which of the following graphs represents the solution set for the inequality - x < 2

Answer:

Step-by-step explanation:

There are several sort of "obvious" properties of equality/congruence. Keeping them sorted out can be a bit of a trick.

  A = A . . . . reflexive property

  A = B ⇔ B = A . . . . symmetric property (erroneously cited in the proof)

  A = B, B = C ⇒ A = C . . . . transitive property (the one needed in the proof)

__

Not to confuse the issue, but there is also the "substitution property of equality" that says if X = Y, then X can be substituted for Y or vice versa. In the end, the transitive property is an application of this, where we're substituting for B in the second equation, or for A in the first equation.

The A=B=C form of Statement 1) in the proof is what gives you the clue it is the transitive property that is wanted here.

Answer:

-5 is in the negatives, and 3 is positive, therefore greater than -5 three is greater than -5

The sequence of the transformations are rotation, then translation, and then reflection.

A transformation refers to the movement of a point from its original (initial) position to a new location.

In Geometry, there are different types of transformation and these include the following:

Based on the diagram (see attachment), we can logically deduce that the sequence of the transformations are rotation, then translation, and then reflection.

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Answer:

Question 1: 29

Question 2: 50

Question 3: AD≅BC

Step-by-step explanation:

question 1: Since it's a parallelogram opposite sides are equal.

4x+5=5x-1   add one to both sides

4x+6 =5x subtract 4x from both sides

6 = x

So AD is equal to 5(6) - 1 = 30-1 =  29=AD

Question 2: Since diagonals in a parallelogram bisect each other AE = EC

So...

5x+5 = 8x- 7 add 7 to both sides

5x+12 = 8x subtract 5x from both sides

12=3x divide both sides by 3

4=x

AC= 5(4) + 5 + 8(4) - 7

AC= 20 + 5 + 32 - 7

AC= 50

Question 3: Lines can only be congruent, represented by ≅, not equal which is represented by =. Values can be equal.

By using the elimination method you get the answer  line AD ≅ line BC

Answer:

9) - 17

11) - 5

13) 30

15) 16

10) - 20

12) - 1

14) 30

16) - 21

1) 16

3) 21

5) - 22

7) - 19

2) 11

4) 7

6) - 9

8) - 6

Step-by-step explanation:

Sorrh I wrote this weirdly I was reading it downwards not sideways but hopefully this helps either way :))

Answer:

251.2

Step-by-step explanation:

The formula for the volume of a cylinder is \(\pi r^2h\). Plugging in your measurements...

Height = 20 inches.

Radius = 2 inches.

The volume is \(\pi2^2h\).

Simplification...

\(\pi2^220 = \pi4(20)= 4\pi 20\).

\(\pi\) ≈ \(3.14\)

3.14 * 4 = 12.56

12.56*20 = 251.2

Answer:

$14.22

Step-by-step explanation:

Bernie is paying the refrigerator at an installment basis, that is, for 1 and 1/2 years or 18 months. If he's paying $69 per month, let's solve the total amount that he'll be paying in 18 months.

$69 x 18 months = $1,242

Now that we know the total amount, we have to subtract the regular price of the refrigerator from the amount with interest in order to know the total amount of interest Bennie's going to pay in 18 months.

$1,242 - $986 = $256

Let's divide the amount into 18 months in order to get the interest per month.

$256 ÷ 18 = $14.22

Bernie pays the average amount of $14.22 as an interest each month.

The value of x is 6 degree that makes m || n.

What is parallel lines?

Parallel lines are coplanar, straight lines in geometry that don't cross at any point. When two planes in the same three-dimensional space are parallel, they never cross. Curves that maintain a set minimum distance from one another and do not touch or intersect are said to be parallel curves.

(8) Given: m || n

We have to find the value of x that makes m || n.

The lines m and n are divides by the line l of angle 90 degree.

⇒ 16x - 6 = 90

Add 6 on both sides,

16x - 6 = 90 + 6

16x = 96

Divide both sides by 16

16x/16 = 96/16

x = 6

Hence, the value of x is 6 degree that makes m || n.

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Answer: 1, 2, and 4.

Step-by-step explanation: Each must be wider than the angle than a "L" has.

Let's assume that the corresponding side of the second triangle is \(\displaystyle\sf x\).

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

To find \(\displaystyle\sf x\), we can solve the proportion above:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

Taking the square root of both sides:

\(\displaystyle\sf \dfrac{x}{6.3} =\sqrt{\dfrac{49}{81}}\)

Simplifying the square root:

\(\displaystyle\sf \dfrac{x}{6.3} =\dfrac{7}{9}\)

Cross-multiplying:

\(\displaystyle\sf 9x = 6.3 \times 7\)

Dividing both sides by 9:

\(\displaystyle\sf x = \dfrac{6.3 \times 7}{9}\)

Calculating the value:

\(\displaystyle\sf x = 4.9\)

Therefore, the corresponding side of the second triangle is \(\displaystyle\sf 4.9 \, cm\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

let's assume that the corresponding side of the second triangle is .

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

To find , we can solve the proportion above:

Taking the square root of both sides:

Simplifying the square root:

Cross-multiplying:

Dividing both sides by 9:

Calculating the value:

Therefore, the corresponding side of the second triangle is 4.9cm


hope it helped u dear...........

Given

To find

Let the purchase value be P,

ATQ,

P -3 x 0.1P = Rs 43,740

P-0.3P = Rs 43,740

0.7P = Rs 43,740

P = Rs 43,740/0.7

P = Rs 62,486 (approx)

Hence, the purchase value of the machine would be Rs 62,486

Answer:

C. I hope this helps! Have a great day.

Answer:

x = 5

Step-by-step explanation:

If it is equilateral, that means all sides are equal

30 = 4x+10

Subtract 10 from each side

30-10 =4x

20 = 4x

Divide by 4

20/4 = 4x/4

5 = x

Answer:

\(8a^3\)

Step-by-step explanation:

\(\sqrt{64a^6}\)

\(\sqrt{64} \times \sqrt{a^6}\)

\(8 \times \sqrt{a^6}\)

\(8 \times a^{6 \times \frac{1}{2} }\)

\(8 \times a^{\frac{6}{2} }\)

\(8 \times a^3\)

Answer:

\(8a^3\)

Step-by-step explanation:

= \(\sqrt{64a^6}\)

= \(\sqrt{8*8*(a^3)^2}\)

= \(8a^3\)

Answer:

After applying the distributive property, Ezra's expression was 8y + 16

After he used the commutative property, his expression was 16 + 8y

Step-by-step explanation:

Distributive property rule: a(x+y) = ax + ay
   Not much to explain here

Commutative property rule: a + b = b + a   or  xy = yx
   We use addition rule in this case, simply place 16 in front of 8y

The measures of the unknown angles are as follows:

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles etc.

The parallel lines are line m and line l .  The parallel lines m and l are cut by two transversals.

Therefore, the measures of the unknown angles are as follows:

∠1 = 27°(vertically opposite angles)

∠1 = ∠4(alternate angles)

∠4 = 27°

Alternate angles are congruent. Vertically opposite angles are congruent.

Therefore,

∠1 + ∠2 = 124

27 + ∠2 = 124

∠2 = 124 - 27

∠2 = 97°

∠3 = 180 - ∠2 - ∠1 (sum of angles on a straight line)

∠3 = 180 -  97 - 27

∠3 = 56°

∠5 = 180 - ∠4 - ∠2

∠5 = 180 - 97 - 27

∠5 = 56°

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Answer:

well you would have to draw two pizzas or circles

Step-by-step explanation:

what you would to is draw lines to separate one of them into 10 peices and the other one into 5. You can shade in the 6 peices Hank ate and then shade the same amount of pizza on Roses. Hope this helped!

D its all about the process of elimination  you just got to un connect the

Hope this helps!

Answer:

Step-by-step explanation:

The sum of 8 and t ⇒ 8 + t

Answer:

\(8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^{14} - 2x^{12}}{x^{10}y^8}\)

Step-by-step explanation:

Given

\(8x^{-10}y^6 - 2x^2y^{-8}\)

Required

Simplify

Rewrite as:

\(8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^6}{x^{10}} - \frac{2x^2}{y^8}\)

Take LCM

\(8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^6*y^8 - 2x^2 * x^{10}}{x^{10}y^8}\)

Apply law of indices

\(8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^{14} - 2x^{12}}{x^{10}y^8}\)

Apply the fraction rule:

\(\text{a}\times\dfrac{\text{b}}{\text{c}} =\dfrac{\text{a}\times\text{b}}{\text{c}}\)

Answer:

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(A) The range and IQR for boxplot 1 is 10 and 6 respectively.

(B) The range and IQR for boxplot 2 is 12 and 7 respectively.

The interquartile range defines the difference between the third and the first quartile.

The formula for the interquartile range is given below.

Interquartile range = Upper Quartile – Lower Quartile = Q­3 – Q­1

The range is the difference between the lowest and highest values.

The formula for the interquartile range is given below.

Range = Maximum – Minimum

(A) For boxplot 1, we need to find the range and IQR from the given data set.

So, let 34 be the maximum and 24 be the minimum.

