HELP PLEASE
Which one of the following absolute value equations and inequalities have a solution set that is NOT the empty set?
O |2x-51|-3 = -2
O |5x-1| +8 < 6
O 3|x-4|+5 < 4
O 2|x + 7| +3 = 2

Time taken by hose B to fill the vat alone = 9 hours

Let 'x' be the capacity of the vat filled in an hour.

Hose A can fill the vat in 3 hours. i.e., 3x quantity is filled in the vat.

After 2 hours of pumping, 2x/3x = 2/3 of the vat is filled.

The remaining to be filled is x/3x = 1/3 capacity of the vat.

It takes 3 hours for hose B to fill the remaining 1/3 capacity of the vat alone.

Let t be the time taken by hose B to fill the whole vat .i.e., 3/3 = 1 capacity of the vat.

In ratio form, 3 : t = 1/3 : 1.

Thus Time taken by hose B to fill the vat alone = 3 ÷ 1/3

                                                                              = 3 x 3

                                                                              = 9 hours

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The range of the composite function (w o r)(x) is (a) (-oo, 0)

From the function, the definition of the functions are given as:

r(x) = 2 - x²

w(x) = x - 2

The composite function (w o r)(x) is calculated as

(w o r)(x) = w(r(x))

This means that:

(w o r)(x) = w(2 - x²)

So, we have

(w o r)(x) = 2 - x² - 2

Evaluate the like terms

This gives

(w o r)(x) = -x²

The above function is a quadratic function, and the range is all set of negative numbers

This can be represented as (-oo, 0)

Hence, the range is (-oo, 0)

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If the hypotenuse of PQR triangle is 5 and perpendicular is [tex]\sqrt{2}[/tex],then value of sin²R is 2/25.

Given that the hypotenuse is 5 and perpendicular is [tex]\sqrt{2}[/tex].

We are required to find the value of sin²R.

Trigonometric ratios are basically the ratios of the sides of the right angled triangle.

Sin is the ratio of perpendicular and hypotenuse of the right angled triangle. We can easily find the value of sin²R with the help of ratio of perpendicular and hypotenuse.

sin R=PQ/PR

sin R=[tex]\sqrt{2}[/tex]/5

Squaring both sides,

sin² R=[tex](\sqrt{2} )^{2}[/tex]/[tex](5)^{2}[/tex]

sin²R=2/25

Hence if the hypotenuse is 5 and perpendicular is [tex]\sqrt{2}[/tex],then value of sin²R is 2/25.

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Answer:

Step-by-step explanation:

the answer would be A because it can be 1 or 6 so if 1/6 means just one number then 2 numbers would 2/6

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). The rectangle's longer side is its length, while its shorter side is its breadth.

A laptop has four sides, with the opposite sides being parallel to one another and having equal lengths. As a result, a laptop stands out as a common example of a rectangle-shaped device in everyday life. The keyboard and a monitor's screen are both rectangular objects in a similar way.

Note that the following are the measurements for a rectangle's perimeter:

(Length Plus Width) = 2

= 2(25x + 12) + 2(7x + 18)

= 50x + 24 + 14x + 46

= 64x + 70

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The graph of  y = -f(x) + 3 is a graph that has a negative slope and is attached.

A graph is a representation of data using the coordinate system. There are different types of graph each defining the required data.

The graph of equation of a straight line is one of the types of graphs. The graph of the form y = mx + c represents the equation of a straight line. The terms are defined as follows

The slope is a function of x and from the question it is negative.

The graph is plotted and attached

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Answer:

Sara has 39 and Jenny has 19.5

Step-by-step explanation:

The volume of the liquid in the chemistry experiment will decrease by 25%.

For the given question.

The percentage decrease would be calculated as follows:

Percentage decrease = (25.2 - 18.9)  / 25.2

Percentage decrease = 6.3/25.2

Percentage decrease = 0.25

Percentage decrease = 0.25 x 100 = 25%

As a result, the volume will decrease by 25%.

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The probability of best simulations to choose one pair of shoes from two and one pair of socks from six can be to flip a coin and roll a die, respectively.

The total number of shoe pairs = 2

The number of pairs that need to be chosen from the total = 1

That is, the probability of choosing one pair out of 2 = 1 ÷ 2 = 0.5

The best simulation for 0.5 probability is flipping a coin, as it has the same probability ratio and has 2 sides to choose from.

The total number of sock pairs = 6

The number of pairs that need to be chosen from the total = is 6

That is, the probability of choosing one pair out of 6 = 1 ÷ 6

The best simulation for 1 ÷ 6 probability is rolling a die, as it has the same probability ratio and has 6 sides to choose from.

Hence, the best simulations are flipping a coin and rolling a die in the given case.

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Dr. Price traveled a total of 1888.86 meters distance between Locations B and A and Locations A and C.

The mileage traveled overall is:

(Distance from B to A) + (Distance from A to C)

Location B = -1098.15

Location A = -895.9

Location C = -12784.75

Distance from B to A:

The distance in absolute terms between B and A

= -1098.15 - (895.9)

= -1098.15 + 895.9

= -202.26

= 202.26

Distance from A to C:

The distance in absolute terms between A and C

= -895.9 - (-2784.75)

= -1098.15 + 2784.75

= 1686.6

The total distance traveled is (202.26 + 1686.6) = 1888.86 meters

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The consecutive even numbers are 12 and 14.

Even numbers can be divided into two equal groups or pairs and are exactly divisible by two. For instance, 2, 4, 6, 8, and so on. These numbers can be divided into equal groups. Consecutive numbers are numbers that follow each other in descending order from smallest to greatest. Consecutive even numbers are even integers that are separated by a factor of two.

Let the consecutive even numbers be x and x+2.

The sum of the numbers is 340. This will be illustrated as:

x² + (x + 2)² = 340

x² + (x + 2)(x + 2) = 340

x² + x² + 4x + 4 = 340

Collect like terms

2x² + 4x + 4 - 340 = 0.

2x² + 4x - 336 = 0

Divide through by 2

x² + 2x - 168 = 0

x² - 14x + 12x -168 = 0

x(x - 14) + 12(x - 14) = 0.

(x + 12)(x - 14) = 0

This shows that the numbers are 12 and 14

Check: 12² + 14² = 144 + 196 = 340.

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Any exponential function will contain a horizontal asymptote of y = 0.

Therefore, the correct answer is as follows:

A horizontal asymptote is a line that runs along the x-axis of a function graph but is not actually a part of the graph itself. "far" right or left, depending on your preference. Eventually, whether it is large enough or little, the graph may cross it.

The initial value of this function exists as the y-intercept, marked as (0, 5). The label on the graph tells you this exists the snake population in year 0.

We note that the snake population goes up by a factor of 2 for each increase of 1 in the number of years. This means the function exists as an exponential function with a base of 2.

y = 5·[tex]$2^t[/tex]

Any exponential function will contain a horizontal asymptote of y = 0.

Therefore, the correct answer is as follows:

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]3x+2y=8\implies 2y=-3x+8\implies y=\cfrac{-3x+8}{2} \\\\\\ y=\cfrac{-3x}{2}+\cfrac{8}{2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{2}}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

3

Step-by-step explanation:

Because Math is math and math

By using all the values of the data set ,

(a) The range for the given set is 9 .

(b) The variance is 6.2045 .

(c) Standard Deviation is 2.49083 .

In the question,

it is given that 12 students gave an arithmetic test , the time (in min) is given as

10, 9, 12, 11, 8,15, 9, 7, 8, 6, 12, 10 .

Arranging the data set in ascending order , we get

6,7,8,8,9,9,10,10,11,12,12,15

Part(a)

the range is calculated by using the formula

Range = highest value - lowest value

Range = 15-6 = 9

Part(b)

calculating , the mean

mean = (6+7+8+8+9+9+10+10+11+12+12+15)/12

= 117/12

= 9.75

Variance can be calculated using the formula

Variance = [tex]\frac{\sum(\(x_i-\bar{x})^{2} }{n-1}[/tex],

where [tex]x_i[/tex] represents the different terms , and

[tex]\bar{x}[/tex] represents the mean .

