Solve 3x + 4x = 2. (2 points)O 2 10 6O 2+210- 3O 2+10- 3O-4 10 3

Solve 3x² + 4x = 2. (2 points)
O 2 ± √10
—————
6
O −2+2√10
——————-
3
O −2+√10
——————-
3
O
-4± √10
————
3

Answers

Answer 1

Answer:

Step-by-step explanation:

As it is a second order equation, it means that it has two possible answers and they are [tex]x_1[/tex] and [tex]x_2[/tex].

The famous quadratic formula for solving any second order equation is the following:

[tex]x_{1} = \frac{-b + \sqrt{b^2 - 4 ac}}{2a}\\x_{2}=\frac{-b - \sqrt{b^2 - 4 ac}}{2a}[/tex]

Where a is the coefficient of [tex]x^2[/tex], b is the coefficient of x, and c is the free term. In other words,

[tex]a = 3\\b=4\\c=-2[/tex]

as the equation should be in the following form:

[tex]a x^2 + bx+c = 0[/tex]

Therefore the possible answer should be the following,

[tex]\frac{-4 + \sqrt{4^2 - 4*3*(-2)}}{2*3}=\frac{-4 +\sqrt{16 + 24}}{6} =\frac{-4 + \sqrt{40}}{6}=\\ \frac{-4 + \sqrt{4*10}}{6} = \frac{-4 + 2\sqrt{10}}{6}[/tex][tex]\frac{2*(-2 + \sqrt{10})}{2*3} = \frac{-2 + \sqrt{10}}{3}[/tex]

by dividing the numerator and denominator by 2, we can deduce the following,

Related Questions

Calculate the Theoretical probability of the following experiments.

Use a tree diagram to visualize your calculations. *** Note that these are independent experiments. Once she has removed a fruit, she will put it back in before removing a second fruit.***

Jane has a bag with 5 oranges, 4 grapefruits, and 3 apples.

What is the probability that she will NOT randomly take out two oranges in a row?

What is the probability that she will NOT randomly take out two grapefruits in a row?

What is the probability that she will NOT randomly take out two apples in a row?

What is the probability that she will NOT take out an orange, then an apple, and finally a grapefruit in that order?

Answers

The probability that she will NOT take out an orange, then an apple, and finally a grapefruit in that order is 0.2917.

What is Probability?

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

A.) The probability that she will NOT randomly take out two oranges in a row,

Probability = 1 - (5/12)² = 0.8264

B.) The probability that she will NOT randomly take out two grapefruits in a row,

Probability = 1 - (4/12)² = 0.8264 = 0.8889

C.) The probability that she will NOT randomly take out two apples in a row,

Probability = 1 - (3/12)² = 0.8264 = 0.9375

D.) The probability that she will NOT take out an orange, then an apple, and finally a grapefruit in that order,

Probability = (7/12) × (9/12) × (8/12) = 0.2917

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I NEED HELP ASAPPPPPP
Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−12)2+81

. Which of the following statements is true?

The airplane reaches its minimum height of 12 feet in 81 seconds.
The airplane reaches its maximum height of 81 feet in 12 seconds.
The airplane reaches its minimum height of 81 feet in 12 seconds.

The airplane reaches its maximum height of 12 feet in 81 seconds.

Answers

Considering the given quadratic equation, the correct statement is given by:

The airplane reaches its maximum height of 81 feet in 12 seconds.

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the equation is given by:

h(t) = -(t - 12)² - 81.

The vertex is (12,81), with a negative leading coefficient, hence it is a maximum point and the correct statement is given by:

The airplane reaches its maximum height of 81 feet in 12 seconds.

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Which of the following situations can be defined using an exponential function?
A The value of the stocks decreased by $100 last year.
B The number of bacteria decreases by 7% each hour.
C The number of bacteria increases by 700 each hours.
D The value of the stocks increases by $10 every year you own them.

Answers

The situation which can be defined using an exponential function is "The number of bacteria decreases by 7% each hour".

What is an exponential function?

An exponential function is used to represent a situation in which values of an event do not increase at a constant or linear rate.

