What is the simplest form of the expression 6x(x − 4) − 16x2 − (9x − 1)?

Answer:

-108

Step-by-step explanation:

We know b is -7 so we have to plug it in.
6(2(-7)-4)

Simplify: 6(-14-4)

Simplify again: 6(-18)

Simplify: -108

Final answer -108

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The team was provided 10 gallons of water.

The second transformation which is (x+0, y-4), 180° rotation, reflection over the x-axis would carry the rectangle onto itself.

What is transformation?

Forms on a coordinate plane can be rotated, reflected, or translated using transformations. Each vector can be translated, any line can be reflected, and any point can be rotated.

We are given a graph on which a rectangle is drawn. This has to be transformed in such a way that it lands onto itself.

Of the given options only the second option is through which it will land on itself.

As when we reflect over x - axis, the rectangle will come in the 3rd quadrant and after rotating it 180°, there will be no change.

Now, to bring it back to its original position, we will have to reduce the y - coordinate by 4 due to which it will shift upwards.

Hence, the second option is the correct option.

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The perimeter of the figure is approximately 32.6 units

What is perimeter ?

Perimeter is a term used in geometry to describe the total length of the boundary or outer edge of a two-dimensional shape. In other words, it is the sum of the lengths of all the sides of a shape.

The concept of perimeter is most commonly used with polygons, which are shapes with straight sides. To find the perimeter of a polygon, we simply add up the lengths of all its sides. For example, the perimeter of a rectangle is given by the formula:

Perimeter = 2(length + width)

where length and width are the dimensions of the rectangle.

According to the question:
To find the perimeter of the figure, we need to add up the lengths of all its sides.

First, let's find the circumference of each semicircle. The diameter of each semicircle is 4, so the radius is 2. The circumference of each semicircle is:

C = πr = π(2) = 2π

Since there are two semicircles, the total length of their circumferences is:

2(2π) = 4π

Now let's find the length of the sides of the rectangle. One side has length 6, and the other side is the diameter of the semicircles, which is also 4. So the length of the other side of the rectangle is 4. Therefore, the perimeter of the rectangle is:

2(6 + 4) = 20

Finally, we can add up the lengths of all the sides to find the perimeter of the figure:

Perimeter = 4π + 20

Using a calculator to approximate π as 3.14 and rounding to the nearest tenth, we get:

Perimeter ≈ 4(3.14) + 20 ≈ 32.6

Therefore, the perimeter of the figure is approximately 32.6 units.

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Answer: The answer is 32.6

Given:-

[tex] \: [/tex]

Solution:-

[tex] \sf \large{↣ \frac{2}{3} + \frac{2}{5} }[/tex]

[tex] \: [/tex]

[tex] \sf \large{ ↣\frac{2 \times 5 + 3 \times 2}{3 \times 5} }[/tex]

[tex] \: [/tex]

[tex] \sf \large{ ↣\frac{10 + 6}{15} }[/tex]

[tex] \: [/tex]

[tex] \large{↣\boxed{ \sf{ \purple{ \: \frac{16}{15} \: }}}}[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps ⸙

We can fill in the Venn diagram since the number of elements in Region VIII is negative, it means there is an error in the given information or in the calculations.

Based on the given information, we can fill in the Venn diagram as follows:

n(A) = 33, n(B) = 36, n(C) = 24, n(B ∩ C) = 14, n(A ∩ C) = 9, n(A ∩ B ∩ C) = 5

n(A ∩ B) = n(A) + n(B) - n(A ∩ B) = 33 + 36 - 17 = 52

Now we can fill in the Venn diagram:

