19.
∠P and ∠Q are supplementary. m∠P = 5x + 3 and m∠Q = x + 3. x = ?

14

0

29

30

AND

P lies in the interior of ∠RST. m∠RSP = 40° and m∠TSP = 10°. m∠RST = ?

100°

50°

30°

10°

AND


6.
What is AB?

The properties of algebra used here are

For first point the algebraic properties used is  Distributive Properties of Addition Over Multiplication.

For Second point the algebraic properties used is  Associative Property of Addition

For third point the algebraic properties used is Associative Property of Multiplication.

For fourth point the algebraic properties used is  Commutative Property of Multiplication

For fifth point the algebraic properties used is  Distributive Properties of Addition Over Multiplication.

For sixth point the algebraic properties used is Associative Property of Addition

The correct question is Write the property that justifies each mathematical statement. Look carefully!!

1. a(c-d) = ac - ad

2. 2x + y = y + 2x

3. — 3(4c) = (- 3 * 4)c

4. 3(4ab) = (4ab)3

5. - 9(3 + 2x) = -9(3) - 9(2x)

6. 3+ (2 + n) = (3 + 2) + n

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The computation shows that the number of pans needed will be 5/6.

From the information given, it should be noted that it was stated that 1/6 of a pan will be needed for one person.

Therefore, the pans that will be needed for the 5 friends will be:

= 1/6 × 5..

= 5/6

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Answer:

$8 + 3t = $25.50

Answer:

  16000

Step-by-step explanation:

You want to know the number of panels produced at plant B if that was 6000 more panels than at plant A, and the total number of defective panels was 820. The defect rate at plant A is 5%, and at plant B is 2%.

Let b represent the number of panels produced at plant B. Then the number produced at plant A is (b-6000). The total number of defects is ...

  0.05(b -6000) +0.02b = 820

Simplifying the equation, we have ...

  0.07b -300 = 820

  0.07b = 1120

  b = 16000

Plant B produced 16000 panels.

<95141404393>

Answer:

58-(14)2

58-28

30

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

You should know the area of a circle, A = πr².

So, all you need to find is the area of half a circle, or A = \(\frac{1}{2}\) πr²

We see that the radius is half of the diameter or r = 6 in.

A = \(\frac{1}{2}\) (3.14)(6)²

A = 56.52 in²

Answer:

1. 87x20(4) divided by 20.

Step-by-step explanation:

Answer:

9. 0.87

10. 1.24

11. 3.4

hello

to solve this question, let's write the standard equation of a straight line

since, this equation passes the given gpoint and it's parallel to it, we will have to modify our equation

the given points are (0, 0)

let's insert it and solve

from the calculation above, the equation of the line is y = 5/8x + 6

Answer:

The half-life of a radioactive substance is the time it takes for half of the initial amount of the substance to decay. We can use the fact that 8% of the original amount remains after 100 days to determine the half-life of the isotope.

Let's assume that the initial amount of the substance is 1 unit (it could be any amount, but we're assuming 1 unit for simplicity). After one half-life, half of the original amount remains, or 0.5 units. After two half-lives, half of the remaining amount remains, or 0.25 units. After three half-lives, half of the remaining amount remains, or 0.125 units. We can see that the amount of substance remaining after each half-life is half of the previous amount.

We can use this information to set up the following equation:

0.08 = (1/2)^n

where n is the number of half-lives that have elapsed. We want to solve for n.

Taking the logarithm of both sides, we get:

log(0.08) = n*log(1/2)

Solving for n, we get:

n = log(0.08) / log(1/2) = 3.42

So the number of half-lives that have elapsed is approximately 3.42. Since we know that 100 days is the time for three half-lives (from the previous calculation), we can find the half-life by dividing 100 days by 3.42:

Half-life = 100 days / 3.42 = 29.2 days (rounded to one decimal place)

Therefore, the half-life of the radioactive isotope that leaked into the stream is approximately 29.2 days.

Answer:

15

Step-by-step explanation:

50 x .3

Answer:15

Step-by-step explanation:

Answer:

3

-1/3

Step-by-step explanation:

up 3 right 1

down 1 right 3

Answer: x = $1.75

Step-by-step explanation:

Let's assume that the cost of each sparking plug is x dollars. Then, the cost of the fan belt is x + $1.75 since it costs $1.75 more than each sparking plug.

According to the problem, the total cost of four sparking plugs and a fan belt is $10.50. We can express this as an equation:

4x + (x + $1.75) = $10.50

Simplifying and solving for x, we get:

5x + $1.75 = $10.50

5x = $8.75

x = $1.75

Therefore, each sparking plug costs $1.75 and the fan belt costs $3.50 ($1.75 + $1.75).

Answer:

-35/-7=5

Step-by-step explanation:

Diviser par de nombre négatif alors sa devient positif pareil pour la multiplication

The first eight terms of the sequence are 27, 27, 39, 87, 117.378, 147.755, 178.132 and 208.509.

By (1) we have that \(a = 27 - A\), and we simplify the system of equations as follows:

\((27-A)+d + A\cdot r = 27\)

\(d + (r-1)\cdot A = 0\) (2b)

\((27-A) +2\cdot d + A\cdot r^{2} = 39\)

\(2\cdot d + (r^{2}-1)\cdot A = 12\) (3b)

\((27-A) +3\cdot d + A\cdot r^{3} = 87\)

\(3\cdot d + (r^{3}-1)\cdot A = 60\) (4b)

By (2b), we simplify the system of equations once again:

\(2\cdot (1-r)\cdot A+(r^{2}-1)\cdot A = 12\)

\([2\cdot (1-r)+(r^{2}-1)]\cdot A = 12\) (3c)

\(3\cdot (1-r)\cdot A + (r^{3}-1)\cdot A = 60\)

\([3\cdot (1-r) + (r^{3}-1)]\cdot A = 60\) (4c)

And by equalising (3c) and (4c) we have an expression in terms of \(r\):

\(\frac{12}{[2\cdot (1-r)+(r^{2}-1)]} = \frac{60}{[3\cdot (1-r)+(r^{3}-1)]}\)

\(12\cdot [3\cdot (1-r)+(r^{3}-1)] = 60\cdot [2\cdot (1-r) + (r^{2}-1)]\)

\(36\cdot (1-r) +12\cdot (r^{3}-1) = 120\cdot (1-r)+60\cdot (r^{2}-1)\)

\(84\cdot (1-r) +60\cdot (r^{2}-1)-12\cdot (r^{3}-1) = 0\)

\(84-84\cdot r +60\cdot r^{2}-60-12\cdot r^{3}-12 = 0\)

\(-12\cdot r^{3}+60\cdot r^{2}-84\cdot r +2 = 0\) (5)

The roots of this third order polynomial are: \(r_{1} \approx 0.0242\), \(r_{2} = 2.488 + i\,0.831\) and \(r_{3} \approx 2.488-i\,0.831\). Since \(r\) must be a real number, then \(r \approx 0.0242\).

By (4c) we have the value of \(A\):

\(A = \frac{60}{3\cdot (1-0.0242)+(0.0242^{3}-1)}\)

\(A \approx 31.130\)

By (2b) we find the value of \(d\):

\(d = (1-0.0242)\cdot 31.130\)

\(d = 30.377\)

And by (1) we find the value of \(a\):

\(a = 27-A\)

\(a = 27-31.130\)

\(a = -4.13\)

The first eight terms are calculated below:

\(n_{1} = 27\)

\(n_{2} = 27\)

\(n_{3} = 39\)

\(n_{4} = 87\)

\(n_{5} = [-4.13 + 4\cdot (30.377)]+(31.130)\cdot (0.0242)^{4} = 117.378\)

\(n_{6} = [-4.13+5\cdot (30.377)+(31.130)\cdot (0.0242)^{5}] = 147.755\)

\(n_{7} = [-4.13+6\cdot (30.377)\cdot (31.130)\cdot (0.0242)^{6}] = 178.132\)

\(n_{8} = [-4.13+7\cdot (30.377)\cdot (31.130)\cdot (0.0242)^{7}] = 208.509\)

The first eight terms of the sequence are 27, 27, 39, 87, 117.378, 147.755, 178.132 and 208.509. \(\blacksquare\)

The statement present typing mistakes and is poorly formatted. Correct form is shown below:

The first four terms of an arithmetic sequence are: \(a\), \(a + d\), \(a + 2\cdot d\), \(a + 3d\). The first four terms of another sequence are: \(A\), \(A\cdot r\), \(A\cdot r^{2}\), \(A\cdot r^{3}\). The eight terms satisfy:

\(a + A = 27\) (1)

\((a+d)+A\cdot r = 27\) (2)

\((a + 2\cdot d) + A\cdot r^{2} = 39\) (3)

\((a + 3\cdot d) + A\cdot r^{3} = 87\) (4)

By using the substitution \(a = 27-A\), or otherwise, find the all eight terms.

