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4 years ago

Mathias and his brother divided 2,029marbles equally.About how many marbles did each of them receive?

Mathematics

2 answers:

sleet_krkn [62]4 years ago

8 0

The answer is 1,014 because half of 29 is 14.5 and you can't have half a marble so your answer is 1,014.

ser-zykov [4K]4 years ago

7 0

If you do 2,029 divided by 2 you will get the answer: 514.5 which is rounded to 515

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One way to prove this quadrilateral is a square is by calculating the slopes of its sides and the slopes of its diagonals.

tatuchka [14]

Answer:

Step-by-step explanation:

<h3>To prove quadrilateral is a square:</h3>

a) Slope of CB

C(-3,-1) ; B = (0,3)

$\sf \boxed{Slope = \dfrac{y_2-y_1}{x_2-x_1}}$

$\sf = \dfrac{3-[-1]}{0-[-3]}\\\\ =\dfrac{3+1}{0+3}\\\\ = \dfrac{4}{3}$

$\sf \text{\bf slope of CB = $\dfrac{4}{3}$}$

b) D(1,-4) ; A(4,0)

$Slope \ of \ DA = \dfrac{0-[-4]}{4-1}\\$

$= \dfrac{0+4}{3}\\\$

$\sf \text{\bf Slope of DA = $\dfrac{4}{3}$}$

Slope of CB = slope of DA

c) C(-3,-1) ; D(1 , -4)

$\sf Slope \ of \ CD =\dfrac{-4-[-1]}{1-[-3]}$

$\sf = \dfrac{-4+1}{1+3}\\\\ = \dfrac{-3}{4}\\$

$\sf Slope \ of \ CD * Slope of CB = \dfrac{-3}{4}*\dfrac{4}{3}=-1$

So, CD is perpendicular to CB

d) B(0,3) ; D(1,-4)

$Slope \ of \ BD = \dfrac{-4-3}{1-0}\\\\=\dfrac{-7}{1}\\\\=-7$

e) C(-3,-1) ; A(4,0)

$\sf Slope \ of \ CA = \dfrac{0-[-1]}{4-[-3]}\\$

$=\dfrac{0+1}{4+3}\\\\=\dfrac{1}{7}$

$\text{Slope of CA *Slope of BD = $\dfrac{1}{7}$*(-7)}=-1$

So, CA is perpendicular to BD

$\sf \text{\bf Slope of DA = \dfrac{4}{3}}$

5 0

2 years ago

How many solutions does the equation 3x-2x+4=2+x+2 have?

ladessa [460]

Answer:

infinitely many solutions

Step-by-step explanation:

3x - 2x + 4 = 2 + x + 2

x + 4 = x + 4

x = x

x = x is a true statement for every value of x, so there is an infinite number of solutions.

Answer: infinitely many solutions

5 0

3 years ago

114

liq [111]

Line <em>q</em> has slope 3, as you've found.

Any line perpendicular to <em>q</em> will then have slope -1/3, as you've found.

Line <em>p</em> thus has slope -1/3 and we know it passes through (6, -5), so from the point-slope formula we get the equation

$y - (-5) = -\dfrac13 (x - 6) \implies \boxed{y + 5 = -\dfrac13 (x - 6)}$

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2 years ago

Triangle A B C is shown. Angle A C B is a right angle. The length of the hypotenuse is 20.

kherson [118]

Answer:

The length of BC is needed because it is the side opposite ∠A.

Step-by-step explanation:

Given the right angles triangle as shown in the attachment, we can get sin(A) without using Pythagoras theorem. Instead we will use SOH CAH TOA trigonometry identity.

According to SOH:

Sin(A) = Opposite/Hypotenuse

Sin(A) = |BC|/|AB|

Opposite side of the triangle is the side facing ∠A.

Based on the formula, we will need to get the opposite side of the triangle which is length BC for us to be able to determine sinA since the hypotenuse is given.

8 0

4 years ago

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Solve (x – 3)2 = 49. Select the values of x.

PIT_PIT [208]

Answer:

Step-by-step explanation:

$(x - 3)2 = 49 \\ \frac{(x - 3)2}{2} = \frac{49}{2} \\ x - 3 = 24.5 \\ x - 3 + 3 = 24.5 + 3 \\ x = 27.5 \\$

6 0

2 years ago

Read 2 more answers