Gordon won the lottery and distributed the prize among his children. Peter received
22% of the prize, Amy received 23% and John and Mary split the rest remaining in
equal parts. If Mary received $14,000, what was the lottery prize worth? Solve the
problem by first formulating an equation(s)/inequality.

Answer:

803000000 is the right answer

Answer:

Step-by-step explanation:

JuJust give it to me please please I need

the derivative of |x| with respect to x is x/|x|.

x/|x|

Answer:

8*5=40

160/40=4

to recheck

V= LxWxH

V=8*5*4

V=160

Step-by-step explanation:

GOOD LUCK

Answer:

9-foot piece is better deal by $0.03 per foot

Step-by-step explanation:

2.80/8 = $0.35 per foot (for 8-foot piece)

2.88/9 = $0.32 per foot (for 9-foot piece)

Answer:

9 foot peice of cord

Step-by-step explanation:

Answer:

Rachael scored 42 points.

Step-by-step explanation:

In order to solve this, we must first find triple Trina's score, so we multiply 16 * 3 which simplifies to 48. Since the question asks for 6 points less than this score, we find subtract 48 - 6 which simplifies to 42.

Answer:

v = 234 / w

Step-by-step explanation:

v varies inversely with w

v = k/w

Find the constnt of variation

v = 18 when w = 13

18 = k/13

k = 18 * 13

k = 234

find the equation that relates v and w

v = 234 / w

Answer:

a+b=5/2a, a+b=5/3b

Step-by-step explanation:

1.2a=0.8b

6/5a=4/5b

6a=4b

b=3/2a, a=2/3b

a+b=3/2a+a

a+b=5/2a

a+b=2/3b+b=5/3b

Answer:

1) Parallel line:  y = 4x + 1

4) Perpendicular line:  y = -5x + 9

6) Perpendicular line: y = 3x + 2

Step-by-step explanation:

I will only provide solutions to question 1, 4, and 6, in accordance with Brainly's guidelines. Since the given problem essentially involves the same type of questions, the solutions that I will provide should allow you to apply the same techniques in solving for the remainder of the questions.

Parallel lines have the same slope.

Perpendicular lines have negative reciprocal slopes. This means that when you multiply the slopes of two lines that are perpendicular from each other will result in a product of - 1.

In other words, if the slope of a line is m₁, and the slope of the other line is  m₂, then it means that they are perpendicular from each other if:  m₁ × m₂ = - 1

According to the definitions provided on parallel lines, since the given linear equation has a slope, m = 4, then it means that the other line parallel to it must have the same slope.

Given the y-intercept of the other line as b = 1, and its slope, m = 4, then the equation of the line parallel to y = 4x + 3 is:

Equation of Parallel line:  y = 4x + 1.

Given the linear equation, y = ⅕x + 4, where its slope,  m₁ = ⅕

Then it means that the negative reciprocal of  ⅕ must be ⇒   [tex]\large\mathsf{-\frac{5}{1}\:\:or\:\:-5}[/tex]

Because:  m₁ × m₂ = - 1

                 ⅕ × -5 = -1

Therefore, if the y-intercept of the other line is b = 9, and its slope is m₂ = -5, then the equation of the line perpendicular to y = ⅕x + 4 is:

Perpendicular line:  y = -5x + 9.

Given the equation of the first line, y = -⅓x - 8, where its slope, m₁ = -⅓.

Then it means that the slope of the other line must be m₂ = [tex]\large\mathsf{\frac{3}{1}\:\:or\:\:3}[/tex]  because:                

       m₁ × m₂ = - 1

       -⅓ ×  3 =  -1

Next, substitute the slope of the other line, m₂ = 3, and the values of the given point, (2, 8) into the slope-intercept form, y = mx + b, in order to solve for the y-intercept of the other line.

y = mx + b

8 = 3(2) + b

8 = 6 + b

Subtract 6 from both sides to isolate b:

8 - 6 = 6 - 6 + b

2 = b

Therefore, the equation of the line perpendicular to y = - ⅓x - 8 is:

Perpendicular line: y = 3x + 2.

Answer:

5.80

Step-by-step explanation:

it is

40.60/7=5.80

Answer:

5.8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

1 pie

Step-by-step explanation:

1/3 + 1/3 +1/3= 3/3

simplified = 1/1 or 1 whole

Answer:

1 pie

Step-by-step explanation:

1/3 +1/3 + 1/3 =3/3 = 1

If the denominator is the same you can keep it the same and just add the numerators.

Hope this helps:)

Answer:

Hiiiiiiii

The answer is 3.58/ 3 7/12

Answer:

50

Step-by-step explanation:

if the given amount (20%) is 10 then to find the whole :

multiply 10 with 100 and then divide the result with 20

10*100/20 = 50

Answer:

x≤90 and 30x+20y≥380,000

Step-by-step explanation:

1. x=original price of shoe

"at most" means inequality where the money you can spend is less than or equal to

so x-10≤80

solve for original price

x≤90

2. x=number of floor tix

y=number of bleacher seats

"at least" means bigger than or equal to

30x+20y≥380,000

Answer:

If you want to solve x it will be 11

If you want to solve y it will be y

=

x

2

44

+

12

Step-by-step explanation:

Answer:

256.5

Step-by-step explanation:

19 · 13.5 = 256.5

I hope this helps

Answer:

281.6

Step-by-step explanation:

=281.6 × 125 %

= 352

Answer:

35.51%, or, if rounded is 36%

Step-by-step explanation:

1. We assume, that the number 352 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 100% equals 352, so we can write it down as 100%=352.

4. We know, that x% equals 125 of the output value, so we can write it down as x%=125.

5. Now we have two simple equations:

1) 100%=352

2) x%=125

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=352/125

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 125 is what percent of 352

100%/x%=352/125

(100/x)*x=(352/125)*x       - we multiply both sides of the equation by x

100=2.816*x       - we divide both sides of the equation by (2.816) to get x

100/2.816=x

35.511363636364=x

x=35.511363636364

now we have:

125 is 35.511363636364% of 352

Answer:

69.6 oz

Step-by-step explanation:

So we have to calculate 45% of 48 then add it to 48 to get the the weight of the new box.

(45/100)*48 = 21.6

48+21.6=69.6

Therefore, the weight of the new box is 69.9oz

Answer:

9/4

Step-by-step explanation:

Just flip it upside down

Answer:

It's 9/4.

<3

(something)

Answer:

well you could write this as  

1) 0.5/3

2) 1/6

so yeah.

if its 1/3 to get one blue ball, for two you would divide the numerator in half so you'd get 0.5/3

Step-by-step explanation:

Answer:

its incorrect

Step-by-step explanation:

the triangles are congruent as they are the exact same but flipped, so it would be the rule of SAS

Answer:

0.3

Step-by-step explanation:

Answer:

14 sets

Step-by-step explanation:

14 x 3 = 42

14 x 5 = 70

Answer:

Step-by-step explanation:

346.62

Answer:

3.4662 times 10^2

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

Step-by-step explanation:

[tex]\large\underline{\sf{Solution-}}[/tex]

[tex]\rm \: f(x) = log(1 + x) - \dfrac{2x}{x + 2}[/tex]

~Let first define the domain of f(x).

[tex]{ \underline { \underline{ {\rule{200cm}{0.4cm}}}}}[/tex]

[tex]\sf \: f(x) = log(1 + x) - \dfrac{2x}{x + 2}[/tex]

w. r. t. x, we get

[tex]\rm {\: \longmapsto\dfrac{d}{dx}f(x) =\dfrac{d}{dx}\bigg[ log(1 + x) - \dfrac{2x}{x + 2}}[/tex]

[tex]\boxed{\sf{ \longmapsto\dfrac{d}{dx}logx \: = \: \dfrac{1}{x}}}[/tex]

[tex]\boxed{\sf{\longmapsto \dfrac{d}{dx} \dfrac{u}{v} = \dfrac{v\dfrac{d}{dx}u \: - \: u\dfrac{d}{dx}v}{ {v}^{2} } \: }}[/tex]

~So, using these results, we get

[tex]\sf {\:\longmapsto f'(x) = \dfrac{1}{x + 1} - \dfrac{(x + 2)\dfrac{d}{dx}2x - 2x\dfrac{d}{dx}(x + 2)}{ {(x + 2)}^{2} }}[/tex]

[tex]\boxed{\rm{\longmapsto \dfrac{d}{dx}x = \sf \pink{ 1 \:} }} [/tex]

And-

[tex]\begin{gathered}\boxed{\sf{\longmapsto\dfrac{d}{dx}k = 0 \: }} \\ \end{gathered}[/tex]

☼︎~So, using this result, we get

[tex]\rm \: f'(x) = \dfrac{1}{x + 1} - \dfrac{(x + 2)2 - 2x(1 + 0)}{ {(x + 2)}^{2} }f′(x)=x+11−(x+2)2(x+2)2−2x(1+0)

[tex]\rm \: f'(x) = \dfrac{1}{x + 1} - \dfrac{(x + 2)2 - 2x(1 + 0)}{ {(x + 2)}^{2} }f′(x)=x+11−(x+2)2(x+2)2−2x(1+0)\rm \: f'(x) = \dfrac{1}{x + 1} - \dfrac{2x + 4 - 2x}{ {(x + 2)}^{2} }[/tex]

[tex]\rm \: f'(x) = \dfrac{1}{x + 1} - \dfrac{4 }{ {(x + 2)}^{2} }f′(x)=x+11−(x+2)24[/tex]

[tex]\rm \: f'(x) = \dfrac{ {(x + 2)}^{2} - 4(x + 1)}{(x + 1) {(x + 2)}^{2} }[/tex]

[tex]\rm \: f'(x) = \dfrac{ {x}^{2} + 4 + 4x - 4x - 4}{(x + 1) {(x + 2)}^{2} }[/tex]

[tex]\rm \: f'(x) = \dfrac{ {x}^{2} }{(x + 1) {(x + 2)}^{2} }[/tex]

[tex]\longmapsto\rm {\: {x}^{2} \geqslant 0x2⩾0}[/tex]

[tex]\longmapsto\sf\:{(x+2)}^{2} > 0[/tex]

[tex]\longmapsto\sf\: x + 1 > 0x+1>0[/tex]

[tex]\sf\longmapsto \:\rm \: f'(x) = \dfrac{ {x}^{2} }{(x + 1) {(x + 2)}^{2} } \geqslant 0[/tex]

[tex]{ \underline { \underline{ \bold {\rule{200cm}{0.4cm}}}}}[/tex]

[tex]\boxed{\begin{array}{c|c} \bf f(x) & \tt \dfrac{d}{dx}f(x) \\ \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf k & \sf 0 \\ \\ \sf sinx & \sf cosx \\ \\ \sf cosx & \sf - \: sinx \\ \\ \sf tanx & \sf {sec}^{2}x \\ \\ \sf cotx & \sf - {cosec}^{2}x \\ \\ \sf secx & \sf secx \: tanx\\ \\ \sf cosecx & \sf - \: cosecx \: cotx\\ \\ \sf \sqrt{x} & \sf \dfrac{1}{2 \sqrt{x} } \\ \\ \sf logx & \sf \dfrac{1}{x}\\ \\ \sf {e}^{x} & \sf {e}^{x} \end{array}}[/tex]

[tex]{ \underline { \underline{ \bold {\rule{200cm}{0.3cm}}}}}[/tex]

Answer:

18 C

19 A

20 C

I am not sure about 16 and 17

Hope it helps

Answer:

Step-by-step explanation:

16) B

17) A

18) C

19) f(X ) = -2x² + 5

f(-3) =-2*(-3)² + 5 =  -2*9 + 5  = -18 + 5 = -13

Ans: A

19)f(x) = - x² - 1

f(-5) = -(-5)² - 1 = -25 - 1 = -16

Ans:  C

Answer:

D- x = 7

Step-by-step explanation: