-12&=8\\y-12+12&=8+12\\y&=20\end{aligned}}[/tex]

Therefore:

[tex]x=\boxed{13}\\\\y=\boxed{20}[/tex]

Answer:

Step-by-step explanation:

6.105 + 10.4 + 3.075 ? ​:19.58

one is the pmf or probability mass function of X = number of children in the family

The Probability Mass Function (PMF) is also called a probability function or frequency function which characterizes the distribution of a discrete random variable.

X takes values: { 3, 4, 5 }

where:  P ( X = 3 ) + P ( X = 4 ) + P ( X = 5 ) = 1

For X = 3 we have : BBB or GGG.

P ( X = 3 ) = ( 1/2 * 1/2 * 1/2 ) * 2 = 1/8 * 2 = 2 / 8 = 1/4

P ( X = 4 ) = ( 1/2 * 1/2 * 1/2 * 1/2 ) * 6 = 6 /16 = 3/8

P ( X = 5 ) = ( 1/2 * 1/2 * 1/2 * 1/2 * 1/2 ) * 12 = 12 / 32 = 3/8

1 / 4 + 3 / 8 + 3 / 8 = 8 / 8 = 1

the complete question is

A family decides to have children until it has three kids of the same gender. Assuming P(B) = P(G) = 0.5, what is the pmf of X = number of children in the family?

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Answer:

[tex]{ \tt{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ \\ { \tt{ - 3 = \frac{ - 3 - ( - 6)}{s - 5} }} \\ \\ { \tt{ - 3(s - 5) = 3}} \\ \\ { \tt{s - 5 = - 1}} \\ \\ { \tt{s = 4}}[/tex]

Step-by-step explanation:

Use the Pythagorean Theorem.

a^2+b^2=c^2

a^2 + 5^2 = 16^2

a^2 + 25 = 256

a^2 = 231

a = square root of 231

a= 15.20

Answer:15.20

Step-by-step explanation:

Answer: Multiplicative inverses or reciprocal, is a number that when multiplied by the given number gives the product as 1.

Step-by-step explanation:

Answer:

Step-by-step explanation:

x

From the word problem given, the number of pizzas each that were delivered are:

Step I

Let a = number of small pizzas delivered

Let b = number of medium pizzas delivered

Let c = number of large pizzas delivered

Step 2 - Creating relevant expressions based on number and type ordered, we have:

a + b + c = 8.............................1

3a + 5b + 11c = 56..................2
4a + 9b + 12C = 4 * 8 + 12.....3a

We can rewrite (3) as
4a + 9b + 12C = 44 ....3b

Step 3

Multiply both sides of (1) by 4

We have

4a +4b +4c = 32

-
4a +4b +4c = 32
5b +8C = 12......................(4)

Multiply both sides of (1) by 3 and subtract from (2), and we have:

3a + 3b + 3c = 24, removing this from (2) we have

3a + 5b + 11c = 56

-
3a + 3b + 3c = 24
2b + 8c = 32.....................(5)

Step 4 - Subtract (4) from (5)

2b + 8c = 32
-
5b + 8c = 12
-3b = 20

b = - 20/3

= - 6.67
Since we cannot have negative values, we work with absolute value to get:

b [tex]\approx[/tex] 7

Since b = 7

2(7) + 8c = 32
8c = 32 - 14
c = 18/8

c [tex]\approx[/tex] 2


Plug in that back into a we have

a + b + c = 8
a + 7 + 2 = 8

a = 8-9
a = -1 (recall we must have absolute values)
a therefore = 1.

Hence the number of pizzas that were ordered are:

1 small
7 medium; and

2 large.

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Answer:

Total = £18,000

9 Office workers = £500

4 Managers = 500 × 2 (twice the bonus of an office worker) = £1,000

Directory = 500 × 3 (3 times the bonus of an office worker) = £1,500

The Solution:

Given the function:

Required:

To determine the domain and the range of the function.

Below is the graph of the function:

Step 1:

The domain of the function is:

Step 2:

The range of the function is:

Therefore, the correct answer is :

The number of animals that are on the farm is 48.

A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 2/3.

The first step is to determine the fraction of the animals that are chickens.

Fraction that are chickens = 1 -  fraction that are pigs and horses.

[tex]\frac{1}{8} + \frac{2}{3}[/tex]

[tex]\frac{3 + 16}{24}[/tex] = [tex]\frac{19}{24}[/tex]

Fraction that are chickens = 1 - 19/24 = 5/24

The next step is to divide the number of chickens by the fraction of the chickens.

Number of animals = number of chickens ÷ fraction of chickens

10 ÷ 5/24

10 x 24/ 5 = 48

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The set which is a function is B = [(1, Z), ( 2, Y), (3, X)]

What is a function ?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Since, we know that function does not repeat any x coordinate

Which means, the first coordinate of every pair does not repeat

Therefore the first coordinates which is repeated is not a function

Now, let's check out the given sets and check whether its a function or not

A = [(4,6), (A, B), (A, 6)], is not a function

Since, its first coordinate is repeated

C = {(6,9), (6,6), (6,9), is not a function

Since, its first coordinate is repeated

B = [(1, Z), ( 2, Y), (3, X)], is a function

Because, its first coordinate is not  repeated

Hence, B = [(1, Z), ( 2, Y), (3, X)], is a function

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               8 square = 64

               5 cube = 125

Step-by-step explanation:

               =8² + 5³

            =64 + 125

                   =189

What are square and cube ?

