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2 years ago

Help me for 10 points!!

Mathematics

1 answer:

attashe74 [19]2 years ago

6 0

-2y + 2

Explanation

We have (x - y + 1) - (x + y - 1)

Let’s expand the Parentheses

= x - y + 1 - x - y + 1

Then let’s group the like terms

= (x - x) + (- y - y) + (1 + 1)

= 0 - 2y + 2

= 2y + 2

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Calculate the area of the triangle with the following vertices (3, -7), (6, 4), (-2, -3)

Monica [59]

Answer:

$\boxed{\mathsf{A} \triangle = \red{\dfrac{67}{2}u.a}}$

Step-by-step explanation:

Let's follow up with the solution. Considering a triangle with the vertices $\mathsf{A(x_A, y_A)}$ , $\mathsf{B(x_B, y_B)}$ and $\mathsf{C(x_C, y_C)}$ , have a look at the representation in the cartesian plan.

From this representation we can say that the area (A) of a triangle through the knowledge of <u>analytical geometry</u> is given by the determinant of the vertices divided by two, mathematically,

$\mathsf{A} \triangle = \dfrac{\left| \begin{array}{ccc} \mathsf{x_A} & \mathsf{y_A }& 1 \\ \mathsf{x_B} & \mathsf{ y_B} & 1 \\ \mathsf{ x_C} & \mathsf{ y_C} & 1 \end{array} \right|}{2}$

So, applying this knowledge we're going to have,

$\mathsf{A} \triangle = \dfrac{\left| \begin{array}{ccc} 3 & -7 & 1 \\ 6 & 4 & 1 \\ -2 & -3 & 1 \end{array} \right|}{2}$

$\mathsf{A} \triangle = \dfrac{1}{2}\left[ \left.\begin{array}{ccc} 3 & -7 & 1 \\ 6 & 4 & 1 \\ -2& -3 & 1 \end{array} \right| \begin{array}{cc} 3 & -7 \\ 6 & 4 \\ -2 & -3 \end{array} \right]$

$\mathsf{A} \triangle = \dfrac{12 + 14 - 18 - (-8 - 9 - 42)}{2}$

$\red{\mathsf{A} \triangle = \dfrac{67}{2} = 33,5u.a}$

Hope you enjoy it, see ya!)

$\green{\mathsf{FROM}}:$ Mozambique, Maputo – Matola City – T-3

DavidJunior17

3 0

3 years ago

Simplify. Write your answer with a positive exponent.<br><br><img src="https://tex.z-dn.net/?f=%285q%5E4%29%5E3" id="TexFormula1

tresset_1 [31]

Answer:

5q^7

Step-by-step explanation:

When multiplying exponents(if positive), you must add them together. So, (5q^4)³ will be 5q^7 because the exponents were positive and they were multiplying so you add them together and leave the variable and number 5 alone.

Hope this helps! :)

4 0

2 years ago

Read 2 more answers

Mark's school trail is 1,425 km long. Mark needs 2850 steps for this. How many centimeters is his step long?

kolezko [41]

Answer:

50 cm

Step-by-step explanation:

Convert 1.425km into cm

1.425 * 1000 * 100 = 142500 cm

Divide the total cm by total no of steps

142500/ 2850 = 50cm

5 0

2 years ago

How much more interest is owed on $900 for 9 months then for 6 months? 6 months = 2.4% rate 9 months = 2.9% rate

stiv31 [10]

Keeping in mind that 6 months is not even a year, since there are 12 months in a year, then 6 months is really 6/12 years, and 9 months is 9/12 years, then

$\bf ~~~~~~ \textit{Simple Interest Earned on 9 months}\\\\
I = Prt\qquad 
\begin{cases}
I=\textit{interest earned}\\
P=\textit{original amount deposited}\to& \$900\\
r=rate\to 2.9\%\to \frac{2.9}{100}\to &0.029\\
t=years\to \frac{9}{12}\to &\frac{3}{4}
\end{cases}
\\\\\\
I=900(0.029)\left( \frac{3}{4} \right)\\\\
-------------------------------$

$\bf ~~~~~~ \textit{Simple Interest Earned on 6 months}\\\\
I = Prt\qquad 
\begin{cases}
I=\textit{interest earned}\\
P=\textit{original amount deposited}\to& \$900\\
r=rate\to 2.4\%\to \frac{2.4}{100}\to &0.024\\
t=years\to \frac{6}{12}\to &\frac{1}{2}
\end{cases}
\\\\\\
I=900(0.024)\left( \frac{1}{2}\right)$

check their difference, that much.

6 0

2 years ago

Question 2: ___ of 5 points)

Luba_88 [7]

Answer:

Slope is - 2 because The slope-intercept form is y=mx+b where m is the slope value. In the equation y=-2x , the m value is - 2 .

6 0

2 years ago