Use the graph f(x) = -x² +8x+20 to determine the values of :
2.2.1 p for which -x² +8x+p=0 will have equal roots.​

Answer:

I don't think this question is phrased correctly. The lesser number is the lesser number...  I think this is asking you to find each of the numbers, so I will do that.

Greater number: -19

Lesser number: -28

Step-by-step explanation:

If the greater number minus the lesser number is 9, the greater number is 9 more than the lesser number. I'll use algebra to solve this problem.

Lets set the lesser number as the variable x.

lesser number = x

Because the greater number is 9 more than the lesser number, the greater number is:

x+9

2x+9 = -47

Subtract 9 on both sides to isolate the variable.

2x + 9 - 9 = -47 - 9

2x = -56

x = -28

Because the greater number is 9 greater than the lesser number, add 9 to x to get the greater number.

-28 + 9 = -19

Step-by-step explanation:

first find distance between ab

then between bc

then ac

in isosceles triangle 2 sides are equal

so if two sides means the distance we find are same

the givan triangle is isosceles

Answer:

the coordinates of vertices triangle ABC are (4,-1), B(5,6) and C (1,3) prove that triangle ABC is an isosceles right triangle.

The volume of the right rectangular prism is 156 cubic centimeters.

We have,

The formula for the volume of a rectangular prism is:

V = l x w x h

where V is the volume, l is the length, w is the width, and h is the height.

Using the given values, we can substitute them into the formula to find the volume of the rectangular prism:

V = 13 cm x 4 cm x 3 cm

V = 156 cm^3

Therefore,

The volume of the right rectangular prism is 156 cubic centimeters.

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Answer:

ans = 6

Step-by-step explanation:

using pythoras theorem:

Hyp^2 = Opp^2 + Adj^2

10^2 = x^2 + 8^2

100 = x^2 + 64

x^2 = 100 - 64

x^2 = 36

x = √36

x = 6.

Hope this helps .

Based on the given information, we can conclude that tuition at Penn State has increased more rapidly than inflation.

The price index measures the average change in prices of a basket of goods and services over time. In this case, the price index increased from 207.34 in 2007 to 226 in 2012, indicating an overall inflation rate of approximately 9% over that period. On the other hand, tuition at Penn State increased from $6,142 to $7,562, representing an increase of approximately 23%.

When comparing the rates of increase, we can see that tuition has outpaced inflation. This implies that the cost of education at Penn State has been rising more rapidly than the general increase in prices for goods and services. It suggests that factors specific to the education industry, such as rising costs of resources, facilities, and personnel, have contributed to the higher tuition rates.

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The complete question is:

Assume tuition at Penn State cost $6,142 (per semester) in 2007 and $7,562 in 2012. If the price index was 207.34 in 2007 and 226 in 2012, then we could say:

Answer:

Step-by-step explanation:

Question 1

Use ratios to solve:

Question 2

Mutya earned Php. 330  

After 37 bounces, the ball's height will be less than 1 foot.

The initial height of the ball is 50 feet.

After first bounce, the ball will reach a height of:

= 50 feet * (1 - 10%)

= 45 feet.

After second bounce, it will reach a height of:

= 45 feet * (1 - 10%)

= 40.5 feet.

Height decreases by 10% after each bounce.

We have to set up an equation:

50 feet * (0.9)^n < 1 foot

Simplifying:

0.9^n < 1/50

Taking the logarithm:

n * log(0.9) < log(1/50)

n > log(1/50) / log(0.9)

n > 37.1298771746

n > 37.13.

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The value of angle Z= 39°, line XY= 21.9 and line XZ= 34.7

A right-angled triangle is a type of triangle which as one of it's sides equal to 90°. Since angle Y is 90°, then ∆ABC is a right-angled triangle

angle Z = 180-(90+51)

angle Z= 180- 141= 39°

using trigonometry ratio

tan51 = 27/XY

XY= 27/tan51

XY= 27/1.2

XY= 21.9

using Pythagoras theorem

XZ²= 21.9²+27²

XZ²= 1208.6

XZ= √1208.6

XZ= 34.7

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Answer:

y=2/3x-7

Step-by-step explanation:

For lines to be parallel, they must have the same slope which is 2/3. However, they can't have the same y-intercept.

