How to factorize this?
[tex]5x {}^{3} - 9x { }^{2} - 17x - 3[/tex]
​

We have the following:

The first thing is to calculate the equation by means of the graph.

For Andrew, we can see that he starts at $ 3 and every hour that passes, he charges $ 2, therefore the equation is:

where x is the number of hours.

For Dave, we can see that he starts at $ 6 and every hour that passes, he charges $ 1.5, therefore the equation is:

where x is the number of hours.

to calculate the number of hours when the value is equal, we must match the equations like this

Which means that at 6 hours they have the same price

For a 44° elevation angle, the grade will be 96%.

Given that,

if the angle of elevation of the road is 44 degrees,

The difference in the road's altitude over a horizontal distance of 100 feet is what is referred to as the percentage grade. For instance, a road with a 5% slope will rise 5 feet for every horizontal 100-foot distance.)

A tangent ?

One of the six basic trigonometric functions is tangent, denoted as tan().

The ratio of the opposite side length to the adjacent side length is the definition of the tangent value of the one sharp angle,, in a right triangle.

[tex]tan \alpha = sin\alpha /cos \alpha[/tex]

The tangent of the angle is the ratio of rise to run.

tan(angle) = grade

tan(44°) ≈ 0.96 = 96%

Therefore, The grade will be 96% for an angle of elevation of 44°.

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Answer:

Step-by-step explanation:

y>3x+1

y≤-2x-4

The three consecutive even integers such that one less than four times the third is equal to five more than the sum of the first two is -4,-2,0.

An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.

Integer ; ....-2 , -1 , 0 , 1 , 2 , .....

Integers are non-decimal numbers and all integers are rational numbers.

Let's assume that first, even integer is x

Then the second and third will be x + 2,x + 4 respectively.

As per the given,

1 less than 4 times the third → 4(x+4) - 1

It is equal to the 5 more than the sum of x and x + 2

So, x + x + 2 + 5

Therefore,  4(x+4) - 1 = x + x + 2 + 5

4x + 16 - 1 = 2x + 7

4x + 15 = 2x + 7

2x = 7 - 15

x = -4

So integers are -4,-2,0

Hence "The three consecutive even integers such that one less than four times the third is equal to five more than the sum of the first two is -4,-2,0".

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(a) 2y=8x

(b) 7x=-2y-7 [ not direct variation ]

We couldn't express in the form x=ky , hence variation is not direct. OR we can say we couldn't express in the form y=kx ....hence variation is not direct

Distance between two coordinates:

Given point: b) (10, -5) and ( -6, 7)

Substitute the value in the expression of distance formula

The distance between coordinates (10,-5) & (-6,7) is 20 unit

A statement which best describes Gary’s error is that: Gary did not use correct factors for 66 in the equation.

The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a given numerical value or factor, the same output would be produced as when each addend is multiplied respectively by the numerical value or factor, and the products are added together.

Mathematically, the distributive property of multiplication is given by this expression:

a(b + c) = ab + ac.

Also, the correct greatest common factor of 66 and 36 is given by:

Greatest common factor (GCF) = 6

By applying the distributive property of multiplication, we have:

66 + 36 = 6(11 + 6)

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Using equation, the cost of small sundae and large sundae are 4 dollars and 6 dollars respectively.

The ice cream  shop sells small and large sundaes .

One day, 30 small sundaes and 50 large sundaes were sold for $420. Another day, 15 small sundaes and 35 large sundaes were sold for $270.

Therefore,

let

x = cost of each small sundae

y = cost of each large sundae

Therefore,

30x + 50y = 420

15x + 35y = 270

multiply equation(ii) by 2

30x + 50y = 420

30x + 70y = 540

subtract equation(i) from equation(ii)

20y = 120

y = 120 / 20

y = 6

Hence,

30x + 50(6) = 420

30x + 300 = 420

30x = 420 - 300

30x = 120

x = 120 / 30

x = 4

Therefore,

cost of small sundae = 4 dollars

cost of large sundae = 6 dollars

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Answer: The answer is B. At least that is what I think the answer would be.

Step-by-step explanation: I hope this helps.

Answer:

A

Step-by-step explanation:

The slope goes up by 11 and over by 1.

Answer: D

Step-by-step explanation:

y= [tex]\frac{1}{55}[/tex]×

Answer: You have to use a calculator

Step-by-step explanation:

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The inequality to show the possible heights of the third tree is 8 ≤ x ≤ 18.

Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤ 

Let the height of the third tree be x.

By the given condition, this will be:

8 + 16 + x ≥ 32 and 8 + 16 + x ≤  42

The first relation will give x ≥ 32 - 24 = x ≥ 8

The second relation will give:

8 + 16 + x ≤  42

24 + x ≤  42

x ≤  42 - 24

x ≤  18

The inequality is 8 ≤ x ≤ 18.

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If sum of three palm tree heights range from 32 to 42 feet. The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet. Then compound inequality is 8 ≤ x ≤ 18.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Let height of the third tree be x.

By the given condition

The sum of three palm tree heights range from 32 to 42 feet

8 + 16 + x ≥ 32 and 8 + 16 + x ≤  42

Solve these inequalities

8 + 16 + x ≥ 32

24+x ≥ 32

x≥ 32-24

x≥ 8

and 8 + 16 + x ≤  42

24+ x ≤  42

x≤  42-24

x ≤ 18

Hence the inequality is 8 ≤ x ≤ 18.

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the size of the wedge for aqua pencils is 43°

Given:

A table showing the pencil collection

To find:

the portion that represents the aqua pencils in degree

The total number of pencils = 23 + 106 + 62 + 47 + 32

The total number of pencils = 270

In degrees:

Total angle in a circle = 360°

Size of the wedge for aqua = number of aqua pencils/total pencils × 360°

To the nearest degree, the size of the wedge for aqua pencils is 43°

A) The ingredient she needed = Fruit juice  = 21 litres

                                                      Lemonade = 14 litres

B) The extra punch she can make = 20litres

C) The ratio of fruit juice and lemonade for second batch = 7:6

What is Ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

A)

Let 3x be fruit juice and 2x be the lemonade

3x + 2x = 35litres

5x = 35

x = 35/5

x = 7

Then, required ingredient she needed

Fruit juice = 3x7 = 21 litres

Lemonade = 2x7 = 14 litres

B)

According to question

The amount of fruit juice she had = 12litre

Let x be 12litre

as we know that the ratio of fruit juice to the lemonade is 3 : 2

Thus,

Fruit juice = 3(x) = 12 litres

                    x = 12/3

                    x = 4

Fruit juice = 3 x 4 = 12litres

putting the value in lemonade

Lemonade = 2(4) = 8 litres

So, The extra punch she can make :

12 + 8 = 20litres

C)

The ratio for new second batch she added 4litres in lemonade

Then it become :

Fruit juice = 21 litres

Lemonade = 14 litres + 4litres = 18

The ratio will be

21:18

7:6

Thus, the ratio of fruit juice to lemonade in second batch will be 7:6

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Answer:

y = [tex]\frac{28+3x}{4}[/tex]

Step-by-step explanation:

- 3x + 4y = 28 ( add 3x to both sides )

4y = 28 + 3x ( isolate y by dividing both sides by 4 )

y = [tex]\frac{28+3x}{4}[/tex]

Answer: Inequality Form: x ≥ 4

lll. 4

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Your answer is x ≥ 4

Step-by-step explanation:

a) Simplify both sides of the inequality.

9 ≤ 4x − 7

b) Flip the equation.

4x − 7 ≥ 9

c) Add 7 to both sides.

4x − 7 + 7 ≥ 9 + 7

4x ≥ 16

d) Divide both sides by 4.

4x/4 ≥ 14/4

x ≥ 4

The value of x in the vertical angles is 12.

When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles.

In other words, vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

Vertically opposite angles are congruent.

Therefore, the vertical angles measures 84 degrees and 8x - 12.

