the length of a rectangle is 2 feet more than the width. Find the minimum dimensions if the perimeter is more than 16 feet and the length and width are integers.

Answer:

(simplify 26³)

26³ = 17,576

= 17,576 + 5 = 3³+57

(simplify 3³)

3³ = 27

= 17,581 = 27+57

= 17,581 ≠ 84

Answer:

58%

Step-by-step explanation:

35/60=0.58333=58/100=58%

The quotient will be x² + 5x + 2 and the remainder will be 1.

Synthetic division method is a method used to divide polynomials. It is used to divide polynomial with a linear factor whose leading coefficient is 1.

We will factorize x³ + 7x² + 12x + 5 by x + 2 using synthetic division method.

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x = 32

Step-by-step explanation:

[tex]{ \tt{p(x) = \frac{x + 7}{3} }}[/tex]

If p(x) = 13, then

[tex]{ \tt{13 = \frac{x + 7}{3}}} [/tex]

[tex]{ \tt{13 \times 3 = x + 7}}[/tex]

[tex]{ \tt{39 = x + 7}}[/tex]

[tex]{ \tt{39 - 7 = x}}[/tex]

[tex]{ \red{ \boxed{ \blue{ \sf{x = 32}}}}}[/tex]

There can be 2184 ways in which three posts can be selected using permutation.

What is permutation?

An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are arranged in a linear or sequential order.

Main Body:

Total members =14

total posts =3

As one person can not hold more than 1 post ,

total ways are = ¹⁴P₃

Therefore total ways = 14!/11!  

                                   = (14*13*12*11!)/11!

                                   = 14*13*12

                                   = 2184 ways

Hence answer is 2184 ways to select 3 members out of 14.

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The derivative of the function f(x) = Sin⁻¹(3x) is f'(x) = 3/√(1-9x²)  , the correct option is (c) .

In the question ,

a function is given as

f(x) = Sin⁻¹(3x) , we need to find the derivative .

we know that the derivative of Sin⁻¹(x) is equal to 1/√(1 - x²) .

So , on differentiating both sides with respect to "x" .

we get

f'(x) = d/dx (Sin⁻¹(3x))

= 1/√1-(3x)² ×  d/dx (3x)

= 1/√(1 - 9x²) × 3

On simplifying further ,

we get

= 3/√(1 - 9x²)

Therefore ,the derivative of the function is 3/√(1-9x²)  , the correct option is (c) .

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It would take Amanda 2.25 hours to catch up with Ben

Speed is the ratio of distance to time. It is given by:

Speed = distance/time

Given that Ben covers a distance d at time t, hence:

3 = d/t

d = 3t

Since Amanda leaves One and a half hours (1.5) after Ben leaves, hence Time = t - 1.5

5 = d/(t - 1.5)

d = 5t - 7.5

Since they catch up, hence:

3t = 5t - 7.5

2t = 7.5

t = 3.75 hours

Time for Amanda = t - 1.5 = 3.75 - 1.5 = 2.25 hours

Hence it would take Amanda 2.25 hours to catch up with Ben.

The cost to rent chair is $1.5  and table is $8.5  .

In the question ,

it is given that

the cost to rent 12 chairs and 2 tables [tex]=[/tex] $35

and the cost to rent 3 chairs and 5 tables  [tex]=[/tex] $47

let the cost for 1 chair ne "c"

and let the cost for 1 table = "t"

So , according to the question ,

the equations are

12c + 2t = 35      ....equation(1)

3c + 5t = 47         ....equation (2)

On multiply equation (2) by 4 and then subtracting equation (1) from it ,

we get

(12c + 20t) - (12c + 2t) = 188 - 35

12c + 20t - 12c -2t = 153

18t = 153

t = 153/18

t = 8.5

and 12c + 2(8.5) = 35

12c + 17 = 35

12c = 18

c = 18/12

c = 1.5

Therefore , The cost to rent chair is $1.5  and table is $8.5  .

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The solution of the linear equation:

3x+4x+5x=4(x+2)

is x = 1

Here we need to solve the following linear equation:

3x + 4x + 5x = 4*(x + 2)

First, we should expand the right side to get:

3x + 4x + 5x = 4x + 8

Now we group like terms:

3x + 4x + 5x - 4x = 8

Taking x as a common factor in the left side:

(3 + 4 + 5 - 4)*x = 8

(3 + 5)*x = 8

8x = 8

x = 8/8

x = 1

The solution is x = 1.

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Answer:

see explanation

Step-by-step explanation:

(a)

parallel line segments are indicated by arrows on the segments pointing in the same direction.

from the diagram EA and DC are parallel lines.

(b)

equal lines are indicated by a dash through the lines.

from the diagram AB and BC are equal.

(c)

perpendicular lines are at right angles (90° ) to each other, usually indicated by a small box between them.

from the diagram AE and CD are perpendicular to DE

Answer:

Step-by-step explanation:

The probability expression when converted from odd's expression is 8/17

From the question, we have the following odd parameters

Odd = 8 to 9

To start with, we need to express the odd as ratio

So, we have the following representation

Odds ratio = 8 : 9

Solving further, we need to express the ratio as fraction

So, we have the following representation

Odds fraction = 8/9

To convert the above odd's expression to probability expression, we make use of the following equation

This is represented as

P = Odds/(Odds + 1)

Substitute the known values in the above equation

So, we have the following equation

P = (8/9)/(8/9 + 1)

Evaluate the sum

This gives

P = (8/9)/(17/9)

Express the quotient as product

P = (8/9) * (9/17)

Evaluate

P = 8/17

Hence, the probability is 8/17

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The percentage of shaded grid is 45% and the number of squares is 5.

a. Percentage of shaded grid

The total number of shaded and unshaded grid is 20 while the total number of shaded area is 9 now let find the percentage of the shaded grid.

Percentage of shaded grid = Shaded grid /Total grid

Percentage of shaded grid = 9/20 × 100

Percentage of shaded grid = 45%

b. Number of squares to be shaded

Number of squares = 20 grid × (70% - 45%)

Number of squares = 20 grid × 25%

Number of squares =  5 squares

Therefore the percentage is 45% .

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Answer:

  f(x) = x² -2x -35

Step-by-step explanation:

You want a quadratic function that has zeros 7 and -5.

Each zero (p) gives rise to a factor (x-p). The zeros 7 and -5 mean the quadratic has factors (x-7) and (x-(-5)).

  f(x) = (x -7)(x +5)

  f(x) = x² -2x -35

__

Additional comment

You may notice that the coefficient of the linear term is the opposite of the sum of the zeros. The constant term is the product of the zeros. Knowing this, we can write the quadratic without any concern for the factors.

  sum: 7-5 = 2

  product: (7)(-5) = -35

  quadratic: f(x) = x² -2x -35

Answer:

5.8 hours

Step-by-step explanation:

First, you just plug it the given information.

Turn the equation to t=d/r by dividing the rate by both sides.

Plug it in 348miles/ 60 miles per hour

It'll take 5.8 hours for the car to travel 348 miles at the rate of 60 miles per hour.

Answer:

a. Given

b. thru any 2 points there exists a line (you can draw a line)

c. Definition of Regular Polygon

d. Definition of Regular Polygon

e. Given

f. Def of Midpoint

g. SAS: Side-Angle-Side congruence

h. CPCTC - Corresponding Parts of Congruent Triangles are Congruent

i. Definition of Regular Polygon

j. Reflexive

k. SSS: Side-Side-Side congruence

l. CPCTC

Step-by-step explanation:

I encourage you to look up all of the above reasons to get a better understanding of what they are!!

Answer:

20 units

Step-by-step explanation:

we find the side lengths by looking at the coordinates and just counting up

Sides are 6,4,6,4

So we just add

6+4+6+4

10+10

20

Hopes this helps please mark brainliest

Answer: Your answer is 20 units, because the height is 6 units, and the length is 4 units, so we then multiply by 2 for both numbers, then add them together, having a sum of 20 units.

Hope that helps.

The probability that a student's mark is more than 75 is 0.0947 and in a class of 50 students, 5 students should have a mark of more than 75.

In the given question,

The Mathematics marks of all the students in the class are normally distributed with mean mark 54 and standard deviation 16.

We have to find the probability that a student's mark is more than 75.

In a class of 50 students, we also have to find how many students should have a mark of more than 75.

From the question the mean = 54

Standard Deviation = 16

So the probability that a student's mark is more than 75.

Using the normal distribution

z = (x−mean)/Standard Deviation

P(x>75) = P(z>(x−mean)/Standard Deviation)

P(x>75) = 1−P(z<(75−54)/16)

Simplifying

P(x>75) = 1−P(z<21/16)

P(x>75) = 1−P(z<1.3125)

From the standard z table value

P(x>75) = 1−0.9053

P(x>75) = 0.0947

Hence, the probability that a student's mark is more than 75 is 0.0947.

Now finding in a class of 50 students, how many students should have a mark of more than 75.

Total student = 50

So the student having mark of more than 75 = Total student * probability that a student's mark is more than 75

The student having mark of more than 75 = 50 * 0.0947

The student having mark of more than 75 = 4.735

The student having mark of more than 75 ≈ 5

Hence, in a class of 50 students, 5 students should have a mark of more than 75.

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Answer:

y=8 x=-19.5

Step-by-step explanation:

Start from the bottom equation and work your way upSolve the fourth equation for w-5w=-15-5w/(-5)=-15/(-5)w = 3 Then use that value of w to plug into the third equation. Notice we're going backwards or up the chain of equations. After w is replaced, solve for zz+w = 2z+3 = 2z+3-3 = 2-3z = -1 Now use z = -1 and w = 3 to plug into the second equation. Solve for y-2y-12z-4w = -16-2y-12(-1)-4(3) = -16-2y+12-12 = -16-2y = -16-2y/(-2) = -16/(-2)y = 8 

Use y = 8, z = -1, w = 3 to plug into the first equation. Solve for x:

2x+4y+z+3w=12x+4(8)+(-1)+3(3)=12x+32-1+9=12x+40=12x+40-40=1-402x=-392x/2=-39/2x = -39/2 The value of x as a fraction is x = -39/2The value of x in decimal form is x = -19.5 

During the first 3 months students club has raised fund of  $1680.

Given that, The Helping Hands Student Club set a goal to raise $4,000 by the end of the school year for a project.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

After 3 months, it reaches 42% of its goal.

The fund raised during the first 3 months is

42% of 4000

= 42/100 × 4000

= 42×40

= $1680

Therefore, during the first 3 months students club has raised fund of  $1680.

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Answer:

$1,680

Step-by-step explanation:

The solution to the equation using graph is x= -0.62 or x = 1.62.

What is equation?

A mathematical equation may be a formula that uses the equals sign to represent the equality of two expressions.

Main Body:

For [tex]-x^{2} +y = 1[/tex]

We make y the subject to obtain

[tex]y = x^{2} +1[/tex]

We can easily graph this function, because we just have to transform the graph [tex]y = x^{2}[/tex] of  by shifting the intercept up to 1.

As for the straight line, -x +y = 2

We find the intercepts as follows,

When y = 0 , x = -2

When x = 0 , y = 2

We plot the points (-2,0)  and (0,2).

We now draw the two graphs on the same graph sheet. The intersection of the two graphs gives the solution to be

x= -0.62 or  x= 1.62

See graph

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The rate of acceleration of a bicycle. if it went from a complete stop to 15 meters per second in 5 seconds is

acceleration is solved using the formula

a = (v - u) / t

definition of variables

final velocity = v

initial velocity = u

time taken  = t

form the question we have that

v = 15 meters per seconds

u = 0 (bicycle went from complete stop)

t = 5 seconds

a = (15 - 0) / 5

a = 15 /5

a = 3 meters per seconds squared

The bicycle is travelling at an acceleration of 3 meters per seconds squared

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Answer: x = -135.59

Step-by-step explanation:

20 = 0.694(x + 150)(2)

Step 1: Simplify both sides of the equation.

20 = 0.694 (x + 150)(2)

20 = 1.388x + 208.2 (use the distributive property)

20 = 1.388x + 208.2

Step 2: Flip the equation.

1.388x + 208.2 = 20

Step 3: Subtract 208.2 from both sides of the equation.

1.388x + 208.2 − 208.2 = 20 − 208.2

1.388x = −188.2

Step 4: Divide both sides by 1.388.

1.388x/1.388 = −188.2/1.388

x = −135.590778

Optional: Simplify

x = -135.59

The measure of the angle for the given trigonometric function is 30°.

Given that, [tex]sin^{-1}(0.5)[/tex].

Trigonometric angles are the angles in a right-angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.

Trigonometry angle can be expressed in terms of trigonometric ratios as,

θ = [tex]sin^{-1[/tex] (Perpendicular/Hypotenuse)

θ =[tex]sin^{-1[/tex] (0.5)

= [tex]sin^{-1[/tex] (1/2)

= 30°

Therefore, the measure of the angle for the given trigonometric function is 30°.

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The domain of the function is [ - 6 , ∞ ]

A radical function is the one provided.

It should be noted that a radical function can only be specified for values that will result in the radicand being larger than or equal to zero.

As a result, either the radicand of the provided function must be larger than or equal to zero, or:

Thus we can write it as

x + 6 ≥ 0

subtract 6 from both LHS and RHS

x + 6 - 6 ≥ 0 - 6

x ≥ - 6

Therefore the domain of the function is [ - 6 , ∞ ]

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Tthe length of PQ and QR.​ is 6 and 8 m

Area of rectangular field ABCD is = 4m x 6m = 24m2

Area of rectangular field PQRS (ABCD with uniform path) = (4 + x)(6 + x)

= 24 + 4x + 6x + x²

48 = 24 + 10x + x²

x² + 10x - 24 = 0

x² + 12x - 2x - 24

x(x + 12) - 2(x + 12)

(x - 2)(x + 12) = 0

x - 2 = 0

x = 2

PQ = 4 + 2 = 6

QR = 6 + 2 = 8

Therefore,  the length of PQ and QR.​ is 6 and 8 m

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The equation a+b+c+d=15 has infinite many solutions

From the question, the equation is given as

a+b+c+d = 15

From the above representation of the equation, we can see that:

When a linear equation that has more than one variable is given, the number of solutions cannot be quantified i.e. infinite number of solutions

Hence, the equation has infinite number of solutions

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