please help














10101010101000

1a) The domain is a set of all real numbers not equal to 5

1b) The domain is a set of all real numbers not equal to 4

Domain of a function is the set of all possible input values that make the function defined.

1a) We are given the function;

C(x) = -3²/(x - 5)

The domain will be a set of values that makes the denominator not equal to zero. Thus;

The domain is a set of all real numbers not equal to 5

1b) The function is; R(x) = 4x/(3x - 12)

The domain will be a set of values that makes the denominator not equal to zero. Thus;

The domain is a set of all real numbers not equal to 4

2a) Function is;

f(x) = (x + 8)/(2x - 1)

f(2) = (2 + 8)/(2(2) - 1)

f(2) = 10/3

f(0) = (0 + 8)/(2(0) - 1)

f(0) = -8

f(-1/2) = (-1/2 + 8)/(2(-1/2) - 1)

f(-1/2) = -15/4

2b) Function is;

r(t) = (t² + 8)/(t³ - 25t)

r(3) = (3² + 8)/(3³ - 25(3)) = -17/48

r(2) = (2² + 8)/(2³ - 25(2)) = -12/42 = -2/7

r(-1) = ((-1)² + 8)/((-1)³ - 25(-1))  = 9/24 = 3/8

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If the average of x and y is 11 and the average of x, y and z is 5, then the value of z is -7

Given,

The average of x and y = 11

We know average = Sum of the terms / Number of terms

Then, the equation will become

[tex]\frac{x+y}{2}=11[/tex]
x+y =11×2

x+y =22

Average of x, y and z = 5

[tex]\frac{x+y+z}{3}=5[/tex]

x+y+z = 5×3

x+y+z =15

Substitute the value of x+y

22+z=15

z =15-22

x = -7

Hence, If the average of x and y is 11 and the average of x, y and z is 5, then the value of z is -7

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The phone numbers that are possible in Wilmington are 10000000. The phone numbers possible in Wilmington if the number cannot be used is 4782969. The phone numbers are possible in Wilmington if they must be divisible by 2 or 5 are 6000000. The phone numbers are possible in Wilmington if there are no repeated digits are 5040.

A positional numeral system uses a single symbol, a numerical digit, to represent numbers. The word "digit" refers to the ten decimal (old Latin adjective decem meaning "ten") digits, which are the equivalent of the ten symbols used in the conventional base-10 numeral system. The word "digit" comes from the Latin word "digiti," which means "fingers."

The absolute value of the base determines the required number of different digits for a given numeral system with an integer basis. For instance, the base-10 decimal system requires ten digits (0 through 9), whereas the base-2 binary system just needs two digits (0 and 1).

Explanation:

The number after area code is of 7 digits.

a) [tex]10^{7} =10000000[/tex]

b) [tex]9^{7} =4782969[/tex]

c) X  X  X  X  X  X  X

    I   I    I   I    I    I    I

   10 10 10 10 10 10  0,2,4,6,8,5,i.e,6digits are possible

=[tex]10^{6} x6=6000000[/tex]

d)7!

=5040

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The measure of angle 1 is 76⁰, the measure of angle 2 is 104⁰, the measure of angle 3 is 76⁰ and the measure of angle 4 is 104⁰.

The sum of angles in a circle is 360 degrees.

In other words, we can say that, the sum of the measures of the central angles of a circle with no points in common is 360 degrees.

In the given diagram, angle 1, angle 2, angle 3 and angle 4 will sum to 360 degrees.

m∠1 + m∠2 + m∠3 + m∠4 = 360⁰

another interesting to observe is that;

m∠1  = m∠3

m∠2 = m∠4

if m∠1 = 76⁰, then

m∠3 = 76⁰

m∠2 + m∠4 = 360 - (76 + 76)

m∠2 + m∠4 = 208

m∠2 = m∠4 = 208/2 = 104⁰

Thus, the measure of angle 1 is 76⁰, the measure of angle 2 is 104⁰, the measure of angle 3 is 76⁰ and the measure of angle 4 is 104⁰.

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Answer:

d,c,a,b

Step-by-step explanation:

Answer:

x=-19

Step-by-step explanation:

For solving for x you will have to use inverse operations

-6=(-5+x)/4

-6(4)=-5+x

-6(4)+5=x

-19=x

x=-19

Answer:

3√2

Step-by-step explanation:

divide both sides by 2

3√2 = n

Answer:

n = 9

Step-by-step explanation:

note that ([tex]\sqrt{a}[/tex] )² = a , then

(3[tex]\sqrt{2}[/tex] )² = 2n

3 × 3 × [tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 2n

9 × 2 = 2n

18 = 2n ( divide both sides by 2 )

9 = n

The type of distributions represented by the given graphs in the question are as follows;

(a) Symmetric

(b) Bimodal

(c) Skewed right

(d) Uniform

(e) Skewed right

The definition and descriptions of the given terms are;

Approximately; The term is used to describe the state of things which is close to an actual thing or situation.

Symmetric; A distribution is symmetric when the area of the side on the left and on the right of the mean are equal and balance each other.

Bell shaped; A distribution that has a bell shaped graph, which usually represents a normal distribution, can be described as a bell shaped distribution.

Skewed left; The graph of a distribution is skewed left if it has a tail (smaller values) on the left of the graph

Skewed right; The graph of a distribution is skewed right if the tail is on the right of the graph.

Uniform; A distribution is uniform if the shape of the graph is approximately rectangular.

Bimodal; A distribution that has two peaks is said to be a bimodal distribution.

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The principal in terms of Simple Interest, Time, and Rate can be expressed as p=(i×100)/(r×t).

Whenever a loan is given to a person it is given for some specific amount of time at a specific rate of interest which is to be paid along with the principal amount. Simple Interest is the method of calculating the interest amount on a loan given for a specific period.

It involves the multiplication of the principal amount, rate of interest, and the time for which the loan is given divided by 100.

Here Simple interest is denoted by i, time in years is denoted by t, the principal is denoted by p, and the rate of interest is denoted by r.

The formula of simple Interest is given by:

Simple interest = (Principal×Rate×Time)/100

i=(p×r×t)/100

Now principal can be denoted as:

p=(i×100)/(r×t)

Thus, the Principal in terms of Simple Interest, Time, and Rate can be expressed as p=(i×100)/(r×t).

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Answer: 17%

Step-by-step explanation:

136,890-117,000=19,890

19,890/117,000=0.17

0.17*100=17% increase in the city population

Answer:

a(c-b)=d

we open the bracket i.e expand it

ac-ab=d

make c the subject formula to get your answer

ac=d+ab

c=d+ab/a

He has enough money to buy all the paving stone for the rectangular garden.

The garden path is rectangular.

He wants to cover the path with a paving stone. The paving stone is square in shape and have side of 40 cm.

Therefore,

area of the square stone = l²

where

Therefore,

area of the square stone = 40²

area of the square stone = 1600 cm²

area of the rectangular garden = lw

where

Therefore,

area of the rectangular garden = 800 × 120

area of the rectangular garden = 96000

area of the rectangular garden = 96000 cm²

Therefore,

number of paving stone required = 96000 / 1600

number of paving stone required = 60

Hence,

cost of covering the path = 4.50 × 60 =  £ 270

Therefore, he has enough money to buy all the paving stone for the rectangular garden.

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Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Part (a)

r = radius

h = height = 5r

SA = Surface area of a cylinder

SA = 2pi*r^2 + 2pi*r*h

SA = 2pi*r^2 + 2pi*r*5r

SA = 2pi*r^2 + 10pi*r^2

SA = (2pi+10pi)*r^2

SA = 12pi*r^2

====================================================

Part (b)

r = radius

h = height = 5r

V = volume of a cylinder

V = pi*r^2*h

V = pi*r^2*5r

V = 5pi*r^3

Set this equal to the stated volume of 1715pi cubic cm and solve for r.

The pi terms cancel

So,

V = 5pi*r^3

1715pi = 5pi*r^3

1715 = 5r^3

r^3 = 1715/5

r^3 = 343

r = CubeRoot(343)

r = 343^(1/3)

r = 7

The board measures 212 inches which is equal to 17.7 feet.

Measurement:

Measurement is used to identify the quantity of the object.

Each object has its own measurements, like solid objects are measured using grams and the liquid one are measured using liters, etc.

For example,

We can buy the vegetables in grams because they are solid objects.

Instead, we have buy the milk in liters because they are liquid.

Given,

A board measures 212 inches.

Here we need to convert this into feet.

We know that,

1 inch = 0.0833333 feet.

So, 212 inches is equal to,

=> 212 x 0.0833333

=> 17.6667 feet.

Here we have to round the answer with one decimal place.

So, that is,

=> 17.7 feet.

Therefore, the board measurement in feet is 17.7 feet.

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Length of the side of cube is ( 3/10 ) ft and the area of two sides of cubical box that sabrina will cover is  ( 9/50 ) sq ft .

Length of the side of cube = s

The given volume of cubical box  = ( 27/1000 ) ft cubed         equation 1

Volume of Cubical box = [tex](length of cube side)^{3}[/tex]

Volume of Cubical box = [tex]s^{3}[/tex]                                          equation 2

On comparing equation 1 and equation 2 , we get

[tex]s^{3}[/tex] = ( 27 / 1000 )

s = ( 3 / 10 ) = 0.3 ft

Sabrina wants to completely cover two of the faces with labels, So we need to calculate the area of two sides of cubical box.

The area of two sides of cubical box = 2 [tex]s^{2}[/tex]

The area of two sides of cubical box = 2 ( 3/10 )² = ( 9 / 50 ) sq ft

Length of the side of cube is ( 3/10 ) ft and the area of two sides of cubical box that sabrina will cover is  ( 9/50 ) sq ft .

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Answer:

c

Step-by-step explanation:

The fact that Jesse is working out at a gym mean that Jesse has a membership to the gym. Therefore, this is a deductive reasoning.

It should be noted that the deductive reasoning is when one arrives at conclusion based on the information that was given earlier.

Based on the information given, it should be noted that one can only work out at the gym if the person has a membership. An individual without a membership will be unable to work out.

In this case, the fact that Jesse is working out at a gym mean that Jesse has a membership to the gym. Therefore, this is a deductive reasoning.

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Answer:

8i

Step-by-step explanation:

[tex] \sqrt{ {4}^{2} - 4(2)(10)} [/tex]

[tex] \sqrt{16 - 80} [/tex]

[tex] \sqrt{ - 64} = 8i[/tex]

Answer:

12

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

BODMAS

start with solving 2^2 which is similar to 2×2 you get 4

2^2=4

4+3 =7

The value of 't' that is nearest entire year is

18 years

Ian made a vehicle investment of $2500.

that would ensure an annual interest rate of 4%.

the function for this  A(t)=2500(1.04).

Find the value of t that makes the equation A(t)=5000 true, to the nearest whole year, using the tables on your calculator.

Give numerical support for your response.

Ian invested $2500

yearly interest 4%

function is A(t)=2500(1.04)

equation A(t)=5000.

[tex]A(t)=2500\times(1.04)^t[/tex]

A ( t ) = 5000

[tex]5000=2500\times(1.04)^t[/tex]

[tex](1.04)^t=5000:2500[/tex]

[tex](1.04)^t=2[/tex]

t = 17.68 ≈ 18

The value of t is 18 years.

Therefore, The value of 't' that is nearest entire year is

18 years

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Answer: 10 times more heavier.

The lateral area of the right octagonal prism is 672 square inches

The formula for lateral area of a right octagonal prism is expressed as;

Lateral area = 8ah

Where;

Substitute the values into the formula

Lateral area = 8 × 7 × 12

Multiply through

Lateral area = 672 square inches

Thus, the lateral area of the right octagonal prism is 672 square inches

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Answer:

∠ B = 23°

Step-by-step explanation:

vertical angles are congruent , so

∠ B = ∠ A , that is

5x - 17 = x + 15 ( subtract x from both sides )

4x - 17 = 15 ( add 17 to both sides )

4x = 32 ( divide both sides by 4 )

x = 8

Then

∠ B = 5x - 17 = 5(8) - 17 = 40 - 17 = 23°

Vertically opposite angles are equal

[tex]x + 15 = 5x - 17 \\ 15 + 17 = 5x - x \\ 32 = 4x \\ x = 8[/tex]

[tex] \sf \: \angle \: a = x + 15 = > 8 + 15 = 23 \degree[/tex]

[tex] \sf \: \angle \: b= 5x - 17 = > 5 \times 8 - 17 = > 40 - 17 = 23 \degree[/tex]

The distance between both the ship and the lighthouse's base is 328 feet.

If a line of sight is slightly down from the horizontal line, it forms an angle with the horizontal line. If the object being observed is below the observer's level, the angle formed between both the horizontal line and also the observer's lines of sight is known as the angle of depression.

Given the circumstances, a right angle triangle is constructed. The lighthouse's height represents the right angle triangle's opposite side.

The adjacent side of a right angle triangle is represented by the horizontal distance, h, between both the ship and thus the base of the lighthouse.

Because they are opposite angles, is if angle of depression to the fire is 26°, the angle of elevation of a lighthouse from the ship is also 26°.

To calculate h, we would use

the trigonometric tangent ratio;

Tan θ = opposite side/adjacent side. Therefore,

Tan 26 = 160/h

h = 160/tan26 = 160/0.4877

h = 328 feet

Therefore, the distance between the ship and the base of the light house is 328 feet.

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Explanation:

The given equation y = -4x+5 has a slope of -4. Compare it to y = mx+b and m is the slope.

Parallel lines have equal slopes, but different y intercepts. The answer will have a slope of -4.

The point we want the answer to go through is (x1,y1) = (0,4)

We'll plug the following values

into the point slope formula below. Solve for y.

y - y1 = m(x - x1)

y - 4 = -4(x - 0)

y - 4 = -4x

y = -4x+4 which is choice A

Answer:

y = 3/4 x - 1

Step-by-step explanation:

We can use the point-slope form of the equation of a line.

y - y_1 = (y_2 - y_1)/(x_2 - x_1)(x - x_1)

y - (-4) = (5 - (-4))/(8 - (-4))(x - (-4))

y + 4 = (9/12)(x + 4)

y + 4 = (3/4)(x + 4)

y + 4 = (3/4)x + 3

y = (3/4)x - 1