What is the answer to 3x^2 +30x+75

Answer:

both are reciprocals

Step-by-step explanation:

15.

\(\frac{5}{8}\cdot \frac{16}{20}\\\\=\frac{5}{8}\cdot\frac{8}{5}=1\)

so they are reciprocals

17.

\(\frac{2}{3}\cdot\frac{12}{18}\\\\=\frac{2}{3}\cdot \frac{3}{2}=1\)

so they are reciprocals

The equivalent ratio to tan F  in  right angles triangle, △EFD is tan F = DE / DF.

For the stated question:

△EFD∼△GHD

So, in right angles triangle, △EFD

Sin Ф = perpendicular / hypotenuse.

Sin E = DF / EF

And,

The ratio is equivalent to tan F = perpendicular / base

tan F = DE / DF

Thus, the equivalent ratio to tan F  in  right angles triangle, △EFD is tan F = DE / DF.

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The complete question is attached:

Answer:

n=1

Step-by-step explanation:

(5 + 4n) + 11 = -5 (3 - 7n)

5+4n+11=−5(3−7n)

simplify

4n+16=−5(3−7n)

expand

4n+16=−15+35n

regroup

4n+16=35n−15

subtract

16=35n−15−4n

simplify

16=31n−15

add

16+15=31n

simplify

31=31n

n=1

Hope this helps :)

(pls mark brainliest)

Answer:

n=22

Step-by-step explanation:

8 (5 + 4n) + 11 = -5 (3 - 7n)

distribute

=> 40+32n+11=-15+45n

add like terms

=> 51+32n=-15+35n

subtract 35n on both sides and subtract 51 on both sides

32n-35n=-15-51

add like terms

-3n=-66

divide both sides by -3

n=22

I ⊆ I' if and only if a' ≤ a and b ≤ b'. This relationship holds true for closed intervals I and I' in R. To show that I ⊆ I' if and only if a' ≤ a and b ≤ b', we will consider two cases:

1. If I ⊆ I', then for any x ∈ I, we have x ∈ I'. Since I and I' are closed intervals, we can write them as I = [a, b] and I' = [a', b']. We want to show that a' ≤ a and b ≤ b' in this case.

Since x ∈ I, we know that a ≤ x ≤ b. Now, since x also belongs to I', we have a' ≤ x ≤ b'. Since this is true for any x in I, we can conclude that a' ≤ a and b ≤ b'.

2. If a' ≤ a and b ≤ b', we want to show that I ⊆ I'. Let x be any element in I, so we have a ≤ x ≤ b. We are given that a' ≤ a and b ≤ b'. Since a' ≤ a and a ≤ x, we can infer that a' ≤ x. Similarly, since x ≤ b and b ≤ b', we can infer that x ≤ b'. Therefore, x ∈ I'.

Since x was an arbitrary element in I, we can conclude that I ⊆ I' when a' ≤ a and b ≤ b'.

In summary, I ⊆ I' if and only if a' ≤ a and b ≤ b'. This relationship holds true for closed intervals I and I' in R.

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Answer:

62

Step-by-step explanation:

JL = JK + KL

5x + 2 = 3x - 1 + 27 add like terms

5x + 2 = 3x + 26

2x = 24

x = 12

JL = 12 × 5 + 2

JL = 62

Answer:

d > 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sample Space

off  even numbers

= {2,4,6,8,10}.

There are 5 outcomes in the sample space,

The sum of the series  Σk=1k(k+2)' is b) 1.5. The correct option is b.

To find the sum of the series Σk=1k(k+2), we can expand the terms and simplify the expression:

Σk=1k(k+2) = 1(1+2) + 2(2+2) + 3(3+2) + ...

Expanding each term:

= 1(3) + 2(4) + 3(5) + ...

= 3 + 8 + 15 + ...

To find a pattern, let's subtract consecutive terms:

8 - 3 = 5

15 - 8 = 7

We observe that the differences between consecutive terms are increasing by 2 each time.

So, the series can be written as:

3 + (3+2) + (3+2+2) + (3+2+2+2) + ...

= 3(1) + 2(1+2) + 2(1+2+3) + 2(1+2+3+4) + ...

= 3Σk=1k + 2Σk=1k(k+1)

Using the formulas for the sum of the first n natural numbers and the sum of the first n squared numbers:

= 3(n(n+1)/2) + 2(n(n+1)(2n+1)/6)

Simplifying this expression, we get:

= (3n^2 + 5n)/2

To determine whether the series converges or diverges, we need to take the limit as n approaches infinity.

lim(n→∞) (3n^2 + 5n)/2

The degree of the numerator and denominator is the same (n^2), so we divide each term by n^2:

lim(n→∞) (3 + 5/n)/2

As n approaches infinity, the term 5/n goes to 0:

lim(n→∞) (3 + 0)/2 = 3/2 = 1.5

Therefore, the sum of the series Σk=1k(k+2) is 1.5, so the correct answer is b) 1.5.

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Answer:

2.25 feet, 45 inches, and 6 yards

Step-by-step explanation:

first, convert all to the same unit of measurement

I will use inches

45 inches = 45 inches

6 yards, 1 yard = 3 feet so 6 yards are equal to 18 feet and 1 foot is equal to 12 inches so 12*18 is 216 inches so 6 yards = 216 inches

Next 1 foot equals 12 inches so 2.25 * 12 = 27 so 2.25 feet = 27 inches.

Now let's look at the complete conversion

45 inches

6 yards = 216 inches

2.25 feet = 27 inches

looking at the inches we can see that 27 is the least then 45 then 216 therefore

2.25 feet < 45 inches <  6 yards so the order is

2.25 feet, 45 inches, and 6 yards

Answer:

why are you cheating

Step-by-step explanation:

whats your reputation

Answer:

Step-by-step explanation:

Yes

The solutions to the quadratic equation x² - x = 5 by completing the square are:

x = (1 + √21)/2 and x = (1 - √21)/2

The quadratic equation is given as:

x² - x = 5

Move the constant term to the right side of the equation:

x² - x - 5 = 0

Take half of the coefficient of x, square it, and add it to both sides of the equation to complete the square. The coefficient of x is -1, so:

x² - x + (-1/2)² = 5 + (-1/2)²

x² - x + 1/4 = 5 + 1/4

Simplify the right side of the equation:

x² - x + 1/4 = 20/4 + 1/4

x² - x + 1/4 = 21/4

Rewrite the left side of the equation as a perfect square:

(x - 1/2)² = 21/4

Take the square root of both sides:

x - 1/2 = ±√(21/4)

Add 1/2 to both sides to isolate x:

x = 1/2 ± √(21/4)

Simplify the right side:

x = 1/2 ± √21/2

Therefore, the solutions to the quadratic equation x² - x = 5 by completing the square are:

x = (1 + √21)/2 and x = (1 - √21)/2

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Complete question:

Solve the below quadratic equation by completing the square.

x²-x = 5.

The diagonal of the base of the box is shorter than the bat.

The length of the interior diagonal of the box is shorter than the bat.

Juilian's  bat will not fit in the box.

The line connecting the opposite vertex of the geometric figure like cube or cuboid or square or rectangle is called the diagonal.

The diagonal of the base `= sq rt (32² + 8²) = 33 in.

The length of the interior diagonal =  sq rt (32² + 8² +6²) =33.5 or 34 in.

Thus, The diagonal of the base of the box is shorter than the bat.

The length of the interior diagonal of the box is shorter than the bat.

Juilian's  bat will not fit in the box.

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Answer:

1. Shorter than

2. Shorter than

3. Will not fit in the box

Step-by-step explanation:

Answer:

Keisha bought 4 boxes of crayons for $0.78 each. How much will she pay for the 4 boxes of crayons?

$3.12

Answer:

there were 91,487.414 gallons of water in the tank before the leak.

Step-by-step explanation:

To find out the number of gallons of water that was in the tank before the leak, you can use the following equation:

Number of gallons before the leak = Number of gallons after the leak + Number of gallons leaked

Plugging in the values given in the problem, we get:

Number of gallons before the leak = 91,468 gallons + 19.414 gallons

Solving this equation gives us:

Number of gallons before the leak = 91,487.414 gallons

So there were 91,487.414 gallons of water in the tank before the leak.

Answer:

B

Step-by-step explanation:

Answer:

\(2\\\\ \frac{2}{4} = 2\)

The \(\frac{2}{4}\) simply means divide 2 by 4.

Each person will get 2 brownies.

a. 11 year growth factor = 1 + (26/100) = 1.26

   1-year growth factor = (1.26)^1/11 = 1.0210

   Therefore,

    1-year growth percent = 1.0210 - 1 = 0.0210 %

     Answer: 2.10

b. 13-year decay factor = 1 - (39/100) = 0.61

   1-year decay factor = (0.61)1/13 = 0.9631

    Therefore,

    13-year decay factor = 1 - 0.9631 = 0.03686 = 3.68%

     Answer: 3.68

c. 5-year growth factor = 3

   1-year growth factor = (3) ^1/5 = 1.245

   Therefore,

   1-year growth factor = 1.2457 - 1 = 0.2457 = 2.45%

   Answer:2.45

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Answer: MQ=16, QL=32

Step-by-step explanation:

The centroid splits the median in a 2:1 ratio.

The measure of MQ and QL are 16 and 32 respectively.

Centroid is the point on the median which divides it in the ratio 2:1.

The ratio of lengths QL and MQ will be 2:1.

\(\frac{QL}{MQ}=\frac{2}{1}\\QL=2MQ\)

It is known that ML is the sum of MQ and QL.

MQ+QL=ML

Substitute QL=2MQ and ML=48 into the obtained equation.

MQ+2MQ=48

3MQ=48

MQ=16

Substitute MQ=16 into QL=2MQ

QL=2(16)

=32

Thus, the lengths are MQ=16 and QL=32.

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Answer:

45 degrees, x,5, 7

Step-by-step explanation:

you just gotta do the math

Answer:

A = 93.31 ft²

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = \(\frac{1}{2}\) h (b₁ + b₂)

where h is the perpendicular height and b₁, b₂ the parallel bases

Here h = 6.2, b₁ = 7.8, b₂ = 14.7 + 7.6 = 22.3 , then

A = \(\frac{1}{2}\) × 6.2 × (7.8 + 22.3) = 3.1 × 30.1 = 93.31 ft²

Answer:

Area= 24ft squared

Step-by-step explanation:

Area= 1/2 Bh

A= 1/2 9(6)

A= 1/2 48

A= 24ft

Step-by-step explanation:

1. Choose arbitrary points A and B in the plane and draw segment AB.

2. Raise a perpendicular m to AB at A.

3. Raise a perpendicular n to AB at B.

4. Choose an arbitrary point C on line n.

5. Drop a perpendicular from point C to line m. Let D be the foot of this perpendicular.

6. Then quadrilateral ABCD is a rectangle.

According to the question (a) An equation of the sphere with center (2, -3, 5) and radius 6 is \($(x - 2)^2 + (y + 3)^2 + (z - 5)^2 = 36$\) ,  (b) The intersection of this sphere with the XZ-plane (where y = 0) is given by \($(x - 2)^2 + z^2 = 36$\).

(a) To find an equation of the sphere with the given center and radius, we use the general equation of a sphere:

\(\((x - h)^2 + (y - k)^2 + (z - l)^2 = r^2\),\)

where (h, k, l) represents the center coordinates and r represents the radius. Plugging in the given values, we have:

\(\((x - 2)^2 + (y + 3)^2 + (z - 5)^2 = 6^2\),\)

Simplifying further, we get the equation of the sphere:

\(\((x - 2)^2 + (y + 3)^2 + (z - 5)^2 = 36\).\)

(b) To find the intersection of this sphere with the XZ-plane (where y = 0), we substitute y = 0 into the equation of the sphere:

\(\((x - 2)^2 + (0 + 3)^2 + (z - 5)^2 = 36\).\)

Simplifying, we have:

\(\((x - 2)^2 + 9 + (z - 5)^2 = 36\),\)

which can be rewritten as:

\(\((x - 2)^2 + (z - 5)^2 = 27\).\)

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Answer:

= 290

Step-by-step explanation:

275 + 8 = 283

283 + 5 = 288

288 + 2 = 290

(If this isn't what you meant just tell me and ill edit my comment)

The like radicals are 3x√x²y and x√yx², and the answer is:

3x√x²y, -2x√xy³², x√yx²,  2√xy

An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. It does not have an equal sign and can be simplified or evaluated by applying the appropriate rules of arithmetic.

According to the given information:

The like radicals have the same radicand (expression under the radical sign) and the same index (the number outside the radical sign). Checking each expression:

Therefore, the like radicals are 3x√x²y and x√yx², and the answer is:

3x√x²y, -2x√xy³², x√yx²,  2√xy

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Answer:

Median without outlier should be 40

For the bottom questions, it should go:

Decreases the mean, does not change the median, does not change the mode

It's decreasing the mean because it goes from 44.7 to 39

Median w/ and without outlier is both 40

Mode also stays the same w/ or without the outlier, which is 96

Answer:

90

Step-by-step explanation:

Answer:

The answer is 3 and 6.

Step-by-step explanation:

3*3 = 9, 6*6 = 36, and 9 + 36 = 45.

Please give brainliest

Applying the distance formula, the distance between the two points (7, 4) and (3, 3) is: 4 units.

If we have two given points with their coordinates, to find the distance between these two points, apply the distance formula that is expressed as:

d = \(\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}\).

Given the two points:

(7, 3) = \((x_1, y_1)\)

(3, 3) = \((x_2, y_2)\)

Substitute the values into the distance formula:

d = √[(3−7)² + (3−3)²]

d = √[(−4)² + (0)²]

d = √16

d = 4 units.

The distance is: 4 units.

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Step-by-step explanation:

1000 is the answer man you want it right