In Exercises 1-4, find the exact values of the six trigono-
metric functions of the angle shown in the figure. (Use the
Pythagorean Theorem to find the third side of the triangle.)
1.
2.
0
8
6
0
13
5


Only number 1 and 2

Nature of roots of the quadratic equation 4x^2 - 12x - 9 = 0 are real and unequal by Discriminant method.

Given quadratic equation is 4x^2 - 12x - 9 = 0

Comparing the given equation with the standard form i.e ax^2 - bx - c = 0.

 Here we have, a = 4

                           b = -12  and

                           c = -9

Now discriminant, D = b^2 - 4ac

                                  = (-12)^2 - 4(4)(-9)

                                  = 144 - (-144)

                               D = 288    

Now check for discriminant D, D=288 and 288 >0

                                 Therefore, (D>0)

Hence the roots of given equation are real and unequal.

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The equation for the given quadratic polynomial is f(x) = x^2-33x+242.

When the highest degree term in a second-degree polynomial equals 2, the polynomial is said to be quadratic. A quadratic equation has the generic form ax^2 + bx + c = 0. Here, x is the unknown variable, a and b are coefficients, and c is the constant term.

A polynomial with an exponent degree of 2 or higher is said to be quadratic. A quadratic polynomial has the general form f (x) = ax^2 + bx + c, where a 0 and b a n d c are real numbers. A parabola is the name of the quadratic polynomial's curve.

f(x) = (x-11)(x-22)

f(x) = x^2-33x+242

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Answer:

--------------------------------

Given system of inequalities:

Plot the inequality and the given points to determine which of them fall into solution area.

See attached.

As we see only two points fall in the solution area, brown zone on the bottom: (6, −2), (6, 0.5).

(Answer:

(6, 5)

Step-by-step explanation:

For this question, there are not two correct choices.

Given systems:

y ≤ 2/3x + 1

y > -1/4x + 2

For the first equation, the y-intercept is 1, and the rate of change is 2/3 (rise over run). The inequality symbol is less than or equal to (≤), meaning this will be a solid line and the area shaded will be below the line.

For the second equation, the y-intercept is 2, and the rate of change is -1/4 (this means it is decreasing in number, therefore the line is going down). The inequality symbol is greater than (>), meaning this will be a dashed line and the area shaded will be above the line.

the area overlapped is where the solution will be. The answer is (6, 5) because it lies on the solid line of the first inequality, indicating it does satisfy the first inequality. Any point on the solid line satisfies the inequality. The point also lies above the second inequality, meaning it is a solution to the system.

Also, if you plug it into the system of inequalities, all the outcomes will make sense.

Answer:[tex]x = 18[/tex]

* also think you meant x instead of c*

Step-by-step explanation:

[tex]\frac{x}{6} - 7 = -4[/tex] --> +7 on both sides

[tex]\frac{x}{6} - 7 + 7 = -4 + 7[/tex]

[tex]\frac{x}{6} = 3[/tex] --> multiple by 6 by both sides

[tex]6 * \frac{x}{6} = 3 * 6[/tex] --> the 6 and the [tex]\frac{x}{6}[/tex] cancel out

[tex]x = 18[/tex]

On solving the provide question, we can say that by plotting data they can own 8 to 10 video games.

The most typical approach to display data using a chart is a graph that shows the relationship between two additional variables. Diagrams created by hand or on a computer are also acceptable. Move 2 units to the right after starting at the origin before going 3 units up. The coordinates for the points 2, 3, should be shown on the coordinate plane. Clearly state your points. The pink dot with the letter P thus stands for 2.3. Before creating a line chart, you need first generate a number line for each value in your data collection. Put an X (or dot) over each value of the data on the number line after that. For each instance when a value appears in a record, place an X over the corresponding number.

Here,

We can therefore deduce from the provided number that the cluster owns between 8 to 10 video games.

How do we know the range is 8 to 10 then? In the example figure, the dots are referred to as the cluster.

Based on this, we may deduce that our range is between 8 and 10, the amount of games that are owned as a minimum and maximum, respectively.

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The complete question is " A group of children, 6 to 10 years old, were asked how many video games they owned. The scatter plot shows the results.

What is the range of video games owned for the cluster?"

As per the given distance, he surrounded around 20 miles

Here we have given that Pete drives from his house to the store and then to the fair.

While we have given the distance covered by the Pete driver as,

=> 6, 5, 4, 3, 2

Then the total travelling distance is calculated by sum up all the details,

Then  we get,

=> 6 + 5 + 4 + 3 + 2

=> 20 units.

