Solve for the roots of x in each of the equations below.

a. x4 - 81 = 0
b. x4 + 10x2 + 25 = 0
c. x4 - x2 - 6 = 0

Answer:

4

Step-by-step explanation:

If two chords intersect externally, then the product of the length of the chord and the length of the part outside the circle is a constant.

Thus from the figure,

we can deduce that:

8×3=6×x

collecting the like terms together we get:

24=6x

x=4

Answer:

x =4

Step-by-step explanation:

Refer the attached figure:

We will use Intersecting secants theorem

Theorem : When two secant lines intersect each other outside a circle, the products of their segments are equal. i.e. [tex]a\times b = c \times d[/tex](refer the attached figure)

So, using this theorem

[tex]x \times 6 = 3 \times 8[/tex]

[tex]x = \frac{24}{6}[/tex]

[tex]x = 4[/tex]

Hence the value of x is 4.

Answer:

(x/4)   -4

Step-by-step explanation:

quotient means divide

quotient of a number x and 4.​

x/4

four less than

x/4   -4

Answer:

This can be written as x/4 - 4

Step-by-step explanation:

To find this, note that quotient denotes a division problem. Then we subtract 4, since it starts with four less than,

Answer:

C. 8x+80.

Step-by-step explanation:

To make this a simple expression, we need to distribute the 8 into x+10. We do this by multiplication. 8*x=8x. 8*10=80. Our new equation is 8x+80.

Answer:

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

From the graph we have the points A(6, 2) and B(0, 10). Substitute:

[tex]AB=\sqrt{(0-6)^2+(10-2)^2}=\sqrt{(-6)^2+8^2}=\sqrt{36+64}=\sqrt{100}=10[/tex]

The length is D. 10

√ (x2 - x1)^2 + (y2 - y1)^2

√ (0-6)^2 + (10 - 2)^2

√ (-6)^2 + (8)^2

√ 36 + 64

√ 100 = 10

Answer:

r = 2 [stream's speed is 2 mph downstream

Step-by-step explanation:

Remark

The distances traveled [upstream and downstream] are the same.

If it takes longer to go upstream, it means the speed of the current is going against him. So the rate is 38 - r where r is the speed of the current.

The rate of the downstream is 38 + r because it takes him less time to go downstream and the current is helping him go.

The times are given

Givens

Formula

d1 = d2

d1 = (38 - r) * 30

d2 = (38 + r) *27

(38 - r) * 30 = (38+r)*27

Solution

Remove the brackets on both sides.

38*30 - 30*r = 38*27 + 27r                    Add 30r to both sides

38*30 - 30r + 30r =38*27 + 27r + 30r  Combine the numbers

1140 = 1026 + 57r                                   Subtract 1026 from both sides.

114 = 57r                                                  Divide by 57

114/57 = 57r/57

r = 2

Answer:

-2

Step-by-step explanation:

8-(-2) = 8 + 2 = 10

7 - 12 = -5

10 / -5 = -2

Answer:

Part a) In the procedure

Part b) Line A and Line B are different parallel lines

Step-by-step explanation:

Part a) we have

[tex]3x-6y=-12[/tex] ----> equation A

[tex]x-2y=-8[/tex] ----> equation B

Isolate the variable x in the equation B

[tex]x=2y-8[/tex]

Substitute the value of x in the equation A

[tex]3(2y-8)-6y=-12[/tex]

[tex]6y-24-6y=-12[/tex]

[tex]-24=-12[/tex] ------> is not true

therefore

The system of equations has no solutions

Part b) What do you know about the two lines in this system of equations?

[tex]3x-6y=-12[/tex] ------> equation A

isolate the variable y

[tex]6y=3x+12[/tex]

[tex]y=(1/2)x+2[/tex]

[tex]x-2y=-8[/tex] -------> equation B

isolate the variable y

[tex]2y=x+8[/tex]

[tex]y=(1/2)x+4[/tex]

Line A and Line B are parallel lines, because their slopes are the same

Line A and Line B are different lines because their y-intercept is not the same

Answer:

C: feature

that is the correct answer

The amount of interest earned is $11908 and the total amount is $21248.

