Paul, Colin and Brian are waiters.
One night the restaurant earns tips totalling £77.40.
They share the tips in the ratio 1:3:5.
How much more does Brian get over Paul?

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( 5^{\frac{3}{2}} \right)^{-\frac{2}{3}}\implies 5^{-\frac{3}{2}\cdot \frac{2}{3}}\implies 5^{-1}\implies \cfrac{1}{5}\implies 0.2 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf (256^{0.5})^{1.25}\implies [(2^8)^{0.5}]^{1.25}\implies [2^{8\cdot 0.5}]^{1.25}\implies [2^4]^{1.25}\implies 2^{4\cdot 1.25} \\\\\\ 2^5\implies 32 \\\\[-0.35em] ~\dotfill\\\\ ( 81^{-\frac{1}{6}} )^{\frac{3}{2}}\implies [(3^4)^{-\frac{1}{6}} ]^{\frac{3}{2}}\implies 3^{4\cdot -\frac{1}{6}\cdot \frac{3}{2}}\implies 3^{-\frac{12}{12}}\implies 3^{-1} \\\\\\ \cfrac{1}{3}\implies 0.33...[/tex]

Step-by-step Answer:

Given points: P1(-3,2), P2(6,2)

Slope given two points = (y2-y1)/(x2-x1)

= (2-2)/(6-(-3))

=0/9

= 0

Answer:

Slope = 0

Step-by-step explanation:

We are given the following points and we are to find the slope of the line which passes through these points:

[tex] ( – 3 , 2 ) [/tex] and [tex] ( 6 , 2 ) [/tex]

We know that the formula of the slope is given by:

Slope = [tex] \frac { y _ 2 - y _ 1 } { x _ 2 - x _ 1 } [/tex]

Slope = [tex] \frac { 2 - 2 } { 6 - (- 3 )} = \frac { 0 } { 9 } [/tex] = 0

Answer:

The Choice N#1 will give more pizza for your money

Step-by-step explanation:

step 1

Find the area of one slice Choice #1

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=22/2=11\ in[/tex] ----> the radius is half the diameter

assume

[tex]\pi =3.14[/tex]

The area of one slice is equal to

[tex]A=(1/8)\pi r^{2}[/tex]

substitute

[tex]A=(1/8)(3.14)(11)^{2}[/tex]

[tex]A=47.4925\ in^{2}[/tex]

Divide the cost by the area

[tex]4.95/47.4925=0.10\frac{\$}{in^{2}}[/tex]

step 2

Find the area of the entire personal pizza Choice # 2

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=6/2=3\ in[/tex] ----> the radius is half the diameter

assume

[tex]\pi =3.14[/tex]

substitute

[tex]A=(3.14)(3)^{2}[/tex]

[tex]A=28.26\ in^{2}[/tex]

Divide the cost by the area

[tex]3.75/28.26=0.13\frac{\$}{in^{2}}[/tex]

therefore

The Choice N#1 will give more pizza for your money

Answer:

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

Step-by-step explanation:

Here we are supposed to find the distance between the two coordinates in a plane. The coordinates given to us are

(5,1) and (9,-6)

We can find the distance using distance formula. The distance formula is given as

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

Where

[tex](x_{2},y_{2}) ; (x_{1},y_{1})[/tex]

are the two coordinates

Hence

[tex]x_{2} = 9 ; y_{2}= -6\\x_{1}=5; y_{1}=1[/tex]

Substituting these values in the distance formula we get

[tex]D=\sqrt{(9-5)^{2} +(-6-1)^{2}}\\D=\sqrt{(4)^{2} +(-7)^{2}}\\D=\sqrt{16+49}\\D=\sqrt{65}\\[/tex]

Hence the Distance is  [tex]D=\sqrt{65}\\[/tex]

Answer:

Excess cash on hand may be a problem for a problem for a company because it may miss an opportunity to:  B) Invest

Answer:

