Multiply the number by 4. Add 10 to the product. Divide this sum by 2. Subtract 5 from the quotient.

The first number is 1 and the result is 2

The second number is 5 and the result is 10

the third number is 9 and the result is 18

the fourth number is 10 and the result is 20

Write a conjecture that relates the result of the process to the original number selected. part a)

Represent the original number as n.

Answer is 2n

part b Represent the original number as n​, and use deductive reasoning to prove the conjecture in part​ (a). Multiply the number by 4.

Help with part b please.

Answer:

56.88

Step-by-step explanation:

2 ways to do this

45.50 x 25% = 11.375

45.50 + 11.375 = 56.875

and that rounds to 56.88

for option 2 I recommend a calculater

45.50 + 25% = 56.875

56.88

Answer:

The second option

Step-by-step explanation:

The rate of change needs to stay constant.

The rate of change can be explained by looking at the "rise" (y) over the "run"(x)

The rate of change for the second option is 2.  We know this because...

Rise(2)

----------

Run(1)

Try looking at one of the points, now go up 2 and over 1, you should now be at the second point, do it again but twice, you should now be at the third point. A proportional relationship must also go through the origin (0,0)

Question:

One number is 7 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 505, Find the numbers.

Answer:

The numbers are 45, 315 and 145

Step-by-step explanation:

Represent the three numbers with A, B and C

Required

Find A, B and C

From the first statement;

[tex]B = 7 * A[/tex]

[tex]B = 7A[/tex] --- (i)

From the second;

[tex]C = 100 + A[/tex]  ---- (ii)

From the third;

[tex]A + B + C = 505[/tex]  ---- (iii)

Substitute 7A for B and 100 + A for C in (iii)

[tex]A + 7A + 100 + A = 505[/tex]

Collect like terms

[tex]A + 7A + A = 505 - 100[/tex]

[tex]9A = 405[/tex]

Divide both sides by 9

[tex]A = 45[/tex]

Substitute 45 for A in (i)

[tex]B = 7A[/tex]

[tex]B = 7 * 45[/tex]

[tex]B = 315[/tex]

Substitute 45 for A in (ii)

[tex]C = 100 + A[/tex]

[tex]C = 100 + 45[/tex]

[tex]C = 145[/tex]

Hence, the numbers are 45, 315 and 145

Answer:

the answer is -10

Step-by-step explanation:

-2 × 5 = -10

Answer:

This problem actually says:

(y + 2), (y + 3) and (2*y^2 - 1) are consecutive terms of an arithmetic progression.

Now, the difference between two consecutive terms in an arithmetic progression is always the same, so we have:

(y + 3) - (y +2) = D

(2*y^2 - 1) - (y + 3) = D

From the first equation we have:

y + 3 - y - 2 = 1  = D

Now we can replace it in the other equation:

2*y^2 - 1 - y - 3 = 1

2*y^2 - y - 5 = 0

Now we need to solve that equation to find the possible values of y.

To solve a quadratic equation of the form:

a*x^2 + b*x + c = 0, we can use the Bhaskara's equation:

[tex]y = \frac{-b +- \sqrt{b^2 -4*a*c} }{2*a}[/tex]

in this case, the solutions are:

[tex]y = \frac{1 +-\sqrt[]{(-1)^2 - 4*2*(-5)} }{2*2} = \frac{1 +- \sqrt{61} }{4} = \frac{1+-6.4}{4}[/tex]

Then the possible values of y are:

y = (1 + 6.4)/4 = 1.85

y = (1 - 6.4)/5 = -1.35

Answer:

F(x)=g'(x)h(X)+g(x)h'(x)

F(x)=90x9tan-1-[9*10/(1+x2)}

The derivative of f(x) is f'(x) = 42x⁵ * cos⁻¹(x) - 7x⁶ / (√(1 - x²))

To find the derivative of the function f(x) = 7x⁶ * cos⁻¹(x), we'll use the chain rule and the power rule of differentiation.

The chain rule states that if we have a function of the form f(g(x)), then its derivative is given by f'(g(x)) * g'(x).

