(SAT Prep) Find the value of x

The equation has two real and equal roots for [tex]k = \frac{5}{6}[/tex]

In this question, we use the concept of the solution of a quadratic equation to solve it, considering that a quadratic equation in the format:

[tex]ax^2 + bx + c = 0[/tex]

has two equal solutions if [tex]\Delta = b^2 - 4ac[/tex] is 0.

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In this question:

The equation is:

[tex](2k+1)x^2 + 2x = 10x - 6[/tex]

Placing in the correct format:

[tex](2k+1)x^2 + 2x - 10x + 6 = 0[/tex]

[tex](2k+1)x^2 - 8x + 6 = 0[/tex]

Thus, the coefficients are: [tex]a = 2k + 1, b = -8, c = 6[/tex]

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Delta:

We want it to be positive, so:

[tex]\Delta = b^2 - 4ac[/tex]

[tex]\Delta = 0[/tex]

[tex]b^2 - 4ac = 0[/tex]

[tex](-8)^2 - 4(2k+1)(6) = 0[/tex]

[tex]64 - 48k - 24 = 0[/tex]

[tex]-48k + 40 = 0[/tex]

[tex]-48k = -40[/tex]

[tex]48k = 40[/tex]

[tex]k = \frac{40}{48}[/tex]

[tex]k = \frac{5}{6}[/tex]

The equation has two real and equal roots for [tex]k = \frac{5}{6}[/tex]

A similar question is found at https://brainly.com/question/12144265

Answer:

1,3,5

Step-by-step explanation:

81 is a perfect square so it can be written as an integer

11.8 is rational because it can be written as a fraction (107/9)

sqrt(6) isn't a perfect square so it is irrational

3/7 is a fraction so it is rational

8.57 is a terminating decimal so it is rational

Try this

(x^2 + x - 12) + (x^2 - 8x + 16)

2y - 1

√36

i wanted to help you! :)

Answer:

[tex]\frac{3}{3}[/tex] = 1   (everything basically cancels)

Step-by-step explanation:

[tex]g(x) = \sqrt{x - 5} + 2 \\ g(5) = \sqrt{5 - 5} + 2 = 0 + 2 \\ g(5) = 2[/tex]

I hope I helped you^_^

Answer:

Hello,

[tex]316^2=99856[/tex]

Step-by-step explanation:

Since

[tex]\\\sqrt{99999} =316,22618...\\\\The\ largest\ 5\ digit\ number\ which\ is\ a \ perfect\ square\ is\ 316^2=99856}\\[/tex]

Answer:

area ≈ 12.505

perimeter ≈  16.1684

Step-by-step explanation:

We are given

- the radius of the circle (and therefore area of the circle)

- the area of the triangle

We want to find

- angle AOB/AOT. We want to find this because 360/the angle gives us how many OABs fit into the circle. For example, if AOT was 30 degrees, 360/30 = 12 (there are 360 degrees in a circle, so that's where 360 comes from). The area of the circle is equal to πr² = π6² = 36π, and because AOT is 30 degrees, there are 12 equal parts of sector OAB in the circle, so 36π/12=3π would be the area of the sector. A similar conclusion can be reached from the circumference instead of the area to find the distance between A and B along the circle, and OA + AB + BO = the perimeter of the minor sector.

First, we can say that OAT is a right triangle because a tangent line is perpendicular to the line from the center to the point on the circle, so AT is perpendicular to OA. This forms two right angles, one of which is OAT

One thing that we can start to solve is AT. We know that the area of a triangle is equal to base * height /2, and the height of this triangle is AO, with the base being AT. Therefore, we can say

15 = AO * AT / 2

15 = 6 * AT / 2

15 = 3 * AT

divide both sides by 3 to isolate AT

AT = 5

Because OAT is a right triangle, we can say that the hypotenuse ² =  the sum of the squares of the two other lengths. The hypotenuse is opposite of the largest angle (in this case, the right angle, as in a right triangle, the right angle is always the largest), so it is OT in this case. The other two sides are OA and AT, so we can say that

OA² + AT² = OT²

5²+6² = OT²

25+36=61=OT²

square root both sides

OT = √61

Next, the Law of Sines states that

sinA/a = sinB/b = sinC/c with angles A, B, and C with sides a, b, and c. Corresponding sides are opposite their corresponding angles, so in this case, AT corresponds to angle AOT, OT corresponds to angle OAT, and AO corresponds to angle ATO.

