What are the solutions of the equation 9x^4 – 2x^2 – 7 = 0? Use u substitution to solve

Answers

Answer 1

Answer:

[tex]x=1\\x=-1[/tex]

Step-by-step explanation:

[tex]9x^{4} -2x^{2} -7=0\\y=x^{2} \\9y^{2} -2y-7=0\\y=\frac{2\pm\sqrt{(-2)^{2} -4*9(-7)} }{2*9} =\frac{2\pm\sqrt{4+252} }{18} =\frac{2\pm\sqrt{256} }{18}[/tex]

[tex]\sqrt{256} =16[/tex]

[tex]y=\frac{2+16}{18} =\frac{18}{18} =1 \\or \\y=\frac{2-16}{18} =-\frac{14}{18} =-\frac{7}{9}[/tex]

[tex]x^{2} = 1 \\or \\x^{2} =-\frac{7}{9}[/tex]

[tex]x=\pm 1[/tex]

[tex]x^{2} =-\frac{7}{9}[/tex] has no solution since fot all [tex]x[/tex] on the real line, [tex]x^{2} \geq 0[/tex] and [tex]-\frac{7}{9} < 0.[/tex]


Related Questions

Hue wants to buy two necklaces, one for her sister and one for herself. The necklace for her sister costs $43.25, and the necklace for herself costs $26.25. The sales tax on the purchases is 3%. Find the total cost of Hue's purchases, including sales tax.

Answers

Answer:

$71.59

Step-by-step explanation:

43.25+26.25

=69.5

69.5×103/100

=71.585

the cost of a leather coat went up from $75 to $90. what is the percent increase?

Answers

Answer:

  20%

Step-by-step explanation:

The increase is ...

  $90 -75 = $15

As a percentage of the original price, that is ...

  $15/$75 × 100% = 0.20×100% = 20%

The increase was 20%.

what expression are equivalent to 4(4x + 9)

Answers

Answer:

16x+36

Step-by-step explanation:

4(4x + 9)

16x+36

____________________________________

Solution,

4(4x+9)

=4*4x+4*9

=16x+36

So the answer is 16x+36

Hope it helps

Good luck on your assignment

___________________________________

Use the following information for questions 34-36: Deanna is the principal at a Midwestern middle school and wants to know the average IQ of all female, seventh grade students. She does not know anything about what the population distribution looks like. She took a simple random sample of 31 seventh-grade girls in her school and found the average IQ score in her sample was 105.8 and the standard deviation was 15. Based on the interval you calculated in question 34, does it seem plausible that the true average IQ score for all seventh-grade female students at this school is 113

Answers

Answer:

Since, 113 is on the confidence interval obtained (97.502, 114.098), so, we can suggest that is plausible that the true average IQ score for all seventh-grade female students at this school is 113.

Step-by-step explanation:

The question isn't complete, the missing part asked us to obtain a 99.5% confidence interval for the true average IQ score

Finding the confidence interval using the sample data provided, we can answer the question of plausibility.

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Sample Mean = 105.8

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.

To find the critical value from the t-tables, we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 31 - 1 = 30

Significance level for 99.5% confidence interval

(100% - 99.5%)/2 = 0.25% = 0.0025

t (0.0025, 30) = 3.03 (from the t-tables)

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample = 15

n = sample size = 30

σₓ = (15/√30) = 2.739

99.5% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 105.8 ± (3.03 × 2.739)

CI = 105.8 ± 8.298

99.5% CI = (97.502, 111.387)

99.5% Confidence interval = (97.502, 114.098)

Since, 113 is on the confidence interval obtained, so, we can suggest that is plausible that the true average IQ score for all seventh-grade female students at this school is 113.

Hope this Helps!!!

Which of the following is a geometric sequence?

Answers

Answer:

D. 1, 1/2, 1/4, 1/8, ...

Step-by-step explanation:

Only one of the listed is a geometric sequence:

D. 1, 1/2, 1/4, 1/8, ... with the common ratio 1/2

Help meee please 15 points!!

Answers

Answer:

B.

Step-by-step explanation:

B.

- 9 ≤ - 3x - 6 ≤ 6

1 part.

- 9  +6 ≤ - 3x - 6 +6

- 3/(- 3) ≤ - 3x/(- 3)

1 ≥ x

2d part

- 3x - 6 +6≤ 6 + 6

- 3x ≤ 12

- 3x/(-3) ≥ 12/(-3)

x ≥ - 4

x ≥ - 4 and x≤ 1

A clothing store determines that in order to sell x shirts, the price per shirt should be p(x)=100−x dollars. Getting x shirts from the supplier costs the store C(x)=1,600+20x dollars. If the store’s revenue from selling x shirts is R(x)=x⋅p(x), for what value of x will the store’s cost and revenue be equal?

Answers

Answer:

x= -40

Step-by-step explanation:

Cost

C(x)=1,600+20x

P(x)=100-x

Revenue=x*p(x)

=x*(100-x)

=100x-x^2

Cost=Revenue

1600+20x=100x-x^2

1600+20x-100x+x^2=0

1600-80x+x^2=0

Solve using quadratic formula

Formula where

a = 1, b = 80, and c = 1600

x=−b±√b2−4ac/2a

x=−80±√80^2−4(1)(1600) / 2(1)

x=−80±√6400−6400 / 2

x=−80±√0 / 2

The discriminant b^2−4ac=0

so, there is one real root.

x= −80/2

x= -40

600000000*100000000000000000000000000000000000000000000

Answers

Answer:

6e+52

Step-by-step explanation:

cAlCuLaToR

Answer:

6e+52

Step-by-step explanation:

multiply

James makes fruit punch by mixing fruit jucie and lemonade in the ratio 1:4 she needs to make 40 liters of punch for a party How much of each ingredient does she need? Fruit juice ? Liters Lemonade ?liters


Part 2

During the party Josie decides to make some more.
She has 4 litres of fruit juice left and plenty of lemonade.
How much extra punch can she make?

Part 3

To make the second batch of punch go further Josie adds 2 more litres of lemonade.
What is the ratio of fruit juice to lemonade in the second batch?

Answers

Answer:

Part 1.

Juice = 8 L.

Lemonade = 32 L.

Part 2.

20 L punch Josie can make.

Part 3.

New ratio juice : lemonade = 2 : 9

Step-by-step explanation:

Part 1.

1+4 = 5 parts altogether, 1 parts for juice and 4 parts for lemonade.

40 : 5 = 8 L is 1 part.

Juice - 1 part - 8 L.

Lemonade - 4 parts - 4*8 = 32 L.

Part 2.

1 parts of juice needs 4 parts of lemonade

4 L of juice     needs  x L of lemonade

1 : 4 = 4 : x

x = 4*4/1 = 16 L lemonade

4+ 16 = 20 L punch Josie can make

Part 3.

It was 4 L of juice and 16 L of lemonade.

After 2 L lemonade was added, we have 4 L of juice and (16+2) = 18 L of lemonade.

4 L juice : 18 L lemonade = 4/2 L juice : 18/2 L lemonade =

= 2 L juice: 9L lemonade

New ratio juice : lemonade = 2 : 9

2/5 plus 1/4 plus 7/10

Answers

The answer is 1 7/20

2/5 x 4/4 + 7/10 x 2/2 + 1/4 x 5/5

=  8/20 + 14/20 + 5/20

= 27/20

= 1 7/20

Answer:

27/20 or 1 and 7/20

Step-by-step explanation:

All you do is find common factors.

I really need help :( anybody ??

Answers

_______________________________

Hey!!

Answer:{2,4,5}

Explanation:

Range

Let R be relation from A to B.The set of second components or the set of elements of B are called range.

Hope it helps..

_______________________________

what is the name of the shape graphed by the function: r=2cos theta

Answers

Answer:

Circle

Step-by-step explanation:

r = 2 cos θ

Multiply both sides by r.

r² = 2r cos θ

Convert to rectangular.

x² + y² = 2x

x² − 2x + y² = 0

Complete the square.

x² − 2x + 1 + y² = 1

(x − 1)² + y² = 1

This is a circle with center (1, 0) and radius 1.

The given function r = 2 cos θ is a circle with a center (1, 0) and radius of 1.

What is a circle?

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

Given function is r = 2 cos θ

Now, Multiply both sides by r.

r² = 2r cos θ

Convert to rectangular form;

x² + y² = 2x

x² − 2x + y² = 0

Using Complete the square.

x² − 2x + 1 + y² = 1

(x − 1)² + y² = 1

Hence, This is a circle with a center (1, 0) and radius of 1.

Learn more about circle here;

brainly.com/question/12512221

#SPJ2

Which of the following sets would have a graph with an open circle on 5 and a ray pointing right on the number line?

Answers

Answer: Choice C  [tex]\{x | x \in \mathbb{R}, \ x > 5 \}[/tex]

The open circle means we do not include the endpoint, hence the use of a greater than symbol. If we were to include the endpoint, then we'd have greater than or equal to. We can rule out choice B due to this reasoning.

The ray pointing to the right indicates we are talking about x values larger than 5, so we can rule out choice A and conclude the answer is C.

Side note: The notation [tex]x \in \mathbb{R}[/tex] is saying "x is a real number"

Shape 1 and shape 2 are plotted on a coordinate plane. Which rigid transformation can you perform on shape 2 to show that shape 2 is congruent to shape 1?

Answers

The answer is B. Take the same point on each of the figures and count how far they are away horizontally and vertically.

Express the following in simplest a + bi form.
V9+1-36
O
-91
O
3 - 61
3 + 6
91

Answers

Answer:

3+6i

Step-by-step explanation:

I did it

Answer:3+6i

Step-by-step explanation:

Flip a fair two sided coin 4 times. Find the probability the first or last flip is a tail.

Answers

Answer:

1/4

Step-by-step explanation:

Flip a fair two sided coin 4 times, the probability the first or last flip is a tail is

P = (1/2) x 1 x 1 x (1/2) = 1/4

(The probability of getting tail in first flip = 1/2, in the 2nd and 3rd flip, tail and head are both accepted, the probability of getting tail in last flip = 1/2)

Hope this helps!

Let A be an n # n matrix, b be a nonzero vector, and x0 be a solution vector of the system Ax D b. Show that x is a solution of the nonhomogeneous system Ax D b if and only if y D x!x0 is a solution of the homogeneous system Ay D 0.

Answers

Complete Question

Let A be an n x n matrix, b be a nonzero vector, and x_0 be a solution vector of the system Ax = b. Show that x is a solution of the non-homogeneous system Ax = b if and only if y = x - x_0 is a solution of the homogeneous system Ay = 0.

Answer:

Step-by-step explanation:

From the question we are told that

    A is an  n × n matrix

   b is a zero vector

  [tex]x_o[/tex] us the solution vector of  [tex]Ax = b[/tex]

Which implies that  

     [tex]Ax_o = b[/tex]

So first we show that

  if [tex]x[/tex] is the solution matrix of [tex]Ax = b[/tex]

  and  [tex]y= x-x_o[/tex] is the solution of  [tex]Ay = 0[/tex]

Then

    [tex]A(x-x_o) = 0[/tex]

=>   [tex]Ax -Ax_o = 0[/tex]

=>   [tex]b-b = 0[/tex]

Secondly to show that

   if  [tex]y= x-x_o[/tex] is the solution of  [tex]Ay =0[/tex]

  then x is the solution of the non-homogeneous system

    [tex]Ax = b[/tex]

Now we know that [tex]y = x-x_o[/tex] is the solution of  [tex]Ay =0[/tex]

So

     [tex]Ay = 0[/tex]

=>  [tex]A(x- x_o) = 0[/tex]

=>   [tex]Ax - Ax_o = 0[/tex]

=>   [tex]Ax - b = 0[/tex]

=>    [tex]Ax = b[/tex]

Thus this has been proved

(-1/4 - 1/2) ÷ (-4/7)

Answers

Answer:

1 5/16

Step-by-step explanation:

(-1/4 - 1/2) ÷ (-4/7)

PEMDAS says parentheses first

Get a common denominator

(-1/4 - 2/4)  ÷ (-4/7)

(-3/4)  ÷ (-4/7)

Copy dot flip

-3/4 * -7/4

21/16

Change to a mixed number, 16 goes into 21  1 time with 5 left over

1 5/16

Which of the following functions is graphed below

Answers

Answer:

B

Step-by-step explanation:

Please answer this correctly

Answers

Answer:

1607.68 square miles

Step-by-step explanation:

use pi r squared

Answer:

Step-by-step explanation:

diameter = 64  miles

r =64/2 = 32 miles

Area of semicircle = πr²/2

                              = 3.14*32*32/2

                             = 1607.68 sq.miles

Indicate in standard form equation of the line passing through the given 

Answers

Answer:

x + y = 6

Step-by-step explanation:

slope is rise/run so -6/6 = -1

y = -x+b

solve for b by plugging in any point

6 = 0 + b -> b = 6

y = -x+6

x + y = 6

A 50 ft kite string is flying on the beach above an umbrella. You are holding the end
of the string and are 12 feet from the umbrella. How high in the air is the kite flying?
Round to the nearest degree.

Answers

Answer:

The height of the kite is 48.54 feet

The angle of elevation is 76.11°

Step-by-step explanation:

To find the height of the kite, we can use the Pythagoras' theorem in the triangle created by the length of the string (hypotenuse), the height of the kite and the distance to the umbrella (catheti).

Then, we have:

50^2 = 12^2 + height^2

height^2 = 2500 - 144

height^2 = 2356

height = 48.54 ft

So the kite is 48.54 feet high in the air.

The angle of elevation can be calculated using the cosine relation:

cos(angle) = 12 / 50

cos(angle) = 0.24

angle = 76.11°

Look at the Picture. Look at the Picture.

Answers

Answer:

325 square inches

Step-by-step explanation:

Consider the attachment below for further reference. Ideally we would split this figure into parts, and solve as demonstrated by the attachment. I have labeled each rectangle as rectangle 1, rectangle 2, rectangle 3 etc. ;

[tex]Rectangle 1 Area = 17 in * 5 in = 85 square in\\Rectangle 2 Area = ( 17 in - 5 in ) * 14 in = 168 square in,\\Rectangle 3 Area = ( 12 in - 3 in ) * 8 in = 72 square in\\\\Total Area = 85 + 168 + 72 = 325 square inches[/tex]

Hope that helps!

Answer: The answer is 325 inches.

Step-by-step explanation: You can divide the rectangle into multiple parts and find the areas of those parts and add all the areas together at the end

How do I find the value of x for which line a is parallel to line b?

Answers

Answer:

x = 20

Step-by-step explanation:

3x + 6x = 180, if you make them supplementary then they will be parallel

9x = 180

x = 20

Round 1040 to the nearest hundred.enter your answer in the box below

Answers

Answer:

1000

Step-by-step explanation:

For rounding questions, you want to look at the place value to the right of the digit it wants you to round to. If that place value to the right of the digit you need to round is less than 5, you round down. If the place value to the right of the digit you need to round is 5 or greater, then you round up. In your situation, the place value you want to round is the hundreds place, so we need to look at the tens value. The tens value is 4, which is less than 5, so we round down. Therefore, the answer would be 1000.

Ariana is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Arians will earn $40 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Ariana earned a total of $500 in royalties on 9 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Arianas songs were played. Define the variables that you use to write the system.

Answers

Answer:

Commercials x = 7

Movies y = 2

Step-by-step explanation:

Let commercials = x

Let's movies = y

$40 is for commercials

$110 is for movies.

Commercials plus movies for the Year = 9

She earned total of $500

X+ y = 9..... equation 1

40x + 110y = 500.... Equation 2

Multipling equation one by 40

40x + 40y = 360

Subtracting equation one from equation 2

70y = 140

Y = 2

If y = 2

X + y = 9

X + 2 = 9

X = 9-2

X = 7

If this rectangle is dilated using a scale factor of One-half through point B, what is the result? Point B is the bottom left corner of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is double the size of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is half the size of rectangle X and point B is at the bottom left corner. Point B is the bottom left corner of rectangle X. Rectangle X prime is double the size of rectangle X and is outside of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is half the size of rectangle X and is outside of rectangle X.

Answers

Answer:

the first one

Step-by-step explanation:

I just took it on edge.

Answer:

It is B just took the unit quiz

Step-by-step explanation:

Suppose that the functions p and q are defined as follows.

Answers

Answer:

Step-by-step explanation:

Hello,

qop(2)=q(p(2))

p(2) = 4+3=7

[tex]q(7) = \sqrt{7+2}=\sqrt{9}=3[/tex]

so

qop(2)=3

and poq(2)=p(q(2))

[tex]q(2)=\sqrt{2+2} = \sqrt{4}=2[/tex]

p(2) = 7

so poq(2)=7

thanks

The answer is "[tex]\bold{(q \circ p)(2)= 3}\ and \ \bold{(p \circ q)(2)=7}[/tex]" and the further explanation can be defined as follows;

Given:

[tex]\to \bold{p(x)=x^2+3}\\\\\to \bold{q(x)=\sqrt{x+2}}[/tex]

Find:

[tex]\bold{(q \circ p)(2)=?}\\\\\bold{(p \circ q)(2)=?}[/tex]

Solve the value for [tex]\bold{(q \circ p)(2)}\\\\[/tex]:

[tex]\to \bold{(q \circ p)(2)= q \circ p(2) =q(p(2))}\\\\[/tex]

[tex]\therefore\\\\ \to \bold{p(2)=2^2+3= 4+3=7}\\\\\ \because \\\\ \to \bold{q(p(2))=\sqrt{7+2}=\sqrt{9}=3}[/tex]

Solve the value for [tex]\bold{(p \circ q)(2)}\\\\[/tex]:

[tex]\to \bold{(p \circ q)(2)= p \circ q(2)= p (q(2))}\\\\[/tex]

[tex]\therefore\\\\ \to \bold{q(2)=\sqrt{2+2}=\sqrt{4}=2}\\\\\ \because \\\\ \to \bold{p(q(2))=2^2+3= 4+3=7}[/tex]

Therefore the final answer of "[tex]\bold{(q \circ p)(2)= 3}\ and \ \bold{(p \circ q)(2)=7}[/tex]"

Learn more:

brainly.com/question/14270968

One-third times the difference of a number and 5 is
Which equation best shows this?
3
One possible first step in solving the equation in the above problem is to
The value of the number is

Answers

Answer:

the value of x is 3

Step-by-step explanation:

Hope this helps!!!! :)

Answer:

one is a

two is c

three is b

Step-by-step explanation:

A group of 8 friends (5 girls and 3 boys) plans to watch a movie, but they have only 5 tickets. If they randomly decide who
what is the probability that there are at least 3 girls in the group that watch the movle?

Answers

Answer:

53.57%

Step-by-step explanation:

We have to calculate first the specific number of events that interest us, if at least 3 are girls, they mean that 2 are boys, therefore we must find the combinations of 3 girls of 5 and 2 boys of 3, and multiply that, so :

# of ways to succeed = 5C3 * 3C2 = 5! / (3! * (5-3)!) * 3! / (2! * (3-2)!)

 = 10 * 3 = 30

That is, there are 30 favorable cases, now we must calculate the total number of options, which would be the combination of 5 people from the group of 8.

# of random groups of 5 = 8C5 = 8! / (5! * (8-5)!) = 56

That is to say, in total there are 56 ways, the probability would be the quotient of these two numbers like this:

P (3 girls and 2 boys) = 30/56 = 0.5357

Which means that the probability is 53.57%

Answer:

Actually, the correct answer for plato users is option D

Step-by-step explanation:

D.  0.821

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