The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

The pencil was reduced by 1/6 of its original length. Hence, the correct option is Option C.

To calculate the fraction, you must divide the remaining length (15 cm) by the original length (18 cm). In order to get a fraction, you have to divide it by their highest common factor, which in this case is 3.

= \frac{15}{18}

= \frac{5}{6}

This is the length of the pencil left at the end of the day. To find the fraction used, you have to subtract this fraction from its whole.

= 1 - \frac{5}{6}

= \frac{5}{6} - \frac{5}{6}

= \frac{6-5}{6}

= \frac{1}{6}

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The percentage of Valeria's action figure collection is 47% which she keeps on her wall.

The percentage is defined as a ratio expressed as a fraction of 100.

To find the percentage of Valeria's action figure collection that she keeps on her wall, we need to divide the number of action figures she keeps on her wall by the total number of action figures in her collection and then multiply by 100%.

Since Valeria has a collection of 500 action figures and she keeps 235 of them on her wall, the percentage of her collection that she keeps on her wall is :

⇒ 235 / 500 × 100% = 47%.

Thus, the percentage of Valeria's action figure collection is 47%

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Answer:

$15400

Step-by-step explanation:

1 year = 12 month

10 years = 120 months

12% = month

1440% = 120 months

1440% = 14.4

Take 1000 times 14.4 = $14400

So, we add the two numbers

1000 + 14400 = $15400

So, $15400 will be in the account at the end of 10 years.

The statements that are true in the right triangle are

A right angled triangle is a triangle in which one of its angles is 90°.

Since the area model at the right shows a right triangle with side lengths a, b, and c such that a² + b² = c².

If the side lengths a increases by a small amount, but the lengths a increases by a small amount, but the lengths b and c do not change, we  need to show which of the following statements will be true.

Now, if the side a increases by a small amount Δa, we have that

a + Δa > a

Squarring both sides, we have that

(a + Δa)² > a²

Adding b² to both sides, we have that

(a + Δa)² + b² > a² + b²

(a + Δa)² + b² > c²  since  a² + b² = c²

So, a² + b² > c² where a is the new value of a = a + Δa

Also, since a is perpendicular to b, we have that angle m∠ACB = 90°. Increasing a by a small amount  Δa does not change a from being perpendicular to b, so we still have that m∠ACB = 90°.

So, the statements that are true in the right triangle are

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The number of red balls Luke has at the start is 47.

blue ball per day = 2

red ball per day = -3 ('-' ve sign as he is loosing them)

let the number of red balls be represented by r

let the number of blue balls be represented by b

after 5 days

b+ 10 = r -15 -(i)

After 9 days

b + 18 =2(r-27)-(ii)

subtracting (i) from (ii)

b + 18 - b - 10 = 2r - r - 54 +15

8 = r - 39

r = 39 + 8

r = 47

The number of red balls Luke has at the start is 47

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Answer: 6.40

Step-by-step explanation:

1.20 times 3 = 3.60

10 - 3.60 = 6.40

The degrees of freedom for the f-ratio evaluating the main effect of factor A would be (1, 8).

A factorial is a mathematical operation denoted by the symbol (!) that multiplies a number (n) by each integer that comes before it. To put it another way, the factorial function instructs you to multiply all the whole numbers starting at the selected number and decreasing by one. The factorial of a number (n!) is equal to n in more mathematical terminology (n-1)

The factorial of a number (n!) is equal to n in more precise mathematical terminology (n-1). For instance, if you wanted to compute the factorial for four, you would write: 4! = 4 x 3 x 2 x 1 = 24.

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Answer:900

Step-by-step explanation:

720=.80x

720/.80=900

to check it

900*.20=720

Step-by-step explanation:

9 hundredths = 9/100

is 9/100 > 6/10 ?

let's bring both to 1/100

9/100 > 6×10/100

9/100 > 60/100

no, this is wrong. 9/100 is not greater than 60/100 (or 6/10).

9/100 would be greater than 6/100. but not greater than 6/10.

Answer:

m∠5 + m∠6 =180°

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

m∠5 + m∠6 are linear pairs, so their sum has to be 180°.

m∠2 + m∠3 = m∠6 because of the exterior angle theorem, which states that the measure of an exterior angle is equal to the sum of the two opposite interior angles. (using this logic, m∠1 equals the sum of m∠5 and m∠3, and m∠4 equals the sum of m∠2 and m∠2).

m∠2 + m∠3 + m∠5 = 180° because the triangle sum property says that the sum of a triangle's interior angles will equal 180°.

The probability of getting exactly 4 heads is 0.26

A loaded coin has 0.48 probability of coming up heads

0.52 probability of coming up tails.

coin is flipped 7 times

let's assume n = 7.

The seven flips of the coin are separate from one another, so what happens on one flip is unaffected by the outcomes of the other tosses.

When calculating the likelihood that two events will occur simultaneously, we must multiply the probabilities of events 1 and 2, presuming that event 1 occurred.

Tosses never affect one another, so the "assuming event 1 happened" part is no longer necessary because it has no effect on the probability. As a result, we just need to multiply the chances for each toss. This supposition is essential. We would have needed to know exactly how tosses are dependent on one another if they were interdependent.

Typically, we would have [tex](n! /(r!)*(n - r)!)*p^r*(1-p)^(n-r)[/tex] is the probability of getting r heads out of n, without taking into account the order.

probability of getting exactly 4 heads r = 4.

out of 7 flipping n =7.

7!/(4!*3!)   = 35

(0.48)^4 = 0.05308416

(0.52)^3 = 0.140608

35*0.05308416*0.140608 = 0.26124201492 = 0.26

so the probability of getting exactly 4 heads is 0.26.

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The line given by the point slope equation y - 8 = 1/2 (x - 4) represents the linear function f(x) = [tex]\frac{1}{2}[/tex] x + 6.

Linear functions are those functions whose graph drawn is a straight line. It consists of one dependent variable and one independent variable.

Linear functions are usually represented as f(x) = y = p + qx.

The given equation of the line in point slope form is,

y - 8 = 1/2 (x - 4)

⇒ y - 8 = (1/2 × x) - (1/2 × 4)

⇒ y - 8 = 1/2x - 2

⇒ y = 1/2x -2 + 8

⇒ y = 1/2x + 6

When x = 0, y = f(0) = (1/2 × 0) + 6 ⇒ f(0) = 6

Hence linear function f(x) = [tex]\frac{1}{2}[/tex] x + 6 represents the line given by the point slope equation y - 8 = 1/2 (x - 4).

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In the distribution system, the water  main sizes most commonly in use up to 3.65m to  tiny 12.7mm.

Water pipes come in a variety of sizes, from enormous mains with a diameter of up to 3.65 m to tiny 12.7 mm pipes used to supply individual outlets within a building.

Any pipe or tube intended to deliver drinking water to consumers is referred to as a water pipe. Depending on the situation, water may be treated either before distribution or at the point of use (POU). Water is typically treated before distribution in well-thought-out water distribution networks, and occasionally it is also chlorinated, to prevent recontamination on the way to the end user.

Polyvinyl chloride (PVC), cast iron, copper, steel, and, in older systems, concrete or fired clay are materials frequently used to build water pipes. Long runs of water pipe can be joined together using flange, nipple, compression, or soldered joints (SCOTT 2011).

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Answer:

Step-by-step explanation:

Answer:

x = 7/10

Step-by-step explanation:

You multiply both sides by "x", to get 7 = 10x. Then divide both sides by 10 to get 7/10 = x, or 0.7 = x.

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We can factor this polynomial with 4 terms without grouping.

Factor is a thing that influence decision or the situation.

How to factor polynomials with 4 term without groupingLet P(x) be a polynomial with four terms.

To factor P(x) without grouping, substitute

x = -1, 1, -2, 2, -3, 3.......

P(-1) = 0 ----> (x + 1) is a factor of P(x)

P(1) = 0 ----> (x - 1) is a factor of P(x)

P(-2) = 0 ----> (x + 2) is a factor of P(x)

P(2) = 0 ----> (x - 2) is a factor of P(x)

If P(-1) ≠ 0, then (x + 1) is not a factor of P(x).

Then, try x = 1, x = -2, x = 2 and so on.

Once one of the linear factors of P(x) is found, the other factors can bound easily (the rest of the process has been explained in the following examples).

Factor the following polynomials without grouping :

d as (x2 + ax + b).

Then,

(x + 1)((x2 + ax + b) = x3 - 2x2 - x + 2

Comparing the coefficients of x and constants,

b + a = -1 ----(1)

b = 2

Substitute b = 2 in (1).

2 + a = -1

a = -3

x2 + ax + b = x2 - 3x + 2

Factors of (x2 - 3x + 2) are (x - 1) and (x - 2).

Therefore,

x3 - 2x2 - x + 2 = (x + 1)(x - 1)(x - 2)

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The expression that is equivalent to (ab⁷)⁴ is (a⁴b²⁸)

What is the integer exponent property?

Exponents that are integers are known as integer exponents. Exponents with positive integer values tell us how many times to multiply the base by itself. We are instructed by negative integer exponents to first flip the numerator and denominator before multiplying the result by the specified number of times.

Here, we have

Given expression:  (ab⁷)⁴

We have to find the expression that is equivalent to this expression.

Using integer exponent property:

= (ab⁷)⁴

= (a⁴b²⁸)

Hence, the expression that is equivalent to (ab⁷)⁴ is (a⁴b²⁸).

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Therefore , Due to a sequence of transformations, polygon ABCD will therefore overlap polygon A'B'C'D'.

A polygon is a closed, two-dimensional, flat or planar structure that is circumscribed by straight sides. There are no curves on its sides. The edges of a polygon are another name for its sides. A polygon's vertices (or corners) are the places where two sides converge.

Here,

a 4 unit translation to the left after reflecting polygon ABCD across the x-axis.

The coordinates for point A in the polygon ABCD are (1, -5).

ABCD's polygon should be mapped onto A'B'C'D',

Reflect the ABCD polygon across the x-axis in accordance with the rule,

A(x, y) → A'(x, -y) (x, -y)

Following this criterion, A's coordinates will be,

A(1, -5) → A'(1, 5) (1, 5)

ABCD is also moved four units to the left.

The rule for the translation is,

A'(x, y)=> A"(x - 4, y) (x - 4, y)

A'(1, 5) => A"(1 - 4, 5) (1 - 4, 5)

=> A"(-3, 5) (-3, 5)

Due to a sequence of transformations, polygon ABCD will therefore overlap polygon A'B'C'D'.

a 4 unit translation to the left after reflecting polygon ABCD across the x-axis.

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x     f(x)
0       0
-2      -4
4       -2
You need to draw y = 2 f (x-1)
So you need to choose x so that  x-1 = 0, -2, 4 then you can use the above values.
New function
x-1 = 0,              x = 1,           y = 2 f (x-1) = 2 f(0) = 2 x 0 = 0
x-1 = -2              x = -1           y = 2 f (x-1) = 2 f(-2) = 2 x -4 = -8
x-1 = 4               x = 5            y = 2 f (x-1) = 2 f (4) = 2 x -2 = -4
So 3 points on the new graph are   (1, 0)   (-1, -8) and (5, -4)
Basically going from y = f(x) to y = f(x-a) where a is a constant positive number you translate (move)  y = f(x)  a units to the right.
y = f(x) to y = 2 f(x),  you dilate f(x) with center (0,0) factor 2,  so  (a,b) > (2a, 2b)
So basically here you are doing both things.
So if (a,b) is on y = f(x) then after the translation (a,b) > (a+1, b) then after the dilation (a+1,b) > (2a+2, 2b).

what is graph?

A diagram or pictorial depiction of facts or values that is arranged might be referred to as a graph. The relationships between two or more items are frequently represented by the points on a graph.

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A statement which describes a translation that would produce ΔDEF from the pre-image of triangle ΔABC include the following: A. To the right five units, and up two units.

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Next, we would determine the translation rule as follows;

ΔABC → ΔDEF = (2 + 5, 1 + 2) = D (7, 3)

ΔABC → ΔDEF = (4 + 5, 4 + 2) = E (9, 6)

ΔABC → ΔDEF = (4 + 5, 1 + 2) = F (9, 3)

Therefore, the translation rule is given by this mathematical expression ΔABC → ΔDEF = (x + 5, y + 2). This ultimately implies that, triangle ABC (ΔABC) was translated by five units to the right and up two units in order to produce triangle DEF (ΔDEF).

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The Domain of the Function is {-2, -1, 0,1 ,2, 3, 4, 5} and the Range of the Function is {4, 3, 2, 1, 0, -1}

What are Functions?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

We neeed to find the Domain and Range of the Function

Domain refers to all the values of x = {-2, -1, 0,1 ,2, 3, 4, 5}

Range refers to all the values of y = {4, 3, 2, 1, 0, -1}

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The approximate total length of iron edging needed to create the square frame and the two diagonals is 43.5 inches. So, option A is correct.

When two vertices of a polygon or polyhedron are not on the same edge, a diagonal in geometry is a line segment that connects them. The term "diagonal" is a colloquial term for any sloping line.

The elements on the line connecting the top left corner and bottom right corner of a square matrix make up the diagonal of a matrix in matrix algebra.

Given, The diagonal of a square is 9 inches.

The side of the square be x as we have assumed.

We have to apply Pythagoras theorem for Δ ABC

AB²+BC²=AC²

x²+x²=9²

x=9/√2

We know that the diagonals in the square bisect each other.

OA = 4.5 inches=OC

OD = 4.5 inches=OB

Therefore, the total length of iron edge that is required for the window is:

=4×Length of square+2 diagonals

= 4×6.36+2×9=43.46 inches

The approximate total length of iron edging needed to create the square frame and the two diagonals is 43.5 inches.

Hence, option A is correct.

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Answer:

24 days

Step-by-step explanation:

you have to divide the balance by the spending money, so £48.00, divided by £2.00 will equal 24 meaning, Claudia can last 24 days without adding money to her account

The system of equations that can be used to determine the sale price of the sets of strings, the guitars, and the amps.

3x + 2y + 2z = 472

2x + y = 212

4x + y = 322

The cost of each amp is $51.

An equation is a mathematical statement made up of two expressions connected by an equal sign.

We have,

3x + 2y + 2z = 472 ____(1)

2x + y = 212 ____(2)

4x + y = 322 ____(3)

From (2) and (3) we get,

Multiply 2 on (2).

4x + 2y = 424

4x + y = 322

(-)    (-)   (-)

       y = 102

Now,

2x + y = 212

2x = 212 - y

2x = 212 - 102

x = 110/2

x = 55

Now,

x = 55

y = 102

From (1) we get,

3x + 2y + 2z = 472

3 x 55 + 2 x 102 + 2z = 471

165 + 204 + 2z = 471

2z = 102

z = 51

Thus,

The system of equations that can be used to determine the sale price:

3x + 2y + 2z = 472

2x + y = 212

4x + y = 322

The cost of each amp is $51.

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The system that contains periodic function and an absolute value function has two solution

In the given system there are two function, those are periodic function and absolute value function

The function is defined as the statement that shows the relationship between one dependent variable and other independent variables. The function consist of different types of variables numbers and the mathematical operators

The periodic function is a function that repeats its value at a regular interval of time

The absolute value function is a function that contains the mathematical expression with absolute value symbols

The system contains periodic and absolute value function and it will contains two solution

Therefore, the system has two solution

I have solved the question in general, as the given question is incomplete

The complete question is:

The system below shows a periodic function and an absolute value function. how many solutions does the system have?

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The probability that the length of the eel is less than 62 centimeters is 0.0985.

In the given question, the length, x centimeters, of eels in a river may be assumed to be normally distributed with mean 53 and standard deviation 7.

An angler catches an eel from the river.

We have to determine the probability that the length of the eel is less than 62 centimeters.

Eels in a river may be assumed to be normally distributed with mean = μ = 53

Eels in a river may be assumed to be normally distributed with standard deviation = σ = 7

Now the probability that the length of the eel is less than 62 centimeters is

P(x > 62) = 1 - P(x < 62)

P(x > 62) = 1 - P((x - μ)/σ < (62 - 53)/7)

P(x > 62) = 1 - P(z < 1.29)

P(x > 62) = 1 - 0.9015

P(x > 62) = 0.0985

Hence, the probability that the length of the eel is less than 62 centimeters is 0.0985.

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The salt that is left after t minutes is y = 16e^[-t/100]

We have to mix problems we use:

dy / dt = (rate in) - (rate out)

The water entering the tank at a speed of 10 L / min but it has no salt, therefore

rate in = 0

The tank has 1000 liters of brine with 16 kg of salt initially, therefore the concentration of salt at time "t" is:

y (t) / 1000

then rate out would be:

rate out = y (t) / 1000 * 10 = y (t) / 100

The difference equation would then be:

dy / dt = 0 - y (t) / 100

1 / y (t) * dy = 1/100 * dt

We integrate from both sides and we have:

ln y = - (1/100) * t + C1

y = e ^ [- (1/100) * t + C1]

y = e ^ [- (1/100) * t] * e ^ [C1]

We assume that C = e ^ [C1]

Thus:

y = C * e ^ [- (1/100) * t]

now y = 16 to t = 0, replacing:

16 = C * e ^ [- (1/100) * 0]

16 = C, therefore we would have:

y = 16*e ^ [- t / 100]

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The modeled epidemic rate cannot be determined from the information provided.

The rate of an epidemic spreading is a complex process that is influenced by many factors such as the population density, the number of people who are vaccinated, and the infectiousness of the virus. Therefore, it is not possible to accurately model the rate of an epidemic spreading after 3 days based on the information provided. To accurately model the rate of an epidemic spreading, additional information such as the population density, the number of people who are vaccinated, and the infectiousness of the virus would be needed.

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