A(-2,3)
Triangle ABC has vertices at A(-2,3), B(-3,6), and
C(2,-1) Is triangle ABC a night triangle? If so, which
angle is the night angle?
O No, the triangle has no right angles.
O Yes, the right angle is angle A
O Yes, the right angle is angle B
O Yes, the right angle is angle C
VA
C (2-1)
B (-3,-6)

Answer:

y - 9 = -1/2 (x - 0)

Step-by-step explanation:

perpendicular slope = -1/2

y - 9 = -1/2 (x - 0)

Answer:

answer is in attachment

Answer:

4

Step-by-step explanation:

Every year, the world grows by 1.1%. Converting to a decimal, we can divide by 100 to get 1.1% = 0.011. This means that the world grows by 0.011 exponentially each year. To put this into an expression, we can add 1 to our percentage to get 1.011. This represents 1 = 100% (the original population) and the growth of 1.1% = 0.011. We multiply the rate including the growth by the population to get the population after one year. After the first year, we have

population * 1.011 as the new population after one year. We do that for every year, so the second year's population is population*(1.011)*(1.011) and so on. If x represents the amount of years, then the population can be represented as

(original population)*1.011ˣ

Therefore, to get from 7 billion to 7.31 billion, we have

7 billion * 1.011ˣ = 7.31 billion

divide both sides by 7 billion to relatively isolate the x

1.011ˣ = 7.31/7

Another way of writing this is

log (base 1.011) (7.31/7) = x

≈ 3.96

Rounding to the nearest whole number, we get 4 as our answer

The number of years it takes for the population to grow from 7 billion to 7.31 billion is;

n = 4 years.

We are told that the population of the world grows exponentially by 1.1% per year. This is equivalent to growth of 0.011 per year exponentially.

Now, since the exponential rate is 0.011 per year, thus, if the original population is P, then after a year, the new population will be;

P_1 = 1.011¹ × P

After 2 years, it will be;

P_2 = 1.011² × P

Thus, if n represents the number of years after the initial population, then population after n years if original population is P is;

P_n = 1.011ⁿ × P

Now, we are told that the population grew from 7 billion to 7.31 billion.

Thus;

P = 7 billion

P = 7 billion P_n = 7.31 billion

Thus;

7 billion × 1.011ⁿ = 7.31 billion

divide both sides by 7 billion to get;

1.011ⁿ = 7.31/7

1.011ⁿ = 1.044285

n log 1.011 = log 1.044285

n = 0.018819/0.004751156

n ≈ 4 years

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The money belongs to Jackie, Avery, and Samantha is $10, $30, and $16 respectively.

Given that,

Avery has three times as Jackie.

Also, Jackie has $6 lower than Samantha.

Together they have $56.

Based on the above information

Let us assume the Jackie be x

So, Avery should be 3x

Samantha should be x + 6

So, the equation should be

x + 3x + x + 6 = $56

5x = $56 - $6

5x = $50

x = $10

So, Jackie has $10

Avery has $30

And, Samantha has $16

Therefore we can conclude that the money belongs to Jackie, Avery, and Samantha is $10, $30, and $16 respectively.

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Answer:

[tex] \frac{1}{3} (2x - y) = z \\ \frac{2}{3} x - \frac{y}{3} = z \\ \frac{2}{3} x = z + \frac{y}{3} \\ \frac{2}{3} x = \frac{3z + y}{3} \\ x = \frac{3z + y}{3} \div \frac{2}{3} \\ x = \frac{3z + y}{3} \times \frac{3}{2} = \frac{3(3z + y)}{6} \\ \\ x = \frac{3z + y}{2} \\ \\ x = \frac{3z}{2} + \frac{y}{2} [/tex]

I hope I helped you^_^

Answer:

[tex]7 \times 6 = 5 \: sixes + 2 \: sixes \\ 7 \times 6 = 30 + 12 \\ = 42 \\ \\ thank \: you[/tex]

Hi ;-)

[tex]7\cdot6=5 \ \text{sixes}+\boxed2 \ \text{sixes}\\\\=\boxed{30}+12\\\\=\boxed{42}[/tex]

Answer:

15.3 L

Step-by-step explanation:

1% of 15 is 15÷100=0.15

0.15×2=0.3, so 2% is 0.3

15+0.3=15.3

Call a bottle of juice costs is x

$2.49 + 12x = $27.57

             12x = $27.57 - $2.49

             12x = $25.08

                 x = $25.08 / 12

                 x = $2.09

SO each bottle of juice costs $2.09.

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Answer:

1.5 hours / 90 minutes

Step-by-step explanation:

time = distance ÷ speed

Answer: x=585

Step-by-step explanation:

thats the answer

The required probabilities are [tex]P(\text{pennies})=\dfrac{13}{28},P(\text{nickels})=\dfrac{27}{140},P(\text{dimes})=\dfrac{3}{14},P(\text{quarters})=\dfrac{9}{70}[/tex].

Given:

Pennies = 65

Nickels = 27

Dimes = 30

Quarters = 18

To find:

The probability of each.

Solution:

The probability formula:

[tex]\text{Probability}=\dfrac{\text{Favorable outcome}}{\text{Total outcomes}}[/tex]

Total number of coins:

[tex]65+27+30+18=140[/tex]

The probability of selecting Pennies is:

[tex]P(\text{pennies})=\dfrac{65}{140}[/tex]

[tex]P(\text{pennies})=\dfrac{13}{28}[/tex]

The probability of selecting nickels is:

[tex]P(\text{nickels})=\dfrac{27}{140}[/tex]

The probability of selecting dimes is:

[tex]P(\text{dimes})=\dfrac{30}{140}[/tex]

[tex]P(\text{dimes})=\dfrac{3}{14}[/tex]

The probability of selecting quarters is:

[tex]P(\text{quarters})=\dfrac{18}{140}[/tex]

[tex]P(\text{quarters})=\dfrac{9}{70}[/tex]

Therefore, the required probabilities are [tex]P(\text{pennies})=\dfrac{13}{28},P(\text{nickels})=\dfrac{27}{140},P(\text{dimes})=\dfrac{3}{14},P(\text{quarters})=\dfrac{9}{70}[/tex].

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Step-by-step explanation:

[tex] \frac{2}{9} + \frac{1}{3} \\ by \: taking \: out \: the \: lcm \: of \: 9 \: and \: 3 \: \\ we \: get \: 9\: as \: lcm \\ now \\ \frac{2 \times 1 + 1 \times 3}{9} \\ \frac{2 + 3}{9} \\ \frac{5}{9} [/tex]

Answer:

[tex] \boxed{d = \frac{5}{3}}[/tex]

Step-by-step explanation:

[tex]given \: points \: (2,1) \: and \: (1, - \frac{1}{3}): \\ d \: = \sqrt{ (x _{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} } \\ d \: = \sqrt{ (1 - 2)^{2} +( - \frac{1}{3} - 1)^{2} } \\ d \: = \sqrt{ ( - 1)^{2} +( - \frac{4}{3})^{2} } \\d \: = \sqrt{ (1) +( \frac{16}{9}) } \\d \: = \sqrt{ 1 + \frac{16}{9} } \\d \: = \sqrt{ \frac{9}{9} + \frac{16}{9} } \\d \: = \sqrt{ \frac{25}{9} }\\d \: = \frac{\sqrt{ 25 }}{\sqrt{ 9 }} \\d \: = \frac{ 5}{3} [/tex]

Answer:

-1/10

Step-by-step explanation:

after (.) we put zero in the denominator according to how many numbers are after .

-0.1= -1/10

hope this will help you

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Answer:

[tex] \frac{x - 5}{3} \geqslant 2.8 \\ \\3 \times ( \frac{x - 5}{3} ) \geqslant \frac{28}{10} \times 3 \\ \\ \\ x - 5 \geqslant \frac{84}{10} \\ \frac{84}{10} = 8.4 \\ \\ x - 5 \geqslant 8.4 \\ \\ x \geqslant 13.4[/tex]

The values of the angles are;

x = 12°

m∠PQS = 71°

m∠PQT = 142°

m∠TQR = 41°

The reason the above values are correct is as follows:

Question: The part of the question that appears missing as obtained online is as follows;

The required angles: x, m∠PQS, m∠PQT, and m∠TQR

Please see attached drawing of the angles from the question

The given parameters are;

[tex]\overset{\longrightarrow}{QS}[/tex] bisects ∠PQT

m∠SQT = (8·x - 25)°

m∠PQT = (9·x + 34)°

m∠SQR = 112°

We have;

m∠PQT = m∠SQT + m∠PQS (Angle addition postulate)

m∠SQT ≅ m∠PQS (Angles formed by angle bisector are congruent)

m∠SQT = m∠PQS Definition of congruency

m∠PQT = 2 × m∠SQT

Therefore;

(9·x + 34)° = 2 × (8·x - 25)° = (16·x - 50)°

Collecting like terms gives;

(34 + 50)° = 16·x - 9·x = 7·x

7·x = 84°

x = 84°/7 = 12°

x = 12°

m∠SQT = (8·x - 25)°

Therefore;

m∠SQT = (8 × 12 - 25)° = 71°

m∠SQT = 71°

m∠PQT = 2 × m∠SQT

∴ m∠PQT = 2 × 71° = 142°

m∠PQT = 142°

m∠PQS = m∠SQT (Angles formed by the same bisector [tex]\overset{\longrightarrow}{QS}[/tex])

∴ m∠PQS = m∠SQT = 71°

m∠PQS = 71°

m∠SQR = m∠SQT + m∠TQR (Angle addition postulate)

m∠SQT = 71°

∴  m∠SQR = 112° = 71° + m∠TQR

m∠TQR = 112° - 71° = 41°

m∠TQR = 41°

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Answer:

Max drove half an hour at 110 miles per hour.

Step-by-step explanation:

185 = 65(2) + 110t

185 = 130 + 110t

-130    -130

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

55 = 110t

/110    /110

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

0.5 = t

Answer:

B. x = 31; m∠ROS = 62°

Step-by-step explanation:

Complementary angles add to 90

∠ROQ + ∠ROS = 90

28+2x = 90

Subtract 28 from each side

2x = 90-28

2x=62

Divide by 2

2x/2 = 62/2

x = 31

∠ROQ =28

∠ROS = 2x=2*31 = 62

Step-by-step explanation:

X = Acceleration × time

=300× (10/60)

=50km/h

Answer:

y = [tex]\frac{4}{3}[/tex] x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

8x - 6y + 12 = 0 ( subtract 8x + 12 from both sides )

- 6y = - 8x - 12 ( divide terms by - 6

y = [tex]\frac{-8}{-6}[/tex] x + 2 , that is

y = [tex]\frac{4}{3}[/tex] x + 2 ← in slope- intercept form

By looking at the dot graph, we can see that the single dot above 12 in the Stony Brook graph, means that the ecologist find that in one of the 42 places measured in the Stony Brooks lake, the nitrate concentration was 12 mg/L

To understand this, first I want to give a brief explanation of how these graphs work.

You know that the ecologist did study the Nitrate pollution at 42 places in two lakes.

Each of these 42 places is represented with a dot in the corresponding graph.  Now looking at the graph, the position of the dots represents the nitrate concentration (you can see it in the horizontal axis) on one of these 42 places (42 dots for 42 places).

So, having a single dot above 12 in the Stony Brook graph, means that the ecologist find that in one of the 42 places measured in the Stony Brooks lake, the nitrate concentration was of 12 mg/L

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When two numbers have no common factors other than 1. In other words there is no value that you could divide them both by exactly (without any remainder). Relatively Prime is also called "coprime" or "mutually prime".

I think this help you Now thank you

The answer is Co-prime

Hope It Help

Answer:

23

Step-by-step explanation:

9x-4=6x+5

3x-4=5

3x=9

x=3

plug in x

6(3)+5 = 23

Answer:

x = 48

Step-by-step explanation:

Multiply both sides by 6

x = 6 * 8

x = 48

Check:

48/6 = 8

8 = 8

Answer:

[tex] \frac{x}{6} = 8 \\ \\ x = 8 \times 6 \\ \\ x = 48[/tex]

Answer:

1: 5 2: 13 3: sqr root of 15 4: 1 5: 1 6: 3

Step-by-step explanation:

Follow the formula a squared plus b squared equals c squared. C is always the longest side of the equation. So figure out your variables to fill in and in the end, square root your remaining answer.

Answer:

12. This is because of the commutative property of addition.

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Using the commutative property of addition

8+4 = 12

4+8 = 12

Answer:

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Step-by-step explanation:

16 - 2t + 5t + 9

16 + 9 -2t + 5t=0

25 + 3t =0

3t= -25

t= -8.3