Region I: n(A ∩ B ∩ C) = 5

Region II: n(A ∩ B) - n(A ∩ B ∩ C) = 52 - 5 = 47

Region III: n(B ∩ C) - n(A ∩ B ∩ C) = 14 - 5 = 9

Region IV: n(B) - n(B ∩ C) - n(A ∩ B) = 36 - 14 - 17 = 5

Region V: n(A) - n(A ∩ C) - n(A ∩ B) = 33 - 9 - 17 = 7

Region VI: n(C) - n(A ∩ C) - n(B ∩ C) = 24 - 9 - 14 = 1

Region VII: n(U) - n(A) - n(B) - n(C) + n(A ∩ B) + n(A ∩ C) + n(B ∩ C) + n(A ∩ B ∩ C) = 70 - 33 - 36 - 24 + 52 + 9 + 14 + 5 = 57

Region VIII: n(U) - (n(I) + n(II) + n(III) + n(IV) + n(V) + n(VI) + n(VII)) = 70 - (5 + 47 + 9 + 5 + 7 + 1 + 57) = -4

Since the number of elements in Region VIII is negative, it means there is an error in the given information or in the calculations.

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Answer:

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Answer:

Step-by-step explanation:

Debt is usually expected in all of the following cases except for option A, which is the purchase of a house.

Debt refers to an amount of money that is owed by one party (the borrower) to another party (the lender). It can be incurred through borrowing money, using credit cards, or other forms of financing. Debt can take many different forms, including personal loans, mortgages, credit card balances, student loans, and other types of financial obligations.

Debt is usually expected in all of the following cases except for option A, which is the purchase of a house. Purchasing a house with a mortgage involves taking on debt, but it is often considered a necessary and responsible investment for many people. The other options - credit card purchases, purchasing a car, and educational loans - often involve taking on debt as well, but they are not typically seen as long-term investments like a house.

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Answer:

8$ is the answer so chose that one

Answer:

18

Step-by-step explanation:

here,

circumference of the circle = 90

[tex]S = r\theta[/tex]

in above equation, S is the length of arch, r is the radius and theta is the angle formed by arc at the center,

As you can see, in a circle of given radius,

[tex]S \propto \theta[/tex]

therefore,

[tex]\dfrac{S_1}{S_2} = \dfrac{\theta_1}{\theta_2}[/tex]

we have the arc length for angle 360 (circumference of the circle).

let S1 be the length of minor arc, S2 be the arc formed by full circle (360 degree),

[tex]\dfrac{S_1}{90} = \dfrac{72}{360}[/tex]

solving the above equation, we get

[tex]S_1 = 18[/tex]

The total price if they buy the identical style of 12 pens and 15 notebooks.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

Hence total cost

= Rs ( 300 + 120 )

= Rs 420

The cost of 15 notebooks

= Rs ( 15 × 20 )

= Rs 300

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Dipesh bought 3 notebooks and 2 pens for Rs. 80. His friend Ramesh said that price of each notebook could be

Rs. 25. Then three notebooks would cost Rs.75, the two pens would cost Rs. 5 and each pen could be for Rs. 2.50.

The function that models the total attendance a (in thousands) at NCAA women's basketball games and the number t of NCAA women's basketball teams over a period of time can be expressed as:

a = 5t + 200 thousands.

The total attendance a (in thousands) at NCAA women's basketball games and the number t of NCAA women's basketball teams over a period of time can be modeled by a function of the form a = kt + b.

where k and b are constants.

Let's determine the slope and y-intercept using the given information: a = kt + b

Given: a = 200 thousand and t = 5 teams

Substitute these values into the equation: a = kt + b200 thousand = 5k + b

The equation can be rewritten as: b = 200 thousand - 5k

We know that b represents the y-intercept,

so when t = 0, the attendance is given by b (in thousands).

Therefore, b represents the initial attendance at the start of the period of time in question.

To find the value of b, substitute t = 0 into the equation:

b = 200 thousand - 5(0) = 200 thousand.

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Answer:

f(x)=2x+x2

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

2x→1

x^2→2

The largest exponent is the degree of the polynomial.

2

Step-by-step explanation:

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First transformation: Reflection across the y-axis

Second transformation: Vertical translation down by 12 units.

