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problem 3 and 4
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find the value of x, y and z​

Answer:

7. (4x +10)/(x^3 +3x^2 -16x -48)

9. -320/93

Step-by-step explanation:

7. As with adding any fractions, first you find a common denominator. When the fractions are rational expressions, it often helps to factor the denominators.

6/(x^2 -16) -2/(x^2 -x -12) = 6/((x -4)(x +4)) -2/((x -4)(x +3))

= (6(x +3) -2(x +4))/((x -4)(x +3)(x +4)) . . . . . using a common denominator

= (6x +18 -2x -8)/((x -4)(x +3)(x +4))

= (4x +10)/((x^2 -16)(x +3))

= (4x +10)/(x^3 +3x^2 -16x -48)

_____

9. First you simplify the denominator:

2/25 -5/16 = (2·16 -5·25)/(25·16) = -93/400

Then you perform the division. This can be done by multiplying by the inverse of the denominator.

(4/5)/(2/5 -5/16) = (4/5)·(-400/93) = -320/93

Try suggested solution, note the answers are marked with green colour.

[tex]\rm \dfrac{HL}{JL}=\dfrac{IL}{KL}=\dfrac{HI}{JK}[/tex]

Step-by-step explanation:

Given :

[tex]\rm \bigtriangleup HLI \sim \bigtriangleup JLK[/tex]  by the SSS similarity theorem.

[tex]\rm \dfrac {HL}{JL} = \dfrac{IL}{KL}[/tex]

Solution :

According to SSS postulate,

KL = IL ----- (1)

HL = JL ----- (2)

HI = JK ------ (3)

From equation (1), (2) and (3) we get,

[tex]\rm \dfrac{HL}{JL}=\dfrac{IL}{KL}=\dfrac{HI}{JK}[/tex]

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Triangle HLI has sides identical in measure to the three sides of triangle JLK, then the two triangles are congruent by SSS postulate. Therefore,

[tex]\rm \dfrac{HL}{JK}=\dfrac{IL}{KL}=\dfrac{HI}{JK}[/tex]

Given :

[tex]\rm \Delta HLI \sim \Delta JLK[/tex] by the SSS similarity.

According to SSS (Side Side Side) postulate:

If all three sides of a triangle are congruent to corresponding three sides of other triangle then the two triangles are congruent.

If triangle HLI has sides identical in measure to the three sides of triangle JLK, then the two triangles are congruent by SSS postulate.

Therefore, from triangle HLI and triangle JLK we get,

KL = IL  ----- (1)

HL = JL ----- (2)

HI = JK ------ (3)

From equation (1) , (2) and (3) we get,

[tex]\rm \dfrac{HL}{JK}=\dfrac{IL}{KL}=\dfrac{HI}{JK}[/tex]

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Answer:

The correct answer is c.

Step-by-step explanation:

This is because it is the first equation being multiplied by 3 and the second being multiplied by 2.

None of the other examples are multiples of the originals.

14-2=12 +4= 16 is the answer to your question

Answer:

Step-by-step explanation:

there you go

Answer:

A) 20.82 > 20.55

Step-by-step explanation:

Hopefully, your issue is with the symbols (< vs >) rather than actually determining which number is larger or smaller.

The wide-open end of the symbol (the left side, in the case of >) indicates the larger (more positive) number.

So, the meanings of the symbols are ...

> — "is greater than"

< — "is less than"

The only true statement of those listed is ...

20.82 is greater than 20.55, or 20.82 > 20.55 . . . . selection A

_____

When writing number comparisons, I like to use the < symbol, because it puts the numbers in number-line order. That is, the smaller (or more negative) number is on the left, just as it is on a number line.

You trade the places of the numbers when changing the symbol. For example, answer choice A could be rewritten as ...

20.55 < 20.82

You know that 20.55 is to the left of 20.82 on the number line, so you know this statement is true.

To get at least a 50% probability of getting at least three heads, you must flip a fair coin at least four times.

To calculate the minimum number of times a fair coin must be flipped before there is at least a 50% probability of getting at least three heads, we can use the concept of probability. Let's assume that flipping a coin is a binary event with two possible outcomes: heads (H) or tails (T).