The value of the given integral is: v = [(4√(3) - 5)π/3]

To evaluate the given integral, let's calculate it step by step:

First, let's integrate with respect to z from 1 to √(4 - x² - y²):

∫[1, √(4 - x² - y²)] dz = √(4 - x² - y²) - 1

Next, let's integrate the above expression with respect to y from -√(3 - x²) to √(3 - x²):

∫[-√(3 - x²), √(3 - x²)] (√(4 - x² - y²) - 1) dy

To simplify the integration, let's convert to polar coordinates:

x = r cosθ

y = r sinθ

The bounds of integration in polar coordinates will be:

r: 0 to √(3)

θ: 0 to 2π

Now, we can rewrite the integral in terms of polar coordinates:

∫[0, 2π] ∫[0, √(3)] (√(4 - r²) - 1) r dr dθ

Evaluating the inner integral with respect to r:

∫[0, 2π] [(-1/3) (4 - r²)\(^{3/2}\) - (1/2) r²] | [0, √(3)] dθ

∫[0, 2π] [(2√(3)/3) - (1/3)(4 - 3)\(^{3/2}\) - (1/2)(√(3))²] dθ

Simplifying further:

∫[0, 2π] [(2√(3)/3) - (1/3) - (3/2)] dθ

∫[0, 2π] [(2√(3)/3) - (5/6)] dθ

Now, integrating with respect to θ:

[(2√(3)/3)θ - (5/6)θ] | [0, 2π]

[(2√(3)/3)(2π) - (5/6)(2π)] - [(2√(3)/3)(0) - (5/6)(0)]

[(4√(3)/3)π - (5/3)π] = [(4√(3) - 5)π/3]

Therefore, the value of the given integral is: v = [(4√(3) - 5)π/3]

Complete Question:

Evaluate the integral:

v = ∫∫∫ [−√3, √3] [−√(3−x²), √(3−x²)] [1, √(4−x²−y²)] dz dy dx

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Answer:

\(-1.30\ and\ -7.70\) (2 decimal places)

Step-by-step explanation:

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

-----------------------------------------------

\(x^2+9x+10=0\)

Plug in values:

\(x=\frac{-9\pm \sqrt{9^2-4\cdot \:1\cdot \:10}}{2\cdot \:1}\)

First value of x:

\(x=\frac{-9+\sqrt{41}}{2}=-1.30\) (2 decimal places)

Second value of x:

\(x=\frac{-9-\sqrt{41}}{2}=-7.70\) (2 decimal places)

Answer: y = -(5/3)x + 8

I assume (6,-2)(6,−2) is actually just (6,−2).

Step-by-step explanation:

A parallel line will have the same slope as the reference line.  Rewite the reference line equation into y=mx+b format:

5x+3y=6

3y = -5x+6

y = -(5/3)x + 6

The parallel line we want will have the same slope, -(5/3):

y = -(5/3)x + b

b will be different since we want this new, parallel, line to go through point (6,-2), so it must be moved to accomodate this point.  Find the value of b we need by entering the point into the new equation and solving for b.

y = -(5/3)x + b  for point (6,-2)

-2 = -(5/3)(6) + b

-2 = -10 + b

b = 8

y = -(5/3)x + 8

Answer:

a1=5

d=9-5=4

a20=5+19×4=81

Answer:

$25

Step-by-step explanation:

We Know

She has saved $15, which is three-fifths of the total cost of the game

How much does the game cost?

$15 = 3/5

$5 = 1/5

We Take

5 x 5 = $25

So, the cost of the game is $25.

For the utility function U(x, y) = \(x^(4/1) * y^(4/3)\), the indifference curve equations for U = 1, U = 2, and U = 3 are derived. The shape of the indifference curves resembles rectangular hyperbolas.

For the utility function U(x, y) = \(x^(4/1) * y^(4/3)\), we derive the indifference curve equations for U = 1, U = 2, and U = 3. By setting the utility function equal to these values, we can solve for the corresponding relationships between x and y.

The resulting equations form rectangular hyperbolas, where the ratio of x to y remains constant along each curve. These curves are concave and exhibit diminishing marginal rates of substitution.

For the utility function U(x, y) = y - 2x, we derive the indifference curve equations for U = 1, U = 2, and U = 3. By setting the utility function equal to these values, we can solve for the relationships between x and y.

The resulting equations represent straight lines with a slope of 2, indicating a constant marginal rate of substitution between x and y. These indifference curves show a positive linear relationship between the two goods.

