Question 4 (3 points)
Use a graphing calculuator, like desmos, to graph the function, then use the graph to determine the number of turning points, global
maximums and minimums, and local maximums and minimums that are not global.
h(x) = x²(x − 3)(x + 2) (x - 2)
-
Turning Points: 4
Local Maximum(2):
Local Minimum(s):
Blank 1: 4
Blank 2:
Blank 3:

Answer:

[tex]y=-\frac{1}{5}x[/tex]

Step-by-step explanation:

Start by finding the slope of the line. Slope is defined as the RISE over the RUN. Find two points on the line with clear coordinate pairs. The line clearly passes through the origin, and the point (5,-1). To get from one point to the other, I have to go DOWN 1 unit. This is the RISE. The rise is -1 because I am going down. I also have to go RIGHT 5 units. This is the RUN. Slope is rise divided by run. Since a positive number divided by a negative number is a negative number, I move the negative sign outside the fraction: [tex]-\frac{1}{5}[/tex]. This is the slope!

The line crosses the y-axis at 0, so the y-intercept is 0.

Point-slope form is a way to write linear equations. It looks like this:

[tex]y=mx+b[/tex]

The letter m represents the slope, and the letter b represents the y-intercept. Let's plug in the values we found for those respectively:

[tex]y=-\frac{1}{5}x+0[/tex]

This simplifies to the equation below! This is the equation of the line!

[tex]y=-\frac{1}{5}x[/tex]

The equation of the line through the point (-6,5) and parallel to the line is    y=[tex]\frac{1}{2}[/tex]x-7 is y=[tex]\frac{1}{2}[/tex]x+8.

What is equation of line ?

Any location with an x and y axis can have a line equation constructed using the slope of the line. To build a line with a certain point, one uses the equation for a straight line. Any two points can be used to find the slope. Slope is the part of a straight line that is steep.

Here the given equation is y=[tex]\frac{1}{2}[/tex]x-7

We know that equation of line is y=mx+c , where m = slope.

Then slope of given line is m= 1/2 . Now the line is parallel to given line so slope of the equation is also equal.

=> slope m=1/2.

Now the given point [tex](x_1,y_1)=(-6,5)[/tex] .

Using equation of the line is ,

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

=> y-5 = 1/2(x+6)

=> 2y-10=x+6

=>2y=x+16

=>y=[tex]\frac{1}{2}[/tex]x+8

Hence the equation of the line is y=[tex]\frac{1}{2}[/tex]x+8.

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The difference is 4[tex]x^{2}[/tex] - 14x - 4

Given,

In the question:

To find the difference:

The difference of [tex]2x^2-9x+8[/tex] subtract from [tex]6x^2 -5x-12[/tex] .

Now, According to the question:

Based on the given condition:

Formulate:

[tex]6x^2 -5x-12[/tex] -  [tex]2x^2-9x+8[/tex]

Simplify and expand:

[tex]6x^2 -5x-12[/tex]  - [tex]2x^2-9x+8[/tex]

Reorder and gather like terms:

[tex](6x^2-2x^2)[/tex] + (-5x - 9x) + (-12 + 8)

Collect coefficient of like terms

(6 - 2)[tex]x^{2}[/tex] + (-5 -9)x + (-12 + 8)

Calculate the sum or difference:

4[tex]x^{2}[/tex] - 14x - 4

Hence, The difference is 4[tex]x^{2}[/tex] - 14x - 4 .

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Daniel's purchasing power will decrease because the interest rate is lower than the historical rate of inflation.

Purchasing power can be portrayed as the quantity of labor and products that a unit of cash or an amount of cash can buy. The connection between financing cost and inflation rate influences the buying force of a saving record.

At the point when the loan cost is higher than the inflation rate, purchasing power increments. Yet, when the interest rate is lower than the expansion rate, buying power falls. For example, In the United States for the 12 months ending April 2022, the annual inflation rate was 8.3%. Since the 0.5% annual interest rate being earned by Daniel is lower than the 8.3% annual inflation rate, the most likely thing to happen to the purchasing power of his savings over time is to fall.

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The percentage of games which Jay won is 44 percent.

This is referred to as a number or ratio expressed as a fraction of 100 and is usually denoted as %.

Percentage is calculated by : parts/whole × 100.

In this scenario we can deduce that the part is 154 while the whole is 350. Therefore: 154/350 × 100 = 44 percent.

Hence the most appropriate choice is 44 percent.

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Answer:

Step-by-step explanation:

4x maybe

The values (d,n) that will be the solution of the equation are

A. (0,445)

D.(118,209)

E.(172,101)

The equation that we have in this problem is:

0.10d+0.05n=22.25

here

d is the number of dimes

n is the number of nickels

Diego collected a total of $22.25 and put it in the jar.

Simply substitute each pair (d,n) into the left term of the equation and see if the answer is 22.25 to determine which values can be the equation's solutions.

Now,

A. (0,445)

0.10d+0.05n=22.25

0.10(0)+0.05(445)=22.25

22.25=22.25

Yes, The point satisfy the condition.

B. (0.50,435)

0.10d+0.05n=22.25

0.10(0.50)+0.05(435)=22.25

21.08≠22.25

No, The point does not satisfy the condition.

C. (233,21)

0.10d+0.05n=22.25

0.10(233)+0.05(21)=22.25

24.35≠22.25

No, The point does not satisfy the condition.

D.(118,209)

0.10d+0.05n=22.25

0.10(118)+0.05(209)=22.25

22.25=22.25

Yes, The point satisfy the condition.

E.(172,101)

0.10d+0.05n=22.25

0.10(172)+0.05(101)=22.25

22.25=22.25

Yes, The point satisfy the condition.

Therefore, The values (d,n) that will be the solution of the equation are

A. (0,445)

D.(118,209)

E.(172,101)

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Answer:

-5

Step-by-step explanation:

We need to find the value of y to find the value of 8y + 3. So,

-11y - 9 = 2

Add 9 on both sides

-11y = 11

Divide 11 by -11

y = -1

Step 2:

8 x -1 + 3

-8 + 3

-5

So the value of 8y + 3 is -5

Answer: Giuseppe is taller.

Step-by-step explanation:

Giuseppe is 74 inches tall, and we know that 12 inches is one foot, so 74/12 is ~6.1677777... versus 6.1.

Another way you can check this is by converting feet to inches. So 6 feet 1 inch would be (6 x 12) + 1 which is ~73.

20 times can you expect to land on yellow if you spin the spinner 100 times.

Given:

A spinner has 8 evenly spaced different colored sections. You spun the spinner 10 times and landed on yellow 2 times.

10 times spinning = landed on yellow 2 times.

divide by 10 on both sides

1 time spinning = landed on yellow 2/10 times

1 time = 1/5 times

multiply by 100 on both sides

1 time * 100 = 1/5*100 landed on yellow

100 times spinning = 20 times landed on yellow.

Therefore 20 times can you expect to land on yellow if you spin the spinner 100 times.

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The measure of angle EBF is  80° .

In the question ,

it is given that ,

point A, B and C lie on a straight line .

and G , B and F lie on a different straight line .

angle GBA = 24° so ,

GBA + GBC = 180°   ...because linear pair

So , GBC = 180 - 24 = 156°

angle CBF = 24°          ......because vertically opposite angles are equal .

from the figure , we see that angle GBC and angle ABF are vertically opposite angles , so ,

156° = ABE + EBF         .....(1)

Since the line AC and DF are parallel and BE is the transversal

So  , angle DEB + angle ABE = 180°

104° + ABE = 180°

ABE = 180-104

ABE = 76°

Substituting ABE = 76° in the equation (1) ,

we get ,

156 = 76+ EBF

EBF = 156 - 76

EBF = 80°

Therefore , The measure of angle EBF is  80° .

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Answer:

1

Step-by-step explanation:

To find the zero of an equation you set the equation equal to 0

That means you do this:

-5x+5=0

Then you solve for x

-5x=-5

x = -5/-5

x= 1

The number 1.23 x 10⁶ without scientific notation is 12,30,000.  

Scientific notation is a way to display extremely big or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper.

We use positive exponents for base 10 when expressing any huge integers in scientific notation. For example:

500000 = 5 x 10⁵, where 5 is the positive exponent.

We use negative exponents for base 10 when expressing any small integers in scientific notation. For example:

0.00005 = 2 x 10⁻⁵, where -5 is the negative exponent.

Here we have

The number 1.23 x 10⁶

We need to write the given number without scientific notation

In the given number the exponent of 10 = 6 and positive

Then we need to move the decimal place 7 places to the right or multiply the given decimal number with 1000000

Therefore,

1.23 x 10⁶ = 1.23 × 1000000 = 12,30,000.  

Hence,

The number 1.23 x 10⁶ without scientific notation is 12,30,000.

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Answer:

Option C: 5

Step-by-step explanation:

1st coin = $8

2nd coin = $16

3rd coin = $32

4th coin = $64

5th coin = $128

Total spent = $248

The equivalent expression of [(1.3^3)/(1.2^4)]^-6 is (1.2^[24])/(1.3^[18]). So option(1) is correct.

