a(n) = -5 + 6(n - 1)a(n)=−5+6(n−1)a, left parenthesis, n, right parenthesis, equals, minus, 5, plus, 6, left parenthesis, n, minus, 1, right parenthesis
Find the 12^\text{th}12
th
12, start superscript, start text, t, h, end text, end superscript term in the sequence.

Answer:

100m

Step-by-step explanation:

x=the height of the tower

100m=the distance from the tower

45 degrees the angle of elevation

Drawing a diagram allows you to see that you can form a 'right-angled triangle'.

Using trig. :

Tan 45=x/100m

multiply both sides by 100m

100m*tan 45=100m

Answer:

[tex]\Huge \boxed{\mathrm{100 \ meters}}[/tex]

Step-by-step explanation:

The base of the right triangle created is 100 meters.

The angle between the base and the hypotenuse of the right triangle is 45 degrees.

We can use trigonometric functions to solve for the height of the tower.

[tex]\displaystyle \mathrm{tan(\theta)=\frac{opposite}{adjacent} }[/tex]

Let the height be x.

[tex]\displaystyle \mathrm{tan(45)}=\frac{x}{100}[/tex]

Multiplying both sides by 100.

[tex]\displaystyle 100 \cdot \mathrm{tan(45)}=x[/tex]

[tex]100=x[/tex]

The height of the tower is 100 meters.

the change in x  is 1 and 2 in y respectively

the points are in order from r (x,y)         to     m (9,8)         to   s (10,10

if we take - 1 from x and 2 from y we will get r, or (8,6)

Answer:

466.7 or 42.003 miles

Step-by-step explanation:

subtract 59.99 from 200.00. Then you have 140.01 and divide or multiply it by 0.30.

Answer:

A 2 by 2 inch square has an area of 4 square inches.

If its area is increased by 21 inches, then its area equals 25 square inches.

To find the length of the side we take the square root of 25 square inches which is 5 inches.

Step-by-step explanation:

Step-by-step explanation:

[tex]\huge{\purple{\underline{\underline{\bf{\pink{Answer}}}}}}[/tex]

in this we have given the value of f(x) = 15

[tex]f(x) = x + 7[/tex]

[tex]f(15) = 15 + 7[/tex]

[tex]f(15) = 22[/tex]

so this is ur answer

hope it helps .

Answer:

The time it takes the rock to reach the canyon floor is approximately 4 seconds.

Step-by-step explanation:

The equation representing the height h (in feet) of an object t seconds after it is dropped is:

[tex]h=-16t^{2}+h_{0}[/tex]

Here, h₀ is the initial height of the object.

It is provided that a small rock dislodges from a ledge that is 255 ft above a canyon floor.

That is, h₀ = 255 ft.

So, when the rock to reaches the canyon floor the final height will be, h = 0.

Compute the time it takes the rock to reach the canyon floor as follows:

[tex]h=-16t^{2}+h_{0}[/tex]

[tex]0=-16t^{2}+255\\\\16t^{2}=255\\\\t^{2}=\frac{255}{16}\\\\t^{2}=15.9375\\\\t=\sqrt{15.9375}\\\\t=3.99218\\\\t\approx 4[/tex]

Thus, the time it takes the rock to reach the canyon floor is approximately 4 seconds.

Answer:

t=4

Step-by-step explanation:

ed2020

Answer:

17.25 miles

1 hour, 56 minutes, and 20 seconds.

4 hours, 47 minutes, and 38 seconds.

Step-by-step explanation:

Part I:

For his three cycling sessions, he had traveled for 25.8 miles, 17.25 miles, and 27.42 miles.

The shortest distance he cycled is 17.25 miles.

Part II:

For his three cycling sessions, he spent: 1) 1 hour, 56 minutes, and 20 seconds, 2) 1 hour, 1 minute, and 13 seconds, and 3) 1 hour 50 minutes and 5 seconds.

The longest time he cycled for was 1 hour, 56 minutes, and 20 seconds.

Part III:

Lance's total cycling time is all the times added together. Therefore:

[tex]1\text{ hr} +1\text{ hr} +1\text{ hr} +56\text{ min} +1\text{ min}+50\text{ min} +20\text{ sec}+13\text{ sec} +5\text{ sec} \\\\=3\text{ hr} +107\text{ min}+38\text{ sec} \\\\=4\text{ hours, }47\text{ minutes}\text{ and 38 seconds}[/tex]

Answer:

i) 17.25 miles.

ii) 1 hrs :56 mins :20 secs

iii) 4 hrs :47 mins: 38 secs total.

Answer:

[tex]{x, y} = {-\frac{2}{3}, \frac{5}{3}}[/tex]

Step-by-step explanation:

7x + 4y = 2

x + y = 1

// Solve equation [2] for the variable  y  

 [2]    y = -x + 1

// Plug this in for variable  y  in equation [1]

  [1]    7x + 4•(-x +1) = 2

  [1]    3x = -2

// Solve equation [1] for the variable  x  

  [1]    3x = - 2  

  [1]    x = - 2/3  

// By now we know this much :

   x = -2/3

   y = -x+1

// Use the  x  value to solve for  y  

   y = -(-2/3)+1 = 5/3  

Solution :

{x,y} = {-2/3,5/3}

Answer: rectangle.

Step-by-step explanation:

Given points: K(0,0) I(2,2) T(5,-5) E(7,-3)

Distance formula to find distance between [tex]A(a,b)[/tex] and [tex]B(c,d)[/tex]: [tex]AB=\sqrt{(d-b)^2+((c-a)^2}[/tex]

[tex]KI=\sqrt{(2-0)^2+(2-0)^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\ units[/tex]

[tex]KT=\sqrt{(5-0)^2+(-5-0)^2}=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}\ units[/tex]

[tex]TE=\sqrt{(7-5)^2+(-3+5)^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\ units[/tex]

[tex]IE=\sqrt{(7-2)^2+(-3-2)^2}=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}\ units[/tex]

i.e. KI = TE and KT= IE, so opposite sides equal.

It can be a parallelogram or rectangle. [if all sides are equal it would be square or rhombus]

[tex]IT=\sqrt{(5-2)^2+(-5-2)^2}=\sqrt{3^2+7^2}=\sqrt{9+49}=\sqrt{58}\ units[/tex]

[tex]KE=\sqrt{(7-0)^2+(-3-0)^2}=\sqrt{7^2+3^2}=\sqrt{9+49}=\sqrt{58}\ units[/tex]

IT= KE, i.e. diagonals are equal.

It means KIET is  a rectangle.

1. The first step here is to arrange the data set's form least to greatest,

Sherelle:  26, 39, 56, 58, 60, 62, 65, 66, 66, 68, 71, 72, 72, 73, 74, 75, 81, 83, 84, 85

Venita:  44, 45, 51, 51, 53, 53, 55, 57, 58, 62, 65, 66, 69, 69, 70, 73, 75, 77, 78, 79

Now we can determine our 5 - number summary based on the numbers respective positions.

First Data Set,

(Five - Number Summary) - Minimum : 26, Quartile 1 : 60, Median : 69.5, Quartile 3 : 75, Maximum : 85

Second Data Set,

(Five - Number Summary) - Minimum : 44, Quartile 1 : 53, Median : 63.5, Quartile 3 : 73, Maximum : 79

2. This part is based on your drawings of the box and whisker plots, so you would have to figure that part out by yourself.

3. First off we know that our data set is composed of the years from 1900, so let's rewrite the set based off of the actual year -

Sherelle:  1926, 1939, 1956, 1958, 1960, 1962, 1965, 1966, 1966, 1968, 1971, 1972, 1972, 1973, 1974, 1975, 1981, 1983, 1984, 1985

Venita:  1944, 1945, 1951, 1951, 1953, 1953, 1955, 1957, 1958, 1962, 1965, 1966, 1969, 1969, 1970, 1973, 1975, 1977, 1978, 1979

( a ) Now in Sherelle's defence, she can say that the lowest coin date in her group is 1926, comparative to Venita's group - the lowest coin date in hers being 1944. Therefore, she is more likely to have the 1916 coin, after all that date is the lowest overall in both their data set.

( b ) In Venita defence, she can say that the mean of her data set is lower than the mean of Sherelle's data set. Take a look at the calculations below,

Sherella's Mean : [tex]\frac{39336}{20}[/tex] = [tex]\frac{9834}{5}[/tex] = 1966.8,

Venita's Mean : [tex]\frac{39250}{20}[/tex] = [tex]\frac{3925}{2}[/tex] = 1962.5

( c ) I would say Sherella's bag would most likely contain the 1916 coin. The mean is a prominent factor, but their mean(s) only differ by a very small quantity. That too, Sherella's bag contains the lowest coin in both their groups, and though that is not a prominent factor, it could be that she does have the 1916 coin.

Answer:

its a mnemonic

Oh  Heck  Another  Hour Of  Algebra

(O = opposite side, H = hypotenuse ) = sine

(A = adjacent side,  H = hypotenuse ) = cosine

(O = opposite side,  A = adjacent ) = tangent

Answer:

A, B, E

Step-by-step explanation:

Solve all equations for x. The equivalent equations are the equations that have the same solution.

A   2 + x = 5; x = 3

B   x + 1 = 4; x = 3

C   9 + x = 6; x = -3

D   x + (-4) = 7; x = 11

E   -5 + x = -2; x = 3

Equivalent equations: A, B, E

Answer:

TRUE

Step-by-step explanation:

Length of other leg [tex]= \sqrt {12^2 - 8^2} \\

= \sqrt {144 -64} \\

= \sqrt {80} \\

= 4\sqrt {5} \\[/tex]

Since, [tex] \sqrt 5[/tex] is an irrational number, hence Perimeter of triangle will also be irrational.

TRUE

Answer:

True.

Step-by-step explanation:

The length of the other side = sqrt ( 12^2 - 8^2)

= sqrt (144 - 64)

= sqrt ( 80) which is irrational so the perimeter is also irrational.

(The sum of a rational number and an irrational is irrational).

Answer:

8

Step-by-step explanation:

x+37+x+37+90 = 180

2x + 74 = 90

2x = 16

x = 8

Answer:

x=8°

Step-by-step explanation:

JI is a diameter and K is on the circumference of a circle.

∴∠JKI=90°

also KJ=KI=x(say)

tan (x+37)=y/y=1=tan 45

so x+37=45

x=45-37=8°

Answer:

Step-by-step explanation:

Volume of the can is expressed as Length *Breadth* Height.

If the area of the can base is Length * Breadth

Volume of the can = area of the base of the can * Height

Given parameters

Volume of the can V = 3416.32cm³

Height of the can h = 17cm

Required

Area of the base of the can

Substituting the given parameters into the formula we have;

V = Ah

A = V//h

A = 3416.32/17

A = 200.96cm²

Hence, the area of the base of the can is 200.96cm²

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]6x^2-8x+k=0\\\\\text{We compute the discriminant.}\\\\\Delta = b^2-4ac=8^2-4*6*k=8*8-8*3*k=8*(8-3k)[/tex]

And the we know that if the discriminant is

***** [tex]\Delta[/tex] < 0, meaning 8-3k<0, meaning

[tex]\boxed{k>\dfrac{8}{3}}[/tex]

then, there is no real solution.

***** [tex]\Delta = 0[/tex], meaning

[tex]\boxed{k=\dfrac{8}{3}}[/tex]

There is 1 solution.

***** [tex]\Delta[/tex] > 0, meaning

[tex]\boxed{k<\dfrac{8}{3}}[/tex]

There are 2 solutions.

Thank you

PS: To give more details...

[tex]8-3k=0\\\\\text{Add 3k}\\\\8=3k\\\\\text{Divide by 3}\\\\k=\dfrac{8}{3}[/tex]

Answer:

No, it does not matter.

Step-by-step explanation:

In prime factorization there is only one way to be factored. Once these numbers are broken down, into prime numbers you will get the same result no matter what list of prime numbers you use and what order you use them in.

Answer:

  6

Step-by-step explanation:

If x represents the last number, to get zero you must subtract 6 from it:

  x - 6 = 0

  x = 6 . . . . . . add 6 (undo the subtraction)

The last number before zero is 6.

Answer:

Step-by-step explanation:

The question is not properly written. Here is the correct question.

You are the owner of Decorama Flooring. Tod and Claudia have asked you to give an estimate for tiling four rooms of their house. The living room is 15 feet*23 feet, dinning room is 12ft*18ft, the kitchen is 9ft*11 ft and the study room is 10ft*12 ft how many square ft of tiles are required for each room. (multiply length by the width).

We must understand that a floor tile is rectangular in nature.

Area of a rectangle = Length * width

To get the amount of square feet required for each room, we must multiply the length and width of each of the rooms together as shown.

For the living room;

Length = 15 feet and Width = 23 feet

Amount of square feet of tiles needed for the living room = 15feet * 23 feet

= 345 ft²

For the dining room;

Length = 12 feet and Width = 18 feet

Amount of square feet of tiles needed for the dining room = 12feet * 18 feet

= 216 ft²

For the kitchen;

Length = 9 feet and Width = 11 feet

Amount of square feet of tiles needed for the kitchen = 11feet *9feet

= 99 ft²

For the study room;

Length = 10 feet and Width = 12 feet

Amount of square feet of tiles needed for the study room = 10feet * 12 feet

= 120 ft²

Answer:

B.

Step-by-step explanation:

First equation: the coefficients of x and y are 3 and -2, and the constant is 4.

So the first row should be [3 -2 4].

Second equation: the coefficients of x and y are 6 and -1, and the constant is 10. Hence, the second row should be [6 -1 10].

Total weight required is half pound, so let the amount of cashews be [tex] a[/tex] , and amount of peanuts be $b$

$\therefore a+b=0.5$ (1)

And we want this to cost $2.80$

Cost of $a$ pound of cashews will be $5.50\times a$ and cost of $b$ pound peanuts will be $2.30\times b$

$\therefore 5.5a+2.3b=2.8$ (2)

Substitute $a=0.5-b$ from equation (1) in equation (2)

$5.5(0.5-b)+2.3b=2.8$

$\implies -3.2b=2.8+5.5\times0.5 $

$\implies -3.2b=0.05$

$b$ comes out to be negative. That means there's no solution with the given conditions.

I checked once , I don't think there's any mistake. Can someone else verify too?

EDIT

I verified all the given options from calculator, and no option gives 2.80

Answer:

[tex]5 \frac{1}{9}[/tex]

[tex]6 \frac{2}{5}[/tex]

Step-by-step explanation:

We can convert these improper fractions into mixed numbers by seeing how many times the denominator goes into the numerator.

In [tex]\frac{46}{9}[/tex], 9 goes into 46 5 times, with a remainder of 1. So:

[tex]5 \frac{1}{9}[/tex].

In [tex]\frac{32}{5}[/tex], 5 goes into 32 6 times with a remainder of 2, so:

[tex]6 \frac{2}{5}[/tex].

Hope this helped!

Answer:

5 1/9 and 6 2/5

Step-by-step explanation:

The simplest way to convert improper fractions into mixed fractions is by long division (see attached).

Supplementary angles are those which sum upto 180°

[tex] \angle 1+\angle2=180^{\circ}[/tex]

Complementary are those which sum to 90°

[tex] \angle 1+\angle2=90^{\circ}[/tex]

so if you know one angle, you can find other.

Answer:Look at my explaination

Step-by-step explanation:The complement of 50 is 90-50 giving us 40degrees

The supplement of 145 is 180-145=35 degrees

The compliment of 27 degrees is 90-27=63 degrees

The supplement of 50 degrees is 180-50=130 degrees

Answer:

y=4

Step-by-step explanation:

An exponential function of the form  has a horizontal asymptote of .

The given function is .

The graph of the given function is shown in the attachment.

From the graph the horizontal asymptote is

Hi there! Hopefully this helps!

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

Answer: 14.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

First we calculate 3 to the power of 2 and get 9.

|

\/

9 + 9 - [tex]\frac{8}{2}[/tex] = 14.

Now we add 9 + 9 to get 18.

18 - [tex]\frac{8}{2}[/tex] = 14.

Then, we divide 8 by 2 to get 4.

18 - 4 = 14.

Then we subtract 4 from 18 to get.....You guessed it, 14!

Answer: 14

PEMDAS

P: Parentheses

E: Exponets

M: Multiplcaction

D: Divison

A: Addition

S: Subtraction

PEMDAS can also be known as Please Excuse My Dear Aunt Sally

P: [tex](9-8/2)[/tex]

E: [tex]3^2[/tex]

M: [tex]3*3[/tex]

D: [tex]8/2[/tex]

A: [tex]9+5[/tex]

S: [tex]9-8/2[/tex]

Multiply

E: [tex]3^2=3*3=9[/tex]

M: [tex]3*3=9[/tex]

Divide

D: [tex]8/2=4[/tex]

Subtract

S: [tex]9-4=5[/tex]

Add

A: [tex]9+5=14[/tex]

Answer: [tex]14[/tex]

The reason why we didn't use P to get our answer because it would of messed up the steps. So instead we separated it by dividing 8/2 in D and 9-4-5 for S.

Answer:

-19

Step-by-step explanation:

(-14)

-5

-------

14+5=19

add the negative

-19

Answer:

5x(25)

Step-by-step explanation:

Answer:2 c^2 - 10c

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

So we have the equation:

[tex]-15=5a+12-2a+6[/tex]

On the right combine like terms:

[tex]-15=5a-2a+12+6\\-15=3a+18[/tex]

Subtract 18 from both sides. The right cancels:

[tex](-15)-18=(3a+18)-18\\-33=3a[/tex]

Divide both sides by 3:

[tex](-33)/3=(3a)/3\\a=-11[/tex]

The answer is A, -11.

Answer:

a = -11

Step-by-step explanation:

-15 = 5a +12- 2a + 6

Combine like terms

-15 = 3a +18

Subtract 18 from each side

-15-18 = 3a+18-18

-33 = 3a

Divide each side by 3

-33/3 = 3a/3

-11 =a

Answer:

[tex]\boxed{0.15}[/tex]

Step-by-step explanation:

Part 1: Solve for the total amount of marbles

To solve for the probability of certain events, a population is needed to derive this information from. In order to find this population, add up the amounts of each marble.

8 + 14 + 12 = 34 marbles

Part 2: Determine the probabilities

Now, given the amounts of marbles, simply multiply the ratios of blue marbles to total marbles and the ratio of clear marbles to total marbles to get the combined probability.

[tex]\frac{12}{34}*\frac{14}{33} = \frac{28}{187} \approxeq 0.1497 \approxeq 0.15 * 100 = 15[/tex]

The probability of these events occurring simultaneously is 15%.