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3 years ago

Two consecutive odd integers have a sum of 32. Find the integers.

1 answer:

6 0

Let
x = first consecutive odd
x + 2 = second consecutive odd

Based on the problem, we equate
x + (x + 2) = 32
Solving for x,
2x + 2 = 32
2x = 32 - 2
2x = 30
x = 30/2
x = 15
and x + 2 = 15 + 2 = 17

Therefore, the integers are 15 and 17.

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A triangle has angle measures of 47 degrees and 92 degrees. What is the measure of the third angle?

ludmilkaskok [199]

Answer:

The missing angle is 41 degrees

Step-by-step explanation:

First of all, a triangle is measured at 180 degrees in total

To find the missing measurement for the third angle, add the 47 and 92 degrees together which would equal 139 degrees.

47+92=139 degrees

Next just subtract 139 from 180 to get your answer.

180-139=41 degrees

The answer is 41 degrees

<u><em>Hope this helps</em></u>

5 0

2 years ago

Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC . What is the leng

Thepotemich [5.8K]

Answer:

Length of side of rhombus is $x=\frac{ab}{a+b}$

Step-by-step explanation:

Given Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC. We have to find the length of side of rhombus.

It is also given that AB=a and AC=b

Let side of rhombus is x.

In ΔCEF and ΔCBA

∠CEF=∠CBA (∵Corresponding angles)

∠CFE=∠CAB (∵Corresponding angles)

By AA similarity rule, ΔCEF~ΔCBA

∴ their sides are in proportion

$\frac{EF}{AB}=\frac{CF}{AC}$

⇒ $\frac{x}{a}=\frac{b-x}{b}$

⇒ $xb=ab-ax$

⇒ $x(a+b)=ab$

⇒ $x=\frac{ab}{a+b}$

Hence, length of side of rhombus is $x=\frac{ab}{a+b}$

6 0

3 years ago

A certain antihistamine is often prescribed for allergies. A typical dose for a 100-pound person is 25 mg every six hours. Comp

koban [17]

Given that a certain antihistamine is often prescribed for allergies.

And typical dose for 100-pound person is 25 mg every 6 hours.

a) Let us calculate dose per 1 hour for 100-pound person= $\frac{25}{6} mg/hr$

Since 1 week means 7X24= 168 hours, dosage per 1 week = dosage per 168 hours

$=168X\frac{25}{6} = 700mg$

The number of 12.8 chew able tablets would be taken in a week= $\frac{700}{12.8}=54.6875$

Hence number of 12.8mg chew able tablets would be taken in a week is 55.

b) Now we can use earlier answer for this problem, since 12.8mg tablet is replaced with 9ml liquid, 55 bottles of 9ml liquid are to be taken in a week.

Hence amount of liquid histamine should a 100-pound person take in a week = 55X9

=495ml

3 0

3 years ago

The angles of elevation froma point X to the top of flagpoles A and B are 35* and 45* respectively. If X lies in the middle of t

BartSMP [9]

Let AB = t. And since X lies in the middle, so AX=BX = t/2 .

Let the height of the smaller flagpole is AO and of larger flagpole is BP .

Using tangent ratio rule in each triangle, we will get

$tan 35 =\frac{AO}{t/2} , tan 45= \frac{BP}{t/2} // AO = \frac{t*tan35}{2}, BP=\frac{t*tan45}{2}$

And there ratio is

$\frac{AO}{BP}= \frac{tan 35}{tan 45}=\frac{0.7}{1}$

5 0

2 years ago

CAN SOMEONE PLEASE HELP? THESE QUESTIONS ARE REALLY HARD AND I HAVE BEEN STUCK ON THEM FOR A WHILE. I REVIEWED THE LESSON AND EV

aniked [119]

Well if I did the right calculations... Kim is 24. The sister is age twelve! Hope I helped.

A. K+S=36

B. Well Simple Addition and Subtraction solves this easily. If you Add 12+12 it equals 24. It still needs to be larger so that Kim is twice as old as her little sister. So you Add another 12 which gives you 36. Or you can easily subtract 12 from it and that will also bring you to 24.

6 0

3 years ago

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