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artcher [175]
3 years ago
10

Someone please help me on this!

Mathematics
1 answer:
Alexxx [7]3 years ago
6 0

Answer & Step-by-step explanation:

This can be proven with the SAS theorem (side-angle-side)

With a perpendicular bisector, the line it bisects is cut directly in half. This creates two equal sides:

GJ=IJ

and it creates two 90° angles:

∠GJH=∠IJH

And because of the reflexive property of congruence:

JH=JH

Side-Angle-Side.

:Done

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A chemist needs 130 milliliters of a 47% solution but has only 35% and 87% solutions available. Find how many milliliters of eac
choli [55]

Answer: Amount of 35% solution required = 100 milliliters

Amount of 87% solution required  = 30 milliliters

Step-by-step explanation:

Given: Total solution required =  130 milliliters

Let x = Amount of 35% solution (in milliliters).

Then, Amount of 87% solution required = 130 - x

As per given,

Concentration = 0.35x +0.87(130-x)=0.47(130)

0.35x +113.1-0.87x=61.1\\\\\Rightarrow\ -0.87x+0.35x=61.1-113.1\\\\\Rightarrow\ -0.52 x= -52\\\\\Rightarrow\ x=\dfrac{52}{0.52}=100

Hence, Amount of 35% solution required = 100 milliliters

Amount of 87% solution required  = 130-100 milliliters =30 milliliters

3 0
2 years ago
WILL GIVE BRAINLEIST PLEASE HURRY DUE AT 9 PM SUPER EASY For exercises 1 and 2, simplify each expression.
Ostrovityanka [42]
1. 13x + 21
2. 33 + 6x
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3 years ago
How do I find the radius, diameter and circumference
Mademuasel [1]


The circumference of a circle is all around the circle

The diameter is a line that crosses straight across a circle

And the radius is half the diameter :)

5 0
3 years ago
A given recipe for soup stock calls for 1 part bone for every 4 parts water. Represent this ratio as a decimal.
Semenov [28]

Answer:

1:4 as a decimal ration is 0.25:1

Step-by-step explanation:

5 0
3 years ago
ASAP!!! LOOK AT THE IMAGE FOR THE GRAPH AND ANSWER CHOICES!! PLEASE HELP URGENT!!
m_a_m_a [10]

Answer:

The answer is D.

4x + y = 2

x - y = 3

____________

When given a graph with an intersection of two lines, first locate the y-intercept (the point where x = 0) of each line, and then find it's slope by evaluating its change in y over the change in x.

It is also possible to eliminate the incorrect systems using substitution when given a point of intersection.

For example, as the point of intersection is apparent on this graph, you can substitute these coordinates from the graph into each of the systems of equations given in the choice answers to verify it.

For it to be a solution, it must satisfy (make true) both equations of the system.

(a, b) : (x, y)

Given that (1,-2) is our point of intersection according to the graph.

Choice A is incorrect because (1, -2) → x + 4y = 3 → (1) + 4(-2) = 3 → 1 + (-8) = 3 →

1 - 8 = 3 → -7 ≠ 3.

And (1, -2) → x + y = 2 → (1) + (-2) = 2 →

-1 ≠ 2.

It is already incorrect as one of the

equations in this system do not satisfy the coordinate.

Choice B is also incorrect because

(1, -2) → x + 4y = 2 → (1) + 4(-2) = 2 →

(1) + (-8) = 2 → 1 - 8 = 2 → -7 ≠ 2.

And (1, -2) → x + y = 3 → (1) + (-2) = 3 →

1 - 2 = 3 → -1 ≠ 3.

Lastly, Choice C is incorrect because

(1, -2) → 4x + y = 3 → 4(1) + (-2) = 3 →

4 + (-2) = 4 - 2 = 3 → 2 ≠ 3.

And (1, -2) → x - y = 2 → (1) - (-2) = 2 →

1 + 2 = 2 → 3 ≠ 2.

Therefore D is correct because it is the last answer remaining.

Also here is proof:

(1, -2) → 4x + y = 2 → 4(1) + (-2) = 2 →

4 + (-2) = 2 → 4 - 2 = 2 → <u>2 = 2</u>

So one equation fits the coordinate, but this cannot yet be verified as the working system unless both equations fit the point.

So (1, -2) → x - y = 3 → (1) - (-2) = 3 →

1 + 2 = 3 → <u>3 = 3</u>

Now we can say that this is the working system.

_____________________________

The next method involves strong observation of the graph to find both equations in slope-intercept form and then back into standard form to find a match of the choice answers as both systems are in standard form (Ax + By = C)

With the first line, it has a y-intercept of 2 because this is where it crosses the y-axis when x = 0. It also has a slope of -4 because it goes down 4 units every 1 unit to the right. This means that the first line has an equation of y = - 4x + 2.

Slope intercept form is the form y = mx + b where m is the slope( rise over run/change in y over change in x) , and b is the y-intercept (where x = 0).

The next line has a y-intercept of -3 because this is where it crosses the axis, and where x = 0. This also has a slope of 1 because it rises by 1 every run or goes up 1 unit every 1 unit to the right. therefore the second line has an equation of y = x - 3.

4 0
3 years ago
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