Let's break down the function f(x) into two parts:

u(x) = 7x⁶

v(x) = cos⁻¹(x)

Now, we'll find the derivatives of u(x) and v(x):

u'(x) = d/dx (7x⁶) = 6 * 7x⁵ = 42x⁵

To find v'(x), we differentiate cos⁻¹(x) using the inverse trigonometric differentiation formula:

d/dx [cos⁻¹(x)] = -1 / (√(1 - x²))

Now, applying the chain rule to the function f(x) = 7x⁶ * cos⁻¹(x), we get:

f'(x) = u'(x) * v(x) + u(x) * v'(x)

f'(x) = 42x⁵ * cos⁻¹(x) + 7x⁶ * (-1 / (√(1 - x²)))

So, the derivative of f(x) is:

f'(x) = 42x⁵ * cos⁻¹(x) - 7x⁶ / (√(1 - x²))

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Answer:

C) =

Step-by-step explanation:

I -56I   = I56I

Absolute value of a number I X I is always non-negative value

Value of I -2 I = 2 &  I 2I = 2

Answer:

C

Step-by-step explanation:

Since they are absolute value, they are both the same distance from zero

Answer:

0.02

Step-by-step explanation:

7⁴ / 7⁶ = 7⁴⁻⁶ = 7⁻² = 1/7² = 1/49 ≈ 0.02

Answer:

.02

Step-by-step explanation:

7^4 ÷ 7^6

We know that a^b ÷ a^c = a^ ( b-c)

7^4 ÷ 7^6  

7^(4-6)

7^(-2)

We know that a^ -b = 1/a ^b

1 / 7^2

1/49

.020408163

Rounding to 2 decimal places

.02

Answer:

a

Step-by-step explanation:

d - 24 = 212

d +24 = 212 + 24

d= 236

Answer:

3 19/20

Step-by-step explanation:

11/5+7/4=

44/20+35/20=

79/20=

3 19/20

Answer:

3. 60/37 hours

4. 35/12 hours

Step-by-step explanation:

3.

Nicole: 1 room in 6 hours; in 1 hour: 1/6 room

Alexandra: 1 room in 5 hours; in 1 hour: 1/5 room

Liana: 1 room in 4 hours; in 1 hour: 1/4 room

Combined in 1 hour:

1/6 + 1/5 + 1/4

When they work together, they paint a room in x hours.

In 1 hour: 1/x room

1/6 + 1/5 + 1/4 = 1/x

10/60 + 12/60 + 15/60 = 1/x

37/60 = 1/x

x = 60/37

Answer: 60/37 hours

4.

Jake: 1 room in 7 hours; in 1 hour: 1/7 room

Karen: 1 room in 5 hours; in 1 hour: 1/5 room

Combined in 1 hour:

1/7 + 1/5

When they work together, they paint a room in x hours.

In 1 hour: 1/x room

1/7 + 1/5 = 1/x

5/35 + 7/35 = 1/x

12/35 = 1/x

x = 35/12

35/12 hours

Answer: 35/12 hours

Answer: ST is equal to 12

Step-by-step explanation:

If RU  is equal to 24 as a whole  and we are given that RS and TU are equal to 6 then we could set up an equation and solve for ST.

6 + 6 +x  = 24   where x is the length of ST

12 + x = 24  

-12         -12

x = 12    

Answer:

Step-by-step explanation:

1) (3 * 7)(8) =3 (7 * 8)

Associative property of multiplication

It states that product of three or more numbers remains same regardless the way they are grouped

2) (7k)5 = 5(7k)

Commutative property of multiplication

3) 8(x +15) = (8)(x) + (8)(15)

distributive property

Answer:

  see below

Step-by-step explanation:

A vertical stretch is accomplished by multiplying the function value by the stretch factor.

  g(x) = 2f(x)

  g(x) = 2(x +3)

Answer:

The correct option are;

Every segment has one perpendicular bisector

Every segment has infinitely many congruent segments

Step-by-step explanation:

1) Every segment in a plane has exactly one perpendicular bisector

2) A congruent segment is a segment of equal length as a given segment, given that there can be infinitely many planes that can contain collinear points, whereby two points define a segment, the number of congruent segments that can be formed on infinitely many planes will therefore, be infinite.

Also given that the number of possible segments is infinite, the number of segments of a given size and therefore, the number of possible congruent segments is infinite.

Answer: $5.84

Step-by-step explanation:

Simple interest is calculated using the formula: PRT/100

where P = principal = $425

R = rate = 5.5%

T = time = 3/12 = 1/4 = 0.25

S.I = PRT/100

= (425 × 5.5 × 0.25)/100

= $584.375/1000

= $5.84

Given :

[tex]\begin{lgathered}\bullet\:\:\textsf{Perimeter of reactangle = \textbf{32 cm}}\\\bullet\:\:\textsf{Width = \textbf{7 cm}}\end{lgathered}[/tex]

[tex]\rule{130}1[/tex]

Solution :

[tex]:\implies\sf Perimeter\:of\: rectangle = 2 (Length + Breadth) \\\\\\:\implies\sf 32 = 2 (l + 7)\\\\\\:\implies\sf 32 = 2l + 14\\\\\\:\implies\sf 32 - 14 = 2l\\\\\\:\implies\sf 2l = 18\\\\\\:\implies\underline{\boxed{\sf Length = 9\:cm}} [/tex]

[tex]\rule{170}2[/tex]

[tex]\dashrightarrow\sf\:\:Area\:of\: rectangle = Length \times Breadth\\\\\\\dashrightarrow\sf\:\: Area\:of\: rectangle = 7\:cm \times 9\:cm\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf Area\:of\: rectangle = 63\:cm^2}}[/tex]

⠀

[tex]\therefore\:\underline{\textsf{The area of reactangle is \textbf{63}}\:\sf{cm^2}}.[/tex]

Answer:

Area of the rectangle is 63 cm².

Step-by-step explanation:

Given :-

To find :-

Solution :-

Consider,

width = 7 cm

Formula used :-

[tex]{\boxed{\sf{Perimeter of rectangle=2(Length+breadth)}}}[/tex]

According to the question ,

2(x+7) = 32

→ x+7 = 32/2

→ x +7 = 16

→ x = 16-7

→ x = 9

★ Length = 9 cm

Area of the rectangle ,

= length × Breadth

= 9 × 7 cm²

= 63 cm²

Therefore, the area of the rectangle is 63 cm².

Answer:

15i[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] and [tex]\sqrt{-1}[/tex] = i

Given

3[tex]\sqrt{-75}[/tex]

= 3 × [tex]\sqrt{25(3)(-1)}[/tex]

= 3 × [tex]\sqrt{25}[/tex] × [tex]\sqrt{3}[/tex] × [tex]\sqrt{-1}[/tex]

= 3 × 5 × [tex]\sqrt{3}[/tex] × i

= 15i[tex]\sqrt{3}[/tex]

Answer:

A) 1/2197

B) 1/5525

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome.

Since there are 52 random cards in a deck of card, the total outcome will be 52.

a) Also in a deck of card, there are 4 aces. If we are to select 3 aces with replacement, this means that each time we pick up an ace from the card, it was returned.

Pr(drawing an ace) = 4/52

Pr(drawing 3 aces and replacing it) = 4/52 *4/52*4/52

Pr(drawing 3 aces and replacing it) = 64/140,608

Pr(drawing 3 aces and replacing it) = 1/2197

b) If we pick 3 aces without replacement then each time we pick an ace, the total number cards keeps reducing.

Pr(picking the first ace) = 4/52

Pr(picking the second ace without replacing) = 3/51 (Since we didn't replace the first one, the total ace in the deck of card will reduce to 3 and the total will be 51)

Pr(picking the third ace without replacing) = 2/50 (since we didn't replace the first two aces, the total ace in the deck of card will reduce to 2 and the total will be 50)

Pr(drawing 3 aces without replacement) =  4/52*3/51*2/50

Pr(drawing 3 aces without replacement) =  24/132,600

Pr(drawing 3 aces without replacement) = 1/5525

Answer:

Step-by-step explanation:

I have listed every number and unbolded the numbers that are divisible by 2 and 3

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

so it is 13/20

The probability of selecting a multiple of 2 or a multiple of 3 from the integers 1-20 is 13/20.

Probability is the likeliness of happening an event among all the events possible to happen. The formula of calculating probability is number/ events/total numbers/ total events. The value of probability lies between 0 and 1.

We have to find out the probability of selecting a multiple of 2 or a multiple of 3 from the integers 1-20.

Multiples of 2 from 1 to 20=2,4,6,8,10,12,14,16,18,20= 10 numbers

Multiples of 3 from 1 to 20=3,6,9,12,15,18=6 numbers

Common multiples 6,12,18=3 numbers

Total numbers from 1 to 20=20

Probability=(10+6-3)/20

[ we have deducted 3 because we have to just take a number once while calculating probability]

=13/20

Hence the probability of selecting a multiple of 2 or a multiple of 3 from the integers 1-20 is 13/20.

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Answer:

x=8

Step-by-step explanation:

x+12=20

Answer:

d. g(x) = 5/3 * f(x)

Step-by-step explanation:

A transformation is the movement of a point from its initial position to a new position. Transforming an object involves transforming all the points in the object. Types of transformation are rotation, reflection, dilation and translation.

From the graph When x = 0, y = f(0)  = 30, also when x = 16, y = f(16) = 40

For the graph of g(x), when x = 0, y = g(0) = 50 and when x = 16, y = g(16) = 67

This means that  g(x) = 5/3 * f(x), g(0)  = 5/3 * f(0) =  5/3 * 30 = 50, also g(16)  = 5/3 * f(16) =  5/3 * 40 = 67

Answer:

D.)

Step-by-step explanation:

Answer:

Write out your decimal as the numerator of a fraction:

0.50 /1

Multiply to remove the 2 decimal places:

0.50 /1 ×  100 /100=  50 /100

Find the Greatest Common Factor of 50 and 100:

GCF is 50

Divide both numerator and denominator by 50:

50 ÷ 50

100 ÷ 50 =  1 /2

therefore your answer is 1/2

Hope this helps! （づ￣3￣）づ╭❤～

Answer:

115/198

Step-by-step explanation:

The correct answer is 115/198.

Answer:

5 cheeseburgers would be 12.50

Step-by-step explanation:

5 / 2 is 2.50 , 2.50 for one cheeseburger times 5 is 12.50

Answer: If two cheeseburgers are $5 the then one cheeseburger is 2.50

So 2.50 x 5 is 12.50

So it's 12.50 for 5 cheeseburgers

Answer:

W is the point of intersection of the lines 'a' and 'b'.

Step-by-step explanation:

Three points lying on line 'b' are points Y, Z and W.

Similarly, three points on line 'a' are points V, X and W.

Common point lying on both the lines 'a' and 'b' is W.

Therefore, point of intersection of the lines 'a' and 'b' is W.

Answer:1/25

Step-by-step explanation: do 5 to the second power which will get all combinations then do 1 as the numerator over the denominator which is the number of combinations.

Answer:

the probability is 5/20 for picking one yellow

and the probability is 4/19 for picking green one right after

Answer:

a) 166x.

Step-by-step explanation:

167x - x

= 166x.

Answer:

The correct answer is A) 166x

Hoped I helped

Answer:

A

Step-by-step explanation:

x²+2x+1)x³+10x²+13x+39 (x+8

           - x³+2x²+x

           +    -       -

           --------------------

                   8x²+12x+39

                   8x²+16x+ 8

                  -      -       -

                  ____________

                          -4x+31

Answer:

Add and subtract the second term to the expression and factor by grouping.

2

x

3

(

3

x

−

1

)

(

x

−

1

)

Step-by-step explanation:

Answer:

3x⁴+2x²+8

Step-by-step explanation:

[tex]6 {x}^{5} + 4 {x}^{3} + 8x[/tex]

[tex] = 2x(3 {x}^{4} + 2 {x}^{2} + 8)[/tex]