a1=5
an=an−1−3

Which sequence is represented by the given information?
{5,8,11,14}
{5,2,−1,−4}
{5,4,3,2}
{0,−3,−6,−9}

[tex]6r+5=11r\ \ \ \ |\text{subtract 6r from both sides}\\\\5=5r\ \ \ \ |\text{divide both sides by 5}\\\\\boxed{r=1}\\-------------------------\\\dfrac{2x-4}{2}=6x+3\\\\\dfrac{2x}{2}-\dfrac{4}{2}=6x+3\\\\x-2=6x+3\ \ \ \ \ |\text{add 2 to both sides}\\\\x=6x+5\ \ \ \ |\text{subtract 6x from both sides}\\\\-5x=5\ \ \ \ \ |\text{divide both sides by -5}\\\\\boxed{x=-1}[/tex]

Step 1

Find the measure of angle x

we know that

If ray NP bisects <MNQ

then

m<MNQ=m<PNM+m<PNQ ------> equation A

and

m<PNM=m<PNQ -------> equation B

we have that

m<MNQ=(8x+12)°

m<PNQ=78°

so

substitute in equation A

(8x+12)=78+78-------> 8x+12=156------> 8x=156-12

8x=144------> x=18°

Step 2

Find the measure of angle y

we have

m<PNM=(3y-9)°

m<PNM=78°

so

3y-9=78------> 3y=87------> y=29°

therefore

the answer is

the measure of x is 18° and the measure of y is 29°

Answer: If NP bisects MNQ, MNQ=8x+12,PNQ=78, and RNM=3y-9, find the values of x and y

x= 18 y=11

Step-by-step explanation:

We know that MNQ= 8x+12

PNQ=78 and MNP is equal to PNQ

Therefore, PNQ=MNP

So since these two angles make up MNQ,

Add 78+78 which is 156

So now we need to find x

The equation to find x is 8x+12=156

8x+12=156

8x=144

x=18

Now that we know x it is time to find y.

So we know that RNM=3y-9

And we know that MNQ is equal to 156

RNM an MNQ form a straight line which means that it is equal to 180 degrees

So the equation to find y is 3y-9+156=180

3y-9+156=180

3y+147=180

3y=33

y=11

So in conclusion, x=18 and y=11

Hope this helped! :3

Answer:

[tex]\displaystyle \large{f\prime(x) = 2x \sin (x) + x^2 \cos (x)}[/tex]

Step-by-step explanation:

We are given a function:

[tex]\displaystyle \large{f(x) = x^2 \sin (x)}[/tex]

Notice that there are two functions multiplying each other. Recall the product rules.

[tex]\displaystyle \large{y=h(x)g(x) \to y\prime = h\prime (x) g(x) + h(x)g\prime (x)}[/tex]

You can let x^2 = h(x), sin(x) = g(x) or sin(x) = h(x), x^2 = g(x) as your desire but I’ll let h(x) = x^2 and g(x) = sin(x).

Therefore, from a function:

[tex]\displaystyle \large{f(x) = x^2 \sin (x) \to f\prime (x) = (x^2)\prime \sin(x) + x^2 (\sin (x))\prime}[/tex]

Recall the power rules and differentiation of sine.

[tex]\displaystyle \large{y = ax^n \to y\prime = nax^{n-1} \ \ \ \tt{for \ \ polynomial \ \ function}}\\ \displaystyle \large{y = \sin (x) \to y\prime = \cos (x) }[/tex]

Therefore, from differentiating function,

[tex]\displaystyle \large{f\prime(x) = 2x \sin (x) + x^2 \cos (x)}[/tex]

And we are done!

[tex]f(x)=2x-5,\ g(x)=x^2-4x-8\\\\(f+g)(x)=f(x)+g(x)=(2x-5)+(x^2-4x-8)\\\\=2x-5+x^2-4x-8=x^2+(2x-4x)+(-5-8)=x^2-2x-13[/tex]

Answer:

[tex]\text{The value of (f+g)(x) is }x^2-2x-13[/tex]

Step-by-step explanation:

Given the two functions

[tex]f(x)=2x-5[/tex]

[tex]g(x)=x^2-4x-8[/tex]

we have to find the value of (f+g)(x)

As we know

[tex](f+g)(x)=f(x)+g(x)=(2x-5)+(x^2-4x-8)[/tex]

[tex]=2x-5+x^2-4x-8[/tex]

[tex]=x^2+2x-4x-5-8=x^2-2x-13[/tex]

[tex]\text{Hence, the value of (f+g)(x) is }x^2-2x-13[/tex]

y = | 3x - 7 |

x-intercept is when y = 0

0 = | 3x - 7 |

0 = 3x - 7

+7       +7

7 = 3x

[tex]\frac{7}{3} = \frac{3x}{3}[/tex]

 [tex]\frac{7}{3} = x[/tex]

[tex](\frac{7}{3}, 0 )[/tex]

y-intercept is when x = 0

y = | 3(0) - 7 |

y = | 0 - 7 |

y = | -7 |

y = 7

(0, 7)

Answer: [tex](\frac{7}{3}, 0 )[/tex] and (0, 7)

The law of large numbers in probability, is a theorem that describes the result of performing the same experiment a large number of times because the average of the results obtained from a large number of trials is close enough to the expected value.

