Which graph shows the system of equations 4 x + y = 3 and 2 x minus 3 y = 3?

A. In the given function, f(x) = x^2 + 3x - 10, the area of the rectangle is represented. However, the function does not directly provide the length and width of the rectangle.

To determine the length and width, we need to factorize the quadratic equation.

By factoring the quadratic equation x^2 + 3x - 10 = 0, we can find its roots or x-intercepts, which will give us the values for x at which the area is equal to zero. Let's factorize it as follows:

(x + 5)(x - 2) = 0

From this factorization, we can see that the roots of the equation are x = -5 and x = 2. These roots represent the values of x at which the area of the rectangle is equal to zero.

B. The reasonable domain for the solution depends on the context of the problem. Since we are dealing with the area of a rectangle, the length and width cannot be negative values. Therefore, the domain for this problem is x ≥ 0, as negative values are not practical for dimensions.

As for the range, the function f(x) = x^2 + 3x - 10 represents the area, which can take any positive value or zero. Hence, the range for the solution is y ≥ 0.

To summarize, the reasonable domain for the solution is x ≥ 0, representing non-negative values for the variable x, while the range is y ≥ 0, indicating non-negative values for the area of the rectangle.

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Answer:

He needs about 12.5 gallons with 0.5 left over.

Step-by-step explanation:

Answer:

answer would be C.

Step-by-step explanation:

x²+2xy+y²=(x+y)²

(x²+2xy+y²)(x+1)=(x+y)²(x+1)

Answer:

No

Step-by-step explanation:

11-(-5)=16

-5+(11)=6

The truth value of the given proposition is "false".

The truth value of the given proposition can be evaluated using the following steps:

Convert the binary representation of the numbers to decimal:

0 = 0

~1 = -1 (invert the bits of 1 to get -2 in two's complement representation and add 1)

10 = 2

Apply the comparison operator "=" between the left and right sides of the equation:

(0 = -1) = 2

Evaluate the left side of the equation, which is false, because 0 is not equal to -1.

Evaluate the right side of the equation, which is true, because 2 is a nonzero value.

Apply the comparison operator "=" between the results of step 3 and step 4, which yields:

false = true

Therefore, the truth value of the given proposition is "false".

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The ratio test is a powerful test used to determine whether a series converges or diverges. It compares the terms of a series to the terms of the same series offset by one position to the right.

When using the ratio test, the criteria for divergence of a series is when the limit is greater than 1.

Option (e) when the limit is greater than 1 is the correct criteria for the divergence of a series when using the ratio test.

If the limit of the ratio is greater than 1, the series is divergent. If the limit of the ratio is less than 1, the series is convergent.

If the limit of the ratio is equal to 1, the test fails and another test must be used.

The ratio test can be used to test the convergence or divergence of infinite series.

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Answer:

Step-by-step explanation:

are the what???

Answer: \(78^{\circ}, 102^{\circ}\)

Step-by-step explanation:

Given

An angle measure \(24^{\circ}\) more than its supplementary angle

Let the first angle be \(x\)

So, another angle is \(x+24^{\circ}\)

Also, the sum of the supplementary angles is \(180^{\circ}\)

\(\therefore x+x+24^{\circ}=180^{\circ}\\\Rightarrow 2x=180^{\circ}-24^{\circ}\\\Rightarrow 2x=156^{\circ}\\\Rightarrow x=78^{\circ}\)

So, the angles are \(78^{\circ}, 102^{\circ}\)

Answer: x-6, x+3, x-3

Step-by-step explanation;

Split the equation into two.

x2(x-6)-9(x-6)

(x-6) is seen as one of the tiles. Now work on x2-9

x2-9 is a difference of squares meaning the last two are (x+3) and (x-3).

The median number of newspapers sold over seven weeks is 223.

The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.

The formula for the median is as follows:

Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)

We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288

The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.

Median = (215 + 231)/2

= 446/2

= 223

In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.

Hence, the median number of newspapers sold over seven weeks is 223.

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Answer:

4-21x

Step-by-step explanation:

Answers R

Step-by-step explanation:

Answer:

n=2

Step-by-step explanation:

5n+4/2 = 7

5n+4=14

5n=10

n=2

:)

The elevation represents a distance from the sea level greater than 5 feet, because the original description specifies a distance greater than 5 feet below sea level.

Physical quantities like mass and electric charge are examples of scalar quantities because they only have magnitudes. In contrast, a vector quantity is a physical quantity like force or weight that has both magnitudes and directions.

The elevation is the height or distance above sea level and is expressed as a distance.

Given that it contains both magnitude (distance) and direction, elevation in the previous description is a vector (above sea level).

Distance is a scalar quantity with only one magnitude that describes the area travelled by a moving object.

A height of less than 5 feet denotes a location that is less than 5 feet above sea level, which is equivalent to a location that is more than 5 feet below sea level.

Greater than 5 feet below sea level = less than -5 feet above sea level, therefore;

A distance from (below) sea level of more than 5 feet is represented by an elevation of less than -5 feet.

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Answer:

A half-filled container will weight 160 oz

Step-by-step explanation:

Weight of container with fruit punch = 275 oz

weight of container excluding fruit punch = 45 oz

Weight of fruit punch = Weight of container with fruit punch - weight of container excluding fruit punch   =  275 oz -  45 oz  =  230 oz

Thus, when container is full, it contains 230 oz.

When container will be half full, it will contain half of 230 oz

half of 230 oz = 1/2 * 230 oz = 115 oz

Thus,

a half-filled container will weight = weight of container + half of the capacity of container(115 oz) = (45 + 115) oz = 160 oz.

Thus,  a half-filled container will weight 160 oz.

The value of x in the given isosceles triangle, is √55 units.

A triangle with two sides equal is called an isosceles triangle.

Given that, an isosceles triangle, with base 6 units and legs 8 units, we need to find the length of the altitude x,

Since, ABC is an isosceles triangle, therefore, BD = DC = 6/2 = 3 units

Using the Pythagoras theorem,

AC² = DC² + AD²

8² = 3² + AD²

AD² = 64-9

AD² = 55

AD = √55

Hence, the value of x in the given isosceles triangle, is √55 units.

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Answer:

refer to the pic attached for steps

6 students are in Janelle's group.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

3x + 5 = 23

now, solving for x

3x = 23 - 5

3x = 18

x= 18/ 3

x= 6

Hence, 6 students are in Janelle's group.

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Answer:

the product of 4 and a number decreased by 7

Step-by-step explanation:

A null hypothesis is a particular kind of statistical hypothesis that asserts that no statistical significance can be found in a given set of observations.

A null hypothesis is a particular kind of statistical hypothesis that asserts that no statistical significance can be found in a given set of observations. The use of sample data in hypothesis testing allows one to judge a hypothesis' veracity.

The null hypothesis states that the estimate is only based on chance. If the observed data (in the sample) do not differ from what would be predicted solely by chance, then the null hypothesis is true. The alternative hypothesis is what the null hypothesis has as its counterpart.

Two population parameters, such as an independent variable and a dependent variable, are said to be unrelated under the null hypothesis. It's possible that an experimental or sampling error caused the result if the hypothesis indicates a relationship between the two parameters.

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Laplace transforms are an essential mathematical tool used to solve differential equations. These transforms transform differential equations to algebraic equations that can be solved easily.

To solve the differential equations given in the question, we will use Laplace transforms. So let's start:Solution:a) y" – y = t y(0) = 1, y'(0) = 1First, we take the Laplace transform of the given differential equation.L{y" - y} = L{ty}

Taking the Laplace transform of both sides gives:L{y"} - L{y} = L{ty}Using the formula, L{y"} = s²Y(s) - s*y(0) - y'(0), and L{y} = Y(s) then we get:s²Y(s) - s - 1 = (1/s²) + (1/s³)Rearranging the above equation, we get:Y(s) = [1/(s²*(s² + 1))] + [1/(s³*(s² + 1))]Now, we apply the inverse Laplace transform to find the solution.y(t) = (t/2)sin(t) + (cos(t)/2)

The solution of the differential equation y" – y = t, with initial conditions y(0) = 1, y'(0) = 1 is y(t) = (t/2)sin(t) + (cos(t)/2).

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The type of variable for,

a. The number of counties in California: Quantitative discrete.

b. The stages of childhood: Qualitative ordinal.

c. In the scenario above, 23 minutes is a statistic, because 28 students is a sample.

d. Between 6 minutes and 8 minutes: Approximately 68% of the athlete's mile times are expected to be between 6 and 8 minutes, according to the empirical rule.

e. Between 4 minutes and 7 minutes: Approximately 68% of the athlete's mile times are expected to be between 4 and 10 minutes, according to the empirical rule.

f. Less than 9 minutes: Approximately 84% of the athlete's mile times are expected to be less than 9 minutes, according to the empirical rule.

In statistics, variables can be categorized into two types: qualitative and quantitative.

Qualitative variables describe characteristics or qualities that cannot be measured numerically, such as gender or hair color.

Quantitative variables, on the other hand, represent numerical values that can be measured or counted.

There are two types of quantitative variables: continuous and discrete. Continuous variables can take any numerical value within a range, such as age or weight.

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There are 720 possible dinner specials.

To calculate the number of dinner specials, we need to multiply the number of options for each course.

The number of dinner specials is the product of the number of options for each course:

So,

3 x 3 x 4 x 5 x 4 = 720 possibilities

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Answer:

£ 4.20

Step-by-step explanation:

1 kg= £1.20

3.5 kg = £1.20*3.5

=£ 4.20

The cost of the apples being weighed on the scales would be £ 4.20

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

We are given that Apples are sold in a supermarket at £1.20 per gram.

Therefore, we know that

1 kg= £1.20

For 3.5 kg

= £1.20 x 3.5

=£ 4.20

The cost of the apples is £ 4.20

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Answer: 0.9 divided by 18 is 0.05.

Step-by-step explanation:

Answer:

D: (4, 6)

Step-by-step explanation:

undefined slope is when the line is vertical

so we are given a point (4, -1)

the best point that will make the slope undefined is D because it will make a vertical slope

The property of the triangle congruence state that a ≅ B then B ≅ A are:

The triangle is a polygon that has 3 edge and vertices. Triangle is one of the basic shape in the geometric. The area of the triangle is formulated as base of the triangle * height of triangle x 0,5. The value of three triangle edge degree is 180°.

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Answer:

Step-by-step explanation:

Find the geometric mean of 16 and 36. Write your answer in the simplest form.

Any obvious wrong answers will be reported.

The number of full test tubes Russel fill with water must be discrete number and not rational. 36 test tubes is the answer.

Volume of a cylinder can be known either by the use of formula (V = πr²h) or by measuring with the volume of a known liquid.

Given that Russel is doing an experiment for a science fair project. He fills a beaker with water three times. He puts 16.5 milliliters of water in each test tube. How many full test tubes can Russel fill with water?

1. Describe one way to estimate the solution to this problem.

By dividing the amount of milliliters of water in the baker by 16.5 ml

2. Russel calculates correctly and says the answer to the problem is 36.36 test tubes. Is Russel's answer reasonable?

No! The reason is based on the fact that the answer must be a whole number and not a decimal number since the question centered on number of full test tubes filled with water.

Therefore, the correct answer should be 36 test tubes.

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The table has a greater rate of change.

The rates of change are equal.

In the given problem, we have a table showing the relationship between x and y values. By comparing the change in y with the change in x, we can determine the rate of change. Looking at the table, we observe that for every increase of 1 in x, there is a corresponding increase of 1 in y. Therefore, the rate of change for this table is 1.

The slopes are equal.

The equation has a greater slope.

In problem 2, we are given a linear equation in the form y = mx + b, where m represents the slope. The given equation is y = 2x + 7, which means the slope is 2. To compare the rates of change, we compare the slopes. If the slopes are equal, the rates of change are equal. In this case, the slopes are equal to 2, so the rates of change are the same.

The function rule has a greater slope.

The slopes are equal.

In problem 3, we are told that as x increases by 1, y increases by 3. This information gives us the rate of change between x and y. The slope of a function represents the rate of change, and in this case, the slope is 3. Comparing the slopes, we find that they are equal, as both have a value of 3. Therefore, the rates of change are the same.

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