1. 34.4°

2. 18.8°

3. 37.7°

4. 36.6°

5. 40.6°

6. 7.5

7. 12.3

8. 14.7

9. 22.0

10. 6.3

Step-by-step explanation:

1. The missing angle is found by the use of the sine.

Sine ∅= opposite/ hypotenuse

=13/23

sin⁻¹(13/23)=34.4°

2. The missing angle is calculated by the use of the tan.

Tan∅=opposite/adjacent

=17/50

Tan⁻¹(17/50)=18.8°

3. The missing angle is calculated by the use of the tan.

Tan∅=opposite/adjacent

=17/22

Tan⁻¹ (17/22) = 37.7°

4. The missing angle is calculated by the use of the tan.

Tan∅=opposite/adjacent

=21/28

Tan⁻¹ (21/28)=36.9°

5. The missing angle is calculated by the use of the tan.

Tan∅=opposite/adjacent

=24/28

Tan⁻¹ (24/28) = 40.6°

6. Missing side is calculated by considering the tan of 58°

Tan 58°=12/x

x=12/Tan 58°

=7.5

7.  Missing side is calculated by considering the sine of 43°

Sin 43°= opposite / hypotenuse

Sin 43 =x/18

x= 18 Sin 43

=12.3

8.  Missing side is calculated by considering the sine of 62°

Sin 62° = 13/x

x=13/Sin 62°

=14.7

9.  Missing side is calculated by considering the tan of 36°

Tan 36°= 16/x

x=16/Tan 36°

=22.0

10. Missing side is calculated by considering the sine of 23°

Sin 23° = x/16

x=16 Sin 23

=6.3

Answer:

A. 19,958,400

Step-by-step explanation:

Answer:

Basically it means to do Keep, Change, Flip. that's a better way to remember "reciprocal". keep the 5, change the ÷ to a × and flip the fraction 2/9 to a 9/2.

After doing that, you'll get the the first answer. 5/1 × 9/2 = 45/2

Answer: First option.

Step-by-step explanation:

When you divide fractions you can multiply the first fraction by the reciprocal of the second fraction.

To find the reciprocal of the fraction, you need to flip it. Then the original denominator will be the new numerator and the original numerator will be the new denominator.

Then, the reciprocal of the fraction [tex]\frac{2}{9}[/tex] is:

 [tex]\frac{9}{2}[/tex]

Therefore, you can find the quotient of [tex]3[/tex]÷[tex]\frac{2}{9}[/tex]  by multiplying [tex]\frac{5}{1}[/tex] by [tex]\frac{9}{2}[/tex]:

[tex]5[/tex]÷[tex]\frac{2}{9}=\frac{5}{1}*\frac{9}{2}=\frac{45}{2}[/tex]

s = number of students books

we know there are many student's books, so since there are "s", and each one weights 2.3 kgs, then all together must weight 2.3s, now the teacher's edition is just 1 alone so that's just 4.3 kgs.

[tex]\bf \stackrel{\stackrel{total}{weight}}{30}~~=~~\stackrel{students'}{2.3s}+\stackrel{teacher's}{4.3}+\stackrel{box's}{0.4}\implies 30=2.3s+4.7 \\\\\\ 30-4.7=2.3s\implies 25.3=2.3\implies \cfrac{25.3}{2.3}=s\implies 11=s[/tex]

Answer:

try 12 Newton seconds

Step-by-step explanation:

I think it's going to be 12 because if you find the slope of the first line you get 1 Newton and the slope of the second line is -1 Newton's. so that means there is a change of -2 newtons. so if you multiply -2 Newton's by the 6 seconds you -12 Newton seconds. let me know if this is correct as it's been a while since I've done this type of stuff.

Answer:

The value of impulse is 9 N-s.

Step-by-step explanation:

The momentum vs time graph shows the impulse

Impulse :

Impulse is the product of force and time.

In mathematical terms,

[tex]I= F\Delta t[/tex]

Where, F = force

t = time

According to graph,

Impulse[tex]I = F\cdot t[/tex]=total area

[tex]I=\dfrac{1}{2}\times3\times6[/tex]

[tex]I=9\ N-s[/tex]

Hence, The value of impulse is 9 N-s.