Simple interest is calculated just on the loan's principal amount, whereas compound interest is calculated on both the principal and the cumulative interest.

Given that 9340.00 is invested into an account that earns 8.5% simple interest for 15 years.

The simple interest will be calculated by the formula below,

Simple interest = ( P x R x T ) / 100

Simple interest = ( 9340 x 8.5 x 15 ) / 100

Simple interest = $11908.5

The total amount will be,

Amount = $11908.5 + $9340

Amount = $21248.5

To know more about simple interests follow

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The simple interest earned on an investment of $9340.00 at a rate of 8.5% over 15 years is $11919.00. The total amount in the account after 15 years is $21259.00.

To calculate the simple interest earned on an investment, you can use the formula I = P ×  r × t, where I is the interest, P is the principal amount, r is the interest rate (in decimal form), and t is the time in years . In this case:

r (Interest Rate) = 8.5% or 0.085 (since 8 1/2% is the same as 8.5%)

t (Time) = 15 years

Using the formula:

I = $9340.00  ×  0.085 ×  15 = $11919.00

The total simple interest earned over 15 years would be $11919.00. To find the total amount in the account after 15 years, we add this interest to the original principal:

Total = Principal Amount + Interest

Total = $9340.00 + $11919.00 = $21259.00

Therefore, the total in the account after 15 years will be $21259.00.

Answer:

B

Step-by-step explanation:

Adams headed the Commission that negotiated the Treaty of Ghent in 1814, which ended the War of 1812 with Great Britain.

Answer:

The total value is £268.20.

Step-by-step explanation:

Given : There are 495 coins in a bottle.

1/3 of the coins are £1 coins.

124 of the coins are 50p coins.

The rest of the coins are 20p.

To find : Work out the total value of the 495 coins?

Solution :

According to question,

Total coins = 495

[tex]\frac{1}{3}[/tex] of the coins are £1 coins.

i.e.  The number £1 coins are

[tex]\frac{1}{3}\times 495 =165[/tex]

So, We have £165

124 of the coins are 50p coins.

50p=£0.50

Number of coins were

[tex]124\times0.50 =62[/tex]

So, We have £62 .

Remaining coins were,

[tex]495-(124+165)=206[/tex]

i.e. remaining coins are 206 are of 20p.

20p=£0.20

Number of coins were

[tex]206\times0.20 =41.20[/tex]

So, We have £41.20 .

Now, Adding all of them together,

i.e. £165+£62+£41.20=£268.20

So, The total value is £268.20.

Answer:

[tex]\large\boxed{\dfrac{1}{3p+15}=\dfrac{1}{3(p+5)}}[/tex]

Step-by-step explanation:

"one over threep + 15":

[tex]\dfrac{1}{3p+15}=\dfrac{1}{(3)(p)+(3)(5)}=\dfrac{1}{(3)(p+5)}=\dfrac{1}{3(p+5)}[/tex]

no, the angles in triangles have to add up to 180 deg. but this adds up to 190

Answer:A,C

Step-by-step explanation:

Answer:

A, C

Step-by-step explanation:

The domain is the set of all possible x-values that will make the function work.

Here, m  is the x-value (the independent variable).

The month number m is an integer, so the appropriate number type for the domain of r is integer.

The month numbers run from 1 to 12, inclusive, so the appropriate domain is 1 ≤ m ≤ 12.

C. Surface area and volume use the same unit of measurement

Answer:

The answer is C.

Step-by-step explanation:

No idea for the Step-by-Step explanation

Answer:

The answer is C for sure

Step-by-step explanation:

I would say the answer is C.  What are the checking account balances of the shoppers in a grocery store?

Hope this helps!

Answer:

Step-by-step explanation:

A diameter is two times longer than a radius. Therefore, if the diameter

d = 15cm, then the radius r = (15cm) : 2 = 7.5cm.

The formula of an area of a circle:

[tex]A=\pi r^2[/tex]

Substitute:

[tex]A=\pi(7.5)^2=56.25\pi\ cm^2[/tex]

[tex]\pi\approx3.14[/tex]

Then

[tex]A\approx(56.25)(3.14)\approx177\ cm^2[/tex]

Answer: The correct answer is choice D.

