Write 50 as a product of three primes

The rectangle with the maximum area, formed by its base on the x-axis and two vertices on the parabola y = 49 - x^2, has dimensions of length 14 units and height 0 units.

To find the dimensions of the rectangle that maximize its area, we need to consider the relationship between the rectangle's dimensions and the parabola.

Let's assume the length of the rectangle is 2x, and the height is y. Since the base of the rectangle lies on the x-axis, the y-coordinate of the two vertices on the parabola will be zero.

Substituting the y-coordinate into the equation of the parabola, we have:

0 = 49 - x^2

Rearranging the equation:

x^2 = 49

Taking the square root of both sides:

x = ±√49

Since we are interested in the positive value of x, we have:

x = 7

Now, substituting this value back into the equation of the parabola, we can find the height:

y = 49 - (7^2)

y = 0

Therefore, the dimensions of the rectangle that maximize its area are:

Length = 2x = 2 * 7 = 14 units

Height = y = 0 units

The rectangle is a degenerate rectangle, which means it has a height of zero. In this case, the maximum area is achieved when the rectangle becomes a line segment on the x-axis with a length of 14 units.

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The given question is incomplete, the complete question is,

What are the dimensions of the rectangle that can be constructed with its base on the x-axis and two vertices on the parabola y = 49 - x^2, in order to maximize its area?

The solution of the given inequality 4(x² - 5) - (x² - 5)² > -12 is x ≥ √3 or x ≤ -√3.

The given inequality is 4(x² - 5) - (x² - 5)² > -12. In order to solve the given inequality, first, we will multiply (x² - 5)² by -1 to get rid of the squared term. Next, we will simplify the terms by using the distributive property. Then, we will collect the like terms and solve the inequality.

Multiply (x² - 5)² by -1. => -(x² - 5)² = -x⁴ + 10x² - 25

Now, the given inequality is:

4(x² - 5) - (x² - 5)² > -12

4(x² - 5) + x⁴ - 10x² + 25 > -12

Simplify the terms by using the distributive property:

4x² - 20 + x⁴ - 10x² + 25 > -12

Simplifying further:

x⁴ - 6x² + 13 > 0

Collect like terms and solve the inequality:

(x² - 3)² + 4 > 0

As the square of any number is always greater than or equal to 0, so

(x² - 3)² ≥ 0 ⇒ (x² - 3)² + 4 ≥ 4

Hence, x² - 3 ≥ 0 ⇒ x² ≥ 3 ⇒ x ≥ ±√3

Therefore, the solution of the given inequality is x ≥ √3 or x ≤ -√3.

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Answer:

parent funiction y=|x|

hozonital shift right 3 units

vertical shift up 1 units

reficlation none

vertical none

Step-by-step explanation:

The decision between the two cities involves tradeoffs: the first city offers a wide range of class sizes but a smaller sample, while the second city has a larger sample but a narrower class size range.

The decision of which city to choose for the study involves tradeoffs. The first city allows for a wide range of class sizes, providing a comprehensive analysis of the relationship between class size and academic performance. However, the smaller sample size limits generalizability.



The second city offers a larger sample size, increasing generalizability, but with a narrower range of class sizes. Researchers should consider their specific research objectives, available resources, and constraints. If the goal is to assess the impact of extreme variations in class size, the first city is suitable. If obtaining highly generalizable results is paramount, the second city, despite the narrower range, should be chosen.



Therefore, The decision between the two cities involves tradeoffs: the first city offers a wide range of class sizes but a smaller sample, while the second city has a larger sample but a narrower class size range.

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Answer:

x=31

Step-by-step explanation:

The area of the triangle whose vertices are (-3, 5), (3, -6), and (7, 2) is 14.

To find the area of a triangle given the coordinates of its vertices, we can use the formula:

Area = 1/2 * |(x1y2 + x2y3 + x3y1) - (y1x2 + y2x3 + y3x1)|

where (x1,y1), (x2,y2), and (x3,y3) are the coordinates of the three vertices.

Substituting the given coordinates, we get:

Area = 1/2 * |(-3*-6 + 32 + 75) - (5*3 - (-6)7 + 2(-3))|

= 1/2 * |(-18 + 6 + 35) - (15 + 42 - 6)|

= 1/2 * |23 - 51|

= 1/2 * |-28|

= 14

Therefore, the area of the triangle is 14 square units.

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If a advertised sofa is $200 but the more costly sofa is $375, the average cost of such a sofa will be $200 is $243.75.

You're planning to purchase a sofa from a furniture store that is having a sale on them.

Let x represent the sofa's price.

Advertised sofa's cost = $200

Expensive sofa's cost = $375

The advertisers are aware that when customers arrive at the store, one out of three switch to an expensive sofa that the one shown in the sale advertisement.

Average cost = 375 x 1/4 + 200 x 3/4

E(x) = 375 x 1/4 + 200 x 3/4

E(x) = 93.75 + 150

E(x) = 243.75

Thus, if a advertised sofa is $200 but the more costly sofa is $375, the average cost of such a sofa will be $200 is $243.75.

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The result of the integral ∫e^(24(3 + 5t - 2)) dt is (1/5) * (1/24) * e^(24(5t + 1)) + C

Reference to Power rule for integrals. To evaluate the integral ∫e^(24(3 + 5t - 2)) dt, we can simplify the expression inside the exponential function first:

3 + 5t - 2 = 5t + 1

Now we can rewrite the integral as:

∫e^(24(5t + 1)) dt

To evaluate this integral, we can use a substitution. Let u = 5t + 1. Then, du = 5dt, and dt = du/5.

Substituting these values into the integral, we have:

∫e^(24u) * (1/5) du

Now the integral becomes:

(1/5) ∫e^(24u) du

To integrate e^(24u), we can use the power rule for integrals. The integral of e^x is e^x, so the integral of e^(24u) will be (1/24)e^(24u). Applying this to the integral, we get:

(1/5) * (1/24) * e^(24u) + C

where C is the constant of integration.

Substituting back u = 5t + 1, we have:

(1/5) * (1/24) * e^(24(5t + 1)) + C

This is the result of the integral ∫e^(24(3 + 5t - 2)) dt.

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Answer:

44

Step-by-step explanation:

1. substitute variables with their constants

(-9)(-3) - (-3)(8) - 7

2. multiply all like terms

(27) - (-24) - 7

3. Combine all like terms

27 + 24 - 7

51 - 7

= 44

Answer:

44

Step-by-step explanation:

Evaluate z x - x y - 7 where x = -3, y = 8 and z = -9:

z x - x y - 7 = -9 (-3) - -3×8 - 7

Hint: | Multiply -9 and -3 together.

-9 (-3) = 27:

27 - -3×8 - 7

Hint: | Multiply -1 and -3 together.

-(-3) = 3:

27 + 3×8 - 7

Hint: | Multiply 3 and 8 together.

3×8 = 24:

27 + 24 - 7

Hint: | Evaluate 27 + 24 using long addition.

| 1 |  

| 2 | 7

+ | 2 | 4

| 5 | 1:

51 - 7

Hint: | Subtract 7 from 51.

| 4 | 11

| 5 | 1

- | | 7

| 4 | 4:

Answer: 44

a. Income tax is the amount of money that an individual is required to pay to the government based on their income.

b. Ramesh's total income in 13 months, including the festival expense, is found as Rs 593,857.

c.   Ramesh's annual income tax, considering the investment in citizens' investment fund, is Rs 85,000.

a. Income tax is described as the amount of money that an individual is required to pay to the government based on their income.  found  using a specific tax rate applied to different income brackets.

b.

Monthly income = Salary + Dearness allowance

= Rs 43,689 + Rs 2,000

= Rs 45,689

Total income for 13 months = Monthly income * 13

= Rs 45,689 * 13

= Rs 593,857

c.

Total income after deducting citizens' investment fund = Total income - Investment amount

= Rs 593,857 - Rs 2000

= Rs 591,857

Hence, the income tax based on the revised total income is:

Tax for income upto 5 lakh which is 1% of the income

= 0.01 * 500000

= Rs 5,000

Tax for income from 5-7 lakh which is the 10% of the income

= 0.1 * 200000

= Rs 20,000

The Tax for income from 7-10 lakh: 20% of the income

= 0.2 * 300000

= Rs 60,000

The Tax for income from 10-20 lakh is 30% of the income

= 0.3 * 0

= Rs 0

The total income tax = Rs 5,000 + Rs 20,000 + Rs 60,000 + Rs 0 + Rs 0

= Rs 85,000

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Answer:

cimcumference = 2 × π × radius of circle ( 2πr)

Answer:

circumference = 2πr

hope it helps

Answer:

yes

Step-by-step explanation:

na sa gutan ko na to eh

Answer:

NOO!

Step-by-step explanation:

\(\tt -7(x+5)=-14\)

First ,let's move all terms to the left:

\(\tt -7(x+5)-(-14)=0\)

Add all numbers together, and all  variables

\(\tt -7(x+5)+14=0\)

Multiply parentheses:-

\(\tt -7x-35+14=0\)

Add all numbers/variables together:

\(\tt -7x-21=0\)

Now, move all terms containing x to the left, and all other terms to the right:

\(\tt -7x=21\)

Divide both sides by -7:-

\(\tt \cfrac{-7x}{-7}=\cfrac{21}{-7}\)

\(\tt x=-3\)

Nope, 10 isn't a solution to -7(x+5)=-14.

~

Answer:

We can solve by using a proportion

4 pages/6 minutes = 6 pages/x minutes      .... cross-multiply.....

4x = 36    divide by 9 on each side

x = 9 minutes

Step-by-step explanation:

Answer:

- 5i and 5i

Step-by-step explanation:

The Fundamental theorem of Algebra states that a polynomial of degree 3 has 3 roots, real and/ or complex.

Complex roots occur in conjugate pairs.

Given 2 real roots x = 5, x = - 5

There cannot be complex roots as they occur in pairs which would result in the polynomial having 4 roots instead of 3.

