How do we determine the function, minimum or maximum, and the value of the minimum or maximum?

The equation of the line in slope intercept form is y = -5 / 9x + 2 / 9

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

y = mx + b

where

Let's find the slope using the points (4, -2)(-5, 3)

Hence,

m = y₂ - y₁ / x₂ - x₁

x₁ = 4

x₂ = -5

y₁ = - 2

y₂ = 3

m = 3 + 2 / -5 - 4

m = 5 / -9

m = - 5 / 9

Therefore, let's find the y-intercept using (4, -2).

-2 = - 5 / 9 (4) + b

-2 = - 20 / 9 + b

b = -2 + 20 / 9

b =  -18 + 20/  9

b = 2 / 9

Therefore, the equation is y = -5 / 9x + 2 / 9

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Answer:the slant height of the triangular pyramid is approximately 11.4132 centimeters.

Answer:

24 people borrowed the books on Friday

Step-by-step explanation:

Every day, the number of books is being subtracted by 2.

56 - Monday (-8)

48 - Tuesday (-8)

40 - Wednesday (-8)

32 - Thursday (-8)

24- Friday

Answer:

the 40th number in the pattern is 9

Answer:

B

Step-by-step explanation:

the side length is equal to sqrt(33)

sqrt(33)  = 5.74, closest to 5 3/4

Answer:

4/5

Step-by-step explanation:

\(y=\dfrac{1}{3}x+\dfrac{11}{15} \\\\1=\dfrac{1}{3}x+\dfrac{11}{15}\\\\\dfrac{4}{15}=\dfrac{1}{3}x\\\\\dfrac{4}{5}=x\)

Hope this helps!

Answer:

x=4/5

Step-by-step explanation:

y=1/3x+11/15

1=1/3x+11/15

4/15=1/3x

multiply both sides by 3

4/5=x

Answer:

f(-3) = -2(-3)^3 - 3

f(-3) = 54 - 3

f(-3) = 51

g(3) = -5(3) + 4

g(3) = -15+4

g(3) = -11

Hope this helps!

Noah earned $160 last month, and his income tax rate is 10%. To calculate how much he earns after tax, we need to subtract the tax amount from his earnings.

The tax amount is equal to 10% of his earnings, which is:

0.1

×

160

=

16

0.1×160=16

Therefore, Noah's earnings after tax is:

160

−

16

=

144

160−16=144

Noah earns $144 after tax.

Answer:

8/25

Step-by-step explanation:

The probability of picking a number less than 9 is 4/5.

The probability of picking an even number is 2/5.

\(4/5 \times 2/5\)

\(=8/25\)

Answer:

the answer is D. F(x) = 1/x(x-3)

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.

The sequence is defined by the following formula:
a1 = 1, a2 = 3,
and
an = (-1)nan - 1 + an - 2 for n ≥ 3.
To find the third term (a3), we substitute n = 3 into the formula:
a3 = (-1)(3)(a3 - 1) + a3 - 2.
Next, we simplify the equation:
a3 = -3(a2) + a1.
Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:
a3 = -3(3) + 1.
Simplifying further:
a3 = -9 + 1.
Therefore, the third term (a3) is equal to -8.
To find the fourth term (a4), we substitute n = 4 into the formula:
a4 = (-1)(4)(a4 - 1) + a4 - 2.
Simplifying the equation:
a4 = -4(a3) + a2.
Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:
a4 = -4(-8) + 3.
Simplifying further:
a4 = 32 + 3.
Therefore, the fourth term (a4) is equal to 35.
To find the fifth term (a5), we substitute n = 5 into the formula:
a5 = (-1)(5)(a5 - 1) + a5 - 2.

Simplifying the equation:
a5 = -5(a4) + a3.
Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:
a5 = -5(35) + (-8).
Simplifying further:
a5 = -175 - 8.
Therefore, the fifth term (a5) is equal to -183.
In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.

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Activity: "Percentage Analysis in Real-Life Situations"

Objective: The objective of this activity is to help learners recognize the practical application of percentages in various social situations. It aims to develop their critical awareness of how percentages are used in real-life contexts and their significance in social, environmental, cultural, and economic relations.

Procedure:

1. Provide learners with a set of real-life scenarios, such as a discount sale, population growth, or budget allocations.

2. Ask them to identify the relevant information and calculate percentages based on the given data.

3. In small groups, learners discuss and analyze the implications of these percentages in the given social situations.

4. Encourage learners to think critically about how percentages impact decision-making, resource allocation, and understanding social phenomena.

5. Have groups present their findings and engage in a class discussion about the significance of percentages in these scenarios.

Teaching and Learning Approach:

This activity promotes an active learning approach by engaging learners in real-life problem-solving. It helps them recognize the practical relevance of percentages and fosters critical thinking skills.

By connecting mathematical concepts to social situations, learners develop a deeper understanding of how percentages are utilized in various aspects of their lives.

The teacher's role is to facilitate discussions, provide guidance, and encourage learners to articulate their understanding of the connections between mathematics and real-world contexts.

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Answer:

3

Step-by-step explanation:

Answer:

6x² - 19x + 15

Step-by-step explanation:

(2x - 3)(3x - 5)

each term in the second factor is multiplied by each term in the first factor , that is

2x(3x - 5) - 3(3x - 5) ← distribute parenthesis

= 6x² - 10x - 9x + 15 ← collect like terms

= 6x² - 19x + 15

If Zach cut his rope into pieces that are half a foot long, then one whole rope is equivalent to two pieces of rope.

If Zack, Gigi, and Ellie each took one piece of rope, then they used a total of three pieces out of two pieces of rope.

To represent this information in a tape diagram, we can draw a rectangle to represent the two pieces of rope and divide it into four equal parts, each representing half a piece of rope. Then, shade in three of these parts to show that three half pieces of rope were used for the science project.

Here is the tape diagram:

        |           |           |           |

        |           |           |           |

        |           |           |           |

        |___________|___________|___________|

        |           |           |           |

        |           |           |           |

        |           |           |           |

        |___________|___________|___________|

Each of the four parts of the tape diagram represents half a piece of rope. Since three parts are shaded in, this means that the three individuals used 3/4 of the whole rope for their science project.

So the fraction of the whole rope used for the science project is 3/4.

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Answer:

8

Step-by-step explanation:

A family of 5 monkeys eat 2 bananas a day.

to figure out how much the monkeys will eat in 4 days

multiply 2 by 4.

make sure the question is not for each monkey or the answer will be

(2 by 4) by 5. witch would be 40

however for the case your saying the answer would be 8

The correct answer is By finding the quotient of the bases to be one third and canceling common factors. Option D.

The Quotient of Powers Property states that when dividing two powers with the same base, you can subtract the exponents. In the given expression, we have three to the fourth power divided by nine.

To simplify this expression using the Quotient of Powers Property, we first need to recognize that nine can be written as three squared, since 3 multiplied by itself gives 9.

So, we have (3^4) / (3^2). According to the Quotient of Powers Property, we subtract the exponents: 4 - 2.

This gives us 3^(4-2), which simplifies to 3^2. Therefore, the expression three to the fourth power all over nine equals three squared.

It states that we find the quotient of the bases to be one third and cancel common factors. In this case, the bases are 3 and 3, and their quotient is indeed one third. Additionally, there are no common factors that can be canceled, as the expression does not contain any variables or additional terms.

Therefore, By finding the quotient of the bases to be one third and canceling common factors. accurately describes the steps involved in simplifying the expression using the Quotient of Powers Property.

We find the quotient of the bases (one third) and cancel common factors (which is not applicable in this case). Option D is correct.

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Note the complete question is

Explain how the Quotient of Powers Property was used to simplify this expression. (1 point)

Three to the fourth power all over nine equals three squared

A.) By simplifying 9 to 32 to make both powers base three and adding the exponents

B.) By simplifying 9 to 32 to make both powers base three and subtracting the exponents

C.) By finding the quotient of the bases to be one third and simplifying the expression

D.) By finding the quotient of the bases to be one third and cancelling common factors

Answer:

After 7 years the car will be worth $ 9,382.78.

Step-by-step explanation:

Given that a car bought for $ 22,959 depreciates at 12% annually, to determine what is its value after 7 years, the following calculation must be performed, using exponential expressions to determine the price decrease:

100 - 12 = 88

22,959 x 0.88 ^ 7 = X

22.959 x 0.4086 = X

9,382.78 = X

Therefore, after 7 years the car will be worth $ 9,382.78.

Answer:

-6l²m

Step-by-step explanation:

v. -54l⁴m³n² / 9l²m²n²

= -6l²m

The unadjusted cost of goods sold for the year is calculated by subtracting the ending inventory from the sum of beginning inventory and purchases. The formula is as follows:

Unadjusted Cost of Goods Sold = Beginning Inventory + Purchases - Ending Inventory

Without knowing the values for beginning inventory, purchases, and ending inventory, we cannot compute the unadjusted cost of goods sold for the year.

5. Given that the $70,000 ending balance in Work in Process includes $24,000 of direct materials, we can calculate the missing information as follows:

Direct Labor = Total Work in Process - Direct Materials - Overhead
Direct Labor = $70,000 - $24,000 - Overhead

Without knowing the value for overhead, we cannot compute the direct labor cost. However, we can rearrange the formula to solve for overhead:

Overhead = Total Work in Process - Direct Materials - Direct Labor
Overhead = $70,000 - $24,000 - Direct Labor

Without knowing the value for direct labor, we cannot compute the overhead cost.

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Answer: x= -3

Step-by-step explanation:

7x = 6+ 15x + 15 - x

7x = 21 + 14x

-7x = 21

x= -3

Answer: 90%

Good Luck!

Answer:

90 / 1 your welcome

The mean is  2,071,798.33

The Median is 1,485,552

The range is 7,425,310

The standard deviation is given as 1961105.68

Mean = (Sum of all populations) / (Number of cities)

= (8,336,817 + 979,576 + 2,693,976 + 2,320,268 + 1,680,992 + 1,584,064 + 1,547,253 + 1,423,851 + 1,343,573 + 1,021,795 + 978,908 + 911,507) / 12

= 24,861,580 / 12

= 2,071,798.33

To find the median, we need to arrange the populations in increasing order and find the middle value. If we arrange these values, we get:

911,507, 978,908, 979,576, 1,021,795, 1,343,573, 1,423,851, 1,547,253, 1,584,064, 1,680,992, 2,320,268, 2,693,976, 8,336,817

Since there are 12 cities (an even number), the median would be the average of the 6th and 7th values:

Median = (1,423,851 + 1,547,253) / 2

= 1,485,552

The mode isn't applicable here as no city population repeats.

The range is the highest population minus the lowest population:

Range = 8,336,817 - 911,507

= 7,425,310

Standard deviation  =  (911507- 2068548.3333333)² +  (978908 - 2068548.3333333)² + (979576  - 2068548.3333333)²  + ( 1021795 -  2068548.3333333)² +  (1343573- 2068548.3333333)²  +( 1423851- 2068548.3333333)² + (1547253- 2068548.3333333)² +( 1584064- 2068548.3333333)² + (1680992- 2068548.3333333)² + ( 2320268- 2068548.3333333)²  +(2693976- 2068548.3333333)² +( 8336817 - 2068548.3333333)² / 12

= 46151226311869 / 12

=  3845935525989.1

\(standard deviation = \sqrt{ 3845935525989.1}\)

=  1961105.6896529

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The expression is equivalent to the expression (12 + 3) ÷ 5 is (3 + 12) ÷ 5

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

(12 + 3) ÷ 5

The above expression is a quotient expression

However, we can apply some algebraic properties

Take for instance;

12 + 3 can be expressed as 3 + 12

So, we have

(12 + 3) ÷ 5 = (3 + 12) ÷ 5

Hence, the expression is equivalent to the expression is (3 + 12) ÷ 5

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Answer:

X = 0, x = -3

Step-by-step explanation:

You have to cancel everything and -3 =3 is 0 and that would make the entire right side zero. If you have x as 0 the first 0 will multiply with everything making everything zero.

\(\text{Find the value of the x's}\\\\x(x+3)(x+3)=0\\\\\text{We know that the x outside of the parenthesis would equal 0}\\\\\text{In order to find the value of the other x's, we must solve by equaling}\\\text{them to 0}\\\\x+3=0\\\\\text{Subtract 3 from both sides}\\\\x=-3\\\\\text{Since there are two of them, you would have two answers as -3}\\\\\boxed{\text{x = 0, or x = -3, or x = -3}}\)

The difference between a root and a factor is roots are zero of the function.

What's the difference between a root and a factor?

You can switch back and forth between a polynomial's factors and roots, according to the factor theorem. In other words, if you are familiar with one, you are familiar with the other. A polynomial of a degree of more than two may occasionally be asked of you by your teacher or your textbook. Finding its causes can help you discover its roots.

You can substitute a number for x and obtain a true assertion by using the root a.

(a – a)(a – b) = 0

The initial factor in this scenario is 0.

In order to produce a true assertion, you can alternatively replace x with the root b's number.

(b – a)(b – b) = 0

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Answer:

(5 - (-1)) or 6

Step-by-step explanation:

Substitute the variables

= (x - y)

=(5 - (-1))

= 6

Hope this was simple enough for you to understand!

All the values of x, y and z are,

z = 12.99

y = 7.01

x = 28.3 degree

We have to given that;

In a triangle,

Two angles are, 61.7 degree and 90 degree

And, One side is, 14.76.

Now, We can formulate;

sin 61.7° = Perpendicular / Hypotenuse

sin 61.7° = z / 14.76

0.88 = z / 14.76

z = 0.88 x 14.76

z = 12.99

And, By Pythagoras theorem we get;

14.76² = z² + y²

14.76² = 12.99² + y²

217.85 = 168.74 + y²

y² = 217.85 - 168.74

y² = 49.1

y = 7.01

And, By sum of all the angles in triangle, we get;

x + 61.7 + 90 = 180

x + 151.7 = 180

x = 180 - 151.7

x = 28.3 degree

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