How many coefficients are in the
expression
5x - 3y - z + 8?
a.
1
b. 2
C. 3
d. 4

Answer:

Refer to pic..........

The area of a trapezoidal region is 1/2h(a+b), where a and b are the lengths of the two parallel sides, and h is the height.

The area of a trapezoidal region is given by the formula A = 1/2h(a+b), where a and b are the lengths of the two parallel sides, and h is the height. This formula can be derived by dividing the trapezoid into two right triangles and a rectangle, and finding the area of each of these shapes.

First, let's consider the two right triangles. The height of each of these triangles is h, and the lengths of their bases are (a-b)/2 and (b-a)/2, respectively. The area of each of these triangles is therefore 1/2h(a-b)/2 = 1/4h(a-b).

Next, let's consider the rectangle. The length of this rectangle is b, and the height is h. The area of this rectangle is therefore bh.

The area of the trapezoidal region is the sum of the areas of the two right triangles and the rectangle. This gives us:

A = 1/4h(a-b) + 1/4h(b-a) + bh

Simplifying this equation gives us:

A = 1/2h(a+b)

Therefore, the area of a trapezoidal region is 1/2h(a+b), where a and b are the lengths of the two parallel sides, and h is the height.

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The inequality for this statement is "x - 5 > 22". So, the solution to this inequality is "x > 27".

To translate the given statement into an inequality, we need to identify the variable, the constant, and the inequality sign. The variable is the unknown number, which we can represent with x. The constant is the number 22, and the inequality sign is greater than (>).

So, the inequality can be written as:
x - 5 > 22

To solve for x, we need to isolate the variable on one side of the inequality. We can do this by adding 5 to both sides of the inequality:
x - 5 + 5 > 22 + 5

Simplifying gives:
x > 27

So, the solution to the inequality is x > 27. This means that any number greater than 27 will make the inequality true.

In conclusion, the inequality that represents the statement "Five subtracted from a number is greater than twenty-two" is x > 27.

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The solution to the equation 1/2 + 3y = y/5 is y = -3/14.

What is the linear equation in one variable?

A linear equation in one variable is an equation that can be written in the form:

ax + b = 0

where x is the variable, a and b are constants, and a is not equal to zero. The solution to the equation is the value of x that makes the equation true.

To solve for y in the equation 1/2 + 3y = y/5, we need to isolate y on one side of the equation.

First, we can simplify the left side of the equation by combining the like terms:

1/2 + 3y = (6/10) + (30y/10) = (6 + 30y)/10

Now we can rewrite the equation as:

(6 + 30y)/10 = y/5

To solve for y, we can start by multiplying both sides of the equation by 10, to eliminate the denominators:

6 + 30y = 2y

Next, we can simplify by subtracting 2y from both sides:

6 + 28y = 0

Finally, we can solve for y by subtracting 6 from both sides and then dividing by 28:

28y = -6

y = -6/28

Simplifying the fraction, we get:

y = -3/14

Therefore, the solution to the equation 1/2 + 3y = y/5 is y = -3/14.

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x1 = 1.3, x2 = 0.3, x3 = 0.7

The solution to the linear programming problem is: x1 = 1.3, x2 = 0.3, x3 = 0.7.

Using the Dual Simplex Algorithm (DSA), we can solve the problem by setting up the initial tableau:

x1 = −5x1 + x2 − 2x3

2x1 + x3 = 0

x1 − x2 ≥ 1

3x1 − x2 + x3 ≤ 3

Once the tableau is set up, we can use DSA to find the optimal solution.

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The main of the given function f(x) is all real numbers except x=-4.

To find the main, we need to find the roots of the function. That is, we need to find out the values of x for which the value of f(x) is equal to 0.


Solving for the roots, we get the following equation:
8x2-9x+1=0


Solving this equation using the quadratic formula yields:
x = (-9 ± √73)/16


Therefore, the roots of the equation are:
x = 0.41 and -4.41


Since the only root which belongs to all real numbers is x = -4, it is the main of the given function.

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The angle of elevation of the sun is 19. 75 degrees

It is crucial to know there are six trigonometric identities.

These identities are;

From the information given,  we have that;

The angle of elevation = θ

The opposite side = The height of the building

The adjacent side = shadow of the building

Using cosine identity, we have;

cos θ = 48/51

divide the values

cos θ = 0. 9412

Take the cosine inverse

θ = 19. 75 degrees

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Answer:

2 tangents

with common points p and O touching both the circles only 2 tangets can be drawn

Answer:

,15

Step-by-step explanation:

ez

The base, which is equal to 1.3, is one of the values in the equation g(x)=18(1.3)x.

The monthly growth rate of the insect population is represented by this number. Since 1.3 is 1 + 30% represented as a decimal, the population is specifically growing by 30% each month. When the growth rate is compounded each month, this indicates that the insect population is expanding quickly over time.

If we enter x=3 into the function, for instance, we obtain g(3)=18(1.3)3=18(2.197)=39.546. This indicates that the anticipated bug population after three months is 39,546. Pest control is frequently required to preserve ecosystem balance since this exponential growth might, if unchecked, result in a very huge insect population.

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The difference in inches between 7 3/4 and 8 whole numbers is 1/4 inch.

What is Subtraction?

One of the four arithmetic operations, along with addition, multiplication, and division, is subtraction, which is denoted by the minus sign. The operation of subtraction represents the removal of items from a collection. In the adjacent image, for instance, there are 5 2 peaches, which means 5 peaches with 2 subtracted, making a total of 3 peaches.

As a result, 5 minus 2 equals 3, or the difference between 5 and 2. Although subtraction is most often used in mathematics with natural numbers, it can also be used with other types of objects, such as negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices, to remove or decrease physical and abstract quantities.

The difference in inches between 7 3/4 and 8 whole numbers is 1/4 inch.

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Answer:

Finding the total accrued amount is necessary before we can determine the interest rate.

Simply multiplying the monthly payment by the number of months in a 12-year period will give us the accrued amount.

144 months in 12 years.

$680 x Monthly Payment

A = 680 * 144

A = $97920

We can use the following formula now that we know the total accrued sum:

A= 97920

P = 72000

t= 12

Let's replace them with our values now.

The percentage value is then obtained by multiplying the r value by 100.

0.03 x 100 = 3%

The interest rate for Alexia is 3%.

The Highest Common Factor is: [tex]{6x^2yz^3}[/tex].

What is HCF ?

HCF stands for "Highest Common Factor", which is the largest number that divides two or more integers without leaving a remainder. It is also known as GCD (Greatest Common Divisor).

The given expressions are:

[tex]$$24x^3yz^4, \quad 30x^2y^2z^3, \quad 36x^3y^2z^3$$[/tex]

To find the HCF, we need to find the common factors of the given expressions.

We can write each expression as a product of prime factors:

[tex]$$24x^3yz^4 = 2^3 \cdot 3 \cdot x^3 \cdot y \cdot z^4$$[/tex]

[tex]$$30x^2y^2z^3 = 2 \cdot 3 \cdot 5 \cdot x^2 \cdot y^2 \cdot z^3$$[/tex]

[tex]$$36x^3y^2z^3 = 2^2 \cdot 3^2 \cdot x^3 \cdot y^2 \cdot z^3$$[/tex]

The common factors among these expressions are [tex]2, 3, $x^2$, $y$, $z^3$.[/tex]

Therefore, the Highest Common Factor is:

[tex]{6x^2yz^3}[/tex].

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Based on the information in the table, we can infer that the number that correctly replaces A is 880.

To find the number that replaces A we must analyze the information in the table. In this case we must find the difference between the distances to the destination in 1, 2, 3, 5 hours.

In this case we can subtract the distance of hour 1 from that of hour 2 to identify the difference.

So, the difference would be 60. To check it we can test with the difference between hour 2 and 3

So we can infer that the distance difference between each hour is 60 miles. Therefore, the value of A would be the value of the distance after 3 hours (940) minus 60.

So the correct option would be option B, 880.

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The 9th term of the geometric sequence 3, -15, 75, ... is 1171875.

