A company makes two chemicals: Type I and Type II. Due to storage problems, a maximum of 100 pounds of Type I and 150 pounds of Type II can be mixed and packaged each year. One pound of Type Itakes 62 hours to mix and 78 hours to package; one pound of Type II takes 44 hours to mix and 46 hours
to package. The mixing department has at most 7220 hours available each year, and packaging has at most 8260 hours available. If the profit for one pound of Type I is $70 and for one pound of Type II is $46, what is the maximum profit possible each year?

To find the value of K, we need to find the point at which the line Y=2x+K is tangent to the parabola Y=x^2-4x+4. This means that the line and the parabola will have the same y-value at this point, and the line will be tangent to the parabola (meaning it will just touch the parabola at this point, without intersecting it).

To find the point at which the line and parabola are tangent, we can set Y=2x+K equal to Y=x^2-4x+4 and solve for x:

2x + K = x^2 - 4x + 4

x^2 - 4x + 4 - 2x - K = 0

(x-2)^2 = K

x = 2 +/- sqrt(K)

Since the line is tangent to the parabola, it will just touch the parabola at this point, which means that the parabola will have a minimum value at this point. This means that the value of K must be nonnegative, because the square root of a negative number is not a real number. Therefore, K must be equal to or greater than 0.

So, the value of K for which Y=2x+K is tangent to Y=x^2-4x+4 is K >= 0.

The equation is equivalent to the r = d/t.

There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

We have to find which equation is equivalent to the formula d = rt.

Formula given: d = rt

Divide both sides by t

d/t = rt / t

d/t = r

Thus, the equation is equivalent to the r = d/t.

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Answer:

its c

Step-by-step explanation:

To answer this question, simply plug in the values that represent the variables into the respective equations.

If z=5 and y =3, then 12z - 3y can be written as:

(12 × 5) - (3 × 3)

(60) - (9)

= 51

If z = 5, then the expression 4z -z can be written as:

(4 × 5) - 5

20-5

= 15

51 and 15 are your answers

Answer:

x=

[tex]3 \sqrt{3} [/tex]

Step-by-step explanation:

because tan30⁰=

[tex] \frac{ \sqrt{3} }{3 } \\ \[/tex]

3/x=root 3 over3

[tex]3 \sqrt{3} [/tex]

$22500 is interest rate of common tock for each year.

What is an explanation of the interest rate?

An interest rate informs you of how much borrowing will cost you and how much saving will pay off.

                      Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the entire loan amount if you are a borrower.

Amount distributed as dividends = $15000

                 Total Preferred dividend to be paid  = $37500

       But Total Preferred dividend paid/avaiable = $15000

                              dividend per share(P.S)   = $0.60    **(15000 / 25000shares)

    Since the preferred stock cumulative dividend to be paid in Next year due to less payment in current year would be = $22500  or $0.90 per share        

                                      Remaining dividend  = 0

                       Equity dividend per share  = 0

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Answer: i think the next number should be 26

Step-by-step explanation:

the equation of the function is y=-2x+10

The function's range is in the interval (1, ∞).

Members of a set can congregate in mathematics.

These sets' constituents are referred to as elements. The correspondence between the two groups is known as a relation when the elements of each group are paired up together.

So, between two sets, a relation is a collection of ordered pairs of elements.

The term "function" refers to a particular type of relation where each element in the first group, referred to as the domain, corresponds to exactly one element in the second group, referred to as the range.

The elements in the domain couple with exactly one element in the range, and this is how a function is a pairing between two sets.

According to our question-

[7, ] is the interval notation.

The function's range falls between the numbers (1, ).

provided function

Determine the function's domain:

You do not want to use a counterargument to the square root in this situation (you cannot find the solution of a negative square root, at least as a real number).

What you actually do is "impose" that the argument always ends in a yes or a no (you know the square root of a positive number or zero).

You then solve for x to determine the variable's ALLOWED values by setting the argument greater than or equal to zero:

Consequently, the function is in the domain.

Find the function's range:

The set of all y values in the function's range is when,

range of the function is in the interval  (1, ∞).

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Answer: first 7,1 second 7, -1

Step-by-step explanation: edge 2023

Answer:

0.7

Step-by-step explanation:

Answer:

The regualar hippo massed 4.45 times as much as the pygmy hippo. (Not sure what I should round to)

Step-by-step explanation:

First, convert each of the fractions to a whole number. To do this get the whole number to the left of the fraction multiply it by the denominator and add the numerator. Once you have found both masses. Get the mass of the regular hippo and divide by the pygmy hippos mass.

Reguar Hippo Mass Calcualtion:

24*2=48

48+1=49kg

Pygmy Hippo Mass Calcualtion:

5*2=10

10+1-11kg

Final Calcuation:

49/11=4.45kg

Answer: 4.45 times as much

Let me know if this helped!

Answer:

50

Step-by-step explanation:

ezpz

Answer:

2

Step-by-step explanation:

: in this context, the y-intercept represents the volume of water already in the tank

In linear equation,3 whole pizzas should they order .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

total people = 4

Each person always eats 3/4 of a cheese pizza.

   3/4 + 3/4 + 3/4 + 3/4  

= 3 + 3 + 3 + 3 /4

= 12/4

= 3

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[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{55}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{55}-\stackrel{y1}{(-11)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-3)}}} \implies \cfrac{55 +11}{8 +3} \implies \cfrac{ 66 }{ 11 } \implies 6[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 6}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 6 ( x +3) \\\\\\ y+11=6x+18\implies {\Large \begin{array}{llll} y=6x+7 \end{array}}[/tex]

The possible values of k are -0.56, -3.56, -2 and -1.

We have the equation of the parabola, y = 0.5 (x- 3 ) ( x+ k)

Substituting x=0, we get that i.e. y =0.5 * (-3) * k -1.5k

So, the y-intercept is (0,-1.5k).

Thus, the height of the triangle becomes |-1.5k| = 1.5k

Again, substituting y=0, 0 = 0.5 (x-3) (x+k) i.e. i.e. x0=(x-3) (x+k)=3 and x=-k

So, the x-intercepts are (3,0) and (-k,0).

Thus, the base of the triangle is 3+k if k>-3 or -3-k if k<-3.

As, area of a triangle = 1/2 * (base )* (height )

Substituting the values, we get,

1.5=1/2 *(3+k)*(1.5k)

i.e.3= 4.5 k + 1.5k ²

i.e. k = -0.56 and k = -3.56

or

1.5=1/2* (-3-k )*(1.5k)

i.e.

3 = -4.5 k - 1.5²

i.e. k = -2 and k = -1.

Thus, the possible values of k are -0.56, -3.56, -2 and -1.

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We can add and subtract 4.5 in the left side to complete squares, then we can rewrite the quadratic equation as:

(x + 13)^2 = 4.5

Here we want to rewrite the quadratic equation:

x^2 + 26x + 164.5 = 0

To rewrite it in the desired way, we need to complete squares, remember that the perfect square trinomial is:

(a + b) = a^2 + 2ab + b^2

We can rewrite the given quadratic as:

x^2 + 26x + 164.5 = 0

x^2 + 2*13*x + 164.5 = 0

The missing term to complete squares is 13^2 = 169, so we can add and subtract 4.5 on the left side of that eqation to get:

x^2 + 2*13*x + 164.5 + 4.5 - 4.5 = 0

x^2 + 2*13*x + 169 - 4.5 = 0

(x + 13)^2 = 4.5

That is the equation we wanted to get.

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The better option is to buy the Granola bar.

What is a unit value?

When the expenditures or value of production of an item is divided by the quantity, the result is known as a unit value. The unit value of a set of homogeneous products is the total value of the purchases/sales divided by the sum of the quantities.

To determine which is the better buy, you need to compare the price per granola bar for each option. To do this, you can divide the price of each pack by the number of granola bars it contains.

For the first pack of 100 granola bars, the price per granola bar is $8.67 / 100 granola bars = $0.09 per granola bar.

For the second pack of 50 granola bars, the price per granola bar is $5.48 / 50 granola bars = $0.11 per granola bar.

Since the price per granola bar is lower for the first pack, it is the better buy. You would save money by purchasing the first pack of 100 granola bars instead of the second pack of 50 granola bars.

Hence, the better option is to buy the Granola bar.

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The new cost per pen based on the information is $6.650.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.

In this case, the pens are sold in a pack of 10 for 95 krona and the price is reduced by 30%, the new price will be:

= 95 - (30% × 95).

= 95 - 28.5

= $66.50

The new cost for every pen will be:

= $66.50 / 10

= $6.650

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If a rubber ball is dropped from a height of 10 feet, The height of the 5th bounce and the population in 12 years

Generally, For the first problem, the height of the 5th bounce can be calculated by plugging in 5 for x in the function

f(x) = 20 (0.6)^x:

f(5) = 20 (0.6)^5

= 20 (0.12)

= 2.4 feet

For the second problem, the population in 12 years can be calculated by plugging in 12 for x in the function f(x) = 1000 (1.04)^x:

f(12) = 1000 (1.04)^12

= 1000 (1.70)

= 1700 pigs

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Answer:

132

Step-by-step explanation: Supplementary=180 So all you have to do is subtract 48 from 180 and should give you 132.

Hope that helps!

It will take the sales of 381 necklaces to reach break-even.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that Tony invest an initial amount of $381 for advertising, and materials cost $8 for each necklace he makes. Tony can sell his creations for $9 per necklace.

Let the number of necklace be x then;

8x + 381 = 9x

Solving;

9x - 8x = 381

x = 381

Therefore, Total expenses = 8x + 381

8(381) + 381

= 3429

Thus, Total sale = 9x = 3429

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Therefore the solution to the given question equation will shift the graph of the original equation up 2 units in  y=2x + 9

equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics. Equations range in complexity from straightforward addition-and-multiplication equations in mathematics through differential equations, exponential equations that use exponential expressions, and integral equations.

Here,

It follows a linear function. y=mx + b

If A is the location where the y-axis intersects, then x = 0 and y = b are the coordinates of A.

In order to move the graph up by 2 units, you must add 2 units to b.

In our case, b was originally equal to 7, so shifting it up makes b become 7+2=9, and the new function is y=2x + 9.

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The values of given functions are Sin2x = 120/169, Cos2x = 119/169 and tan2x = 120/119.

Trigonometric equation is a condition including at least one trigonometric ratios of obscure points. It is communicated as proportions of sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec), cosecant(cosec) points. For instance, cos2 x + 5 sin x = 0 is a mathematical condition.

We have,

Cosx = 12/13

Use sin^2(x) + Cos^2(x) = 1

sinx = [tex]\sqrt{1-cos^{2}x}[/tex] = 5/13

We know that

Sin2x = 2sinxcosx

Sin2x = 2(5/13)(12/13)

Sin2x = 120/169

Using cos2x = 2cos^2x - 1

cos2x = 2(12/13)^2 - 1

Cos2x = 119/169

Then, using tanx = sinx/cosx

tan2x = sin2x/cos2x

tan2x = [tex]\frac{\frac{120}{169} }{\frac{119}{169} }[/tex] = 120/119

Thus, required values Sin2x = 120/169, Cos2x = 119/169 and tan2x = 120/119

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Required solution is

[tex]Sin2x=-\frac{120}{169} \\\\\\Cos2x=-\frac{119}{169} \\\\\\Tan2x=\frac{120}{119}[/tex]

What is trigonometric ratios?

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

[tex]cos2x=cos^2x-sin^2x[/tex]

[tex]sin2x=2sinxcosx\\\\tan2x=(2tanx)/(1-tan2x)[/tex]

..

[tex]sinx= -\frac{12}{13}[/tex]

you are working with a (5-12-13) reference right triangle in quadrant IV where sin<0,cos>0,tan<0

[tex]sinx=-\frac{12}{13} (given)\\\\\cosx=\frac{5}{13} \\\\tanx=-\frac{12}{5}[/tex]

..

[tex]cos2x=cos^2x-sin^2x=\frac{25}{169-144} \times \frac{1}{69} =-\frac{119}{169} \\\\\\sin2x=2sinxcosx=2\times(-\frac{12}{13}) \times (\frac{5}{13} )=-\frac{120}{169} \\\\\\tan2x=\frac{2tanx}{1-tan^{2}x } \\\\\\=2(-12/5)/(1-(144/25))=(-24/5)/(-119/25)=(-24/5)(25/119)=\frac{120}{119}[/tex]

required solution is

[tex]Sin2x=-\frac{120}{169} \\\\\\Cos2x=-\frac{119}{169} \\\\\\Tan2x=\frac{120}{119}[/tex]

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Answer:

m = 2/5

:)))))))))))))))))))))))))))

Answer:

Each egg costs $0.60

Each piece of toast costs $0.30

Step-by-step explanation:

Let's assume that the cost of a single egg is E

And the price of a toast as T

Kendra charges $1.50 for one toast and two eggs

The equation above will be

2E + T = $1.50

And the other equation is

E + T = $0.90

For the second equation, we make E the subject of the formula

E = 0.90 - T

Now substitute for this in equation 1

2E + T = 1.50

It will now be 2(0.90 - T) + T = 1.50

1.80 - 2T + T = 1.50

T= $0.30

price of one toast is $0.30

And now, for the price of an egg, we substitute T = 0.30 in the equation

E= $0.60

The given expression is simplified as -4/7. So, the correct option is D.

To simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

Given that, (8-(4)(3))/(∛8 +5).

The given expression can be simplified as follows

Numerator of fraction simplified as 8-(4)(3)

= 8-12

= -4

Numerator of fraction simplified as (∛8 +5)

We know that, cube root of 8 (∛8) is 2

=(2 +5)

= 7

Thus, the fraction is -4/7

So, the expression (8-(4)(3))/(∛8 +5) is reduced to -4/7.

The simplified form of expression is -4/7. Therefore, option D is the correct answer.

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Answer:

see explanation

Step-by-step explanation:

vertical angles are congruent , then

2x - 3 = x + 16 ( subtract x from both sides )

x - 3 = 16 ( add 3 to both sides )

x = 19

Then

x + 16 = 19 + 16 = 35°

since the angles are congruent , then

the measure of each angle is 35°

Step-by-step explanation:

Formula 1: V = lwh

V = 10 x 8 x 6

V = 480

Formula 2: V = 2lw + 2lh + 2wh

V = 2(10 x 8) + 2(10 x 6) + 2(8 x 6)

V = 480

Because the value of x is 126° and the value of cos 2x is -0.301, which is fractionally identical to -7/25, the value of cos 2x will be -7/25.

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry. The sine, cosine, and tangent are the three fundamental trigonometric operations. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical concepts are built.

Here,

sin x=4/5

x=126°

Cos 126°=-0.588

cos (2*126)=-0.310

The value of cos 2x will be -7/25 because value of x is 126° and that of cos 2x is -0.301 that is fractionally equal to -7/25.

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Answer:

B

Step-by-step explanation:

on edge