What is the value of the expression 5 5/12-3 1/4

Answer:

0.16

Step-by-step explanation:

Its 0.16 because it would be easiest to make 8/50 into 16/100 to make it easier to turn into a decimal.

Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(4x^2+5xy+y^4=370\)

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)

Differentiate the terms in x only (and constant terms):

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Use the product rule to differentiate terms in both x and y.

\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)

\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)

Therefore, slope of the tangent line to the curve at the given point is -11/7.

Answer:

1 answer

Answer:lower bound = 147.5gupper bound = 152.5gStep-by-step explanation:if you were rounding a single digit number to the nearest 5, ...

Step-by-step explanation:

Answer:

0.0625 is the answer.

Hope it helps you!!!

They can buy 120 vans, 60 small trucks, and 80 large trucks.

The truck company plans to spend 10 million on 260 vehicles. Each commercial van cost 25,000 dollars. Each small truck 50,000 dollars and each large truck 50,000 dollars. They needed twice as many van as small truck

Therefore,

let

s = number of small truck

number of van = v

let

l = number of large truck

v + s + l = 260

25,000(v) + 50,000(s) + 50,000(l) = 10,000, 000

v + 2s + 2l = 400

Hence,

v = 2s

So,

2s + 2s + 2l = 400

4s + 2l = 400

2s + s + l = 260

3s + l = 260

2s + l = 200

s = 60

l = 200 - 2(60)

l = 200 - 120

l = 80

v = 2(600 = 120

Therefore, they can buy the following:

number of small truck = 60

number of van = 120

number of large truck = 80

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Using a trigonometric identity, it is found that the equivalent expression is given by 1.

Relating sine and cosine, we have that:

\(\sin^{2}{\beta} + \cos^{2}{\beta} = 1\)

Then:

\(\cos^{2}{\beta} = 1 - \sin^{2}{\beta}\)

For the tangent, we have that:

\(\tan{\beta} = \frac{\sin{\beta}}{\cos{\beta}}\).

For the secant, we have that:

\(\sec{\beta} = \frac{1}{\cos{\beta}}\).

In this problem, the expression is:

\(\frac{(1 - \sin{\beta})(1 + \sin{\beta})}{\cos^{2}{\beta}} = \frac{1 - \sin^2{\beta}}{\cos^2{\beta}} = \frac{\cos^2{\beta}}{\cos^2{\beta}} = 1\)

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Answer:

is a measure of the average absolute distance between each data value and the mean of a data set.

Answer:

2hole square and six whole square (a+b) (a-b) finish...

Answer:

First, find two points on the graph:

Slope = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{8-2}{2-0} =\frac{6}{2}=3\)

16 + (-3) = 16 - 3 = 13

Hello!

the equation of the blue line is 3y + 0.5x

Answer:

y - 1 = (1/2)(x - 2)^2

Step-by-step explanation:

The appropriate equation for such a parabola has the form

y - k = a(x - h)^2, where (h, k) is the vertex:

y - 1 = a(x - 2)^2.  Since the y-intercept is (0, 3), we substitute 3 for y and 0 for x, obtaining:

3 - 1 = a(0 - 2)^2, or

2 = a(4).  Therefore, a = 1/2, and the equation of this parabola is:

y - 1 = (1/2)(x - 2)^2

Answer:D

Step-by-step explanation:

please mark brainliest

Answer:

(-4,3)

Step-by-step explanation:

Hope this helps. :)

So, Gina's farm produced approximately 471.8 tons of sweet potatoes this year. Rounded to the nearest whole number, this is 472 tons.

When we talk about an increase, we are referring to a change in quantity or value that is greater than the original amount. In other words, an increase means that something has gotten bigger, larger, or more than it was before.

Given by the question.

To find out how much sweet potatoes Gina's farm produced this year, we need to add 40% of last year's production to the amount produced last year:

40% of 337 tons = 0.4 x 337 = 134.8 tons

Adding this to last year's production gives:

337 + 134.8 = 471.8 tons

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$27.71 is the amount Steve spend if he shops at S2.

Given that Steve is going shopping

The shopping list of steve has 2 cereal, 4 soups , 2 soda, 1 milk and 4 candy.

We have to find the cost spend by Steve when he purchase in shop 2, S2.

In S2, the cereal cost 2.15, soup cost 2.75, soda cost is 3.00, Milk cost 3.25 and candy costs 0.79.
Total cost = 2×2.15 + 4×2.75+2×3+1×3.25+4×0.79

=4.3+11+6+3.25+3.16

=27.71

Hence, $27.71 is the amount Steve spend if he shops at S2.

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Answer:

w or x

Step-by-step explanation:

the square root of 40 is 6.3

9514 1404 393

Answer:

  about 71.6°

Step-by-step explanation:

The relevant trig function is ...

  Tan = Opposite/Adjacent

Here, the "opposite" side of the right triangle is the height of the tower. The "adjacent" side is the distance to the tower. Then if the angle is x, we have ...

  tan(x) = 900/300 = 3

  x = arctan(3) ≈ 71.6°

Megan's angle of elevation is about 71.6°.

Answer:

Angle required = Height of Eiffel Tower/Megan standing place × arctan

=> (900/300) × arctan

=> 3 × arctan

=> 3arctan

=> 71.6⁰

Hence,

Angle = 71.6⁰

\( \\ \)

The obtained answers for the given line segments are as follows:

9. The value of the line segment \(\overline {DE}\) = 43; Where \(\overline { DF}\) = 61 and \(\overline {EF}\)

10. The value of x is 6; Where \(\overline {DE}\) = 4x - 1, \(\overline {EF}\) = 9, and \(\overline { DF}\) = 9x - 22

11. The value of line segment \(\overline {EF}\) = 32; Where  \(\overline { DF}\) = 78, \(\overline {DE}\) = 5x - 9, and \(\overline {EF}\) = 2x + 10

12. The value of line segment \(\overline { DF}\) = 57; Where \(\overline {DE}\)  = 4x + 10 \(\overline {EF}\) = 2x - 1, and \(\overline { DF}\) = 9x - 15.

The calculation for the required values is as follows:

9. Finding \(\overline{DE}\):

It is given that,

\(\overline{DF}\) = 61; \(\overline{EF}\) = 18

From the figure, we can write

\(\overline{DF} = \overline{DE} + \overline{EF}\)

On substituting the given values,

61 = \(\overline{DE}\) + 18

⇒ \(\overline{DE}\) = 61 - 18

∴ \(\overline{DE}\) = 43

10. Finding x:

It is given that,

\(\overline {DE}\) = 4x - 1, \(\overline {EF}\) = 9, and \(\overline { DF}\) = 9x - 22

From the figure we have

\(\overline{DF} = \overline{DE} + \overline{EF}\)

On substituting,

(9x - 22) = (4x - 1) + 9

⇒ 9x - 22 = 4x - 1 + 9

⇒ 9x - 4x = 8 + 22

⇒ 5x = 30

∴ x = 6

11. Finding \(\overline{EF}\):

It is given that,

\(\overline { DF}\) = 78, \(\overline {DE}\) = 5x - 9, and \(\overline {EF}\) = 2x + 10

From the figure we have

\(\overline{DF} = \overline{DE} + \overline{EF}\)

On substituting,

78 = (5x - 9) + (2x + 10)

⇒ 78 = 5x - 9 + 2x + 10

⇒ 7x + 1 = 78

⇒ 7x = 78 - 1

⇒ 7x = 77

∴ x = 11

On substituting x = 11 in \(\overline {EF}\) = 2x + 10; we get

\(\overline {EF}\) = 2(11) + 10

      = 22 + 10

      = 32

Therefore, the value of the line segment \(\overline {EF}\) is 32.

12. Finding \(\overline {DF}\):

It is given that,

\(\overline {DE}\)  = 4x + 10 \(\overline {EF}\) = 2x - 1, and \(\overline { DF}\) = 9x - 15

From the figure we have

\(\overline{DF} = \overline{DE} + \overline{EF}\)

On substituting,

(9x - 15) = (4x + 10) + (2x - 1)

⇒ 9x - 15 = 4x + 10 + 2x - 1

⇒ 9x - 15 = 6x + 9

⇒ 9x - 6x = 9 + 15

⇒ 3x = 24

∴ x = 8

On substituting x = 8 in \(\overline { DF}\) = 9x - 15; we get

\(\overline { DF}\) = 9(8) - 15

      = 72 - 15

      = 57

Therefore, the value of the line segment \(\overline { DF}\) is 57.

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Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

The answer is:

g(x + 1) = 6x + 1

g(4x) = 24x -5

Work/explanation:

To evaluate, I plug in x + 1 into the function:

\(\sf{g(x)=6x-5}\)

\(\sf{g(x+1)=6(x+1)-5}\)

Simplify

\(\sf{g(x+1)=6x+6-5}\)

\(\sf{g(x+1)=6x+1}\)

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

Do the same thing with g(4x)

\(\sf{g(4x)=6(4x)-5}\)

\(\sf{g(4x)=24x-5}\)

Hence, these are the answers.

The graph solution of the function is attached below;

For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)

Given in the question;

points to be plotted;

(-4,9) , (-1,3) , (0,1) , (2,-3)

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Answer:

Step-by-step explanation: evagline has 3/5 of box of nuts.she uses it to fill 6 bowls

Answer:

2229 thanks, merry early Christmas

The required function y = 7 cos (2π * 0.1 * x) and period of the function is 10 seconds, which is the time it takes for one complete cycle of the wave.

he cosine function can be used to model periodic motion, and its general form is:

y = A cos (Bx + C) + D

where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.

In this case, we know that a 14 in. wave occurs every 10 s, so we can use this information to find the frequency, which is the reciprocal of the period. The period is the time it takes for one complete cycle of the wave, which in this case is 10 s.

Therefore, the frequency is:

\(f = \frac{1}{T}=\frac{1}{10} = 0.1 Hz\)

We can also see that the amplitude of the wave is 7 inches, since the wave has a height of 14 inches from its highest point to its lowest point.

Now we can write the function that models the height of the particle in inches y as it moves in seconds x:

y = 7 cos (2π * 0.1 * x)

Here, the frequency is expressed in radians per second (2π * 0.1 = 0.2π), since the cosine function takes radians as its argument. The phase shift and vertical shift are both zero in this case, since the wave starts at its highest point and has no vertical shift.

Therefore, the period of the function is 10 seconds, which is the time it takes for one complete cycle of the wave.

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The inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

Inverse of a function can be calculated by following the steps mentioned below -

According to the question, the equation given is as follows

y = f(x) = 2x + 5

y = 2x + 5

Replace 'y' with 'x', we get -

x = 2y + 5

Now, solve for y -

2y = x - 5

y = (x/2) - (5/2)

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = (x/2) - (5/2)

Hence, the inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

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Answer:

B i think uodate me the answer

Answer:

Step-by-step explanation:

Perimeter:  

     \(P=(x+y+z) \ cm\)

Semi-perimeter:

     \(SP=\frac{1}{2} (x+y+z) \ cm\)

Answer:

2, 3  and 5

Step-by-step explanation:

Answer:

2,3,5

Step-by-step explanation:

Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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