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3 years ago

Five less than twice the value of a number is equal to three times the quantity of

Mathematics

1 answer:

Elden [556K]3 years ago

8 0

Answer:

a) x = 34

b) yes, it checks out

Step-by-step explanation:

2x - 5 = 3(4 + 1/2x)

multiply both sides by 2 to eliminate fraction

2[2x - 5 = 3(4 + 1/2x)] = 4x - 10 = 24 + 3x

x - 10 = 24

x = 34

<u>check</u>

2(34) - 5 = 3(4 + 34/2)

68 - 5 = 3(4 + 17)

63 = 3(21)

63 = 63

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How many non perfect squares are there in between 35square and 36square

vampirchik [111]

1 square sorry if I’m wrong

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3 years ago

What additional congruence statement could you use to prove ΔCAB≅ΔCAD by HL?

AleksAgata [21]

Answer:

AB≅AD; ΔADC≅ΔEBC; SAS only; VY; AB≅CE

Step-by-step explanation:

For HL, we must have the hypotenuse and a leg of each triangle congruent to the corresponding hypotenuse and leg of the other triangle.

We can see from the diagram that AC≅AC by the reflexive property. AC is a leg in each right triangle. This means we need the hypotenuse of each triangle congruent to the corresponding hypotenuse of the other triangle; this means we need AB≅AD.

ASA means "angle side angle." It states that if two angles and the included side of one triangle is congruent to the corresponding two angles and the included side of the other triangle, then the triangles are congruent.

We can see that BC≅CD from the diagram. This is the side; this means we need two angles.

We know that ACD≅ECB by the diagram. This is one angle and the side; we need one more angle.

Since m∠ADE = 90°, this means that m∠ADC must be 90° as well. Since m∠EBA = 90°, this means that m∠EBC must be 90° as well. This gives us the last corresponding pieces for the two triangles to be congruent using ASA.

Since ∠CBA≅∠DEA, and ∠BAC≅∠EAD, this means the third pair of angles, ∠ACB and ∠ADE, must be congruent as well. This is because all triangles have a sum of 180°.

This means we have two sides and the angle between them; this is SAS.

ΔUTW is similar to ΔVTX. This means the angle measures are the same for both triangles. We can also see that ∠VXW ≅ ∠UWT.

∠UWX and ∠UWT make a linear pair; this makes them supplementary. Since ∠VXW≅∠UWT, this means that ∠UWX and ∠UWT are supplementary as well.

This means that ∠UYX, which is opposite ∠UWX, will be congruent to it. This makes VYU≅VXT.

This gives us a pair of congruent angles at the bottom of ΔVYU, which makes it isosceles. This means that the sides adjacent to the base angles are congruent, which means that VU≅VY.

We are given that ΔABC≅ΔECD. This means corresponding pieces are congruent. From the similarity statement, we can see that AB corresponds to EC.

5 0

4 years ago

Read 2 more answers

Find the endpoint of the line segment

blondinia [14]

Answer:

(29,-13)

Step-by-step explanation:

You can tackle this for x and y coordinate separately.

For x, the line starts at -9 and is halfway at 10. The distance between -9 and 10 is 19 so it has another 19 to go, which puts the endpoint at 10+19=29.

Same for y: from 7 to -3 is 10 down, another 10 to go, puts you at -13.

Formula: x,y of midpoint is ((x1+x2)/2, (y1+y2)/2)

3 0

4 years ago

NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. There are 21 mathem

saveliy_v [14]

Mathematics majors $=21$

Computer science majors $=325$

We need to use product rule because the first event is picking the mathematics major and second event is picking the computer science major

$21\times325=6825$

We need to use sum rule because the first event is picking OR mathematics major and second event is picking the computer science major

$21+325=346$

What is mathematics ?

One of the most essential disciplines is mathematics.
Math is a topic that involves numbers, forms, facts, measurements, and logical processes.
Every aspect of our lives, including medical, engineering, finance, the natural sciences, economics, etc., are greatly affected by it.
The universe of mathematics is all around us.
Mathematical ideas, theories, and formulae have a wide range of practical applications.
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So the more about mathematics visit.

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4 0

2 years ago

Mathswatch? Help <br><br> Angles and parallel lines

GrogVix [38]

The answer is

a) x° = 80

reasons) the reason is a line is 180°
the angle 100°
that would leave you 80° to make a straight line

i hope this helped :)

3 0

4 years ago