The third term of an arithmetic progression is 6 while the sum of the first twelve terms is 282. Find the common difference and the first term​

Answer:

  A.  4·10⁴

Step-by-step explanation:

The problem statement tells you ...

  6×10⁵ miles = 15 × (last year's mileage)

Dividing by 15 gives ...

  (60×10⁴ miles)/15 = (last year's mileage) = 4×10⁴ miles

_____

Further explanation

An exponent is an indication of repeated multiplication.

  10⁵ = 10·10·10·10·10 = 100,000

We can use the associative property of multiplication to rewrite the number of miles:

  6×10⁵ = 6·(10·10·10·10·10) = 600,000 = (6·10)·(10·10·10·10) = 60×10⁴

An inequality is comparing the relation of two equations that are not equal.

Depending on a persons cell phone plan, if they can only talk for so many minutes per month or send so many texts per month, this is an inequality written as number of minutes/ texts per month needs to be less than or equal to the allowable amount.

Answer:

y = 3x - 11

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 4 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes, hence

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (2, - 5) into the partial equation

- 5 = 6 + c ⇒ c = - 5 - 6 = - 11

y = 3x - 11 ← equation of parallel line

the equation of the line that is parallel to y = 3x - 4 and passes through the point (2, -5) is:

To find the equation of a line that is parallel to a given line and passes through a certain point, we need to use the concept that parallel lines have the same slope. The slope-intercept form of a line's equation is y = mx + b, where m is the slope and b is the y-intercept. Given that the line is parallel to y = 3x - 4, it will have the same slope, which is 3. Thus the slope of our new line is also 3.

We want our line to pass through the point (2, -5). Plugging these values into the slope-intercept form, we get:

which simplifies to:

Thus, the y-intercept b of our new line is:

Therefore, the equation of the line that is parallel to y = 3x - 4 and passes through the point (2, -5) is:

Answer:

26 m

Step-by-step explanation:

Perimeter = 92 m

Length = 8 m more than width

Width: 20 m

Therefore,

The width of the rectangular lot is 19 m and the length is 27 m.

The subject of this question is the calculation of the length of a rectangular lot. The perimeter of a rectangle is the sum of all its sides, given by the formula 2*(length + width). From the question, we know that the perimeter is 92 m, and the length is 8 m more than the width. Suppose 'w' is the width. Thus the length is 'w + 8' m.

So, we can set up the equation 2*(w + w + 8) = 92. Solving this equation will give us the value for the width (w) and consequently, the length by adding 8 to it.

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48 more miles

Coyote= 43h

Rabbit= 35h

Coyote= 43(6)= 258

Rabbit= 35(6)= 210

Now subtract 258 by 210

258-210= 48

Typo is probably in "sun" being really "sum".

Just write an equation.

[tex]4(q+p)=4q+4p[/tex]

Hope this helps.

r3t40

Answer:

(x-4)^2 + (y-1)^2 = 6^2

or

(x-4)^2 + (y-1)^2 = 36

Step-by-step explanation:

The equation for a circle is given by

(x-h)^2 + (y-k)^2 = r^2

where (h,k) is the center and r is the radius

(x-4)^2 + (y-1)^2 = 6^2

or

(x-4)^2 + (y-1)^2 = 36

Answer:

(x - 4)^2 + (y - 1)^2 = 6^2

Step-by-step explanation:

Adapt the standard equation of a circle with center at (h, k) and radius r:

(x-h)^2 + (y-k)^2 = r^2

Here we have:

(x - 4)^2 + (y - 1)^2 = 6^2

Answer:

12

Step-by-step explanation:

The general formula for this is

Formula

1/t1 + 1/t2 = 1/t_tot

givens

t1 = 6 hours

t2 = x

t_tot = 4 hours

Solution

1/6 + 1/x = 1/4                 Subtract 1/6 from both sides.

1/6-1/6 + 1/x = 1/4 - 1/6   Change to 12 as your common denominator

1/x = 3/12 - 2/12              subtract

1/x = 1/12                         Cross multiply

x = 12

Tom would need 12 hours to do the job alone.

Answer:

Option D. 12 hours

Step-by-step explanation:

Let the work done by Tom to do the job alone = x hours

So per hour work done by Tom = [tex]\frac{1}{x}[/tex]

Jerry can do the job alone in the time = 6 hours

Per hour work done by Jerry = [tex]\frac{1}{6}[/tex]

Similarly job done by both together in the time = 4 hours

Per hour work done by both together = [tex]\frac{1}{4}[/tex]

Now we know,

Per hour work done by both together = per hour work done by Tom + Per hour work don by Jerry

[tex]\frac{1}{4}=\frac{1}{x}+\frac{1}{6}[/tex]

[tex]\frac{1}{x}=\frac{1}{4}-\frac{1}{6}[/tex]

[tex]\frac{1}{x}=\frac{3-2}{12}[/tex]

[tex]\frac{1}{x}=\frac{1}{12}[/tex]

x = 12 hours

Option D. will be the answer.

Answer:

Step-by-step explanation:

Look at the picture.

Use the long division.

Step-by-step explanation:

[tex]\dfrac{a}{b}\cdot(-1)=-\dfrac{a}{b}[/tex]

On the number line, fractions a/b and -a/b lie on the opposite sides of the number 0, at the same distance (look at the picture).

Answer:

Step-by-step explanation:

A better way to write the first function would be:

c(n) = 4*c(n-1), meaning that the number of likes is equal to four times the number of likes from the previous day. 

On the first day, c(n)=c(0) = 100

Therefore:

C(n) = 100 * 4^n 

Let's plug in a view values to test our function: 

When n= 0 (first day)

C(0) = 100 * 4 ^0 = 100*1 = 100 likes

C(1) = 100 * 4^1 = 100 * 4 = 400 likes, four times the previous day

C(2) = 100 * 4^2 = 100 * 16 = 1600 likes, four times the previous day

And so on. Our function is an accurate descriptor of the model. 

Answer: 8

Step-by-step explanation: 8 divided by 1 is 8

8 is the whole number equal to fraction 8/1.

A number system is defined as a system of writing to express numbers.

The given fraction is 8/1

Eight divided by one.

A fraction represents a part of a whole or, more generally, any number of equal parts.

8 is the numerator and 1 is the denominator.

The complete set of natural numbers along with '0' are called whole numbers.

If a number is divided by another number then the result will be the numerator which is whole number.

8/1=8

Hence, 8 is the  whole number equal to fraction 8/1.

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The equation of a circle is written as ( x-h)^2 + (y-k)^2 = r^2

h and k is the center point of the circle and r is the radius.

In the given equation (x+3)^2 + (y-1)^2 = 81

h = -3

k = 1

r^2 = 81

Take the square root of both sides:

r = 9

The center is (-3,1) and the radius is 9

Answer:

Perimeter= 36mm

Area= 81mm

Step-by-step explanation:

Answer:

The phosphate groups that are the polar of the phospholipid because they are charged - A.

The phosphate groups that are the polar of the phospholipid because they are A. charged

It is group of polar lipids that consist of two fatty acids ,  a glycerol unit and a phosphate group .

A phosphate group has a negatively charged oxygen and a positively charged nitrogen to make this group ionic. A single phospholipid molecule  has a phosphate group on one end and two chains of fatty acids . The phosphate group is negatively charged making the head polar and hydrophilic .

correct answer A) charged

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Answer:

D.

Step-by-step explanation:

First, put your original equation in slope-intercept form to find your slope.

[tex]y=mx+b\\2x+4y=-5\\4y=-2x-5\\y=-\frac{1}{2} x-\frac{5}{4}[/tex]

Now that you have your slope ([tex]-\frac{1}{2}[/tex]) and a point, you can use point-slope form to find your y-intercept.

[tex]y-y1=m(x-x1)\\y-(-8)=-\frac{1}{2} (x-(-4))\\y+8=-\frac{1}{2} (x+4)\\y+8=-\frac{1}{2} x-2\\y=-\frac{1}{2} x-10[/tex]

Your answer choices are all in [tex]Ax+By=C[/tex] form, so lets convert our equation into that form.

[tex]y=-\frac{1}{2} x-10\\1/2x+y=-10\\x+2y=-20[/tex]

If we multiply all of our terms by 2, we can get answer choice D.

Answer:

The age of triplets is 42 years old

Step-by-step explanation:

The question in English is

The sum of the ages of twins and triplets is 150 years if the ages are exchanged the new sum is 120 years. What is the age of triplets?

