The quadratic function f(x) has roots of −2 and 3 and point (2, −4) lies on f(x). What is the equation of f(x)? f(x) = 2(x + 2)(x − 3) f(x) = 2(x − 2)(x + 3) f(x) = (x + 2)(x − 3) f(x) = (x − 2)(x + 3)

Answer:

-1/5

Step-by-step explanation:

When a line is perpendicular to another line, it's gradient will be a reciprocal.

To calculate the reciprocal of a number you have to flip the fraction the other way around.

So, in the case our current gradient is 5/1 (5/1 is the same as just 5) and we need to flip in over to get 1/5, which is our new gradient.

The final step is to make the number negative because the line is going down. This gives us the final answer of -1/5.

Using a standard normal distribution table or calculator, the probability (percent) of a z-score less than 1.415 is approximately 92.18%.

a) To find the percent of SAT verbal scores less than 700, we need to calculate the z-score: (700 - 516) / 130 ≈ 1.415.

Using a standard normal distribution table or calculator, the probability (percent) of a z-score less than 1.415 is approximately 92.18%.

b) To determine the number of scores greater than 575, we first find the z-score: (575 - 516) / 130 ≈ 0.453.

Using a standard normal distribution table or calculator, the probability of a z-score greater than 0.453 is approximately 1 - 0.675 = 0.325.

With 1000 randomly selected scores, about 325 (0.325 * 1000) would be expected to be greater than 575.

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The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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The profit-maximizing levels of labor and output is 25 and 5

We have wage given as $10

VMPL = 100 dollars * MPL

The profit-maximizing level of labor and output is achieved where VMPL = wage(w), where

w = $10. [Given in question]

VMPL = $100 * MPL

VMPL = $100 * 0.5* (L^-1/2)

10 = 100 * 0.5* (L^-1/2)

We would have the value of L = 25

Next we have to find the quantity

Q = 1^1/2 * L^1/2 =

1^1/2 * (25)^1/2 =

= 5

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Answer:

\(34 < 2x \\ 34 \div 2 < 2x \div 2 \\ 17 < x \\ x = 18 \\ 19 \\ 20...\)

Infinitely many position vectors with length 2 in xyz-space are orthogonal to the nonzero position vector v. (D)

A position vector in xyz-space is a vector that starts at the origin and ends at a point in xyz-space. The length of a position vector is the distance from the origin to the point it ends at.

If we want to find position vectors with length 2 that are orthogonal (perpendicular) to a given nonzero position vector v, we can use the dot product.

Let w be a position vector with length 2 that is orthogonal to v. Then, the dot product of v and w must be zero, since they are orthogonal. That is, v · w = 0. Since the length of w is 2, we can write w as 2u for some unit vector u. Thus, v · w = v · (2u) = 2(v · u) = 0.

This means that v and u are orthogonal as well, since the dot product of two vectors is zero if and only if they are orthogonal.

There are infinitely many unit vectors u that are orthogonal to v, and therefore, there are infinitely many position vectors with length 2 that are orthogonal to v. Therefore, the answer is (d) infinitely many.

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Answer:

No

Yes

Step-by-step explanation:

Let's find the inclination of the 3 lines.

m:

((-4) -3)/(0 - (-4))

-7/4

n:

((-2) -2)/(3 - 1)

-4/2

-2

k:

(1 -(-3)/(4 -(-3)

(1 +3)/4 +3

4/7

Okay, we find the inclination of all the three lines. For two lines be parallel, they have to have the same inclination. The inclination of m = -7/4 and the inclination of n = -2, so they're not parallel. And now, to know if m is perpendicular to k, they inclination have to be the opposite of the inverse of each other, so it means that they have to have opposite signals, and they need to be inverted fractions (for example a/b are inverted to b/a), and they are these two things: m = -7/4 and n = 4/7, so they're perpendicular

Answer:

No, the slopes are not equal.

Yes, the slopes are negative reciprocals.

Step-by-step explanation:

Just did it on edge.

We are increasing every professor's salary by 4000, let this new salary be Yi for every professor then mean of new salary Y will be

Y = 1/n∑Yi

Y  = 1/n∑(Xi + 4000)

Y  = 1/n(∑Xi + ∑4000/n)

Y  = X + 4000

Median Xm is the middle most value of the Professor's old salary, since new salary is

            Yi = Xi + 4000

then new median salary Ym will be

            Ym = Xm + 4000

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Answer:

Step-by-step explanation:The mean and Median salary would increase by $4,000.

Let sum of the salaries be n1+n2+n3+.......... +n30

   Mean = sum of observation / no. of observation

Thus,

   Initial mean, M1 = n1+n2+n3+.......... +n30 / 30

When $4,000 is added to every salary 4000 is added 30 times to the sum.

Thus,

  New mean, M2 = n1+n2+n3+.......... +n30 +( 4000 * 30)

                                                30

                           = M1 + ( 4000 * 30)

                                              30

  Thus,         M2 = M1+ 4000

Therefore, The mean salary increase by $4,000.

