Solve the system algebraically. Make sure that any points you name satisfy both equations.

Answer:

-72

Step-by-step explanation:

Answer:

Step-by-step explanation:

12x-6 = 90 because opposite angles are equal if intercepted in parallel lines

12x=96

x= 8

Step-by-step explanation:

if I understand you correctly, then you got

sin(60°) = sqrt(3/2)

and now we have to find cos(60°) based on that.

but : sin(60°) = sqrt(3/4) = sqrt(3)/2

I will continue with that.

one major observation with the trigonometric functions in a norm circle (radius = 1) is that sine and cosine are the legs of a right-angled triangle.

the radius at the angle is the Hypotenuse.

and so, Pythagoras applies

c² = a² + b²

c is the Hypotenuse, a and b are the legs.

so,

radius² = sin²(x) + cos²(x)

and because radius = 1

1² = 1 = sin²(x) + cos²(x)

in our case

1 = sin²(60) + cos²(60)

1 = (sqrt(3)/2)² + cos²(60) = 3/4 + cos²(60)

cos²(60) = 1 - 3/4 = 1/4

cos(60) = sqrt(1/4) = 1/2

To make red brass alloy ratio of copper : zinc is 16 :3 ,then zinc should be combined for making red brass alloy of 40kg copper is 7.5kg.

As given,

Ratio given to make red brass alloy using copper and zinc is:

Copper :Zinc=16 :3

Given quantity of copper to make red brass alloy=40 kg

Let y kg be the quantity required to make red brass alloy using 40 kg copper

Using ratio and proportion we get,

40 :y=16 :3

⇒y ×16=40×3

⇒y=120/16

⇒y=7.5 kg

Therefore, to make red brass alloy ratio of copper : zinc is 16 :3 , then zinc should be combined for making red brass alloy of 40kg copper is 7.5kg.

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The answer is the option C. (h + j + k)/3

Because to find the average of 3 quantities, you have to add them all and then divide the result by 3

The most appropriate choice for stocks and net proceeds will be given by-

Net proceeds of Erin = $3533.9

What is stock and net proceeds?

Stock

Stock is a part of share set up by the company so that people can buy.

Net proceeds

After deducting all expenses, amount recieved by the seller after selling of stocks is called net proceeds.

Worth of stocks purchased by Erin  = $23510

Percentage paid to her broker = 1%

Amount paid to broker = [tex]\frac{1}{100}\times 23510[/tex]

                                      = $235.1

Now price of stocks increased to $27300

Net profit = $(27300 - 23510)

                = $3790

Net proceeds = $(3790 - 235.1 - 21)

                        =$3533.9

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Given:

The dimensions of the room are,

The dimensions of the carpet are,

To find:

The number of rolls of carpet.

Explanation:

The number of rolls of carpet is calculated by,

Therefore, the number of rolls of carpet is 8.

Final answer:

The number of rolls of carpet is 8.

The expression with a rational exponent as a radical expression is [tex]\sqrt[9]{3}[/tex]. Therefore, option B is the correct answer.

The given expression is [tex](3^{\frac{2}{3} } )^{\frac{1}{6} }[/tex].

Rational exponents are exponents of numbers that are expressed as rational numbers, that is, in [tex]a^\frac{p}{q}[/tex], a is the base and p/q is the rational exponent where q ≠ 0.

Now, the given expression can be solved as follows:

Using power law [tex](a^m)^n=a^{m\times n}[/tex], we get

[tex](3^{\frac{2}{3} } )^{\frac{1}{6} }=3^{\frac{2}{3}\times \frac{1}{6}}[/tex]

[tex]=3^{\frac{1}{9} }[/tex]

The equivalent expression to [tex]=3^{\frac{1}{9} }[/tex] is [tex]\sqrt[9]{3}[/tex].

The expression with a rational exponent as a radical expression is [tex]\sqrt[9]{3}[/tex]. Therefore, option B is the correct answer.

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Since (2,1) is the turning point, let's write the function in its vertex form:

Let's use one of the points:

Therefore:

For Wesley:

distance = 7.7miles, time = 3.5h

For Xavier:

distance = 3.5 miles, time = 1.25h

For Yvette:

distance = 4.224 miles, time = 1.76h

For Zubin:

distance = 5.175 miles, time = 2.25h

Therefore, the complete table is as given below

Answer: C(x) > a(x) , meaning c(X) has the greatest average rate of change over the given interval.

Explanations :

• The greatest average rate of change = slope

• given by formula :

• The average rate of change over the given interval = 7-1 = 6

and

• We can see that b(x) has constant average rate of change at 2 , therefore this will not be considered for this purpose of the exercise.

and

• The average rate of change over the given interval =, 8 -1 = 7

in conclusion , C(x) = 7 , whereas a(x) = 6 ,

Therfore C(x) > a(x)

A premise or premiss is a true or false statement that helps form the body of an argument, By law of syllogism the statement is true. Your cat will chase mice.

A premise or premiss is a true or false statement that helps form the body of an argument, which logically leads to a true or false conclusion.

If the following two statements are true: (1) If p , then q . (2) If q , then r . Then we can derive a third true statement: (3) If p , then r .

If you have a cat, then it will chase mice.

is the given statement.

Let p is you have a cat

q is chase mice.

r is cat will chase mice.

iby the law of syllogism Your cat will chase mice. because  (1) If p , then q . (2) If q , then r . Then we can derive a third true statement: (3) If p , then r .

Hence by law of syllogism the statement "if you have a cat, then it will chase mice" is true.

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We need to graph the following inequality:

First, let's apply the same operations on both sides of the inequality to isolate the variable y on the left side of the inequality. We obtain:

Now, notice that:

represents a line containing all points with coordinates (x,y) such that y=-4x.

The solution to the inequality includes those points, and also the points for which y is greater than -4x.

Thus, the solution to this inequality consists of all the points on that line (solid line) and the whole region above that line:

Notice that, to graph the solid line, we can choose two points on the line, and then join them. We can use the points:

The methods which can be used to prove that the two triangles are congruent are:

Prove all three sets of corresponding angles are congruent.

Prove all three sets of corresponding sides are congruent.

Option C and Option D are the correct answer.

Corresponding angles are angles that occur on the same side of the transversal line and are equal in size.

We have,

To prove that two triangles are congruent, we need to show that the corresponding sides and corresponding angles are congruent.

So,

Prove all three sets of corresponding angles are congruent.

Prove all three sets of corresponding sides are congruent.

These two methods can be used to prove that the two triangles are congruent.

Thus,

The methods which can be used to prove that the two triangles are congruent are:

Prove all three sets of corresponding angles are congruent.

Prove all three sets of corresponding sides are congruent.

Option C and Option D are the correct answer.

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Answer: 74.43%

Let us first list down the probabilities of the machine working.

First is the probability that none of the components will fail. We can write this probability as:

Next, the probability that one of the components will fail. This will give us:

Then, the probability that 2 of the components will fail.

Adding all of these probabilities and we will have:

Therefore, the probability that the machine will be working would be 74.43%.

Length has 5 cubes

width has 3 cubes

height has 7 cubes

Volume = length x width x height

5/2 * 3/2 * 7/2 = 105/8 = 13.125 ft^2

see the attached figure below to better understand the problem

Please give me a minute

The price is about $38

therefore

The answer is option C

The image of C under the translation described by this translation rule (x, y) → (x + 11, y - 8) is: (4, -6)

In Geometry, the translation of a geometric figure to the right simply means adding a digit (11) to the value on the x-coordinate (x-axis) of the pre-image while translating a geometric figure down simply means subtracting a digit (8) from the value on the y-coordinate (y-axis) of the pre-image.

Note: Each point on this graph represents 2 units.

Next, we would translate the image of C 11 units to right and 8 units down. Therefore, this transformation can be modeled by this translation rule:

(x, y)                              →               (x + 11, y - 8)

Point at C = (-7, 2)        →      Point at C' = (-7 + 11, 2 - 8) = (4, -6)

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We need to solve the inequality:

We can start by sketching the graph of the parabola:

Then, we need to find the points of the parabola below the x-axis.

The zeros of that parabola are given by:

And since the coefficient of x² is positive, the parabola opens upwards. So, its graph looks like this:

Thus, the points on the parabola below the x-axis are those for which:

The probability that at most 3 of light bulbs will be defective will be 0.998.

Probability may be defined as an expression which may be used to determine the possibility of occurring of any event. The probability of happening an event surely is 1 and probability of not happening an event is zero. Since, 5 percent of bulbs are defective then

5% = 0.05 Now,

Non defective bulbs = 1 - 0.05 = 0.95

n = number of light bulbs = 7

We can calculate this using binomial distribution.

p(x) = ⁿCₓ × (pˣ)(1-p) ^n-x

Our question says at most 3 is defective, so it will be

(⁷C₀ × 0.05⁰ × 0.95⁷) + (⁷C₁ × 0.05¹ × 0.95⁶) + (⁷C₂ × 0.05² × 0.95⁵) + (⁷C₃ × 0.05³ × 0.95⁴)

= 0.698 + 0.257 + 0.040 + 0.003

= 0.998 which is the required probability.

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The function f(6) has a value of 1./3

The graph that completes the question is added as an attachment

From the graph, we have the following points

(x, y) = (4, 1) and (1, 2)

We start by calculating the slope of the points using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where x and y are defined above

So, we have

Slope = (2 - 1)/(1 - 4)

Evaluate

Slope = -1/3

At f(6), we have

x = 6

So, the point can be represented as (6, y)

Using the slope formula again, we have

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (4, 1) and (6, y)

This gives

Slope = (y - 1)/(6 - 4)

Evaluate

Slope = (y - 1)/2

So, we have

(y - 1)/2 = -1/3

Evaluate

y = -2/3 + 1

Evaluate

y = 1/3

Hence, the value of f(6) is 1/3

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Question 8

We are to solve

This can be simplified to

Raising both sides of the equation to a power of 5 we have

By raising both sides of the equation to power of 1/14, we get

Simplifying this we get

To solve the exercise, replace in the expression the given values of c and d and then operate:

Therefore, the value of the evaluated expression is 38.1

We are given a rectangle ABCD

Recall that a rectangle is a quadrilateral in which all angles are right angles (90°)

Each pair of interior angles are supplementary. The two right angles add to a straight angle which means that the opposite sides of a rectangle are parallel.

In quadrilateral ABCD, if m∠A = m∠B = m∠C = m∠D = 90° then AB || DC and AD || BC

Hence, a rectangle is also a parallelogram.

Option B is the correct answer.

10. |x - 4| - 4 = 1/2x

⇒ Multiplying by 2,

2 |x - 4| - 8 = x

So, x - 4 = (x + 8)/2

             = -(x + 8)/2

When,

x - 4 = (x + 8)/2

2x - 8 = x + 8 (Multiplying by 2)

2x - x = 8 + 8 (Adding 8 and subtracting x to both sides)

x = 16

When,

x - 4 = - (x + 8)/2

2x - 8 = -x - 8 (Multiplying by 2)

2x + x = -8 + 8 (Adding 8 and x to both sides)

3x = 0

x = 0

Hence, the solution is x = 16 and x = 0.

13. (3/4)x = 2x - 10

⇒ Subtract 2x from both sides.

-5x/4 = -10

Multiply both sides by 4/(-5).

(-5x/4)×4/(-5) = -10 × 4/(-5).

x = 8 is the solution of the equation.

15. x² - 7x - 8 > 0

⇒ Solve the quadratic equation by splitting the middle term,

x² - 8x + x - 8 > 0

x(x - 8) + 1(x -8) > 0

(x + 1)(x- 8) > 0

-1 and 8 are the critical points of the inequality.

x < -1 and x > 8 are the solutions of the inequality which are represented by the shaded red region in the graph.

16. x - 5 > - 2x + 4

⇒ Adding 2x to both sides.

3x - 5 > 4

Adding 5 to both sides.

3x > 9

Divide both sides by 3.

x > 3 is the required solution represented by blue shade region in the graph.

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No, becuase not all the posible values of x make the inequality true.

For example, if x = 0

7(0) - 5 > 2

0 - 5 > 2

- 5 > 2 This is not true.

Given:

There are 11 letters in the word 'MISSISSIPPI'

The number of P's are 2.

The probability that the randomly chosen slip of paper have the letter P written on it is,

The probability that the randomly chosen slip of paperdoes not have the letter P written on it is,

The odd against event is calculated as,

Answer: The odds against the paper having the letter P written on it is 9/2 (9:2)

Tommie will make $12.65 per hour after his raise.

We will perform addition of value equal to mentioned percentage. So, representing this as equation -

Amount of money earned after raise = 11.5 + 10%×11.5

Converting percentage to whole number

Amount of money earned after raise = 11.5 + (10/100×11.5)

Performing multiplication and division on Right Hand Side of the equation

Amount of money earned after raise = 11.5 + 1.15

Performing addition on Right Hand Side of the equation

Amount of money earned after his raise = $12.65

Therefore, after increase in 10% raise, Tommie will earn total $12.65.

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Solution:

If a profit of $1.45 was earned on each bag of oranges sold, then the profit, if all 13 bags were sold, would be:

13 x $1.45 = $18.85

so that, the correct answer is:

$18.85