How do you check if a number is rational?
How do you check if a number is irrational?



Thanks!

P.S. 50 points & brainiest to whoever answer first!

Using the distance formula, the length of segment PQ is:

C. √68 units

The distance formula is given as:

d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Segment PQ has the following endpoints:

P(-2, 3)

Q(6, 1)

To find the length of segment PQ using the distance formula, we can apply the formula, where:

\((x_1, y_1)\)are the coordinates of point P

\((x_2, y_2)\) are the coordinates of point Q.

Given:

P(-2, 3) = \((x_1, y_1)\)

Q(6, 1) = \((x_2, y_2)\)

Let's substitute the values into the formula:

PQ = √[(6 - (-2))² + (1 - 3)²]

PQ = √[(8)² + (-2)²)

PQ = √(64 + 4)

length of segment PQ = √68 units

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Answer:

what does the stem-and-leaf plot look like?

1. Figure STUV is congruent to Figure KLMN because rigid motions can be used to map Figure STUV onto Figure KLMN.

2. Figure STUV is also similar to Figure KLMN because rigid motions and/or dilations can be used to map Figure STUV onto Figure KLMN. The scale factor is 2.

When it is said that two figures are congruent, like the ones shown on the graph, This means that they have the same shape and size.

Similar figures have the same shape, but they may have different sizes and be located in different positions.

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29/2 ÷ 5/4

2/29 × 5/4

To get your answer its just a matter of understanding the question, they are asking you to find how many 1¼ gallons of water can fit in a tank that can hold 14½ gallons of water so, to find the answer we need to divide 14½ by 1¼ ( these fractions are mixed numbers so, you need to change them into improper fraction)

Now when dividing the fractions you always invert the fraction on the left side and the division sign turns into a multiplication sign...

29/2÷5/4 = 2/29×5/4.

Answer: 2x+5

Step-by-step explanation:

(5x + 3) – (3x – 2)

5x+3-3x+2

2x+5

Answer:

\(\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}\)

╭⋟───────────────

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

───────────────⋞╯

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꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

The true statement based on the relationship depicted in the Venn diagram is that no rhombuses are trapezoids (option D).

To identify the true statement using the relationship represented in the Venn diagram, we need to analyze the overlapping regions and the properties of the shapes involved.

A trapezoid is a quadrilateral with at least one pair of parallel sides, while a rhombus is a quadrilateral with all sides of equal length. Let's evaluate the options:

A. All trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region between the trapezoids and rhombuses shows that there are trapezoids that are not rhombuses. Therefore, option A is incorrect.

B. All rhombuses are trapezoids: This statement is true based on the diagram. The entire region representing rhombuses is also included within the region representing trapezoids. Every rhombus can be considered a trapezoid because it has at least one pair of parallel sides. Thus, option B is correct.

C. No trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region indicates that there are trapezoids that are indeed rhombuses. Therefore, option C is incorrect.

D. No rhombuses are trapezoids: This statement is true based on the diagram. There is no overlap between the regions representing rhombuses and trapezoids, implying that no rhombus can be considered a trapezoid. Hence, option D is correct.

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Answer:

1. List (in order) the five phases a single 2 solar mass will go through in its life.

2. List (in order) the five phases a single 25 solar mass will go through in its life.

3. List (in order) the five phases a single 60 solar mass will go through in its life.

Phase options (can be used more than once, some may not be used at all):

Type II Supernova

Protostar

White Dwarf

Giant Phase

Main sequence

Neutron Star

Brown Dwarf

Black Hole

Type 1a Supernova

Planetary Nebula

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the number that Grace thought:

We'll represent the unknown number as "x."

"Added 7": This can be represented as (x + 7).

"Multiplied by 3": This becomes 3 * (x + 7).

"Took away 5": This is represented as 3 * (x + 7) - 5.

"Divided by 4": This gives (3 * (x + 7) - 5) / 4.

"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.

Now we can solve for x:

(3 * (x + 7) - 5) / 4 = 7

Multiply both sides by 4 to eliminate the denominator:

3 * (x + 7) - 5 = 28

Simplify the left side:

3x + 21 - 5 = 28

Combine like terms:

3x + 16 = 28

Subtract 16 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Therefore, the number that Grace thought of is 4.

Answer:

$30 on CDs

$20 on Makeup

hope it helps

Step-by-step explanation:

The money spent on each product is $20 and $30 respectively.

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

Given that,

The money spent by Lauren on make up and CDs is $50.

Suppose the money spent on CDs be x.

Then, the money spent on make up is  x + 10.

As per the question the following equation can be formed,

x + x + 10 = 50

=> 2x + 10 = 50

=> 2x = 40

=> x = 20

Thus, money spent on make up is 20 + 10 = 30 dollars.

Hence, the money spent on CDs and make up is $20 and $30 respectively.

