what is 32 – 21 + 10x – 12x

Answer:

2520

Step-by-step explanation:

The n th term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference.

To find the number of terms given [tex]a_{n}[/tex] = - 10 , d = - 2 and a₁ = 100, then

100 - 2(n - 1) = - 10 ( subtract 100 from both sides )

- 2(n - 1) = - 110 ( divide both sides by - 2 )

n - 1 = 55 ( add 1 to both sides )

n = 56 ← number of terms

Given n, a₁ and a₅₆ , then the sun of the terms is

[tex]S_{56}[/tex] = [tex]\frac{n}{2}[/tex] (a₁ + a₅₆ )

      = [tex]\frac{56}{2}[/tex] (100 - 10) = 28 × 90 = 2520

Everything you answered so far looks good. Nice work.

For question 10, we need to find two numbers that multiply to 3(-1) = -3 and also add to 2. The 3 and -1 are the first coefficient and last term. The 2 is the middle coefficient.

Through trial and error, the two numbers we're after are 3 and -1

3 times -1 = -3

3 plus -1 = 2

We break up the 2x into 3x - 1x and factor like so...

3x^2 + 2x - 1

3x^2 + 3x - 1x - 1 ... replace 2x with 3x-1x

(3x^2+3x) + (-1x-1) ... pair up terms

3x(x+1) - 1(x+1) .... factor each parenthesis group

(3x-1)(x+1) ... pull out the gcf (x+1)

You can use FOIL, the box method, or distribution to go from (3x-1)(x+1) back to 3x^2+2x-1 again.

Answer:

Step-by-step explanation:

Answer:

star or asterisk if you are talking about (*)

Answer:

(*) is similar to (×)

and it means multiply

Answer:

x = 60

Step-by-step explanation:

Given

[tex]\sqrt{x+4}[/tex] - 7 = 1 ( add 7 to both sides )

[tex]\sqrt{x+4}[/tex] = 8 ( square both sides )

([tex]\sqrt{x+4}[/tex] )² = 8² , that is

x + 4 = 64 ( subtract 4 from both sides )

x = 60

Answer:

To be honest with u my mom says she has know idea and nitherr do i and were math people so sorry.

Step-by-step explanation:

Answer:

3y + x = -15

Step-by-step explanation:

gradient = 3

gradient of the perpendicular = -⅓

[tex] \frac{y - ( - 4)}{x - ( - 3)} = - \frac{1}{3} [/tex]

-x -3 = 3y + 12

3y + x = -15

Answer:

see below

Step-by-step explanation:

The sum of the interior angles of any polygon can be found with the formula 180(n - 2) where n = number of sides. In this case, n = 6 so the answer is 180(6 - 2) = 180 * 4 = 720°.

Answer:

The sum of the interior angles of a regular hexagon is 720°

Step-by-step explanation:

As we know that the sum of interior angle is 180(n-2). So the number of sides of hexagon is 6. Now, 180(6-2)=180*4=720°

Answer: 48

Step-by-step explanation:

Given, A box has a white, a green, a blue, and an orange marble.

Total possible outcomes of pulling marbles = 4

There is also a fair 12-sided die labeled with the numbers 1 through 12.

Total possible outcomes of rolling the die = 12

By Fundamental counting principle , we have

Possible outcomes are in the sample space for pulling a marble out of the box and rolling the die = (Total possible outcomes of pulling marbles ) x (Total possible outcomes of rolling the die)

= 4 x 12

= 48

Hence, the correct answer is "48".

Answer:

The correct option is;

b) 0 sq, units

Step-by-step explanation:

The vertices of the triangle are;

(4, 0), (2, 3), (8, -6)

The distance formula fr finding the length of a segment is given as follows;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

Where, (x₁, y₁) and (x₂, y₂) are the coordinates of the end points of the line

For the points (4, 0) and (2, 3) , we have;

√((3 - 0)² + (2 -4)²) = √13

Distance from (4, 0) to (2, 3) = √13

For the points (4, 0) and (8, -6) , we have;

√((-6 - 0)² + (8 -4)²) = √13 =

Distance from (4, 0) to (8, -6) = 2·√13

For the points (2, 3) and (8, -6) , we have;

