us
Find a formula for the nth term in this
arithmetic sequence:
a₁ = 7, a2 = 4, a3 = 1, a4 = -2, ...
an = [? ]n +

9x - 4(x - 2) =x + 20

We move all terms to the left:

Multiply

We get rid of the parentheses.

We add all the numbers and all the variables.

We move all terms containing x to the left hand side, all other terms to the right hand side

Answer:

B (2nd option)

Step-by-step explanation:

Factor each one.

6x^2+39x-21 is divisible by 3 -> 3(2x^2+13x-7) -> 3(2x-1)(x+7)

6x^2+54x+84 is divisble by 6 -> 6(x^2+9x+14) -> 6(x+2)(x+7)

The greatest common factor is 3(x+7), so taking that out of each polynomial, we have (2x-1) and 2(x+2). The least common multiple is the greatest common factor*(2x-1)*2(x+2) which, simplifying, is 12x^3+102x^2+114x-84, or B.

Answer:

-32x^5

Step-by-step explanation:

using binomial expression we have (1-2x)^6

Answer:

Step-by-step explanation:

a-b=21

5a-2b=18

Using elimination, we have

5a-5b=105

5a-2b=18

So:

3b=-87 so b=-29

Substituting, a=-8

(a,b)=(-8,-29)

The  x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.

Given the equation;

8x - 9y = 15

First, we find the x-intercepts by simply substituting 0 for y and solve for x.

8x - 9y = 15

8x - 9(0) = 15

8x = 15

Divide both sides by 8

8x/8 = 15/8

x = 15/8

Next, we find the y-intercept by substituting 0 for x and solve for y.

8x - 9y = 15

8(0) - 9y = 15

- 9y = 15

Divide both sides by -9

- 9y/(-9) = 15/(-9)

y = -15/9

y = -5/3

We list the intercepts;

x-intercept: ( 15/8, 0 )

y-intercept: ( 0, -5/3 )

Therefore, the  x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.

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Explanation:

Angles EBA and DBC are congruent because of the similar arc marking. Both are x each.

Those angles, along with EBD, combine to form a straight angle of 180 degrees. We consider those angles to be supplementary.

So,

(angleEBA) + (angleEBD) + (angleDBC) = 180

( x ) + (4x+12) + (x) = 180

(x+4x+x) + 12 = 180

6x+12 = 180

6x = 180-12

6x = 168

x = 168/6

x = 28

Angles EBA and DBC are 28 degrees each.

This means angle D = 3x+5 = 3*28+5 = 89

-----------

Then we have one last set of steps to finish things off.

Focus entirely on triangle DBC. The three interior angles add to 180. This is true of any triangle.

D+B+C = 180

89 + 28 + C = 180

117+C = 180

C = 180 - 117

C = 63 degrees

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:x + 4x + 12 + x=180°[/tex]

( Angle EBA= Angle DBC, and the three angles sum upto 180° due to linear pair property )

[tex]\qquad❖ \: \sf \:6x + 12 = 180[/tex]

[tex]\qquad❖ \: \sf \:6x = 180 - 12[/tex]

[tex]\qquad❖ \: \sf \:6x = 168[/tex]

[tex]\qquad❖ \: \sf \:x = 28 \degree[/tex]

Next,

[tex]\qquad❖ \: \sf \: \angle C + \angle D + x = 180°[/tex]

[tex]\qquad❖ \: \sf \: \angle C +3x + 5 + x = 180°[/tex]

[tex]\qquad❖ \: \sf \: \angle C +4x = 180 - 5[/tex]

[tex]\qquad❖ \: \sf \: \angle C +4(28) = 175[/tex]

( x = 28° )

[tex]\qquad❖ \: \sf \: \angle C +112 = 175[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 175 - 112[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

Answer:

No solution

Step-by-step explanation:

[tex]\sqrt{6x-3}=2\sqrt{x} \\ \\ 6x-3=4x \\ \\ -3=2x \\ \\ x=-\frac{3}{2} [/tex]

However, this would make the right hand side of the equation undefined over the reals, so there is no solution.

The coefficient of 2(3)(6)Q is 2(3)(6)

The expression is given as:

2(3)(6)Q

For an expression

AQ

Where A is a number or product of numbers and Q is a variable

The number A represents the coefficient

By comparing:

AQ and 2(3)(6)Q

We have

A = 2(3)(6)

Hence, the coefficient of 2(3)(6)Q is 2(3)(6)

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Answer:

-8 5/12

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

Let the number of hamburgers be h and the number of cheeseburgers be c.

This means that:

Substituting c=3h into the first equation, it follows that 4h=336, and thus h=84.

When we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.

Given two expressions be [tex]x^{3} +6x^{2} +3x+1[/tex] and (x-2).

We are required to divide the first expression by second expression.

Division means distributing parts of something. The number which is being divided is known as quotient.Divisor is a number which divides the number.

Expressions refers to the combination of numbers, fractions, coefficients, determinants, indeterminants. It expresses some relationship or show equation of line.

We know that  relationship between quotient, divisor, divident and remainder is as under:

Dividend=Divisor*Quotient+Remainder

[tex]x^{3} +6x^{2} +3x+1[/tex]=(x-2)*([tex]x^{2} +8x+19[/tex])+39

Quotient=[tex]x^{2} +8x+19[/tex]

Remainder=39

Hence when we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.

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The time taken for the smaller pipe to fill the pool by itself is 15.71 hours

1/6 = 1/x + 1/(x+6)

1/6 = (x+6)+(x) / (x)(x+6)

1/6 = (x+6+x) / x²+6x

1/6 = (2x+6)(x² + 6x)

1(x² + 6x) = 6(2x+6)

x² + 6x = 12x + 36

x² + 6x - 12x - 36 = 0

x² - 6x - 36 = 0

x = 9.71 or -3.71

The value of x cannot be negative

Therefore, the

Time taken for long pipe = x

= 9.71 hours

Time taken for small pipe = x + 6

= 9.71 + 6

= 15.71 hours

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Answer:

[tex] \frac{\pi}{4} [/tex]

Step-by-step explanation:

[tex] \sf let \: y = { \tan }^{ - 1} ( \tan \frac{3\pi}{4} ) \\ \\ \sf \hookrightarrow \tan y = \tan \frac{3\pi}{4} \\ \\ \sf \hookrightarrow \tan y = \tan(\pi - \frac{\pi}{4} ) \\ \\ \sf \hookrightarrow \tan y = \tan( - \frac{\pi}{4} ) \\ \\ \sf \hookrightarrow \tan y = - \tan \frac{\pi}{4} \\ \\ \boxed {\hookrightarrow{ \bold{y = - \frac{\pi}{4} } } }[/tex]

Answer:

45

Step-by-step explanation:

Assuming this is a trapezoid,

[tex]\frac{29+WZ}{2}=37 \\ \\ 29+WZ=74 \\ \\ WZ=45[/tex]

Step-by-step explanation:

(7m - 3)² = 49m² - 42m + 9

play it through and do the actual multiplication behind the square :

(7m - 3)² = (7m - 3)(7m - 3) =

= 7m×7m + 7m×(-3) + (-3)×7m + (-3)(-3) =

= 49m² - 2×21m + 9 = 49m² - 42m + 9

Answer:

3

Step-by-step explanation:

First we look at our problem 1/2 + 5/2. We can see our denominator is the same so we can add our numerators. 1/2 + 5/2 equals 6/2 = 3.

Answer:

If you add this fraction in fraction strip instead of equivalent fraction method

Step-by-step explanation:

firstly draw 5 1/2 fraction strip

then draw 12 1/4 fraction strip

we taking 1/4 bcoz 1/4 is multiple of 1/2, under 1/2 there is 2 1/4.

The end product will be 12/4

cancel out it 12/4 by 2 ans = 6/2 still we can cancel so cancel out 6/2 by 2 at the end ans will be 3/1 = 3

if you think it wrong then use the equivalent fraction method to see the answer..

1/2 + 5/2

denominators are same so we will take only one denominator and will directly add the numerators

1 + 5 = 6 so

6/2 cancel it the ans will be 3/1 and it's equal to 3.

Answer: y = 5.4

Step-by-step explanation: This is a proportional statement. So we can set up a system of proportions.

So we know when x is 5, y is 3. Thus, we can set up a proportion [tex]\frac{x}{y}[/tex] such that substituting will give [tex]\frac{5}{3}[/tex].

Now, we know when x is 9, y is some unknown number. So we can set up the second proportion as [tex]\frac{9}{y}[/tex].

Since 5/3 and 9/y are directly proportional, these 2 expressions are therefore equal. So we have [tex]\frac{5}3}[/tex] [tex]= \frac{9}{y}[/tex].

Cross multiplying, we get [tex]5y = 27[/tex].

Dividing by 5, we get [tex]y = 5.4[/tex]

Hope this helped!

The correct option regarding the sampling is C. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.

Sampling is a process that is used in statistical analysis in which a predetermined number of observations are taken from a larger population

In this case, since the claim is mean pulse rate of students in a large statistics classes is greater than 72. The sample mean pulse rate was found to be 98.9 then the sample is not unusual if the claim is true. The sample is unusual if claim is false. Therefore there is sufficient evidence to support the claim.

The correct option is C.

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The relation that is also a function is described as follows:

A nonlinear function on a coordinate plane vertex at (minus 3, minus 2) passes through (minus 7, 0), and (minus 6, minus 4).