The square of a number is the multiplication by itself. That means, for any integer, we can obtain the square by multiplying the integer itself. For example, the square of an integer 4 will be: 4 × 4 = 16, i.e., the square of 4 is equal to 16.

The cube of a number is the multiplication by itself thrice. That means, for any integer, we can obtain the cube by multiplying the integer by its square. For example, the cube of an integer 5 will be: 52 × 5 or 5 × 5 × 5, i.e., the cube of 5 is equal to 125.

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Answer:

Explanation: Each year a volume of 15,000 cubic meters is taken from the lake for 15 years, the lake has a surface area of 1.35 square kilometers and a depth of 4m. We have to find the fall in the depth of the river after 15 years:

The total water taken out of the lake in 15 years is:

Therefore the fall in height is:

Therefore the height of the lake will reduce by 0.17me.

The line that passes through the point -1, four and is parallel to the line 2 X plus Y equals one is y + 2x = 2.

Slope is measure of steepness of a line.

The Equation of line is y = mx + c

where,

m is slope

c is y intercept

To find equation of the parallel line we must first find the slope of the original line

The original line is 2x + y = 1

We must first write equation in the general form above

That's

y = - 2x + 1

Comparing with general equation above

Slope = - 2

Since lines are parallel their slope are also same

Slope of parallel line = - 2

So the equation of line using point

( - 1 , 4) and the slope - 2 is

y-4= -2(x+1)

y-4= 2x-2

y+2x= -2+4

We have final answer as

y + 2x = 2

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answer:

8.037m

step-by-step explanation:

the total of two or more addends is the sum of the numbers added.

your two addends are 5.89 and 2.147, so add them together.

5.89+2.147

=5.89+2.147

=8.037

the answer is 8.037m

The relationship between the volume, V, and temperature, T, of a given mass of gas, found by the French scientist Jacques Charles, gives;

a) The slope–intercept form of the equation that expresses the volume in terms of the temperature of the gas is; [tex] \displaystyle{ V = 1. \bar 6 \cdot T + 455}[/tex]

b) The volume at 60 °C is 555 cm³

c) Interpolation originates from the verb interpolare

d) The temperature at 300 °Cis 955 cm³

e) Extrapolation originates from 'extra' (meaning outside) and the shortened form of Interpolation

f) The temperature–intercept is -273 °C

g) The special name is the absolute zero temperature

Charles law states that the volume of a given mass of gas is directly proportional to its temperature given in Kelvin.

Mathematically, Charles Law states that; V = K•T

Where;

V = The volume of the gas

T = The gas temperature

K = The proportionality constant

The volume occupied by the gas at 27 °C = 500 cm³

The volume occupied at 90 °C = 605 cm³

a) To write the equation in slope–intercept form, we have;

[tex] \displaystyle{ Slope = \frac{605 - 500}{90 - 27} =1. \bar{6} =1. \bar{6}}[/tex]

The equation of the line in point and slope form is therefore;

Point–slope form; [tex] \displaystyle{ V - 500 = 1. \bar{6} \times (T - 27) }[/tex]

[tex] \displaystyle{ V = 1. \bar{6} \cdot T -45 + 500 = 1. \bar{6} \cdot T + 455}[/tex]

The equation in slope–intercept form of expressing the volume, V, in terms of the temperature, T, is therefore;

Volume equation; [tex] \displaystyle{ V = 1. \bar{6} \cdot T + 455}[/tex]

b) The volume at 60 °C is given from the equation that gives the volume, V, in terms of time, T as follows;

[tex] \displaystyle{ V(T) = 1. \bar{6} \cdot T + 455}[/tex]

When T = 60 °C

[tex] \displaystyle{ V(60) = 1. \bar{6} \times 60 + 455=555}[/tex]

c) The word interpolate originated from the Latin word interpolare which means to alter or refurbish

d) The volume occupied by the gas at 300 °C is given by the function for the volume, V, in terms of temperature, T, equation as follows;

When T = 300 °C

[tex] \displaystyle{ V(300) = 1. \bar{6} \times 300 + 455 = 955}[/tex]

e) Extrapolation originate from the word 'extra' which refers to the outside of an area. Extra is combined with a short form of interpolate to give the word, extrapolation

f) When the volume is zero, the volume function equation can be used to find the temperature as follows;

Volume function; [tex] \displaystyle{ V = 1. \bar{6} \cdot T + 455}[/tex]

When V = 0

[tex] \displaystyle{ V = 0 =1. \bar{6} \cdot T + 455}[/tex]

[tex] \displaystyle{ -455 = 1. \bar{6} \cdot T }[/tex]

[tex] \displaystyle{T = \frac{3 \times (-455)}{5}= -273 }[/tex]

g) The special name given to -273 °C of the gas is the absolute zero temperature.

