If f(x) = –4x + 3 and g(x) = 3x2 + 2x – 4, find (f + g)(x).

A. (f + g)(x) = –2x – 1
B. (f + g)(x) = 3x2 + 6x + 7
C. (f + g)(x) = 3x2 – 2x – 1
D. (f + g)(x) = 4x – 1

Answer:

Perimeter of triangle 1 = p1 = 66

Perimeter of triangle 2 = p2 = 44

Cody started with 54 stamps in his collection. The problem was solved using basic algebra by setting up an equation and working backwards.

The subject of this question is mathematics, specifically dealing with a basic algebra problem that requires working backwards to find the original number of items in a collection. To solve the problem, we can set up an equation to represent the scenario given:

Let's call the original number of stamps 'x'. After selling half of them, Cody would have ½x. When he buys seventeen more stamps, the equation to represent this situation is ½x + 17 = 44. To find the value of 'x', we need to subtract 17 from both sides of the equation, which gives us ½x = 44 - 17 or ½x = 27. To find the full value of x, we multiply both sides of the equation by 2, which gives us x = 27 * 2 or x = 54.

Therefore, Cody started with 54 stamps in his collection.

Final answer:

To estimate the value of 9.9 squared times 1.79, round 9.9 to 10, square it to get 100, and multiply by 1.79 to get an estimate of 179.

Explanation:

The question asks to estimate the value of 9.9 squared times 1.79. To estimate this value, we can round 9.9 to the nearest whole number, which is 10. Then we square 10 to get 100, and multiply this by 1.79.

So, the estimated value would be:

102 × 1.79 = 100 × 1.79 = 179

This estimation approach uses basic arithmetic principles and rounding techniques to simplify the calculation.

Answer:

Answer is C

Step-by-step explanation:

The calorie content of foods that contain 14 grams of fat is about 410.

A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Since they can demonstrate the degree of connection, if any, between the values of observed quantities or events, scatter plots are crucial in statistics (called variables).

A scatter plot is made up of a vertical axis that represents the measurements of the other variable and a horizontal axis that contains the measured values of the independent variable (dependent variable).

We have,

A scatter plot shows the association between the amount of fat and the total amount of calories in a few food items.

From the scatter plot, for 14 grams of fat the calories lies in between 300 and 400.

So, we can conclude from the scatter plot is 340.

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Answer:

[tex]\displaystyle\frac{x^r}{x^s} = x^{r-s}[/tex]

Step-by-step explanation:

The quotient rule of exponential power states that:

[tex]\displaystyle\frac{x^r}{x^s} = x^{r-s}[/tex]

This can be easily understood with the help of an example:[tex]\displaystyle\frac{x^4}{x^2} = \displaystyle\frac{x\times x\times x\times x}{x\times x}  = x^2 = x^{4-2}[/tex]

Basically, this quotient rule helps us to reducing the fractions. Since the numerator and the denominator is same as we have same base, we could simply subtract the powers to get the answer as illustrated in the above example.

When dividing powers with the same base, subtracting exponents simplifies the expression due to the quotient of powers rule is [tex]a^m / a^n = a^{(m - n).[/tex]

When dividing powers with the same base,  subtract the exponents because of the properties of exponents.

The rule is known as the "quotient of powers" rule, and it states that when you divide two powers with the same base,

subtract the exponents to simplify the expression.

The rule can be stated as follows:

[tex]a^m / a^n = a^{(m - n).[/tex]

Here's why this rule works,

Let's say you have a number 'a' raised to two exponents 'm' and 'n':

[tex]a^m[/tex]= a × a × a ×... (m times)

[tex]a^n[/tex] = a × a × a × ... (n times)

Now, to divide these two powers, cancel out the common factors:

[tex]a^m / a^n[/tex] = (a × a × a ×... ... × a) / (a × a × a ×...... × a)

In the numerator and denominator, there are 'm' and 'n' occurrences of 'a', respectively.

Since we are dividing, we can cancel out 'n' occurrences of 'a' from the numerator and denominator:

[tex]a^m / a^n[/tex] = (a × a × a ×... ... × a) / (a × a × a ×...... × a)

          = [tex]a^{(m - n)[/tex]

Therefore, when divide powers with the same base, subtract the exponents to simplify the expression and apply this property of exponents.

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Answer:

The answer is 7/8.

Step-by-step explanation:

If you add 11/16 to 3/16, you'll get 14/16.  14/16 has two numbers that are divisible by 2,  so when you divide 14/16 by 2 you'll get 7/8 which is 14/16 in a simplified form.  7 is prime and you can't divide it down any more, but 8 i'snt the same way.  The rule is, whatever you do to one side, you have to do to the other.  You can divide 8, but not 7; therefore, you cannot simplify the fraction any further.

To add fractions with the same denominator, simply add the numerators together, while keeping the denominator the same.

To add fractions with the same denominator, simply add the numerators together, while keeping the denominator the same. In this case, we have 11/16 + 3/16. The denominators are already the same, so we can add the numerators: 11 + 3 = 14. The fraction 14/16 cannot be simplified further.

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Answer:

Draw a square and shade half of it. Then draw 2 lines to divide the square into 3 equal parts. There will be one shaded piece in each group, and there are 6 pieces total, so the answer is 1

6

of a gallon.

Step-by-step explanation:

Distributive Property

Addition or Subtraction Property of Equality

Multiplication or Division Property of Equality

The calculation that is NOT a relevant way to find the value of 14/20 is given by option a: 0.5 + 0.05.

Let's find the value of 14/20 first:

To find 14/20, divide 14 by 20:

14 ÷ 20 = 0.7

Now, let's check each calculation:

a. 0.5 + 0.05 = 0.55 (Not relevant to finding 14/20)

b. 0.75 - 0.05 = 0.7 (Relevant, as this gives us 14/20)

c. 14 ÷ 20 = 0.7 (Relevant, as this is the correct calculation for 14/20)

d. 14 × 0.05 = 0.7 (Relevant to finding 14/20)

Therefore, the calculation that is NOT a way to find 14/20 is option a: 0.5 + 0.05.

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Answer:

Subtracting  −7n+2 ​​from 2n−1 ​ is 9n - 3.

Step-by-step explanation:

As the expression given in the question be as follow.

−7n+2 and 2n - 1 .

Subtracted −7n+2 from 2n - 1 .

= 2n - 1 - (-7n + 2)

Open the bracket

= 2n - 1 + 7n - 2

Simplify the above

= 9n - 3

Therefore Subtracting  −7n+2 ​​from 2n−1 ​ is 9n - 3.

The prices you can pay per fish can be represented by the inequality 5x ≤ 12. After solving the inequality, the maximum price you can pay per fish is $2.40.

To write the inequality that represents the prices you can pay per fish, let's assume that the price of each goldfish is 'x' dollars. Since you have $12 in total, the inequality can be written as:

5x ≤ 12

To solve this inequality, divide both sides by 5:

x ≤ 2.4

Therefore, you can pay at most $2.40 per fish.

On USATestprep the answer is C) (c-a,-b)

The coordinates of point R' are (-c, b-d).

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

Given that, a translation of trapezoid PQRS (blue) to trapezoid P'Q'R'S' (green).

Translation rules:

When the shape is moved down by k units, then replace y with y - k.

So, the coordinates of point R' are (-c, b-d)

Therefore, the coordinates of point R' are (-c, b-d).

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Answer:

[tex]\dfrac{5}{24}[/tex]

Step-by-step explanation:

There are 24 hours in a day, therefore:

The total hour used for sleeping, studying and travelling=7+6+6=19 hours

Hours used for other things=24-19=5 hours

Therefore, the fraction of the day used for other things=[tex]\dfrac{5}{24}[/tex]