In geometry, what’s the difference between a postulate and a theorem? Give an example of each

Answer:

6.476

Step-by-step explanation:

use a calculator or just subtract

Answer:

6.476

Step-by-step explanation:

Should the answer need to be rounded to a given place value, proceed accordingly

Answer:

Option D. Segment BC

Step-by-step explanation:

we know that

The external secant is a segment contained by a secant segment with an endpoint on the circle and at the fixed point outside the circle

In this problem

AC is a secant segment and BC is a external secant

EC is a secant segment and DC is a external secant

Without a diagram, an external secant segment is defined as the portion of a secant line that lies outside the circumference of a circle, extending from the point of tangency to another point outside the circle.

An external secant segment is part of a secant line that extends from the point of tangency on the circle's circumference to the point outside the circle where the secant line ends. Without the specific diagram referenced in the question, we can use the given information to assume that segments A, B, C, and D may connect in some way to a circle, since secant lines and segments are defined in relation to circles.

Typically, a secant line will intersect the circle at two points, while an external part of the secant would be the part that lies outside the circle. Given options A. segment EC, B. segment AC, C. segment ED, and D. segment BC, the segment that would qualify as an external secant segment is the one that extends from the circle's edge without entering the circle itself again.

Answer:

1

Step-by-step explanation:

1*1=1

Answer:

Step-by-step explanation:

An Irrational Number is a real number that cannot be written as a simple fraction. Irrational means not Rational.

and in order to get irrational number product equal to one

we shall multiply by its reciprocal for example

[tex]\sqrt{2}[/tex] is an irrational number

in order to get the product equal 1 we shall multiply it by [tex]\frac{1}{\sqrt{2} }[/tex]

[tex]\sqrt{2} X\frac{1}{\sqrt{2} } =1[/tex]

Answer:

15 ml

Step-by-step explanation:

If we mix 1 part concentrate and 5 parts water, we have 6 parts in total.

To create 90ml medicine, how many "6 parts" are there?

There would be 90/6 = 15 total "6 parts".

Each of the "6 parts's" 1 part is concentrate, so concentrate would be 1 * 15 = 15 ml.

In ratio:

[tex]\frac{Concentrate}{Total(Water+Concentrate)}=\frac{1}{5+1}=\frac{1}{6}\\\frac{1}{6}*90=15[/tex]

In a 90ml dose of medicine that requires a 1:5 ratio of concentrate to water, 15ml of concentrate is needed. This calculation uses the method of dilution, a common means of preparing solutions.

The question asks about the quantity of concentrate needed for a 90ml dose of medicine, given that one part of concentrate is diluted with 5 parts of water. This represents a ratio of 1:5, so for every 6 parts of the total mixture, 1 part is the concentrate.

To calculate this, we need to divide the total volume by the overall ratio (which is 6 in this case: the sum of the ratios 1:5). So take 90 ml and divide by 6, which gives 15 ml. This means there should be 15ml of the concentrate in a 90ml dose of medicine.

Dilution is a common means of preparing medicines and other solutions of a desired concentration by adding a solvent (like water in this example) to a more concentrated stock solution (the concentrate in this case).

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Answer:

A.) QRT and QST both measure 78 degrees

Step-by-step explanation:

I used process of elimination for this they had to be the same and the both aren't obtuse

Answer:

∠QRT and ∠QST both angles have measure 78°

Step-by-step explanation:

Given the figure in which measure of arc QVT is 156°

we have to choose the correct statement.

As given arc QVT=156° i.e ∠QPT=156°

By theorem angle made by same arc i.e inscribed angle formed by same arc are equal.

⇒ ∠QRT=∠QST

Also another theorem angle subtended at the centre is twice the angle at the circumference

⇒ ∠QPT=2∠QRT=2∠QST

[tex]2\angle QRT=\angle QPT=156^{\circ}[/tex]

[tex]\angle QRT=\frac{156}{2}=78^{\circ}[/tex]

⇒ ∠QRT and ∠QST both angles have measure 78°

Hence, option 1 is correct.

9/30 cubic feet

Multiply the base area times the height to find the volume, which is the amount of packing material required.

First, multiply the numerators, or the top numbers. 9 * 1 = 9

Then, multiply the denominators, or the bottom numbers. 10 * 3 = 30

So, the amount of packing material required is 9/30 cubic feet.

The probabilities of all possible outcomes in a distribution must sum to 1.

[tex]\dfrac5{12}+\dfrac16+\dfrac13+x=1\implies x=\dfrac1{12}[/tex]

Answer:

1/12 C

Step-by-step explanation:

5/12

1/6=2/12

1/3=4/12

5/12-3=2/12

2/12+2=4/12

4/12-3= 1/12

The answer would be 10 units.

I hope this helped!

Answer: 10

Step-by-step explanation:

You need to apply the Pythagorean Theorem:

[tex]a^2=b^2+c^2[/tex]

Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.

Since you need to calculate the value of the hypotenuse, you need to solve for "a":

[tex]a=\sqrt{b^2+c^2}[/tex]

You know the lenght of two sides of the right triangle (6 and 8) Then, you can  substitute these values into [tex]a=\sqrt{b^2+c^2}[/tex].

Therefore, the hypotenuse of this right triangle is:

 [tex]a=\sqrt{6^2+8^2}[/tex]

 [tex]a=10[/tex]

Answer:

c

Step-by-step explanation:

The Correct statements are

B.⇒The circumcenter of triangle is the point where perpendicular bisector of sides meet.

Because three sides of triangle acts as a chord of the circle,and perpendicular bisector of chords intersects at the center of the circle.

C:⇒ Give any three non collinear points , there exist only one circle that passes through all the three points.

Join these points you will get two line segment .Draw perpendicular bisector of these segments.The point where these perpendicular bisectors meet is center of the circle.

E:⇒ The incenter of triangle is the point where internal bisector of angles meet.

Internal bisector of angle divide angle into two equal parts.The three line segements which is bisector of three angles meet at a point called Incenter of triangle.  

The correct statements are: 1. The capital of France is Paris. 2. The United States has 50 states. 3. The Great Wall of China is the largest man-made structure.

The correct statements are:

1. The capital of France is Paris.

2. The United States has 50 states.

3. The Great Wall of China is the largest man-made structure.

These are the correct statements from the options provided.

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Answer:

The answer is 58 I don't know if it's correct but that what I got.

Step-by-step explanation:

Answer:

1. C.

2. B.

3. Add 6.1 to both sides

Step-by-step explanation:

1. Your equation here is "w + 2 < -1"

You must get w by itself, so to do that, subtract 2 from both sides.

w + 2 < -1

w < -3

Notice that the symbol is "w is less than -3" not "w is less than or equal to -3," so our plot must have a closed circle (or no open circle).

The larger the number behind the negative sign, the smaller it is.

ex: -3 is smaller than -1

So, the answer is C.

2. Here, you have the inequality -15 > q - 5

To find out which number set best fits the inequality, substitute the numbers in for the q value.

[I'll skip to answer B.]

B.'s number set is {-11, -12, -14}

So, plug in each value for q

For -11:

-15 > (-11) - 5

-15 > -16

This works.

(As I mentioned earlier, the larger the number in front of the negative, the smaller it is.)

For -12:

-15 > (-12) - 5

-15 > -17

This works as well

For -14:

-15 > (-14) - 5

-15 > -19

This works too

Thus, the answer is B.

3. And finally, you have the equation p - 6.1 = 10

To solve for p, make sure its alone on one side of the equation.

To do this, add 6.1 to both sides.

This is the first (and pretty much only) step to solve this equation

I hope this helps!!! :)

Answer:

William is 18, Monica is 6... 6 x 3=18 Three times as old.. in 6 years William will be 24, Monica will be 12.. Twice as old... 12 x 2= 24

Step-by-step explanation:

Answer:

Current age of Monica=6 years

and current age of William=18 years

Step-by-step explanation:

Let Monica's current age be x years and William's current age be y years.

William is 3 times elder than Monica.

⇒  y=3x

In 6 years William will be twice as old as Monica.

⇒ y+6=2(x+6)

⇒ y+6=2x+12

⇒3x+6=2x+12

⇒ x=6

Hence, y=3×6=18

That means, current age of Monica=6 years

and current age of William=18 years

ANSWER

The answer is

B

[tex] \frac{1}{27} [/tex]

EXPLANATION

The given expression is

[tex] {3}^{ - 3} [/tex]

Use the negative index property;

[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]

We apply this property to get:

[tex]{3}^{ - 3} = \frac{1}{ {3}^{3} } [/tex]

This gives us:

[tex]{3}^{ - 3} = \frac{1}{3 \times 3 \times 3 } [/tex]

[tex]{3}^{ - 3} = \frac{1}{27} [/tex]

The correct option is B.

For this case we must evaluate the following expression:

[tex]3 ^ {3}[/tex]

We have by definition of properties of powers that:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then, rewriting the expression:

[tex]3 ^ {- 3} = \frac {1} {3 ^ 3} = \frac {1} {27}[/tex]

ANswer:

[tex]3 ^ {- 3} = \frac {1} {27}[/tex]

OptionB

Answer:

$335.15

Step-by-step explanation:

(2012 price) - 11.1% · (2012 price) = (2013 price)

$377(1 - 0.111) = (2013 price)

$377 · 0.889 = $335.15 = (2013 price)

The average price of that type of smartphone in 2013 was $335.15.

Answer:

Price of smartphone in 2013 is $335.153.

Step-by-step explanation:

We are given the following information in the question.

Price of smartphone in 2012 = $377

Decline percentage of average price of phone from 2012 to 2013 = 11.1%

We have to calculate the the average price of mobile in 2013:

Formula:

Decrease in average price = [tex]\text{Price of smartphone in 2012}\times \text{Decline percent in average price}[/tex]

[tex]= \displaystyle\frac{11.1}{100}\times 377\\\\ =41.847\$[/tex]

Average price of smartphone in 2013 = [tex]\text{ Average price of smartphone in 2012 - Decrease in price of smartphone}\\= 377 - 41.847\\= 335.153[/tex]

Thus, the price of smartphone in 2013 is $335.153.

Answer:

We need 4/5 cups of oil

Step-by-step explanation:

We can use ratios to solve.  Put the amount of oil over the number of batches

2/3  cup          x cups                    

---------------- = --------------

2.5 batches      3 batches

Using cross products

2/3 * 3 = 2.5 *x

2 = 2.5 x

Divide each side by 2.5

2/2.5 = 2.5x/2.5

.8 =x

Changing this back to a fraction

4/5 =x

We need 4/5 cups of oil

Answer:

A. Cafeteria plan

Step-by-step explanation:

Heidi's employer offers paid vacations and health and life insurance as well as a 401(k) but she is only participating in the 401(k) plan.

This is a part of Cafeteria plan.

A Cafeteria Plan is a reimbursement plan that allows the employees to contribute some amount of their gross income to a designated account before taxes are calculated.

Answer:

[tex]0.328\ l[/tex]

Step-by-step explanation:

Remember that

[tex]1\ l=1,000\ cm^{3}[/tex]

step 1

Find the volume of the aquarium

The volume is equal to

[tex]V=b^{3}[/tex]

we have

[tex]b=12\ cm[/tex]

substitute

[tex]V=(12)^{3}=1,728\ cm^{3}[/tex]

step 2

Convert to liters

[tex]1,728\ cm^{3}=1,728/1,000=1.728\ l[/tex]

step 3

Calculate how much more water is needed to fill the aquarium completely

Find the difference between the volume of the aquarium and the water that contains the aquarium

[tex]1.728\ l-1.40\ l=0.328\ l[/tex]

Answer:

[tex] log(4) + log( {x}^{2} ) - log(3) + log(y) + log(z) [/tex]

I think the answer would be something like this. but please correct me if I'm wrong

The first set of numbers are in standard form while the other is in scientific notation.

Scientific Notation is a process in which makes a long numbered number into a shorter version.

To make a number scientific notation, you must put the first number between 0-10.    

The problem would be 6.7 x 10^-4 - 2.3 x 10^5. The answer would be 4.4 x 10^1. First you have to know what to do with the powers. You subtract them because it is a subtraction problem. Then you subtract the numbers and then you have the answer.

Answer:

4.4 x 10^1

Step-by-step explanation:

Answer:

m∠A = 42°

Step-by-step explanation:

* Lets revise some facts in the circle

- If the vertex of an angle on the circle and the two sides of the

 angle are chords in the circle, then this angle is called

 an inscribed angle

- Each inscribed angle subtended by the opposite arc, the arc name

 is the starting point and the ending point of the angle

# Ex: ∠CAB is subtended by arc CB

- There is a relation between the inscribed angle and its

  subtended arc, the measure of the inscribed angle equals half

  the measure of its subtended arc

* Now lets solve the problem

- ∠CAB is an inscribed angle subtended by arc CB

∴ m∠CAB = (1/2) measure of arc CB

∵ The measure of arc CB = 84°

∴ The measure of ∠A = 1/2 × 84° = 42°

* m∠A = 42°

Answer:

8 15/16 inches

Step-by-step explanation:

just multiply 2 3/4 by 3 1/4

Answer:

8.94 inches or [tex] 8\frac { 1 5 } { 1 6 } [/tex] inches

Step-by-step explanation:

We know that the current height of the photo is [tex]3\frac{1}{4}[/tex] inches and the customer wants it to be enlarged by a factor of [tex]2\frac{3}{4}[/tex] its current height.

[tex]  3\frac { 1 } { 4 } = 3.25 [/tex]

[tex] 2 \frac { 3 } { 4 } = 2.75 [/tex]

To find the enlarged height, we will multiply the scale factor with the photo's current height.

Enlarged height = [tex]3.25 \times 2.75 = 8.94 inches or [tex] 8\frac { 1 5 } { 1 6 } [/tex] inches

Answer:

[tex](9x^7-4y^4)^2[/tex]

Step-by-step explanation:

This is a difference of squares, so we are able to square root each of them and that is our factor

Answer:

y = 7/5x + 18/5

Step-by-step explanation:

so we have y = mx + b

f(1) = 5

f(-4) = -2

so let's find b

so like if you do (5 - (-2))/(1 - (-4)) you get (5 + 2)/(1 + 4) = 7/5

y = 7/5x + b

so now we can plug in a value like f(1) = 5

5 = (7/5)1 + b

b = 18/5

Answer:

-1/2

Step-by-step explanation:

The slope of a line is found by using

m = (y2-y1)/(x2-x1)

    = (9-10)/(6-4)

    = -1/2

Create equivalent fractions:

23/x = 40/17

Cross multiply and divide:

x = 9.8

ANSWER

D. 224

EXPLANATION

The given series is

[tex]\sum_{n=1}^{14}(2n+1)[/tex]

The first term of this series is

[tex]a_1=2(1) + 1 = 3[/tex]

The last term of this series is:

[tex]l = 2(14) + 1 = 29[/tex]

The sum of the first n-terms of the series is calculated using the formula,

[tex]S_n= \frac{n}{2} (a + l)[/tex]

[tex]S_ {14}= \frac{14}{2} (3+ 29)[/tex]

[tex]S_ {14}= 7 \times (32)[/tex]

[tex]S_ {14}= 224[/tex]

90 is 50% of 180

50% = half

90 • 2 = 180

The expression is 180 is 50 percent of 90

From the question, we have the following parameters that can be used in our computation:

90 is 50 percent of what number

Represent the percentage with x

So, we have

90 is 50 percent of x

Mathematically, we have

50% * x = 90

So, we have

x = 90/50%

Express percentage as decimal

x = 90/0.50

Evaluate the expression

x = 180

Hence, the number in the percentage is 180

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Answer:

≈ 3.8928

Step-by-step explanation:

log base 3 of 72 is approximately 3.8928

you would need to plug this into a calculator to solve

To evaluate log3 72, given that log3 8 is approximately 1.8928, we use properties of logarithms. We can express 72 as 8×9, and since log3 9 equals 2, log3 72 is 1.8928 + 2, which is 3.8928.

The student is asking to evaluate log3 72 given that log3 8 ≈1.8928. We can use the properties of logarithms to solve this. Since 72 can be expressed as 8×9, and we know that log3 8, we can find the log3 9 by understanding that 9 is 3²and therefore log3 9 is 2, because the base and the argument are the same.

Now, using the property of logarithms that loga (xy) = loga x + loga y, we can write log3 72 as:

log3 (8 ∙9) = log3 8 + log3 9

log3 72 = 1.8928 + 2

log3 72 = 3.8928

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Answer:

a=2, b=4

Step-by-step explanation:

32=ab²

128=ab³

1) Divide second equation by first one

128/32 = ab³/ab²

4 = b

2) ab²=32

a*4²=32

16a=32

a=2