Simplify the expression to a polynomial in standard form: (4x-1)(3x-2)(x+1)

The percent decrease in the number of people who went to the pool over these four weeks is 15%.

The number of people in each week will be recorded below:

First week = 1020

Second week = 1020 - 100 = 920

Third week = 920 + 145 = 1065

Fourth week = 1065 - 198 = 867

The percent decrease in the number of people who went to the pool over these four weeks will be:

= (1020 - 867) / 1020 × 100

= 153 / 1020 × 100

= 15%

The percentage decrease is 15%.

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Answer:

98 laps

Step-by-step explanation:

(5x 14) + (2 x 14)

70+ 28 =98

With the slope and one point of the line, Using the formula of equation of line with slope and a point, The answer is [tex](y-y_1)= m (x-x_1)[/tex] .

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.

points= ([tex]x_1 , y_ 1[/tex])

slope = m

Required equation,

[tex](y-y_1)= m (x-x_1)[/tex]

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Answer:

Can you make another post showing us a picture of the Geometry book page 599? I may be able to help :-)

The vertex of the graph of f(x) = |x - 5| - 6 is (5, -6). It lies in the fourth quadrant.

Therefore the answer is (5, -6).

The graph f(x) = |x - 5| - 6 is symmetrical about the axis  x = 5.

A vertex of a graph is a node of a graph. For a graph of the form f(x) = a|x - h| + k, the vertex is (h, k). So in this case where f(x) = |x - 5| - 6, a = 1, h = 5 and k = -6. Therefore the vertex of the given graph f(x) is

(5, -6)

--The question is incomplete, answering to the question --

"What is the vertex of the graph of f(x) = |x - 5| - 6?"

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The probability that two red balls are chosen from the vase would be = 1/9

Probability is defined as the concept that proves that an event may occur or not.

The number of red balls = 7

The number of black balls = 2

The number of green balls = 9

The total number of balls in the vase = 18

The probability of getting 2 red balls = 2/18 = 1/9

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You can locate your SSS loan number scrawled on the upper right corner of your E-1 form if you applied for one in 2015 or earlier and still have a copy of it.

The personal information of an SSS member is contained on the SSS E1 form (also known as the E-1 form). Prior to receiving a social security number, a person must submit the E1 form to apply for membership in the Social Security System.

The applicant must complete the form with his personal data (such as name, date of birth, and home address), a list of dependents or beneficiaries, and, if self-employed, his profession or company.

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On a frictionless horizontal table, the rocket-powered hockey puck moves at an angle of 61.9° above the horizontal in 3 seconds.

The significance of non-zero digits is constant. Between any two significant digits, there can be no zeros. Only the final or trailing zeros in the decimal section are important. Between any two non-zero digits, all zeros are important. Seven significant digits are seen in, for instance, 108.0097. There is never any significance for any zeros that are both to the right and left of the decimal point and a digit that is not zero.

given

Then, using the formula that relates the tangent of angle, vertical component of velocity, and horizontal component of velocity to find the direction in which the puck is moving.

Displacement is the smallest distance between the two points.

The vector representation of velocity is,

s = 1/2at2

= 1 .80 m

The puck moves at an angle 61.9° above the horizontal.

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The polynomial function p(x) = 5x³ - 5x² - 10x have zeros of 0, -1 and 2

The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero. They are interesting to us for many reasons, one of which is that they tell us about the x-intercepts of the polynomial's graph. We will also see that they are directly related to the factors of the polynomial.