A relation is a function if each value of the input is mapped to only one value of the output.

In this problem, we have that:

Hence a function is given by:

A nonlinear function on a coordinate plane vertex at (minus 3, minus 2) passes through (minus 7, 0), and (minus 6, minus 4).

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The probability that the value of p(x) is greater than 315 is 0.063754

From the question, the given parameters about the distribution are

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (315 - 283)/21

Evaluate the difference of 315 and 283

z = 32/21

Evaluate the quotient of 32 and 21

z = 1.524

The probability that the value of p(x) is greater than 315 is then calculated as:

P(x > 315) = P(z > 1.524)

From the z table of probabilities, we have;

P(x > 315) = 0.063754

Hence, the probability that the value of p(x) is greater than 315 is 0.063754

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Answer:

no solutions

Step-by-step explanation:

Answer:

It is the second answer

Step-by-step explanation:

The standard form of an ellipse is

x^2/a^2 + y^2/b^2  or x^2/b^2 + y^2/a^2 = 1

If the x is the main axis we use the first form.  If the y is the main axis we use the second form.  We will use the second form.

our a is 3 and our b is 4

x^2/3^2 + y^2/4^2

Using the z-distribution, the p-value for the test is of 0.0040.

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

For this problem, the parameters are given as follows:

[tex]\overline{x} = 33.8, \mu = 32, \sigma = 4.3, n = 40[/tex]

Hence the value of the test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

z = (33.8 - 32)/(4.3/sqrt(40))

z = 2.65.

Using a z-distribution calculator, with z = 2.65 and a right-tailed test, as we are testing if the mean is greater than a value, the p-value is of 0.0040.

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Answer:

25.2

Step-by-step explanation:

I'll assume you wrote:

[tex]f(x) = 4e^{x-2} - 4[/tex]

So when x = 4:

[tex]4e^{4-2} - 4 = 4e^2 - 4[/tex] ≅ [tex]4\cdot 7.3 - 4 = 25.2[/tex]

Answer:

68?

Step-by-step explanation:

multiples of 5 end in 5 or 0

_ _ _

last digit has 2 choices ( 5 and 0 )

1,3,5,7,9 are odd

so tens digit has 5 choices but we see that 5 is repeated so we split into more cases

when last digit is 0, tens digit has 5 choices then hundreds digit has 8 choices so 1*5*8=40

when last digit is 5, tens digit has 4 choices and hundreds digit has 7 choices (0 can't be first digit) 1*4*7=28

40+28=68

Answer:

96 degrees

Step-by-step explanation:

The angle bisectors splits the two angles mentioned down the middle so the 2 angles are equal to each other.

4x + 4 = 2(x + 13)  Distribute the 2

4x + 4 = 2x + 26  Subtract 2x from both sides

2x + 4 = 26  Subtract 4 from both sides

2x = 22  Divide both sides by 2

x = 11  Plug that back into either the right side or the left side of the original equation

4x + 4

4(11) + 4

44 + 4

48.  Each angle is 48 degrees.  48 + 48 is 96

Answer:

9x3 - 6x2 + 3x

Step-by-step explanation:

(27x 4 - 18x 3 + 9x 2) ÷ 3x

Dividing each term between 3x we have:

9x3 - 6x2 + 3x

We can check the result:

(9x3 - 6x2 + 3x) * (3x)

= (27x4 - 18x3 + 9x2)

Answer:

show the image because we cant answer it if there's no picture or image

Step-by-step explanation:

Mathematically speaking, the Riemann sum of the linear function is represented by A ≈ [[4 - (- 6)] / 5] · ∑ 2 [- 6 + i · [[4 - (- 6)] / 2]] - [[4 - (- 6)] / 5] · ∑ 1, for i ∈ {1, 2, 3, 4, 5}, whose representation is represent by the graph in the lower left corner of the picture.

Graphically speaking, Riemann sums with right endpoints represent a sum of rectangular areas with equal width with excess area for positive y-values and truncated area for negative y-values generated with respect to the x-axis. Mathematically speaking, this case of Riemann sums is described by the following expression:

A ≈ [(b - a) / n] · ∑ f[a + i · [(b - a) / n]], for i ∈ {1, 2, ..., n}

Where:

a - Lower limit

b - Upper limit

n - Number of rectangles

i - Index of a rectangle

If we know that f(x) = 2 · x - 1, a = - 6, b = 4 and n = 5, then the Riemann sum with right endpoints of the area below the curve is:

A ≈ [[4 - (- 6)] / 5] · ∑ 2 [- 6 + i · [[4 - (- 6)] / 2]] - [[4 - (- 6)] / 5] · ∑ 1, for i ∈ {1, 2, 3, 4, 5}

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