Answer:

36

Step-by-step explanation:

36 because 3x12 =36 so 36 feet above kite

Answer:

15 + 7c or 15 + 7 * c

Hope this helps!

Total amount of drink in the jug is 1 1/10 litre.

To find the total amount of drink in the jug, we need to add the amount of water and the amount of lemon juice:

Amount of water = 3/5 litre

Amount of lemon juice = 1/2 litre

We need to find a common denominator to add these fractions. The smallest common multiple of 5 and 2 is 10. So we can rewrite the fractions with denominators of 10:

Amount of water = (3/5) x (2/2) = 6/10 litre

Amount of lemon juice = (1/2) x (5/5) = 5/10 litre

Now we can add the fractions:

Total amount of drink = 6/10 + 5/10 = 11/10 litre

Since the numerator is greater than the denominator, we have an improper fraction. We can convert it to a mixed number by dividing the numerator by the denominator:

11 ÷ 10 = 1 with a remainder of 1

So the total amount of drink in the jug is 1 1/10 litre.

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Answer:

If friction did not exist, it would be hard for us to slow down in running, or putting breaks on a car, and more!

If friction did not exist, your car will slide down the road even if you try your best to put the brakes on a car. Friction is a very important force to slow down things that are moving very fast

Step-by-step explanation:

Hoped this helped.

\(GeniusUser\)

Answer:

83

Step-by-step explanation:

Solve using order of operations

First do the parentheses

8+3(20+5) -----> 8+3(25)

Then Multpily

8+3(25) -----> 8+75

Then add

8+75 =83

Based on the calculations,  it would not be very unusual to have more than 153 dentists recommend mintyfresh toothpaste.

The proportion of dentists who recommend mintyfresh toothpaste is 7/8 = 0.875. The expected number of dentists who recommend mintyfresh toothpaste in a sample of 170 is 170 x 0.875 = 148.75. The standard deviation of the sampling distribution is √(np(1-p)) = √(170 x 0.875 x 0.125) = 4.71.

To find the probability of having more than 153 dentists recommend mintyfresh toothpaste, we calculate the z-score as (153 - 148.75) / 4.71 = 0.91. Using a standard normal distribution table, we find that the probability of having a z-score greater than 0.91 is approximately 0.1826, or 18.26%.

Therefore, it would not be very unusual to have more than 153 dentists recommend mintyfresh toothpaste.

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Answer:

265

Step-by-step explanation:

It's a cube, so all sides are the same, so 6.5 x 6.5 x 6.5

This equals 264.625. They want 3 significant figures, so u round to the nearest whole number. Significant numbers are whole numbers. This becomes, 265.

If the probabilities of their outcomes are 20%, 60%, and 20% respectively, the expected value of these outcomes is $346.

To calculate the expected value of the outcomes, we multiply each outcome by its corresponding probability and then sum up the results.

In this case, the projected outcomes are $240, $310, and $560, with probabilities of 20%, 60%, and 20% respectively.

To calculate the expected value, we use the formula:

Expected value = (Outcome 1 * Probability 1) + (Outcome 2 * Probability 2) + (Outcome 3 * Probability 3) + ...

Expected value = ($240 * 0.20) + ($310 * 0.60) + ($560 * 0.20)

Expected value = $48 + $186 + $112

Expected value = $346

The expected value represents the average value or the long-term average outcome we can expect from the given probabilities and outcomes. It provides a summary measure that helps in understanding the central tendency of the distribution of outcomes.

In this case, the expected value indicates that, on average, we can expect the project's outcome to be around $346.

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Answer: B.) -4+3

Step-by-step explanation:

The model represents "-4+3" because the blue arrow (top) stops at 3 which is a positive and the red arrow (bottom) stops at -4 which is a negative.

Answer:

75.398

Step-by-step explanation:

The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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It is quadratic

Option B is the correct answer.

The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y -axis

The scatterpot looks like parabola. Hence it is Quadratic.

The answers that  best explains how we check to make sure that this condition is met is: c. Make sure there is similar spread around the sample mean of y.

The equal spread condition states that the residuals (differences between the actual and predicted values of y) should have roughly equal variance at each value of x.

To check if this condition is met, we examine the residual plot, which is a scatterplot of the residuals versus the independent variable x. If the spread of residuals around the mean is roughly equal for all x, then the equal spread condition is satisfied.

Therefore the correct option is C.

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Answer:

Step-by-step explanation:

3

Answer:

6

Step-by-step explanation:

triangle area

1/2bh

1/2 * 4 * 6

= 12

same area as parallelogram

parallelogram area

= bh

= 2 * ___

to get 12

= 2 * 6

= 12

so 6

Answer:

15

Step-by-step explanation:

Break the shape into a rectangle and a triangle. The rectangle is 3 x 4 = 12. The triangle is 2 x 3 / 2 = 3

3 + 12 = 15

Answer:

Area = 18

Step-by-step explanation:

Width x height.

The width is 6 cm, as opposed to 4 cm and 2 cm. Add any remainder width lengths that add up to the width. Next, multiply the width by the shapes' height. In this situation, we get 18 cm.