The least common multiple of 20, 24, and 45 is _____.
a) 30
b) 180
c) 360
d) 21,600

The standard form of a quadratic equation is :

ax² + bx + c = 0

And the quadratic formula is:

[tex] x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} [/tex].

So, first step is to compare the given equation with the above equation to get the value of a, b and c.

So, a = 9, b = 6 and c = - 17.

Next step is to plug in these values in the above formula. Therefore,

[tex] x=\frac{-6\pm\sqrt{6^2-4*(9)*(-17)}}{2*9} [/tex]

[tex] =\frac{-6\pm\sqrt{36+612}}{18} [/tex]

[tex] =\frac{-6\pm\sqrt{648}}{18} [/tex]

[tex] =\frac{-6\pm\sqrt{324*2}}{18} [/tex]

[tex] =\frac{-6\pm\sqrt{324}*\sqrt{2}}{18} [/tex]

[tex] =\frac{-6\pm18*\sqrt{2}}{18} [/tex]

[tex] =-\frac{6}{18} \pm\frac{18\sqrt{2}}{18} [/tex]

[tex] =-\frac{1}{3} \pm\sqrt{2} [/tex].

So, x = [tex] -\frac{1}{3} \pm\sqrt{2} [/tex]

Answer: x= -1 + 3 sq root 2 /3

Step-by-step explanation:

the plus has a Line under it

Answer:

You can find a width of 9 feet.

Step-by-step explanation:

The width of the rectangular shaped garden should be 9 feet

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the perimeter of the rectangle be P = 48 feet

We can use the equation given to solve for the width w of the garden:

2l + 2w = 48

Substituting l = 15, we get:

2(15) + 2w = 48

30 + 2w = 48

Subtracting 30 from both sides, we get:

2w = 18

Dividing both sides by 2, we get:

w = 9 feet

Hence , the width of the garden should be 9 feet

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The growth rate of the hedge maple tree is 0.75 feet per year, and the tree's original height when it was planted was 6 feet.

We are tasked with finding the growth rate of a hedge maple tree and its original height when it was planted based on the given data. The tree's height was recorded at two different times: Four years after it was planted, its height was 9 feet, and eight years after planting, its height reached 12 feet.

To calculate the growth rate per year, we take the difference in height over the difference in time:
Growth rate = (Height at 8 years - Height at 4 years) / (Time at 8 years - Time at 4 years)
Thus, Growth rate = (12 feet - 9 feet) / (8 years - 4 years) = 3 feet / 4 years = 0.75 feet per year.

To determine the original height when the tree was planted, we can subtract the total growth over the four years from the height at four years after planting:
Original height = Height at 4 years - (Growth rate * 4 years)
Original height = 9 feet - (0.75 feet/year * 4 years) = 6 feet.

Answer:

False

Step-by-step explanation:

A five number summary consists of these five statistics: the minimum value, the first quartile, the median, the third quartile, and the maximum value of a set of numbers

A standard deviation is  a measure that is used to quantify the amount of variation or dispersion of a set of data values.

Std deviation is the square root of variance

Variance is the average of squares of deviations of each entry from the mean.

Hence from five point summary, we cannot calculated standard deviation of the distribution

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

 3.1    3x3+9x2+x+3  is not a perfect cube 

 3.2      Factoring:  3x3+9x2+x+3 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  x+3 
Group 2:  3x3+9x2 

Pull out from each group separately :

Group 1:   (x+3) • (1)
Group 2:   (x+3) • (3x2)
               -------------------
Add up the two groups :
               (x+3)  •  (3x2+1) 
Which is the desired factorization

 3.3    Find roots (zeroes) of :       F(x) = 3x2+1
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which  F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q  then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  3  and the Trailing Constant is  1. 

 The factor(s) are: 

of the Leading Coefficient :  1,3 
 of the Trailing Constant :  1 

 Let us test ....

Polynomial Roots Calculator found no rational roots

Processing ends successfully

Answer:

D

Step-by-step explanation:

its reflected off the L-axis

Answer: The sample space showing the possible orders of the other three runners is

[tex]S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}[/tex]

Step-by-step explanation:

Since we have given that

Number of runners = 4

Four runners are as follows:

Fran, Gloria, Haley, and Imani.

Since Haley is the first runner in the relay,

So, Sample space showing the possible order of the other three runners.

[tex]S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}[/tex]

Hence, the sample space showing the possible orders of the other three runners is

[tex]S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}[/tex]

Answer:

the answer is D, TRUST ME

Step-by-step explanation:

The coefficient of the term (5/3) x y is 5/3.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

(5/3) x y

The coefficient of any expression is the numerical term,

Numerical term in the expression is 5/3.

So, the coefficient of the term (5/3) x y is 5/3.

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The value of x is 12 and Shakeel got 18 points.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Adam scored x points. Imran scored 3 points fewer than Adam. Shakeel scored twice as many points as Imran. together they scored 39 points

Establishing the equation, we get

Adam scored x points.

Imran scored x-3 points.

Shakeel scored 2(x-3) points.

Together they scored 39 points:

x + (x-3) + 2(x-3) = 39

x + x -3 + 2x - 6 = 39

4x = 48

x = 12

∵ Shakeel scored = 2(x-3) points.

Putting x = 12, to get the marks scored by him,

Shakeel's score = 2(12-3) = 18

Hence, The value of x is 12 and Shakeel got 18 points.

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Answer:

[tex]cos\Theta =\frac{4}{5}[/tex]

[tex]tan\Theta =\frac{3}{4}[/tex]

Step-by-step explanation:

Given : sin θ = 3/5

To Find : value of cos θ and tan θ

Solution :

use the identity:

[tex]sin^{2}\Theta +cos^{2}\Theta =1[/tex]

putting value of sin θ

⇒ [tex](\frac{3}{5})^{2} + cos^{2}\Theta =1[/tex]

⇒[tex]\frac{9}{25} +cos^{2}\Theta =1[/tex]

⇒[tex]cos^{2}\Theta = 1-\frac{9}{25}[/tex]

⇒[tex]cos^{2}\Theta = \frac{16}{25}[/tex]

⇒[tex]cos\Theta = \sqrt{\frac{16}{25}}[/tex]

⇒[tex]cos\Theta =\frac{4}{5}[/tex]

Thus , [tex]cos\Theta =\frac{4}{5}[/tex]

Now to find value of tan θ

Since we know that

⇒ [tex]tan\Theta =\frac{sin\Theta }{cos\Theta }[/tex]   (identity)

⇒[tex]tan\Theta =\frac{\frac{3}{5} }{\frac{4}{5} }[/tex]

⇒[tex]tan\Theta =\frac{3}{5}\div \frac{4}{5}[/tex]

⇒[tex]tan\Theta =\frac{3}{5}\times  \frac{5}{4}[/tex]

⇒[tex]tan\Theta =\frac{3}{4}[/tex]

Thus , the value of

[tex]tan\Theta =\frac{3}{4}[/tex]

[tex]cos\Theta =\frac{4}{5}[/tex]

Final answer:

This detailed answer provides the values of cos θ and tan θ for an angle θ in the second quadrant given sin θ = 3/5. It explains the process using the Pythagorean identity and the characteristics of the second quadrant.

Explanation:

cos θ = -4/5

tan θ = -3/4

Given sin θ = 3/5 and the angle θ lies in the second quadrant, we can determine cos θ using the Pythagorean identity. Since sin θ = 3/5 is positive in the second quadrant, the x-coordinate in the triangle would be negative. Therefore, cos θ = -4/5. Similarly, tan θ can be calculated as tan θ = sin θ / cos θ = (3/5) / (-4/5) = -3/4.

Answer:

yoo hoo

Step-by-step explanation: This was in 2016 but its 1/5

Answer:

The coefficient of the term 13a is, 13

Step-by-step explanation:

Coefficient term are the numbers that multiply the variables or letters

In the given expression: [tex]13a+6b[/tex]

13a means 13 times a , and a is the variable,

so 13 is the coefficient .

6b means 6 times b , and b is the variable ,

so 6 is the coefficient .

therefore, the coefficient of the term 13a in the given expression is, 13.

tan(θ) = -1/6.

Given that sec(θ) = √37/6 and sin(θ) < 0, we can find tan(θ) using the trigonometric identity:

sec²(θ) - tan²(θ) = 1

First, we need to find the value of tan(θ) using the given information:

Since sec(θ) = √37/6, we know that sec(θ) = 1/cos(θ), so cos(θ) = 6/√37.

Since sin²(θ) + cos²(θ) = 1, we can find sin(θ):

sin²(θ) + (6/√37)² = 1

sin²(θ) + 36/37 = 1

sin²(θ) = 1 - 36/37

sin²(θ) = (37-36)/37

sin²(θ) = 1/37

Given that sin(θ) < 0, sin(θ) is negative. Therefore, sin(θ) = -1/√37.

Now that we have sin(θ) and cos(θ), we can find tan(θ):

tan(θ) = sin(θ)/cos(θ)

tan(θ) = (-1/√37) / (6/√37)

tan(θ) = -1/6

Therefore, tan(θ) = -1/6.

Answer:

[tex]y=2x^2-10x-12[/tex]

Step-by-step explanation:

[tex]y=2(x+1)(x-6)[/tex]

write the given function in standard form

Standard form is [tex]y=ax^2+bx+c[/tex]

[tex]y=2(x+1)(x-6)[/tex] multiply the parenthesis using FOIL method

[tex]y=2(x^2-6x+1x-6)[/tex]

multiply 2 inside the parenthesis

[tex]y=2(x^2-6x+1x-6)[/tex]

[tex]y=2x^2-12x+2x-12[/tex]

Combiene like terms

[tex]y=2x^2-10x-12[/tex]

1. Infinite many solution.

2. No solution

3. One solution

4. No solution

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Depending upon the situation we have three case

[tex]a_1/ a_2 = b_1/ b_2 = c_1 / c_2[/tex] then line is Coincident and have infinite many solution.

and, [tex]a_1/ a_2 \neq b_1/ b_2[/tex] then line is Intersecting and have one solution.

and, [tex]a_1/a_2 = b_1/ b_2 \neq c_1/ c_2[/tex] then line is Parallel and have No solution.

1. 3x = -12y + 15 and x+4y=5

3x + 12y - 15= 0 and x+ 4y- 5 = 0

So, [tex]a_1/ a_2 = b_1/ b_2 = c_1 / c_2[/tex] then line is Coincident and have infinite many solution.

2. 4x - y +3 = 0 and -8x + 2y -3 = 0

So,  [tex]a_1/a_2 = b_1/ b_2 \neq c_1/ c_2[/tex] then line is Parallel and have No solution.

3. x+ 4y - 12= 0 and 5x - 20y -60 = 0

So,  [tex]a_1/ a_2 \neq b_1/ b_2[/tex] then line is Intersecting and have one solution.

4. -5x + y +6 = 0 and -15x + 3y +12 = 0

So,  [tex]a_1/a_2 = b_1/ b_2 \neq c_1/ c_2[/tex] then line is Parallel and have No solution.

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The set of possible rational roots for the polynomial is {±1, ±2, ±4, ±5, ±10, ±20}.

Thus, option (B) is correct.

Given:

[tex]x^3+5x^2-8x-20=0[/tex]

Using Rational Root Theorem

if a rational number p/q is a root of the polynomial, then p is a factor of the constant term, and q is a factor of the leading coefficient.

Here, p= -20 and q= 1.

So, the factors of -20 are:

-20, -10, -5, -4, -2, -1, 1, 2, 4, 5, 10, 20.

The factors of 1 (leading coefficient) are:

-1, 1.

Therefore, the possible rational roots are the combinations of these factors, where the numerator is a factor of -20, and the denominator is a factor of 1.

Combining the factors, the set of possible rational roots:

{±1, ±2, ±4, ±5, ±10, ±20}

Thus, option (B) is correct.

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