What value of x will make each equation below true? 4x-1=4x+7

Answer:

i)-240*a^4*b^3*c^2

ii)-15*x^2*y^2+3*x^3*y^2

iii)x^4*y^3*z^2-x^2*y^3*z^3+x^3*y^2*z^3

iv)p*q+6*q-7*p-42

v)2*x^3-3*x^2-23*x+42

vii)2*x^2-2*y^2+7*x-12*y-15

Step-by-step explanation:

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Work Shown:

We have two sequences, which we'll call A and B

Both sequences are arithmetic. The first sequence starts at 2, and increases by 3 each time. Sequence B starts at 3 and increases by 7 each time.

The terms in bold are what the two sequences have in common.

-----------

It turns out that the bold terms follow an arithmetic sequence of their own.

The sequence {17, 38, 59, ...} is arithmetic.

Call this sequence C. This sequence starts at 17 and increases by 21 each time. The nth term for sequence C is

C(n) = a+d(n-1)

C(n) = 17+21(n-1)

C(n) = 17+21n-21

C(n) = 21n-4

Plugging in n = 1 leads to C(n) = 17. Also, plug in n = 2 and you should get C(n) = 38. Plugging in n = 3 leads to C(n) = 59. And so on.

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The question is now "what is the largest term in sequence C such that it is less than 500?".

In other words, we want to find the term C(n) where C(n) < 500 and C(n) is as large as possible.

Use a bit of algebra to get

C(n) < 500

21n - 4 < 500

21n < 500+4

21n < 504

n < 504/21

n < 24

So n must be smaller than 24 to get what we want.

Because n is a natural number (positive whole number), we drop to n = 23 to find that

C(n) = 21n-4

C(23) = 21(23)-4

C(23) = 479

The largest value, less than 500, the two original sequences have in common is 479.

If we didn't have the restriction "less than 500", then there would be no largest value as sequence C goes on forever.

Answer:

467

Step-by-step explanation:

We have two sequences, which we'll call A and B

A = {2,5,8,11,14, 17 ,20,23,26,29,32,35, 38, 41,44,47,50,53,56, 59 ,62...}

B = {3,10, 17 ,24,31, 38 ,45,52, 59 , 66...}

Both sequences are arithmetic. The first sequence starts at 2, and increases by 3 each time. Sequence B starts at 3 and increases by 7 each time.

The terms in bold are what the two sequences have in common.

-----------

It turns out that the bold terms follow an arithmetic sequence of their own.

The sequence {17, 38, 59, ...} is arithmetic.

Call this sequence C. This sequence starts at 17 and increases by 21 each time. The nth term for sequence C is

C(n) = a+d(n-1)

C(n) = 17+21(n-1)

C(n) = 17+21n-21

C(n) = 21n-4

Plugging in n = 1 leads to C(n) = 17. Also, plug in n = 2 and you should get C(n) = 38. Plugging in n = 3 leads to C(n) = 59. And so on.

-----------

The question is now "what is the largest term in sequence C such that it is less than 500?".

In other words, we want to find the term C(n) where C(n) < 500 and C(n) is as large as possible.

Use a bit of algebra to get

C(n) < 500

21n - 4 < 500

21n < 500+4

21n < 504

n < 504/21

n < 24

So n must be smaller than 24 to get what we want.

Because n is a natural number (positive whole number), we drop to n = 23 to find that

C(n) = 21n-4

C(23) = 21(23)-4

C(23) = 479

The largest value, less than 500, the two original sequences have in common is 479.

If we didn't have the restriction "less than 500", then there would be no largest value as sequence C goes on forever.We have two sequences, which we'll call A and B

A = {2,5,8,11,14, 17 ,20,23,26,29,32,35, 38, 41,44,47,50,53,56, 59 ,62...}

B = {3,10, 17 ,24,31, 38 ,45,52, 59 , 66...}

Both sequences are arithmetic. The first sequence starts at 2, and increases by 3 each time. Sequence B starts at 3 and increases by 7 each time.