A coordinate is a value that specifies the position of a point in a particular system or framework of reference. Coordinates are typically expressed as numerical values that describe the location of a point in relation to some predefined origin, axis, or set of reference points. The most common type of coordinate system is the Cartesian coordinate system, which uses two or three axes to describe points in a plane or in three-dimensional space, respectively. In this system, coordinates are typically expressed as ordered pairs (for two-dimensional points) or ordered triplets (for three-dimensional points), such as (x, y) or (x, y, z), where x, y, and z represent the distances along each axis from the origin. Other types of coordinate systems include polar coordinates, cylindrical coordinates, and spherical coordinates, which are used in various branches of mathematics and science to describe points in different contexts.

To find the two transformations, we can use the fact that applying multiple transformations to a figure is the same as applying a single transformation that is the composition of the individual transformations.

Let's start with the final vertices of the transformed figure: (-2,0), (2, 0), (2,-6), and (0,-2).

We can see that the first two vertices have the same x-coordinate and are located on the x-axis. This suggests a reflection across the y-axis, which would swap the x-coordinates of the vertices.

So, the first transformation is a reflection across the y-axis.

After this transformation, the transformed figure has vertices (-WXYZ).

Next, we need to find the second transformation that maps WXYZ to (-WXYZ) with the given final vertices.

We can see that the vertex (2,-6) has a lower y-coordinate than the other three vertices. This suggests a vertical translation that moves this vertex down to its final position.

To determine the amount of vertical translation, we can subtract the y-coordinate of the vertex in its initial position (6) from the y-coordinate of the vertex in its final position (-6), which gives a total downward movement of 12 units.

So, the second transformation is a vertical translation down by 12 units.

Therefore, the two transformations that Nelson applies to WXYZ are a reflection across the y-axis followed by a vertical translation down by 12 units.

First transformation: Reflection across the y-axis

Second transformation: Vertical translation down by 12 units.

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Answer:

x=7 y=14

Step-by-step explanation:

2x-x=11-4

x=7

y-4=x+3

y-4=7+3

y=7+3+4

y=14

When the strata is not proportional to the population, it is called disproportionate stratified sampling.

The sampling method used in this case is a stratified sampling method. What is Stratified Sampling? Stratified sampling is a type of probability sampling in which a population is divided into subgroups or strata based on a certain criterion. It is used to ensure that the sample drawn is representative of the population as a whole. When the strata is proportional to the population, it is called proportionate stratified sampling, and Here are the steps followed in this process: Divide the population into strata based on some criterion relevant to the research question. Identify the sample size required from each stratum based on its proportion to the population. Draw a random sample from each stratum to arrive at the final sample.

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Answer: If I'm correct, an equivalent expression to v could be (2y)+10+2(5x+3)

Sorry I don remember how to do the other 2.

Step-by-step explanation

PEMDAS

2x + 10 + 2(5y + 3)

2x = 2

5y = 5

2+10=12 12+16

2 x (5+3=8) = 16

12+16= 28

x=1 y=1

An equivalent algebraic expression could be

(2y)+10+2(5x+3) if I'm correct because the

The answer is equal to the previous answer

The total surface area of the triangular prism is 1008cm² with dimensions 13cm, 5cm, 12cm, 9cm, 15cm, and 20cm.

To find the total surface area of a triangular prism with dimensions 13cm, 5cm, 12cm, 9cm, 15cm, and 20cm, we first need to identify the different faces of the prism. The triangular prism has two triangular faces and three rectangular faces.

The area of one triangular face can be calculated as

(1/2) x base x height, where the base is 12cm and the height is 9cm. Therefore, the area of one triangular face is

(1/2) x 12cm x (9+5)cm = 84cm²

Since there are two triangular faces, the total area of the triangular faces is 2 x 84cm² = 168cm².

The area of one rectangular face can be calculated as length x width, where the (length, width) is (13cm, 20cm), (14cm, 20cm) and (15cm, 20cm) = 15 × 20 + 13 × 20 + 14 × 20

= 840cm²

Thus, the total surface area of the triangular prism is the sum of the areas of the two triangular faces and three rectangular faces, which is

168cm² + 840cm² = 1008cm²

Therefore, the total surface area of the triangular prism is 1008cm².

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Answer:

proofs attached to answer

Step-by-step explanation:

proofs attached to answer

Answer: - 6

Step-by-step explanation:

Since n is c in [tex]ax^{2}[/tex] + bx + c, that means that n is the y - intercept of the graph. The y - intercept in the graph is -6 which means that n = -6.

(a)The probability that a call is answered during the first two minutes is 50%.

(b)The probability that a customer waits more than four minutes is infinite.

(a)The probability that a call is answered during the first two minutes is 50%. This is because, if the average waiting time is four minutes, then the call is equally likely to be answered during the first two minutes as it is during the last two minutes. Therefore, the probability of being answered within the first two minutes is 50%.

(b)The probability that a customer waits for more than four minutes can be calculated by assuming that the waiting time follows the same continuous uniform distribution from 0 to 4 minutes. The probability density function (PDF) for this distribution is:

f(x) = 1/4 0 <= x <= 4

The probability that a customer waits more than four minutes is the area under the PDF from 4 to infinity:

P(x > 4) = integral from 4 to infinity of f(x) dx

= integral from 4 to infinity of 1/4 dx

= [1/4 * x] evaluated from 4 to infinity

= lim(x -> infinity) (1/4 * x) - (1/4 * 4)

= infinity

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To find the distance they traveled, we can use the formula:

distance = rate × time

In this case, the rate is 65 miles per hour and the time is 3 hours.

So, the distance they traveled is:

distance = 65 × 3 = 195 miles

Therefore, Lily's family traveled 195 miles from Chicago to Wisconsin Dells.

The subject of this question is Mathematics and it involves counting and working with coins.

The subject of this question is Mathematics as it involves counting and working with coins.

Tia has 12 coins in total, consisting of 6 pennies, 3 nickels, and 3 dimes. Will has 15 coins, with an equal number of pennies, nickels, and dimes. Ana has a total of 9 coins, with 2 pennies, 4 nickels, and 3 dimes.

In summary, the question involves counting the number of coins each person has, which can be solved using basic arithmetic and understanding of coin values.

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According to the question the value of x in the right triangle with a 30-degree angle and hypotenuse of 15 is 7.5.

We can use trigonometric ratios to find the value of x in a right triangle with a 30-degree angle and hypotenuse of 15.

First, we can use the fact that in a 30-60-90 triangle, the length of the shorter leg is half the length of the hypotenuse. So, we know that:

x/15 = 1/2

Multiplying both sides by 15 gives:

x = 7.5

Therefore, the value of x in the right triangle with a 30-degree angle and hypotenuse of 15 is 7.5.

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Answer:

[tex]\textsf{D.}\quad f(x)=\dfrac{(x-1)}{x(x-3)}[/tex]

Step-by-step explanation:

An asymptote is a line that the curve gets infinitely close to, but never touches.

Vertical asymptotes of a rational function occur when the denominator equals zero.

From inspection of the given graph, the vertical asymptotes are:

Therefore, for the denominator to equal zero, it must include the factors:

Since the only answer option that has the factors x and (x - 3) is option D, the graphed rational function is:

[tex]f(x)=\dfrac{(x-1)}{x(x-3)}[/tex]

Answer:

[tex]- 8 {g}^{15} {h}^{6} [/tex]

Step-by-step explanation:

[tex] {( - 2 {g}^{5} \times {h}^{2} )}^{3} [/tex]

Use the property of exponents (raise each term by a degree separately):

[tex] {( - 2 {g}^{5} \times {h}^{2} )}^{3} = ( { - 2})^{3} \times {( {g}^{5} })^{3} \times {( {h}^{2}) }^{3} = - 8 \times {g}^{15} \times {h}^{6} = - 8 {g}^{15} {h}^{6} [/tex]

60$

if you add $25.50 + $32.75 + 1.75 you get a sum of 60 (this being with no tax)

Answer:

Step-by-step explanation: ???