Here are the first terms of an arithmetic sequence
5,12,19,26
Write down an expression in terms of n for the nth term of the sequence

Answer: -2

Step-by-step explanation: 4-8= -4 then it ends up being -2r-4=0

Then you add 4 to 0 so -2r=4 then divide

Answer/Step-by-step explanation:

✔️Using trigonometric ratio, find width of the rectangle, BD:

Thus:

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

Where,

[tex] tan(\theta) = tan(60) = \sqrt{3} [/tex]

Opposite = BD

Adjacent = 7 cm

Plug in the values

[tex] \sqrt{3} = \frac{BD}{7} [/tex]

Multiply both sides by 7

[tex] 7\sqrt{3} = BD [/tex]

[tex] BD = 7\sqrt{3} [/tex]

✔️Using trigonometric ratio, find height of the rectangle, BF:

Thus:

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

Where,

[tex] tan(\theta) = tan(60) = \sqrt{3} [/tex]

Opposite = 6 cm

Adjacent = BF

Plug in the values

[tex] \sqrt{3} = \frac{6}{BF} [/tex]

[tex] BF = \frac{6}{\sqrt{3}} [/tex]

Rationalize

[tex] BF = \frac{6 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} [/tex]

[tex] BF = \frac{6\sqrt{3}}{3} [/tex]

[tex] BF = 2\sqrt{3} [/tex]

✔️Perimeter of rectangle BDEF:

Perimeter = 2(BD + BF)

Plug in the values

[tex] Perimeter = 2(7\sqrt{3} + 2\sqrt{3}) [/tex]

[tex] Perimeter = 2(9\sqrt{3}) [/tex]

[tex] Perimeter = 18\sqrt{3} [/tex]

✔️Area of the rectangle BDEF:

Area = BD × BF

Plug in the values

[tex] Area = 7\sqrt{3} \times 2\sqrt{3} [/tex]

[tex] Area = 7 \times 2\sqrt{3 \times 3} [/tex]

[tex] Area = 14 \times 3 [/tex]

[tex] Area = 42 [/tex]

Answer:

point b is twice the distance

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

100

Answer:

5 + 3a

Step-by-step explanation:

5 - a + 4a =

5 + ( -a + 4a ) =

5 + ( 4a - a ) =

5 + ( 3a )

Answer:

49 cents per ounce

Step-by-step explanation:

Answer:

ab, ac, bc

Step-by-step explanation:

a=30, b=60, c=180-(30+60) = 180-90=90

Just to avoid some confusion: the first picture is a graph of function A, and the second picture is a graph of function B.

Answer:

D. Function A is non-linear and Function B is linear.

Step-by-step explanation:

A good way to find out if a function is linear is by graphing it. If you graph it and it is a straight line, then it is linear.

So, let's graph the given points from the table of Function A and see if it forms a straight line. When you connect the dots, it's not straight, so Function A is non-linear.

Now let's look at function B. We can graph that too with the given information from the equation - the slope is -1 and the y-intercept is 5. (If you are a bit confused on how to graph it, don't hesitate to ask!) It does form a straight line, so Function B is linear.

The solution is Option D.

Function A is non-linear and Function B is linear.

What is Linear Equation in 2 variables?

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Given data ,

Let the first equation be A

Let the second equation be B

where

The function A is represented by y = x³

The function B is represented by y = -x + 5

Now ,

We can see that the linear equation A is of the form y = x³ , and this is a cubic relation and it is a non linear graph

The function B is a linear equation of the form y = mx + c , which is the linear equation for a line with slope -1

So , the function B y = -x + 5 is linear

Hence , the Function A is non-linear and Function B is linear.

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Answer:

15/24

Step-by-step explanation:

hope this helps u.

Answer:

15/24

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

The line is going to the right side so that means that x must be greater than -53 and the dot is filled in so it is also equal to

Answer:

7x+1

Step-by-step explanation:

Use the distributive property to multiply 7 by x−1.

7x−7+8

Add −7 and 8 to get 1.

7x+1

Answer:

the answer is 60 dollars.

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

Work Shown:

x = original price

20% = 20/100 = 0.20

20% of x = 0.20x = discount

x - 0.20x = 0.80x = final price

0.80x = 50

x = 50/0.80

x = 62.50

The original price of the jeans was $62.50

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

Note how,

20% of x = 0.20*x = 0.20*62.50 = 12.50

Tara saves $12.50 (this is the discount).

The price she pays is x - 0.20x = 62.50 - 12.50 = 50 dollars, which matches with what your teacher gave in the instructions. This confirms we have the correct original price.

Answer:

:

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The system of equations representing the rates for two duplicating companies are -

C[1] = 5 + 0.06x

C[2] = 10 + 0.04x

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the rates for two duplicating companies. There are two different rates as-

[1] > initial fee of $5 and $0.06 per page.

[2] > initial fee of $10.00 and $0.04 per page.

