7 + z < 3

Can someone help me solve this inequality please?

Answer:

Option 1 : x=4

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.

Learn more about elimination method here

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The horizontal distance between Point C (10, 3) and Point D (4, 3) is calculated by subtracting the smaller x-coordinate from the larger one. The result is 6 units.

The question is asking for the horizontal distance between two points on a coordinate plane, Point C (10, 3) and Point D (4, 3). In this context, the horizontal distance is the distance along the x-axis of the coordinate plane.

The x-coordinate of Point C is 10 and the x-coordinate of Point D is 4. To find the horizontal distance, we simply subtract the smaller x-coordinate from the larger one:

10 - 4 = 6

Therefore, the horizontal distance between Point C and Point D is 6 units.

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In a coordinate plane, when two points share the same y-coordinate, the horizontal distance between them is the difference in their x-coordinates. For Point C(10, 3) and Point D(4, 3), the horizontal distance is 6 units.

The question you are asking relates to the concept of distance in a coordinate plane. In particular, you are looking at the horizontal distance between two points that share the same y-coordinate.

When the y-coordinates are the same, the horizontal distance between the two points is simply the difference in their x-values. So, if you have Point C located at (10, 3) and Point D at (4, 3), you can calculate the distance between them by subtracting the x-coordinate of Point D from the x-coordinate of Point C.

Therefore, the horizontal distance between Point C and Point D is 6 units.

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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: 287

Step-by-step explanation:

Given : A store owner bought a large box of 5135 paper clips

He wants to repackage the paper clips into 18 smaller boxes each box that contain the same amount of paper clips .

Then by using the division operation ,  the number of clips should the store owner put into each the box :-

[tex]5135\div18=285.277777778\approx285[/tex]  [Rounded to the nearest whole number.]

∴ The store owner should put 287 paper clips into each the box.

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 '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.

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.

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.

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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.

The expression (20-6)÷2 already equals 7, as applying the order of operations inside the parentheses followed by the division gives the correct result. The second expression, 20-(6÷2), cannot be altered with parentheses to equal 7; it currently equals 17 without any additional changes.

The question involves understanding how parentheses alter the order of operations in arithmetic expressions. We are asked to determine where to place the parentheses in two different expressions to make them equivalent to 7. Let's evaluate both provided expressions:

The first expression, with parentheses around (20-6), results in the value 7 after performing the operations inside the parentheses followed by the division. Therefore, (20−6)÷2 is already equivalent to 7 and does not require any additional parentheses. The second expression, 20−(6÷2), without modifying its current state with the given parentheses, results in 17 and not 7. Hence, we cannot make this expression equivalent to 7 by altering or moving the parentheses.

Answer:

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

Step-by-step explanation: