Please help with the 4 questions.

Final answer:

To find where the tangent line is horizontal on the curve y = 2x^3 + 3x^2 - 12x + 8, set its derivative to zero and solve for x, resulting in points (-2, 8) and (1, 1) where the tangent lines are horizontal.

Explanation:

To find the points on the curve y = 2x^3 + 3x^2 − 12x + 8 where the tangent line is horizontal, we look for where the derivative of the curve equals zero because horizontal tangent lines have a slope of zero. The derivative of the given function is y' = 6x^2 + 6x - 12. This derivative represents the slope of the tangent at any point on the curve.

Setting the derivative equal to zero gives us the quadratic equation 6x^2 + 6x - 12 = 0, which can be simplified to x^2 + x - 2 = 0. Factoring this quadratic equation, we get (x + 2)(x - 1) = 0, leading to two solutions for x: x = -2 and x = 1. Substituting these x-values back into the original equation gives us the y-coordinates and therefore the points on the curve where the tangent line is horizontal: (-2, 8) and (1, 1).

The cost of producing one more item is 4 if 50 are currently being produced.

A linear equation is defined as an equation in which the highest power of the variable is always one.

The slope-intercept form is y = mx+c, where the slope is m and the y-intercept is c.

We have been given that linear cost function is C(x) = 4x + 300.

Here, the slope (4) is the cost per unit,

We have to determine the cost of producing one more item

Since 50 are currently being produced, so substitute the value of x = 51,

So the cost of producing one more item as

⇒ C(51) - C(50) = 4(51) +300 - (4(50) + 300) = 504 - 500 = 4

Therefore, the cost of producing one more item is 4 if 50 are currently being produced.

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Final answer:

To find (g x h)(5), calculate h(5) first, then substitute the result into g(x) and calculate. The equivalent expression is (5)^2 - 7.

Explanation:

To solve (g x h)(5), we need to find g(h(5)). Given h(x) = x - 7 and g(x) = x^2, we first find h(5) = 5 - 7 = -2. Then, we evaluate g(-2) = (-2)^2 = 4. So, (g x h)(5) = g(h(5)) = g(-2) = 4, which corresponds to the option (5)^2 - 7.

Answer:

3.50p>(or equal to) 140; p>(or equal to)40

Step-by-step explanation:

To find the length of cable remaining on the spool, subtract the weight of the empty spool from the total weight, and then divide the result by the weight of cable per metre.

The question involves the process of subtracting, conversion and division. First, we need to subtract the weight of the empty spool from the total weight of the partly-used spool and the remaining cable to find the weight of the remaining cable alone. This means 1540 grams - 260 grams = 1280 grams. Then, we convert the weight of the remaining cable (which is in grams) to metres by dividing it by the weight of one metre of cable (which is 85 grams). So, 1280 grams ÷ 85 grams/metre = approximately 15 metres. Therefore, this is the quantity of cable that Ted has left on the spool.

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Answer:

its devon

Step-by-step explanation:

Answer:

[tex](4x+9)[/tex]

Step-by-step explanation:

we know that

The perimeter of triangle is equal to the sum of the three length sides

therefore

[tex]P=(x+4)+(x+8)+(2x-3)\\ \\P=(x+x+2x)+(4+8-3)\\ \\P=(4x+9)\ units[/tex]

I am sure the answer is |10.5−(−6.1)| hope this helps and if correct give me the brainliest please

the correct answer is

|10.5-(6.1)|

I took the test

Exponential notation is used to express very large and very small numbers as a product of two numbers. We can cube the digit term in the usual way and multiply the exponent of the exponential term by 3 to write expressions in exponential form using the digit 3 and 5.

Exponential notation is used to express very large and very small numbers as a product of two numbers. In the case of writing expressions in exponential form using the digit 3 and 5, we can cube the digit term in the usual way and multiply the exponent of the exponential term by 3. For example, if we want to write 3 to the power of 5 in exponential form, it can be written as 3³ x 5³ = 243 x 125. Therefore, there are multiple different ways to use the digits 3 and 5 to write expressions in exponential form.

Final answer:

To write expressions in exponential form using the digits 3 and 5, follow the rules of exponential arithmetic.

Explanation:

To write expressions in exponential form using the digits 3 and 5, we can follow the rules of exponential arithmetic. In exponential form, a number is written as the digit term multiplied by 10 raised to the power of the exponential term.

For example, if we want to write 35 in exponential form, we can write it as 3×105. If we want to write 53 in exponential form, it would be 5×103.

By using these rules, you can create different expressions by combining the digits 3 and 5 with different exponential terms.

Answer:

Inverse function, [tex]f^{-1}=2^x[/tex]

Step-by-step explanation:

We are given a function [tex]f(x)=\log_2x[/tex]

We need to find the inverse of f(x)

Step 1: Set f(x)=y

[tex]y=\log_2x[/tex]

Step 2: Switch x and y

[tex]x=\log_2y[/tex]

Step 3: Solve for y (isolate y)

[tex]y=2^x[/tex]              [tex]\because \log_ab=x\Rightarrow b=a^x[/tex]

Inverse of function [tex]f(x)\rightarrow f^{-1}(x)=2^x[/tex]

The inverse of the logarithmic function is [tex]f^{-1}(x) = 2^x[/tex]

The logarithmic expression is given as:

[tex]f(x) = \log_2(x)[/tex]

Replace f(x) with y

[tex]y = \log_2(x)[/tex]

Swap the positions of x and y

[tex]x = \log_2(y)[/tex]

Apply the change of base rule of logarithm

[tex]2^x = y[/tex]

Rewrite as:

[tex]y = 2^x[/tex]

Express y as an inverse function

[tex]f^{-1}(x) = 2^x[/tex]

Hence, the inverse of the logarithmic function is [tex]f^{-1}(x) = 2^x[/tex]

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Maria and her family drove 885 miles, and the first '8' in this number represents the hundreds place, meaning it has a value of 800 miles.

The student's question is related to place value in numbers. Maria and her family drove 885 miles on their summer vacation, and the query specifically asks about the value represented by the first digit '8' on the left side of this three-digit number. In this case, the digit '8' is in the hundreds place, which means it represents the hundreds component of the overall number. Therefore, the first '8' has a value of 800. This is because in the number 885, the first '8' represents 8 hundreds, the second '8' represents 8 tens (or eighty), and the '5' represents 5 ones.

Answer:

The simplified product has a degree of 2.

The simplified product, in standard form has exactly 2 negative terms.

Step-by-step explanation:

[tex](b - 2c)(-3b + c)[/tex]

LEts multiply it using FOIL method

[tex]b* -3b= -3b^2[/tex]

[tex]b*c= bc[/tex]

[tex](-2c) * (-3b)= 6bc[/tex]

[tex](-2c) * c= -2c^2[/tex]

The product is [tex]-3b^2 +bc+6bc-2c^2[/tex]

[tex]-3b^2+7bc-2c^2[/tex]

The simplified product has a degree of 2.

It has two negative terms

Answer: The correct options are,

The simplified product has a degree of 2,

The simplified product, in standard form, has exactly 2 negative terms.

Step-by-step explanation:

Here, the given expression,

[tex](b-2c)(-3b+c)[/tex]

By distributive property,

[tex]=(b-2c)(-3b)+(b-2c)(c)[/tex]

Again by distributive property,

[tex]=b(-3b)-2c(-3b)+bc-2c(c)[/tex]

[tex]=-3b^2+6bc+bc-2c^2[/tex]

[tex]=-3b^2+7bc-2c^2[/tex]

Which is the simplified form of the given expression,

That having three terms in which two terms are negative and the degree ( The highest sum of the exponents of the variables) is 2,

Hence, the correct options are,

The simplified product has a degree of 2,

The simplified product, in standard form, has exactly 2 negative terms.

35 pounds of $0.20 coffee beans and 85 pounds of $0.68 coffee beans create a 120-pound mixture valued at $0.54 per pound when mixed. Solving the system of linear equations confirms these amounts as reasonable and correct.

To solve the problem of determining how much of each type of coffee bean is used in a mixture, we can use a system of equations to model the scenario. Let's define x as the number of pounds of the $0.20 coffee beans and y as the number of pounds of the $0.68 coffee beans. Given the total weight of the mixture is 120 pounds, we can formulate our first equation:

x + y = 120

The total value of the coffee mixture is $0.54 per pound, hence the second equation representing the total value of the mixture is:

0.20x + 0.68y = 0.54(120)

By solving this system of equations, we can find the precise quantities of each type of bean used in the mixture.

Step 1: Multiply the second equation by 100 to clear the decimals for easier calculation:

20x + 68y = 54 times 120

Step 2: Solve for one of the variables, let's say x:

x = 120 - y

Step 3: Substitute x in the second equation:

20(120 - y) + 68y = 54 times 120

This simplifies to:

2400 - 20y + 68y = 6480

48y = 4080

Step 4: Solve for y:

y = 4080 / 48

y = 85

Step 5: Substitute y back into the first equation to find x:

x = 120 - 85

x = 35

If 35 pounds of the $0.20 beans and 85 pounds of the $0.68 beans are mixed together, we achieve the desired mixture weighing 120 pounds valued at $0.54 per pound. This solution is reasonable because the sum of the weights equals the total weight of the mixture, and the calculated total value per pound matches the desired value.

The value of the solution of expression is, r = 7

We have to give that,

An expression to simplify,

r + 15 = 4r - 6

Now, Simplify the expression by combining like terms as,

r + 15 = 4r - 6

Subtract r on both sides,

r + 15 - r = 4r - r - 6

15 = 3r - 6

Add 6 into both sides,

15 + 6 = 3r

21 = 3r

Divide 3 on both sides,

r = 21/3

r = 7

Therefore, the solution is, r = 7

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To solve the equation 67 times a number minus 58 is equal to 36 less than the number, we can use algebraic manipulation to isolate the variable x. The solution is x = 1/3.

To solve the equation, we can set up the equation as follows:

67x - 58 = x - 36

Next, we can simplify the equation by combining like terms:

67x - x = 58 - 36

66x = 22

Finally, we can solve for x by dividing both sides of the equation by 66:

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