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The required answers are 1) \($$A = x^2 + 28x + 192$$\) 2) 300000 3) \($$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$\).

area of the land purchased is given as 480m², and the dimensions of the land are (x+12)mx(x+16)m. Therefore, the area of the land can be expressed as:

\($$A = (x+12)(x+16)$$\)

Expanding this expression, we get:

\($$A = x^2 + 28x + 192$$\)

Hence, the area of the land purchased is given by the polynomial expression \($x^2 + 28x + 192$\).

The total budget for the expenses is Rs. 5,00,000. If Mr. Chand's daughter is ready to share 3/5 of the expenses, then the fraction of the expenses she will pay is:

\($\frac{3}{5}=\frac{x}{500000}$$\)

Simplifying this expression, we get:

\($x = \frac{3}{5}\times 500000 = 300000$$\)

Therefore, Mr. Chand's daughter will pay Rs. 3,00,000 towards the expenses.

We can solve the polynomial \($x^2 + 28x + 192$\) into different factors by using the quadratic formula:

\($x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$\)

Here, the coefficients of the polynomial are:

\($$a = 1, \quad b = 28, \quad c = 192$$\)

Substituting these values in the quadratic formula, we get:

\($x = \frac{-28 \pm \sqrt{28^2 - 4\times 1 \times 192}}{2\times 1}$$\)

Simplifying this expression, we get:

\($$x = -14 \pm 2\sqrt{19}$$\)

Therefore, the polynomial \($x^2 + 28x + 192$\) can be factored as:

\($$x^2 + 28x + 192 = (x - (-14 + 2\sqrt{19}))(x - (-14 - 2\sqrt{19}))$$\)

or

\($$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$\)

So, we have factored the polynomial into two factors.

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Answer:

<YTZ

Step-by-step explanation:

Vertical angles are congruent.

<VTW measures 40°.

<YTZ is vertical to angle VTW.

m<YTZ = m<VTW

m<YTZ = 40°

Answer: <YTZ

Answer:

(2,0)

Step-by-step explanation:

point D is on point (2,0)

that is what it means

Answer:

Improper fraction for 2 1/24

49/24

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Answer:

Theta=60

Step-by-step explanation:

Lets start to get the value of x in \(sin(x)=\frac{1}{2}\)

Just do the opposite which is \(sin^{-1}(\frac{1}{2}) = 30\)

So \(sin(30)=\frac{1}{2}\)

Still we got only the value of x not theta then

The value of x = theta/2

Theta/2=30 multiply each side by 2

Theta = 60

To solve these equations, we can aply algebraic operations on both sides of each equation. We do so until

Answer:

15

Step-by-step explanation:

180-15

Hello!

the sum of the angles in the triangle = 180°

so the 3rd angle = 180° - 165° = 15°

Answer:O 18+3

O-18+3

O-18+(-3)

Step-by-step explanation:O 18+3

O-18+3

O-18+(-3)

If the archaeologist found a fossil whose length is 489.44 inches, using the conversion table, the length in feet, to the nearest tenth, is 40.8 feet.

The conversion table refers to the tabulated standard units of measurement, showing temperature, length, area, volume, weight, and metric conversions

For instance, the conversion table shows that 12 inches equal 1 foot.

The length of the fossil = 489.44 inches

12 inches = 1 foot

489.44 inches = 40.8 feet (489.44 ÷ 12)

Thus, using the conversion table, which relies on multiplication or division operations using the conversion factors, the length in feet of the fossil is 40.8 feet.

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Answer:

5

Step-by-step explanation:

u do 2x2 cuz of the square root and add the 1

Answer:  $1.40

Work Shown:

x = cost before markup

1.45x = cost after the 45% markup

1.45x = 2.03

x = (2.03)/(1.45)

x = 1.40

Yes, they are quite similar. the p-value obtained using the theory-based method (p < 0.0001) agree with that obtained using the randomization/simulation - based method (p < 0.0001)

P- value is the probability of obtaining a value of test statistic more extreme in the direction of alternative hypothesis than the observed one. In easy words if p -value < level of significance we reject H0 in favor of H1.

Here:

p-value < 0.0001 => we reject H0.

If the statistical software renders a p value of 0.000 it means that the value is very low, with many "0" before any other digit.

So the interpretation would be that the results are significant, same as in the case of other values below the selected threshold for significance.

Therefore, yes they are quite similar.

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Incomplete Question:

Student researchers investigated whether balsa wood is less elastic after it has been immersed in water. They took 60 pieces of balsa wood and randomly assigned half to be immersed in water and the other half not to be. They measured the elasticity by seeing how far (in inches) the piece of wood would project a dime into the air.

Does the p-value obtained using the theory-based method (p < 0.0001) agree with that obtained using the randomization/simulation-based method (p < 0.0001)?

A. No, they are different.

B. Yes, they are quite similar.

Answer:

1. isosceles and acute

2. Scalene and acute

3. Equilateral and equiangular

4. Right (and isosceles ?)

(not sure ab isosceles for the last one but everything else is fine)

:)

Answer:

To solve the equation:

2/3x - 1/5x = x - 1

First, we need to find a common denominator for 2/3 and 1/5, which is 15. So we can rewrite the equation as:

(10/15)x - (3/15)x = 15/15 x - 1

Simplifying the left side:

(7/15)x = 15/15 x - 1

Multiplying both sides by 15:

7x = 15x - 15

Subtracting 7x from both sides:

-8x = -15

Dividing both sides by -8:

x = 15/8 or 1.875

Therefore, the solution to the equation is x = 1.875.

Answer:14.4222

Step-by-step explanation:

Answer:

Her total pay is 2,887.50 since she did not make over 4000$ she will not receive the extra 500$ bonus

Step-by-step explanation:

82,500 X 3.5% = 2,887.50

Given the function :

We will find the inverse of the function analytically as following :

Solve for x

make y in the place of x. so,

The graph of both function will be as shown in the following picture .

The given function f(x) = 5^x - 1 is the graph of the blue color

And the inverse with the red color

each function is written closer to its graph

The equation that models the relationship between the number of guests, x, and the total charge, y is A. y = 450 + 125x. The base charge for a single guest is $450, and for each additional guest, the charge increases by $125. So, we add 125 times the number of additional guests to the base charge of $450.

Answer: We can use the trigonometric identity cos(A - B) = cosA cosB + sinA sinB and the given value of cos(A - B) to find the value of cosA cosB - sinA sinB. Then, we can use the given value of secA to find the value of cosA, and use the fact that secA = 1/cosA to find the value of sinA. Finally, we can solve for sinB using the equation we obtained earlier.

cos(A - B) = cosA cosB + sinA sinB

84/85 = (17/8) cosB + sinA sinB

We can rewrite the expression (17/8) cosB + sinA sinB as (17/8) (cosB + (1/17) sinA sinB), and then square both sides of the equation to obtain:

(84/85)^2 = (17/8)^2 (cosB + (1/17) sinA sinB)^2

Simplifying, we get:

(cosB + (1/17) sinA sinB)^2 = (84/85)^2 / (17/8)^2

cosB + (1/17) sinA sinB = ± (84/85) / (17/8)

cosB + (1/17) sinA sinB = ± 32/85

Now, we can substitute the values of secA and cos(A - B) to obtain:

cosA = 1/secA = 8/17

cosA cosB - sinA sinB = cos(A - B) = 84/85

Substituting these values into the expression we obtained earlier, we get:

(8/17) cosB - sinA sinB = 84/85

Multiplying both sides by 17/8, we get:

cosB - (17/8) sinA sinB = (17/8) (84/85)

Adding this equation to the previous equation, we get:

2 cosB = (17/8) (84/85) + (32/85)

Solving for cosB, we get:

cosB = [(17/8) (84/85) + (32/85)] / 2 = 83/85

Using the identity sin^2(A) + cos^2(A) = 1 and the fact that secA = 1/cosA, we can find the value of sinA:

sin^2(A) + cos^2(A) = 1

sin^2(A) = 1 - cos^2(A)

sinA = ±sqrt(1 - cos^2(A))

sinA = ±sqrt(1 - (8/17)^2) = ±15/17

Since secA = 17/8, we know that cosA is positive, and therefore sinA must also be positive. Therefore, sinA = 15/17.