So, according to this definition and the situation given , the correct answer is option B - if 800 people are randomly surveyed about the TV shows they watch, about 400 of them will be women; because there are larger number of experiment.

Part B:

To get the expected value of a t-shirt we will multiply each of the 3 prices by the associated probability, and then add up these three products-

[tex](24\times\frac{1}{6})+(30\times\frac{1}{2})+(36\times\frac{1}{3})[/tex]

=4 + 15 + 12 = $31

Hence, option C is correct.

Answer:

1.  If 800 people are randomly surveyed about the TV shows they watch, about 400 of them will be women.

2. $31

Step-by-step explanation:

Got it right on the test.

[tex]E=\{-1,\ 0,\ 1,\ 2,\ 3,\ 4\}\\\\F=\{3,\ 4,\ 5,\ 6,\ 7,\ 8\}\\\\E\ \cup\ F=\{-1,\ 0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8\}[/tex]

All elements from set E and from the set F. The same elements are only once.

use the amount for each quantity to obtain theratio

choc chips : sugar = 5 : 3 = [tex]\frac{5}{3}[/tex]

Answer:

[tex]\frac{5}{3}[/tex]

Step-by-step explanation:

Hi, here is the solution.

The doubling each dimensions increases the volume by 8. That is (2 * 2* 2)

There 1000 toothpicks in a regular box.

The jumbo box hold  8 *1000 = 8000 toothpicks.

Thank you.

p = -4

q could be 6.5 units to the right   ...   or to the left   ...   of point p.

to the right: p + q   ⇒  [tex]-4 + (6\frac{1}{2}) = 2\frac{1}{2}[/tex]

to the left: p - q  ⇒ [tex]-4 - (6\frac{1}{2}) = -10\frac{1}{2}[/tex]

Answer: [tex]2\frac{1}{2}[/tex] or [tex]-10\frac{1}{2}[/tex]

Answer:

Option B 0.11

Step-by-step explanation:

Given that  the population proportion of 0.58, a simulation of 200 trials is run, each with a sample size of 50 and a point estimate of 0.42. The minimum sample proportion from the simulation is 0.31, and the maximum sample proportion from the simulation is 0.53.

This gives an idea that confidence interval is

(0.31, 0.53) with mean being in the middle of this interval

Margin of error = 1/2 (length of this interval)

Length of confidence interval =[tex]0.53-0.31 =0.22[/tex]

Margin of error =± 1/2(0.22) = ±0.11

Hence option B is correct

7×2=14e

7×1=7

14e-7-11=6+6e

   -6e             -6e

8e-7-11=6

    +7      +7

8e-11=13

     +11    +11

8e=24

8e÷8=e

24÷8=3

e=3

To solve the equation 7(2e-1)-11=6+6e for e, distribute, combine like terms, subtract, add, and divide until you have isolated e. The solution is e=3.

To solve for e in the equation 7(2e-1)-11=6+6e, first distribute the 7 on the left side of the equation:

14e - 7 - 11 = 6 + 6e

Now, combine like terms on both sides:

14e - 18 = 6 + 6e

Next, subtract 6e from both sides:

8e - 18 = 6

Add 18 to both sides:

8e = 24

Finally, divide by 8:

 e = 3.

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Given

ratio of elinor's age to his mother is 3 : 8

after 15 years

 the ratio will become 6:11

Find out the  elinor's age today and find her mothers age after 15 years.

To proof

As given in the question

ratio of elinor's age to his mother is 3 : 8

let x be the variable describe age.

let the elinor age = 3x

let the mother age = 8x

after 15 years

ratio will become 6:11

[tex]\frac{elinor\ age + 15 }{Mother\ age + 15 } = \frac{6}{11}[/tex]

As assume ealier elinor age be 3x and mother age be 8x

put this in the above equation

we get

[tex]\frac{3x + 15 }{8x + 15 } = \frac{6}{11}[/tex]

now sloving the above equation

we get

11 ( 3x + 15) = 6 ( 8x + 15 )

33x + 165 = 48x + 90

75 = 15x

[tex]x = \frac{75}{15}[/tex]

x = 5

Therefore

elinor's age today = 3x

                              = 3 × 5

                              = 15years

mothers age after 15 years = 8x + 15

                                              = 8× 5 + 15

                                              = 40 + 15

                                              = 55years

Hence proved

The problem is about solving a system of equations established from the given ratios of Elinor's and her mother's ages. Substitution method is used to find their present ages, and to find mother's age after 15 years, we add 15 to her current age.

This is a problem related to ratios and ages, which can be solved as an algebraic system of equations. Let's denote Elinor's present age as 'e' and her mother's age as 'm'. Then, from the problem we know that:

e/m = 3/8 (1), and

(e+15)/(m+15) = 6/11 (2).

From equation (1), we can express e as (3/8)m. We then substitute e in equation (2) to find the value of 'm'. Once we have 'm', we substitute its value in equation (1) to get 'e'. And to find her mother's age after 15 years, we add 15 to 'm'.

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To solve an absolute value equation of the form |X| = k, where X is an expression with a variable and k is a non-negative number or an expression, you must solve the compound equation X = k or X = -k.

The first step is to divide both sides by 9 to get the absolute value of an expression equal to a non-negative number.

9|9 – 8x| = 2x + 3

Divide both sides by 9.

[tex] |9 - 8x| = \dfrac{2x + 3}{9} [/tex]

Now we eliminate the absolute value by rewriting this as a compound equation.

[tex] 9 - 8x = \dfrac{2x + 3}{9} ~~~or~~~ 9 - 8x = -\dfrac{2x + 3}{9} [/tex]

We must solve both equations.

Multiply both sides by 9.

[tex] 9(9 - 8x) = 2x + 3 ~~~or~~~ 9(9 - 8x) = -(2x + 3) [/tex]

[tex] 81 - 72x = 2x + 3 ~~~or~~~ 81 - 72x = -2x - 3 [/tex]

[tex] -74x = -78 ~~~or~~~ -70x = -84 [/tex]

[tex] x = \dfrac{-78}{-74} ~~~or~~~ x = \dfrac{-84}{-70} [/tex]

[tex] x = \dfrac{39}{37} ~~~or~~~ x = \dfrac{6}{5} [/tex]

Answer: x = 39/37 or x = 6/5

To check for extraneous solutions, we plug in each solution into the original equation and check if it works.

Check 39/37:

9|9 – 8(39/37)| = 2(39/37) + 3

|81 - 72(39/37)| = 78/37 + 3

|2997/37 - 2808/37| = 78/37 + 111/37

|189/37| = 189/37

189/37 = 189/37

The solution 39/37 is valid.

Check x = 6/5.

9|9 – 8x| = 2x + 3

9|9 – 8(6/5)| = 2(6/5) + 3

|81 - 72(6/5)| = 12/5 + 15/5

|405/5 - 432/5| = 27/5

|-27/5| = 27/5

27/5 = 27/5

The solution x = 6/5 is also valid.

There are no extraneous solutions.

Given equation is [tex]x^3-5x^2+2x+6=0[/tex]

Usually we solve this type of problem by factoring but this equation is not factorable. If we solve by grouping then also we are not getting any common factor. So factoring method is not going to help. I this type of situation we may use graphing calculator. From graph we just need to pick those points where graph crosses the x-axis. Those values will be the final answer.

Using graphing calculator we see that there are three solutions at x=-0.856, x=1.678, x=4.177 which are approx x=-0.8, x=1.7 and x=4.2

Hence final answers are x=-0.8, x=1.7 and x=4.2.

Answer:

-0.9, 1.7, and 4.2

Step-by-step explanation:

8,5 and 6,1

The slope is 2

One marker would cost approx. $0.03

the answer to your question :[tex]4\sqrt{5}[/tex]

hope this helps! ❤ from peachimin

Exact Form:√5

Decimal Form:2.23606797…

least to greatest: -0.51, -1/2, 0.42, 11/20

greatest to least: 11/20, 0.42, -1/2, -0.51

you answer is 5/8 please mark as brainliest if you need more help with questions like this lemme know

[tex]g(x)=\dfrac{x-1}{4}\to y=\dfrac{x-1}{4}\\\\\text{change x to y and y to x}\\\\x=\dfrac{y-1}{4}\ \ \ \ |\text{solve for y}\\\\\dfrac{y-1}{4}=x\ \ \ \ \ |\cdot4\\\\y-1=4x\ \ \ \ |+1\\\\y=4x+1\\\\\boxed{g^{-1}(x)=4x+1}[/tex]