The longer base of an isosceles trapezoid measures 18 ft. The nonparallel sides measure 8 ​ft, and the base angles measure 75 degrees.
​a) Find the length of a diagonal.
​b) Find the area.

Answer: 72

Step-by-step explanation:

There are 9 students to choose from to go the library. After that person is chosen there are 8 students remaining.

First student  and   Second student

           9           x               8                 = 72

There are 36 ways for a teacher to choose 2 students out of 9 to go to the library, using combinations where the order of selection is not important.

The student is asking how many ways there are to choose 2 students out of 9 to go to the library, with the order of selection being irrelevant. This is a classic combinatorics problem that involves calculating combinations. Combinations are used in mathematics to count selections where order does not matter.

To find the number of combinations, denoted as C(n, k), where n is the total number of available options and k is the number of selections made, you can use the formula C(n, k) = n! / (k! * (n - k)!), where ! denotes a factorial. For this specific problem, the formula becomes C(9, 2) = 9! / (2! * (9 - 2)!), which simplifies to C(9, 2) = 9 * 8 / (2 * 1) = 36 ways to choose 2 students out of 9.

Answer:

System of equations of x^2+3x+1=2x^2+2x+3 is x^2-x+2=0.

Step-by-step explanation:

We need to make system of equations of:

x^2+3x+1=2x^2+2x+3

Solving,

Adding -2x^2 on both sides

x^2+3x+1-2x^2=2x^2+2x+3-2x^2

-x^2+3x+1=2x+3

Adding -2x on both sides

-x^2+3x+1-2x=2x+3-2x

-x^2+x+1=3

Adding -3 on both sides

-x^2+x+1-3=3-3

-x^2+x-2=0

Multiplying with -1

x^2-x+2=0

System of equations of x^2+3x+1=2x^2+2x+3 is x^2-x+2=0.

[tex]10x^2-7x-12=\\10x^2-15x+8x-12=\\5x(2x-3)+4(2x-3)=\\(5x+4)(2x-3)[/tex]

Answer:

(2x - 3)(5x + 4)

Step-by-step explanation:

Given

10x² - 7x - 12

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 10 × - 12 = - 120 and sum = - 7

The factors are - 15 and + 8

Use these factors to split the x- term

10x² - 15x + 8x - 12 ( factor the first/second and third/fourth terms )

= 5x(2x - 3) + 4(2x - 3) ← factor out (2x - 3) from each term

= (2x - 3)(5x + 4) ← in factored form

Answer:[tex]\large\boxed{C.\ (x-5)^2}[/tex]Step-by-step explanation:

[tex]f(x)=x-5,\ g(x)=x^2\\\\g\bigg(f(x)\bigg)-\text{put}\ x-5\ \text{expression instead of}\ x\ \text{in}\ g(x):\\\\g\bigg(f(x)\bigg)=(x-5)^2[/tex]

Answer:

-4z-6y-9

Step-by-step explanation:

7z-[(2z+y)-(-5y+3z)+9]-12z

=7z-[2z+y+5y-3z+9]-12z

=7z-2z-y-5y+3z-9-12z

=7z-2z-12z+3z-y-5y-9

=-4z-6y-9

Answer:

A'(0, -8), B'(6, 0), C'(0, 8), D'(-6, 0)

Step-by-step explanation:

Whenever you are doing a 90° clockwise rotation ABOUT THE ORIGIN, it is in the form of [y, -x], meaning you take the y and make it your x, then take your original x and put its OPPOSITE.

90° counterclockwise rotation → [-y, x]

90° clockwise rotation → [y, -x]

I hope this helps, and as always, I am joyous to assist anyone at any time.

can you please add the answers to choose from? I'd like to help

Answer:

B. The second graph displayed.

Step-by-step explanation:

Recieved an 100% on my test with this question!!

Hope I could help! (´⊙◞⊱​◟⊙｀)

[tex](f-g)(x)=2x-6-(3x+9)=2x-6-3x-9=-x-15[/tex]

Answer:

The correct option is C.

Step-by-step explanation:

The correct option is C.

We have given:

f(x) = 2x - 6 and g(x) = 3x + 9

Now we have to find (f-g)(x)

(f-g)(x) = f(x)- g(x)

Now subtract g(x) from f(x)

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

Open the parenthesis. When we open the parenthesis the signs of second bracket will become negative because there is a negative sign outside the bracket.

(f-g)(x)= 2x-6-3x-9

Now solve the like terms:

(f-g)(x)= -x-15

Thus the correct option is C....

Answer:

[tex]\arge\boxed{B.\ (3x^2+4x-7)(x)+(3x^2+4x-7)(-3)}[/tex]

Step-by-step explanation:

[tex]\text{The distributive property:}\ a(b+c)=ab+ac.\\\\(3x^2+4x-7)(x-3)=(3x^2+4x-7)(x)+(3x^2+4x-7)(-3)[/tex]

Answer:

here you go

Step-by-step explanation:

W = (0.6) L

       P = 2  (  L + W  )

       P = 2  [  L + (0.6) L  ]

       P = 2  ( 1.6 L  )

       P = (3.2) L  

       P = (3.2) x

The perimeter of the soccer field with the length of [tex]x[/tex] feet is equal to

[tex]3.2x[/tex] feet.

" Perimeter is defined as the total length around the given geometrical shape."

Formula used

Perimeter of the soccer field [tex]= 2 ( L + W)[/tex]

[tex]L=[/tex] length of the soccer field

[tex]W =[/tex] width of the soccer field

According to the question,

Given,

[tex]'x'[/tex] represents the length of the soccer field

As per the given condition,

Width = [tex]60\%[/tex] of length

          [tex]= \frac{60}{100} \times x\\\\= 0.6x[/tex]

Substitute the value in the formula to get the perimeter,

Perimeter of the soccer field [tex]= 2 ( x+ 0.6x)[/tex]

                                                 [tex]= 2(1.6x)\\\\= (3.2x) feet[/tex]

Hence, the perimeter of the soccer field with the length of [tex]x[/tex] feet is equal to [tex]3.2x[/tex] feet.

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Answer:

The first term of the sequence is 1/5

Step-by-step explanation:

The first term is 1/5.

The reason is that there is a common ratio between each term. In this case multiplying the previous term in the sequence by 5 would give the next term.

So in this case 1/5 is the first term.

If we multiply 1/5 by 5, it will give the next term which is 1.

1/5*5=1

Thus the first term in the sequence = 1/5....

Answer:

C. 86°

Step-by-step explanation:

I just did it on A p 3 x

Answer:

[tex]\frac{15}{61}+\frac{18}{61}i[/tex]

Step-by-step explanation:

[tex]\frac{3}{5-6i}[/tex]

To simplify or to write in the form a+bi, you will need multiply the top and bottom by the bottom's conjugate like so:

[tex]\frac{3}{5-6i} \cdot \frac{5+6i}{5+6i}[/tex]

Keep in mind when multiplying conjugates you only have to multiply first and last.

That is the product of (a+b) and (a-b) is (a+b)(a-b)=a^2-b^2.

(a+b) and (a-b) are conjugates

Let's multiply now:

[tex]\frac{3}{5-6i} \cdot \frac{5+6i}{5+6i}=\frac{3(5+6i)}{25-36i^2}[/tex]

i^2=-1

[tex]\frac{15+18i}{25-36(-1)}[/tex]

[tex]\frac{15+18i}{25+36}[/tex]

[tex]\frac{15+18i}{61}[/tex]

[tex]\frac{15}{61}+\frac{18}{61}i[/tex]

For this case we must simplify the following expression:

[tex]\frac {3} {5-6i}[/tex]

We multiply by:

[tex]\frac {5 + 6i} {5 + 6i}\\\frac {3} {5-6i} * \frac {5 + 6i} {5 + 6i} =\\\frac {3 (5 + 6i)} {(5-6i) (5 + 6i)} =\\\frac {3 (5 + 6i)} {5 * 5 + 5 * 6i-6i * 5- (6i) ^ 2} =\\\frac {3 (5 + 6i)} {25-36i ^ 2} =\\\frac {3 (5 + 6i)} {25-36 (-1)} =\\\frac {3 (5 + 6i)} {25 + 36} =\\\frac {3 (5 + 6i)} {61} =\\\frac {15 + 18i} {61}[/tex]

Answer:

[tex]\frac {15 + 18i} {61}[/tex]

Answer:

Distance between points  (5, -3) and (0, 2) is √50 or 7.07

Step-by-step explanation:

We need to find distance between two points (5,-3) and (0,2)

The distance formula used is:

[tex]d= \sqrt {\left( { x_2-x_1 } \right)^2 + \left( {y_2-y_1} \right)^2 }[/tex]

here

x₁= 5, y₁=-3, x₂=0 and y₂=2

Putting values in the formula:

[tex]d= \sqrt {\left( {x_2-x_1} \right)^2 + \left( {y_2-y_1} \right)^2 }\\d= \sqrt {\left( {0-5} \right)^2 + \left( {2-(-3)} \right)^2 }\\d= \sqrt {\left( {-5} \right)^2 + \left( {2+3} \right)^2 }\\d= \sqrt {25+25}\\d= \sqrt {50}\\d= 7.07[/tex]

So, distance between points  (5, -3) and (0, 2) is √50 or 7.07

Answer:

(E) (20k - 150)/(k - 10)

Step-by-step explanation:

Sum of all scores = average × number of scores = 20 × k = 20k

                   Sum of 10 scores = 15 × 10 =150

      Sum of remaining scores = 20k - 150

Number of remaining scores = k -10

Average of remaining scores = sum of remaining/no. remaining

= (20 k -150)/(k-10)

Answer:

Step-by-step explanation:

Distance of yellow to white = 8 inches which is given

The green ball is at the midpoint of red to white.

Since the green ball is 10 inches to the red ball, the green ball is also 10 inches from the white ball. That's what a midpoint is.

The yellow ball is closer.

Answer:

B. 3.64 to the nearest hundredth.

Step-by-step explanation:

3tan1/3theta=8

tan1/3theta = 8/3

1/3 theta =  1.212 radians, 1.212 + π radians.

theta = 1.212 * 3 = 3.636 radians,    3(1.212 + π) radians.

The second value is greater than 2π radians.

The correct answer is C. 1.21, 2.26, 3.31, 4.35, 5.40.

To solve the equation [tex]\( 3 \tan \frac{1}{3}\theta = 8 \)[/tex] in the interval[tex]\( 0 \) to \( 2\pi \)[/tex], we first isolate [tex]\( \tan \frac{1}{3}\theta \):[/tex]

[tex]\[ \tan \frac{1}{3}\theta = \frac{8}{3} \][/tex]

Next, we take the inverse tangent (arctan) of both sides to solve for

[tex]\[ \frac{1}{3}\theta = \arctan\left(\frac{8}{3}\right) \][/tex]

Now, we multiply both sides by 3 to solve for [tex]\( \theta \)[/tex]:

[tex]\[ \theta = 3 \cdot \arctan\left(\frac{8}{3}\right) \][/tex]

Using a graphing calculator, we find the values of [tex]\( \theta \)[/tex] that satisfy the equation within the interval [tex]\( 0 \)[/tex] to[tex]\( 2\pi \)[/tex]. The calculator will give us the principal value and we need to consider all solutions within the given interval, taking into account the periodicity of the tangent function.

The principal value for [tex]\( \arctan\left(\frac{8}{3}\right) \)[/tex] is approximately[tex]\( 1.21 \)[/tex] radians. Since the tangent function has a period of[tex]\( \pi \)[/tex], we add multiples of[tex]\( \pi \)[/tex] to find other solutions within the interval [tex]\( 0 \)[/tex] to [tex]\( 2\pi \).[/tex]

[tex]\[ \theta \approx 1.21 + k\pi \][/tex]

where [tex]\( k \)[/tex] is an integer such that[tex]\( \theta \)[/tex] remains within the interval [tex]\( 0 \)[/tex] to[tex]\( 2\pi \).[/tex]

For[tex]\( k = 0 \):[/tex]

[tex]\[ \theta \approx 1.21 \][/tex]

For [tex]\( k = 1 \):[/tex]

[tex]\[ \theta \approx 1.21 + \pi \approx 4.35 \][/tex]

For[tex]\( k = 2 \):[/tex]

[tex]\[ \theta \approx 1.21 + 2\pi \approx 7.49 \][/tex]

However, this value is outside our interval, so we do not include it.

For[tex]\( k = 3 \):[/tex]

[tex]\[ \theta \approx 1.21 + 3\pi \approx 10.63 \[/tex]]

This value is also outside our interval, so we do not include it.

Since the tangent function is periodic with a period of [tex]\( \pi \),[/tex] we also need to consider the solutions in the second half of the interval[tex]\( 0 \)[/tex] to [tex]\( 2\pi \),[/tex] which are obtained by subtracting the principal value from[tex]\( 2\pi \):[/tex]

[tex]\[ \theta \approx 2\pi - 1.21 + k\pi \][/tex]

[tex]\[ \theta \approx 2\pi - 1.21 + k\pi \][/tex]

For [tex]\( k = 0 \)[/tex]:

[tex]\[ \theta \approx 2\pi - 1.21 \approx 5.40 \][/tex]

For [tex]\( k = 1 \)[/tex]:

[tex]\[ \theta \approx 2\pi - 1.21 + \pi \approx 8.54 \][/tex]

This value is outside our interval, so we do not include it.

Therefore, the solutions within the interval[tex]\( 0 \)[/tex] to [tex]\( 2\pi \)[/tex], rounded to the nearest hundredth, are: [tex]\[ \boxed{1.21, 2.26, 3.31, 4.35, 5.40} \][/tex]

Note that [tex]\( 2.26 \)[/tex] and [tex]\( 3.31 \)[/tex] are obtained by adding [tex]\( \pi \) to \( 1.21 \)[/tex] and [tex]\( 2.26 \)[/tex]respectively, which are the first two solutions in the first half of the interval. These values are within the interval [tex]\( 0 \) to \( 2\pi \)[/tex] and are also solutions to the original equation.

Step-by-step explanation:

hi I have answered ur question

To make n the subject of the formula t = square root of n+3/n, we can isolate the square root term by squaring both sides of the equation and rearranging the equation to make n the subject.

To make n the subject of the formula t = √(n+3)/n, we can start by isolating the square root term. To do this, we square both sides of the equation:

t2 = √(n+3)/n2

Next, we can multiply both sides by n2 to get rid of the denominator:

t2n2 = n + 3

Finally, we can rearrange the equation to make n the subject:

n = (t2n2 - 3)/t2

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Answer:

f(8) = 8.25(1.1)^7 ; f(8) = 16.077 ⇒ answer B

Step-by-step explanation:

* Lets explain how to solve the problem

∵ The x-coordinate is the number of the obstacle

∵ The y-coordinate is the average time to complete the obstacle

∵ The order pairs of function are (1 , 8.25) , (2 , 9.075) , (3 , 9.9825) ,

  (4 , 10.98075)

- From these order pairs

# The time to finish the 1st obstacle is 8.25 minutes

# The time to finish the 2nd obstacle is 9.075 minutes

# The time to finish the 3rd obstacle is 9.9825 minutes

# The time to finish the 4th obstacle is 10.98075 minutes

∵ 2nd ÷ 1st = 9.075/8.25 = 1.1

∵ 3rd ÷ 2nd = 9.9825/9.075 = 1.1

∵ 4th ÷ 3rd = 10.98075/9.9825 = 1.1

∴ There is a constant ratio 1.1 between each 2 consecutive terms

∴ The order pairs formed a geometric series

- Any term in the geometric series Un = a r^(n - 1) , where a is the 1st

 term in the series , r is the constant ratio and n is the position of the

 term in the series

∵ a = 8.25 ⇒ the time of the first obstacle

∵ r = 1.1

- Sheila wants to find the average time she will need for the 8th

 obstacle

∴ n = 8

∵ The explicit formula is f(x) = a r^(n - 1)

∴ f(8) = 8.25 (1.1)^(8 - 1)

∴ f(8) = 8.25(1.1)^7

∴ f(8) = 16.076916 ≅ 16.077

* f(8) = 8.25(1.1)^7 ; f(8) = 16.077

Answer:

Option) BEE is the correct answer!

Step-by-step explanation:

Answer:

The left end goes up and the right end goes down.

Step-by-step explanation:

Lets solve the function first and then find out the end behavior of the polynomial:

The given function is  f(x)=-x^3+x^2-4x+2

First step is: Identify the degree of the polynomial. For this we have to  find out the variable with the largest exponent.

The variable with the largest exponent in the given function is -x³

The degree of the polynomial is the largest exponent on the variable.

3 is the degree of the polynomial.

Since the degree is Odd, the ends of the function will point in the opposite direction.

Now find out the leading coefficient of the polynomial which is -1.

Since the leading coefficient is negative the graph falls to the right.

To find the behavior we have to use the degree of the polynomial as well as the sign of leading coefficient.

If it is ODD and NEGATIVE then the the left end goes up and the right end goes down.

Therefore the end behavior of the given function will be described as "the the left end goes up and the right end goes down"....

Answer:

The graph of g(x) is a translation of f(x) 3 units down.

Step-by-step explanation:

The given function is

[tex]g(x) = f(x) - 3[/tex]

The parent function now is f(x).

The -3 tells us that there is a vertical translation of the parent function 3 units down.

Therefore the graph of g(x) is obtained by translating the graph of f(x) down by 3 units.

Answer:

Option B

center (3,2)

radius 3

Step-by-step explanation:

Given:

x^2+y^2-6x+4y+4=0

x^2+y^2-6x+4y=-4

Now completing square of x^2-6x by introducing +9 on both sides:

x^2-6x+9+y^2+4y=-4+9

(x-3)^2+y^2+4y=5

Now completing square of y^2+4y by introducing +4 on both sides:

(x-3)^2+y^2+4y+4=5+4

(x-3)^2 + (y-2)^2= 9

Now comparing with the circle equation:

(x-h)^2 + (y-k)^2= r^2

where

r= radius of circle

h= x-offset from origin

k= y-offset from origin

In given case

r=3

h=3

k=2

Hence, option B is correct with radius =3 and center =(3,2)!

Answer:

Center (3,-2); radius 3

Answer:

C. 4, 7, 11, 11, 16, 17

Step-by-step explanation:

The mean is the average of the numbers'

The median is the middle number

The mode is the number that occurs most often.

Let's look at each data set I turn.

A. 10, 10, 12, 12, 13, 13

Mean = 11. 7; Median: = 12; Modes: 10, 12, 13

All three measures are different.

B. 2, 3, 4, 4, 5, 7

Mean = 4.2; median = 4; mode = 4

Median and mode are the same, but the mean is different.

C. 4, 7, 11, 11, 16, 17

Mean = 11; median = 11; mode = 11

All three measures are the same.

D. 1, 2, 3, 3, 5, 6

Mean = 3.3; median = 3; mode = 3

Median and mode are the same, but the mean is different.

Step-by-step explanation:

simplify the equation

5-x(2)-3x(4x-7)/(5-x)(3x)

=10-2x-12x²+21x/15x-3x²

=-12x²-23x+10/15x-3x³

the answer is B

yes, Robot is correct but Irum is not

Answer:

simplify the equation first

5-x(2)-3x(4x-7)/(5-x)(3x)

=10-2x-12x²+21x/15x-3x²

=-12x²-23x+10/15x-3x³

the answer is B

Step-by-step explanation:

:)

Explanation:

Using the rule that x = x^1, we can rewrite the p as p^1

So 11m^3n^2p is the same as 11m^3n^2p^1

The exponents are: 3, 2, 1

Those exponents add up to 3+2+1 = 6

The degree of a monomial like this is simply equal to the sum of the exponents.

Answer:

6

Step-by-step explanation:

First of all, recall that 1.5m is the same as 150cm.

Now, we simply build a proportion where we consider 48 to be 100, and wonder what 150 will be:

[tex]48\div 100 = 150 \div x[/tex]

Solving for x, we have

[tex]x = \dfrac{150\cdot 100}{48}=\dfrac{15000}{48} = 312.5[/tex]

Which actually makes sense, because we're stating that 1.5m is about 300% of 48cm, which means three times as much. Which is true, because three times 48cm means 144cm, which is about 1.5m

Answer:

Step-by-step explanation:

To solve this problem, you must first have the numbers in the same units, that is, convert the meters to centimeters and operate with them or transform to meters and work with them, therefore, I decide to work with centimeters, like this:

Then, you can make a simple rule of three, where 150 centimeters corresponds to 100% and you look for the percentage of 48 centimeters:

So:

Therefore, the percentage of 48 centimeters is equal to 32%.

Answer:

Answer is x>3

Step-by-step explanation:

The last step is: divide -2 to both sides and since the 2 is negative the sign flips so it would be x>3.

Hope my answer has helped you and if not i'm sorry.

Answer:

2 /√3 or  2√3 / 3.

Step-by-step explanation:

Referring to the 30-60-90 triangle: hypotenuse = 2 , smaller leg = 1 and longer leg = √3 and the shorter side is opposite the 30 degree angle.

So cos 30 = √3/2

Sec 30 = 1 / cos 30

= 2 /√3

or  2√3 / 3.

The exact value of sec(30º) using trigonometric identity for secant is 2.

To find the exact value of sec(30º), use the trigonometric identity for secant:

sec(θ) = 1/cos(θ)

Using the special right triangle with angles 30º, 60º, and 90º, it is known that the side lengths are in the ratio 1:√3:2.

The cosine is defined as the adjacent side divided by the hypotenuse.

For a 30º angle, the adjacent side = 1 and the hypotenuse = 2.

So, cos(30º) = 1/2

Substituting this into the formula for secant:

sec(30º) = 1/cos(30º)

               = 1/(1/2)

               = 2

Therefore, the exact value of sec(30º) is 2.

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Answer:

the cost of each notebook is $4.8

Step-by-step explanation:

Cost of each notebook= ?

Cost of a poster = $6

Total amount she spent = $20.40

If we subtract the cost of poster from total amount we get the cost of 3 notebooks.

$20.40-$6

=$ 14.4

It means the cost of 3 notebooks = $14.4

To find the cost of each notebook divide the cost of 3 notebooks by the number of books.

=14.4/3

=$4.8

Thus the cost of each notebook is $4.8....