Choose the two steps that are part of factoring the trinomial 6x2 + 17x + 5 by grouping.

An expression for the volume V of the rectangular prism in terms of its width w is V = ( 3W³ + 12W² ) Units³

Given data :

we know that

The volume of a rectangular prism is equal to

V = LWH ------> Equation A

where

L is the length

W is the width

H is the height

we know that

L = 3W ----> Equation B

H = W + 4 ------> Equation C

substitute equation B and equation C in equation A

V = ( 3W ) (W) ( W + 4 )

Apply distributive property

V = ( 3W³ + 12W² ) units³

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Answer:

[tex]65.1\text{cm}^2[/tex]

Step-by-step explanation:

Area of Rectangle

[tex]A=bh=(8\text{cm})(5\text{cm})=40\text{cm}^2[/tex]

Area of Semicircle

[tex]\displaystyle A=\frac{\pi r^2}{2}=\frac{\pi (4\text{ cm})^2}{2}=8\pi\text{ cm}^2[/tex]

Combined Area

[tex]A_{total}=A_{rectangle}+A_{semicircle}=40\text{cm}^2+8\pi\text{cm}^2\approx65.1\text{ cm}^2[/tex]

Answer:

he is not because triangles can be different sides but they always have to equal 180 if it's a right triangle but if it does not it's a ln acute or obtuse triangle

The calculation would have three significant figures, since both original numbers have three significant figure.

The number of significant figures in a calculation is determined by the number of significant figures in the original numbers used in the calculation. For example, if we have the calculation 3.14 + 2.7 = 5.84, the answer will have three significant figures because the original numbers, 3.14 and 2.7, each have three significant figures.

In general, significant figures are determined by counting all non-zero digits, plus any zeros that come between non-zero digits, such as in the numbers 10.0 and 0.07. If a number is a decimal, the zeros after the decimal point are also significant, such as in the number 0.07. Zeros that come before the first non-zero digit are not significant, such as in the number 0.0007.

In the above example, the calculation would have three significant figures, since both original numbers have three significant figures.

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Complete quetion:

What is the number of significant figures in the calculation 3.14 + 2.7 = 5.84?

Answer:

below

Step-by-step explanation:

x^2 - 19x    ± 39       take 1/2 of the 'x' coefficient square it and add and subtract it

x^2 - 19x +  90.25    - 90.25   ±39

(x-9.5)^2   - 90.25 ±39     so I guess the answer is  90.25

The different ways of arranging these categories will be 720.

The factor of n is given as the production of the number n, (n - 1), (n - 2)... and 1. Then the factorial of n is given as,

n! = n x (n - 1) x (n - 2) x ... 3 x 2 x 1

We have the group letter (A-F). Then the number of letters is given as,

n = 6 (A, B, C, D, E, F)

Then the different ways of arranging these categories will be given as,

⇒ 6!

⇒ 6 x 5 x 4 x 3 x 2 x 1

⇒ 720

The different ways of arranging these categories will be 720.

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The probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

The problem involves exponential distribution which is a standard continuous distribution. The probability density function of this distribution is given by -

f(x) = θe^(-θx) ; where θ is a parameter and characteristic of the distribution, x is the random variable.

Also, the mean for an exponential distribution is given by u = 1/θ .

In the question it is 22 seconds.

So, the value of θ is 1/22.

Now, we have to find P(X<30) where X is the random variable denoting the calling time in seconds.

P(X<30) is nothing but F(x) at x = 30 seconds, i.e. cumulative distribution function. For an exponential distribution , F(X) is given by -

P(X<x)= F(X) = 1- e^(-θ x) , where x>0.

Putting θ = 1/22 and x= 30 in F(X) , we get -

F(X) = 1-e[(-1/22)30] = 1- 0.2555 = 0.7445 which is P(X<x) = P(X<30) = 0.7445.

So, the probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

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The probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

The problem involves exponential distribution which is a standard continuous distribution. The probability density function of this distribution is given by -

f(x) = θe^(-θx) ; where θ is a parameter and characteristic of the distribution, x is the random variable.

Also, the mean for an exponential distribution is given by u = 1/θ.

In the question, it is 22 seconds.

So, the value of θ is 1/22.

Now, we have to find P(X<30) where X is the random variable denoting the calling time in seconds.

P(X<30) is nothing but F(x) at x = 30 seconds, i.e. cumulative distribution function. For an exponential distribution , F(X) is given by -

P(X<x)= F(X) = 1- e^(-θ x) , where x>0.

Putting θ = 1/22 and x= 30 in F(X) , we get -

F(X) = 1-e[(-1/22)30] = 1- 0.2555 = 0.7445 which is P(X<x) = P(X<30) = 0.7445.

So, the probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.

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The angle of depression is 32°.

The angle of depression is the angle formed when the item being seen is below the observer's level between the horizontal line and the line of sight of the observer.

The angle of depression is the angle formed by the horizontal axis and the downward axis of a line of sight. As an example, if you were perched on top of a hill or other structure and looked down at an object, you might determine the angle of depression. To measure these angles, a theodolite or a clinometer can be used. The maximum depression angle is 90 degrees. It can't be possible because any rational spectator would turn around the instant the object passed beneath him.

Due to the fact that AB is perpendicular to B and AD is the horizontal line of sight, we can conclude that AD AB (given).

∴ ∠DAB = 90°.

We can express this as DAB = DAC + BAC.

alternatively, 90° = ∠DAC + 58°

alternatively, ∠DAC = 90° - 58° = 32°.

The angle of depression is 32°.

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Answer:

Translation and dilation

Step-by-step explanation:

Translation because the points move spaces on the graph, and dilation because it gets bigger/smaller than the other.

The probability of getting 15 or more heads is :

P (Z > -0.18) = 1 - 0.4289 =  0.5714

Now, According to the question:

Normal Approximation to Binomial:

The normal distribution is used to approximate for the binomial distribution. The condition when binomial distribution is approximated to normal is that n should be large and probability should be close to 0.5

"Information available from the question"

n = 30

Probability, p(heads) = 1/2

Since sample size is large, we check for normal approximation.

np = 30(1/2) = 15

and, n(1 - p) = 30(1 - (1/2)) = 15 both are greater than 5, we use normal approximation.

Mean, μ = np = 30(1/2) = 15

Standard deviation, σ = [tex]\sqrt{np(1-p)}[/tex]

Standard deviation, σ = [tex]\sqrt{30(1/2)(1-1/2)}[/tex]

Standard deviation, σ =2.739

We have to find P (X ≥ 15). Using continuity correction, we deduct 0.5

P(X ≥ 15) = P(X > 14.5)

The respective Z-score with X = 14.5 is

Z = (x - μ)/ σ

Z = (14.5 - 15)/2.739

Z = -0.18

Now, we use z-tables to find probability greater than -0.18

P (Z > -0.18) = 1 - 0.4289 =  0.5714

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The expression to represent the total cost to have 'x' burritos delivered is y = 10x + 5

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

A linear expression can either have two variables or one variable. For example y = 2+3x is an example of linear expression with two variables where x and y are the variable.

Represent the total cost by y

A burritos cost $10 and with $5 delivery fee. This means that the delivery for one burrito will be for x' burrito

therefore y = 10x +5

therefore the equation for x burritos to be delivered is y = 10x+5

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Answer: y = 3x + 0 OR y = 3x

Step-by-step explanation:

M = slope. rise/run. compare the points on the line by how much they rise and how much they run. In this case it is 3/1 (3). the B = the y-intercept. (the point where the line meets the y line, in this case the line meets at the origin which is 0.)

4 over 6 because when you multiply 2 over 3 by 2 over two the answer is 4 over 6.

Answer: The answer is 3.

Step-by-step explanation:

Not all square matrices can be diagonalized. If there are just two eigenvectors (up to multiplication by a constant), then the matrix cannot be diagonalized.

A collection of integers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix, are the integers. In addition to several mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital uses as well.

Thus, Not all square matrices can be diagonalized. If there are just two eigenvectors (up to multiplication by a constant), then the matrix cannot be diagonalized.

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The given lines are parallel.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: The two equations given are  y = 3/8x +3 &  y = 3/8x + 8/3

We can observe that both the equations are in slope-intercept form we get

the slope of both the lines m=3/8

Two lines are parallel if their slopes are equal and they have different y-intercepts. In other words, perpendicular slopes are negative reciprocals of each other.

Clearly the two given lines have the same slope and different y intercept

Hence, The two lines are parallel

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Answer:

The slope of the line that passes through G(-3, 2) and H(7, 2) is 0.

Step-by-step explanation:

The slope of a line can be found using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

In this case, we have two points G(-3, 2) and H(7, 2):

m = (2 - 2) / (7 - (-3))

m = 0

Therefore, the slope of the line that passes through G(-3, 2) and H(7, 2) is 0.

The solutions of x = 0 or x = y  and y = 0 or y = 1 can then be found. Therefore, the solutions of the equation are (0,0), (0,1), (1,0), and (1,1).

x2 - xy + y2 - x = 0

x(x - y) + y(y - 1) = 0

x(x - y) = 0  and  y(y - 1) = 0

x = 0 or x = y  and y = 0 or y = 1

Therefore, the solutions are (0,0), (0,1), (1,0), and (1,1).

The equation z2 z 1 = 0, when written as (x,y)(x,y) (x,y) (1,0) = (0,0), can be manipulated to x2 - xy + y2 - x = 0. By factoring out the x and y terms, the equation can be rearranged to x(x - y) + y(y - 1) = 0. This then can be further simplified to x(x - y) = 0  and  y(y - 1) = 0. The solutions of x = 0 or x = y  and y = 0 or y = 1 can then be found. Therefore, the solutions of the equation are (0,0), (0,1), (1,0), and (1,1).

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The largest box that can be formed has a volume of 20 cubic feet.

Let's call the side length of the square cutout x. The original piece of cardboard measures 3 feet by 4 feet, so the dimensions of the piece of cardboard after the cutouts are made are (3 - 2x) by (4 - 2x).

When this piece is folded into a box, the length and width of the box will be (3 - 2x) and (4 - 2x) respectively. The height of the box will be x, as that is the height of the cutout squares.

The volume of the box can be found by multiplying the length, width, and height: V = (3 - 2x)(4 - 2x)x

We want to find the maximum volume, so we need to differentiate the expression for the volume and set it equal to zero, and then solve for x.

dV/dx = 2x(4 - 2x) - (3 - 2x)(2x) = 0

2x(4 - 2x) = (3 - 2x)(2x)

2x(4 - 2x) = 2x^2 - 6x^2

-4x^2 + 4x = 0

x(4 - x) = 0

x = 0 or x = 4

Since the side length of the cutout square cannot be negative, we reject x = 0 and keep x = 4. So, the maximum volume will occur when the side length of the cutout squares is 4 feet.

Substituting x = 4 into the expression for the volume, we find:

V = (3 - 2x)(4 - 2x)x = (3 - 2x)(4 - 2x) = (3 - 2x)(4 - 2x) = (3 - 8)(4 - 8) = -5 * -4 = 20 cubic feet

So, the largest box that can be formed has a volume of 20 cubic feet.

Therefore, The largest box that can be formed has a volume of 20 cubic feet.

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The largest box that can be formed has a volume of 20 cubic feet.

Let's call the side length of the square cutout x. The original piece of cardboard measures 3 feet by 4 feet, so the dimensions of the piece of cardboard after the cutouts are made are (3 - 2x) by (4 - 2x).

When this piece is folded into a box, the length and width of the box will be (3 - 2x) and (4 - 2x) respectively. The height of the box will be x, as that is the height of the cutout squares.

The volume of the box can be found by multiplying the length, width, and height: V = (3 - 2x)(4 - 2x)x

We want to find the maximum volume, so we need to differentiate the expression for the volume and set it equal to zero, and then solve for x.

dV/dx = 2x(4 - 2x) - (3 - 2x)(2x) = 0

2x(4 - 2x) = (3 - 2x)(2x)

2x(4 - 2x) = 2x² - 6x²

-4x² + 4x = 0

x(4 - x) = 0

x = 0 or x = 4

Since the side length of the cutout square cannot be negative, we reject x = 0 and keep x = 4. So, the maximum volume will occur when the side length of the cutout squares is 4 feet.

Substituting x = 4 into the expression for the volume, we find:

V = (3 - 2x)(4 - 2x)x = (3 - 2x)(4 - 2x) = (3 - 2x)(4 - 2x) = (3 - 8)(4 - 8) = -5 * -4 = 20 cubic feet

So, the largest box that can be formed has a volume of 20 cubic feet.

Therefore, The largest box that can be formed has a volume of 20 cubic feet.

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The fully factored form of the equation is 2x(x + 3) (2x - 1) that is option B.

Synthetic division and the rational root theorem can be used to demonstrate this. According to the rational root theorem, p must divide the constant term and q must divide the leading coefficient if p/q is a rational root of the polynomial f(x). The constant term in this example is -6, the leading coefficient is 4, and the potential rational roots are 1, 2, 3, and 6.

When we divide 4x3 + 10x2 - 6x by 2x - 1 using synthetic division, we arrive at the following result:

4x^3 + 10x^2 - 6x = (2x - 1) (2x^2 + 8x + 6)

We can then factor the remaining quadratic, 2x^2 + 8x + 6, as (x + 3)(2x + 2).

Thus, the completely factored form of 4x^3 + 10x^2 - 6x is:

4x^3 + 10x^2 - 6x = 2x(x + 3)(2x - 1)

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It follows that continuity at infinity is provided by having the same limit while approaching it from either side, i.e., the limit towards + and, which makes sense based on your understanding.

When a function can be extended to P1, it is said to be "continuous at infinity" (R).

Calculus's idea of the limit describes how a function behaves as its input gets closer to a particular value. As long as the limit is present, the value that f(x) approaches as x moves closer to c is represented by the notation lim(x -> c) f(x), which stands for the limit of a function at the point x = c.

You must demonstrate that all three of the following conditions are true in order to prove that a function f is continuous on an interval:

Every point in the interval has f specified, and the interval has f's bound.

For each and every > 0, there is a corresponding > 0 such that |x - c| implies |f(x) - f(c)| for all x and all c in the interval.

F is considered to be continuous on the interval if these requirements are met.

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Answer:

B. m2=50 and m3=50

Step-by-step explanation:

Angle m1 and angle m3 combined make a straight line, the angle of a straight line is 180°, so you can do 180-130=50 amd theres you m3. Looking at m1 and m2 its the same thing, we already know m1 is 130° so its the same equation, 180-130=50 and thats m2 angle.

Ps. My hand writing is bad but this is how I solved it.

The second graph is correct

Answer:

second graph

Step-by-step explanation:

just wanted to help the first person who answered get brainlist

Ohm's Law states that the current passing through a conductor is proportional to the voltage across the conductor, and inversely proportional to the resistance of the conductor.

Mathematically, this can be expressed as:

V = IR,

where V is the voltage, I is the current, and R is the resistance of the conductor. The resistance of a conductor is given by:

R = ρℓ/a,

where ρ is the resistivity of the material, ℓ is the length of the conductor, and a is the cross-sectional area.

From Ohm's Law, we can also derive an expression for the electric field inside the conductor:

E = V/ℓ = IR/ℓ = ρI/a

In the case of conductors 1 and 2, the voltage across both conductors is the same (v2 = v1), so the electric field in conductor 2 can be expressed as:

E2 = V2/ℓ2 = v1/(2ℓ1) = ρI2/a2 = (ρ/2a1)I2

Similarly, the electric field in conductor 1 can be expressed as:

E1 = V1/ℓ1 = v1/ℓ1 = ρI1/a1 = (ρ/a1)I1

Finally, the ratio of the electric fields in conductors 1 and 2 can be calculated as:

E2/E1 = (ρ/2a1)I2 / (ρ/a1)I1 = a1/2a1 = 1/2

So, the ratio of the electric fields, E2/E1, is equal to 1/2. This means that the electric field in conductor 2 is half the electric field in conductor 1, despite the fact that the voltage across both conductors is the same. This happens because the cross-sectional area of conductor 2 is twice that of conductor 1, which compensates for the fact that the length of conductor 2 is also twice that of conductor 1.

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The correct answer is option A which is the ordered pair of point P’ will be (8.75, 5.25).

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

here, we have,

If pentagon OPQRS is dilated by a scale factor of 7/4 from the origin, to create O’P’Q’R’S’, what is the ordered pair of point P’

Multiply the coordinates of point P by the scale factor 7/4  to get the coordinates of P'.

Given : P(-5,3)

P' (x,y) = P (-5 x 7/4 , 3 x 7/4)

           = P(-8.75, 5.25)

Therefore the correct answer is option A which is the ordered pair of point P’ will be (-8.75, 5.25).

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Answer:

each member's lunch costs $3.62

Step-by-step explanation:

$209.96 is the total cost of all the members' lunches.  To find the price of 1 lunch, divide 209.96 by 58. You will get 3.62.

Answer: 7

Step-by-step explanation:

a = 11, b = 7 a = 11, b = 10 a = 28, b = 7 a = 28, b = 10

✓ a = 11, b = 7You just needed to multiply the terms together

The average CPI of the processor is 1.95, which means that on average, it takes 1.95 clock cycles to execute one instruction.

The average CPI such as cycles per instruction of a processor is a measure of its performance.

In a processor with 3 instruction classes, A, B, and C, with relative frequencies of 45%, 35%, and 20% respectively, and individual CPIs of 1, 2, and 4 respectively, the average CPI can be calculated as follows:

Average CPI = (relative frequency of class A * individual CPI of class A) + (relative frequency of class B * individual CPI of class B) + (relative frequency of class C * individual CPI of class C)

Average CPI = (45% * 1) + (35% * 2) + (20% * 4)

Average CPI = 0.45 + 0.70 + 0.80 = 1.95

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