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For every 21 liters of petrol a car can run for 80 km- 58.2 liters of petrol would be required to ensure the car has enough petrol of a trip that is 224 km unitary method

It is provided that to run 80km car requires 21 liters of petrol

To know how much petrol is required for a trip of 224 km, we first would require to know how much petrol is required to run 1 km

This is called unitary method

Petrol required by car to run 1 km would be petrol required by car to cover 80kms of distance divided by 80 km of distance = 21 liters of petrol/ 80 km distance

                                                      = 21/80

                                                      =0.26 liters

So, petrol required by car for a trip of 224 km= 0.26 liters  ×224km

                                                                          = 0.26× 224

                                                                           =  58.24 liters

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Step-by-step explanation:

\(15^{10}+15^{11}+15^{12}+15^{13}\)

You can look at it like this:

\(15^{10}+15^{11}+15^{12}+15^{13}=15^{10}+15^{10}\cdot15+15^{10}\cdot15^2+15^{10}\cdot15^3\\\\=15^{10}\cdot(1+15+15^2+15^3)=15^{10}\cdot(1+15+225+3375)\\\\=15^{10}\cdot3616=15^{10}\cdot32\cdot113=15^{10}\cdot2^5\cdot113=2.085.167.812.500.000\)

Answer:

Below.

Step-by-step explanation:

15^10 + 15^11 + 15^12+ 15^13

= 15^10(1 + 15 + 15^2 + 15^3)

= 15^10 * 3616

= 2,085,167,812,500,000

instantaneous rate of change of the search length 0.1667 seconds per

We need to take the derivative of the function S(n) with respect to n and evaluate it at n=12 in order to determine the instantaneous rate of change of the search length for a set of 12 articles.

Taking the derivative of S(n) with respect to n using the chain rule, we get:

S'(n) = 1.6 * (1/(0.8n)) * 0.8 = 2/n

Evaluating this expression at n=12, we get:

S'(12) = 2/12 = 0.1667 seconds per article

This indicates that the search time will increase by approximately 0.1667 seconds per article if the set contains 12 articles by one unit. Alternately, the search time per article will decrease by approximately 0.1667 seconds if the set's number of articles decreases by one unit from 12.

Therefore, the units for the instantaneous rate of change are "seconds per article", indicating the change in search time for each additional or fewer article in the set.

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Answer:

1 and 7

Step-by-step explanation:

supplementary means that they add up to 180º

1,3                    5,6              1,7          

2,4                   7,8              2,8

1,2                    5,7              3,5

3,4                   6,8              4,6

There are still some more but my hands are tired of typing.

Answer:

A: 1 and 7

Step-by-step explanation:

when 2 angles are put next to each other on a straight line with a line going through the middle those two angles always add to 180 since 180 is equal to a straight line.

supplementary angles are 2 angles that together make 180.

out of the options given, all of them except 1 and 7 are equal angles and as a result would not add to 180. if you put angles 1 and 7 on a straight line together, they do, thus the answer is A, aka 1 and 7.

Answer: A

Step-by-step explanation: 14/20 = 70%

1. The distance all the way across the cooker. In this case, 136 cm.

1. The coordinates of the edges of the cooker can be determined by considering the distance from the vertex to the edge of the cooker. Given that the distance from the vertex to the edge is 68 cm, and the vertex is at (-32, 0), we can find the coordinates of the edges as follows:

One edge of the cooker: (-32 + 68, 0) = (36, 0)

The other edge of the cooker: (-32 - 68, 0) = (-100, 0)

The distance all the way across the cooker. In this case, it is 36 - (-100) = 136 cm.

2. To write an equation for the parabolic mirror, we can use the standard form of a parabolic equation, which is y = a(x - h)² + k, where (h, k) represents the vertex of the parabola.

In this case, the vertex is at (-32, 0).

The equation becomes y = a(x + 32)² + 0.

Substituting these coordinates into the equation, we get:

0 = a(36 + 32)² + 0

0 = a(68)²

0 = 4624a

From this, we can see that a = 0, which means the equation simplifies to y = 0, indicating that the parabolic mirror is a straight line along the x-axis.

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Answer:

A

Step-by-step explanation:

I don't really understand the numbers but if both X and Y are negative, then adding the 2 will result in a negative value.  Multiplying 2 negative values will be positive, as will dividing them, and sometimes subtracting will too.

The probability of drawing two slips of paper containing numbers that are the lengths of two sides of a triangle in the (3,4,5) family is 1/50.

The (3,4,5) family of triangles is a set of triangles that are similar to the triangle with side lengths 3, 4, and 5. In particular, the sides of any triangle in the (3,4,5) family must satisfy the Pythagorean theorem, i.e., the sum of the squares of the two shorter sides must equal the square of the longest side.

We can start by listing all the possible pairs of numbers that can be drawn from the hat

(3,4), (3,5), (3,6), (3,7), (3,8), (3,10)

(4,5), (4,6), (4,7), (4,8), (4,10)

(5,6), (5,7), (5,8), (5,10)

(6,7), (6,8), (6,10)

(7,8), (7,10)

(8,10)

Out of these 20 possible pairs, we need to count the pairs that satisfy the conditions for being lengths of two sides of a triangle in the (3,4,5) family. For any such triangle, the longest side must be either 5 or 10. Therefore, we can split the pairs into two groups

Pairs that include 5: (3,4), (5,6), (5,8), (5,10)

Pairs that include 10: (6,8), (7,10), (8,10)

For a pair to be the lengths of two sides of a triangle in the (3,4,5) family, the sum of the squares of the two shorter sides must equal the square of the longest side. We can check this condition for each of the pairs in the two groups

Pairs that include 5

(3,4): not a valid triangle

(5,6): not a valid triangle

(5,8): the sum of the squares of the two shorter sides is 5^2 + 8^2 = 89, which is not equal to 10^2

(5,10): the sum of the squares of the two shorter sides is 3^2 + 4^2 = 25, which is equal to 5^2

Pairs that include 10

(6,8): the sum of the squares of the two shorter sides is 6^2 + 8^2 = 100, which is equal to 10^2

(7,10): not a valid triangle

(8,10): the sum of the squares of the two shorter sides is 4^2 + 8^2 = 80, which is not equal to 10^2

Therefore, out of the 20 possible pairs, only 2 pairs satisfy the conditions for being lengths of two sides of a triangle in the (3,4,5) family. The probability of drawing one of these pairs is 2/20 = 1/10.

Once the first number is drawn, there are only 5 slips of paper left in the hat, and only one of them is the other side of the triangle, so the probability of drawing the second number is 1/5. Therefore, the probability of drawing two numbers that are the lengths of two sides of a triangle in the (3,4,5) family is (1/10) × (1/5) = 1/50.

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Answer:

watch me whipzdudbbd iv ex

The compound interest earned is $1412.13.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

Compound interest is accelerated, and not linear.

"Interest on interest," or the power of compound interest, is believed to have originated in 17th-century Italy. It will make a sum grow faster than simple interest, which is calculated only on the principal amount.

Compounding multiplies money at an accelerated rate and the greater the number of compounding periods, the greater the compound interest will be.

Here, for this question, we will have to use the compound interest formula.

A = P(1 + r/n)^nt (Amount earned after compounding)

A = 12000(1 + .09/4)^[4(1.25)]

A = 12000(1.0225)^5

A ≈ 12000(1.117678)

A ≈ $13,412.13

i = A - P (interest earned)

i = 13,412.13 - 12000

i ≈ $1412.13

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1. The exponential growth function for Jennifer's investment account balance, I(t), can be expressed as: I(t) = a * (1 + b)ⁿ

2. The value of $50,000 after 10 years with an annual interest rate of 15% would be approximately $202,300.

3. Jennifer would have approximately $271,790 in her investment account after 8 years with an initial investment of $100,000.

1. The exponential growth function for Jennifer's investment account balance, I(t), can be expressed as:

I(t) = a * (1 + b)ⁿ

Therefore, the function for Jennifer's investment account balance after t years is:

I(t) = $50,000 * (1 + 0.15)ⁿ

2. In order to calculate how much money Jennifer will have after 10 years, we can substitute t = 10 into the function:

I(10) = $50,000 * (1 + 0.15)¹⁰

= $50,000 * (1.15)¹⁰

A ≈ $202,300

3. In order to calculate how much money Jennifer would have after 8 years using this new function, we substitute t = 8 into the equation:

N(8) = $100,000 * (1 + 0.15)⁴ × (1 + 0.15)⁴

≈ $271,790

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The value of m + n is given as follows:

A. 18.

The exponential expression for this problem is defined as follows:

\((x^5y^6)^{\frac{1}{5}}(x^3y^4}^{\frac{1}{4}}\)

Applying the power of power rule, we have that the exponents are given as follows:

Then the values of m and n are given as follows:

m = 7, n = 11.

Thus the sum is given as follows:

m + n = 7 + 11 = 18.

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Answer:

The medians intersect at 4-4 (i think).

Step-by-step explanation:

Every triangle has three medians and they all intersect in the triangles centroid. i believe that the medians intersect at 4-4.

i am not a very trustworthy source so you should probably ignore this awnser.

Answer:

Domain= {x:x £|R}

|R=any real number