Step-by-step explanation: In order to answer this question you need to calculate the volume of each of the cubes.

Cube A has a side which is 3 meters, so the volume = 3 x 3 x 3 = 27

Cub B has a side which is 6 meters, so the volume = 6 x 6 x 6 = 216

216/27 = 8. Therefore, the volume of cube B is 8 times the volume of cube a.

The volume of cube A is 27 cubic meters and the volume of cube B is 216 cubic meters. Cube B's volume is 8 times greater than cube A's. The correct answer is option D)

The volume of a cube is calculated by cubing the length of its side. So, the volume of cube A is 3 meters x 3 meters x 3 meters = 27 cubic meters. The volume of cube B is 6 meters x 6 meters x 6 meters = 216 cubic meters. Comparing the volumes, cube B's volume is 216/27 = 8 times greater than the volume of cube A. Therefore, the statement that accurately represents the relationship between the two volumes is option D) The volume of cube B is 8 times the volume of cube A.

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The constant term is "240." The number represents the daily revenue when the price of a taco is 0 dollars.

Answer:

The constant term is 240. It represents the initial daily revenue.

Step-by-step explanation:

It is given that Tico's Taco Truck is trying to determine the best price at which to sell tacos, the only item on the menu,  to maximize profits.

The owner can calculate the daily revenue using the polynomial  expression

[tex]-7x^2+32x+240[/tex]

where x is the number of $1 increases in the taco price.

Constant term does not contain any variable.

In the given expression 240 is free from variable x. So, the constant term is 240.

The value of expression is 240 for x=0. Since x is the number of $1 increases in the taco price, therefore 240 is the daily revenue when the taco price is not increased or the taco price increased by 0.

Therefore the constant term is 240 and it represents the initial daily revenue.

Answer:

70%

Step-by-step explanation:

1. divide the number of games won (33) by the total number of games (47)

    33/47 = 0.702

2. Move the decimal two places to the right = 70.2%

3. round down to 70%

Final answer:

The soccer team won 70% of its games after calculating the fraction of games won, converting it to a decimal, then to a percent, and finally rounding to the nearest whole number.

Explanation:

To calculate the percent of games won by the soccer team, we divide the number of games won by the total number of games played and then multiply by 100 to convert the fraction to a percentage.

Step 1: Find the fraction of games won: 33 (games won) ÷ 47 (total games).

Step 2: Convert the fraction to a decimal: 33 ÷ 47 = 0.7021.

Step 3: Convert the decimal to a percent: 0.7021 × 100 = 70.21%.

Step 4: Round to the nearest whole number: 70.21% rounded to the nearest whole number is 70%.

Therefore, the soccer team won 70% of its games.

Answer: Last option.

Step-by-step explanation:

To find the inverse of the function f(x), you must follow the proccedure shown below:

- Rewrite the function,as following:

[tex]y=4x+12[/tex]

- Solve for x. Then:

[tex]y-12=4x\\x=\frac{1}{4}y-\frac{12}{4}\\\\x=\frac{1}{4}y-3[/tex]

- Now, substitute y with x.

Therefore, you obtain that the inverse function g(x) is the following:

[tex]g(x)=\frac{1}{4}x-3[/tex]

Then, the answer is the last option.

Answer:

Last choice is the answer.

Step-by-step explanation:

We have given a function.

f(x) = 4x+12

We have to find the inverse of given function.

Let y  = f(x)

y = 4x+12

Solving for x, we have

x = 1/4y-3

Since, x =  f⁻¹(y)

 f⁻¹(y) =  1/4y-3

Replacing y with x , we have

f⁻¹(x) = 1/4x-3

Given that g(x) = f⁻¹(x)

g(x) = 1/4x-3 which is the answer.

Answer:

-25

Step-by-step explanation:

You use the PEMDAS order of operations to find this out

So first you do exponents

-1^3 is positive

so you then rewrite the equation as 3*4(-2)-1

Then you multiply and divide

12(-2)

That equals -24

Then you add the remaining

-24+-1= -25

Answer:

Final answer is 1/3.

