In Exercises 29–34, graph the function and identify intervals on which
the function is increasing, decreasing, or constant.

30. ƒ1x2 = 0 x + 1 0 + 0 x - 1 0 - 3

32. h1x2 = 0.51x + 222 - 1

34. ƒ1x2 = x3 - x2 - 2x


In Exercises 41– 46, use a grapher to find all local maxima and minima
and the values of x where they occur. Give values rounded to two decimal
places.


42. g1x2 = x3 - 4x + 1

44. ƒ1x2 = 1x + 321x - 122


In Exercises 47–54, state whether the function is odd, even, or neither.

48. g1x2 = x3

50. g1x2 = 3/
1 + x2

52. ƒ1x2 = x3 + 0.04x^2 + 3

Answer:

[tex]6/k[/tex]

Step-by-step explanation:

It's in the attachment!

I am pretty sure that the answer is x=6/k

Answer:

2.61 pounds of apples are left.

Step-by-step explanation:

Amount of green apples is 3.42 pounds and amount of red apples is 2.19 pounds.

So, the total amount of the two types apples will be:  [tex](3.42+2.19)pounds = 5.61[/tex] pounds.

Simone uses 3 pounds of apples to make a pie.

Thus, the amount of of apples left will be:  [tex](5.61-3)pounds= 2.61[/tex] pounds.

varies directly formula: [tex]\frac{r}{s} = k[/tex]

[tex]\frac{r}{2} = 13[/tex]

[tex](2)\frac{r}{2} = (2)13[/tex]

r = 26

Answer:

158 tickets would be sold.

Step-by-step explanation:

Since,

[tex]\text{Number of tickets}=\frac{\text{Total cost of tickets}}{\text{Cost of each ticket}}[/tex]

We have,

Total cost of tickets = $ 2212,

Cost each ticket = $ 14,

Hence,

[tex]\text{Number of tickets that are sold}=\frac{2212}{14}=158[/tex]

Let

x-----> the purchase price of the house

we know that

1) Marika paid [tex]80\%[/tex] of the purchase price of the house with a loan

2) Marika paid the remaining [tex]\$49,400[/tex] of the purchase price with her savings

3) [tex]\$49,400[/tex] represent the [tex]20\%[/tex] of the purchase price

so

[tex]0.20x=49,400[/tex]

Solve for x

Divide by [tex]0.20[/tex] both sides

[tex]0.20x/0.20=49,400/0.20[/tex]

[tex]x=247,000[/tex]

therefore

the answer is

the purchase price of the house is [tex]\$247,000[/tex]

Marika's house's total purchase price was $247,000, calculated by determining 1% of the purchase price from the known 20% and then multiplying it by 100.

To find the total purchase price of Marika's house, we can use the information that 80% of the purchase price was covered by a loan, while the remaining 20% (which is $49,400) was paid from Marika's savings. To find the full purchase price, we first find what 1% of the purchase price is by dividing the known 20% amount by 20.

1% of purchase price = $49,400 / 20

1% of purchase price = $2,470

To find the full 100% purchase price, we multiply the 1% value by 100.

Purchase price = 100 * (1% of purchase price)

Purchase price = 100 * $2,470

Purchase price = $247,000

Thus, the total purchase price of the house was $247,000.

To find the missing measures in a figure, utilize the properties or formulas associated with that specific shape. For example, use the Pythagorean theorem for right triangles.

To find the missing measures in each figure, you would typically use the properties of the specific geometrical shape presented.

For example, triangles have properties that are different from squares, rectangles, or circles. So, if you have a right triangle where you know the lengths of two sides, you can use the Pythagorean theorem to find the missing side.

This theorem states that a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the other two sides. For other shapes, you may use different formulas or identities based on their properties.

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Answer: 15 3/5 feet

Step-by-step explanation:

Answer:

Bonus of Brianna = 125 $

Explanation:

 Amount of Brianna's yearly bonus = 155$

 Amount taken away for each customer care complaint = 2.50$

 Number of complaints received against Brianna in the year = 12

 Total amount lost by Brianna due to complaint = 12*2.50 = 30$

 Amount of bonus received by Brianna after reduction of complaint loss = 155-30 = 125$

  Bonus of Brianna = 125 $

Answer: 125 dollars

Step-by-step explanation:

Final answer:

In a situation where a transversal crosses parallel lines, several congruent angles and vertical angles can form, and supplementary angles are also a possibility. Complementary angles are formed only under specific conditions. The formation of obtuse angles depends on the transversal's orientation relative to the parallel lines.

Explanation:

When a transversal crosses parallel lines, several outcomes are possible, and we can determine which statements could be true. Let's go through the options provided:

The average weight for a typical passenger car is roughly estimated to be around 1,400 kilograms. However, this can vary significantly depending on the type, size, and model of the vehicle. Exact weights should be confirmed from the vehicle's specifications.

The weight of an automobile can significantly vary depending on the specific model and brand. The average weight of contemporary passenger cars is estimated to be around 1,400 kg. This weight is taken from a general approximation as weight can change based on the vehicle's size, materials, and included accessories.