Let's find the value of x using the principle of vertically opposite angles.

Therefore,

84 = 8x - 12

add 12 to both sides of the equation

84 + 12 = 8x - 12 + 12

96 = 8x

divide both sides by 8

x = 96 / 8

x = 12

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Answers:

==========================================================

Explanation:

Question 1

27x^6 = (3x^2)^3 which is one cube and y^3 is another cube

Therefore 27x^6+y^3 is a sum of two cubes.

It might help to think of it like A^3+B^3 where in this case A = 3x^2 and B = y.

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

Question 2

81 isn't a perfect cube since 81^(1/3) = 4.3267 approximately, which isn't a whole number. We need 81^(1/3) to be a whole number if we wanted 81 to be a perfect cube.

We don't even need to check b^15 since 81 being a non-perfect cube means the entire expression cannot be a sum of two cubes, nor a difference of cubes.

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

Question 3

64x^3 = (4x)^3 is a perfect cube

but 9z^9 is not a perfect cube

We can see this if we computed 9^(1/3) and the result is a non-whole number.

The answer here is the same as the previous question.

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

Question 4

36^(1/3) is not a whole number, so 36 isn't a perfect cube. By extension  36m^12 isn't a perfect cube either. The answer is the same as questions 2 and 3.

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

Question 5

1 is a perfect cube since 1 = 1^3

d^12 is a perfect cube because d^12 = (d^4)^3

Therefore, we have a difference of two cubes.

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

Question 6

729^(1/3) = 9 which rearranges to 9^3 = 729, showing 729 is a perfect cube.

However y^29 is not a perfect cube since the exponent 29 is not a multiple of 3.

The overall expression is "neither".

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

Question 7

343^(1/3) = 7 rearranges to 7^3 = 343, showing 343 is a perfect cube

y^6 is a perfect cube since (y^2)^3, i.e. the exponent 6 is a multiple of 3.

We have a difference of cubes.

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

Question 8

4 isn't a perfect cube since 4^(1/3) results in some decimal value that isn't a whole number. The entire expression is neither a sum nor difference of cubes.

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

Question 9

144^(1/3) isn't a whole number, so we get a similar result to problem 8.

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Question 10

64j^6 = (4j^3)^3 is one cube

k^9 = (k^3)^3 is another cube

We have a difference of cubes

P = 2L + 2W

P = 72

L = 12W (that's an odd way to put it -- 6x 2x)

P = 2(12W) + 2W

P = 24W + 2W

72 = 26W

W = 2.769

Answer:

with?

Step-by-step explanation:

Answer

The height of the child in a year time = 124.8 cm

Explanation

The child is currently 120 cm tall.

The child grows 4% bigger in 1 year.

We now need to calculate how tall the child is in that 1 year.

New height for the child = (Current height) + (Increase in height)

Current height = 120 cm

Increase in height = 4% of 120 cm = 0.04 × 120 = 4.8 cm

New height for the child = (Current height) + (Increase in height)

= 120 + 4.8

= 124.8 cm

Hope this Helps!!!

The area of the rectangle is 104 inches²

Define Area of Rectangle

The area of a rectangle is the space occupied by the rectangle inside its perimeter.

Given that, the perimeter is 42 inches

we know, the formula of perimeter of rectangle = 2(L + W)

so, the first equation will be

2(L + W) = 42

or, 2L + 2W = 42       ----------eq(i)

Next, the length of a rectangle is 5 inches longer than its width, so

L = W + 5

or, L - 5 = W              --------------eq(ii)

Now, the eq(i) is

2L + 2W = 42

Put W value from eq(ii),

2L + 2(L- 5) = 42

=> 2L + 2L - 10 = 42

=> 4L - 10 = 42

=> 4L = 52

=> L = 13

We got, L = 13 put this value in any of the equation

I'm putting the value in eq(ii) as it easy for to solve

=> 13 - 5 = W

=> W = 8

If you want to cross verify the values of L and W , then simply put the values in both the equation and LHS = RHS like that

2(13) + 2(8) = 42  (correct)

13 - 5 = 8 (correct)

Now, we got length and width so now just put the values of L and W in area of rectangle formula,

Area of rectangle = Length * width

                            = 13 * 8

Area of rectangle = 104 inches²

Hence, The area of the rectangle is 104 inches²

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The given expression is

It's important to know that the rules of significant figures state that the resulting number of a sum of decimal numbers may have no more significant numbers than the least number of significant figures.

In other words, the answers can't be more precise than the least precise number in the sum.

The relation between the events Y and W prevents us from completing the analysis.

The relation between the events Y and W prevents us from completing the analysis.

Case 1: W is more likely than Y then we have the following analysis:

Z, X, Y, and W are arranged in ascending order of more likeliness.

Case 2: Y is more likely than W then we have the following analysis:

Z, X, W, and Y are arranged in ascending order of more likeliness.

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Given

V(5, -2)

T(10, -3)

Procedure

For V:

The equation of the horizontal straight line corresponds to y = -2.

The equation of the vertical straight line corresponds to x = 5

For T:

The equation of the horizontal straight line corresponds to y = -3.

The equation of the vertical straight line corresponds to x = 10

Part A: The multiplication expression is  L×w

Part B: The expression is written as N= r+ g + w + b

The final product = 200 boxes

It is crucial to note that the formula for determining the area of a rectangle is expressed as;

Area = lw

Given that;

The area can be calculated by multiplying the length and the width and also by then adding the number of boxes.

We have the expression as;

10( 4 + 5 + 4 + 7)

Also,

L × w =  r + g + w + b

Hence,  we have that L×w is a multiplication expression.

Total number of boxes for the length = 20

Total number of boxes for the width = 10

Total area = L×w = 20×10=200

We have;

N= r+ g + w + b

but r = g = b

Also,

L×B =  3r + w

Hence, a multiplication expression is an expression that has its variables or numbers being multiplied.

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Answer:

12.5 hours

Step-by-step explanation:

The flat rate is the base, in which no matter how long you rent it for, they'll still charge you that much. You have 200 dollars, and negative 75 is 125 dollars, which you can spend on the hours. Assuming you can rent the jet ski for half an hour, you can divide 125 by 10 for the amount of hours, and the answer is 12.5 hours. However, if you can't rent the jet skis for half an hour, the answer is 12 hours.

Using ratios and assuming the given values, the rate of the total cost for items in the United Kingdom to that of the total cost of items in Australia is 2/3.

Assume that the costs are:

The ratio would be:

So, we have:

Simplify:

Express as rate

Therefore, using ratios and assuming the given values, the rate of the total cost for items in the United Kingdom to that of the total cost of items in Australia is 2/3.

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Percent of the original is the radius of the reduced artery is 0.070 times the original radius.

Given that,

A blood clot has lowered the flow rate in an artery to 8.5% of its usual value, and the average pressure difference has increased by 20.5%.

p1 = 8.5 % ,

p2 = 20.5 %

The equation is using here is From Poiseuille's equation

Q = \Delta p \pi r4 / 8 \eta L

now

Q1 = \Delta p1\pi r14 / 8 \eta L

and

Q2 = \Delta p2\pi r24 / 8 \eta L

Q1 = \Delta p1\pi r14 / 8 \eta L / Q2 = \Delta p2\pi r24 / 8 \eta L

Q1 / Q2 = \Delta p1 ro4 / \Delta p2 r24

r24 = ( 0.085 Q1 / Q1 ) ( \Delta p1 / \Delta p1 + 0.20 \Delta p1 ) ro4

r24 = 0.085 X ( 1 / ( 1 + 0.20 ) ro4  

r2 = 0.070 ro  

As a result, the shortened artery's radius is 0.070 times its original radius, or percent of the original.

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Answer:

(x+6)+x=20 Andy

Step-by-step explanation:

X represents Andy

X+6 represents juana who did 6 more problems

(X+6)+x=20

2x+6=20

2x=14

X=7