Question 3 (2 marks)
Reginald is a furniture salesman. He is paid a weekly retainer of $370 plus 4.5% of the
value of furniture he sells. Calculate his income for a week when he sells $67 000 worth
of furniture.
752 words
09 English (Australia)
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Answer: 86

Step-by-step explanation:

This is a cyclic quadilateral in which opposite angles adds upto 180.

Let the unknown angle be x

ATQ

x + 94 = 180

x = 180 - 94

x = 86

please click thanks and mark brainliest if you like :)

Answer:

5/9

Step-by-step explanation:

In short, the absolute value of a number turns that number into a positive value no matter what. Here is a small representation:

Negative -> Positive

Positive -> Positive

Since we are working with a negative value, it will turn positive.

Best of Luck!

Answer:

C

Step-by-step explanation:

using the theorem of Pythagoras

x = sqrt * 10.2^2 - 9.6^2 *

using the calculator

x = 3.4 units

rounded to 1 decimal place

Answer:

R35625

Step-by-step explanation:

(R30,000×.125×18/12)+R30000

=R35625

Answer:

d) 6

Step-by-step explanation:

natural number = +ve numbers, so -1/2 is out

4.9 and π arent whole numbers nor intergers

Answer:

31 PTS

Step-by-step explanation:

Answer:

The mean is about 68 (67.5555)

Step-by-step explanation:

(63+64+66+66+67+68+69+71+74) / 9 ≈ 68

Answer:

15 months old.

Step-by-step explanation:

Let m = months and h = height:

h = 1/3(m + 75) ⇔ h = 1/3m + 25

Let h = 30:

[tex]30=\frac{1}{3}m+25\\5=\frac{1}{3}m\\15=m[/tex]

Therefore, when Asia is 30 inches tall, she will be 15 months old.

Answer:

hello thereeeee

ans is 23.5

Step-by-step explanation:

so lets start

first of all remove decimal of divisor 1.1/25.85 multiplying by 10

11/258.5

now first multiply by 2

now we get 22 and subtract with 25 => 25-22 = 3

so left is

38

now 11*3 = 33

so now by 3

38-33= 5

bringing another 5 down

we get 55

now quotient is 23. something ( as we bought .5 down)

and now 11*5 = 55

so

23.5 is answer

Answer:

2 sin(2x)

Step-by-step explanation:

sin x stretched vertically by a factor 2 and compressed horizontally by a factor 2.

The solution is : A. y = cos(x) - 2, is the equation of the sinusoidal function shown.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

The word "sinusoid" means the graph has a shape of the sine function that smoothly goes up and down.

so, we get,

However, the cosine function also has the same shape but the only thing is that it is horizontally translated. Thus, the cosine function is the sinusoid.

Hence, The solution is : A. y = cos(x) - 2, is the equation of the sinusoidal function shown.

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9514 1404 393

Answer:

  1 11/49 ≈ 1.224 miles

Step-by-step explanation:

Let m represent the length of the morning walk. Then the length of the evening walk is 2.5m, and the total each day is m+2.5m = 3.5m.

The total for 7 days is ...

  7(3.5m) = 30

  m = 30/24.5 = 60/49 ≈ 1.224 . . . . miles

Mia's morning walks are 1 11/49 miles, about 1.224 miles.

Answer:

0

Step-by-step explanation:

for y= -2*(3^x), as x is greater, the slope is steeper, and since the two graphs don't intercept in the picture we can see, they won't ever intercept because the slop of y=-2x+3 stays the same. as x becomes greater the distance between the two graphs is larger

Answer:

Hello,

Step-by-step explanation:

This a method knowing nothing.

1+3+5+7+9=25

425-25=400

400/5=80

Numbers are 80+1,80+,80+5,80+7,80+9 whose sum is 425.

Answer:

Differentiation is concerned with things like speeds and accelerations, slopes and curves ect. These are Rates of Change, they are things that are defined locally. The Fundamental Theorem of Calculus is that Integration and Differentiation are the inverse of each other.