Let

x -----> twins age

y ----> triplets age

we know that

2x+3y=150 ------> equation A

2y+3x=120 -----> equation B

Solve the system by graphing

The intersection point both graphs is the solution of the system

The solution is the point (12,42)

see the attached figure

therefore

The age of triplets is 42 years old

Answer:

21

Step-by-step explanation:

you can arrange 7×3 ways

Answer with explanation:

Number of trophies possessed by me= 7

Number of trophies that is to be selected from 7 trophies =3

⇒⇒So, Chosing 3 out of 7 trophies and arranging them on a shelf requires Concept of Permutation, as order of arrangement is also taken into consideration

    [tex]=_{3}^{7}\textrm{P}\\\\=\frac{7!}{(7-3)!}\\\\=\frac{7!}{4!}\\\\=\frac{4!*5*6*7}{4!}\\\\=5*6*7\\\\=210\text{Ways}[/tex]

Or

⇒First place can be filled in 7 ways,second place can be filled in 6 ways and third place can be filled in 5 ways.

So total number of ways of selecting 3 trophies from 7 trophies

                             =7 *6 *5

                             =210 ways

⇒Now, 3 trophies can be arranged in a shelf in 3! =3 *2*1=6 ways.

Answer:

$179.17

Step-by-step explanation:

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Answer: The investment be worth $ 174.05 in 2 years .

Step-by-step explanation:

Given : The principal amount invested  : A= $125

Interest rate : r = 18% =0.18   [ Percent convert into decimal if we divide it by 100]

Time : t = 2 years

The formula to find the accumulated amount if compounded continuously :-

[tex]A=Pe^rt\\\\=(125)(1+0.18)^{2}\\\\= 125 (1.18)^2\\\\ = 125 (1.3924)\\\\=174.05[/tex]

Hence, the investment be worth $ 174.05 in 2 years .

Answer:

Explanation:

The formula for permuations is nPk:

Where n is the total number of elements from which you must choose combinations of k number of elements, and where the order of selection is relevant.

In this case n = 22 (the number of participants), k = 5 (the number of top participants). Since, the order in which the participants finish is relevant, then you have to use the formula of permutations, such as the question states.

Calculations:

The full length of one line times the length of the line outside the circle is equal the the other line.

(x-1) +5 x 5 = (2+x)+4 x 4

Simplify:

(x+4) x 5 = (x +6) x 4

5x +20 = 4x +24

Subtract 20 from each side:

5x = 4x +4

Subtract 4x from each side:

x = 4

The answer is B. 4

Answer:

The correct ordered pair is (7,1)

Step-by-step explanation:

The given system has equations:

[tex]2x - 6y = 8....(1)[/tex]

[tex]5x- 4y = 31....(2)[/tex]

We make x the subject in the first equation to get:

[tex]x = 4 + 3y...(3)[/tex]

Put equation 3 into equation 2 to get:

[tex]5(4 + 3y) - 4y = 31[/tex]

Expand:

[tex]20 + 15y - 4y = 31[/tex]

[tex]15y - 4y = 31 - 20[/tex]

[tex]11y = 11[/tex]

[tex]y = 1[/tex]

Put y=1 into equation 3 and solve for x.

[tex]x = 4 + 3( 1) = 7[/tex]

The correct ordered pair is (7,1)

Answer:

[tex](x-6i)(x+6i)(x-3)(x+3)[/tex]

Step-by-step explanation:

If 6i is a zero then -6i is a zero.

In general, if a+bi is a zero then a-bi is a zero (if the polynomial has real coefficients which this one does: 1,27,-324).

Let's test it to see:

Check [tex]x=6i[/tex]

[tex]P(6i)=(6i)^4+27(6i)^2-324\\

P(6i)=6^4(i^4)+27(6)^2(i^2)-324\\

P(6i)=1296(1)+27(6^2)(-1)-324\\

P(6i)=1296-27(36)-324\\

P(6i)=1296-972-324\\

P(6i)=1296-1296\\

P(6i)=0\\[/tex]

Check [tex]x=-6i[/tex]

[tex]P(-6i)=(-6i)^4+27(-6i)^2-324\\

P(-6i)=(6i)^4+27(6i)^2-324\\

P(-6i)=P(6i)\\

P(-6i)=0\\[/tex]

So yep they both give us 0 when we plug it in.

