MATHEMATICS HIGH SCHOOL

Solve for p in the literal equation 7p + 9r = 9.
p =

Answers

Answer 1
Answer:

Answer:

       p = -7

Step-by-step explanation:

7p + 9r = 9

      -9    -9

      7p = 0

      -7     -7

        p = -7

     

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A certain liquid has a density of 2.67 g/cm3. 30.5 mL of this liquid would have a mass of ________ Kg. 0.0114
11.4
0.0814
0.0875 81.4

Answers

Answer:

One ml is equal to a cm3, then

m=2.67g/cm3*30.5cm3

m=81.435g

If we divide this quantity by 1000 to pass this to Kg we get:

m=81.435/1000=0.081435kg

Step-by-step explanation:

Remember the formula of density is density=mass/volume, if we solve for mass we get:

mass=density*volume

Ed is doing a survey of popular colors for cars for a school report. He decides to take a sample by sitting near a busy intersection and noting the colors of the cars as they go by him. Ed counts 23 black cars, 9 red cars, 17 blue cars, 25 white cars, and 21 silver cars during 20 minutes of watching. How many more white and blue cars are there than silver and red cars?

Answers

The answer is 12.

If we represent the cars in this way:
Black cars  A = 23
Red cars    B = 9
Blue cars   C = 17
White cars D = 25
Silver cars E = 21

Then sum of white and blue cars is D + C = 25 + 17 = 42
And the sum of silver and red cars is E + B = 21 + 9 = 30

Using the subtraction:
(D+C) - (E+B) = 42 - 30 = 12

Therefore, there are 12 more white and blue cars than silver and red cars.

Answer:

12

Step-by-step explanation:

Y=tan(x-30) period and amplitude ​

Answers

Answer:

No amplitude

Period is pi

Step-by-step explanation:

How to distribute this problem:
(x-8)^2 + 16

Answers

Answer:

We conclude that:

\left(x-8\right)^2+16=x^2-16x+80

Step-by-step explanation:

Given the equation

\left(x-8\right)^2\:+\:16

First, solve (x - 8)²

Apply Perfect Square formula:    (a - b)² = a² - 2ab + b²

a=x,\:\:b=8

\left(x-8\right)^2=x^2-2x\cdot \:\:8+8^2

             =x^2-16x+64

so the expression becomes

\left(x-8\right)^2+16=x^2-16x+64+16

                     =x^2-16x+80           Add the numbers: 64+16=80

Therefore, we conclude that:

\left(x-8\right)^2+16=x^2-16x+80

One leg of a right triangle is 7 units long, and its hypotenuse is 16 units long. What is the length of the other leg? Round to the nearest whole number.

Answers

Answer:

14 units

Step-by-step explanation:

To find the length of the other leg of a right triangle, where one leg is 7 units long and the hypotenuse is 16 units long, use Pythagoras Theorem.

Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the legs.  

Let the legs of the right triangle be "a" and "b", and the hypotenuse be "c". Therefore:

\begin{aligned}a^2+b^2&=c^2\na^2+7^2&=16^2\na^2+49&=256\na^2+49-49&=256-49\na^2&=207\n√(a^2)&=√(207)\na&=14.3874945...\na&=14\;\sf(nearest\;whole\;number)\end{aligned}

Therefore, the length of the other leg is 14 units (rounded to the nearest whole number).

Answer:

7^{2} + x^{2} = 16^{2}

49+x^2=256

x^2=207

x=14.387=14

Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

Answers

1. The first theorem used is that vertical angles are congruent.
2. The next theorem used is that adjacent angles in a parallelogram are supplementary. 
3. The definition of supplementary angles is then used for angle formed by intersecting  lines.
4. The theorem on vertical angles is used again.
5. Finally, the definition of the transitivity property is used to prove that alternate exterior angles are congruent.

Using the Corresponding Angles Theorem, Vertical Angles Theorem, and the Transitive Property of Congruence, we can prove that alternate exterior angles (e.g, <4 and <5) are congruent by the alternate exterior angles theorem.

Recall:

  • Alternate exterior angles are angles that lie outside the two lines that is cut across by a transversal but on opposite sides along the transversal.
  • Examples of alternate exterior angles are <2 and <7; <4 and <5 as shown in the figure attached below.

If we are given that m \parallel n in the diagram attached below, the following are theorems and definitions we can use to prove that \angle 4 \cong \angle 5 (alternate exterior angles).

Statement 1: \angle 4 \cong \angle 8

Reason: Corresponding Angles Theorem

The corresponding angles theorem states that when two parallel lines (lines m and n) are intersected by a transversal line (line w), the two corresponding angles formed (e.g. <4 and <8) are congruent.

Statement 2: \angle 8 \cong \angle 5

Reason: Vertical Angles Theorem

The Vertical Angles Theorem states that the opposite vertical angles (e.g. <8 and <5) formed when two lines (lines n and w) intersect are congruent to each other.

Statement 3: \angle 4 \cong \angle 5

Reason: Transitive Property of Congruence

The Transitive Property of Congruence states that if a = b; and b = c; then a = c.

Therefore, using the Corresponding Angles Theorem, Vertical Angles Theorem, and the Transitive Property of Congruence, we can prove that alternate exterior angles (e.g, <4 and <5) are congruent by the alternate exterior angles theorem.

Learn more here:

brainly.com/question/16182992
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