The given sequence is 3, -15, 75, ... We can see that each term is obtained by multiplying the previous term by -5. Therefore, the common ratio is -5.

We can use the formula for the nth term of a geometric sequence to find the 9th term. The formula is given by:

aₙ = a₁ x rⁿ⁻¹

where,

aₙ = nth term of the sequence

a₁ = first term of the sequence

r = common ratio of the sequence

n = index of the term we want to find

Using the given sequence, we have:

a₁ = 3 (first term)

r = -5 (common ratio)

To find the 9th term, we substitute n=9 into the formula:

a₉ = a₁ x r⁹⁻¹

a₉ = 3 x (-5)⁸

a₉ = 3 x 390625

a₉ = 1171875

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The length of the diagonal is between 4 - 5 and closer to 4

First, we need to know the properties of a rectangle;

Given that the diagonal measures;

√18

Find the value

4. 2

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Using the graph, we can find that Enrique can fill 4 glasses from the container.

A structured representation of the data is all that the graph is. It assists us in comprehending the info. Data are the numerical details gathered by observation.

Data is a derivative of the Latin term datum, which means "something provided." Data is continuously gathered through observation once a research question has been formulated. After that, it is arranged, condensed, and categorised before being graphically portrayed.

Here,

We can see that the point on the graph suggests that for filling one glass,

8 fl oz of juice is required.

So, let the no. of glasses that will be filled be = x.

Now, x = Total amount of juice/ Amount of juice per glass

= 32/8

= 4 glasses.

Therefore, 4 glasses will be filled from the container.

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The complete question is:

8 Enrique has a container of 32 fl oz of orange juice. He is filling glasses with 1 cup of juice. The point on the graph shows the ratio of fluid ounces to cups. Based on this ratio, how many glasses can Enrique fill from the container? Plot a point on the graph to show the number of cups in 32 fl oz. Show your work.

x≤8 is the inequality of the number line.

A number system is defined as a system of writing to express numbers.

A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

In the given number line the shaded dot is at 8 at the arrow is to the left side of the number line which means the value of x is decreasing from point 8.

x≤8 is the inequality

Hence, x≤8 is the inequality of the number line.

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The average number of fruit flavored pieces you get in a bowl is 18.

To find the number of fruit flavored pieces you get in a bowl, you can calculate the average of the fruit flavored pieces in the five bowls you poured.

Here's how:

1: Add the number of fruit flavored pieces in each bowl: 3 + 23 + 20 + 23 + 21 = 90

2: Divide the total number of fruit flavored pieces by the number of bowls: 90 / 5 = 18

Therefore, the average number of fruit flavored pieces you get in a bowl is 18.

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The Euclidean algorithm can be applied to Gaussian integers in the same way it is applied to ordinary integers. In this case, we are given x = 3+2i and y = 2-5i and we need to find q and r such that x = qy + r and d(r) < d(y).

First, we divide x by y to get a quotient and remainder:
x/y = (3+2i)/(2-5i) = (3+2i)(2+5i)/(2-5i)(2+5i) = (16+7i)/29 = 0.551724 + 0.241379i

Since q and r must be Gaussian integers, we round the real and imaginary parts of the quotient to the nearest integer to get q = 1 + 0i = 1.

Next, we multiply q by y and subtract from x to get the remainder:
r = x - qy = (3+2i) - (1)(2-5i) = 1+7i

Finally, we check that d(r) < d(y):
d(r) = 1^2 + 7^2 = 50
d(y) = 2^2 + (-5)^2 = 29

Since d(r) > d(y), we need to adjust our quotient and remainder. We can do this by subtracting 1 from the real part of q and adding y to the remainder:
q = 0 + 0i = 0
r = (1+7i) + (2-5i) = 3+2i

Now, d(r) = 3^2 + 2^2 = 13 < 29 = d(y), so our final answer is q = 0 and r = 3+2i.

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The completed statement for the congruence of triangles is ΔXYZ ≅ ΔABC, the correct option is (d).

