How do you solve an inequality step by step?.

The ordered pair that makes both inequalities true is (-2,2)

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

All you have to do is substitute each choice into the equation.

(X,Y) is the format, now plug the numbers that's in that order into both the equations to see if it's true

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Question:

Which ordered pair makes both inequalities true? y < –x + 1 and y > x?

A.-3,5

B.-2,2

C.-1,-3

D.0,-1

The greatest possible area for the garden is  135200 ft^2 with a shorter side at 260 ft and a longer side at 520 ft

Let L be the length and W be the width of the garden.

So,  L + 2W = 1040

Area = A

= LW

=(1040 - 2W)W

= 1040W - 2W^2

To maximize the area:

take the derivative of A and set = 0

That is:

A' = 1040 - 4W = 0

4W = 1040

W = 1040/4

= 260

And L = 1040 - 2W

= 1040 - 520

= 520

So,

shorter side =260 ft

longer side =520 ft

Computing the greatest possible are using the length of the shorter and the longer side we get:

greatest possible area: =LW=(260)(520)=135200 ft2

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According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal  to the other triangle.

ASA (angle, side, angle) ASA, which translates for "angle, side, angle," denotes the existence of two triangles whose included side and two known angles are equal.

Thus, when two angles with the included side with one triangle are equal to two angles the included side of another triangle, two triangles are said to be congruent.

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Answer:

The simplest ratio of squares to triangles would be: 1 to 5, 1:5, or 1/5.

Either one works, they mean the same thing.

Step-by-step explanation:

In order to find out the simplest form, see how you can divide the numbers with the highest number and the numbers coming out as low as they can. In this case the number to divide the numbers we already have would be 3:

3 divided by 3 = 1

15 divided by 3 = 5

That's why we end up with 1:5.

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Anthony's expected earning would be $175 in a day when he waits in 20 tables.

According to the question,

We have the following information:

Each day Anthony works, Anthony will make a guaranteed wage of $35, however the additional amount that Anthony earns from tips depends on the number of tables he waits on that day. From past experience, Anthony noticed that he will get about $7 in tips for each table he waits on.

Now, for waiting on 20 tables, he will get the fixed amount of 35 dollars and the amount for 20 tables.

So, the total amount will be:

35+7*20

35+140

$175

Hence, Anthony would expect to earn $175 in a day when he waits in 20 tables.

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[tex]\huge \boxed{\sf 8+4\sqrt{5} }\\\\\\\sf Using\ the\ distance\ formula \\\\\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

[tex]\sf A(0,4)\ and\ B(2,0)\\\\d = \sqrt{(2 - 0)^2 + (0-4)^2}=2\sqrt{5} \\\\B(2,0)\ and\ C(2,-2)\\\\d = \sqrt{(2 - 2)^2 + (-2-0)^2}=2 \\\\C(2,-2)\ and\ D(0,-2)\\\\d = \sqrt{(0 - 2)^2 + (-2-(-2))^2}=2 \\\\D(0,-2)\ and\ E(-2,2)\\\\d = \sqrt{(-2 - 0)^2 + (2-(-2))^2}=2\sqrt{5} \\\\E(-2,2)\ and\ F(-2,4)\\\\d = \sqrt{(-2 - (-2))^2 + (4-2)^2}=2\\\\F(-2,4)\ and\ A(0,4)\\\\ d=\sqrt{(0-(-2))^2+(4-4)^2} =2[/tex]

[tex]\sf Adding\ all\ the\ distances \\\\2\sqrt{5} +2+2+2\sqrt{5}+2+2 =8+4\sqrt{5} =16.94427190...[/tex]

Answer:

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Four of the segments are horizontal or vertical with the length of 2 units:

Two of the segments have same length (parallel segments) with 4 units vertical and 2 units horizontal difference of coordinates:

The perimeter is:

The correct equivalent expression is 6x - 24.

