50 people purchase item 5( the item 5 cost $18.94). seven of these customers use a coupon for 15% off. how much money do you make off the sales of item 5?

The value of each trigonometric identity is:

3/2

5/6

14/3

We have,

We will use the trigonometric formula and substitute the given values.

So,

Cosec θ

This can be written as,

= 1/ sin θ

= 1/(2/3)

= 3/2

And,

Sin θ

This can be written as,

= 1/ cosec θ

= 1/(6/5)

= 5/6

And,

Sec θ

This can be written as,

= 1/cosθ

= 1/(3/14)

= 14/3

Thus,

The value of each trigonometric identity is:

3/2

5/6

14/3

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Answer:

C

Step-by-step explanation:

The answer is C, 12 and 13, because the exact square root of 156 is about 12.5. On a number line, 12.5 is in between 12 and 13. Hope this helps, good luck, and God bless!

In the second step of solving the inequality 5x - 9 < 91, the property used is the addition property of inequalities.

This property states that adding the same value to both sides of an inequality does not change the inequality's direction. By adding 9 to both sides of the inequality, we aim to isolate the variable term. The inequality becomes 5x < 100.

The addition property allows us to perform this operation and maintain the validity of the inequality. It is a fundamental property in solving inequalities, enabling us to simplify and manipulate expressions.

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Thus, Shawn runs 3.6 miles per hour. Russ needs  3.57 hours to run every mile.

A unit is one of a particular object. An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator.

A particular kind of ratio is a unit rate ( known as a single-unit rate). One unit of one quantity will be compared to a distinct number of units of another quantity. Unit rates are frequently employed in practical contexts, such as when converting between measuring systems.

Given data:

Shawn runs - 18 miles in 5 hours.

Russ run - 25 miles in 7 hours.

Unit rate: in 1 hour.

Shawn runs - 18/5 miles = 3.6 miles per hour.

Russ run - 25 /7 = 3.57 miles per hour.

Thus, Shawn runs 3.6 miles per hour. Russ needs  3.57 hours to run every mile.

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The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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the dimensions of the dumpster that will minimize its surface area

length l = 6.32

width w =  1.58

height h = 0.39

Length = l

width = w

height = h

given that length is four times its width

l = 4w

Now, the formula for the surface area of a cube is;

S = 2lh + 2lw + 2wh

substitute l = 4w in the above equation

S = 2(4w)h+2(4w)w+2wh

S = 8wh+8\(w^{2}\)+2wh

S = 10wh + 8\(w^{2}\)

formula for the volume of a cube is;

V = lwh

now substitute l=4w in the above equation

V = (4w)wh

V = 4\(w^{2}\)h

h = 4\(w^{2}\)/V

Put V/2w² for h in the surface area equation to get;

S= 8w² + 10w(V/4w²)

 = 8w² + 5V/2w

given that volume V = 25.6 substitute that in the above equation

S = 8w² + 5(25.6)/2w

  = 8w² + 128/2w

Since we want to minimize the surface area, let us find the first derivative of S to get;

S' = 16w - 128/2w²

At S' = 0

0 = 16w-  128/2w²

16w =  128/2w²

32w³ = 128

w³ = 128/32

w³ = 4

w = \(\sqrt[3]{4}\)

w = 1.58 yds

since l = 4w substitute the value of w in that

l = 4(1.58) = 6.32

h = 4\(w^{2}\)/V = 4(\(1.58^{2}\))/25.6

h = 0.39

the dimensions are

length l = 6.32

width w =  1.58

height h = 0.39

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Answer:

2,3 and 4

Step-by-step explanation:

Answer: Using the absolute value function, the value that is the opposite of being short $3.96 is: x + 3.96.

Step-by-step explanation:

The absolute function is defined by:

|x| = x, x ≥ 0.

|x| = -x, x < 0.

It measures the distance of a point x to the origin, that is, |2| = |-2| = 2.

For this problem, the number is of $3.96, that is:

|x| = 3.96.

Hence:

Short of $3.96 means that x = -3.96.

The opposite is the other solution, of x = 3.96.

The value of x at which the slope of the tangent line to the given function is equal to 5 is 4. Thus, the correct answer is option (b).

The incline of the digression line to the capability y=x²-3x+2 at some random point (x₀, y₀) on the bend is given by the subordinate of the capability by then. To find the worth of x for which the slant of the digression line is equivalent to 5, we want to separate the given capability and set it equivalent to 5 and afterward tackle for x.

Therefore, let's distinguish the function from x: dy/dx = 2x - 3 Now, we need to set this derivative to 5: 2x - 3 = 5. If we solve for x, we get: 2x = 8x = 4. This means that the value of x at which the tangent line to the given function is equal to 5 is 4. Accordingly, the right response is choice (b).

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The concentration of hydrogen ions in seawater is 3.126 × 10⁻⁶ mol / dm³.

The pH level of seawater is 8.5.

If the pH is 8.5, and If the pH is 8.5, Assuming that this is measured under normal circumstances, we can apply the following relationship:

pH + pOH = pK_(w)

At 25 degrees Celcius, pK_(w) = 14

Where K_(w) is the dissociation constant for water = 1.0 × 10⁻¹⁴,

(At 25° C) but pK_(w) is the negative logarithm of K_(w).

pK_(w) = − log₁₀[ K_(w) ]

From this, we can convert pH, the measure of H₃O⁺ ions, into pOH, the measure of OH⁻ ions in the seawater:

pH + pOH = 14

8.5 + pOH = 14

pOH = 14 - 8.5

pOH = 5.5

Now,

pOH = − log₁₀[ OH⁻ ]

10^{−pOH} = [ OH⁻ ]

So,

10⁻⁵·⁵ = [ OH⁻ ] ≈ 3.126 × 10⁻⁶ mol / dm³

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Answer:

7 x 12

Step-by-step explanation:

\(a=l *w\)

\(84=l*w\\w=l+5\\\)

these equations we know, so we can use them like this

\(84=l*(l+5)\\84=l^2 +5l\\\)

I then plugged this equation into the desmos calculator to get the answer

\(l=7\)

we then plug this into a previous equation

\(w=l+5\\w=7+5\\w=12\)

to get our answer l=7, w=12

-0.477  is the value of log 1 by 3 .

A logarithm is defined simply?

The logarithm represents the power to which a number must be raised to obtain another number (see Section 3 of this Math Review for more about exponents).

For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2: log 100 = 2.

log (1/3)

= log1 - log3

= 0 - 0.477

 = -0.477

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Answer:

2m-17

Step-by-step explanation:

-20+1/4(8m+12)

-20+2m+3

2m-20+3

2m-17

the answer is -20+ (8m+12/4)

Answer:

(-2/7,2/3)

Step-by-step explanation:

Let's solve for x.

−7x+3y=2

Step 1: Add -3y to both sides.

−7x+3y+−3y=2+−3y

−7x=−3y+2

Step 2: Divide both sides by -7.

−7x/ −7 = −3y+2/ −7

x= 3/ 7 y+ −2/ 7

Answer:

x= 3/ 7 y+ −2/ 7

Let's solve for y.

−7x+3y=2

Step 1: Add 7x to both sides.

−7x+3y+7x=2+7x

3y=7x+2

Step 2: Divide both sides by 3.

3y/ 3 = 7x+2/ 3

y= 7/ 3 x+ 2/ 3

Answer:

y= 7/ 3 x+ 2/ 3

The equation of the line passing through the points (-2, 3) and (5, 4) is y = (1/7)x + 23/7.

A straight line is a geometric object that extends infinitely in both directions and has no curvature or angles. It can be defined as the shortest distance between two points in a two-dimensional plane. A straight line can be represented algebraically using the slope-intercept form:

y = mx + b

To find the equation of a line passing through two given points, we can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

where m is the slope of the line and (x₁, y₁) is one of the given points.

First, we need to find the slope of the line passing through the points (-2, 3) and (5, 4). We can use the slope formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (-2, 3) and (x₂, y₂) = (5, 4):

m = (4 - 3) / (5 - (-2))

m = 1/7

Now we have the slope of the line, we can use one of the given points to write the equation in point-slope form. Let's use the point (5, 4):

y - y₁= m(x - x₁)

y - 4 = (1/7)(x - 5)

To convert this equation into slope-intercept form (y = mx + b), we can simplify and solve for y:

y - 4 = (1/7)x - (5/7)

y = (1/7)x - (5/7) + 4

y = (1/7)x + 23/7

Therefore, the equation of the line passing through the points (-2, 3) and (5, 4) is y = (1/7)x + 23/7.

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The point (9, -7) is the only solution to the system of linear inequalities given.

To determine which point would be a solution to the system of linear inequalities, let's substitute the given points into the inequalities and see which point satisfies both inequalities.

The system of linear inequalities is:

y > -4x + 6

y > (1/3)x - 7

Let's test each given point:

For the point (9, -7):

Substituting the values into the inequalities:

-7 > -4(9) + 6

-7 > -36 + 6

-7 > -30 (True)

-7 > (1/3)(9) - 7

-7 > 3 - 7

-7 > -4 (True)

Since both inequalities are true for the point (9, -7), it is a solution to the system of linear inequalities.

For the point (-12, -2):

Substituting the values into the inequalities:

-2 > -4(-12) + 6

-2 > 48 + 6

-2 > 54 (False)

-2 > (1/3)(-12) - 7

-2 > -4 - 7

-2 > -11 (False)

Since both inequalities are false for the point (-12, -2), it is not a solution to the system of linear inequalities.

For the point (12, 1):

Substituting the values into the inequalities:

1 > -4(12) + 6

1 > -48 + 6

1 > -42 (True)

1 > (1/3)(12) - 7

1 > 4 - 7

1 > -3 (True)

Since both inequalities are true for the point (12, 1), it is a solution to the system of linear inequalities.

For the point (-12, -7):

Substituting the values into the inequalities:

-7 > -4(-12) + 6

-7 > 48 + 6

-7 > 54 (False)

-7 > (1/3)(-12) - 7

-7 > -4 - 7

-7 > -11 (True)

Since one inequality is true and the other is false for the point (-12, -7), it is not a solution to the system of linear inequalities.

In conclusion, the point (9, -7) is the only solution to the system of linear inequalities given.

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