A roller coaster carries riders up a ramp that is 39 meters long. This ramp
forms a right triangle with the ground and a vertical support beam. What is
the height of the support beam?
Support
Roller coaster 9
Ground
15 m
OOOO
A. 36 m
24 m
C. 42 m
D. 54 m

Answer:

c. 1; rational

Step-by-step explanation:

k² − 10k + 25 = 0

The discriminant of ax² + bx + c is b² − 4ac.

If the discriminant is negative, there are no real roots.

If the discriminant is zero, there is 1 real root.

If the discriminant is positive, there are 2 real roots.

If the discriminant is a perfect square, the root(s) are rational.

If the discriminant isn't a perfect square, the root(s) are irrational.

Finding the discriminant:

a = 1, b = -10, c = 25

(-10)² − 4(1)(25) = 0

The discriminant is zero, so there is 1 rational root.

Answer:

Option C 3 + 4 = 9 or 5 · 2 = 11 is correct answer

Step-by-step explanation:

Disjunction states that if we have p or q then the disjunction is true if either p is true or q is true or p and q are true.

The disjunction is false when both p and q both are false.

1. 2 · 3 = 6 or 4 + 5 = 10

Disjunction is true because 2.3 =6 is true while 4+5=10 is false

2.  5 - 3 = 2 or 3 · 4 = 12

Disjunction is true because 5-3 =2 is true and 3.4=12 is also true.

3. 3 + 4 = 9 or 5 · 2 = 11

Disjunction is false because 3+4 =7 and not 9 and 5.2 =10 and not 11. Since both are false so, this disjunction is false.

4. 6 · 2 = 11 or 3 + 5 = 8

Disjunction is true because 6.2=12 and not 11 is false but 3+5 = 8 is true.

So, Option C 3 + 4 = 9 or 5 · 2 = 11 is correct answer.

Answer:

4i sqrt(2)

Step-by-step explanation:

sqrt(-2) + sqrt(-18)

We know sqrt(ab)= sqrt(a) sqrt(b)

sqrt(-1)sqrt(2) + sqrt(9) sqrt(-2)

sqrt(-1)sqrt(2) + sqrt(9) sqrt(2)sqrt(1)

We know the sqrt(-1) is equal to i

i sqrt(2) +3 sqrt(2) i

i sqrt(2) +3i sqrt(2)

4i sqrt(2)

Answer:

153938040.0259 ft2

Step-by-step explanation:

R= Square root of A/π

Answer:

153,860,000 ft^2.

Step-by-step explanation:

The area = 3.14 * r^2

= π * 7,000^2

= 153,860,000 ft^2.

Check the picture below.

bearing in mind that in essence, a reference angle is the angle made with the x-axis from any terminal point.

Answer:

○C. x + 2

Step-by-step explanation:

x^4 + 2x^3 -x-2

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

x^3 -1

Factor the numerator by grouping.  Take an x^3 from the first 2 terms and -1 from the last 2 terms

x^3( x + 2) -1(x+2)

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

x^3 -1

now lets factor out the x+2

( x + 2)(x^3 -1)

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

x^3 -1

Canceling out the x^3-1, we are left with

x+2

Answer:

C. x+2

Step-by-step explanation:

The given expressions are two polynomials which have to be divided in order to find the quotient. The long division method will be used to find the quotient of the two terms.

The long division is done and the picture is attached for detail.

From the picture, we can see that the correct answer is:

C. x+2 ..

Answer:

x² + y² = 36

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ← r is the radius

here r = 6, so

x² + y² = 6², that is

x² + y² = 36

The circle's equation is x² + y² = 36.

Given:

length of its radius is 6.

To find:

the circle's equation

The equation for a circle in center, radius form is

(x - h)² + (y - k)² = r²  

The equation of a circle centered at the origin is

x² + y² = r²  

Where, r is the radius of the circle

Here radius of the circle = 6

If the center is (0,0) then h = 0 and k = 0

x² + y² = 6²,

x² + y² = 36

Therefore, the circle's equation x² + y² = 36.

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Answer:

[tex]a_n=9.5 \cdot (0.2)^{n-1}[/tex]

Step-by-step explanation:

If this is a geometric sequence, it will have a common ratio.

The common ratio can be found by dividing term by previous term.

The explicit form for a geometric sequence is [tex]a_n=a_1 \cdot r^{n-1} \text{ where } a_1 \text{ is the first term and } r \text{ is the common ratio}[/tex]

We are have the first term is [tex]a_1=9.5[/tex].

Now let's see this is indeed a geometric sequence.

Is 0.076/0.38=0.38/1.9=1.9/9.5?

Typing each fraction into calculator and see if you get the same number.

Each fraction equal 0.2 so the common ratio is 0.2.

So the explicit form for our sequence is

[tex]a_n=9.5 \cdot (0.2)^{n-1}[/tex]

Final answer:

A geometric sequence follows a specific pattern where each term is obtained by multiplying the previous term by a constant ratio. The explicit rule for a geometric sequence is defined by the first term, the term number, and the common ratio.

Explanation:

Geometric series are sequences in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. The explicit rule for a geometric sequence is of the form an = a₁ * r⁽ⁿ⁻¹⁾, where a₁ is the first term, n is the term number, and r is the common ratio.

Answer:

AB=20

Step-by-step explanation:

Given:

r= 14.5

AB cuts r=14.5 in two parts one parts length=4

remaining length, x = 14.5 - 4 =10.5

draw a line from center of circle to point A making right angled triangle

Now hypotenuse=r=14.5

and one side of triangle=10.5

Using pythagoras theorem to find the third side:

c^2=a^2+b^2

14.5^2=10.5^2+b^2

14.5^2-10.5^2=b^2

b^2=100

b=10

AB=2b

     =2(10)

     =20

Hence length of cord AB=20!

Answer:

a) P(z>1.16) = 0.8770

b) P(z>-0.75) = 0.2266

Step-by-step explanation:

Mean = 205 cm

Standard Deviation = 8.6 cm

a) Find the probability that an individual distance is greater than 215.00

We need to find P(X>215)

x = 215

z = x - mean /standard deviation

z = 215 - 205 / 8.6

z = 1.16

P(X>215)=P(z>1.16)

Finding value of z =1.16 from the table

P(z>1.16) = 0.8770

b) Find the probability that the mean for 25 randomly selected distances is greater than 203.70 cm

Sample size n= 25

x = 203.70

mean = x- mean / standard deviation / √sample size

mean = 203.70 - 205 / 8.6 / √25

mean = -1.3/8.6/5

mean = -0.75

Finding value from z-score table

P(mean >-0.75) = 0.2266

c) Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

If the original problem is normally distributed, then for any sample size n, the sample means are normally distributed.

Answer: cos(C)

Step-by-step explanation: Use SohCahToa. Sin(A) is opposite over hypotenuse. The opposite is line BC. Use angle C. To get line BC, you will need the adjacent, and also the hypotenuse. Cos will get you this. Therefore, your answer is Cos(C).

The one which is equivalent to [tex]sin(A)[/tex] will be [tex]Cos(C)[/tex] .

Trigonometric ratios are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

There are six trigonometric ratios [tex]Sin\theta,Cos\theta,Tan\theta,Cot\theta,Sec\theta,Cosec\theta[/tex] .

We have,

[tex]\triangle ABC[/tex] Right angled at  [tex]B[/tex] .

So,

[tex]sin(A)=\frac{Perpendicular}{Height}[/tex]

So, in  [tex]\triangle ABC[/tex] ,

[tex]sin(A)=\frac{BC}{AC}[/tex]

Now,

To find its equivalent we will look from angle [tex]C[/tex] ,

So, in options we two  trigonometric ratios from angle [tex]C[/tex],

So, take  [tex]Cos(C)[/tex] ,

[tex]Cos(C)=\frac{Base}{Hypotenuse}[/tex]

[tex]Cos(C)=\frac{BC}{AC}[/tex]

i.e. Equivalent to [tex]sin(A)[/tex]  is [tex]Cos(C)[/tex]

Hence, we can say that the one which is equivalent to [tex]sin(A)[/tex] will be [tex]Cos(C)[/tex] which is in option [tex](c)[/tex] .

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[tex]\huge{\boxed{y=-\frac{5}{6} x+4}}[/tex]

Parallel lines share the same slope, so the slope of the parallel line in this case must be [tex]-\frac{5}{6}[/tex].

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex] is any known point on the line.

Plug in the values. [tex]y-(-1)=-\frac{5}{6} (x-6)[/tex]

Simplify and distribute. [tex]y+1=-\frac{5}{6} x+5[/tex]

Subtract 1 from both sides. [tex]\boxed{y=-\frac{5}{6} x+4}[/tex]

Answer:

y = -5/6x   +   4        (slope - intercept form)

OR

5x + 6y -24 = 0          (standard form)

Step-by-step explanation:

What is the equation of the line that goes through the point (6,-1) and is parallel to the line represented by the equation below?

y=-5/6 x+3

To solve this;

We need to first find the slope of the the equation given

Comparing the equation given with y=mx + c, the slope (m) = -5/6, any equation parallel to this equation will have the same slope as this equation.

Since our new equation is said to be parallel to this equation the slope(m) of our new equation is also -5/6.

Now we will proceed to find the intercept of our new equation, to find the intercept, we will simply plug in the value of the points given and the slope into the formula y=mx + c and then simplify

The value of the points given are; (6, -1) which implies x=6 and y=-1  slope(m)= -5/6

y = mx + c

-1 = -5/6 (6)  +  c

-1 = -5  +  c

Add 5 to both-side of the equation to get the value of c

-1+5 = -5+5 + c

4 = c

c=4

Therefore the intercept(c) of our new equation is 4

We can now proceed to form our new equation. To form the equation, all we need to do is to simply insert the value of our slope (m) and intercept (c) into y = mx +  c

y = -5/6x   +   4

This above equation is in slope-intercept form, we can further simplify it to be in the standard form.

6y = -5x + 24

5x + 6y -24 = 0

Answer:

1 4/21

Step-by-step explanation:

(5/9*3/5)+6/7

The 5's cancel

(3/9)+6/7

Cancel a 3 in the numerator and a 3 in the denominator

1/3 + 6/7

We need to get a common denominator of 21

1/3 *7/7  + 6/7 *3/3

7/21 + 18/21

25/21

This is an improper fraction

21 goes into 25 1 time with 4 left over

1 4/21

Answer: [tex]\frac{25}{21}[/tex]

Step-by-step explanation:

The first step is to make the multiplication of the fractions inside the parentheses. To do this, you must multiply the numerator of the first fraction by de numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction:

[tex](\frac{5}{9}*\frac{3}{5})+\frac{6}{7}=\frac{15}{45}+\frac{6}{7}[/tex]

Now you can reduce the fraction  [tex]\frac{15}{45}[/tex]:

[tex]=\frac{1}{3}+\frac{6}{7}[/tex]

 And make the corresponding addition: in this case the Least Common Denominator (LCD) will be the multiplication of the denominators.   Divide each denominator by the LCD and multiply this quotient by the corresponding numerator and then add the products. Therefore you get:

[tex]=\frac{7+18}{21}=\frac{25}{21}[/tex]

Answer:

6

Step-by-step explanation:

imputing 5 into g which makes the equation: 2(5) - 4

2(5) - 4

10 - 4

6

Answer:

6

Step-by-step explanation:

2(5)-4

2*5 is 10

10 subtracted by 4 is 6

Hope this helps ^-^

Answer:

The smaller angle= 68°

The larger angle=112°

Step-by-step explanation:

Supplementary angles add up to 180°

Let the smaller of the angles to x then the larger angle will be x+44.

Adding the two then equating to 180°:

x+(x+44)=180

2x+44=180

2x=180-44

2x=136

x=68

The smaller angle= 68°

The larger angle=68+44=112°

Answer:

The angles are 68° , 112°

Step-by-step explanation:

Let the smaller angle be x

so the larger angle = x + 44

x , x + 44 are supplementary.

so,    x  + (x + 44) = 180

         x  + x + 44  = 180

                      2x  = 180 - 44 = 136

                          x = 136/2 = 68    

 the larger angle = x + 44 = 68 + 44 = 112

[tex]\huge{\boxed{553}}\ \ \huge{\boxed{554}}[/tex]

The numbers can be represented as [tex]x[/tex] and [tex]x+1[/tex].

We know that [tex]x+x+1=1107[/tex].

Combine like terms. [tex]2x+1=1107[/tex]

Subtract 1 on both sides. [tex]2x=1106[/tex]

Divide both sides by 2. [tex]x=553[/tex]

The first number is [tex]x[/tex], which equals [tex]\boxed{553}[/tex].

The second number is [tex]x+1[/tex], which equals [tex]553+1[/tex], which is [tex]\boxed{554}[/tex].

These numbers can be presented as n and n + 1 = 1107

2n = 1106 because we combine the n terms and subtract 1 from each side.

2n ÷ 2 = n

1106 ÷ 2 = 553

We now know that n = 553.

Our second consecutive integer must be 554. This is because our second

consecutive integer represents n + 1 so 553 + 1 =554.

Therefore, are two consecutive integers are 553 and 554.  

Answer:

A''(1,-1) B''(2,2) C''(5,2)

Step-by-step explanation:

Points A(1,−5) B(2,−2) C(5,−2)

reflection over y=-1

Perpendicular distance between points y-coordinates of points (A, B and C) and y=-1 are 4,1 and 1

after reflections, the perpendicular distance will be 8,2,2 and the points will be at

A'(1,3) B'(2,0) C'(5,0)

again  reflection over y=1

Perpendicular distance between points y-coordinates of points (A', B' and C') and y=1 are 2,1 and 1

after reflections, the perpendicular distance will be 4,2,2 and the points will be at

A''(1,-1) B''(2,2) C''(5,2)!

Answer:

f(- 5) = 13

Step-by-step explanation:

To evaluate f(- 5) substitute x = - 5 into f(x)

f(- 5) = - 3 × - 5 - 2 = 15 - 2 = 13

Answer:

d = 6.67s

Step-by-step explanation:

This is the answer because if you take 100 and divide it by 15, then you get d as 6.6666, which rounds up to 6.67s.

[tex]\displaystyle\\\text{We will use numbers from 1 to 9.}\\\\1+2+3+4+5+6+7+8+9=\frac{9(9+1)}{2}=\frac{9\times10}{2}=\frac{90}{2}=\boxed{\bf45}\\\\\text{the sums of the numbers in each row, in each column are }=\frac{45}{3}=\boxed{\bf15}\\\\\text{Solution:}\\\\\boxed{\,2\,}\boxed{\,7\,}\boxed{\,6\,}\\\boxed{\,9\,}\boxed{\,5\,}\boxed{\,1\,}\\ \boxed{\,4\,}\boxed{\,3\,}\boxed{\,8\,}\\\\\text{Convenient rotation of the square gives 8 solutions.}[/tex]

Answer:

3 is the correct option.

Step-by-step explanation:

The given expression is:

3k+6/(k-2)+(2-k)

Break the numerators:

3k/(k-2) + 6/(2-k)

Now Re-arrange the term (2-k) in the denominator as (-k+2)

3k/(k-2) + 6/(-k+2)

Now takeout -1 as a common factor from (-k+2)

3k/(k-2) + 6/-1(k-2)

Now  move a negative (-1)from the denominator of 6/-1(k-2) to the numerator

3k/(k-2) + -1*6/(k-2)

Now take the L.C.M of the denominator which is k-2 and solve the numerator

3k - 6/ (k-2)

Take 3 as a common factor from the numerator:

3(k-2)/(k-2)

k-2 will be cancelled out by each other:

Thus the answer will be 3.

The correct option is 3....

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=-2x+12&(1)\\3y-x+6=0&(2)\end{array}\right\qquad\text{substitute (1) to (2):}\\\\3(-2x+12)-x+6=0\qquad\text{use the distributive property}\\(3)(-2x)+(3)(12)-x+6=0\\-6x+36-x+6=0\qquad\text{combine like terms}\\(-6x-x)+(36+6)=0\\-7x+42=0\qquad\text{subtract 42 from both sides}\\-7x=-42\qquad\text{divide both sides by (-7)}\\\boxed{x=6}\qquad\text{put it to (1)}\\\\y=-2(6)+12\\y=-12+12\\\boxed{y=0}[/tex]

Answer:

[tex]\text{\fbox{(6,~0)}}[/tex]

Step-by-step explanation:

[tex]\left \{ {{\text{y~=~-2x~+~12}} \atop {\text{3y~-~x~+~6~=~0}} \right. \\ \\ \text{We~already~have~the ~value~of ~y ~so~ substitute~ this~ value~~ of ~y ~into~ the ~second ~equation.} \\ \\ \text{3(-2x~+~12)~-~x~+~6~=~0} \\ \\ \text{Distribute~ 3 ~inside~ the~ parentheses.} \\ \\ \text{-6x~+~36~-~x~+~6~=~0} \\ \\ \text{Combine~ like~ terms. ~You ~can~ subtract~ -6x ~and ~x ~and ~add ~36 ~and ~6.} \\ \\ \text{-7x~+~42~=~0} \\ \\ \text{Subtract~ 42 ~from~ both~ sides ~of~ the ~equation.} \\ \\ \text{-7x~=~-42} \\ \\ \text{Now ~solve~ for ~x ~by ~dividing~ both~ sides ~by~ -7.} \\ \\ \text{\fbox{x~=~6}} \\ \\ \text{To~ find~ y, ~substitute~ 6 ~for~x~ into~ the~first~ equation.} \\ \\ \text{y~=~-2(6)~+~12} \\ \\ \text{Multiply ~-2~ and~ 6.} \\ \\ \text{y~=~-12~+~12} \\ \\ \text{Combine~ like ~terms~ to ~complete~ solving~ for ~y.} \\ \\ \text{\fbox {y~=~0}} \\ \\ \text{The~ solution~ to ~this ~system ~of ~equations ~is ~\fbox{(6~,~ 0)}~.}[/tex]

Answer:

1st piece = 15 inch

2nd piece = 15 inch

3rd piece = 30 inch

Step-by-step explanation:

2.

Let length of first piece be x

since 2nd piece is same, so 2nd piece's length is also x

third piece is TWICE, so its length is 2x

Total length of all the 3 pieces is 60, so we setup an equation and solve for x:

x + x + 2x = 60

4x = 60

x = 60/4 = 15

Hence, first piece is 15, second piece is 15, third piece is 2(15) = 30

Answer: C

Step-by-step explanation:

First, you should see that the bottom right corner is an angle on the other side. So subtract 180 from 95 to get 85. Since all angles in a triangle add up to 180, You do 85 + 60 + x = 180. You simplify further to get 145 + x = 180.

Subtracting 145 from both sides leaves you with x = 35, which gives you C.

So C is the correct answer.

Answer:

The other two vertices are (4 , -2) and (4 , 2) ⇒ 2nd answer

Step-by-step explanation:

* Lets explain how to solve the problem

- All the points on a vertical line have thee same x-coordinates

- In the vertical segment whose endpoints are (x , y1) and (x , y2)

 its length = y2 - y1

- All the points on a horizontal line have thee same y-coordinates

- In the horizontal segment whose endpoints are (x1 , y) and (x2 , y)

 its length = x2 - x1

* Lets solve the problem

- The two vertices of the garden are (-1 , 2) , (-1 , -2)

- The side joining the two vertices is vertical because the points have

  the same x-coordinate

∴ The length of the height = 2 - -2 = 2 + 2 = 4

∴ The length of the height of the garden is 4 feet

∵ The garden shaped a rectangle

∵ The area of the garden is 20 feet²

- The area of the rectangle = base × height

∵ The height = 4 feet

∴ 20 = base × 4 ⇒ divide both sides by 4

∴ Base = 5 feet

∴ The length of the base of the garden is 5 feet

- The adjacent side to the height of the rectangle is horizontal line

∵ The points on the horizontal line have the same y-coordinates

∴ The adjacent vertex to vertex (-1 , 2) has the same y-coordinates 2

∵ The length of the horizontal segment is x2 - x1

∴ 5 = x - (-1)

∴ 5 = x + 1 ⇒ subtract 1 from both sides

∴ x = 4

∴ The adjacent vertex to (-1 , 2) is (4 , 2)

- Lets find the other vertex by the same way

∵ The adjacent vertex to vertex (-1 , -2) has the same y-coordinates -2

∵ x-coordinate of this vertex is the same with x- coordinate of point

 (4 , 2) because these two points formed vertical side

∴ The other vertex is (4 , -2)

∴ The adjacent vertex to (-1 , -2) is (4 , -2)

* The other two vertices are (4 , -2) and (4 , 2)

Answer: Option B

(B) (4,-2) and (4,2) <======+ 100%

Step-by-step explanation:

Answer:

x= [tex]\frac{-1}{6}y+\frac{-11}{6}[/tex]

y=6x+11

Step-by-step explanation:

4x + 3y = –5 -2x + 2y = 6

- 4x - 3y  –5 -2x + 2y = 6

- 4x - 3y -2x + 2y = 6+5

-4x - 3y -2x +2y =11

-6x-y= 11

Answer:

A

Step-by-step explanation:

if he had multiplied the 2nd equation by 9 throughout successfully, he would have gotten :

6x - y = 16  (multiply by 9)

54x - 9y = 144

Answer:

(a) The error is in step 1.

See below.

Step-by-step explanation:

They did not multiply the 16 by 9.

Answer:

The correct answer option is B. 2.1 inches.

Step-by-step explanation:

We are given that the cylinder is to hold 42 in³ of liquid while the height of this container is 3 inches tall.

We are to find the best approximation for the radius of this container.

We know that the formula for the volume of a cylinder is given by:

Volume of cylinder = [tex]\pi r^2h[/tex]

Substituting the given values in the above formula to get:

[tex]42=\pi \times r^2 \times 3[/tex]

[tex]r^2 = \frac{42}{\pi \times 3 }[/tex]

[tex]\sqrt{r^2} = \sqrt{4.46}[/tex]

r = 2.1 inches

Answer:

f(-5) = 1/ 243

Step-by-step explanation:

f(x) = 3^x

Let x=-5

f(-5) = 3^-5

Since the exponent is negative, it will move to the denominator

f(-5) = 1/3^5

f(-5) = 1/ 243

For this case we have the following function:

[tex]f (x) = 3 ^ x[/tex]

We must evaluate the function for[tex]x = -5[/tex]

So, we have:

[tex]f (-5) = 3 ^ {-5}[/tex]

By definition of power properties it is fulfilled that:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Thus:

[tex]f (-5) = \frac {1} {3 ^ 5} = \frac {1} {3 * 3 * 3 * 3 * 3} = \frac {1} {243}[/tex]

Answer:

[tex]\frac {1} {243}[/tex]

Answer:

B

Step-by-step explanation:

(74+72+76+80+73+(AnswerB)75)÷6(total number of quizzes include the one she needed to take)=75(minimum average because she needs to get average of 75)