Multiply. (-4/3) * (-3/5) Write your answer in simplest form.

Using the pythagoras theorem to set the appropriate hypotenuse, perpendicular and base to make a right angled triangle, the correct option the would for a right angled triangle would be option c i.e 2, 2, [tex]\sqrt{8}[/tex].

A right angled triangle is a triangle in which one of the angles is a right angle (90 degrees). The side opposite the right angle is called the hypotenuse and the other two sides are called the legs or catheti. The two legs are perpendicular to each other and the hypotenuse is the longest side of the triangle. The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, applies to all right-angled triangles.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs or catheti). This can be written as: c^2 = a^2 + b^2 where c is the length of the hypotenuse, and a and b are the lengths of the legs.

So applying the pythagorean theorem on  provided options to choose the best option for making a right angled triangle, we find that the option c suites best to form a right angled triangle as show below,

[tex](\sqrt{8}) ^{2} = 2^{2}+2^{2}[/tex] , which satisfies the equation.

i.e 8 = 8

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The efficiency of the motor rated at 2.0 hp and delivering only 1.6 hp to a transmission system is 75%

Efficiency of the machine is the ratio of the work input to the machine to the work output of the machine\

This represented mathematically as

= work input / work output * 100 / 1

Form the problem we have that

work input = motor rated at 1.5 hp

work output = motor rated at 2.0 hp

Efficiency = 1.5 / 2.0 * 100 / 1

Efficiency = 0.75 * 100 / 1

Efficiency = 75%

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Answer:

b = 4

Step-by-step explanation:

Solve for b?

1/2b + 9 = 11     Subtract 9 from both sides

1/2b = 11 -9

1/2 b = 2    Multiply both sides by 2

b = 4

16 potatoes

according to the question:

we can formulate it as, (12*4)/3

= 48/3= 16

use the BODMAS rule to solve

that is Brackets Of Division Multiplication Addition Subtraction

so first (12*4) will be calculated.

multiply means adding equal groups

the first value that is used to multiply is called the multiplicand (12)

the second value that is been multiplied is called the multiplier. (4)

the result that we get when we multiply the multiplicand and the multiplier is called the product. (48)

then, divide the product with the denominator

48/3

The division is the process of splitting a specific amount into equal parts.

therefore, 16 potatoes are there.

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The cost-area proportional situations are:

The cost-area non-proportional situation is:

The situation where there is no enough information is

As a general rule:

Proportional situations are situations that can be represented as unit rates

When represented as a graph, they pass through the origin as in graph (d)

Other possible scenarios are:

The information in (b) a concrete patio quoted at a bulk cost for 50 square feet is incomplete because it does not state if the bulk cost is a unit rate

Other scenarios are non-proportional

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Answer:

4.5 meters

Step-by-step explanation:

If the pins were placed 30 cm apart, and there were a total of 15 pins, then the length of the string is 30 cm * 15 pins = <<30*15=450>>450 cm.

To convert this length to meters, we divide the number of centimeters by 100: 450 cm / 100 = 4.5 meters.

Therefore, the length of the string is 4.5 meters.

Answer:

5mg/kg

Step-by-step explanation:

1/5 of 25 = 5

The inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

Inverse of a function can be calculated by following the steps mentioned below -

According to the question, the equation given is as follows

y = f(x) = 2x + 5

y = 2x + 5

Replace 'y' with 'x', we get -

x = 2y + 5

Now, solve for y -

2y = x - 5

y = (x/2) - (5/2)

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = (x/2) - (5/2)

Hence, the inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

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The answer choice which represents a statement which is false among the given answer choices as required to be determined is; Choice B; Complementary and supplementary angles must share a common side.

It follows from the task content that the statement which represents na false statement is to be identified among the given answer choices.

First, acute angles have measures between 0 and 90° and hence, Choice C is correct.

Also, vertical angles are congruent and their measures are equal. Choice D is true.

Also, it is noteworthy to know that; If two supplementary angles are adjacent to each other; then they are called linear pair. Hence, Choice A is correct.

However, complementary and supplementary angles are angles whose sum amount to 90 and 180 respectively and do not necessarily need to share a side.

Therefore, Choice B represents a statement which is false.

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The number of pounds of food that the pig ate every day, given that it was the same amount of food daily, was 3. 94 pounds per day

To find the food that the pigs ate each day, you first need to find the total number of pounds of food that Angela bought and this amount in total is :

= 250 + 145 + 200

= 595 pounds of food

The number of days from the start of November through March is :

= 30 days November + 31 days December + 31 days January + 28 Days February + 31 Days March

= 151 days in total

The amount of food that Angela's pigs ate per day is therefore:

= Total food purchased / Number of days

= 595 / 151

= 3. 94 pounds per day

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To solve the equation x - 9 = 0, B. add 9 to both sides.

