MATHEMATICS HIGH SCHOOL

The greater of two numbers is twice the lesser if the greater is increased by 18 the result is 4 less than 4 times the lesser that the numbers

Answers

Answer 1

Answer:

Answer:

In short, 5 is the lesser number and 19 is the greater number.

Step-by-step explanation:

So for this, we will be doing a system of equations. Using the info from our question, our two equations are:

(let x = greater number and y = lesser number)

Now, for this I will be using the substitution method. Since we know that x = 4y - 1, substitute that into the second equation:

From here we can solve for y. Firstly, combine like terms:

Next, subtract 4y on both sides of the equation:

Next, multiply both sides by -1:

Now that we know the value of y, substitute it into either equation to solve for x:

Answer:

In short, 5 is the lesser number and 19 is the greater number.

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two cars leave an intersection at the same time, one travelling at 70km/h along one road and the other car travelling at 80km/h along the other road. After 2 hours they are 218 km apart. At what angle, to the nearest minute, do the roads meet at the intersection.

Answers

$v_1=70\ km/h\nv_2=80\ km/h\nt=2h\n\nv=(s)/(t)\to s=vt\n\ns_1=70\ km/h\cdot2h=140\ km\ns_2=80\ km/h\cdot2h=160\ km\n\nlook\ at\ the\ picture$

$218^2=140^2+160^2-2\cdot140\cdot160\cdot cos\alpha\n\n47524=19600+25600-44800cos\alpha\n\n47524=45200-44800cos\alpha\n\n44800cos\alpha=45200-47524\n\n44800cos\alpha=-2324\ \ \ \ /:44800\n\ncos\alpha\approx-0.051875\Rightarrow\alpha\approx92^o58'$

What is 6.99 × 10−4 in standard form? A) 0.0000699 B) 0.000699 C) 0.0699 D) 6,990

Answers

Option B: 0.000699 is the standard form

Explanation:

Given that the expression $6.99* 10^{-4$

We need to determine the standard form of the expression $6.99* 10^{-4$

Since, the power is in negative four, then we need to move the decimal point four places before the number 6.

Moving the decimal point four places before the number 6, we get,

0.000699

Thus, the standard form of the given expression is $6.99* 10^{-4$

Therefore, Option B is the correct answer.

Answer:

It is B

Step-by-step explanation:

I just took it on USA test prep :)

Solve the system of equations 3x+2y=14 2x-4y=4

Answers

3x + 2y = 14....multiply by 2
2x - 4y = 4
----------------
6x + 4y = 28 (result of multiplying by 2)
2x - 4y = 4
----------------add
8x = 32
x = 32/8
x = 4

2x - 4y = 4
2(4) - 4y = 4
8 - 4y = 4
-4y = 4 - 8
-4y = -4
y = -4/-4
y = 1

solution is (4,1)

Divide 7/15 by 3/5.
A. 75/21
B. 7/9
C. 7/25
D. 21/75

Answers

In this question there is nothing complicated. Only thing is to know the way fractions can be divided. Once that is known the problem would be one of the easiest to solve. Now let us get back to the problem and look at all the information's that are given in the question.
Divide 7/15 by 3/5 = (7/15)/(3/5)
      = (7 * 5)/(15 * 3)
   = (35/45)
Dividing the numerator and the denominator by 5 for simplifying purpose, we get
   = 7/9
So from the above deduction we can easily conclude that 7/9 is the correct answer and option "B" is the correct option among all the options given in the question.

If you would like to solve 7/15 / 3/5, you can calculate this using the following steps:

7/15 / 3/5 = 7/15 * 5/3 = 7/9

The correct result would be B. 7/9.

5. Seven times a number is equal to 12 more than 3 times the number. Find the number.

Answers

Answer:

Step-by-step explanation:

3 times 3 is 9 plus 12 is 21....3 times 7 is 21.

1. Determine whether the regular hexagon has reflection symmetry, rotation symmetry, both, or neither. If it has reflection symmetry, state the number of axes of symmetry. If it has rotation symmetry, state the angle of rotation. For each type of symmetry, explain how you can tell the figure does or does not have the given symmetry.

Answers

A hexagon is a 6 sided polygon which has a 720° total of internal angles.
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In Rotational symmetry, the image is rotated around a central point and still looks the same. The regular hexagon is rotated 12 times at an angle of 60°.

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