4x=3x+10 transversal

Answer:

Step-by-step explanation:

To determine whether an ordered pair is a solution to a system of equations or inequalities, we need to substitute the values for x and y into each equation or inequality and see if the resulting expression is true. If it is true for all of the equations or inequalities, then the ordered pair is a solution to the system.

Here's the step-by-step process for each ordered pair:

(1,3):

Substitute x = 1 and y = 3 into y < 4x - 1: 3 < 4(1) - 1 = 3 < 3, which is true.

Substitute x = 1 and y = 3 into y > x: 3 > 1, which is true.

Since both inequalities are true, the ordered pair (1,3) is a solution to the system y < 4x - 1 and y > x.

(0,0):

Substitute x = 0 and y = 0 into y < 4x - 1: 0 < 4(0) - 1 = -1, which is false.

Substitute x = 0 and y = 0 into y > x: 0 > 0, which is false.

Since at least one inequality is false, the ordered pair (0,0) is not a solution to the system y < 4x - 1 and y > x.

Answer:

Step-by-step explanation:

m=3-1/2-7= -2/5

c⇒ -2

y=mx+c

y=-2/5x-2

Answer: The answer is A. (-∞0, +00)

The rule A(x,y) ⇒  (-y,x) describes a transformation. The correct option is D.

The concept of rotation in mathematics has its roots in geometry. Any rotation is a movement of a certain area while maintaining at least one point. It may be used to describe, for instance, how a rigid body moves around a fixed point.

Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x, and y, making y negative.

The transformation is described by the rule A(x,y) (-y,x). The right answer is D.

To know more about rotation follow

https://brainly.com/question/28354740

#SPJ1

The percentage of middle school students that prefer each season and the percentage of high school students that prefer each season is 57.93% and 42.07% respectively.

The percentage is the ratio of the composition of value to the overall composition of value multiplied by 100.

Here,
Total number of students = 93 + 31 + 36 + 54 = 214

The percentage of students in middle school prefer spring,
= number of students in middle school prefer spring / total student × 100%
= 93/214 × 100%
= 43.45%

Similarly,
The percentage of students in middle school prefer winter,
= number of students in middle school who prefer winter/ total students × 100%
= 31/214 × 100%
= 14.48%

Thus, the percentage of middle school students that prefer each season and the percentage of high school students that prefer each season are 43.45 + 14.48 = 57.93% and 100-57.93% = 42.07%.

Learn more about percentages here:

brainly.com/question/13450942

#SPJ9

Answer:

Step-by-step explanation:

6(x+5) = 6x+30

-2(x-3)=-2x+6

6x+30=-2x+6

8x+30=6

8x=-24

x=-3

Answer: x = -3

Step-by-step explanation:

6(x + 5) = -2(x-3)

1. Distribute: 6x + 30 = -2x + 6

2. Add 2 to both sides: 8x + 30 = 6

3. Subtract 30 on both sides: 8x = -24

4. Divide by 8 on both sides: x = -3

Vertex A: (90°, 3) and Vertex B: (90°, -1) of the sine function.

The vertex A of the curve y = sin x + 2 is obtained by shifting the vertex of y = sin x upward by 2 units. Since the vertex of y = sin x is (90°, 1), the vertex of y = sin x + 2 will be:

A = (90°, 1 + 2) = (90°, 3)

Therefore, the coordinates of the vertex A of the curve y = sin x + 2 are (90°, 3).

b) The curve y = -sin x is obtained by reflecting the curve y = sin x about the x-axis. Since the vertex of y = sin x is (90°, 1), the vertex of y = -sin x will be:

A = (90°, -1)

Therefore, the coordinates of the vertex A of the curve y = -sin x are

(90°, -1).

To know more about Sine Function, click here,

https://brainly.com/question/11881676

#SPJ1

Following are the values of the functions -

1) f(a) = 8a - 4

2) f(a+h) = 8a+ 8h - 4

3)[tex]\frac{f (a+h)-(a) }{h}= 8[/tex]

An expression or relationship with one or more variables is called a function. Both its inputs and outputs are numerous. There is just one output per input. The function explains how the inputs and outputs are related.

To evaluate f(a), we simply substitute the value of "a" into the function:

1) f(a) = 8a - 4

To evaluate f(a+h), we substitute the value of "a+h" into the function:

2) f(a+h) = 8(a+h) - 4

f(a+h) = 8a+ 8h-4

To find the expression for [tex]\frac{f (a+h)-(a) }{h}[/tex], we divide the result by h: L(a+h)-f(a) h we can subtract f(a) from f(a+h) and then

3) [tex]\frac{f (a+h)-(a) }{h}[/tex]

[tex]= \frac{ (8a+8h-4-(8a-4)}{h} \\= \frac{8h}{h}= 8[/tex]

To know more about Function visit,

brainly.com/question/22340031

#SPJ1

Step-by-step explanation:

please see the attached picture

Answer:

x=5 and LN= 30, MP= 40

Step-by-step explanation:

Add like terms to both sides of the equation and you will get your answer

Answer: look at the image for the answer and explanation

Step-by-step explanation:

A. The value of the function at x = 8 will be 4. Then the correct option is B.

B. The average rate of change of the function in the interval of [2, 6]  will be 24. Then the correct option is D.

C. The total mass of 5,000 of these microorganisms will be 0.012 g. Then the correct option is C.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

A. The function is f(x) = 8 / (x - 6), then the value of the function at x = 8 is given as,

f(8) = 8 / (8 - 6)

f(8) = 4

Then the correct option is B.

B.  The function is f(x) = 3x² - 5, then the average rate of change of the function in the interval of [2, 6] is given as,

Average rate = [3(6² - 4²)] / (6 - 2)

Average rate = 24

Thus, the correct option is D.

C.  The average mass of a certain type of microorganism is 2.4 × 10⁻⁶ grams. Then the total mass of 5,000 of these microorganisms is given as,

⇒ 2.4 × 10⁻⁶ × 5,000

⇒ 0.012 grams

Thus, the correct option is C.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ1

The value of sin B rounded to the nearest hundredth is 0.80.

Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

The right triangle represented in the question is given below.

We know that sine of an angle in a right angled triangle is the ratio of it's opposite side to hypotenuse.

In the triangle ABC, AB is the hypotenuse and AC is the opposite side of B.

Sin B = AC / AB

Sin B = b / c

Sin B = 20 / 25

Sin B = 0.8

Hence the value of sine of B is 0.8.

Learn more about Trigonometric Ratios here :

https://brainly.com/question/29156330

#SPJ1

The probability that at least 1 of the 4 cards drawn is a face card is 0.6.

A typical deck contains 52 cards in total. There are 51 cards left in the deck after the first spectator draws a card. The replacement card leaves 52 cards in total, which is the same as before. The number of cards remains 52 for all four draws since each succeeding audience member will draw a card and replace it.

Finding the likelihood that none of the four cards are face cards and subtracting it from one will give us the chance that at least one of the four cards is a face card.

A deck of cards has 12 face cards (4 jacks, 4 queens, and 4 kings). Consequently, the likelihood that a single draw will not provide a face card is:

P(not a face card)=(52 - 12)/(52)=(40/(52)=(10/13).

The likelihood that none of the four draws will produce a face card is:

P(no face cards are present) = (10/13)4 = 0.432

As a result, the likelihood that at least 1 of the four cards revealed is a face card is as follows:

P(none are face cards) = 1 - P(at least one is a face card) = 1 - 0.432 = 0.568

The chance, rounded to one decimal place, is roughly 0.6.

Consequently, there is a 0.6 percent chance that at least one of the four cards will be a face card.

To know more about Standard Deck visit:

brainly.com/question/13935092

#SPJ1

The composite function has its value to be g o h(x) = -20x^2 - 30x

from the question, we have the following parameters that can be used in our computation:

h(x) = 4x + 6

g(x) = -5x

Using the above as a guide, we have the following:

g o h(x) = g(x) * h(x)

substitute the known values in the above equation, so, we have the following representation

g o h(x) = (4x + 6) * -5x

Evaluate

g o h(x) = -20x^2 - 30x

Hence, the value is g o h(x) = -20x^2 - 30x

Read more about composite function at

https://brainly.com/question/10687170

#SPJ1

Answer: The equation "x + y = mb" represents a linear equation in two variables, x and y. In this equation, m is a constant and b is another constant or a known value. The equation states that the sum of x and y is equal to the product of m and b.

This equation can be used to model a variety of real-world situations where two quantities are related and their sum is equal to a constant value. For example, it could represent the amount of money saved by two people, where x and y are the savings of the two people and mb is the total amount of money saved.

To solve for x and y, we can use either substitution or elimination method, or any other method for solving systems of linear equations. The values of x and y that satisfy the equation "x + y = mb" are called the solutions of the equation.

Step-by-step explanation:

The amount of money which would be in the account after 14 years is; $18,123.77.

The number of years it'd take for the money to double is; 13.86 years.

Since the given model of the account is;

A (t) = 9000e^0.05t

After 14 years, it follows that; t = 14.

Therefore;

A (14) = 9000e^0.05(14)

A (14) = 9000 × 2.013752707

A (14) = $18,123.77.

Also, the doubling time implies that; A (t) = 18,000

Therefore, 18000 = 9000e^0.05t

2 = e^0.05t

0.05t = ln (2)

t = ln (2) / 0.05

t = 13.86 years.

Read more on Continuous compounding;

https://brainly.com/question/30460031

#SPJ1

The more basic function that has been shifted, reflected, stretched, or compressed to create q(x) = -1/x + 1 is the function f(x) = 1/x.

The transformation applied to f(x) to obtain q(x) is divided into several steps:

Reflection: The negative sign in front of 1/x reflects the graph of f(x) across the x-axis, causing the y-values to change sign.

Vertical shift: Adding "+1" to -1/x raises the graph of f(x) by one unit.

Horizontal shift: Although there is no explicit horizontal shift in q(x), we can see that the graph of q(x) has a vertical asymptote at x=0, whereas the graph of f(x) does not. This means that the graph of q(x) has been shifted to the right by one unit.

The more basic function that has been shifted, reflected, stretched, or compressed to create q(x) = -1/x + 1 is the function f(x) = 1/x.

To know more about Graph visit:-

https://brainly.com/question/17267403

#SPJ1

Answer:

the scale factor that Samir used in his drawing is 5/1.

Step-by-step explanation:

Here's a step by step explanation of how to find the scale factor of a drawing:

Identify the scale used in the drawing. In this case, the scale used in Samir's drawing is 5 inches = 1 yard.

Express the scale as a ratio between the two sizes. In this case, the ratio is 5 inches : 1 yard.

Simplify the ratio, if possible. In this case, the ratio 5 inches : 1 yard can be simplified to 5/1.

The simplified ratio, 5/1, is the scale factor of the drawing. This means that for every 5 inches on the drawing, the actual length in the real world is 1 yard.

So, the scale factor that Samir used in his drawing is 5/1.

Answer:

Step-by-step explanation:

To factorise the expression, we can use the factor theorem which states that if a polynomial p(x) has a factor (x - r), then p(r) = 0.

We can use this theorem to find the factors of the polynomial expression:

(a - 2b)^3 + (2a - b)^3

We can write (a - 2b)^3 as (a - 2b)(a^2 - 4ab + 4b^2). Using the factor theorem, we see that:

(a - 2b)(a^2 - 4ab + 4b^2) = 0 when a = 2b

Similarly, we can write (2a - b)^3 as (2a - b)(4a^2 - 4ab + b^2). Using the factor theorem, we see that:

(2a - b)(4a^2 - 4ab + b^2) = 0 when a = b/2

Now we have two equations: a = 2b and a = b/2, which we can use to solve for a and b in terms of each other. We see that:

a = 2b = b/2

Multiplying both sides by 2, we get:

2a = b

We can substitute this back into the original expression:

(a - 2b)^3 + (2a - b)^3 = (a - 2(2a))^3 + (2a - (2a))^3 = (-3a)^3 + (0)^3 = -27a^3

So the factorised form of the expression is:

(a - 2b)^3 + (2a - b)^3 = -27a^3.

Work Shown:

Use the sum of cubes factoring rule

x^3 + y^3 = (x+y)(x^2 - xy + y^2)

In this case,

So,

x^3 + y^3 = (x+y)(x^2 - xy + y^2)

(a-2b)^3 + (2a-b)^3 = (a-2b+2a-b)((a-2b)^2 - (a-2b)(2a-b) + (2a-b)^2)

(a-2b)^3 + (2a-b)^3 = (3a-3b)((a^2-4ab+4b^2) - (2a^2-ab-4ab+2b^2) + (4a^2-4ab+b^2))

(a-2b)^3 + (2a-b)^3 = (3a-3b)((a^2-4ab+4b^2) - (2a^2-5ab+2b^2) + (4a^2-4ab+b^2))

(a-2b)^3 + (2a-b)^3 = (3a-3b)(a^2-4ab+4b^2 - 2a^2+5ab-2b^2 + 4a^2-4ab+b^2)

(a-2b)^3 + (2a-b)^3 = (3a-3b)(3a^2-3ab+3b^2)

(a-2b)^3 + (2a-b)^3 = 3*3(a-b)(a^2-ab+b^2)

(a-2b)^3 + (2a-b)^3 = 9(a-b)(a^2-ab+b^2)

The answer has been fully confirmed with WolframAlpha.

Since f(f1(y)) = y and f1(f(x)) = x, we can conclude that f1 is the correct inverse function for f.

Function can be defined in which it relates an input to output.

Given function ,

The function f(x) = x³ +9 is one-to-one.