√((-6 - 3)² + (8 -2)²) = 3·√13 =

Distance from (2, 3) to (8, -6) = 3·√13

Therefore, the perimeter of the triangle = 6·√13

The semi perimeter s = 3·√13

The area of the triangle,  [tex]A = \sqrt{s\cdot \left (s-a \right )\cdot \left (s-b \right ) \cdot \left ( s-c \right )}[/tex]

Where;

a, b, and c are the length of the sides of the triangle;

[tex]A = \sqrt{3\cdot \sqrt{3} \cdot \left (3\cdot \sqrt{3} -\sqrt{3} \right )\cdot \left (3\cdot \sqrt{3} -2 \cdot \sqrt{3} \right ) \cdot \left ( 3\cdot \sqrt{3} -3\cdot \sqrt{3} \right )} = 0[/tex]

Therefore, the area = 0 sq, units.

Answer:

3d + f -2

Step-by-step explanation:

= 4f+4+3d-6-3f

= f+3d-6

= 3d+ f - 6

Answer:

9108

Step-by-step explanation:

23^3+(-12)^3+(-11)^3                              remove parentheses

= 23^3-12^3-11^3                                  group difference of two cubes

= (23-12)(23^2+23*12+12^2) + 11^3      factor difference of two cubes

= 11 (23^2+23*12+12^2-11^2)                factor ou 11

= 11(23(23+12) + (12+11)(12-11))              apply difference of two squares

= 11 (23*35+23*1)                                  factor out 23

= 11(23*(35+1))                                       simplify

= 11*23*36                                             convert 11*23 into difference of 2 squares                                                                    

= (17^2-6^2)*6^2                                   expand parentheses

= 102^2-36^2                                       evaluate squares

= 10404 - 1296                                     subtraction

= 9108

(no calculator required)

Answer:

6+x=24

Step-by-step explanation:

he has 6 more marbles than the blue

the amount of blue marbles is unknown

so let blue marble be x

we know that the total number of marbles is 24

so 6+x=24

Answer:

m = -1/2 and b = 6.5

Step-by-step explanation:

To find the slope of the original line segment, we have to do the change in y/the change in x:

(4-8)/(-5--3) = -4/-2 = 2

2 is the slope of the original line segment, but since this is the perpendicular bisector, we have to take the negative reciprocal of 2 so m = -1/2

To find b we substitute the values of x, y, and m into the equation. Let's use the x value of -3 and the y value of 8:

y = mx + b

8 = -1/2(-3) + b

8 = 3/2 + b

6.5 = b

Answer:

Step-by-step explanation:

Hello, the vertex is (1,2), right?

You remember that when the parabola equation is in standard form like below

[tex]y=ax^2+bx+c[/tex]

The vertex is for , and we apply with this example where a = 1, b = -2, c=3

[tex]x=-\dfrac{b}{2a}=\dfrac{-(-2)}{2}=1\\\\1^2-2*1+3=4-2=2[/tex]

So this is the first graph.

Thank you

Answer:

A

Step-by-step explanation:

I just took the test

Answer:

2x-2

Step-by-step explanation:

Being specifically asked to rationalise the denominator we focus on it as required.

To rationalise a term it has to be multiplied by its inverse.

The inverse of

[tex] \sqrt{x} - \sqrt{2 - x} [/tex]

is

[tex] \sqrt{x} + \sqrt{2 - x} [/tex]

Multiplying this two vives us a difference of two squares

[tex] {( \sqrt{x} })^{2} - {( \sqrt{2 - x} )}^{2} [/tex]

which gives us

x-(2-x)

=2x-2

Answer:

The answer is below

Step-by-step explanation:

From the diagram of the flask attached, the diameter of the cylinder is 1 inch and its height (h) is 3 inches. The radius of the cylinder (r) = diameter / 2 = 1/2 = 0.5 inch

The volume of the cylinder = πr²h = π(0.5)² × 3 = 2.36 in³

While for the sphere the diameter is 4.5 in. The radius of the sphere R = diameter / 2 = 4.5/2 = 2.25

The volume of the sphere = 4/3 (πR³) = 4/3 × π × 2.25³ = 47.71 in³

Volume of the flask = The volume of the cylinder  + The volume of the sphere = 2.36 + 47.71 = 50.07 in³

If the sphere and the cylinder are dilated by a scale factor of 2. For the cylinder its height (h') = 3/2 = 1.5 inch and its radius (r') = 0.5/2 = 0.025

The new volume of the cylinder = πr'²h' = π(0.25)² × 1.5 = 0.29 in³

While for the sphere The radius of the sphere R' = 2.25 / 2 = 1.125

The new volume of the sphere = 4/3 (πR'³) = 4/3 × π × 1.125³ = 5.96 in³

New Volume of the flask = The new volume of the cylinder  + The new volume of the sphere = 0.29 + 5.96 = 6.25 in³

The ratio of the new volume to original volume = New Volume of the flask / Volume of the flask = 6.25 / 50.07 = 1/8 = 0.125

The resulting volume would be 0.125 times the original volume

Answer:

50.07 and 8 times

Step-by-step explanation:

1) Calculate volume of each figure using according formulas.

You should get:

Sphere: 47.71in^3

Cylinder: 2.36in^3

Now let's add, and you should get 50.07.

2) Let's dilate the dimensions/flask by 2 (multiply by 2)

4.5 * 2 = 9

1 * 2 = 2

3 * 2 = 6

Now with these dimensions you should get:

Sphere: 381.7in^3

Cylinder: 18.85in^3

This should add up to 400.55in^3

Divide new by original. 400.55 / 50.07 = 8

So it is 8 times larger.  

Answer:

Step-by-step explanation:

The daily charge will be 17x for x days of rental. Added to the flat rate, the total becomes ...

  y = 130 +17x

__

For 9 days, the cost is ..

  y = 130 +17·9 = 130 +153 = 283 . . . . dollars charge for 9 days

Answer:

( -5, 1)

Step-by-step explanation:

When we reflect over the x axis

(x,y)→(x,−y)

( -5, -1) becomes ( -5, - -1)  which is ( -5, 1)

Answer:

Volume = 5×8×10.5 = 420 meters3

Step-by-step explanation:

5×8×10.5

Answer:

once upon a time a dude went to a store. there was a dude jacket for 20% off.

Step-by-step explanation:

Now do the opposite. for exapmle, the price increased by 20 %.

Answer:

Sample because it's only the first ten games of the season not of all the games in the season

Step-by-step explanation:

Answer:

Sample but the power of a study is its ability to detect an effect when there is one to be detected. ... A sample size that is too small increases the likelihood of a Type II error skewing the results, which decreases the power of the study.

Within accompaniment order to be a population then it would need to be justifiable to be comparable to a larger cross section same teams different players that could be at the end of the season, and a population that shows cross section of change, such as the inevitable and include distractions that occur in sports as season starts and progresses till end. Examples of this would include ie) playing with man down etc. or against a team with man down or during penalties etc..

It only becomes a population when it defines all home games only being used as a population as this would show less distraction for each team. Which would be unlikely event in first 10 games, just like it would be unfair to not show the differences for away games within a population.

The higher proportion showing the whole season, thereafter would show population as things change too fast in seasonal events.

Answer: 4t - 3 < 12

Step-by-step explanation:

Answer:

-15

Step-by-step explanation:

We proceed as follows;

In this question, we want to fill in the blank so that we can have the resulting expression expressed as the product of two different linear expressions.

Now, what to do here is that, when we factor the first two expressions, we need the same kind of expression to be present in the second bracket.

Thus, we have;

2a(b-3) + 5b + _

Now, putting -15 will give us the same expression in the first bracket and this gives us the following;

2a(b-3) + 5b-15

2a(b-3) + 5(b-3)

So we can have ; (2a+5)(b-3)

Hence the constant used is -15

Answer:

$6,291.70

Step-by-step explanation:

You're given the equation and you're given an x-value; 75,834. Just plug it in to get m = 2500 + 0.05(75,834) = 2500 + 3791.70 = 6,291.70.

Answer:

$6,291.70

Step 1:

To find the monthly salary for somebody who sells $75,834 in cars, we need to first multiply that by 0.05, or 5%, since 0.05 has to get multiplied by s (sales) in the equation they provide us. We don't do anything with $2,500 (yet).

[tex]75,834*0.05=3791.70[/tex]

One of the options for our answer shows 3,791.7, but we are not finished with solving this problem, so 3,791.7 is not our answer.

Step 2:

After completing step 1, Superb Auto already provides new salespeople with $2,500. This means that whatever they sell (or don't sell), they would still get that $2,500. In step 1, we found out that our first number that replaces 0.05s is 3791.7, so we just have to add that to 2,500 to get our final answer.

[tex]3791.7+2500=6291.7[/tex]

Our final answer is $6,291.70, and that is the third option on our list of choices.

The area of the shaded region in the regular polygon is 161.3 cm²

A regular polygon is a polygon in which all the sides are equal.

From the diagram, the regular polygon is a square which is composed of a small square and a large square. In a square, all the sides are equal.

For the small square, half of the diagonal is 4 cm, therefore the length of the diagonal is 8 cm (2 × 4 cm). Let the length of the side be a cm, using Pythagoras theorem:

a² + a² = 8²

2a² = 64

a² = 32

a = √32 = 5.7 cm

The area of the small square = length × length = 5.7 × 5.7 = 32.5 cm²

For the large square, half of the diagonal is 9 cm, therefore the length of the diagonal is 18 cm (2 × 9 cm). Let the length of the side be b cm, using Pythagoras theorem:

b² + b² = 18²

2b² = 324

b² = 162

b = √162 = 12.7 cm

The area of the large square = length × length = 12.7 × 12.7 = 161.3 cm²

The area of the shaded region = Area of large square - Area of small square = 161.3 cm² - 32.5 cm² = 128.8 cm²

The area of the shaded region in the regular polygon is 161.3 cm²

Find out more on regular polygon at: https://brainly.com/question/1592456

Answer:

it’s actually 130 or 130.0

Step-by-step explanation:

Answer:

[tex]W= 4700+0.02S[/tex]

Step-by-step explanation:

Given that

W is the monthly wage

S is the monthly sales

According to the problem statement, salesperson receives a monthly salary of $4700 (sales or no sales made he/she gets that amount)

Also plus 2%  commission of sales made for the month added to the wage

we can model his/her wage as follows

[tex]W= 4700+ (2/100)S\\\\ W= 4700+0.02S[/tex]

Hence the model for the monthly wage is [tex]W= 4700+0.02S[/tex]

Answer:

the answer

Step-by-step explanation:

D) 0.13 (325)

HOPE THIS HELPS!

do you need the workout?

Answer:

y = 1.48 or y = - 0.193 to 3 s f.

Step-by-step explanation:

By comparing the 2 equations term by term we see that x = 1/y

So 1/y =  0.676

giving y = 1 / 0.676

= 1.48 to 3 s f.

an

1/y = -5.18

y = - 0.193 to 3 s f.

Answer:

The answer is 17.

Step-by-step explanation:

200/3 is approximately 67, and divided by 4 again to represent the second checkpoint will become 16.75. Obviously there can't be a fraction of a bag, so the answer is 17.

Answer:

16

Step-by-step explanation:

the lcm for 3 and 4 is 12

200 ÷ 12 = 16.667

≈16

Answer:

320 square inches

Step-by-step explanation:

4 * 1/2(8)(16) + 8*8 = 320

Answer:

320 sq. in.

Step-by-step explanation:

The formula for finding the area of a triangle is:

[tex]\frac{hb}{2}[/tex] (basically multiplying the height and the base and then dividing by 2)

Since there are 4 triangles, we can multiply the area of 1 triangle by 4 (64 times 4 is 256).

Then, on the bottom we have a (8 times 8) square (64).

Triangles: 256

Square: 64

256 + 64 = 320 sq. in!

Hope that helps and maybe earns a brainliest!

Have a great day!

Answer:

$153

Step-by-step explanation:

Divide by 100-sale%

102/.66666=

$153

Check: 153x.666666=102 YES

Answer:

the original price is 153

Step-by-step explanation:

leather jacket is 102 sale price

the sale is 1/3 of original price

the original price=1/2 its price=sale price

x-1/3x=102

2/3 x=102

2x=306

x=306/2

x=153 dollars