Both utility functions satisfy the assumptions of completeness, transitivity, and monotonicity. Completeness implies that the consumer can rank all bundles of goods, transitivity ensures consistent preferences, and monotonicity states that more of a good is preferred to less.

The derived indifference curves reflect these assumptions by providing a consistent ranking of bundles based on utility. The shapes of the indifference curves are well-defined, allowing for clear visual representations of the preferences of the consumer.

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Answer:

2 is the value that provides the same result with f(x) and g(x).

Step-by-step explanation:

You can solve this by saying:

f(x) = g(x)

and then solving for x.

So let's do it:

\(f(x) = g(x)\\-0.5x + 2 = 2x - 3\\2x + 0.5x = 2 + 3\\2.5x = 5\\x = 2\)

This tells us that when x = 2, the two functions will have identical values.  Let's try them out to confirm it!

f(x) = -0.5x + 2

f(2) = -0.5 * 2 + 2

f(2) = -1 + 2

f(2) = 1

g(x) = 2x - 3

g(2) = 2 * 2 - 3

g(2) = 4 - 3

g(2) = 1

So we can see that 2 is the value that produces the same result in both charts.

The input value that produces the same output value in both charts is 2. so the correct answer is option D.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

here, we have,

You are given two functions  f (x) = -0.5X +2 and g(x) = 2x - 3

x      f(x)

-3     3.5

-2     3

-1     2.5

0     2

1      1.5

2     1

3     0.5

The second table is given below:-

x      g(x)

-3      

-2      

-1      

0    

1      

2      

3      

We will put the points and will find the value of functions:-

g(-3) = 2(-3) - 3 = -6 -3 = -9

g(-2) = 2 -(-2) -3 = -7

g(-1) = 2( -1) -3 = -3

g(0) = 2 - 0  - 3 = -3

g(1) = 2.1 - 3 = -1

g(2) = 2.2 -3 = 1

g(3) = 2.3 -3 = 3

Hence the second table will be

x      g(x)

-3      -9

-2      -7

-1       -5

0       -3

1        -1

2       1

3       3

The input value that produces the same output value in both charts is 2.

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bisects x = -12AB / (2AB - 6BD)

m∠ABC = 6x

= 6 × (-12AB / (2AB - 6BD))

To solve for x and find the measure of angle ABC (m∠ABC), we will apply the angle bisector theorem and use the given information.

According to the angle bisector theorem, the ratio of the lengths of the segments created by an angle bisector is equal to the ratio of the measures of the angles formed by the bisector.

Let's set up the equation using the given information:

m∠ABD = 6x (angle ABD)

m∠DBC = 2x + 12 (angle DBC)

Using the angle bisector theorem, we have:

AB/BD = m∠ABD/m∠DBC

Since BD bisects ∠ABC, we can substitute the given measures into the equation:

AB/BD = (6x) / (2x + 12)

To solve for x, we can cross-multiply:

AB × (2x + 12) = BD × (6x)

Expanding both sides of the equation:

2ABx + 12AB = 6BDx

Rearranging the equation:

(2AB - 6BD)x = -12AB

Now we can isolate x:

x = -12AB / (2AB - 6BD)

The measure of angle ABC (m∠ABC), we substitute the value of x back into the expression:

Simplifying this expression further would require additional information about the lengths of AB and BD.

Without this information, we cannot find the exact value of m∠ABC.

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The probability that exactly two customers in the sample will default on their payments is 0.9997.

This is a binomial probability problem with n = 5 trials and p = 3% = 0.03 probability of success (default) on each trial.

The probability of exactly two defaults can be calculated using the binomial probability formula:

P(x = r) = nCr * p^r  * q^n-r

where q = 1 - p = 1 - 0.03 = 0.97

P(x = 2) = (5C0 × 0.03⁰ × 0.97⁵⁻⁰) + (5C1 × 0.03¹ × 0.97⁵⁻¹) + (5C2 × 0.03² × 0.97⁵⁻²)

P(x = 2) = 0.9997

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T(110) is used to calculate the value of T when w = 110.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change (slope) and b is the y intercept.

Given the linear equation:

T(w) = 530 - w

Hence T(110) is used to calculate the value of T when w = 110.

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The summation of the given number sequence can be written as below:

  \(\sum\limits_{n=1}^6 \frac{n}{13-n}\)

What is meant by number series?

