What is the sum of the polynomials? (–x2 + 9) (–3x2 – 11x + 4) a. –4x2 – 2x + 4 b. –4x2 – 11x + 13 c. 2x2 + 20x + 4 d. 2x2 + 11x + 5

The area of triangle PQR is 25/2 * √(5).

In geometry, a triangle is a two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and has many important properties and applications.

The sum of the interior angles of a triangle is always 180 degrees, and the exterior angles sum to 360 degrees. The three sides of a triangle can be classified according to their lengths and their angles.

To find the area of triangle PQR, we can use the formula:

Area = (1/2) * base * height

where the base and height are the lengths of two sides of the right triangle that meet at a 90-degree angle.

We can use the distance formula to find the lengths of the sides of triangle PQR:

PQ = √[(x_Q - x_P)² + (y_Q - y_P)²] = √[(-1 - (-6))² + ((-1) - 9)²] = √[25 + 100] = 5√(5)

PR = √[(x_R - x_P)² + (y_R - y_P)²] = √[(-9 - (-6))² + (5 - 9)²] = √[9 + 16] = 5

QR = √[(x_R - x_Q)² + (y_R - y_Q)²] = √[(-9 - (-1))² + (5 - (-1))²] = √[64 + 36] = 2√20) = 4√(5)

Since triangle PQR is a right triangle, the base and height are PQ and PR, respectively. Therefore, the area of triangle PQR is:

Area = (1/2) * PQ * PR = (1/2) * 5√(5) * 5 = 25/2 * √(5)

So the area of triangle PQR is 25/2 * √(5).

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Step-by-step explanation:

See image

Step-by-step explanation & Answer

f(x) = x² - 4x -5, factored is simply f(x) = (x - 5)(x + 1).

If you zero out f(x), namely 0=(x-5)(x+1), that simply gives you the zeros of 5 and -1.

Now, from ----- -1------0---------------------------------5,

Notice from -1 to 5, there are 6 units, and half of 6 is 3, so, the half-way is 3 units away from either zero.

We can get to the half-way point by -1 + 3, or 2, x = 2, that's where the vertex is at, but you already knew that, and of course the y-coordinate is at f(2) = (2)² - 4(2) - 5, which is -9, so the vertex is indeed at (2, -9).

Well, surely you can, simply use the zeros location, -1 and 5, and draw a bowl between them, with the bottom of the bowl at 2, -9.

Answer:

1/2 it’s like flipping a coin it can either come up heads or tails.

Step-by-step explanation:

The probability that the other child is a daughter is 1/2 or 50%.

The gender of each child is independent, and there are two equally likely outcomes for each child (male or female). Therefore, the probability of having a son is 1/2 and the probability of having a daughter is also 1/2. Since one child is already known to be a son, that does not affect the probability of the other child being a daughter. Thus, the probability of having a daughter as the other child is also 1/2 or 50%.

Therefore, the answer to the question is that the probability that the other child is a daughter is 1/2 or 50%

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Answer:

the value for p will be 162

Answer:

I think it will help u (:

Step-by-step explanation:

Assuming the given measurement is the diameter of the sphere, we can find the radius as follows:Radius (r) = Diameter / 2 = 7.2 / 2 = 3.6 cmThe formula for the volume of a sphere is:V = (4/3) * π * r³Substituting the values, we get:V = (4/3) * 3.14 * (3.6)³

V = 4.19 * 46.656

V = 195.4 cm³Rounding this to the nearest tenth, we get:V ≈ 195.4 cm³Therefore, the volume of the sphere is approximately 195.4 cm³.

Answer: To have infinitely many solutions, the equation must simplify to a true statement, such as 0=0.

So, let's simplify the given equation:

4(x-4) = 4x + ?

We need to choose a value for the constant on the right-hand side so that the equation simplifies to a true statement.

We can start by distributing the 4 on the left-hand side:

4x - 16 = 4x + ?

Now we can see that the 4x terms cancel out, leaving:

-16 = ?