For the [1] company, we can write the equation as -

C[1] = 5 + 0.06x

For the [2] company, we can write the equation as -

C[2] = 10 + 0.04x

So, the system of equations will be -

C[1] = 5 + 0.06x

C[2] = 10 + 0.04x

Therefore, the system of equations representing the rates for two duplicating companies are -

C[1] = 5 + 0.06x

C[2] = 10 + 0.04x

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Answer:

2.275%

Step-by-step explanation:

We start by calculating the z-score

Mathematically;

z-score = (x-mean)SD

here, x = 70.5

mean = 65.5

SD = 2.5

Substituting these values;

z = (70.5-65.5)/2.5

= 5/2.5 = 2

So we want to calculate the probability that;

P( z> 2)

We check the standard normal distribution table for this

That will be

0.02275

In percentage, this is 2.275 %

Answer:

X= -4

Step-by-step explanation:

Hello. For to solve that, you need to use the sustitution method:

1. You need clear X in the first equation and put in the second

X+Y = -10

X = -10-Y

2.  Y = X-2, then you replaced the X in this equation:

Y = (-10-Y) - 2

Y+2=-10-Y

2Y=-10-2

2Y= -12

Y= -12/2

Y=-6

3. Now you use the Y value for to solve X:

X=-10-Y, then

X =- 10-(-6)

X = -4

Answer:

Step-by-step explanation:

From the information given:

[tex]\mathbf{H_o: \mu = 9.7 \ hours}[/tex]

[tex]\mathbf{H_1: \mu > 9.7 \ hours}[/tex]

The type 1 error is rejecting [tex]\mathbf{H_o}[/tex] when

The meaning of Type 1 error is rejecting the claim that the mean running time is 9.7 hours when actually the mean running time is greater than 9. 7 hour.

The equation of the line is y = 3x - 9 if the line with a slope of 3 passes through the point (6,9).

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have:

A line with a slope of 3 passes through the point (6,9).

m = 3

The line equation:

y = mx + c

y = 3x + c

9 = 3(6) + c

c = -9

y = 3x - 9

Thus, the equation of the line is y = 3x - 9 if the line with a slope of 3 passes through the point (6,9).

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Answer:

12 staples

Step-by-step explanation:

So the first thing we have to do is find the G.C.D (Greatest Common Denominator) between 21/4 and 7/16 which of course is 16 so your new fractions would be 84/16 and 7/16.

Now we have to divide both numbers I just used a fraction calculator for this but basically you multiply 84/16 by the reciprocal of 7/16 which is 16/7 and simplify which equals 12.

So it would take 12 staples to bind the booklet

Answer:

1 4/5 meters

Step-by-step explanation:

Juniors brother = 1 1/2 meters tall

Junior is 1 1/5 of his brother height

Junior = 1 1/5 of 1 1/2

= 6/5 × 3/2

= 6 * 3 / 5 * 2

= 18/10

= 1 8/10

= 1 4/5 meters

Junior is 1 4/5 meters tall

Answer:

1 4/5

Step-by-step explanation:

its on khan (: trust me

Answer:

4:3

Step-by-step explanation:

16:12=8:6=4:3

Answer:

4:3

Step-by-step explanation:

16 and 12 can both be divided by 4

16/4 = 4 12/4 = 3

so your simplified ratio is 4:3

Answer:

20

Step-by-step explanation:

when a letter and a number are next to each other u have to multiply, so x is 5 so 3 x 5 is 15. 15 plus 5 is 20 so 20 is ur answwer

Answer:

20

Step-by-step explanation:

x= 20

3x+5 replace x with 5 than do 3x5=15+5=20

Answer:

6/5

Step-by-step explanation:

Answer:

the slope is -6/5

Step-by-step explanation:

Answer:

The scale factor is 1/2

Step-by-step explanation:

I have a different one but it was supposed to be 1/4

1 goes on the first on -1 goes on the second

- 1/125 goes on the last one and -125 the third one

Answer:

A. -4< n<8 B.-4< n< 8

Step-by-step explanation:

Answer:

D.-4<n<8

Step-by-step explanation:

Answer:

70 miles.

Step-by-step explanation:

In this question we are given the speed of the migrating bird. If we remember the definition of speed we will remember that speed is distance the object/body traveled, divided by the time it took the object/body to travel this distance.

Solution:

Firstly we need to find out what distance will the bird travel in 1 hour.  We can easily do that science we know the distance it travels in 3 hours. So we just use the property of a fraction that states that if we multiply or divide the denominator and the numerator by the same number we will get a fraction of the same value but written a bit differently. So we divide the numerator and the denominator by 3 and get

[tex]\frac{42 miles}{3 hours}[/tex] = [tex]\frac{14 miles}{1hour}[/tex]

Now we know what distance the bird travels in one hour so we can easily figure how much the bird will travel in 5 hours by multiplying the numerator and the denominator by 5. So we do...

[tex]\frac{14 miles}{1 hour}[/tex] = [tex]\frac{70 miles}{5 hours}[/tex]

And we get that the bird will travel 70 miles in 5 hours.