Why is it a good idea to check to see if your answer is reasonable?

The equation of the line tangent to y = 9 - x^2 that passes through the point (1, 12) is y = -2x + 14.

To find the equations of all lines tangent to y = 9 - x^2 that pass through the point (1, 12), we need to find the slope of the tangent line at the point (1, 12) and use it to form the equation of the line.

y - y1 = m(x - x1)

y - 12 = -2(x - 1)

Rewrite the equation in slope-intercept form:

y = -2x + 14

Therefore, the equation of the line tangent to y = 9 - x^2 that passes through the point (1, 12) is y = -2x + 14.

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Explanation on dividing £42 in the ratio of 4:6 into two parts accurately.

Divide £42 in a ratio of 4:6:

Calculate the total parts in the ratio, which is 4 + 6 = 10.

Divide £42 by 10 to find the value of one part: £42 ÷ 10 = £4.20.

Multiply £4.20 by the parts in each ratio: £4.20 x 4 = £16.80 for the first part (4 parts),

£4.20 x 6 = £25.20 for the second part (6 parts).

The value "7" is approximately 9.09 percent of the number "77".

To calculate what percent of 77 is 7, we need to find the proportion of 7 in relation to 77. The concept of percent is based on the idea of expressing a fraction of a whole as a value out of 100.

To find the percentage, we divide the given value (7) by the total value (77) and multiply by 100.

⇒ (7/77) × 100 = 0.0909 × 100 ≈ 9.09%,

Therefore, 7 is approximately 9.09% of 77. This means that 7 represents about 9.09% of the total value of 77. It reflects the proportion of 7 within the whole value of 77, expressed as a percentage.

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Answer:

Saturated hydrocarbons are relatively unreactive except in the presence of high temperatures and oxygen.      

Step-by-step explanation:

we have to choose the option in which saturated hydrocarbons react.

Saturated hydrocarbons do contain double and triple bonds that make molecule reactive. They only contains sigma bonds, which are very stable and difficult to break and hence these are unreactive.

In saturated hydrocarbons the percentage of carbon is lower which gets easily oxidised in oxygen of the air to form [tex]CO_2[/tex] completely.

Saturated hydrocarbons are generally unreactive, but when exposed to high temperatures and oxygen they react in a combustion reaction to produce Carbon Dioxide and Water.

Hence, Saturated hydrocarbons are relatively unreactive except in the presence of high temperatures and oxygen.

Option option 1 is correct.

The Vertical Angles Theorem states that if two angles are vertical angles, then they are congruent .Given <A and <B are vertical angles so they are equal.

<A=<B.

Measure of <A=x and <B=5x-80

Or  5x-80=x

Adding 80 both sides

5x-80+80=x+80

5x=x+80

Subtracting x both sides

5x-x=x-x+80

4x=80

Dividing both sides by 4

x=20

Measure of <A= x= 20 degrees.

Sample Response: Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.

What did you include in your response? Check all that apply.

Louise is missing the term 30x3.

Louise could have used the formula for a perfect square trinomial.

Louise squared each term in the binomial rather then using the distributive property.

Using the square of the sum notable product, it is found that Louise's answer is not correct, as she forgot to add the multiplication of 2 by both terms.

It is represented by the following relation:

[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]

Hence, for Louise's expression, we have that:

[tex](5x^3 + 3)^2 = (5x^3)^2 + 2(5x^3)(3) + 3^2 = 25x^6 + 30x^3 + 9[/tex]

She forgot the middle term, hence her answer is not correct.

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The correct answer is: The original price is = x = $500

Explanation:

Mathematically, we can write it as:

[tex] \frac{15}{100} * x = 75 [/tex]

x = Original Price

The above equation can be read as: "The 15% of the original price is $75."

Now we need to find the value of x:

[tex] x =\frac{75 * 100}{15} = 500 [/tex]

Hence,

The original price is = x = $500

The slope of the given equation 12x = 7y - 10y is -4 (constant) thus it will be a linear equation.

