What is the value of the 6 in 13.76?

Answer:

Step-by-step explanation:

The triangle inequality theorem states that the sum of any two sides of a triangle os greater than the third side.

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First triangle:

Let a,b and c be the sides of the triangle:

● a = 10

● b = 20

● c = 30

Now let's apply the theorem.

● a+b = 10+20=30

That's equal to the third side (c=30)

●b+c = 50

That's greater than a.

● a+c = 40

That's greater than b.

These aren't the sides of a triangel since the first inequality isn't verified.

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Second triangle:

● a = 122

● b = 257

● c = 137

Let's apply the theorem.

● a+b = 379

That's greater than c

● a+c = 259

That's greater than b

● b+c = 394

That's greater than a

So 122,257 and 137 can be sides of a triangle.

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The third triangle:

● a = 8.6

● b = 12.2

● c = 2.7

Let's apply the theorem:

● a+b = 20.8

That's greater than c

● b+c = 14.9

That's greater than a

● a+c = 11.3

That isn't greater than b

So theses sides aren't the sides of triangle.

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● a = 1/2

● b = 1/5

● c = 1/6

Let's apply the theorem.

● a+b = 7/10

That's greater than c

● a+c = 2/3

That's greater than b

● b+c = 11/30

That isn't greater than a

So these can't be the sides of a triangle.

If 11 is subtracted from 3 times the number, the result is the square of 5 less than the number. What are the set of numbers that satisfy

Answer:

B. f(n) = 56(0.5)^n-1

Step-by-step explanation:

 First, You have to find out the starting population, if you look at the problem you see the population starts at 56

f(x) = 56

Second, you know that the population goes down 50% each week so it has a decay of 0.5

f(x) = 56(0.5)

 Third,  you need to add the exponent of n to make it exponential.  But, if you just add n then the the population would be 28 on week 1 which is incorrect. To fix that you make the exponent n-1 so when you are on week 1 it doesn't become 28 but it stays on 56, and on week 2 it's 28, ect

f(x) = 56(0.5)^n-1

Answer:

Step-by-step explanation:

Given the functions  f(x) =  3x² + 4 and g(x) = 2x − 3, to know that statements that is  true about f+g, we will need to add the functions together first.

f(x)+g(x) = 3x² + 4 + 2x - 3

f(x)+g(x) = 3x²+2x +4 - 3

f(x)+g(x)  = 3x²+2x + 1

The highest degree of a quadratic function is 2 and since the highest degree of the resulting function is 2, hence the resulting sum of the equations is quadratic.

Also the range of the values is all real numbers because the presence of x² in the function will always return a positive value greater than x.

Hence the correct statements are 'the range is all real numbers and it is a quadratic function'

Answer:

B AND D

Step-by-step explanation:

Answer:

Option (1)

Step-by-step explanation:

Given equation is,

[tex]2^x=1-3^x[/tex]

To determine the solution of the equation we will substitute the values of 'x' given in the options,

Option (1)

For x = -0.75

[tex]2^{-0.75}=1-3^{-0.75}[/tex]

0.59 = 1 - 0.44

0.59 = 0.56

Since, values on both the sides are approximately same.

Therefore, x = -0.75 will be the answer.

Option (2)

For x = -1.25

[tex]2^{-1.25}=1-3^{-1.25}[/tex]

0.42 = 1 - 0.25

0.42 = 0.75

Which is not true.

Therefore, x = -1.25 is not the answer.

Option (3)

For x = 0.75

[tex]2^{0.75}=1-3^{0.75}[/tex]

1.68 = 1 - 2.28

1.68 = -1.28

Which is not true.

Therefore, x = 0.75 is not the answer.

Option (4)

For x = 1.25

[tex]2^{1.25}=1-3^{1.25}[/tex]

2.38 = 1 - 3.95

2.38 = -2.95

It's not true.

Therefore, x = 1.25 is not the answer.

Answer: Line EF=2

Step-by-step explanation: 11 minus 9 is equal to 2. So line EF is equal to 2.

Answer:

Domain is all real numbers, x ≠ -5

Range is all real numbers, y ≠ 0

Step-by-step explanation:

Answer:

1 1/8

Step-by-step explanation:

1/4 of 4 1/2 is Pepsi.

1/4 * 4 1/2 = (1/4) * 4 + (1/4) * (1/2) = 1 1/8

Answer:

5.84 x10.^4

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  

10

If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

the horizontal distance is the x-intercept, and the vertical distance is the y-intercept

1) x-int=1, y-int=1

2) x-int=6, y-int=5

Answer:

F , D, E

Step-by-step explanation:

The smallest angle is opposite the smallest side

The largest angle is opposite the largest side

DE is smallest so F is smallest

Then EF so D

DF is largest so E is the largest angle

AC will be 4√2 when AB = 4 and BC = 4, in the given right triangle.

According to Pythagoras' Theorem, in a right triangle, the square of the length of the longest side, that is, the hypotenuse, that is, the side opposite to the right angle is equal to the sum of the squares of the lengths of the other two sides.

In the question, we are given a right triangle, with sides AB = 4 and BC = 4.

We are asked to find AC.

To find AC, we will use the Pythagoras theorem, according to which, we can write:

AC² = AB² + BC²

or, AC² = 4² + 4²,

or, AC² = 16 + 16,

or, AC² = 32,

or, AC = √32,

or, AC = √(16 * 2) = 4√2.

Therefore, AC will be 4√2 when AB = 4 and BC = 4, in the given right triangle.

Learn more about Pythagoras' Theorem at

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X - (-20) = 5

When you subtract a negative, change it to addition:

X + 20 = 5

Subtract 20 from both sides:

X = -15

Answer:

[tex]\boxed{x=-15}[/tex]

Step-by-step explanation:

[tex]x-(-20)=5[/tex]

[tex]\sf Distribute \ negative \ sign.[/tex]

[tex]x+20=5[/tex]

[tex]\sf Subtract \ 20 \ from \ both \ sides.[/tex]

[tex]x+20-20=5-20[/tex]

[tex]x=-15[/tex]

Answer: 880 cm

Step-by-step explanation:

Given: Radius of the hula hoop = 35 cm

Hula hoop is  circular in shape

Then, Circumference = [tex]2\pi r[/tex] , where r = radius

Now , Circumference of hula hoop = [tex]2\times \dfrac{22}{7}\times35=220\ cm[/tex]

Now , the distance the hula hoop rolls in 4 full rotations = 4 × (Circumference of hula hoop)

[tex]= 4 \times 220=880\ cm[/tex]

Hence, the required distance = 880 cm

Answer:

880

Step-by-step explanation:

Answer:

Proof in the explanation.

Step-by-step explanation:

I expanded both sides as a first step. (You may use foil here if you wish and if you use that term.)

This means we want to show the following:

[tex]3-9\tan^2(\theta)-4\sin^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]

[tex]=12\cos^2(\theta)-9-4\cos^2(\theta)\tan^2(\theta)+3\tan^2(\theta)[/tex].

After this I played with only the left hand side to get it to match the right hand side.

One of the first things I notice we had sine squared's on left side and no sine squared's on the other. I wanted this out. I see there were cosine squared's on the right. Thus, I began with Pythagorean Theorem here.

[tex]3-9\tan^2(\theta)-4\sin^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]

[tex]3-9\tan^2(\theta)-4(1-\cos^2(\theta))+12\sin^2(\theta)\tan^2(\theta)[tex]

Distribute:

[tex]3-9\tan^2(\theta)-4+4\cos^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]

Combine like terms and reorder left side to organize it based on right side:

[tex]4\cos^2(\theta)-1+12\sin^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

After doing this, I since that on the left we had products of sine squared and tangent squared but on the right we had products of cosine squared and tangent squared. This problem could easily be fixed with Pythagorean Theorem again.

[tex]4\cos^2(\theta)-1+12\sin^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

[tex]4\cos^2(\theta)-1+12(1-\cos^2(\theta))\tan^2(\theta)-9\tan^2(\theta)[/tex]

Distribute:

[tex]4\cos^2(\theta)-1+12\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

Combined like terms while keeping the same organization as the right:

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

We do not have the same amount of the mentioned products in the previous step on both sides. So I rewrote this term as a sum. I did this as follows:

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

Here, I decide to use the following identity [tex]\cos\theta)\tan(\theta)=\sin(\theta)[/tex]. The reason for this is because I certainly didn't need those extra products of cosine squared and tangent squared as I didn't have them on the right side.

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\sin^2(\theta)-9\tan^2(\theta)[/tex]

We are again back at having sine squared's on this side and only cosine squared's on the other. We will use Pythagorean Theorem again here.

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\sin^2(\theta)-9\tan^2(\theta)[/tex]

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8(1-\cos^2(\theta))-9\tan^2(\theta)[/tex]

Distribute:

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8+8\cos^2(\theta)-9\tan^2(\theta)[/tex]

Combine like terms:

[tex]12\cos^2(\theta)-9+3tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)[/tex]

Reorder again to fit right side:

[tex]12\cos^2(\theta)-9+4\cos^2(\theta)\tan(\theta)+3\tan^2(\theta)[/tex]

This does match the other side.

The proof is done.

Note: Reordering was done by commutative property.

Answer:

[tex]4\frac{1}{2}[/tex] feet further.

Step-by-step explanation:

Since these are mixed numbers that are both in fourths, we can easily subtract the two numbers. However, I find it easier if we first convert both mixed numbers into improper fractions.

[tex]5\frac{1}{4} = \frac{5\cdot4+1}{4} = \frac{21}{4}[/tex]

[tex]9\frac{3}{4} = \frac{9\cdot4+3}{4} = \frac{39}{4}[/tex]

Now we can subtract the numerators:

[tex]\frac{39}{4} - \frac{21}{4} = \frac{39-21}{4} = \frac{18}{4}[/tex]

[tex]\frac{18}{4}[/tex] simplifies down to [tex]\frac{9}{2}[/tex].

Converting  [tex]\frac{9}{2}[/tex] to a mixed number is easy - 2 goes into 9 4 times (8) with one remainder so:

[tex]4\frac{1}{2}[/tex] .

Hope this helped!

Answer:

10 cm is the answer because 30÷3 angles

Answer:

x=27

Step-by-step explanation:

expanding the above expression we get

5x+5=4x+32

grouping numbers with coefficient of x at the left side and constant at the right side we get

5x-4x=32-5

x=27

Answer:

x = 9/4

y = 3/5

z = 2/3

w = -9/5

Step-by-step explanation:

Technically, the matrix is in reduced row echelon form. If there are zeros above and below the ones, it is RREF. If there are zeros only below the ones, then it's REF.

Since it is in RREF, the augmented numbers to the right of the bar are already your solutions. Simply label the variables.

Answer:

The number to be added is 6.89

Step-by-step explanation:

Here, we want to know what number must be added to the expression to make it equal to zero.

Let the number be x

Thus;

-6.89 + 14.52 -14.52 + x = 0

-6.89 + x = 0

x = 6.89

Answer:

never crosses the x-axis.

Step-by-step explanation:

     A quadratic equation with a negative discriminant has a graph that - never crosses the x-axis.

Answer:

The graph of a quadratic equation that has a negative discriminant is the one that never intersect x-axis. The graph of a quadratic equation that has a zero discriminant is the one that intersect x-axis at only one point. To be clearer, it can be seen in the attached image.

