PQ has endpoints at P(-5, 4) and Q (7,-5). What is the length of PQ?

Answer:

See diagram below

Step-by-step explanation:

arctan (angle ) = 18 / (6 sqrt3)  = 60 degrees

Step-by-step explanation:

height of pole = 18m = p

length of shadow = 6\(\sqrt{3}\) m = b

now,

tan α = p/b

        = 18/6\(\sqrt{3}\)

        = \(\sqrt{3}\)

or, tan α = tan 60

           α = 60

Therefore angle of elevation of the sun is 60.  

Answer:

A≈50.27in²

Step-by-step explanation:

Answer:

9.1 units

Step-by-step explanation:

formula of a distance of two points:

\(\sqrt{(x1-x2)^2+(y1-y2)^2}\) where x and y indicate the coordinates of the points

\(\sqrt{(4+5)^2 + (-1)^2} = \sqrt{81 + 1} = \sqrt{82} = 9.1 units\)

Answer:

-2

Step-by-step explanation:

4y - 7 = - 15

4y = -15 + 7

4y = -8

y = - 8 / 4

y = - 2

Answer:

T=7+2x

Step-by-step explanation:

It just makes sense

Answer:

[1, ∞)

Step-by-step explanation:

1) Solve for x

-4x + 21 \(\leq\) 3x + 14

21 \(\leq\) 7x + 14

7 \(\leq\) 7x

1 \(\leq\) x

2) 1 is the lowest possible value of x and since it's a smaller or equal to inequality, you use a square bracket. If it was 1 < x, it would be a round bracket. Since there isn't a boundary for the highest value of x, you write an infinity. When you have an infinity, it's always a round bracket.

Answer:

x ≥ 1

 [1, ∞)

Step-by-step explanation:

Note: 3 < 7 and 8 > 2 this is obvious

2,3,7,8 are on the RIGHT SIDE of the number zero "0"

now look at this sequence :

-3 > -7 and -8 < -2

the numbers are the same but thy are on the opposite side of the ZERO.

now notice that the <> signs flipped from the fist to the second set...

when you do these problems, "Multiplying or dividing by a negative number"

effectively moves you from one side of the zero to the other....

the "thing" you have to do is REMEBER AFTER EACH STEP...

IF YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER (not add or subtract)  

YOU HAVE TO FLIP THE SIGN...

-4x+21 ≤ 3x +14

-4x ≤ 3x - 7          |||| subtracted 21 NO sign flip

-7x ≤ -7                ||| subtracted 3X NO sign flip

x ≥ 1                     ||| Divided by "-1" SIGN MUST FLIP !!!

Answer:

4

Step-by-step explanation:

:)

Answer:

The perimeter of a 4-sided polygon: P = x²-3x+1

Step-by-step explanation:

Given the lengths of the sides of a given polygon

The perimeter of a 4-sided polygon can be determined by adding the lengths of all 4 sides.

Perimeter = (3x²+2) + (-2x²+10) + (2x-7) + (-5x-4)

Remove the parentheses

                =3x²+2-2x²+10+2x-7-5x-4

Group like terms

                =3x²-2x²+2x-5x+2+10-7-4

Add similar elements:   3x²-2x²=x²

                 =x²+2x-5x+2+10-7-4

Add similar elements:   2x-5x=-3x

                 =x²-3x+2+10-7-4

                 =x²-3x+1

Therefore, the perimeter of a 4-sided polygon: P = x²-3x+1

Answer:

5 km = 5000 m

Step-by-step explanation:

1 km = 1000 m

5 km × 1000 m = 5000 m

Hopw this helps and stay safe, happy, and healthy, thank you :) !!

Answer:

To prove that n^3 + 3n + 4 is Θ(2^n), we need to show that it is both O(2^n) and Ω(2^n).

First, let's show that it is O(2^n). To do this, we need to find constants c and n0 such that n^3 + 3n + 4 <= c * 2^n for all n >= n0.

We can start by simplifying the left-hand side: n^3 + 3n + 4 <= n^3 + n^3 + n^3 (since 3n <= n^3 and 4 <= n^3 for all n >= 1).

So we have: n^3 + 3n + 4 <= 3n^3

Now, for n >= 1, we know that 2^n <= 3^n, so we can write: 3n^3 >= 2^n

Therefore, we have: n^3 + 3n + 4 <= 3n^3 <= c * 2^n for c = 3 and n0 = 1.

So, n^3 + 3n + 4 is O(2^n).

Next, let's show that it is Ω(2^n). To do this, we need to find constants c and n0 such that n^3 + 3n + 4 >= c * 2^n for all n >= n0.

One way to approach this is to try to find a lower bound for n^3 + 3n + 4 by removing some terms (because we want to show that the left-hand side is at least as big as some constant times 2^n, and the more terms we have on the left-hand side, the harder that is to do).

If we remove the 3n and the 4, we have n^3 <= n^3.

If we remove only the 4, we have n^3 + 3n >= n^3.

Either way, we have: n^3 + 3n >= n^3 >= c * 2^n for c = 1 and n0 = 1.

Therefore, n^3 + 3n + 4 is Ω(2^n).

Since we have shown that n^3 + 3n + 4 is both O(2^n) and Ω(2^n), we can conclude

Step-by-step explanation:

We have shown that n^3 + 3n + 4 is in the order of e(2n^3), as required.

To prove that n^3 + 3n + 4 is in the order of e(2n^3), we need to show that there exist positive constants c and n0 such that:

n^3 + 3n + 4 <= c * e(2n^3) for all n >= n0

Taking natural logarithm on both sides of the inequality, we get:

ln(n^3 + 3n + 4) <= ln(c) + 2n^3

Now, we need to show that there exist positive constants c and n0 such that the inequality holds.

Taking the derivative of the left-hand side of the inequality, we get:

d/dn (ln(n^3 + 3n + 4)) = (3n^2 + 3) / (n^3 + 3n + 4)

For n >= 1, we have:

3n^2 + 3 <= 3n^3 + 3n^2 <= 6n^3

n^3 + 3n + 4 >= n^3

Therefore,

d/dn (ln(n^3 + 3n + 4)) <= (6n^3) / n^3 = 6

This means that the function ln(n^3 + 3n + 4) is bounded above by a constant of 6. Thus, we can set c = e^6 and n0 = 1.

For all n >= 1, we have:

ln(n^3 + 3n + 4) <= 6 + 2n^3

n^3 + 3n + 4 <= e^(6 + 2n^3) = e^6 * e^(2n^3)

Therefore, we have shown that n^3 + 3n + 4 is in the order of e(2n^3), as required.

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The probability of picking a block of 5 digits from a random-digit table that is less than 30000 is 0.3 or 30%.

To calculate the probability, we need to consider the range of possible outcomes for the block of 5 digits. Since we want the block to be less than 30000, the first digit can be any digit from 0 to 2.

For the first digit, there are three options (0, 1, and 2) that satisfy the condition. For the remaining four digits, each digit can be any digit from 0 to 9, allowing for a total of 10 options for each digit.

To find the total number of possible outcomes, we multiply the number of options for each digit: 3 options for the first digit and 10 options for each of the remaining four digits. Therefore, the total number of possible outcomes is 3 * 10 * 10 * 10 * 10 = 30,000.

Since each possible outcome is equally likely, the probability of picking a block of 5 digits less than 30000 is given by the number of favorable outcomes (30,000) divided by the total number of possible outcomes (100,000). Thus, the probability is 30,000 / 100,000 = 0.3 or 30%.

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Answer:

65x + 60x = 500

Step-by-step explanation:

65x + 60x = 500

add 65x and 60x

this will equal 125x

divide 500 by 125

this will give you x = 4

which gives you the answer that the trucks will meet in 4 hours

please mark as brainliest

hope this helps : )

Answer:

16.35

Step-by-step explanation:

Using an inverse normal distribution, we can calculate the z score given the percentile, which can then be used to find our value.

First, we can use an inverse normal distribution calculator to figure out that the z score given the 75th percentile is 0.674.

Next, we know that the z score is (observed value - mean) / standard deviation. We can plug our values in to get

\(\frac{x-15}{2} = z\\\frac{x-15}{2} = 0.674\\x-15 = 0.674 * 2\\x = 0.674 * 2 + 15\\x= 16.348\)

Rounding, we get x = 16.35 as our answer

Answer:

14

Step-by-step explanation:

There are 3 even and 3 odd sides meaning its a 50/50 chance for either to happen each time you roll. This means half of the results are expected to be odd and even.

The value of x is 49/58 − 7/58 = 42/58.

This states that in a triangle, the square of the length of a side is equal to the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of the angle between them.

The value of x can be calculated using the Law of Cosines.

For triangle ABC, the Law of Cosines can be written as follows:

AB2 = AC2 + BC2 − 2AC × BC × cos60

(2x + 1)2 = (2x − 1)2 + (−7)2 − 2 × (2x − 1) × (−7) × cos60

4x2 + 4x + 1 = 4x2 − 4x + 1 + 49 + 14x − 14 × cos60

0 = 58x + 49 − 14 × cos60

58x = 49 − 14 × cos60

x = 49 − 14 × cos60/58

Substituting the value of cos60 = 0.5 into the equation, we get:

x = 49 − 7/58

Therefore, the value of x is 49/58 − 7/58 = 42/58.

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The corollary states that for every positive real number ε, there exists a positive integer n such that

The corollary of the Archimedean principle states that for any positive real number ε, there exists a positive integer n such that ε is greater than the reciprocal of n, i.e., ε > 1/n. In other words, there exists a positive integer n such that the fraction 1/n is smaller than any given positive real number ε.

To prove this corollary, we can assume that ε is a positive real number. By the Archimedean principle, there exists a positive integer m such that m > ε. Now, consider the positive integer n = ⌈1/ε⌉ + 1, where ⌈x⌉ denotes the ceiling function, rounding up x to the nearest integer.

We have:

1/ε < 1/(⌈1/ε⌉ + 1) ≤ 1/(1/ε) = ε.

Therefore, we can conclude that for any positive real number ε, there exists a positive integer n = ⌈1/ε⌉ + 1 such that ε > 1/n.

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Answer:

Step-by-step explanation:

cosx=(adjacent side)/(hypotenuse)

cosB=3/5

Answer:

Y = 3/2x + 8

Step-by-step explanation:

Slope (AKA M) can be found searching for each point on the graph. Since the graph starts at 8 it is the Y intercept (AKA B)

Answer:

5/6

Step-by-step explanation:

Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.

Answer:

5/6

Step-by-step explanation:

Keep the first fraction the same, then flip the second fraction, then multiply

2/3 * 5/4

10/12

simplify: divide numerator and denominator by 2

5/6

Answer

Step-by-step explanation:

because all  you have to do is look at the total after "car".

Answer:

38%

Step-by-step explanation:

Your looking for the total of the car.

Answer:

546

Step-by-step explanation:

subtract how much he has left by how much he started with

Answer:

The standard repayment plan.

Step-by-step explanation:

Here is the complete question :

SARAH makes $43,000 per year, is single, and lives in Connecticut. She has $19,000 in subsidized loans and $8000 in unsubsidized loans. Which repayment plan will be the cheapest for her in total?

The standard repayment plan is a repayment plan where a fixed sum is paid monthly for 10 years. This makes a total of 120 payments. The advantage of the standard repayment plan over the federal repayment plan is that less interest is paid and payment is made over a shorter period

Because unsubsidized loans accrue a higher interest expense when compared to subsidized loans, Sarah should pay off her unsubsidized loan first. This would minimise interest payment

Answer:

The unit rate is 32/25 Walls per gallons.

Step-by-step explanation:

Gallons of paint used by Martin =  5/8 gallons

Portion of wall Martin wants to paint in pints = 4/5 wall.

Rate at which Martin paints the wall: Rate =  Portion of wall covered/Paints Used.

Rate = 4/5 Gallons/5/8 Gallons = 32/25 Wall Gallons.

Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

Answer: He bought 5 sandwiches.

Step-by-step explanation:

We know that he purchased sandwiches (let's suppose that he bought X ) and one gallon of milk.

The cost of each sandwich is $8, then the cost of the X sandwiches will be X times $8, or: X*$8.

The cost of the gallon of milk is $4.

The total cost will be:

$4 + X*$8.

And we know that the total cost was $44, then we have the equation:

$4 + X*$8 = $44

We can solve this for X

X*$8 = $44 - $4

X*$8 = $40

X = $40/$8 = 5

This means that he bought 5 sandwiches

The rate at which it rained during the storm was 1.89 inches per hour.

To find the rate at which it rained during the storm, we can use the formula:

rate = amount of rain / time

In this case, the amount of rain is 5.1 inches and the time is 2.7 hours.

So, we can plug those values into the formula:

rate = 5.1 inches / 2.7 hours

Simplifying this expression, we get:

rate = 1.89 inches/hour

Therefore, the rate at which it rained during the storm was 1.89 inches per hour.

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The graph that represents the systems of linear equations 2x - y ≥ -3 and y < -2x + 4 is option d

information gotten from the question include

inequality graph showing shaded regions

rearranging the equation to be in the form

y = mx + c

2x - y ≥ -3

2x + 3 ≥ y

y ≤ 2x + 3

The two equations are

y ≤ 2x + 3

y < -2x + 4

some interpretation on the information from the question include

The both inequalities are less than hence the shading for the both will be below the line

This interpretation helps to conclude that last options is the best choice

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You have the following operation:

958 ÷ 10

To determine what is the missing number, calculate the given division:

95

10 | 958

- 90

58

-50

8

as you can notice, the missing number is 58 in the given procedure of the division 958 ÷ 10.

Hence, the asnwer is C. 58