Please helppppppppppp

The rational zeros for f(x) = 3x^4 - 4x^3 + x^2 + 6x - 2 are x = -1 and x = 1/3 whereas the linear factors of f(x) are (x + 1) and (3x - 1).

We will use the synthetic division method to determine the rational zeros and linear factors of given polynomials.

Polynomials are divided via synthetic division.

The procedure entails of synthetic division:

Step 1: Create a synthetic divide.

Step 2: Bring the leading coefficient down to the bottom row.

Step 3: Divide this by the value stated in the bottom row.

Step 4: Finally, add the column you defined in step 3.

This can proceed as:

Given: f(x) = 3x⁴- 4x³ + x² + 6x - 2

3x⁴ - 4x³ + x² + 6x - 2 = 0

We will put x = -1 in f(x). In this case, replace x with -1. This will be:

f(-1) = 3 * 1⁴ - 4 * 1³ + 1² + 6 * 1 - 2 = 0

Since f(-1) = 0, so (x + 1) is a factor of f(x).

Using synthetic division:

-1)....3....-4....1....6....-2

.........3.....-7...8....-2..|..0

Remainder = 0

Quotient = 3x³ - 7x² + 8x - 2

For 3x³ - 7x² + 8x - 2,  f(1/3) = 0, so (x - 1/3) is a factor.

1/3)....3....-7....8....-2

..........3.....-6...6...|..0

Remainder = 0

Quotient = 3x² - 6x + 6 = 3(x² - 2x + 2)

Because x² - 2x + 2 has no more rational zeros or linear components. The rational zeros are hence x = -1 and x = 1/3.

Thus, the rational zeros for f(x) = 3x^4 - 4x^3 + x^2 + 6x - 2 are x = -1 and x = 1/3 whereas the linear factors of f(x) are (x + 1) and (3x - 1).

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Max gain 10.3 pounds of weight between the time he was a puppy and his 1-year check-up.

Two or more expressions with an Equal sign is called as Equation.

Given,

When Max was a puppy, he weighted [tex]5\frac{1}{2}[/tex] pounds

At his 1-year check-up with the vet, Max weighted 15.8 pounds

We need to find the weight did Max gain between the time he was a puppy and his 1-year check-up.

To find this we need to find the difference when Max was a puppy and after one year check up.

Difference is nothing but subtracting one value from another value.

Let us convert mixed fraction  [tex]5\frac{1}{2}[/tex] pounds to improper.

[tex]5\frac{1}{2}[/tex] =11/2=5.5

Now subtract 15.8-5.5

10.3 pounds.

Hence, max gain 10.3 pounds of weight between the time he was a puppy and his 1-year check-up.

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Answer:

50 miles per hour

Step-by-step explanation:

80 km         1 mi        

---------- x ------------ = 50 mi/hr

  1 hr         1.6 km

The equation of a line perpendicular to -5x + y = 9 that passes through the point (0, -9) is [tex]y = -\frac{1}{5}x -9[/tex]

The equation of the line in slope intercept form can be represented as follows:

y = mx + b

where

Perpendicular lines follows the following rules as follows:

m₁ m₂ = -1

Let's find the slope of -5x + y = 9 .

y = 5x + 9

Hence,

slope = 5

Let's find the slope of the equation of the line that passes through (0, -9) and perpendicular to  -5x + y = 9 .

5m₂ = -1

m₂ = -1 / 5

m₂ = - 1 / 5

Therefore, let's find the y-intercept of the line using (0, -9)

-9 = - 1 / 5(0) + b

b = -9

Therefore, the equation of the line is y = - 1 / 5 x - 9

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78 meals are eaten in a restaurant, 58 meals are eaten in a car, 33 meals are eaten at home and the question is solved by using linear equations.

What is the linear equation?

A linear equation is an algebraic equation of the form y =mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given that the total number of meals is 169.

Assume that,

a = number of meals eaten in a restaurant

b = number of meals eaten in a car

c = number of meals eaten at home

a + b + c = 169 .....(i)

Since the total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13.

