Find the required information to fill out the missing words in the sentence

f(x) = [tex]x^{2}[/tex] -> f(x) = [tex]x^2[/tex] - 18 (translation) -> f(x) = [tex](x-3)^2[/tex] - 18 (horizontal translation) -> f(x) = -6[tex](x-3)^2[/tex] + 18 - 6x (vertical stretching)

To transform the function f(x) =[tex]x^{2}[/tex] into f(x) = [tex]x^{2}[/tex] - 6x + 18, we need to apply a series of transformations. Here are the steps:

Translation: We need to shift the graph of f(x) = [tex]x^{2}[/tex] down by 18 units to obtain f(x) = [tex]x^{2}[/tex] - 18. This can be done by subtracting 18 from the function, which results in f(x) = [tex]x^2[/tex]- 18.

Horizontal translation: Next, we need to shift the graph of f(x) = [tex]x^{2}[/tex] - 18 to the right by 3 units to obtain f(x) =[tex](x-3)^2[/tex] - 18. This can be done by replacing x with (x-3) in the function, which results in f(x) =[tex](x-3)^2[/tex]- 18.

Vertical stretching: Finally, we need to vertically stretch the graph of f(x) = [tex](x-3)^2[/tex] - 18 by a factor of -6 to obtain f(x) = [tex](x-3)^2[/tex] - 6x + 18. This can be done by multiplying the function by -6, which results in f(x) = -6[tex](x-3)^2[/tex] + 18 - 6x.

So, the series of transformations required to transform f(x) = [tex]x^{2}[/tex] into f(x) = [tex]x^{2}[/tex] - 6x + 18 is:

f(x) = [tex]x^{2}[/tex] -> f(x) =[tex]x^{2}[/tex] - 18 (translation) -> f(x) =[tex](x-3)^2[/tex] - 18 (horizontal translation) -> f(x) = -6[tex](x-3)^2[/tex]+ 18 - 6x (vertical stretching)

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Answer: D. $722

Step-by-step explanation:

$2,000 - $375 (initial airfare cost which will only be once)

= 1,625

7 x 129 = 903 (cost of the 7 nights in a hotel)

1,625 - 903 = 722

$722 left for the trip

You could try factoring.

[tex]6x^2-x-1=(2x-1)(3x+1)\\3x^2+25x+8=(x+8)(3x+1)\\x^2+4x-32=(x+8)(x-4)\\2x^2+7x-4=(x+4)(2x-1)[/tex]

So your expression becomes...[tex]\frac{(2x-1)(3x+1)}{(x+8)(3x+1)}*\frac{(x+8)(x-4)}{(x+4)(2x-1)}=\frac{x-4}{x+4}[/tex].

a. The total length of cloth required to make shirts for 15 students is 345 meters.

b. At least 23 meters of cloth to make one shirt

c. The length of cloth required for one shirt in decimal form is 23.00 meters.

d. 13.25 meters of cloth is left after making 1 shirt from a piece of cloth that is 36.25 meters long.

What is total length?

Whole Length (TL) is the measurement taken in a straight line, with the fish lying on its side, from the tip of the snout to the end of the tail (caudal fin).

(a) Total cloth required = 15 × 23 meters = 345 meters

Therefore, the total length of cloth required to make shirts for 15 students is 345 meters.

(b) Number of shirts = 9.5 meters ÷ 23 meters/shirt ≈ 0.413

Therefore, only 0 shirts can be made from a piece of cloth 9.5 meters long. We need at least 23 meters of cloth to make one shirt.

(c) 23 meters = 23.00 meters

Therefore, the length of cloth required for one shirt in decimal form is 23.00 meters.

(d) Number of shirts = 36.25 meters ÷ 23 meters/shirt ≈ 1.576

The amount of cloth left over after making 1 shirt is:

Cloth left over = 36.25 meters - 23 meters = 13.25 meters

Therefore, 13.25 meters of cloth is left after making 1 shirt from a piece of cloth that is 36.25 meters long.

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Answer:

Step-by-step explanation:

The width of the soccer field in the drawing is 116 inches if the ratio is 2 inches to 1 yard

If 2 inches on the drawing represents 1 yard in reality, then 1 inch on the drawing represents 1/2 yard in reality.

So, to find the width of the soccer field in the drawing, we can use the following proportion:

1 inch on drawing / (1/2) yard in reality = x inches on drawing / 58 yards in reality

Simplifying this proportion, we get:

x inches on drawing = (1 inch on drawing / (1/2) yard in reality) * 58 yards in reality

x inches on drawing = 2 * 58

x inches on drawing = 116

Therefore, the width of the soccer field in the drawing is 116 inches.