A straight line on the coordinate plane is represented by a linear function.

A linear function is a function that varies linearly with respect to the changing variable.

Given the line,

12x = 7y - 10y

12x = -3y

-3y = 12x

Divide both sides by -3

y = -4x

The slope of any function is given as dy/dx or first differential

dydx = -4 so the slope is constant thus the line will be a linear equation.

The graph of the line also has been attached for refernce.

Hence "The slope of the given equation 12x = 7y - 10y is -4 (constant) thus it will be a linear equation".

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The equation 12x = 7y - 10y simplifies to 12x = -3y and is a linear equation because it can be rewritten in the form y = mx + b, where m is the slope (-4) and b is the y-intercept (0).

The equation 12x = 7y - 10y simplifies to 12x = -3y, which can then be written in the slope-intercept form as y = -4x. This is a linear equation because it can be expressed in the standard form y = mx + b, where m represents the slope and b is the y-intercept. In this equation, m equals -4 and b equals 0, indicating that the line crosses the y-axis at the origin (0,0).

Similar examples of linear equations include 7y = 6x + 8, 4y = 8, and y + 7 = 3x. These equations all have a constant rate of change, which is characteristic of linear relationships, where one variable is a constant multiple of the other plus a constant (y = a + bx). As a real-life example, the equation y = 55x + 75 represents the total labor charges to fix a car, with y being the dependent variable and x the independent variable, showcasing the linear relationship between hours worked and total charges.

The distributive property is demonstrated best by equations in the form a(b + c) = ab + ac. The correct choices that illustrate this property are: 1. C, 2. B, 3. A, 4. A, 5. A, 6. B, 7. C, and 8. C.

To determine which choice best shows the distributive property of multiplication, we need to find the equation that demonstrates the format a(b + c) = ab + ac. This property states that you can distribute the multiplication over addition inside the parentheses.

1 Correct choice: C. (7 × 2) + (7 × 4) = 7 × (2 + 4)

2 Correct choice: B. (7 × 3) + (7 × 2) = 7 × (3 + 2)

3 Correct choice: A. (2 × 10) + (2 × 8) = 2 × (10 + 8)

4 Correct choice: A. (9 × 4) + (9 × 5) = 9 × (4 + 5)

5 Correct choice: A. 2 × (3 + 5) = (2 × 3) + (2 × 5)

6 Correct choice: B. 9 × (3 + 7) = (9 × 3) + (9 × 7)

7 Correct choice: C. 5 × (4 + 6) = (5 × 4) + (5 × 6)

8 Correct choice: C. (2 × 6) + (2 × 0) = 2 × (6 + 0)

This demonstrates the distributive property effectively.

Complete question:

Determine which choice best shows the distributive property of multiplication.

1) A. 7 × 1 = 7, B. 7 × 2 = 2 × 7, C. (7 × 2) + (7 × 4)=7 × (2 + 4), D. (7 × 2) × 4 = 7 × (2 × 4)

2) A. (7 × 3) × 2 = 7 × (3 × 2), B. (7 × 3) + (7 × 2) = 7 × (3 + 2), C. 7 × 1 = 7, D. 7 × 3=3 × 7

3) A. (2 × 10) + (2 × 8) = 2 × (10 + 8), B. (2 × 10) × 8 = 2 × (10 × 8), C. 2 × 1 = 2, D. 2 × 10 = 10 × 2  

4) A. (9 × 4) + (9 × 5) = 9 × (4 + 5), B. (9 × 4) × 5 = 9 × (4 × 5), C. 9 × 1 = 9, D. 9 × 4 = 4 × 9

5) A. 2 × (3 + 5) = (2 × 3) + (2 × 5), B. 2 × 3 = 3 × 2, C. 2 × (3 × 5) = (2 × 3) × 5, D. 1 × 2 = 2

6) A. 9 × (3 × 7) = (9 × 3) × 7, B. 9 × (3 + 7) = (9 × 3) + (9 × 7), C. 9 × 3 = 3 × 9, D. 1 × 9 = 9

7) A. 5 × (4 × 6) = (5 × 4) × 6, B. 1 × 5 = 5, C. 5 × (4 + 6) = (5 × 4) + (5 × 6), D. 5 × 4 = 4 × 5

8) A. 2 × 1 = 2, B. 2 × 6 = 6 × 2, C. (2 × 6) + (2 × 0) = 2 × (6 + 0), D (2 × 6) × 0 = 2 × (6 × 0)

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay.

The logarithmic function [tex]\bold{y=log_ax}[/tex] is defined to be equivalent to the exponential equation x = ay.

Real life example:

Some examples of this include sound (decibel measures), earthquakes (Richter scale), the brightness of stars, and chemistry (pH balance, a measure of acidity and alkalinity)

Three of the most common applications of exponential and logarithmic functions have to do with interest earned on an investment, population growth, and carbon dating.

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Answer:

27

Step-by-step explanation:

Make a tree-diagram for all three-letter code words starting with A. Each path from the top to the bottom contains 3 letters, which is one of the code words beginning with A. There are 9 such code words. Clearly, there are 9 code words starting with B and 9 starting with C. In all, there are 27 code words.

Answer:

Option. B) 2x² = 3x

Step-by-step explanation:

Susan wants to make 2 square flags to sell at a craft fair.

She wants to buy a fabric of 3 meters wide. She doesn't want any fabric left over.

It means area of fabric purchased should be same as area of the flags.

Since x = length of one side of the flag

So area of one flag = x² meter²

Area of 2 flags = 2x² meter²

Area of the fabric = length × width

Area of fabric = x.3 = 3x

Now as per question both the areas should be same

2x² = 3x

Option B. is the correct option.

Final answer:

The length of the arc of a circle with a radius of 3 and a central angle of 340 degrees is 17π. This is calculated by converting the angle to radians and finding the proportion of this angle to the full circle's circumference (2πr).

Explanation:

To find the length of the arc of a circle with a radius of 3 and a central angle of 340 degrees, we first need to understand that arc length (Δs) is proportional to the central angle when measured in radians. The circumference (Δ4) of a circle is given by the formula Δ = 2πr. Since there are 360 degrees in a complete circle, which corresponds to 2π radians, we can set up a proportion to solve for the arc length of the 340-degree angle.

The proportion will look like this:

Convert the central angle from degrees to radians by multiplying it by π/180.

340 degrees * π/180 = 340π/180 radians.

Use the ratio of the angle in radians to the entire circle in radians (2π) to find the arc length: Δs = (Angle in radians/2π) * Circumference.

Δs = (340π/180) / (2π) * 2π * 3.

Simplify to find the arc length Δs.

The final step yields the arc length for the given central angle and radius:

Δs = (340/360) * 2π * 3 = (17/18) * 2π * 3.

Therefore, the length of the arc is Δs = 17π.

(x + f) + 2 = j    subtract 2 from both sides

x + f = j - 2       subtract f from both sides

x = j - f - 2

Answer:

B.3287

Step-by-step explanation:

We are given that

b(x) varies directly with x.

b(x)=4325 when x=25

We have to find the value of b(x) when x=19

According to question

[tex]b(x)\propto x[/tex]

[tex]b(x)=kx[/tex]

Where k=Proportionality constant

Substitute the values then we get

[tex]4325=k(25)[/tex]

[tex]k=\frac{4325}{25}=173[/tex]

[tex]k=173[/tex]

Now, substitute the value of k then, we get

[tex]b(x)=173 x[/tex]

Substitute the value of x=19

Then, we get

[tex]b(x)=173 \times 19=3287[/tex]

Hence, option B is true.