How many triangles will there be in the 7th term of the following
sequence?
Δ, ΔΔΔ, ΔΔΔΔΔ..
Ο
Α. 19
Ο
Β. 22
Ο
C 16
D. 8

Answer:

(42.26/100)*120 = $50.712

Step-by-step explanation:

Answer: tip = 8.452

Step-by-step explanation:

Answer:

10ab + 4a + 5b + 2

= 10ab + 5b + 4a + 2

= 5b(2a+1) + 2(2a+1)

= (5b+2)(2a+1)

Answer:

y = 2 + ((-)6/5)x

Step-by-step explanation:

-6x-5y=-10

add 6x to both sides.

-5y = -10 +6x

divide both sides by -5

y = 2 - (6/5)x

Plug in 0 for x to get the y intercept:

f(0) = 2 - (6/5) (0)

y = 2

(0, 2) is the y intercept.

Do the same for values such as -1, -2, 1, and 2, etc.

Then graph it.

To find the correct graph for -6x - 5y = -10, transform it to the slope-intercept form y = 6/5x - 2, which reveals a slope of 6/5 and a y-intercept at -2. Seek a graph with a line that increases 6 units vertically for every 5 units horizontally and intersects the y-axis at -2.

To find the graph that represents the equation -6x - 5y = -10,

we first need to manipulate the equation into slope-intercept form,

which is y = mx + b where m is the slope and b is the y-intercept. Starting with the given equation:

-6x - 5y = -10

Let's isolate y by adding 6x to both sides:

-5y = 6x - 10

Now, divide each term by -5 to solve for y:

y = -6x / -5 + 10 / -5

y = 6/5x - 2

The slope-intercept form of the equation is now y = 6/5x - 2. This tells us that the slope (m) of the line is 6/5 and the y-intercept (b) is -2. You will look for the graph with a line that rises 6 units for every 5 units it moves to the right (since the slope is positive) and crosses the y-axis at -2.

Answer:

The solution of the inequality is:

[tex]x>2[/tex]

Step-by-step explanation:

Given inequality:

[tex]-1 >-2(x - 4)-5(4x-7)[/tex]

Solving the inequality.

Using distribution.

⇒ [tex]-1 >(-2x) +((- 4)(-2))+(-5\times4x)+((-5)(-7))[/tex]

⇒ [tex]-1 >-2x +8-20x+35[/tex]

Combining like terms

⇒ [tex]-1 >-2x-20x+35+8[/tex]

⇒ [tex]-1 >-22x +43[/tex]

Adding [tex]22x[/tex] both sides.

⇒ [tex]-1+22x >-22x +43+22x[/tex]

⇒ [tex]-1 +22x> 43[/tex]

Adding 1 both sides.

⇒ [tex]-1+1 +22x> 43+1[/tex]

⇒ [tex]22x>44[/tex]

Dividing both sides by 22.

⇒ [tex]\frac{22x}{22}>\frac{44}{22}[/tex]

⇒ [tex]x>2[/tex]

Thus, the solution of the inequality is:

[tex]x>2[/tex]

Answer: D. 9

Step-by-step explanation: If BD is 18 then BE is 9

Answer:

can confirm that it is 9

Step-by-step explanation:

slay have a nice day!

Just multiply the total length by the fraction:

14.3 * 1/10 = 1.43 miles

Answer:

1.43

Step-by-step explanation:

NOTE: This is the way I do it , other people may have a other/faster way to do it.

For this question you simpily have to divide 14.3 by 10:

1. Convert 14.3 into a mixed number - 14 3/10

2. Divide 14 by 10 - 1.4

3. Divide 3/10 by 10 - 3/100

4. Convert 3/100 into a decimal- 0.03

5. Add the two decimals - 0.03 + 1.4 = 1.43

Answer:

The coordinates of point Q will be given by (11,-2)

Step-by-step explanation:

See the attached diagram.

Given that R is the midpoint of PS and Q is the midpoint of RS.

Therefore, the point Q divides the line PS in the ratio 3 : 1.

Now, coordinates of P are (8,10) and that of point S is (12,-6).

Therefore, the coordinates of point Q will be given by  

[tex](\frac{3\times 12 + 1 \times 8}{3 + 1}, \frac{3 \times (- 6) + 1 \times 10}{3 + 1})[/tex]  

= (11,-2) (Answer)

Answer:

C. Starting with a given set of rules and figuring out what must be  true . TRUE

Step by step explanation:

Mathematical Induction

Mathematical Induction is a mathematical technique which we can use to prove any given mathematical statement, result, theorem or corollary with help of induction.

Here, we assume the statement to be true for a smaller natural number            (Usually 1) and then prove the statement to be true for ANY ARBITRARY NUMBER say k.

Now, from the given options:

A. Writing down the steps to solve a complicated math problem .

FALSE as the induction method is based on ASSUMPTION and INDUCTION.

B. Forming rules based upon observations and experiences .

FALSE as the induction method is based on ASSUMPTION and INDUCTION.  We need to induce the needed  statement or Result.

C. Starting with a given set of rules and figuring out what must be  true .

TRUE as the induction method is based on ASSUMPTION and INDUCTION.

We try and find out  the result with the given existing data.

D. Reducing the solution to a problem in lowest terms.

FALSE as the induction method is based on ASSUMPTION and INDUCTION.  

Explanation:

When the inequality symbol is replaced by an equal sign, the resulting linear equation is the boundary of the solution space of the inequality. Whether that boundary is included in the solution region or not depends on the inequality symbol.

The boundary line is included if the symbol includes the "or equal to" condition (≤ or ≥). An included boundary line is graphed as a solid line.

When the inequality symbol does not include the "or equal to" condition (< or >), the boundary line is not included in the solution space, and it is graphed as a dashed line.

Once the boundary line is graphed, the half-plane that makes up the solution space is shaded. The shaded half-plane will be to the right or above the boundary line if the inequality can be structured to be of one of these forms:

Otherwise, the shaded solution space will be below or to the left of the boundary line.

_____

Just as a system of linear equations may have no solution, so that may be the case for inequalities. If the boundary lines are parallel and the solution spaces do not overlap, then there is no solution.

_____

The attached graph shows an example of graphed inequalities. The solutions for this system are in the doubly-shaded area to the left of the point where the lines intersect. We have purposely shown both kinds of inequalities (one "or equal to" and one not) with shading both above and below the boundary lines.

Answer:

Andrew did not reason that he could save the $10 per hour he would make cutting lawns by preparing his own meal

Step-by-step explanation:

If Andrew cuts lawns for $10 per hour, he would have $4 more to save by preparing his own meal rather than spending the $4 at Taco Bell

Answer:

Instead of spending time making food, he drives and buys food by a total of $4.

Now, he is not considerating the amount of gas that he is spending by going to buy food and returning.

Also, he was not working, so he is not producing money at the beginning, so making his own lunch actually does not implies that he stops working and loses money.

Answer: D

Step-by-step explanation: I just did the quiz

Answer: D

Step-by-step explanation:

Yeah the quiz was like, dud the answers D, so I was like okay it's D

Answer:

The cost of the sofa is $216

Step-by-step explanation:

The sofa was sold at cost plus 25% profit

let the cost of the sofa be                               = x

therefore                                     x + 25% of x = 270

                                                    x + .25x        =  270

                                                    1.25x            =   270

                                                    1.25x/1.25    =   270/1.25

                                                     x                  =   $216

Answer:

D

Step-by-step explanation:

The diagram shows Pascal's triangle. Pascal's triangle is a triangular array of the binomial coefficients.

The entry in the [tex]n^{th}[/tex] row (start counting rows from 0) and [tex]k^{th}[/tex] column (start counting columns from 0) of Pascal's triangle is denoted by

[tex]C^n_k=\left(\begin{array}{c}n\\ k\end{array}\right)[/tex]

Coefficient 20 stands in 6th row, then n = 6 and in 3rd column, so k = 3.

Hence,

[tex]20=C^6_3=\left(\begin{array}{c}6\\ 3\end{array}\right)=\dfrac{6!}{3!(6-3)!}[/tex]

Answer:

25

Step-by-step explanation:

60 per day 25 in sales 63.75-60=3.75

3.75÷.15=25

If Nicole's earns 15% commission of her total sales, then Nicole's total sale of Monday is 25.

Percentage is a part of the whole number. It is denoted by % sign.

1 %= 1/100.

Given that,

Total salary of Nicole's = $60.

Also,

Nicole gets 15% commission of her total sales,

Total earning on Monday = $63.75

The commission earned on Monday = 63.75 - 60 = 3.75

According to given condition,

15 % = 3.75

1 % = 3.75 / 15

100 % = 3.75 / 15 x 100

100 % = 25

Total sale of Nicole's on Monday is 25.