Calculating the equivalent expression in this question is a one step process and requires multiplication. We will simply multiply the values in bracket with number outside the bracket. In the process, ensure copying the correct sign while writing the result.

Rewriting the expression 6(x - 4)

Equivalent expression = 6×x - 6×4

Performing multiplication on Right Hand Side of the equation

Equivalent expression = 6x - 24

Thus, the desired equivalent expression is 6x - 24.

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The complete question is -

Which expression is equivalent to 6(x-4)? 6x + 4 6x - 4 0 6x-24 0 46x + 24

The slope of a ki run that rise 5 feet for every horizontal change of 12 feet. The horizontal change of 12 feet is 2.0833.

The The slope of a line is "upward thrust over run". That could be 6/30 on this case. That may be simplified to 1/5 (via way of means of dividing each numbers via way of means of 6).That makes the slope 1/5 (or 0.2 as a decimal.

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The correct option is b which tells that an optimal solution to a linear programming problem must lie at the intersection of at least two constraints.

Linear programming is an optimization technique that is fine for the purpose of getting the best solution such as maximizing profit or certain 4th-era quantities.

When there are just two choice variables, the graphic method of solving a linear programming issue can be employed.

It is fine by modelling real-life problems into mathematical models that have linear relationships or constraints such as in the form of objective functions.

In linear programming, an objective function defines the formula for quantity optimization and the goal from this is to determine variable values that maximize or minimize the objective function depending on the problem robbery solved.

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Answer:117,649

Step-by-step explanation:

Answer:

the degree of f(x) is at least 4

Step-by-step explanation:

Answer:

one pen costs 0.5 euros

one rubber costs 0.75 euros

Step-by-step explanation:

4p+5r=5.75

p+4r=3.5

  -4r.   -4r

p=3.5-4r

4(3.5-4r)+5r=5.75

14-16r+5r=5.75

14-11r=5.75

-14.     -14

-11r=-8.25

r=0.75

One rubber cost 0.75 euros

Now to find cost of one pen we just fill in what we know

p+4(0.75)=3.5

p+3=3.5

 -3.  -3

p=0.5

1 pen cost 0.5 euros

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Step-by-step explanation:

Hello, I need the function in order to give you a exact answer.

90% confidence interval would be less than a 95% confidence interval.

Given,

A random sample has been taken from a population. A statistician, using this sample, needs to decide whether to construct a 90 percent confidence interval for the population mean or a 95 percent confidence interval for the population mean;

We have to find the difference between the intervals;

Here,

Confidence intervals are a range that depict the accuracy of the measurement. If a statistician chooses to use a 90% C I instead of a 95% C I, it informs you that you have a 10% probability of being incorrect as opposed to a 5% possibility when using the 95%.

That is, a 90% confidence interval would be less than a 95% confidence interval.

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If the width of a rectangle is 8t-5.5 feet and the length is 5.5t + 7 feet. The perimeter of the rectangle will be 27t+3

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is given that, The width of a rectangle is 8t-5.5 feet and the length is 5.5t + 7 feet.

We have to find find the perimeter of the rectangle.

The perimeter of a rectangle is two times the sum of the length and breadth as,

P = 2(l+w)

P=2(8t-5.5+5.5t + 7)

P=2(13.5t+1.5)

P=27t+3

Suppose the value of t is 1, the perimeter of the rectangle is found as,

P=27×1+3

P=30

Thus, if the width of a rectangle is 8t-5.5 feet and the length is 5.5t + 7 feet. The perimeter of the rectangle will be 27t+3

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The year in which only 38,000 items of clothing will be donated to the homeless shelters in new york city. is 2020, using the concept of linear equation.

The above problem is related to a linear equation, A linear equation is a condition in which the highest power of the variable is always 1. It is additionally known as a one-degree equation. The standard form of a linear condition in one variable is of the form Ax + B =0 .from the given graph we can  come  up with the equation which bests fits for x to be the number of the year from 1992 and y  to be the number of clothes donated in thousands, which is  y=-0.375x+48.5

now for the given situation:

-0.375x+48.5 = 38

=>-0.375x= 38-48.5

=-0.375x = -10.5

=>x = -10.5/ 0.375 = 28

so it is 2020

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the complete question attached herewith.

The Central angle and the radius are not the same.

What is the Radius of a circle?

Any circular object's radius is the measurement from the center to its outermost border or boundary. A radius is a dimension that applies to spheres, semispheres, cones with circular bases, and cylinders with circular bases in addition to circles.

It is possible to define a circle as the locus of a point moving in a plane while maintaining a constant distance from a fixed point. The radius of a circle is the distance from any point on the circle to its center. The fixed point is referred to as the center of the circle.

So, According to the question:

The angle formed by any two-circle radii is known as the central angle. The arc length, or the distance between the two places where the two radii cross the circumference, and the radius length must be determined in order to determine the central angle.

Hence,

The Central angle and the radius are not the same.

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The solution to the equation is x = 2/3.

The number of times a number is multiplied by itself is referred to as an exponent.

The given equation is (1/2)ˣ ⁻ ¹ = 2³ˣ ⁻ ⁴.

Solve the equation as follows:

(1/2)ˣ ⁻ ¹ = 2³ˣ ⁻ ⁴

Recall that xᵃ = (1/x)⁻ᵃ, therefore,

2ˣ⁻¹ = 2³ˣ ⁻ ⁴

Since the base of the exponents is the same, it follows:

x - 1 = 3x - 4

3x - x = -1 + 4

2x = 3

x = 2/3

Hence, the solution to the equation is x = 2/3.

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Reponse Rate , is the indicator which is used for review the researcher's overall quality of a data collection efforts .

Reponse Rate:

It provides valuable insight into the accuracy of the data collected. Simply put, the response rate is the number of people who completed the survey divided by the number of people who make up the entire sample group.

It is important to note that response rates can only be calculated for defined sample groups.

Example:

We have a survey with the following stats:

Message sent: 1000

Number of respondents surveyed: 250

Number of surveys completed: 300

Let's calculate the response rate .

response rate = number of surveys completed / number of emails sent

response rate = 30%.

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The maximum number of functions that can be defined from the power set of A, P(A), to the power set of B, P(B) is 4096.

The Collection of well-defined objects or elements is known as a set. The objects in a set are called elements. The Set contains a finite number of elements. The Set is denoted by any capital letter like A, B etc. Elements of the set can be numbers, alphabets etc.

The elements of the set are listed inside the curly brackets { ..... }. There are various types of sets. The set of all subsets of the set X is called a Power set including the null set, empty set and the set itself. Cardinal number or cardinality denotes the number of elements in the set. Cardinality is denoted by n( X ) where X is a set. The number of subsets of the set is given by 2^n.

As per the question,

⇒  n ( A )   =   3 elements

Number of subsets of A   =   2³

                                          =   8 subsets

⇒   n ( B )   =   2 elements

Number of subsets of B   =   2²

                                          =   4 subsets

By using the product rule,

Total number of functions from P ( B ) to P ( A )   =   8 × 8 × 8 × 8

                                                                                =   4096

Therefore, 4096 is the maximum number of functions that can be defined from the power set of A, P(A) to the power set of B.

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Answer:

Step-by-step explanation:

did you watch the video-

A root of a transformed equation that is not the root of the original equation because it was excluded from the original equation's domain is known as an extraneous solution.

What are extraneous solutions?

A "false" solution to an equation is known as an extraneous solution. Even if we appeared to follow sound procedures when solving the equation, an extraneous solution did not fulfill the original equation.

So,

When we solve an equation, an extraneous solution is a result that does not fulfill the equation. As an illustration, if we square both sides of the equation x = -1, we obtain the value x = 1, which does not satisfy the original equation, indicating that x = 1 is an extraneous solution.

when we wanted to solve the equation √x = -1.  After squaring both sides, we get a value of x = 1.

