Sarah bought a pair of shoes that were discounted 12.5%. If the non-sale price was s,
which expression represents the cost Sarah paid for the shoes?
a. 1-0.125
b. 1-0.125s
c. 0.875s
d. 5-0.875

Answer:

I) ∠CAB measures 60°.

II) BC measures approximately 15.23 cm.

*Please read notes.

Step-by-step explanation:

We are given ΔABC, where AB measures 10√3 cm, AC measures 6 cm, and the triangle has an area of 45 square cm.

And we want to find I) the measure of ∠CAB and II) the length of BC.

I) First, we should always draw a representative triangle so we can determine the sides and angles. This is shown below.

Note that ∠CAB (or simply ∠A) is the angle between the two sides. Thus, we can find the angle by using the alternative formula for the area of a triangle:

[tex]\displaystyle A=\frac{1}{2}ab\sin(C)[/tex]

Where a and b are two side lengths, and C is the angle between the two sides.

Substitute:

[tex]\displaystyle 45=\frac{1}{2}(10\sqrt{3})(6)\sin(A)[/tex]

Simplify:

[tex]\displaystyle 45=30\sqrt{3}\sin(A)[/tex]

So:

[tex]\displaystyle \sin(A)=\frac{45}{30\sqrt{3}}=\frac{3}{2\sqrt3}=\frac{\sqrt{3}}{2}[/tex]

Take the inverse sine of both sides. Use a calculator. Thus:

[tex]\displaystyle m\angle A=\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)=60^\circ[/tex]

II) To find BC, we will use the Law of Cosines. We do not know whether or not ΔABC is a right triangle, so we cannot use right triangle trigonometry or special right triangles.

The law of cosines is:

[tex]\displaystyle c^2=a^2+b^2-2ab\cos(C)[/tex]

Where a and b are side lengths and C is the angle between the side lengths. c is the side length opposite to the angle.

BC is opposite to A. Substitute:

[tex](BC)^2=(10\sqrt{3})^2+(6)^2-2(10\sqrt{3})(6)\cos(60^\circ)[/tex]

Simplify:

[tex]\displaystyle BC^2=336-120\sqrt{3}\left(\frac{1}{2}\right)=336-60\sqrt{3}[/tex]

Take the square root of both sides:

[tex]\displaystyle BC=\sqrt{336-60\sqrt{3}}\approx 15.23[/tex]

BC measures about 15.23 cm.

Notes:

In this case, the inverse sine of √3/2 will yield two answers: 60° and 120°. This is an example of an ambiguous case. Both of these angles will work. However, BC will be different. If ∠A is 60°, then BC is about 15.23. However, if ∠A is 120°, then BC is about 20.97. Both will result in the triangle having an area of 45 square cm, as well as AB measuring 10√3 and AC measuring 6.

Answer:

Step-by-step explanation:

10 games, 8 rides

Answer:

The first line

Step-by-step explanation:

Answer:

-3=3x+12

Step-by-step explanation:

Answer:

1) <2 ; 60

2) <3 ; 60

3) <4 and <3. <4 = 120 and <3 = 60

4) <1, <3, and <4 = 125. <2 = 55

Step-by-step explanation:

1)

Corresponding angles are equal

2)

Alternate interior angles are equal

3)

<4 and <3 are same-side interior angles. This makes them supplementary angles

<4 = 120

<3 = 60

4)

<1 = <4 = <3. All of these angles equal 125.

<2 + <1 = 180

<2 + 125 = 180

<2 = 55

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{x-\dfrac{3}{2}=3}[/tex]

[tex]\large\textsf{You have to SIMPLIFY the SIDES of The given EQUATION}[/tex]

[tex]\mathsf{x + (-\dfrac{3}{2}) = 3}[/tex]

[tex]\large\textsf{ADD by } \mathsf{\dfrac{3}{2}}\large\textsf{ to BOTH of the SIDES}[/tex]

[tex]\mathsf{x + (-\dfrac{3}{2})+ \dfrac{3}2{}=3+\dfrac{3}{2}}[/tex]

[tex]\large\textsf{CANCEL out: } \mathsf{-\dfrac{3}{2}+\dfrac{3}{2}}\large\textsf{ because that gives you 0}[/tex]  

[tex]\large\textsf{Keep: } \mathsf{3+ \dfrac{3}{2}}\large\textsf{ because that helps solve for your x-value }[/tex]

[tex]\large\textsf{New equation: }\mathsf{x = 3 + \dfrac{3}{2}}[/tex]

[tex]\mathsf{3+\dfrac{3}{2}}[/tex]

[tex]\large\textsf{SOLVE above and you have your ANSWER}[/tex]

[tex]\mathsf{3+\dfrac{3}{2}=\bf \dfrac{9}{2}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Therefore, your answer is: }\mathsf{\bf x = \dfrac{9}{2}}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

200.96

or

201 (if you round it up)

Step-by-step explanation:

1) Well, if we know that the diameter (D) is 16 cm, then we know that the radius (r) is 8 cm (D = 2 * r).

2) Next, we square (^2) the radius, and we get 64 (r^2 = r * r = 8*8 = 64)

3) Finally, we multiply π by 64, and we get 200.96 cm^2 (3.14 * 64) which is very close to 201 cm^2.

Answer:

12mm (triangle)

165mm (whole shape)

Step-by-step explanation:

The triangle is 6 x 4 = 24 ÷ 2= 12

(divide by 2 because its a teiangle)

2nd shape is 10 x 8 = 80

3rd shape is 6 x 12 = 72

72 + 80 + 12 = 165mm

Answer:

x+10=45

x+10-45=0

x-35=0

x=35

Answer:

x = 4.5

Step-by-step explanation:

Since the perimeters are equal , then the equation relating them is

2x + 3 + 2x - 3 + x = x + 3 + x + 3 + x + 3 , that is

5x = 3x + 9 ( subtract 3x from both sides )

2x = 9 ( divide both sides by 2 )

x = 4.5

Answer:

2

Step-by-step explanation:

9 ÷ 3 - 2 × 2

3 - 2 × 2

1 × 2

2

Answer:

4

Step-by-step explanation:

3/2x -1 = 5

then

3/2x = 5+1

then

3/2x = 6

then

x = 6 / (3/2)

then

x = 6 *2/3

then

x = 4

Answer:

I believe it is D.

Step-by-step explanation:

This shows all the combinations of the dice roll as could go along with any of the coin toss solutions.

I hope I didn't confuse you lol! Hope this helps :)

Answer: Approximately normal, because we expect 19.2 successes and 20.8 failures from people in their twenties, and 16.8 and 43.2 from people in their fifties, and all of these counts are at least 10.

Step-by-step explanation:

Answer:

-500

Step-by-step explanation:

Answer:

lol xdxdxd how you not know fraction? this is basic math this is why you failed lolol

Step-by-step explanation:

Answer:

this is the answer in the image above

Answer:

look attachment

Answer: 12

Step-by-step explanation:

Since Duane has 30 pairs of socks in a drawer and he has 6 matched pairs and the rest are of the socks are mismatched, the number if mismatched socks will be:

= 30 - 6

= 24 mismatched socks

Since he packed 1/2 of his mismatched pairs in his duffle bag for a week at summer camp, therefore, the number of socks he packed will be:

= 1/2 × 24

= 12

Therefore, he packed 12 socks for summer camp.

Answer:

21.5sqft

Step-by-step explanation:

The area of the square is 10ft*10ft = 100sqft

The area of the circle is 5ft*5ft*pi = 25pi sqft

We're supposed to use 3.14 for pi, so the circle is around 25*3.14 sqft = 78.5sq ft

The area left over is 100sqft - 78.5sqft = 21.5sqft

Answer:

21.5 sq. feet

Step-by-step explanation:

Answer:

6 centimetres

Step-by-step explanation:

Square root 36 = 6

Answer:

6

Step-by-step explanation:

A = x^2

x = √A

x = √36

√36 = 6

Answer:

$1.50

Step-by-step explanation:

The computation is shown below:

Given that

The cost of each cupcakes be 0.50 cents

And, the cost of doughnuts be $25

So for two doughnuts the cost would be 2.50

And, for two cupcakes, the cost would be 0.50 × 2 = 1

So, the more amount would be

= 2.50 - 1

= $1.50

Hence, the same would be considered and relevant too

Answer:

The radius of these cylinders is approximately 1 foot.

Step-by-step explanation:

According to this graph, the volume of the cylinder is directly proportional to its height, that is, radius remains constant. The expression of direct proportionality:

[tex]V \propto h[/tex]

[tex]V = k\cdot h[/tex] (1)

Where:

[tex]V[/tex] - Volume of the cylinder, in cubic feet.

[tex]h[/tex] - Height of the cylinder, in feet.

[tex]k[/tex] - Proportionality constant, in square feet.

Besides, the proportionality constant is described by this expression:

[tex]k = \pi \cdot R^{2}[/tex] (2)

Where [tex]R[/tex] is the radius of the cylinder, in feet.

If we know that [tex]h = 9\,ft[/tex] and [tex]V = 28.26\,ft^{2}[/tex], then the radius of the cylinder is:

[tex]k = \frac{V}{h}[/tex]

[tex]k = 3.14[/tex]

[tex]R = \sqrt{\frac{k}{\pi} }[/tex]

[tex]R \approx 1\,ft[/tex]

The radius of these cylinders is approximately 1 foot.

Answer:

10000 possible combinations

Step-by-step explanation:

Number of digits = 4

Range of values of each digit = 0 - 9

Number of digits in range = 10

Hence, each digit could be = (1 - 10)

1st digit = 10

2nd digit = 10

3rd digit = 10

4th digit = 10

Total possible combination :

10 * 10 * 10 * 10 = 10000 possible combinations

Answer:

The fewest square tiles he can use without cutting any of them = 12 square tiles

Step-by-step explanation:

The given dimensions of Mr. Pete's rectangular patio = 108 inches by 144 inches

The area of the patio = 108 in. × 144 in. = 15,552 in.²

We note that when square tiles are used the must fit both the length and the with of the rectangular patio

Therefore, we have;

The dimensions of the square tiles that the fewest number of tiles is the highest common factor, HCF, of 108 inches and 144

The HCF of 108 and 144 are found from by the prime factors as follows;

108 = 2² × 3³ = 2² × 3² × 3

144 = 2⁴ × 3² = 2² × 3² × 4

From which we have;

The HCF of 108 and 144 = 2² × 3² = 36

Therefore, the size of the sides of the square tiles that will give the fewest number of tiles is 36 inches

The number of the 36 inches square tiles that fit into the length of the rectangular patio = 144 inches/(36 inches/tile) = 4 tiles

The number of the 36 inches square tiles that fit into the breadth of the rectangular patio = 108 inches/(36 inches/tile) = 3 tiles

The total number of tiles he will use = (4 × 3) tiles = 12 tiles = The fewest square tiles he can use without cutting any of them.

Answer:

-4

Step-by-step explanation:

Given the expression

h(x) = -x^2 +4x

h(-2) = (-2)^2 + 4(-2)

h(-2) = 4  + (-8)

h(-2) = 4 -  8

h(2) = -4

Hence the value of the function when x = -2 is -4

Answer:

2/3

Step-by-step explanation:

rise/run

2 up, 3 right

Answer:

[tex]m=\frac{2}{3}[/tex]

Step-by-step explanation: