The number of people waiting in a line to buy tickets x minutes after a ticket booth opened is given by the expression 70 − 5x.

What does the value 70 represent?

A. the number of people in the line when the ticket booth opened

B. the number of people who bought tickets every minute

C. the number of minutes it takes to sell all the tickets

D. the total number of tickets available

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

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

x = j - f - 2

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 prime factorization of 19 is 19, as it is a prime number and can only be divided by 1 and itself.

To determine the prime factorization of a number, we identify all the prime numbers that multiply together to give the original number. In the case of 19, we need to check if it can be divided by any primes (like 2, 3, 5, 7, 11, 13, 17).

After testing, we find that 19 is only divisible by 1 and itself, making it a prime number. Therefore, the prime factorization of 19 is simply 19.

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).

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.

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.

associative means that you can move the parenthesis around the problem and still get the same answer. like (4+2)+3=4+(2+3)
first & sixth are the true

Basic number properties:

For the expression 6 + (x + 5):

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.

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 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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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)

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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