If x=6i is a zero then x-6i is a factor by factor theorem.

If x=-6i is a zero then x+6i is a factor by factor theorem.

What is (x-6i)(x+6i)?

Let's use the multiply conjugates formula: [tex](u-v)(u+v)=u^2-v^2[/tex].

[tex](x-6i)(x+6i)=x^2-36i^2=x^2-36(-1)=x^2+36[/tex]

Now we know [tex](x^2+36)[/tex] is a factor of [tex]x^4+27x^2-324[/tex].

We can use long division or we could try to find two numbers that multiply to be -324 and add up to be 27 since this is a quadratic in terms of [tex]x^2[/tex] with leading coefficient of 1.

Well we already know we are looking for number times 36 that would give us -324.

So -324=-9(36) and 27=-9+36

So the factored form in terms of real numbers is:

[tex](x^2+36)(x^2-9)[/tex]

We already know the first factor can be factored as (x+6i)(x-6i).

The other can factored as (x-3)(x+3) since (-3)(3)=-9 and -3+3=0.

So the complete factored form is

[tex](x-6i)(x+6i)(x-3)(x+3)[/tex].

To find the remaining zeros of the polynomial, we use synthetic division and find a quadratic factor. The remaining zeros are the solutions to the quadratic equation x^2 + 9 = 0, which are 3i and -3i.

To find the remaining zeros of the polynomial, we can use polynomial long division or synthetic division. Let's use synthetic division:

Since 6i is a zero of P(x), the conjugate -6i is also a zero. We can divide P(x) by (x - 6i)(x + 6i) to find the remaining quadratic factor.

Performing the synthetic division, we get a quadratic factor of x^2 + 9. Therefore, the remaining zeros of the polynomial are the solutions to the equation x^2 + 9 = 0.

Solving the quadratic equation x^2 + 9 = 0, we find that the remaining zeros are x = 3i and x = -3i.

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Using the Pythagorean theorem:

x = √(11.7^2 - 8.6^2)

x = √(136.89 - 73.96)

x = √62.93

x = 7.9

The answer is D.

Answer:

111

Step-by-step explanation:

because the lines are parallel and they are on opposite sides its like having two angles on the same line but on different sides so they are supplementary meaning they add up to 180 and 180-69 = 111

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Answer:

Option 3 [tex]\frac{67}{441}[/tex]

Step-by-step explanation:

step 1

Find the roots of the quadratic equation

we have

[tex]3x^{2}+5x-7=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]3x^{2}+5x-7=0[/tex]

so

[tex]a=3\\b=5\\c=-7[/tex]

substitute in the formula

[tex]x=\frac{-5(+/-)\sqrt{5^{2}-4(3)(-7)}} {2(3)}[/tex]

[tex]x=\frac{-5(+/-)\sqrt{109}} {6}[/tex]

[tex]x=\frac{-5+\sqrt{109}} {6}[/tex]

[tex]x=\frac{-5-\sqrt{109}} {6}[/tex]

step 2

Let

[tex]\alpha=\frac{-5+\sqrt{109}} {6}[/tex]

[tex]\beta=\frac{-5-\sqrt{109}} {6}[/tex]

we need to calculate

[tex]\frac{1}{(3\alpha+5)^{2}}+ \frac{1}{(3\beta+5)^{2}}[/tex]

step 3

Calculate   [tex](3\alpha+5)^{2}[/tex]

[tex](3\alpha+5)^{2}=[3(\frac{-5+\sqrt{109}} {6})+5]^{2}[/tex]

[tex]=[(\frac{-5+\sqrt{109}} {2})+5]^{2}[/tex]

[tex]=[(\frac{-5+\sqrt{109}+10} {2})]^{2}[/tex]

[tex]=[(\frac{5+\sqrt{109}} {2})]^{2}[/tex]

[tex]=[(\frac{25+10\sqrt{109}+109} {4})][/tex]

[tex]=[(\frac{134+10\sqrt{109}} {4})][/tex]

[tex]=[(\frac{67+5\sqrt{109}} {2})][/tex]

step 4

Calculate   [tex](3\beta+5)^{2}[/tex]

[tex](3\beta+5)^{2}=[3(\frac{-5-\sqrt{109}} {6})+5]^{2}[/tex]

[tex]=[(\frac{-5-\sqrt{109}} {2})+5]^{2}[/tex]

[tex]=[(\frac{-5-\sqrt{109}+10} {2})]^{2}[/tex]

[tex]=[(\frac{5-\sqrt{109}} {2})]^{2}[/tex]

[tex]=[(\frac{25-10\sqrt{109}+109} {4})][/tex]

[tex]=[(\frac{134-10\sqrt{109}} {4})][/tex]

[tex]=[(\frac{67-5\sqrt{109}} {2})][/tex]

step 5

substitute

[tex]\frac{1}{(3\alpha+5)^{2}}+ \frac{1}{(3\beta+5)^{2}}[/tex]

[tex]\frac{1}{[(\frac{67+5\sqrt{109}} {2})]}+ \frac{1}{[(\frac{67-5\sqrt{109}} {2})]}[/tex]

[tex]\frac{2}{67+5\sqrt{109}} +\frac{2}{67-5\sqrt{109}}\\ \\\frac{2(67-5\sqrt{109})+2(67+5\sqrt{109})}{(67+5\sqrt{109})(67-5\sqrt{109})} \\ \\\frac{268}{1764}[/tex]

Simplify

Divide by 4 both numerator and denominator

[tex]\frac{268}{1764}=\frac{67}{441}[/tex]

Answer:

  3)  67/441

Step-by-step explanation:

Comparing the given equation to the expressions you need to evaluate, you find there might be a simplification.

  3x² +5x -7 = 0 . . . . . given equation

  3x² +5x = 7 . . . . . . . add 7

  x(3x +5) = 7 . . . . . . . factor

  3x +5 = 7/x . . . . . . . . divide by x

Now, we can substitute into the expression you are evaluating to get ...

  1/(3α +5)² +1/(3β +5)² = 1/(7/α)² +1/(7/β)² = (α² +β²)/49

__

We know that when we divide the original quadratic by 3, we get

  x² +(5/3)x -7/3 = 0

and that (α+β) = -5/3, the opposite of the x coefficient, and that α·β = -7/3, the constant term. The sum of squares is ...

  α² +β² = (α+β)² -2αβ = (-5/3)² -2(-7/3) = 25/9 +14/3 = 67/9

Then the value of the desired expression is ...

  (67/9)/49 = 67/441

Answer:

13.69%.

Step-by-step explanation:

The probability he scores in 1 shot = 1 - 0.63 = 0.37.

The probability that he scores twice in 2 shots = 0.37 * 0.37

= 0.1369

= 13.69%.

The probabilities are multiplied because the 2 events are independent.

Answer:

For plato user the answer is 13.69 %.

Step-by-step explanation:

If this player shoots twice, the probability that he scores a goal both times is  

13.69 %.

It would be C. they are skew on ED :)

Answer: C

Step-by-step explanation: your welcome

Answer:

9. 75°

10. 60°

Step-by-step explanation:

Note the angle-intercept theorem. If you create an angle in the opposite side of a circle from 2 points on other side, the arc will have a measure TWICE that of the intercepted angle created on other side.

Question 9

Arc WX has a measure 76, thus the angle created is Angle V, which should be HALF of that. So angle V is  76/2 = 38

Now looking at the triangle inside the circle, we know three angles of a triangle add up to 180, thus we can write and solve for "?" angle:

X + W + V = 180

? + 67 + 38 = 180

? + 105 = 180

? = 180 - 105 = 75°

Question 10

Using the theorem we can say that Angle B is HALF of ARC XYZ.

So,

2*Angle B = Arc XY + Arc YZ

2*102 = Arc XY + 124

204 = Arc XY + 124

Arc XY = 204 - 124 = 80°

Also, Arc BX + Arc XY is twice that of Angle Z (which is 70), thus

Arc BX + Arc XY = 70 *2

Arc BX + Arc XY = 140

Arc BX + 80 = 140

Arc BX = 140 - 80 = 60°

Answer:

convert from Celsius to Fahrenheit

Step-by-step explanation:

i work with thermometers i know

For this case we have that by definition, to convert degrees Celsius to Fahrenheit we use the following formula:

[tex]F = \frac {9} {5} C + 32[/tex]

Where:

C: Represents the degrees Celsius

So, we can write a function:

[tex]F (C) = \frac {9} {5} C + 32[/tex]

Answer:

The function allows to convert degrees Celsius to Fahrenheit