Solve for the variable k

[tex]6 {x}^{2} - 5x - 6 = 0 \\ 6 {x}^{2} - 9x + 4x - 6 = 0 \\ (6 {x}^{2} - 9x) + (4x - 6) = 0 \\ 3x(2x - 3) + 2(2x - 3) = 0 \\ (3x + 2)(2x - 3) = 0 \\ 3x + 2 = 0 \\ \\ \\ or \\ 2x - 3 = 0 \\ x = \frac{ - 2}{3} \\ \\ or \\ \\ x = \frac{3}{2} [/tex]

I FACTORISED THE EQUATION FIRST WITH A SIMPLE METHOD OF MULTIPLYING THE COEFFICIENT OF

[tex] {x}^{2} [/tex]

and the constant number then find the factors that will give me the coefficient of x.

ATTACHED IS THE SOLUTION

Step-by-step explanation:

are you sure this is the whole information ?

because

6² = 5x + 6

is not called a quadratic equation.

it is a quadratic equation, when there is one term in x² involved.

I assume therefore, that your problem is

6x² = 5x + 6

that is then as basic quadratic equation

6x² - 5x - 6 = 0

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

a = 6

b = -5

c = -6

x = (5 ± sqrt((-5)² - 4×6×-6))/(2×6) =

= (5 ± sqrt(25 + 144))/12 = (5 ± sqrt(169))/12 =

= (5 ± 13)/12

x1 = (5 + 13)/12 = 18/12 = 3/2

x2 = (5 - 13)/12 = -8/12 = -2/3

so, the 2 solutions for the quadratic equation are

x = 3/2 and x = -2/3

If the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units

The length of the hypotenuse = 13.5 units

The angle = 41 degrees

Here we have to use the trigonometric function

sin θ = Opposite side / Hypotenuse

cos θ = Adjacent side / Hypotenuse

tan θ = Opposite side / Adjacent side

In this question hypotenuse and angles are given and we have to find the opposite side.

sin θ= opposite side /  Hypotenuse

Substitute the values in the equation

sin 41 = Opposite side / 13.5

Opposite side = sin 41×13.5

= 8.86 units

Hence, if the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units.

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Answer:

x = 1 +sqrt(5)

x = 1 -sqrt(5)

Step-by-step explanation:

y= x^2 -2x -3

Let y = 1

1= x^2 -2x -3

Subtract 1 from each side

1-1= x^2 -2x -3-1

0 = x^2 -2x -4

Using the quadratic formula

x = - (-2) ±sqrt( (-2) ^2 -4(1)(-4))

     ----------------------------------------

                      2(1)

x = 2 ±sqrt( 4 +16)

     ------------------------

                      2

x = 2 ±sqrt( 20)

     ------------------------

                 2

x = 2 ±sqrt( 4*5)

     ------------------------

                 2

x = 2 ±sqrt(5)

     ------------------------

                 2

x = 1 ±sqrt(5)

0.020 is a probability for student selects at least 6 .

What is a probability simple definition?

There are two ways to do it. You can either interpret this as

One minus the probability that the student will guess 5 or fewer

correct answers with a probability of a correct answer being = 1/4  ⇒      

0.0197277069

The probability that the student will guess 4 or fewer wrong answers

with a probability of a wrong answer being = 3/4

  binomcdf (10,3/4,4)

     = 0.0197277069

Either way it rounds to 0.020

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Let Bailey drive x miles.

So, Kacie drove 2x miles.

Kaiden drove 2x + 10 miles.

According to the question,

x + 2x + 2x + 10 = 50

x = 8

Therefore, Bailey drove 8 miles and Kacie drove 16 miles, while Kaiden 36 miles.

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The simplified form of like terms in -3(u+6) -4(u+5) is 7u = -38.

Similar variables and powers are defined as like terms. It is not necessary for the coefficients to agree. When two or more terms do not share the same variables or powers, they are said to be unlike terms. Unless there is a power, the variables' order is irrelevant.

Two expressions joined by an equal sign form a mathematical statement known as an equation.

Given that,

Expression is -3(u+6) -4(u+5)

Simplifying the equation,

-3u-18-4u–20 = 0

-7u -38 = 0

-7u = 38

7u = -38

Therefore 7u = -38 is the simplifief form of like term in -3(u+6) -4(u+5).

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Answer: y=x2+3x−1

Hope this helps! :)

The domain and the range pf the curve was solved and the correct answer to the question is the last option which is

The domain are the input values and are represented in the x axis while the range are the output values and represented in the y axis

From the graph

We can conclude that the last option is the correct answer

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Answer:

the formula for the vertex is f(x)=a(x-h)²+k

so if you replace -4= a(0-5)²+-2

so a=-0.08

The formula would end up like this f(x)=-0.08(x-5)²+-2

Step-by-step explanation:

Applying the slope formula, we have:

16. Slope = -9/4; Parallel slope = -9/4; Perpendicular slope = 4/9.

17. Slope = -4; Parallel slope = -4; Perpendicular slope = 1/4.

See explanation below for the rest answers.

Slope of a line = change in y / change in x.

The slope of parallel lines are the same, while the slopes of two lines that are perpendicular to each other are negative reciprocals of each other, i.e. 1/a and -a can be the slopes of two lines that are perpendicular to each other.

In an equation given in slope-intercept form, y = mx + b, the slope is represented as "m".

16. Given, (3, 7) and (7, -2):

Slope (m) = (-2 - 7)/(7 - 3)

Slope = -9/4

Parallel slope = -9/4

Perpendicular slope = 4/9.

17. Given, y = -4x + 2,

Slope = -4

Parallel slope = -4

Perpendicular slope = 1/4.

18. Rewrite 5x - 2y = 8 in slope-intercept form:

-2y = -5x + 8

y = 5/2x - 4

Slope = 5/2

Parallel slope =  5/2

Perpendicular slope = -2/5.

19. Rewrite  4x + 3y = 2 in slope-intercept form:

3y = -4x + 2

y = -4/3x + 2/3

Slope (m) = -4/3

Substitute (a, b) = (2, -5), and m = -4/3 into y - b = m(x - a):

y - (-5)) = -4/3(x - 2)

y + 5 = -4/3(x - 2) [point-slope form]

20. Given, y = -5x + 2

Slope (m) = -5

Substitute (a, b) = (-4, -6), and m = -5 into y - b = m(x - a):

y - (-6) = -5(x - (-4))

y + 6 = -5(x + 4) [point-slope form]

21. Rewrite 9x - 3y = 6 in slope-intercept form:

-3y = -9x + 6

y = 3x - 2

The slope of y = 3x - 2 (9x - 3y = 6) is 3.

The slope of -3x - 5 is -3.

Therefore, the lines are neither parallel nor perpendicular.

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US$ the tourist received finally is US$985.

BD$2000 is there.

BD$1 = US$0.50

Bank charged a commission of 1.5%.

Solution:

For one BD i.e., BD$1 he gets US$0.50.

It is half the value of BD$.

By cross multiplication technique, you can find this.

Then for,

BD$2000 he will get US$ 1000.

Bank charges =  1.5%.

That is,

1.5/100*1000 = $15

US$ the tourist received finally = 1000-15

= $985

US$ the tourist received finally is US$985.

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Scientific notation of the given expression divided -6.5 × 10^-7 by

9.88 ×10^-8 with two decimal places is equal to  6.58 × 10^0.

As given in the question,

Divided  -6.5 × 10^-7 by  9.88 ×10^-8 we have,

= ( -6.5 × 10^-7 ) /( 9.88 ×10^-8 )

= ( -6.5 / 9.88) × 10^(-7 +8)

= 0.65789 × 10^1

Express above quotient in scientific notation form with two decimal is equal to

= 6. 58 × 10^0

Therefore, scientific notation of the given expression divided -6.5 × 10^-7 by  9.88 ×10^-8 with two decimal places is equal to 6.58 × 10^0.

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Answer:

5

Step-by-step explanation:

he needs $85 and he has $25,

so it will be 85-25=60

that means he would need $60 more. if he saves $13 every week, it will 60÷13= 4.6 weeks or approximately 5.

The interval where the product will at least break even is [tex]$\left[\begin{array}{cc}\text { Solution: } & x \leq-5 \\ \text { Interval Notation: } & (-\infty,-5]\end{array}\right]$[/tex]

Given C= 305 x+1350C

R=60 x

To find the interval where the product will at least break even we must have [tex]$R(x) \geq c(x)$[/tex]

[tex]$\Rightarrow \quad 35 x \geq 305 x+1350$[/tex]

[tex]$$35 x \geq 305 x+1350$$[/tex]

Subtract 305 x from both sides

[tex]$$35 x-305 x \geq 305 x+1350-305 x$$[/tex]

Simplify

[tex]$$-270 x \geq 1350$$[/tex]

Multiply both sides by - 1 (reverse the inequality)

[tex]$$(-270 x)(-1) \leq 1350(-1)$$[/tex]

Simplify

[tex]$$270 x \leq-1350$$[/tex]

Divide both sides by 270

[tex]\frac{270 x}{270} \leq \frac{-1350}{270}$$[/tex]

Simplify

[tex]$$x \leq-5$$[/tex]

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

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In a case whereby triangle ABC is congruent to triangle DEC, angle B = 2x + 31 and angle E = 7x - 24, the X is 11.

It should be noted that when a Triangles are exactly the same in term of size and shape then it is congruent.

Since the angle E and angle B is the same, then we can equate it so that we can find the value of X , then this can be calculated as

(2x + 31) = (7x - 24)

The we have

(7x - 2x) = (31 +24)

The we will have

(5x) =( 55)

Then

x = 11

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Answer:

perpendicular

Step-by-step explanation:

The equations represent a vertical and horizontal line, respectively, which are perpendicular to each other.

Answer: C

Step-by-step explanation:

Starting off we need to understand what the circles are in inequalities.

A closed circle means that the number on the inequality is included in the solution. An open circle means that the number in the inequality is not included in the solution. A closed circle would use [tex]\leq or \geq[/tex]. An open circle would use < or >.

So, using these processes, -2<x[tex]\leq[/tex]7 would be the answer.

Step-by-step explanation:

the set of prime numbers that, when multiplied together, give

13824:

2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3

Answer:

24

Step-by-step explanation:

The best plot for these results is given by:

C. Plot C.

The mean result for each group is given as follows:

Then we have to look at the vertical bars of each plot, and see the scores given.

For plot A, the scores are given as follows:

For plot B, the scores are given as follows:

For plot C, the scores are given as follows:

For plot D, the scores are given as follows:

Plot C has the closest value readings to the actual values of 36.8 and 52.4, hence it is the best option to plot the scores for each group.

The problem is missing and is given by the image at the end of the answer.

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Answer:

1/4^3

Step-by-step explanation:

Answer:

y + 2 = -2(x - 2) (point-slope form)

y = -2x + 2 (slope-intercept form)

2x + y = 2 (standard form)

Step-by-step explanation:

[tex]m = \frac{ - 4 - ( - 2)}{3 - 2} = - \frac{2}{1} = - 2[/tex]

[tex]y + 2 = - 2(x - 2)[/tex]

[tex]y + 2 = - 2x + 4[/tex]

[tex]y = - 2x + 2[/tex]

[tex]2x + y = 2[/tex]

Each person gets 1/12 fraction of the original cake.

What is a fraction?

A fraction, which derives from the Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. A common, vulgar, or simple fraction is one that has a non-zero denominator shown below (or after) the line that separates the numerator from the denominator. Composite fractions, complicated fractions, and combined numeral fractions are examples of uncommon fractions that use numerators and denominators.

Each person gets = 1/2 x 1/6 = 1/12

Hence, each person gets 1/12 fraction of the original cake.

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I WILL TAKE THE POINTS (0,7) AND (2,1) FROM THW GRAPH AND USE THEM TO GET THE GRADIENT.

[tex]m \frac{y2 - y1}{x2 - x1} \\ = \frac{1 - 7}{2 - 0} \\ m = \frac{ - 6}{2} \\ m = - 3[/tex]

I WILL USE THE POINT (0,7) TO FIND THE VALUE OF C IN THE GENERAL EQUATION.

[tex]7 = - 3(0) + c \\ c = 7[/tex]

THE EQUATION IS

[tex]y = - 3x + 7[/tex]

ATTACHED IS THE SOLUTION

The function to show how quickly the weeds grow each day is "f(x) = 4(1.02)7x; spreads at a rate of approximately 2% daily. Option B

f(x) = 4(1.15)x = 4(1+ 0.15)x ................... (1)

Given that there are seven days in a week, the daily growth rate of the weeds may be estimated using equation (1) by dividing 0.15 (which stands for the 15% weekly growth rate) in the following manner:

f(x) = 4(1.15)x = 4(1+ 0.15/7)x

f(x) = 4(1 + 0.02)x

f(x) = 4(1.02)x

Since 0.02 is the same as 2%, this implies that the rate at which the weeds grow each day is 2%.

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Because the angles on the first quadrant of the bottom horizontal line are equal, we conclude that the two parallel lines are FM and GB,

We know that two lines are parallel if when intersected by the same line, the two give the same angles.

In the image, we can see only one pair of equal angles, which are the two ones represented by a red quarter circle.

Both of these angles are on line MB, this means that the two parallel lines are the ones that intersect MB (in this case are the two vertical lines).

Then we can conclude that the two parallel lines are FM and GB.

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Diameter = 13.93771776 cm

To solve this question, find the 4 first terms of the sequence.

The first term is a₁

a₁ is given and a₁ = 7

The second term is a₂

Given:

Then, let's find a₂ using the value of a₁

The third term is a₃

let's find a₃ using the value of a₂

The fourth term is a₄

let's find a₄ using the value of a₃

Answer:

The four first terms are:

a₁ = 7

a₃ = 12

a₃ = 17

a₄ = 22