Step-by-step explanation:

Answer D

Answer:

c

Step-by-step explanation:

Answer:

A. Proper fractions have a greater numerator than denominator.

Answer:

x = -4

Step-by-step explanation:

logs (8 - 3x) = log20

Since we are taking the log on each side

log a = log b  then a = b

8 -3x = 20

Subtract 8  from each side

8 -3x-8 =20 -8

-3x = 12

Divide by -3

-3x/-3 = 12/-3

x = -4

Answer:

[tex] \boxed{\sf x = -4} [/tex]

Step-by-step explanation:

[tex] \sf Solve \: for \: x \: over \: the \: r eal \: numbers:[/tex]

[tex] \sf \implies log(8 - 3x) = log 20[/tex]

[tex] \sf Cancel \: logarithms \: by \: taking \: exp \: of \: both \: sides:[/tex]

[tex] \sf \implies 8 - 3x = 20[/tex]

[tex] \sf Subtract \: 8 \: from \: both \: sides:[/tex]

[tex] \sf \implies 8 - 3x - 8 = 20 - 8 [/tex]

[tex] \sf \implies - 3x = 12 [/tex]

[tex] \sf Divide \: both \: sides \: by \: - 3:[/tex]

[tex] \sf \implies \frac{-3x}{-3} = \frac{12}{-3} [/tex]

[tex] \sf \implies x = - 4[/tex]

Answer:

LOOK BELOW

Step-by-step explanation:

Mean= add all of the numbers together and divide by total amount of

            numbers

            aka=3

Median= put all the numbers in order and find the number in the middle

               aka=2.5

Minimum=0

Maximum=8

This data can only be found using a Box and Whisker Plot....

I can't really explain a box and whisker plot so you have to look that up to understand that..  SRY!!!

------------------------------------

First Quartile=1

Third Quartile=5

Interquartile Range=4

Answer:

Mean= add all of the numbers together and divide by total amount of

           numbers

           aka=3

Median= put all the numbers in order and find the number in the middle

              aka=2.5

Minimum=0

Maximum=8

This data can only be found using a Box and Whisker Plot....

I can't really explain a box and whisker plot so you have to look that up to understand that..  SRY!!!

------------------------------------

First Quartile=1

Third Quartile=5

Interquartile Range=4

Step-by-step explanation:

Answer:

B) Associative Property of Multiplication

Step-by-step explanation:

*if it's wrong idk how, but I apologise*

The perpendicular distance of the trapezoid is 3.5 cm

The given parameters are:

The area of a trapezoid is:

Area = 0.5 * (Sum of parallel sides) * perpendicular distance

So, we have:

14.7 = 0.5 *(5.3 + 3.1) * perpendicular distance

Evaluate

Perpendicular distance = 3.5

Hence, the perpendicular distance of the trapezoid is 3.5 cm

Read more about area at:

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Answer:

554

Step-by-step explanation:

The largest number (5) should go in the hundreds place, the second-largest number (also 5) should go in the tens place and the smallest number (4) should go in the units place so the answer is 554.

Answer:

You can write in

Step-by-step explanation:

Lakhs

First write 100,203.

Put ones,tens,hundreds,thousands,ten thousands and lakh on top of each number from the extreme left.

This is how you can write 100,203 in another way. You can't write in any other way than this one.

Hope this helps....

Have a nice day!!!!

Answer:

y=−2x−13.

Step-by-step explanation:

The equation of the line in the slope-intercept form is y=−2x−5.

The slope of the parallel line is the same: m=−2.

So, the equation of the parallel line is y=−2x+a.

To find a, we use the fact that the line should pass through the given point: −1=(−2)⋅(−6)+a.

Thus, a=−13.

Therefore, the equation of the line is y=−2x−13.

Answer:

809.915$

Step-by-step explanation:

Amount of money = Principal x e^(rate x year)

                              = 600 x e^(0.05 x 6)

                              = 809.915$

Answer:

$809.92

Step-by-step explanation:

(see attached for reference)

Recall that the formula for compound interest (compounded continuously) is

A = P e^(rt)

where,

A = final amount (we are asked to find this)

P = principal = given as $600

r = interest rate = 5% = 0.05

t = time = 6 years

e = 2.71828 (mathematical constant)

Substituting the known values into the equation:

A = P e^(rt)

= 600 e^(0.05 x 6)

= 600 (2.71828)^(0.30)

= $809.92