Step-by-step explanation:

Question says that Mrs Jenkins picked some tomatoes from her garden. She used 5/9 of the tomatoes to make pasta sauce. After that  she used 3/4 of the remainder to make a salad. Now we need to find about what fraction of the tomatoes did Mrs Jenkins use to make the salad.

As she used 5/9 of the tomatoes to make pasta sauce.

Now remaining amount of tomatoes = 1- 5/9 = 9/9 -5/9 = 4/9

Then she used 3/4 of the remainder to make a salad. So fraction of the tomatoes did Mrs Jenkins use to make the salad = (4/9)(3/4)=12/36=1/3

Hence final answer is 1/3.

Answer:

Step-by-step explanation:

1/4x20=5 so Maria ate 5 slices of pizza.

Answer:

Choices A and C

Step-by-step explanation:

Answer:

A, C

Step-by-step explanation:

We can see in the graph that it is done by ticks of 1/10s

Therefore we can determine that point A is on 1.6.

Since 1.6 > 1.27, this is true.

1 one and 7 hundreths is 1.07

And since 1.07 < 1.27, this is not true.

Finally 27 tenths is the equivalent of 2.7

2.7 > 1.27 so this is true.

Answer:

18

Step-by-step explanation:

⅓g + 6 = 12

⅓g       =  6     Subtracted 6 from each side

   g      = 18     Multiplied each side by 3

18 games remain in the season.

Check:

⅓ × 18 + 6 = 12

   6     + 6 = 12

           12 = 12

Answer:

[tex]\large\boxed{y=a(x+8)(x+1)(x-3)}[/tex]

Step-by-step explanation:

[tex]\text{Factored form:}\\\\y=a(x-x_1)(x-x_2)(x-x_3)\\\\x_1,\ x_2,\ x_3-zeros\\\\\text{We have}\ x_1=-8,\ x_2=-1\ \text{and}\ x_3=3.\ \text{Substitute:}\\\\y=a(x-(-8))(x-(-1))(x-3)\\\\y=a(x+8)(x+1)(x-3)\\\\\text{Where}\ a\neq0\ (\text{any real number except 0})[/tex]

Answer:  [tex]\bold{\bigg(\dfrac{1}{2},2\dfrac{1}{2}\bigg)}\qquad \implies \qquad \bold{\bigg(\dfrac{1}{2},\dfrac{5}{2}\bigg)}[/tex]

Step-by-step explanation:

y = x + 2       x + y = 3

Solve using Substitution Method by replacing y with x + 2:

                    x + (x + 2) = 3

                         2x + 2 = 3

                         2x       = 1

                           x        = [tex]\dfrac{1}{2}[/tex]

Next, replace x with 1/2 in one of the original equations and solve for y:

y = x + 2

  = [tex]\dfrac{1}{2}[/tex] + 2

  = [tex]2\dfrac{1}{2}[/tex]

Answer:

x = 1/2

y = 5/2

Step-by-step explanation:

So we're gonna use the elimination method, by eliminating one of x or y to find the value of the other one.

y = x + 2 --------------(1)

x + y = 3 --------------(2)

In (1), x is in LHS and y is in RHS. To make things simpler, we take both x and y to the same side.

y           = x + 2

y - x      = x + 2 - x ( take x to the other side)

y - x      = 2-------------------------(3)

Note that in (2), x is positive and in (3), x is negative. So by adding these two, we can single out y because +x and -x cancels out. So we can eliminate x.

(3) +  (1) : (x+y) + (y- x) = 3 + 2

              2y                 = 5

              y                   = 5/2

Substituting y = 5/2 for (1),

5/2 - x  = 2

5/2       = 2 + x

5/2 - 4/2 = x

x   = 1/2

∴ x = 1/2

  y = 5/2

Hope i helped you :)

The correct answer is 9>n since it doesn't say greater than or equal to, we can cross out the 2 and that leaves us with 9<n and 9>n but it actually says 9 is more than a number so that leaves us with 9>n

Answer:

Rational number

Step-by-step explanation:

A rational number is one which can be expressed in the form

[tex]\frac{a}{b}[/tex] where a and b are integers

- 3 can be expressed as [tex]\frac{-3}{1}[/tex] -3 and 1 are integers

Hence - 3 is a rational number