Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample.If two angles are congruent, then they are vertical angles.

Step-by-step explanation:

Daniela : nice definition

Ori : part is right, but part is not

Kaori : incorrect

Daniela would not even have to say, that the lines are distinct. in any case, yes if you don't change anything about the appearance of the lines, but can move them on top of each other. and they completely blend in with each other, then yes they are parallel.

Ori is wrong about the part that they have to be close together. the second line could be in another galaxy, but if they are in the same plane and never intersect each other, then they are parallel.

Kaori is wrong by understanding that parallel means to opposite of perpendicular. perpendicular just means that the 2 lines are intersecting each other at a right angle (90°). but they can intersect at any other angle. that makes them not perpendicular, but they still intersect each other. so, they are not parallel.

The unknown angles on the straight line are as follows:

∠RQT is a straight angle.

Therefore,

∠RQT = 180 degrees(angle on a straight line)

Therefore, let's find m∠RQS and m∠TQS

∠RQT = m∠RQS + m∠TQS

where,

m∠RQS = 10x + 9

m∠TQS = 7x + 1

Therefore,

∠RQT = 10x + 9 + 7x + 1

∠RQT = 17x + 10

180 - 10 = 17x

170 = 17x

divide both sides by 17

x = 170 / 17

x = 10

Therefore,

m∠RQS = 10(10) + 9 = 109°

m∠TQS = 7(10) + 1 = 71°

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Answer:

c= 24

Step-by-step explanation:

Manny would save $729.50 per paycheck

What are dollar savings on new motorcycle and retirement?

The amount of savings on new motorcycle and retirement can be determined by multiplying the fractions by the earnings per paycheck

savings for new motorcycle=$2918*2/20

savings for new motorcycle=$291.80

savings on retirement=$2918*3/20

savings on retirement=$437.70

total savings=$291.80+$437.70

total savings=$729.50

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The inverse of y = 7x² - 10 is √(x+10)÷7

Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effects of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One is the result when a number is multiplied by its reciprocal, or inverse.

based on the available facts;

y = 7x^2 - 10

Switch y and x.

x = 7y^2 - 10

Solve for y.

Add 10 to both sides.

x + 10 = 7y^2

Divide both sides by 7.

(x + 10)/7 = y^2

√ both sides.

√(x + 10)/7 = y

Replace y with f^-1(x)

f^-1(x) = √(x + 10)/7y = 7x^2 - 10

Switch y and x.

x = 7y^2 - 10

Solve for y.

Add 10 to both sides.

x + 10 = 7y^2

Divide both sides by 7.

(x + 10)/7 = y^2

√ both sides.

√(x + 10)/7 = y

Replace y with f^-1(x)

f^-1(x) = √(x + 10)/7

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Answer:

14

Step-by-step explanation:

the fist 20 characters equal 14

Answer:

110

Step-by-step explanation:

integers are basically whole numbers

first 10 even integers would be 2,4,6,8,10,12,14,16,18,20

if you add all those numbers, it would be 110

The total number of different permutations of the set is 5040

The set of elements is given as

Set =  {a, b, c, d, e, f, g}.

The cardinality of the above set is

n = 7

So, the total number of different permutations of the set is

Permutation = n!

This gives

Permutation = 7!

Expand

Permutation = 7 * 6 * 5 * 4 * 3 * 2 * 1

Evaluate

Permutation = 5040

Hence, the total number of different permutations of the set is 5040

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Answer:

$25.23

Step-by-step explanation:

Answer:

53/30

Step-by-step explanation:

Just got to derive the lowest common multiple of the denominator and make it same for all fraction. Don't forget to multiply the numerator just the same.

Answer: 53/30

Step-by-step explanation:

[tex]\displaystyle\\\frac{4}{6}+\frac{2}{4} +\frac{3}{5} =\\\\\frac{2*2}{2*3} +\frac{2}{2*2}+\frac{3}{5}=\\\\\frac{2}{3} +\frac{1}{2} +\frac{3}{5}=\\\\\frac{2*10+1*15+3*6}{3*2*5} =\\\\\frac{20+15+18}{30} =\\\\\frac{53}{30}[/tex]

The equation that can be used to determine the cost of one drink is 29.18 = 22 + 2x - 5 where the cost of each drink is $6.9

= $22

29.18 = 22 + 2x - 5

29.18 = 17 + 2x

29.18 - 17 = 2x

12.18 = 2x

x = 12.18 / 2

x = 6.9

Therefore, the equation that can be used to determine the cost of one drink is 29.18 = 22 + 2x - 5 where the cost of each drink is $6.9

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In linear equations, 64% of samples have nitrogen levels and phosphorus levels that are low.

