Isaiah recorded the grade-level and instrument of everyone in the middle school School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar 11
Bass 3
Drums 3
Keyboard 4
Eighth Grade Students
Instrument # of Students
Guitar 4
Bass 10
Drums 6
Keyboard 3

Based on these results, express the probability that an eighth grader chosen at random will play the guitar as a decimal to the nearest hundredth.

Vertex form of x-int: y-int: is .(2,3)

f(x)=−2x2+8x−5

Write

f(x)=−2x2+8x−5

as an equation.

y=−2x2+8x−5

Rewrite the equation in vertex form.

Tap for more steps...

y=−2(x−2)2+3

Use the vertex form,

y=a(x−y)2+k

, to determine the values of

a, h, and k.a=−2h=2k=3

Since the value of

a

is negative, the parabola opens down.

Opens Down

Find the vertex

(x,y).(2,3)

x-int: y-int: is .(2,3)

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The value of x is  x < 2

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

-x-7> -9

Add 7 on both the sides

-x -7 + 7 > -9 +7

-x > -2

divide by -1 and change inequality sign

x < 2

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To find the side x, we can use the Law of Cosines, which states that in any triangle, the square of the length of any side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those two sides and the cosine of the angle between them. In symbols, if a, b, and c are the lengths of the sides of a triangle, and C is the measure of the angle opposite the side of length c, then we have the equation:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we are given the lengths of two sides (a = 10 and b = 6) and the measure of the angle opposite the unknown side (C = 0 degrees), so we can plug those values into the equation to solve for c:

x^2 = 10^2 + 6^2 - 2 * 10 * 6 * cos(0)

x^2 = 100 + 36 - 120

x^2 = 16

x = sqrt(16) = 4

Therefore, the length of the side x is 4.

To find the indicated angle, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is constant. In symbols, if a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the measures of the angles opposite those sides, then we have the equations:

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

In our case, we are given the lengths of two sides (a = 10 and c = 12) and the measure of the angle opposite one of those sides (A = 0 degrees), so we can use those values to solve for the measure of the angle opposite the other side:

10/sin(0) = 12/sin(C)

sin(C) = 0

Therefore, the measure of the angle C is 0 degrees.

this is original answer

To find the side x, we can use the Law of Cosines, which states that in any triangle, the square of the length of any side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those two sides and the cosine of the angle between them. In symbols, if a, b, and c are the lengths of the sides of a triangle, and C is the measure of the angle opposite the side of length c, then we have the equation:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we are given the lengths of two sides (a = 10 and b = 6) and the measure of the angle opposite the unknown side (C = 0 degrees), so we can plug those values into the equation to solve for c:

x^2 = 10^2 + 6^2 - 2 * 10 * 6 * cos(0)

x^2 = 100 + 36 - 120

x^2 = 16

x = sqrt(16) = 4

Therefore, the length of the side x is 4.

To find the indicated angle, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is constant. In symbols, if a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the measures of the angles opposite those sides, then we have the equations:

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

In our case, we are given the lengths of two sides (a = 10 and c = 12) and the measure of the angle opposite one of those sides (A = 0 degrees), so we can use those values to solve for the measure of the angle opposite the other side:

10/sin(0) = 12/sin(C)

sin(C) = 0

Therefore, the measure of the angle C is 0 degrees.

The statement about the functions that is true is (a) only g(x) is an even function.

From the question, we have the following parameters that can be used in our computation:

f(x) = √(x + 1) - 3

The graph of g(x)

The graph of g(x) is an even function

This is so because the graph remains unchanged under reflection in the y-axis.

However, the function f(x) is neither even nor odd

This is so because

Hence, the true statement is (a)

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Answer:

y=x-1

Is the line equation.

Step-by-step explanation:

As we know that general equation of line is given by

y=mx + c

M is the slope and C is is Y intercept

Know m = 1 and point (x,y) as (5,4)

So plug in the values and solve for c

4=1*(5)+c

c=-1

So, equation of the line is

y=x-1

Answer:

Ordered pair: (- 8, 1)

x = - 8,y = 1

Step-by-step explanation:

[tex]1.5x-9y=-21\\-1.5x-3y=9[/tex]

Add together.

- 12y = - 12

y = 1

1.5x - 9(1) = - 21

1.5x - 9 = - 21

1.5x = - 12

x = - 8

By ASA, the two triangles are congruent.  They share 2 angles and the line in between them.