We want to find angle AOT, as stated earlier, so we have

sin(OAT)/OT = sin(ATO)/OA = sin(AOT)/AT

We know the side lengths as well as OAT/sin(OAT) and want to figure out AOT/sin(AOT), so one equation that helps us get there is

sin(OAT)/OT = sin(AOT)/AT, encompassing our 3 known values and isolating the one unknown. We thus have

sin(90)/√61 = sin(AOT) /5

plug in sin(90) = 1

1/√61 = sin(AOT)/5

multiply both sides by 5 to isolate sin(AOT)

5/√61 = sin(AOT)

we can thus say that

arcsin(5/√61) = AOT ≈39.80557

As stated previously, given ∠AOT, we can find the area and perimeter of the sector. There are 360/39.80557 ≈ 9.04396 equal parts of sector OAB in the circle. The area of the circle is πr² = 36π, so 36π / 9.04396 ≈ 12.505 as the area. The circumference is equal to π * diameter = π * 2 * radius = 12 * π, and there are 9.04396 equal parts of arc AB in the circumference, so the length of arc is 12π / 9.04396 ≈ 4.1684. Add that to OA and OB (both are equal to the radius of 6, as any point from the center to a point on the circle is equal to the radius) to get 6+6 + 4.1684 = 16.1684 as the perimeter of the sector

Answer:

$109 and 35%

Step-by-step explanation:

49.05 is the sale price and the discount is 55%. What’s the original price?

price/ 1- discount

49.05/ 1 - 0.55

49.05/ 0.45

109

for the other part

to find the discount subtract final price from original price

94 - 61.10 = 32.9

Which would be 35% in percent form.

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

[tex]\frac{14}{30}[/tex] is not equivalent to [tex]\frac{2}{5}[/tex] in the list of fractions [tex]\frac{18}{45}, \frac{14}{30} , \frac{x}{y} \frac{10}{25}, \frac{8}{20}, \frac{16}{40}[/tex].

Equivalent fractions represent the same value even though they look different.

We know we can find an equivalent fraction of a given fraction by or dividing both the numerator and denominator of the given fraction with the same number (maybe LCM or HCF of the numerator or denominator).

[tex]\frac{18}{45}=\frac{18/9}{45/9}=\frac{2}{5}[/tex] (since [tex]9[/tex] is HCF of [tex]18, 45[/tex])

[tex]\frac{14}{30}=\frac{14/2}{30/2}=\frac{7}{15}[/tex] (since [tex]2[/tex] is HCF of [tex]7, 15[/tex])

[tex]\frac{10}{25} =\frac{10/5}{25/5} =\frac{2}{5}[/tex] (since [tex]5[/tex] is HCF of [tex]10, 25[/tex])

[tex]\frac{8}{20} =\frac{8/4}{20/4} =\frac{2}{5}[/tex] (since [tex]4[/tex] is HCF of [tex]8, 20[/tex])

[tex]\frac{16}{40} =\frac{16/8}{40/8} =\frac{2}{5}[/tex] (since [tex]8[/tex] is HCF of [tex]16, 40[/tex])

Thus, [tex]\frac{14}{30}[/tex] is not equivalent to [tex]\frac{2}{5}[/tex].

Learn more about Equivalent fractions here- https://brainly.com/question/17912

#SPJ2

We conclude that the equation x = y^4 satisfies x = 256.

First, we know that:

y^4 - 256 = 0

With this equation, we can find the value of y, it will give:

y^4 = 256

Then:

y = 256^(1/4) = 4

Now if we have the equation x = y^4, we can write:

x = y^4 = 256

x = 256

We conclude that the equation x = y^4 satisfies x = 256.

If you want to learn more about equations:

https://brainly.com/question/13763238

#SPJ1

Answer:

∠ DFE = 15°

Step-by-step explanation:

The inscribed angle DFE is half the measure of its intercepted arc, that is

∠ DFE = [tex]\frac{1}{2}[/tex] DE = [tex]\frac{1}{2}[/tex] × 30° = 15°

Answer:

<DFE = 15

Brainliest, please!

Step-by-step explanation:

<DFE is an inscribed angle. An inscribed angle measures half as much as it's opposite arc.

30 x 1/2 = 15

Answer:

upper quartile

Step-by-step explanation:

upper quartile

The choose C. –2/15

(-2/15) +(-13/5) =(-13/5) +a/b

a/b = (-2/15)+(-13/5) - (-13/5)

a/b = (-2/15) - ( 39/15) +(39/15)

a/b = –2/15

I hope I helped you ^_^

Answer: option 3: a/b = (-2/15)

Step-by-step explanation:

See here when we solve this

(-2/15)+(-13/5) = (-13/5)+a/b

(-2/15) = (-13/5)+a/b-(-3/15)

(-2/15) = a/b

please click thanks and mark brainliest if you like :)

Answer:

5

Step-by-step explanation:

[tex]5^{2}[/tex] = 25

25 * 2 = 50

50 - 3 = 47

Hope that this helps!

Answer:

Step-by-step explanation:

let the number be x

Square of a number: x²

Twice the square of a number = 2*x² = 2x²

Three less than twice the square of a number = 2x² - 3

2x² - 3 = 47     {Add 3 to both sides}

2x² = 47 + 3

2x² = 50        {Divide both sides by 2}

 x² = 50/2

x² = 25          Take square root

x = √25

x = 5

Answer:

n=1/8

Step-by-step explanation:

-8n+34=6(5+4n)

We move all terms to the left:

-8n+34-(6(5+4n))=0

We add all the numbers together, and all the variables

-8n-(6(4n+5))+34=0

We calculate terms in parentheses: -(6(4n+5)), so:

6(4n+5)

We multiply parentheses

24n+30

Back to the equation:

-(24n+30)

We get rid of parentheses

-8n-24n-30+34=0

We add all the numbers together, and all the variables

-32n+4=0

We move all terms containing n to the left, all other terms to the right

-32n=-4

n=-4/-32

n=1/8

Answer:

n= 0.125 or 1/8

Step-by-step explanation:

Distrubute 6 into (5+4n). It should give you 30+24n.

The equation should now look like this: -8n+34=30+24n.

Swap -8n with 30, giving -30+34=8n+24n. Add the numbers and the pronumerals together.

Now it will look like 4=32n. Divide the numbers, but unfortunately the number is small so the answer will have to be a decimal or a fraction. So it's 0.125 or 1/8.

If I didn't explain everything or something is wrong, please comment. I just signed up, so it's my first time using this.

Answer:

Step-by-step explanation:

6. Yes: these two angles are opposite 2 equal line.

7. No: We don't know that AC bisects <JAD

8. No: We don't know that JCA or DCA are right angles.

9. Yes. Both angles have AC in common. JD is a straight line which has 180 degrees. AC intersects a JD and creates 2 angles. We know their total but not their equality.

10. Yes. They are given as equal.

Not everything you see is true just because it looks that way.

Answer:

c. 5 - 17

Step-by-step explanation:

a. -15 - 3 = -18

b. -3 - (-9) = 6

c. 5 - 17 = -12

d. -6 - (-6) = 0

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{Option A. \boxed{\bf \downarrow}}[/tex]

[tex]\huge\textsf{- 15 - 3}\\\huge\textsf{= -15 + (-3)}\\\huge\textsf{= \bf -18}\\\boxed{\huge\textsf{\bf -18 \boxed{\neq} -12}}\\\bullet\huge\text{ \bf Option A. cannot be your result.}[/tex]

[tex]\huge\text{Option B. }\boxed{\downarrow}[/tex]

[tex]\huge\textsf{-3 - (-9)}\\\huge\textsf{= -3 + 9}\\\huge\textsf{= \bf 6}\\\boxed{\huge\textsf{\bf 6 \boxed{\neq} -12}}\\\bullet\huge\text{\bf Option B. cannot be your result.}[/tex]

[tex]\huge\text{Option C. \boxed{\downarrow}}[/tex]

[tex]\huge\textsf{5 - 17}\\\huge\textsf{= 5 + (-17)}\\\huge\textsf{= \bf -12}\\\boxed{\bf -12 \ \boxed{=} -12}\\\huge\text{\bf Option C. could be the result.}[/tex]

[tex]\huge\text{Option D. \boxed{\downarrow}}[/tex]

[tex]\huge\textsf{-6 - (-6)}\\\huge\textsf{= -6 + 6}\\\huge\textsf{= \bf 0}\\\boxed{\bf 0 \ \boxed{\neq} -12}\\\huge\text{\bf Option D. cannot be your result.}[/tex]

[tex]\boxed{\huge\textsf{Answer: \bf Option C. \underline{\underline{5 - 17}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\boxed{\huge \boxed{\frak {Amphitrite1040:)}}}[/tex]

Answer:

-35

Step-by-step explanation

A predecessor is something that came before the current version, and -36 is negative so before -36 is -35

Answer:

the correct answer is -34

Step-by-step explanation:

A predecessor is something that came before the current version.

hope it helps you

Answer:

56

Step-by-step explanation:

Answer:

56 hours

Step-by-step explanation:

I divided 384 dollars by 3w hours and then was Sue made 12 an hour. Then I tried mukyiplong different times until I discovered 12×56=672. So, 56 hours

Answer:

wqhg

Step-by-step explanation:

its situated in u.s, in quahog , rhode island

Answer:

Step-by-step explanation:

Iihgghh

[tex]\sf \longrightarrow \: \:Surface \: area \: of \: cylinder \: = \: 2\pi \: r \: h \: + \: 2\pi \: {r}^{2} [/tex]

[tex]\sf \longrightarrow \: \: r \: = \: \frac{Diameter}{2} \\ [/tex]

[tex]\sf \longrightarrow \: \: r \: = \: \frac{12}{2} \\ [/tex]

[tex]\sf \longrightarrow \: \: r \: = \: \cancel\frac{12}{2} \: \: ^{6} \\ [/tex]

[tex]\sf \longrightarrow \: \: r \: = \:6 \: ft[/tex]

[tex]\sf \longrightarrow \: \: h \: = \: 15 \: ft[/tex]

[tex]\sf \implies \: \:2 \: \times \: \pi \times \: 6 \: \times \: 15 \: \: + \: \: 2 \: \times \: \pi \times \: {6}^{2} [/tex]

[tex]\sf \implies \: \:2 \: \times \: \pi \times \: 90 \: \: + \: \: 2 \: \times \: \pi \times \: 36[/tex]

[tex]\sf \implies \: \:180 \: \pi \: + \: \: 72 \: \pi[/tex]

[tex]\sf \implies \: \:252 \: \pi[/tex]

Hence, the surface area of cylinder is 252 π ft²

Using Pythagorean theorem

[tex]\\ \sf\longmapsto BC^2=AB^2+AC^2[/tex]

[tex]\\ \sf\longmapsto BC^2=7^2+3^2[/tex]

[tex]\\ \sf\longmapsto BC^2=49+9[/tex]

[tex]\\ \sf\longmapsto BC^2=58[/tex]

[tex]\\ \sf\longmapsto BC=\sqrt{58}[/tex]

Answer:

O Yes, because 1 kilogram = 1000 grams, and 1 liter = 100 centiliters.

Yes, because 1 gram per liter is the same as 1 kilogram per centiliter.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

No solution because the line will never intersect each other (cuz the gradient is the same)

Answer:

7 and - infinity

Step-by-step explanation:

The function is decreasing in nature. The function has a maxima when x is near 7 and as the function is decreasing, the function will approach -infinity as x approaches positive infinity.

Answer:

hope it helps you

Step-by-step explanation:

mark it brainliest answer