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3 years ago

Kari drew two parallel lines PQ and RS intersected by a transversal KL, as shown below:

Mathematics

1 answer:

Archy [21]3 years ago

5 0

Answer: Same-Side Interior Angles Theorem

Step-by-step explanation:

Same-Side Interior Angles Theorem says that when two lines are parallel and a transversal intersects it , then the angles on the same interior side are supplementary.

We are given that Two parallel lines PQ and RS are drawn with KL as a transversal intersecting PQ at point M and RS at point N.

Angle QMN is shown congruent to angle LNS.

Also, angle QML and angle SNK are the angles lies on the same side of the transversal.

It means the measure of angle QML is supplementary to the measure of angle SNK [ By Same-Side Interior Angles Theorem ]

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Earth orbits the sun in an elliptical pattern. The equation of Earth's path is.... where the measurements represent millions of

Triss [41]

General equation of Ellipse centered at (h,k) is given as

$\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} =1\\$

where a is the radius along x-axis

and b is radius along y-axis.

Given : The equation of elliptical path of Earth as

$\frac{(x+2.5)^{2}}{22350.25} + \frac{y^{2}}{22344} = 1\\$

Comparing the equation with the general equation, we get

(h,k) as (-2.5,0)

a = $\sqrt{22350.25} = 149.5$

b = $\sqrt{22344} = 149.48$

We have the Sun located at the coordinate (0,0).

Hence, the distance between Sun and Earth in July = 149.5 + 2.5 =152

∴ Earth's distance from the Sun in July is 152 million kilometers.

5 0

3 years ago

Write Equivalent Fractions

Viktor [21]

Answer:

Step-by-step explanation:

Find equivalent fractions. Enter a fraction, mixed number or integer to get fractions that are equivalent to your input. Example entries:

Fraction - like 2/3 or 15/16

Mixed number - like 1 1/2 or 4 5/6

Integer - like 5 or 28

What are Equivalent Fractions?

Equivalent fractions are fractions with different numbers representing the same part of a whole. They have different numerators and denominators, but their fractional values are the same.

For example, think about the fraction 1/2. It means half of something. You can also say that 6/12 is half, and that 50/100 is half. They represent the same part of the whole. These equivalent fractions contain different numbers but they mean the same thing: 1/2 = 6/12 = 50/100

How to Find Equivalent Fractions

Multiply both the numerator and denominator of a fraction by the same whole number. As long as you multiply both top and bottom of the fraction by the same number, you won't change the value of the fraction, and you'll create an equivalent fraction.

Example Equivalent Fractions

Find fractions equivalent to 3/4 by multiplying the numerator and denominator by the same whole number:

34×22=68

34×33=912

34×44=1216

34×55=1520

34×66=1824

Therefore these are all equivalent fractions:

34=68=912=1520=1824

Note that if you reduce all of these fractions to lowest terms, they equal 3/4.

For additional fraction help see our Fractions Cal

3 0

3 years ago

Can some please help and explain your steps thanks

boyakko [2]

For A you would have to convert from that equation to the slope-intercept form of the equation. To do that, first add 2x to both sides, because you want to have x on the right side of the equation. And that's it! That gives you 4y = 2x + 8. And from that equation you can identify the slope (2) and the y-int (8)

For B, the same thing. Converting to slope-intercept form, just with an extra step. First, you would subtract 1y from both sides to move it to the left of the equal sign, since that's where it needs to be for slope-intercept form. That gives you -1y + 7 = -x. Don't worry about the negatives for now. Next, subtract 7 from both sides to get y by itself on the left (because that's how it is in slope-intercept form) which gives you -1y = -x - 7. Then, because you can't have negative variables, divide both sides by negative 1 (a negative divided by a negative equals a positive), to equal y = x + 7. (I've attached a picture showing my steps if the words are too confusing)

For C, you need to find the slope first, then use the slope to find the y-intercept. So subtract. (I've shown in the picture) that equals -8 over 4 which simplifies to -2. So -2 is the slope! Now to find the y-intercept, plug in an ordered pair from the problem (doesn't matter which one) and the slope to find the y-intercept (b). I'm just going to use (-2, 5). So plug in the y from the pair (5) and the slope (-2) and the x from the pair (-2) into the slope-intercept equation to equal 5 = -2(-2) + b. Since you don't know b (the y-intercept) leave it blank and solve like a one step equation! (steps in the picture). And there you have it, the slope is -2 and the y-int is 1!

For D, it's like C, but you dont have the chart. Use subtraction to find the slope. Change in y over change in x (which means subtract the y values and divide them by the difference in x values). So. You'd do 0 - 3 over -6 - 3 which equals -3 over -9, which simplifies to 1/3. And that's your slope! So to find the y-int just do the same thing you did in the last problem, plug in an ordered pair and the slope into the slope-intercept equation and solve as a one step equation (steps in picture). And there you have it, the slope which is 1/3, and the y-int which is 2.