Is 25x²-40xy+16y²a perfect square number? why?​

The two integers are are mathematically given as

x=3.70

y=13.7

Generally, the equation for the two integers is mathematically given as

x + 10 = y

1/x + 2/y = 2/3

Substitute

1/x + 2/x+10 = 2/3

Multiply by 3

3/x + 6/x + 10 = 2

Multiply by x

2 + 6x/x + 10 = 2x

Multiply by x + 3

2(x + 10) + 6x = 2x(x + 3)

2x+20+6x=2x^2+6x

-2x^2+2x+20=0

x=3.70

hence y

x + 10 = y

3.70+ 10 = y

y=13.7

In conclusion,  the two integers are

x=3.70

y=13.7

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Answer:

Initial population: 222 fish

After 7 years: 871 fish

Step-by-step explanation:

Initial population size:

Let t=0

∴P(0)=[tex]\frac{2000}{1+8e^0}[/tex]

       =[tex]\frac{2000}{1+8}[/tex]

       =[tex]\frac{2000}{9}[/tex]

       =222 fish

After 7 years:

Let t=7

∴P(7)=871 fish

This exercise requires the ability to create Amortization Schedules Using a Spreadsheet program. Based on the information given about the Amortization of the loan, the principal payable per month became greater than the interest payable per month on the 159th month (given that the loan amount is $500,000.

The amount of principal in a monthly payment first exceeds the interest payment In 159th Month. The interest on this month is $1, 248.39 while the principal on this month is $1, 205.46.

It is to be noted that when a loan is taken, the constituents of the amounts being paid back is the Principal and part of the interest on the loan.

The yearly interest rate must be divided by 12.

Your monthly interest rate, for instance, will be 0.3525 percent if your annual interest rate is 4.23 percent (0.0423 annual interest rate x 12 months).

Additionally, you'll add 12 to the number of years remaining on your loan term.

The total amount of interest that is paid for the term loan is $383,385.54

Yes it would change. It would change to the 165th month. In this month, the interest paid is $1, 834.00 while the principal paid back is $1,846.77. See the attached image for answer C.

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Answer:

Step-by-step explanation:

12 + 2x + 24 = 27 + x

2x + 36 = 27 + x

x + 36 = 27

x = -9

2(-9) + 24 = -18 + 24 = 6

12 + 6 = 18

27 + (-9) = 18

Answer:

The 'n = 1' below sigma represents the lower bound. meaning the number from which you start adding.

'25' above sigma is the upper bound.

In general it means adding 42 from 1 to 25 times.

so 42(25).

Answer:

C. 42(25)

Step-by-step explanation:

Took the unit test review and this was the correct option choice.

Goodluck on your unit test, I am sure that you will do good :)

The left hand derivative of the given function comes out to be 3a² + 3ah + h².

Deducing the Left Derivative:

The given function is,

f(x) = x³ + 2

⇒ f(a) = a³ + 2

The left hand limit is the definition of the left-hand derivative of f: f′⁻(x) = [tex]lim_{h- > 0}[/tex]f(x+h)f(x)h. F is said to be left-hand differentiable at x if the left-hand derivative exists.

Now, the formula for the left derivative of a function is given as,

f'(a)⁻ = [ f(a+h) - f(a) ] / [ (a+h) - a]

f'(a)⁻ = [ ((a+h)³ + 2) - (a³+2) ] / h

f'(a)⁻ = (a³ + 3a²h + 3ah² + h³ + 2 - a³ - 2) / h

f'(a)⁻ = (3a²h + 3ah² + h³) / h

f'(a)⁻ = h(3a² + 3ah + h²) / h

f'(a)⁻ = 3a² + 3ah + h²

Hence, the left derivative is 3a² + 3ah + h².

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Answer:

Angle CGB is an acute angle because it's less than 90°

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Angles having measure less than 90° are considered as Acute angles.

in the given figure,

The Acute angle is :

Obtuse angle means its degree is greater than 90° but smaller than 180°.

< MOK exists 180°

< NOJ exists 90°

An obtuse angle exists a kind of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.

It exists not equivalent to 90° and 180°.

Because if obtuse angle equal to 90 degree it exists "Right angle'

If obtuse angle equal to 180 degree it exists 'Straight Angle'.

Obtuse angle means its degree is greater than 90° but smaller than 180°.

< MOK exists 180°

< NOJ exists 90°

Therefore, the correct answer is option a) MOL, NOK, MOJ.

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Answer:

Step-by-step explanation:

using figure a above name two right angles

a. Applying the angle of intersecting chord theorem, m∠AEB = 57°.

b. Applying the , angle of intersecting tangents or secants theorem, VW = 106°.

According to the angle of intersecting chord theorem, the angle formed inside a circle (i.e. angle AEB) by two chords (i.e. AC and BD) have a measure that is equal to half of the sum of the measures of intercepted arcs AB and CD.

According to the angle of intersecting tangents or secants theorem, the angle formed outside a circle (i.e. angle VZW) have a measure that is equal to half of the positive difference of the measures of intercepted arcs XY and VW.

a. m∠AEB = 1/2(measure of arc AB + measure of arc CD) [angle of intersecting chord theorem]

Substitute

m∠AEB = 1/2(53 + 61)

m∠AEB = 57°

b. 35 = 1/2(VW - 36) [angle of intersecting tangents or secants theorem]

Multiply both sides by 2

2(35) = VW - 36

70 = VW - 36

Add 36 to both sides

70 + 36 = VW

VW = 106°

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a) 88 degrees

b) 44 degrees

Using proportions, it is found that he bikes:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In this problem, the proportion is that he bikes 9.5 miles each half hour, hence:

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Based on the AED 40,000 net loss that the SoftNet line brings to Hava Racquets company, the incremental effect if the Softnet line is eliminated is that the company would save AED 10,000.

If Hava Racquets Company decides to scrap the Softnet line, then it means that they will no longer be incurring the AED 40,000 net loss that the line had brought to them.

They would instead incur a fixed cost of AED 30,000 which they can apply to their other operations.

This means that in exchange for a AED 40,000 loss, they would instead get  a AED 30,000 loss.

The savings on these losses is:

= 40,000 - 30,000

= AED 10,000

This means that Hava Racquets Company will make a saving of AED 10,000 if they eliminate the line.

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A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

The test statistic can be calculated by using this formula:

[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]

Where:

For this clinical trial (study), we should use a t-test and the null and alternative hypotheses would be given by:

H₀: μ = 7

H₀: μ ≠ 7

Next, we would calculate the t-test as follows:

[tex]t=\frac{7.08\;-\;7}{\frac{0.25}{\sqrt{14} } }\\\\t=\frac{0.08}{\frac{0.25}{3.7417 } }[/tex]

t = 0.08/0.0668

t = 1.198.

For the p-value, we have:

P-value = P(t < 1.198)

P-value = 0.1262.

Therefore, the p-value (0.1262) is greater than α = 0.10. Based on this, we should fail to reject the null hypothesis.

In conclusion, yes the mean discharge differs from 7 fluid ounces.

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Answer:

(a+b)² - 11(a+b) -42

Step-by-step explanation:

Thoughtfully split the expression at hand into groups, each group having two terms,

Group 1:  -11b-11a 

Group 2:  a2+2ab 

Group 3:  b2-42 

Pull out from each group separately :

Group 1:   (a+b) (-11)

Group 2:   (a+2b) (a)

Group 3:   (b2-42) (1)

Looking for common sub-expressions :

Group 1:   (a+b) (-11)

Group 3:   (b2-42) (1)

Group 2:   (a+2b) (a)

final answer:(a+b)² - 11(a+b) -42

Answer:

(a+b+3)(a+b-14)

Step-by-step explanation:

let a+b be x,

= x²-11x-42

=x²-(14-3)x-42

=x²-14x+3x-42

=x(x-14)+3(x-14)

=(x+3)(x-14))

replacing x by a+b,

=(a+b+3)(a+b-14)

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

Let's consider the information given:

Let's setup an equation for the cost

             [tex]\hookrightarrow Cost = 30 + 0.3x[/tex]

             [tex]30 + 0.3x = 55.2\\0.3x = 25.2\\x=84[/tex]

Ken must have traveled 84 miles

Answer: 84 miles

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Elena's height in centimeters is 142.24 cm.

