The two polygons are similar. What is the side length of ​ QR?
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Part 1
The side length of is

enter your response here mm.

Answer:

1/15,1/14,1/13

Step-by-step explanation:

the total number of pool balls decrease as you try and pick all 3 balls one after the other

in other word ur probability gets bigger as you pull each ball.

hope this helps

Answer:

1/15,1/14,1/13

Step-by-step explanation:

Hope that help s

\({\Large \begin{array}{llll} y=2x^2+bx+c \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=-1\\ y=-5 \end{cases}\implies -5=2(-1)^2+b(-1)+c \implies -5=2-b+c \\\\\\ -7=-b+c\implies b-7=c \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=2\\ y=10 \end{cases}\implies 10=2(2)^2+b(2)+c\implies 10=8+2b+c\)

\(2=2b+c\implies \stackrel{\textit{substituting "c"}}{2=2b+(b-7)}\implies 2=3b-7\implies 9=3b \\\\\\ \cfrac{9}{3}=b\implies \boxed{3=b}\hspace{5em}\stackrel{\textit{we know that}}{b-7=c}\implies \boxed{-4=c} \\\\\\ ~\hfill~ {\Large \begin{array}{llll} y=2x^2+3x-4 \end{array}} ~\hfill\)

Check the picture below.

The following can be determined about the slopes and y-intercepts of the system of equations: A. The slopes are different, and the y-intercepts are different.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, we have the following system of equations in standard form:

4x + 2y = −2

x − 3y = 24

By rewriting system of equations in slope-intercept form, we have:

y = -2x - 1  ⇒ m = -2, b = -1

y = x/3 - 8  ⇒ m = 1/3, b = -8

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Answer:

35

Step-by-step explanation:

x2 + 2y ÷ 2W + 3z

plug in the numbers

5(2) + 2(8) ÷ 2(2) + 3(3)

solve and use order of operations

=35

Answer:

its 119

Step-by-step explanation:

The angle formed by the two hands have a measure less than 1/4 turn

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

A clock with the hour hand at 12 and the minute hand at 2

The turn represented by the above is represened as

Turn = (2 * 30)/360

When simplified, we have

Turn = 1/6

Next, we have

Angle at the turn = 1/4

1/6 is less than 1/4

This means that the angle formed by the two hands have a measure less than 1/4 turn

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The image coordinates of K′ if the preimage is reflected across y = −7 is (-4, -8)

Based on the given question, we have certain variables that can be utilized for our calculations.

K = (-4, -6)

First, find the equation of the reflection line

The reflection line is y = -7.

This can be expressed as

y = a = -7

The image of the reflection is then calculated as

K' = (x, -(y + 2|a|))

Replace the given or established values in the equation mentioned earlier, resulting in the following expression

K' = (-4, -(-6 + 2 * 7))

Evaluate

K' = (-4, -8)

Hence, the image coordinates of K′ are (-4, -8).

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Answer:

IQR= 3

Step-by-step explanation:

Hello!

The data represents the number of classes taught by each teacher at Broxin High School.

To calculate the IQR you have to do the following steps:

1) Arrange the data from least to greatest:

Raw data: 5, 7, 5, 1, 1, 9, 4, 5, 3, 4, 6

Arranged: 1, 1, 3, 4, 4, 5, 5, 5, 6, 7, 9

2) Calculate the 1st Quartile (Q₁):

The first quartile divides the bottom 25% of the data from the top 75%, to know which value of the data set corresponds to it you have to calculate its position:

PosQ₁= (n+1)/4= (11+1)/4= 3

This means that the 1st quartile corresponds to the 3rth observation:

1, 1, 3, 4, 4, 5, 5, 5, 6, 7, 9

Q₁= 3

3) Calculate the 3rd Quartile (Q₃)

The third quartile divides the bottom 75% of the data from the top 25%, as before, you have to calculate its position and then identify the value in the data set.

PosQ₃= (n+1)*(3/4)= (11+1)*(3/4)= 9

The third quartile corresponds to the 9th observation:

1, 1, 3, 4, 4, 5, 5, 5, 6, 7, 9

Q₃= 6

4) Interquartile range (IQR)

The IQR shows you the distance where the middle 50% of the data set is.

IQR= Q₃-Q₁= 6-3 = 3

I hope this helps!

Answer:

Hydro static force is =18377 N

Step-by-step explanation:

The hydro static force is equals to the hydro static pressure times the area.

The hydro static pressure of a fluid increases as the depth of the fluid increases and the formula of it is given below.

Hydro static Pressure, P = d·g·ρ

Where, d is the depth of the object

g is the gravitational constant

ρ is the density of the fluid

Density of water   ρ = \(1000 kg/m3\)

=1000 kg/m^3 * 9.8m/s^2 which is √(3/2).a below the water level.

