What is this expression in simplified form 5/2 times 9/6? A.90 B.90/3 C.45/2 D. 45/3

Following the instructions for the inequalities gives the following results:

1. 4<7, both sides multiplied by 7

= 28<49, both sides multiplied by 6

= 168<294, both sides multiplied by 3

= 504<882, both sides multiplied by 10

= 5,040<8,820

2. 11>2, add 5 to both sides

= 16>3, add 3 to both sides

= 19>9, add -4

= 15>5

3. -4<-2, subtract 6

= -10<-8, subtract 8

= -18<-16, subtract 2

= -20<-18

4. -8<8, divide by -4

= 2>-2, divide by -2

= -1<1

5. The inequalities remain correct at the end because the same mathematical operations are performed on both sides simultaneously.

Inequality is a relationship of a non-equal comparison between two numbers or algebraic expressions.

Inequality can be represented as greater than, greater than or equal to, less than, or less than or equal to.

Thus, the rules for inequalities show that if one adds to, subtracts from, multiplies by, or divides by the same number on both sides of an inequality, the inequality remains true.

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Answer:

x = - 4

Step-by-step explanation:

using the rule of indices

[tex]\frac{1}{a^{n} }[/tex] = [tex]a^{-n}[/tex] , then

[tex]3^{x}[/tex] = [tex]\frac{1}{81}[/tex] = [tex]\frac{1}{3^{4} }[/tex] = [tex]3^{-4}[/tex] , that is

[tex]3^{x}[/tex] = [tex]3^{-4}[/tex] , thus

x = - 4

Answer:

five-hundredths

Step-by-step explanation:

Answer:

We call the denominator rational.

Step-by-step explanation:

For example:

[tex]\frac{1}{\sqrt{2}} = \frac{\sqrt2}{\sqrt2 \cdot \sqrt2} = \frac{\sqrt2}{2}[/tex]

It's clear that the denominator is now a rational number, not an irrational one anymore.

Answer:

A, C

Step-by-step explanation:

See attached image.

Answer:

2/3rds of liad's run

Step-by-step explanation:

3 min 45s = 3 3/4 min = 15/4 min; 10/(15/4) = 8/3 laps

2min 30s = 2 1/2 min = 5/2 min; 10/(5/2) = 4 laps

(8/3)/4 = 2/3

a) The slope of the secant lines are: q = 5, f(q) = 2,076: m = - 131.1, q = 10, f(q) = 1,299: m = - 106.8, q = 20, f(q) = 357: m = - 81.6, q = 25, f(q) = 84: m = - 68.1, q = 30, f(q) = 0: m = - 51.

b) The estimated slope of the line tangent to the curve at the point (x, y) = (15, 765) is - 94.2 gallons per minute.

In this problem we must determine the slope of several lines based on the information given by the table and using the secant line formula:

m = [f(q) - f(p)] / (q - p)     (1)

If we know that a = 15 and p = 765, then the slope of the secant lines are:

q = 5, f(q) = 2,076

m = [2,076 - 765] / (5 - 15)

m = - 131.1

q = 10, f(q) = 1,299

m = [1,299 - 765] / (10 - 15)

m = - 106.8

q = 20, f(q) = 357

m = [357 - 765] / (20 - 15)

m = - 81.6

q = 25, f(q) = 84

m = [84 - 765] / (25 - 15)

m = - 68.1

q = 30, f(q) = 0

m = [0 - 765] / (30 - 15)

m = - 51

The slope of the line tangent to the curve at the point (x, y) = (15, 765) can be estimated by averaging the slopes of the closest secant lines:

m' = [(- 106.8) + (- 81.6)] / 2

m' = - 94.2

The estimated slope of the line tangent to the curve at the point (x, y) = (15, 765) is - 94.2 gallons per minute.

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Answer:

3 :8

Step-by-step explanation:

12 : 32 = 3:8

I believe that is right.

Answer: x = 9

Step-by-Step Solution:

Hypotenuse = 15 units

Base = 12 units

Altitude = x units

Using Pythagoras Theorem,

=> Hypotenuse^2 = Base^2 + Altitude^2

(15)^2 = (12)^2 + x^2

225 = 144 + x^2

225 - 144 = x^2

81 = x^2

x^2 = 81

x = √81

=> x = 9

Therefore, Altitude = 9 units

Answer: C. 5.4 Blocks

Step-by-step explanation:

Given information

5 bags = 3 blocks

Set variable

Let x be the number of blocks

Constructure proportional equation

[tex]\frac{3}{5} } ~=~\frac{x}{9}[/tex]

Cross multiply the fraction

[tex](3)~*~(9)~=~(5)~*~(x)[/tex]

[tex]27~=~5x[/tex]

Divide 5 on both sides

[tex]27~/~5~=~5x~/~5[/tex]

[tex]\Large\boxed{x=5.4~blocks}[/tex]

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Answer:

oc

Step-by-step explanation:

5 times .6 equals 3

9 times .6 equals 5.4

An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B

The term triangle refers to a figure that has three sides. There are several types of triangles such as the;

Despite all these types of triangle, the basic geometric properties of triangles can be applied to all types of triangle that we have mentioned above.

Considering the question, an equation that could be used to represent one of the exterior angles and a logical conjecture about the exterior angles of a triangle is that; m<4 = m<1 + m<2. An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B

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Answer:

6x⁴ - 2x² +3

Step-by-step explanation:

[tex]\frac{12x^6-4x^4+6x^2}{2x^2}=6x^4 - 2x^2 + 3[/tex]

Given the measure of side a, b and c of the triangle, the measure of angle C to the nearest tenth is 104.5°.

From the law of cosines;

cosC = ( a² + b² - c² ) / 2ab

Where C is the angle C and a, b, and c are the three sides of the triangle.

Given the data in the question;

Using law of cosine;

cosC = ( a² + b² - c² ) / 2ab

We substitute the values into the equation.

cosC = ( 2² + 3² - 4² ) / ( 2 × 2 × 3 )

cosC = ( 4 + 9 - 16 ) / ( 12 )

cosC = -3 / 12

cosC = -0.25

We find the inverse of cosine.

C = cos⁻¹( -0.25 )

C = 104.477°

C = 104.5°

Given the measure of side a, b and c of the triangle, the measure of angle C to the nearest tenth is 104.5°.

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First find volume of both the cylinders:

Cylinder Volume Formula: πr²h

(r => radius, h => height)

*Container A:

r = 8

h = 15

πr²h = π(8)²(15) = 960π³

*Container B:

r = 11

h = 13

πr²h = π(11)²(13) = 1573π³

What % of container B is empty after the pumping is complete?

The water pumped from A to B, and we want to know remaining that is empty: A < B: 1573π³- 960π³ = 613π³. Now to find %:

[tex]\frac{613\pi^{3} }{1573\pi ^{3}} * 100 = 0.39 * 100 =[/tex] 39% or 40% (Nearest Tenth)

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Based on the time taken by the jet when flying with the wind versus against it, the rate of the jet and jet streams are:

The speed of the jet flying against the wind is:

= 3,000 / 3

= 1,000 mph

The speed with the jet stream is:

= 5,360 / 4

= 1,340 mph

Assuming the speed of the jet is x and the rate of wind is y, the formulas are:

x - y = 1,000

x + y = 1,340

Solving gives:

2x = 2,340

x = 1,170 mph

The rate of jet stream is:

x - y = 1,000

1,170 - y = 1,000

y = 170 mph

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Mathematical expression involves an equation that may consist of numbers only or combined with alphabets, which may also be given in the form of a statement. Therefore the required statement in the question is option C. Add 3 to the product of one-fourth and 8, then divide by 5.

Mathematical expression involves an equation that may consist of numbers only or combined with alphabets, which can be given in the form of a statement. When a given expression consists of both numbers and alphabets, then it forms an algebraic expression. It can also be given in the form of a statement.

Given in the question:

([tex]\frac{1}{4}[/tex] x 8 + 3) ÷ 5

This can be given in a statement form as; Add 3 to the product of one-fourth and 8, then divide by 5.

The appropriate statement that describes the given expression is: Add 3 to the product of one-fourth and 8, then divide by 5 i.e Option C.

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Part (a)

[tex]z=\frac{85-75}{11.4} \approx \boxed{0.88}[/tex]

By similar logic, the answers to the other parts are

(b) 1.75

(c) -2.19

(d) 0

Answer:

The answer is 2970

Step-by-step explanation:

Collectively, all the students can make about 54 books rds per minute (27 * 2)

Therefore in 55 minutes there should be 2970

(54*55) :)

The domain and range of the given graphs are as follows,

(b) Domain: x ∈ (-∞, ∞), Range: y ∈ (-∞, ∞)

(c) Domain: x ∈ [-2, ∞), Range: y ∈ [1, ∞)

Determining the Domain and Range from a Graph

The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The various output values are represented on the y-axis as the range.

Thus, in graph (b),

Since the values of the given curve extends infinitely (denoted by arrowhead of the curve) on positive as well as negative sides for both the axes, x and y, its domain and range both are (-∞, ∞).

Similarly, in graph (c),

The minimum value on x-axis or abscissa is -2 and maximum is infinity. Hence, its domain is [-2, ∞). The minimum ordinate value or y-coordinate is 1 and maximum is infinity. Thus, its range is [1, ∞).

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Step-by-step explanation:

b + 35° = 180° ( supplementary angle )

b = 180° - 35°

b = 145°

Answer: [tex]\Large\boxed{b=145^\circ}[/tex]

Step-by-step explanation:

Given information

∡1 = 35°

∡b = ?

Total Angle = 180° (Supplementary Angle)

Derived formula from the given information

∡1 + ∡b = Total Angle

Substitute values into the given formula

(35) + b = 180

Subtract 35 on both sides

35 + b - 35 = 180 - 35

[tex]\Large\boxed{b=145^\circ}[/tex]

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Answer:

250.

Step-by-step explanation:

if one coin covers 1.14 cm, then the required number can be calculated according the equality:

required_number=(given_length/given_diameter);

Then:

[tex]number=\frac{2.85*100}{1.14} =\frac{285}{1.14} =250[coins].[/tex]

P.S. note, the given length is in [meter], the diameter is in [cm].

Answer:

810 is the number that represents the same amount.

Hope this helps :)

The decimal notation for the given value in scientific notation is 215400.

Very large or very small numbers are denoted in scientific notation to simplify complex calculations.

The scientific notation is represented by: a × 10ⁿ

Wher a - any number or decimal number

n - the power of 10; it is an integer number

To convert this into decimal notation,

The given number is in the scientific notation,

2.154 × 10⁵

Since the power of 10 is positive, the decimal point in the number 2.154 moves towards the right. I.e,

2.154 × 10⁵ = 215400

Here power is 5. So, the decimal point moved five places to the right.

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Answer:

36

Step-by-step explanation:

75/100

75/100=0.75

0.75*48 =36

Since the values on both sides are equal, hence the system of equation given has no solution

Simultaneous equations are equations that consists of two or more equation and unknowns.

Given the equation below

2х+4у=4

x + 2y = 3

​

From equation 2;

x = 3 - 2y

Substitute into equation 1

2(3-2y) + 4y = 4

Expand

6 - 4y + 4y = 4

6 = 4

Since the values on both sides are equal, hence the system of equation given has no solution

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The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.

In this problem we have a cubic equation and the nature of their roots must be inferred according to a algebraic method.

Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, there is a method to infer the nature of the roots of such polynomials: The discriminant from Cardano's method, an analytical method used to solve polynomials of the form a · x³ + b · x² + c · x + d = 0.

The discriminant is described below:

Δ = 18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d²      (1)

Where:

If we know that a = 1, b = 2, c = 4 and d = 8, then the nature of the roots is:

Δ = 18 · 1 · 2 · 4 · 8 - 4 · 2³ · 8 + 2² · 4² - 4 · 1 · 4³ - 27 · 1² · 8²

Δ = - 1024

The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.

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