Find the value of the constant a for which the polynomial x^3 + ax^2 -1 will have -1 as a root. (A root is a value of x such that the polynomial is equal to zero.)

I am trying to simplify a difference quotient with the form

f(x+h)−f(h)/h

if f(x)=2/x2 I have attempted to cancel out the denominator of the numerator by the least common denominator method. I know that I can solve this using implicit differentiation, but am trying to use the difference quotient to get the partial derivative

Here is my work so far:

f(x+h)−f(x)(h)

=f(2/(x+h)2)−f(2/x2)h

=(2/(x+h)2)−(2/x2)h

here I multiply by the LCD

=(2(x2)−2(x+h)2)/(x2(x+h)2)h

Here I expand out the top and cancel out 2x2

=(2x2−(2x2+4xh+2h2))/(x2(x+h)2)h

=−(4xh+2h2)/(x2(x+h)2))h

Here I think I should multiply by 1/h to get rid of the h on the bottom

I end up with:

=4xh+2h2hx2(x+h)2

factor out an h

=−4x+2hx2(x+h)2

Answer:

It is 7.5

Step-by-step explanation:

Answer:

exponential growth

Step-by-step explanation:

f(x) is in the form  a* b^x

where a is the initial value and b is the growth/ decay factor

since b > 1 it is growth

This is the exponential form of a function

We have exponential growth

Answer:

Step-by-step explanation:

Correct choice is C

[tex]\\ \sf\longmapsto \dfrac{2x}{3}-7=5[/tex]

[tex]\\ \sf\longmapsto \dfrac{2x-21}{3}=5[/tex]

[tex]\\ \sf\longmapsto 2x-21=5(3)[/tex]

[tex]\\ \sf\longmapsto 2x-21=15[/tex]

[tex]\\ \sf\longmapsto 2x=15+21[/tex]

[tex]\\ \sf\longmapsto 2x=36[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{36}{2}[/tex]

[tex]\\ \sf\longmapsto x=18[/tex]

Answer:

Below

Step-by-step explanation:

Part A: -1 and 2.5

Part B: The vertex is a minimum

Part C: tbh, I'm not quite sure about this part but just use parts A and B to answer :)

(you can also use the website desmos. com/calculator as a graphing calculator)

Answer:

sqrt(3) + sqrt(7)

Step-by-step explanation:

3*sqrt(7) / sqrt(21) = 3/sqrt(3)

If you rationalize the denominator, you get 3*sqrt(3)/3. The threes cancel

You are left with sqrt(3)

7sqrt(3)/sqrt(21) = 7 / sqrt(7)

If you rationalize the denominator, you get

7  sqrt(7)/ 7 = sqrt(7)

The 7s have been canceled out

The answer is

sqrt(3) + sqrt(7)

$\sf\underline\bold\blue{Information\:given\:in\:the\:question:}$

$\space$

$\sf\underline\bold\blue{What\:we\:have\:to\:find?}$

$\space$

$\sf\underline\bold\blue{Answer:}$

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$\sf\underline\bold\blue{Calculations:}$

Here we have the value of the circle's diameter that is 20inches. So, first we have to calculate the radius of the circle using the formula :

$\mapsto$ $\sf\bold{Radius=}$ $\sf\dfrac{Diameter}{2}$

$\space$

$\sf\underline\bold\blue{Calculating\:the\:required\:values:}$

$\mapsto$ $\sf\bold{Radius=}$ $\sf\dfrac{20}{2}$

$\sf{Convert \: to \: the\:lowest\:term(Divide),}$

$\mapsto$ $\sf\underline\bold{Radius=10}$

☆Now we know the value of the radius . So now let's calculate the area of the circle.

$\space$

$\sf\bold{Area\:of\:circle:}$ π$\sf{ r \: ^{2} }$

$\sf\bold{Evaluating \: the\:required\:values:}$

$\sf\bold{Area\:of\:circle=3.1415(10)^2}$

$\space$

$\sf\bold{Area\:of\:the\:circle=3.1415\times10\times10}$

$\sf\bold{Now,}$

$\sf\bold{Area\:of\:the\:circle:3.1415\times100}$

$\space$

$\sf\underline\bold\green{Thus,Area\:of\:the\:circle\: is \: 314.15}$

____________________________

You're going to have to break all of these identities into sin and cos, and then just resolve them like normal.

The expression [tex]\frac{tan x + cot x}{cosec x* cos x} = sec ^{2} x[/tex] is proved .

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.

formulas for trigonometric ratios is:

sin θ = 1/cosec θ

cos θ = 1/sec θ

tan θ = 1/cot θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

According to the question

[tex]\frac{tan x + cot x}{cosec x* cos x} = sec ^{2} x[/tex]

[tex]\frac{\frac{sin x}{cos x} + \frac{cos x}{sin x}}{\frac{1}{sin x}*cosx } = sec^{2} x[/tex]

[tex]\frac{\frac{sin^{2}x + cos^{2}x }{sinx cosx} }{\frac{cosx}{sinx} } = sec^{2} x[/tex]

[tex]\frac{\frac{1}{sinx cosx} }{\frac{cosx}{sinx} } = sec^{2} x[/tex]

[tex]\frac{\frac{1}{cosx} }{\frac{cosx}{1} } = sec^{2} x[/tex]

[tex]\frac{1}{cos^{2} x} =sec^{2} x[/tex]

[tex]sec^{2} x =sec^{2} x[/tex]

L.H.S = R.H.S

Hence, The expression [tex]\frac{tan x + cot x}{cosec x* cos x} = sec ^{2} x[/tex] is proved  .

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Answer:

x=0,1,±2

Step-by-step explanation:

x^3(x^2-5)=-4x

x^2(x^2-5)=-4

Take x^2=a, we have

a*(a-5)=-4, a^2-5a+4=0, (a-1)(a-4)=0, a=1,4

x^2=0, 1, 4. x=0,1,±2

Answer:

x = 1 and x = 2

Step-by-step explanation:

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

x² = 4 or x² = 1

Since x > 0, the negative integers are rejected and the solutions to this equations are x = 1 and x = 2

Positive parabola that has a minimum.

It’s positive if it opens upward, negative if it opens downward. It has a minimum if it opens upward, and maximum when it opens downward.

Answer:

x=27

y=25

c=12

n=70

Step-by-step explanation:

a- x-10=17

isolate the x by adding 10 to both sides

x=27

b- y+7=32

isolate the y by subtracting 7 from both sides

y=25

c- 4c=48

isolate c by dividing both sides by 4

c=12

d- n/5=14

isolate the n by multiplying both sides by 5

n=70

Answer:

a) [tex]x-10=17[/tex]

Add 10 to both sides:-

----------

b) [tex]y+7=32[/tex]

Subtract 7 from both sides

------------

c) [tex]4c=48[/tex]

Divide both sides by 4

------------

d) [tex]\frac{n}{5}=14[/tex]

Multiply both sides by 5

OAmalOHopeO

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

Answer:

=2^5+5^5

=32+3125

=3157

Hi there!

[tex]\large\boxed{\frac{1}{4}, -\frac{3}{2}}[/tex]

13y² + 10y - 3 = 5y²

Begin by moving all terms to one side:

13y² + 10y - 3 - 5y² = 0

Combine like terms:

8y² + 10y - 3 = 0

Factor using the guess-and-check method.

(4y - 1)(2y + 3) = 0

Set each factor equal to 0 to find the solutions:

4y - 1 = 0

4y = 1

y = 1/4

2y + 3 = 0

2y = -3

y = -3/2

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].

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Step-by-step explanation:

a fraction of a number out of 100%

Answer and step-by-step explanation:

Percent (%) means per 100

A percentage is a number or ratio expressed as a fraction of 100

Example 50% of 8 = 8*50/100 = 4

Answer:

Number of batches of soup = 8 2/3 batches

Step-by-step explanation:

Each batch of soup = 3/4 pounds of potatoes

Total pounds of potatoes available = 6 1/2 pounds

How many batches of soup did Monique make?

Number of batches of soup = Total pounds of potatoes available / Each batch of soup

= 6 1/2 pounds ÷ 3/4 pounds

= 13/2 ÷ 3/4

= 13/2 × 4/3

= (13 * 4) / (2 * 3)

= 52/6

= 8 4/6

= 8 2/3

Number of batches of soup = 8 2/3 batches

Answer:

B 13/2 divided by 3/4
E 13/2 (4/3)

The perimeter = sum of all sides

= 120 + 80 + 50

= 250

So 250 - 3

247

Left space for gate

Now cost of fencing = Rs 20/per meter

= 247 × 20

= Rs 4,940

Now the area of the triangular park can be found using heron's formula

S = (a+b+c)/2

S = (120+80+50)/2

S = 250/2

S = 125

Now

Herons formula = √s(s-a)(s-b)(s-c)

√125(125-120)(125-80)(120-50)

√125(5)(45)(70)

√5×5×5×5×5×3×3×5×14

After Making pairs

5×5×5×3√14

375√14

Therefore 375√14m is the area of the triangular park

Must click thanks and mark brainliest

$\sf\underline\bold{Answer:}$

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$\sf\underline\bold{Step-by-Step:}$

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$\sf\bold{Given(In \:the\:Q):}$

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$\sf\bold{To \: find:}$

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$\sf\small{☆Area\:to\:be\:planted=Area \: of \: ∆ABC}$

$\space$

$\sf\underline\bold{Calculating\:area\:of\:∆ABC:}$

$\space$

Use heron's formula to find the area of the triangle.

$\space$

$\mapsto$ $\sf\small{Heron's\:formula=}$

[tex]\sf\sqrt{s(s-a)(s-b)(s-c)}[/tex]

$\space$

$\sf\bold{Now,find\:semi\:parameter:-}$

$\sf\small{Perimeter\:of\:the\:∆=120+80+50=250}$

$\sf\small{Semi-Perimeter:}$ $\sf\dfrac{250}{2}$ $\sf\small{=125m}$

$\space$

$\sf\small{Substitute \: the\:values\:in\:heron's\:formula:}$

$\sf{Area\:of\:the\:∆:-}$

$\mapsto$ [tex]\sf\sqrt{125(125-120)(125-80)(125-50)}[/tex]

$\space$

$\mapsto$ $\sf\sqrt{125\times(5)\times(45)\times(75)}$

$\space$

$\mapsto$ $\sf\small\sqrt{2109375}$ $\sf\small{=375}$ $\sf\small\sqrt{15}$

$\space$

$\longmapsto$ $\sf\underline\bold\purple{1452.56m^2}$

______________________________

$\sf\underline\bold{Now,find\:the\:cost\:of\:fencing:}$

$\sf{Cost\:of\:fencing-}$

$\space$

$\sf\underline{Hence,the\:gardener\:has\:to\:fence:}$

$\space$

So,total cost of fencing at the rate of Rs.20 per m:-

___________________________________

Answer:

The bike will travel approximately 1,272 inches or 106 feet.  

Step-by-step explanation:

The diameter of a circle (wheel) can be used to find the circumference, which is the total perimeter around the wheel.  The formula used to find circumference is:  C = dπ, where 'd' is the diameter and π = 3.14.  In this case C = 27 x 3.14 ≈ 84.78 inches.  Since this measurement represents the perimeter of wheel, we would need to multiply this number by 15 in order to find the total distance after 15 complete rotations of the wheel:  84.78 x 15 ≈ 1,272 inches.  1,272 inches is a large measurement, so we can easily convert this to feet by dividing by the number of inches per foot, or 12:  1272/12 = 106 feet.

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

Fill up the .3 container and then pour it into the .5

fill up the .3 again and fill up the .5 ... if all is poured in the .5 will overflow over the top.

stop when the .5 is totally full... only .3 will fit... the liquid left in  the .3 will be .1

Step-by-step explanation:

Given the five number summary, christina has scored 70 marks which is equal to the median of the test scores, therefore about [tex]\frac{1}{2}[/tex] class scored higher than her and  [tex]\frac{1}{2}[/tex] class scored lower than her, making option (d) correct.

The five number summary is the descriptive summary of a data where in you are provided the lowest observation, first quartile, median, third quartile and the maximum observation.

Here, the first quartile is the observation which lies at a point in the ordered data that 25% observations are lesser than it and 75% are greater than it.

the median is the observation which lies at a point in the ordered data that 50% observations are lesser than it and 50% are greater than it.

the third quartile is the observation which lies at a point in the ordered data that 75% observations are lesser than it and 25% are greater than it.

As given in the data,

Christina's marks = 70

median marks = 70

christina's marks = median marks

therefore, by definition of median, about half class scored lower than christina and half more than her.  

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The complete question is given below:

Given the five number summary  as:

minimum = 2

first quartile = 50

median = 70

third quartile = 85

maximum = 96

Christina earned 70 on the test. Describe how the scores of Christina's

classmates compared to Christina's score.

A. about 1/4 scored higher, about 3/4 scored lower

B. about 314 scored higher, about 1/2 scored lower

C. about 3/4 scored higher, about 1/4 scored lower

D. about 1/2 scored higher, about 1/2 scored lower

Answer:

12

Step-by-step explanation:

F(x)=x^2−2x+4

Let x = |-4| = 4

F(|-4|)=4^2−2(4)+4

     = 16 -8+4

    = 8+4

     = 12

Answer:

Adrenaline: A stress hormone produced within the adrenal gland that quickens the heart beat, strengthens the force of the heart's contraction, and opens up the bronchioles in the lungs, among other effects. The secretion of adrenaline is part of the human 'fight or flight' response to fear, panic, or perceived threat.

Step-by-step explanation:

Answer:

hey sol, ok so im guessing you have to either divide or multiply, im stuck on this problem to lol

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{sinxcos^3x-cos xsin^3x}{cos^42x-sin^42x} \\=\frac{sin x cos x(cos^2x-sin ^2 x)}{(cis^2 2x+sin^2 2x)(cos^2 2x-sin ^22x)} \\=\frac{2sin x cos x cos 2x}{2(1)(cos 4x)} \\=\frac{sin 2x cos 2x}{2 cos 4x} \\=\frac{2 sin 2x cos 2x}{4 cos 4x} \\=\frac{sin 4x}{4 cos 4x} \\=\frac{1}{4} tan 4x[/tex]

Answer:

the answer is c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

y=mx+b

b is the y intercept

b=0, so 0 is the y intercept

Step-by-step explanation:

From the given information; Let the unknown different positive integers be (a, b, c and d).

An integer is a set of element that are infinite and numeric in nature, these numbers do not contain fractions.

Suppose we make an assumption that (a) should be the greatest value of this integer.

Then, the other three positive integers (b, c and d) can be 1, 2 and 3 respectively in order to make (a) the greatest value of the integer.

Therefore, the average of this integers = 9

Mathematically;

[tex]\mathbf{\dfrac{(a+b+c+d)}{4} =9}[/tex]

[tex]\mathbf{\dfrac{(a+1+2+3)}{4} =9}[/tex]

[tex]\mathbf{\dfrac{(6+a)}{4} =9}[/tex]

By cross multiplying;

6+a = 9 × 4

6+a = 36

a = 36 - 6

a = 30

Therefore, we can conclude that from the average of four positive integers which is equal to 9, the greatest value for one of the selected integers is equal to 30.

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The greatest value for one of the four positive integers is 30.

To find the largest positive integer, you have to minimize the other three positive integers.

Find the average of the four positive integers and equate it to the given value of the average.

[tex]\frac{6 + y}{4} = 9\\\\6+ y = 36\\\\y = 36-6\\\\y = 30[/tex]

Thus, the greatest value for one of the positive integers is 30

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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 3. -7.5 is located to the left of 6.5 on a number line oriented from left to right.