Suppose that a>1/2 and the parabola with equation y=ax^2+2 has vertex V. The parabola intersects the line with equation y=-x+4a at points B and C, as shown. If the area of triangle VBC is 72/5, determine the value of A.

The solutions are (4.5, 4.5) and (6, 3).

Here,

The equations are;

x + y = 9

x²- 3xy + 2y² = 0​

We have to solve the equations.

What is Expression?

Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division

Now,

The equations are;

x + y = 9

x²- 3xy + 2y² = 0​

Since, x + y = 9 ⇒ y = 9 - x

And, solve the equation as;

x²- 3xy + 2y² = 0​

x²- 2xy - xy + 2y² = 0​

x (x - 2y) - y (x - 2y) = 0

(x - y) (x - 2y) = 0

(x - y) = 0 or (x - 2y) = 0

For, (x - y) = 0

Given, x + y = 0

Hence, Solve equation (x - y) = 0 and (x + y) = 9 we get;

2x = 9

x = 4.5

And, y = 4.5

For  (x - 2y) = 0

x = 2y put in equation (x + y) = 9 we get;

(x + y) = 9

2y + y = 9

3y = 9

y = 3

And, x = 6

Therefore, The solutions are (4.5, 4.5) and (6, 3).

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Solutions are (4.5,4.5) and (6,3)

What are Quadratic equations ?

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).

Given,

x + y = 9 => y = 9-x  equation 1

x^2 - 3xy + 2y^2 = 0  equation 2

(x - y)(x - 2y)=0

x - y = 0 or x - 2y = 0

1. Equating x-y=0 and x + y = 9,

x + y = 9

x - y = 0

2x = 9

x = 4.5

y = 4.5

because y = x

2. Equating x - 2y = 0 and x + y = 9,

2x + 2y = 18

x - 2y = 0

3x = 18

x = 6

y = 9 - x = 3

therefore, possible solutions are (4.5,4.5) and (6,3)

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If two hikers are 11 miles apart and walking towards each other and they meet in 2 hours, then if one hiker walks 0.3mph faster than the other, then the rate at which the slow hiker and fast hiker walk towards each other is equal to 2.6 and 2.9 mph respectively.

Consider, the speed of the slow hiker = s

Then, the speed of the fast hiker = s + 0.3

The distance covered by both the hikers in 1 hour = 2s + 0.3 miles

The distance covered by both the hikers in 2 hours = 2(2s + 0.3) = 4s + 0.6 miles

We can find the value of s by forming an algebraic expression as follows,

4s + 0.6 = 11

4s = 11 - 0.6

4s = 10.4

s = 10.4 / 4

s = 2.6

Speed of the slow hiker = s = 2.6 mph

Speed of the fast hiker = s + 0.3 = 2.6 + 0.3 = 2.9 mph

Hence, the rate at which the slow hiker and the fast hiker walk toward each other is equal to 2.6 and 2.9 mph respectively.

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Answer: four friends went out for dinner. the bill , including tax , totaled $64.00 if they want to leave a 15% tip and want to share the bill and tip equally

Step-by-step explanation:

Yes, the given expressions i.e., 3m^2+2m^2 and 5m^2 are equivalent expression.

An expression is defined as a combination of various terms or numbers that are combined by using mathematical operations in addition, subtraction, multiplication, and division.

Equivalent expressions are expressions that have similar value or worth but do not look the same. When considering if the expressions given are equivalent, at least two expressions are must.

A) Yes, by considering the above definitions we can conclude that 3m^2+2m^2 and 5m^2 are equivalent expressions.

B) Given, 3m^2+2m^2 and 5m^2

Now, solve 3m^2+2m^2 we simply get the value which is similar to other expression given to us in the question i.e., 5m^2.

Hence, 3m^2+2m^2 and 5m^2 are similar or equivalent expression.

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Answer:

Step-by-step explanation:

1) Use multiplication distributive property [tex](xy)^a=x^ay^a[/tex]

= [tex]\frac{(x^4)^2y^2}{3}[/tex]

2) Use Power rule [tex](x^a)^b = x^{ab}[/tex]

= [tex]\frac{x^8y^2}{3}[/tex]

Answer:

this is the answer of about the image is even

The water gauge pressure at the house will be 9.63×10⁵ N/m².

Firstly we will be calculating the total height which will comprise of height from tank to house and elevated height. The formula for total height will be -

Total height = 5 + 110 sin 58°

Keep the value of sin 58° in formula and performing multiplication followed by addition

Total height = 5 + 110×0.848

Total height = 5 + 93.28

Total height = 98.28 meters

Now, calculating the water gauge pressure at house. The formula to be used is -

P = ρ×g×h, where P is pressure, ρ is density of water, g refers to acceleration due to gravity and h represents total height. We are aware that density of water is 1000 kg/m³ and accelerate due to gravity is 9.8 m/s².

Keep the values in formula to find the gauge pressure.

P = 1000 × 9.8 × 98.28

Performing multiplication

P = 963,144 N/m² or 9.63×10⁵ N/m²

Hence, the water gauge pressure at the house will be 9.63×10⁵ N/m².

The complete question is -

A house at the bottom of a hill is fed by a full tank of water 5m deep and connected to the house by a pipe that is 110m long at an angle of 58 degrees from the horizontal. Determine the water gauge pressure at the house.

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Answer:

focus

Step-by-step explanation:

Answer:

Step-by-step explanation:

Focus = (8,-6¹/2), directrix is y= -5¹/2

The value of the functions are:

(a) ( f - g )( 1 ) = - 1

(b) ( f · g )( 4 ) = 0

Before performing operations on functions, we must first comprehend the various function rules and how to get the function value at a given x-value. By applying this concept, we can determine the function value.

From the graphs, we have the functions,

f(x) = 2( | x - 2 | )

g(x) = - x + 4

Now,

(a) ( f - g )( 1 )

( f - g )( 1 ) = f( 1 ) - g( 1 )

( f - g )( 1 ) = 2 ( | 1 - 2 | ) - ( - 1 + 4 )

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

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

( f - g )( 1 ) = - 1

(b) ( f · g )( 4 )

( f · g )( 4 ) = f( 4 ) · g( 4 )

( f · g )( 4 ) = 2( | 4 - 2| ) · ( - 4 + 4 )

( f · g )( 4 ) = 0

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The approximation of -8 plus the square root of 20 is given by:

-3.5.

To round a number to the nearest tenth, it will have only one decimal digit, and the rule is as follows:

The square root of 20 is given by:

sqrt(20) = 4.47.

7 > 5, hence, rounded to the nearest tenth:

sqrt(20) = 4.5.

Then:

-8 + 4.5 = -3.5.

Which is the approximation.

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The measure of side HI is 10.74 for the triangle EFG which is similar to HIJ.

Similar triangles are those triangles which have corresponding sides in proportion to each other and the corresponding angles of two triangles are equal to each other. Similar triangles look the same but they differ in terms of the sizes of the two triangles.

In short, If two triangles are similar that means,

All corresponding angle pairs of triangles will be equal.

All corresponding sides of triangles will be proportional.

Now, it is given in the question that ΔEFG is similar to ΔHIJ then, their corresponding sides will be in proportion.

⇒ GE/EF = HJ/HI

⇒ 19/34 = 6/HI

⇒ HI = 6 x 34/19

⇒ HI = 10.74

Therefore, the measure of side HI is 10.74.

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Answer:

85%

Step-by-step explanation:

Answer:

85%

Step-by-step explanation:

85% because, $40 X .85 = $34 which means, $34 is 85% of $40

Answer:

[tex]volume = 653.71 {cm}^{3} [/tex]

Step-by-step explanation:

Volume = πr^2h

=

[tex] \frac{22}{7} \times {4}^{2} \times 13 \: c {m}^{3} [/tex]

= 22*16*13/7 cm^3

= 653.714cm^3

Rounding off = 653.71 cm^3

Answer:

653.45

Step-by-step explanation:

it told me the answer

Each side of the triangle should contain four numbers whose sum is 28.