From the above,

The value of the stocks decreased by $100 last year is a linear function.The number of bacteria increases by 700 each hour is a linear function.The value of the stocks increases by $10 every year you own them is a linear function.

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any help is great find the missing length?

Answers

Answer:

Step-by-step explanation:

Similar = proportional

solve with an equation

12 : 9 = 4 : x

x = 4 * 9 : 12

x = 3

A group of students from your school is part of the audience for a TV game show. The total number of people in the audience is . What is the theoretical probability of students from your school being selected as contestants out of possible contestant spots?

Answers

A group of students from your school is part of the audience for a TV game show, the theoretical probability of students is mathematically given as

P=2.7%

What is the theoretical probability of students from your school being selected as contestants out of possible contestant spots?

Generally, the equation for Probability is mathematically given as

[tex]P=\frac{Desired outcomes}{Total outcomes}[/tex]

Where Desired outcomes

D=40C5 *110C3

D=1420112865560

And Total outcomes

T=150C8 *

T=5.2572*10^10{12}

Hence, Probability

[tex]P=1420112865560/ 5.2572*10^10{12}[/tex]

P=0.0270

P=2.7%

In conclusion, the theoretical probability

P=2.7%

Answers

see the attachment photo!

When graphing f(x)=a sin(bx) you would determine the functions period using which of the following?

A. The period is 2pi/b

B. The period is a

C. The period is pi/b

Answers

Answer: A. The period is 2pi/b

Explanation:

The value of 'a' out front in y = a sin(bx) determines the amplitude.

The b term helps us compute the period, which is 2pi/b for sine, cosine, secant, and cosecant functions.

For example, y = 2sin(3x) has an amplitude of 2 and period of 2pi/3

For tangent and cotangent functions, the period would be pi/b.

(giving 100 points) What is the equation of the line of best fit for the following data? Round the slope and y-intercept of the line to three decimal places.

x y

4 3

6 4

8 9

11 12

13 17

A: y = 1.560x - 4.105

B: y = -4.105x + 1.560

C: y = 4.105x - 1.560

D: y = -1.560x + 4.105

please hurry

Answers

Answer:

Slope-intercept form of a linear equation: [tex]y=mx+b[/tex]

where:

[tex]m[/tex] is the slope[tex]b[/tex] is the y-intercept

To determine the equation of the line of best fit from the given answer options, examine the relationship between the x and y values.

From inspection of the data, we can see that as x increases, y increases. Therefore, the slope of the equation will be positive.

(If the y-values decrease as the x-values increase, then the slope would be negative).

Therefore, we can immediately discount answer options B and D as they have negative slopes.

The x and y values are not very far away from each other. The options given for the slope are either 1.560 or 4.105. If the slope was 4.105, we would expect to see values of y that were further away from the x-values.

Therefore, the line of best fit is:

A: y = 1.560x - 4.105

To prove this, plot the 5 points on a graph and draw a line of best fit (see attached).

Choose 2 points on the line of best fit: (4, 2) and (11, 13)

Use the slope formula with these points to calculate the approximate slope:

[tex]\implies \sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}\approx\dfrac{13-2}{11-4}=\dfrac{11}{7}=1.57[/tex]

Thus proving that y = 1.560x - 4.105 is an appropriate option for the equation of the line of best fit.

help me please i still struggle

Answers

Answer:

59 degrees

Step-by-step explanation:

Angles on a straight line add up to 180 degrees

Angles in a triangle add up to 280 degrees

180 minus 149 is 31

31 add 90 is 121

180 minus 121 is 59

If sin Q = 4/5, cos P + cos Q

Answers

The value of the cos P + cos Q is 7/5 if sin Q = 4/5 after applying the identities of trigonometric.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We know that:

P + Q are complementary, which means that

P+Q = 90°

Then R is a right angle, i.e. it measures 90°.

sin(90-x) = cos (x)

cos(90-x) = sin (x)

Then sinQ = 4/5

cos(90-Q) = cosP = 4/5

Now sin²(P) + cos²(P) = 1

sin²(P) = 1 - cos²(P)

sin²(P) = 1 -[4/5]² =9/25

sin(P) = 3/5

cos(Q) = sin(P) = 3/5

cos(P) + cos(Q) = 4/5 + 3/5 = 7/5

Thus, the value of the cos P + cos Q is 7/5 if sin Q = 4/5 after applying the identities of trigonometric.

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Can I get help with this pls

Answers

Answer:

2 [tex]\leq[/tex] x [tex]\leq[/tex] 7

Step-by-step explanation:

See attachment.

4x what = 364

please put the calculation

Answers

Answer:

Step-by-step explanation:

4 x 91 = 364

To work this out, we must do the inverse operation. The inverse (opposite) of x (times or multiply) is ÷ (divide).

So, we do 364 ÷ 4 = 91

Hope this helps!

- profparis

A stack of 30 science flashcards includes a review card for each of the following: 10 insects, 8 trees, 8 flowers, and 4 birds.

What is the probability of randomly selecting an insect?
Express the probability as a reduced fraction

Answers

Answer:

1/3

Step-by-step explanation:

[tex]|\Omega|=30\\|A|=10\\\\P(A)=\dfrac{10}{30}=\dfrac{1}{3}[/tex]

Bentley leans a 22-foot ladder against a wall so that it forms an angle of 74 degrees with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary

Answers

The Sine or Sin(θ) in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. The Height on the wall till which the ladder reaches is 21.148 ft.

What is Sine (Sinθ)?

The Sine or Sin(θ) in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

Sin(θ) = Perpendicular/Hypotenuse

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

The height of the wall can be found by using the trigonometry ratios, therefore, the height of the wall can be determined as,

Sin(74°) = (Height on the wall)/(Length of the wall)

Sin(74°) = (Height on the wall)/22 ft

(Height on the wall) = 21.148 ft

Hence, the Height on the wall till which the ladder reaches is 21.148 ft.

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Answer:

21.15

Step-by-step explanation:

If a baseball player hits 10 home runs in the first 45 game, at the same rate how many home runs can he expect to hit during the 162 game season

Answers

Using proportions, it is found that he can be expected to hit 36 home runs during the 162 game season.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the player hits 10 home runs in 45 games, hence the proportion is:

p = 10/45.

Then, in 162 games, the amount is:

HR = 10/45 x 162 = 36.

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which method is best for solving the system of equations,

3x+2y=4

-3x+y=2

Answers

The method which is best for solving the system of equations when you remove one variable by adding them is B Elimination

To answer the question, we need to know what system of equations are

What are system of equations?

System of equations are pairs of equations that contain two unknowns

Ways of solving system of equations

We have different ways of solving systems of equations which include

Guess and CheckEliminationGraphing and Substitution

Since we have the system of equations

3x + 2y = 4

-3x + y = 2

The method which we can use to remove one variable by adding them is the elimination method.

Adding them, we have

3x + 2y = 4

-3x + y = 2

3y = 6

y = 6/3

y = 2

So, the method which we can use to remove one variable by adding them is B Elimination

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which unit of measure would be appropriate for the area of a bulletin board that is 2 meters tall and 6 meters wide

Answers

Answer:The entire area would be 12 square meters.

Step-by-step explanation:

2 x 6 square meters = 12 square meters. which is the entire area.

what is the answer to −1.4+(−1.2)

Answers

Answer:

-2.6

Step-by-step explanation:

-1.4+(-1.2)

-1.4-1.2=-2.6

Hope this helps!

If not, I am sorry.

Is this relation a function? Justify your answer.

Answers

Answer:

Can't see the problem. Send a picture of it.

[tex] \frac{2}{3} n (4p + \sqrt{36} - 2 {n}^{2} [/tex])

n= -3
p=5

need urgent help

Answers

Answer:

-16.

Step-by-step explanation:

2/3 * (-3) * (4*5 + 6 - 2(-3)^2)

= -2(20 + 6 - 18)

= -2 * 8

= -16.

simplify (x^3+2x-3)-(x^2-2x+4)

Answers

Answer:

x³ - ((x+1)(x+1))

Step-by-step explanation:

x³ + 2x -3 - x² - 2x + 4

x³ - x² + 1

x³ - ((x+1)(x+1))

Answer:

x^3−x^2+4x−7

Step-by-step explanation:

Hope this helps! Have a great day!!

Suppose that y varies directly with x and inversely with z, and y = 4 when x = 8 and z = 14. find z when x = 36 and y = 6. first, what is the equation of variation? y =

Answers

The value of z if x = 36 and y = 6 is 42

Direct and inverse variation

Suppose that y varies directly with x and inversely with z, hence the required expression will be:

y = kx/z

If y = 4 when x = 8 and z = 14 then;

4 = k(8)/14

8k = 56

k = 7

To find z when x = 36 and y = 6, we will have:

6 = 7(36)/z
1 = 7(6)/z

z = 42

Hence the value of z if x = 36 and y = 6 is 42

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Answer:

Keep it simple. Answer:

y=kx/z

k=7

z=42

Step-by-step explanation:

The diagram shows a rectangle. The area of the rectangle is 310 m². Work out the value of w when 5x-9 is the length and 3x+7 is the another length

Answers

Answer:

w = 10

Step-by-step explanation:

First we take the two values for the breadth of the rectangle

So:

5x - 9 = 3x + 7

now we solve this equation as follows:

5x - 3x = 9 + 7

2x = 16

x = 8

now that we have found the value for x, we can substitute it in the equation, 5x - 9,or in the equation, 3x + 7.

when we substitute x in any of these equations, we get

5(8) - 9 = 31

3(8) + 7 = 31

now that we have the value for the breadth we can form the following equation:

31 × w = 310

31w = 310

w = 310/31 = 10

Answer:

Step-by-step explanation:

Firstly, we find the value of X

since 5X-9 and 3X+7 are lenghts

5X-9= 3X+7

5X-3X= 7+9

2X = 16

dividing bothsides by 2

2X/2= 16/2

X = 8

Hence,

5X-9= 5(8)-9= 40-9 = 31

3X+7=3(8)+7= 24+7= 31

To find the width

Area= lenght×width

310= 31×w

31w= 310

w= 310/31

W= 10

Anyone know the answer

Answers

Step-by-step explanation:

-2g(1+g)

-2g - 2g²

(-2)g - (2)g²

I have a bag with 6 marbles numbered from 1 to 6. mathew has a bag with 12 marbles numbered from 1 to 12. matthew chooses one marble from his bag and i choose two from mine. in how many ways can we choose the marbles (where the order of my choices does matter) such that the sum of the numbers on my marbles equals the number on his?

Answers

Answer:

It would be 30.

Step-by-step explanation:

If we make a list of all the sums that we can get, we have:

1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6

These 15 sums can be chosen in two ways, since order matters, and we could do 2+1 instead of 1+2.

That gets us to 15x2 which is 30.

The number of ways that we can choose the marbles such that the sum of the numbers on my marbles equals the number on his would be 30.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

I have a bag with 6 marbles numbered from 1 to 6.

Mathew has a bag with 12 marbles numbered from 1 to 12.

1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6

These 15 sums can be chosen in two ways,

Since order matters, and we could do 2+1 instead of 1+2.

15 x 2 which is 30.

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Help please i need this

Answers

Answer:

i can't see the question i would love to help though

Step-by-step explanation:

HELP MEE ,20 POINTS !!!!
Celina says that each of the following expressions is actually a binomial in disguise:
5abc-2a^2+6abc
5x^3∙2x^2-10x^4+3x^5+3x∙(-2) x^4
(t+2)^2-4t
5(a-1)-10(a-1)+100(a-1)
(2πr-πr^2 )r-(2πr-πr^2)∙2r

Answers

Celina says true that each of the following expressions is actually a binomial expression.

What is binomial?

The binomial is a polynomial of two-term only. For example, x + 5 where x and 5 are the two separate terms.

Celina says that each of the following expressions is actually a binomial in disguise:

a. 5abc - 2a² + 6abc = 11abc - 2a²