According to descartes's rule of sign, how many possible positive and negative roots are there for the equation 0=−4x6−3x5 2x2−4x 1?

The equation of the tangent line to the curve are  [tex]y=x-1 , y=\frac{xe-e^{2}+8 }{e}[/tex].

It is required to find the solution.

A tangent is a line that touches the edge of a curve or circle at one point, but does not cross it. The tangent line to a curve at a point is that straight line that best approximates (or “clings to”) the curve near that point.

Given:

[tex]y=8\frac{lnx}{x} \\\\y'=8(\frac{1/x*x-lnx*1}{x^{2} } \\\\y'=\frac{1-lnx}{x^{2} }[/tex]

Now, we find the slope of the tangent by inserting the point (1,0) into the derivative.

[tex]m_{tangent}=\frac{1-ln1}{1^{2} }\\\\m_{tangent}=1-0/1\\\\m_{tangent} =1[/tex]

We can now find the equation, because we know the slope and a point (1, 0).

[tex]y-y_{1} =m(x-x_{1} )\\[/tex]

y-0=1(x-1)

y=x-1

We can now find the equation, because we know the slope and a point (e, 8/e).

[tex]y-y_{1} =m(x-x_{1} )\\\\y-8/e=1(x-e)\\\\y=\frac{xe-e^{2}+8 }{e}[/tex]

Therefore, the equation of the tangent line to the curve are  [tex]y=x-1 , y=\frac{xe-e^{2}+8 }{e}[/tex].

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Answer:

9

Step-by-step explanation:

The expression for g(x) is 9x + 26

A function can be defined as an expression, law or rule explaining the relationship between an independent and dependent variable.

Given the function;

g(x) = f(x + 4) - 10  

Where f = 9

Substitute into the function;

g(x) = 9( x + 4) -10

expand the bracket

g(x) = 9x + 36 - 10

collect like terms

g(x) = 9x + 26

Thus, the expression for g(x) is 9x + 26

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Answer:

1) 6a

2) 8

3) 18a

Step-by-step explanation:

1) [tex] \sf {2a}^{ - 1} \times {3a}^{2} [/tex]

Simplify using exponent rule with the same base

[tex] \sf \: 2 \times {3a}^{ - 1 + 2} [/tex]

Multiply the monomials

[tex] \sf \: 6a {}^{ - 1 + 2} [/tex]

Calculate the sum or difference.

[tex] \sf \: {6a}^{1} [/tex]

Calculate the power

[tex] \sf \: 6a[/tex]

2) [tex] \sf( \frac{1}{2} ) {}^{ - 3} [/tex]

simplify using negative exponents rule [tex] \sf {a}^{-n} = \frac{1}{{a}^{n}} [/tex]

[tex] \sf {2}^{3} [/tex]

calculate the power

[tex] \sf \: 8[/tex]

3) [tex] \sf {2a}^{ - 1} \times {(3a)}^{2} [/tex]

Simplify using exponents rule with the same exponent

[tex] \sf {2a}^{-1} × {3}^{2} × {a}^{2}[/tex]

Simplify using exponents rule with the same base a ^ n + a ^m = a ^n+m

[tex] \sf 2×{3}^{2} ×{a}^{-1+2} [/tex]

Calculate the power

[tex] \sf 2 × 9a {}^{-1+2}[/tex]

[tex] \sf 18a[/tex]

2(I) We round a number to three significant figures in the same way that we would round to three decimal places. We count from the first non-zero digit for three digits. We then round the last digit. We fill in any remaining places to the right of the decimal point with zeros.

8348 = 8350(rounded to 3 SF)

2(ii) 0.00796 = 0.0080

2(II) 6.329 = 6

2(III) 0.05684 = 0.0568

Step-by-step explanation:

1.i

2a^-1 × 3a²

remember, when we multiply factors with the same base value or variable, we keep that base value or variable and simply add the exponents.

-1 + 2 = 1

so, we get

2×3 × a¹ = 6a

1.ii

(1/2)^-3

remember, the "-" on the exponent just means 1/...

so, it is actually

1 / (1/2)³ = 1 / 1/8 = 8

1.iii

2a^-1 × (3a)²

similar to the first one, but remember, when we put the product of factors to a certain power, we need to do this for every factor of the inner multiplication :

2a^-1 × 9a² = 2×9 × a¹ = 18a

2.

the first significant figure is the first digit in the number reading from the left, that is not 0. it can be before or after the decimal point.

any digit (now continuing to read further to the right) after the first significant figure is again a significant figure even if it is 0.

i.

8.348 is rounded to 3 significant figures : 8.35

ii.

0.00796 is rounded to 2 significant figures :

0.0080 or 0.008 (because if the last digit after the decimal point is a 0, we can ignore it).

iii.

6.329 is rounded to 1 decimal place : 6.3

iv.

0.05684 is rounded to 3 decimal places : 0.057

3.

the sum of interior angles in a polygon is (n − 2) × 180°. where n is the number of sides.

as deca stands for 10, a decagon has 10 sides and 10 vertexes.

the sum of its inner angles is

(10 - 2) × 180° = 8 × 180° = 1440°

1170° of that is already covered by the first 7 angles.

so, we have left

1440 - 1170 = 270°

for the remaining 3 angles (that are all equal).

so,

270 = 3×angle

angle = 270/3 = 90°.

so, all of the 3 remaining angles are 90°.

Answer:51 degrees

Step-by-step explanation:

At noon the temperature is 75 degrees

the temperature drops 3 degrees every half hour.

First solve for time elapsed between noon and 4, which is 4 hours.

Next, we can change our rate to be in terms of full hours instead of half hours using the fact that 1 hr = 2 half hours, so the temperature drops 6 degrees every hour.

Four hours have elapsed so multiply 6*4 = 24 degrees and then subtract it from the starting 75

75 - 24 = 51.

Answer:

For A.) there are only 2 so 2/8 would become0.25

B.) 4 even number 4/8= 1/2 = 0.50

C.) 1 Red  1/8= 0.125

D.) 5 Not blue 5/8 = 0.625

E.)3 Blues 3/8= 0.375

F.) 0 because there are no 9 so it's not possible

Step-by-step explanation:

Answer:

5 m/s²

Step-by-step explanation:

To find the acceleration we apply Newton's second law of motion

F = ma   where F is the net force in Newtons, m the mass of the object (kg) and a the acceleration in  meters/second² (m/s²)

Given

F = 200 N

m = 40 kg

we have 200 = 40a

So a = 200/40=5 m/s²

The solution to the inequality where the inequality expression is given as: -1 < x + 3 < 5 is -4 < x < 2

The inequality expression is given as:

-1 < x + 3 < 5

Subtract 3 from all parts of the inequality expression

So, we have:

-3 -1 < x + 3 -3 < 5 - 3

Evaluate the difference and sum

So, we have:

-4 < x < 2

Hence, the solution to the inequality where the inequality expression is given as: -1 < x + 3 < 5 is -4 < x < 2

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Answer: 80 degrees because a line is 180°.

So if you subtract

180 - 100 = 80°

Answer:

x=80°

Step-by-step explanation:

The measures of angle x and the 100° angle form a straight angle.

This straight angle is 180°.

You can subtract the measure of one angle from the whole to find the measure of the other angle.

180°-100°=80°

This means angle x is 80°.

Answer: 116 61/100 miles

Step-by-step explanation: Road trip is 245 7/50 miles long

They have already driven 128 53/100

Those are mixed fraction. To facilitate the calculation, we should transform them into improper fractions (numerator > denominator)

245 7/50 = (50*245+7)/50 = 12257/50

128 53/100 = 12853/100

To find out much farther they have to drive, we need to subtract how much they have already driven to the total lenght of the trip:

12257 - 12853 = 24514 - 12853 = 11661

50         100             100                100

They still have 11661/100 to drive. In mixed fraction:

116 61/100 miles

Answer:

A person will pay $2.31 for a 1.7 pound of banana.

Step-by-step explanation:

1.7 pounds of bananas x $1.36 per pound = $2.31

Step-by-step explanation:

Fact 1: Alternate angles are equal.

Angles, (5x-11)° and (3x+17)° are ALTERNATE angles and so,

(5x-11)° = (3x+17)°

5x - 3x = 17 + 11

2x = 28

x = 28 ÷ 2

x = 14

NB: x does NOT have the degree sign because it's NOT an angle on its own, but rather within the bracket/part of the calculation to get the angle degree.

Fact 2: Opposite angles are equal.

Y° and (3x+17)° are OPPOSITE angles

y = (3x+17)°

y = (3x14) + 17

y= 42 + 17

y = 59°

Hope this helps!

Answer:

14 cents

Step-by-step explanation:

because 4.48 divided by 4 = 1.12 BUT since there are 8 ounces in a cup 1.12 divided by 8 = 0.14

A = 2p and B = 1/p  are the values of a and b.

What does math division mean?

To divide this,

[tex]\frac{6p^{2} }{3p} = 2p[/tex]

Multiplying back through, we have

[tex]3p * 2p = 6p^{2}[/tex]

Subtracting this from the first term under the box, we have

[tex]6p^{2} - 6p^{2} = 0[/tex]

Bring down the next term, 9p.

See how many times 3p goes into 9p = 9p/3p = 3

Multiplying back through, we have 3(3p) = 9p.  

Subtract this from the line above; 9p-9p = 0.  

Bring down the last term, 3.  

Since this is not 0, this is the remainder.  

This gives us

2p + 3 R 3;

writing this as a rational expression, we have

2p + 3 + 3/3p

The remainder term 3/3p will simplify to 1/1p or 1/p;

this gives us

2p + 3 + 1/p

Therefore, the answer is  A = 2p and B = 1/p

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The multiplicity that would be in a 1H NMR spectrum for the indicated proton(s) is triplet.

The correct answer is an option (b)

NMR spectroscopy is used to examine the structure of molecules.

Another type of additional data available from 1H NMR spectroscopy is called multiplicity.

It is useful because it reveals how many hydrogens are on the next carbon in the structure.

1H NMR is a technique to confirm the structure of organic compounds or those that contain protons.

In 1H NMR technique, multiplicity provides information about the number of proton neighbors for a particular proton atom or group of atoms (neighboring typically refers to  atoms within 3 bonds).

A solution-state proton spectrum is relatively fast to acquire, compared with other nuclei, and a lot of information about the structure of a compound can be deduced from it.

Therefore, the multiplicity that would be in a 1H NMR spectrum for the indicated proton(s) is triplet.

The correct answer is an option (b)

Answer:

1.73 repeated

Step-by-step explanation:

Answer:

1. 15          2. 30

Step-by-step explanation:

1. (2/5)x = 20

20/(2/5) = x

x = 50

50 × (3/10) = 15

2.  (2/3)y = 24

24/(2/3) = y

y = 36

36 × (5/6) = 30

Check the picture below.

Answer: The graph of g(x) is wider than f(x) and is shifted to the left 3 units and down 3 units.

Step-by-step explanation: I took the quiz and got it right

The function f(x) = x² is transformed and became g(x) = 3(x+2)² -1 has the graph of g(x) is wider than f(x) and is shifted to the left 3 units and down 3 unit.

By applying suitable graph transformation we can shift, stretch, shrink, a given graph along x and y axis.

According to the given question given a graph f(x) = x² and g(x) is                        3(x+3)² - 3.

Let us break transformations of g(x) one by one.

g(x) = 3f(x) which implies it's amplitude or vertical stretch is increased by a factor of 3.

Now, g(x) = 3(x+3)² implies the graph is shifted towards left by 3 units as x + 3 = 0 is x = -3.

Now, g(x) = 3(x+3)² - 3 implies that the whole graph has been shifted 3 units down along the y axis.

Hence the graph of g(x) is wider than f(x) and is shifted to the left 3 units and down 3 units.

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The 5 ordered pairs whose second component is the opposite of the first component are (-1,1), (-2,2), (-3,3), (-4,4) and (-5, 5).

Ordered pairs:

An ordered pairs is a composition of the x coordinate and the y coordinate (ordinate), having two values written in a fixed order within parentheses.

It can be written as (a,b).

Here

a represents the x coordinate and

b represents the y coordinate.

It helps to locate a point on the Cartesian plane for better visual comprehension.

Given:

The second component is the opposite of the first component.

Here we need to find the 5 ordered pairs for that.

For the given statement,

Let x be the first component and y be the second component.

So it can be written as,

=> y = -x

So, the five ordered pairs are,

=> 1 = -1

=>2 = -2

=> 3 = -3

=> 4 = -4

=> 5 = -5

So, the ordered pairs are,

(x,y) => (-1,1), (-2,2), (-3,3), (-4,4) and (-5, 5).

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Answer:

Pretty sure it’s x>12

Step-by-step explanation:

Answer x > 12

thats the whole thing

These forecasts illustrate bias.

Therefore, these forecasts illustrate bias.

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Answer:

There are many exponents that will give you 8.

I will list a few for you. :)

→ 2³

→ 8¹

→ [tex]\sf 4^{1.5}[/tex]

Hope this helps.

The numeric value of the b is 0.23 which satisfy the given equation.

According to the statement

We have to find that the value of the b.

So, For this purpose, we know that the

The numeric value refers to the worth of each digit depending on where it lies in the number.

From the given information:

The equation is a

3(2b + 3)² = 36

then to find the value of b rearrange the terms then

(2b + 3)² = 12

(2b + 3) =  \sqrt{12}

(2b) =   \sqrt{12}  -3

then

b  = \sqrt{12}  -3/ 2

b = 3.46 - 3/2

b = 0.46/2

b = 0.23.

So, The numeric value of the b is 0.23 which satisfy the given equation.

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Answer: 6.8*10⁻⁴=0.00068

Step-by-step explanation:

[tex]6.8*10^{-4}=0.00068[/tex]

Justin should have multiplied 3.8 and 7.9 first

He is trying to evaluate the expression 12.5 + 3.8x, when x = 7.9.

This was Justin solution to the expression

12.5 + 3.8(7.9)

16.3(7.9)

128.77

Now let's do our own arithmetic,

12.5 + 3.8x

we have to substitute the value of x in the equation.

12.5 + 3.8(7.9)

Using PEMDAS principle, we have to multiply before addition.

Therefore,

12.5 + 3.8(7.9)

12.5 + 30.02

42.52

Hence, Justin should have multiplied 3.8 and 7.9 first

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