Susan used 9 5/8 kilowatts of electricity to power her house for 5 1/2 hours. ON average, how many kilowatts did Susan use per hour?

By using elimination method, (11,-12) point is the solution to the system of equations.

"The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables."

Given system of equations

x + 2y = 10...................(1)

3x + 4y = 8.................(2)

By using elimination method, multiply equation (1) with (3).

Equation (1): 3x + 6y = 30..................(3)

Subtract equation (2) from (3)

3x + 6y - (3x + 4y) = 30 - 8

3x +6y - 3x - 4y = 22

2y = 22

y = [tex]\frac{22}{2}[/tex]

y = 11

Substituting y = 11 in equation (1)

x + 2y = 10

⇒ x + 2(11) =10

⇒ x = 10 - 22

⇒ x = -12

Hence, (11,-12) point is the solution to the system of equations.

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Answer:

Amount of granola is more than quantity of cashews

Step-by-step explanation:

Amount of cashews bought by Ally = 1/12 pound

Amount of granola bought by Ally = 5/6 pound

We need to plot the fraction on the number line and also to state which quantity is greater .

First, we will make these fractions equivalent.

[tex]\frac{1}{12}=\frac{1}{12}\\\\\frac{5}{6}=\frac{5\times 2}{6\times 2}=\frac{10}{12}[/tex]

Here, denominator of both the fractions are same.

Numerator of [tex]\frac{1}{12}[/tex] is 1

Numerator of [tex]\frac{10}{12}[/tex] is 10

Since [tex]10> 1[/tex], [tex]\frac{10}{12}>\frac{1}{12}\Rightarrow \frac{5}{6}>\frac{1}{12}[/tex]

So, amount of granola is more than quantity of cashews.

Number Line:

Answer:

Option 1 : x=4

X = number of turkey sandwiches

Y = number of steak sandwiches

X   + Y    = 925 total sandwiches sold

4X + 6Y = 4524 dollars made

-4(X + Y = 925)

-4X + (-4Y) = -3700

 4X +  6Y    = 4524

           2Y    = 824

Y = 412

X + Y = 925

X + 412 = 925

Answer:

4

Step-by-step explanation:

Answer:- D.It is not a function because there are two different y-values for a single x-value.

Explanation:-

From the given graph we can see that there are 2 different values of y i.e. y=-2 and y=4 for single x=4.

Therefore, D is the right answer. The graph is not a function because it is not a function because there are two different y-values for a single x-value.

The graph is not a function because there are two different y-values for a single x-value. Option (d) is correct.

Further explanation:

Given:

The options are as follows,

(a). It is not a function because the points are not connected to each other.

(b). It is not a function because the points are not related by a single equation.

(c). It is not a function because there are two different x-values for a single y-value.

(d). It is not a function because there are two different y-values for a single x-value

Explanation:

The output values of the function are known as range and the input values on which function is defined is known as the domain of the function.

The one-to-one function is a function in which every value of the range has exactly one pre-image in the domain.

One-to-one function always passes the vertical line test and the horizontal line test.

The given graph doesn’t pass the vertical line test.

The given graph has two values for [tex]x=4.[/tex]

The graph is not a function because there are two different y-values for a single x-value. Option (d) is correct.

Option (a) is not correct.

Option (b) is not correct.

Option (c) is not correct.

Option (d) is correct.

Kindly refer to the image attached.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Relation and Function

Keywords: relations, functions, all relation are functions, all functions are relations, no relations are functions, no functions are relation, one-to-one, onto, graph representation, paired, y-value, x-values, origin.

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

At noon, the temperature was = -3 degrees

Temperature reduced by = 2.5 hours per day

Temperature reaches = -18 degrees

Let the number of hours be 'x'.

According to question,

[tex]-3-2.5x=-18\\\\-2.5x=-18+3\\\\-2.5x=-15\\\\x=\dfrac{15}{2.5}=6[/tex]

Hence, it will take 6 hours for the temperature to reach.

Option 'A' is correct.

Final answer:

Solving the equation 3x=9 involves multiplying both sides by the reciprocal of 3, which is 1/3. By doing so, both sides simplify to x=3, thereby providing the solution to the equation.

Explanation:

To solve the equation 3x=9, we can use the principle of multiplying both sides by a reciprocal to isolate the variable. The reciprocal of 3 is 1/3 because 3 multiplied by 1/3 equals 1, which leaves us with the identity property of multiplication (any number multiplied by 1 results in the number itself). Therefore, we can solve the equation as follows:

Multiply both sides of the equation by the reciprocal of 3, which is 1/3: (1/3) * (3x) = (1/3) * 9.

Simplify both sides: (1/3) * 3 = 1 and 1 * x is just x, so we get x on the left side. On the right side, (1/3) * 9 = 3.

You are left with the simplified equation x = 3, which is the solution.

This demonstrates that dividing by a number is the same as multiplying by its reciprocal. In other words, we used a form of inversion on 3x = 9 to find the value of x. By following this method, we've effectively divided both sides of the original equation by 3 to solve for x.

Answer:

Centimeters are smaller than meters, so the number of meters will be less than 8.

Step-by-step explanation:

Answer:

A stenographer will type 80 words.

Step-by-step explanation:

In this question it is given that average typing speed of a stenographer is 100 words per minute and we have to calculate the words a stenographer will type in 4/5 of a minute.

By using unitary method we will calculate the number of words a stenographer will type.

∵ In 1 minute stenographer is typing words = 100

∴ in 4/5 minutes stenographer will type = 100 × (4/5) words

                                                                  = 400/5 = 80 words

So the answer is a stenographer will type 80 words in 4/5 of a minutes.

Three-dimensional objects can grow from both one-dimensional and two-dimensional objects when subjected to thermal expansion, which causes areas and volumes, as well as lengths, to increase with temperature.

A three-dimensional object can grow or expand from two-dimensional objects, such as areas (length and width), as well as from one-dimensional objects, such as lengths. When considering thermal expansion in two and three dimensions, it is important to understand that unconstrained objects expand in all dimensions: their areas (two-dimensional) and volumes (three-dimensional), as well as their lengths (one-dimensional), increase with temperature.

For example, if we have a metal plate (a two-dimensional object) with a circular hole in it and we increase the temperature, the area of the plate including the circular hole will increase (Figure 13.11 (a)). Similarly, if we have a solid metal block (a three-dimensional object), its volume will increase with temperature (Figure 13.11 (c)).

The thermal expansion process is explained by the fact that, as temperature increases, the atoms or molecules making up a material move farther apart, causing expansion. This is true for both holes and solid parts of a material, they both grow larger with increased temperature. Therefore, all one-dimensional, two-dimensional, and three-dimensional aspects of an object expand proportional to the increase in temperature.