can someone help me solve this logarithm function

Answer:

  k = -35.5

Step-by-step explanation:

When α and β are zeros of the polynomial 2x² +5x +k, it can be written in factored form as ...

  2x² +5x +k = 2(x -α)(x -β)

When the factored form is expanded, it becomes ...

  = 2x² -2(α+β)x +2αβ

Comparing this to the original, we see that ...

__

Then the given expression can be used to find k:

  α +β = -5/2 . . . . . solved the first relation for α+β

  (α +β)² = (α² +β² +αβ) +αβ = 24 +αβ

  (-5/2)² = 24 +αβ . . . . . . . use -5/2 for α+β

  αβ = 25/4 -24 = -17.75 . . . . . solve for αβ

Then the value of k is ...

  k = 2αβ = 2(-17.75)

  k = -35.5

Answer:

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms. This would create the effect of a constant multiplier.

-- Credit -- libretexts

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!

Answer:

An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference. A geometric sequence is a sequence with the ratio between two consecutive terms constant. This ratio is called the common ratio.

Step-by-step explanation:

Answer:

B. [0.802], [0.978]

Step-by-step explanation:

n=49

p=.89

confidence level of 95% has a z value of 1.960

z*= 1.960

z*=qnorm(1.95/2)

p+/-z* multiplied by sqrt[ P * ( 1 - P ) / n ]

p+/-z*times(√(p)(1-p)/n)

.89+/-1.960* (square root of (.89)(.11)/49))

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mathuheducathyMath2311TestsTest2032311PT3helppdf

Answer:

[tex]4 \cot {}^{2} (45) - 3 \tan {}^{2} (60) + 2 \sec {}^{2} (60) = 3 \\ [/tex]

[tex]LHS = 4 \cot {}^{2} (45) - 3 \tan {}^{2} (60) + 2 \sec {}^{2} (60) \\[/tex]

let us first take a look at the values of the trigonometric ratios given in the question so that we get quite clear about what is to be done.

here ,

[tex] \cot(45) = 1 \\ \\ \tan(60) = \sqrt{3} \\ \\ \sec(60) = 2[/tex]

now ,

we just have to plug in the values considering certain other things given in the question and we're done!

so let's start ~

[tex]4(1) {}^{2} - 3( \sqrt{3} ) {}^{2} + 2(2) {}^{2} \\ \\ \dashrightarrow \: 4(1) - 3(3) + 2(4) \\ \\ \dashrightarrow \: 4 - 9 + 8 \\\\ \dashrightarrow \: 12 - 9 \\ \\\dashrightarrow \: 3 = RHS[/tex]

hence , proved ~

hope helpful :D

Answer:

x = ±1

Step-by-step explanation:

x² - 1 = 0

x² = 1

x = ±1

I hope this helps!

Answer:

|-86| = 86

The absolute value of -86 is 86!

Tip : The absolute value is always positive.

Answer:

|-86| = 86

Step-by-step explanation:

Answer:

x/4

Step-by-step explanation:

Answer:

See below for answers and explanations

Step-by-step explanation:

Part A

The equation is in the form of [tex](x-h)^2+(y-k)^2=r^2[/tex], which happens to be the equation of a circle

Part B

For the equation of the circle, its center is at [tex](h,k)\rightarrow(5,-11)[/tex]

Part C

Since [tex]r^2=49[/tex], then the radius of the circle is [tex]r=7[/tex]

Part D

The area of a circle is [tex]A=\pi r^2[/tex], so the area is [tex]49\pi[/tex] square units.

Answer:

shorter than, shorter than, will not

Step-by-step explanation:

First, we can find out the diagonal of the base of the box using Pythagoras' theory - a² + b² = c²

32² + 8² = 1088

c = √1088 = 32.984845

This means that the diagonal of the base of the box is shorter than the bat (32.984845 is less than 34)

Next, we can work out the interior diagonal, again using Pythagoras' theory - a² + b² = c²

32.984845² + 6² = 1124

c = √1124 = 33.52610923

This means that the length of the interior diagonal of the box is shorter than the bat (33.52610923 is less than 34)

Therefore, Julian's bat will not fit in the box.

Hope this helps!

1 is the answer......

WHATS UP KID

Answer:

the answer is

[tex] \frac{12 {c}^{8} }{ {d}^{2} } [/tex]

Step-by-step explanation:

[tex] \frac{12}{ {c}^{ - 8} {d}^{2} } [/tex]

Step-by-step explanation:

Answer:

\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149

Step-by-step explanation:

Standard equation of a circle:  \sf (x-a)^2+(y-b)^2=r^2(x−a)2+(y−b)2=r2

(where (a, b) is the center and r is the radius of the circle)

Substitute the given center (-14, -5) into the equation:

The time when Hank's Movers will cost less is the point when the total charges is both Movers are Equal, the time is at 3 hours

Given Data

For Acme, the expression for the total charges is

Total = 45+40x ----------1

For Hank, the expression for the total charges is

Total = 55x ----------------2

Equating both expressions we have

45+40x = 55x

collect like terms

45 = 55x-40x

45 = 15x

divide both sides by 15

x = 45/15

x = 3 hours

Learn more about algebra here:

https://brainly.com/question/22399890

Polynomial is an expression that consists of indeterminates(variable) and coefficients. The degree of the polynomial will be 5.

What are polynomials?

Polynomial is an expression that consists of indeterminates(variable) and coefficients, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

The polynomial with zeros 0,-3, and 2 with multiplicities 2,1, and 2, respectively, can be written as,

[tex](x-0)^2(x+3)^1(x-2)^2\\\\= x^2(x+3)(x^2+4-4x)\\\\=(x^3+3x^2)(x^2+4-4x)\\\\=x^5 +4x^3-4x^4+3x^4+12x^2-12x^3\\\\=x^5 -x^4-8x^3+12x^2\\[/tex]

Hence, the degree of the polynomial will be 5.

Learn more about Polynomial:

https://brainly.com/question/17822016

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Answer:

x = 63  units

Step-by-step explanation:

130 tan 39   = entire  L side

130 tan 39  -  130 tan 18 = x = 63

Answer:

1/2

Step-by-step explanation:

3/4 of 2/3 = 3/4 × 2/3 = 6/12 = 1/2

Answer:

Divide 108 by 12 since there are 12 inches in a foot.

108 ÷ 12 = 9

Veronica needs to divide 108 inches by 12 to get 9 feet.

To convert inches to feet, Veronica needs to divide the number of inches by 12, as there are 12 inches in a foot.

Given that Veronica wants to convert 108 inches to feet, she should perform the following calculation:

108 inches ÷ 12

= 9 feet

Therefore, Veronica needs to divide 108 inches by 12 to get 9 feet.

To learn more on Conversion factor click:

https://brainly.com/question/32020768

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Answer:

Step-by-step explanation: first one way that you can answer this question is to use a numberline, so you start at zero and go to the left of the numberline and the numbers behind -7 would be -8,-9, and or ,-10 they are all less than negative seven

Answer:

17

Step-by-step explanation:

...................

[tex]12x\sqrt{\cfrac{3}{2}}~~ = ~~6\sqrt{3}\implies (6)(2)x\cdot \cfrac{\sqrt{3}}{\sqrt{2}}~~ = ~~6\sqrt{3}\implies \cfrac{(2x)(6\sqrt{3})}{\sqrt{2}}=6\sqrt{3} \\\\\\ \cfrac{2x}{\sqrt{2}}=\cfrac{6\sqrt{3}}{6\sqrt{3}}\implies \cfrac{2x}{\sqrt{2}}=1\implies 2x=\sqrt{2}\implies x=\cfrac{\sqrt{2}}{2}[/tex]

Answer:

180-108=72.

72/3=24.

24x2=48

Step-by-step explanation:

[tex]see \: if \: 10 \: are \: left \: then \: we \: hve \: spent \\ 250 - 10 = 240 \: dollars \\ [/tex]

hence

[tex]six \: flasks \: cost \: 240 \: dollars \\ so \: if \: we \: divide \: 240 \: by \: 6 \: we \: get \: 40 \: \\ [/tex]

so one flask costs 40$

Answer:

y+6.75

Step-by-step explanation:

Answer: y+6.75

Follow Order of Operations

y+9*3/4

9*3/4 = 6.75

y+6.75

Answer:

30%

Step-by-step explanation:

The sign means that x can be equal to or LESS than -3. The only ones are -3 and -5. 0.17+0.13=0.30

Answer: A: The data is a random sample from the population of interest

Step-by-step explanation: kahn