Which arithmetic sequence has a common difference of -21? ( only one is correct )

a) {873, 894, 915, 936, …}

b) {32, 20, 8, -4, …}

c) {1,245; 1,224; 1,203; 1,182; …}

d) {1,563; 1,587; 1,611; 1,635; …}

Answer:

scalene

Step-by-step explanation:

hidhihihihihihi

Answer:

[tex]2x+5y=41[/tex]

Step-by-step explanation:

Median of a triangle:  A line segment that connects a vertex of a triangle to the midpoint of the opposite side.

Vertex:  The point where any two sides of a triangle meet.

Given vertices of a triangle:

Find the midpoint of BC (Point D) by using the Midpoint formula.

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

Define the endpoints:

Substitute the defined endpoints into the formula:

[tex]\textsf{Midpoint of BC}=\left(\dfrac{-21-33}{2},\dfrac{25+13}{2}\right)=(-27,19)[/tex]

Therefore, D = (-27, 19).

Find the slope of the median (line AD) using the Slope formula.

Define the points:

Substitute the defined points into the Slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{19-9}{-27-(-2)}=-\dfrac{2}{5}[/tex]

Therefore, the slope of the median is -²/₅.

Substitute the found slope and one of the points into the Point-slope formula to create an equation for the median.

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-9=-\dfrac{2}{5}(x-(-2))[/tex]

Simplify and rearrange the equation so it is in standard form Ax+By=C:

[tex]\implies 5(y-9)=-2(x+2)[/tex]

[tex]\implies 5y-45=-2x-4[/tex]

[tex]\implies 2x+5y-45=-4[/tex]

[tex]\implies 2x+5y=41[/tex]

Therefore, the equation of the median is:  

2x + 5y = 41

Yes, companies that provide mobile wifi hotspots can see your history.

A Wi-Fi hotspots can be defined as  the hotspots that makes it possible for other mobile user connected to a wifi hotspots to browse or to connect to the internet.

For a mobile user to connect to the internet through the mobile wifi hotspot, the mobile hotspot wifi owner must have giving access to mobile user to browse .

Hence, companies that provide mobile wifi hotspots can see your history of the site you visit.

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Answer: 15

Step-by-step explanation: Using the pythagorean theorem A^2 + B^2 = C^2 where C is the hypotenuse of the triangle and any A and B are any sides of the triangle that are not the hypotenuse; we can rewrite this as A^2 = C^2 - B^2 to find out the missing side. I picked A to be the unknown side but you could also choose B. We know the hypotenuse is 39, and side B is 36. 39^2 - 36^2, or 1521 - 1296, is 225.

Now we have A^2 = 225. To get rid of the square, we have to take the square root of both sides. The A^2 cancels to be A, and sqrt(225) is 15. Thus, side A, or the missing side is 15.

Hope this helped!

hope this helps

by

aman10we

The value of x after solving this equation is 2

Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11

Given here, the equation as : (4x - 5)^4 = 81.​

(4x - 5)^4 = 3⁴.​

4x - 5    = 3

      x     = 2

Hence, the value of x is equal to 2

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Answer: a) $ 6,487.47

b) $ 1,487.47

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

the price of one pound of trail mix is $3

the price of one pound of jelly beans is $2.5

Step-by-step explanation :

let t be the price of one pound of trail mix.

and b be the price of one pound of jelly beans.

This statement:

“For 3 pounds of trail mix and 8 pounds of jelly beans,

the total cost is $29”

Can be translated mathematically like this :

3t + 8b = 29

This statement:

“For 5 pounds of trail mix and 2 pounds of jelly beans,

the total cost is $20”

Can be translated mathematically like this :

5t + 2b = 20

We obtain a system of two equations :

3t + 8b = 29

5t + 2b = 20

Solving the system:

3t + 8b = 29  (equation 1)

5t + 2b = 20. (equation 2)

3t + 8b = 29

20t + 8b = 80   [4×(equation 2)]

3t + 8b = 29

17t = 51  [4×(equation 2) - equation 1]

3t + 8b = 29

t = 51/17 = 3

9 + 8b = 29

t = 3

8b = 20

t = 3

b = 20/8 = 5/2

t = 3

b = 5/2

t = 3

Therefore ,the solution to our system is (3 , 2.5)

The slope of the line that passes through between (0, -6) and (2, 0) is: C. 3.

The slope of a line can be defined as the measure of the ratio of the vertical distance to the horizontal distance that exists between two points on a coordinate plane.

If we are given two points on a line, (x1, y1) and (x2, y2), the slope (m) is the rise/run = change in y / change in x = (y2 - y1)/(x2 - x1).

Given the following coordinates of two points as follows, (0, -6) and (2, 0), let:

(0, -6) = (x1, y1)

(2, 0) = (x2, y2)

Plug in the values into the slope formula to find the slope:

Slope (m) = (0 - (-6)) / (2 - 0)

Slope (m) = (0 + 6) / (2 - 0) [minus multiplied by minus is plus]

Slope (m) = (6) / (2)

Slope (m) = 3

Thus, the slope of the line that passes through between (0, negative 6) and (2, 0) is calculated as: C. 3.

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Answer:

51,840

Step-by-step explanation:

The format of P(n, r) is used for permutations,

where      [tex]P(n, r) = \frac{n!}{(n - r)!}[/tex]

To evaluate this expression, P(9,2), we use the formula of permutation,

We have the value of n = 9 and r = 2, thus,

[tex]P(n, r) = P(9, 2) = \frac{9!}{(9 - 2)!} =\frac{9!}{7!} =\frac{9*8*7!}{7!} = 9 *8 =72\\[/tex]

To evaluate this expression, P(6, 5), we use the formula of permutation,

We have the value of n = 6 and r = 5, thus,

[tex]P(n, r) = P(6, 5) = \frac{6!}{(6 - 5)!} =\frac{6!}{1!} =\frac{6*5*4*3*2*1!}{1!} = 6*5*4*3*2 = 720[/tex]

Therefore the product of P(9, 2) · P(6, 5) is

72 · 720 = 51,840

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the statement is false, as there no exist a value of t such that cos(t) > 1.

Here we have the statement:

"There are values of t so that the equation cos(t) = 5/3"

Now, remember that the range of the sine and cosine equations is given by:

R: -1 ≤ y ≤ 1

And 5/3, the value in the statement, is larger than 1, which is the maximum in the range.

Then the statement is false, as there no exist a value of t such that cos(t) > 1.

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The sequence of transformation carried out on ABCD is; B: Reflection about the y-axis followed by a translation left by 2 units

As in rotation, reflection and translation the transformed image is congruent to the original figure (i.e all the points undergo same change). Thus, analyzing any one point will give the series of transformation undertaken.

Taking point A(3, 1) into consideration; Reflecting a point (x, y) over y axis, it becomes (-x, y).

Thus, reflecting A(3, 1) over y - axis gives the the new coordinates as (-3, 1)

Now, translating a point (x, y) k units left, gives a new coordinate (x - k, y).

Thus, translating point (-3, 1) 2 units left, gives the new coordinates as A'(-5, 1).

This is the coordinates for A'.

Thus, we can conclude by saying that the sequence of transformation carried out on ABCD is reflected about the y-axis followed by a translation left by 2 units.

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Answer:

376.99112cm²

Step-by-step explanation:

A=2 pi rh + 2 pi r²

A=(2 x pi x 5 x 7) + (2 x pi 5²)

pi 22/7

Answer:

=====================================

We know that diagonals of rhombus are perpendicular to each other.

Hence its area is half the product of diagonals.

The diagonals are JL and KM and one of them is vertical and the other one horizontal since x- or y-coordinates are equal in pairs.

Let's find the length of diagonals, using the difference of coordinates:

Now find the area:

Answer:

c

Step-by-step explanation:

The measure of the angle ∠CRQ is 103° and the measure of the angle ∠CRS will be 103°.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

In the figure, lines BD and QS are parallel. Two parallel lines B D, and Q S are intersected by a line AT at C, and R respectively such that the angle ∠DCR is 77 degrees.

We know that the angle ∠DCR & ∠SRT and ∠DCR & ∠SRT are corresponding angles. Then they are equal to each other.

∠DCR = ∠SRT = 77°

∠CRQ = ∠CRS

We know that the angle ∠CRQ and ∠CRS are supplementary angles. Then we have

∠CRQ + ∠SRT = 180°

∠CRQ + 77° = 180°

∠CRQ = 103°

Then the measure of the angle ∠CRQ is 103° and the measure of the angle ∠CRS will be 103°.

The diagram is given below.

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Answer:

[tex]-3(x-2)^2+5[/tex]

Step-by-step explanation:

First we can factor a -3 from the [tex]x^2[/tex] term and the [tex]x[/tex] term to get [tex]-3(x^2-4x)-7[/tex].

Then we want the stuff in the parentheses to have the form of [tex](x+b)^2[/tex], or equivalently, [tex](x^2+2b+b^2)[/tex] . So we can let [tex]2b = -4[/tex]. By solving it, we get [tex]b = -4/2 = -2[/tex]. Then our [tex]b^2[/tex] term should be [tex]b^2 = (-2)^2 = 4[/tex].

In order to make our [tex]b^2[/tex] term appear in the parentheses, we need to add and subtract our [tex]b^2[/tex] term, so we get [tex]-3(x^2 - 4x + 4 - 4) -7[/tex].

What we to keep inside our parentheses is [tex](x^2 - 4x + 4)[/tex] , so we can factor the [tex]-4[/tex] out of parentheses to get [tex]-3(x^2-4x+4-4)-7 = -3(x^2-4x+4)+(-3)(-4) - 7 = -3(x^2 - 4x + 4) + 12 - 7 = -3(x^2 - 4x + 4) + 5[/tex]

Finally, plugging  [tex]b = -2[/tex]  that we computed earlier into the equation [tex](x^2+2b+b^2) = (x+b)^2[/tex], we get  [tex](x^2 - 4x + 4) = (x-2)^2[/tex].

So we have [tex]-3(x^2-4x+4)+5 = -3(x-2)^2+5[/tex].

In summary, the procedure is

[tex]-3x^2+12x-7 \\= &-3(x^2-4x) -7 \\= &-3(x^2-4x+4-4)-7 \\= -3(x^2-4x+4) + (-3)(-4)-7\\=-3(x^2-4x+4)+12-7\\= -3(x^2-4x+4)+5 \\= -3(x-2)^2+5[/tex]

A) RSB&T's operating profits are 2,625,000.

B) The profit from Customer A = 42 and Customer B=42.

C) The profit from Customer A=77.7 and Customer B=-207.75(loss)

Data on two representative customers follow.

[A] Compute RSB&T's operating profits.

Computation of Operating Profits:-

Revenue                                   19,500,000

Interest to Depositors            (1,875,000)

Overheads                          (15,000,000)

Total operating Profit              2,625,000

[B] Costs are based only on Deposits

Particulars       A          B

Revenue               312           312

Interest Cost        -30         -30

Operating Cost    -240       -240

Profits                42        42

[C] As per Activity based costing

Particulars                       A              B

Revenue                              312      312

Interest Cost                       -30      -30

ATM Uses                       -75     -150

Branch Visit                       -30     -120

Processing Transaction      -3.3   -123.75

Managing Function        -96      -96

Profits/Loss                        77.7     -207.75

Therefore,

A) RSB&T's operating profits are 2,625,000.

B) The profit from Customer A = 42 and Customer B=42.

C) The profit from Customer A=77.7 and Customer B=-207.75(loss)

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Answer:

For example, 8f + 4g is one of the most used expression

Another example is 4 (2f + g), is correct too

By solving the equations x+2y=5, 4x-12y=-20 through elimination or substitution method we will get the value of x=1 and y=2.

Given two equations x+2y=5 and 4x-12y=-20.

We are required to solve the equations through elimination and substitution method.

Firstly we will solve the equations through elimination method.

x+2y=5-------------1

4x-12y=-20--------2

Multiply the equation 1 by 4 and then subtract the equation 2 from equation 1.

4x+8y-4x+12y=20+20

20y=40

y=2

Use the value of y in 1

x=5-2*2

x=5-4

x=1

From substitution method.

First find the value of x from first equation in terms of y.

x=5-2y-----4

Now put this value in second equation to get the value of y.

4(5-2y)-12y=-20

20-8y-12y=-20

20-20y=-20

-20y=-40

y=2

Put the value of y in equation 4.

x=5-2y

x=5-2*2

x=5-4

x=1

Hence by solving the equations x+2y=5, 4x-12y=-20 through elimination or substitution method we will get the value of x=1 and y=2.

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Answer:

2

Step-by-step explanation:

If he sells and makes x paintings, his expenses will he 10+45x and his revenue will be 50x.

The break-even point is the point at which total cost and total income are equal. For breakeven, Lamar needs to sell 2 paintings.

In economics, business, and especially cost accounting, the break-even point is the point at which total cost and total income are equal, i.e. "even."

Let the number of paintings that Lamar makes and sells at the break-even point be represented by x.

Given that Lamar bought some brushes for $10, and paint and canvas for each painting cost $45. Therefore, the total cost of making x number of paintings is,

Total cost of x painting = $10 + $45(x)

Also, the selling price of each painting is $50. Therefore, the revenue generated from x paintings is,

Revenue generated = $50(x)

Further, at the breakeven point, the total cost of production of any product is equal to the revenue generated by the product. Therefore, we can write,

Total cost of x painting = Revenue generated

$10 + $45(x) = $50(x)

10 + 45x = 50x

10 = 50x - 45x

10 = 5x

x = 10/5

x = 2

Hence, For breakeven Lamar needs to sell 2 paintings.

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Peter:

£2.30 ÷ 6 = £0.38 each sausage

Paul:

£3.50 ÷ 10 = £0.35 each sausage

As you can tell, it is cheaper to buy from Paul because each sausage is £0.35 which is 3 pence less than buying from Peter.

In other words, the best value for money would go to the 10 pack sausage, saving £0.03 per unit of sausage.

However, that doesn't answer the question. You need to find how many packages you can get with your available £10.

£10 ÷ £2.30 = 4.34...

So, you can buy 4 packs of sausage from Peter - meaning you will get 24 sausages in total. This is because each pack contains 6 sausages, and you have 4 of this. (6x4=24)

£10 ÷ £3.50 = 2.85...

So, you can buy 2 packs of sausages from Paul & meaning you will get 20 sausages in toal because each package contains 10 sausages. (2x10 = 20)

Thus, you should buy from Peter because you get 24 sausages, instead of 20 sausages from Paul, in accordance to the £10 you can spend in both shops.

Hope this helps!

we conclude that the store where you can get more sausages is in Peter the Butcher.

You have £10.

Peter the Butcher sells 6 sausages for £2.30

The number of packages that you can buy is:

£10/£2.30 = 4.3

Rounding down to the next whole number, we conclude that here you can buy 4 packages, then:

4*6 = 24 sausages

4*£2.30 = £9.20

So here you can buy 24 sausages for £9.20

In Paul the butcher, you can buy 10 sausages for £3.50

Notice that here you can only buy 2 packages (because the cost of 3 packs would be  £10.50, which is more than the amount you can spend).

Then here you only can get 20 sausages.

Then, we conclude that the store where you can get more sausages is in Peter the Butcher.

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Answer:

-14

Step-by-step explanation:

[tex]\sqrt{16} = 4\\\\(\sqrt{16} - 1) = (4 -1) =3\\\\(3-9) = (-6)\\\\(3-9) ^2 = (-6)^2 = 36\\\\25 - 3 - 36 = 25 - 39 = -14\\[/tex]

Answer:

1. 2A + 3A

2. 2A - B

3. 2A

4. 2(A-B)

Step-by-step explanation:

When multiplying matrix by a number you just multiply each number in the matrix by whatever you are multiplying. When adding 2 matrices you just add the corresponding number in each matrix. Ex: You add the top left number to the top left number. The same goes with subtraction.

Answer:

Behold!

Step-by-step explanation:

Answer:

It could be 105, 112 or 133.

Step-by-step explanation:

Having 7 as a factor means it is a multiple of 7.

The first 3 digit multiple of 7: 100 ÷ 7 = 14 2/7 → first 3 digit multiple of 7 is 15 × 7 = 105

Last 3 digit multiple of 7 less than 140: 140 ÷ 7 = 20 → last 3 digit multiple of 7 less than 140 is 19 × 7 = 133

→ The possible multiples of 7 to consider are [15..19] × 7 which gives 105, 112, 119, 126 and 133.

The sum of the digits of these number is:

105 → 1 + 0 + 5 = 6

112 → 1 + 1 + 2 = 4

119 → 1 + 1 + 9 = 11

126 → 1 + 2 + 6 = 9

133 → 1 + 3 + 3 = 7

Of these sums only 6, 4 and 7 are less than 9, thus the possible numbers are 105, 112 or 113.

Answer:

Slope: [tex]-\frac{1}{5}[/tex]   Y-intercept: (0,0)

Step-by-step explanation:

By putting this into a graph you can see that the y-intercept is (0,0). Also, by looking at the chart and using the walk, rise rule you can see that the slope is [tex]-\frac{1}{5}[/tex].

Answer:

[tex]4 < x < 20[/tex]

Step-by-step explanation:

By the triangle inequality theorem, the sum of the length of the two smaller sides must be greater than the length of the largest side. If 12 cm was the length of the largest side, notice that [tex]8+x > 12 \Rightarrow x > 4[/tex]. Similarly, if x was the length of the largest side, we'd get the inequality [tex]12+8 > x \Rightarrow 20 > x[/tex]. Combining these inequalities, we get [tex]\boxed{4 < x < 20}[/tex].

The inverse equation of x = y is y = x

Inverse equations are the opposite of an original equation

The equation is given as

x = y

Swap the positions of x and y in the above equation

y = x

This means that the inverse equation of x = y is y = x

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The expression that represents the perimeter of the rectangle is 30h - 2

The dimensions of the rectangle are given as:

Length = 7h + 3

Width = 8h - 4

The perimeter of the rectangle is given as:

P = 2 * (Length + Width)

Substitute the known values in the above equation

P =2 * (7h + 3 + 8h - 4)

Evaluate the like terms

P = 2 * (15h - 1)

Evaluate the product

P = 30h - 2

Hence, the expression that represents the perimeter of the rectangle is 30h - 2

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The value of the probability P(A and B) is 0.20

The given parameters about the probability are

P(A or B) = 0.9

P(A) = 0.5

P(B) = 0.6

To calculate the probability P(A and B), we use the following formula

P(A and B) = P(A) + P(B) - P(A or B)

Substitute the known values in the above equation

P(A and B) = 0.5 + 0.6 - 0.9

Evaluate the expression

P(A and B) = 0.2

Hence, the value of the probability P(A and B) is 0.20

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The amount he can spend on marketing is $8,333.33.

The amount he can spend on supplies is $16,666.67

The amount he can spend on trainings is $12,500

The amount he can spend on travel is $2,500

The amount he can spend on equipment is $10,000

The amount he can spend on each category can be determined by multiplying the fraction of that category by the total department's budget.

The amount he can spend on marketing : 1/6 x $50,000 = $8,333.33.

The amount he can spend on supplies: 1/3 x $50,000 =  $16,666.67

The amount he can spend on trainings: 1/4 x 50,000 =  $12,500

The amount he can spend on travel $2: 1/20 x 50,000 = 2,500

The amount he can spend on equipment $: 1/5 x 50,000 = 10,000

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