Which of the following could be the product of two consecutive prime numbers?​

The wheel is rotating 600 times per minute, find how many times rotate in 1 second:

1 minute = 60 seconds

Then, if in 1 second it rotates 10 times in 1/2 seconds it rotates:

Multiply the number of times it rotates (5 times) by 360 (a wheel has 360º)

To perform a two column proof, we should give a statement and give a reason of it.

So we start with the initial statement.

1. Statement: x-4 =(1/2)(8x+6)+4x. Reason: Given

Next, we distribute the multiplication (1/2) with(8x+6). If we do so, we get the following statement.

2. Statement x-4 = (4x+3) + 4x. Reason: Distributive property of addition and multiplication.

Now, on the right we can add 4x with 4x, due to the associative property of additon, we get

3. Statement: x-4 = (4x+4x)+3 = 8x+3. Reason: Associative property of addition.

Now, we can subtract x on both sides, so we get

4. Statement: -4 = 7x+3. Reason: Subtraction property of equality.

By the same reason, we should subtract 3 on both sides. We get

5. Statement: -7 = 7x. Reason: Subtraction property of equality.

Finally, we divide by 7 on both sides, so we get

6. Statement: -1=x. Reason: Division property of equality.

7. Statement: x=-1. Reason: Symmetric property of equality.

1) In this question let's calculate the sin(θ) and cos(θ)

Given that

2) In this question, we're calculating the value of the sine and the cosine in radians.

We must remember that 5π/4 ⇒ to 225º, and that it's in the Quadrant III

If we subtract

225 -180 =45 So the sine of 5π/4 is -√2/2 and the cosine (5π/4 ) = -√2/2

2.3) The sign of the Quadrant

Since 225º is in Quadrant III both results are negative ones.

The two composite functions have their values to be (w o s)(x) = 7x² - 49x + 33 and (s o w)(x) = (7x - 2)² - 7(7x - 2) + 5

Composite function 1

The given parameters are

w(x) = 7x - 2

s(x) = x² - 7x + 5

To calculate (w o s)(x), we make use of

(w o s)(x) = w(s(x))

So, we have

(w o s)(x) = 7s(x) - 2

Substitute s(x) = x² - 7x + 5

(w o s)(x) = 7(x² - 7x + 5) - 2

Expand

(w o s)(x) = 7x² - 49x + 35 - 2

Simplify

(w o s)(x) = 7x² - 49x + 33

Composite function 2

Here, we have

w(x) = 7x - 2

s(x) = x² - 7x + 5

To calculate (s o w)(x), we make use of

(s o w)(x) = s(w(x))

So, we have:

(s o w)(x) = w(x)² - 7w(x) + 5

Substitute w(x) = 7x - 2

(s o w)(x) = (7x - 2)² - 7(7x - 2) + 5

So, the composite functions are (w o s)(x) = 7x² - 49x + 33 and (s o w)(x) = (7x - 2)² - 7(7x - 2) + 5

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part A. We are given that a hiker will increase the distance covered by 10% each day. Let "S" be the distance, then on the first day the distance is:

On the second day, we must add 10% of the first day, we get:

Simplifying we get:

On the third day, we add 10% of the second day, we get:

On the fourth day, we add 10% of the third day, we get:

If we continue this pattern and we set "n" as the number of days, then a formula for the distance after "n" days is:

Now, we are given that for n = 7 the distance is 75897, therefore, we substitute n = 7 in the formula:

Substituting the value of the distance:

Now we can solve for S1, we do that by dividing both sides by 1.1 together with its

exponent:

Now we solve the operations:

Solving the operations:

Therefore, the distance the first day was 42842 miles.

part B. The formula for Sn is the given previously but we replace the known value of S1:

Part C. To determine the distance after 10 days, we substitute the value n = 10 in the formula, we get:

Solving the operations we get:

Therefore, the distance after 10 days is 101019.19 miles.

Answer:

Explanation:

Here, we want to get the number that could be inserted into the parentheses to make it true

From the logical operator given, we can see that we need a number greater than -10

From the options given, only -3 is greater than -10, which makes it the correct answer choice

Given:

Resolving it to its radical form can be gotten based on the general laws of indices.

We have:

I.e. the number is raised to the power of the numerator and then we get the denominator's root of the number obtained.

Thus:

Now, we have our value in the square root form as:

Problem

Solution

5. E-D

Procedure

-3-2 =-5

-4-1=-5

0-7=-7

1-5=-4

2-3=-1

6- (-4)=10

And the answer would be:

-5 -5

-7 -4

-1 10

6. 3F

Procedure

3* -2=-6

3 *5 = 15

3* 1= 3

3*3 = 9

3*14=12

3 * -6= -18

And the answer would be:

-6 15 3

9 12 -18

We have the following:

The first thing is to find the slope of the line, like this:

replacing:

now, the equation has the following form:

for b,

m = -1/2

y = 2

x = 0

replacing:

Therefore, the equation in standard form is:

Given the following systems of linear equations,

6x + 20y = -62 (Equation 1)

3x - 9y = -12 (Equation 2)

Step 1 : Solve 6x+20y=−62 for x:

6x + 20y + (−20y) = −62 + (−20y) (Add -20y to both sides)

6x = −20y −62

6x/6 = (−20y −62)/6 (Divide both sides by 6)

x = (-10y/3) + (-31/3)

Substitute to Equation 2:

3x−9y=−12

3[(-10y/3) + (-31/3)] - 9y = -12

−19y−31=−12 (Simplify both sides of the equation)

−19y−31+31=−12+31 (Add 31 to both sides)

−19y=19

-19y/-19 = 19/-19 (Divide both sides by -19)

y= −1

Step 2: Substitute −1 for y in x =(-10y/3) + (-31/3)

x =(-10(-1)/3) + (-31/3)

x = -7

Answer:

x=−7 and y=−1

The number of different ways in which Ms. Bell's can select 3-member committee of sophomores is 20 ways.

For the given question;

Ms. Bell's mathematics class consists -

Ms. Bell create a 3-member committee of sophomores with unbiased outcomes.

The section of 3 sophomores can be done as;

⁶C₃ = 6!/3!(6-3)!

⁶C₃ = 6/3!.3!

⁶C₃ = 20 ways.

Thus, the number of different ways in which Ms. Bell's can select 3-member committee of sophomores is 20 ways.

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Answer:

A, C, E

Step-by-step explanation:

4^10 = 1048576

A: (4^5)^2 = 1048576

C: 4^20 / 4^10 = 1048576

E: (4^2 x 4^3)^2 = 1048576

EXPLANATION

The intercept-form of a quadratic function is as follows:

y = a(x - p)(x - q)

Now, as the roots are (-5,0)

Since the parabola passes through the point (−5,0), then 0=25a−5b+c

Since the parabola passes through the point (−1,0), then 0=a−b+c.

Since the parabola passes through the point (−7,−24), then −24=49a−7b+c.

Thus, we have obtained the following system:

Solving it we get that a=−2, b=−12, c=−10.

Thus, the equation of the parabola is y=(−2x−10)(x+1)

Ok, so he started at 38 feet below and ended at 92 feet above. 38 below = -38.

The difference in the height is given by

92-(-38) =

92+38 =

130 feet

Devin was 130 feet higher at the end of climbing.

height of tree = 65 ft

length of shadow = 13 ft

Let draw a diagram to illustrate the question effectively

The proportion can be set up below

Th shadow will be 4 ft. do you

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

8x - 3x + 4x = -36

x = ?

Step 02:

We must apply the algebraic rules to find the solution.

8x - 3x + 4x = -36

12x - 3x = - 36

9x = - 36

x = - 36 / 9

x = - 4

The answer is:

x = - 4

This is a compound interest question and we have been given:

Principal (P) = $24000

Rate (r) = 7.25%

Years (t) = 10

However, we are told this value is compounded continuously. This means that for every infinitesimal time period, the value keeps being compounded.

The formula for finding the compound interest is:

But because the compounding period is continuous and therefore, infinitesimal,

This is similar to the general formula for Euler's number (e) which is:

Thus, we can re-write the Amount formula in terms of e:

Therefore, we can find the amount of money in the account after 10 years:

Therefore the amount after compounding continuously for 10 years is:

$49553.55

Evaluate the value of expression.

So answer is 1.

The equation of a circle is given by the next formula:

Where the center is the point (h, k) and r means the radios. Therefore:

Answer is letter C

Trigonometric Ratios

The figure is a triangle with hypotenuse of h = 25 feet. The angle of elevation is 35°.

Answer:

B(2) = -1

Step-by-step explanation:

Assuming each division on the grid is 1 unit

Locate 2 on the x-axis. That is two divisions to the right of the origin. The y value corresponding to this is -1

When a, b, c changes from -1 to +1, the parabolas opens and widens.

Given,

The quadratic function, f(x) = ax² + bx + c

We have to find the change in graph when a, b, c changes from -1 to 1.

First lets consider:

a and b as constants and c is varying.

That is,

x² + x + c

Then,  the parabola will move up and down.

Now, lets consider:

a and c as constants and b is varying.

That is,

x² + bx + 1

Then, the vertex will move but  all parabolas passes through the points (0, c)

Now, we can move to the question.

What happens to graph when +1 changes to -1.

So,

b and c should keep constant and a is varying.

Then,

ax² + x + 1

Here, the parabolas opens and widens.

That is,

When a, b, c changes from -1 to +1, the parabolas opens and widens.

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The graph of the given line is attached below.

We are given the line:-

y = (3/5)x - 4

We will find the x and y intercepts of the line to plot in the graph.

As the equation is already in the slope intercept form, we can write,

The y-intercept of the line is -4.

Hence, the coordinates of the point will be (0,-4).

To find the x - intercept of the line we will put y = 0 in the given line.

0 = (3/5)x - 4

4 = 3x/5

x = 20/3

The coordinates of the point will be (20/3,0).

We can plot these points to get the desired graph.

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ANSWER

Quadrant III

STEP-BY-STEP EXPLANATION:

Firstly, we need to draw the cardinal points and label each quadrant on it

Looking at the ordered pair (-x, -y), you will see that the x and y-values both fall on the negative side of the x-ais and y-axis

Hence, it falls on the quadrant III

To find out how much Katherin have left we need to substrac the amount she spent:

Therefore she has $1.9 left.

To do this same problem in fraction form we need to convert the 2.6 in fraction, to do this we multiply the number by 10 and divided by ten. Then:

then we have:

Therefore, the answer in decimal form is 19/10 dollars.

Answer:

Explanation:

Here, we want to create a table of values to represent the given equation

To do this, we need to select a range of values for x

This can be a range of any set of numbers

With respect to this question, we shall be choosing -2 to +2 with an increment of 1

The values of x are thus: -2,-1 , 0, +1 and +2

So, now let us get the corresponding y-values using the equation rule

Now, let us get the y-values

when x = -2

y = -2-9 = -11

when x = -1

y = -1-9 = -10

when x = 0

y = 0-9 = -9

when x = 1

y = 1-9 = -8

when x = 2

y = 2-9 = -7

Thus,we have the table of values as follows:

The given equation is

To write the equation in standard form, first, we have to use the distributive property.

Now, we subtract 5x and 5 on both sides.

Now, we add 9 on each side

Answer:

3.34

Step-by-step explanation:

625 is 5^4

Using the log rule [tex]log_b(x^a)=alog_b(x)[/tex],

log_b(5^4) = 4*log_b(5)

4*0.835 = 3.34

By definition, a relation is a function if each input value (x-value) has one and only one output value (y-value).

In this case, you have the following relation:

Notice that each ordered pair has this form:

Where "x" is the input value and "y" is the output value.

You can identify that each input value has one and only output value. Therefore, you can conclude that this relation is a function.

Hence, the answer is: It is a function.