A series in mathematics is the addition of an unlimited number of quantities, one after the other, to an initial quantity. A list of elements or objects that have been arranged sequentially is referred to as a sequence. The total of all the terms in a sequence can be used to very broadly define a series. All of the terms in the sequence must, however, clearly relate to one another. We must identify the laws that lead to the production of a number series in order to answer the questions about number series.

The given series is:

 1/12 + 2/11 + 3/10 + 4/9 + 5/8 + 6/7

We can observe from the sequence at the numerator of the terms is increasing by one and the numerator of the first term is 1.

The denominator, on the other hand, is decreasing by 1 and the denominator of the first term is 12.

The number of terms is 6.

So we can write the limit of n as 1 to 6.

The value of n is the numerator of the sequence.

The denominator value will be (13 - n).

Therefore the summation of the given number sequence can be written as below:

  \(\sum\limits_{n=1}^6 \frac{n}{13-n}\)

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After 4 hours of discharging, the volume left in the tank would be 500 liters. The correct option is C.

Initially, the tank has a water capacity of 1500 liters.

After three hours of discharging, half of the water is discharged, which means 1500/2 = 750 liters have been removed from the tank.

To find the volume left after 4 hours of discharging, we need to subtract the additional amount discharged in the fourth hour.

Since the discharge rate remains the same, we can calculate the amount discharged in one hour as 750/3 = 250 liters.

Therefore, in the fourth hour, 250 liters would be discharged. Subtracting this from the remaining water after three hours (750 liters), we get 750 - 250 = 500 liters.

Therefore, the correct answer is c. 500 liters.

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The two most commonly used measures of variability are variance and standard deviation.

1. Variance: Variance measures how spread out a set of data points is from the mean. It calculates the average of the squared differences between each data point and the mean. The formula for variance is sum of squared differences divided by the number of data points.

Example: Let's say we have a set of data points: 2, 4, 6, 8, and 10. The mean of these data points is 6. The differences between each data point and the mean are: -4, -2, 0, 2, and 4. Squaring these differences gives us: 16, 4, 0, 4, and 16. The sum of these squared differences is 40. Dividing this sum by the number of data points (5) gives us a variance of 8.

2. Standard Deviation: Standard deviation is the square root of variance. It measures the average distance between each data point and the mean. Standard deviation is often preferred over variance because it is in the same unit as the data points, making it easier to interpret.

Example: Using the same set of data points as above, the variance is 8. Taking the square root of 8 gives us a standard deviation of approximately 2.83.

In summary, variance measures how spread out the data points are from the mean, while standard deviation gives us a more intuitive understanding of the variability by providing a measure in the same unit as the data points. These measures help us understand how the data is distributed and how much it deviates from the average.

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Answer:

\(2 \sqrt{ - 2 } \)

maybe?

The correct definition for the term "Circular flow diagram" is a diagram that pictures the economy as consisting of four main sectors that interact with each other through different markets, and in which financial institutions help to facilitate some of the interactions.

A circular flow diagram is a visual representation of how money, goods, and services flow within an economy. It illustrates the interconnectedness of various sectors in the economy, including households, firms, government, and the foreign sector. The diagram shows the flow of money and goods between these sectors through different markets such as the product market and the factor market. It demonstrates how households supply factors of production (such as labor) to firms in exchange for income, and how firms supply goods and services to households in exchange for revenue. Additionally, the circular flow diagram highlights the role of financial institutions in facilitating the flow of funds between sectors, such as banks providing loans to businesses. Overall, the circular flow diagram provides a simplified representation of the economic interactions and relationships between different sectors in an economy.

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Answer:the second one

Step-by-step explanation: hope this helps

The value of h in terms of x when the volume of cylinder is equal to that of cone is h = 6x²

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Sometimes, volume is also termed capacity.

The volume of a cone is linked to the volume of a cylinder. A cone is one third of the volume of a cylinder. The volume of a cone is ¹/₃ × π × r² × l. To calculate the volume we multiply these values together.

The volume of cylinder = πr²h

and volume of cone = 1/3 πr²h

since the volume of the cone and cylinder are equal

πr²h = 1/3 πr²h

r in cylinder = x cm and h is 2x

r in cone = x cm

therefore πx²×2x = 1/3πxh

divide both side by πx

π2x³/πx = h/3

2x² = h/3

therefore h = 3×2x²

h = 6x²

therefore the value of h in terms of x is h = 6x²

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