Answer:

see below

Step-by-step explanation:

3 > w/2

Multiply each side by 2

2*3 > w/2 *2

6 > w

w < 6

There is an open circle at 6 since there is no equal sign

The line goes to the left since w is less then 6

Each ticket cost $3

8+5x=23

5x=15

x=3

Answer: 26 dollars

Step-by-step explanation:

8-5=3

23+3=26

Answer:

[tex]\sqrt{\frac{3}{64} }[/tex] in simplified form is [tex]\frac{\sqrt{3}}{8}[/tex]

Step-by-step explanation:

We need to solve the expression

[tex]\sqrt{\frac{3}{64} }[/tex]

We know that [tex]\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}[/tex]

and 64 = 8*8

Solving we get

[tex]=\frac{\sqrt{3}}{\sqrt{64}}\\=\frac{\sqrt{3}}{\sqrt{8*8}}\\=\frac{\sqrt{3}}{\sqrt{8^2}}\\=\frac{\sqrt{3}}{8}[/tex]

So [tex]\sqrt{\frac{3}{64} }[/tex] in simplified form is [tex]\frac{\sqrt{3}}{8}[/tex]

To simplify the given radical expression √3/64, first express the fraction as a power of a fraction. Apply the power rule of radicals and simplify the expression.

To simplify the given radical expression √3/64, we first express the fraction under the radical sign as a power of a fraction. 3/64 can be written as 3/(26). Next, we can apply the power rule of radicals, which states that √(a/b) = √a/√b. Applying this rule, we can rewrite the radical expression as √3/(26). Finally, we can simplify the expression by evaluating the square root of 3 and 26. The simplified expression is √3/23 or 3/(23).

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Answer:

The first choice, 8.64 sq. ft.

Step-by-step explanation:

Formula for area of triangle:

(Length x Height) / 2

4.8 * 3.6 = 17.28

17.28 / 2 = 8.64

A = 8.64 sq. ft. so, the first choice

Answer:

8.42ft square

Step-by-step explanation:

Base × height/2

base=4.8ft

height =3.6ft

4.8 × 3.6= 17.28

17.28/2=8.64ft

Answer:

A

Step-by-step explanation:

Recall the general equation for a straight line is

y = mx + b

where m is the gradient and b is the y-intercept

given 2 points whose coordinates are (x1, y1) and (x2, y2), m can be found with the following formula:

m = [tex]\frac{y1-y2}{x1-x2}[/tex]

in this case, x1 = -8, y1 = 11, x2 = 4, y2=7/2

applying these values to the formula for m will give

m = -(5/8)

We can see immediately that the only 2 possible answers are A or B.

If we substitute this back into the general equation, we get:

y = -(5/8)x + b

In order to find the value for b, we substitute any one of the 2 given points back into this equation. Lets choose (-8,11)

11 = -(5/8) (-8) + b

11 = -(5/8) (-8) + b

11 = 5 + b

b = 6

hence A is the answer.

Answer:

-2x^2-8x+12 if you meant the second function to be g(x)=5x^2+6x-8

If you didn't mean that please let me know in the comments so I can change my answer

Step-by-step explanation:

f-g=

 3x^2-2x+4

-(5x^2+6x-8)

--------------------

-2x^2-8x+12

Answer:

C. 120°

Step-by-step explanation:

m∠d = 150°

m∠ a = 90°

The sum of angles at a point add up to 360°

m∠b + m∠c +m∠e = 360° - (90° + 150°) = 120°

Answer:

c 120

Step-by-step explanation:

m∠d = 150°

m∠ a = 90°

The sum of angles at a point add up to 360°

m∠b + m∠c +m∠e = 360° - (90° + 150°) = 120°

Answer:

186 minutes.

