Solve 2x2 – 6x + 10 = 0 by completing the square.

Answer:

D. ⅔

Step-by-step explanation:

I hope it helps :)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\ m = \frac{3 - 1}{5 - 2} = \frac{2}{3} \\ m = \frac{2}{3} [/tex]

Answer:

2√2−3

Step-by-step explanation:

Simplify each term.

Since there are no imaginary terms, the complex conjugate is the same as the simplified expression.

Hope this can help

Answer:

35 degree angle a cute angle

Answer:

Step-by-step explanation:

A and B are supplementary angles since the lines are parallel

A + B = 180

6x-18 + 14x+38 = 180

Combine like terms

20x +20 = 180

Subtract 20 from each side

20x+20 -20 =180-20

20x = 160

Divide by 20

20x/20 =160/20

x = 8

Answer:

  $2192.60

Step-by-step explanation:

March 4 is day 63 of the year. So, the amount of tax that Kelly needs to refund to Mason is the tax for the remaining 365 -63 = 302 days of the year.

Kelly will owe Mason ...

  (302/365)($2650) = $2192.6027 ≈ $2192.60

Answer:

  (4y +1)(y +6)

Step-by-step explanation:

We can rewrite the middle term and factor by grouping.

  4y^2 + 25y + 6 = (4y^2 +24y) +(y +6)

  = 4y(y +6) +1(y +6)

  = (4y +1)(y +6)

Answer:

answer is B

Step-by-step explanation:

Answer:

see details.

Step-by-step explanation:

Graphs from question not yet uploaded, so read attached graph to make a match.

Answer:

hope this is right y=74

Step-by-step explanation:

have not done this since two years ago so...

but anyway 148-180 = 32

32 is that angle

if this were a right triangle my answer would be different but 148/2 still completes this triangle and somewhat makes sense.

The correct answer is 90.

A - No

B - No

C - Yes

D - Yes

.

C and D are alternate exterior angles

Answer:

0

Step-by-step explanation:

3^2 is 9, and (-3)^2 is 9.

so, 9-9=0

Answer: The concentration will be 8 milligrams per liter at 2 hours and 4 hours.

Step-by-step explanation:

GIven: The concentration of a certain painkiller supplied by serum varies in its effectiveness over time according to the following function, [tex]C (t) = - t^2 + 6t[/tex] where C is the concentration of the painkiller in the serum measured in milligrams per liter so that it takes effect during t hours.

Put C(t)=8, then we get

[tex]8=-t^2+6t\\\\\Rightarrow\ t^2-6t+8=0\\\\\Rightarrow\ t^2-2t-4t+8=0\\\\\Rightarrow\ t(t-2)-4(t-2)=0\\\\\Rightarrow\ (t-2)(t-4)=0\\\\\Rightarrow\ t=2,4[/tex]

At t=2, [tex]C(t)=-(2)^2+6(2)=-4+12=8[/tex]

At t=4, [tex]C(t)=-(4)^2+6(4)=-16+24=8[/tex]

Hence, the concentration will be 8 milligrams per liter at 2 hours and  4 hours.

Answer:

[tex]\boxed{\frac{1}{8} }[/tex]

Step-by-step explanation:

[tex]\frac{5}{4} / 10[/tex]

Changing "division" into multiplication and inverting the term after it:

[tex]\frac{5}{4} * \frac{1}{10}[/tex]

=> [tex]\frac{1*1}{4*2}[/tex]

=> 1/8

Answer:

1/8

Step-by-step explanation:

Well to do 5/4 ÷ 10 let's set up the following.

[tex]\frac{5}{4} / \frac{10}{1}[/tex]

Then we use the keep, change, and flip rule.

So keep 5/4 change the / to a * and flip the 10/1 ro a 1/10.

[tex]\frac{5}{4} * \frac{1}{10}[/tex]

Now we multiply them to get,

5/40

simplified

1/8

Thus,

the answer is 1/8.

Hope this helps :)

Answer:

a. $849.45

Step-by-step explanation:

In the above question, we are given the following information

Coupon rate = 10%

Face value = 1000

Maturity = n = 20 years

t = number of periods = compounded semi annually = 2

Percent yield = 12% = 0.12

Bond Value formula =

C/t × ([1 -( 1/ 1 + r/t)-^nt ÷] r/t) +( F/ (1 + r/t)^nt)

C = coupon rate × face value = 10% × 1000 = 100

Bond value:

= 100/2 × ( [1 - (1 /1 + 0.12/2)^-20×2]÷ 0.12/2)+ (1000/( 1 + 0.12/2)^20×2

= 50 × ( [1 - (1 /1 + 0.06) ^40] ÷ 0.06) + ( 1000/ (1 + 0.06) ^40

= 50 × ( [1 - (1/ (1.06) ^40] ÷ 0.06 ) + (1000/(1.06)^40)

= 50 × 15.046296872 + 97.222187709

= $849.45

Bond value = $849.45

Answer:

x = 1/2

Step-by-step explanation:

2(4x+2) = 4x - 12(x-1)

Distribute

8x +4 = 4x - 12x +12

Combine like terms

8x + 4 = -8x +12

Add 8x to each side

8x+4+8x = -8x+12 +8x

16x+4 = 12

Subtract 4 from each side

16x +4-4 = 12-4

16x = 8

Divide by 16

16x/16 =8/16

x = 1/2

Answer:

x = 1/2

Step-by-step explanation:

2(4x+2) = 4x - 12(x-1)

Expand brackets.

8x + 4 = 4x - 12x + 12

Subtract 4 on both sides.

8x = 4x - 12x + 12 - 4

Subtract 4x and add 12x on both sides.

8x - 4x + 12x = 12 - 4

Combine like terms.

16x = 8

Divide both sides by 16.

x = 8/16 = 1/2

Hey there! I'm happy to help!

We want to find the probability that the player makes at least seven out of eight free throws. First, we find the probability of them making seven free throws.

[tex]\frac{1}{2}^7=\frac{1}{128}[/tex]

Then, we find the probability of them making eight, which is another possibility that fits this.

[tex]\frac{1}{2}^8=\frac{1}{256}[/tex]

Now, we add the probability of these two events happening.

[tex]\frac{1}{128}+\frac{1}{256}=\frac{3}{256}[/tex]

Therefore, the probability that the player makes at least seven of eight free throws is 3/256 or about 1.17%

Have a wonderful day! :D

Step-by-step explanation:

If f(x) =x, is the father function, then all it's child function would be equally inclined to x and y-axis respectively.

If f(x) =x, is the father function, then all its child functions would be equally inclined to the x and y-axis respectively.

Each family of capabilities has a determining feature. A discern function is the best function that also satisfies the definition of a certain sort of function. As an instance, whilst we think about the linear capabilities which make up our own family of capabilities, the parent feature could be y = x.

Key commonplace points of linear determine features encompass the reality that the equation is y = x. Domain and variety are actual numbers. Slope, or fee of alternate, is steady.

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Answer:

a) Fixed cost = $50

b) Total variable cost is $15, while variable cost per unit is $0.15.

c) C = 50 + d0.15

d) Direct variation

e) The cost of renting a car for a day and driving a total of 800km is $170,

Step-by-step explanation:

a) What is the fixed cost?

Fixed cost is a cost that does not change with the level of activity. Fixed is incurred whether there is an activity, or there is no activity at all, that is, when the activity is zero.

Since cost, C, is equal to $50 when distance, d (km), is equal to zero in the table, the fixed cost is therefore equal to $50, i.e.:

Fixed cost = $50

b) What is the variable cost?

Variable cost is a cost that changes as the level of activity changes. From the table, the variable cost can be obtained by deducting the fixed cost from the total cost. This can be calculated using any of the distance, d (km), in the table.

Using the distance of 100 as an example, the total variable cost can be obtained as follows:

Variable cost = Total Cost at 100 distance - Fixed cost = $65 - $50 = $15

Note that variable cost per distance at 100 distance can be obtained as follows:

Variable cost per distance = $15 / 100 = $0.15

c) Write an equation relating your answer from part (a) and part (b)

Since,

C = Cost

d = distance (km)

Fixed cost = $50

Variable cost per distance = $0.15

Therefore, suppressing the dollar sign for simplicity purpose, an equation relating the above can be given as follows:

C = 50 + d0.15 ............................................. (1)

d) What kind of variation is this relationship showing?

This is a direct variation.

Direct variation is a variation in which an increase in one variable will lead to an increase in another variable.

For example in equation (1), a increase in d which is multiplied by $0.15 will lead to an increase in C.

e) Calculate the cost of renting a car for a day and driving a total of 800km.

This implies that d = 800.

Substituting d = 800 into equation (1), we have:

C = 50 + (800 * 0.15) = 170

Therefore, the cost of renting a car for a day and driving a total of 800km is $170.

Answer:

11 / 12 or 0.9167

Step-by-step explanation:

Given:

3/4 + 1/6

Find:

Value with expression

Computation:

"3/4 added to number 1/6"

3/4 + 1/6

By taking LCM

[9 + 2] / 12

11 / 12 or 0.9167

Answer:

y > 2x + 1

Step-by-step explanation:

(1 is the y intercept) 2/1 is the gradient so 2 up and 1 across

Concepts:

Answer:

First option and fifth option

-2x-1=3^(-x) and 2^(-x)+2= -5^x + 3 don't intersect.

Therefore, the graphs have no solution.

4x+21+3x-5=121

7x+16=121

x=15

angle ABD =4(15)+21=81

Answer:

15 pt

Step-by-step explanation:

to convert qt to pt you multiply by 2 so 7 and 1/2 times 2 is 15

Answer:

See below.

Step-by-step explanation:

So, we have the zeros -4 with a multiplicity of 1, zeros 2 with a multiplicity of 3, and f(0)=64.

Recall that if something is a zero, then the equation must contain (x - n), where n is that something. In other words, for a polynomial with a zero of -4 with a multiplicity of 1, then (x+4)^1 must be a factor.

Therefore, (x-2)^3 (multiplicity of 3) must also be a factor.

Lastly, f(0)=64 tells that when x=0, f(x)=64. Don't simply add 64 (like what I did, horribly wrong). Instead, to keep the zeros constant, we need to multiply like this:

In other words, we will have:

[tex]f(x)=(x+4)(x-2)^3\cdot n[/tex], where n is some value.

Let's determine n first. We know that f(0)=64, thus:

[tex]f(0)=64=4(-2)^3\cdot n[/tex]

[tex]64=-32n, n=-2[/tex]

Now, let's expand:

Expand:

[tex]f(x)=(x+4)(x^2-4x+4)(x-2)(-2)[/tex]

[tex]f(x)=(x^2+2x-8)(x^2-4x+4)(-2)[/tex]

[tex]f(x)=(x^4-4x^3+4x^2+2x^3-8x^2+8x-8x^2+32x-32)(-2)[/tex]

[tex]f(x)=-2x^4+4x^3+24x^2-80x+64[/tex]

This is the simplest it can get.

Answer:

Step-by-step explanation:

Given,

Radius ( r ) = 10

Height ( h ) = 6

pi ( π ) = 3.14

now, let's find the volume of given cone:

[tex]\pi {r}^{2} \frac{h}{3} [/tex]

Plug the values

[tex] = 3.14 \times {10}^{2} \times \frac{6}{3} [/tex]

Evaluate the power

[tex] = 3.14 \times 100 \times \frac{6}{3} [/tex]

Calculate

[tex] = 628 \: {units}^{3} [/tex]

Hope this helps..

Best regards!!

Answer:

The answer is 200π units³ .

Step-by-step explanation:

Given that the formula of volume of cone is V = 1/3×π×r²×h where r represents radius and h is height. Then, you have to substitute the value of radius and height into the formula :

[tex]v = \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]

[tex]let \: r = 10 \: , \: h = 6[/tex]

[tex]v = \frac{1}{3} \times \pi \times {10}^{2} \times 6[/tex]

[tex]v = \frac{1}{3} \times \pi \times 600[/tex]

[tex]v = 200\pi \: {units}^{3} [/tex]

Answer:

15%

Step-by-step explanation:

To calculate the margin of error, we can adopt this formula

Margin of error = critical value* (standard deviation/sqrt of sample size)

Where critical value is 2.33, sd is 0.78 and sample size is150.

Thus, we have:

Margin of error = 2.33*(0.78/√150)

Margin of error = 2.33*(0.78/12.2474)

Margin of error =2.33*0.06369

Margin of error = 0.1484 which is a 15% margin of error

If it has a single zero that means it has to be just touching the x-axis with its tip.

We know that if it has only one zero, the discriminant equals 0.

So,

[tex]D=b^2-4ac=0\implies (-k)^2-4(1)(9)=0[/tex]

Solving for k,

[tex]k=\pm\sqrt{36}=\boxed{\pm{6}}[/tex].

Hope this helps.

Answer:

C and E

Step-by-step explanation:

He got it on ap.ex

The area of the pyramid can be found using the formula SA = BA + LA and SA= BA + 1/2ps option (C) and (E) are correct.

In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the center of the square.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a pyramid with a square base:

The perimeter of the base is p

The slant height is s.

The base area is BA

The lateral area is LA.

We can find the area of the pyramid as follows:

SA = BA + LA

SA= BA + 1/2ps

Thus, the area of the pyramid can be found using the formula SA = BA + LA and SA= BA + 1/2ps option (C) and (E) are correct.

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Answer:

Step-by-step explanation:

A basketball is basically a sphere, so it suffices to calculate the surface are of the ball to determine the amount of required material. Given a sphere of radius r we have that the surface area is [tex]4\pi r^2[/tex]

In this case, r = 11.14 cm. So the area is aproximately 1159.48 squared cm. (1159.48 = [tex]4\pi (11.14)^2[/tex])

Answer:

S = [0.2069,0.7931]

Step-by-step explanation:

Transition Matrix:

[tex]P=\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

Stationary matrix S for the transition matrix P is obtained by computing powers of the transition matrix P ( k powers ) until all the two rows of transition matrix p are equal or identical.

Transition matrix P raised to the power 2 (at k = 2)

[tex]P^{2} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

[tex]P^{2} =\left[\begin{array}{ccc}0.2203&0.7797\\0.2034&0.7966\end{array}\right][/tex]

Transition matrix P raised to the power 3 (at k = 3)

[tex]P^{3} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

[tex]P^{3} =\left[\begin{array}{ccc}0.2203&0.7797\\0.2034&0.7966\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

  [tex]P^{3} =\left[\begin{array}{ccc}0.2086&0.7914\\0.2064&0.7936\end{array}\right][/tex]

Transition matrix P raised to the power 4 (at k = 4)

[tex]P^{4} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

[tex]P^{4} =\left[\begin{array}{ccc}0.2086&0.7914\\0.2064&0.7936\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

[tex]P^{4} =\left[\begin{array}{ccc}0.2071&0.7929\\0.2068&0.7932\end{array}\right][/tex]

Transition matrix P raised to the power 5 (at k = 5)

[tex]P^{5} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

[tex]P^{5} =\left[\begin{array}{ccc}0.2071&0.7929\\0.2068&0.7932\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

[tex]P^{5} =\left[\begin{array}{ccc}0.2069&0.7931\\0.2069&0.7931\end{array}\right][/tex]

P⁵ at k = 5 both the rows identical. Hence the stationary matrix S is:

S = [ 0.2069 , 0.7931 ]

Answer:

The answer for dy/dx is 3/4t .

Step-by-step explanation:

First, you have to differentiate x and y expressions in term of t :

[tex]x = a {t}^{4} [/tex]

[tex] \frac{dx}{dt} = 4a {t}^{3} [/tex]

[tex]y = a {t}^{3} [/tex]

[tex] \frac{dy}{dt} = 3a {t}^{2} [/tex]

Next, we can assume that dy/dt ÷ dx/dt = dy/dx. So we have to substitute the expressions :

[tex] \frac{dy}{dt} \div \frac{dx}{dt} = \frac{dy}{dt} \times \frac{dt}{dx} = \frac{dy}{dx} [/tex]

[tex] \frac{dy}{dx} = 3a {t}^{2} \div 4a {t}^{3} [/tex]

[tex] \frac{dy}{dx} = 3a {t}^{2} \times \frac{1}{4a {t}^{3} } [/tex]

[tex] \frac{dy}{dx} = \frac{3}{4t} [/tex]