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tatyana61 [14]
3 years ago
15

. Sara collected $135 in donations for the hospital. This represents 5% of the total amount collected by her class. How much did

the class collect in all? *
$6.75
$130
$140
$2700
Mathematics
2 answers:
AfilCa [17]3 years ago
6 0
5 percent of 2700 is 135 so the answer is $2700

Drupady [299]3 years ago
5 0
$2700

I know $135 is 5%, so $270 is 10% (because 5% + 5% = 10%). If you know what 10% of an amount is, you can just multiply that number by 10 to get to 100%. 270x10=2700

Another way to do this would be to say an unknown number, x, times 5% (0.05) equals $135. That equation would be 0.05x=135. Divide each side by 0.05 to get x = 2700

I hope this helps!
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Anyone know this i need help this is for a final
Nuetrik [128]
For every week that goes on, the tiger’s weight increases by 4 lbs.

(1+4=5, 5+4=9, 9+4=13, 13+4=17)

hopefully this helps, good luck on your final! <3
5 0
3 years ago
Decide if the following statement is valid or invalid. If two sides of a triangle are congruent then the triangle is isosceles.
Naya [18.7K]

Answer:

Step-by-step explanation:

Properties of an Isosceles Triangle

(Most of this can be found in Chapter 1 of B&B.)

Definition: A triangle is isosceles if two if its sides are equal.

We want to prove the following properties of isosceles triangles.

Theorem: Let ABC be an isosceles triangle with AB = AC.  Let M denote the midpoint of BC (i.e., M is the point on BC for which MB = MC).  Then

a)      Triangle ABM is congruent to triangle ACM.

b)      Angle ABC = Angle ACB (base angles are equal)

c)      Angle AMB = Angle AMC = right angle.

d)      Angle BAM = angle CAM

Corollary: Consequently, from these facts and the definitions:

Ray AM is the angle bisector of angle BAC.

Line AM is the altitude of triangle ABC through A.

Line AM is the perpendicular bisector of B

Segment AM is the median of triangle ABC through A.

Proof #1 of Theorem (after B&B)

Let the angle bisector of BAC intersect segment BC at point D.  

Since ray AD is the angle bisector, angle BAD = angle CAD.  

The segment AD = AD = itself.

Also, AB = AC since the triangle is isosceles.

Thus, triangle BAD is congruent to CAD by SAS (side-angle-side).

This means that triangle BAD = triangle CAD, and corresponding sides and angles are equal, namely:

DB = DC,

angle ABD = angle ACD,

angle ADB = angle ADC.

(Proof of a).  Since DB = DC, this means D = M by definition of the midpoint.  Thus triangle ABM = triangle ACM.

(Proof of b) Since angle ABD = angle ABC (same angle) and also angle ACD = angle ACB, this implies angle ABC = angle ACB.

(Proof of c) From congruence of triangles, angle AMB = angle AMC.  But by addition of angles, angle AMB + angle AMC = straight angle = 180 degrees.  Thus 2 angle AMB = straight angle and angle AMB = right angle.

(Proof of d) Since D = M, the congruence angle BAM = angle CAM follows from the definition of D.  (These are also corresponding angles in congruent triangles ABM and ACM.)

QED*

*Note:  There is one point of this proof that needs a more careful “protractor axiom”.  When we constructed the angle bisector of BAC, we assumed that this ray intersects segment BC.  This can’t be quite deduced from the B&B form of the axioms.  One of the axioms needs a little strengthening.

The other statements are immediate consequence of these relations and the definitions of angle bisector, altitude, perpendicular bisector, and median.  (Look them up!)

Definition:  We will call the special line AM the line of symmetry of the isosceles triangle.  Thus we can construct AM as the line through A and the midpoint, or the angle bisector, or altitude or perpendicular bisector of BC. Shortly we will give a general definition of line of symmetry that applies to many kinds of figure.

Proof #2 (This is a slick use of SAS, not presented Monday.  We may discuss in class Wednesday.)

The hypothesis of the theorem is that AB = AC.  Also, AC = AB (!) and angle BAC = angle CAB (same angle).  Thus triangle BAC is congruent to triangle BAC by SAS.

The corresponding angles and sides are equal, so the base angle ABC = angle ACB.

Let M be the midpoint of BC.  By definition of midpoint, MB = MC. Also the equality of base angles gives angle ABM = angle ABC = angle ACB = angle ACM.  Since we already are given BA = CA, this means that triangle ABM = triangle ACM by SAS.

From these congruent triangles then we conclude as before:

Angle BAM = angle CAM (so ray AM is the bisector of angle BAC)

Angle AMB = angle AMC = right angle (so line MA is the perpendicular bisector of  BC and also the altitude of ABC through A)

QED

Faulty Proof #3.  Can you find the hole in this proof?)

In triangle ABC, AB = AC.  Let M be the midpoint and MA be the perpendicular bisector of BC.

Then angle BMA = angle CMA = right angle, since MA is perpendicular bisector.  

MB = MC by definition of midpoint. (M is midpoint since MA is perpendicular bisector.)

AM = AM (self).

So triangle AMB = triangle AMC by SAS.

Then the other equal angles ABC = ACB and angle BAM = angle CAM follow from corresponding parts of congruent triangles.  And the rest is as before.

QED??

8 0
2 years ago
Mr. Champion invests 34,000 into a money-market fund that pays 4.8% simple interest. How long will it take for him to earn $8,16
Tanzania [10]

Answer:

5 years

Step-by-step explanation:

Step one:

Given Information

Principal= $34,000

rate = 4.8%

SImple interest = $8,160

Required

The time T of the investment

Step two:

the expression for simple interest is

SI= PRT/100

substitute

8160 = 34000*4.8*T/100

cross multiply we have

8160*100= 34000*4.8*T\\\\816000= 163200T\\\\

divide both sides by 163200

816000/163200= T\\\\T= 5 years

4 0
3 years ago
It takes Leon 17 hours to seal his driveway working by himself. If Michael helps Leon, they can seal the driveway in 2 hours. Ho
Norma-Jean [14]

Answer:

It takes Michael 1 hour, 14 minutes and 7 seconds to seal the driveway close

Step-by-step explanation:

Hi

Leon do the work in 17 hours that means the rate of his work is \frac{1}{17} work/hr, so he do \frac{2}{17} of the work in two hours, therefore Michael do the other \frac{15}{17} of the work, thus Michael rate will be \frac{15}{17} \div\frac{1}{2} =\frac{30}{17} work/hour.

So it takes Michael 1h+\frac{4}{17}h to complete the work, or \frac{4h}{17} \times \frac{60min}{1hour} =14\frac{2}{17} min\\\\\frac{2}{17} min \times \frac{60 secs}{1min}=7secs

1h \ 14 min \ 7secs

8 0
3 years ago
The primary purpose of the passage is to
Charra [1.4K]

The main purpose of the passage is to describe the purpose, methods, and results of an experiment. The correct option is B.

Given a passage shown in the attached pictures.

Option B is the best answer. The first paragraph of the passage identifies and describes "Texas squash vines" (line 1), but the main focus of the passage is introduced in the first sentence of the second paragraph. The remainder of the passage focuses on describing the purpose, process, and results of recent research conducted on these Texas squash vines.

Option A is incorrect because the passage doesn’t focus on the assumptions behind a theory but rather on the way in which that theory was tested. Option C is incorrect because the passage does not contain a lot of conflicting data; most of them support the idea that there may be too many scents for the Texas squash. Option D is incorrect because the passage explains the procedures used in a study were “’very labor intensive’” (line 58) but does not present them as particularly innovative.

Hence, the primary purpose from the given passage is to describe the aim, method, and results of an experiment.

Learn more about the passage from here brainly.com/question/12555695

#SPJ4

5 0
2 years ago
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