a bonus of 4200 is shared by 10 people who works for a company.40% of the bonus is shared equally between 3 managers the rest of the bonus is shared equally between 7 sales people.Peter, one of the sales people says," if the bonus is shared equally between 10 people i will get 25% more money. Janet a manager, says," no you wont get that much extra. show that Janet is correct by working out how much peter thinks he would get and how much he would actually get.

Answer: CPCTC

Step-by-step explanation:

because in the step before that it was proved that the triangles were congruent and CPCTC is used after they are proved congruent.

By CPCT [Corresponding Part of congruent Triangle]

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hope i helped

-lvr

Answer:

1024 pi

Step-by-step explanation:

r = 32 units.

Area = pi * r^2

Area = 3.14 * 32^2

Area = 1024 * pi

Tt = pi??

For this question, the time given confuses me.  I know the rate of return is just total return divided by divided by investment, Assuming that Matt received the $400 in dividends as cash payouts, and they weren't reinvested into buying shares of the stock, then his total return over two years was $500, Now, if Matt's dividends were reinvested into the stock - and if you have a 401(k) or IRA, that's what usually happens - then his ROI would have been only 6% because he only made a profit of $100 on an investment of $1500. Note:  In the real world, in current market conditions, Matt probably would have got about a 5% return on a good stock, and Bella would have received about 0.05% on a savings account.

hope this helped you ;)

Matt probably would have got about a 5% return on a good stock.

The rate of return is just the total return divided by investment.

Consider that Matt received the $400 in dividends as cash payouts, and they weren't reinvested into buying shares of the stock, then his total return over two years was $500.

Now, if Matt's dividends were reinvested into the stock then his ROI would have been only 6% because he only made a profit of $100 on an investment of $1500.

In the real, current market conditions, Matt probably would have got about a 5% return on a good stock, and Bella would have received about 0.05% on a savings account.

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Answer:

Option D is correct.

The equation with roots 3 plus or minus square root 2 is x² - 6x + 7

Step-by-step explanation:

The roots of the unknown equation are

3 ± √2, that is, (3 + √2) and (3 - √2)

The equation can then be reconstructed by writing these roots as the solutions of the quadratic equation

x = (3 + √2) or x = (3 - √2)

The equation is this

[x - (3 + √2)] × [x - (3 - √2)]

(x - 3 - √2) × (x - 3 + √2)

x(x - 3 + √2) - 3(x - 3 + √2) - √2(x - 3 + √2)

= x² - 3x + x√2 - 3x + 9 - 3√2 - x√2 + 3√2 - 2

Collecting like terms

= x² - 3x - 3x + x√2 - x√2 - 3√2 + 3√2 + 9 - 2

= x² - 6x + 7

Hope this Helps!!!

Answer:

-7 and -4

Step-by-step explanation:

The graph of the function f(x) = (x + 4)⁶ (x + 7)⁵ cross the X axis at x = -4 and x = -7.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given is a function,

f(x) = (x + 4)⁶ (x + 7)⁵

When the function cross the X axis, the value of the function will be 0.

Let f(x) = 0

(x + 4)⁶ (x + 7)⁵ = 0

This implies that, either x + 4 = 0 or x + 7 = 0

x + 4 = 0 ⇒ x = -4

x + 7 = 0 ⇒ x = -7

Hence the roots are -4 and -7 where the function crosses the X axis.

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Answer:

If it is on the maximum, then the y-value of the point cannot be any higher and  still be on the graph of the function. If it is on the minimum, the the y-value of the point cannot be any lower and still be on the graph of the function. If it isn't either the maximum or the minimum, it is neither.

Answer:

22.467

Step-by-step explanation:

Hello,

You just have to do the computation in XL or using a calculator, and round each number to the nearest hundred

x sqrt(x)

1 1

2 1.414

3 1.732

4 2

5 2.236

6 2.449

7 2.646

8 2.828

9 3

10 3.162

and do the sum which is 22.467

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

300

Step-by-step explanation:

First let's square all the integers from 1 to 10 inclusive. We get:

1^2 = 1

2^2 = 4

3^2 = 9

4^2 = 16

5^2 = 25

6^2 = 36

7^2 = 49

8^2 = 64

9^2 = 81

10^2 = 100.

Rounding to the nearest hundred, we get that 1, 4, 9, 16, 36, and 49 all round to 0 and 64, 81, and 100 round to 100.

Therefore, we obtain 

0+0+0+0+0+0+0+100+100+100,

or 300.

Answer:

Solution,

[tex] \frac{5}{8} = \frac{12}{g} \\ or \: 5 \times g = 12 \times 8 \: ( \: cross \: multiplication) \\ or \: 5g = 96 \\ or \: g = \frac{96}{5} \\ g = 19.2[/tex]

Hope this helps..

Good luck on your assignment...

Answer:

Step-by-step explanation:

5/8=12/g

*8      *8

5=12*8/g

*g    *g

5g=12*8=96

:5              :5

g=96/5

g=19.2

Answer:

A

Step-by-step explanation:

Descending order is where the monomials of a polynomial are arranged in decreasing exponent order so the answer is A.

Answer:

the answer is option a because all the expression in option a is written descending power form.

Answer:

5/18

Step-by-step explanation:

Let's say the original packaging was 1 lb of packaging for $1.

The cost was $1/lb.

Then the weight went down by 10% and the price went up by 15%.

Now 0.9 lb of packaging cost $1.15.

The new unit cost is $1.15/(0.9 lb)

The difference is

$1.15/(0.9 lb) - $1/lb =

= $1.15/(0.9 lb) - $0.9/(0.9 lb)

= $0.25/(0.9 lb)

=$25/(90 lb) = $5/(18 lb)

The price went up by 5/18.

Answer:

A,C,and D are parralelograms

The parallelogram are shapes with figures having opposite sides which are parallel

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The sum of angles of a parallelogram is 360°

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as ABCD

Now , from the figure 1

a)

The figure is having opposite sides are parallel

where AB = CD

And , BC = AD

So , it is a parallelogram

b)

The figure does not have any sides parallel

So , it is not a parallelogram

c)

The shape is having 2 sides as parallel

And , AB = CD

So , it is a parallelogram

d)

The shape is having 2 sides as parallel

And , AB = CD

So , it is a parallelogram

Hence , the parallelogram is solved

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Answer:

4 lb

Step-by-step explanation:

Answer:

144 cm^2

Step-by-step explanation:

8x6+4x10+4x8+4x6

48+40+32+24

80+40+24

120+24

144

Answer:

Around 10/3 or 3.33 times farther.

Step-by-step explanation:

We simply divide the larger distance by the smaller distance to find our ratio:

2(10⁸)/6(10⁷)

10/3

*Remember when you divide exponents, you subtract them

Answer:

2 cm

10 cm

Step-by-step explanation:

14/7 = 2

This helps to find because area of rectangle = bh or base times height.

A = 1/2 bh

30 = 1/2 b 6

30 = 3b

b = 10

Answer:

b = 2 cm

b = 10 cm

Step-by-step explanation:

Area of a Rectangle: A = lw

Area of a Triangle: A = 1/2bh

We are given area and length, so simply plug it in:

14 = 7w

w = 2 cm

We are given area and height, so simply plug it in:

30 = 1/2(6)(b)

30 = 3b

b = 10 cm

Answer:

Step-by-step explanation:-

-

-8239910.76

Answer:

115/5 23 so 20% =23 23x4 =92

Answer:

507x223 is greater than 530 x 200

914x385 is less than 900 x 400

Answer:

Maximum =  756

Minimum =  600

Step-by-step explanation:

A square is a shape that has the large areas of a defined perimeter out of available rectangles. It implies they want the two parentheses to be as similar in value. as a result, to establish the maximum value of P.

And to establish the minimum value, to have the greatest difference for them. 1 + 2 + 3 ... +10=55, which wasn't even but which can be split as similarly as possible into 27 and 28 which have a product of 756. In this question it can be done in a variety of ways, one of which is:

(1 + 3 + 5 + 8 + 10) ×  (2 + 4 + 6 + 7 + 9) = 756

At the very least, the biggest difference can be created if one term is made of the smallest numbers, while the other full of the highest, or:

(1 + 2 + 3 + 4 + 5) × (6 + 7 + 8 + 9 + 10)=600

Answer:

1) [tex]7 \frac{11}{16} [/tex]

2) [tex] \frac{7}{15} [/tex]

Step-by-step explanation:

1) Let's convert the mixed fraction into a improper fraction.

[tex]5\frac{1}{8} \\ = \frac{5(8) + 1}{8} \\ = \frac{41}{8} [/tex]

Let the number be x.

[tex] \frac{2}{3} x = \frac{41}{8} \\ x = \frac{41}{8} \div \frac{2}{3} \\ x = \frac{41}{8} \times \frac{3}{2} \\ x = \frac{123}{6} \\ x = 7 \frac{11}{16} [/tex]

2)[tex]4 \frac{3}{8} = \frac{35}{8} [/tex]

[tex]9 \frac{3}{8} = \frac{75}{8} [/tex]

[tex]4 \frac{3}{8} \div 9 \frac{3}{8} \\ = \frac{35}{8} \div \frac{75}{8} \\ = \frac{35}{8} \times \frac{8}{75} \\ = \frac{7}{15} [/tex]

Step-by-step explanation:

a, 3

b,

draw lines through the corresponding corners of each shape  These lines will cross at the centre of enlargement O

Answer:

2.5

Step-by-step explanation:

1/2x5=?

5/2=?

2.5=?

Answer:

[tex]\boxed{2.5}[/tex]

Step-by-step explanation:

=> [tex]\frac{1}{2} of 5[/tex]

The word "of" means "to multiply"

=> [tex]\frac{1}{2} * 5[/tex]

=> [tex]\frac{1*5}{2}[/tex]

=> [tex]\frac{5}{2}[/tex]

=> 2.5

Answer:

√3 + 1

Step-by-step explanation:

Step below are self-explanatory

Answer:

16.59

Step-by-step explanation:

Given:

[tex](ax+b)(bx+a)=26x^2+\Box\cdot x+26[/tex]

Expanding the left hand side, we have:

[tex](ax+b)(bx+a)=abx^2+a^2x+b^2x+ab\\=abx^2+(a^2+b^2)x+ab\\=26x^2+\Box\cdot x+26\\ab=26 \implies b=\frac{26}{a}[/tex]

Therefore:

[tex]a^2+b^2=a^2+\dfrac{26}{a} =\dfrac{a^3+26}{a}[/tex]

To find the minimum value, we take the derivative and solve for its critical point.

[tex]\frac{d}{da} (\frac{a^3+26}{a})=\frac{2a^3-26}{a^2}\\$Setting the derivative equal to zero, we have:\\2a^3-26=0\\2a^3=26\\a^3=13\\a=\sqrt[3]{13}[/tex]

Recall that:

[tex]\Box=a^2+b^2=\dfrac{(\sqrt[3]{13}) ^3+26}{\sqrt[3]{13}}\\=\dfrac{13+26}{\sqrt[3]{13}}\\\\\Box=16.59[/tex]

The minimum possible value of the coefficient of x is 16.59.

Answer:

173

Step-by-step explanation:

For sympliciy let the box equal y.

Expanding the left side we get (a*x+b)(b*x+a) = (a*b*(x)^2 + (a^2 + b^2)x + a*b). Hence we have that  (a*b*(x)^2 + (a^2 + b^2)x + a*b) = 26*(x)^2 + x*y + 26. Scince the coefficients of like terms in our equation must be equal, ab=26. Hence (a,b) = (1,26),(26,1),(-1,-26),(-26,-1),(2,13),(13,2),(-2,-13),(-13,-2). Since a^2 + b^2 = y we can see that the only 2 values of y are 677 and 173 (by simply plug in the values of (a,b)), taking the smaller of the two our answer is [173].

Answer: 28

Step-by-step explanation:

The shape is grouped into 4 identical parallelograms.  

Thus, as the combined area of the figure is 308, you can divide 308/4 to get 77.  Thus, each parallelogram has an area of 77.

Then, divide 14/2 to get that the height of each parallelogram is 7.  

The area of a parallelogram is l*w.  Thus, because l = 7, each parallelogram has a width of 11 because 77/7 = 11.  

Then, simply add 11+11+6 to get y.

Hope this helps <3

Answer: B. rectangular pyramid

Answer:

Option (1). 17

Step-by-step explanation:

Length of a segment having coordinates (x₁, y₁) and (x₂, y₂) is given by the formula,

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

Coordinates of points A and C are (4, 3) and (19, 11).

To get the length of segment AC we will substitute the coordinates in the formula,

AC = [tex]\sqrt{(19-4)^2+(11-3)^2}[/tex]

     = [tex]\sqrt{(15)^2+8^2}[/tex]

     = [tex]\sqrt{225+64}[/tex]

     = [tex]\sqrt{289}[/tex]

     = 17

Therefore, length of segment AC = 17 units.

Option (1) will be the answer.

Answer:

x = 4

x = -10

Step-by-step explanation:

(x + 3)² = 49

Take the square root of both sides.

x + 3 = ±7

The equation is x + 3 = 7 or x + 3 = -7.

x + 3 = 7

Subtract 3 on both sides.

x = 4

x + 3 = -7

Subtract 3 on both sides.

x = -10

Answer:

x₁ = -10

x₂ = 4

Step-by-step explanation:

(x + 3)² = 49

x + 3 = ± 7

x + 3 = -7 → x = -10

x + 3 = 7 → x = 4

Hope this helps! :)