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Answer:

[tex]a_n=42n-621[/tex]

Step-by-step explanation:

This is arithmetic sequence so you should go to linear equations in your head.

Think of the question asking you to find the equation of line going through the points:

(14,-33) and (15,9).

First, let's find the slope.

You need to compute y's change over x's change.

The way I like to do that is line up the points vertically, subtract them, and then put 2nd difference over first.

Like this:

(  15  ,   9)

-(  14  ,  -33)

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

   1         42

So the slope is 42/1=42.

(The slope is our common difference.)

Now point slope form is:

y-y1=m(x-x1) where m is the slope and (x1,y1) is a point you know on the line.

So we have m=42 and (x1,y1)=(15,9).  (You could have chose the other point.)

y-9=42(x-15)

I'm going to put in slope-intercept form.  Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

y-9=42(x-15)

Solve for y by adding 9 on both sides:

y=42(x-15)+9

Distribute 42 to terms in the ( ) :

y=42x-42(15)+9

y=42x-630+9

y=42x-621

So we can which back to n now:

[tex]a_n=42n-621[/tex]

Answer:

2/3

Step-by-step explanation:

Ah, I see. A 1-6 die.

Probability of one number = 1/6

2 numbers? = 2/6

6/6-2/6=4/6

4/6=2/3

[tex]\huge{\boxed{\frac{2}{3}}}[/tex]

There are [tex]4[/tex] numbers on a number cube that are greater than [tex]2[/tex]. They are [tex]3, 4, 5, 6[/tex].

Write this as a fraction. [tex]\frac{\text{4 favorable outcomes}}{\text{6 total outcomes}}[/tex]

Divide both the numerator and denominator by [tex]2[/tex] to simplify. [tex]\boxed{\frac{2}{3}}[/tex]

Answer:

First part:

Set h(t) = 231and solve for t.

-16t²+ 152t + 9= 231

-16t² + 152t - 222= 0

Solve this quadratic equation for t. You should get 2 positive solutions. The lower value is the time to reach 231 on the way up, and the higher value is the time to reach 231 again, on the way down.

Second part:

Set h(t) = 0 and solve the resulting quadratic equation for t. You should get a negative solution (which you can discard), and a positive solution. The latter is your answer.

The constructions will NOT result in a point of concurrency is C. the three midsegments of a triangle.

The central segment is parallel to the sides of the non-intersecting triangles. There are three congruent triangles formed by the central segment and sides of the triangle. Every triangle has three central segments.

The central segment is a line segment connecting the midpoints of the two sides of a triangle. Each triangle has three central segments because each triangle has three sides. The center segment of the triangle is parallel to the third side of the triangle and half the length of the third side.

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Answer:

The correct answer options are:

Circle E

Circle F

Step-by-step explanation:

We are given that a circle A has a radius of 6 and we are to determine whether which of the circles from the answer options are congruent to circle A.

We know that radius is the distance from the center of the circle to any point on circle's circumference.

Circle E, F show the radius of 6, therefore they are congruent to circle A.

Answer:

There is a scale factor of 1

Step-by-step explanation:

the ratio 1:1 means that there is no difference between the two triangles, and that they are congruent.

Answer:

Therefore the probability of 10 - 12 inclusive = 0.20613 + 0.21862 + 0.17004  

= 0.59479  

+ 59.5% to one place of decimals

Step-by-step explanation:

P(exactly 10) = 15C10 * (0.70)^10 * (0.30)^5  

=15! / (10! * 5!) * (0.70)^10 * (0.30)^5  

= (15*14*13*12*11) /(5*4*3*2*1) * (0.70)^10 * (0.30)^5  

= 0.20613  

P(exactly 11) = 15C11 * (0.70)^11 * (0.30)^4  

= (15*14*13*12)/(4*3*2*1) *(0.70)^11 *(0.30)^4  

= 0.21862  

P(exactly 12) = 15C12 * (0.70)^12 * (0.30)^3  

= (15*14*13)/(3*2*1) * (0.70)^12 * (0.30)^3  

= 0.17004  

Answer:

The expression is 5⁵-1 (=3124)

Step-by-step explanation:

Answer:

[tex]\large\boxed{2\dfrac{2}{3}+12\dfrac{6}{8}=15\dfrac{5}{12}}[/tex]

Step-by-step explanation:

[tex]2\dfrac{2}{3}+12\dfrac{6}{8}=2\dfrac{2}{3}+12\dfrac{6:2}{8:2}=2\dfrac{2}{3}+12\dfrac{3}{4}\\\\\text{Find}\ LCD:\\\\\text{List of multiples of 3:}\ 0,\ 3,\ 6,\ 9,\ \boxed{12},\ 15,\ ...\\\text{List of multiples of 4:}\ 0,\ 4,\ 8,\ \boxed{12},\ 16,\ ...\\\\12=3\cdot4\\\\\text{therefore}\\\\\dfrac{2}{3}=\dfrac{2\cdot4}{3\cdot4}=\dfrac{8}{12}\\\\\dfrac{3}{4}=\dfrac{3\cdot3}{4\cdot3}=\dfrac{9}{12}\\\\2\dfrac{2}{3}+12\dfrac{3}{4}=2\dfrac{8}{12}+12\dfrac{9}{12}=(2+12)+\dfrac{8+9}{12}=14+\dfrac{17}{12}\\\\=14+1\dfrac{5}{12}=15\dfrac{5}{12}[/tex]

Answer:

-6

Step-by-step explanation:

This means what value can I plug into -3x-8 so that I get output 10.

g(x)=-3x-8

g(a)=-3a-8

So we are going to solve g(a)=10 for a.

g(a)=10

-3a-8=10

Add 8 on both sides:

-3a   =18

Divide both sides by -3:

 a     =-6

Check it!

g(-6)=-3(-6)-8=18-8=10 and it's good! :)

Answer:

Step-by-step explanation:

To find the zeros, set y=-4(x - 3)2 + 8 = 0.  Then -4(x - 3)^2 = -8, and:

4(x - 3)^2 = 8.  Dividing both sides by 4 yields (x - 3)^2 = 2.

Taking the square root of both sides yields x - 3 = ±2, so that

x = 3 ±2, or x = 5 and x = 1.  These are the zeros. The correct interpretatioon is A:  where the daily profit is $0.

Answer:

Interpretation: The zeros are where the daily profit is $0.00.

Zeroes are x = 1.58 and x = 4.41.

Step-by-step explanation:

Given function,

[tex]y=-4(x-3)^2+8[/tex]

For finding the zeros,

y = 0,

[tex]-4(x-3)^2+8=0[/tex]

[tex]-4(x-3)^2=-8[/tex]

[tex](x-3)^2=2[/tex]

[tex]x-3=\pm \sqrt{2}[/tex]

[tex]\implies x = 3\pm \sqrt{2}[/tex]

[tex]\implies x\approx 4.41\text{ or }x=1.58[/tex]

Hence, the zeroes of the function are x = 1.58 and x = 4.41,

∵ x represents the price of a taco and y represents daily profit,

Therefore, the zeroes are where the daily profit is $ 0.00.

Answer:

A) 1:1

Step-by-step explanation:

Each leg is the same value and the hypotenuse is [tex]\sqrt{2}[/tex] of the value.

Answer:

Answer A:  1:1

Step-by-step explanation:

In a 45-45-90 triangle, the two legs are of equal length.

Thus, Answer A:  1:1, is the correct one.

Answer:

Option c). 5 square root 3 over 2

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle AOC

we know that

m∠AOC+m∠BOC=180° ----> by supplementary angles

m∠BOC=60° ---> given value

m∠AOC+60°=180°

m∠AOC=180°-60°=120°

step 2

we know that

The triangle AOC is an isosceles triangle

OA=OC=2.5 in -----> the radius of the circle

m∠CAO=m∠OCA ----> base angle

we have that

2m∠CAO=180°-m∠AOC

2m∠CAO=180°-120°

m∠CAO=30°

step 3

Find the measure of the chord AC

we know that

Applying the law of sines in triangle AOC

sin(30°)/2.5=sin(120°)/AC

AC=(2.5)sin(120°)/sin(30°)

sin(30°)=1/2

AC=(2.5)sin(120°)/(1/2)

AC=(5)sin(120°)

Remember that

sin(120°)=sin(60°)

sin(60°)=√3/2

substitute

AC=(5√3)/2

5 square root 3 over 2

Answer:

[tex]cos^{-1}[\frac{6.3}{9.8}][/tex]

[tex]sin^{-1}[\frac{7.5}{9.8}][/tex]

Step-by-step explanation:

step 1

Find the measure of angle ABC using the function cosine

we know that

The function cosine of angle ABC is equal to divide the adjacent side to angle ABC by the hypotenuse of the right triangle

cos(∠ABC)=BC/AB

substitute

cos(∠ABC)=6.3/9.8

[tex]ABC=cos^{-1}[\frac{6.3}{9.8}][/tex]

step 2

Find the measure of angle ABC using the function sine

we know that

The function sine of angle ABC is equal to divide the opposite side to angle ABC by the hypotenuse of the right triangle

sin(∠ABC)=AC/AB

substitute

sin(∠ABC)=7.5/9.8

[tex]ABC=sin^{-1}[\frac{7.5}{9.8}][/tex]

Answer:

D is the correct option

Step-by-step explanation:

2x-3/x ÷ 7/x²

Change the division sign into multiplication and the second term will be flipped(denominator will become numerator)

2x-3/x * x²/7

x will be cancelled out by x²

2x-3/1 * x/7

Now multiply 2x-3 by x

2x²-3x/7

Take x as a common:

x(2x-3)/7

Thus the correct option is D....