For example, a luxury sports car like a 2014 Lamborghini Aventador Roadster weighs considerably less due to the use of lightweight materials in its construction. Some small cars or compact cars may weigh less than the typical average, while trucks and larger vehicles will likely exceed this weight.

Lastly, remember that the weight of the vehicle can influence factors such as speed, fuel efficiency, and momentum. Always ensure to confirm the specific weight for any particular vehicle from its manufacturer's specifications or verified sources.

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x-intercept (48,0)

y intercept(0,6)

[tex]2-3(x+4)=8\qquad|\text{use distributive property}\\\\2+(-3)(x)+(-3)(4)=8\\\\2-3x-12=8\\\\-3x+(2-12)=8\\\\-3x-10=8\qquad|\text{add 10 to both sides}\\\\-3x=18\qquad|\text{divide both sides by (-3)}\\\\\boxed{x=-6}}\to\boxed{a.}[/tex]

All you have to do is simplify the equation, then isolate x to find its value:

2 - 3 ( x + 4 ) = 8

- 3 ( x + 4 ) + 2 = 8

- ( 3x + 12 ) = 2 = 8

-3x - 12 + 2 = 8

-3x - 10 = 8

-3x = 18

x = [tex]\frac{18}{-3}[/tex]

x = -6

The answer is A= -6

Hope that helps!

Answer:

The answer is 44%

Step-by-step explanation:

The solutions to the equation 4z² − z − 7 = 0 will be negative 1.2 and 1.45.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have

The quadratic equation is given below.

4z² − z − 7 = 0

Then we have

a = 4, b = -1, and c = -7

Then solutions to the equation will be

[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-(-1) \pm \sqrt{(-1)^2 - 4* 4 * (-7)}}{2 * 4}\\\\x = \dfrac{1 \pm \sqrt{1 + 112}}{8}\\\\x = \dfrac{1 \pm \sqrt{113}}{8}[/tex]

On further solving we have

x = (1 ± 10.63) / (8)

x = 1 - 10.63 / 8 , 1 + 10.63 / 8

x = - 1.2, 1.45

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Final answer:

To find the cost of four tickets for each route, multiply the price matrix [150 160 180] by the matrix [4], giving [600 640 720] as the cost matrix for four tickets to Chicago, Boston, and Dallas respectively.

Explanation:

To find the cost of four tickets for each of the three routes from Atlanta (Chicago, Boston, and Dallas), we need to multiply the given matrix representing the prices of each route by a matrix that contains the number of tickets for each route. The cost matrix for one ticket is [150 160 180]. To calculate the cost for four tickets, we can multiply this matrix by a column matrix that has the value 4 for each route since we want to buy four tickets for each destination.

The column matrix will thus be [4] since we only have one column (for the number of tickets) and three rows (one for each destination). The multiplication process is straightforward:

[150 160 180] x [4] = [600 640 720]

So, the matrix representing the cost of four tickets to each destination is: [600 640 720].

This is a pemdas problem. The basic rule of pemdas is:

Multiplication/division and addition/subtraction are in no particular order; they are solved from left to right.

Since you solve inside the parentheses first, you would first add 1 and 2 together and then rewrite the problem.

6 ÷ 2(3)

Now you have 6 divided by 2 multiplied by 3. Pemdas shows that division and multiplication are solved in no particular order, so that means that you will solve this expression from left to right.

Start by dividing 6 and 2, then rewrite the problem.

3(3) is what you are left with.

Multiply 3 and 3 together and you will be left with your final answer of:

Hello!

Answer: ⇒⇒⇒⇒ =9

Step-by-step explanation:

This question it should be pemdas.

Hint:

↓

P-parenthesis

E-exponents

M-multiply

D-divide

A-add

S-subtract

First you had to calculate with parenthesis.

[tex](1+2)=3[/tex]

[tex]=6\div \:2*3[/tex]

Then you multiply and divide from ("left to right").

[tex]6\div \:2=3[/tex]

[tex]3*3=9[/tex]

Hope this helps!

Thank you for posting your question at here on brainly.

Have a great day!

-Charlie

One way is to create a factor tree for each number.  Then see which factors they have in common.

Example:

   12                30

   ^                  ^

2    6             3  10

      ^                   ^

    2  3               2  5

The factors are the underlined numbers above:

12: 2 x 2 x 3

30: 2 x 3 x 5

The common factors are: 2, 3, and 6    why 6? because 2 x 3 = 6

The greatest common factor is: 6

To find the common factors and the greatest common factor (GCF) of numbers, list all factors of each number, find the common ones, and identify the largest as the GCF. The factor-label method can simplify locating the GCF.

To find the common factors and the greatest common factor (GCF) of two numbers, you start by listing all the factors of each number. These are whole numbers that can divide the numbers without a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, and the factors of 18 are 1, 2, 3, 6, 9, and 18.

Common factors are factors that the two numbers share. In our example, the common factors of 12 and 18 are 1, 2, 3, and 6.

The greatest common factor (GCF) is the largest of these common factors. This helps in multiplication and division of numbers, particularly when simplifying fractions. Here, the GCF of 12 and 18 is 6.

To find the GCF more quickly, you can use the factor-label method. Divide both numbers by a common factor and continue this process with the resulting numbers until you can't find any common factors other than 1. The GCF is the product of all the common factors you used to divide.

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x > 7                     x < 10

7 o---------------------o 10

This is not an empty set.  x contains all of the values between 7 and 10.

The correct answer is (2,−1)

If an ant has six legs, then:

So, if you saw between 35 and 50 legs, there are between six and eight ants.

The equation that models the value of the coin, t years after 2016, is [tex]Y = 75(1 + 0.04)^t.[/tex] It demonstrates an exponential growth where the coin's value increases at a rate of 4% each year since 2016.

The value of the coin changes at an annual rate of 4%, which suggests an exponential growth model. The general form of an exponential growth equation is  [tex]Y = P(1 + r)^t[/tex], where Y is the future value, P is the initial (or present) value, r is the rate of interest, and t is time in years. In this case, we know the present value (P) as of 2016 is $75, the rate of interest (r) is 4% or 0.04 per year, and the time (t) indicates the number of years since 2016.

Therefore, the equation that models the value of this coin, t years after 2016, should be  [tex]Y = 75(1 + 0.04)^t.[/tex] This equation can be used to estimate the future value of an 1858 flying eagle penny given the past rate of appreciation.

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The equation that models the value of the coin in dollars, t years after 2016, is A = 75(1 + 0.04)^t.

To model the value of the coin in dollars, t years after 2016, we can use the exponential growth formula:

A = P(1 + r)^t,

where A represents the final amount, P is the initial amount, r is the growth rate, and t is the number of years.

In this case, the initial amount is $75, the growth rate is 4%, and the number of years is t. So the equation would be: A = 75(1 + 0.04)^t.

Using this equation, you can calculate the value of the coin in dollars for any given year after 2016 by plugging in the number of years into the equation.

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ANSWER

[tex]B=63\degree[/tex]

EXPLANATION

We want to solve the trigonometric equation;

[tex]tan^2(B)=4[/tex], where [tex]0\degree \le B \le 90\degree[/tex].

Taking square root of both sides gives,

[tex]tan(B)=\pm \sqrt{4}[/tex]

[tex]tan(B)=\pm 2[/tex]

Since B is in the first quadrant, we proceed with;

[tex]tan(B)=2[/tex], because the tangent ratio is positive in the first quadrant.

[tex]\Rightarrow B =arctan(2)[/tex]

[tex]\Rightarrow B =63.43\degree[/tex].

Correct to the nearest degree,

[tex]B =63\degree[/tex]

Answer:

Emma has dog food worth of 6 weeks 6 days.

Step-by-step explanation:

Lets take number of weeks the dogs can eat dog food as [tex]x[/tex].

Then,

Number of bags dogs eat per week * number of weeks = number of dog food

will give the number of weeks the dogs can eat the dog food.

Now we substitute the given values to the equation,

[tex]8\frac{1}{4}*x=56\frac{37}{40}[/tex]

[tex]\frac{33}{4} *x=\frac{2277}{40}[/tex]

[tex]\frac{330}{40} *x=\frac{2277}{40}[/tex]

[tex]330*x=2277[/tex]

[tex]x=\frac{2277}{330}[/tex]

[tex]6.9[/tex] weeks

Which mean she has dog food worth of 6 weeks 6 days.

Hey there!!

Given equation :

4x² - 2

And x is given by 3

Now substitute the value of 3 in the equation :

... 4×(3)² - 2

... 4×3×3 -  2

... 12×3 - 2

... 36 - 2

Hence, the answer is 34.

Hope my answer helps!

The required expression is 34 when evaluating the given expression for x = 3.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The expression is given in the question following as:

4x² - 2

We have to evaluate the expression given 4x² - 2 when x = 3

As per the question, we have

⇒ 4x² - 2

We can substitute the value of x = 3 into the expression to get:

⇒ 4(3)² - 2

⇒ 4(9) - 2

⇒ 36 - 2

Apply the subtraction operation, and we get

⇒ 34

Therefore, the result of the expression when x = 3 is 34.

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the answer would be -4 because it's when the axis touches the y-axis. in that case it would be c. -4

hope this helps! ❤ from peachimin

The goal is to raise AT LEAST $180, so this automatically indicates that the amount of keychains sold with the price must be the same or more than $180.

k = number of keychains

each keychain is $2.25

2.25k ≥ 180

divide both sides by 2.25 to get the k alone

k ≥ 80

The answer is 2.25k ≥ 180, k ≥ 80

(Hope this isn't confusing)

Set up a proportion like 64/x = 80/100 and solve for x. x=80

Final answer:

Explaining how to write and solve the equation to find 80% of 64.

Explanation:

Write the equation: 64 = 0.80x, where x represents the unknown value.

Solve for x: Divide both sides by 0.80 to isolate x. x = 64 / 0.80 = 80, so 64 is 80% of 80.

Answer: 64 is 80% of 80.