Write an equation to model the distance between the point (2,4) and any point along the curve
y=4x3 + 1.

Write it out as an equation:

(48 /(5+(11-8))) -7

Simplify:

(48/(5+3))-7

(48/8)-7

6-7 = -1

The answer is -1

Answer:

Below

Step-by-step explanation:

All figures are squares. The area of a square is the side times itself

Let A be the area of the big square and A' the area of the small one in all the 5 exercices

51)

● (a) = A - A'

A = c^2 and A' = d^2

● (a) = c^2 - d^2

We can express this expression as a product.

● (b) = (c-d) (c+d)

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52)

● (a) = A-A'

A = (2x)^2 = 4x^2 and A'= y^2

● (a) = 4x^2 - y^2

● (b) = (2x-y) ( 2x+y)

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53)

● (a) = A-A'

A = x^2 and A' = y^2

● (a) = x^2-y^2

● (b) = (x+y) (x-y)

■■■■■■■■■■■■■■■■■■■■■■■■■■

54)

● (a) = A-A'

A = (5a)^2 = 25a^2 and A' =(2b)^2= 4b^2

● (a) = 25a^2 - 4b^2

● (a) = (5a-2b) (5a+2b)

■■■■■■■■■■■■■■■■■■■■■■■■■■

55)

● (a) = A - 4A'

A = (3x)^2 = 9x^2 and A'= (2y)^2 = 4y^2

● (a) = 9x^2 - 4 × 4y^2

● (a) = 9x^2 - 16y^2

● (a) = (3x - 4y) (3x + 4y)

Answer:

  55°

Step-by-step explanation:

Perhaps you want the measure of angle B. (There is no "b" in the figure.)

That measure is half the measure of the intercepted arc:

  m∠B = 110°/2 = 55°

Angle B is 55°.

Answer:

Difference : 4th option

Step-by-step explanation:

The first thing we want to do here is to factor the expression x² + 3x + 2. This will help us if it is similar to the factored expression " ( x + 2 )( x + 1 ). " The denominators will be the same, and hence we can combine the fractions.

x² + 3x + 2 - Break the expression into groups,

( x² + x ) + ( 2x + 2 ) - Factor x from x² + x and 2 from 2x + 2,

x( x + 1 ) + 2( x + 2 ) - Group,

( x + 2 )( x + 1 )

This is the same as the denominator of the other fraction, and therefore we can combine the fractions.

x - 1 / ( x + 2 )( x + 1 )

As you can see this is not any of the options present, as we have not expanded ( x + 2 )( x + 1 ). Remember previously that ( x + 2 )( x + 1 ) = x² + 3x + 2. Hence our solution is x - 1 / x² + 3x + 2, or option d.

Answer:

Step-by-step explanation:

Adding both equations

4x+5y+5y-4x=19+38

10y = 57

y= 5.7

Subtracting equation i from ii

5y-4x-4x-5y=38-19

-8x=9

x= -0.9

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

If we have 3 red spaces, 5 white spaces, and one blank space, there are a total of 9 spaces.

Since there are 3 red spaces, there is a [tex]\frac{3}{9} = \frac{1}{3}[/tex] chance of getting a red. However, the question asks the probability of not getting a red, so the chances of not getting a red are [tex]1 -\frac{1}{3} = \frac{2}{3}[/tex].

Hope this helped!

Answer: 15

Step-by-step explanation:

General terms in AP

f, f+d, f+2d, f+3d, ....  , where f= first term and d= common difference.

The given A.P. : 18, a, b, - 3

here, f= 18    

[tex]f+d= a ...(i)\\\\f+2d = b ...(ii)\\\\f+3d= -3 ...(iii)\\\\[/tex]

Put f= 18 in (iii) ,

[tex]18+3d=-3\\\\\Rightarrow\ 3d= -3-18\\\\\Rightarrow\ 3d= -21\\\\\Rightarrow\ d=-7[/tex]

Put f= 18 and d= -7 in (i) and (ii) , we get

[tex]a=18+(-7)=11\\\\b=18+2(-7)\\\\\Rightarrow\ b=18-14\\\\\Rightarrow\ b=4[/tex]

Now, [tex]a+b= 11+4=15[/tex]

Hence, the correct answer is "15".

Answer:

360

Step-by-step explanation:

Answer: x = 3

Step-by-step explanation:

Sqrt(x+7) - 1  = x

Sqrt(x+7) = x + 1

x+7 = x^2 + 1

x = x^2 - 6

x=3

Answer:

the percentage share for BBC2 remained almost the same at about 11 % each year

if you look at the chart the BBC2 almost remains stable between 10 and 12 %

1980 ( between 39 and 51)

1985 ( between 37 and 49 ) and so on

( these numbers are not exactly the same , it is about or approximately)

Answer:

f(x) = 5 * ( 8/5) ^x

Step-by-step explanation:

f(x) = a b^x

Let x = 0

5 = a * b^0

5 = a*1

a = 5

Let x = 1

8 = 5 * b^1

Divide each side by 5

8/5 = b

f(x) = 5 * ( 8/5) ^x

Answer:

x = 3

Step-by-step explanation:

j(x) = 4/5(-5) + 7

= -4 + 7

= 3

Answer:

15

Step-by-step explanation: -4/5 x has to be -12 because -12+7 equals 5. Since we want to figure out x, we have to flip -4/5 x to 4/5x which would change the -12 to 12. What is a fourth of 12? It is three. 12+3 equals 15. This is the first right answer on all of the internet for this question!

Answer:

5(12 : 3) -8

Step-by-step explanation

when you solve the first half of the equation you get 1.

so 9-1 is 8.

Answer:

For "Negative 23 greater-than x" , highlight the left half of the number line starting at -23 and use a parenthesis ) on -23.

For "x greater-than-or-equal-to negative 23", highlight the right half of the number line starting at -23, and use a square bracket [ on -23.

Step-by-step explanation:

Start by locating the number -23 on the number line. Please see attached image to accompany the explanation.

In the first case:  "Negative 23 greater-than x" , which is expressed mathematically as:

[tex]-23 >x[/tex]

notice that "x" has to be strictly smaller than the number -23, therefore those sought x values must reside to the left of the number -23, so we have to highlight that half of the number line. Apart from that, we need to include a symbol on top of the number -23, that indicates that -23 itself shouldn't be considered as part of the set, that symbol is by convention a parenthesis ).

In the second case: "x greater-than-or-equal-to negative 23", which is expressed mathematically as:

[tex]x\geq -23[/tex]

notice that "x" has to be greater than or equal to the number -23, therefore those sought x values must reside to the right of the number -23, so we have to highlight that half of the number line. Apart from that, we need to include a symbol on top of the number -23, that indicates that -23 itself should be considered as part of the set, that symbol is by convention a square bracket [.

Answer:

the answer is A

Step-by-step explanation:

Answer:

5x(25)

Step-by-step explanation:

Answer:

C. [tex]x[/tex] and $(x-6)$

Step-by-step explanation:

The roots of the quadratic equation are $0$ and $6$.

Hence the equation is $(x-0)(x-6)=x(x-6)$

Answer:

See below

Step-by-step explanation:

Answer:

  £67.50

Step-by-step explanation:

On each metre of material, the shop makes a profit of ...

  £6.90 -4.65 = £2.25

So, for 30 metres, the profit will total ...

  30 × £2.25 = £67.50

A profit of £67.50 would be made on a 30-metre roll of material.

Answer:

the other factor is (x+7)

Step-by-step explanation:

Given x^2+11x+28

factor into

x^2+7x + 4x + 28

=x(x+7) + 4(x+7)

= (x+4)(x+7)

Answer: the other factor is (x+7)

Answer:

[tex]\huge\boxed{f = 5\ Hz}[/tex]

Step-by-step explanation:

Given:

Time period = T = 0.2 sec

Required:

Frequency = f = ?

Formula:

f = 1/T

Solution:

f = 1/0.2

f = 5 Hertz

Answer:

[tex] \boxed{\sf Frequency \ (f) \ of \ the \ wave = 5 \ Hz} [/tex]

Given:

Time Period (T) = 0.2 s

To Find:

Frequency (f) of the wave

Step-by-step explanation:

[tex] \sf Frequency (f) = \frac{1}{Time Period (T)} [/tex]

[tex] \sf f = \frac{1}{0.2} [/tex]

[tex] \sf f = \frac{1}{0.2} \times \frac{10}{10} [/tex]

[tex] \sf f = \frac{10}{2} [/tex]

[tex] \sf f = \frac{ \cancel{2} \times 5}{ \cancel{2}} [/tex]

[tex] \sf f = 5 \: Hz[/tex]

Answer:

The correct option is;

B. s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t

Step-by-step explanation:

The given parameters are;

The number of T-shirts, t, and shorts, s, Tim must design a day = 12

The maximum number of T-shirts and shorts Tim can design a day = 30

The maximum number of hours Tim can work = 18 hours

Therefore, we have;

The number of shorts Tim designs in a day is ≥ The minimum number of T-shirts and shorts Tim must design a day less the number of T-shirts Tim designs

Which gives;

s ≥ 12 - t

Also the number of shorts Tim designs in a day is ≤ The maximum number of T-shirts, and shorts, Tim can design a day less the number of T-shirts Tim designs

Which gives;

s ≤ 30 - t

The number of 45 minute period for the design of shorts in 18 hours = 18×60/45 = 24

The fraction of 36 minutes in 45 minutes = 36/45 = 0.667

Therefore we have;

The number of shorts Tim designs in a day is ≤ The number of 45 minute periods in 18 hours less the number of 36 minutes periods used to design T-shirts

Which gives;

s ≤ 24 - 0.66·t

The correct option is s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t.

Answer:

B. s> 12-tss 30 - t Ss 24 -0.66t, s 2 0; t> 0

Step-by-step explanation:

Hope this helps!!

Answer:

[tex] \boxed{13}[/tex]

Step-by-step explanation:

Arranging the data in ascending order:

8 , 8 , 10 , 11 , 13 , 13 ,13 , 14 , 14 , 15 , 16 , 17 , 18 , 18 ,

In the case of discrete data, mode can be found just by inspection, i.e just by taking an item with highest frequency.

Here, 13 has the highest frequency

So, Mode = 13

Extra information

Mode

The mode of a set of data is the value with the highest frequency. A distribution that has two modes is called bimodal. The mode of a set of data is denoted by Mo.

Hope I helped!

Best regards!

Answer:

The correct option is;

f(x) = -2·x² + 5·x - 1

Step-by-step explanation:

Given the points

(-1, -8), (0, -1), (1, 2), we have;

The general quadratic function;

f(x) = a·x² + b·x + c

From the given points, when x = -1, y = -8, which gives

-8 = a·(-1)² + b·(-1) + c = a - b + c

-8 =  a - b + c.....................................(1)

When x = 0, y = -1, which gives;

-1 = a·0² + b·0 + c = c

c = -1.....................................................(2)

When x = 1, y = 2, which gives;

2 = a·1² + b·1 + c = a + b + c...............(3)

Adding equation (1) to (3), gives;

-8 + 2 = a - b + c + a + b + c

-6 = 2·a + 2·c

From equation (2), c = -1, therefore;

-6 = 2·a + 2×(-1)

-2·a  = 2×(-1)+6 = -2 + 6 = 4

-2·a = 4

a = 4/-2 = -2

a = -2

From equation (1), we have;

-8 =  a - b + c = -2 - b - 1 = -3 - b

-8 + 3 = -b

-5 = -b

b = 5

The equation is therefore;

f(x) = -2·x² + 5·x - 1

The correct option is f(x) = -2·x² + 5·x - 1.

Answer:

n = 5

Step-by-step explanation:

To start off, we know that whenever the bases are the same, their exponents are equal to each other. Therefore, since both of the numbers bases are the same (both are z), we know that they will be equal.

The n can be distributed to the [tex]z^2[/tex] so that it now reads to be:

[tex]z^2^n = z^{10}[/tex]

Exponents are equal, so:

2n=10

Divide the 2 on both sides:

n=5

Answer:

n =5

Step-by-step explanation:

z^2^n

We know that a^b^c = a^ (b*c)

z^(2n)

This is equal to z^10

Since the bases are the same, the exponents are the same

2n = 10

Divide by 2

2n/2 = 10/2

n = 5

Answer:

n = 24

Step-by-step explanation:

Given the fraction:

[tex]$\frac{n}{n+101}$[/tex]

To find:

Smallest positive integer [tex]$n$[/tex] such that the fraction is equal to a terminating decimal.

Solution:

The rule that a fraction is equal to a terminating decimal states that, the denominator must contain factors of only 2 and 5.

i.e. Denominator must look like [tex]2^m\times 5^n[/tex], only then the fraction will be equal to a terminating decimal.

Now, let us have a look at the denominator, [tex]n+101[/tex]

Let us use hit and trial method to find the value of [tex]n[/tex] as positive integer.

n = 1, denominator becomes 102 = [tex]2 \times 3 \times 17[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 4, denominator becomes 105 = [tex]5 \times 3 \times 7[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 9, denominator becomes 110 = [tex]2 \times 5 \times 11[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 14, denominator becomes 115 = [tex]5 \times 23[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 19, denominator becomes 120 = [tex]5 \times 3 \times 2^3[/tex] not of the form [tex]2^m\times 5^n[/tex].

n = 24, denominator becomes 125 = [tex]2^0 \times 5 ^3[/tex] It is of the form [tex]2^m\times 5^n[/tex].

