If the first equation is multiplied by 3 and then the equations are added, the result is _____.

3x + y = 3
x - 3y = -2

10x = 11
10x = 7
8x = 7

The answer is: [tex]\( 28x^2 - 23x - 15 \)[/tex]

To multiply the expression  (7x+3)(4x-5)  we apply the distributive property, also known as the FOIL method for binomials.

This involves multiplying each term in the first binomial by each term in the second binomial and then combining like terms.

Here's the step-by-step process:

 1. Multiply the first terms: [tex]\( (7x) \cdot (4x) = 28x^2 \)[/tex]

2. Multiply the outer terms: [tex]\( (7x) \cdot (-5) = -35x \)[/tex]

3. Multiply the inner terms: [tex]\( (3) \cdot (4x) = 12x \)[/tex]

4. Multiply the last terms: [tex]\( (3) \cdot (-5) = -15 \)[/tex]

Now, combine the like terms:

[tex]\( 28x^2 - 35x + 12x - 15 \)[/tex]

Therefore, the correct final expanded form of the expression is:

[tex]\( 28x^2 - 23x - 15 \)[/tex]

The measure of the exterior angle of the circle ∠ABC = 55°

In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.

The formula for Area of a sector is given as;

A = θ/360 x πr²

where;

θ is the central angle of the sector

r is radius

Given data ,

Let the measure of the arc be represented as A = 235°

So , the difference of the measures of arc = 235 - 125°

Now , the measure of the external angle ∠ABC = ( 235 - 125 ) / 2

So , the external angle ∠ABC = 55°

Hence , the measure of angle ∠ABC = 55°

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Answer:

The upper quartile median value is 40. Therefore second option is correct.

Step-by-step explanation:

Stem is first digit of a number and leaf is last digit of a number.

Stem 1 leaf 4 can be written as 14.

From the given table, the observations can be written as

[tex]16,18,23,25,26,34,37,37,40,41,46[/tex]

Total number of observations is 11, which is an odd number.

[tex]median=\frac{n+1}{2}\text{th term}[/tex]

[tex]median=\frac{11+1}{2}\text{th term}=6\text{th term}[/tex]

Therefore median is 34.

We have 5 terms before 34 and 5 terms after 34.

[tex]Q_1=\frac{n+1}{4}\text{th term}=3\text{th term}[/tex]

[tex]Q_1=23[/tex]

[tex]Q_3=\frac{3(n+1)}{4}\text{th term}=9\text{th term}[/tex]

[tex]Q_3=40[/tex]

Q₃ is also known as upper quartile median value. Therefore second option is correct.

The value that shows the extraneous solution to the logarithmic equation below is x = -4

Given the logarithmic function expressed as:

log3(18x^3)-log3(2x)=log3(144)

This can also be written as:

log3(18x^3/2x)  = log3(144)
log3 (9x^2) -= log3 (144)

Cancel out the log function to have:

9x^2 = 144

Divide both sides by 9

x^2 = 144/9
x^2 = 16

x = ±4

Hence the value that shows the extraneous solution to the logarithmic equation below is x = -4

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Hello, I hope this will help you out!

The ratio of oranges to apples is 10/3! Hope that helped!

Answer:

Given condition: A grocery store display has 60 oranges and 18 apples.

Then,

Number of oranges = 60 and

Number of apples = 18.

Then, we use ratios to make comparisons between two things.

When we express a ratios in words we use the word ''to'' then we say that the ratio of something to something else.

Ratio of oranges to apples = [tex]\frac{Number of oranges}{Number of apples}[/tex]

then,

Ratio of oranges to apples =[tex]\frac{60}{18}[/tex]

Divide numerator and denominator by 6, we get

Ratio of oranges to apples =[tex]\frac{10}{3}[/tex] which is in the simplest fractional form.

Final answer:

A rational number is a number that can be written as a ratio of two integers, with the denominator not equal to zero.

Explanation:

The definition of a rational number is a number that can be written as a ratio of two integers, where the numerator and the denominator are both integers and the denominator is not zero. For example, fractions such as 2/3, where both 2 and 3 are integers, represent rational numbers. This is different from irrational numbers like √2 or transcendental numbers like π, which cannot be expressed as a ratio of two integers.

Furthermore, while all integers are themselves rational numbers (since any integer 'a' can be written as 'a/1'), not all rational numbers are integers, particularly when the numerator is not a multiple of the denominator.

To rewrite the rational expression x^3+5x^2+3x-10/x+4 in the form q(x) + r(x)/b(x), we can use polynomial division.

To rewrite the rational expression x^3+5x^2+3x-10/x+4 in the form q(x) + r(x)/b(x), we can use polynomial division. Here are the steps:

Therefore, the rational expression x^3+5x^2+3x-10/x+4 can be rewritten as q(x) + r(x)/b(x), where:

The average rate of change from x = 0 to x = 2 for the parabola described in the question is -4. Hence the correct option is 1.

The average rate of change of a function between two points is calculated by subtracting the y-values (function outputs) and dividing by the difference in x-values (inputs). In this case, to find the average rate of change of the parabola from x = 0 to x = 2, we use the points (0, 3) and (2, -5).

The average rate of change = (y2 - y1) / (x2 - x1)

Substitute in the given points: ( -5 - 3 ) / ( 2 - 0 )

Simplify the expression: -8 / 2 = -4

To solve the word problem, we set up and solved an algebraic equation. Maggie's original number is approximately 4.31 after converting the written problem into the equation 3x - 8 + 10x = 48 and solving for 'x'.

The goal is to translate the word problem into an algebraic equation and solve for the unknown number. If Maggie is thinking of a number, let's use 'x' to represent this unknown number. According to the problem, she multiplies the number by 3, subtracts 8, and then adds 2 times the original number 5 times. The result of these operations is 48. Here's how you set up the equation:

3x - 8 + 10x = 48

The next step is to combine like terms:

13x - 8 = 48

Now we add 8 to both sides of the equation:

13x = 56

The last step is to divide both sides by 13 to solve for x:

x = 56 / 13

x = 4.3077 or approximately 4.31 if rounded to two decimal places.

Therefore, Maggie's number is approximately 4.31.

Answer:

D

Step-by-step explanation:

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its b i done the test