Here we have also given that 1 unit is equal to 1 miles.

Therefore, the resulting distance is 20 miles.

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Answer:

formula:

c^2 = a^2 + b^2 - 2abcos(C)

where c is the length of the diagonal, a and b are the lengths of the legs of the triangle (the non-parallel sides of the trapezoid), and C is the angle between them.

In this case, a = b = 7 feet and C = (180 - 140)/2 = 20 degrees. We can plug these values into the formula to find:

c^2 = 7^2 + 7^2 - 2(7)(7)cos(20)

c = sqrt(98 + 49cos(20))

To use the Law of Sines to find the length of the shorter base, we can use the following formula:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the sides of the triangle and A, B, and C are the angles opposite those sides.

Since we know a and b, we can use the formula to find:

x/sin(140) = 7/sin(20)

x = 7sin(140) / sin(20)

Note that the value of c will be in squared units, so you need to take the square root to get the actual length of the diagonal.

The missing coefficient of the linear equation 4 · x + 10 = __ · x + 8 such that it has no solutions is equal to 4.

In this problem we find a linear equation of the form a · x + b = c · x + d, where a, b, c, d are real coefficients. This kind of equation has no solution for the case when a = c. The complete procedure is shown below.

First, write the incomplete expression:

4 · x + 10 = __ · x + 8

Second, add the missing coefficient according to the definition for linear equations with no solutions:

4 · x + 10 = 4 · x + 8

Third, use algebra properties to simplify the expression:

10 = 8 (CRASH!)

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The size of the final unknown interior angle is 157°

Given the interior angles of a polygon are 162°,115°,125°,138°,105°, and 98°.

Considering the given polygon to be 7-sided,

The sum of the interior angles of a polygon is:

(n-2) x 180

where n= number of sides of the polygon

Substituting the values:

(7 - 2) x 180

= 5 x 180

= 900

Let the unknown angle be x°

So,

162+115+125+138+105+98+x = 900

x = 900 - 743

x = 157°

Thus the final interior angle is 157°

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The coin will be worth $299.23 in 11 years when increasing at the rate of 11% Option A is the correct answer.

A steady rate of expansion that is proportionate to the quantity's current size is referred to as exponential growth. In other words, a quantity expands more quickly the larger it is. The exponential function, which has the formula y = ab raised to x, can be used to mathematically represent exponential growth. Here, "a" stands for the beginning quantity or value, "b" is the growth factor or base, and "x" stands for the duration or number of growth periods. Population expansion, compound interest, and the spread of infectious illnesses are a few examples of real-world processes that show exponential growth.

The exponential growth is given by the formula:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

For the given situation we have:  (P) = $115, the interest rate (r) = 11% or 0.11, and the number of years (t) = 11.

Thus,

[tex]A = $115(1 + 0.11/1)^{(1*11)}\\A = $115(1.11)^{11}[/tex]

A = $299.23

Hence, the coin will be worth $299.23 in 11 years. Option A is the correct answer.

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The length of the rectangle is 2.4 and breadth is 1.8

Now, According to the question:

The given information is :

The length of a rectangle multiplied by 3 is equal to 4 times its width.

The perimeter is 8[tex]\frac{2}{5}[/tex].

To find the length and the width.

We take,

Length=L

Width=W

3L=4W

Divide by 3 on both sides

L = [tex]\frac{4}{3}[/tex]W

We know that, The perimeter of rectangle:

Perimeter of rectangle is = 2(L + W)

2W + 2L=8.4

2W + 2([tex]\frac{4}{3}[/tex]W) = 8.4

2W + [tex]\frac{8}{3}[/tex]W=8.4

[tex]\frac{6}{3}[/tex]W +  [tex]\frac{8}{3}[/tex]W = 8.4

[tex]\frac{14}{3}[/tex]W =  8.4

14W = 25.2

Divide by 14 on both sides.

W = [tex]\frac{25.2}{14}[/tex]

W =1.8

L = 4/3W

L= [tex]\frac{4}{3}1.8[/tex]

L=2.4

L=2.4; W=1.8

Hence, The length of the rectangle is 2.4 and breadth is 1.8

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Answer: The answer is 3

Step-by-step explanation:

(-7)-(-10)

=(-7)+10

=10-7

=3

Answer: 3

Step-by-step explanation: First, to make this easy, let's rewrite the equation:

-7 + 10

I did this because whenever you change subtraction to an addition problem, with decimals, you need to change the sign of the number on the right side (always) So, (-7) - (-10) is the same as (-7) + 10.