Step-by-step explanation:

33.63 to start.

take away the service fee of 18.75

14.88

divide 14.88 by 0.08

186

Answer:

Step-by-step explanation:

$33.63-$18.75= $14.88

$14.88/.08=186

You used 186 minutes last month,

Answer:

31 over 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Without parentheses, you have 11 - 2 (which is 9) plus 8 (totalling 17).

Then you have 17/6.

That's "divided."

Answer:

Step-by-step explanation:

radius=4 as it is tangent to x-axis.

y co-ordinate of center is 4 so radius=4

eq. of circle is (x-2)²+(y-4)²=4²

or x²-4x+4+y²-8y+16=16

or x²+y²-4x-8y+4=0

Final answer:

The standard equation of a circle tangent to the x-axis with center (2,4) is (x - 2)² + (y - 4)² = 16.

Explanation:

To write the standard equation of a circle that is tangent to the x-axis with the center located at (2,4), we must recognize that the distance from the center of the circle to the x-axis is equal to the radius of the circle. Since the center is at (2,4), the distance to the x-axis (which is y=0) is 4 units; thus, the radius of the circle is 4.

The standard form of the equation of a circle with center (h,k) and radius r is (x - h)² + (y - k)² = r². Substituting the given center (2,4) and the radius 4 into this formula, we get:

(x - 2)² + (y - 4)² = 4²

Simplifying the radius squared term, we obtain the final equation:

(x - 2)² + (y - 4)² = 16

Answer:

It is -24/11

Step-by-step explanation:

This is a system of equations. Using substitution should give the answer.

Taking the first equation, q = 3p - 6. Plug this into the second equation.

2p + 3(3p - 6) = 4. Distributing gives 2p+ 9p - 18 = 4. Subtract 4 from both sides to give: 11p - 14 = 0. p = 14/11

Plug this back into the first equation.

42/11 - q = 6

q = 42/11 - 6, which equals -24/11

Hope this helps!

Answer:

Correct Answer: Option A

Explanation

3p - q = 6 ........ 1

2p + 3q = 4 ....... 2

Multiply eqn 1 by 3

9p - 3q = 18 ........ 3

2p - 3q = 4 ......... 2

Add eqn3 and eqn2

11p = 22 => p = 22/11 = 2

Substitute for p =2 in eqn1

3p - q = 6

3x2 - q = 6 => 6 - q = 6 => -q = 6 - 6  

q = 0

Step-by-step explanation:

F irst

O uters

I nners

L ast

We first need to expand the equation By finding what adds up to 16 and multiples to 48

X^2 + 16x + 48 = x^2 + 12x + 4x + 48.

According to the foil method

(a + b)(c + d) = ac + ad + bc + bd

ac = x^2

ad = 12x

bc = 4x

bd = 48.

Answer:

(-1)(-1)(-1)

(-1)(-1)(-1)(-1)(-1)

These, since they are all negatives and there are an odd number of terms.

Step-by-step explanation:

Answer:

A and D

Step-by-step explanation:

Answer:

Step-by-step explanation:

The point-slope form of an equationo f a line:

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

m - slope

We have

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

Therefore we have

the slope: m = -2

the point: (5, -2) not (-5, 2)!!!

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

Convert:

[tex]y+2=-2(x-5)[/tex]           use the distributive property a(b + c) = ab + ac

[tex]y+2=-2x+10[/tex]         subtract 2 from both sides

[tex]y=-2x+8[/tex]

Answer:

1.8 x [tex]10^{13}[/tex]

Step-by-step explanation:

( 9 x 10²) (2 x [tex]10^{10}[/tex] )

= (9)(2) x  [tex]10^{10+2}[/tex]

=18 x [tex]10^{12}[/tex]

= 1.8 x [tex]10^{13}[/tex]

Answer:

(9x10^2)(2x10^10)

= 1.9 x 10^13 (In scientific notation)

Step-by-step explanation:

Expression to be simplified is given as:

(9x10^2)(2x10^10)

= 9x10^2x2x10^10

= 9x2x10^2x10^10

The base here in the expression is same so the power will add up:

= 18 x 10^(2+10)

= 1.8 x 10^12

Using Scientific notation on the expression, we know that the decimal point must after the first digit so that the number let us say x is such that x > 0 and x < 10. To move decimal one place back, we will multiply it with 10^1:

18 x 10^12

= 1.8 x 10 x 10^12

= 1.8 x 10^(1+12)

= 1.8 x 10^13

The characteristics a rhombus and a rectangle always have in common is opposite sides with equal length.