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The first term of the arithmetic progression is 5

An arithmetic sequence can simply be defined as a sequence of numbers or terms in which the differences between successive or consecutive terms are always equal.

The formula for the nth term of an arithmetic sequence is expressed as;

Tn = a + (n-1)d

Where;

Given that the first term of the sequence is a, the 43rd term is 26 and the common difference is 1/2

Substitute the values into the formula

26 = a + (43 -1)1/2

expand the bracket

26 = a + (42)1/2

Multiply through

26 = a + 21

collect like terms

a = 26 - 21

a = 5

Thus, the value is 5

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Answer:

Green Pens : 21

Step-by-step explanation:

Let the number of
green pens = x

Three more blue pens than green pens translates to
=> number of blue pens = number of green pens + 3
=> blue pens  = x + 3

Total number of pens = blues + green = x + 3 + x = 2x + 3

Probability of taking 2 green pens:
The first time a green pen is taken out, the probability
P( 1s green pen) = Number of green pens/Total number of pens

= [tex]\dfrac{x}{2x + 3}[/tex]

After the first green pen is removed, the number of green pens will be one less and so will the total number of pens

Number of green pens = x - 1
Total number of pens = 2x + 3 - 1 = 2x + 2

P(second green pen | first green pen)

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

P(2 green pens) = P(first green pen) x P(second green pen)
[tex]= \dfrac{x}{2x + 3} \times \dfrac{x-1}{2x + 2}\\\\=\dfrac{x(x -1)}{(2x +3)(2x+2)}[/tex]          [1]

Probability of 2 blue pens

P( 1st blue pen) = number of blue pens/total number of pens
[tex]=\dfrac{x + 3}{2x + 3}[/tex]

P(second blue pen = (number of pens remaining if first was blue) ÷ total number of pens - 1

If the first pen taken was blue then there will be 2x + 3 - 1 blue pens out of a total of 2x + 3 - 1 pens

P(2nd blue pen | first blue pen)

[tex]=\dfrac{x + 2}{2x + 2}[/tex]

[tex]\text{P(2 blue pens)} =\dfrac{x + 3}{2x + 3} \times \dfrac{x + 2}{2x + 2}[/tex][tex]=\dfrac{(x + 3)(x+2)}{(2x + 3)({2x + 2})}[/tex]  [2]

The probability of either 2 green pens or 2 blue pens is the sum of the two probability expressions [1] and [2]

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

[tex]= \dfrac{x(x - 1)+ (x + 3) (x +2)}{(2x + 3)(2x + 2)}\\\\\\= \dfrac{2x^2+4x+6}{(2x + 3)(2x + 2)}\\\\\\\\[/tex]

Numerator: factor out 2 to get 2(x² + 2x + 3)

denominator = 4x²+10x+6 = 2 (2x² + 5x + 3)

2 of numerator and 2 of denominator cancel out to give the final expression:

[tex]\dfrac{x^2\:+\:2x\:+\:3}{2x^2+\:5x\:+\:3}[/tex]

But we are given that the probability of picking 2 pens of the same color = 27/55

This will give us:
[tex]\dfrac{x^2\:+\:2x\:+\:3}{2x^2+\:5x\:+\:3} = \dfrac{27}{55}[/tex]

Cross-multiplying we get

[tex]55\left(x^2+\:2x\:+\:3\right)=27\left(2x^2+\:5x\:+\:3\right)[/tex]

=> [tex]55x^2+110x+165 = 54x^2+135x+81[/tex]

Grouping like terms and simplifying gives
[tex]x^2-25x+84=0[/tex]

This is a quadratic equation which can be solved using a scientific calculator (as I did)

The solution set is

x = 21, x = 4

Remember x = number of green pens. We can ignore x = 4 because the total number of pens given by the expression 2x + 3 will be less than 12 and we are told there are more than 12 pens total

So the solution is x = 21 (number of green pens)
Number of blue pens = x + 3 = 21 + 3 = 24

Answer: Green Pens : 21   and Blue Pens: 24

The value of a negative number such that the sum of that number and its square is 42 is -7.

Let the negative number be -x.

According to the question, the sum of the negative number and its square is 42.

So, we form an equation

- x + (-x)² = 42

x² - x - 42 = 0

Solving the quadratic equation,

x² - 7x + 6x - 42 = 0

x(x - 7) + 6(x - 7) = 0

(x - 7)(x + 6) = 0

x = -6 and x = 7

We have taken the number -x to be negative.

So, -x = -6 and -x = 7

x = 6 and x = -7

Hence, the value of the negative number is -7.

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The correct question is: "Determine the value of a negative number such that the sum of that number and its square is 42."

Answer:

slope of perpendicular line = - [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

calculate the slope m of the given line using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 0) and (x₂, y₂ ) = (3, 3) ← 2 points on the line

m = [tex]\frac{3-0}{3-1}[/tex] = [tex]\frac{3}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{2} }[/tex] = - [tex]\frac{2}{3}[/tex]