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2 years ago

Complete the two-column the proof by filling in the blanks.

Mathematics

1 answer:

Alborosie2 years ago

3 0

Applying the vertical angles theorem and other properties, the two-column proof that shows that <2 ≅ <4 is explained below.

<h3>What are Vertical Angles?</h3>

The adjacent angles that form a pair of angles that are directly opposite to each other, when two lines intersect, are referred to as verticals. They do not share the same side both share a common vertex.

According to the vertical angles theorem, angles that are vertical angles have equal angle measure.

<h3>What is the Transitive Property of Congruence?</h3>

The transitive property of congruence states that, if angle A is congruent to angle B, and angle B is congruent to angle C, then, angles A and C are congruent.

The two-column proof that proves that angles 2 and 4 are congruent is given below.

<u>Statement Reasons </u>

∠1 ≅ ∠3 Given

∠3 ≅ ∠2 Vertical angles are congruent

∠1 ≅ ∠2 Transitive property of congruence

∠1 ≅ ∠4 Vertical angles are congruent

∠2 ≅ ∠4 Transitive property of congruence

In summary, applying the vertical angles theorem and other properties, the two-column proof that shows that <2 ≅ <4 is given above.

Learn more about the vertical angles on:

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Find the distance between the points on the graph.

allsm [11]

Answer:

√41

Step-by-step explanation:

Use the distance formula.

(3, 1) and (-2,-3)

The distance between 3 and -2 is 5. 5 squared is 25.

The distance between 1 and -3 is 4. 4 squared is 16.

25+16 = 41

the root of 41 is √41.

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3 years ago

Find the equation of the line that passes through (0, -3) and is parallel to

Tresset [83]

Hey there!

$\\$

Answer:

$\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

$\\$

Explanation:

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be $\: \sf{d_1} \:$ and the line that is parallel to $\: \sf{d_1} \:$ be $\: \sf{d_2} \:$ .

$\sf{d_2} \:$ passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

$\sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}}$

$\\$

⇒Subtitute the values :

$\sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )}$

$\implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}$

$\sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}}$ .

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

$\sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.}$

$\implies \sf{y = \bold{\dfrac{7}{6}}x + b}$ $\\$

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line $\: \sf{d_1} \:$ . Now, replace y with -3 and x with 0:

$\implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore, the equation of the line $\: \bold{d_1} \:$ is $\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

$\\$

▪️Learn more about finding the equation of a line that is parallel to another one here:

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100 men and 100 women were surveyed and asked what there favorite ice ream flavor was, chart below

ser-zykov [4K]

Answer:

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Step-by-step explanation:

So starting off with chocolate. 200 people were surveyed. So 100 people would be 0.50 (or half or 50%). So 107 people who prefer chocolate would be a bit more than 0.50. 0.535 prefer chocolate.

Going to vanilla, 93 people prefer it. this is LESS than half so it has to be under 0.50. There is only one that is less than 0.50, which is 0.465. Also using addition, this would be the only logical one.

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Step-by-step explanation:

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