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RSB [31]
3 years ago
11

At the beginning of a science experiment, Caleb found the temperature of a solution to be 31°C. During the experiment, the chang

e in the temperature of the solution was – 17°C. What is the final temperature of the solution?
Mathematics
1 answer:
Paul [167]3 years ago
3 0

Answer:

Final temperature of the solution is 14°C.

Step-by-step explanation:

Given that,

Initial temperature of the solution, T_i=31^{\circ}\ C

The change in temperature of the solution, \Delta T=-17^{\circ}\ C

We need to find the final temperature of the solution.

Change in temperature = Final temperature - initial temperature

\Delta T=T_f-T_i\\\\T_f=\Delta T+T_i\\\\T_f=-17+31\\\\T_f=14^{\circ} C

So, the final temperature of the solution is 14°C.

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( x, y) satisfies both equations y+18=x(x-3) and x=y+6
antoniya [11.8K]

Answer:

(- 2, - 8 ) , (6, 0 )

Step-by-step explanation:

y + 18 = x(x - 3) ← distribute

y + 18 = x² - 3x → (1)

x = y + 6 → (2)

Substitute x = y + 6  into (1)

y + 18 =(y + 6)² - 3(y + 6) ← expand parenthesis using FOIL

y + 18 = y² + 12y + 36 - 3y - 18

y + 18 = y² + 9y + 18 ( subtract y + 18 from both sides )

0 = y² + 8y = y(y + 8)

Equate each factor to zero and solve for y

y = 0

y + 8 = 0 ⇒ y = - 8

Substitute these values into (2) and evaluate for x

y = 0 : x = 0 + 6 = 6 ⇒ (6, 0 )

y = - 8 : x = - 8 + 6 = - 2 ⇒ (- 2, - 8 )

3 0
3 years ago
Write the coordinates of the vertices after a translation 4 units left.
DENIUS [597]

Answer:

Step-by-step explanation:

8 0
2 years ago
A meteorologist was monitoring the temperature outside in degrees Fahrenheit (°F) and wrote the expression 78 + (-6). James beli
tatuchka [14]

Answer:

James is correct

Step-by-step explanation:

Given the expression wrote by a meteorologist as 78 + (-6), If James believes that this expression is the same as 78-6 then James is correct because if the parenthesis is expanded the product of the addition and the subtraction sign will produce a negative sign i.e + * - = -

78 + (-6) =  78 - 6 = 72

Based on the conclusion, we can say that James is correct in his reasoning

7 0
3 years ago
Find the area and perimeter of the compound figure below. (6 points)
fenix001 [56]

Answer:

  • area: 27.8 square units
  • perimeter: 21.2 units

Step-by-step explanation:

The area of a compound figure is the sum of the areas of its parts. The perimeter is the sum of the lengths of all of the edges.

<h3>Area</h3>

This compound figure is conveniently divided into a semicircle of radius 2.5 and a trapezoid with bases 5 and 7, and height 3.

<u>Semicircle</u>

The area of the semicircle is half the area of a circle with the same radius. It will be ...

  A = 1/2πr²

  A = 1/2π(2.5²) = 3.125π . . . . square units

<u>Trapezoid</u>

The area of the trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

  A = (1/2)(5 +7)(3) = 18 . . . . square units

Then the total area of the figure is ...

  3.125π +18 ≈ 27.8 . . . . square units

__

Perimeter

The perimeter will be the sum of the lengths of the straight line segments and the length of the semicircular arc.

<u>Arc</u>

  The arc length is half the circumference of the circle, so is ...

  arc = 1/2(2πr) = πr = 2.5π . . . . units

<u>Diagonal segments</u>

The figure is bounded by two congruent line segments that are each the hypotenuse of a triangle 1 unit wide and 3 units high. The Pythagorean theorem tells us that length is ...

  diagonal length = √(1² +3²) = √10 . . . . units

The two diagonal sides have a total length of 2√10 units.

<u>Horizontal segments</u>

The figure is bounded by two congruent horizontal segments of length 1 unit each, and one horizontal segment of length 5 units. Their total length is ...

  horizontal length = 1 + 1 + 5 = 7 . . . . units

The total perimeter is ...

  perimeter = horizontal length + diagonal length + arc length

  7 +2√10 +2.5π ≈ 21.2 . . . . units

7 0
3 years ago
Is the midpoint of a line segment is found by averaging the x coordinates and averaging the y coordinates of the endpoints
Serhud [2]
Yes, that's the definition of "midpoint."

                      xa + xb
xmidpoint = --------------
                           2

                      ya + yb
ymidpoint = --------------
                           2
6 0
3 years ago
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