3+5+9+11=28

3+10+8+7=28

11+6+9+7=28

The pain of numbers that can be used for A and B is [5,9] The pain of numbers that can be used for C and D is [10,8] and the pain of numbers that can be used for E and f is [6,4].

The hypotenuse of a right triangle is its longest side; its "opposite" side is the one that faces the angle in question; and its "adjacent" side is the one that faces it. We use special terminology to define the sides of right triangles.

We use special terminology to define the sides of right triangles.

The side opposite the right angle is always the hypotenuse of a right triangle. It is the longest side in a right triangle.

The opposing and neighboring sides are the other two sides. The labels on these sides relate to an angle.

One side is across from another at a particular angle.

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The coordinates of the point on the directed line segment will be (1, -6).

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

The coordinates of the point on the directed line segment from (-1, -8) to (5, -2). The ratio is 1: 2.

Then the coordinates of the point will be

x = (1(5) + 2(-1)) / (1 + 2)

x = (3 / 3)

x = 1

y = (1(-2) + 2(-8)) / (3)

y = - 18 / 3

y = - 6

The coordinates of the point on the directed line segment will be (1, -6).

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Answer:

(30.00)

Step-by-step explanation:

(30.00) is the correct answer for your question/ statement you have asked. the answer is (30.00) again.

Answer:

12 cm

Step-by-step explanation:

Volume of total shape = Volume of big rectangle - Volume of small rectangle

Volume of big rectangle = L×B×H

Volume of big rectangle = 10 cm×3 cm×2 cm

Volume of big rectangle = 60 cm

Volume of small rectangle = l×b×h

l = 10 cm - 6 cm = 4cm

Volume of small rectangle = 4 cm×3 cm×4 cm

Volume of small rectangle = 48cm³

Volume of total shape = 60cm³ - 48cm³

Volume of total shape = 12cm³

highest common factor (HCF) of 32, 48 and 72= 8

HCF - Highest Common Factor

The Highest Common Factor (HCF) of two numbers is the highest possible number that divides both the numbers completely. The Highest Common Factor (HCF) is also called the Greatest Common Divisor (GCD).

There are many ways to find the HCF of two numbers. One of the quickest ways to find the HCF of two or more numbers is by using the prime factorization method. Explore the world of HCF by going through its various aspects and properties. Find answers to questions like what is the highest common factor for a group of numbers, easy ways to calculate HCF, HCF by division method, its relation with LCM, and discover more interesting facts around them.

HCF by Prime Factorization

In order to find the HCF of numbers by the prime factorization method, we use the following steps. Let us understand this method using the example given below.

Step 1: Find the common prime factors of the given numbers.

Step 2: Then, multiply these common prime factors to obtain the HCF of those numbers.

highest common factor (HCF) of 32, 48 and 72

32 = 2x2x2x2x2

48= 2x2x2x2x3

72= 2x2x2x3x3

highest common factor (HCF) of 32, 48 and 72 = 2x2x2= 8

highest common factor (HCF) of 32, 48 and 72= 8

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The firefighter needs to climb a height of 22.91 foot to reach the cat.

What is the Pythagorean Theorem ?

Pythagorean Theorem states that the square of the hypotenuse of a right triangle equals the sum of squares of the lengths of the other two sides.

It is given that the hypotenuse of the ladder is 25 foot and it's base is 10 feet away from base of tree.

Using the Pythagorean theorem which states that :

H² = P² + B²

where ;

H = Hypotenuse , P = Perpendicular and B = base

We can find out the height up to which the firefighter needs to climb to reach the cat. And it is given by :

25² - 10² = P²

625 - 100 = P²

or

P = √525

P = 22.91 foot

Therefore , the firefighter needs to climb a height of 22.91 foot to reach the cat.

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A local maximum occurs over the interval (-2,0).

A local minimum occurs over the interval (0,2).

If the graph of the function increases first and decreases after a particular point, then the function acquires a local maximum at that point.

Similarly, if the graph of the function decreases first and then increases after a point, then the function acquires a local minimum at that point.  

