6. Calculate the number that you need to add to each side of the equation w 2– 3w = 350 to create a perfect square trinomial. Add this number to each side of the equation. Show your work. (3 points)
7. Factor the trinomial. (3 points)

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

e8=56+ 34 x 3 (45 x -2) = 4

Step-by-step explanation:

Answer:

56+34×3

Step-by-step explanation:

hope it helps

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The coefficient of \(x^{7}\) is 16796160.

For this, we have to find the coefficient of \(x^{7}\) in \((3x+4)^{10}\)

General Term: This term symbolizes all of the terms in the binomial expansion of (x + y)^n.

The general term in the binomial expansion of (x + y)^n is

T(r+1) = nCr x^(n-r)y^r.

Here the r-value is one less than the number of the term of the binomial expansion. Also, nCr is the coefficient, and the sum of the exponents of the variables x and y is equal to n.

We can use the general term for this.

\(T_{r+1} = (nCr) a^{n-r} x^{r}\)

Since we have to find  \(x^{7}\),

\(T_{3+1} = (10C3)(3x)^{7} 4^{3} \\T_{3+1} = [(10C3)3^{7} 4^{3} ]x^{7}\)

This is the coefficients of \(x^{7}\)

Calculating,

10C3 = 120 (using combinations)

\(3^{7} = 2187\\4^{3} = 64\)

Therefore, multiplying the 3,

Coefficients of \(x^{7}\) = 120 * 2187 *64

= 16796160

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\(\frac{x}{3x}+\frac{8x}{3x}=\frac{1}{3}+\frac{8}{3}=3\)

y = 1/3x - 21 is the equation of the line in slope-intercept form.

What is a slope?

Slope is a measure of the steepness or incline of a line. It describes how much the dependent variable (usually y) changes for a given change in the independent variable (usually x).

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

We are given that the slope is 1/3 and that the line passes through the point (3, -20). We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

where (x1, y1) is the point through which the line passes, and m is the slope. Plugging in the values we have:

y - (-20) = 1/3(x - 3)

Simplifying this equation:

y + 20 = 1/3x - 1

Subtracting 20 from both sides:

y = 1/3x - 21

This is the equation of the line in slope-intercept form.

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Answer:

The value of E [Z]  is 0.50.

Step-by-step explanation:

The expected value is computed using the formula:

\(E(X)=\sum x\cdot P(X= x)\)

Denote the three dices as follows:

X₁ = a four-sided die

X₂ = a six-sided die

X₃ = a 12-sided die

Define the indicator variables as follows:

\(I_{1}=\left \{ {{1;\ X_{1}=4} \atop {0;\ X_{1}\neq 4}} \right. \\\\I_{2}=\left \{ {{1;\ X_{2}=4} \atop {0;\ X_{2}\neq 4}} \right. \\\\I_{3}=\left \{ {{1;\ X_{3}=4} \atop {0;\ X_{3}\neq 4}} \right.\)

The probability of rolling a 4 in the three dices are as follows:

\(P(X_{1}=4)=\frac{1}{4}\\\\P(X_{2}=4)=\frac{1}{6}\\\\P(X_{3}=4)=\frac{1}{12}\)

Compute the value of E [Z] as follows:

\(E(Z)=E(I_{1})+E(I_{2})+E(I_{3})\)

         \(=(1\times\frac{1}{4})+(1\times\frac{1}{6})+(1\times\frac{1}{12})\\\\=\frac{3+2+1}{12}\\\\=\frac{6}{12}\\\\=\frac{1}{2}\\\\=0.50\)

Thus, the value of E [Z]  is 0.50.

The value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08

Simplifying an equation is simply another way of saying solving a math problem. When you simplify a phrase, you are attempting to write it in the simplest way feasible. In conclusion, there should be no more adding, subtracting, multiplying, or dividing to do.

Given expression 1. -4\(x^{-2}\) + 3\(y^{0}\)  2. 2\(x^{0}\)\(y^{-2}\)

Expression for x =2 and y=5

-4x-2 + 3y0

= -4(2)-2 + 3(5)0

= 16+3

=19

Now

2x0y-2

= 2(2)0x(5)-2

= 2 x (1/25)

= 2 x 0.04

= 0.08

Therefore the value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08

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The probability of selecting blue, yellow and blue marble without replacement is 3/170

Number of red marbles = 7

Number of blue marbles = 4

Number of yellow marbles = 6

Total number of marbles = 17

Probability of selecting a red marble = 7/17

Probability of selecting a blue marble = 4/17

Probability of selecting a yellow marble = 6/17

Now the probability of selecting the first blue marble = Number of blue marbles/Total number of marbles. = 4/17

Probability of selecting the yellow marbles = Number of yellow marbles/Number of marbles left after the first draw = 6/16

Probability of selecting the third blue marble = Number of blue marbles/Total number of marbles left after the second draw = 3/15

So the probability of blue, yellow and blue marble is:

4/17*6/16*3/15 = 3/170

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The required, general solution for x that satisfies the equation cos(x + 30) = -1 is x = (2n + 1)π - 30.

To find the general solution for the equation cos(x + 30) = -1, we can start by considering the general form of the cosine function. The cosine function has a period of 2π, meaning it repeats every 2π radians.

In this equation, we have cos(x + 30) = -1. Since the cosine function has a maximum value of 1 and a minimum value of -1, the only way for cos(x + 30) to equal -1 is if x + 30 is an odd multiple of π. We can write this as:

x + 30 = (2n + 1)π

Here, n is an integer representing the number of periods of the cosine function. To find the general solution, we can solve for x by subtracting 30 from both sides:

x = (2n + 1)π - 30

This equation gives us the general solution for x that satisfies the equation cos(x + 30) = -1. We can see that for each integer value of n, we have a different solution.

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Answer:

it's 6

Step-by-step explanation:

You can think of it 2 ways the first one is called the "bat and ball" method which is 12x15 then u divide it by 30. The other methos only works on very few if you look at the 30/15 one 15 is half of 30 so when you look at 12 half of that would be 6. Hope this helps :)

Answer:

9.16515138991

Round of :-

9.17...ans

Step-by-step explanation:

The number of square meters that the space that Araceli rents is, is 30. 66 square meters.

The space that Araceli rents has a rectangular space so to find the area of the rectangular space that Araceli rents, we need to multiply the length by the width.

The given width is 4. 2 meters and the length is 7. 3 meters.

The area of the space in square meters is therefore :

Area = Length × Width

Area = 7. 3 meters × 4. 2 meters

Area = 30. 66 square meters

In conclusion, the space that Araceli rents has an area of 30. 66 square meters.

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Answer:

75 yards

Step-by-step explanation:

375/5=75

Answer:

dsseeeseeeeeeeeeeeeee33ee3e33ee2eew3wwwwwwwwwwwewqee

Answer:

Bonnie is correct.

Step-by-step explanation:

Input 5 for the amount of shirts for letter X then follow the steps for a multistep equation:

12(5) - 10 = 50

60 - 10 = 50

50 = 50

x = x or 1

So, Susan, as Bonnie said, can buy 5 shirts.

Here b is =0, According to the Zero Product Property, if ab=0, then either a=0 or b=0 (or both). If and only if one or more of the factors in a product are zero, the product is zero. This is very helpful when attempting to solve quadratic problems.

The product of two nonzero items is not zero, according to the algebraic definition of the zero product property. In other terms, the following claim:

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Answer: B) Outside the triangle

Step-by-step explanation:

The circumcenter of a obtuse triangle is always outside of the triangle

The most convincing explanation I can give for why a = c is supplementary property a+ b

= 180° and b+c = 180° and substraction operation and also one more reason is a = c is also true because they are vertically opposite angles.

A supplementary angle is an angle that sums to 180 degrees. For example, the 130° and 50° angles are complementary because the sum of 130° and 50° is 180°.

We know that, supplementary angles are angles whose sum is 180°. From the above figure, using the property that linear pairs are supplementary , we have b+c = 180° , c+d = 180° , d+a = 180° ,

a+b = 180°

Therefore, consider a+b = 180° and b+c = 180°

Using subtraction property of equality, we have

180°- b = a .........(1)

180°-b = c ..........(2)

Substitute 180°- b = a in equation (2) , we get

=> a = c

Hence, we get the required results.

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When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

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Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

The similar triangles for this problem are given as follows:

RST and VUT.

Then the measure VT is given as follows:

VT = 5.4 units.

Similar triangles are triangles that share these two features listed as follows:

Hence the similar triangles for this problem are given as follows:

RST and VUT.

The proportional relationship for the side lengths is given as follows:

6/14 = (x + 2)/(4x - 1).

Applying cross multiplication, the value of x is obtained as follows:

14(x + 2) = 6(4x - 1)

14x + 28 = 24x - 6

10x = 3.4

x = 3.4.

Then the length VT is given as follows:

VT = 3.4 + 2

VT = 5.4 units.

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The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer:

-12

Step-by-step explanation:

a(b - c)

b = 3, c = -3 and a = -2

-2( 3- -3)

-2(3+3)

-2(6)

-12

Answer: -12

Explanation: It's a good idea to get into the habit of

using parenthses when substituting numbers in for variables.

If you have parenthses in your original problem,

change them to brackets as you substitute to avoid confusion.

Since your brackets replace your original parenthses,

your first step will be to simplify what's inside the brackets.

So we have (-2) [(3) - (-3)].

Simplifying inside the brackets, we get 6.

So we have (-2) [(6)].

Multiplying from here, our answer is -12.

Answer:

A. = 27 B. = 16

Step-by-step explanation:

A. 36/4 = 9 3X9 = 27

B. 36/9 = 4 4X4 =16

If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~

Answer:

56+8x

Step-by-step explanation:

Answer:

Step-by-step explanation:

sp = 504

gain = 12%

in this case

sp =100%+12%=504

112%=504

1%=504/112 =4.5

100%=450

so cost =$450

Hope im correct, if i am im glad to be of service.

To hold 1,000,000 inflated balloons,

38 classrooms are needed.

In three-dimensional space,

the amount of space taken by an object is the volume of that object.

The volume of the cubic,

= length x width x height

Given:

The dimensions of the normal classroom are 15 ft × 50 ft × 35 ft.

The volume of the classroom,

= 15 ft by 50 ft by 35 ft.

= 26250 cubic feet.

The number of classrooms,

= 1,000,000 / 26250

Simplifying the fraction,

we get,

= 38.09

≈ 38 to the nearest whole number.

Therefore, 38 classrooms are required.

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Answer:

A is the answers for the question

Step-by-step explanation:

please mark me as brainlest

\(\underline{\underline{\large\bf{Solution:-}}}\\\)

\(\longrightarrow\)Given is a quadratic equation which can be solved by splitting the middle term.

\(\leadsto\)For this we have to look at factors of the constant term . Since here constant term term is- 6 so splitted middle term should have product equal to -6

\(\begin{gathered}\\\implies\quad \sf x^2-x-6=0 \\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf x^2-3x+2x-6=0 \\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf x(x-3)+2(x-3)=0 \\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf (x-3)(x+2) =0 \\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf (x-3) =0 \quad or \quad (x+2) =0\\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf x=3 \quad or \quad x= -2\\\\\end{gathered} \)

\(\quad\therefore\: \sf x \:is \: \:3 \:or -2 \)

Answer:

in fraction form is 6/20 in decimal form its 0.3

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

(-6 - 4) ÷ -5 = 2