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Answer: 9 3/10

Step-by-step explanation:

6 + 2/5 + 2 + 9/10= 6 + 2 = 8 = 2/5 + 9/10= 4/10 + 9/10= 13/10= 1  3/10= 8 + 1 + 3/10= 9 3/10

Answer:

$6235 1

' 1 . ' 8

Answer:

Step-by-step explanation:

As a result, the two new streets formed by reflecting and translating the expression original streets will be parallel and 5 units apart, with one to the left.

In mathematics, an expression is a group of representations, digits, and conglomerates that resemble a statistical correlation or regimen. An expression can be a real number, a mutable, or a combination of the two. Addition, subtraction, rapid spread, division, and exponentiation are examples of mathematical operators. Arithmetic, mathematics, and shape all make extensive use of expressions. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.  

If we reflect the line segment that represents Maple Street in the y-axis, the resulting street will be to the left of the y-axis, and if we translate it down 5 units, the new street will be parallel to but 5 units below the original Maple Street. Similarly, reflecting the line segment that represents Hazel Street in the y-axis results in a street to the right of the y-axis, and translating it down 5 units results in a new street parallel to the original Hazel Street but 5 units below it.

As a result, the two new streets formed by reflecting and translating the original streets will be parallel and 5 units apart, with one to the left.

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The 3 correct answers of the figures that could be the base for the pyramid that has a height of 5 inches and a volume of 60 cubic inches are:

The formula to find the base of a pyramid given its height and volume,

Volume of pyramid = (1/3) * Base area * Height

Substituting in the given values, we have:

60 = (1/3) * Base area * 5

Base area = 36 square inches

In conclusion, any figure with a base area of 36 square inches could be the base for this pyramid.

The following figures have a base area of 36 square inches:

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Answer:

B.......................

Answer:

In each statement:

The rate is the percentage or ratio that relates the quantity being described to the base.

The base is the total quantity or amount that the rate is applied to.

The percent is the rate expressed as a percentage, or the part of the base that corresponds to the rate.

Step-by-step explanation:

the answer will be 1272.7cm3

the formula of the volume of the cylinder is pie×radius squared×height so,

we will get the radius and the radius is half of the diameter and the diameter is 9 so 9÷2=4.5 and then it will be squared so it will be 20.25cm2 and so we will write it this way

3.14×20.25×20=1271.7cm3

hope this helped

xoxo adham

By  inverse proportions, 6.4 is the value of y .

What are some examples of inverse proportions?

In the case of two quantities that are inversely proportional, one quantity falls as the other rises. The number of hours needed to construct a wall serves as an illustration of inverse proportion. The time required to build a wall decreases as more people work on the same project.

 suppose that y =√kx

 enter (0.25,16) to y =√kx

    0.5k = 16

      k = 5

   y = 8√x

  when x = 0.64

  y = 8√0.64

 y = 6.4

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1. Option a, c and e fulfill the Pythagorean triplet rule.

2. Option a, e, and f are the correct options.

3. Yes as per the Pythagoras theorem, all the sides will be proportional to the similar triangle.

The formula for the Pythagoras theorem is written as c² = a² + b², where c is the hypotenuse of the right triangle and a and b are its other two legs.

As a result, the Pythagoras equation can be used to any triangle that has one angle that is exactly 90° to create a Pythagoras triangle.

In question 1,

The Pythagorean triplets we have are:

5, 12, 13 as they fulfill the c² = a² + b², formula.

5, 10, 5√5 and 20, 99, 101

In the second question, we have the triplet 7, 24, 25

So the triangles similar to this will have proportionate sides.

So 14, 48, 50(sides have been doubled)

√7, √24, √25 (sides have been square rooted) and

35, 120 and 125(sides have been multiplied by 5)

are the sides that are proportional.

In the last question,

If the triangle has Pythagorean triplets, then for the other triangle to be similar the sides has to be multiples of the triplets or proportionate to them.

In this case its true, so the triangles are similar to each other.

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The binary number 1001100 is equivalent to the decimal number 76.

HOW TO CONVERT BINARY TO DECIMAL?

To convert a number in base 2 (binary) to base 10 (decimal), we need to multiply each digit of the binary number with its corresponding power of 2 and then sum up the results. The rightmost digit corresponds to 2, the next digit to 2 the next to 2², and so on, with each successive digit corresponding to the next higher power of 2.

For example, to convert the binary number 1001100 to decimal, we would start by multiplying the rightmost digit (0) by 2 raise the power 0, which equals 1. We would then multiply the next digit (0) by 2 raise the power 1, which equals 0, and so on, until we reach the leftmost digit (1), which corresponds to 2 raise the power 6. We then add up all of these products to get the decimal equivalent of the binary number.

So, using this method, we have:

1 x 2⁶ + 0 x 2⁵ + 0 x 2⁴ + 1 x 2³+ 1 x 2² + 0 x 2¹ + 0 x 2°= 64 + 0 + 0 + 8 + 4 + 0 + 0 = 76

Therefore, the binary number 1001100 is equivalent to the decimal number 76.

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Answer:

24328.49 cm

Step-by-step explanation:

as (A = π r²). r is 88 so and is 24328.49cm

To convert 2/5 to a fraction, it is already a fraction in its simplified form, so we can leave it as is.

To convert 2/5 to a decimal, we can divide the numerator (2) by the denominator (5):

2 ÷ 5 = 0.4

Therefore, 2/5 is equivalent to the fraction 2/5 and the decimal 0.4.

The number of triangles formed or the interior angle sum to each regular polygon:

Number of triangles formed is 4 - Regular octagon

Interior angle sum is 1,440 - Regular dodecagon

Interior angle sum is 1,800 - Regular decagon

Number of triangles formed is 6 - Regular hexagon

A triangle is a geometric shape that consists of three straight line segments that are connected to form three angles. The three line segments are called sides and the three angles are located at the vertices (corners) where the sides meet.

Here,

The number of triangles formed in a regular polygon is related to the number of sides it has. For a regular polygon with n sides, the number of triangles formed is (n-2). For example, a regular hexagon has six sides, so the number of triangles formed is (6-2) = 4. The interior angle sum of a regular polygon is related to the number of sides it has as well. The formula to find the interior angle sum of a regular polygon with n sides is: Interior angle sum = (n-2) x 180 degrees

For example, a regular dodecagon has 12 sides, so its interior angle sum is (12-2) x 180 = 1,800 degrees. Similarly, a regular octagon has 8 sides, so its interior angle sum is (8-2) x 180 = 1,080 degrees.

Therefore, based on the given information, we can match the number of triangles formed and the interior angle sum to each regular polygon as follows:

Regular octagon: Number of triangles formed is 4 (column 1) and Regular octagon is matched to 1 (column 2).

Regular hexagon: Number of triangles formed is 6 (column 1) and Regular hexagon is matched to 2 (column 2).

Regular decagon: Interior angle sum is 1,800 (column 1) and Regular decagon is matched to 3 (column 2).

Regular dodecagon: Interior angle sum is 1,440 (column 1) and Regular dodecagon is matched to 4 (column 2).

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We are given the following lengths:

We will solve it by using this formula:

[tex]\boxed{\mathfrak{\purple {Median = \frac{1}{2}(lower \: base+upper \: base)}}}[/tex]

[tex]\boxed{\mathcal{\purple { XY = \frac{1}{2}( CO+PY)}}}[/tex]

[tex] \green{ \sf4m + 3 = \frac{1}{2} (2m - 10 + 3m + 37)}[/tex]

[tex] \red \implies \green{ \sf4m + 3 = \frac{1}{2} (5m+ 27)}[/tex]

[tex] \red \implies \green{ \sf4m + 3 = \frac{5}{2} m + \frac{27}{2} }[/tex]

[tex] \red \implies \green{ \sf8m + 6 = 5m + 27 }[/tex]

[tex] \red \implies \green{ \sf8m + 6 - 5m = 27 }[/tex]

[tex] \red \implies \green{ \sf8m - 5m= 27 - 6 }[/tex]

[tex] \red \implies \green{ \sf3m = 21 }[/tex]

[tex] \boxed{ \mathfrak{ \red{m = 7}}}[/tex]

[tex] \blue \longmapsto \orange{ \tt \: XY =4m + 3}[/tex]

[tex] \blue \longmapsto \orange{ \tt \: XY =4(7) + 3}[/tex]

[tex] \blue \longmapsto \orange{ \tt \: XY =28 + 3}[/tex]

[tex] \boxed{ \underline{ \underline{ \blue \longmapsto \orange{ \tt \: XY =31}}}}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: CO = 2m - 10}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: CO = 2(7) - 10}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: CO = 14 - 10}[/tex]

[tex] \boxed{ \underline{ \underline{ \purple \longmapsto \pink{ \tt \:CO=4}}}}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: PY = 3m + 37}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: PY = 3(7) + 37}[/tex]

[tex] \purple \longmapsto \pink{ \tt \: PY = 21 + 37}[/tex]

[tex] \boxed{ \underline{ \underline{ \purple \longmapsto \pink{ \tt \:PY=58}}}}[/tex]

Answer:

[tex]\textsf{16.}\quad m = 7[/tex]

[tex]\textsf{17.} \quad \overline{XY}=31[/tex]

[tex]\textsf{18.} \quad \overline{CO}=4[/tex]

[tex]\textsf{19.} \quad \overline{PY}=58[/tex]

[tex]\textsf{20.} \quad \overline{EV}=80.5\; \sf meters[/tex]

Step-by-step explanation:

The median of a trapezoid is the line segment that connects the midpoints of the non-parallel sides. It is parallel to the bases, and its length is equal to the average of the lengths of the two bases.

Given line segments:

    [tex]\bullet \quad \overline{CO}=2m-10[/tex]

    [tex]\bullet \quad \overline{PY}=3m+37[/tex]

    [tex]\bullet \quad \overline{XY}=4m+3[/tex]

As the length of the median XY is equal to the average of the lengths of the two bases we can set up the following equation:

[tex]\overline{XY}=\dfrac{\overline{CO}+\overline{PY}}{2}[/tex]

Substitute the expressions for each line segment into the equation and solve for m:

[tex]\begin{aligned}4m+3&=\dfrac{(2m-10)+(3m+37)}{2}\\2(4m+3)&=(2m-10)+(3m+37)\\8m+6&=5m+27\\8m+6-5m&=5m+27-5m\\3m+6&=27\\3m+6-6&=27-6\\3m&=21\\3m \div 3&=21 \div 3\\m&=7\end{aligned}[/tex]

Therefore, the value of m is 7.

Now we have calculated the value of m, simply substitute this value into each line segment expression to determine their measures:

[tex]\begin{aligned} \overline{XY}&=4m+3\\&=4(7)+3\\&=28+3\\&=31\end{aligned}[/tex]

[tex]\begin{aligned} \overline{CO}&=2m-10\\&=2(7)-10\\&=14-10\\&=4\end{aligned}[/tex]

[tex]\begin{aligned} \overline{PY}&=3m+37\\&=3(7)+37\\&=21+37\\&=58\end{aligned}[/tex]

[tex]\hrulefill[/tex]

The length of the median of a trapezoid is equal to the average of the lengths of the two bases.  

Given the bases of trapezoid LOVE are LO and EV, and the median is XY, we can set up the following equation:

[tex]\overline{XY}=\dfrac{\overline{LO}+\overline{EV}}{2}[/tex]

Given line segments:

    [tex]\bullet \quad \overline{LO} = 48.5[/tex]

    [tex]\bullet \quad \overline{XY} = 64.5[/tex]

To find the measure of the lower base EV, substitute the given values of the line segments into the equation and solve for EV:

[tex]\begin{aligned}\overline{XY}&=\dfrac{\overline{LO}+\overline{EV}}{2}\\\\64.5&=\dfrac{48.5+\overline{EV}}{2}\\\\2(64.5)&=48.5+\overline{EV}\\\\129&=48.5+\overline{EV}\\\\129-48.5&=48.5+\overline{EV}-48.5\\\\\overline{EV}&=80.5\end{aligned}[/tex]

Therefore, the measure of the lower base EV is 80.5 meters.

the vertex of the quadratic  function is (4,-25).

A quadratic function is a polynomial function with one or more variables where the highest exponent of the variable is 2. Due to the fact that the biggest degree term in a quadratic function is of second degree, it is sometimes referred to as the polynomial of degree two. It carries out algebraic functions.

examples of quadratic functions are:

f(x)=x²-8x-9

x-coordinate of vertex:

x=-b/2a

Putting the values, we get

x=-(-8)/2=4

Y-coordinate vertex:

y(4)=16-32-9=-16-9=-25

Vertex(4,-25)

Hence, the vertex of the function =(4,-25).

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Answer: 5.6 kilograms.

Step-by-step explanation:

We know that 1,000 paperclips have a mass of 1 kilogram.

Therefore, one paperclip has a mass of 1/1000 kilograms, or 0.001 kilograms.

To find out how many kilograms 5,600 paperclips have, we can multiply the mass of one paperclip (0.001 kilograms) by the number of paperclips:

0.001 kilograms/paperclip * 5,600 paperclips = 5.6 kilograms

Therefore, 5,600 paperclips have a mass of 5.6 kilograms.

The correct function that expresses the town's population after n decades is: p(n) = 8000 × 2ⁿ. So the initial population of the town is 8,000, which is consistent with the problem statement.

A function is a mathematical concept that describes the relationship between a set of inputs, called the domain, and a set of outputs, called the range.

A function assigns a unique output to each input, meaning that for a given input, there is only one possible output.

Starting with a population of 8,000, the population doubles every decade, which means it multiplies by 2.

After n decades, the population will have doubled n times, so we can express the population as 8,000 multiplied by 2 raised to the power of n:

p(n) = 8000 × 2ⁿ

This function gives us the population of the town after n decades, where n is a non-negative integer. If we substitute n=0 into the function, we get:

p(0) = 8000 × 2⁰ = 8000

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Answer:

Step-by-step explanation:

The corresponding equal angles must be written in the same order. So the first one is the correct answer.

With a significance level of 0.05, the. option that shows the correct test statistic, P- value, and conclusion is A. Test statistic, -1.952; P-value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.

In statistics, the significance level (denoted by α) is the probability of making a Type I error, which is rejecting a true null hypothesis. In other words, it is the maximum allowable probability of observing a result as extreme as or more extreme than the one observed, assuming the null hypothesis is true.

The significance level is typically set by the researcher before conducting a hypothesis test and is usually set to 0.05 (5%) or 0.01 (1%). If the p-value of the test is less than or equal to the significance level, the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than the significance level, the null hypothesis is not rejected.

The correct option is A.

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With a significance level of 0.05, which of the following shows the correct test statistic, P- value, and conclusion?

Test statistic, -1.952; P-value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.

Test statistic, = 0.3619; P-value, 0.6392. There is insufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.

Test statistic, -1.952; P-value, 0.0509. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.

Test statistic, t=0.3651; P-value, 0.6425. There is insufficient evidence to reject the null hypothesis of

no difference between the triglyceride test levels.

by simplifying the expression, option d ,sec θ is the correct answer.

how can we solve this expression?

We can simplify the given expression as follows:

(tan θ - [tex]sec^2[/tex] θ) / tan θ

= (tan θ / tan θ) - ([tex]sec^2[/tex] θ / tan θ) ,

by diving it by tan θ

= 1 - (1/[tex]cos^2[/tex] θ)([tex]sin^2[/tex] θ / cos θ),

since sec = 1/cos and tan=sin/cos

placing the value in expression and solving it , we get

= 1 - ([tex]sin^2[/tex] θ / ([tex]cos^3[/tex] θ))

= [tex]cos^3[/tex] θ / [tex]cos^3[/tex] θ - [tex]sin^2[/tex] θ

= [tex]cos^3[/tex]θ / [tex]cos^2[/tex] θ (1 - [tex]tan^2[/tex] θ)

We can simplify the given expression as follows:

= cos θ ( [tex]cos^2[/tex]θ -  [tex]sin^2[/tex]θ) / ([tex]cos^2[/tex] θ)

= cos θ (cos θ / [tex]cos^2[/tex]θ)

= 1/cos θ is equal to sec θ

Therefore, the simplified expression is sec θ.

Hence, the answer is option (d) sec θ.

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Answer:

260

Step-by-step explanation:

First you find the area of the triangle

1/2×base×height

1/2×20×10

=100

Then you find the area of the rectangle

A=l×b

=20×8

=160

Then you add the area of the triangle with the area of the rectangle

160+100=260

As a result, the length of the hypotenuse AB is three times that of the side that is perpendicular to angle B, denoted by the symbol x.

Length, which is typically expressed in units like meters, feet, or inches, is a measurement of an object's size or the separation between two locations. It alludes to the measurement of an object's longest dimension or the separation between two ends. The term "length" can also be used to describe the extent of a line or the linear separation between two locations, such as the length of a triangle's side, a road, or a length of rope. In geometry, length is a crucial mathematical notion that is used to gauge an object's size, shape, and location.

given

The length of the side directly across from the angle divided by the length of the hypotenuse is known as the sine of an angle. Here are the facts:

60° sine + (BC/AB)

Using sin 60°, whose value is 3/2, as an example:

√3/2 = (BC/AB)

Multiplying AB by both sides:

BC = AB * √3/2

The hypotenuse's length is determined by adding the squares of the lengths of the other two edges. Here are the facts:

We have the following by substituting the earlier-obtained formulas for AC and BC:

Adding 3 to both sides:

4AB2 + 9AB2 = 12AB2

AB = 3x

As a result, the length of the hypotenuse AB is three times that of the side that is perpendicular to angle B, denoted by the symbol x.

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