\(\text{Range}=\sf 34-24\)

\(\text{Range}=\sf10\)

Therefore, the range is 10.

Now time to find the IQR.

So, let 33 be Q3 and 27 be Q1.

\(\text{IQR}=\sf 33-27\)

\(\text{IQR}=\sf 6\)

Therefore, the IQR is 6.

(B) Now for boxplot 2, we will do the same thing as from part A.

Let's find the range.

So, let 24 be the maximum and 12 be the minimum.

\(\text{Range}=\sf 24-12\)

\(\text{Range}=\sf12\)

Hence, the range is 12.

Now for the IQR.

So, let 22 be Q3 and 15 be Q1.

\(\text{IQR}=\sf 22-15\)

\(\text{IQR}=\sf 7\)

Hence, the IQR is 7.

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The fraction represented by point A, it is crucial to have information about the scale, intervals, and the relative position of point A on the number line.

With these details, you can calculate the fraction accurately.

Point A on the number line represents a fraction that requires additional information to determine its precise value.

I can provide you with a general approach to finding the fraction corresponding to a given point on the number line.

A number line represents a range of values, typically with a specific scale or interval.

The scale can be divided into equal parts, such as units or fractions.

To determine the fraction represented by point A, we need to know the scale and the position of point A relative to that scale.

Let's consider a number line that ranges from 0 to 1, with evenly spaced tick marks representing tenths.

If point A is located halfway between the tick marks representing 0.4 and 0.5, then it represents the fraction 0.45 (or 9/20 in simplified form).

If the number line has a different scale or is divided into different intervals, the fraction represented by point A will be different.

Without specific details about the number line and the position of point A, it is impossible to determine the fraction precisely.

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The value of the z-score for the number 15  in a data set is 0.93.

Define z-score.

A data point's z-score, also known as a standard score, indicates how far it deviates from the mean. In practical terms, however, it's a measurement of how many standard deviations a raw number is from or above the population mean.

You can plot a z-score on a normal distribution graph. Z-scores can be anywhere between -3 and +3 standard deviations.

                     ∴  z = (x – μ) / σ

Given:

σ = 4.32

x = 15

Data set: 5, 7, 9, 11, 13, 15, 17

So, mean = 5 + 7 + 9 + 11 + 13 + 15 + 17/7

                = 77/7

            μ = 11

z = (x – μ) / σ

  = (15 - 11)/4.32

   = 4/4.32

z  = 0.93

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Answer:

3y

Step-by-step explanation:

Answer:

y intercept is 4

the equation is y= 3/4 + 4

Slope intercept equation y=mx+b

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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The annualized return for the entire period is the closest to 10.5%.

To calculate the annualized return for the entire period, we need to consider the returns for each year and the return in the first quarter of Year 4. Since the returns are given for each period, we can use the geometric mean to calculate the annualized return.

The formula for calculating the geometric mean return is:

Geometric Mean Return = [(1 + R1) * (1 + R2) * (1 + R3) * (1 + R4)]^(1/n) - 1

Where R1, R2, R3, and R4 are the returns for each respective period, and n is the number of periods.

Given the returns:

Year 1 return: 5% or 0.05

Year 2 return: 12% or 0.12

Year 3 return: -6% or -0.06

First quarter of Year 4 return: 2% or 0.02

Using the formula, we can calculate the annualized return:

Annualized Return = [(1 + 0.05) * (1 + 0.12) * (1 - 0.06) * (1 + 0.02)]^(1/3) - 1

Annualized Return = (1.05 * 1.12 * 0.94 * 1.02)^(1/3) - 1

Annualized Return = 1.121485^(1/3) - 1

Annualized Return ≈ 0.105 or 10.5%

Therefore, the annualized return for the entire period is approximately 10.5%.

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(3 x 7) x a and 3 x (7 x a) are equivalent expressions due to the associative property of multiplication.

The associative property of multiplication allows you to change the grouping of factors in a multiplication operation without changing the result. According to the associative property of multiplication, you can rearrange the parentheses to group the factors in any way you like.

For example, let's consider the expression 3 x 7 x a.

According to the associative property of multiplication, you can regroup the factors as (3 x 7) x a or 3 x (7 x a) without changing the result. This means that you can multiply 3 and 7 first, and then multiply the result by a, or you can multiply 7 and a first, and then multiply the result by 3, and you will get the same result either way.

This is because multiplication is associative, which means that the order in which you multiply numbers does not affect the final product. You can group the factors in different ways using parentheses, and you will still get the same result.

This property allows us to simplify and rearrange expressions in different ways to make them easier to work with or to solve equations. So, (3 x 7) x a and 3 x (7 x a) are equivalent expressions due to the associative property of multiplication.

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