We can choose any value for the constant on the right-hand side, and the equation will be true. For example:

-16 = -16

So the complete equation with infinitely many solutions is:

4(x-4) = 4x - 16

Step-by-step explanation:

Answer:

Isabelle is taking a survey to find the most popular music group of students in her community. Which of these is not a way for her to get a representative sample of this information?

 ask every tenth student she sees ac a concert

 ask every fifth student entering her school in the morning

 ask every third student she encounters at the mall

 ask every student at a local movie theater

Step-by-step explanation:

After answering the presented question, we can conclude that As a expression result, the laptop costs $2500 without GST.

An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

To get the laptop's price without GST, divide the inclusive price by (1 + GST rate as a decimal).

As a result, the laptop's price without GST can be estimated as follows:

Price excluding GST = Price including GST / (1 + GST rate as a decimal)

Price excluding GST = 2675 / (1 + 0.07)

Without GST, the price is $2500.

As a result, the laptop costs $2500 without GST.

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The recursive and explicit formulae of the given arithmetic expression are:

Recursive formular = [tex]a_{n+1} = a_{n-13}[/tex]

Explicit formular is Tn = 75 - 13n

You can determine the value of any term in a series by using an explicit formula. The integers are divided into the natural numbers, which are 1, 2, 3, 4, and so on. If you know the value of the (n-1)th term in a sequence, you may use a recursive formula to determine the value of the nth term in the sequence. Recursive formulas give the value of a specific phrase depending on the previous term, whereas explicit formulas give the value of a specific term based on the position.

Given:

a1 = 52

a2 = 75 = 52 - 13 = a1 - 13

Recursive formular = [tex]a_{n+1} = a_{n-13}[/tex]

a = 52, d = -13

F(11) = a + (n - 1)d = 52 + (n - 1)-13 = 52 - 13n + 13 = 75 - 13n

Explicit formular is Tn = 75 - 13n

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The arithmetic sequence has a common difference of 23, recursive rule of this sequence is xₙ = [tex]x_{n-1}[/tex] + 23 and explicit rule is xₙ = 23n + 29. The 11th term is 282.

An arithmetic sequence is a mathematical progression in which each term is generated by adding a constant value to the preceding term, with the exception of the first term. This constant value is known as the common difference, and it governs the pattern of the sequence. There are two types of arithmetic sequences, one is an increasing sequence and the other is a decreasing sequence. Increasing sequence is obtained if the common difference is a positive number. Decreasing sequence is obtained if the common difference is a negative number.

The general format of the recursive rule is xₙ = [tex]x_{n-1}[/tex] + d, where xₙ is the nth term, [tex]x_{n-1}[/tex] is the (n-1)th term and d is the common difference of the arithmetic sequence.

In the given sequence x₁ = 52 and x₂ = 75

Common difference can be calculated by subtracting first term from second term = x₂ - x₁ = 75 - 52 = 23

Hence recursive rule for this sequence is xₙ = [tex]x_{n-1}[/tex] + 23

The general format of explicit rule is xₙ = x₁ + (n-1) × d.

For this sequence it is xₙ = x₁ + (n-1) × 23 = 52 + 23n - 23 = 23n + 29

To find f(11) we can use the explicit rule

f(11) = 23 × 11 + 29 = 282

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The car wheel will make approximately 840 revolutions as the car travels a distance of one mile.

To calculate the number of revolutions that a car wheel of diameter 24 in. will make as the car travels a distance of one mile, we need to use the formula:

number of revolutions = distance traveled / distance per revolution

The distance traveled is given in miles, and we need to convert the diameter of the wheel, given in inches, to the distance per revolution in miles.

The diameter of the wheel is 24 in., which means the radius is 12 in. The distance per revolution is equal to the circumference of the wheel, which is given by the formula:

circumference = 2 * pi * radius

Substituting the values, we get:

circumference = 2 * pi * 12 in. = 75.4 in.

To convert this to miles, we divide by 63,360 inches per mile:

distance per revolution = 75.4 in. / 63,360 in./mi = 0.00119 mi/rev

Now, we can calculate the number of revolutions as:

number of revolutions = 1 mi / 0.00119 mi/rev ≈ 840 revolutions

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The number of electoral votes does the state of nevada have in the electoral college is 6 electoral votes.

Nevada will be having a total of 6 electoral votes in the electoral college. The number of electoral votes for each state is equal to the total number of its members in Congress, which will be including its representatives in the House of Representatives and its two senators.

Therefore, since Nevada has 4 members in the House of Representatives and 2 senators, the state has a total of 6 members in Congress, and hence it can be concluded that a total of 6 electoral votes will be there in the Electoral College.

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Potentially hazardous cold food that requires time and temperature control for safety (TCS food) should not be kept at a temperature above 41°F (5°C) for more than 6 hours total time, according to the FDA Food Code.

According to the U.S. Food and Drug Administration (FDA) Food Code, potentially hazardous cold food that requires time and temperature control for safety (TCS food) should not be kept at a temperature above 41°F (5°C) for more than 6 hours total time.

After that, the food must be thrown out to prevent the growth of harmful bacteria. These food are harmful to the health of consumer.

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Let Ramanujan pick a complex number $a+bi$, where $a$ and $b$ are real numbers. Then the product of the numbers chosen by Ramanujan and Hardy is:

(

�

+

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)

(

5

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3

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)

=

5

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+

3

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+

5

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3

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2

=

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5

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+

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−

3

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(a+bi)(5+3i)=5a+3ai+5bi+3bi

2

=(5a+3b)+(5b+3a)i−3b

We want this product to be equal to $32-8i$. Equating the real and imaginary parts gives us two equations:

5

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+

3

�

=

32

(1)

5a+3b=32(1)

5

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+

3

�

=

−

8

(2)

5b+3a=−8(2)

We can solve this system of equations to find $a$ and $b$. Multiplying equation (1) by 3 and equation (2) by 5, and subtracting the resulting equations gives:

15

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+

9

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−

25

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−

15

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=

−

96

15a+9b−25b−15a=−96

Simplifying:

−

16

�

=

−

96

−16b=−96

Therefore, $b=6$. Substituting $b=6$ into equation (1) gives:

5

�

+

18

=

32

5a+18=32

Therefore, $a=2$. Thus, Ramanujan picked the complex number $2+6i$.

Based on the given conditions and informations provided, the complex number that was picked by thr Ramanujan is calculated to be  2+6i.

Let Ramanujan pick a complex number a+bi, where a and b are real numbers. Then the product of the numbers chosen by Ramanujan and Hardy is:

(a+bi)(5+3i) = 5a+3ai+5bi+3bi² = (5a+3b)+(5b+3a)i-3b

We want this product to be equal to 32-8i. Equating the real and imaginary parts gives us two equations:

5a+3b=32 (1)

5b+3a=-8 (2)

We can solve this system of equations to find a and b. Multiplying equation (1) by 3 and equation (2) by 5, and subtracting the resulting equations gives:

15a+9b-25b-15a=-96

Simplifying:

-16b=-96

Therefore, b=6. Substituting b=6 into equation (1) gives:

5a+18=32

Therefore, a=2. Thus, Ramanujan picked the complex number 2+6i.

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Answer:

(- 12, - 16 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

(- 12, 16 ) → (- 12, - 16 )

If a point's preimage is P(x, y), then its image after a dilation with a scale factor of k and centered at the origin (0, 0) is P'(kx, ky).

The set of all points in a function's domain that correspond to a given point in the range is known as the preimage of a point in mathematics.

Formally, let f be a function that goes from a set A to a set B, and let y be a point in B. The preimage of y is the set of all points x in A where f(x) = y, or the set of all points in the domain that the function maps to the given point in the range.

If the preimage of the point P has facilitates (x, y), and the expansion focused at the beginning with a scale component of k is applied, then the directions of the picture point P' can be tracked down utilizing the accompanying recipe:

The x- and y-coordinates of P' are determined by multiplying the corresponding coordinates of the preimage point P by the scale factor k; consequently, the coordinates of the image point P' following the dilation with the origin centered on k would be (kx, ky).

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Complete question: If P(x,y) is the preimage Of a point, then it’s image after a dilation centered at the origin (0,0) with the scale factor k is the point P'.

What are the coordinates of point P'?

Answer: Let's call the length of the slide "x". From the problem, we know that Kenji walks 5 feet after he slides down and climbs 8 feet to get to the top of the slide again. This means that the total vertical distance he traveled (height of the slide) is equal to 5 + 8 = 13 feet.

Using the Pythagorean theorem, we can find the length of the slide:

x^2 = 13^2 + h^2

where h is the height of the slide.

We know that h = 13 feet, so we can substitute that into the equation:

x^2 = 13^2 + 13^2

x^2 = 338

x ≈ 18.4 feet

Therefore, the length of the slide is approximately 18.4 feet. Rounded to the nearest tenth, this is 18.4 feet.

Step-by-step explanation:

The minimum value of multiplication of AxB is 245,376.72, which is obtained when A = 450 (rounded down from 495) and B = 545 (rounded up from 537.03).

Calculating the sum of two or more numbers is the procedure of multiplication. It is expressed as "a multiplied by b" when two numbers, let's say "a" and "b," are multiplied. Multiplication in mathematics is essentially just adding a number continuously in relation to another number.

The given values are:

A = 900 rounded to the nearest 10 = 900

B = 90.7 rounded to 1 decimal place = 90.7

We need to find the minimum value of AxB.

Multiplying A and B directly, we get:

AxB = 900 x 90.7 = 81,630

To find the minimum value of AxB, we can use the concept of AM-GM inequality which states that for two positive real numbers a and b, their arithmetic mean (AM) is greater than or equal to their geometric mean (GM):

AM ≥ GM

or

(a+b)/2 ≥ √(ab)

Applying this to our values of A and B, we get:

(A+B)/2 ≥ √(AxB)

Substituting the given values of A and B, we get:

(900 + 90.7)/2 ≥ √(AxB)

Simplifying this, we get:

495.35 ≥ √(AxB)

Squaring both sides, we get:

245,376.72 ≥ AxB

Therefore, the minimum value of multiplication of AxB is 245,376.72, which is obtained when A = 450 (rounded down from 495) and B = 545 (rounded up from 537.03).

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Complete question:

A = 900 rounded to the nearest 10

b = 90.7 rounded to 1 DP

Find the minimum of a x b​

a) 1)  x=0 or x=-2 ,    2) x=0 or x=2    3)  x=0 or x=-2    4) x=0 or x=-2  

b) 1) x=0 or x=-5/3   2)x=0 or x=5/3   3) x=0 or x=5/3  4) x=0 or x=-5/3 .this equations can be solved by factorization and simplification.

what is factorization?

Factorization is the process of expressing a given number or algebraic expression as a product of two or more factors. The factors are the numbers or expressions that when multiplied together result in the original number or expression.

In the given question,

a) x²+2x=0:

x(x+2)=0

x=0 or x=-2

x²-2x=0:

x(x-2)=0

x=0 or x=2

x²+2x=0:

x(x+2)=0

x=0 or x=-2

-x²-2x=0:

-x(x+2)=0

x=0 or x=-2

b)

3x²+5x=0:

x(3x+5)=0

x=0 or x=-5/3

3x²-5x=0:

x(3x-5)=0

x=0 or x=5/3

-3x²+5x=0:

x(-3x+5)=0

x=0 or x=5/3

-3x²-5x=0:

x(-3x-5)=0

x=0 or x=-5/3

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Answer:

It is 9 1/4

Step-by-step explanation:

This is because 9 stays the same as the whole number, and 25 divided by 100 is 4. To check our work we can multiply 25 by 4 to get 100. Now we know we have the right answer.

"The beautiful part of learning is that no one can take it away from you" (:

The total surface area of the triangular prism is 200 square inches.

A triangular prism is a three-dimensional geometric shape that consists of two parallel triangular bases connected by three rectangular faces.

To find the surface area of the triangular prism using the net provided, we need to find the area of each face and then add them together.

Using formulas,

Area of rectangle= [tex]length\times width[/tex] square unit.

Area of triangle = [tex]\frac{1}{2}\times Base \times Height[/tex] square unit.

The blue rectangle has a length of 5 inches and a width of 4 inches, so its area is

=> 5 x 4 = 20 square inches.

The orange rectangle has a length of 12 inches and a width of 4 inches, so its area is

=> 12 x 4 = 48 square inches.

The red rectangle has a length of 13 inches and a width of 4 inches, so its area is

=> 13 x 4 = 52 square inches.

The green triangles have a base of 12 inches and a height of 5 inches, so each triangle's area is

=> [tex]\frac{1}{2}\times12\times5[/tex]=  30 square inches.

To find the total surface area, we add the area of each face:

=> 20 + 20 + 48 + 52 + 30 + 30 = 200 square inches.

Therefore, the surface area of the triangular prism is 200 square inches.

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Answer:

x=2

Step-by-step explanation:

33=32x-31

64=32x

2=x

Answer:  [tex]x = 2[/tex]

Answer:

right angles

Step-by-step explanation:

The required area of the shape is 2014.88 sq units.

Region is the proportion of a locale's size on a surface. The region of a plane district or plane region alludes to the region of a shape or planar lamina, while surface region alludes to the region of an open surface or the limit of a three-layered object.

Given shape consist of a square and four half circles.

Radius of circle = 14 units, side length of the square is 28 units

Area of the shape = are of square + area of four half circles

= 28×28 + 4(π(14)²)/2

= 784 + 2π(14)²

= 784 + 1230.88

= 2014.88 sq units

Thus, required area of the shape is 2014.88 sq units.

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For the point (5, 4) to the directrix, the distance to the directrix is equal to the distance to the focus. For the other points on the list, the distance to the directrix is equal to the distance to the focus. The distance to the directrix is equal to the distance to the focus, we can conclude that (-1, 5) is on the parabola.

A perfect, U-shaped curve is referred to by the term parabola in mathematics. It is described as the collection of all plane points that are equidistant from a focus and a fixed broadband (the directrix). The point where the parabola's curve changes direction is known as its vertex, and the line that runs through it and is perpendicular toward the directrix is known as its axis of symmetry. The behavior of electromagnetic waves, projectile motion, reflector and antenna forms, and other real-world phenomena are frequently modelled using parabolas.

To determine whether a point is on a parabola with a given focus and directrix, we can use the definition of a parabola: a parabola is the set of all points that are equidistant to the focus and the directrix.

In this case, the focus is the point (0, 2) and the directrix is the line y = -2.

Let's first consider the point (5, 4). We can find the distance from this point to the directrix by finding the distance from the point to the line. The formula for the distance from a point (x1, y1) to a line [tex]Ax + By + C = 0[/tex] is:

[tex]|Ax1 + By1 + C| / \sqrt(A^2 + B^2)[/tex]

In this case, A = 0, B = 1, and C = -2, so the equation of the directrix is y = -2, which can be written as [tex]0x + 1y - 2 = 0.[/tex] Plugging in (5, 4), we get:

[tex]|0(5) + 1(4) - 2| / \sqrt(0^2 + 1^2) = 6[/tex]

So the distance from (5, 4) to the directrix is 6.

Next, we can find the distance from (5, 4) to the focus (0, 2):

[tex]\sqrt((5-0)^2 + (4-2)^2) = \sqrt(29)[/tex]

Since the distance from (5, 4) to the directrix is not equal to the distance from (5, 4) to the focus, we can conclude that (5, 4) is not on the parabola.

We can repeat this process for each point on the list. For the point (-1, 5), we get:

Distance to directrix: |-1 - 2| / 1 = 3

Distance to focus: [tex]\sqrt((-1-0)^2 + (5-2)^2) = \sqrt(26)[/tex]

Since the distance to the directrix is equal to the distance to the focus, we can conclude that (-1, 5) is on the parabola.

Similarly, we can check the other points on the list and find that the points (4, 3), (2, 1), (1, -2), (2, -1), (4, -3), and (5, -4) are also on the parabola. The points (3, 5), (6, 7), (8, 0), and (0, 8) are not on the parabola.

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Answer:

Here is the correct answer:

15 m, 20 m, 25 m

Answer:

In the images

Hope this helps!

Step-by-step explanation:

Clockwise is the direction the arrow is pointing, counter-clockwise is the other direction.

Answer:

Step-by-step explanation:

125,000 x 16% = $20,000

(23%) 28,750 + (8%) 10,000 + (9%) 11,250 + (12%) 15,000 + (16%) 20,000 + (19%) 23,750 + (13%) 16,250 = $125,000