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Yanka [14]
2 years ago
11

May someone please help me on which to graph?

Mathematics
1 answer:
olga_2 [115]2 years ago
6 0

Answer:

Option (4)

Step-by-step explanation:

Proportional relationship means,

y ∝ x

y = kx

k=\frac{y}{x}

Here, k = proportionality constant

Therefore, if the graph of a line passes through the origin (0, 0) table will represent the proportional relationship.

From table 1,

For a point (1, 2)

k=\frac{2}{1}=2

For another point (3, 2)

k=\frac{3}{2}=1.5

In both the cases 'k' is not same of constant.

Therefore, table (1) is not proportional.

For table (2),

Line passes through (2, 0).

That means there is a x-intercept → (2, 0)

Therefore, table doesn't represent a proportional relationship.

For table (3),

Line passes through a point (0, 1)

It means given line has a y-intercept → y = 1

Therefore, table doesn't represent a proportional relationship.

For table (4),

Line of this table passes through two points (1, 3) and (2, 6)

k=\frac{3}{1}=3

k=\frac{6}{2}=3

Therefore, proportionality constant for the given table is 3.

Now we can graph table (4).

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Answer:

22

Step-by-step explanation:

add everything in the parentheses first, then multiply by 1/2  (or divide by 2)

(28 + 7 + 6 + 3) x 1/2 = 44 x 1/2 = 22

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3 years ago
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The vertices of a triangle ABC are A(7, 5), B(4, 2), and C(9, 2). What is measure of angle ABC? 30° 45° 56.31° 78.69°
GenaCL600 [577]

The measure of angle ABC is 45°

<em><u>Explanation</u></em>

Vertices of the triangle are:   A(7, 5), B(4, 2), and C(9, 2)

According to the diagram below....

Length of the side BC (a) =\sqrt{(4-9)^2+(2-2)^2}= \sqrt{25}= 5

Length of the side AC (b) = \sqrt{(7-9)^2 +(5-2)^2}= \sqrt{4+9}=\sqrt{13}

Length of the side AB (c) = \sqrt{(7-4)^2 +(5-2)^2} =\sqrt{9+9}=\sqrt{18}

We need to find ∠ABC or ∠B . So using <u>Cosine rule</u>, we will get...

cosB= \frac{a^2+c^2-b^2}{2ac} \\ \\ cos B= \frac{(5)^2+(\sqrt{18})^2-(\sqrt{13})^2}{2*5*\sqrt{18} }\\ \\ cosB= \frac{25+18-13}{10\sqrt{18}} =\frac{30}{10\sqrt{18}}=\frac{3}{\sqrt{18}}\\ \\ cosB=\frac{3}{3\sqrt{2}} =\frac{1}{\sqrt{2}}\\ \\ B= cos^-^1(\frac{1}{\sqrt{2}})= 45 degree

So, the measure of angle ABC is 45°

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Answer:

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What is the slope of the line that passes through (-1,-2) and (-1,-3)
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Gnesinka [82]

\huge \boxed{\mathfrak{Question} \downarrow}

  • Simplify :- 1 + - w² + 9w.

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

\large \sf1 + - w ^ { 2 } + 9 w

Quadratic polynomial can be factored using the transformation \sf \: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where \sf x_{1} and x_{2} are the solutions of the quadratic equation \sf \: ax^{2}+bx+c=0.

\large \sf-w^{2}+9w+1=0

All equations of the form \sf\:ax^{2}+bx+c=0 can be solved using the quadratic formula: \sf\frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

\large \sf \: w=\frac{-9±\sqrt{9^{2}-4\left(-1\right)}}{2\left(-1\right)}  \\

Square 9.

\large \sf \: w=\frac{-9±\sqrt{81-4\left(-1\right)}}{2\left(-1\right)}  \\

Multiply -4 times -1.

\large \sf \: w=\frac{-9±\sqrt{81+4}}{2\left(-1\right)}  \\

Add 81 to 4.

\large \sf \: w=\frac{-9±\sqrt{85}}{2\left(-1\right)}  \\

Multiply 2 times -1.

\large \sf \: w=\frac{-9±\sqrt{85}}{-2}  \\

Now solve the equation \sf\:w=\frac{-9±\sqrt{85}}{-2} when ± is plus. Add -9 to \sf\sqrt{85}.

\large \sf \: w=\frac{\sqrt{85}-9}{-2}  \\

Divide -9+ \sf\sqrt{85} by -2.

\large \boxed{ \sf \: w=\frac{9-\sqrt{85}}{2}} \\

Now solve the equation \sf\:w=\frac{-9±\sqrt{85}}{-2} when ± is minus. Subtract \sf\sqrt{85} from -9.

\large \sf \: w=\frac{-\sqrt{85}-9}{-2}  \\

Divide \sf-9-\sqrt{85} by -2.

\large \boxed{ \sf \: w=\frac{\sqrt{85}+9}{2}}  \\

Factor the original expression using \sf\:ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \sf\frac{9-\sqrt{85}}{2}for \sf\:x_{1} and \sf\frac{9+\sqrt{85}}{2} for \sf\:x_{2}.

\large \boxed{ \boxed {\mathfrak{-w^{2}+9w+1=-\left(w-\frac{9-\sqrt{85}}{2}\right)\left(w-\frac{\sqrt{85}+9}{2}\right) }}}

<h3>NOTE :-</h3>

Well, in the picture you inserted it says that it's 8th grade mathematics. So, I'm not sure if you have learned simplification with the help of biquadratic formula. So, if you want the answer simplified only according to like terms then your answer will be ⇨

\large \sf \: 1 + -  w {}^{2}  + 9w \\  =\large  \boxed{\bf \: 1 -  {w}^{2}   + 9w}

This cannot be further simplified as there are no more like terms (you can use the biquadratic formula if you've learned it.)

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2 years ago
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