So, to make this even easier, we can model this as 10 - 7, which is 3. As we know, it's the same as (-7) + 10 because we are adding 10 more to (-7) which is 3. Also, if you can, using a numberline really helps to! I hope this helped!

The probability that the hand contains 4 jacks is solved to be

0.003697

Probability is solved using the formula

= required outcome / possible outcome

The required outcome

= number of ways of picking 4 jacks * number of ways of 10 cards from 48

= ⁴C₄ * ⁴⁸C₁₀

= 1 * 6540715896

= 6540715896

The possible outcome

= number of ways of picking 14 card from possible 52 cards

= ⁵²C₁₄

= 1.768966345 * 10¹²

The probability

= required outcome / possible outcome

=  6540715896 / 1.768966345 * 10¹²

= 11 / 2975

= 0.00369747

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1 and 7/12

Divide the 2 fractions (multiply by reciprocal.)

1/4 + 1/2 × 8/3

1/4 + 8/6

Find common denominators.

6/24 + 32/24

38/24

Turn that into a mixed number.

1 14/24

Simplify.

1 7/12

The cost of pizza and salad will be $8.54 and $2.64 respectively.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

The equation will be represented as;

Let p = pizza

Let s = salad

2p + 3s = 25

3p + 2s = 30.90

Multiply equation i by 3

Multiply equation ii by 2

6p + 9s = 75

6p + 4s = 61.80

Subtract.

5s = 13.20

Divide

s = 13.20 / 5

s = $2.64

Pizza will be

2p + 3s = 25

2p + 3(2.64) = 25

2p = 25 - 7.92

p = 17.08 / 2

p = 8.54

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l

Complete question

Two groups of students went to pizza delight one group paid 25 dollars 2 pizzas and 5 salads the other group paid 30.90 dollars for 3 pizzas and 2 salads. Find the cost of the pizza and salad.

The area of the triangle ΔKLM, obtained using Routh's theorem is 4/13

Routh Theorem outlines the ratio relationship between the triangle formed by three cevians of a triangle and the area of the original triangle.

Mathematically it states that the ratios (x, y, and z) of the segments formed the intersection of the cevians and the three sides of the triangle produces the area of the triangle when expressed in the form;

A = (x·y·z - 1)² ÷ ((x·y + y + 1)·(y·z + z + 1)·(z·x + x + 1)).

The specified dimensions are;

BD : DC = CE : EA = A_F: FB  = 1 : 3

The point of intersection of AD, BE and CF = K, L, and M

Area of triangle ΔABC = 1

The area of triangle ΔKLM is found as follows;

Where the length of AB = 4 units, we get;

Length of A_F = 1 unit and the length of FB = 3 units

We get;

BD/DC = x, CE/EA = y, A_F/FB = z

x = y = z = 1/3

Routh's theorem states that the area of the triangle formed by AD, BE, and CF is obtained using the formula;

Area of ΔKLM = (x·y·z - 1)² ÷ ((x·y + y + 1)·(y·z + z + 1)·(z·x + x + 1))

Plugging in the values of x, y, z, we get;

x = y = z, therefore;

Area of ΔKLM, A = (x³ - 1)² ÷ ((x² + x + 1)·(x² + x + 1)·(x² + x + 1))

A = (x³ - 1)² ÷ ((x² + x + 1)³)

x = 1/3, therefore;

A = ((1/3)³ - 1)² ÷ (((1/3)² + (1/3) + 1)³) = 4/13

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Three ratios that are equivalent to 18:21 are 6 : 7, 36 : 42 and 72 : 84

An equivalent ratio is a ratio that represents the same relationship between numbers as another ratio, but with different values.

You can create equivalent ratios by multiplying or dividing both parts of the ratio by the same non-zero number. For example, if a ratio is 4:8, an equivalent ratio would be 2:4.

Thus, 3 ratios that are equivalent to 18:21 can be:

18 : 21 = 6 : 7 (divide both sides by 3)

18 : 21 = 36 : 42 (multiply  both sides by 2)

18 : 21 = 72 : 84 (multiply  both sides by 4)

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The only value of c that satisfies the conclusion of the Mean Value Theorem on the closed interval [0,3] is c = 2.

The Mean Value Theorem states that if a function f is continuous on a closed interval [a, b], then there exists some c in the interval such that

f'(c) = (f(b) - f(a)) / (b - a).

In the case of f(x) = x(x-3) , on the closed interval [0,3], we can solve for c using the equation above.

We begin by calculating f'(c), which is equal to 2c - 3. Then, we set the equation equal to (f(3) - f(0)) / (3 - 0), which is equal to -3 / 3.

Substituting this into our equation for f'(c), we get 2c - 3 = -1, which simplifies to c = 2.

Therefore, the only value of c that satisfies the conclusion of the Mean Value Theorem on the closed interval [0,3] is c = 2.

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The population in this study would be adolescent boys.

The researcher is interested in the effect of the electrolytic sports drink on the endurance of adolescent boys. The sample of 30 boys that are selected for the study is representative of the larger population of adolescent boys, and the results of the study will be generalized to this population. The study is designed to draw inferences about the population of adolescent boys based on the sample that is selected.

The population in this study would be adolescent boys.

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The solution for the compound inequality is -2>x≥-4. Therefore, option C is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is 3<-2x-1≤7.

Here, 3<-2x-1

Add 1 on both the sides of an inequality, we get

4<-2x

Divide -2 on both the sides of an inequality, we get

-2>x

Here, -2x-1≤7

Add 1 on both the sides of an inequality, we get

-2x≤8

Divide -2 on both the sides of an inequality, we get

x≥-4

The solution is -2>x≥-4

Therefore, option C is the correct answer.

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Step-by-step explanation and Answer

Since the interest rate is 5%, and the first loan was borrowed on May 1, we can calculate the interest on the first loan by using the formula:

Interest = Principal x Rate x Time

In this case, the principal is 2000, the rate is 5% (expressed as a decimal), and the time is (September 24 - May 1) = 4.5 months

So, Interest = 2000 x 0.05 x 4.5/12 = 50

The same applies to the second loan of 1000, so the interest on this loan is:

Interest = 1000 x 0.05 x (4.5/12) = 25

To find the total amount returned, we add the interest on both loans to the total principal borrowed:

total = 2000 + 1000 + 50 + 25 = 3075

Therefore, the total amount returned is Ks 3075

Answer:

We know that the distance between Paris and Nice is about 920,000 meters. To convert this distance to kilometers we divide by 1000: 920,000/1000= 920 kilometers

We also know that the train travels at a speed of 230 kilometers per hour. To find out how long it will take Lola to travel from Paris to Nice, we divide the distance by the speed:

920/230 = 4 hours

So it will take Lola 4 hours to travel from Paris to Nice by train.

Answer: 4 hours actually kinda ez not gonna lie

Step-by-step explanation: 230 kilometers = 230000 meters. 230 * 1000 = 230000. Distance / speed = time. 920000/230000 = T(as in time). T = 4

The following algebraic expression are trinomial.

The term expression in math is also known as algebraic expression consists of unknown variables, numbers and arithmetic operators.

Here we must know what is meant by trinomial,

The term trinomial is referred as

Here we have given algebraic expression that is written as  x³ + x² - √x is a trinomial with one variable ‘x’ and it having three non-zero terms.

Then the next given algebraic expression which is 2x³ - x², is NOT a trinomial. Because this expression is a binomial with one variable ‘x’, having two non-zero terms.

Then the another given algebraic expression that is 4x³ + x² - 1/x, is a trinomial with one variable ‘x’, having three non-zero terms.

Finally the given algebraic expression which can be written as x⁶ - x +√6, is a trinomial with one variable ‘x’, having three non-zero terms.

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When the tone's height, h, equals 0, we can determine when the tone will fall to the ground. The equation that expresses the height of the tone as a function of time is as follows:

    h = -16t^2 + 32t + 40

  where t is the number of seconds since the tone was launched, and h is the tone's height in feet.

  We can set the formula equal to 0 because we are aware that h = 0 when the tone strikes the ground:

   -16t^2 + 32t + 40 = 0

Here is the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / 2a

where a = -16, b = 32, and c = 40.

With these values entered into the formula, we obtain:

t = (-32 ± √(32^2 - 4(-16)(40))) / 2(-16)

t = (-32 ± √(1024 + 2560)) / (-32)

t = (-32 ± √(3584)) / (-32)

t = (-32 ± 64) / (-32)

t = (32) / (-32) or (-96) / (-32)

t = -1 or 3

The duration of the tone before it reaches the ground is -1 or 3 seconds.  

       However, as there is no such thing as a negative amount of time, it takes 3 seconds for the tone to reach the earth.

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Answer:

x = 5

y = -4

Step-by-step explanation:

3x+4y = -1

-2x-5y = 10

We time the first equation by 2 and the second equation by 3

6x + 8y = -2

-6x -15y = 30

-7y = 28

y = -4

Now put -4 back in for y and solve for x

3x+4(-4) = -1

3x - 16 = -1

3x = 15

x = 5

Let's check

3(5) + 4(-4) = -1

15 - 16 = -1

-1 = -1

So, x = 5 & y = -4 is the correct answer.

Answer:

Step-by-step explanation:

The system of inequalities can be written as follows:

x ≥ 14

x + y ≥ 15

0.5x + 0.1y ≤ 1

We can graph the system by plotting the three lines representing the three inequalities.

The first inequality, x ≥ 14, is a vertical line with x-intercept at (14, 0).

The second inequality, x + y ≥ 15, is a line with a slope of 1, passing through the point (0, 15) and with y-intercept at (0, 15).

The third inequality, 0.5x + 0.1y ≤ 1, is a line with a slope of -5, passing through the point (2, 0.2) and with y-intercept at (0, 0.2).

The solution to the system of inequalities is the region below the line representing the first inequality, above the line representing the second inequality, and to the right of the line representing the third inequality.

One possible solution is x = 16 and y = 1. This means that Taylor has 16 nickels and 1 dime, which is exactly 15 coins worth a maximum of $1 combined.

Answer: the person is right above just made sure that .5 is .05 since it’s cents. A nickel is worth .05 cents not .5 cents.

Step-by-step explanation:

The probability that their total completion time in the maze for all rats is between 5.75 and 6.25

To solve this problem, you would need to use the properties of the normal distribution and the central limit theorem. The central limit theorem states that the sum of a large number of independent and identically distributed random variables will tend to be normally distributed, regardless of the underlying distribution of the individual variables.

Since the completion time for each rat is normally distributed with a mean of 1.5 and a standard deviation of 0.35, the total completion time for 5 rats will also be normally distributed with a mean of 7.5 (5 x 1.5) and a standard deviation of 0.7 (√(5) x 0.35).

Then, you can use the cumulative distribution function (CDF) of the normal distribution to find the probability that the total completion time is between 5.75 and 6.25. This would involve finding the area under the normal distribution curve between those two values, which can be calculated using a table of the standard normal distribution or a calculator with the normal distribution function.

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Answer:

x^2 +9

Step-by-step explanation:

expand and simplify

(2x-3)^2-3x(x-4)

First expand the squared term

4x^2 -6x -6x+9 -3x(x-4)

Distribute the -3x

4x^2 -6x -6x+9 -3x^2 +12x

Combine like terms

4x^2 -3x^2-6x -6x +12x+9

x^2 +9

Answer:

[tex]{x}^{2} - 12x + 21[/tex]

Step-by-step explanation:

We know that,

[tex] {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} [/tex]

Accordingly, let us solve the sum.

[tex] {(2x - 3)}^{2} - 3x(x - 4)[/tex]

Expand and solve the brackets.

[tex]4 {x}^{2} - 12x + 9 - 3 {x}^{2} + 12[/tex]

Combine like terms.

[tex] {x}^{2} - 12x + 21[/tex]

A visual representation of data where numbers on the left side of a chart show one part of each value and numbers on the right side of the chart show the other is called a bar chart. A bar chart is a chart that uses rectangular bars to represent different values or categories. Each bar has a length that represents a value or a category. The left side of the chart is called the y-axis, or the vertical axis, and the right side of the chart is called the x-axis, or the horizontal axis. The x-axis typically shows the categories, and the y-axis shows the values of those categories. The height of each bar represents the value of the data point, with the height on the y-axis and the categories on the x-axis. This type of graph is useful for comparing the relative sizes of different groups or categories, as well as spotting trends and patterns.

Two fractions are equivalent if they represent the same decimal number. For example, the three previous fractions represent the same decimal: 0.5. 1/2 is 1 between 2, which is 0.5

The converse is:

If a number is a whole number, then it is a natural number.

The following information should be considered:

Considering the conditional:

In the case when the number is a natural number, then it is a whole number.

>If a number is not a whole number, then it is not a rational number. The converse is false. ( converse must be true)

>If a number is a rational number, then it is a whole number. The converse is false. (converse must be true)

>If a number is not a rational number, then it is a whole number. The converse is false. (hypothesis should've been "then it is not a whole number")

In the Law of Detachment, if both conditional and hypothesis are true, then the conclusion is true.

All whole numbers are rational numbers.

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