Find and simplify each of the following for f(x) = 4x² - 6x + 9.


(A) f(x + h) =
(Do not factor.)

The zeros of the quadratic equation y=4(x+9)²-36 are -6 and -12.

What is a quadratic equation?

Any equation of the form  ax² + bx + c = 0where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

Given:

y=4(x+9)²-36

on solving the bracket ,we get

y = 4x² + 324 + 72x - 36

or

y = 4x² + 72x + 288

or

y = 4(x² + 18x + 72)

or

y = 4(x² + 12x + 6x + 72)

or

y = 4(x(x+12)+6(x+12))

or

y = 4(x+6)(x+12)

Therefore , zeroes are -6 and -12.

Hence , the zeros of the quadratic equation y=4(x+9)²-36 are -6 and -12.

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Both cash and credit sales for the period are reported on the income statement of a retail company. So the correct statement is option (b) Both cash and credit sales for the period.

An income statement shows the income, expenses, and profitability of a company for a specified period. It is also sometimes referred to as the Income Statement (P&L) or Income Statement. it shows you:

Revenue from sales of products or services. 

An income statement shows how much revenue a company has generated, what expenses it has spent, and what income it has allocated over a period of time. You can use it to understand your company's business model and understand how your company is competitive within your industry. 

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The actual value of $10 in currency A would be of $1.7 in currency B.

$17.

The actual value is obtained applying the proportions in the context of this problem.

The exchange rate is given as follows:

$1 in currency A - $1.7 in currency B.

Hence the value in currency B of $10 in currency A is obtained as follows:

1.7 x 10 = $17.

The problem asks for the value in currency B of $10 in currency A.

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Answer:

111.76

Step-by-step explanation:

My attempt:

To find the number that 95 is 85% of, we can set up an equation using the information given. Let's call this number "x".

According to the problem, 95 is 85% of x, so we can write this as an equation:

95 = 0.85x

Now we can solve for x by dividing both sides by 0.85:

x = 111.76

So 95 is 85% of 111.76.

Answer:

111.76

Step-by-step explanation:

1.We have, 85% × x = 95 or,  85 100 × x = 95

2. Multiplying both sides by 100 and dividing both sides by 85,

we have x = 95 × 100/85

x = 111.76

Answer: To find the angle θ in a right triangle given the cosine value, we can use the inverse cosine function, also known as arccos.

cos θ = A/H = 22/38

θ = arccos (22/38)

Using a table of trigonometric values or a calculator, we can find the value of arccos (22/38) to be approximately 56.3 degrees.

So, θ = 56.3° (rounded to the nearest degree).

Step-by-step explanation:

The solution of the system of equations is equal to (3, 4).

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (3, 4).

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The proportion could be used to find the length of the actual wall, in feet is 2/5=13x/2, the correct option is B

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Given;

1 inch: 2 1/2 feet

One wall of the house was represented by a line 6 1/2 inches long on the floor plan.

Now,

6 1/2 inches= 13/2inch

1 inch: 2 1/2 feet=5/2feet

13/2inch=13/2 * 5/2

=65/4

b. 2/5=13x/2

Therefore, according to the given proportion the answer will be 2/5=13x/2.

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The expression that represents the cube root of 1+i​ is ∛(1 + i)

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

The cube root of 1+i​

In mathematics and algebra, the cube root is represented as ∛

Using the above as a guide, we have the following:

The cube root of 1+i​ is ∛(1 + i)

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Answer:

6000 bushels per hour.

Step-by-step explanation:

Let's assume that the rate at which the conveyor unloads wheat is proportional to its width.

If a 14-inch conveyor unloads 4000 bushels per hour, we can write this as:

Rate = 4000 bushels/hour * (Width of conveyor) / 14 inches

Now, if we want to find the rate at which an 21-inch conveyor would unload wheat, we can simply plug in the width into the equation:

Rate = 4000 bushels/hour * (21 inches) / 14 inches

Rate = 6000 bushels/hour

Therefore, an 21-inch-wide conveyor would unload 6000 bushels per hour.

1) The Mathematical curriculum teaches a combination of mathematical concepts, problem solving.

2) Some mathematical instructions that are promoted include understanding of mathematical concepts, computational fluency.

3) Yes, there are specific procedures used to teach basic mathematical instruction.

The Mathematical curriculum can be said to:

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The relative frequency or proportion of a given category is the number of sample items in that category divided by the total sample size.

The relative frequency or proportion of a given category is a measure of how often that category appears in a sample of categorical data. It is calculated by dividing the number of sample items in that category by the total sample size. For example, if a sample contains 10 items and three of them are in category A, then the relative frequency for category A is 3/10 or 0.3. This indicates that 30% of the sample items are in category A. Relative frequencies are used to compare categories within a sample, as well as to compare samples of different sizes. This allows us to draw conclusions about the frequency of occurrence of different categories within a population.

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Answer:

$44.236.20

Step-by-step explanation:

First, we need to calculate the cost of purchasing new seats for all the buses. The company has 13 buses and each bus has 28 seats, so the total number of seats to be replaced is 13 * 28 = 364 seats. The cost of purchasing each seat is $89.40, so the total cost of purchasing new seats for all the buses is 364 * $89.40 = $32,610.40.

Next, we need to calculate the cost of installing new seats for all the buses. The cost of installing each seat is $31.70, so the total cost of installing new seats for all the buses is 364 * $31.70 = $11,625.80.

Finally, we need to add the cost of purchasing and installing new seats to get the total cost the company will pay. The total cost of purchasing new seats is $32,610.40 and the total cost of installing new seats is $11,625.80, so the total cost the company will pay is $32,610.40 + $11,625.80 = $44,236.20.

a) Strings of probability 0s and 1s, which reflect the results of the coin flips, make up the sample space, S.

In (b), I A wins equals (1, 01, 001, 0001), (ii) B wins equals (0, 10, 010, 0010), and (iii) (A U B) equals (1, 0, 01, 10, 001, 010, etc.).

(a) Strings of 0s and 1s, which reflect the results of the coin flips, make up the sample space, S. Each 0 denotes a tail, while each 1 denotes a head. Since there is no restriction on the number of coin flips that can take place, the sample space is unlimited. Due to the fact that every result can be expressed as a string of 0s and 1s, it is also a finite collection. (b) I A wins means that A flipped a head before B or C, and the results are 1, 01, 001, 0001, etc. (ii) B wins = 0 (zero), 10 (one), 010 (zero), 0010 (zero), etc., indicating that B flipped a head before A or C. (iii) (A U B) = 1, 0, 01, 10, 001, 010, etc., indicating that either A or B turned over a coin before C. Presumably, A flips first, followed by B, C, then A, and so on.

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(AUB) will be equal to {2,4,6,7,6,10,11, .....even numbers). The empty set, or 0, is one of the most significant sets in mathematics.

A set that contains items from all related sets, without any repetition of elements, is known as a universal set (often symbolized by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.

A set with no elements is referred to as a null set or empty set.  The null set is the intersection of two disjoint sets, or sets that have no elements in common.

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The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

It is a statistical calculation that provides a way of summarizing how much a set of values deviates from the mean, or average, of those values.

The standard deviation is calculated by first finding the difference between each value in the set and the mean, squaring these differences, summing the squares, and dividing by the number of values in the set. The square root of this result gives the standard deviation.

A low standard deviation indicates that the values in a set are closely clustered around the mean, while a high standard deviation indicates that the values are more spread out. The standard deviation is useful in many applications, including quality control, finance, and social sciences, as it provides a way to quantify the variability of a set of values and to make meaningful comparisons between different sets of data.

We can estimate the answer by using the cumulative distribution function (CDF) of the normal distribution. The CDF gives us the probability that a random variable is less than or equal to a certain value. We would need to use a calculator or software to determine the exact value of the CDF, but we can estimate it using the empirical rule.

Since approximately 68% of regular grade gasoline falls within one standard deviation of the mean, we can estimate that roughly 68% of gasoline is less than 83.75.

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The y-coordinate of center of mass is 1.2819 kg.

The center of mass, also known as the center of gravity, is a point in a system of objects where the total mass of the objects is concentrated. It represents the balance point of the system and is the point at which the system would balance if it were suspended from that point. The position of the center of mass is dependent on the distribution of mass in the objects making up the system.