Answer:

12

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

PC * PA = PB^2

(PA+AC) * PA = PB^2

(4+32) * 4 = PB^2

36*4 = PB^2

144 = PB^2

Taking the square root of each side

sqrt(144) = sqrt(PB^2)

12= PB

Answer:

a

Step-by-step explanation:

Given a tangent and a secant to a circle from an external point, then

The square of the tangent is equal to the product of the external part and the whole of the secant , that is

PB² = PA × PC = 4(4 + 32) = 4 × 36 = 144 ( take square root of both sides )

PB = [tex]\sqrt{144}[/tex] = 12 → a

Answer: (7, 20)

Concept:

There are three general ways to solve systems of equations:

Since the question has specific requirements, we are going to use substitution to solve the equations.

Solve:

Given equations

y = 3x - 1

2x + 6 = y

Substitute the y value since both equations has isolated [y]

2x + 6 = 3x - 1

Add 1 on both sides

2x + 6 + 1 = 3x - 1 + 1

2x + 7 = 3x

Subtract 2x on both sides

2x + 7 - 2x = 3x - 2x

[tex]\boxed{x=7}[/tex]

Find the value of y

y = 3x - 1

y = 3(7) - 1

y = 21 - 1

[tex]\boxed{y=20}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

2x^2+4x-16

Step-by-step explanation:

The quadratic can be written as

f(x) = a(x-z1)(x-z2) where z1 and z2 are the roots

f(x) = a (x-2)(x- -4)

a is the leading coefficient

f(x) = 2(x-2)(x+4)

     = 2(x^2 -2x+4x-8)

     = 2(x^2 +2x-8)

     = 2x^2 +4x-16

Answer:

No.

Step-by-step explanation:

Using the order of operations:

4 · 6 - 4 = 20 (Multiplication is done first.)

4 · (6 - 4) = 8 (Parentheses is done first.)

Answer:

750,. is answer

I hope it helps

Answer:

401 more people per square mile

Step-by-step explanation:

Find how many people there are per square mile in both cities by dividing the number of people by the number of square miles:

672,800/142.9

= 4708 people per square mile (Detroit)

195,100/45.3

= 4307 (Grand Rapids)

Find how many more people per square mile live in Detroit by finding the difference between these two numbers:

4708 - 4307

= 401

So, there are 401 more people per square mile living in Detroit versus Grand Rapids.

Answer:

The state can issue 456,976,000 license plates.

Step-by-step explanation:

For digits, it is assumed that we can use 0-9. Thus, there are 10 options for each slot with a digit.

For letters, it is assumed that we can use the 26 letters of the alphabet (i.e. A through Z). Thus, there are 26 options for each slot with a letter.

For this particular problem, the slot method can be used. Assuming that repetition of letters/digits is allowed:

[tex]\frac{10}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{10}[/tex] [tex]\frac{10}[/tex]

= 10*26*26*26*26*10*10

=456,976,000.

Therefore, the state can issue 456,976,000 license plates.

Answer:

32%

Step-by-step explanation:

The slope of the road is measured as

slope = [tex]\frac{rise}{run}[/tex] = [tex]\frac{16}{50}[/tex]

To express as a percentage multiply the fraction y 100% , that is

slope = [tex]\frac{16}{50}[/tex] × 100% = 16 × 2 = 32%

Answer: (x+4) ( x-4i)(x+4i)

Discussion:

Factor the polynomial:

x^3+4x^2+16x+64 =  (x +4 ) ( x^2 + 16)     (*)

Factor x^2 +1 6 over the complex numbers:

x^2 + 16 = (x -4i)(x+4i)                               (**)

Combing (*) and (**) gives the full factorization

(x+4) ( x-4i)(x+4i)

After completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].

"It is a polynomial equation with degree two."

"It is a method that is used for converting a quadratic expression of the form [tex]ax^2 + bx + c[/tex] to [tex]a(x - h)^2 + k[/tex] "

For given example,

We have been given a quadratic equation.

[tex]3x^{2} -12x-15=0[/tex]

First we divide above quadratic equation by 3,

[tex]x^{2} -4x-5=0\\\\x^2-4x=5[/tex]                             ................(i)

Now for completing the square first find [tex](\frac{-b}{2a} )[/tex]

[tex]\frac{-b}{2a}\\=\frac{-(-4)}{(2)(1)}\\\\ =\frac{4}{2}\\\\ =2[/tex]

Add [tex](\frac{-b}{2a} )^2[/tex] on both the sides of equation (i),

[tex]x^{2} -4x+4=5+4\\\\(x-2)^2=9\\\\(x-2)^2=3^2[/tex]

Therefore, after completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].

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Answer:

[tex]\displaystyle F(b + 3) = b^2 + 4b + 7[/tex]

Step-by-step explanation:

We are given the function:

[tex]\displaystlye F(x) = x^2 - 2x + 4[/tex]

And we want to find F(b + 3).

We can substitute:

[tex]\displaystyle F(b + 3) = (b + 3)^2 - 2(b+3) + 4[/tex]

Expand:

[tex]\displaystyle = (b^2 + 6b + 9) + (-2b -6) + 4[/tex]

Rearrange:

[tex]\displaystyle = (b^2) + (6b-2b) + (9 - 6 + 4)[/tex]

Combine like terms. Hence:

[tex]\displaystyle = b^2 +4b + 7[/tex]

In conclusion:

[tex]\displaystyle F(b + 3) = b^2 + 4b + 7[/tex]

Answer:

Remainder is -53/8

Step-by-step explanation:

the divisor is (2x - 3):

make x the subject:

[tex]2x - 3 = 0 \\ 2x = 3 \\ x = \frac{3}{2} [/tex]

substitute for x in the function:

[tex]f(x) = {x}^{3} - 6 {x}^{2} + 3x - 1 \\ f( \frac{3}{2} ) = {( \frac{3}{2}) }^{3} - 6 {( \frac{3}{2}) }^{2} + 3( \frac{3}{2} ) - 1 \\ \\ f( \frac{3}{2} ) = \frac{ - 53}{8} [/tex]

Answer:

21.9 ft

Step-by-step explanation:

Answer:

Part A)

About 74.2°.

Part B)

About 21 feet.

Step-by-step explanation:

A 22 feet ladder is leaning against a building, where the base of the ladder is six feet from the base of the building.

This is shown in the diagram below (not to scale).

Part A)

We want to determine the angle of elevation of the ladder. That is, we want to find the value of θ.

Since we know the values adjacent to θ and the hypotenuse, we can use the cosine ratio. Recall that:

[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]

The adjacent is 6 and the hypotenuse is 22. Thus:

[tex]\displaystyle \cos \theta = \frac{6}{22} = \frac{3}{11}[/tex]

Take the inverse cosine of both sides:

[tex]\displaystyle \theta = \cos^{-1}\frac{3}{11}[/tex]

Use a calculator. Hence:

[tex]\displaystyle \theta = 74.1733...\approx 74.2^\circ[/tex]

The angle of elevation is approximately 74.2°

Part B)

We want to find how high up the ladder reaches on the building. In other words, we want to find x.

Since x is opposite to θ and we know the adjacent side, we can use the tangent ratio. Recall that:

[tex]\displaystyle \tan \theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]

The opposite side is x and the adjacent side is 6. The angle θ is cos⁻¹(3/11) (we use the exact form to prevent rounding errors). Thus:

[tex]\displaystyle \tan \left(\cos^{-1}\frac{3}{11}\right) = \frac{x}{6}[/tex]

Solve for x:

[tex]\displaystyle x = 6 \tan \left(\cos^{-1}\frac{3}{11}\right)[/tex]

Use a calculator. Hence:

[tex]x = 21.1660... \approx 21\text{ feet}[/tex]

The ladder reaches about 21 feet up the building.

Answer:

990/23

Step-by-step explanation:

Step 1

Multiply the denominator by the whole number

23 × 43 = 989

Step 2

Add the answer from Step 1 to the numerator

989 + 1 = 990

Step 3

Write answer from Step 2 over the denominator

990/23