Thus b + c = a + 13 .....(ii)

Again twenty more restaurant-purchased meals will be eaten in a restaurant than at home.

a = 20 + c .....(iii)

Subtract equation (ii) from (i)

a + b + c - b - c = 169 - a - 13

2a = 156

Divide both sides by 2

a = 78

Substitute a = 78 in equation (iii)

78 = 20 +c

c = 58

Putting c =58  and a =78  in equation (ii)

b + 58 = 78 + 13

b = 33

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Question:

The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 169. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13. Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of​ restaurant-purchased meals eaten in a​ restaurant, the number eaten in a​ car, and the number eaten at home.

Part A Write an inequality to represent the possible lengths of time

the tent can be rented

[tex]6.11\leq h\leq 11.66[/tex]

Part B. Using your inequality in Part A, what is one possible length of

time the tent could be rented

[tex]6hr 6min\leq h\leq 11hr39min[/tex]

The definition of a linear inequality

The inequality symbol is used to compare two mathematical expressions in what are referred to as linear inequalities. The expression could be both numerical and algebraic, or it could just be one.

What does a linear inequality in mathematics look like?

What Is an Example of Linear Inequality? An example is the linear inequality x - 5 > 3x - 10. The LHS is obviously greater than the RHS because the greater than symbol is being utilized in this inequality. After being resolved, the inequality appears as follows: 2x 5 x (5/2).

Given That

45h+225 is total cost in dollars for renting tent and parents are willing to spend between $500 and $750 for the tent.

Part A

[tex]500\leq 45h+225\leq 750\\500-225\leq 45h+225-225\leq 750-225\\275\leq 45h\leq 525\\\frac{275}{45} \leq h\leq \frac{525}{45} \\6.11\leq h\leq 11.66[/tex]

Part B

[tex]6.11hr\leq h\leq 11.66hr[/tex]

6.11 hr = 366 minute approx.

11.66 hr = 699 minute approx.

[tex]6hr 6min\leq h\leq 11hr39min[/tex]

Hence this is the answer

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[tex]{ \pink{ \boxed{ \purple{ \sf{f(3) = 98}}}}}[/tex]

Step-by-step explanation:

[tex]{ \blue{ \tt{f(x) = 2 {x}^{4} - 8 {x}^{2} + 5x - 7}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 2( {3})^{4} - 8( {3})^{2} + 5(3) - 7}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 2(81) - 8(9) + 15 - 7}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 162 - 72 + 8}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 162 - 64}}}[/tex]

[tex]{ \red{ \boxed{ \green{ \sf{f(3) = 98}}}}}[/tex]

Answer:

Slope = 0.75

Step-by-step explanation:

Slope Formula: y2-y1/x2-x1

4-1/5-1=3/4=0.75

The function is positive and increasing from 0 to 2.5, at negative and decreasing  from 0 to -2.5,  respectively.

How to find returns to scale?

Returns to scale involves an increase in an output more than when all the inputs increase proportionately.

Using the graph, there is a line segment from the origin to a point. at the middle of the third block making 2.5.

This shows an increase which is positive and on the other hand, there is a line segment from the origin towards left hand side on the number line showing a decrease and a negative from 0 to -2.5.

In conclusion, the line pointing upwards towards right hand side shows both positive and increase while the line pointing leftward shows decrease and negative.

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Answer: There are 52 cards in a standard deck and half of them, 26 in all, are red.

Suppose that you are drawing 4 cards without replacement from a thoroughly shuffled deck. You have 26 cards choose 4 over 52 choose 4.

∴  P(pulling 4 cards from deck) =  (264)(524)

Using mathematical operations of addition and subtraction, Rodrigo needs to buy additional 2⁷/₂₄ pounds of vegetables.

The basic mathematical operations are addition, subtraction, division, and multiplication.

These mathematical operations can be used to determine the results of mathematical expressions.