The terms in bold are what the two sequences have in common.

-----------

It turns out that the bold terms follow an arithmetic sequence of their own.

The sequence {17, 38, 59, ...} is arithmetic.

Call this sequence C. This sequence starts at 17 and increases by 21 each time. The nth term for sequence C is

C(n) = a+d(n-1)

C(n) = 17+21(n-1)

C(n) = 17+21n-21

C(n) = 21n-4

Plugging in n = 1 leads to C(n) = 17. Also, plug in n = 2 and you should get C(n) = 38. Plugging in n = 3 leads to C(n) = 59. And so on.

-----------

The question is now "what is the largest term in sequence C such that it is less than 500?".

In other words, we want to find the term C(n) where C(n) < 500 and C(n) is as large as possible.

Use a bit of algebra to get

C(n) < 500

21n - 4 < 500

21n < 500+4

21n < 504

n < 504/21

n < 24

So n must be smaller than 24 to get what we want.

Because n is a natural number (positive whole number), we drop to n = 23 to find that

C(n) = 21n-4

C(23) = 21(23)-4

C(23) = 479

The largest value, less than 500, the two original sequences have in common is 479.

If we didn't have the restriction "less than 500", then there would be no largest value as sequence C goes on forever.

Answer:

x = 5.98

Step-by-step explanation:

Step 1: Use tangent to solve for x

tan50.1 = [tex]\frac{x}{5}[/tex]

x = 5tan50.1

x = 5.98

Therefore x is equal to 5.98

Answer:

90 degrees

Step-by-step explanation:

I don't really have an explanation but I'm 100% sure that it is

Answer:

90 degrees

Step-by-step explanation:

Answer:

i. 179.775 kg

IIa)the weight=585.225 kg

IIb) percentage=75.6%

3)=30240 kg

Step-by-step explanation:

From the question were given the total area of the land as 1000 sq. meter

Amount of cultivated rice= 765 kg

the percentage of wastage rice =23.5%.

But we can convert the amount of the wastage rice from percentage to kilogram which is

23.5/100=0.235

Then to kilogram 0.235× 765 kg= 179.775 kg

Then amount of wastage rice= 179.775 kg

I)Find the weight of the wastage. ?

The amount of wastage rice is the conversion of it's percentage to kilogram which I did above

Then amount of wastage rice= 179.775 kg

II) Find the weight and percentage of rice cultivated.

Since we know amount of wastage as 179.775 kg, then the amount of cultivated will b difference between the cultivated and wastage=765 - 179. 775 = 585.225 kg

Then it's percentage is the substraction of the percentage of wastage from 100%

= 75.6%

3)If the area has been increased 40 times in size, how much rice will be cultivated (excluding the wastage)

Increase in the land in 40 times= 40×1000= 40,000sm

Then the rice cultivated= 75.6% ×40000

=30240 kg

Answer:

1.3888888888889 mps

Step-by-step explanation:

1 kph = 0.27777777777778 mps, so just multiply that by 5.

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Work Shown:

b = unknown number

2b = 2 times a number

2b+3 = the sum of 2 times a number and 3

2b+3 = 7, since the expression above is set equal to 7

The equation represents the given algebric phrase is 2b + 3 = 7 and that number will be 2.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

As per the given phrase,

The sum of 2 times a number and 3 equals 7.

2 times b = 2b

The Sum of 2b with 3 equal to 7 will be 2b + 3 = 7

2b = 7 - 3

2b = 4

b = 4/2 = 2

Hence"The equation represents the given algebric phrase is 2b + 3 = 7 and that number will be 2".

For more about the equation,

https://brainly.com/question/10413253

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Answer:

[tex]\Large \boxed{k=2x + \frac{-7}{3}} \\ \\ \\ \Large \boxed{x=\frac{1}{2} k+\frac{7}{6}}[/tex]

Step-by-step explanation:

Solving for k:

[tex]\sf 3k+16=9+6x[/tex]

Subtracting 16 from both sides.

[tex]\sf 3k=6x-7[/tex]

Dividing both sides by 3.

[tex]\displaystyle \sf k=2x + \frac{-7}{3}[/tex]

Solving for x:

Flipping the original equation.

[tex]\sf 6x+9=3k+16[/tex]

Subtracting 9 from both sides.

[tex]\sf 6x=3k+7[/tex]

Dividing both sides by 6.

[tex]\sf \displaystyle x=\frac{1}{2} k+\frac{7}{6}[/tex]

Answer:

perimeter = 322.5 ft ( to the nearest tenth of a foot)

Step-by-step explanation:

Length the length of the sides of the square be L

Area of a square = L²

∴ 6,500 = L²

L = √(6,500)

L = 80.6226

Next Let us calculate the perimeter

Perimeter of a square = L + L + L + L = 4L

perimeter = 4 × 80.6226

Perimeter = 322.4904 ft

perimeter = 322.5 ft ( to the nearest tenth of a foot)

N:B rounding to the nearest tenth of a foot is same as rounding to 1 decimal place.

Answer:

Step-by-step explanation:

[tex] \sf{9 - 4x = 17}[/tex]

Move 9 to right hand side and change it's sign

⇒[tex] \sf{ - 4x = 17 - 9}[/tex]

Subtract 9 from 17

⇒[tex] \sf{ - 4x = 8}[/tex]

Divide both sides of the equation by -4

⇒[tex] \sf{ \frac{ - 4x}{ - 4} = \frac{8}{ - 4}} [/tex]

Calculate

⇒[tex] \sf{x = - 2}[/tex]

Hope I helped!

Best regards!!

Answer:

Area of the triangle = 12 square feet

Step-by-step explanation:

Area of a triangle is calculated by the formula,

Area = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

From the picture attached,

Height of the given triangle = Vertical distance of the top vertex = 4 feet

Base of the triangle = 6 feet

Area of this triangle = [tex]\frac{1}{2}(6)(4)[/tex]

                                 = 12 square feet

Therefore, area of the given triangle will be 12 square feet.

Answer:

a = 49

b = - 20√2

Step-by-step explanation:

5 - 2√6 / 5 + 2√6

We can rationalise the denominator as follow:

5 - 2√6 / 5 + 2√6

Multiply the numerator and the denominator by the conjugate of

5 + 2√6. The conjugate of 5 + 2√6 is

5 - 2√6

(5 - 2√6 / 5 + 2√6) x (5 - 2√6 / 5 - 2√6)

(5 - 2√6) (5 - 2√6) /(5 + 2√6) (5 - 2√6)

Expand

(25 - 10√6 - 10√6 + 4×6) / (25 - 10√6 + 10√6 + 4×6)

25 - 20√6 + 24 / 25 - 24

25 + 24 - 20√6 / 1

49 - 20√6

Equating 49 - 20√6 with a + b√3, we can obtain the value of a and b as follow:

49 - 20√6 = a + b√3

From the above

a = 49

b√3 = - 20√6

Divide both side by √3

b = - 20√6/√3

Rationalise

b = - 20√6/√3 x √3/√3

b = - 20√(6×3)/ √3×√3

b = - 20√18 / 3

b = - 20√(9×2) / 3

b = - 20 × 3√2 / 3

b = - 20√2

Given info:- Rationalise the denominator and find out the value of "a" and "b"

Given expression: {(5-2√6)/(5+2√6)} = a+b√3

Explanation:-

{(5-2√6)/(5+2√6)} = a+b√3

We know that Rationalising factor of a+b√c is a-b√c.

Therefore, the rationalising factor of 5+2√6 is 5-2√6.

⇛{(5-2√6)/(5+2√6)} × {(5-2√6)/(5-2√6)} = a+b√3

⇛{(5-2√6)(5-2√6)}/{(5+2√6)/(5-2√6)} = a+b√3

⇛{(5-2√6)²}/{5+2√6)(5-2√6)} = a+b√3 [∵(a-b)(a-b)=(a-b)²]

⇛{(5-2√6)²}/{(5)²-(2√6)²} = a+b√3 [∵(a+b)(a-b)=a²-b²]

⇛{(5-2√6)²}/({5*5)-(2*2√6*6)} = a+b√3

⇛{(5-2√6)²}/(25 - 4√6) = a+b√3

⇛{(5-2√6)²}/(25-24) = a+b√3

⇛{(5-2√6)²}/1 = a+b√3

⇛(5-2√6)² = a+b√3

⇛(5)²-(2√6)²+2(5)(2√6) = a+b√3

⇛(5*5) - (2*2√6*6) - 10 - 2√6 = a+b√3

⇛25 - 10 - 4√6 - 2√6 = a+b√3

⇛15 - 4√6 - 2√6 = a+b√3

⇛15 + 6√6 = a+b√3

∴ 15 + 6√6 = a+b√3

On, comparing with both RHS we notice that:

The value of a = 15 and b = 6.

Hope this helps!!

If you have any doubt, then you can ask me in the comments.

Answer:

y = -5, 1

Step-by-step explanation:

2y² - 10y + 44 = (y - 7)²

expand (y - 7)²

(y - 7)² = y² - 14y + 49

move it to the left

(2y² - 10y + 44) - (y² - 14y + 49) = 0

distribute the (-)

2y² - 10 y + 44 - y² + 14y - 49 = 0

combine like terms

y² - 4y -5

factor with factoring X

y² + 5y - y - 5 = 0

factor by grouping ↓

factor out a y from first half of equation

y(y + 5) - y - 5 = 0

factor out a (-) from second half of equation

y(y +5) - (y + 5) = 0

(y +5)(y - 1) = 0

y = -5, 1

Answer: 153.94cm

Step-by-step explanation:

Answer:

A  =  49 cm ²

Step-by-step explanation:

A = πr²

   = 22/7 * 7 *7

      = 49 cm²

Answer:

This will be -8x^3y^9.

Answer:

Two other exponents that results in 256 are [tex]16^2[/tex] and [tex]4^4[/tex]

Step-by-step explanation:

Given

[tex]2^8 = 256[/tex]

Required

Write two exponential expression that equals 256

[tex]2^8 = 256[/tex]

Expand 8 as 4 * 2

[tex]2^{4*2} = 256[/tex]

Using laws of indices, we have

[tex](2^4)^2 = 256[/tex]

2⁴ = 16; So, we have

[tex]16^2 = 256[/tex] --- This is one

Recall that

[tex]2^{4*2} = 256[/tex]

This can also be rewritten as

[tex]2^{2*4} = 256[/tex]

Using laws of indices, we have

[tex](2^2)^4 = 256[/tex]

2² = 4; So, we have

[tex]4^4 = 256[/tex] --- This is another one

Hence, two other exponents that results in 256 are [tex]16^2[/tex] and [tex]4^4[/tex]

Answer:

true

Step-by-step explanation:

Answer:

False, if you get a negitive it would be - square root symbol 9

This is just an example

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Hello!

Since y varies directly with x what happens to y also happens to x

From y = -12 to y = -4 you divide by 3 so we do that to x

6 / 3 = 2

The answer is 2

Hope this helps!

Answer:8640 square inches

Step-by-step explanation:

Answer:

rational numbers are the number which can not expressed into simpler fraction

Answer:

25°

Step-by-step explanation:

180-130=50

50÷2=25°

Answer:

0.00432 km = 4320 mm

Step-by-step explanation:

There are 1000000 millimeters in a kilometer. To convert kilometers to millimeters, multiply the kilometer value by 1000000.

Quick check 0.00432 * 1000000 = 4320 mm

Answer:

4320

Step-by-step explanation:

Answer:

b so  it doesnt tell you how many people come to the hospital a day

Step-by-step explanation:

a--->b--->=c

Answer:

A) A nonresponse occurred

Step-by-step explanation:

We understand that in the span of 10 years, 1000 patients were monitored, and among those were some individuals who had moved. These certain individuals are not responsive anymore, and can not be a source of data, and the poll would be incorrect if the hospital decided to switch out the patients in the midst of the decade. Therefore we are to assume a nonresponse occurred. (To define nonresponse, it is simply a failure to respond, which is indeed what is defined for those who had moved.)

It is not B for the two variables have no correlation, it is not C for all patients were at first patrons and the problem did not explicitly state there was missing info, and D is incorrect for it said the sample group was selected at random. Therefore, with process of elimination, A would still be correct.

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question the equation of the line is

y = - 4x + 9

Comparing the equation with the general equation of a line above

Slope / m = - 4

Hope this helps you

Answer:

r = (5000 - [(5000 x 0.3) + (4000 x 0.6) + (300 x 0.25)])0.8

Simplified - r = 820

Step-by-step explanation:

I don't know how to explain it exactly, but I know you have to find out how much the carnations, tulips, and irises all cost,subtract that from how much money he has, and divide what left by the cost of the roses (by multiplying the 0.8 cents, because it's a decimal).

r = (5000 - [(5000 x 0.3) + (4000 x 0.6) + (300 x 0.25)])0.8

r = (5000 - [1500 + 2400 + 75])0.8

r = (5000 - 3975)0.8

r = 1025(0.8)

r = 820

Answer:

21x-7/7x

=7x(3x-1)/7= 3x-1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

To find the area of a rectangle, you must multiply its length with its width.

We know that either the length or it's width is 7x.

To find the length of the other side, we essentially have to figure out what 7x you to be multiplied by to get 14x (21x-7x can be simplified to that by combining like terms)

To reverse multiplication, we can use division.

Let's set up the following expression:

14x/7x

2x/x

2

The length of its other side is 2.

Answer:

[tex]\Huge \boxed{-x^2+2x}[/tex]

Step-by-step explanation:

2 times x subtracted by x².

[tex]\Rightarrow 2 \cdot x-x^2[/tex]

[tex]\Rightarrow 2x-x^2[/tex]

Rearranging the expression.

[tex]\Rightarrow -x^2+2x[/tex]

Answer:

2x -x^2

Step-by-step explanation:

[tex]2(x) - x^2\\= 2x-x^2[/tex]

Answer:

Jake can use 19.70 ccf to not exceed $ 64.00 in water bill.

Step-by-step explanation:

The cost function of water bill is:

[tex]C = C_{f}+C_{v}[/tex]

Where:

[tex]C_{f}[/tex] - Fix costs, measured in USD.

[tex]C_{v}[/tex] - Variable costs, measured in USD.

The fix and variable costs are, respectively:

[tex]C_{f} = 24.60[/tex]

[tex]C_{v} =2\cdot \left(\frac{Q}{100} \right)[/tex]

Where [tex]Q[/tex] is the water capacity consumed within a month, measured in cubic feet. Therefore, first formula is expanded:

[tex]C = 24.60+2\cdot \left(\frac{Q}{100} \right)[/tex]

If [tex]C = 64\,USD[/tex], the maximum water capacity is:

[tex]64 = 24.60+2\cdot \left(\frac{Q}{100} \right)[/tex]

[tex]39.40 = 2\cdot \left(\frac{Q}{100} \right)[/tex]

[tex]Q = 1970\,ft^{3}[/tex]

Which is equivalent to 19.70 ccf.

Answer:

D. divide by -8

Step-by-step explanation:

Answer:

x≤9

Step-by-step explanation:

x−6≤3

Add 6 to both sides.

x≤3+6

Add 3 and 6 to get 9

x≤9

Answer: x ≤ 9

Step-by-step explanation: When solving an inequality, your goal is the same as it would be if you were solving an equation – to get the variable by itself or isolated on one side of the equals sign.

Since 6 is being subtracted from x, add 6 to both sides of the inequality.

On the left, the -6 +6 cancel out and on the right, 3 + 6 is 9.

So we have x ≤ 9.