Can someone please answer and explain this.

Given the expression:

We will use the following rule to simplify the expression:

so, the given expression will be:

Your answer is that all angles are equal to 66.

Angle 3 and angle 7 are equal, which we know because corresponding angles are equal (angles that make an ‘F’ shape).

This means we can form an equation because we know what angle 3 and angle 7 are:

2x + 40 = 3x + 27

- 2x

40 = x + 27

- 27

13 = x

Therefore angle 7 is 3(13) + 27 = 66, and so is angle 3.

We also know that angle 5 is equal to 66, because it is vertically opposite to angle 7 and vertically opposite angles are equal.

I hope this helps!

Answer: Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Answer:

A. y = square root of 2x

We are given the function

y = 2 √x

We are asked for the function that has the same domain as the given function

First, the domain for the given function is this

{ x | x ≥ 0 }

So, any function that has a domain of x that is equal to or greater than 0. Some examples:

f(x) = √x  -  2

f(x) = 5 √x

Answer:

a= 78

Step-by-step explanation:

To solve subtract:

180-102= 78

Hope this helps!

Answer:

78 is the missing angle

Step-by-step explanation:

180 - 102 = 78

The Y values are increased from one interval to the next by multiplying by 3 and 3 represents the base in the exponential equation

Given that the input-output table of the function \(y=3^{x}\) , asked to describe how the Y values are increasing from one interval to the next and the other question is what does the 3 represents in the exponential equation

Given the functions  \(y=3^{x}\), it is an exponential function, always increasing and always greater than zero. as the x increases the value of y increases exponentially by the factor of 3 i.e.Y values are increasing from one interval to the next by multiplying by 3.

An exponential equation has a base and power, here given function \(y=3^{x}\)the base of the given function is 3 and the power is x

Therefore, Y values are increased by multiplying with 3, and 3 is the base of the equation.

Hence, The Y values are increased from one interval to the next by multiplying by 3 and 3 represents the base in the exponential equation

complete question: image attached

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Answer:

\(QT = 10\)

Step-by-step explanation:

Given

\(Perimeter = 55\)

See attachment for triangle

The perimeter is calculated as:

\(Perimeter = QR + RS + QS\)

This gives:

\(55 = 3x + 18 + 2x +12\)

Collect like terms

\(3x + 2x = 55 - 18 - 12\)

\(5x = 25\)

\(x = 5\)

From the attachment:

\(QT = 2x\)

\(QT = 2 * 5\)

\(QT = 10\)

Triangle QRS has a perimeter of 55. If RT bisects angle R, then the length of QT is 10 and this can be determined by using the formula of the perimeter of a triangle.

Given :

The perimeter of the triangle QRS is given by:

Perimeter = QR + RS + QS

55 = QR + RS + QS

Now, put the values of sides QR, RS, and QS in the above equation.

55 = 3x + 18 + 2x + 12

55 = 5x + 30

25 = 5x

x = 5

Now, the length of the QT is given by:

QT = 2x

QT = 10

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Step-by-step explanation:

directly proportional means

y = kx

with k being a constant factor for all values of x.

we get k by using the given data point (10, 15).

15 = k×10

k = 15/10 = 1.5

so, now for the other tree we know k and x and calculate y

y = 1.5×14.4 = 21.6 m

it is 21.6 m tall (its height is 21.6 m).

Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.

To calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.

Given:

Cost per KWH: $0.75

Average monthly usage: 120 KWHs

To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:

Monthly Cost = Cost per KWH * Average monthly usage

Plugging in the values, we have:

Monthly Cost = $0.75/KWH * 120 KWHs

Calculating the result:

Monthly Cost = $90

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Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

The average speed over the time interval from 9 A.M. to noon was of 33.33 mph.

Step-by-step explanation:

The average speed is given by the following equation:

\(v = \frac{d}{t}\)

From 10A.M. to noon.

You traveled at 50mph during 2 hours. So how long you traveled?

\(50 = \frac{d}{2}\)

\(d = 50*2\)

\(d = 100\)

You traveled 100 miles.

What was your average speed over the time interval from 9 A.M. to noon

From 9 A.M. to 10 A.M, you did not travel.

From 10 P.M. to noon, 100 miles.

So 100 miles during 3 hours.

\(v = \frac{d}{t} = \frac{100}{3} = 33.33\)

The average speed over the time interval from 9 A.M. to noon was of 33.33 mph.

Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.

We have,

For Matthew's investment, the continuous compounding formula can be used:

\(A = P \times e^{rt}\)

Where:

A = Final amount

P = Principal amount (initial investment)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (in decimal form)

t = Time (in years)

In this case,

Matthew's money has tripled,

So A = 3P.

For Parker's investment, the formula for compound interest compounded annually is used:

\(A = P \times (1 + r)^t\)

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

t = Time (in years)

We need to find t when Matthew's money has tripled in value.

Let's set up the equation:

\(3P = P \times e^{rt}\)

Dividing both sides by P, we get:

\(3 = e^{rt}\)

Taking the natural logarithm of both sides:

ln(3) = rt

Now we can solve for t

t = ln(3) / r

For Matthew's investment,

r = 3 1/8% = 3.125% = 0.03125 (as a decimal).

For Parker's investment,

r = 2 3/4% = 2.75% = 0.0275 (as a decimal).

Now we can calculate t for Matthew's investment:

t = ln(3) / 0.03125

Using a calculator, we find t ≈ 22.313 years.

Now, we can calculate how much money Parker would have in his account at that time:

\(A = P \times (1 + r)^t\)

\(A = $8,000 \times (1 + 0.0275)^{22.313}\)

Using a calculator, we find A ≈ $13,774.

Therefore,

Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.

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Answer:

20,763

Step-by-step explanation:

I saw the answer after I got it wrong

The solution of the composite function fog(x) = 3x + 3 at x > 2.

Let the two function f(x) and g(x) generate a new function h(x) using an operation.

The operation is composition of functions and h(x) is a composite function.

We have three piecewise function.

First we have to show that,

the composite function,

fog(x) at x > 2.

For that,

g(x) at x > 2 is,

g(x) = 3x.

Now, f(g(x)),

= f(3x)

= 3x + 3 at x > 2.

Therefore, the function is fog(x) = 3x + 3.

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The complete question:

Find the fog(x) at x > 2

Answer:

That would be 3x=50-10y

Step-by-step explanation:

If 10y and 3x add up to 50 then the expression above is checking to see if 3x is the correct answer to 50. Therefore 3x= 50- 10y. Thank you for submitting this question.

By solving simultaneous linear equation, it can be calculated that

The two numbers are 82 and 48

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Let the numbers be x and y

The sum of two numbers is 130

so, x + y = 130 .... (1)

The difference of two numbers is 34

so, x - y = 34 ..... (2)

Adding  (1) and (2),

2x = 164

\(x = \frac{164}{2}\\x = 82\)

Putting the value of x in (1)

82 + y = 130

y = 130 - 82

y = 48

The two numbers are 82 and 48

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Based on the data, the mean would be the best measure of center to describe a typical value in the data set.

To create a dot plot, we can list the numbers in order and place a dot above the corresponding value on the number line.

20 ••

21 ••

22 •

23 ••••

24 •••••

25 ••

26 ••

27 •

The dot plot shows a relatively symmetric distribution of the data, with the majority of values clustered around the middle. Therefore, the mean would be a good measure of center to describe a typical value of the data set.

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Answer:

C

Step-by-step explanation:

We know that secant is the same as \(\frac{1}{cos}\) , so knowing that we can immediately find cosΘ by flipping the given secant value to be \(\frac{12}{-13}\) . Since only C has this for cosΘ, this is your answer. However, if you wanted to check further using a triangle. Using the knowledge that secant is \(\frac{1}{cos}\) and cosine is adjacent over hypotenuse (SOH CAH TOA), we can find that our hypotenuse is -13 and the adjacent side is 12. From there we can find the remaining functions using 5 as your opposite (given in the solutions) and SOH CAH TOA for each sine, cosine and tangent, flipping each for cosecant and cotangent.

Answer

138

Step-by-step explanation:

The answer is 138 because, when you take 258 and subtract it by 120, you will end up with 138!  

Answer:

It was most likely raised by 46%

Step-by-step explanation:

120/258

8 < x < 8.5 is your answer

other sides has to always be less than the hypotenuse

9514 1404 393

Answer:

  0.5 < x < 16.5

Step-by-step explanation:

The sum of the two shortest sides of a triangle must always exceed the length of the longest side.

If x and 8.0 are the short sides, then ...

  x + 8.0 > 8.5

  x > 0.5

If 8.0 and 8.5 are the short sides, then ...

  8.0 +8.5 > x

  16.5 > x

So, for the given triangle to exist, we must have ...

  0.5 < x < 16.5

_____

Additional comment

You will notice that the value 0.5 is the difference of the given sides, and 16.5 is their sum. This will always be the case for a problem like this. The third side length always lies between the difference and the sum of the other two sides.

Answer:

The formula for density (ρ) is:

Density (ρ) = Mass (m) / Volume (V)

Step-by-step explanation:

Where:

Answer:

draw the diagram and multiply 5x20

We have that the unit cost is given by a parabola, and the leading coefficient is given by 0.6 (it is positive), then, we have a minimum in the shape of the parabola.

A way to find the minimum is to find the vertex of the parabola (in this given case, the vertex is the minimum point) which coordinates are as follows:

Since we need to find the minimum unit cost, we need to find the value for y. Then, we have:

a = 0.6

b = -324

c = 56258

Then

Therefore, the minimum unit cost is equal to $12,518.

Answer: 9.625 cups..

So, b) and e) are subspaces of R3, and a), c), and d) are not.

a) {(x,y,z) ∈R3 : x = 0} is not a subspace of R3, because it doesn't contain the zero vector (0,0,0) which is a requirement for a subspace. It's also not closed under scalar multiplication.

b) {(x,y,z) ∈R3: x + y = 0} is a subspace of R3, because it's closed under scalar multiplication and addition and it contains the zero vector (0,0,0).

c) {(x,y,z) ∈R3 : xz = 0} is not a subspace of R3, because it's not closed under scalar multiplication and it's not closed under addition

d) {(x,y,z) ∈ R3: y ≥0} is not a subspace of R3, because it's not closed under addition, it doesn't contain the zero vector (0,0,0) and it's not closed under scalar multiplication.

e) {(x,y,z) ∈ R3: x = y = z} is a subspace of R3 because it satisfies all the properties of a subspace, it is closed under addition, scalar multiplication, it contains the zero vector (0,0,0) and the negative of any vector in the set is also in the set. This set contains all the vectors that are multiples of (1,1,1) which forms a subspace.

So, b) and e) are subspaces of R3, and a), c), and d) are not.

Complete Question: For each of the following subsets of R3 determine whether it is a vector subspace of R3 or not. Justify your answer.                                                                                                                                                      

a) {(x,y,z) ∈R3 : x = 0}

b) {(x,y,z) ∈R3: x + y = 0}

c) {(x,y,z) ∈R3 : xz = 0}

d) {(x,y,z) ∈ R3: y ≥0}

e) {(x,y,z) ∈ R3: x = y = z}

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Answer:

90

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

(((95 × 26) - 470)/16) - 35

Step 2: Evaluate

The experimental probability of tossing a tail and spinning a 2 is given by: Option H: 1/8

Experimental probability calculates the probability of some event from the results of experiments.

For an event E, we get the experimental probability of that event

\(P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}\)

where, \(P_e(E)\) is denoting experimental probability of occurrence of E.

For this case, the table is missing, the results recorded were:

Toss         Spin        Frequency

Head          1                 2

Head          2                6

Head          3                7

Tail             1                 7

Tail             2                5

Tail             3                13

That means total number of times experiment was done was: 2+6+7+7+5+13=40

Let we take E = event of  tossing a tail and spinning a 2

Thus, from the table, we see that E occurred 5 times.

Thus, based on this, the experimental probability of occurrence of E is:

\(P_e(E) = \dfrac{5}{40} = \dfrac{1}{8}\) (option H)

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