The total pounds of vegetables required for a stew = 3 pounds

Available pounds of vegetables:

Onions = 3/8 pounds

Tomatoes = 1/3 pounds

The total available pounds = 17/24 pounds

Additional pounds required = 3 - 17/24 pounds

= 2⁷/₂₄ pounds

Thus, based on addition and subtraction, Rodrigo needs additional 2⁷/₂₄ pounds of vegetables.

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The factor of the difference of two squares (x + 2)² - (y - 2)² is (x + y)(x - y + 4).

If for any two squares say a² and b², then their difference a² - b² = (a + b)(a - b).

Given the two squares (x + 2)² and (y - 2)²

then their difference will yeild the factors derived as follows;

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

open brackets

(x + 2)² - (y - 2)² = (x + 2 + y - 2)(x + 2 - y + 2)

collect like terms

(x + 2)² - (y - 2)² = (x + y + 2 - 2)(x - y + 2+ 2)

so

(x + 2)² - (y - 2)² = (x + y)(x - y + 4)

Thus, by application of the rule of difference of two squares, we have the factors of (x + 2)² - (y - 2)² to be (x + y 2 - 2) and (x - y + 2+ 2).

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Step-by-step explanation:

your teacher gave you the solution to the real problem of this question : how many cups are in 1 gallon. 16 cups.

and if you remember that a year has 365 days, then the rest is rant simple and straight forward :

8 cups per day

so

365 × 8 = 2920 cups per year.

2920 cups = 2920/16 = 182.5 gallons

therefore, she drinks 182.5 gallons of water per year.

Step-by-step explanation:

there are 18 dogs to choose 1 dog.

therefore, these are 18 options.

for each of these 18 options there are 24 cats to choose from.

so, altogether, there are

18×24 = 432

dog-cat options.

There are are 432 ways to choose dog-cat options are possible for the producer.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

Total Number of Dogs= 18

Total Number of cats= 24

so, the number easy to select

= 18 x 24

= 432

Hence, there are 432 ways to choose dog-cat options are possible for the producer.

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Answer: 10 squares

Step-by-step explanation:

The answer for the area is 10 squares but I’m not sure that’s what they’re asking for.

Answer:

Step-by-step explanation:

-28,100 if you subtract 29,700.00 - 1,600.00  =  -28,100

By using property of triangle and trapezium, it is obtained that

a) value of x is 35°

b) Third option is correct

What is a triangle and trapezium?

Triangle is a three sided two dimensional figure.

Trapezium is a quadrilateral whose one pair of opposite side is parallel and another pair of opposite side is non parallel

Here property of triangle is used

[tex]m \angle D = (2x)^{\circ}, \ m\angle E = (2x - 4)^{\circ}, m \angle F = (x +9)^{\circ}[/tex]

[tex]m \angle D + m\angle E + m \angle F = 180\\2x + 2x - 4 + x + 9 = 180\\5x + 5 = 180\\5x = 180 - 5\\5x = 175\\x = \frac{175}{5}\\x = 35^{\circ}[/tex]

In the second question, if the trapezoid is rotated 90° clockwise, then (x, y ) will change to (y, -x) and new coordinate of A is (1, 5)

Third option is correct

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Answer: 1) C- the survey participants should be randomly selected

2) C- how interested would you be in purchasing a blue car?
3) C- the stadiums front gate

Step-by-step explanation: I took the quick check.

Answer:

1. c

2. d

3. c

Step-by-step explanation:

The two numbers that are compatible are 0.25 and 8. The property which helps to calculate it is commutative property.

What is the commutative property?

This law merely asserts that while adding and multiplying integers, you can rearrange the numbers in a problem without changing the solution.

Given numerical expression is (0.25 x 12.3) x 8.

First remove the parenthesis from the numerical expression:

(0.25 x 12.3) x 8 = 0.25 x 12.3 x 8

Now apply commutative property:

(0.25 x 12.3) x 8 = (0.25 x 8) x 12.3

(0.25 x 12.3) x 8 = 2.00 x 12.3

(0.25 x 12.3) x 8 = 24.6

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Complete steps to find domain of function is describe below.

Domain is defined as the all input values which satisfy the function or can say all inputs any function have.

suppose we have a function f(x) = 6x^2 + 5x - 4

For domain solve it for x

⇒ 6x^2 + 5x - 4

⇒ 6x^2+ 8x - 3x - 4

⇒ 2x(3x + 4)· -1(3x + 4)

⇒ (3x + 4) (2x - 1)

values of x are positive for quadratic  equation,

⇒ (3x + 4) (2x - 1)≥0

⇒ x ≥ 1/2  or  x ≥ -4/3

These  are the domain of function.

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Answer:

See below

Step-by-step explanation:

Eight minus unknown quantity 'x' equals two.

At the end of 6 months she will have $410 when calculated using simple interest.

What is simple interest?

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

Main Body:

Principle =$400

Rate = 5%

Time = 6 months = 1/2 years

Simple interest = P*R*T/100

S.I. = 400*5*(1/2)/100

S.I. = 10

Hence total amount is 400+ 10= $410.

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a) The coefficients are the costs of the respective shirts.

b) The graph can be seen on the image at the end, the intercepts are (0, 25) and (30, 0)

c) 3 solutions are:

(0, 25), (30, 0), (25, 4)

Here we know that:

And we have the linear equation:

10x + 12y = 300

The first coefficient is the one in the term "10x"

The coefficient 10 will mean the cost, in dollars, of each short-sleeved shirt.

The second coefficient is on the term "12y"

And 12 means the cost in dollars of each long-sleeved shirt.

b) The graph of the linear equation can be seen on the image at the end.

The y-intercept (when x = 0) is the number of long-sleeved shirts you can buy if you don't buy any short-sleeved one.

The x-intercept is the number of short-sleeved shirts you can buy if you don't buy any long-sleeved one.

c) 3 possible solutions can be seen on the graph, some examples are:

(0, 25), (30, 0), (25, 4)

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Answer:

7

Step-by-step explanation:

13x - 7 + 30 = 30 + 84

13x - 7 + 30 - 30 = 30 - 30 + 84

13x - 7 = 84

13x = 84 + 7

13x = 91

x = 91 / 13

x = 7

The equation of the line perpendicular to the given line is, y = 3x + 1.

What is slope of the line?

The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.

Consider, the given equation of line

[tex]y = -\frac{1}{3}x+4[/tex]

We have to find the equation of line passes through the point (-2, -5) and perpendicular to the given line.

Here, the point is (-2, 5).

First to find the slope of the line.

Since, the slope of the line, perpendicular to the given line is negative reciprocal of the slope of given line.

Here, the slope of given line is, -1/3.

So, the slope of perpendicular line is [tex]-(\frac{1}{(-\frac{1}{3}) }) = 3[/tex]

Therefore, the slope of the line is 3.

Now to find the equation of the line.

Consider, the point - slope form of the line

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex](x_1, y_1) = (-2, -5) , m = 3[/tex]

⇒

[tex]y-(-5)=3(x-(-2))\\y+5=3(x+2)\\y+5=3x+6\\y=3x+6-5\\y=3x+1[/tex]

Hence, the equation of line in slope - intercept form, is y = 3x + 1.

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The expected value of the proposition is -$1007.41

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]

In which [tex]C_{x},x[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{x},x= \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Suppose a basketball player has made 215 out of 322 free throws.

This means that p = 215/322 = 0.6677

2 free throws:

This means that

Probability of making two free throws.

This is P(X = 2).

P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]

P(X = 2) = [tex]C_{2},2.(0.6677)^2.(0.3323)^0[/tex] = 0.29629

Expected value:

If he makes both free throws, you earn $24. So 0.29629 probability of you earning $24.

Otherwise, you have to pay $32. 1 - 0.29629 = 31.70371 probability of you losing $32.

E = 0.29629*24 - 31.70371*32 = -1007.41

Hence, The expected value of the proposition is -$1007.41

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