To find the inverse function f1, we need to switch the roles of x and y in the equation for f(x). So, we have:

y = x³ + 9

Next, we need to solve for x in terms of y:

x³ + 9 = y

x³ = y - 9

x = (y - 9[tex])^{(1/3)}[/tex]

So, the inverse function is:

f1(y) = (y - 9[tex])^{(1/3)}[/tex]

To verify that f1 is the correct inverse function, we need to show that f(f1(y)) = y and f1(f(x)) = x:

f(f1(y)) = f((y - 9[tex])^{(1/3)}[/tex] = (y - 9[tex])^{(1/3)}^3[/tex] + 9 = y - 9 + 9 = y

And:

f1(f(x)) = f1(x³ + 9) = (x³ + 9 - 9[tex])^{(1/3)}[/tex] = [tex]\mathrm{ x^3^{(1/3)}}[/tex] = x

Therefore, Since f(f1(y)) = y and f1(f(x)) = x, we can conclude that f1 is the correct inverse function for f.

To learn more about Function from given link.

https://brainly.com/question/12431044

#SPJ1

Answer:

Step-by-step explanation:

To determine which option is faster, we need to determine the total number of nights required for each option.

First, let's find the number of pages Nora still needs to read by subtracting the number of pages she's already read from the total number of pages: 280 pages * 30% = 84 pages

So, Nora still needs to read 280 pages - 84 pages = 196 pages.

For Option 1, Nora would read 25% of the remaining pages each night, so the number of pages she reads each night would be: 196 pages * 25% = 49 pages

The total number of nights required would be 196 pages / 49 pages/night = 4 nights.

For Option 2, Nora would read 28 pages each night, so the total number of nights required would be 196 pages / 28 pages/night = 7 nights.

Since 4 nights is less than 7 nights, Nora should choose Option 1 to finish reading the book in the least amount of time.

The parameters for the home mortgage, and the monthly payment, PMT,  for the mortgage are as follows;

Part 1;

P = $175,000, APR = 7%, n = 12, Y = 30

Part 2;

The monthly payment for the mortgage, PMT ≈ $1,164.28

A mortgage is a loan agreement, with the possession of the collateral presented for the loan such as a house being bought with the loan amount, being relinquished by the debtor, upon default

Part 1

The value of the mortgage  = $175,000

The fixed Annual Percentage Rate, APR = 7%

The duration of the payment = 30 years

Part 2; The monthly payment PMT loan formula can be presented in the following format;

Therefore;

[tex]PMT = \frac{175000\times \frac{0.07}{12} }{1-\left(1+\frac{0.07}{12}\right)^{(-12\times 30)} } \approx 1164.28[/tex]

Learn more on the payment loan here: https://brainly.com/question/15949383

#SPJ1

An equation to show the sequence is -25n.

When all the terms of the geometric sequence are added, than that expression is known as geometric series.

The sum of terms of a geometric sequence;

Now, lets suppose its initial term is   , multiplication factor will be r

and let it has total n terms, then, its sum is given as:

[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]

(sum till nth term)

We are given that;

The first term of sequence=-25

D= -50-(-25)

=-25

Now,

an = a + (n-1)d

=-25+(n-1)-25

=-25-25n+25

=-25n

Therefore, the answer of the sequence will be -25n.

Learn more about sum of terms of geometric sequence visit:

brainly.com/question/1607203

#SPJ9

Answer: 994 beads

Step-by-step explanation:

Red Beads = 275

Blue Beads = 825 (275 x 3)

825 + 275 = 1100 beads (total)

1100 - 156 = 994 beads

A rectangle that has been divided into equal parts is referred to as a rectangular fraction. Depending on how many equal pieces you divide the whole into, the equal parts may be divided into halves, thirds, fourths, and so on.

1/2 of 2/3 is equal to 1/3

What is the equation?

The equation is defined as a mathematical statement with at least two terms that contain variables or values that are equal.

To represent the multiplication of 1/2 and 2/3, we can draw a rectangle and divide it into equal parts.

1) First, we draw a rectangle.

2) Then, we divide it into 2 equal parts horizontally.

3) Next, we divide each half vertically into 3 equal parts.

4) Now we can see that each small rectangle represents 1/6 of the whole rectangle.

So, 1/2 of 2/3 is equal to 1/2 of 1/3.

Therefore, 1/2 of 2/3 is equal to 1/3.

To know more about multiplication equation visit,

https://brainly.com/question/30315410

#SPJ1

Answer:

3ab2+1 = -23

3a^2b-1 =-25

Step-by-step explanation:

Answer:

360 degrees

2 pi radians, means you have 2 pi of something and they are radians. It is the same 360 degrees. A radius is the line from the side of the circle to the center.

Reason: pi radians is 180 degrees. Double each value to find that 2pi radians is 360 degrees. It's a full revolution of a circle. Use a unit circle if necessary.