Plz help! I don't understand these problems!


Find the value of x in each case.

Answer:

The answer will be -45/4 or -11 1/4

Step-by-step explanation:

The first thing you will do is convert both numbers into improper fractions. -4 1/2 will be -9/2 and 2 1/2 will be 5/2. Once you do that, you will multiply each fraction and you should get -45/4. Finally, you would convert that into a mixed number which would be -11 1/4.

Hope that helps and if not, let me know!!

The relationship between the two variables is y=4/3 x+3.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The coordinate points are (0, 3) and (3, 7)

Here, slope (m) = (7-3)/(3-0)

= 4/3

Substitute m=4/3 and (x, y)=(0, 3) in y=mx+c, we get

3=4/3(0)+c

c=3

So, the equation is y=4/3 x+3

Therefore, the relationship between the two variables is y=4/3 x+3.

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The ways to select the candidates from the total is (c) 142,506

From the question, we have

Total number of members, n = 30

Numbers to selection, r = 5

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 30 and r = 5

Substitute the known values in the above equation

Total = ³⁰C₅

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 30!/25!5!

Evaluate

Total = 142,506

Hence, the number of ways is 142,506

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Answer:

15

Step-by-step explanation:

The inverse of the equation is determined as \(y = \log_{6}(-3x)\).

option D is the correct answer.

The inverse of the equation is calculated by applying the following method;

The given equation;

y = - 6ˣ/3

The inverse of the equation is calculated as;

multiply through by 3

\(-3x = 6^y\)

Take the logarithm of both sides of the equation with base -6:

\(\log_{6}(-3x) = y\)

Finally, replace y with x to obtain the inverse equation as follows;

\(y = \log_{6}(-3x)\)

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Answer:

the are so many numbers but here's one of them

Step-by-step explanation:

Since the number is less than 700, it cannot begin with a 7 or an 8.

So the hundreds digit can only be a 2 or a 5.

Now the tens digit can be any digit not occupying the hudreds digit. So there would be 3 possibilities, and there remain two possibilities for the units digit.

Hence, the number of such numbers is 2x3x2 which is 12.

The number of two-digit or three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 will be 150.

A sample is a group of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

The number of two-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 5 x 5

⇒ 25

The number of three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 5 x 5 x 3

⇒ 125

The number of two-digit or three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 125 + 25

⇒ 150

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The solution to the given scatter plot is:

a)  Exponential

b) y = 587.52x

c) 894

Scatter plots are basically al type of data visualization that shows us the relationships that exists between variables.

a) The best model for the given scatter plot is definitely exponential because of the nature of the points and curve.

b) The regression equation for the model has the general formula:

Y = a + bx

Thus, from the given scatter plot, we can say that the equation is:

y = 587.52x

c) Using the equation that you found, in part B, using an online regression equation calculator, we can say that the prediction of the point total in the 10th level is: 894

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The measure of the angle which is twice it's complementary angle are 30° and 60°.

Let the angle be x. As we know, the sum of complementary angles is 90°. So, forming the equation and solving accordingly.

x + 2x = 90

Performing addition on Left Hand Side of the equation

3x = 90

x = 90/3

Performing division on Right Hand Side of the equation

x = 30°

One angle = 30°

Second angle = 2×30

Performing multiplication on Right Hand Side of the equation to calculate the second angle.

Second angle = 60°

So, one angle is 30° and the other angle is 60°.

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Answer:

y=2x-4

Step-by-step explanation:

Given the points (0, -4) and (5, 6), -4 is the y-intercept because it's given.

Use the slope-intercept form to solve for the slope: y=mx+b.

6=5(m)-4

+4        +4         add both sides by 4

---------------

\(\frac{10}{5} =\frac{5m}{5}\)              divide both sides by 5 to isolate m

2=m

The equation of the line is y=2x-4

Answer:

(7, 7)

Step-by-step explanation:

We are given the formula 7(x, y) = (x+5, y+4) for a pair of coordinates (x,y).

P is given as the coordinates: (2, 3), therefore if we substitute P into the equation, we can replace x and y in the given equation for the coordinates of P (2,3).

P is given as (2,3), so 7(P) = 7(2,3).

Using the given formula:

7(2,3) = (2+5, 3+4)

2+5 = 7, 3+4 = 7

Therefore 7(P) = (7, 7)

Hope this helped!

Answer:

If only Jim purchased a cup of coffee, we will subtract its cost from the total;

9.50 - 1.00 = 8.50

Assuming that the two purchased nothing else for breakfast, and that the cost of an egg scramble was the same for both, let's call the price of the egg scramble x.

Since they both bought eggs, then 2x = 8.50

x = $4.25, the price for each egg scramble

Answer:

m<S=63°

Step-by-step explanation:

The angle formed with the radius and a tangent is 90 degrees. (<T)

180-90-27=63

The two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.

It is given that two triangles that are JKL and MNP are considered in which:

Now, from ΔJKL and ΔMNP, we have

∠K = ∠N (Given in the question)

∠L = ∠P(Given in the question)

Thus, by AA rule of similarity,

ΔJKL is similar to ΔMNP.

Therefore, the two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

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Answer:

Step-by-step explanation:

1)  DE = 6/sin63 = 6.7

DF = 6/tan63 = 3.1

m∠E = 180 - 90 - 63 = 27°

2)  tan30 = 1/√3 = UV / (27√10)

UV = (27√10) / √3 · (√3/√3) = (27√30) / 3 = 9√30

3)  cosV = 3/8

cos⁻¹(3/8) = 68

m∠V = 68°

We know that one yards is 36 inches, then to determine how many inches 5 yards are we just multiply 5 by 36, then we have:

Therefore 5 yards is 180 inches.

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

700

Step-by-step explanation:

You multiply the two numbers together

20x35=700

700/20=35

Answer:

\(a_2=3\)

Step-by-step explanation:

The arithmetic sequence is given as: \(1,\ a_2, \ a_3, \ a_4, \ \cdots,\ a_{10}\)

We are told that the 10 numbers add up to 100.

\(S_n=\frac{n}{2}(a_1+l)\\ $Where: \\n=number of terms\\l=last term\\a_1$=first term\)

\(S_{10}=100\\100=\dfrac{10}{2}(1+l)\\100=5(1+l)\\$Divide both sides by 5$\\20=1+l\\$Last term, $l=20-1=19\)

We know that the nth term of an arithmetic sequence

\(l=a_1+(n-1)d\\19=1+(10-1)d\\19=1+9d\\9d=19-1\\9d=18\\d=2\)

Therefore, the second number

\(a_2=a_1+2\\=1+2\\a_2=3\)

Answer:

Set your calculator to Degree mode.

55^2 = 90^2 + 50^2 - 2(90)(50)cos(C)

3,025 = 10,600 - 9,000cos(C)

-7,575 = -9,000cos(C)

cos(C) = 101/120

C = cos^-1 (101/120) = 32.7°

The value of such that = k * 180, where k is an integer, is the value at which cotangent is undefinable.

Cotangent, or cot, is one of the six standard trigonometric functions. Cotangent of an angle is defined as the ratio of the adjacent side to the opposite side of a right-angled triangle.

The value of cotangent is undefined when the denominator is zero. This implies that cotangent is undefined at angles where the value of sine is zero.

Since the sine function is periodic and has a period of 360 degrees, the values of sine repeat themselves after every 360 degrees.

For this reason, cotangent is undefined at angles such that θ = k * 180, where k is an integer.

That is, cotangent is undefined at 0°, 180°, 360°, and so on. It is also important to note that cotangent is a periodic function, and its values repeat every 180 degrees.

Therefore, cotangent is undefined at 0° + k * 180°, where k is an integer.

To summarize, the value of Θ at which cotangent is undefined is such that θ = k * 180, where k is an integer.

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Answer:

Step-by-step explanation:

-2x<-4

x=2

-2×2<-4

-4<-4

which is not true.

Hence x=2 is not a solution.

Answer: No

Step-by-step explanation: To determine whether x = 2 is a

solution to the inequality, substitute a 2 in for x.

So we have -2(2) < -4 or -4 < -4 which is a false statement.

No, 2 is not a solution to the inequality.

The given expression :

set up the expressions next to each other in parenthesis:

Distribute the first term in the first set of parenthesis throughout each term in the second set of parenthesis:

Now, distribute x over 2x^2+3x-10 and 5 too

Answer: 11 × x = 8x + 9

Step-by-step explanation:

The system of equations -9x+8y = 9x and 7y+8=8x is linear.

A system of equations is considered linear if each equation in the system is linear, meaning that the highest power of any variable in each equation is 1.

In this case, the first equation -9x+8y = 9x is linear because the highest power of any variable is 1 (x is raised to the first power).

Similarly, the second equation 7y+8=8x is also linear because the highest power of any variable is 1 (x is raised to the first power and y is not raised to any power).

Therefore, the system of equations is linear.

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The lines intersect at only one specific point (-5, 9)

The correct answer is: There is one unique solution (-5, 9).

When two straight-line equations intersect at a point, it means that there is one unique solution to the system of equations. In this case, the point of intersection is (-5, 9), which indicates that the system has a single solution. This means that there is a unique set of values for the variables that satisfy both equations simultaneously.

If the system had no solution, it would mean that the two lines are parallel and will never intersect. However, since the lines in the given system intersect at (-5, 9), it implies that there is a solution.

Alternatively, if the system had infinitely many solutions, it would mean that the two equations represent the same line. In this case, the lines intersect at every point along their entire length, resulting in an infinite number of solutions. However, the fact that the lines intersect at only one specific point (-5, 9) indicates that there is one unique solution to the system of equations.

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