Factor completely: 21x3 + 35x2 + 9x + 15 ...?

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

Answer:

The required equation is : [tex]2x+4[/tex]

Step-by-step explanation:

Tommy's monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana that Tommy eats.

Let Tommy eats x bananas, then the monkey eats 2x bananas.

Then, the required equation will be :

[tex]2x+4[/tex]

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:

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.

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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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

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.

The confidence interval is calculated based on the given values and can help determine if deaths are temporarily postponed during holidays.

To construct a confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and after the holiday, we can use the formula:

p ± z √(p(1- p/ n)

where p is the sample proportion, z is the z-score, and n is the sample size.

In this case, the sample proportion is p = 4968/10000 = 0.4968.

The z-score corresponding to a 90% confidence interval is approximately 1.645. The sample size is n = 10000.

Substituting these values into the formula, we get:

0.4968 ± 1.645 √((0.4968 * 0.5032) / 10000)

Calculating this expression gives us the confidence interval estimate.

Based on the result, we can assess whether there is an indication that people can temporarily postpone their death to survive the holiday. If the lower limit of the confidence interval is significantly lower than the proportion of deaths in the week after the holiday, it suggests that there is a decrease in deaths in the week before the holiday. However, if the lower limit is close to or higher than the proportion of deaths in the week after the holiday, it indicates that there is no evidence of a significant decrease in deaths before the holiday.

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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.

Susan invested $6,000 in municipal bonds and $13,000 in certificates of deposit. For the bond investment scenario, given the increase in market interest rate to 9%, you would pay less than $10,000 for the bond. The calculation shows you would be willing to pay approximately $9,724.77.

To solve Susan's investment problem, we can set up a system of equations using the information provided in the problem. Let x be the amount invested in municipal bonds and y be the amount invested in certificates of deposit (CDs). We can then set up the following equations:

x + y = $19,000 (Total investment amount)

0.07x + 0.09y = $1,590 (Total annual income from investments)

Now, we solve the system of equations. Multiplying the second equation by 100 to get rid of decimals:

7x + 9y = 159,000

Next, we can multiply the first equation by 7 to help us eliminate one variable:

7x + 7y = 133,000

Subtracting the modified first equation from the second equation:

9y - 7y = 159,000 - 133,000

2y = 26,000

y = $13,000

Using y = $13,000 in the first equation:

x + 13,000 = 19,000

x = $6,000

Therefore, Susan invested $6,000 in municipal bonds and $13,000 in certificates of deposit.

Regarding the bond investment scenario:

a. Since the market interest rate has risen to 9%, higher than the bond's 6% interest rate, you would expect to pay less than $10,000 for the bond.

b. To calculate the price you would be willing to pay, you need to find the present value of the expected payment from the bond one year from now:

The expected payment is $10,000 (the face value) plus $600 (the final interest payment), which totals $10,600.

Using the market interest rate of 9%, the present value (PV) formula is:

PV = Payment / (1 + market interest rate)

PV = $10,600 / (1 + 0.09)

PV = $10,600 / 1.09

PV ≈ $9,724.77

Therefore, you would be willing to pay approximately $9,724.77 for the bond.

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]

How many friends?

40

____

X

40/ x

Answer:

[tex]5/14[/tex]

Step-by-step explanation:

Let

x-----> the shaded area

we know that

[tex]x+\frac{1}{7}=\frac{1}{2}[/tex]

solve for x

Multiply by [tex]14[/tex] both sides

[tex]14x+2=7[/tex]

[tex]14x=7-2[/tex]

[tex]14x=5[/tex]

Divide by [tex]14[/tex] both sides

[tex]x=5/14[/tex] ----> fraction irreducible

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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From the diagram below , x = t ( r - h ) / h

Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

There are several trigonometric identities that need to be recalled, i.e.

[tex]cosec ~ A = \frac{1}{sin ~ A}[/tex]

[tex]sec ~ A = \frac{1}{cos ~ A}[/tex]

[tex]cot ~ A = \frac{1}{tan ~ A}[/tex]

[tex]tan ~ A = \frac{sin ~ A}{cos ~ A}[/tex]

Let us now tackle the problem!

Look at ΔADE in the attachment.

We will use the following formula to find relationship between variable t and h:

tan ∠A = opposite / adjacent

[tex]\tan \angle A = \frac{DE}{AD}[/tex]

[tex]\large {\boxed{ \tan \angle A = \frac{h}{t} } }[/tex] → Equation 1

Look at ΔABC in the attachment.

We will use the following formula to find relationship between variable r , t and x:

tan ∠A = opposite / adjacent

[tex]\tan \angle A = \frac{BC}{AB}[/tex]

[tex]\large {\boxed{ \tan \angle A = \frac{r}{x + t} } }[/tex] → Equation 2

Next we can substitute equation 1 to equation 2 :

[tex]\tan \angle A = \frac{r}{x+t}[/tex]

[tex]\frac{h}{t} = \frac{r}{x+t}[/tex]

[tex](x + t)h = r ~ t[/tex]

[tex](x + t) = \frac{(r ~ t)}{h}[/tex]

[tex]x = \frac{(r ~ t)}{h} - t[/tex]

[tex]x = \frac{(r ~ t)}{h} - \frac{(h ~ t)}{h}[/tex]

[tex]\large {\boxed {x = \frac{t(r - h)}{h}} }[/tex]

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle

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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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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