When we substitute x = 1 into the original equation, we get:

x = -1  [original equation]

√1 = -1  [substitute x = 1]

1 = -1  [this is not true]

Hence,

This equation is called an extraneous solution.

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Answer:

y=x-10

Step-by-step explanation:

y=ax+b - linear equation

y=-x+7

a=-1

y=cx+d - perpendicular equation to y=ax+b

a*c=-1

(-1)*c=-1

c=1

y=x+d

(4,-6) => x=4, y=-6

y=x+d => -6=4+d

d=-10

y=x-10

There are 35 students that have only dogs

What is subset?

If every element of set A is also an element of set B, then set B is a superset of set A and set A is a subset of set B. A and B could be equal; if they are not, then A is a legitimate subset of B. Include refers to the property that one set is a subset of another.

Total students =350

Cats only student = 175

Having both pets student= 140

Students having dog= 350- 175 = 175

Dogs only student = 175 - 140 = 35

So, There are 35 students which have dog only.

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To find the measure of side of triangle using the law of cosines , we use  a² = b² + c² − 2bc·cosA.

The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them.

Let a, b, and c be the lengths of the three sides of a triangle and A, B, and C be the three angles of the triangle. Then, the law of cosine states that:

a² = b² + c² − 2bc·cosA.

The law of cosine is also known as the cosine rule. This law is useful to find the missing information in any triangle.

To find the measure of the side of triangle using the law of cosines :

Let  a and b be the length of two sides of triangle and the angle between them measuring ∅ . So , to find the third side

Using the law of cosines formula,

a² = b² + c² − 2bc·cosA.

=> a² = b² + c² − 2bc·cos ∅

Replace all the values ,You will able to find third side .

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Diana should reject the null hypothesis because the p-value is less than the value α=0.05.

Given that,

Let's say Diana, a researcher in education at a nearby university, wants to assess the effectiveness of a brand-new Spanish course that combines cultural immersion teaching methods with conventional teaching methods. She chooses a simple random sample of 72 freshmen, matches their IQs and high school GPAs, and then divides them into 36 pairs. She chooses one student from each pair at random to enroll in the new course, while the other student in the pair enrolls in the standard course.

We have to find the p-value.

We know that,

Let

t= difference/standard error =(0.11791)/(0.05242)=2.249

From excel: p value =t distance(2.249,36,2)=0.031

Since p value <0.05

Therefore, Diana should reject the null hypothesis because the p-value is less than the value α=0.05.

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The federal government only has powers written in the constitution and the rest or for the states

If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.

How do you know if a number has no solution?

Normally when solving problems you end up with something at the end saying, x= [some number]. When a problem has no solution you'll end up with a statement that's false. For example: 0=1 This is false because we know zero can't equal one. Therefore we can conclude that the problem has no solution.

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The number of students in 2001 is 150.4 thousand and the number of students in 2018 is 467.5 thousand

From the question, we have the following function that can be used in our computation:

y = 123.1(1.069)ˣ

Such that

x = Number of years after 1998

In the year 2001, the value of x is calculated as

x = Current year - 1998

So, we have

x = 2001 - 1998

Evaluate

x = 3

Substitute x = 3 in the equation y = 123.1(1.069)ˣ

y = 123.1(1.069)³

Evaluate

y = 150.4

In the year 2018, the value of x is calculated as

x = Current year - 1998

So, we have

x = 2018 - 1998

Evaluate

x = 20

Substitute x = 20 in the equation y = 123.1(1.069)ˣ

y = 123.1(1.069)²⁰

Evaluate

y = 467.5

Hence, the number of students in 2018 is 467.5

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The two consecutive integers that will make the inequality true are 13 and 14.

inequality, is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

If you check for the square root of 181 [tex]\sqrt{181}[/tex] is 13.453

And the two consecutive integers smaller than 13.45 and greater than 13.45 are 13 and 14 respectively.

In conclusion, the two consecutive integers for the expression are 13 and 14.

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