Side of the plate  x = 10 m

The hydrostatic force = the pressure at the center x the area =\([sqrt(3)/2 m][1000 kg/m^3 * 9.8m/s^2]\)\([(1/2)(3)(8)(sqrt(3)/2) m^2]\)=18377 N

Answer:

70 cans

Step-by-step explanation:

2 cups / 10 cans = 14 cups / ? cans

Cross-Multiply

10 x 14 = 2 x ?

140 = 2?

? = 70 cans

Hope this helps!! :)

The unknown angle in the cyclic quadrilateral is as follows:

∠R = 86 degrees

The diagram above is cyclic quadrilateral. A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees. The opposite angles in a cyclic quadrilateral is supplementary.

Hence, let's find the unknown angle.

∠R = 1 / 2 (92 + 80)

∠R = 1 / 2 (172)

∠R = 86 degrees

Therefore, the unknown angle is 86 degrees.

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To prove: If one angle of a triangle is 90°, then the sum of the other two angles is equal to 90°. is sum of angles on a triangle is 180 degrees

In a triangle, the sum of the interior angles in the triangle is 180 degrees

For right triangle, that is angle that has one side as 90 degrees, the sum of the other two sides will be 90 degrees

Assuming the other angles are x and y, then a side is 90 degrees

x + y + 90 = 180 (sum of interior angles on a triangle)

x + y = 180 - 90

x + y = 90 degrees

hence the sum of the interior angles is 90 degrees

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The company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.

What is the Gaussian method?

The Gaussian method, also known as Gaussian elimination or row reduction, is a technique for solving systems of linear equations. It involves performing a sequence of operations on the rows of a matrix to transform it into an equivalent matrix that is in row echelon form or reduced row echelon form.

To use the Gaussian method, we need to set up a system of linear equations based on the given information. Let x, y, and z be the number of units of Metakeb, Mewesson, and Metekem produced per month, respectively. Then we have:

Machining department: 1200x + 1800y + 3000z = 1050(60)

Inspection department: 2400x + 1200y = 1160(60)

Assembly department: 600x + 3000y = 830(60)

Simplifying these equations, we get:

Machining department: 20x + 30y + 50z = 3150

Inspection department: 8x + 4y = 232

Assembly department: x + 5y = 139

Now we can use the Gaussian method to solve for x, y, and z:

Step 1: Write the augmented matrix:

| 20 30 50 | 3150 |

| 8 4 0 | 232 |

| 1 5 0 | 139 |

Step 2: Use row operations to get the matrix in row echelon form:

R2 → R2 - 4/5 R3

R1 → R1 - 20R3

| 0 -2 50 | 850 |

| 0 2 -4   | -28 |

| 1 5 0     | 139 |

R2→ -1/2 R2

R1 → R1 + R2

| 0 1 -25 | 407 |

| 0 1 -2 | 14 |

| 1 5 0 | 139 |

R1→ R1 - R2

| 0 0 -23 | 393 |

| 0 1 -2 | 14 |

| 1 5 0 | 139 |

R3→ R3 - 5R2

| 0 0 -23 | 393 |

| 0 1 -2 | 14 |

| 1 0 10 | 65 |

R1→ -1/23 R1

| 0 0 1 | -17 |

| 0 1 -2 | 14 |

| 1 0 10 | 65 |

R2 → R2 + 2R3

| 0 0 1 | -17 |

| 0 1 0 | 96 |

| 1 0 10 | 65 |

R3 → R3 - 10R1

| 0 0 1 | -17 |

| 0 1 0 | 96 |

| 1 0 0 | 235 |

Step 3: Read off the solution from the row echelon form:

z = -17

y = 96

x = 235

Therefore, the company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.

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Answer:

leg lengths are 5 units and 3 units.

Step-by-step explanation:

ヾ(•ω•`)o

Answer:

1/4

Step-by-step explanation:

\((\stackrel{x_1}{-14}~,~\stackrel{y_1}{-16})\qquad (\stackrel{x_2}{-18}~,~\stackrel{y_2}{-17}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-17}-\stackrel{y1}{(-16)}}}{\underset{run} {\underset{x_2}{-18}-\underset{x_1}{(-14)}}}\implies \cfrac{-17+16}{-18+14}\implies \cfrac{-1}{-4}\implies \cfrac{1}{4}\)

I’m sorry but I could not find a pdf version of the Envision volume 2 book for 5th grade online. However, I found some websites that have answer keys and lesson plans for the book. You can check them out by searching for the following queries:

I hope this helps you with your homework.

Answer:

31

Step-by-step explanation:

Substitute -10 for x in b(x)=|x+41|, obtaining f(-10) = |-10 + 41|.  This result simplifies to f(-10) = |31| = 31

The digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number,

A rational number is a number that can be expressed as a ratio or fraction of two integers (a numerator and a non-zero denominator).

We can see that the next three digits in the decimal points are 6, 6 and 6, respectively. Therefore, the decimal equivalent of 22/6 is:

22/6 = 3.666666...

We notice that the digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number, which means that its decimal representation either terminates (ends) or repeats in a pattern. In this case, it repeats in a pattern of 6's.

Each of the digits after the decimal point will be 6 because this number is a rational number and repeating decimal with a repeating digit of 6.

The difference between 40 and the product of these digits and 6 is always 4.

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This is due to the fact that angles 2, 3, and 5 are interior angles of the triangle, and the total of the inner angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

A triangle is a closed, two-dimensional geometric object composed of three line segments, known as sides, that intersect at three locations, known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all sides equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles less than 90 degrees), right (one angle equal to 90 degrees), or obtuse (all angles greater than 90 degrees). The area of a triangle can be computed using the formula A = (1/2)bh, where A is the area, b is the triangle's base, and h is the triangle's height.

Regarding the given diagram, the following claims are always true:

m∠3 + m∠4 + m∠5 = 180°

m∠5 + m∠6 = 180°\s= m∠2 (the measure of the external angle at angle 2). (the measure of the exterior angle at angle 2). And because angles 2 and 3 are likewise interior triangle angles, we get m2 + m3 = m6, which can be rearranged to yield m5 + m6 = m3 + m4 + m5 = 180°.

m∠2 + m∠3 + m∠5 = 180°

This is due to the fact that angles 2, 3, and 5 are interior angles of the triangle, and the total of the inner angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

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Answer:

\( \huge{ \boxed{ \sf{5 \: and \: 7}}}\)

☪ Question :

☇ Both numbers are prime in which of the following pairs of numbers ?

☐ 5 and 9

☐ 7 and 9

☐ 5 and 6

☑ 5 and 7 ---- Answer !!

☐ 7 and 8

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

☥ Let's explore about prime numbers and composite numbers !!

\( \underline{ \text{Still \: confused ?}}\)

Alright , Let's check all the options :

☐ 5 and 9

⤿ 5 is a prime number as it can only be divided by 1 and itself but 9 is not a prime number as it can be divided by more than two numbers ( i.e 1 , 3 and 9 )

☐ 7 and 9

⤿ 7 is a prime number as it can only be divided by 1 and itself but 9 is a composite number as it can be divided by 1 , 3 and 9.

☐ 5 and 6

⤿ 5 is a prime number as it can only be divided by 1 and itself but 6 is a composite number as it can be divided by more than two numbers ( i.e 1 , 3 and 6 )

☑ 5 and 7

⤿ Yeah ! 5 and 7 are prime numbers as they only have two factors which are one and itself.

☐ 7 and 8

⤿ 7 is a prime number as it can only be divided by 1 and itself but 8 is a composite number as it can be divided by more than two numbers ( i.e 1 , 2 , 4 and 8 )

Hope I helped!

Have a wonderful day ! ツ

~TheAnimeGirl ♡

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Here we just need to identify the pair of prime numbers, we will see that the correct option is D: 5 and 7.

Prime numbers are the numbers that can only be divided by themselves and 1.

So we just need to test each one of the given numbers to see if these are primes or not, for example for 6 we have:

6/3 = 2

6/2 = 3

So 6 is not a prime.

Similarly for 8 we have:

8/2 = 4

8/4 = 2

So 8 is not a prime.

In the other hand, 5 and 7 can only be divided by themselves, thus 5 and 7 are primes.

Then the correct option is D, 5 and 7.

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Answer:

y=4/5x1

Step-by-step explanation:

Answer:

A model of a shopping centre is drawn to scale where 1 cm on the model represent 4 m on the ground. Music shop Thabo's Sports Ware Fati's Clothing shop Grocery store PARKING Coffee shop Toilets Restaurant Shoe store Physiotherapy Health and Fitness center 1.1 Which shop is on the right of the physiotherapy? (2) 1.2 Describe the position of the Coffee Shop in relation to the Toilets. (2)

Answer:

Step-by-step explanation:

5p(6L/p)=30L

30 liters can be made with the five pots.

Answer is in the photo. I can only upload it to a file hosting service. link below!

tinyurl.com/wpazsebu

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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1)

The axis of symmetry is x = -6.

2)

Vertex is (-6, 26).

3)

f(x) has a maximum value.

4)

f(x) is concave down.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

f(x) = -x² - 12x - 10

This is in the form of ax² + bx + c.

a = -1, b = -12, c = -10

The axis of symmetry is x = -b/2a

x = 12/(-2)

x = -6

Now,

f(x) = -x² - 12x - 10

f(x) = -(x² + 12x + 10)

f(x) = - { (x² + 12x + 36) - 36 + 10}

f(x) = -(x + 6)² + 26

This is in the form of f(x) = a (x - h)² + k

a = -1, h = -6, k = 26

Vertex = (h, k) = (-6, 26)

Now,

f(x) = -x² - 12x - 10

f'(x) = -2x - 12

f''(x) = -2

It is a negative value.

This means f(x) has a maximum value.

Now,

From the graph, we see that f(x) is concave down.

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The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.