Catherine sketched the slope triangle on the previous slide. Notices that the slope triangle has a 2 and 4, so she thinks the slope is 2/4 or 1/2

Given:

In a geometric sequence,

First term = 11

Common ratio = 4

To find:

The function for the geometric sequence.

Solution:

We have,

First term: a = 11

Common ratio: r = 4

We know that, nth term of a geometric sequence is

[tex]a_n=ar^{n-1}[/tex]

Putting a=11 and r=4, we get

[tex]a_n=(11)(4)^{n-1}[/tex]

The function notation is

[tex]f(n)=(11)(4)^{n-1}[/tex]

Therefore, the function for the geometric sequence is [tex]f(n)=(11)(4)^{n-1}[/tex], where n is a positive integer.

The slope of this line is 0. If you graph the line y=10, for any x value, the y-value remains 10 (denoted because x is equal to 0 in the actual equation shown, which means that x will not be shown in the equation). The graph would basically just be a straight horizontal line, neither curving up or down.

Answer:

[tex]x=\frac{3\pi}{4}\\\\x=\frac{5\pi}{4}[/tex]

Step-by-step explanation:

Trigonometric Equations

It's required to solve:

[tex]\cos x+\sqrt{2}=-\cos x[/tex]

for [tex]x\in [0,2\pi)[/tex]

Adding cos x:

[tex]2\cos x+\sqrt{2}=0[/tex]

Subtracting [tex]\sqrt{2}[/tex]

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

Dividing by 2:

[tex]\displaystyle \cos x=-\frac{\sqrt{2}}{2}[/tex]

Solving for x:

[tex]\displaystyle x=\arccos\left(-\frac{\sqrt{2}}{2}\right)[/tex]

We need to find the angles whose cosine is [tex]-\frac{\sqrt{2}}{2}[/tex] over the given interval.

These angles lie on the quadrants III and IV respectively and they are:

x=135°, x=225°

Converting to radians:

135 * π / 180 = 3π/4

225 * π / 180 = 5π/4

The two solutions are:

[tex]\mathbf{x=\frac{3\pi}{4}}[/tex]

[tex]\mathbf{x=\frac{5\pi}{4}}[/tex]

Answer:

The correct answer is option C

Step-by-step explanation:

Answer: H

Step-by-step explanation:

Answer:

1.01 m8

Step-by-step explanation:

Answer:

s = 1

t = -10

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

15s + t = 5

4s = 3t + 34

Step 2: Rewrite

15s + t = 5

Step 3: Redefine Systems

45s = -3t + 15

4s = 3t + 34

Step 4: Solve for s

Elimination

Step 5: Solve for t

Answer:

Explanation is below

Step-by-step explanation:

Here ya go

Step 1

15s+t=5,4s=3t+34  Question

Step 2

4s=3t+34  Substitute  -15s+5

4s=3(-15s+5)+34

s=1

Step 3

t=-15s+5  Substitute 1 for s

t=(-15)(1)+5

t=-10

answer

s=1

t=-10

Answer:

Let's see

Step-by-step explanation:

Two triangles are same ∆1 and ∆2

They have same height and breath

Now ∆1= ∆2

=> ar(∆1)= ar(∆2)

The same is for quadrilaterals

Answer:

h = — 10.071

Step-by-step explanation:

Look at the picture for my work.

Answer:

The answer is x= -4/3

Step-by-step explanation:

3(x-4)=12x

=3x-12=12x

=3x-3x-12=12x-3x

-12=9x

To find x divide both sides by 9.

-12÷9=9x÷9

-4/3=x

Answer:

Equation 2

Step-by-step explanation:

Equation 2 is the only one possible to be linear. All of the other answers have an exponents. For instance, say you have y=x^3. For 1, it is 1*1*1. (1,1). For 2, it is 2*2*2. (2,8). For 3, 3*3*3. (3,27) It escalates into a curve and is non-linear.

Answer:

96000

Step-by-step explanation:

N=4years

R=4 %

We have S.I.=

100

PNR

=

100

P×4×4

=

100

16P

=0.16P

And on interest being compounded for 3 years and R=5 %, Amount=P(1+

100

R

)

N

=P(1+

100

5

)

3

=P×(1.05

3

)=1.157625P

So, C.I.=A−P=1.157625P−P=0.157625P

Given, S.I.−C.I=Rs228

=>0.16P−0.157625P=Rs228

=>0.002375P=Rs228

=>P=Rs96,000

Answer:

to be entirely honest i do not know

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

140-180= 40

Answer:

-14.2

Step-by-step explanation:

f(x)=-3x+5 Write original equation

f(6.4)=-3(6.4)+5 Substitute 6.4 in for x.

=-14.2 Solve

Answer:

equation form: 12 + 2x = 18

x = 3

lets check the work see if its true

12 + 2(3) = 18

12 + 6 = 18

It Checks!

therefore your answer is 3. He can get 3 different toppings

Step-by-step explanation:

Answer:

Both graphs are proportional

Step-by-step explanation:

in the first graph the x is multiplied by 3 to get y. in the second, you are getting rid of 1/3 of x to get y

Answer:

3

Step-by-step explanation:

Took quiz

Answer:

D.

Step-by-step explanation:

Answer:

I got this! Basically, the instructions say 12 gallons per 3 minutes. So you plug in the 12/3 to find the ratio of how many gallons per 1 minute.

Step-by-step explanation:

So, for the chart you just mulitply and evauluate

Time (min)           | 2 |  3 |  4 |   5  |   6 |

Water used (gal) | 8 | 12 | 16 | 20 | 24 |

Part (a)

Focus on triangle PSQ. We have

angle P = 52

side PQ = 6.8

side SQ = 5.4

Use of the law of sines to determine angle S

sin(S)/PQ = sin(P)/SQ

sin(S)/(6.8) = sin(52)/(5.4)

sin(S) = 6.8*sin(52)/(5.4)

sin(S) = 0.99230983787513

S = arcsin(0.99230983787513)

S = 82.889762826274

Which is approximate

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

Use this to find angle Q. Again we're only focusing on triangle PSQ.

P+S+Q = 180

Q = 180-P-S

Q = 180-52-82.889762826274

Q = 45.110237173726

Which is also approximate.

A more specific name for this angle is angle PQS, which will be useful later in part (b).

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

Now find the area of triangle PSQ

area of triangle = 0.5*(side1)*(side2)*sin(included angle)

area of triangle PSQ = 0.5*(PQ)*(SQ)*sin(angle Q)

area of triangle PSQ = 0.5*(6.8)*(5.4)*sin(45.110237173726)

area of triangle PSQ = 13.0074347717966

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

Next we'll use the fact that RS:SP is 2:1.

This means RS is twice as long as SP. Consequently, this means the area of triangle RSQ is twice that of the area of triangle PSQ. It might help to rotate the diagram so that line PSR is horizontal and Q is above this horizontal line.

We found

area of triangle PSQ = 13.0074347717966

So,

area of triangle RSQ = 2*(area of triangle PSQ)

area of triangle RSQ = 2*13.0074347717966

area of triangle RSQ = 26.0148695435932

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

We're onto the last step. Add up the smaller triangular areas we found

area of triangle PQR = (area of triangle PSQ)+(area of triangle RSQ)

area of triangle PQR = (13.0074347717966)+(26.0148695435932)

area of triangle PQR = 39.0223043153899

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

This value is approximate. Round however you need to.

===========================================

Part (b)

Focus on triangle PSQ. Let's find the length of PS.

We'll use the value of angle Q to determine this length.

We'll use the law of sines

sin(Q)/(PS) = sin(P)/(SQ)

sin(45.110237173726)/(PS) = sin(52)/(5.4)

5.4*sin(45.110237173726) = PS*sin(52)

PS = 5.4*sin(45.110237173726)/sin(52)

PS = 4.8549034284642

Because RS is twice as long as PS, we know that

RS = 2*PS = 2*4.8549034284642 = 9.7098068569284

So,

PR = RS+PS

PR = 9.7098068569284 + 4.8549034284642

PR = 14.5647102853927

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

Next we use the law of cosines to find RQ

Focus on triangle PQR

c^2 = a^2 + b^2 - 2ab*cos(C)

(RQ)^2 = (PR)^2 + (PQ)^2 - 2(PR)*(PQ)*cos(P)

(RQ)^2 = (14.5647102853927)^2 + (6.8)^2 - 2(14.5647102853927)*(6.8)*cos(52)

(RQ)^2 = 136.420523798282

RQ = sqrt(136.420523798282)

RQ = 11.6799196828694

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

We'll use the law of sines to find angle R of triangle PQR

sin(R)/PQ = sin(P)/RQ

sin(R)/6.8 = sin(52)/11.6799196828694

sin(R) = 6.8*sin(52)/11.6799196828694

sin(R) = 0.4587765387107

R = arcsin(0.4587765387107)

R = 27.3081879220073

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

This leads to

P+Q+R = 180

Q = 180-P-R

Q = 180-52-27.3081879220073

Q = 100.691812077992

This is the measure of angle PQR

subtract off angle PQS found back in part (a)

angle SQR = (anglePQR) - (anglePQS)

angle SQR = (100.691812077992) - (45.110237173726)

angle SQR = 55.581574904266

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

This value is approximate. Round however you need to.

Answer:

2x + 3y - 9 = 0

Step-by-step explanation:

Answer:

The solutions to the system of equations are:

[tex]x=\frac{325}{9},\:y=\frac{65}{9}[/tex]

Step-by-step explanation:

Given the system of the equations

[tex]\begin{bmatrix}2x-y=65\\ 5y=x\end{bmatrix}[/tex]

isolate 'x' for 2x-y

[tex]2x-y=65[/tex]

Add y to both sides

[tex]2x-y+y=65+y[/tex]

[tex]2x=65+y[/tex]

Divide both sides by 2

[tex]\frac{2x}{2}=\frac{65}{2}+\frac{y}{2}[/tex]

[tex]x=\frac{65+y}{2}[/tex]

[tex]\mathrm{Subsititute\:}x=\frac{65+y}{2}[/tex]

isolate 'y' for  [tex]5y=\frac{65+y}{2}[/tex]

[tex]5y=\frac{65+y}{2}[/tex]

[tex]10y=65+y[/tex]

subtract y from both sides

[tex]10y-y=65+y-y[/tex]

[tex]9y=65[/tex]

Divide both sides by 9

[tex]\frac{9y}{9}=\frac{65}{9}[/tex]

[tex]y=\frac{65}{9}[/tex]

[tex]\mathrm{For\:}x=\frac{65+y}{2}[/tex]

[tex]\mathrm{Subsititute\:}y=\frac{65}{9}[/tex]

[tex]x=\frac{65+\frac{65}{9}}{2}[/tex]

[tex]x=\frac{325}{9}[/tex]

The solutions to the system of equations are:

[tex]x=\frac{325}{9},\:y=\frac{65}{9}[/tex]

Answer:

Either C or B I’m not quite sure which one. I’m sorry

Step-by-step explanation:

Answer:

the answer is the second choice

Step-by-step explanation:

hopefully this helps :)

Answer:

i think its B but i'm not 100 percent sure sorry if im not but i think i am

Step-by-step explanation:

Answer:

It's D

Step-by-step explanation:

You l*w is the area.