The amount of each type of table that will seat everyone is given as follows:

The combination is obtained with a system of equations, in which the variables of the system are given as follows:

There is a total of 52 tables, hence:

x + y = 52.

There will be a total of 280 people, hence:

4x + 10y = 280.

Hence the system is:

Multiplying the first equation by -4 and then adding them, the variable y is obtained as follows:

6y = 280 - 52 x 4

y = (280 - 52 x 4)/6

y = 12 tables.

Hence the variable x is obtained as follows:

x + y = 52

x + 12 = 52

x = 40 tables.

The problem is given as follows:

Mina's Catering Service is organizing a formal dinner for 280 people. The hall has two kinds of tables, one that seats 4 people and one that seats 10 people. The hall can contain up to a total of 52 tables. Which combination of tables sits everyone?

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On the graph, the graph equation has been drawn, crossing the y and x-axis points (0, 10) and (20, 0).

To calculate the slope m and the y-intercept, write the equation y = MX + b.

The slope and y-intercept can then be used to graph the equation (0, b).

The three primary forms of linear equations are point-slope, standard, and slope-intercept.

So, the equation is as follows:

8x+16y=160

Now,

The short sleeves are symbolized by an x.

y is a symbol for the long sleeves.

The equation must now be plotted as follows:

(Please see the graph below.)

As a result, the y and x-axis points (0, 10) and (20, 0) intersected by the equation.

Therefore, on the graph, the graph equation has been drawn, crossing the y and x-axis points (0, 10) and (20, 0).

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Answer:

If Doug has $100,000 in a savings account that earns 13% interest per year and the interest is not compounded, then after four years he will earn $52,000 in interest. This is because 13% of $100,000 is $13,000, and since the interest is not compounded, this amount will remain constant for each year. Therefore, after four years Doug will earn a total of $13,000 + $13,000 + $13,000 + $13,000 = $52,000 in interest.

In general, if a savings account earns x% interest per year and the initial amount in the account is y dollars, then after n years the account will earn n * (x/100) * y dollars in interest. For example, if the interest rate is 13% and the initial amount is $100,000, then after four years the account will earn 4 * (13/100) * $100,000 = $52,000 in interest.

Step-by-step explanation:

Answer: He will earn about $3,756.66

Step-by-step explanation:

Answer:

Mr. Conners will use 144 fence posts.

Step-by-step explanation:

Given question is incomplete; please find the question attached herewith.

As we can see from the attachment, Mr Corner's yard is in the rectangular shape.

Total distance around the yard = Perimeter of a rectangle = 2(Length + width)

Length of the yard = 330 ft

And width of the yard = 102 ft

So perimeter of the yard = 2(330 + 102                                         = 864 f

Mr. Conners wants to put a fence post at every 6 feet.

So number of posts used =

                                   =

                                         = 144

The solution is 42 : 98 : 105

The ratio of the number of songs Gerald , Harold and James downloaded is in the ratio 42 : 98 : 105

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Let the ratio of number of songs downloaded by Gerald and Harold be =

3 : 7

Let the ratio of number of songs downloaded by Harold and James be =

14 : 15

So , the number of songs downloaded by Gerald = 3x

The number of songs downloaded by Harold = 7x

And ,

The number of songs downloaded by Harold = 14y

The number of songs downloaded by James = 15y

So , substituting the values in the equation , we get

7x = 14y

x = 2y

And ,

The number of songs downloaded by Gerald = 3 x 14 z

The number of songs downloaded by Gerald = 42z

The number of songs downloaded by Harold = 7 x 14z

The number of songs downloaded by Harold = 98z

The number of songs downloaded by James = 7 x 15z

The number of songs downloaded by James = 105z

So , the ratio of the number of songs Gerald , Harold and James downloaded = 42z : 98z : 105z

On simplifying the proportion , we get

The ratio will be = 42 : 98 : 105

Hence , The ratio of the number of songs Gerald , Harold and James downloaded is in the ratio 42 : 98 : 105

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Answer:

81

Step-by-step explanation:

81 * 1 = 81

If the 81x1 is = 81 * 1 then it should be 81.

If its not I will redo my answer.

Answer:

81 x 1 is 81

81

x 1

81

Domain - the set of possible x-coordinates of a function.

Range - the set of possible y-coordinates of a function.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Domain is:

Range is:

This is not a function as it fails the vertical line test.

