Question
After attending a car show, Katrina decides to start saving for a car. She places $50 of her most recent paycheck into a jar and
commits to adding $150 every month to save for a down payment. Her total amount saved for the car, y, after x months can
represented by this equation:
y 150x + 50

Answer and Explanation:

No, they did not use a ruler to compute the values of trig functions. They used geometry to prove theorems about trigonometry, then used those results and ordinary computations involving addition, subtraction, multiplication, division, and square roots to determine the entries in trigonometric tables.

Claudius Ptolemy (85 C.E.–165) created the first trig tables that we know of, and he included proofs of the theorems he used. One of the main theorems he used is what is now called Ptolemy’s theorem.

In order to prove his sum and difference forumlas, Ptolemy first proved what we now call Ptolemy’s theorem.

Ptolemy’s theorem. The product of the diagonals of a cyclic quadrilateral is equal to the sum of the products of the opposite sides.

A cyclic quadrilateral is a quadrilateral inscribed in a circle as ABCD. Ptolemy’s theorem says:

AC ⋅ BD = AB ⋅ CD + AD ⋅ BC

When one of the diagonals (like ) is a diameter of the circle, that gives you a way to determine the trig functions for sum and differences of angles.

Sometimes, the sum and difference formulas for sine and cosine are still called Ptolemy’s formulas.

sin(α + β) = sin α cos β + cos α sin β

cos(α + β) = cos α cos β − sin α sin β

sin(α − β) = sin α cos β − cos α sin β

cos(α − β) = cos α cos β + sin α sin β

Ptolemy started with angles he knew the trig functions for. These included angles in various isosceles triangles: 45°-45°-90°, 60°-60°-60°, and 36°-72°-72°, the last one described by Euclid in Proposition IV.10. That gave him the trig functions for 36°, 60°, and 90°. Using half-angle formulas (mentioned by Hipparchus (190–120 B.C.E.), he could compute trig functions for half of those angles and a quarter of those angles. Then using the sum and difference formulas he computed the rest of the numbers in his trig table.

Hope this helps! :)

Answer:

300

Step-by-step explanation:

if it is 300 feet ABOVE sea level, then it is a positive answer.

you would want to look for the words 'above' or 'below' if it is talking about sea level.

Answer:

Step-by-step explanation:

Using a linear function, it is found that he would have to ride his bicycle 7.9 miles a day to meet his goal.

A linear function is modeled by:

y = mx + b

In which:

For this problem, we have that:

When x = 4, y = 39.6, hence:

39.6 = 4m + 8

4m = 31.6

m = 31.6/4

m = 7.9.

He would have to ride his bicycle 7.9 miles a day to meet his goal.

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Answer:

1758 years

Step-by-step explanation:

0.693/t1/2 = 2.303/t log No/N

t1/2 = half life of the C-14

t= time taken

No= amount of radioactive material originally present

N= amount of isotope after time t.

But N= 0.81 No

0.693/5715= 2.303/t log No/0.81No

0.00012 = 0.211/t

t =0.211 /0.00012

t= 1758 years

Answer:

$5.86

Step-by-step explanation:

12% of 50=6 pennies

40% of 50= 20 dimes

6+5= 11 nickels

11+20+6= 37 coins

50 total coins-37= 13 quarters

13 quarters = $3.25

20 dimes = $2.00

11 nickels = $0.55

6 pennies = $0.06

$3.25+$2.00+$0.55+$0.06=$5.86

Answer:

$5.86

Step-by-step explanation:

Answer:

x=

−32/9y +14/9

Step-by-step explanation:

Answer:

The answer is A: 1,260

Step-by-step explanation:

I took the test on Edge

Answer:

A-1,260

Step-by-step explanation:

Answer:

0 < cc + dd ≤ 11

Step-by-step explanation:

≤ means equal to or less than.

It has to be more than zero, obviously.

Answer:

c+d≤11

Step-by-step explanation:

welcome

you need more information to finish this question. You can't get an answer for a math question like this one with that little information.

Answer:

Step-by-step explanation:

lol it means 4/5,

your in rsm i aleready know

Answer:

id.   k

Step-by-step explanation:

I.  dk

Answer: y=8 and x=8 radical 3

According to the given statement the volume of medicine will give to the patient = 0.27ml.

A substance's density is defined as its mass per unit volume. The most common symbol for density is, but the Latin letter D is also an option.

Density is an important topic because it tells us which compounds will float and which will sink when placed in some kind of liquid. Substances float in general if their density is smaller than the density of the liquid in which they are immersed.

ρ = m/v

ρ = density

m = mass

V = volume

Medicine = 4500mg

The medication comes in 5g/0.3mL

We know that:

mL = mg / 1000

So,

ml = 4500/1000

    = 4.5ml

Formula for finding volume = weight/density

                                              = 4.5/(5/.3)

                                              = (4.5 * 0.3)/5

                                               = 0.27ml

According to the given statement the volume will give to the patient = 0.27ml.

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Answer:

For these types of problems, You must look at the coefficients and variables separately and find the GCF for each. Then, combine the two

First, take 12 and 9

Factors of both

9- 1, 3, 9

12- 1, 2, 3, 4, 6, 12

So the gcf of 12 and 9 is 3

Now do the variables a and a^2

a^2 is just a twice

The GCF is a

Now combine a and 3

Answer: GCF is 3a

Answer:

GCF is 3a

Step-by-step explanation:

I just know LOLLL

Answer:

93

Step-by-step explanation:

Let the digit in tens place be 'x' & digit in ones place be 'y'.

So , the original number = [tex]10x+y[/tex]

According to the question , [tex]x+y=12[/tex]......... .eqn(1)

When digits are interchanged ,

The new number formed = [tex]10y+x[/tex]

According to the question , [tex]10y+x=10x+y-54[/tex] ............ eqn(2)

Solving eqn(2) further ,

[tex]10y+x=10x+y-54\\=>10x-x-10y+y=54\\=>9x-9y=54\\=>9(x-y)=54\\=>x-y=\frac{54}{9}=6.......... eqn(3)[/tex]

Adding eqn(1) and eqn(3) ,

[tex](x+y)+(x-y)=12+6\\=>x+y+x-y=18\\=>2x=18\\=>x=\frac{18}{2} =9[/tex]

Putting the value of x in eqn(1),

[tex]9+y=12\\=>y=12-9=3[/tex]

∴ Original number = 93

Answer:

The Martins used their sprinkler for 35 hours, while the Kellys used their sprinkler for 25 hours.

Step-by-step explanation:

As the Martins and the Kellys used their sprinklers for 60 hours combined last summer, and the water output rate of the Martins' sprinkler is 30 liters per hour, while the Kelly's is 35 liters per hour To determine how many hours each family used their sprinklers, knowing that in total 1925 liters of water were used, the following logical reasoning must be carried out:

There is a 5 liter difference between the Kelly sprinkler and the Martin sprinkler. If both used 30 liters of water per hour, for 60 hours 1800 liters (30 x 60) would have been used. Therefore, there is an excess of 125 liters that corresponds to an excess of consumption, attributable to the Kelly sprinkler, which consumes 5 liters more of water per hour than the Martin's. Thus, since 125/5 equals 25, in total the Kellys used their sprinkler for 25 hours, while the Martins did it for 35 hours.

This reasoning is proved with the following calculation:

25 x 35 = 875

35 x 30 = 1,050

875 + 1,050 = 1,925

Answers:

Row 1: 4 sig digits, 1.705*10^4

Row 2: 5 sig digits, 1.9080*10^-5

Row 3: 300, 1 sig digit

Row 4: 0.00246, 3 sig digits

Answer:

Unknown

Step-by-step explanation:

ajkdfhlkhalukdjglahgfjhgdljhdfjgajdfgaiufgyhj

Answer:

2.3 is the mid point of gh

Answer:

[tex]\frac{1}{\sin \left(10^{\circ \:\:}\right)}\:\:\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=4[/tex]

Step-by-step explanation:

Given the expression

[tex]\frac{1}{\sin \left(10^{\circ \:}\right)}-\frac{\sqrt{3}}{\cos \left(10^{\circ \:}\right)}=4[/tex]

Taking the left-hand side and solving it

[tex]\frac{1}{\sin \left(10^{\circ \:}\right)}-\frac{\sqrt{3}}{\cos \left(10^{\circ \:}\right)}[/tex]

as

[tex]\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=5.76[/tex]

and

[tex]\frac{\sqrt{3}}{\cos \left(10^{\circ \:\:}\right)}=1.76[/tex]

so the expression becomes

[tex]\frac{1}{\sin \left(10^{\circ \:\:}\right)}\:\:\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=5.76-1.76[/tex]

                           [tex]=4[/tex]

Thus, we conclude that

[tex]\frac{1}{\sin \left(10^{\circ \:\:}\right)}\:\:\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=4[/tex]

Answer:

15 because the 2 tickets were originally 105

Step-by-step explanation:

52.50 x 2 = 105 because 52 + 52 = 104 and .50 + .50 = 1 so 104 + 1 = 105

Answer:

yes this is right that you have have done

Answer:

What is the constant speed of Fast Freddy?: 1/4

What is the constant speed of Speedy Sam? : 1/8

Who ran faster?: Freddy

Step-by-step explanation:

2021 edge

Answer:

Step-by-step explanation:

y=-3/4 x-3

Answer:

Step-by-step explanation:

You want the simplified form of (5b^1c^-5)^-3(4b^0a^2)^-5.

There are several useful rules of exponents here:

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

  a^-b = 1/(a^b)

Simplifying the top-level exponents first, we have ...

  [tex](5b^1c^{-5})^{-3}(4b^0a^2)^{-5}=(5^{-3}b^{1(-3)}c^{(-5)(-3)})(4^{-5}b^{0(-5)}a^{2(-5)})\\\\=(5^{-3}4^{-5})a^{-10}b^{-3+0}c^{15}=\dfrac{1}{5^34^5}a^{-10}b^{-3}c^{15}=\boxed{\dfrac{1}{128000}a^{-10}b^{-3}c^{15}}[/tex]

In terms of answer requirements:

  n = 1/128000

  r = -10

  s = -3

  t = 15

Answer:

10.4 feet per year

Step-by-step explanation:

Divide the tree growth by the number of years.

78/7.5=10.4