factorise

1)
8a(3x–2y)²–12x +8y​

Answer:

x=3.00 or x= 8.00

Explanation:

Let us denote side of the cut-out square as x inches

Then base of box = 16-2x by 6-2x

The volume = V = (16-2x)(6-2x)

= 96-3x-12x+4x

dV/dx = 96-44x+4x^2

= 0 for a max V

divide by 4

X^2 -11x +24=0

Using quadratic formula to solve the equation

X= (11± √11^2-(4×1×24)/2

(11± √25)/2

x= 3 or 8inches

From the equation of volume = V = x(16-2x)(6-2x)

Substitute

let x = 3 , V = 3(16-6)(6-6) = 0

let x = 8 , V = 8(16-16)(6-16) = 0

Therefore, the maximum volume exist at both point x=3 or x= 8

Answer:

(x + 4)² + (y + 1)² = 4

Step-by-step explanation:

From the graph attached,

Extreme ends of the diameter of the circle,

(-4, 1) and (-4, -3)

Center of the circle = Midpoint of the diameter

Center = [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

           = [tex](\frac{-4-4}{2},\frac{1-3}{2})[/tex]

           = (-4, -1)

Radius of the circle = Distance between the center and extreme end

                                = 2 units

Since standard equation of the circle is,

(x - h)² + (y - k)² = r²

where (h, k) is the center and 'r' is the radius of the circle

By substituting the values in the standard equation,

(x + 4)² + (y + 1)² = 2²

(x + 4)² + (y + 1)² = 4

Answer:

-6

Step-by-step explanation:

x(-y + z)

Let x= 3 y =3 and z =1

3( -3+1)

Parentheses first

3 ( -2)

Then multiply

-6

Answer:

Hello! The answer to your question is -6

Steps will be provided below.

Step-by-step explanation:

This is how to solve your question:

Question:

Evaluate x(-y + z) for x = 3, y = 3, and z = 1.

Answer and how to solve:

The answer is -6 because....

If you do the steps correctly it will be...

Do the Parentheses first.

3x-(2)

Now you just multiply and you will get your answer.

Which will give you -6

SO THE ANSWER TO YOUR QUESTION IS -6

⭐️Hope this helps! :) ⭐️

Have a wonderful day! :D

Answer:

look below

Step-by-step explanation:

hi

Answer:

6

Step-by-step explanation:

I think the answer is 6

Answer:

A. 4x¹¹ + x⁷ + 3x³ - 5x + 9

Step-by-step explanation:

order the exponents from largest to smallest. variables always come first; therefore, -5x before 9

Answer:

RS and plane RSU

Step-by-step explanation:

I think not to sure

Answer:

Table B

Step-by-step explanation:

Note that for y to vary inversely as x, an increase in x will cause a decrease in y. Therefore, by careful observation of tables A, B, C, and D, we would notice the following:

In table C:

As x increases from 1 to 2 to 3, y also increases from 26 to 52 to 78. Which means that an increase in x causes an increase in y. This is not an inverse variation.

In table D:

As x increases from 1 to 2 to 3, y also increases from -7 to -1 to 6. Which means that an increase in x causes an increase in y. This is also not an inverse variation.

We are left with options A and B

If y varies inversely as x, the following relationship must hold:

[tex]y \alpha \frac{1}{x}\\y = \frac{k}{x}[/tex]

Where k is a constant of proportionality

considering option B:

When x = 1, y = 36

36 = k/1

k = 36 * 1

k = 36

when x = 2, y = 36/2

y = 18

when x = 3, y = 36/3

y = 12

These tally with all that is indicated in the table. Option B is an inverse variation

Answer:

i will say c

Step-by-step explanation:

c

Answer:

B. Whole numbers from 0 to 10

Step-by-step explanation:

this is a dot graph, so only those dots, whole numbers of tickets, are valid input, that is, domain of the graph.

Answer:

[tex]=3/4[/tex]

Step-by-step explanation:

[tex]\frac{4\sqrt{18}}{16\sqrt{2}}[/tex]

First, simplify the fraction:

[tex]=\frac{\sqrt{18}}{4\sqrt2}[/tex]

Now, simplify the radical in the numerator (the radical in the denominator cannot be simplified:

[tex]\sqrt{18}=\sqrt{9\cdot2}=\sqrt{9}\cdot\sqrt{2}=3\sqrt{2}[/tex]

Substitute:

[tex]=\frac{3\sqrt{2}}{4\sqrt{2}}[/tex]

The radicals cancel:

[tex]=3/4[/tex]

Answer:

b) 36 inches

Step-by-step explanation:

Length  of the  wire = Outside circumference of the cylindrical tube * length of the cylinder

= 4 * 9

= 36 inches

Length of the wire will be same to the surface area of the cylinder

Surface area of cylinder = circumference * length

Answer:

The triangle has two sides that are equivalent and the angle where the two meet are also equivalent.

In other words, two sides and the angle between them are congruent.

Hope this helps, if it does please give me brainliest, it will help me a lot :)

Have a good day

Answer:

A on edge

Step-by-step explanation:

Answer:

The probability that a man in this age category does NOT die of cancer during the course of the​ year is 0.997.

Step-by-step explanation:

Suppose the probability of an event occurring is [tex]P_{i}[/tex].

The probability of the given event not taking place is known as the complement of that event.

The probability of the complement of the given event will be,

[tex]1 - P_{i}[/tex]

In this case an events X is defined as a man, aged 55​ - 59, will die of cancer during the course of the year.

The probability of the random variable X is:

[tex]P (X) = \frac{300}{100000}=0.003[/tex]

Then the event of a man in this age category not dying of cancer during the course of the​ year will be complement of event X, denoted by X'.

The probability of the complement of event X will be:

[tex]P(X')=1-P(X)[/tex]

          [tex]=1-0.003\\=0.997[/tex]

Thus, the probability that a man in this age category does NOT die of cancer during the course of the​ year is 0.997.

Answer:

to be honest I'm not sure how to do

Step-by-step explanation:

Given

Opp=8

Adj=6

Hyp=10

Answer

1)Sin<A=Opp/Hyp

8/10=4/5... Yes

2)Cos<A=Opp/Adj

8/6=4/3... No

Given

Opp=6

Adj= 8

Hyp= 10

Answer

1)Sin<B= Opp/Hyp

6/10=3/5... No

2)Cos<B= Opp/Adj

6/8=3/4... No

Hope this helps ❤❤❤

Answer:

3

Step-by-step explanation:

We are adding 2 each time

-3 +2 = -1

-1 +2 = 1

To get the next term add 2

1 +2 = 3

Answer: 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,

[tex] - \frac{2}{3} [/tex]

Now, let's find the value of 9x + 6

[tex]9x + 6[/tex]

plug the value of X

[tex] = 9 \times (- \frac{2}{3} ) + 6[/tex]

Multiplying a positive and negative equals a negative

[tex]( + ) \times ( - ) = ( - )[/tex]

[tex] = - 9 \times \frac{2}{3} + 6[/tex]

Reduce the number with Greatest Common Factor 3

[tex] = - 3 \times 2 + 6[/tex]

Multiply the numbers

[tex] = - 6 + 6[/tex]

The sum of two opposites equals 0

[tex] = 0[/tex]

Hope this helps..

best regards!!

Answer:

Step-by-step explanation:

The two have a total of 5+2 = 7 "ratio units" so have a total of 140 cars.

can you mark me as brainliest?

Answer:

Mark as BRAINLIEST plz

|x-323|<50: answer

Step-by-step explanation :

For water to be a liquid, the temperature must be within 50 Kelvin of 323 K.

So, the range of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323.

The equation that can be used to determine the maximum temperature at which water is a liquid can be given by :  x < 323 + 50

The equation that can be used to determine the minimum temperature at which water is a liquid can be given by : x > 323 - 50

So the resultant equation can be written as :

|x-323|<50

The solution of inequality equation is  | x - 323 | < 50

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the temperature of the water be = x Kelvin

Now , the equation will be

For water to be in the liquid state, the temperature must be within 50 kelvin (K) of 323 K

So , the value of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323

Substituting the values in the inequality equation , we get

For maximum temperature ,

x should be 50 more than 323 and

For minimum temperature ,

x should be 50 less than 323

So ,

The inequality relation is

x > 50 + 323   be equation (1)

x < 323 - 50   be equation (2)

So , the modulus function is expressed as

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

Therefore , the value is | x - 323 | < 50

Hence , The solution of inequality equation is  | x - 323 | < 50

To learn more about inequality equations click :

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Answer:

[tex]Side\ B = 6.0[/tex]

[tex]\alpha = 56.3[/tex]

[tex]\theta = 93.7[/tex]

Step-by-step explanation:

Given

Let the three sides be represented with A, B, C

Let the angles be represented with [tex]\alpha, \beta, \theta[/tex]

[See Attachment for Triangle]

[tex]A = 10cm[/tex]

[tex]C = 12cm[/tex]

[tex]\beta = 30[/tex]

What the question is to calculate the third length (Side B) and the other 2 angles ([tex]\alpha\ and\ \theta[/tex])

Solving for Side B;

When two angles of a triangle are known, the third side is calculated as thus;

[tex]B^2 = A^2 + C^2 - 2ABCos\beta[/tex]

Substitute: [tex]A = 10[/tex],  [tex]C =12[/tex]; [tex]\beta = 30[/tex]

[tex]B^2 = 10^2 + 12^2 - 2 * 10 * 12 *Cos30[/tex]

[tex]B^2 = 100 + 144 - 240*0.86602540378[/tex]

[tex]B^2 = 100 + 144 - 207.846096907[/tex]

[tex]B^2 = 36.153903093[/tex]

Take Square root of both sides

[tex]\sqrt{B^2} = \sqrt{36.153903093}[/tex]

[tex]B = \sqrt{36.153903093}[/tex]

[tex]B = 6.0128115797[/tex]

[tex]B = 6.0[/tex] (Approximated)

Calculating Angle [tex]\alpha[/tex]

[tex]A^2 = B^2 + C^2 - 2BCCos\alpha[/tex]

Substitute: [tex]A = 10[/tex],  [tex]C =12[/tex]; [tex]B = 6[/tex]

[tex]10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha[/tex]

[tex]100 = 36 + 144 - 144 *Cos\alpha[/tex]

[tex]100 = 36 + 144 - 144 *Cos\alpha[/tex]

[tex]100 = 180 - 144 *Cos\alpha[/tex]

Subtract 180 from both sides

[tex]100 - 180 = 180 - 180 - 144 *Cos\alpha[/tex]

[tex]-80 = - 144 *Cos\alpha[/tex]

Divide both sides by -144

[tex]\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}[/tex]

[tex]\frac{-80}{-144} = Cos\alpha[/tex]

[tex]0.5555556 = Cos\alpha[/tex]

Take arccos of both sides

[tex]Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)[/tex]

[tex]Cos^{-1}(0.5555556) = \alpha[/tex]

[tex]56.25098078 = \alpha[/tex]

[tex]\alpha = 56.3[/tex] (Approximated)

Calculating [tex]\theta[/tex]

Sum of angles in a triangle = 180

Hence;

[tex]\alpha + \beta + \theta = 180[/tex]

[tex]30 + 56.3 + \theta = 180[/tex]

[tex]86.3 + \theta = 180[/tex]

Make [tex]\theta[/tex] the subject of formula

[tex]\theta = 180 - 86.3[/tex]

[tex]\theta = 93.7[/tex]

Answer:

First car: 30 gallons

Second car: 35 gallons

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations:

Total gas consumption was 65:

x+y=65

Where:

x = gallons consumed by the first car

y = gallons consumed by the second car

The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas, the two cars went a combined total of 1650 miles:

x 20+y 30 = 1650

The system is:

x+y=65 (1)

x 20+y 30 = 1650 (2)

Isolating y on (1)

y = 65-x

Replacing y= 65-x on (2):

x 20+(65-x)30 = 1650

20x +1,950-30x= 1650

20x-30x= 1650-1950

-10x= -300

x= -300/-10

x = 30 gallons

Back to (1)

y =65-x

y =65-30

y= 35 gallons

Feel free to ask for more if needed or if you did not understand something.  

Answer:

m = 187

Step-by-step explanation:

Given m and n are inversely correlated then the equation relating them is

m = [tex]\frac{k}{n}[/tex] ← k is a constant

To find k use the condition when m = 22, n = 51

22 = [tex]\frac{k}{51}[/tex] ( multiply both sides by 51 )

1122 = k

m = [tex]\frac{1122}{n}[/tex] ← equation of correlation

When n = 6, then

m = [tex]\frac{1122}{6}[/tex] = 187

The value of m will be equal to 187 when both the numbers are an inverse function of each other.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that m and n are inversely correlated then the equation relating them is

m = K / n ← k is a constant

To find k use the condition when m = 22, n = 51

22 = k / 51 ( multiply both sides by 51 )

1122 = k

m =  1122 / n ← equation of correlation

When n = 6, then

m = 1122 / 6  = 187

Therefore, the value of m will be equal to 187 when both the numbers are an inverse function of each other.

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Answer:

Market price = Rs. 15,000

Step-by-step explanation:

Let Market price = x

discount = 20% of x

              = 0.20 *x = 0.2x

Selling price after discount = x - 0.2x = 0.8x

Value added tax = 15% of 0.8x

                            = 0.15 * 0.8x

                           = 0.12x

Selling price with VAT = 0.8x + 0.12x = 0.92x

Differences between SP with vat and SP after discount = rs.1800

0.92x - 0.8x = 1800

0.12 x = 1800

x = 1800/0.12

x = Rs. 15,000

Answer:

The eigen values obtained are not real and thus according to the notation in the question, the eigen values DNE in R

Step-by-step explanation:

Here, we are to find the eigen value and the eigen vector of matrix A over the real numbers R

Please kindly check attachment for complete solution and explanation

Answer:175

Step-by-step explanation:

1. Turn 28% into a decima: 0.28

2. Multiply 1250 by 0.28 to get the amount of ninth grade students:350

3. Half the amount of ninth grade students:175

Answer:

The answer is 175

Step-by-step explanation:

Because I read the problem carefully and identified that the explanation is way too long so I am gonna make this short and easy for you. I am correct, just Trust me :)

Answer:

  11

Step-by-step explanation:

The Law of Cosines is useful when you have two sides of a triangle and the angle between.

  v^2 = w^2 +u^2 -2wu·cos(V)

  v^2 = 6^2 +16^2 -2·6·16·cos(27°)

  v^2 = 292 -171.0733

  v ≈ 10.9966

  v ≈ 11

Answer:

Step-by-step explanation:

Side AC is the side opposite the reference angle of 70 degrees while side BC is the side adjacent to the reference angle. AB is the hypotenuse since it is across from (or opposite) the right angle. The trig ratio that uses the sides opposite from and adjacent to the reference angle is the tangent. Setting up to solve for AC:

[tex]tan(70)=\frac{?}{3}[/tex] and

3tan(70) = ? so

? = 8.24

Answer:

40

Step-by-step explanation:

We're given an angle that forms a linear pair, and we're given an isosceles triangle. The angle to the right of 110 is 70, since they have to add up to 180. Since this is an isosceles triangle (denoted by the two dashes), we know that the other base angle has to be 70. 70 + 70 = 140; all angles add up to 180 so 180 - 140 = 40 degrees.

Answer:

40 degrees

Step-by-step explanation:

Since this is an isosceles triangle the 2 bottom angles are congruent

The bottom angles will be 70 degrees bc the exterior angle is 110 and 180-110=70

Because a triangle adds up to 180 degrees you need to use the equation 70 + 70 + x = 180 and you should get x = 40 degrees

Answer: 90,000

Step-by-step explanation:

From the question, we are informed that in a local town, 54,000 families have incomes less than $25,000 per year. We are further told that this number of families is 60% of the families that had this income level 12 years ago.

To calculate the number of families who had incomes less than 25,000 per year 12 years ago goes thus:

Let the the number of families who had incomes less than 25,000 per year 12 years ago be represented by x.

Since we are told that this number of families is 60% of the families that had this income level 12 years ago. This means that:

60% of x = 54,000

60/100 × x = 54,000

0.6 × x = 54,000

0.6x = 54,000

Divide by 0.6

0.6x/0.6 = 54000/0.6

x = 90,000

The number of families who had incomes less than 25,000 per year 12 years ago was 90,000.

Answer:

8 scoops of flour

Step-by-step explanation:

It asks for you to solve using unit rates so we need to find out the rate of how much flour you need to bake a single cookie since the question is about how many scoops of flour Shelby needs to bake 64 cookies.

So first, do 6/48, which is 1/8.

It takes 1/8 scoop of flour to bake one cookie.

Unit rate: 1/8 scoop of flour per cookies.

Now, we can multiply 1/8 by 64 since 64 is the number of cookies Shelby needs and 1/8 is the amount of flour for one single cookies. 1/8 * 64 = 8.

Shelby needs 8 scoops of flour to bake 64 cookies