Solve the nonlinear inequality. Expr
x³-9x>0
(-3,0) U (3,00)
Graph the solution set.

How would I graph this on a number line ?

Answer:

8%: $295

10% : $6005

15%: $595

Step-by-step explanation:

Let's break this down:

Let's call the amounts invested at 8% and 10% combined = x
Then call the amount invested at 15% = x + $300
8% of x = 0.08x
10% of (6300 - x) = 0.1(6300 - x)
15% of (x + $300) = 0.15(x + $300)
0.08x + 0.1(6300 - x) + 0.15(x + $300) = $773
0.18x = $53
x = $53/0.18 = $295

a = amount invested at 8%

how much is 8% of "a"? (8/100) * "a", namely 0.08a.

b = amount invested at 10%

how much is 10% of "b"? (10/100) * "b", namely 0.10b.

c = amount invested at 15%

how much is 15% of "c"? (15/100) * "c", namely 0.15c.

we know the total amount invested is 6300, so whatever "a", "b" and "c" might be, we know that a + b + c = 6300.

we also know that the yielded amount in interest is 773, so if we simply add their interest, that'd be 0.08a + 0.10b + 0.15c = 773.

we also know that the combined amounts of "a + b" plus 300 bucks is "c", so really c = a + b + 300.

\(c = a + b + 300 \\\\[-0.35em] ~\dotfill\\\\ a+b+c=6300\implies c=6300-a-b\implies \stackrel{\textit{substituting from the equation above}}{a+b+300=6300-a-b} \\\\\\ 2a+2b+300=6300\implies 2a+2b=6000\implies 2(a+b)=6000\)

\(a+b=\cfrac{6000}{2}\implies a+b=3000\implies \boxed{b=3000-a} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{c = a + b + 300}\implies \stackrel{\textit{substituting from above}}{c=a+(3000-a)+300}\implies {\Large \begin{array}{llll} c=3300 \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{we also know that} }{0.08a+0.10b+0.15c=773}\implies \stackrel{\textit{now, substituting "b" and "c"}}{0.08a+0.10(3000-a)+0.15(3300)=773}\)

\(0.08a+300-0.10a+495=773\implies -0.02a+300+495=773 \\\\\\ -0.02a+795=773\implies -0.02a=-22\implies a=\cfrac{-22}{-0.02}\implies {\Large \begin{array}{llll} a=1100 \end{array}} \\\\\\ \stackrel{\textit{now, we know that}}{b=3000-a}\implies {\Large \begin{array}{llll} b=1900 \end{array}}\)

To write the height of Debbie as a fraction of the height of Leo in its simplest form is this: 17/18.

Writing one figure as a fraction of another can be done by representing the figures as numerators and denominators. In this case, what we will have is 85/90. That is the height of Debbie divided by the height of Leo.

To express this fraction in its simplest form will mean dividing the figures until they can no longer be divided. Using 5 as a common factor for dividing, we can conclude that the simplest form of the answer is 17/18.

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Answer:

6

Step-by-step explanation:

Let that number be x.

\(2x = 9 + 3\)

\(2x = 12\)

\(x = 6\)

Answer:

Step-by-step explanation:The line parallel to y = -2x + 5 that passes through the point(1,1)

Has the same slope, m but a different y intercept (0,b)

So lets start by using the given point (1, 1) and the slope intercept form of the line to calculate b

y = mx + b

m = -2

1 = -2(1) + b

1 = -2 + b

Add 2 to both sides of the equation to solve for b

1 + 2 = b

3 = b

The line is

y = -2x + 3

Answer:

Step-by-step explanation:

The angle of depression is the downward angle the air traffic controller

looks down from in the tower.  It also equals the angle of elevation which is the angle formed by the runway and the line of sight.

With this information you can find the remaining angle:

180 - (90 + 18)

180 - 108 = 72

Let Angle B = 72°

Angle A = 18°

Angle C =90°

We have one side - 140 feet - this is side a - it is across from angle A.

There is a right triangle formed by the runway (side b) the tower, side a, and the line of sight (side c)

Using the law of sines:

sin A/a = sinB/b

sin 18°/a = sin72°/b

.3090/140 = .9510/x

cross multiply and then divide

140 × .9510/.3090

133.14/.3090

430.873 ft

round to a tenth = 430.9 ft

Answer:

x = 10

Step-by-step explanation:

I don't really get what you mean, so I just solved for x.

1/2x-2=3

We add 2 on both sides.

1/2x=5

Times both sides by 2 to cancel out the 1/2

x=10.

Hope this helped. :)

(sorry if I didn't do what you wanted me to.)

The statement that is true about the function is:

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

Given:

The minimum value of the curve = (1.9, -5.7),

The maximum value = (0, 2)

The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)

The point the function crosses the y-axis (the y-intercept) = (0, 2)

The given points can be plotted using MS Excel, from which we have:

F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5.

Hence, the correct option is A.

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69200000 in scientific notation is  6.92 × 10⁷.

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.

Scientific Notation is a special way of writing numbers:

For example 800 is written as 8 × 10² in Scientific Notation.

Therefore, let's write the scientific notation of the number 69200000.

Hence,

69, 200, 000 = 6.92 × 10⁷

The logic is that we will count backwards until we meet the last number. Since we counted towards the left side, the exponent will be positive.

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Step-by-step explanation:

Slope is 1/3 while the intercept is 10/3

These symbolic representations use the symbols ∧ (and) to indicate that all conditions must be true, ∨ (or) to indicate that at least one condition must be true, and ¬ (not) to negate a statement.

Using the given symbols ∧ (and), ∨ (or), and ¬ (not), we can represent the statements as follows:

Let h = "John is healthy," w = "John is wealthy," and s = "John is wise."

John is healthy and wealthy but not wise.

Symbolic form:

h ∧ w ∧ ¬s

John is not wealthy but he is healthy and wise.

Symbolic form:

¬w ∧ h ∧ s

John is neither healthy, wealthy, nor wise.

Symbolic form:

¬h ∧ ¬w ∧ ¬s

John is neither wealthy nor wise, but he is healthy.

Symbolic form:

¬w ∧ ¬s ∧ h

John is wealthy, but he is not both healthy and wise.

Symbolic form:

w ∧ (¬h ∨ ¬s)

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The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.

Let's suppose its initial term is a , multiplication factor is  r and let it has total n terms,

then, its sum is given as:

\(S_n = \dfra\)\(\dfrac{a(r^n-1)}{r-1}\)

(sum till nth term)

Given geometric sequence;

85 +85(.9) +85(.9)² + ...

a = 85

r = 0.9

its sum is given as:

\(S_n = \dfra\)\(\dfrac{a(r^n-1)}{r-1}\)

\(S_n = \dfrac{85(0.9^5-1)}{0.9-1}\\\\S_n = \dfrac{85(0.5904-1)}{-0.1}\\\\\\S_n = \dfrac{85(-0.4095)}{-0.1}\\\\S_n = 348.08\)

Thus,

The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.

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Answer:

Here are the angles in each quadrant with a common reference angle of 165°:

First quadrant: angle is 15° (subtract 165° from 180°)

Second quadrant: angle is 195° (subtract 165° from 180° and add the result to 180°)

Third quadrant: angle is 195° (subtract 165° from 180° and then subtract the result from 180°)

Fourth quadrant: angle is 195° (subtract 165° from 360°)

Answer:

\(-3(t+1)(8t-3)\)

Step-by-step explanation:

First, factor both the denominators completely:

\(9-24t\\= 3(3-8t)\\= 3(-8t+3)\\= -3(8t-3)\)

\(8t^2+5t-3\\= 8t^2+8t-3t-3\\= 8t(t+1)-3(t+1)\\= (8t-3)(t+1)\)

Now, we can see that the factors of the first denominator are -3 and 8t-3.

The factors of the second denominator are t+1 and 8t-3.

To find the LCD, multiply all of these factors together:

\(-3(t+1)(8t-3)\)

Notice how we only multiply 8t-3 in the equation once. This is because it was present in both denominators, unlike the other factors.

I hope this helps!

The solution is: Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1, the following functions is graphed below.

Option C is correct.

Explanation:

We are given a graph of piece-wise function which break at x=1

We need to choose correct option for graph.

Function is break at x=1.

We will get two function

For x≤1 and x>1

As we can see x≤1, graph is linear and x>1 graph is parabolic.

Equation of linear graph, x≤1

Take two point of graph (0,6) and (-6,0)

Equation of line:

y-y1/y2-y1 = x-x1/x2-x1

y = x+1

f(x)=x+6 , x≤1

Equation of parabolic graph, x>1

f(x) = x^2 + 3

Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1

Please see the attached figure.

Hence, The option C is correct.

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Answer:

95

Step-by-step explanation:

Answer:

95

Step-by-step explanation:

Answer:

b ≤ -26

Step-by-step explanation:

3(b+16) ≤ -30

3b + 48 ≤ -30

3b ≤ -78

b ≤ -26

The ordered pairs for the equation y = -7x + 8 are (0, 8), (1, 1), and (-1, 15).

To find ordered pairs for the equation y = -7x + 8, we can substitute different values of x and solve for y.

Let's choose three values of x:

When x = 0, y = -7(0) + 8 = 8. So one ordered pair is (0, 8).

When x = 1, y = -7(1) + 8 = 1. So another ordered pair is (1, 1).

When x = -1, y = -7(-1) + 8 = 15. So another ordered pair is (-1, 15).

Therefore, the ordered pairs  are (0, 8), (1, 1), and (-1, 15).

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Answer:

x=-1

Step-by-step explanation:

x+11+x+13=22

2x+24=22

2x=-2

x=-1

The equation that represent the gross pay is y = 0.12x + 1760. The commission was $10896 and gross pay was $12656

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Let y represent the gross pay for x total sales.

Donald Simmons a $1760 monthly salary plus a 12% commission on merchandise he sells each month, hence:

y = 1760 + 12% of x

y = 0.12x + 1760

Donald's sales were $90,800 for last month. Hence:

a) Commission = 0.12 * $90800 = $10896

b) Gross pay:

y = 10896 + 1760 = $12656

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Area of centre rectangle

Area of right rectangle

Area of triangle

Total

The expression for h(x) is,

⇒  h (x) = √(x - 2) + 4

Now, Given that;

Initially the graph f (x) is shifted horizontally to the right.

When the graph shifts to right the function then becomes

f (x) → f (x-b)

Where b is the units by which it is shifted towards right .

So, in the figure we can see that it is shifted 2 units to the right .

So, f(x) → f(x-2)

Since f(x) is,

⇒ f (x) = √x

So, f (x-2) = √x - 2

Now, the new obtained graph is again shifted vertically upward

When the graphs shifts upward;

⇒ f(x) → f(x) + b

where b is the units by which it is shifted upward

So, our obtained f(x-2) when shifted upward by 4 units so using the above given transformation of upward shift

i.e. f(x) → f(x) + b

So, Our new graph h(x) = f(x-2) + 4

⇒  h (x) = √(x - 2) + 4

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The answers isssssssss

$300

:)

The representation table given indicates that the function is linear, as the difference between consecutive y-values (9-8, 8-7, and 7-6) is constant. Therefore, we can represent the function with a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of the function, we can use the x- and y-values given in the table to solve for m and b. For example, using the x- and y-values (-3,9) and (-2,8), we can solve the equation 9 = m(-3) + b for m and b:

9 = -3m + b

8 = -2m + b

Subtracting the second equation from the first equation gives us:

1 = -m

So the slope of the function is -1. Substituting this value back into either equation gives us:

9 = -3(-1) + b

9 = 3 + b

6 = b

So the y-intercept of the function is 6. Therefore, the equation of the function is y = -1x + 6.

The other two representations can be solved in the same way to find the equations of those functions.

Answer: Triangle 1 = 30 m2

Triangle 2 = 15 cm2

Step-by-step explanation:

Triangle area formula = 1/2 x base x height

Area1 = 1/2 x 10 x 6

= 30

Area2 = 1/2 x 6 x 5

= 15

Answer:

The area of the triangle is 15 cm and rectangle is 30 or 60

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

sense its between -2 and -4

*question

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer:

a)  \(\frac{2}{3} \,\frac{lb}{bread}\)

b)  \(1\frac{1}{4} \,\frac{in}{domino}\)

Step-by-step explanation:

Part a:

every 4 lbs of flour, she makes 6 loaves of bread. this as a rate in simplest fraction form is:

\(\frac{4}{6} \,\frac{lb}{bread} = \frac{2}{3} \,\frac{lb}{bread}\)

Part b:

every 10 inches , 8 dominoes can be placed. then the rate can be written as:

\(\frac{10}{8} \,\frac{in}{domino} = \frac{5}{4} \,\frac{in}{domino} =1\frac{1}{4} \,\frac{in}{domino}\)