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Answer:

To simplify the square root of 252 means to get the simplest radical form of √252.

Step-by-step explanation:

Step 1: List Factors

List the factors of 252 like so:

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252

Step 2: Find Perfect Squares

Identify the perfect squares* from the list of factors above:

1, 4, 9, 36

Step 3: Divide

Divide 252 by the largest perfect square you found in the previous step:

252 / 36 = 7

Step 4: Calculate

Calculate the square root of the largest perfect square:

√36 = 6

Step 5: Get Answer

Put Steps 3 and 4 together to get the square root of 252 in its simplest form:    

6 √ 7  

Answer:

12

Step-by-step explanation:

Answer:

W = 15900 ft.lb

Step-by-step explanation:

From the given information.

Consider y to be the distance from the ground towards the bucket of the cement.

At height y, suppose the bucket is lifted by Δy.

Then, the workdone can be = 500Δy + 0.5(75 - y) Δy

where;

The bucket of the cement =  500Δy

The remaining of the rope =  0.5(75 - y) Δy

However; the workdone (W) can be calculated as:

\(W = \int^{30}_{0} \ 500 \ dy + \int^{30}_{0} \ 0.5 (75-y ) \ dy\)

\(W = 500 \times 30 + 0.5 \bigg(75 \times 30 - \dfrac{1}{2} \times 30^2 \bigg )\)

W = 15000 + 0.5 ( 2250 - 450)

W = 15000 + 900

W = 15900 ft.lb

The required work is \(15,900 \ ft-lb\).

Integral Calculus is the branch of calculus where we study integrals and their properties. Integration is an essential concept which is the inverse process of differentiation. Both the integral and differential calculus are related to each other by the fundamental theorem of calculus.

Let \(x\) be the distance from the ground to the bucket of cement.

At the height \(x\), if the bucket is lifted by \(\Delta x\), the work done is,

\(500\Delta x+0.5\left ( 75-x \right )\Delta x\).

(See the attached figure below).

The \(500\Delta x\) term is due to the bucket of cement; the \(0.5\left ( 75-x \right )\Delta x\) term is due to the remaining cable.

So, the total work, \(W\), required to lift the bucket is,

\(W=\int_{0}^{30}500dx+\int_{0}^{30}0.5\left ( 75-x \right )dx \\ =500.30+0.5\left ( 75.30-\frac{1}{2}30^{2} \right ) \\ =15,900 \ ft-lb.\)

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The given membership dues are enough for 1.34 months therefore for one month it is on side of profit.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Given that,

Fixed operating costs amounted to $95

Variable cost = $265

Let's say it can be used for x months

Now,

265x + 95 ≤ 450

265x ≤ 355

x ≤ 1.34

Hence "The given membership dues are enough for 1.34 months therefore for one month it is on side of profit".

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Answer:

771 is the absolute value of -771.

Step-by-step explanation:

The absolute value is the distance of that number from 0. Therefore, negative or not, the number shown will always be the positive number that it is.

Examples:

|-8| = 8.

|2|=2

|-9912|=9912

|236|=236

Continued explanation:

Because the absolute value is the distance of that number from zero, the value will always be positive. And then the distance is going to be the same number.

I hope this helps!

-No one

Answer:

  a)  |sec(θ)|

  b) 2cot(2x)

Step-by-step explanation:

Trig identities are used to simplify these expressions. Several are used:

__

  \(\sqrt{1-\tan(180^\circ-\theta)\cot(90^\circ-\theta)}=\sqrt{1-(-\tan(\theta))\tan(\theta)}\\\\=\sqrt{1+\tan^2(\theta)}=\sqrt{\sec^2(\theta)}=\boxed{|\sec(\theta)|}\)

__

  \(\dfrac{\cos(2x)\tan(x)}{\sin^2(x)}=\dfrac{\cos(2x)}{\sin^2(x)}\cdot\dfrac{\sin(x)}{\cos(x)}=\dfrac{\cos(2x)}{\sin(x)\cos(x)}\\\\=\dfrac{\cos(2x)}{\left(\dfrac{\sin(2x)}{2}\right)}=2\dfrac{\cos(2x)}{\sin(2x)}=\boxed{2\cot(2x)}\)

Answer:

Cohen's d : 1.00

Step-by-step explanation:

We know that M₁ = 18, and M₂ = 14. Given that the pooled variance for the these two samples are 16, S²Pooled = 16, and therefore S - pooled = 4.

The formula to solve for the value of Cohen's d is as follows,

d = M₁ - M₂ / S - pooled,

d = 18 - 14 / 4 = 4 / 4 = 1

Therefore the value of Cohen's d = 1

Answer in the picture.

A function assigns the values. The value of f(g(x)) is 50x² + 140x + 93.

A function assigns the value of each element of one set to the other specific element of another set.

Given the value of f(x)=2x²-5 and g(x)=5x+7, therefore, the value of f(g(x)) can be written as,

f(g(x)) = 2(5x+7)²-5

f(g(x)) = 2(25x²+49+70x)-5

f(g(x)) = 50x² + 98 + 140x - 5

f(g(x)) = 50x² + 140x + 93

Hence, the value of f(g(x)) is 50x² + 140x + 93.

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Answer:

The answer is d for problem 3

Step-by-step explanation:

I hope this helps now have a good and blessed day.

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer:

Just do 60 divided by 10

Step-by-step explanation:

60=10 x  10 times 6 = 60 so x=6

Answer: \(x=6\)

Divide both sides by 10

\(10x=10=60/10\\x=6\)

Answer:

he put it on one brownie so 1/7

Translated the the images 5 units down in the second attachment.

A translatiοn in math mοves a shape left οr right and/οr up οr dοwn. The translated shapes lοοk exactly the same size as the οriginal shape, and hence the shapes are cοngruent tο each οther. They just have been shifted in οne οr mοre directiοns. Since it is just mοving οf the shape frοm οne place tο οther, there is nο change in the shape.

The directiοn οr the path οf this change in pοsitiοn οf the οbject can vary i.e., initially the οbject can mοve left, then turn right, and sο οn. While translating, all the pοints οn the shape will shift by the same number οf units. Fοr example, if οne pοint shifts 2 units tο the right, then all the pοints will alsο mοve 2 units tο the right.

Here to translate the shape you simply need to move down every point x value of the point to x - 5 value of the point.

Then you have your translated shape. (see attachment)

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Answer:

\(a=\dfrac{3b-7}{3}\)

Step-by-step explanation:

Given that,

The given equation is :

5b + 6a – 7 = 2b + 9a

We need to solve the above equation for a. Taking he terms having a and b in LHS and constants in RHS.

5b+6a-2b-9a=7

taking like terms together

(6a-9a)+(5b-2b)=7

-3a+3b=7

Subtracting both sides by 3b. So,

-3a+3b-3b=7-3b

-3a=7-3b

Dioviding both sides by (-3). So,

\(a=\dfrac{7-3b}{-3}\\\\a=\dfrac{3b-7}{3}\)

Hence, the value of a is \(a=\dfrac{3b-7}{3}\).

Answer:

\(a = \frac{3b-7}{3}\)

Step-by-step explanation:

1 yard = 36 inches

2 1/2 yards x 36 = 90 inches

Answer: 90 inches

Answer:

\(y=\frac{4}{3} x-9\)

Step-by-step explanation:

Here this is in standard form. Hope this helps!

Answer:

y=4/3x-9

Step-by-step explanation:

equasion for linear function is y=mx+b where y is m is slope and b is y intercept. just plug in your variables

Given:

A line segment AB.

A point is \(\dfrac{3}{10}\) of the way from A to B.

To find:

The coordinates of that point.

Solution:

Section formula: If a point divide a line segment in m:n, then

\(Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)\)

From the given figure, it is clear that the two end points of the line segment are A(-4,-5) and B(12,4).

Let the unknown point be P. The point is \(\dfrac{3}{10}\) of the way from A to B. It means,

\(\dfrac{AP}{AB}=\dfrac{3}{10}\)

Let AP and AB are 3x and 10x, then

\(\dfrac{AP}{PB}=\dfrac{AP}{AB-AP}\)

\(\dfrac{AP}{PB}=\dfrac{3x}{10x-3x}\)

\(\dfrac{AP}{PB}=\dfrac{3x}{7x}\)

\(\dfrac{AP}{PB}=\dfrac{3}{7}\)

It means, point P divided the line segment in 3:7.

Using section formula, we get

\(P=\left(\dfrac{3(12)+7(-4)}{3+7},\dfrac{3(4)+7(-5)}{3+7}\right)\)

\(P=\left(\dfrac{36-28}{10},\dfrac{12-35}{10}\right)\)

\(P=\left(\dfrac{8}{10},\dfrac{-23}{10}\right)\)

\(P=\left(0.8,-2.3\right)\)

Therefore, the coordinates of the required point are (0.8, -2.3).

❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤

\(11x + 16 = (9x + 2) + 32\)

\(11x + 16 = 9x + 34\)

Subtract sides 16

\(11x + 16 - 16 = 9x + 34- 16\)

Simplification

\(11x = 9x + 18\)

Subtract sides 9x

\( - 9x + 11x = - 9x + 9x + 18\)

Simplification

\(2x = 18\)

Divide sides by 2

\( \frac{2x}{2} = \frac{18}{2} \\ \)

\(x = 9\)

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Answer:

x=9

Step-by-step explanation:

angle 4 = angle 1 + angle 2

11x + 16 = 9x + 2 + 32

combine like terms

11x - 9x = 2 + 32 - 16

2x = 34 - 16

2x = 18

x = 18/2

x = 9