Is a reference angle always in the first quadrant or can it be in other quadrants? HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

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:

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:

[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]

[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]

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

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

Answer:

The values of x are : [tex]2i[/tex] and [tex]-2i[/tex]

Step-by-step explanation:

Given equation is:   [tex]2x^2= -8[/tex]

First, we will divide both sides by 2 for getting rid of that 2 from the left side. So........

[tex]\frac{2x^2}{2}= \frac{-8}{2} \\ \\ x^2=-4[/tex]

Now, we need to take square root on both sides. So, we will get......

[tex]\sqrt{x^2}= \pm \sqrt{-4} \\ \\ x=\pm \sqrt{4(-1)} \\ \\ x=\pm 2\sqrt{-1}= \pm 2i[/tex]

(Replacing [tex]\sqrt{-1}[/tex] as  [tex]i[/tex] )

So, the solutions are: [tex]x= 2i, -2i[/tex]

Answer:

2i or -2i

Step-by-step explanation:

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.

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

One marker would cost approx. $0.03

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

[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]

Answer:

[tex]\dfrac{1}{3,357,900}[/tex]

Step-by-step explanation:

There are

[tex]C^{42}_4=\dfrac{42!}{4!(42-4)!}=\dfrac{42!}{4!\cdot 38!}=\dfrac{38!\cdot 39\cdot 40\cdot 41\cdot 42}{2\cdot 3\cdot 4\cdot 38!}=39\cdot 10\cdot 41\cdot 7=111,930[/tex]

different ways to select the  four numbers between 1 and 42. Only one of this ways is correct (successful to win).

There are 30 different ways select the single number between 1 and 30. Only one of them is correct.

The  probability of winning the jackpot is

[tex]\dfrac{1}{111,930}\cdot \dfrac{1}{30}=\dfrac{1}{3,357,900}[/tex]

The probability of winning the jackpot in the particular lottery is 1 in 9,335,082,240.

To find the probability of winning the jackpot, we need to calculate the probability of selecting the correct four numbers between 1 and 42 and the correct single number between 1 and 30.

For the four numbers, the probability of choosing each number correctly is 1/42 since there are 42 numbers to choose from and only one is correct. Since the selections are independent, we can multiply the probabilities together to get the overall probability of choosing all four numbers correctly: (1/42) * (1/42) * (1/42) * (1/42) = 1/311,169,408.

For the single number, the probability is 1/30 since there are 30 numbers to choose from and only one is correct.

To find the overall probability of winning the jackpot, we multiply the probabilities of selecting the four numbers correctly and the single number correctly: (1/311,169,408) * (1/30) = 1/9,335,082,240.

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[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.

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

hope this helps! ❤ from peachimin

Exact Form:√5

Decimal Form:2.23606797…

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:

[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!

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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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.

The answer is:

                                    1919=2

Let us assume the numbers as follows:

9=1

8=2

1=0

6=4

2=0

Hence, when we substitute the assumed values in each of the given numbers we obtain the result for each as follows:

1)

9999=1+1+1+1

9999=4

2)

8888=2+2+2+2

8888=8

3)

1816=0+2+0+4

1816=6

4)

1212=0+0+0+0

i.e.

1212=0

5)

1919=0+1+0+1

i.e.

1919=2

Answer

The value of 1919 is 2

Explanation:  

Now find the value of 1919,

1 ⇒ 0

9 ⇒ 1

So, 1919 ⇔ 0101 ⇔ 0+1+0+1 = 2

Therefore, 1919 = 2

Further Explanation

Given, 9999= 4, 8888= 8, 8816= 6, 1212= 0,

If assume 9 as 1 for 9999 and add each 1 to get 4

So,  9999 ⇔ 1111 ⇔ 1+1+1+1 = 4

Therefore, 9 represents 1

If assume 8 as 2 for 8888 and add each 2 to get 8

So,  8888 ⇔ 2222 ⇔ 2+2+2+2 = 8

Therefore, 8 represents 2

If assume 1 as 0 and assume 6 as 2 for 8816 and add each digit to get 6

So,  8816 ⇔ 2202 ⇔ 2+2+0+2 = 6

Therefore, 1 represents 0 and 6 represents 2

If assume 2 as 0 for 1212 and add each digits to get 0

So,  1212 ⇔ 0000 ⇔ 0+0+0+0 = 0

Therefore, 2 represents 0

Learn More

Learn more about logical reasoning: https://brainly.com/question/8815372; Answered by:  Empathictruro

Keywords

Logical reasoning, high school mathematics, numbers, mathematical sum