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3 years ago

The table below shows the scores for two teams playing a series of four card games.

Mathematics

2 answers:

zlopas [31]3 years ago

4 0

Team 1 has -2 points and team 2 has -1 points team 2 is the winner and the results of four games would not change anything as both games 3 and 4 when added together would end up as zero extra points so it would not change anything

nadya68 [22]3 years ago

4 0

Answer:

A. team 1: -2 points; team 2: -1 points;

B. team 2

C. no, it wouldn't

Step-by-step explanation:

A. After two games, team 1 made -3 +1 = -2 points, and team 2 made 4 -5 = -1 points.

B. -1 is greater than -2, then team 2 won.

C. After four games, team 1 made -3 +1 -4 +4 = -2 points, and team 2 made 4 -5 +9 -9 = -1 points. The results are the same as before.

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X - 4y = 1 and 3x + 2y = -11. What is the solution to the system of equations?

Pepsi [2]

Answer:

x=-3 y=-1

Step-by-step explanation:

3 0

3 years ago

Firefighters need to use a 60-foot ladder to save a child. She is 50 feet above street

mr_godi [17]

Answer:

The ladder must be placed at a distance of 33.2 feet from the bottom of the building

Step-by-step explanation:

From what we have here, we are looking at a right angled triangle with the hypotenuse which is the length of the ladder

The height of the child is 50 feet from ground level

So we need to get the third side of the triangle

We can get this by considering the use of Pythagoras’ theorem

This will give us the length of the third side of the triangle

From Pythagoras’ the square of the hypotenuse is equal the sum of the squares of the two other sides

Let the unknown side be x

Thus;

60^2 = 50^2 + x^2

x^2 = 60^2 - 50^2

x^2 = (60-50)(60+50)

x^2 = (10)(110)

x^2 = 1100

x = square root of 1100

x = 33.166

To the nearest tenth, this is 33.2 feet

3 0

3 years ago

3 cos 2x + Sinx = 1 for 0° ≤x ≤ 360

Archy [21]

Answer:

x = 41.81°, 138.19°, 210°, 330°

Explanation:

3cos(2x) + sin(x) = 1

subtract one from both sides

→ 3cos(2x) + sin(x) − 1 = 0

rewrite using trigonometry identities

→ 2 + sin(x) − 6sin²(x) = 0

solve x by substitution

f(x) = 2 + sin(x) − 6sin²(x)

= 2 + 4sin(x) - 3sin(x) − 6sin²(x)

= −2sinx(3sinx −2) − (3sinx−2)

= (3sinx −2)(−2sinx−1)

= −(3sinx −2)(2sinx+1)

f(x) = 2 + sin(x) − 6sin²(x) = 0

= −(3sinx −2)(2sinx+1) = 0

(3sinx −2) = 0 (2sinx+1) = 0

→sinx = 2/3 →sinx = −1/2

x = 41.81°, 138.19° x = 210°, 330°

(Please heart the answer if you find it helpful, it's a motivation for me to help more people)

3 0

3 years ago

Derivatives concept: Exercises using the definition of derivatives: (Full development)

krok68 [10]

(A) f(x) = 7 is constant, so f(x + h) = 7, too, which makes f(x + h) - f(x) = 0. So f'(x) = 0.

(B) f(x) = 5x + 1 ==> f(x + h) = 5 (x + h) + 1 = 5x + 5h + 1

==> f(x + h) - f(x) = 5h

Then

$\displaystyle f'(x) = \lim_{h\to0}\frac{5h}h = \lim_{h\to0}5 = 5$

(C) f(x) = x ² + 3 ==> f(x + h) = (x + h)² + 3 = x ² + 2xh + h ² + 3

==> f(x + h) - f(x) = 2xh + h ²

$\implies\displaystyle f'(x) = \lim_{h\to0}\frac{2xh+h^2}h = \lim_{h\to0}(2x+h) = 2x$

(D) f(x) = x ² + 4x - 1 ==> f(x + h) = (x + h)² + 4 (x + h) - 1 = x ² + 2xh + h ² + 4x + 4h - 1

==> f(x + h) - f(x) = 2xh + h ² + 4h

$\implies \displaystyle f'(x) = \lim_{h\to0}\frac{2xh+h^2+4h}h = \lim_{h\to0}(2x+h+4) = 2x+4$

5 0

3 years ago

A high school is having a pancake breakfast fundraiser. They have 4 packages of pancake mix that each feed 120 people. The funct

horrorfan [7]

Answer:

$1 \leqslant no \: packages = m \leqslant 4$

then

$x = no \: members \: cooking \: team \leqslant n$

Step-by-step explanation:

Imagine the space they need to host at least 120 people so they could open the second package and finish before noon

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4 years ago