The centre of mass of region R is given by

[tex]$\mathrm{\bar{y}=\frac{\int_{R}\rho y_{e}dA}{Mass_{regionR}} \ \ where \ y_{e} \ center \ of \ mass \ of \ element}[/tex]

For the vertical element,

[tex]\mathrm{y_{e}=\dfrac{y}{2}}[/tex]

Find the numerator of the y coordinate of Center of Mass

[tex]$\mathrm{\frac{1}{2}\int_{R}\rho yydx=\frac{\rho}{2} \int_{\frac{-\pi}{3}}^{\frac{\pi}{3}} (3cosx)^2dx=\frac{9\rho}{2} \int_{\frac{-\pi}{3}}^{\frac{\pi}{3}} cos^2xdx=\frac{9\rho}{2} \int_{\frac{-\pi}{3}}^{\frac{\pi}{3}} (\frac{1+cos(2x)}{2})dx}[/tex]

[tex]$\mathrn{\frac{9\rho}{4} \int_{\frac{-\pi}{3}}^{\frac{\pi}{3}} (1+cos(2x))dx=\frac{9\rho}{4} [x+\frac{sin(2x)}{2}]_{\frac{-\pi}{3}}^{\frac{\pi}{3}}}[/tex]

[tex]$\mathrm{\frac{9\rho}{4} \left[\frac{\pi}{3}+\frac{sin(2(\frac{\pi}{3}))}{2}\right ]-\frac{9\rho}{4} \left[\frac{-\pi}{3}+\frac{sin(2(\frac{-\pi}{3}))}{2}\right ]}[/tex]

[tex]$\mathrn{\frac{9\rho}{4} \left[\frac{\pi}{3}+\frac{\sqrt{3}}{4}\right ]-\frac{9\rho}{4} \left[\frac{-\pi}{3}-\frac{\sqrt{3}}{4}\right ]=\frac{9\rho }{4} \left[\frac{2\pi}{3}+\frac{\sqrt{3}}{2}\right ]}[/tex]

Therefore, the y-coordinate of center of mass is

[tex]$\mathrm{\bar{y}=\frac{\dfrac{9\rho }{4}\left [\dfrac{2\pi}{3}+\dfrac{\sqrt{3}}{2}\right ]}{3\rho \sqrt{3}}=\frac{\sqrt{3}}{4}\left [\frac{2\pi}{3}+\frac{\sqrt{3}}{2}\right ]=\frac{3}{8}+\frac{\sqrt{3}\pi}{6}=1.2819}[/tex]

Thus, The y-coordinate of center of mass is 1.2819 kg

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The center of mass of a thin plate of constant density is determined by its area and the distribution of its mass.

To find the center of mass of this plate, we first need to calculate its area. We can do this by using the formula for the area of a region bounded by the x-axis and a curve y=f(x):

A = ∫[tex]a^{b}[/tex] ydx = ∫-pi/3^pi/3 3cosx dx

A = 3∫-pi/3^pi/3cosx dx

A = 3(sin(pi/3) - sin(-pi/3))

A = 3(sin(pi/3) + sin(pi/3))

A = 6sin(pi/3)

A = 6*(1/2)

A = 3

Now that we know the area of the plate, we can calculate its center of mass. To do this, we need to use the formula for the center of mass of a region bounded by the x-axis and a curve y=f(x):

xcm = 1/A ∫[tex]a^{b}[/tex] xydx

xcm = 1/3 ∫-pi/3^pi/3 x(3cosx) dx

xcm = 1/3 ∫-pi/3^pi/3 3xcosx dx

xcm = 1/3(3(sin(pi/3) - sin(-pi/3)) - 3xsin(pi/3) + 3xsin(-pi/3))

xcm = 1/3(6sin(pi/3) - 3pi/3sin(pi/3) + 3(-pi/3)sin(-pi/3))

xcm = 1/3(6sin(pi/3) - 3pi/3sin(pi/3) + 3pi/3sin(pi/3))

xcm = 0

Therefore, the center of mass of the plate is located at (0, 0).

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After solving (c+3)², the procedure is an illustration of the distributive property of equations, and c = -3.

Perhaps the most basic form has just been assumed to represent the fraction with the least process. How or when to decide mostly on fundamental form. Look for components that are present in both the denominator and the numerator. Sometimes it is possible to determine if a fractional integer is a power of two.

A algebraic theorem is a statement with two equal sides and an equal sign in the center. The degrees earned by each variable are stated in descending order, similar to an equation's general form. A linear equation has the formula x + b = 0. A three distinct linear function has the general form x + b y + c = 0. (or something similar). Mathematics can be categorized as identities or conditioned equations.

given:

[tex]( c+ 3 ) ^ 2[/tex]

= by using formulas of [tex]( a+ b ) ^2[/tex]

by distributive property

[tex]c^2 + 3^2 + 6c[/tex]

[tex]= c^2 + 9 + 6c[/tex]

[tex]c^2 + 3c + 3c + 9 = 0[/tex]

= (c + 3 )(c+ 3)

c = -3

After solving (c+3)², the procedure is an illustration of the distributive property of equations, and c = -3.

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If C.)Angle B is congruent to angle E then ∆ABC and ∆DEF are congruent by the ASA criterion.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

According to the ASA congruence postulate, two triangles are congruent when two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.

Looking at our diagram, we can see that the angle C and side CB of ABC are, respectively, congruent with the angle F and side FE of DEF.

Since CB is a side of ABC between angles C and B and FE is a side of DEF between angles F and E, angle B must be equal to angle E for these two triangles to be congruent by ASA.

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1. If , _____ then ∆ABC and ∆DEF are congruent by the ASA criterion.

A.) AB=DE

B.)CA=FD

C.)Angle B is congruent to angle E

D.)Angle A is congruent to angle D

If a translation is applied to square ABCD,  the y-coordinate of B' = y_coordinate of B - 8 = -8.

What is the translation?

The translation is a term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way. It is not rotated, reflected or re-sized. In a translation, every point of the object must be moved in the same direction and for the same distance.

When a translation of T-3, -8 is applied to square ABCD, it means that each point in the square is moved 3 units to the left and 8 units down.

The y-coordinate of B is found by moving 8 units down from the original y-coordinate of B.

Therefore, If a translation is applied to square ABCD,  the y-coordinate of B' = y_coordinate of B - 8 = -8.

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Answer:

4. y = 3x

Step-by-step explanation:

A proportional relationship is one in which the ratio of two variables is always constant. This is also known as direct proportion.

Out of the given options, the equation that shows a proportional relationship is:

4. y = 3x

In this equation, the ratio of y to x (y/x) is always 3, so the relationship between y and x is proportional. As x increases, y also increases at a constant rate, and as x decreases, y decreases at a constant rate. This type of relationship is often represented by the equation y = kx, where k is the constant of proportionality.

Answer:

$108

Step-by-step explanation:

The tax amount is $89.25 x 6% = $5.35.

The tip amount is $89.25 x 15% = $13.39.

So the total cost is $89.25 + $5.35 + $13.39 = $108.

Answer:

[tex]m^3+3m^2+3m+1[/tex]

Step-by-step explanation:

[tex](m^2+2m+1)(m+1)=(m^2)(m)+(m^2)(1)+(2m)(m)+(2m)(1)+(1)(m)+(1)(1)=m^3+m^2+2m^2+2m+1m+1=m^3+3m^2+3m+1[/tex]

You could also use the binomial theorem because the expression is equivalent to [tex](m+1)^3[/tex] but either method works.

Because f is analytic variable in D, it is differentiable, and every place in D has a zero derivative. Therefore, f in D must be constant.

A function f must be differentiable in the domain D if it is analytic there. The derivative of f must therefore exist and be continuous in D. The derivative of f must be zero everywhere in D if the absolute value of f, |f(z)|, is constant in D since the derivative of an absolute value of a function is always zero. As a result, f must be constant in D since the derivative of f is zero everywhere in D. Due to the fact that the derivative of |f(z)| is always zero, this holds true regardless of the value of |f(z)|. As a result, the function f(z) is constant in the domain D if f is analytical in D and |f(z)| is constant in D.

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Dustin walk at the rate of 6 miles per hour.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Dustin can run 2 miles per hour faster than he can walk around the track. If Dustin walks around the track in 20 minutes and runs around the track in 15 minutes.

Let the speed of Dustin walking = x

We know that;

Speed = Distance / Time

For walking;

Speed = Distance / Time

x = Distance / (20/60)

x × 20/60 = Distance

Distance = x/3 miles

For run;

Speed = Distance / Time

⇒ x + 2 = (x/3) / (15/60)

⇒ 3 (x + 2) = 4x

⇒ 3x + 6 = 4x

⇒ 4x - 3x = 6

⇒ x = 6

Thus, Dustin walk at the rate of 6 miles per hour.

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