Here the given x and f(x) values for the continuous function f(x) are:

x        f(x)

-3       -16

-2        -1

-1         2

0         -1

1          -4

2          -1

As we can see by examining the table values, the function is increasing in the intervals (-3,2) and (-2,-1).The function acquires value f(x) = 2 at x = -1 and then it starts to decrease. So this value f(x) = 2 is the local maximum and is acquired on the interval (-2,0).

The graph is then decreasing from x = -1 to x = 1. The function has the value f(x) = -4 at x = 1. Then the function starts to increase from x = 1 to x = 2. So f(x) = -4 is the local minimum of the function and is acquired on the interval (0,2).

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Answer:

3

Step-by-step explanation:

y=mx+b

m is the slope

The correct representation of x + 5 using algebra tiles is one green rectangle box and one small yellow box.

Algebra tiles are the tiles or square or rectangular boxes which are use to represent the polynomial expression whether of linear , monomial or quadratic.

There are three types of algebra tiles :

All of these tiles has different color to represent positive and negative value :

Square Type                      Positive color                      Negative Color

Small squares                     Yellow                                 Red

Rectangles                          Green                                  Red

Large Squares                     Blue                                    Red

For the given question, Expression is x + 5

that means, there is one Green rectangle and one Yellow small square.

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Answer:

Step-by-step explanation:

Angles in a triangle add up to 180 degrees.

Therefore A+B+C = 180

This means 4x+34+7x-10+5x+12 = 180

Simplies down to 16x+36 = 180

Rearrange to have 16x = 144

Divide by 16 on both side to get x = 9

Substitue the value of x back into the equation of A

A = 4(9)+34 = 70 degrees

Answer:

Rounded to the nearest inch: 10

Rounded to the nearest tenth: 10.2

Rounded to the nearest hundredth: 10.25

Step-by-step explanation:

To find the area of a square, we multiply the side length by itself, or in other words, SQUARE the side length!

[tex]A=s^2[/tex]

We are given the area, so plugging that into our equation looks like this:

[tex]105=s^2[/tex]

To eliminate the exponent, take the square root of both sides of the equation!

[tex]\sqrt{105}=s[/tex]

From here, there are a few paths to take, depending on what your teacher is looking for. I will evaluate the approximate of the square root by finding the nearest perfect squares.

The nearest perfect square less than √105 is √100, and the nearest perfect square greater than √105 is √121.

105 is closer to 100 than to 121, so √105 is closer to √100.

√100 is equal to 10, so the √105 is approximately 10 inches!

Using a calculator to check:

[tex]\sqrt{105}=10.247[/tex] inches

Answer:

a=15, b=14

Step-by-step explanation:

We know all angles must add up to 360, so lets add all angles and set them equal to 360.

[tex]7a+33+3b+10a-12+6b-42=360\\17a+9b-21=360[/tex]

We also know that any angle opposite another is equal. Lets take 6b-42 and 3b and set them equal.

[tex]3b=6b-42[/tex]

Now solve for b in both equations

[tex]3b=6b-42\\-3b=-42\\b=14[/tex]

[tex]17a+9b-21=360\\9b-21=360-17a\\9b=381-17a\\b=\frac{381-17a}{9}[/tex]

Now we set the two equations equal to each other to solve for a:

[tex]14=\frac{381-17a}{9} \\126=381-17a\\-255=-17a\\15=a[/tex]

This gives a=15, b=14.

calculate the total of the bills= 300+200+225+275 =1000

the average monthly bill= 1000/12 = 83.333

Total =0

for i in range(4):

  bill = float(input("Enter bill for quarter " + str (i+1) + ": "))

  total += bill

average = total / (4 * 3)

if average > 75:

  print("Average monthly bill is $" + str(average) + ". Too much water is being used")

if 25 <= average < 75:

  print("Average monthly bill is $" + str(average) + ". A typical amount of water is being used")

if average < 25:

  print("Average monthly bill is $" + str(average) + ". Thank you for conserving water")

calculate the total of the bills= 300+200+225+275 =1000

the average monthly bill= 1000/12 = 83.333

Total =0

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