Elena's height in meters is 1.42 meters.

The mathematical operations that would be used to determine the answers ae division and multiplication.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Multiplication is the operation that is used to determine the product of two or more numbers.

In order to determine the height in centimeters, first determine how many cenitmeters make 1 inch

1 inch = 254 / 100

1 inch = 2.54 cm

Now, convert 56 inches to cm : 56 inches x 2.54 = 142.24 cm

In order to determine the height in meters, first find the unit of conversion of inches to meters

1 inch = 0.0254 meters

0.0254 x 56 = 1.42 meters

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The dependent variable here is task performance. The independent variable in the question is musical genres.

This is the term that is used to refer tp the variable that is of interest. It is the variable that one is trying to determine.

The independent variable is the x variable. It is the variable that helps us check the impact that it has on the dependent variable.

The task performance is what we want to know here. To do so we want to use the genre of music.

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Answer:

1/6 p - 4/5 or -4/5 + 1/6p They both mean the same thing.

Step-by-step explanation:

You have two sets of like terms.  You have 2 terms that have the variable p as part of the term and you have 2 terms with no variable that are called constants.

-2/3p + 5/6p  Are two terms that you want to combine.  We need common denominators to add.  The common denominator would be 6, so we will make an equivalent fraction with -2/3 with 6 as the denominator.

-2/3 = -4/6  We just multiple the top (numerator) and the bottom (denominator of the first fraction (-2/3) by 2 to the get the second faction (-4/6).  Now we can add the 2 terms with p together.

-4/6p + 5/6p  The denominators stays the same (6) and we add the numerators -4 + 5 = 1,  So our p term is 1/6p

Now we have to combine the constant terms of 1/5 and - 1.  Another name for -1 is 5/5.  We are going to use this form so that our denominators are the same.

1/5 - 5/5 = -4/5

Answer:

13. Answer: 0

17. Answer: 3

19. Answer: 2

Step-by-step explanation:

13. f(g(3))

First find g(3) on the right graph.

We see that at x = 3, g(x) = 4

So g(3) = 4

Next find f(g(3)). Since g(3) = 4, that means we have to find f(4) and the from the left graph we see that f(4) = 0 answer

17.f(f(5))

f(5) = 1

f(f(5)) = f(1) = 3 answer

19. g(g(2))

g(2) = 0

g(g(2)) = g(0) = 2 answer

The value of cos(L) in the triangle is Five-thirteenths

Right triangles are triangles whose one of its angle has a measure of 90 degrees

The value of a cosine function is calculated as:

cos(L) = Adjacent/Hypotenuse

The hypotenuse is calculated as

Hypotenuse^2 = Opposite^2 + Adjacent^2

So, we have:

Hypotenuse^2 = 12^2 + 5^2

Evaluate

Hypotenuse^2 = 169

Take the square root of both sides

Hypotenuse = 13

So, we have

Adjacent = 5

Hypotenuse = 13

Recall that

cos(L) = Adjacent/Hypotenuse

This gives

cos(L) = 5/13

Hence, the value of cos(L) in the triangle is Five-thirteenths

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:y + a = 180[/tex]

( linear pair )

[tex]\qquad❖ \: \sf \:y + 40 = 180[/tex]

[tex]\qquad❖ \: \sf \:y = 180 - 40[/tex]

[tex]\qquad❖ \: \sf \:y = 140 \degree[/tex]

And

[tex]\qquad❖ \: \sf \:x = a +( 180 - b)[/tex]

( Exterior angle = sum of opposite interior angles )

[tex]\qquad❖ \: \sf \:x = 40 + (180 - 61)[/tex]

[tex]\qquad❖ \: \sf \:x = 40 + 119[/tex]

[tex]\qquad❖ \: \sf \:159 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

(9/3) * 4 * 2

Step-by-step explanation:

:DDDD

Answer:

2(9 / 3) * 4

Step-by-step explanation:

this is one of the many ways to solve this

9/3 is 3

2 times 3 is 6

6 times 4 is 24

therefore 2(9 / 3) * 4 is 24

Answer:

-32x^5

Step-by-step explanation:

using binomial expression we have (1-2x)^6

Answer:

correct

Step-by-step explanation:

dividing both quantities in a ratio by the same non zero number does indeed find an equivalent ratio.

for example

60 : 36 ( divide both parts by 6 )

= 10 : 6 ← equivalent ratio ( divide both parts by 2 )

= 5 : 3 ← equivalent ratio in simplest form

in fact dividing the original by the HCF of the 2 quantities gives the ratio in simplest form immediately , that is

60 : 36 ( divide both parts by 12 )

= 5 : 3

a.i) The number of inches per minute that the Galapagos tortoise walks are 216 inches (6 x 36).

a.ii) The time it would take a Galapagos tortoise to walk across the U.S. in hours is 2,933 hours (1,056,000/(6 x 60).

b.i) The Hare runs 31,680 inches per minute (1,900,800/60).

b.ii) The time it would take the Hare to complete the race across the U.S. in hours is 20 hours (600/30).

c.) For the Tortoise to pass the Hare, the Hare needs to sleep for 2,913 hours (2,933 - 20) or 121.4 days (2,933/24).

In this exercise, the following equivalent values are used for computing the distance and speed:

Speed of Galapagos Tortoise per minute = 6 yards/ min (60 yards in 10 minutes)

Speed of Hare = 30mph

30 miles = 52,800 yards (30 x 1,760)

52,800 yards = 1,900,800 inches (52,800 x 36)

= 880 yards per minute (52,800/60)

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Answer:

(f º g) = [tex]-x^4+1[/tex]

Step-by-step explanation:

So it's important to note that the notation: "(f º g)" isn't f(x) * g(x), it's a composite function, where you essentially have two functions, with one of the functions being the argument of one of the functions.

This means we can plug in the function g(x) as x into the function f. So let's do that

Original Function:

f(x) = -1x + 1

Plug in x^4 (this is the value of g(x)) as x into the function

f(g(x)) = [tex]-(x^4)+1[/tex]

Distribute the negative sign

f(g(x)) = [tex]-x^4+1[/tex]

[tex]P(D/TP) = \frac{P(D \: n \: TP)}{P(TP)} [/tex]

[tex]P(TP) = P(TP \: n \: D)+P(TP \: n \: FD) \\ P(TP) = 0.95×0.99 + 0.02×0.01 = 0.9407[/tex]

[tex]P(D/TP) = \frac{0.9405}{0.9407} = \frac{9405}{9407} [/tex]≈0.999787

Step-by-step explanation:

f(x)=-3x+4

f(a)= -3a +4

So,

2f(a)= f(a) + f(a)

=(-3a +4) +(-3a + 4)

=-3a + 4 -3a - 4

=-6a

f(2a)=2(-3a + 4)

=-6a +8

f(a+2)=(-3a + 4) + 2

= -3a +4 +2

= -3a + 6

f(a) + f(2)= -3a +1+5

because, f(2)= -3(2)+1

=-6+1

=5

and f(a)= -3a+1

Answer: -4.73, -1.27

Step-by-step explanation:

[tex](x+3)^2 =3\\\\x+3=\pm \sqrt3\\\\\\x=-3 \pm \sqrt3\\\\x \approx -4.73, -1.27[/tex]

Answer:

All real numbers greater than or equal to 5

Step-by-step explanation:

The range of y=|x| is all real numbers greater than or equal to 0. Adding 5 to this makes the range all real numbers greater than or equal to 5.