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8 litres (amount of 20% solution needed) and 7 litres for (amount of 50% solution needed)

Step-by-step explanation:

Let consider ‘x’ for 20% acid solution and (15 – x) for 50% acid solution. And so, the equation would be as below,

                         20% in x + 50% in (15 – x) = 15 litres of 34%

Convert percentage values, we get

                              0.20(x) + 0.50 (15 – x) = 15 (0.34)

                              0.20 x + 7.5 – 0.50 x = 5.1

                              -0.3 x + 7.5 = 5.1

                              0.3 x = 7.5 – 5.1

                              0.3 x = 2.4

[tex]x = \frac{2.4}{0.3} = 8 litres (amount of 20 \% solution needed)[/tex]

Apply ‘x = 8’ value in (15 – x) we get,

                         15 – 8 = 7 litres

The value of 7 litres for (amount of 50% solution needed)

Answer:

Therefore

m∠ DAB is 105°

Step-by-step explanation:

Given:

ABCD is a parallelogram. The diagram is not drawn to scale.

m∠CDA = 75°,

To FInd

m∠DAB  = ?

Solution:

ABCD is a parallelogram.

AB || CD .......{opposite sides of a parallelogram are parallel}

∴∠CDA+∠DAB = 180°{SUM of the interior angles between parallel are supplementary}

substituting the values we get

[tex]75+m\angle DAB=180\\\\m\angle DAB =180-75=105\\\\m\angle DAB =105\°[/tex]

Therefore

m∠ DAB is 105°

Answer:

x^3 - 3x^2 - 3x + 9 + (-36/(x+3))

OR

x^3 - 3x^2 - 3x + 9 - (36/(x+3))

Step-by-step explanation:

First set the divisor equal to 0:

x + 3 = 0

Subtract 3 from both sides

x = -3

This is what you'll divide the dividend by in synthetic division.

Take the coefficents of each term in the dividend. Do not forget the 0 placeholders:

x^4 + 0x^3 - 12x^2 + 0x -9

Coefficents: 1. 0.  -12. 0 -9.

Please see the image for the next steps.

The remainder is -36. Put the remainder over the divisor and add it to the polynomial (shown in image)

-36/(x+3)

Divide using synthetic division the remainder is -36. Put the remainder over the divisor and add it to the polynomial -36/(x+3).

First set the divisor equal to 0:

x + 3 = 0

Subtract 3 from both sides

x = -3

This is what you'll divide the dividend by in synthetic division.

Take the coefficents of each term in the dividend. Do not forget the 0 placeholders:

[tex]x^4 + 0x^3 - 12x^2 + 0x -9[/tex]

Coefficents: 1. 0.  -12. 0 -9.

The remainder is -36. Put the remainder over the divisor and add it to the polynomial -36/(x+3).

Answer:

Step-by-step explanation:

-3w+9-8

=-3w+1

Answer: [tex]4\ feet[/tex]

Step-by-step explanation:

The exercise provides you the following Quadratic function:

[tex]h(t)=4+60t-16t^2[/tex]

You know that it represents the height (in feet) of the ball as a function of the time (in seconds) since the ball hit the bat.

Based on this, you can conclude that when the ball strikes the bat the time in seconds is:

[tex]t=0[/tex]

Therefore, in order to calculate the height in feet of the ball when it strikes the bat, you need to subsititute [tex]t=0[/tex] into the function and    then evaluate.

So, you get:

 [tex]h(0)=4+60(0)-16(0)^2\\\\h(0)=4[/tex]

You got the equations correct, great job on that!

Let "s" be the variable that represents how many shirts were bought. Let "p" represent the total price/cost.

Equation for the store at Town Center mall:

p = 80 + 3.5s (80 is base cost, and cost increases 3.5 per shirt)

Equation for the store in Arlington:

p = 120 + 2.5s (120 is base cost, and cost increases 2.5 per shirt)

We want to find a point where the systems are equal; thus, we are solving for a system of linear equations, and we already have the equations we need.

p = 80 + 3.5s

p = 120 + 2.5s

We know that variable "p" is equal for both equations; thus, we can combine both equations into:

80 + 3.5s = 120 + 2.5s

Subtract both sides by 2.5s

80 + 3.5s - 2.5s = 120 + 2.5s - 2.5s

80 + s = 120

Subtract both sides by 80

s = 40

Thus, both equations are equal when 40 shirts are bought.

To find the cost, use any of the two equations (or both) to find the total cost, which should be equal.

p = 80 + 3.5(40) = 220

p = 120 + 2.5(40) = 220

Thus, the total price/cost at both stores is $220.

Let me know if you need any clarifications, thanks!

