when 4a - a x 3a + 7a is simplified it is equivalent to?

Answer:

the range in interval notation is (-4, 4).

Step-by-step explanation:

"Range" refers to the set of numbers that contains all possible values of y that a given function can take on.  In this diagram we see that the smallest possible y-value is -4 and the largest is +4, not inclusive (the set does not contain either -4 or +4).  Thus, the range in interval notation is (-4, 4).

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??

Yes, This statement is valid.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The two sides of a triangle are congruent.

Then, In ΔABC;

⇒ AB ≅ BC

So, ΔABC is isosceles.

Now,

Since, The two sides of a triangle are congruent.

We know that;

In a triangle if two sides are equal then it is an Isosceles triangle.

So, The given statement '' ΔABC is isosceles'' is valid.

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Let's find the slope (m) :

y - intercept (c) = -6

so, the equation of line will be :

Answer:

8

Step-by-step explanation:

mark me as brainliest ppls :)

Answer:

the one you have selected is correct

Step-by-step explanation:

Answer:

The most successful is Peptone (C)

Answer:

126

Step-by-step explanation:

Answer:

77

Step-by-step explanation:

Rate as BRAINLIEST

x + 9y

we plug in x and y

5+9(8)

=5+72

= 77

Answer:

77

Step-by-step explanation:

substitute the values in the equation

that'll give you 5+9(8)

then evaluate, 9(8)=72

72+5=77

Answer:

c: 35/2

Step-by-step explanation:

70/4 = 35/2

35/2 is the simplest answer and how much Jacob earns for each yard he mows.

Answer:

my answer is 8

because 4 6 8

Answer:

To the second one:

Step-by-step explanation:7x-11>=-74

Add 11 on both sides

7x>=-63

You divided by a positive, the sign does not change, However when you multiply or divide by a Negative, It does.

x>=-9

This is greater than or equal to, the hole would be closed and pointing right

The answer would be B.

Answer:

[tex]\dfrac{2}{8}=25\%[/tex]

Answer: 2/8 (1/4 simplified.) 0.25(decimal form)

Step-by-step explanation:

If 6/8 are dog bones, then we subtract 8/8-6/8. We get 2/8. If the fraction needs to be simplified, then we get 1/4. If a decimal is needed, then we divide 2 by 8. We get 0.25.

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The given statement can be represented as :

where, the number is assumed to be " b "

therefore, the correct choice is B. 2b³ - b

Answer:

312.5 cm²

Step-by-step explanation:

Since the figures are similar , then

ratio of heights = a : b

ratio of areas = a² : b²

Here linear ratio = 12 : 15 = 4 : 5 , then

ratio of areas = 4² : 5² = 16 : 25

let x be the area of B , the using proportion

[tex]\frac{200}{16}[/tex] = [tex]\frac{x}{25}[/tex] ( cross- multiply )

16x = 5000 ( divide both sides by 16 )

x = 312.5

Area of shape B is 312.5 cm²

Answer:

$200

Step-by-step explanation:

first you find the percentage of the money

so 60% of $500

second add/subtract the answer you get to/from the amount given

in this case subtract the answer you get from 500 and thats it there's your answer.

Answer:

i did the math and person above is right :)

Step-by-step explanation:

Answer:

.

Step-by-step explanation:

Hope this helps, if not sorry.

The sets can either be presented in set builder form or roaster form. The

given sets presented in the required form are;

a. The set B is the set of days in the week that starts with letter S

Therefore;

The elements of B are; Saturday, Sunday

In roster method, we have; B = {Saturday, Sunday}

In set builder notation, we have; B = {x | x is a days in the week that starts with letter S}

b. C is the set of letters in PHILIPPINES

In roster form, we have; C = {P, H, I, L, I, P, P, I, N, E, S}

In set builder notation, we have; C = {Letters in the word PHILLIPINES}

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Answer:

8d : 8r = Ratio =  1 : 4

Step-by-step explanation:

Area of 8cm diameter = 4cm radius = formula pi x 4^2

= 50.2654825

= 50.27 m^2     rounded to 2dp as meters

Area of 8cm radius = formula pi x 8^2

=201.06193

= 201.06,^2     rounded to 2dp as meters

201.06193 / 50.2654825 = 4

4 x 50.265 = 201.061

    =        1    :   4

8d : 8r = Ratio =  1 : 4

The ratio of  the area of circle with an 8m diameter to a circle with an 8m radius is 1:4.

A term that is used to compare two or more numbers and to indicate how big or small a quantity is when compared to another is called ratio.

Area of a circle is the region covered or enclosed within its boundary.

The formula for the area of circle is give by

[tex]Area = \pi r^{2}[/tex]

Where,

r is the radius of the circle

According to the given question.

We have two circle.

One with the diameter 8m.

⇒ Radius, [tex]r_{1} = \frac{8}{2} =4m[/tex]

Therefore,

the area of circle with 4m radius

= [tex](4)^{2} \pi[/tex]

[tex]=16\pi[/tex]

Also, another circle with the radius 8m.

Therefore,

The area of the circle with the radius 8m

[tex]\pi (8)^{2} \\= 64\pi[/tex]

So,

the ratio of the area of circle with  an 8m diameter to a circle with an 8m radius = [tex]\frac{16\pi }{64\pi } =\frac{1}{4}[/tex]

Hence, the ratio of  the area of circle with an 8m diameter to a circle with an 8m radius is 1:4.

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The Above expression can we showed as :

here, the squared number is x

Answer:

1.6 litre of milk is left

Answer: $165

Step-by-step explanation: Divide the new price by 1, + the percent of increase. 198 / 1.20 = 165

MARK AS BRAINLIEST PLEASE! ;D

Answer:

Any Help On This Would Make Me So Grateful

Answer:

hello

Step-by-step explanation:

there is my answer

hope it helps

Answer:

28.914

Step-by-step explanation:

Answer:

Step-by-step explanation:

Aooalalslslslslpapwlqllslwlsposlskskskwkwjsjsjisisisw

Answer:0.012345

Step-by-step explanation: km=mm/1000000 so 12345/1000000=0.012345mm

Answer:

D. x = 12

Step-by-step explanation: