Which expression describes the distance between point A and point B on the number line?

Combinations are a method of calculating the total outcomes of an event where the order of the outcomes is irrelevant. We will use the formula nCr = n! / r! * (n - r)! to calculate combinations.

They can select one  republican from the four  republican by 4 ways, and than select the remaining 4 members

from the 7 republicans by  [tex]C^{4} _{7}[/tex]= 7 x5 = 35 ways.

In all,  4 × 35= 140 selections are possible.

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Answer:

Step-by-step explanation:123123km equals to 110m

2(m + 1) + 5m​

step 1

Apply distributive property

2*(m)+2*(1)+5m

2m+2+5m

Combine like terms

Given:

There are given the function:

And,

The transferred function is:

Explanation:

According to the question:

We need to describe the transformation:

So,

We can see that in the transfer function, there is given that a negative sign.

So,

The transformation is:

Reflection on the x-axis: reflected:

Final answer:

Hence, the correct option is A.

The problem says Seth earns $25 a day and $3 for each ticket he sells.

Let's for each ticket he sells.

Let's

Part A:

By Angle-Angle Theorem,

Triangle BCA is similar with triangle BDC (∠B ≅ ∠B, and ∠C ≅ ∠D)

Triangle CDA is similar with triangle BCA (∠CBA ≅ ∠DCA, and ∠BCA ≅ ∠CDA)

By transitive property

ΔBCA ~ ΔCDA ~ BDC

Part B:

Part C:

Cross multiplying the proportions we have

The equation of the line that passes through the points (-2,4) and (-4,3) is y = (1/2)x + 5.

We know the slope intercept form of a line is given by:-

y = mx + c

Where,

m represents the slope of the line,

c represents the y-intercept, and

(x,y) represents the ordered pair of each point on the line

We know that,

m = (3-4)/(-4-(-2)) = -1/-2 = 1/2

We can write,

4 = (1/2)(-2) + c

4 = -1 + c

4 + 1 = c

c = 5

Hence, the equation of the line is :-

y = (1/2)x + 5

The graph of the equation is attached below.

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If the Busy Bee store bottles fresh jars of honey at a constant rate and In 3 hours, it bottles 36 jars, and in 7 hours, it bottles 84 jars of honey, then the constant of  proportionality is 12

The Busy Bee store bottles fresh jar of honey at a constant rate.

That means number of bottle is directly proportional to the time taken

Number of bottle they bottles =  k × Time taken

Where k is the constant of proportionality

In 3 hours, it bottles 36 jar

36 = k ×3

k = 36/3

k = 12

In 7 hours, it bottles 84 jar

84 = k × 7

k = 84/7

k = 12

Hence, if the Busy Bee store bottles fresh jars of honey at a constant rate and In 3 hours, it bottles 36 jars, and in 7 hours, it bottles 84 jars of honey, then the constant of  proportionality is 12

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Answer: 7 months

Step-by-step explanation: by 7 months you would have paid both memberships $300

We need to complete the perfect square. A perfect square has the following form:

In our case we have:

We can immediately deterine the value of "a", which is the root of number multiplying x², since this number is 1, then:

This also means we can find "b", because the second term is equal to the product of 2, a, and b. So we have:

With this we can determine the blank, because it is b². So we have:

The first missing space is 16 and the second is 4.

The value of the amount after the second year is $10163.817.

In order to compute compound interest, we multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. Then we are left with the principal amount of the loan plus compound interest.

Amount after Compound Interest [tex]A = P(1+\frac{r}{nt} )^{nt}[/tex] where A is the amount, P is the Principle value, r is the rate of interest, n is the number of times it is compounded daily, and t is the time.

Given Information :

For 1st year, Principal Amount (P) = $5000

Interest (r) = 1.5 %

Time = 1 year

The amount is calculated compounded daily,

So, Calculating the amount after 1 year,

[tex]A = P( 1+\frac{r}{nt}) ^{nt} \\A = 5000(1+\frac{1.5}{365*100}) ^{365*1} \\A = 5000(1+0.00004109)^{365} \\A = 5000*1.015\\A =5075.55[/tex]

For 2nd Year, Principal Amount= (P) $5000

Rate of Interest (r) = 1.75%

Time (t) = 1 year

The amount is calculated compounded daily,

So, Calculating the amount after 1 year,

[tex]A =P(1+\frac{r}{nt}) ^{nt\\}\\A= 5000(1+\frac{1.75}{365*100}) ^{365*1} \\ A = 5000(1.00004795)^{365} \\A =5000*1.077\\A =5088.26[/tex]

Now, the value of the amount after the second year = $5075.55 +$5088.26 =$10163.817.

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start by writing a relation

find x using the relationship

To translate a point given its coordinate and a vector to translate by, we can simply add each value of the vector to the corresponding x and y coordinates of the point, so:

So, the image of the translations is (2, -7).

Given:

The lengths of two sides of a triangle are 55 and 20.

Required:

To find the possible lengths of the third side.

Explanation:

So, if the third side is x cm, then

So, we got

Now

Hence the conclusion is the value of x lies between 35 and 75.

Therefore, the possible third sides are 45, 72 and 60.

Final Answer:

The possible third sides are 45, 72 and 60.

The question asks us to find the vertex of the equation below:

The question asks us to find the vertex using two methods.

For the first method, we will use is to plot the graph of the equation and highlight the coordinate of the vertex on the graph.

The second method will employ completing the square method to find the vertex of the equation.

Method 1:

Plotting the graph of the equation, we have:

From the plot above, we can see that the vertex is: (31.765, 22.953)

The next method must get the same values for the vertex coordinates.

Method 2:

This method is the completing the square method. It converts quadratic equations into their vertex forms.

The general equation for a vertex form of a quadratic equation is:

In order to apply "completing the square" method, we need to complete the following steps:

1. Factor out the coefficient of x-squared

2. Divide the coefficient of x by 2 and square the result

3. Add and subtract the answer from step 2 to the equation; then factorize to get the quadratic equation

in its vertex form.

Now, let us proceed to find this vertex form:

1. Factor out the coefficient of x-squared

2. Divide the coefficient of x by 2 and square the result

3. Add and subtract the answer from step 2 to the equation; then factorize to get the quadratic equation

in its vertex form.

Now that we have the equation in vertex form, we just need to compare the equation with the general formula for the vertex form, to get the coordinates of the vertex.

Therefore, the final answer is: (31.7647, 22.9529)

Answer:

5.

Step-by-step explanation:

1. the formula of the required distance:

[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2} ;[/tex]

2. according to the formula above:

[tex]d=\sqrt{3^2+4^2}=5.[/tex]

Explanations:

• Take note that the sides of a rectangle are parallel

• All 4 angles are 90 degrees, when they intercept they form a perpendicular line .

• The reflection, rotation and the transformation, will still maintain and preserve the properties of rectangle,

• opposite side are still going to be parallel and congruent,

90 degrees angles will still remain the same .

This shows that the properties of a rectangle are maintained

To find the scale factor, we have to divide two corresponding sides

Using the given information, we have

The product of the polynomials (3x+2) and (-x^3-3) is:

(3x+2)*(-x^3-3) = (3x)*(-x^3) + (3x)*(-3) + 2*(-x^3) + 2*(-3) = -3x^4 - 2x^3 -9x - 6

Multiplying it by (3 + x), we got:

(3 + x)*(-3x^4 - 2x^3 -9x - 6) = 3*(-3x^4) + 3(-2x^3) + 3*(-9x) +3*(-6) + x*(-3x^4) + x*(-2x^3) + x*(-9x) + x*(-6) = -3x^5 -11x^4 -6x^3 -9x^2 - 33x - 18

Therefore, the coefficient of x^4 is -11.

Answer:

Slope Intercept Form

y = mx + b

Where

m is slope

b is y- intercept (y axis cutting point)

Now,

Slope is change in y's over change in x's:

[6-1]/[2--3] = 5/5 = 1

So, we have:

y = 1x + b

y = x +b

We can just plug in a point (let it be (2,6) ) in x and y and solve for b:

y = x + b

6 = 2 + b

b = 6-2

b = 4

Final equation:

If triangle HJK has a centroid P then we know that the side HP will be the double of PM so we can made an equation for HM

Now we can replace the value of HM and solve for PM so:

After performing some mathematical operations, the length of RA is 15 feet.

So, the length of RA is:

As both the pentagons are similar, then:

Similarly,

Therefore, after performing some mathematical operations, the length of RA is 15 feet.

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Answer:

m^8a+8m^6a+24m^4a+32m^2a+16

Step-by-step explanation:

Simple binomial theorem.

(x+y)n = nC0 xny0 + nC1 xn-1y1 + nC2 xn-2 y2 + ... + nCn-1 x1yn-1 + nCn x0yn

OR

(x+y)n = ∑nk=0nCk xn-kyk = ∑nk=0nCk xkyn-k

plugging the numbers into this theorem yields that answer.

Answer:

The solution is x < - 11/4.

Step-by-step explanation:

In inequality notation, 7(x+4) less than 2(-5)+3(x+9) simply means:

7(x+4) < 2(-5)+3(x+9) ⇒7x + 28 < - 10 +3x +27

To collect like terms, subtract 3x and 28 from both sides of the inequality, thus:

7x - 3x < - 10 + 27 - 28 ⇒ 4x < -11 ⇒ x < -11/4 [by dividing both sides of the inequality by 4]

Therefore, the solution is x < - 11/4.

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An expression for the combined total dollar Josh earned this month is X = 15t + 13(95 - t).

A mathematical expression is a statement using a combination of numbers, variables, and mathematical operands.

Mathematical expressions may also use the equal symbol (=) to show that the two expressions are equal.  Sometimes, the inequality signs are used when two expressions are not equivalent.

The pay rate per hour as a tutor = $15

The pay rate per hour as a waiter = $13

The combined total hours worked for the month = 95 hours

Let t = the number of hours worked as a tutor

Let X = Josh's total dollars earned for the month.

Josh's total earnings as a tutor for the month, A = 15t

Josh's total earnings as a waiter for the month, B = 13(95 - t)

The combined total dollar Josh earned this month, X = A + B

X = 15t+ 13(95 - t).

Thus, the total earnings by Josh for this month can be expressed as X = 15t+ 13(95 - t).

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The equation of the line in point-slope form passing through ( - 1, - 4 ) and slope 3 is y + 4 = 1( x + 1 ).

The set of points that make up a line in a coordinate system is represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y.

The point-slope form of an equation of the line is given as:

y - y₁ = m( x - x₁ ) where m is the slope and ( x₁, y₁ ) is the point on the line.

Now, the equation of line passes through ( - 1, - 4 ) and m = 1

Then,

y - y₁ = m( x - x₁ )

y - ( - 4 ) = 1( x -  ( - 1 ) )

y + 4 = x + 1

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40 people are seated. (Solved using the equation 4x + x = 50)

What is an equation?

An equation can be compared to a scale on which objects are weighed. When the two pans are filled with the same amount of anything (like grain), the scale will balance and the weights will be considered equal. To maintain the scale in balance, if any grain is taken out of one of the balance's pans, an equal amount must be taken out of the other pan. More broadly, if the identical operation is carried out on both sides of an equation, the equation remains in balance. Equations involving one or more functions and their derivatives are known as differential equations. By identifying a derivative-free formulation for the function, they may be resolved. Processes are modeled using differential equations.

The equation below is formed according to the question

4x + x = 50

or, 5x = 50

or, x = 50/5 = 10

Hence, no. of people seated = 4x10 = 40

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Explanation

To solve the question, we will make use of PEMDAS

So, in solving the question

We will have

Combining the above, we will have

Thus, we have our answer as 20

Answer = 20