Find the zeroes of the polynomial 100x^2 - 81

Answers

Answer 1

Answer:

x = ±0.9

Step-by-step explanation:

The algebraic identity to be used here :

a² - b² = (a + b)(a - b)

We know that :

100x² = (10x)²81 = 9²

Therefore,

100x² - 81 (10x + 9)(10x - 9)

The zeros are :

10x + 9 = 0 ⇒ 10x = -9 ⇒ x = -9/10 ⇒ x = -0.910x - 9 = 0 ⇒ 10x = 9 ⇒ x = 9/10 ⇒ x = 0.9
Answer 2

Answer:

[tex]x=-\dfrac{9}{10} \quad x=\dfrac{9}{10}[/tex]

Step-by-step explanation:

[tex]\begin{aligned}100x^2-81 & =(10^2)x^2-9^2\\ & = (10x)^2-9^2\end{aligned}[/tex]

[tex]\textsf{Difference of Two Squares Formula}: \quad a^2-b^2=\left(a+b\right)\left(a-b\right)[/tex]

[tex]\implies a=10x \: \textsf{ and } \: b=9[/tex]

[tex]\implies 100x^2-81=(10x+9)(10x-9)[/tex]

[tex]\begin{aligned}\textsf{To find the zeros}: \quad 100x^2-81 & = 0\\\\\implies (10x+9)(10x-9) & =0\\\implies 10x+9 & =0 \implies x=-\dfrac{9}{10}\\\implies 10x-9 & =0 \implies x=\dfrac{9}{10}\end{aligned}[/tex]


Related Questions

ANSWER QUICK, FIRST ANSWER GETS BRAINLIEST! What is the interquartile range of this data set?



Enter your answer in the box.

Answers

Answer:

13

Step-by-step explanation:

13 will go inside this box  

Answer:

13

Step-by-step explanation:

Finding Upper Quartile (Q₃)

31, 40, 41, 4940 + 41 / 2Q₃ = 40.5

Finding Lower Quartile (Q₁)

20, 25, 30, 3025 + 30 / 2Q₁ = 27.5

Interquartile Range = Q₃ - Q₁

40.5 - 27.513

Find the magnitude of the sum of the vectors <4,5> and <-2,2>. Round your answer to the nearest 100th.

Answers

Answer:

[tex]||v||\approx7.28[/tex]

Step-by-step explanation:

Sum of the vectors

[tex]\langle4,5\rangle+\langle-2,2\rangle=\langle4+(-2),5+2\rangle=\langle2,7\rangle[/tex]

Magnitude of the resultant vector

[tex]||v||=\sqrt{x^2+y^2}=\sqrt{2^2+7^2}=\sqrt{4+49}=\sqrt{53}\approx7.28[/tex]

Suppose that two lines, AB and CD, are intersected by a transversal.
Which of the following reasons alone could be used to show that the lines are parallel?

Answers

Answer: A, B

Step-by-step explanation:

A and B are unique to parallel lines, C and D are not.


find the area to the nearest hundredth use 3.14 for π​

Answers

Answer:

50.24

Step-by-step explanation:

you can use pi r^2

7.
Lines AE and BD are tangent to circles O and P at A, E, B, and D, as shown in the diagram below. If
AC: CE = 5:3, and BD = 56, determine and state the length of CD.
145
U.
Р
56
3
E
B
2

Answers

Answer: 21

Step-by-step explanation:

The measure of the tangent to the circle CD = 21

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the 2 tangents to the circle be AE and BD respectively

The measure of the line segment BD = 56

Now , the ratio of the line AE is

AC : AE = 5 : 3

The measure of AE = measure of CD

Let the value of AC = 5x

Let the value of AE = 3x

Now , the measure of AE = measure of BD

Substituting the values in the equation , we get

5x + 3x = 56   be equation (1)

On simplifying the equation , we get

8x = 56

Divide by 8 on both sides of the equation , we get

x = 7

Now , the measure of CD = 3x

Substituting the value of x in the equation , we get

CD = 3 ( 7 ) = 21

Therefore , the measure of CD = 21

Hence , the measure of CD = 21

To learn more about circle click :

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Michael glues pipe cleaners around the edges of a rectangular poster. he uses a total of 14 pipe cleaners with 5 pipe cleaners each on the longer sides of the poster. how many pipe cleaners does he use for each of the shorter sides of the poster?

Answers

The total pipe used for each of the shorter sides of the poster is 2 if Michael uses a total of 14 pipe cleaners, with 5 pipe cleaners each on the longer sides of the poster.

What is the area of the rectangle?

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have:

Michael glues pipe cleaners around the edges of a rectangular poster. He uses a total of 14 pipe cleaners, with 5 pipe cleaners each on the longer sides of the poster.

Total pipe Michael uses = 14

He used a total of 5 pipe cleaners on each long side.

Total pipe cleaner on two long sides = 5×2 = 10

The pipe used on shorter side = 14 - 10 = 4

Total pipe for each of the shorter sides of the poster = 4/2 = 2 pipes

Thus, the total pipe for each of the shorter sides of the poster is 2 if Michael uses a total of 14 pipe cleaners, with 5 pipe cleaners each on the longer sides of the poster.

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what is equivalent to -3/2

Answers

Answer:

-6/4

Step-by-step explanation:

equivalent, that means something that is equal to so if you break -6/4 to the lowest you get -6/4

Does anyone know how to do these two questions I have to turn this in ( I will be very grateful

Answers

Answer:1.  72.5

Step-by-step explanation: in number one you add so is equal to 0.2 ÷ 14.5

number to we put 1÷25(42,000) so is equal to 1680 the we substract 42000-1680=40,320

Please answer fast i really need this so i can get good grades.

Answers

B and C for the first two

PLEASE HELP WITH THE PICTURE BELOW NEED IT IMMEDIATELY!
50 POINTS!

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's use slope - point form of line to get the required equation ~

[tex]\qquad \sf  \dashrightarrow \:y - y_1 = m(x - x_1)[/tex]

where,

m = slope of the line ( given in question )

[tex] \sf{y_1 = 6} [/tex]

[tex] \sf{x_1 = 9} [/tex]

Now, let's put in the values ~

[tex]\qquad \sf  \dashrightarrow \:y - 6= \dfrac{5}{9} (x - 9)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y - 6 = \dfrac{5}{9} x - 5[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = \dfrac{5}{9} x - 5 + 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = \dfrac{5}{9} x + 1[/tex]

So, the correct choice is A

Idil wants to ride her bicycle 41.4 miles this week. She has already ridden 15 miles. If she rides for 4 more days, what is the average number of miles she would have to ride each day to meet her goal?

Answers

Answer:

6.6

Step-by-step explanation:

41.4-15 = 26.4

26.4 divided by 4 equals 6.6

Idil would need to ride an average of 6.6 miles per day for the next 4 days to meet her goal of 41.4 miles for the week.

How find the average number of miles she would have to ride each day to meet her goal?

To find the average number of miles Idil would have to ride each day to meet her goal, we can use the following formula:

Average miles per day = (Total miles - Miles already ridden) / Number of days remaining

Given information:

Total miles she wants to ride = 41.4 miles

Miles already ridden = 15 miles

Number of days remaining = 4 days

Now, let's calculate the average miles per day:

Average miles per day = (41.4 - 15) / 4

Average miles per day = 26.4 / 4

Average miles per day = 6.6

So, Idil would need to ride an average of 6.6 miles per day for the next 4 days to meet her goal of 41.4 miles for the week.

Learn more about the miles at https://brainly.com/question/28935014

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Sum= 5; Product = 6

Answers

Answer:

2 and 3

Step-by-step explanation:

[tex]3*2=6\\3+2=5[/tex]

The Hormel Corporation has an annual dividend rate of $1.04. If you owned 5,000 shares of
Hormel, how much would you receive annually in dividends?
$4,900
$5,000
$5,100
$5,200

Answers

Answer:

$4,900

Step-by-step explanation:

[tex]\frac{\mbox{number of shares}}{\mbox{annual dividend}} = \frac{5,000}{1.04}[/tex]

This simplifies to 4807.7, which you can round to $4,900.

help please
What is e in math? ​

Answers

e is the Exponential Constant or Euler's Number.

It has a value of 2.718281828...

[tex]\huge\mathfrak\colorbox{white}{}[/tex]

e to the n is given by:

[tex]\huge{e}^{n}= [\sum_{k=0}^{∞} (\frac{{n}^{k}}{k!})][/tex]

Luca's science class is making slime from cornstarch and glue. Luca is helping pass out materials. He gives each student 80 grams of cornstarch from a 2-kilogram bucket. If Luca's class has a total of 21 students, how many grams of cornstarch will he have left?

Answers

Answer:5

Step-by-step explanation:

What fraction is equal to 0.4 (with a line over the four)

A. 44/9
B. 4/99
C. 4/9
D. 9/4

Answers

Answer:

4/9 = 0.4 with a line over the 4

Step-by-step explanation:

Answer:

C. 4/9

Step-by-step explanation:

On dividing 4/9 :

4/90.444....0.4 (bar on the 4)

Option C gives the right answer.

Select the correct graph for the function f(x) = 3x + 4 .

Answers

Answer:

No graph was provided but Ive attached my own

Step-by-step explanation:

f(x) = 3x + 4 → y = mx + b

y - intercept (b) is 4

slope (m) is 3 so the rise / run = 3 / 1

Need help please answer ASAP!

Answers

Problem 16

Answer: Choice (3)  

Work Shown:

[tex]2ax - 5x = 2\\\\x(2a - 5) = 2\\\\x = \frac{2}{2a-5}\\\\[/tex]

I factored out x, then divided both sides by (2a-5)

=========================================================

Problem 17

Answer: Choice (2)

Work Shown:

1 yard = 3 feet

1/3 yard = 1 foot

x/3 yards = x feet

In the second step, I divided both sides by 3. Afterward, I multiplied both sides by x.

#16

2ax-5x=2x(2a-5)=2x=2/2a-5

Option C

#17

3feets=1yard

So

xfeet=1/3×x yard=x/3yard

Can someone give me a simple explanation on how to simplify radicals.

Answers

Answer:

Step 1: Determine the prime factors of the number under the root. Step 2: Write the prime factors in groups. Step 3: Simplify any multiplication and exponents. Step 4: Simplify the radical until no further simplification can be done.

Step-by-step Have explanation:

a great day

An airliner has 40 rows of seats. Each row has 2 seats on one side, 3 seats in the middle and 2 seats on the other side. How many seats are in the crows ? a) 280 b) 950 c) 400 d) 3,590​

Answers

Answer:

280 seats

Step-by-step explanation:

40*7 = 280

Answer:

18

Step-by-step explanation:

100 points! plus brainlyist!

Answers

Answer:

x=2

Step-by-step explanation:

We must equate f(x)=g(x) ;

x+3=2x^2-3

2x^2-x-6=0, when we solve for x in this equation we get 2 solutions:

x=2, x=-1.5

Since -1.5 is not seen in the table, we consider the value 2.

At x=2 in the table both f(x) and g(x) have the same value 5 and proves f(x)=g(x) has a solution at x=2.

Answer:

x = 2

Step-by-step explanation:

Given:

f(x) = |x| + 3

g(x) = 2x² - 3

From inspection of the table, the equation f(x) = g(x) has a solution when

x = 2 as this is the only value of x when the two functions have the same value of 5.

See attached graph for proof.  The points of intersection are the solutions:  (-2, 5) and (2, 5).  (Since x = -2 is not in the given table, this is not included in the answer to this question).

A customer in Arizona where sales tax is 5.6% orders a cheeze pleeze bites subscription that cost 5.40 every 2 months how much sales tax is collected in a year

Answers

Answer:

see the attachment.

the answer is $ 32. 40/ Year

Which function is increasing?

Answers

The answer is b………..

Which is the rational number?

Answers

Answer:

F

Step-by-step explanation:

Evaluating the expression :

√8 × √2√164

4 is clearly a rational number.

Hence, the right option is F.

Helppppppppppp meeeeer

Answers

Answer:

the answer will be (A)

Step-by-step explanation:

i think the closest will be the first option..

(sorry that i made a mistake earlier)

hope it helps .. please mark brainliest ♡

Answer:

the answer is A

Step-by-step explanation:

5 - 9 round up

1 - 4 round down

pls help in geometry

Answers

Answer:

58.5; 300; 196.5

Step-by-step explanation:

Area of triangle 1 = (1/2) * 9 * 13 = 58.5 inches^2

Area of whole figure = (1/2) * (14+26) * 15 = 300 inches ^2

Area of shaded region = 300 - 58.5 - [(1/2) * 6 * 15] = 241.5 - 45 = 196.5 inches^2

Andy has 36 CDs. He buys a case
that holds 4 CDs in each section.
How many sections can he fill?

Answers

hey there

Number of sections he can fill = 36/4 = 9

He can fill 9 sections

Answer:

9 sections

Step-by-step explanation:

We can find the number of section by dividing the total number of CDs by the number of CDs that each case holds.

    [tex]\sf \text{Number of CDs =$\dfrac{36}{4}$}[/tex]

                              = 9

DOES ANYONE KNOW THE ANSWER ???? Please I can’t fail this test !

Answers

Answer:

the answer I believe will be 25.16

last option is the answer to the question

A triangle has sides with lengths of 25 kilometers, 60 kilometers, and 61 kilometers. Is it a
right triangle?
yes
no

Answers

no
if u use the pythagorean theorem
25^2 + 60^2 ≠ 61^2
625 + 3600 ≠ 3721
4225 ≠ 3721

Question 12 of 14
The perimeter of a rectangle is 32 inches. The length is 1 foot. What is the width of the rectangle in inches?

A.
4 inches

B.
10 inches

C.
15 inches

D.
20 inches

Answers

The answer is A) 4 inches
how?: knowing that rectangle are parallels to its opposite side and the length is 1 ft which is 12 inches, adding both side you get 24 inches which you would have to subtract from your original 32 inches which would be 8 inches remaining. now dividing that by 2 because you still have two more side and they should be equal you get 4 inches on both side.
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