Equivalent expressions are expressions that work the same way despite their appearance. When we plug in the same value(s) for the variable, two algebraic expressions have the same value (s).

Equivalent means that different terms and expressions with similar values are considered equal in mathematical form.

The given expression is

[(1.3^3)/(1.2^4)]^-6

Apply the indices power law to the above expression.

[(1.2^4)/(1.3^3)]^6

The exponents are then expanded using the power law of indices.

(1.2^[4x6])/(1.3^[3x6])

(1.2^[24])/(1.3^[18])

Hence, the equivalent expression of [(1.3^3)/(1.2^4)]^-6 is (1.2^[24])/(1.3^[18])

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Answer:

153.9 units squared

Step-by-step explanation:

A = pi*r^2

A = pi* 7^2

A = pi* 49

A = 153.9

Answer: 21

Step-by-step explanation:

If she makes 7 out of 10 shots she makes 70% of her shots (7/10 x 100 = 70%)

So if she makes 30 shots, 21 will go in the basket

(30)(0.70) = 21

The given system of equations has solutions (-2, -1) and (-2, -1) respectively.

Calculating the unknown variables while keeping the equations balanced on both sides is the process of solving a system of equations.

Finding the value of the variable that makes the condition of all the given equations true is how we solve an equation system.

Given the system of equation below:

-2x² + y = -5

y = -3x² +5

Substitute equation 2 into 1 to have:

-2x² + (-3x+5) = -5

-2x²-3x² +5 = -5

-2x²-3x² +10=0
-5x² = -10

x²  = 10/5

x²  = 2

x = ±√2

If x = -√2

y = -3x² +5

y = -3(2) + 5

y = -1

If x = √2

y = -3x² +5

y = -3(2) + 5

y = -1

Hence the solutions to the given system of equations are (-√2, -1) and (√2, -1).

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The amount earned as commission in 2011 is $44928

From the question, we have the following parameters that can be used in our computation:

Commission percentage = 12%

Average sales per week = $7200

The amount earned as commission in the 2011 is then calculated as

Amount = Commission percentage x Average sales per week x Number of weeks

Substitute the known values in the above equation

So, we have

Amount = 12% x 7200 x 52

Evaluate

Amount = 44928

Hence, the commission amount is $44928

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Answer:

y = mx + b

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Answer: 9 students will be on a bus that is not full

Step-by-step explanation:

123/38 = 3.23684210526 = 3 bus that is full.
38 x 3 = 114, 123 - 114 = 9

So, 9 students will be on a bus that is not full while the other 3 bus will be full of students.

Answer:

there will be nine students in the bus that is not full.

Step-by-step explanation:

if each bus holds 38 in your first bus you have 38 and then there are 85 students left so in the second bus there are also 38 and you should have 47 students left that need to go in a bus so then again in bus 3 there are also 38 which means in the fourth/last bus there are only 9 students left  

The value of x in the given equation is x = -12/35

From the question, we are to solve the given linear equation.

The given linear equation is

-4 1/5x = 1.44

To solve the given equation, we will determine the value of x in the equation.

First, we will convert 4 1/5 to an improper fraction

-4 1/5 = -21/5

Also,

We will convert 1.44 to a fraction

1.44 = 144/100 = 36/25

Now,

-21/5(x) = 36/25

-21(x) × 25 = 36 × 5

x = (36 × 5) / (-21 × 25)

x = -180/525

x = -12/35

Hence, the value of x is x = -12/35

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The probability that the household contains 3 people must be 0.16

The probability of finding 3 people in a household is the same as the probability of finding 4 people.

The probability = Number of favorable outcomes / Total number of outcomes

The probability is the occurrence of the random event. The value of the probability varies from 0 to 1

Therefore if we add all the probability together, the result will be one

Also The probability of finding 3 people in a household is the same as the probability of finding 4 people.

Consider the probability of finding 3 people = Probability of finding 4 people = x

Then the equation will be

0.25 + 0.32 + x + x + 0.07 + 0.03 + 0.01 = 1

Add the terms

0.68 + 2x = 1

2x = 1 - 0.68

2x = 0.32

x = 0.32 / 2

x = 0.16

Hence, the probability that the household contains 3 people must be 0.16

The complete question is:

In government data, a household consists of all occupants of a dwelling unit. choose an American household at random and count the number of people it contains. here is the assignment of probabilities for the outcome. the probability of finding 3 people in a household is the same as the probability of finding 4 people. what is the probability of finding 3 people in the household ?

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The inequality is represented by the polynomial y ≥ 3.6 · (x - 11.5) · (x + 3.5).

What is the expression of the quadratic inequality?

Herein we must derive the quadratic expression within an inequality of the y ≥ f(x) based on its two roots and a known point on the curve. We can find the coefficients of the quadratic function by solving this system of linear equations:

(x₁, y₁) = (- 3.5, 0)

12.25 · a - 3.5 · b + c = 0       (1)

(x₂, y₂) = (11.5, 0)

132.25 · a + 11.5 · b + c = 0       (2)

(x₃, y₃) = (8.5, - 54)

72.25 · a + 8.5 · b + c = - 54     (3)

The solution of the system is a = 3.6, b = - 54, c = 144.9.

Thus, the inequality is represented by the polynomial y ≥ 3.6 · x² - 54 · x + 144.9, whose factored form is determined by the quadratic formula:

y ≥ 3.6 · (x² - 15 · x + 40.25)

y ≥ 3.6 · (x - 11.5) · (x + 3.5)

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The function for the transformation "The cubic function shifts 7 units right and 5 units up. is written as  f(x) = (x - 7)^3 + 5.

Let the cubic function be = f(x) = x^3

The transformation required include shifts 7 units right and 5 units up

shifting 7 units to the right is achieved by subtracting 7 units from x in the function hence f(x) = (x - 7)^3

moving 5 units up is achieved by adding 5 units to the function hence

f(x) = (x - 7)^3 + 5

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The ratio of flower seeds to the total amount of seeds is 2/7 = 0.2857.

The greatest common divisor of two or more numbers that are not all equal to zero is the largest positive integer that divides each of the integers. This term is used in mathematics. The symbol represents the two integers x and y's greatest common factor. The GCF of two or more numbers is the greatest number among all the common factors of the given numbers.

Given that,

The local stores have donated 30 packets of flower seeds and 105 packets of vegetable seeds.

30/105

We have to find the GCF of 30 and 105=15

30/15=2

105/15=7

So, the answer is 2/7

The ratio of flower seeds to the total amount of seeds is 2/7.

By converting fractions as a decimal number we get,

2/7=0.2857

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The probability that exactly two marbles are red, is 0.365.

In the given question we have to find the probability that exactly two marbles are red.

A bag contains 10 red marbles, 5 white marbles, and 6 blue marbles.

Total marbles is

10+5+6=21

We draw 5 marbles out at random, without replacement.

Marbles taken out =5

Total possibility of taking 5 marbles out of 21 marbles is [tex]^{21}C_{5}[/tex].

Using [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]

So [tex]^{21}C_{5}=\frac{21!}{5!(21-5)!}[/tex]

[tex]^{21}C_{5}=\frac{21!}{5!16!}[/tex]

[tex]^{21}C_{5}=\frac{21\times20\times19\times18\times17\times16!}{5\times4\times3\times2\times1\times16!}[/tex]

Simplifying

[tex]^{21}C_{5}[/tex] =7×19×9×17

[tex]^{21}C_{5}[/tex] = 20,349

Probability of exactly two marbles are red is

Possible out comes of exactly two red marbles equal to 2 red and other color marble 3.

Total red marbles are 10. So [tex]^{10}C_{2}[/tex]

The remaining marble except red marble is 11. So [tex]^{11}C_{3}[/tex]

[tex]=^{10}C_{2}\times^{11}C_{3}[/tex]

Simplifying

[tex]=\frac{10!}{2!(10-2)!}\times\frac{11!}{3!(11-3)!}[/tex]

[tex]=\frac{10!}{2!8!}\times\frac{11!}{3!8!}[/tex]

[tex]=\frac{10\times9\times8!}{2\times1\times8!}\times\frac{11\times10\times9\times8!}{3\times2\times1\times8!}[/tex]

=5×9×11×5×3

=7,425

So the probability that exactly two marbles are red

P(R)=7,425/20,349

P(R)=0.365

Hence, the probability that exactly two marbles are red, is 0.365.

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By the zero vector property x=y.

Suppose for full generality that V is any vector space and x,y,z is any vector in V. Suppose, x+z = y+z. Show that x=y. Since z is in v, there exists a vector z in v, such that

= z + (-z) = 0, because x+y=y+z

Thus x+z=y+z

= (x+z)+(-z) = (y+z)+(-z) and thus

= x+(z+(-z)) = y + (z+(-z)) because addition is associative in vector

= x+0 = y+0 because additive inverse exists in a vector

= and thus x=y by the properties of zero vector

Also according to the question, it is now proved that x+z=y+z implies x=y and v has the cancellation property.

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