The Congruence of triangles is a term used in geometry which refers to the equality of shape and size of two triangles. The "Two-triangles" are  congruent if their "corresponding-sides" and angles are equal.

On observing both the triangles, we can say that,

The first triangle is right-angled at "X", and the second triangle is right-angled at "A",

the hypotnuse of first triangle is "ZY" and the hypotnuse of second triangle is "CB",

So, the "vertex X" similar to "vertex A", "vertex Z" similar to "vertex C", and "vertex Y" similar to "vertex B",

Therefore, triangle XYZ is congruent to triangle ABC, Option (d) is correct.

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Answer:

ACB

Step-by-step explanation:

Trust me

Answer:

380

Step-by-step explanation:

To find out what number is 600% of another number, we need to divide that number by 600% (or 6).

So:

x = 2,280 ÷ 6

x = 380

Therefore, 600% of 380 is equal to 2,280.

Hope this helped !

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

The correlation coefficient, denoted by r, tells us how closely data in a scatterplot fall along a straight line. The closer that the absolute value of r is to one, the better that the data are described by a linear equation. If r =1 or r = -1 then the data set is perfectly aligned. Data sets with values of r close to zero show little to no straight-line relationship.

Due to the lengthy calculations, it is best to calculate r with the use of a calculator or statistical software. However, it is always a worthwhile endeavor to know what your calculator is doing when it is calculating. What follows is a process for calculating the correlation coefficient mainly by hand, with a calculator used for the routine arithmetic steps.

He makes $8/49 for every 7 cups of juice, so his overall profits will be some multiple of $8/49.

Finding the worth of one unit of a quantity, then using this value to determine the value of a specified number of units of the quantity, is known as the unitary technique. When solving issues involving rates, ratios, and proportions, this approach is helpful. The fundamental tenet of the unitary technique is that we can use the value of one unit of a quantity to determine the value of any number of additional units of the same quantity.

given

Let's symbolise the cost of a cup of apple juice by the variable x.

So, a cup of lemon juice is sold for 3/2 times x, or (3/2)x.

Mr. Tan offers 5 cups of apple juice for every 2 cups of lemon juice. This indicates that there are 2.5 sales of lemon juice for every 1 sales of apple juice.

Assume Mr. Tan sells 5y cups of apple juice and 2y cups of lemon juice.

Based on the information provided, we can conclude that apple juice generates $12 more revenue than lemon juice.

in order to create an equation:

5yx = 2(3/2)x + 12

Simplifying:

5yx = 3x + 12

adding two to both sides:

10yx = 6x + 24

x(10y - 3) = 12

x = 12 / (10y - 3) (10y - 3)

We can now re-use this number of x to represent the revenue from apple juice in the equation:

5yx = 3x + 12

5y(12 / (10y - 3)) = 3(12 / (10y - 3)) + 12

Therefore, Mr. Tan charges $1/7 for each cup of apple juice and (3/2)($1/7) Equals $3/14 for each cup of lemon juice.

He charges (5/7)($1/7) = $5/49 for 5y = 5(1/7) = 5/7 glasses of apple juice.

For a sum of (2/7)($3/14) = $3/49, he sells 2y = 2(1/7) = 2/7 cups of lemon juice.

For each 7 cups of juice sold, Mr. Tan makes a sum of $5/49 + $3/49 = $8/49.

Consider that he offers 2n cups of lemon juice and 5n glasses of apple juice. (2n)($3/14) + (5n)($1/7) = $6n/49 + $5n/49 = $11n/49

He makes $8/49 for every 7 cups of juice sold, so his overall profits will be some multiple of $8/49.

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The sample proportions of male births that are at least as extreme as the sample proportion of 472/960 are 0.0026 for both the lower and upper tails.

A proportion is an equation in which two ratios are set equal to each other.

Part 1:

a. The values of p and q can be identified as follows:

p = proportion of male births in the population = 0.512

q = proportion of female births in the population = 1 - p = 1 - 0.512 = 0.488

So, p = 0.512 and q = 0.488.

Part 2:

b. The sample proportion of male births is:

P = 472/960 = 0.4917

To find the sample proportions of male births that are at least as extreme as this value, we need to calculate the z-scores corresponding to the upper and lower tails of the distribution under the null hypothesis (i.e., p = 0.512). The formula for the z-score is:

z = (P - p) / √(p*q/n)

where n is the sample size.

For the lower tail, we have:

z = (0.4917 - 0.512) / √(0.512*0.488/960) = -2.79

For the upper tail, we have:

z = (0.512 - 0.4917) / √(0.512*0.488/960) = 2.79

Using a standard normal distribution table or calculator, we can find the probabilities associated with these z-scores:

P(z < -2.79) = 0.0026

P(z > 2.79) = 0.0026

Hence, the sample proportions of male births that are at least as extreme as the sample proportion of 472/960 are 0.0026 for both the lower and upper tails.

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Complete Question:

A random sample of 960 births in New York State included 472 ​boys and that sample is to be used for a test of the common belief that the proportion of male births in the population is equal to

0.512.

Complete parts​ (a) through​ (c).

Question content area bottom

Part 1

a. In testing the common belief that the proportion of male babies is equal to 0.512​, identify the values of p and p. p=enter your response here p=enter your response here

Part 2

b. For random samples of size 960​,

what sample proportions of male births are at least as extreme as the sample proportion of 472960​?

The simplified result of is (6m^(2) + 13m - 15) / (m^(2) + 9m + 18).

Step 1: Flip the second fraction:

(mn)/(m^(2)+9m+18) ÷ (m)/(6m^(2)+13m-15) = (mn)/(m^(2)+9m+18) × (6m^(2)+13m-15)/(m)

Step 2: Change the division sign to multiplication:

(mn)/(m^(2)+9m+18) × (6m^(2)+13m-15)/(m)

Step 3: Multiply the numerators and denominators:

= (mn)(6m^(2)+13m-15) / (m^(2)+9m+18)(m)

Step 4: Simplify the result:

= (6m^(3)n + 13m^(2)n - 15mn) / (m^(3) + 9m^(2) + 18m)

= (mn)(6m^(2) + 13m - 15) / (m)(m^(2) + 9m + 18)

= (6m^(2) + 13m - 15) / (m^(2) + 9m + 18)

So the simplified result is (6m^(2) + 13m - 15) / (m^(2) + 9m + 18).

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The domains of each function and each composite function are as follows:

domain of f: (-∞, ∞)
domain of g: (-∞, ∞)
domain of f ∘ g: (-∞, ∞)
domain of g ∘ f: (-∞, ∞)

To find the composite functions f ∘ g and g ∘ f, we need to substitute the function g(x) into f(x) for f ∘ g, and the function f(x) into g(x) for g ∘ f.

(a) f ∘ g = f(g(x)) = f(x3 + 1) = 3(x3 + 1) − 8 = 3x3 + 3 − 8 = 3x3 − 5

(b) g ∘ f = g(f(x)) = g(3x − 8) = (3x − 8)3 + 1 = 27x3 − 72x2 + 64x − 511

The domain of a function is the set of all values of x for which the function is defined.

The domain of f is all real numbers, since there are no restrictions on the values of x. So the domain of f is (-∞, ∞).

The domain of g is also all real numbers, since there are no restrictions on the values of x. So the domain of g is (-∞, ∞).

The domain of f ∘ g is the same as the domain of g, since the values of x are first substituted into g(x) before being substituted into f(x). So the domain of f ∘ g is (-∞, ∞).

The domain of g ∘ f is the same as the domain of f, since the values of x are first substituted into f(x) before being substituted into g(x). So the domain of g ∘ f is (-∞, ∞).

Therefore, the domains of each function and each composite function are as follows:

domain of f: (-∞, ∞)
domain of g: (-∞, ∞)
domain of f ∘ g: (-∞, ∞)
domain of g ∘ f: (-∞, ∞)

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The expression when evaluated is 256

From the question, we have the following parameters that can be used in our computation:

8 power of 8/3

Mathematically, this can be expressed as

8^(8/3)

When evaluated using a calculator, we have

8^(8/3) = 256

Hence, the solution is 256

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