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2 years ago

Jess says that two of the three points below are on a line through the origin.

Mathematics

2 answers:

natima [27]2 years ago

8 0

Answer:

3, 8) and (9, 24) lie on the same line

Step-by-step explanation:

Marrrta [24]2 years ago

6 0

Answer:

(3, 8) and (9, 24) lie on the same line through the origin.

because (9, 24) is the result of dilatation of (3, 8) with scale factor 3.

(6, 21) is not the result, because 21 ≠ 2×8, even 6 = 2×3

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Find the amount of time. I=$237. 90, P=$1525, r=2. 6% Find the amount of time. __ Years

Virty [35]

$~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$237.90\\ P=\textit{original amount deposited}\dotfill & \$1525\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ t=years \end{cases} \\\\\\ 237.90 = (1525)(0.026)(t)\implies \cfrac{237.90}{(1525)(0.026)}=t \implies 6=t$

3 0

2 years ago

Which of the following could be the ratio of the length of the longer leg of a 30-60-90 to the length of its hypotenuse? CHECK A

8_murik_8 [283]

Answer:

A. √3 : 2

D. 3√3 : 6

Step-by-step explanation:

In a triangle described as 30°-60°-90° triangle, the base angles are 90° and 60°

The side with angles 90° and 60° is the shortest leg and can be represented by 1 unit

The hypotenuse side is assigned a value twice the shorter leg value, which is 2 units

From Pythagorean relationship; the square of the hypotenuse side subtract the square of the shorter leg gives the square of the longer side

This is to say if;

The given the shorter leg = 1 unit

The hypotenuse is twice the shorter leg= 2 units

The longer leg is square-root of the difference between the square of the hypotenuse and that of the shorter leg

$=2^2-1^2\\\\=4-1=3\\\\\\b^2=3\\\\\\b=\sqrt{3}$

where the longer leg is represented by side b in the Pythagorean theorem, the hypotenuse by c and the shorter leg by a to make;

$a^2+b^2=c^2$

Hence the summary is

a=shorter leg= 1 unit

b=longer leg = √3 units

c=hypotenuse=2 units

The ratio of longer leg to its hypotenuse is

=√3:2⇒ answer option A

This is the same as 3√3:6 ⇒answer option D because you can divide both sides of the ratio expression by 3 and get option A

$=3\sqrt{3} :6\\\\\\\frac{3\sqrt{3} }{3} :\frac{6}{3} \\\\\\=\sqrt{3} :2$

Answers are :option A and D

4 0

3 years ago

Solve sin theta + 1 = cos 2 theta on the interval 0 less than or equal to theta <2 pi

hjlf

Answer:

Ф = 0 and Ф = π

Step-by-step explanation:

* Lets explain how to solve the problem

∵ sin Ф + 1 = cos²Ф, where 0 ≤ Ф < 2π

- To solve we must to replace cos²Ф by 1 - sin²Ф

∵ sin²Ф + cos²Ф = 1

- By subtracting sin²Ф from both sides

∴ cos²Ф = 1 - sin²Ф

- Lets replace cos²Ф in the equation above

∴ sin Ф + 1 = 1 - sin²Ф

- Subtract 1 from both sides

∴ sin Ф = - sin²Ф

- Add sin²Ф for both sides

∴ sin²Ф + sin Ф = 0

- Take sin Ф as a common factor from both sides

∴ sin Ф(sin Ф + 1) = 0

- Equate each factor by 0

∵ sin Ф = 0

∴ Ф = 0 OR Ф = 2π

∵ sin Ф + 1 = 0

- Subtract 1 from both sides

∴ sin Ф = -1

∴ Ф = π

∵ 0 ≤ Ф < 2π

∵ Ф < 2π

∴ We will refused the answer Ф = 2π

∴ Ф = 0 and Ф = π

7 0

3 years ago

a car needs fixing and Abe can fix it for $70 per hour with a $60 part, but Gabe can fix it for $80 an hour with a $40 part. How

Nat2105 [25]

After 2 hours time , both Abe and Gabe to cost the same amount .

Step-by-step explanation:

Here we have , a car needs fixing and Abe can fix it for $70 per hour with a $60 part, but Gabe can fix it for $80 an hour with a $40 part. We need to find How long will it take for both Abe and Gabe to cost the same amount .Let's find out:

Let the time for which both Abe and Gabe to cost the same amount be x hours, so according to question scenario we will have equation as :

⇒ $70x+60=80x+40$