Which function is shown in the graph? A. f(x) = x2 – 3x – 10 B. f(x) = x2 + 3x – 10 C. f(x) = x2 + x - 12 D. f(x) = x2 – 5x – 8

Answer: 20 is the answer

Step-by-step explanation:

Answer: 20 students

Step-by-step explanation

40% of 20 can be written as 40% × 20.

= 40/100 × 20

= 8

I assume the natural logarithm, and not the base-10 log. Parameterize the integral as

[tex]\displaystyle I(a) = \int_0^1 \frac{(x^a - 1)^2}{\log^2(x)} \, dx[/tex]

Differentiate twice with respect to [tex]a[/tex].

[tex]\displaystyle I'(a) = 2 \int_0^1 \frac{x^{2a} -x^a}{\log(x)} \, dx[/tex]

[tex]\displaystyle I''(a) = 2 \int_0^1 (x^{2a} - x^a) \, dx[/tex]

Evaluate the last integral, then solve for [tex]I(a)[/tex] with the fundamental theorem of calculus, noting that [tex]I(0)=I'(0)=0[/tex].

[tex]\displaystyle I''(a) = 2\left(\frac1{2a+1} - \frac1{a+1}\right)[/tex]

[tex]\displaystyle I'(a) = 2 \int_0^a \left(\frac1{2t+1} - \frac1{t+1}\right) \, dt \\\\ ~~~~ = \log(2a+1) - 2 \log(a+1)[/tex]

[tex]\displaystyle I(a) = \int_0^a (\log(2t+1) - 2\log(t+1)) \, dt \\\\ ~~~~ = (2a+1) \log(2a+1) - 2(a+1) \log(a + 1)[/tex]

Let [tex]a=\phi[/tex] to recover the original integral.

[tex]\displaystyle I(a) = (2\phi+1) \log(2\phi+1) - 2(\phi+1) \log(\phi + 1)[/tex]

Using various properties of the golden ratio [tex]\phi[/tex], namely

[tex]\phi = 1 + \dfrac1\phi \implies \phi^2 = \phi + 1 \implies \phi^3 = \phi^2 + \phi[/tex]

[tex]2\phi+1 = \phi\left(2+\dfrac1\phi\right) = \phi(1 + \phi)[/tex]

[tex]\phi=\dfrac{1+\sqrt5}2 \implies \phi^3 = 2 + \sqrt5[/tex]

we can simplify the result to

[tex]\displaystyle I(\phi) = \int_0^1 \frac{(x^\phi-1)^2}{\log^2(x)} \, dx = \boxed{\sqrt5\,\log(\phi)}[/tex]

A stack of 20 identical boxes are 180 cm tall, then after removing 3 boxes from the top it is 153 cm tall.

As given in the question,

Number of identical boxes in a stack=20

Stack of 20 identical boxes are 180 cm tall

Height of 1 box=180/20

                         =9cm

Julia removes 3 boxes from the top

Height of 3 identical boxes=9 × 3

                                             =27 cm

Height of stack after removing 3 boxes from the top

=Original height - height of 3 boxes

=180 -27

=153cm

Therefore, a stack of 20 identical boxes are 180 cm tall, then after removing 3 boxes from the top it is 153 cm tall.

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Answer:I believe it is 15-25

Step-by-step explanation:

The coordinates of D' are (4,0)

A Trapezoid is regarded as a quadrilateral that has only one pair of opposite sides that are said to be parallel.

The coordinates of the given trapezoid are:

A = (-6,2)

B = (-5,4)

C = (-2,4)

D = (1,2)

It is given that the trapezoid is moved to the points of (x+3, y-2) on the graph.

Now, consider A = (-6,2)

A' = (-6+3, 2-2)

A' = (-3,0)

Consider B = (-5,4)

B' = (-5+3, 4-2)  

B' = (-2,2)

Consider C = (-2,4)

C' = (-2+3, 4-2)  

C' = (1,2)

Consider D = (1,2)

D' = (1+3, 2-2)  

D' = (4,0)

Therefore, D' has the coordinates (4,0)

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Given the rigth triangle, you have to determine the length of the missing side marked with an x.

To do so you have to apply the trigonometric functions, these are calculated as:

Where

θ is one of the inner angles of the triangle.

"opposite" indicates the opposite side to than angle

"adjacent" is the side in contact or next to the angle

and "hypotenuse" is the longest side of the triangle.

In this exercise we know the measure of the angle and the hypotenuse, the trigonometric function you have to use to determine the length of "x" is the Sine:

Replace with:=46º

hypotenuse=14

opposite=x

Correct option is b. 10.1

The fact that Fats, sugars, and proteins molecules have in common is that all of these are macronutrients.

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Answer:

They all have carbon atoms.

Step-by-step explanation:

Based on the number of shares outstanding and the market value, the price the stock is currently selling for is  $31.40

To find the selling price of the stock the formula is:

= Equity value of stock / Number of stock outstanding

The number of stock outstanding is 19,000 shares. The equity value of the stock is $596,600.

The selling price of the stock today then is:

= Equity value of stock / Number of stock outstanding

= 569,600 / 19,000

= $31.40

Full question is:
What is the stock selling for today?

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The rate at which the distance between the buses is changing when they are 13mi apart, heading toward each other is 101.54 km per hour.

Let l = distance further away at which they'll meet. This will be illustrated as:

l = ✓13² - ✓5²

= ✓169 - 25

= ✓144

= 13m

Assuming that each bus drives a constant 55mph. The passes towards each other will be:

= -(55 + 55)

= -110m/h

Therefore, h² + l² = b².

Differentiate

2hdh/dt + 2ldl/dt = 2bdb/dt

= 2 × 5 × 0+ 2 × 12 (-110)

= 3 × 13db/dt

= -101.54 m/h

The rate is 101.54 m/h.

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Answer:

  x = 8

Step-by-step explanation:

You want to know the value of x in an expression for an angle measure at parallel lines.

Where at transversal crosses parallel lines, all acute angles created are congruent, all obtuse angles created are congruent, and the acute angles are supplementary to the obtuse angles.

The angle marked 83° is acute. The angle marked (12x+1)° is obtuse, so these angles are supplementary:
  83° +(12x +1)° = 180°

  12x +84 = 180 . . . . . . . divide by ° and simplify

  12x = 96 . . . . . . . . . . subtract 84

  x = 8 . . . . . . . . . . . . divide by 12

The value of x is 8.

Using proportions, it is found that your walk and jogging rates are given as follows:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations.

One example of application, in the context of this problem, is for the relation between velocity, distance and time, as velocity is distance divided by time, that is:

v = d/t.

From the graph, the walk takes 40 minutes = 2/3 of an hour, and you walk 1.25 x 2 = 2.50 miles, as you walk 1.25 miles and then you come back home, hence the rate is given as follows:

v = 2.50/(2/3) = 3 x 2.50/2 = 3.75 miles per hour.

For the jog, you jog the same distance twice in one hour, hence you jog 5 miles in one hour, and the rate is given as follows:

v = 5/1 = 5 miles per hour.

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The perimeter of the given triangle having vertices H(3,-1); I(-6,-1) and J(3,-9) is 29.04.

The points which form a triangle are:

H(3,-1) ; I(-6,-1) and J(3,-9)

Perimeter of the given triangle with vertices H(3,-1); I(-6,-1) and J(3,-9) is required:

To find the length we have to find the distance between the points.

Using distance formula i.e.

[tex]\sqrt{ [ (x2 - x1)^2 + (y2 - y1)^2 ][/tex]

Let the length of the sides be A1, A2 , A3

On applying the distance formula to H(3,-1) and I(-6,-1) ;

We get,

A1 =  [tex]\sqrt{[ (-6-3)^2 + (-1+1)^2 ][/tex]

    = [tex]\sqrt{ [ (-9)^2 + (0)^2 ][/tex]

    = [tex]\sqrt[ 81 + 0 ]}[/tex][tex]\sqrt{[ 81 + 0 ][/tex]

    = [tex]\sqrt{81}[/tex]

    = 9

On applying the distance formula to  I(-6,-1) and J(3,-9);

We get,

A2 = [tex]\sqrt{ [ (3+6)^2 + (-9+1)^2 ][/tex]

     = [tex]\sqrt{[ (9)^2 + (-8)^2 ][/tex]

     = [tex]\sqrt{[ 81 + 64 ][/tex]

     = [tex]\sqrt{145}[/tex]

    = 12.04

On applying the distance formula to J(3,-9) and H(3,-1);

We get,

A3 = [tex]\sqrt{[ (3-3)^2 + (-9+1)^2 ][/tex]

     =  [tex]\sqrt{[ (0)^2 + (-8)^2 ][/tex]

     = [tex]\sqrt{ [ 0 + 64 ][/tex]

     =[tex]\sqrt{64}[/tex]

     = 8

Hence,

The perimeter is 9 + 12.04 + 8 = 29.04

The perimeter of the triangle having vertices H(3,-1); I(-6,-1) and J(3,-9) is 29.04.

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Answer:

324

Step-by-step explanation:

20%-> 0.2

0.2(270)= 54

270+54=324

Answer:The answer is 324

Step-by-step explanation:20% of 270 is 54 so add 54 and 270 because you increase by 20 to get the answer

Answer

Tan (A) = 0.109 radians

Explanation:

The figure given is a right angles triangle

Given that AB = c is the hypotenus

AC = b = adjacent

BC = a = opposite

Tan A can be calculated using SOH CAH TOA

Tan A = opposite / adjacent

Tan A = BC / AC

BC = a = 4.020

We need to find b uisng pythagoras theorem

b = 11.307

Tan A = 4.020 / 11.307

Tan A = 0.3555

A = tan ^-1 (0.3555)

A = 19.570 degrees

Convert degrees to radian

since 1 pi = 180 degrees

x pi = 19.570

Cross multiply

19.570 * 1 = x * 180

x = 19.570 / 180

x = 0.109

Therefore, tan (A) is 0.109 radians

When the fraction n/12 is between 1/4 and 2/3, the possible values of n will be 4, 5, 6, and 7.

It should be noted that a fraction simply means a number that isn't whole. It can be illustrated as a/b where a is the numerator and b is the denominator.

It should be noted that 1/4 is equivalent to 3/12.

It should be noted that 2/3 is equivalent to 8/12.

Therefore, the values of n will be numbers between 3 and 8. They are 4, 5, 6, and 7.

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Answer:

(x+1)(x-5)

Step-by-step explanation:

The option that is an equivalent expression of 15x² +12x + 8 is C. 12x + 15x² + 8.

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same values for the variable, two algebraic expressions that are equivalent have the same values.

If two systems of equations have the same solution, they are equivalents. In algebra, 2(2x - 3y + 6) is equal to 4x -6y + 12 as an example of an equivalent expression.

In this case, it should be noted that 15x² +12x + 8 is the same as 12x + 15x² + 8. Therefore, the correct option is C.

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Answer: The answer is D.

Step-by-step explanation: Because I use a graphing calculator

The equation of the line in slope intercept form is y = -5 / 9x + 2 / 9

The slope intercept form of the equation of a line  can be represented as follows:

y = mx + b

where

Let's find the slope using the points (4, -2)(-5, 3)

Hence,

m = y₂ - y₁ / x₂ - x₁

x₁ = 4

x₂ = -5

y₁ = - 2

y₂ = 3

m = 3 + 2 / -5 - 4

m = 5 / -9

m = - 5 / 9

Therefore, let's find the y-intercept using (4, -2).

-2 = - 5 / 9 (4) + b

-2 = - 20 / 9 + b

b = -2 + 20 / 9

b =  -18 + 20/  9

b = 2 / 9

Therefore, the equation is y = -5 / 9x + 2 / 9

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The integers that are in order from least to greatest will be C. -13, -2, 6, 20.

It should be noted that an integer simply means a natural number or a whole number that given. It should be noted that they can either be positive or negative.

In this case, the numbers will be illustrated as thus:

The smallest number is -13.

The biggest number is 20.

Therefore, the arrangement is -13, -2, 6, 20.

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To make a specific shade of green paint, 4.8 gallons of yellow paint is needed to mix with 3 gallons of blue paint.

In the question ,

it is given that

to make a specific shade of green paint , the painter mixes 1/2 gallon of blue paint and 4/5 gallon of yellow paint .

so , the ratio of yellow paint to blue paint  [tex]=\frac{\frac{4}{5} }{\frac{1}{2} }[/tex]

writing in the simplified form , we get

= 4/5 × 2/1

= 8/5

So, for the given specific shade of green , the ratio of yellow : blue paint will remain same ,

let the amount of yellow paint used to mix with 3 gallons of blue paint be x gallons .

[tex]\frac{8}{5} =\frac{x}{3}[/tex]

On simplifying

x = 24/5

x = 4.8

so yellow paint required is 4.8 gallons

Therefore , to make a specific shade of green paint , 4.8 gallons of yellow paint is needed to mix with 3 gallons of blue paint.

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The new coordinates of the point N after the given dilation transformation is; (-2, 6)

From the attached image, we see the given triangle MNP. We see that it's coordinates are;

M(-1, -2)

N(0, 2)

O(2, -2)

Now, when we talk about dilation in transformation, we are simply referring to a transformation that produces an image that is the same shape as the original, but is a different size.

Thus, triangle MNP will be dilated according to the rule  (x,y), where point P is the center of dilation.

Given the coordinate N = (0, 2)

The rule of dilation with scale factor k =2 and point P is the center of dilation is given by:

(x, y) = (2x - 2), (2x + 2)

Thus;

N = (0, 2) → N'(2(0) - 2), (2(2) + 2)

= N'(-2, 6)

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The value of 30/cos40° rounded to 1 d.p. (decimal point) is 39.2.

How to round off any decimal number to one decimal place?

When you round to the first decimal place, or to the nearest tenth, the number in the hundredth point place will determine whether you round up or down. If the hundredths digit is a number between 5 and 9, round up to the nearest whole number. If it's a number between 0 and 4, you would "round down" by keeping the tenths place the same.

We have 30/cos40°

Value of 30/cos40° = 30/0.766044 = 39.162241 (cos40° = 0.766044)

Since the number in the hundredths place is 6, which is between 5 and 9, we would round the tenth decimal point up to 2.

Therefore, the value of 30/cos40° rounded to 1 d.p. (decimal point) is 39.2.  

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Answer:

5 degree Celsius

Explanation:

Using the formula for conversion included in the image attached, we have:

Therefore, 41 degrees Fahrenheit is equivalent to 5 degrees Celsius

When the given proportion is solved the value of w is calculated to be 6.

What is proportion?

A proportion can be commonly understood as two ratios that have been set equal to each other; a proportion is an equation that can be solved.

When it is said that proportion is two ratios that are equal to each other, it means in the sense of two fractions being equal to each other.

for example 5/10 = 1/2, 5:10 = 1: 2

7:42 = 1 : w

[tex]\frac{7}{42} = \frac{1}{w} \\[/tex]

w = 1 x 6

w = 6

When the given proportion is solved the value of w is calculated to be 6

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Answer:

x = 10

The interior angles measure 93°, 126°, 60°, and 81°.

Step-by-step explanation:

[tex]9x + 3 + 12x + 6 + 6x + 8x + 1 = 360[/tex]

[tex]35x + 10 = 360[/tex]

[tex]35x = 350[/tex]

[tex]x = 10[/tex]

9(10) + 3 = 90 + 3 = 93°

12(10) + 6 = 120 + 6 = 126°

6(10) = 60°

8(10) + 1 = 80 + 1 = 81°

Notice that this set of angles is congruent

herefore,

Solving for y ,

nswer: 116