Now, we can use the equation we obtained earlier to find the value of sinB:

cosB - (17/8) sinA sinB = (17/8) (84/85)

Substituting the values we obtained for cosB, sinA, and the given value of secA, we get:

83/85 - (17/8) (15/17) sinB = (17/8) (84/85)

Simplifying, we get:

sinB = [(83/85) - (17/8) (15/17) (85/84)] / [(17/8) (85/84)]

sinB = -24/85

Therefore, the value of sinB is -24/85.

Step-by-step explanation:

Answer:

After 10 weeks, Susan will have $295 and CiCi will have $259.

Step-by-step explanation:

Susan: y= 65+23x

CiCi: y = 119+14x

65+23(6)=203

119+14(6)=203

After 6 weeks, Susan and CiCi will both have $203 in their accounts.

65+23(10)=295

119+(14)(10)=259

Therefore, After 10 weeks, Susan will have $295 and CiCi will have $259.

Answer: 15

Step-by-step explanation: Use the formula: \(a^{2}+b^{2}=c^{2}\)

Remember \(c^{2}\) should always be the hypotenuse or the longest side.

\(112^{2}+b^{2}=113^{2}\) ---> evaluate the exponents

\(12544+b^{2}=12769\) ----> subtract 12544 to the other side

\(b^{2}=225\) ---> take the square root of both sides

\(b=15\)

The number of sodas sold at the baseball game was 119, while the number of hot dogs sold was 72.

Let's assume the number of sodas sold as 'x' and the number of hot dogs sold as 'y'.

According to the problem, the total number of sodas and hot dogs sold is 191, so we can write the equation:

x + y = 191   ...(1)

The problem also states that the number of hot dogs sold was 47 less than the number of sodas sold. Mathematically, we can express this as:

y = x - 47   ...(2)

To find the values of x and y, we can solve the system of equations (1) and (2). Substituting equation (2) into equation (1), we have:

x + (x - 47) = 191

Simplifying the equation:

2x - 47 = 191

2x = 191 + 47

2x = 238

Dividing both sides by 2:

x = 238/2

x = 119

Substituting the value of x back into equation (2):

y = 119 - 47

y = 72

As a result, the total amount of sodas sold is 119, and the total amount of hot dogs sold is 72.

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Answer:

A dilation did not take place.

Step-by-step explanation:

Answer:

Dilation

Step-by-step explanation:

A Dilation didn't take place. They are of the same size.

Answer:

The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.4137.

Step-by-step explanation:

The point estimate is the sample proportion.

Sample proportion:

103 out of 249, so:

\(p = \frac{103}{249} = 0.4137\)

The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.4137.

Answer:

18

Step-by-step explanation:

\(\frac{6}{1/3} =\frac{6*3}{1} \\=18\)

The circles are similar because you can translate circle 1 using the transformation rule (x + 10, y) and then dilate it using a scale factor of 2/5.

First analyze the centers, the original center is at (-3, 5) and the new center is at (7, 5)

The change is in the x-value, the change is:

7 - (-3) = 10

So there is a translation of 10 units to the right,

And the original radius is R = 10, the new one is R' = 4

if the scale factor of the dilation is k we can write:

10*k = 4

k = 4/10 = 2/5

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Answer:

I think it's PEMDAS, but I'm not sure- sorry if it's wrong.

Step-by-step explanation:

Answer:

pls include a screenshot of the graphs

Step-by-step explanation: