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Lelechka [254]
3 years ago
5

There are exclusions that make the expression

Mathematics
2 answers:
Gnom [1K]3 years ago
8 0

Answer:

<h2>True.</h2>

Step-by-step explanation:

The given expression is

\frac{x^{3}-1}{x^{3}+x^{2}+x}

This expression is rational, which means the denominator must be different to zero, otherwise, the function will be undefined. So, let's find if there are values that make the denominator zero.

\frac{x^{3}-1}{x^{3}+x^{2}+x}=\frac{x^{3}-1}{x(x^{2}+x+1)}

So, if we evaluate the expression with x=0, we would have

\frac{x^{3}-1}{x(x^{2}+x+1)}=\frac{0^{3}-1}{0(0^{2}+0+1)}=\frac{-1}{0}

As you can observe, there must be one exclusion, because it makes the expression undefined.

Therefore, the answer is true.

sveticcg [70]3 years ago
4 0
Truer hi s hm Ken mallow’s
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Someone, please help me lol I'm small brain
Eddi Din [679]

Answer:

Measure of EF: 1.98

Measure of AB: 6.16

Measure of HI: 12.2

Step-by-step explanation:

Trick I learned that's very helpful when solving these problems: SOH (Sine, Opposite, Hypotenuse)- CAH (Cosine, Adjacent, Hypotenuse)- TOA (Tangent, Opposite, Adjacent)

MEASURE OF EF

you're starting with angle D which is 26 degrees. You have the measure of the Hypotenuse (DF) and you're trying to find the measure of EF (the segment opposite the angle) so you would use Sine

to do the equation, i'm going to use x in place of EF. 0.44 = sin(26)

Formula: sin(angle) = (opposite)/(hypotenuse)

Equation:

0.44 = x/4.5       <----------- multiply by 4.5 to get x by itself

4.5*0.44 = x       <---------- 4.5 times 0.44

1.98= x       <----------------answer

MEASURE OF AB

trying to find hypotenuse and you already have the adjacent angle so you would use cosine. Using y in place of AB. 0.616 = sin(52)

cos(angle) = (adjacent)/(hypotenuse)

cos(52) = 10/y      <------ divide by y

y*0.616 = 10       <------------ divide by 0.616

y = 10/0.616    <----------- next you'll divide 10 by 0.616

y = 6.16    <-----------answer

MEASURE OF HI

trying to find adjacent, already have opposite so you would use tangent. tan(42) = 0.90. using z in place of HI

tan(angle) = (opposite)/(adjacent)

tan(42) = 11/z   <------------ multiply z on both sides

z*0.90 = 11  <--------- divide by 0.90 to get z by itself

z = 11/0.90    <-------- divide 11 by 0.90

z = 12.2

4 0
2 years ago
The table shows data from a travel agency, representing the number of guests on a trip (x) and the estimated dollar
Arlecino [84]

The slope of the best fit for the 3 given points is 500, so the correct option is b.

<h3>How to find the slope?</h3>

Remember that for a line that passes through two points (x₁, y₁) and (x₂, y₂) the slope is:

s = \frac{y_2 - y_1}{x_2 - x_1}

With the 3 given points we can find 3 slopes, and then we will need to find the average of these 3.

The 3 points are: (3, 2,750), (6, 4,200), and (9,5,750)

Then the 3 slopes are:

s_1 = \frac{4,200 - 2,750}{6 - 3} = 483.3\\\\s_2 =  \frac{5,750 - 2,750}{9 - 3} = 500\\\\s_3 =  \frac{5,750 - 4,200}{9 - 6} = 516.7

The average slope is:

S = (483.3 + 500 + 516.7)/3 = 500

So the correct option is b.

If you want to learn more about slopes:

brainly.com/question/1884491

#SPJ1

6 0
2 years ago
A carrot has
4vir4ik [10]

Answer:

B- For an equal number of servings, the bananas will have three times as much sugar

Step-by-step explanation:

The complete question is

A carrot has 5 grams of sugar per serving. A banana has 15 grams of sugar per serving. Which statement is true?

A- There will always be more sugar in 10 servings of carrots than in a smaller number of servings of bananas.

B- For an equal number of servings, the bananas will have three times as much sugar.

C- For an equal number of servings, the bananas will always have 10 more grams of sugar.

D- The amount of sugar in two servings of carrots is 30 grams.

<u><em>Verify each statement</em></u>

A- <u>There will always be more sugar in 10 servings of carrots than in a smaller number of servings of bananas</u>

The statement is False

Because

In 10 servings of carrots there are 10(5)=50 grams of sugar

In 5 servings of banana there are 5(15)=75 grams of sugar

therefore

50 g < 75 g

B- <u>For an equal number of servings, the bananas will have three times as much sugar</u>

The statement is true

Because

In one serving of carrots there are 5 grams of sugar

In one serving of bananas there are 15 grams of sugar

The ratio of grams of sugar in a serving of bananas to grams of sugar in a serving of carrots is 15:5

Simplify

3:1

therefore

An equal number of servings, the bananas will have three times as much sugar

C- <u>For an equal number of servings, the bananas will always have 10 more grams of sugar. </u>

The statement is False

Because

In 10 servings of carrots there are 10(5)=50 grams of sugar

In 10 servings of banana there are 10(15)=150 grams of sugar

so

50+10\neq 150

D- <u>The amount of sugar in two servings of carrots is 30 grams</u>

The statement is False

Because

In 2 servings of carrots there are 2(5)=10 grams of sugar

10\neq 30

3 0
3 years ago
The irrational number square root 67 is less than [blank]
Solnce55 [7]

Answer:

The square root of 67 is less than the whole number of 9

Step-by-step explanation:

8 squared is 64

9 squared is 81

67 is in between them

4 0
2 years ago
PLEASEEE I DONT KNOW HOW TO DO ITTTT. THE 35.8 IS RIGHT BUT I CANT GET MEASURE OF ANGLE C AND A I GOT 46.2 for A AND 70.8 for C
Rashid [163]

Answer:

Hope it helps....!!!!!

Step-by-step explanation:

AB = c = 38

BC = a = 29

AC = b

Angle ABC = 63 degrees

Solving for AC   "b":

Cosine rule: c^2 = a^2 * b^2 -2ab * cos C

38^2 = 29^2 * b^2 - (2* 29) * b * (cos 38)

1444 = 841 * b^2 - 58 * b * 0.955

(1444 + 58)/0.955 = b^2 * b

1572.77486911 = b^3

11.62935 = b

11.63 = b (rounded to two decimal places)

Now solving for angle A:

Sine rule: a/sinA = b/sinB

29/sinA = 11.63/sin(63)

sinA/29 = sin(63)/11.63

sin A = (sin(63)/11.63) * 29

sin A = 0.41731

A = sin^-1 (0.41731)

A = 24 degrees 39 minutes 53 seconds

Now solving for angle C:

Sine rule: c/sinC = b/sinB

38/sinC = 11.63/sin(63)

sinC/38 = sin(63)/11.63

sin C = (sin(63)/11.63) * 38

sin C = 0.54682

C = sin^-1 (0.54682)

C = 33 degrees 8 minutes 56 seconds

3 0
3 years ago
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