Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?

AB = 25
27 < AB < 81
AB = 85
AB< 27 or AB > 81

Using it's concept, the probability that a randomly selected student is in music/drama is: 25%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Hence, in this problem, the probability will be found dividing the number of students that are in music or drama by the total number of students.

These data is given in a table, which is not given in this exercise. Researching this problem on the internet, we have that there are 20 + 7 + 3 + 20 + 13 + 2 + 25 + 5 + 5 = 100 students, of which 7 + 13 + 5 = 25 are in music/drama, hence the probability is:

P = 25/100 = 25%.

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Answer:

No

Step-by-step explanation:

Lets simplify both expressions:

We will start with Gloria's first expression:

[tex]1/4 (12x + 24) -9x[/tex]

Apply distributive property:

[tex](3x + 6) -9x[/tex]

Combine like terms, we are then left with:

[tex]6-6x[/tex]

Now lets simplify the second expression

[tex]-6(x+1)[/tex]

Apply distributive property

[tex]-6x-6[/tex]

Rearrange:

[tex]-6-6x[/tex]

Now we can see that the two equations are not equal, as the first is 12 greater than the second. Another way we could have tested this was plugging in a value for x and then solving.

Answer:

  A.  The volumes are the same, based on Cavalieri's principle.

Step-by-step explanation:

Cavalieri's principle tells us the volumes of solids will be identical if their cross sectional areas are identical at every height.

A right cylinder and an oblique cylinder of the same height and radius will both have circular cross sections of the given radius at any height. Since the radius is the same, the area of the circle is the same. Hence the requirements of Cavalieri's principle are met, and the cylinders have the same volume.

Considering the volume of a rectangular prism, since the new volume is greater than the filled volume, the new dimensions would work, and 90.29% of the infuser would be filled.

The volume of a rectangular prism of length l, width w and height h is given by:

V = lwh.

The original dimensions are:

h = 7.9 cm, l = 3 cm, w = 1.5.

Hence the volume in cm³ was:

V = 7.9 x 3 x 1.5 = 35.55 cm³.

The infuser was filled to 80% capacity, hence:

Vf = 0.8 x 35.55 = 28.44 cm³.

For the new dimensions, we have that h = 7 cm, hence the volume is:

Vn = 7 x 3 x 1.5 = 31.5 cm³.

28.44/31.5 x 100% = 90.29%.

Since the new volume is greater than the filled volume, the new dimensions would work, and 90.29% of the infuser would be filled.

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Based on the graph of the cupcakes done, we find that w(2) = 5.

Herein we have an application of linear equations to the production of cupcakes. In accordance with the graph, the horizontal axis is for the preparation time (x) and the vertical axis is for the quantity of cupcakes done (w). Based on the graph, we find that w(2) = 5.

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The common difference is (1,0.38).

An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. In this type of progression, there is a possibility to derive a formula for the nth term of the AP. For example, the sequence 2, 6, 10, 14, … is an arithmetic progression (AP) because it follows a pattern where each number is obtained by adding 4 to the previous term.

x1 = 1 , y1 = 24

x2 = 2, y2 = 24.38

x3 = 3 , y3 = 24.76

x4 = 4 , y4 = 25.14

Thus the common difference equals :-

x2 - x1 = x3 - x2 = x4 - x3 = 1

y2 - y1 = y3 - y2 = y4 - y3 = 0.38.

Thus the common difference is (1,0.38).

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Answer:

D. [tex]\displaystyle{\dfrac{5^8}{9^8}}[/tex]

Step-by-step explanation:

The law of exponent defines that:

[tex]\displaystyle{\left(\dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n}}[/tex]

In word, you simplify the expression by expanding an exponent to both numerator and denominator.

So from the expression [tex]\displaystyle{\left(\dfrac{5}{9}\right)^8}[/tex], you expand the exponent 8 in both numerator and denominator then you'll end up with D choice!

If you have any questions then please let me know in comment!

The length of diagonal is 9.5 ft

What is Pythagoras theorem?

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

We will find the length of diagonal as shown below:

l= 7 ft

h= 5 ft

w= 4 ft

Let diagonal be d.

Let v be the diagonal of the base.

Using Pythagoras theorem

[tex]v=\sqrt{7^2+4^2}[/tex]

[tex]=\sqrt{49+16}[/tex]

[tex]v=\sqrt{65}[/tex]

For finding the value of d again using Pythagoras theorem

[tex]d=\sqrt{v^2+h^2}[/tex]

[tex]=\sqrt{(\sqrt{65})^2+5^2 }[/tex]

[tex]=\sqrt{65+25}[/tex]

[tex]=\sqrt{90}[/tex]

=9.4868

Rounding to nearest tenth

=9.5

Hence, the length of diagonal is 9.5 ft

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answer:

+16

steps:

number without the x should be 9

number without the x should be 9c to be 9 needs +16

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divide the number next to the x by 2

-6 divided by 2 is -3

find the square

-3 squared is 9

number without the x should be 9

x²-6x=7

make the equation = 0

x²-6x-7=0

a is the number next x²

b is the number next to x

c is the number without the x

c has to be 9

c is -7

c to be 9 needs +16

x²-6x+9 =0

x²-6x+(-3)² =0

(x-3)²

Answer:

9

Step-by-step explanation:

Completing the square  is a method used to solve the quadratic equation.

        Coefficient of x is '6'. 6 ÷ 2 = 3

       3² = 9

            x² - 6x + 9 = 7 + 9

Answer: To make into a perfect square, 9 must be added.

Answer:

88

Step-by-step explanation: make me brainliest if it is correct

The expression (quotient) which is modelled by the given diagram as in the task content is; (x²+x-2)/(x-1) = x +2.

It follows from the task content that the diagram model in discuss by observation involves a quotient in which case, the division is; (x-1).

Additionally, the dividend in the quotient by observation is the sum of terms as follows;

x² + x +x -x -1 -1 = x²+x -2.

Ultimately, the result of the division according to the model is; (x +2).

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The amount  Tyshawn earn per hour is $13.5

Fractions are written as a ratio of two integers

If after working 80 hours at his job, Tyshawn earned a total of $1080, then;

80 hrs = $1080

In order to calculate the amount earned per hour

Amount per hour = 1080/80

Amount per hour = $13.5

Hence the amount  Tyshawn earn per hour is $13.5

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The values that complete the conversions are

a = 10000

b = 100

c = 1000000

From the question, we are to complete the given conversions

i)

1 m² = a cm²

NOTE: 1 m² =  10000 cm²

∴ a = 10000

ii)

1 cm² = b mm²

NOTE: 1 cm² = 100 mm²

∴ b = 100

iii)

1 km² = c m²

NOTE: 1 km² = 1000000 m²

∴ c = 1000000

Hence, the values that complete the conversions are

a = 10000

b = 100

c = 1000000

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1) Correct.

2) The y-intercept is when x=0, so it is (0,5).

Answer:

706.86ft² or 225π ft²

Step-by-Step Explanation:

r = 15ft

Now solve the area of the circle! :)

A=πr²

A=π15²

A=225π ft²

or to simplify further!

A=706.86ft²

The dimension of the box should be 1.7×1.7×3.58 in inches, applying minimization of surface area.

Dimensions to Minimize the Surface Area of the Box

It is given that the box is square based with an open top.

⇒ The box has one square and 4 rectangles

Thus, the total surface area of the box is given as,

S= a²+ab+ab+ab+ab  

S= a²+4ab ______________ (1)

Here, a is the side of the squared base and length of the rectangular sides of the box, b is the breath of the rectangular sides of the box.

This equation is later used for minimization of the surface area.

Also, the volume, V = a²b

It is also given that volume of the box is 184 in³.

⇒ 184 = a²b _____________ (2)

Forming a One-Variable Equation

From equation (2), b=184/a²

Now, substitute this value of b in equation (1) to get,

S = a² + 4a(184/a²)

S = a² + 4(184/a)

S = a² + 736/a

Minimization of Surface Area to find the Dimension

We require a dimension that will minimize the surface area of the box. Hence, applying minimization surface area, dS/da = 0

dS/da = 2a -736/a²

0 = 2a -736/a²

⇒ 0 = 2a³- 736

2a³ = 736

a³ = 736/2

a³ = 368

a = ∛368

a= 7.17 in

∵V = a²b

184 = (7.17)²b

b = 184/7.17²

b = 184/51.4089

b = 3.58 in

Therefore, 1.7×1.7×3.58 in inches is the required dimension for the box, using minimization of surface area..

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based on the given exponential functions, we can tell that C. Both functions are increasing, but function g increases at a faster average rate.

function g is represented by the model:
g(x) = -18 x (1/3)^x + 2

g(x)=-18(1/3)^x In(1/3)

In1/3 < 0

this means that:

g (x) > 0

for any interval, g(x) > f(x)

this means that g is increasing at a faster rate than f which is increasing as shown by the table given in the question.

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Answer:

100

Step-by-step explanation:

Lets first find the area of the greater square:

[tex]8*14=112[/tex]

And now the area of the cut inside of the square:

[tex]3*4=12[/tex]

Now subtract the area cut from the area of the greater square:

[tex]112-12=100[/tex]

The initial amount of the element is 16

The function is given as:

f(t) = 16(1/2)^t

Set t = 0, to determine the initial amount

f(0) = 16(1/2)^0

This gives

f(0) = 16 * 1

Evaluate

f(0) = 16

Hence, the initial amount of the element is 16

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Answer:

C. Best models this relationship

Step-by-step explanation:



Answer:

C: y=1/3x

Step-by-step explanation:

I'll set up an equation for this.

When x = 6, y needs to be 2.

--> 2 = 6 times ___

since 6 times 1/3 is 2, ___ is 1/3.

Now we know that 1/3 is the slope. In a complete equation, this will be shown as y = 1/3 x.

This can be proven by reinserting the value of x and y.

2 = 1/3 (6)

Since this equation works, we can be sure that C: y=1/3 x is correct.

Answer:

see below

Step-by-step explanation:

90 degree clockwise will change x, y coordinates to  y, -x

point D  1,3    becomes   3,-1

point E   4, 4   becomes  4,-4

point F  4, -2  becomes   -2,-4

point G  1,-1    becomes    -1, -1

Answer:

8.8

Step-by-step explanation:

If DEF///ABC

AB=4.4

Solving an inequality, we will see that there is less than $280 in the pile of money.

Let's say that the amount of money is defined by the variable.

First, we know that Jeri keeps $80, so now in the pile we have:

M - $80.

Now she gives one third of that, then the leftover is:

(2/3)*(M - $80) + $80

We know that this is more than:

M - $200

Then we have the inequality:

(2/3)*(M - $80) + $80 > M - $200

And we can solve this for M.

(2/3)*M  - (2/3)*$80 + $80 > M - $200

(1/3)*$80 + $200 > M - (2/3)*M

(1/3)*$80 + (1/3)*$200 > (1/3)*M

$280 > M

Then we conclude that there is less than $280 in the pile of money.

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The point (12, 190) means that the temperature after 12 hours is 190 degrees Celsius

To do this, we make use of the following points

(12, 190), (14, 201), (15, 301), (16, 305), (18, 350), (20, 40), (25, 450)

Where x represents the number of hours and y represents temperature

See attachment for the scatter plot.

To do this, we make use of the point (12, 190)

This means that the temperature after 12 hours is 190 degrees Celsius

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Answer:

2.5 pounds

Step-by-step explanation:

Answer:

12/5

Step-by-step explanation:

to find tan D you need the opposite and the adjacent sides.

12 is opposite D and 5 is adjacent to D

so using the equation tan=Opposite/adjacent

tanD=12/5

The sine, cosine, cosecant, and secant functions have period 2π; the tangent and cotangent functions have period π.

Definition for Period of a Trigonometric Function :

The pause between any function's repetitions is known as the function's period. The duration of one complete cycle is the period of a trigonometric function. Trigonometric functions include three basic types: sin, cos, and tan, which have periods of -2π, 2π, and π respectively.

If a function repeats itself repeatedly at a predetermined frequency, it is said to be periodic. The formula for t is f(x) = f(x + p), where p is a real number that denotes the period of the function. Period is the interval between two occurrences of the wave.

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Step-by-step explanation:

When evaluating piecewise function, make sure the x value satisfies the function we use.

since 5>3, we use the second equations

That function is a constant function, this means at any x>3, exclusive, we will have a y value of -1.

So

[tex]f(5) = - 1[/tex]

The given magic numbers are placed in the appropriate squares, so that the sum in each row, column and diagonal is all equal as shown below.

First of all, we would rewrite all the rational numbers in their lowest forms:

Next, we would write the sum of the numbers in each row as follows:

First row: 16/19 + 9/19 + 2/19 + (-7/-19) = 34/19

Second row: (-6/-19) + (-3/-19) + 12/19 + 2/1 = 34/19

Third row: 11/19 + 14/19 + 5/19 + (-4/-19) = 34/19

Fourth row: 1/19 + (-8/-19) + 15/19 + 10/19 = 34/19

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