What is linear equations?

P(low nitrogen) = 46% = 0.46

P(low phosphorus) = 28% = 0.28

P(low nitrogen and low phosphorus) = 10% = 0.10

P(low nitrogen or low phosphorus) = P(low nitrogen) + P(low phosphorus) - P(low nitrogen and low phosphorus)

= 0.46 + 0.28 - 0.10

= 0.64 = 64%

Hence , 64% of samples have nitrogen levels and phosphorus levels that are low.

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The value of x and BD are 29 and 62

From the diagram shown, we can see that AC and BD are diagonals of the rectangle

It is important to note that the diagonals of a rectangle are equal

Then,

AC = BD

4x - 54 =  33 + x

collect like terms

4x - x = 33 + 54

Add/ subtract like terms

3x = 87

Make 'x' the subject

x = 87/ 3

x = 29

But BD = 33 + 1x = 33 + 1(29) = 33 + 29 = 62

Thus, the value of x and BD are 29 and 62

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Answer:

h = -4/3

Step-by-step explanation:

Worked out on paper

We have proved the trigonometric expression cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A) by using C/D formula.

We are given the expression:

cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A)

We need to prove the expression.

We know that:

Cos C + Cos D = 2 cos ( C + D / 2) cos ( C - D / 2)

Using this identity, we get that:

= cos 5 A + cos A + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= 2 cos ( 5A + A / 2) cos ( 5A - A / 2) + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= 2 cos 3 A cos 2 A + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= cos 2 A ( 2 cos 3A + 1) = cos 2 A (1 + 2 cos 3 A)

= cos 2 A (1 + 2 cos 3 A) = cos 2 A (1 + 2 cos 3 A)

LHS = RHS

Hence proved.

Therefore, we have proved the trigonometric expression cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A) by using C/D formula.

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An equation that can  can be used to find the number of sales Luke made this week is; 191 + 16.55x = ¹/₃(573 + 49.65x)

We are told to represent the number of sales as x.

Now, Luke works at a store and earns a fixed amount of $191 plus $16.55 per sale. This is represented as; 191 + 16.55x

Noah works at a different store and earns a fixed amount of $573 plus $49.65 per sale. This is represented as; 573 + 49.65x

We are told that they both made the same number of sales but Luke earned a third of what Noah earned. Thus;

191 + 16.55x = ¹/₃(573 + 49.65x)

An equation that can  can be used to find the number of sales Luke made this week is;

191 + 16.55x = ¹/₃(573 + 49.65x)

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Answer:

6x-9=2

Step-by-step explanation:

Answer:

2.47

Step-by-step explanation:

Perform long division.

[tex]Borrow\:8\:and\:2.\:You\:will\:see\: :)\\6 \cdot 2 = 12\\= 14 - 12 \\= 2\\Drop\:8\\= 28\\6 \cdot 4 = 24\\= 28 - 24\\= 4\\Drop\:2\\= 42\\6 \cdot 7 = 42\\= 42 - 42\\= 0\\\\= \boxed{2.47}[/tex]

➲ Hope it helps.

Answer:

-5

Step-by-step explanation:

(-12)+7 is the same as 7-12 which gives us - 5

Answer:

∠ TVW = 65°

Step-by-step explanation:

∠ UVW = ∠ TVW + ∠ UVT ( substitute values )

21x + 6 = 8x + 9 + 88

21x + 6 = 8x + 97 ( subtract 8x from both sides )

13x + 6 = 97 ( subtract 6 from both sides )

13x = 91 ( divide both sides by 13 )

x = 7

Then

∠ TVW = 8x + 9 = 8(7) + 9 = 56 + 9 = 65°

Answer:

Step-by-step explanation:

Proportional relationship equation:

Use given values in table to find the value of k:

So the equation is:

Answer: B. 3x+6<6 or -2x+9>3

               C. 3x-5<10 and -2x+9>3

Answer:

?

Step-by-step explanation:

Response bias results from the possibility that not all sophomore students provided accurate information about their drug use, which will immediately result in the response bias because of false data.

Response bias is a catch-all phrase for a variety of inclinations for participants to give misleading or inaccurate answers to queries. These biases are common in studies involving participant self-report, such as structured interviews or surveys. The validity of questionnaires or surveys can be significantly impacted by response biases.

The idea that human subjects do not passively respond to stimuli but rather actively integrate several sources of information to develop a response in a specific scenario is central to the concept that response bias can be induced or caused by a variety of causes. As a result, practically every element of an experimental condition has the ability to sway a respondent.

Explanation:

The remedy is to conduct a survey by licensed social workers since licensed social workers didn't explicitly ask sophomore students about drug use; instead, they interacted with the students as their friends before gathering the data.

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The product of two rational numbers is a rational number.

Definition and importance Imbalance or monetary disparity alludes to the contrast between the rich and poor, the endlessly the less wealthy it is shown by individuals' various situations inside the financial conveyance abundance, pay and pay. Imbalance is huge in a general public where hardly any individuals own a lopsided measure of the financial pie. Social imbalance alludes to the lopsided economic wellbeing in any general public, coming about because of inconsistent open doors, and lower awards for exertion. This sort of divergence is brought about by a sensation of being unjustifiably treated, or of segregation in host of regions, like restricted admittance to quality training and occupations. Notwithstanding pay imbalance, individuals who have specific individual attributes, either from birth, or which have been constrained on them by others, are in many cases the subject of inconsistent social treatment. These attributes incorporate such things as race, skin tone, and eye shape, as well as parentage, the guardians' societal position, inability, orientation and orientation character.

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Answer: A rational Number

Step-by-step explanation:

Answer:

x is 50.

Explanation:

3.5 and 1.4 are both at the bottom of the fraction (denominators), so divide 3.5 by 1.4 to get 2.5.

Then, multiply 20 by 2.5.

This makes sense because 3.5 is greater than 1.4, and the final answer (50) is greater than 20.

We can always check by dividing 50 by 3.5 and 20 by 1.4. See if it is the same number.

Answer:

irrational number

Step-by-step explanation:

cause it just is

stan bts,txt,enhypen,ateez, and straykids

If a chip is randomly drawn from the bag, the probability it is not a red one is P(not red)  = 12/19.

Probability of an event A is the number of event A divided by all possible outcomes. Mathematically,

P(A) = n(A)/n(S)

where:

n(A) = number of event A

n(S) = number of all possible outcomes or sample space.

Suppose there 3 possible outcomes, A, B, and C, then:

n(S) = n(A) + n(B) + n(C)

1 = P(A) + P(B) + P(C)

The probability the outcome is not event A is equal to the probability of (B or C), or in other words,

However,

    P(B or C) =  P(B) + P(C)

It means,

     P(not A)  = 1 - P(A)

In the given problem:

Number of chips:

Blue = 3

Red = 7

Yellow = 4

Green = 5

Total chips = 3 + 7 + 4 + 5 = 19

If a chip is randomly drawn, the probability it will be a red one is:

P(red) = 7/19

Hence

P(not red) = 1 - 7/19 = 12/19

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Answer:

Find the revenue function R when x energy drinks are sold.

Step-by-step explanation:

The inequality to represent the number of students who can attend the field trip on the bus will be C. s≤48 s is less than or equal to 48.

From the information, Mrs. Milleman's math class is planning to going on a field trip. The school bus which is taking them can hold at most 48 people.

Therefore, the inequality to represent the number of students who can attend the field trip on the bus will be C. s≤48 s is less than or equal to 48.

In conclusion, the correct option is C.

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1.  For the spring, the sugar-water mixture is in the ratio of 3:2 that is for 2 cups of water, 3 cups of sugar are required. For the fall, for every cup of water, 2 cups of sugar are required, giving a ratio of 2:1.

2. To get the ratio for the mixtures, order the pairs (e.g. (6, 4), (15, 10), and check the proportion of each variable in the other variable, using the least common divisor.

A ratio is the proportion of each variable in the other.

Ratios are expressed using the ratio sign (:) or in fractions, decimals, or percentages.

Spring Sugar-Water Mixture
Cups of Sugar   Cups of Water

          6                         4

        15                        10

        18                        12

       27                        18

The ratio of the spring sugar-water mixture is 3:2.  For instance, 27:18 can be reduced to 3:2 by divisor 9.

Fall Sugar-Water Mixture

Cups of Sugar   Cups of Water

          4                         2

        10                         5

        14                         7

       30                        15

The ratio of the fall sugar-water mixture is 2:1.

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