We know Median of even number of observation =  [(n/2)th term + ((n/2) + 1)th term]/2

Here n/2th term is n15 and (n/2 +1)th term is n16

Thus,

    Initial Median, Median 1 = n15 + n16  

                                                     2

When $4,000 is increased in each salary

    New Median, Median 2 = n15 + 4000 + n16 + 4000

                                                                 2

                                         = Median 1 + 2 * 4000

                                                                    2

Thus,                  Median 2= Median 1 + 4000

Therefore, The median salary increases by $4,000

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The perimeter of triangle JKL is  determined as 68 units.

The perimeter of triangle JKL is calculated as follows;

The perimeter of triangle JKL is the sum of all the distance round the triangle.

Perimeter = length JK + length LK + length JL

AL = CL = 12

Length LK = CL + CK = 12 + 8 = 20

JA = JB = 14

KB = CK = 8

Length JK = JB = KB = 14 + 8 = 22

Length JL = JA + AL = 14 + 12 = 26

The perimeter of triangle JKL is calculated as;

Perimeter = 20 + 22 + 26

Perimeter = 68 units.

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x = 10 is the solution to the equation

Here, we want to find the value of x.

To find the value of x, we need to bring like terms together.

Answer:

x=10

Step-by-step explanation:

24-4=20 divided by 2 is 10

Answer:

h ≈ 9.9 cm

Step-by-step explanation:

By applying tangent rule for the given angle in the given right triangle,

tan(51°) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(51°) = \(\frac{h}{8}\)

h = 8 × tan(51°)

h = 9.879

h ≈ 9.9 cm

Therefore, measure of side 'h' is 9.9 cm.

Check the picture below.

\(\stackrel{\textit{\Large Areas}}{\stackrel{rectangle}{(5)(3)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(4)(3)}~~ + ~~\stackrel{semi-circle}{\cfrac{1}{2}\pi (2)^2}}\implies 15~~ + ~~6~~ + ~~2\pi \stackrel{using~\pi =3.14}{\implies 27.28}\)

Step-by-step explanation:

Para hacer las porciones para 32 personas, multiplique cada cantidad de ingrediente por 4 ya que la receta proporciona 8 porciones y 8 * 4 = 32

Papa seca = \(\frac{1}{2} *4\)

                     = 2 papas secas

Cerdo = \(\frac{1}{2} *4\)

       = 2 kg de carne de cerdo

Cebollas = 1 * 4

            = 4 cebollas grandes

Aji panca = 3 * 4

               = 12 cucharadas de aji panca

Ajo molido = \(1\frac{1}{2} *4\)

                       = \(\frac{3}{2} *4\)

                       = 6 cucharadas de ajo molido

Sal = 1 * 4

      = 4 cucharadas de sal

Answer:

16in^2

Step-by-step explanation:

4 x 4

The value of x in sequence of number is 10.

Here, first term of sequence is x and each term there after is twice the previous term. Also Fifth term is 160.

What is geometric series?

Geometric series is an infinite series of the form:

\(a+ar+a r^{2} +ar^{3} +..........\)

where r is known as common ratio.

Now, first term is x and each term there after is twice the previous term.

So the series will be;

x , 2x , 4x , 8x, ..........

Clearly this series is geometric series with common ratio 2.

And the nth term of geometric series is \(ar^{n-1}\)

⇒ fifth term is 160

\(ar^{5-1} = 160\\ar^{4} = 160\\a 2^{4} =160\\a=\frac{160}{16} \\a=10\)

Here, first term is x.

The value of x in sequence of number is 10.

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Answer:

C

Step-by-step explanation:

use 0 and 3 for example:

replace x with 0 give you 2*0=0

add 0 with 3 and you get 3

The volume of the box is 72 cubic feet.

We have,

To find the volume of the box, we need to multiply its length, width, and height.

Given:

Length = 4 ft

Breadth = 6 ft

Height = 3 ft

The volume of the box is:

Volume = Length x Breadth x Height

Volume = 4 ft x 6 ft x 3 ft

Volume = 72 cubic feet

Therefore,

The volume of the box is 72 cubic feet.

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Answer:

3g means 3*g, but g^3 means g*g*g

Step-by-step explanation:

Answer:

The difference between each of those expressions is that one is that the one on the left is 3 x g. while the one on the right is g x g x g. if that makes sense!

Step-by-step explanation:

The difference in commission for selling goods worth Rs. 20 lakhs and Rs. 30 lakhs is Rs. 7,500.

The commission on sales worth Rs. 20 lakhs would be:

1% of (20 lakhs) = 0.01 x 20,00,000 = Rs. 20,000

The commission on sales worth Rs. 30 lakhs would be:

1% of (25 lakhs) + 1.5% of (5 lakhs) = (0.01 x 25,00,000) + (0.015 x 5,00,000) = Rs. 27,500

The difference in commission between the two sales would be:

Rs. 27,500 - Rs. 20,000 = Rs. 7,500

Therefore, the difference in commission for selling goods worth Rs. 20 lakhs and Rs. 30 lakhs is Rs. 7,500.

