William spent $132.75 on books, including the shipping fee , that he orderd from an online company. each book cost $4.75. how many books did william buy.
A.33 B.32 C.15 D.34

The property used to simplify the expression is 12 × 47 = 12 × (40 + 7) is  distributive property.

The distributive property states that an expression which is given in form of x (y + z) can be solved as x × (y + z) = xy + xz.

In other words,  distributive property is a rule that states that you can distribute the terms of an expression.

Therefore, let's check the property used on the expression as follows:

12 × 47 = 12 × (40 + 7)

12 × 40 + 12 × 7

480 + 84

564

Hence, the property used on the expression is distributive property.

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Answer:

17 ounce cereal

Step-by-step explanation:

It is only a 53. cent difference so the better option would be the 17 ounce bag

The inequality graphed on the number line can be written as:

-3 ≤ x < 2

Here we can see an inequality graphed on a number line, we can see that we start with a closed circle at x = -3

A closed circle means that x = -3 is a solution.

And we can see that it ends with an open circle at x = 2, the open circle means that the point is not a solution.

Then the inequality thati is shown in the number line is written as:

-3 ≤ x < 2

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The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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Answer:

C. 129

Apply : Angles of Intersecting Chords Theorem

m∠x is half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

m∠x = 1/2(54+204)

Add numbers in brackets.

m∠x = 1/2(258)

Expand brackets.

m∠x = 129

The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.

To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.

Since the owner wants the total cost to be under $2000, we can set up the inequality:

43H + 750 < 2000

Now, let's solve this inequality for H, the number of hours:

43H < 2000 - 750

43H < 1250

Dividing both sides of the inequality by 43:

H < 1250/43

To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.

Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:

H < 29

Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.

By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.

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Answer:

A) (3,-2)

Step-by-step explanation:

A) (3,-2)

Answer:D and E I think

Step-by-step explanation:

The possible exact values of the trigonometric functions of θ are:

sin θ = -1/√3,  cos θ = √3/3, sec θ = √3

The law of sines, also known as the sine rule, is a mathematical principle that relates the sides and angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides of the triangle.

Trigonometric functions are mathematical functions that relate angles to the ratios of the sides of a right triangle. The six primary trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Each function represents a different ratio of two sides of a right triangle and can be used to solve problems in geometry, physics, engineering, and other fields that involve angles and triangles.

According to the given information,

Given that tan θ = -√(1/3) and 0 < θ < 180°, we can use the trigonometric identities to find the values of the other trigonometric functions of θ.

First, we can use the definition of the tangent function:

tan θ = opposite/adjacent

Since tan θ = -√(1/3), we can assign opposite = -1 and adjacent = √3 as their ratio equals -√(1/3). This means that the terminal side of the angle θ will lie in the fourth quadrant of the unit circle since the opposite is negative and the adjacent is positive.

Next, we can use the Pythagorean identity:

sin²θ + cos²θ = 1

to find the value of sin θ. Since we know that θ is in the fourth quadrant, we can assign sin θ = -1/√3, since sin θ is negative in the fourth quadrant and the ratio of opposite/hypotenuse of a 30-60-90 triangle is √3/2, which means the ratio of hypotenuse/opposite is 2/√3 = √3/3.

Then, we can use the definition of the cosine function:

cos θ = adjacent/hypotenuse

to find the value of cos θ. We know that adjacent = √3 and the hypotenuse is positive (since it is a length), so we can assign cos θ = √3/3.

Finally, we can use the reciprocal identity:

sec θ = 1/cos θ

to find the value of sec θ. We know that cos θ = √3/3, so we can assign sec θ = √3.

Therefore, the possible exact values of the trigonometric functions of θ are:

sin θ = -1/√3

cos θ = √3/3

tan θ = -√(1/3)

sec θ = √3

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For the given number 4 x 5³/₈. The whole part is 4 and the fraction part is 5³/₈. Both are added together to form a fraction of 43/8.

An inappropriate fraction can be created by converting a mixed fraction. Follow the instructions below to accomplish that.

For the given number 4 x 5³/₈.

The whole part is 4.

The fraction part is 5³/₈.

Solving the mixed fraction:

= 5³/₈.

= (5*8 + 3) /8

Both are added together to form a fraction:

= 43/8

The final number becomes:

= 4 x 5³/₈

= 4 x 43/8

= 43/2

Thus, the result of the final number obtained is 43/2.

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Answer:

A. down

Step-by-step explanation:

The parent graph is

f(x)=x

If this graph is transformed to obtain

g(x)=f(x)−4

The subtracttion means the graph will shift downward vertically

The graph of g(x) is obtained by shifting f(x) down by 4 unit.

Therefore the direction is down.

Mark this as brainliest please.

Answer:

Step-by-step explanation:

what is 12/21 + 18/21 + 14/21

(12 + 18 + 14)/21 =

44/21

Answer:

RC,\α is a rigid motion.

Here C, is the rotacenter which is the fixed point and around C all other points move in a fixed distance by the definition of rotation.

the motion follows in a circularmanner with C as the center.

consider a point Q which changes to Q1 after rotation by an angle\alpha

Step-by-step explanation:

When considering rotational motion and subsequently rotational mechanics every point on the body must have same angular velocity and angular acceleration. If the body is not rigid different points on the body will have different angular velocity and angular acceleration.

Answer:

Area of play ground = Length × Breadth = 750 × 250 = 187500. a Cost of levelling the ground = 187500 × 16 100 = Rs . 30000 

Answer: F

Step-by-step explanation:

(i) The interval is meant to have infinitesimal width because the limit is approaching 0.

(ii) This gives the derivative at \((x, f(x))\), which is the same as the slope of the tangent line.

(iii) False, this deals with the tangent line, not the secant.

(iv) True by definition.

a) The Present Value of the annuity that arrives at one-year intervals is $386,858.92.

b) The Present Value of the annuity if the first payment arrives in six months while subsequent payments arrive at one-year intervals is $388,022.68.

The present value is the discounted value of future cash inflows at a stated discount rate.

Calculating the present value removes the effects of inflation from the future value of money.

N (# of periods) = 10 years

I/Y (Interest per year) = 5%

PMT (Periodic Payment) = $50,100

FV (Future Value) = $0

Results:

PV = $386,858.92

Sum of all periodic payments = $501,000 ($50,100 x 10)

Total Interest = $114,141.08

PV of $50,100 at six months = $48,878.05

PV of $50,100 at 12 months = $47,714.29

Difference in present value = $1,163.76

PV for yearly annuity = $386,858.92

Difference in PV between 6 and 12 months = $1,163.76

PV for first 6 month annuity and subsequent 12 months = $388,022.68

Thus, the PV of a) is $386,858.92 while the PV of b) is $388,022.68.

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The missing variables on item 2 are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle of 60º, we have that:

Hence the length o is given as follows:

tan(60º) = o/12.

\(\sqrt{3} = \frac{o}{12}\)

\(o = 12\sqrt{3}\)

Applying the Pythagorean Theorem, the length i is given as follows:

i² = 12² + \((12\sqrt{3})^2\)

i² = 576

i² = 24²

i = 24.

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Answer:

o = 12√3

i = 24

Step-by-step explanation:

From observation of the given right triangle, we can see that two of its interior angles measure 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, the triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #2, the shortest leg is 12 units.

As "a" is the shortest leg, the scale factor "a" is 12.

The side labelled "o" is the longest leg opposite the 60° angle. Therefore:

\(o = a\sqrt{3}=12\sqrt{3}\)

The side labelled "i" is the hypotenuse of the triangle. Therefore:

\(i= 2a = 2 \cdot 12=24\)

Therefore:

Answer:

232/15 [as an improper fraction] or 15 7/15 [as a mixed fraction]

Explanation:

16 - 8 / 15 =

(16) - (8 / 15) =

((16 × 15) / 15) - ((8) / 15) =

((240) / 15) - ((8) / 15) =

(240 - 8) / 15 =

232 / 15 =

15 7/15

Dilation involves changing the size of a figure

The endpoints of the image are (-2,-1) and (6,1)

The coordinates of the pre-image are give as:

(2,2) and (6,2)

The scale factor is given as:

k = 2

The center of dilation is given as:

(a,b) = (6,5)

The coordinates of the image are then calculated as:

\((x,y) \to (k(x -a) + a, k(y -b) + b)\)

For (2,2), we have:

\((x,y) \to (2(2 -6) + 6, 2(2 - 5) + 5)\)

\((x,y) \to (-2, -1)\)

For (6,2), we have:

\((x,y) \to (2(6 -6) + 6, 2(2 - 5) + 5)\)

\((x,y) \to (6, -1)\)

Hence, the endpoints of the image are (-2,-1) and (6,1)

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12x + 98

Step-by-step explanation:

AB=14x +25 +73-2x=12x+98

Answer: \(5\sqrt 5\)

Step-by-step explanation:

Sol \(\sqrt 125\) = \(\sqrt{25.5}\)

= \(\sqrt{25}\)  x  \(\sqrt{5}\)

\(5 \sqrt{5}\)

Answer:

\(=-6w^2-31w-35\)

Step-by-step explanation:

Apply Foil.
\(\left(3w+5\right)\left(-2w-7\right)=3w\left(-2w\right)+3w\left(-7\right)+5\left(-2w\right)+5\left(-7\right)\)
\(=3w\left(-2w\right)+3w\left(-7\right)+5\left(-2w\right)+5\left(-7\right)\)
\(=-6w^2-31w-35\)

Answer:

D) h=2t+5

Step-by-step explanation:

Length of scarf before unraveling = 4.75 + 0.75 = 5.5.

Equation: Length before unraveling = 4.75 + 0.75

Sadie is knitting a striped scarf for her grandfather for his birthday, but discovers a mistake and has to unravel 0.75 of the scarf. After unraveling, the remaining part of the scarf is 4.75 long. To calculate the length of the scarf before it was unraveled, we can use an equation. The equation we will use is Length before unraveling = 4.75 + 0.75. We can interpret this equation as the length before unraveling being equal to the length after unraveling plus the amount unraveled. Therefore, the length of the scarf before unraveling is 4.75 + 0.75, which is equal to 5.5. This equation is useful for finding the original length of the scarf, as it takes into account the amount that was unraveled. Therefore, the original length of the scarf is 5.5.

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i Got u Bro!

Ov=zo « = 192 +8 5 Or = 1/2 (x + 2)² – 8 20 Ov=« 2)2-4 DELL.

The length of the third side or c=30 feet.

Length is defined as the measurement of distance of an object from one end to the other.

The  length of the sides of a triangle is given by ,

a=24 feet, b=18 feet. c=?.

By Pythagorean theorem,

“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

\(c^{2}=a^{2} +b^{2}\)

\(c^{2} = 24^{2} +18^2\)

   = 900

⇒c=30 feet.

Hence, the length of the third side or c=30 feet.

Question:

The given diagram forms the triangle with the length of the sides ,

a=24 feet, b=18 feet. Find the length of the side c.

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Answer:

a.) near the low end of frequencies that can be detected by humans.

Step-by-step explanation:

Humans can hear frequencies in the range of 20 Hz to 20,000 Hz, so the frequency range of a cat's purr is near the low end of this range.

The the length of each side of the triangle are: 5 units, 8.7 units and 10 units respective

A triangle is a polygon with three sides, three angles, three vertices and sum of angles equal to 180 degrees

From the triangle, Using the trigonometric ratio of sine

Sin C = opposite/Hypothenuse

Sin30 = 5/H

Making h the subject of the relation we have

h= 5/sin30

h=5/0.5

Therefore the value of h=10 units

To find the third side use Pythagoras theorem

10² = 5²+p²

100-25 = p²

75 = p²

Taking the square of both sides

p=√75

p=8.7 units

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