The probability of getting three or more heads in one flip is zero, since we can only get a maximum of two heads in one flip. However, we can calculate the probability of getting three or more heads in a series of flips.

The probability of getting at least three heads in one flip is zero, but we can calculate the probability of getting at least three heads in two flips, three flips, four flips, and so on. We continue calculating the probability until we find the number of flips that gives us a probability of at least 50%.

Using this method, we find that we need to flip the coin at least 4 times to have a probability of at least 50% of getting at least three heads. This means that after flipping the coin four times (or more), there is a better than 50% chance of getting at least three heads.

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Answer:

x > 2

Step-by-step explanation:

The inequality has constants and variables on both sides. It is convenient to find the variable term with the smallest (most negative) coefficient. Add the opposite of that term to both sides of the inequality.

2x -3 +5x > 11 -5x +5x . . . . added 5x

7x -3 > 11 . . . . . . . . . . . . . . . simplify

Now, find the constant on the side of the inequality that has the variable term. Add the opposite of that constant to both sides.

7x -3 +3 > 11 +3 . . . . . added 3

7x > 14 . . . . . . . . . . . . simplify

Finally, divide by the coefficient of x. It is positive, so we do not need to do anything to the relation symbol.

x > 14/7 . . . . . . . . . . divided by 7

x > 2 . . . . . . . . . . . . simplify . . . . This is your solution.

See the attached picture for the complete answers to both questions:

Question A asked how much more water was required to fill the tank, so you need to calculate the full volume, then subtract 3/4 of the volume.

Question B, volume is cubed, so you need to cube the scale factor of 3. 3^3 = 27, so the larger tank is 27 times more.

Question C) Area is squared so you need to square the scale factor. Surface area would be 9 times more. 3^2 = 9

For the 2nd question, calculate the volume of each box and divide to find the number of boxes.

Then see the picture for total surface area for part B.

Answer:

  $4212

Step-by-step explanation:

18% of $23,400 is ...

  18/100 · $23,400 = $4212

Answer:

4212

Step-by-step explanation:

23400 * 0.18

Answer:

B) 5000x^2

Step-by-step explanation:

The exponent of x starts at 5 in the first term and decreases by 1 as the term numbers increase by 1. Hence, the 4th term will have 2 as the exponent of x. (It will have 5-2=3 as the exponent of 5.)

Pascal's triangle tells you the coefficients of the 6 terms in the expansion will be 1, 5, 10, 10, 5, 1, so the 4th term has a coefficient of 10.

The 4th term will be ...

10(2x)^2(5)^3 = 10·4·125·x^2 = 5000x^2

Answer:

a) 4/5

b) 1/3

Step-by-step explanation:

Put the numbers in the formula and evaluate.

a) pitch = (rise)/(1/2·span)

= (12 ft)/(1/2·30 ft) = 12/15 = 4/5

___

b) pitch = (4 ft)/(1/2·24 ft) = 4/12 = 1/3

The pitch of a roof is calculated by dividing the rise of the roof by half the span of the roof. The pitch of a roof with a 12 feet rise and 30 feet span is 0.8. The pitch of a roof with a 4 feet rise and 24 feet span is 0.333.

The pitch of a roof can be calculated using the equation: pitch = rise of roof / (½ span of roof).

For the first part of your question, where the rise is 12 feet and the span is 30 feet, you substitute these values into the above equation: pitch = 12 / (½ * 30) = 0.8

For the second part, where the rise is 4 feet and the span is 24 feet, when these values substituted into the equation you get: pitch = 4 / (½ * 24) = 0.333

So, the pitch of the first roof is 0.8 and the pitch of the second roof is 0.333

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Subtract the two given numbers:

81 - 3 = 78

Divide by the number of missing numbers +1, so divide by 3:

78/3 = 26

This gives you the difference of each number in the sequence, so now subtract 26 from each one:

81 -26 = 55

55 - 26 = 29

29-26 = 3

The two missing numbers are 55 and 29.

To find the missing terms of a geometric sequence, divide each term by a common ratio.

The given sequence is 81, ____, _____, 3.

To find the missing terms, we need to determine the common ratio of the geometric sequence.

Using the given sequence, we can see that each term is obtained by dividing the previous term by a constant factor. Therefore, the common ratio is 81 divided by the first missing term, which is then divided by the second missing term divided by the third missing term, which is then divided by 3.

To find the first missing term, we can divide 81 by the common ratio. Similarly, to find the second missing term, we can divide the first missing term by the common ratio. The missing terms of the geometric sequence are 27 and 9. Therefore, the complete sequence is 81, 27, 9, 3.

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Here is your answer

D. [tex]\frac{8788}{3}[/tex]π [tex]{units}^{3}[/tex]

REASON:

Formula for volume of sphere

= 4/3×π× r^3

Here, r= 13

So,

volume=4/3×π× 13^3

= 4/3×π× 2197

= 8788/3 ×π

HOPE IT IS USEFUL

The volume of the sphere is [tex]\bold{\frac{8788}{3} \pi ~~unit^3}[/tex]

The correct answer is option (D).

V = (4/3) × π × r³, where 'r' is the radius of the sphere

For given example,

radius of the sphere (R) = 13

Using the formula o the volume of the sphere,

V = (4/3) × π × R³

V = (4/3) × π × 13³

V = 8788/3 π cubic units.

Therefore, the volume of the sphere is [tex]\frac{8788}{3} \pi[/tex] cubic units.

The correct answer is option (D) [tex]\frac{8788}{3} \pi ~~unit^3[/tex]

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Dividing the total batter of 12 cups by the amount needed per muffin, which is 2/3 cup, reveals that the baker made 18 muffins. The answer is option C.

To find out how many muffins the baker made, we need to use the information given about the amount of batter used and how much batter is required for one muffin. According to the problem, the baker used 12 cups of batter in total and each muffin requires 2/3 cup of batter.

We start by setting up a simple division to find the answer:

(Total amount of batter) \/ (Amount of batter per muffin) = Number of muffins

12 cups \/ 2/3 cups per muffin = 18 muffins

This calculation reveals that the baker made 18 muffins. Therefore, the correct answer is (C) 18 muffins.

Answer:

A, B, E

Step-by-step explanation:

Permutations are involved when order matters, as in lane assignment, passwords, and seating charts.

When the end result is a "group of 10 students", "3 employees", or "4 cashiers", clearly order does not matter. One student, employee, or cashier is as good as another in these cases.

Using it's definition, it is found that these following situations involve permutations:

A) Determining how many different ways 7 runners can be assigned lanes on a track for a race.

B) Determining how many 5-letter passwords can be made using the word "graph."

E) Determining how many different seating charts can be made placing 6 people around a table.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem:

You can learn more about permutations at brainly.com/question/25247153

Total number of people: 65 + 85 +38 +12 = 200

Total male =  65 +38 = 103

Total women: = 200-103 = 97

Total Type A = 65+85 = 150

Total Type B = 38+12 = 50

P(male or type b ) = 103/200 + 50/200 - 38/200 = 0.515 + 0.25 - 0.19 = 0.765 - 0.19 = 0.575

P(male | type b )  = 38/50 = 0.76

The answer is P(male or type b ) < P(male | type b )

Answer:

45.55 m

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relationship between adjacent and opposite sides of an angle is ...

Tan = Opposite/Adjacent

Then the side opposite the angle of elevation will have length ...

tan(26°) = Opposite/(90 m)

Opposite = (90 m)·tan(26°) ≈ 43.90 m

This is the height of the top of the dam above Scarlett's height, so the total height to the top of the dam is ...

43.90 m + 1.65 m = 45.55 m

Answer:

Step-by-step explanation:

The problem can be solved by putting the equation into vertex form.

  s - 6 = -16(t^2 -15/4t)

  s -6 -16(15/8)^2 = -16(t^2 -15/4t +(15/8)^2) . . . . add the square of half the x-coefficient inside parentheses and equivalent amount on the other side of the equation

  s -62.25 = -16(t -15/8)^2 . . . . write as a square, simplify the constant

  s = -16(t -1.875)^2 +62.25 . . . . put in vertex form

The vertex of the downward-opening parabola is at (t, s) = (1.875, 62.25).

1. It took 1.875 seconds for the ball to reach its maximum height.

2. The ball went up to 62.25 feet.

Answer:

Alan: 200 m/min

Brian: 150 m/min

Step-by-step explanation:

Let "a" and "b" represent Alan and Brian's rates in meters per minute, respectively. The rate at which Alan is lapping Brian is the difference in their rates:

a - b = (450 m)/(9 min) = 50 m/min

This lets us write Brian's rate in terms of Alan's as ...

a -50 = b

The time to complete one oval differs by 3/4 minute (45 seconds), so we have ...

time = distance/speed

450/b - 450/a = 3/4

Multiplying by 4ab/3 gives ...

600(a -b) = ab

Substituting from above, we can rewrite this as ...

600·50 = a(a -50)

a^2 -50a -30000 = 0 . . . . . quadratic rearranged to standard form

(a -200)(a +150) = 0 . . . . . . .factored

a = 200 or -150 . . . . only the positive solution is useful here

Alan's rate is 200 m/min; Brian's rate is 150 m/min.

_____

Check

It takes Alan 450/200 min = 2.25 min to complete one oval. It takes Brian 450/150 = 3 min to complete one oval. That is 3-2.25 = 0.75 min = 45 seconds longer than Alan.

After 9 minutes, Alan will have gone (200 m/min)·(9 min) = 1800 m = 4 laps, while Brian will have gone (150 m/min)·(9 min) = 1350 m = 3 laps. Hence Alan will overtake Brian at the 9-minute mark.

Answer:

5

Step-by-step explanation:

the roots are:

[tex]\left \{ {{x_1+x_2=6} \atop {x_1*x_2=5}} \right.  \ => \ \left \{ {{x_1=1} \atop {x_2=5}} \right.[/tex]

Answer:

C. increases rapidly.

Step-by-step explanation:

tan(θ) =  sin(θ)/cos(θ)

Now, when sin 90 = 1

and cos 90 = 0

so, tan(90) = 1/0 = not defined.

(1/0 is infinity and its value is not defined)

So, when angle θ increases to 90°, then the value of tan(θ) increases rapidly, as shown in the figure below.

Answer:

  B)  maximum at 15

Step-by-step explanation:

Factor the leading coefficient from the first two terms.

  -(x^2 +6x) +6

Add the square of half the x-coefficient inside parentheses and subtract the same quantity outside.

  -(x^2 +6x +9) +6 -(-9)

  -(x +3)^2 +15

Compared to the form

  a(x -h)^2 +k

we find a=-1, h=-3, k=15. The negative vertical scale factor (a=-1) means the parabola opens downward. The vertex is located at (h, k) = (-3, 15).

The maximum value is 15.

Answer:

Step-by-step explanation:

You do x+75=250 using the information given

Answer:

the answer is 175

Step-by-step explanation:

$250

-

$75

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

$175

Answer:

8 21/100

Step-by-step explanation:

8.21 is read "eight and twenty-one hundredths". The mixed number "eight and twenty-one hundredths" is written ...

8 21/100

Answer:

3-,3,0,3

Step-by-step explanation:

For this case we must evaluate the following quadratic equation, [tex]y = -x ^ 2 + 3,[/tex] for [tex]x = -3[/tex], [tex]x = 0[/tex]and [tex]x = 3[/tex]

For [tex]x = -3[/tex]:

[tex]y = - (- 3) ^ 2 + 3\\y = -9 + 3 =\\y = -6[/tex]

For [tex]x = 0[/tex]:

[tex]y = - (0) ^ 2 + 3\\y = 0 + 3\\y = 3[/tex]

For [tex]x = 3[/tex]:

[tex]y = - (3) ^ 2 + 3\\y = -9 + 3\\y = -6[/tex]

Answer:

[tex](-3, -6)\\(0,3)\\(3, -6)[/tex]

Answer:

Part 1) The base is [tex]25\ in[/tex]  and the height is [tex]10\ in[/tex]

Part 2) The base is [tex]7.5\ in[/tex]  and the height is [tex]18.75\ in[/tex]

Step-by-step explanation:

case 1) Right isosceles triangle of the left

Let

x------> the base of the rectangle

y----> the height of the rectangle

Remember that

In a right isosceles triangle the lengths of the legs of the triangle is the same

[tex]y+x+y=45[/tex]

[tex]2y+x=45[/tex] ----> equation A

[tex]\frac{x}{y} =\frac{5}{2}[/tex]

[tex]x=2.5y[/tex] -----> equation B

substitute equation B in the equation A

[tex]2y+2.5y=45[/tex]

[tex]4.5y=45[/tex]

[tex]y=10\ in[/tex]

Find the value of x

[tex]x=2.5(10)=25\ in[/tex]

case 2) Right isosceles triangle of the right

Let

x------> the base of the rectangle

y----> the height of the rectangle

Remember that

In a right isosceles triangle the lengths of the legs of the triangle is the same

[tex]y+x+y=45[/tex]

[tex]2y+x=45[/tex] ----> equation A

[tex]\frac{y}{x} =\frac{5}{2}[/tex]

[tex]y=2.5x[/tex] -----> equation B

substitute equation B in the equation A

[tex]2(2.5x)+x=45[/tex]

[tex]6x=45[/tex]

[tex]x=7.5\ in[/tex]

Find the value of y

[tex]y=2.5(7.5)=18.75\ in[/tex]

In Case 1, the sides of the rectangle are 5x, 45, 45, and 2x. In Case 2, the sides of the rectangle are 5x, 45/sqrt(2), 45/sqrt(2), and 2x.

Let's denote the length of one side of the rectangle as 5x and the length of the other side as 2x. Since the triangle is right isosceles, the two legs are of equal length. Let's denote the length of each leg as a. Using the Pythagorean theorem, we can write an equation: a^2 + a^2 = 45^2. Solving for a, we find that a = 45/sqrt(2).

Case 1: Since two vertices of the rectangle lie on the hypotenuse, the length of the rectangle's side that is parallel to the hypotenuse will be equal to the length of that hypotenuse, which is 45. Therefore, the sides of the rectangle will be 5x, 45, 45, and 2x.

Case 2: Since the two vertices of the rectangle lie on the legs of the triangle, the length of the rectangle's side that is parallel to the hypotenuse will be equal to the lengths of the legs, which is 45/sqrt(2). Therefore, the sides of the rectangle will be 5x, 45/sqrt(2), 45/sqrt(2), and 2x.

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Answer:

yesterday 9 today 10

Step-by-step explanation:

46/5= 9.2

52/5= 10.4

Answer:

large box weights 40 pounds & small box weights 35 pounds

Step-by-step explanation:

We can write 2 equations and solve simultaneous.

Let x be weight of large box and y be weight of small box

"The combined weight of a large box and a small box is 75 pounds.":

[tex]x+y=75[/tex]

"The truck is transporting 70  large boxes and 65 small boxes. If the truck is carrying a total of 5075  pounds":

[tex]70x+65y=5075[/tex]

Now we can solve for x in the first equation, which is x = 75 -y

We now substitute this into the 2nd equation and solve for y:

[tex]70x+65y=5075\\70(75-y)+65y=5075\\5250-70y+65y=5075\\-5y=5075-5250\\-5y=-175\\y=35[/tex]

Using y = 35 and plugging that into the 1st equation, we can solve for x:

[tex]x+y=75\\x+35= 75\\x= 75 - 35\\x=40[/tex]

Hence, large box weights 40 pounds & small box weights 35 pounds

Answer:

  9x² -6xy +y²

Step-by-step explanation:

The square of the binomial can be written directly using the relationship ...

  (a +b)² = a² +2ab +b²

where you have a=3x and b=-y.

  area = (3x -y)² = (3x)² + 2(3x)(-y) + (-y)²

  area = 9x² -6xy +y²