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(x1 , y1) = (-4, -2)

(x2 , y2) = (5 , -2)

A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation.

How to Translate a Triangle

Step 1: Identify the coordinates of each of the vertices of the triangle.

Step 2: Translate each point by adding the horizontal translation value to the x-coordinate of each vertex and the vertical translation value to the y-coordinate of each point. For these translations, add a negative number if the horizontal translation is to the left or if the vertical translation is downward.

Step 3: Plot the three translated points and draw the triangle by connecting each pair of points with a straight line.

Coordinates are written as (x, y) meaning the point on the x axis is written first, followed by the point on the y axis.

Given data

(x1 , y1) = (-4, -2)

(x2 , y2) = (5 , -2)

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Answer:60

Step-by-step explanation:a triangle always equals 180 so if you dived that by the three angles it equals 60 degrees

X = 7  divid both sides

8x = 56

8x/8 and 56/8 .





Answer:

Function decreasing: where x is (-4; 0) and (2; 4)

Function increasing: where x is (0; 2)

Step-by-step explanation:

Decreasing is the part in graph where function goes down. Increasing is the part where function goes up.

Answer:

13/25 is the correct answer

Step-by-step explanation:

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To gain your original salary again you need 23.46% increment

Lets say your salary was $100

Given that doing work fever hours per week resulted 19% decrease in your pay

Salary after deduction 19% = 100 - (100  × 19/100)

cancelling 100 from numerator and denominator

= 100 - ( 19) = $81

To gain original salary you need total amount = Original salary - Deducted salary

= 100 - 81

= $19

Percentage of $19 of $81 = (19/81)  × 100

= 1900 / 81

= 23.46 %

23.46% increment in pay would you have to receive in order to gain your original salary again.

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Answer:30%

Step-by-step explanation:you divide 18 by 100 and then multiply that by 30 and it gives you 5.4 which is close to 5 players. So 30% is the answer

The bearing of R from P is found using trigonometry and the angle addition formula. The bearing is 210 degrees, with a distance of 3 from Q and 5 from P.

To find the bearing of R from P, we can use the bearings and distances given in the problem. Let P be a point, and line segment from P to Q with length 5. Then, from Q to R with length 3.

The angle of bearing of Q from P is 150 degrees, which means that the angle between the line segment PQ and the North direction is 150 degrees. We can say this angle as ∠PQ North. Similarly, the bearing of R from Q is 60 degrees, so we can say the angle ∠Q R North as 60 degrees.

Use trigonometry to find the angle between PR and the North direction. We can use the Law of Cosines to find the angle between PR and PQ:

cos(∠PQR) = (5^2 + 3^2 - PR^2) / (2 * 5 * 3)

cos(∠PQR) = (25 + 9 - PR^2) / 30

cos(∠PQR) = (34 - PR^2) / 30

Solving for cos(∠PQR), we get:

cos(∠PQR) ≈ 0.388

Taking the inverse cosine, we get:

∠PQR ≈ 67.6 degrees

Use the angle addition formula to find the bearing of R from P. Since we know the bearings of Q from P and R from Q, we can use the angle addition formula to find the bearing of R from P:

∠P R North = ∠PQ North + ∠Q R North

∠P R North = 150 degrees + 60 degrees

∠P R North = 210 degrees

Therefore, the bearing of R from P is 210 degrees (correct to the nearest degree).

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Based on the coordinates of the vertices of the quadrilateral ABCD, the perimeter is 18.64 units and the area is 18.96 units².

First, find the distance between the points of the quadrilateral:

Distance formula is:

d = √( (x₂ - x₁)² + (y₂ - y₁)²)

Distance for AB:

= √( (6 - 3)² + (5 - 5)²)

= 3

Distance for BC:

= √( (4 - 6)² + (-1 - 5)²)

= 6.32

Distance of CD:

= √( (1 - 4)² + (-1 - (-1)²)

= 3

Distance of AD:

= √( (1 -3)² + (-1 -5)²)

= 6.32

Perimeter is:

= 6.32 + 6.32 + 3 + 3

= 18.64 units

The area of the quadrilateral would be:

= 3 x 6.32

= 18.96 units²

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Answer:

a - b and a + b.

Step-by-step explanation:

Let's say the area of a rectangle is represented by the expression 100a^2 - 49b^2.

According to an algebraic formula, a^2 - b^2 = (a - b) * (a + b) = a^2 - ab + ab - b^2.

In this case, the square root of 100 is 10, and the square root of 49 is 7. That means that we have (10a - 7b) * (10a + 7b).

We can check that by doing... (10a - 7b)(10a + 7b) = 100a^2 - 70ab + 70ab - 49b^2 = 100a^2 - 49b^2.

Since it matches to the expression given, the expressions that represent the dimensions of the rectangle are (a - b) and (a + b).

Hope this helps!

Answer:

x = 2

Step-by-step explanation:

14x = 28

x = 28/14

x = 2

Hope it helps ⚜

Answer:

\(solution;\\here,\\14x=28\\or,x=28/14\\x=2\\\)hope ,it will help you:)

Step-by-step explanation: