Find the value of b.a=5 and c = 10A.9.5B.10C.9D.8.7Please can you explain.

If you subtract 2x from both sides of the equation you have:

Therefore, if you subtract 2x both sides, the equation will look like

Answer:

(D). f(x) = [tex]-\frac{3}{2}[/tex] x² + [tex]\frac{17}{2}[/tex] x - 7  

Step-by-step explanation:

( x , y )

ax² + bx + c = y ............ ( 1 )

~~~~~~~~~~~~~~

( 2 , 4 ) --------> ( 1 )

a(2)² + b(2) + c = 4

4a + 2b + c = 4 .............. (2)

( 3 , 5 ) ---------> ( 1 )

a(3)² + b(3) + c = 5

9a + 3b + c = 5 ............... (3)

( 4 , 3 ) ----------> ( 1 )

a(4)² + b(4) + c = 3

16a + 4b + c = 3 .............. (4)

[tex]delta[/tex] = Δ = [tex]\left[\begin{array}{ccc}4&2&1\\9&3&1\\16&4&1\end{array}\right][/tex] = - 2

[tex]delta_{a}[/tex] = [tex]\left[\begin{array}{ccc}4&2&1\\5&3&1\\3&4&1\end{array}\right][/tex] = 3

[tex]delta_{b}[/tex] = [tex]\left[\begin{array}{ccc}4&4&1\\9&5&1\\16&3&1\end{array}\right][/tex] = - 17

[tex]delta_{c}[/tex] = [tex]\left[\begin{array}{ccc}4&2&4\\9&3&5\\16&4&3\end{array}\right][/tex] = 14

a = [tex]delta_{a}[/tex] / [tex]delta[/tex] = [tex]-\frac{3}{2}[/tex]

b = [tex]delta_{b}[/tex] / [tex]delta[/tex] = [tex]\frac{-17}{-2}[/tex] = [tex]\frac{17}{2}[/tex]

c = [tex]delta_{c}[/tex] / [tex]delta[/tex] = [tex]\frac{14}{-2}[/tex] = - 7

f(x) = [tex]-\frac{3}{2}[/tex] x² + [tex]\frac{17}{2}[/tex] x - 7   (D)

SOLUTION:

Step 1:

In the question, we are given the following:

Find intervals of concavity and points of inflection of function

Step 2:

The details of the solution are as follows:

PART A:

Find intervals of concavity of function:

PART B:

Find the points of inflection of the function:

Answer: 2096 work hours per year

Hello there. To solve this question, we need to calculate the percentage of households that owns a 4K TV with the values given in the sample and compare with the other percentage to see if the value has increased.

Using that sample of 300 households, in which 60 of them owns a 4K TV, we get that the percentage will be calculated by the ratio:

60/300

Simplify the fraction by a factor of 60

1/5

Multiply it by 100%

20%, equal to 0.20

In 2014, we had that percentage being equal to 18%, which is equal to 0.18

So, we do have sufficient evidence that the percentage of households satifying this situation have increased with the time.

We have the following equation of the area of a square:

where s is the length of the side.

In this case, we have that the area is 36 square meters, then:

if we apply the square root on both sides we get:

therefore, the measure of the side of the square is 6 meters

We are given the equation:

Where x is the height over the sea level, where d is in miles, and x in feet. We want to know the value of the function at x = 18 feet. Thus:

We can now simplify by dividing 18 by 2:

Now, using properties of radicals:

The answer in simplified radical form is:

Using the calculator, we can find the answer to the nearest tenth of a mile d(18)= 5.2 miles

The value of x for the given triangle is 65°.

According to the question,

We have the following information:

A figure of triangle is given where two of its angles are 68° and 47°.

We know that the sum of all three angles of a triangle is 180°.

(More to know: all angles in an equilateral triangle are equal and in an isosceles triangle two angles are equal however the sum of three angles is 180°.)

So, we have the following expression:

x+68+47 = 180

x+115 = 180

x = 180-115

x = 65°

Hence, the value of x for the given triangle is 65°.

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Since the triangles are similar, that means the the prop

The functions are:

So the product (p*q) is

So the solution is is B)

A = P ( 1 + r/n ) ^ nt

P is the principle which is 36000

r is the rate which is 13.7 % or .137 in decimal form

n is the number of time per year, semi annual means 2 times per year

t is the time = 2

A = 36000( 1 + .137/2) ^ (2*2)

36000( 1 + .137/2) ^ (4)

The equation that can be used to determine the length and width of the garden is x² + 2x - 24 =0, the length is 6 feet and the width is 4 feet.

There is a rectangular garden with an area of 24 square feet

The garden is 2 feet longer than it is wide

Let the width of the garden be x

Then, the length of the garden is x + 2

The area of a rectangular garden = length of the garden x width of the garden

24 = x (x + 2)

x² + 2x - 24 =0

x² + 6x - 4x - 24 = 0

x(x + 6) -4(x + 6) = 0

(x - 4)(x + 6) = 0

x - 4 = 0

x = 4

Width of the rectangular garden is 4 feet

Length of the rectangular garden is (4 + 2) feet = 6feet

Therefore, the equation that can be used to determine the length and width of the garden is x² + 2x - 24 =0, the length is 6 feet and the width is 4 feet.

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35. 06 286 = 35.0629

For the information given in the statement, you have the inequality:

Now, to solve the inequality, subtract $37 from both sides of the inequality.

Now, divide by $9.40 into both sides of the inequality

Therefore, the math club could rent the meeting room for a maximum of 6 hours.

we will take two points on the line,

first is (0,2) and other is (1, 4)

the rate of change will be the slope of the line,

so the rate of the change is 2 km per trip

so the answer is 2

Given the following equation:

You must solve for "x" as following:

1. Apply the Distributive property:

2. Observe the equation. You can notice that left side is equal to right side. If you try to solve for "x", you get:

0x cannot be combined with other terms

Because when it is combined it always results in 0.

Given:

• Perimeter of the rectangle = 24 inches

• The length is 3 inches greater than it's width.

Let's find the dimensions of the rectangle.

To find the dimensions, apply the formula for perimeter of a rectangle:

P = 2l + 2w

Where l is the length and w is the width.

Given that the length is 3 inches greater than the width, the length can be expressed as:

l = (w + 3) inches

Substitute 24 for P and (w + 3) for l in the formula:

P = 2l + 2w

24 = 2(w + 3) + 2w

Let's solve the equation for w:

24 = 2(w + 3) + 2w

APply distributive property:

24 = 2(w) + 2(3) + 2w

24 = 2w + 6 + 2w

Combine like terms:

24 = 2w + 2w + 6

24 = 4w + 6

Subtract 6 from both sides:

24 -6 = 4w + 6 - 6

18 = 4w

Divide both sides by 4:

The width of the rectangle is 4.5 inches.

Since the lengh is 3 inches greater than the width, add 3 to 4.5 inches to get the length of the rectangle.

l = w + 3

l = 4.5 + 3

l = 7.5

The length of the rectangle is 7.5 inches.

Therefore, the dimensions of the rectangle are:

Length = 7.5 inches

Width = 4.5 inches

ANSWER:

Length = 7.5 inches

Width = 4.5 inches

Answer:

[tex]y = 100 - \frac{17}{3} x[/tex]

Here you go the visual explanation should be there for you, if your still confused i suggest asking your teacher for help on how to find the slope.

The factoYou ar/zero product property is the most efficient method for solving the equation

The given quadratic equation can be factored as:

The factor/zero product property is the most efficient method for solving the equation

ANSWER

EXPLANATION

The tour bus can seat 55 passengers.

A minimum of 15 people must register for the tour to book the bus.

This means that the number of people that must register for the tour must be greater than or equal to 15 and less than or equal to 55.

Let the number of people that must register be x.

Then we have that the inequality that represents the situation is:

That is the inequality.

SOLUTION

To identify or determine which relation in the graph is a function, we use the vertical line test.

The vertical line test explains that If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x-value has more than one output. A function has only one output value for each input value.

Hence, from the explanation above, we cam see that

Graph 1 is a Function

Graph 2 is a Function

Using similar approach

Graph 3 is not a function

Graph 4 is not a function

The distance travelled by the ball is 0.9076 feet.

Foucault used a pendulum to demonstrate the earth’s rotation. There are now over 30 Foucault pendulum displays in the United States. The Foucault pendulum at the Smithsonian Institution in Washington, DC, consists of a large brass ball suspended by a thin 52-foot cable. The ball swings at an angle of 1°. We have to find the distance travelled by the ball.

The ball travels in a circular motion. The radius of the circle is equal to the length of the cable. The distance travelled by the ball is equal to the arc length traversed in circular motion. Let the radius, angle, and distance be denoted by the variables "r", "θ", and "d", respectively.

r = 52 feet

We need to convert the angle from degrees into radians.

θ = 1°

θ = 1°*(π/180°)

θ = π/180

The formula for arc length is used below to calculate the distance.

d = r*θ

d = 52*(π/180)

d = 0.9076

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Looking at the restrictions over the variable x, we know that the domain is:

To find the range, notice that:

On the other hand, the function:

is an increasing function (its value grows when x grows), and can get as large as we want provided a sufficiently large value for x. Then, the range of such a function would be:

Which does not get altered when we multiply the square root of (x-2) by 4.

Since the function:

is a 5-units shift downwards, then the variable y can take any value from -5 onwards.

Then, the range of the function is:

Another way to find the range is to isolate x from the equation:

Since we already know that x must be greater than 2, then:

From here, there are two options:

Since we know an equation for y, then:

Or:

The second case is not true for every x.

Therefore:

Therefore:

we have that

they have 24 boxes of markers 56 coloring books and 72 packages of modeling clay

so

24=(2^3)(3)

56=(2^3)(7)

72=(2^3)(3^2)

24/8=3

56/8=7

72/8=9

the number of backpacks is 8

therefore

teh answer is option B

We know by the pythagorean theorem that

We know that the length of the hypotenuse squared will be equal to the sum of the legs squared. The problem says that the legs have the exact same length and the hypotenuse is 6cm longer, so we can write

Where "a" is the leg length, see that we can apply the pythagorean theorem here, and it will be

See that now c = a + 6, and b = a.

We can simplify that expression

We know that

Therefore our equation will be

Now we pass all the terms for one side and we will have a quadratic equation

We can use the formula for the quadratic equation and find out the solutions

Using it

Now we can just do all the calculus

Then the solution are

Even though we have two solution, see that the second one is negative, and we can't have negative length! Then the length of its legs will be

And the hypotenuse will be a + 6, then

Therefore, the legs and the hypotenuse length is

We can write it approximately as

If we want a more rough approximation we can say it's

For finding the solutions, you need to match the equations

For the next step, you should replace the value for x in any of the equations given

y=x+2

y=-2+2

y=0

(-2,0) Letter a

Answer:

252,5 or 2,525 rounded.

Step-by-step explanation:

Rounding explanation:

2525_

You rounded to the nearest one's place. The 5 in the ones place rounds down to 5, or stays the same because the digit to the right in the tenth place is _.

2,525

When the digit to the right is less than 5 we round toward 0.2525 was rounded down toward zero to 2,525

Solution

For this case we have the following number given:

We can see that x = -3 and y = - sqrt(3)

The angle is given by:

The radius would be:

And the polar form would be given by:

Answer:

The answer is D!!

Step-by-step explanation:

Right on edg 2022