The right option is B. opposite sides with equal length

From the question,

We are to determine which of the given characteristics do a rhombus and a rectangle always have in common.

To determine which of the characteristics, we will list some of the characteristics of the two shapes

Characteristics of a Rhombus

Characteristics of a Rectangle

Now, from above,

We have that all the sides of rhombus are equal in length, which makes the opposite sides to be equal as well.

Also, among the characteristics of a rectangle is that, opposite sides are equal in length

Hence, the characteristics a rhombus and a rectangle always have in common is opposite sides with equal length. The right option is B. opposite sides with equal length

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The option B is correct. A rhombus and a rectangle always have opposite sides with equal length in common. This is a defining property of all parallelograms.

In geometry, both a rhombus and a rectangle are types of parallelograms. To determine what characteristics they have in common, we must identify their properties. A rhombus has all sides of equal length, but its angles are not necessarily right angles. In contrast, a rectangle has all angles as right angles, but its sides are not necessarily of equal length. Therefore, the characteristic that both a rhombus and a rectangle always have in common is:

This means that in both a rhombus and a rectangle, the opposite sides are parallel and equal in length, which is a defining property of all parallelograms.

Answer:

[tex]15a^2b^2-20a^2b+6ab^2-4ab+7[/tex]

Step-by-step explanation:

The sum of two polynomials is

[tex]10a^2b^2-8a^2b+6ab^2-4ab+2[/tex]

First addend is

[tex]-5a^2b^2+12a^2b-5[/tex]

Second addend x.

Hence,

[tex]x+(-5a^2b^2+12a^2b-5)=10a^2b^2-8a^2b+6ab^2-4ab+2\\ \\x=10a^2b^2-8a^2b+6ab^2-4ab+2-(-5a^2b^2+12a^2b-5)=\\ \\=10a^2b^2-8a^2b+6ab^2-4ab+2+5a^2b^2-12a^2b+5=\\ \\=(10a^2b^2+5a^2b^2)+(-8a^2b-12a^2b)+6ab^2-4ab+(2+5)=\\ \\=15a^2b^2-20a^2b+6ab^2-4ab+7[/tex]

Answer:  The correct option is (A) [tex]15a^2b^2-20a^2b+6ab^2-4ab+7.[/tex]

Step-by-step explanation:  Given that the sum of two polynomials is [tex](10a^2b^2-8a^2b+6ab^2-4ab+2)[/tex] and one addend is [tex](-5a^2b^2+12a^2b-5).[/tex]

We are to find the other addend.

Let P(x) be the other addend.

Then, according to the given information, we must have

[tex]-5a^2b^2+12a^2b-5+P(x)=10a^2b^2-8a^2b+6ab^2-4ab+2\\\\\Rightarrow P(x)=(10a^2b^2-8a^2b+6ab^2-4ab+2)-(-5a^2b^2+12a^2b-5)\\\\\Rightarrow P(x)=10a^2b^2-8a^2b+6ab^2-4ab+2+5a^2b^2-12a^2b+5\\\\\Rightarrow P(x)=15a^2b^2-20a^2b+6ab^2-4ab+7.[/tex]

Thus, the other addend is [tex]15a^2b^2-20a^2b+6ab^2-4ab+7.[/tex]

Option (A) is CORRECT.

Answer:

never occur at the same time

Step-by-step explanation:

In Statistics, two events that are mutually exclusive never occur at the same time. For instance, in tossing a coin we can either land heads or tails but not both. The two events are said to be mutually exclusive.