In a typical equation that is algebraic in nature, as in, has a variable, the value of that variable can be solved by isolating the variable on such a way that it would stand alone on one side of the equation.

We can solve by applying the appropriate properties of equality to isolate the variable.

Given the equation x - 9 = 0, solve for the value of x by isolating the variable x to one side of the equation by applying the addition property of equality. Tod of this, add 9 to both sides of the equation:

x - 9 = 0 + 9

x = 9

Therefore, the correct answer is: B. add 9 to both sides.

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The statement which is correct about each inequality as required to be assigned are as follows;

It follows from the task content that the statement which is correct about each of the inequalities is to be matched accordingly.

It is noteworthy to know that the underlying rule while solving inequalities is such that;

If the coefficient of a variable upon isolation on one side of the inequality is negative, it follows that the inequality sign must be flipped while multiplying or dividing both sides of the inequality by a negative number.

On the other hand, if the coefficient of the variable is positive, the inequality sign is not to be flipped.

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Answer: [tex]y = \frac{1}{2}x + \frac{1}{2}[/tex]

Step-by-step explanation:

Step 1: Find the slope using the two points given

[tex](3,2)[/tex]and [tex]-(5,-2)[/tex]

use the slope formula ->[tex]slope = \frac{y2 - y1}{x2 - x1}[/tex]

[tex]= \frac{-2-2}{-5 - 3}[/tex]

[tex]= \frac{-4}{-8}[/tex]

[tex]= \frac{1}{2}[/tex]

Plug in the slope into the slope-intercept form -> [tex]y = mx + b[/tex]

[tex]y = \frac{1}{2}x + b[/tex]

Step 2: Find the y-intercept (also known as b in the formula above):

Do this by taking any point (3,2) or (-5,-2) and plugging it into the slope equation in Step #1

[tex](3,2)\\y = \frac{1}{2}x + b\\2 = \frac{1}{2}(3) + b\\2 = \frac{3}{2} + b\\4 = 3 + 2b\\1 = 2b\\b = \frac{1}{2}[/tex]

Step 3: Plug in the slope we found in step 1 and the y intercept in step 2

[tex]y = mx + b\\y = \frac{1}{2}x + \frac{1}{2}[/tex]

The domain of the rational function given; f (x) = x / ( x² - 64 ) as required to be determined in the task content is; All real values of x such that x ≠ −8 and x ≠ 8.

Recall that the domain of a rational function includes all real number values except those which render the rational function undefined; i.e the denominator is equal to 0.

On this note, the only exceptions for the domain of the rational function can be determined as follows;

x² - 64 = 0

x² = 64

x = ± 8

On this note, the values which are exceptions to the possible real number values of x are; -8 and 8.

Ultimately, the domain of the given rational function as required is; All real values of x such that x ≠ −8 and x ≠ 8.

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The given expression is equivalent to z(i) = 21 + 12i.

       [tex]${\displaystyle z=re^{i\varphi }=r(\cos \varphi +i\sin \varphi )}[/tex]

       where {r} is the absolute value of z, and {φ} is the argument of z.

Given is the complex expression -

z(i) =  (3 - 4i)(1 + 5i) - (2 - i)

The given complex expression is -

z(i) =  (3 - 4i)(1 + 5i) - (2 - i)

z(i) = 3(1 + 5i) - 4i(1 + 5i) - (2 - i)

z(i) = 3 + 15i - 4i - 20i² - 2 + i

z(i) = 3 - 2 + 15i - 4i + i - 20i²

z(i) = 1 + 12i - 20i²

z(i) = 1 + 12i + 20

z(i) = 21 + 12i

Therefore, the given expression is equivalent to z(i) = 21 + 12i.

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{Complete question -

Simplify the expression (3-4i)(1+5i)-(2-i). Please show your work}

The size of sample space is 8.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. This is the fundamental theory of probability, which is applied to the probability distribution.

Given Jennifer first spins a spinner and then flips a coin,

Table for sample space is

                                         Result of spin

Coin result       Red                Green            Yellow           Blue

Heads      Red, heads     Green, heads  Yellow, heads      Blue, heads

Tails          Red, tails     Green, tails  Yellow, tails     Blue tails

Total sample space is 8.

Hence the number of sample space is 8.

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Answer:

Step-by-step explanation:

Answer:

420 = 4.2 x 100 = 4.2 × 102

Step-by-step explanation:

The amount of production in the economy to meet the final consumer demand which is 80 units of agriculture, 60 units of manufacturing and 50 units of energy

The given parameters that will help us to calculate the amount are

(1) Pe =0.2Pa + 0.2 Pm + 0.1pe

Pm = 0.2P + 0.4 Pm + 0.1 Pe

Pa = 0.1 Pa + 0.2Pm -0.3 Pa

(2) The free variable Pa = 100

We create a table of outputs using the given Units economy distribution

Agriculture        Manufacture       Energy           Purchased by

0 .2                      0.2                       0.1                 Agriculture

0.2                    0.4                       0.1                    manufacturing

0.1                    0.2                       -0.3                    Energy

Let Pa, Pm, Pe represent the prices for each sector

We then create an income equation using the expenses of the table above we have

(1) Pa =0.2Pa + 0.2 Pm + 0.1pe =80

Pm = 0.2P + 0.4 Pm + 0.1 Pe = 60

Pe = 0.1 Pa + 0.2Pm -0.3 Pa=50

Making pa, pm and pe the subjects of the relation and summing them to have the amount

pa = 0.5x = 80

Pa=80/0.5= 160

Pm = 0.7pm = 60

Making pm the subject of the formula

pm= 60/0.7 = 86

Pe = 0

Therefore the amount is 160+86+0 = 246

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The two equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p include the following:

B. 2.3p – 10.1 = 6.49p – 4

C. 230p – 1010 = 650p – 400 – p

From the information provided, we have the following equation:

2.3p – 10.1 = 6.5p – 4 – 0.01p

Next, we would simplify the given equation by collecting like terms as follows;

2.3p - 10.1 = 6.5p - 0.01p - 4 = 6.49p - 4

2.3p - 10.1 = 6.49p - 4

In Mathematics, the multiplication property of equality states that both sides of an equation will remain the same and equal, when both sides of the equations are multiplied by the same number.

By multiplying both sides of the given equation by 100, we have;

100 × (2.3p - 10.1) = 100 × (6.5p - 4 - 0.01p)

230p - 1010 = 650p - 400 - p

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Answer:

x ≤ 5

Step-by-step explanation:

That inequality best matches the graph.

On solving the provided question, we can say that from the graphs, line segment should you remove to make the relation a function of x  the line segment with endpoints (-3,2) and (-4,-2)

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

from the graphs,

line segment should you remove to make the relation a function of x

the line segment with endpoints (-3,2) and (-4,-2)

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She will need to pay 1068.75 dollar.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time peroid.

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

Given that Gabriella borrowed $3,600 to finance a large-screen television at a rate of 6.25% for 4.75 years.

Amount = $3,600

Rate = 6.25%

Time =  4.75  years

Therefore, Simple Interest = (Principal × Rate × Time) / 100

Simple Interest = 3,600× 6.25% × 4.75

Simple Interest = 3,600× 6.25/100 × 4.75

Simple Interest = 1068.75

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Answer:

$1,068.75

Step-by-step explanation:

$3,600 x 0.0625 x 4.75 = $1,068.75

A graph of the linear equation 3x - 4t = 12 has been plotted as shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.

Next, we would use an online graphing calculator to plot the relationship between the value of x and the value of t as shown in the image attached below.

In conclusion, a graph which represents the linear equation (3x - 4t = 12) does not represent or show a proportional relationship between the value of x and t because they didn't pass through the origin (0, 0).

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The value of x and y are 5 and 3 respectively.

The value of x and y when (x , 2y) = (5, 6) can be found as follows:

Therefore, the x coordinates of the graph is given as 5 while the double of y coordinates is equals to 6. Then, we have to equate the values as follows:

x = 5

2y = 6

The value of x is known by mere equating.

Hence, let's find the value of y.

2y = 6

divide both sides of the equation by 2

2y / 2 = 6 / 2

y = 3

Therefore, the value of y = 3 and x = 5.

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Answer:

D. x > 15

Step-by-step explanation:

To solve, we must isolate x:

[tex]175+35x > 700\\35x > 525\\x > 15[/tex]

Step-by-step explanation:

let change the playing yes /no question from direct speech to direct speech

My sister asked me, "Have you seen my dog?" ____________________________________________ Vijay asked "Have you gone to market?" ____________________________________________ My mother asked, "Why are you crying?" ____________________________________________ The rickshaw puller asked me, "Do you speak English?" ____________________________________________

Answer:

If there are 24 coins in total and some of them are nickels, then there must also be some dimes. Let's call the number of dimes "x" and the number of nickels "y". We know that y = 1/3 * x. We can set up an equation to represent this relationship: y + x = 24. We can also substitute 1/3 * x for y to get the following equation: 1/3 * x + x = 24. We can combine like terms to get: (4/3) * x = 24. We can divide both sides by 4/3 to solve for x: x = 18.

Therefore, there are 18 dimes in the bag.

Step-by-step explanation: