Vhat is the value of the expression below when a -5.b = 7, and c = 6?
9b - 4a + 2c

Answer:

A but im not sure

Step-by-step explanation:

Answer:

The correct answer is B: Saturday.

The relationship between Monday and Thursday is that they are two days apart in a typical Monday-to-Sunday week. Similarly, Friday is also two days apart from Tuesday in a typical week, so the relationship between Friday and Tuesday would be the same as the relationship between Monday and Thursday. Therefore, the correct answer is B: Saturday.

The answer is A, rhombus.

Answer: a) 10x-6x and c) 12x+2x-10x

Step-by-step explanation:

Lets start by simplifying all the expressions

a) 10x-6x=4x

b)7x+3x=10x

c)12x+2x-10x=14x-10x=4x

d)x-x+2x=2x

As you can see a and c both simplify to 4x meaning that is our answer.

Options A and C

Hope it helps.

Do comment if you have any query.

Answer:

x = 5

Step-by-step explanation:

x^2/(x + 5) = 25/(x+5)      Subtract the right side from both sides.

x^2/(x + 5) - 25/(x + 5) = 0

x^2 - 25

=======   = 0

x + 5

(x + 5)(x - 5)

============= = 0

(x + 5)

Cancel x + 5 in the numerator and denominator.

x - 5 = 0

x = + 5

Does it check?

x^2/(x + 5) = 25/(x + 5)

x = 5

5^2/(10) = 25/10

25/10 = 25/10 Yes it checks.

The equation y = -|x - 3| + 2 written as a piecewise function is;

f(x) = {y = x - 1, if x < -3

        {y = -x + 1, if x ≥ -3

A function can be written as piecewise function if it changes its behavior ( increasing or decreasing ) about a point.

The function f(x) = y = |x| changes its behavior at |x| = 0 i.e , x = 0 .

y = | x | = x , if x < 0

= - x , if x > 0

| x | = a => x = ± a

• | x | ≥ a ( a ≥ 0 ) => x € ( -∞ , -a ] U [ a , ∞ )

• | x | ≤ a ( a ≥ 0 ) => x € [ -a , a ]

The given function is : y = -|x - 3| + 2

The function will change its behavior when; -| x - 3 | = 0

-x + 3 = 0

x = -3

If x < -3 , then ;

y =  -(-(x - 3)) + 2

y = x -3 + 2

y = x - 1

If x ≥ -3, then ;

y = -(x - 3) + 2

y = -x + 3 + 2

y = -x + 1

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The answer should be 2, 4.

The teacher can thus use social sciences as a vehicle to develop mathematical skills by facilitating the development of skills such as data interpretation and analysis.

As an instructor, I would use social sciences to develop mathematical skills in the following manner:Consider a social science topic like demography. In this case, a teacher could use mathematics to assist students in interpreting population statistics.

Teachers might guide students to gather information about population size, growth rate, and geographical distribution from various countries and then use statistics to analyze the data.

For example, a teacher could give students graphs or charts to help them understand population growth rates. They can be asked to make comparisons and identify trends.

In this way, students' understanding of the population is improved, as is their mathematical reasoning.Aside from using mathematics to interpret population statistics,

the teacher can also incorporate mathematical skills development in social sciences by using methods that involve understanding and analysis of data. In other words, students learn how to use data to reach conclusions and make decisions.

They learn how to interpret data and how to extract information from it.This method of teaching creates opportunities for the use of the same skills in different contexts and areas of learning.

It enables students to see connections between subjects and fosters an integrated approach to learning.

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Answer:

2 and 10

Step-by-step explanation:

The profit per month will be, R1 044 000 / 12 = R87 000.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, To calculate the profit per month, we need to divide the profit per year by the number of months in a year.

Hence, Calculate the profit per month, divide the profit per year by 12 as;

⇒ R1 044 000 ÷ 12

⇒ R87 000 per month

Thus, The profit per month will be, R1 044 000 / 12 = R87 000.

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The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

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Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(4x^2+5xy+y^4=370\)

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)

Differentiate the terms in x only (and constant terms):

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Use the product rule to differentiate terms in both x and y.

\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)

\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)

Therefore, slope of the tangent line to the curve at the given point is -11/7.

Answer:

Step-by-step explanation:

We know that:

Work:

Divide the RHS:

Multiply the RHS:

Hence, for 15 pens, the cost is $7.2

Hoped this helped.

\(BrainiacUser1357\)

The function that grows at the fastest rate for increasing values of x is f(x) = 4×2ˣ.

We can see this by comparing the growth rates of the three functions for larger and larger values of x.

As x gets larger, the exponential function f(x) grows much faster than the other two functions, which are both polynomial functions.

if we plug in x = 10, we get:

f(10) = 4×2¹⁰ = 4×1024 = 4096

h(10) = 9×10² + 25 = 925

g(10) = 15×10 + 6 = 156

As we can see, f(10) is much larger than h(10) and g(10), indicating that f(x) grows at a much faster rate than the other two functions.

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Answer:

x = 21.52

Step-by-step explanation:

Given:

hypotenuse (That has to be found out)

Side adjacent to the given angle

and an angle,

Hence we can say that Cos ratio would be used;

Cos(28) = 19 / x

x = 19 / Cos(28)

x = 21.52

Hope this helps!

The missing value E, the total revenue for the period 2017/18, is approximately 186.67.

To calculate the missing value E, the total revenue for the period 2017/18, we need to determine the total revenue of the provincial sector first.

Given that the revenue of the local government sector is 20, 12% of the provincial sector, we can set up the following equation:

20 = 0.12 × Provincial sector revenue

To find the value of Provincial sector revenue, we divide both sides of the equation by 0.12:

Provincial sector revenue = 20 / 0.12

Provincial sector revenue = 166.67

Now that we know the revenue of the provincial sector is 166.67, we can find the missing value E, which represents the total revenue for the period 2017/18. Since the local government sector always receives a larger share than the provincial sector, we can assume that the total revenue is the sum of the revenues of both sectors:

E = Local government sector revenue + Provincial sector revenue

E = 20 + 166.67

E = 186.67

Therefore, the missing value E, the total revenue for the period 2017/18, is approximately 186.67.

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2x + 3x + 140 = 360 (being complete turn angle)

5x + 140 = 360

5x = 360-140

5x = 220

x = 44

now 2x = 2 × 44 = 88

3x = 3 × 44 = 132

Answer:

Hi

Step-by-step explanation:

Please paste your question so I can solve it

Thanks

Answer:

-60

It is -60 because if it takes away 6 points for each cone you hit and you hit 10, then it would be -60 times 10, which equals -60.

Pythagorean theorem is represented by triangle B.

In this question we find four cases of triangle, of which we must determine what triangle can be explained by Pythagorean theorem. This theorem offers a relationship between the three sides of the triangle:

r² = x² + y²

Where:

Please notice that hypotenuse is the longest side of the triangle. Graphically speaking, there is a right triangle, that is, a triangle with one right angle. Then, triangle B express the relationship according to Pythagorean theorem.

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Answer:

Here's an interesting project idea for mathematics that can relate three different topics:

Topic 1: Fractals

Topic 2: Chaos Theory

Topic 3: Differential Equations

Research Question: Can fractals be used to model chaotic systems described by differential equations?

In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.

Your research paper can cover the following areas:

Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.

Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.

Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.

Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.

Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.

Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.

Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.

Step-by-step explanation:

The value of x is -12.07, and y is 3.07 for equation 1/2x + 6y = 12, y = x + 15.

We have to solve the given equations,  1/2x + 6y = 12 y = x + 15.

Equation; 1/2x + 6y = 12 and y = x + 15.

The given equations are solved by using the elimination method following all the steps given below.

The equations are,

\(\dfrac{1}{2}x + 6y = 12\\\\y = x+15\)

Substitute the value of y in equation 1 from equation 2,

\(\dfrac{1}{2}x + 6(x+15) = 12\\\\\dfrac{1}{2}x + 6x + 90 = 12\\\\\dfrac{x+12x+180}{2} = 12\\\\13x + 181 = 12 \times 2\\\\13x + 181 = 24\\\\12x = 24-181\\\\12x = -157\\\\x = \dfrac{-157}{13}\\\\x = -12.07\)

Substitute the value of x in equation 2,

\(y =- 12.07+15\\\\y = 3.07\)

Hence, The required value of x is -12.07, and y is 3.07 for equation 1/2x + 6y = 12, y = x + 15.

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Part 1

The equation is \(y=a(x+8)(x-72)\).

Using the point \((62, -490)\) to solve for \(a\),

\(-490=a(62+8)(62-72) \implies a=\frac{7}{10}\\\\\therefore \boxed{y=\frac{7}{10}(x+8)(x-72)}\)

Part 2

When \(x=-8\), \(y=0\).

When \(x=2\), \(y=-490\).

So, the average rate of change is \(\frac{-490-0}{2-(-8)}=\boxed{-49}\)

true

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The correct option is that C. Carmen disagreed and said, "No, the answer is 72x^12"

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

It should be noted that when dividing exponents with same base, we will subtract the powers and when multiplying them, we will add the powers.

Here, the study team was discussing how to multiply 6x^10 by 12x^2. Therefore, this will be:

= 72 × x^(10 + 2)

= 72x^12.

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Answer:

Answer is 7.

Step-by-step explanation:

(a + 2)^4- 20(a + 2)^2+ 64 = 0

2a^4- 20(2a)^2+ 64 = 0

16a-20(4a)+64=0  

-4a    -64  -4a          -64

12a-84=0

    +84 +84

12a=84

84/12=7

Answer:

$0.64 per cup

Step-by-step explanation:

There are 16 cups in 1 gallon, so the number of cups in 2 gallons is:

1 gallon: 16 cups

2 gallon = 2 x 1 gallon = 2 x 16 cups = 32 cups

So we need to find the price of each cup:

1 cup = ($20.48 / 32 cups) = $0.64 per cup.

The equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is: R(x) = 250000 + 375x - 2.5x²

Equations are mathematical statements with two algebraic expressionsοn either sideοf an equals (=) sign. It illustrates the equality between the expressions writtenοn the left and right sides. To determine the valueοf a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

N(x) = 625 + 2.5x

The revenue R(x) will be the productοf the numberοf students enrolled and the fee charged per student. The fee charged per student will be (400 - x) dollars. So, the revenue function can be represented as:

R(x) = (625 + 2.5x)(400 - x)

Simplifying the expression, we get:

R(x) = 250000 + 375x - 2.5x²

Therefore, the equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is:

R(x) = 250000 + 375x - 2.5x²

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The interest amount is $622.85

The given parameters are:

The interest amount is calculated as:

I = P(1 + r/n)^(nt) - P

This gives

I = 1000 * (1 + 4.5%/1)^(1 * 11) - 1000

Evaluate the products and the quotient

I = 1000 * (1 + 0.045)^(11) - 1000

Evaluate the sum

I = 1000 * (1.045)^(11) - 1000

Solve

I = 622.85

Hence, the interest amount is $622.85

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Answer:

15cm and 45cm

Step-by-step explanation:

If one part is one third of the other, then the long one is three times as long as the short one.

If the short one has length x

x + 3x = 60cm

4x = 60cm

x = 15cm

So short one is 15cm and the long one is 3*15cm = 45cm