Substituting the values from the data given ,  we get

Variance = [(6-9.75)²+(7-9.75)²+(8-9.75)²+(8-9.75)²+(9-9.75)²+(9-9.75)²+(10-9.75)²+(10-9.75)²+(11-9.75)²+(12-9.75)²+(12-9.75)²+(15.9.75)²] / (12-1)

On further simplifying , we get

= 68.25/11

= 6.2045

Part(c)

Standard Deviation = √Variance

Substituting the value of variance from above

we get ,

standard deviation = √6.2045 = 2.49083

Therefore , By using all the values of the data set ,

(a) the range is 9.

(b) Variance is 6.2045

(c) Standard Deviation is 2.49083

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Answer: 16 times longer

Step-by-step explanation: 6.4 divided by 0.4 is equal to 16.

Answer:rerrrrrrrrrrrrrrrrrrrrrrrrrrrrr

Step-by-step explanation:eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answer:

[tex]{ \rm{ \sqrt{ \frac{1 + \cos(x) }{1 - \cos(x) } } }} \\ \\ [/tex]

- Rationalize the denominator of the above expression;

[tex]{ \rm{ = \sqrt{ \frac{(1 + \cos(x)).(1 + \cos(x)) }{(1 - \cos(x)).(1 + \cos(x)) } } }} \\ \\ = { \rm \sqrt{ \frac{( {1}^{2} + 2 \cos(x) + \cos ^{2}(x)) }{( {1}^{2} - { \cos }^{2}(x)) } } } \\ \\ = { \rm\sqrt{ \frac{(1 + 2 \cos(x) + { \cos }^{2} (x)) }{(1 - { \cos }^{2}(x)) } } }[/tex]

- From the above expression, 1 - cos²x = sin²x

[tex] = { \rm{ \sqrt{ \frac{1 + 2 \cos(x) + { \cos }^{2}(x) }{ { \sin }^{2}(x) } } }} \\ [/tex]

[tex] = { \rm{ \sqrt{ \frac{ {(1 + \cos(x)) }^{2} }{ { \sin}^{2}x } } }} \\ \\ = { \rm{ \frac{ \sqrt{(1 + \cos(x)) {}^{2} } }{ \sqrt{ { \sin}^{2} x} } }} \\ \\ = { \rm{ \frac{1 + \cos(x) }{ \sin(x) } }} \\ \\ = { \rm{ \frac{1}{ \sin(x) } + \frac{ \cos(x) }{ \sin(x) } }} \\ \\ = { \boxed{ \rm{ \: \csc(x) + \cot(x) \: }}}[/tex]

Given the angles in the trapezoid:

• 36 degrees

• 113 degrees

Let's find the values of a and b.

In a trapezoid, the angles on the same side of one transversal are supplementary angles and supplementary angles sum up to 180 degrees.

Hence, we have:

a° + 36° = 180°

b° + 113 = 180°

Now, let's solve for a and b.

a° + 36° = 180°

Subtract 36° from both sides:

a° + 36° - 36° = 180 - 36°

a° = 144°

b° + 113° = 180°

Subtract 113 from both sides:

b° + 113° - 113° = 180° - 113°

b = 67°

Therefore, the values of a and b are:

a = 144

b = 67

ANSWER:

• a = 144

• b = 67

1275 spaces are in the parking garage.

What is linear addition?
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Two whole numbers added together result in another whole number. Two natural numbers added together will provide the original natural number once again. Two integers added together will result in an integer; two positive integers added together will result in a positive integer; two negative integers added together will result in a negative number; and one positive and one negative integer added together will result in an integer with the same sign as the largest number.

Given, total number of cars parked in garage = 551
Empty spaces available in first floor = 128
Empty spaces available in second floor = 294
Empty spaces available in third floor = 302
Therefore, total spaces in the parking garage = 551 + 128 + 294 + 302
= 1275
Thus, 1275 spaces are in the parking garage.

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a) If function be [tex]$f(x)=\frac{x^2+(17-4 x)}{9 x}$[/tex] then the value of f(5) = 22/45.

b) If function be g(x) = 3 x² - 6x + 9 then the value of g(x + 3) = 3x² + 12x + 18.

c)  If the function be [tex]$h(y)=\frac{y^3-5}{7 y}$[/tex] then the value of [tex]$h(2x) =\frac{8 x^3-5}{14 x}$$[/tex].

a) Let the function be [tex]$f(x)=\frac{x^2+(17-4 x)}{9 x}$[/tex]

substitute the value of x = 5, then

[tex]$f(5) = \frac{5^2+(17-4 \cdot 5)}{9 \cdot 5}$$[/tex]

simplifying the above equation, we get

[tex]$=\frac{22}{45}$$[/tex]

Therefore, the correct answer is 22/45.

b) Let the function be g(x) = 3 x² - 6x + 9

substitute the value of g(x) = g(x + 3), then we get

To estimate the value of g(x + 3) = 3(x + 3)² - 6(x + 3) + 9

= 3x² + 18x + 27 - 6(x + 3) + 9

simplifying the above equation, we get

=3x² + 18x + 27 - 6x - 18 + 9

Group like terms, we get

= 3x² + 18x - 6x + 27 - 18 + 9

=3x² + 12x + 27 - 18 + 9

= 3x² + 12x + 18

Therefore, the value of g(x + 3) = 3x² + 12x + 18.

b) Let the function be [tex]$h(y)=\frac{y^3-5}{7 y}$[/tex]

substitute the value of y = 2x, then we get

[tex]$h(2x)=\frac{(2x)^3-5}{7 (2x)}$[/tex]

simplifying the above equation, we get

[tex]$=\frac{8 x^3-5}{7 \cdot 2 x}$$[/tex]

[tex]$=\frac{8 x^3-5}{14 x}$$[/tex]

Therefore, the value of [tex]$h(2x) =\frac{8 x^3-5}{14 x}$$[/tex].

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In order to find how much stronger was the first gust than the second, we just need to subtract their values.

So we have that:

So the strongest wind gust was 4 miles per hour stronger than the second strongest wind gust.

Given data:

The given principal is P=$20,000.

The given rate of interest is r=6%.

The given time is t=20 years.

The expression for the interest is,

Substitute the given values in the above expression.

Thus, the interest earned after 20 years is $44,142.71, so (C) option is correct.

ABC =ADE

WILL BE ITS ANSWER

Using Pythagoras's theorem we can calculate that the bucket must reach57.134 feet .

We know from the Pythagoras theorem of aright angled triangle , the sum of squares of the two legs of a right triangle is equal to the square of the hypotenuse of the same triangle.

From the question we can ascertain that the height at which the cat is stuck is 40.4 feet.

Now it is given that the rescue ladder came in at 45 ° . So the length of the legs are equal.

Therefore length of ladder which is the hypotenuse = √(2×40.4²)

Length = 57.134... feet

length ≈ 57.13 feet

Therefore the bucket must reach 57.13 feet which is the height at which the cat is stuck on the tree of length 40.4 feet.

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Hello, the detailed answer is given below. Good luck!

Step-by-step explanation:

The function in option number C is a linear function.

Here, we are given 4 functions. Let us check them one by one to see if they are linear or not-

A. In this function, if x = 0, y =11

if x = 1, y = 7

Thus, if x increases by 1, y increases by 4.

but now if we see when x = 2, y = 5 which is not an increase of 4.

Thus, the given function is not linear.

B. In this function, if x = 0, y = 0

if x = 1, y = 0

Thus, if x increases by 1, y increases by 0.

but now if we see when x = 2, y = -1 which is not an increase of 0.

Thus, the given function is not linear.

C. In this function, if x = 0, y = 6

if x = 1, y = 12

Thus, if x increases by 1, y increases by 6.

when x = 2, y = 18 which is an increase of 6.

similarly, when x = 3, y = 24 which is an increase of 6.

Thus, the given function is linear.

Hence function in option number C is a linear function.

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Applying precedence of operations, the missing expressions are given as follows:

a) Step 2: [tex]\left(\frac{8^2 + 2}{0.5}\right)[/tex] - 12.4/4.

b) Step 6: 132 - 3.1.

The precedence of operations is defined according to the PEMDAS acronym, with the meaning of each letter being given as follows:

In Step 2, the absolute value operation is interpreted as a parenthesis, hence having a higher precedence over the exponent 8², then the expression is given by:

[tex]\left(\frac{8^2 + 2}{0.5}\right)[/tex] - 12.4/4.

In Step 6, the division of 12.4 by 4, with a result of 3.1, has a higher precedence than the subtraction, hence the expression is given as follows:

132 - 3.1.

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