The polynomial function given is

p(x) = 5x³ - 5x² - 10x

The zeros of the function are 0, 2, -1

To test the zeros if they are the roots of the polynomial

p(0) = 5(0)³ - 5(0)² - 10(0)

p(0) = 0

p(2) = 5(2)³ - 5(2)² - 10(2)

p(2) = 0

p(-1) = 5(-1)³ - 5(-1)² - 10(-1)

p(-1) = 0

The zeros are 0, -1, and 2 to the polynomial

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The value of k is 9 for quadratic equation 3x²+2kx+27=0 whose roots are real and equal.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given equation 3x²+2kx+27=0

Here, a=3,b=2k,c=27

It is given that roots are real and equal.

b²-4ac=0

(2k)²-4(3)(27)=0

4k²-324=0

4k²=324

Divide both sides by 4

k²=81

Take square root on both sides

k=±9

Hence, the value of k is 9 for quadratic equation 3x²+2kx+27=0 whose roots are real and equal.

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All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.

Congruent Figures :

Those figures which covers each other/one another exactly then they are congruent Figures.

There are 4 ways by which we can prove any 2 triangles as congruent :

If they are having -

Three pairs of side are equal then the triangles are congruent.

If any 2 pairs of angles and 1 side are equal then the triangles are congruent.

If any two pairs of sides and the included angle are equal then the triangles are congruent.

If any right angle triangles are having their hypotenuse and a pair of sides equal then they are congruent.

So, all three pairs of corresponding sides are equal then are congruent to each other.

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Answer:

a) $13.75

b) $41.24

Step-by-step explanation:

Original price: $54.99

Discount: 25%

Amount of discount: 25% of $54.99 = 25/100 × $54.99 = 0.25 × $54.99 = $13.75

Sale price: $54.99 - $13.75 = $41.24

The option that has correct quotient is option A = 4.15 ÷ 2.5 and Option B = 0.415÷0.25

How to find which has a quotient?

Quotient * Dividend  =  Divisor

A. 4.15 ÷ 2.5

Quotient = 1.66

Divisor = Quotient * 2.5

= 1.66 * 2.5

= 4.15

So, Option A is a correct answer.

B. 0.415÷0.25

Divisor = Quotient * 0.25

= 1.66 * 0.25

= 0.415

So, Option B is a correct answer.

C. 41.5÷0.25

Divisor = Quotient * 0.25

= 1.66 * 0.25

= 0.415 ≠ 41.5

So, Option C is not a correct answer.

D. 4.15÷0.25

Divisor = Quotient * 0.25

= 1.66 * 0.25

= 0.415 ≠  4.15

So, Option D is not a correct answer.

E. 0.415 ÷ 2

Divisor = Quotient * 0.25

= 1.66 * 2

= 3.32 ≠  0.415

So, Option E is not a correct answer.

Hence, The option that has correct quotient is option A = 4.15 ÷ 2.5 and Option B = 0.415÷0.25

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The slope of the given line y = -(4/5)x + 3 is -(4/5).

The slope of a line is defined as the gradient of the line.

The slope of a line is a measure of its steepness. It is defined as the change in y (the "rise") divided by the change in x (the "run") between two points on the line.

The equation is given in the question as:

y = - (4/5)x + 3

To find the slope of a line given by the equation y = mx + b, where m is the slope and b is the y-intercept, we can just take the coefficient of x, which is m.

As per the question, the coefficient of x is -(4/5), so the slope of the line is -(4/5).

Therefore, the slope of the given line is -(4/5).

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The relation is not a function because the element 17 is paired with two elements in the range (17 and 0). Therefore, the relation is not a function.

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Yes,  All equilateral triangles are similar to each other.

No,  All equilateral triangles are not congruent to each other.

The fact that every angle in an equilateral triangle is equal to 60 degrees is one of its characteristics.

According to the AAA Triangle Similarity Postulate, two triangles are similar  if all of their angles are identical to their corresponding angles in another triangle.

According to the AAA Postulate, all equilateral triangles are similar because their angles are all 60 degrees.

The reason is that although an equilateral triangle's angles are all 60 degrees, their corresponding sides are not necessarily the same .

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The correct answer is 138 students.

x = .24 * 575

x = 138 students

Therefore, the correct answer is 138 students.

The required length of licorice for $1.80 is given as 18 in.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

here,
The price of licorice is proportional to its length. It costs $0.50 to buy 5 in; it is uncertain how much licorice you can get for $1.80.
Let the price be y and the length be x,
according to the quesiton,
y = kx,
put y = 0.50 and x = 5
0.50 = 5k
k = 0.1

Now

y = 0.1 x
for
y = 1.8
1.8 = 0.1x
x = 18

Thus, the length of licorice necessary for $1.80 is specified as 18 in.

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The value of the sum of the functions f(x) and g(x), (f + g)(x) is 5x³ - 4x.

The outputs for a certain set of inputs can be referred to as a function.

A function's inputs are referred to as its independent variables, while its outputs are referred to as its dependent variables.

Given, f(x) = x³ + 8 and g(x) = 4x³ - 5x - 8.

Let, f(x) = x³ + 0x + 8.

We know, (f + g)(x) = f(x) + g(x).

Therefore, (f + g)(x) = (x³ + 0x + 8) + (4x³ - 5x - 8).

(f + g)(x) = x³ + 4x³ + 0x - 4x + 8 - 8.

(f + g)(x) =  5x³ - 4x.

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The percent that the average score on the test increased during the two months is 12.5%.

It should be noted that mean simply means the average of a set of numbers that are given. In this case, the average test score of RSM students in September increased by 10%. In October it increased by another 15%..

The average of the increase will be:

= (10% + 15%) / 2

= 25% / 2

= 12.5%

The average is 12.5%.

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Mode of the distribution 3, 5, 7, 4, 2, 1, 4, 3, 4 is 4.

As per the question the data given is 3, 5, 7, 4, 2, 1, 4, 3, 4.

Now we have to determine the mode of the given distribution.

Mode: A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.

The simple way to determine the mode is the most repeated data.

The number or the value which is "repeated more number of times compared to the other values".

From the data given:

3 repeated two times.

5 repeated one time.

7 repeated one time.

4 repeated three times.

2 repeated one time.

1 repeated one time.

Therefore the value of mode is 4.

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Divide the base for that period by the appropriate commission rate to determine your commission for that period. Mark earns more money.Since $1680 > $1080, Mark earns more.

This is a pretty straightforward computation based on percentages. Simply take the selling price, multiply it by the commission rate, then divide the result by 100.

Mark: $24/h; 150% OT

Calculate Mark's overtime (OT) pay

Convert OT rate to decimals --> 150% = 1.5

Mark's OT wage is 1.5*$24 = $36

Mark worked for 20h OT. (60h-40h = 20h)

(Regular pay X regular hours worked) + (OT wage X OT hours worked)

= ($24 X 40h) + ($36 X 20h)

= $1680

Joe: 5% commission

Convert 5% to decimals --> 0.05

(Jewelry sold) X (commission rate)

= $21000 X 0.05

= $1050

Since $1680 > $1080, Mark earns more.

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The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.

The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane. The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

V=b*h

b=base area of prism

h=height of prism

The volume of a prism is calculated as V=Bh, where B is the base area and h is the height.

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Answer:

40 minutes

Step-by-step explanation:

rate = distance/time = miles/hr

rate = 240 mi/2 hr = 120 mi/hr

time = distance / rate = (80 mi)/(120 mi/hr) = 0.67 hr = 40 minutes

(0.67 hr)(60 min/hr) = 40 minutes

The Multiplicative Inverse of the number 6 is "1/6" .

The Inverse (Multiplicative) of the number is the number that when multiplied by the original number gives the product as 1 .

which means the product of the number and its multiplicative inverse is 1 .

the number is given to be 6 .

So , let the multiplicative inverse of 6 be = x .

So , According to Definition of Multiplicative Inverse ,

we can write : x * 6 = 1

dividing both side by "6" .

we get ;

x = 1/6 .

Therefore , the multiplicative inverse is 6 .

The given question is incomplete , the complete question is

What is the Multiplicative Inverse of 6 ?

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199 feet in meters

1 foot = 0.3048 meters

[tex]0.3048(meters)\times199(feet)[/tex]

[tex]=\fbox{60.66}[/tex]

10800 mm³ is the volume of the unsharpened pencil.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that the unsharpened pencil is in the shape of a hexagonal prism with base area of 54 mm².

The length of hexagonal prism is  20 cm.

Let us convert cm to mm

1 cm = 10 mm

20 cm =200 mm.

Volume of hexagonal prism V=Ah.

A is the base area and h is the height.

V=54×200

=10800 mm³.

Hence,  volume of an unsharpened pencil is in the shape of a hexagonal prism with base area of 54 mm² and length of 20 cm is 10800 mm³.

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The value of x° and y° are 26.8° and  86.2°.

What is rounding to tenth?

Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5.

The length of sides of the triangle are 8, 6, and 5.

Assume that AB = c = 6, BC = a = 5, and AC = b = 8

m∠A = x° and m∠B = y°.

Cosine law:

c² = a² + b² - 2ab cos C  ....(i)

b² = a² + c² - 2ac cos B  ....(ii)

a² = b² + c² - 2bc cos A  ....(iii)

Putting a = 5, b = 8, c = 6, and A = x° in law (iii)

5² = 8² + 6² - 2×8×6 cos x

25 = 64 + 36 - 84 cos x

84 cos x = 75

cos x = 75/84

x = 26.76°

x = 26.8°  (nearest tenth)

Putting a = 5, b = 8, c = 6, and B = y° in law (ii)

8² = 5² + 6² - 2×5×6 cos y

64 = 25 + 36 - 60 cos y

60 cos y = 4

cos y = 4/60

y =86.177°

y =86.2°

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Median is the only average to be used while dealing with qualitative data which cannot be measured quantitatively but still can be arranged in ascending or descending order of magnitude,

e.g., to find the average intelligence among a group of people.

It is to be used for determining the typical value in problems concerning wages, distribution of wealth, etc.

It helps us to identify if the distribution is symmetric or not.

The mean and median of a symmetric distribution are close together.

If the distribution is exactly symmetric, the mean and median are exactly the same.

In a skewed distribution, the mean is farther out in the long tail than the median.

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Answer:

Step-by-step explanation:

To find the exact value of x, we need to solve the given equation for x. The equation is:

32^1/25 x 2^x = 8^1/4

To solve this equation, we need to rewrite it in a form that allows us to isolate the variable x. We can start by using the properties of exponents to simplify the left-hand side of the equation. We can use the property that says that raising a number to a fractional power is the same as taking the square root of that number, raised to the power of the denominator of the fraction. So, we can write:

(32^1/25)^2 = (32^1/25)^25/25 = 32^1/25

This simplification allows us to rewrite the left-hand side of the equation as follows:

32^1/25 * 2^x = (32^1/25)^2 * 2^x

Next, we can use the property of exponents that says that the product of two numbers raised to the same power is equal to the product of the numbers, raised to that power. So, we can rewrite the left-hand side of the equation as follows:

(32 * 2)^1/25 * 2^x = (32^1/25)^2 * 2^x

Then, we can use the property of exponents that says that raising a product to a power is the same as raising each factor to that power. So, we can rewrite the left-hand side of the equation as follows:

(32^1/25) * 2^(1/25 + x) = (32^1/25)^2 * 2^x

Finally, we can use the property of exponents that says that the exponent of a power is equal to the product of the exponents of the base and the power. So, we can rewrite the left-hand side of the equation as follows:

(32^1/25) * 2^(1/25 * 25 + 1 * x) = (32^1/25)^2 * 2^x

Since the right-hand side of the equation is already in a form that allows us to isolate the variable x, we can now use the property of exponents that says that raising a number to a power and then taking the square root of that number is the same as