Answer:

V = 942.48cm³

Step-by-step explanation:

The volume of a right circular cylinder with a radius of 5 cm and a height of 12 cm is 942.48.

Formula: V=πr2h

V=πr2h=π·52·12≈942.4778cm³

Answer:

Step-by-step explanation:

[tex]-2<\dfrac{x}{3}+1<5\qquad\text{subtract 1 from both sides}\\\\-2-1<\dfrac{x}{3}+1-1<5-1\\\\-3<\dfrac{x}{3}<4\qquad\text{multiply both sides by 3}\\\\(3)(-3)<3\!\!\!\!\diagup^1\cdot\dfrac{x}{3\!\!\!\!\diagup_1}<(3)(4)\\\\-9<x<12[/tex]

Answer:

Observe the attached image

Step-by-step explanation:

The inequality we have is:

[tex]y <2[/tex]

This means that the region represented by this inequality includes all the values below the horizontal line [tex]y = 2[/tex].

To graph this region, draw a dotted horizontal line that intersects the y axis at [tex]y = 2[/tex]. Then shade all the region that is below the horizontal line, as shown in the attached image.

Answer:

C. Hours

Step-by-step explanation:

It wouldn't take minutes or seconds to travel 2,442 miles so A and B don't make sense.

Also, it wouldn't take days to travel in the same country, it might a day but not days.

So the only answer that would make sense would be C. Hours

Hope This Helps!!

Answer:

Step-by-step explanation:"

The electrician charges an initial fee of $42", AND "The electrician charges $22 for every hour worked" is true.

The equation is y=22x+42. The formula is y=mx+b.m is the slope, or is this case, the number of dollars for every "x", which is the number of hours worked. So you have to pay $22 for every hour the electrician works.b is the y-intercept, or the amount it starts with, in this case, you have to pay a fee of $42 even when the electrician worked 0 hours. This is because $42 is the amount it starts with.On a graph, the line will start at (0,42) because that is when you start paying. And then it will increase by 22 for each hour, so the next coordinate would be (1,64).

The given function y=22x+42 represents the electrician’s charges. The electrician charges $22 for each hour worked and has a flat service fee of $42.

The given function y=22x+42 stands for the electrical work charges in terms of hours worked. Here 'y' represents the total amount charged, 'x' represents the number of hours worked, '22' is the hourly rate and '42' is likely a fixed service fee regardless of the hours worked. So the aspects that holds true for this function are: (1) The electrician charges $22 per hour of work, (2) The electrician has a fixed service fee of $42 whether or not they have worked any hours

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Answer:

Henry's monthly payment is $457.5

Henry pays up for the boat at the end overall $35,960

Step-by-step explanation:

* Lets explain how to solve the problem

- Henry buys a large boat with full amount of $32,000

- He cannot pay the full amount at once

- He puts a down payment of $14,000

- He receives a loan for the rest of the payment

∵ The rest of payment = 32,000 - 14,000 = $18,000

- The loan has an interest rate of 5.5%

∴ The rate of interest = 5.5/100 = 0.055

- It is to be paid out over 4 years

∵ The amount of interest = P × r × t , where

# P is the principle amount

# r is the rate

# t is the time

∵ P = 18, 000 , r = 0.055 , t = 4

∴ The amount of interest = 18,000 × 0.055 × 4 = $3960

- The total remaining amount is the sum of the rest of payment and

 the amount of interest

∵ The rest of payment is $18,000

∵ The interest amount = $3,960

∴ The total remaining amount = 18,000 + 3,960 = $21960

- The number of monthly payments = 12 × t

∵ t = 4

∴ The number of monthly payment = 12 × 4 = 48 months

- The monthly payment = the total remaining ÷ the number of

  monthly payment

∵ The total remaining is 21960

∵ The number of monthly payment = 48

∴ The monthly payment = 21960 ÷ 48 = $457.5

* Henry's monthly payment is $457.5

- The total paying for the boat is the sum of the payment down and

  the remaining total payment

∵ The payment down is $14,000

∵ The remaining total payment is 21,960

∴ The total payment for the boat = 14,000 + 21,960 = $35,960

* Henry pays up for the boat at the end overall $35,960

Answer:

The measure of angle xba is 43°

Step-by-step explanation:

we know that

If ray ba bisects the angle xby, then the measure of angle xby is divided into two equal angles

see the attached figure to better understand the problem

so

∠xba=∠aby

∠xba+∠aby=∠xby

we have

∠xby=86°

therefore

∠xba=∠xby/2=86°/2=43°

Answer:

f(g(-1)) = -8 and g(f(1/2) = 4/19.

Step-by-step explanation:

The question specifies f(x) = x^2 + 9x and g(x) = 1/x. The question requires that there should be composite functions. This means a function in a function. Therefore, f(g(x)) means that the function g(x) is taken is an input in the function f(x). Simply replace g(x) instead of x in f(x). This gives:

f(g(x)) = (1/x)^2 + 9(1/x) = x^(-2) + 9/x.

Similar process for g(f(x)) gives:

g(f(x)) = 1/(x^2 + 9x).

Now there are two separate composite functions. Now taking inputs in the composite functions:

f(g(-1)) = (-1)^(-2) + 9/(-1) = 1 - 9 = -8.

g(f(0.5) = 1/(0.5^2 + 9(0.5)) = 1/(0.25+4.5) = 1/4.75 = 100/475 = 4/19.

Therefore f(g(-1)) = -8 and g(f(1/2) = 4/19!!!

Answer: The direction of the rotation is counterclockwise about the origin.

Step-by-step explanation:

          [tex](x,y)[/tex] → [tex](-y, x)[/tex]

In this case, we can observe that the coordinates of the Pre-image of the Point G are:

[tex](7 ,-5)[/tex]

And the coordinates of its Image are:

[tex](5, 7)[/tex]

Then:

[tex](x,y)[/tex] → [tex](-y, x)[/tex]

[tex](7 ,-5)[/tex] → [tex](5, 7)[/tex]

Therefore, the direction of the rotation is counterclockwise about the origin.

Answer:

-140

Step-by-step explanation:

Plug in -4 for x, and -6 for y, in the expression:

-7(x - 4y) = -7((-4) - 4(-6))

Simplify. First, solve the terms within the parenthesis. Multiply:

-7((-4) (-4 * -6))

-7((-4) (+24))

-7(-4 + 24)

Solve the parenthesis. Add:

-7(20)

Fully simplify.

-7 * 20 = -140

-140 is your answer.

~

Answer:

The answer Is B.

Step-by-step explanation:

In "A" I believe japanese should be capatalized and in "C" "genji" should be capitalized but In "B" Murasaki Shikibu’s is a name so it should be capitalized.

Answer:

yes; 4² + 3² = 5²

Step-by-step explanation:

Pythagorean theorem.

In a right triangle the square of the hypotenuse is equal to  the sum of the squares of the other two sides. Hypotenuse is the longest side of the triangle.

4² + 3² = 5²

16 + 9 = 25

25 = 25  

Answer:

[tex]\Huge \boxed{\frac{1}{4}}[/tex]

Step-by-step explanation:

Slope formula:

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\displaystyle \frac{3-2}{3-(-1)}=\frac{1}{4}[/tex]

Therefore, the slope is 1/4, and the correct answer is 1/4.

Answer:

C 1/4

Step-by-step explanation:

To find the slope of the line given two points, we use the formula

m = (y2-y1)/(x2-x1)

   = (3-2)/(3--1)

   = (3-2)/(3+1)

   = 1/4

Answer:

x = 6 + 3√10

Step-by-step explanation:

Since this is an unfactorable expression, we need to apply the Quadratic Formula, -b ± √b² - 4ac\2a [radical wrapped around b² - 4ac]. Evaluate, then you will end up with the answer above.

I am joyous to assist you anytime.

Answer:

D

Step-by-step explanation:

From any point (x, y ) on the parabola the focus and directrix are equidistant

Here the focus = (- 6, 0) and the directrix is x = 6

Using the distance formula

[tex]\sqrt{(x+6)^2+(y-0)^2}[/tex] = | x - 6 |, that is

[tex]\sqrt{(x+6)^2+y^2}[/tex] = | x - 6 |

Squaring both sides

(x + 6)² + y² = (x - 6)² ← distribute factors on both sides

x² + 12x + 36 + y² = x² - 12x + 36

Subtract x² - 12x + 36 from both sides

24x + y² = 0 ( subtract y² from both sides )

24x = - y² ( divide both sides by 24 )

x = - [tex]\frac{1}{24}[/tex] y² → D