Domain is:

Range is:

This is a function as it passes the vertical line test.

Answer:

17

Step-by-step explanation:

You need to use the formula for Arithmetic Sequences.

[tex]a_{n}=a_{1}+(n-1)d[/tex]

You need to plug in the value for [tex]a_{1}[/tex] which is just the first value in your sequence. As well as [tex]n[/tex] which is the term your looking for, in this case it's 48. Lastly [tex]d[/tex] which is the amount that the pattern is increasing or decreasing by. If the sequence is increasing then the [tex]d[/tex] is positive but if the sequence is decreasing then the [tex]d\\[/tex] is negative.

The combined area of the shaded triangles in figure one is 2ab. We have four congruent right triangles given, with legs a and b. The formula to calculate the area of a right triangle is (leg * leg) / 2. So the area of one of the triangles is ab/2. We have four of these triangles, so ab/2 * 4 = 2ab.

The area of the unshaded square in figure one can be represented as c^2. Since the side of the square is given as c, its area must be c^2 (calculate the area of a square by multiplying its side length by itself).

The combined area of the unshaded squares in figure 2 can be represented by a^2 + b^2. Again, we find the areas of each square by multiplying the side lengths togther: (a * a) + (b * b) = a^2 + b^2.

Finally the areas of the squares in figure one and figure two show that a^2 + b^2 = c^2. This is because the shaded triangles in figure one take up the same area as that of figure two. And since the total figure areas are the same, the unshaded parts of each figure must be equal to each other. Therefore, we have a^2 + b^2 = c^2. This is also known as the Pythagorean Theorem.

Using the AAS rule.

ST ≅ UT (given)

∠SRT≅∠UVT (given)

∠RTS ≅ ∠UVT (opposite angles)

∠RST ≅ ∠VUT (AAS rule)

Proved.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

AAS rule:

When two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

From the figure we have,

ST ≅ UT (given)

∠SRT≅∠UVT (given)

∠RTS ≅ ∠UVT (opposite angles)

∠RST ≅ ∠VUT (AAS rule)

Thus,

∠RST is congurent to ∠VUT using the AAS rule.

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If Group 1 trees produce 25 percent more coconuts than Group 2, proportionately, Group 2 trees produce 120 coconuts.

Proportion refers to the two ratios equated to each other.

Proportion shows how much quantity or value is contained in another.

We depict proportions using fractional values, such as fractions, decimals, and percentages.

The number of coconuts produced by Group 1 trees = 150

The percentage by which Group 1 trees produce more than Group 2 = 25%

Let Group 1's production compared to Group 2's = 1.25 (100% + 25%)

Let Group 2's production = 100% = 150/125 x 100

= 120 coconuts

Thus, Group 2 trees would produce 120 coconuts compared to Group 1 trees that produced 150, which was proportionately, 25% more.

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Angle K has  a value of 63 degrees.

Given,

The triangle KLM

Angle L = 4x + 7

Angle K = 6x - 9

Angle M = 118° (Exterior)

We have to find the value of angle K.

Here,

Angle M (Interior) = 180 - 118 = 62° (linear pair of angles)

Now,

Angle L + Angle K + Angle M = 180° (Sum of interior angles of a triangle)

Then,

4x + 7 + 6x - 9 + 62 = 180

10x - 2 + 62 = 180

10x  + 60 = 180

10x = 180 - 60

x = 120/10

x = 12

Now,

Angle K = 6x - 9  = 6 × 12 - 9 = 72 - 9 = 63

That is,

The value of Angle K is 63 degrees.

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Answer:

A.124

Step-by-step explanation:

Because it's like that

Answer:

A. 124

Step-by-step explanation:

<3

There are no local extrema since there isn't any x value that causes the first derivative to be equal to 0.

z = 5x + 3 y

Discover the function's first derivative.

By applying the Sum Rule, the derivative of 5 x + 3 y with respect to x is d d x [ 5 x ] + d /d x [ 3 y ].

d/d x [ 5 x] + d /d x [ 3 y]

Analyze d /d x [ 5 x ].

Tap to take other actions...

5 + d /d x [ 3 y]

Because 5 is independent of x, its derivative is 5 d d x [ x ] since 5 is constant with respect to x.

5 d/ d x [ x ] + d /d x [ 3 y]

The Power Rule, which asserts that d d x [ x n ] is n x n 1 where n = 1. 5 1 + d d x [ 3 y ] is a method of differentiation, says that you should differentiate.

Subtract 1 from 5 and multiply the result by 5 + d /d x [ 3 y ]

The Constant Rule can be used to differentiate.

Because 3 y is constant in relation to x, its derivative in relation to x is 0 (5 + 0).

Subtract 5 from 0 to get 5.

Since 5 is constant in relation to x, its derivative in relation to x is 0 (f " (x ) = 0).

By setting the derivative to 0, you can solve the problem and discover the function's local maximum and lowest values.

5 = 0

There are no local extrema since there isn't any x value that causes the first derivative to be equal to 0.

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Answer:

=(3,-4)

Step-by-step explanation:

At two points [tex]x_{1}[/tex] = π/6 and [tex]x_{2}[/tex] = 5π/6 (using trigonometric function)

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

⇒[tex]x_{1}[/tex] = π[tex](2n + \frac{1}{6} )[/tex] or [tex]x_{2}[/tex] = π[tex](2n + \frac{5}{6} )[/tex]

where n is an integer

But hence x belongs to [-3π , 3π]

the acceptable solutions are

[tex]x_{1}[/tex] = π/6 and [tex]x_{2}[/tex] = 5π/6

What are Trigonometric Functions?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides.

There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Function of Sine

The ratio of the opposing side's length to the hypotenuse is known as an angle's sine function. According to the diagram above, sin is worth:

Sin a =Opp/Hypo = CB/CA

Function of Cosine

The cosine of an angle is the ratio of the neighbouring side's length to the hypotenuse's length. The cos function will be derived as follows from the diagram up top.

Cos a = Adjacent/Hypotenuse = AB/CA

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Answer:

9/56

Step-by-step explanation:

Area of a rectangle = width x length

Area = (3/8) x (3/7) = 9/56

Mutiplying fractions is easy, just multiply the numerator, then multiply the denominator.

The height of the flagpole in this problem is calculated as follows:

12.9 feet.

The height of the flagpole in this problem is obtained using similar triangles, as shown by the image given at the end of the answer.

Similar triangles are used because the equivalent sides have proportional side lengths.

From the image given at the end of the answer, the equivalent sides of each triangle are given as follows:

Then the proportional equation is given as follows:

8/20 = 5.1667/x

Applying cross multiplication, the height of the flagpole is calculated as follows:

8x = 20 x 5.1667

x = 20 x 5.1667/8

x = 12.9 feet.

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The system of equation is 45x+75y=1455.

The number of small boxes is 14 and large boxes is 11.

In the given question,

The paper will be shipped in small boxes and large boxes.

Each small box of paper weights 45 pounds.

Each large box of paper weights 75 pounds.

There were 3 more small boxes shipped than large boxes and the total weight of all boxes was 1455 pounds.

We have to write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped.

We also have to define the variables that we use to write the system.

Let x be the number of small boxes.

Let y be the number of large boxes.

There were 3 more small boxes shipped than large boxes.

So x = y+3

Weight of x number of small boxes = 45x

Weight of y number of small boxes = 75y

Total weight of boxes = 1455

So; 45x+75y=1455

Now putting the value of x to this system of equation

45(y+3)+75y=1455

45y+135+75y=1455

120y+135=1455

Subtract 135 on both side, we get

120y=1320

Divide by 120 on both side, we get;

y=11

Now putting the value of y in x=y+3

x = 14

Hence, the number of small boxes is 14 and large boxes is 11.

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Answer:

Ax + By = C is standard form.

Step-by-step explanation:

It is standard form because slope intercept is y = mx + b and point slope is y-y₁=m(x-x₁)

Hope this helps

Answer:

Standard form.

Step-by-step explanation:

y=mx + b is the slope-intercept form.

The product of the polynomials (4 + 2x³)(4 − 2x³) is 16 - 4x⁶

From the question, we have the following parameters that can be used in our computation:

Polynomial products: (4 + 2x3 )(4 − 2x3 )

Rewrite the above product properly

So, we have the following representation

Polynomial products = (4 + 2x³)(4 − 2x³)

Using the difference of two squares identity

We have the following representation

Polynomial products = (4)² - (2x³)²

Evaluate the exponents

Polynomial products = 16 - 4x⁶

Hence, the product is 16 - 4x⁶

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