Answer:

1036 students

Step-by-step explanation:

Let the number of students at West High be "w" and the number of students at East High be "e"

West High population is 250 FEWER than TWICE of East High, we can write:

w = 2e - 250

Total students in both schools is 2858, so we can write 2nd equation as:

e + w = 2858

We can replace 1st equation in 2nd to get an equation in e, and find "e":

e + w = 2858

e + (2e - 250) = 2858

3e - 250 = 2858

3e = 2858 + 250

3e = 3108

e = 3108/3

e = 1036

Hence,

number of students attending East High School = 1036 students

First, do distributive property:

2(5+3x)+(x+10)  Distribute the 2 to the 5 and the 3x; multiply them

10+6x+x+10      Since (x+10) would be 1 times x and 10, it's just x+10

Then, do communitive property:

10+6x+x+10     What we found in the last step, now combine the like terms

20+7x              This is what you get since 10+10=20 and 6x+x=7x

The answer:

20+7x or 7x+20

Hope that helps!

Answer:

∠ZPB and ∠APZ are two adjacent supplementary angles

Step-by-step explanation:

we know that

Two angles are Adjacent when they have a common side and a common vertex

Two angles are supplementary if their sum is equal to 180 degrees

In this problem we have that

[tex]m\angle ZPB=90^o[/tex] ----> given problem

[tex]m\angle APZ=90^o[/tex] ----> given problem

so

[tex]m\angle ZPB+m\angle APZ=180^o[/tex]

∠ZPB and ∠APZ are supplementary angles

and

∠ZPB and ∠APZ have a common side (ZP) and a common vertex (P)

therefore

∠ZPB and ∠APZ are two adjacent supplementary angles

Answer: ∠ZPB and ∠APZ are two adjacent supplementary angles

Step-by-step explanation: Its the way the cookie crumbles.

Answer:

5

Step-by-step explanation:

1.24 times 3 = 3.72

.95 (the value of pence to a pound in decimal form) = 2.85

6.18 for the teapot

2.72+2.85+6.18=11.75

She now has £8.25 left (20-11.75).

8.25/1.57=the amount of plates she can buy: 5.25477707006, so 5 with some money left

Polar form: (r,θ)

Using these formulas:

x²+y²=r²

tan(θ)=y/x

We have the point (1,1) in cartesian coordinates. We need to find r and θ to get it in polar form.

r²=1²+1²

r²=2

r=±√2

tan(θ)=1/1

tan(θ)=1

θ=π/4 radians or 45 degrees

Polar coordinates: (√2,π/4)

Those answer choices look strange. Are you sure these are the right answer choices?

Answer:

Step-by-step explanation:

The way I see it, (1, 1) corresponds to a point which is √2 units from the origin and has an angle of 45° (or π/4 radians).

25 cakes can be completely decorated using 4 gallons of icing.

Step-by-step explanation:

Given:

4 gallons of icing

16 cups =1 gallon

No. of icing cups = [tex]4\times16[/tex] cups

       =64 cups

No. of cups required to decorate and frost a cake= 4% of total no. of icing cups

          = [tex]\frac{(4\times64)}{100}[/tex]

          = 2.56

2.56 cups of icing is required to decorate each cake.

Maximum no. of cakes decorated = [tex]\frac{ (64\times1)}{2.56}[/tex]

                    = 25

25 cakes can be completely decorated using 4 gallons of icing.

Final answer:

To maintain the same weekly revenue after reducing her pot price from $24 to $16, a potter working 4 days a week must increase her daily production from 14 pots to 21 pots, which is an increase of 7 pots per day.

Explanation:

The question involves a potter who initially makes 14 pots per day and works 4 days a week, charging $24 per pot. To find out by how many pots per day she must increase her production after lowering her price to $16 per pot, to make the same amount of money, we first calculate her current weekly revenue:

After reducing the price to $16 per pot, we need to determine how many pots per day she needs to sell to maintain the same weekly revenue of $1,344:

Therefore, she needs to sell 7 more pots per day (21 pots - 14 pots) to maintain her weekly revenue.

Answer:

1/20

Step-by-step explanation:

Answer:

12/5-2p

Step-by-step explanation:

2/5(6-5p)

12/5-10/5p

12/5-2p

The simplified form of the expression 2/5 (6 -5p) is 12 / 5 - 2p.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

2/5 (6 -5p)

Simplify the expression by solving bracket term,

(2/5) x 6 - (2/5) x 5p

12 / 5 - 2p

The simplified form of the expression 2/5 (6 -5p) is 12 / 5 - 2p.

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