So, the answer is n = 24

The statements that can be used to describe the reasoning used to determine if Kelsey’s inequality is correct include:

It should be noted that the inequality symbol is incorrect because she can spend up to and including $65.

Based on the information given, the correct expression that can be used to solve the question should be:

65 - (5.50b + 7.5)

In conclusion, the correct options are B and C.

Read related link on:

https://brainly.com/question/16904821

Answer:

B and C

Step-by-step explanation:

Answer:

The total amount left by Manavi and Kuber is: (1) 399

Step-by-step explanation:

Manavi

saving account +  amount spent at the mall:  1/'2 + 1/4 =  3/4

left over: 1 - 3/4 = 4-3/4 = 1/4

1260 ( 1/4) = 315

The total leftover for Manavi is Rs.315.

Now do the same steps with Kuber.

Kuber

saving account +  amount spent at the mall: 1/3+ 3/5 = 14/15

left over: 1- 14/15 = 15-14/15 = 1/15

1260 (1/15) = 84

The total leftover for Kuber is Rs.84.

Lastly, just add both left over amount together.

315+84 = 399

The total amount left by Manavi and Kuber is: (1) 399

Answer:

≈ 36.1%

Step-by-step explanation:

In any circle the following ratio is equal

[tex]\frac{arc}{circmference}[/tex] = [tex]\frac{centralangle}{360}[/tex] = [tex]\frac{130}{360}[/tex] , thus

percentage = [tex]\frac{130}{360}[/tex] × 100% ≈ 36.1%

an arc measuring 130° is approximately 36.11% of the circumference of the circle.

To find the percentage of the circumference that an arc measuring 130° represents, we need to calculate the ratio of the arc length to the circumference of the circle and then convert it to a percentage.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.

Let's assume the radius of the circle is r.

The circumference of the circle is C = 2πr.

To find the length of the arc corresponding to 130°, we need to calculate the fraction of the total angle (360°) that 130° represents:

Fraction of the angle = (130° / 360°) = (13/36).

Since the fraction of the angle is equal to the fraction of the arc length to the circumference, the length of the arc can be calculated as:

Arc length = Fraction of the angle * Circumference = (13/36) * (2πr).

Now, to find the percentage of the circumference that the arc length represents, we divide the arc length by the circumference and multiply by 100:

Percentage = (Arc length / Circumference) * 100

Percentage = [(13/36) * (2πr)] / (2πr) * 100

Percentage = (13/36) * 100

Percentage = 36.11%

Therefore, an arc measuring 130° is approximately 36.11% of the circumference of the circle.

Learn more about arc length here

https://brainly.com/question/10266974

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Answer:

358.125

Step-by-step explanation:

Answer:

358 3/24

Step-by-step explanation:  

Answer:

3053.5517 cm^3 ; 1/8

Step-by-step explanation:

Given the following :

Volume (V) of sphere = (4/3)πr^3 where r = radius

Diameter of sphere = 18 ; radius(r) = diameter / 2 = 18/2 = 9cm

V = (4/3) × π × 9^3

V = 1.3333 × π × 729

V = 3053.5517 cm^3

When diameter(d) is reduced to half

d = d/2

Volume (V1) of sphere with diameter 'd' =

V1 = (4/3)π(d/2)^3

Volume (V2) of sphere with diameter 'd' reduced to half, d = d/2, d/2 * 1/2 = d/4

V2 = (4/3)π(d/4)^3

V1 / V2 = [(4/3)π(d/2)^3] / [(4/3)π(d/4)^3]

V1 / V2 = (d/2)^3 / (d/4)^3

V1 / V2 = [d^3 / 2^3] / [d^3 / 4^3]

V1 / V2 = 8 / 64

V1 / V2 = 1 / 8

Answer:

first blank is 972

second blank is 1/8

yup

Step-by-step explanation:

Answer:

vertex(-3,27)

Step-by-step explanation:

f(x)= x^2+ 6x + 36 ( a=1,b=6,c=36)

V(h,k)

h=-b/2a=-6/2=-3

k=f(-3)=3²+6(-3)+36

f(-3)=9-18+36=27

vertex(-3,27)