A strong foundation in mathematics is most necessary for which career?

Education
Engineering
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Medicine

A. 20

Begin by substituting the known value. I have removed the symbols for now just to make the equation easier to read. 55 = 3.5x - 15

Add 15 on both sides of the equation to cancel out the subtraction. 70 = 3.5x

Finally, divide both sides by 3.5 to cancel out the subtraction. 20 = x

So, Starla bought 20 napkins.

Answer:

[tex]5y=24x[/tex]

Step-by-step explanation:

The question in English is

If 4x= 5/6y then 5y=

we have

[tex]4x=\frac{5}{6}y[/tex]

Solve for 5y

Multiply both sides by 6

[tex]6*4x=(6)*\frac{5}{6}y[/tex]

Simplify

[tex]24x=5y[/tex]

Rewrite

[tex]5y=24x[/tex]

Answer:

[tex]\large\boxed{x=\dfrac{9}{8}-\dfrac{\sqrt{109}}{8},\ y=-\dfrac{1}{2}-\dfrac{\sqrt{109}}{18}}\\or\\\boxed{x=\dfrac{9}{8}+\dfrac{\sqrt{109}}{2},\ y=-\dfrac{1}{2}+\dfrac{\sqrt{109}}{18}}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}4x\times9y=7&(1)\\4x-9y=9&(2)\end{array}\right\\\\(2)\\4x-9y=9\qquad\text{subtract}\ 4x\ \text{from both sides}\\-9y=-4x+9\qquad\text{change the signs}\\9y=4x-9\qquad\text{substitute it to (1)}\\\\4x(4x-9)=7\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\(4x)(4x)+(4x)(-9)=7\\(4x)^2-36x=7\\(4x)^2-2(4x)(4.5)=7\qquad\text{add}\ 4.5^2\ \text{to both sides}\\(4x)^2-2(4x)(4.5)+4.5^2=7+4.5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2[/tex]

[tex](4x-4.5)^2=7+20.25\\(4x-4.5)=27.25\to 4x-4.5=\pm\sqrt{27.25}\\\\4x-\dfrac{45}{10}=\pm\sqrt{\dfrac{2725}{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{2725}}{\sqrt{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25\cdot109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25}\cdot\sqrt{109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{5\sqrt{109}}{10}\qquad\text{add}\ \dfrac{45}{10}\ \text{to both sides}\\\\4x=\dfrac{45}{10}\pm\dfrac{5\sqrt{109}}{10}[/tex]

[tex]4x=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 4}\\\\x=\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\\\\\text{Put the values of}\ x\ \text{to (2):}\\\\9y=4\left(\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\right)-9\\\\9y=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}-\dfrac{18}{2}\\\\9y=-\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 9}\\\\y=-\dfrac{1}{2}\pm\dfrac{\sqrt{109}}{18}[/tex]

Answer:

The function is neither even nor odd.

Step-by-step explanation:

the function is even if f(-x) = f(x)

The function is odd if f(-x) = -f(x)

We are given the function:

f(x) = 3(x-1)^4

Solving

f(x) = 3(x^4 -4x^3+6x^2-4x+1)

f(x) = 3x^4-12x^3+18x^2-12x+3

Now putting -x instead of x i,e f(-x)

f(-x) = 3(-x)^4-12(-x)^3+18(-x)^2-12(-x)+3

Solving

f(-x) =3x^4+12x^3+18x^2+12x+3

so, f(-x) ≠ f(x) The function is not even

and f(-x) ≠ -f(x) The function is not odd

Hence the function is neither even nor odd.

The answer is C. y = -3x - 7

The equation of the line that is parallel to the line 3x + y = 5 and passing through (-1, -4) will be 3x + y + 7 = 0.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The equation of the line that is parallel to the line 3x + y = 5 and passing through (-1, -4).

We know the equation of a parallel line is given as 3x + y = C

The equation is passing through (-1, -4).

Then we have

C = 3 × (-1) + (-4)

C = - 3 - 4 C = -7

Then the equation of the parallel line will be

3x + y = -7

3x + y + 7 = 0

More about the linear system link is given below.

https://brainly.com/question/20379472

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Answer:

4(3n+2) or 12n+8

Step-by-step explanation:

Given expression is:

[tex](\frac{8}{6n-4})(9n^{2}-4)[/tex]

The numerator of the fraction will be multiplied with 9n^2- 4

So, Multiplication will give us:

[tex]=\frac{8(9n^2-4)}{6n-4}[/tex]

We can simplify the expression before multiplication.

The numerator will be broken down using the formula:

[tex]a^2 - b^2 = (a+b)(a-b)\\So,\\= \frac{8[(3n)^2 - (2)^2]}{6n-4}\\ = \frac{8(3n-2)(3n+2)}{6n-4}[/tex]

We can take 2 as common factor from denominator

[tex]=\frac{8(3n-2)(3n+2)}{2(3n-2)}\\After\ cutting\\= 4(3n+2)[/tex]

Hence the product is 4(3n+2) or 12n+8 ..

Answer: 1 and the second part is 12n+8

Step-by-step explanation:Edgen2020

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~\stackrel{origin}{(\stackrel{0}{ h},\stackrel{0}{ k})}\qquad \qquad radius=\stackrel{15}{ r} \\\\\\ (x-0)^2+(y-0)^2=15^2\implies x^2+y^2=225[/tex]

Answer:

66 (B.)

Step-by-step explanation:

I hust got an 100% on the unit test

Final answer:

Using the formula C = πd with pi (3.14) and the given diameter 21 cm, the circumference is calculated to be 65.94 cm, which rounds to 66 cm, making the correct answer B. 66.

Explanation:

The circumference (C) of a circle is calculated by the formula C = πd, where π (pi) is a constant approximately equal to 3.14, and d is the diameter of the circle.

Given the diameter of 21 cm for the circle, we calculate the circumference as follows:

When rounded to the nearest whole number, the circumference is 66 cm.

Therefore, the correct answer is choice B. 66.

Answer:

Step-by-step explanation:

Answer:

The correct answer is R0, 270°

Answer:

ln 27x²

Step-by-step explanation:

Using the rules of logarithms

• log[tex]x^{n}[/tex] ⇔ nlogx

• logx + logy ⇒ logxy

Given

3 ln 3 + 2 ln x, then

= ln 3³ + lnx²

= ln 27 + lnx² = ln 27x²

This prompt involves calculating total revenue, marginal revenue, total cost, and marginal cost for a competitive firm and finding the profit maximizing quantity of dog coats sold. The analysis is done by constructing a table and graphing relevant curves to identify where marginal revenue equals marginal cost.

The question regards the calculation of total revenue, marginal revenue, total cost, and marginal cost for a perfectly competitive firm, Doggies Paradise Inc., and the identification of the profit maximizing quantity of dog coats sold. To find these values, a table must be constructed with output levels from one to five units. The price per unit is $72, and fixed costs are $100, with variable costs increasing with each additional unit produced. The total revenue (TR) is the price multiplied by the quantity sold, while the marginal revenue (MR) is the additional revenue from selling one more unit. Total cost (TC) is the sum of fixed costs and variable costs at each output level, and marginal cost (MC) is the change in total costs when production is increased by one unit. The profit maximizing quantity is determined where MR equals MC or where the additional cost of producing one more unit no longer yields an additional profit.

Total Revenue and Total Cost Curves

Sketching these curves will show the relationship between the cost of producing dog coats and the revenue generated from sales at different production levels. The TR curve shows a steady increase as more units are sold, while the TC curve reflects the fixed costs and the upward slope as variable costs increase with higher output.

Marginal Revenue and Marginal Cost Curves

Graphing MR against MC allows for visual determination of the profit maximizing output, which is the point where the two curves intersect. This indicates that producing any more units beyond this point will not increase profit.

Answer:

Step-by-step explanation:

3√2 sec(x) + 2 = 2√2 sec(x)       Subtract    2√2 sec(x)   from both sides

√2 sec(x)  + 2 = 0                         Subtract 2 from both sides.

√2 sec(x)  = - 2

The secant is related to the cosine. sec(x) = 1/cos(x). The statement tells you that wherever the cos(x) < 0 , the secant will be as will. That means your answer will be in quad 2 and quad 3 and you are to use the appropriate rules for theta in those two quads.

It turns out that you could do this by using the reciprocal of 2

cos-1(- 0.5) = 120 degres. In terms of pi (which is 180 degrees)

120/180 * pi = (2/3) * pi

In quad three you would get pi + pi/3 = 4/3 pi

So your answers are

2/3 pi and 4/3 pi

[tex]\bf -\cfrac{1}{4}(vq^4)(-8v^3q)^2\implies -\cfrac{1}{4}(vq^4)\stackrel{\textit{distributing the exponent}}{[(-8)^2v^{2\cdot 3}q^2]}\implies -\cfrac{1}{4}(vq^4)(64v^6q^2) \\\\\\ -\cfrac{1}{4}(vq^4 64v^6q^2)\implies -\cfrac{64}{4}(v v^6 q^4q^2)\implies -16v^{1+6}q^{4+2}\implies -16v^7q^6[/tex]

Answer:

f(x) = 3x² -21x + 30

Step-by-step explanation:

Polynomial function of lowest degree with roots as 'a' and 'b' and leading coefficient as 'c' is given by:

P(x) = c (x - a) (x - b)

Given: Leading coefficient = 3, Roots = sqrt 5 and 2

P(x) = 3 (x - 5) (x - 2)

      = 3 ( x² - 2x - 5x +10)

       = 3 ( x² - 7x +10)

       = 3x² - 21x + 30

Only one person can win gold, silver, and bronze. The order of the winner does matter. So it’ll be 18 times 17 times 16.

Answer: 4,896

Stwhiep-by-step explanation:

Given, There are 18 skaters competing in the competition.

To find : The number of ways in which they can win gold, silver, and bronze medal.

Since, in distribution of medals(gold, silver, and bronze) we require 3 winners in a particular order, so for this we use Permutations.

According to permutation , number of ways of selecting r things out of n = [tex]\dfrac{n!}{(n-r)!}[/tex]

Then, The number of ways in which 18 skaters can win 3 medals= [tex]\dfrac{18!}{(18-3)!}=\dfrac{18\times17\times16\times15!}{15!}=4,896[/tex]

Hence, the required number of ways =4,896

Answer:

The system of inequalities is

[tex]y\leq x+3[/tex]

[tex]y\leq -2x+3[/tex]

Step-by-step explanation:

step 1

Find the equation of the solid line that goes through the points negative 3, 0, negative 4, negative 1

Let

A(-3,0),B(-4,-1)

Find the slope

m=(-1-0)/(-4+3)

m=-1/-1=1

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

we have

m=1

point A(-3,0)

substitute

y-0=(1)(x+3)

y=x+3

The solution is the shaded area below the solid line

therefore

The equation of the first inequality is equal to

[tex]y\leq x+3[/tex]

step 2

Find the equation of the solid line that goes through the points 1, 1, 2, negative 1

Let

C(1,1),D(2,-1)

Find the slope

m=(-1-1)/(2-1)

m=-2/1=-2

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

we have

m=-2

point C(1,1)

substitute

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

y=-2x+2+1

y=-2x+3

The solution is the shaded area below the solid line

therefore

The equation of the first inequality is equal to

[tex]y\leq -2x+3[/tex]

therefore

The system of inequalities is

[tex]y\leq x+3[/tex]

[tex]y\leq -2x+3[/tex]

Answer:

In two similar geometric figures, the ratio of their corresponding sides is called the scale factor. To find the scale factor, locate two corresponding sides, one on each figure. Write the ratio of one length to the other to find the scale factor from one figure to the other

Step-by-step explanation:

Answer:

its 8 i just finished the test

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

If

[tex]f(x)=-x^2 +3x+5[/tex]

and

[tex]g(x)=x^2 +2,[/tex]

then

[tex](f+g)(x)=-x^2+3x+5+x^2+2=3x+7[/tex]

This is the linear function. To plot the graph of this function, find x- and y- intercepts:

x-intercept:

[tex]y=0\Rightarrow 3x+7=0\\ \\3x=-7\\ \\x=-\dfrac{7}{3}[/tex]

y-intercept:

[tex]x=0\Rightarrow y=3\cdot 0+7\\ \\y=7[/tex]

Plot these two points on the coordinate plane and connect them with a straight line.

The answer is y=2 !!!!!!!!!!!!!!

Answer:

y = 2

Step-by-step explanation:

3x + 5y = 1

7x + 4y = −13

We will use the elimination method to eliminate the x variable. Then we will solve for y. We need the coefficients of the x-terms in the two equations to be additive inverses, so they will add to zero, eliminating x.

Multiply both sides of the first equation by -7, and multiply both sides of the second equation by 3.

-21x - 35y = -7

21x + 12y = -39

Now add the equations to eliminate x.

-23y = -46

Divide both sides by -23.

y = 2

B. 6

C. 4

D. 7

E. 1

F. 2

G. 6

Hope this helps :)

It took me a min to understand how they were doing the numbers corresponding to the letters lol

Answer with explanation:

a → 3

b → 5

c→ 4

d →7

e→ 1

f→2

g→6

Answer: (-1,3,1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the formula of an area of a triangle:

[tex]A=\dfrac{1}{2}bc\sin A=\dfrac{1}{2}ac\sin B=\dfrac{1}{2}ab\sin C[/tex]

Therefore we have the equation:

[tex]\dfrac{1}{2}bc\sin A=\dfrac{1}{2}ac\sin B[/tex]     multiply both sides by 2

[tex]bc\sin A=ac\sin B[/tex]           divide both sides by c

[tex]b\sin A=a\sin B[/tex]          divide both sides by sin A

[tex]b=\dfrac{a\sin B}{\sin A}[/tex]

We have

[tex]\sin A=0.3,\ \sin B=0.4,\ a=12[/tex]

Substitute:

[tex]b=\dfrac{(12)(0.4)}{0.3}=\dfrac{4.8}{0.3}=\dfrac{48}{3}=16[/tex]

Using the Law of Sines and given values sinA, sinB, and side a, we can determine that the length of side b in the triangle is 16 units.

To find the length of side b in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant:

a / sin A = b / sin B = c / sin C

Given that sinA = 0.3, sinB = 0.4, and a (side opposite angle A) is 12, we can write

12 / 0.3 = b / 0.4

Multiplying both sides of the equation by 0.4 and solving for b gives us:

b = (12 / 0.3) * 0.4

b = 40 * 0.4

b = 16

Therefore, the length of side b is 16 units.

Answer:

Region A is the region represents the graph of the feasible region

for the given constraints

Step-by-step explanation:

* Lets look to the graph to answer the question

# y ≥ 2x represented by the orange line

∵ The sign of inequality is greater than, then the shaded part will

   be over the line

∴ The solution is in A region

# x + y ≤ 14 represented by the purple line

∵ The sign of inequality is smaller than, then the shaded part will

   be under the line

∴ The solution is in A or B or C regions

# y ≥ 1 represented by the pink line

∵ The sign of inequality is greater than, then the shaded part will

   be over the line

∴ The solution is in A or B or C regions

# 5x + y ≥ 14 represented by the blue line

∵ The sign of inequality is greater than, then the shaded part will

   be over the line

∴ The solution is in A or B or C regions

# x + y ≥ 9 represented by the green line

∵ The sign of inequality is greater than, then the shaded part will

   be over the line

∴ The solution is in A or B regions

* From all above The common region in the five inequalities is A

∴ Region A is the region represents the graph of the feasible region

  for the given constraints

Answer:

A. Region A

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

To find the y- intercept let x = 0 in the function

g(0) = 0 - 0 - 84 = - 84 ← y- intercept

To find the x- intercepts let y = 0, that is

x² - 5x - 84 = 0

To factor the quadratic

Consider the factors of the constant term (- 84) which sum to give the coefficient of the x- term

The factors are - 12 and + 7, since

- 12 × 7 = - 84 and - 12 + 7 = - 5, thus

(x - 12)(x + 7) = 0

Equate each factor to zero and solve for x

x - 12 = 0 ⇒ x = 12

x + 7 = 0 ⇒ x = - 7

x- intercepts are x = - 7 and x = 12

Answer:

option C

{-11/3 , 19/3}

Step-by-step explanation:

Given in the question an equation

|3x-4| = 15

To solve the absolute equation we need to add ± on right side of equation.

3x-4 = ±15

3x = 15+4 or 3x = -15 + 4

3x = 19  or  3x = -11

x = 19/3  or  x = -11/3

The solution of |3x-4| = 15 is {-11/3 , 19/3}

Answer:

The solution of I3x - 4I = 15 is {-11/3 , 19/3}

Step-by-step explanation:

* Lets explain the meaning of I I (absolute value)

- The absolute value of any number is the magnitude of the number

means the value of the number without its sign, we ignore the sign

of the number

- The absolute never equal a negative value

- If IxI = a, then x = a or x = -a

* Now lets solve the problem

∵ I3x - 4I = 15

∴ 3x - 4 = 15 OR 3x - 4 = -15

* Lets solve the two equation

∵ 3x - 4 = 15 ⇒ add 4 to both sides

∴ 3x = 19 ⇒ divide both sides by 3

∴ x = 19/3

∵ 3x - 4 = -15 ⇒ add 4 to both sides

∴ 3x = -11 ⇒ divide each side by 3

∴ x = -11/3

* The solution of I3x - 4I = 15 is {-11/3 , 19/3}

For this case we must find the quotient of the following expression:

[tex]\frac {-8x ^ 6} {4x ^ {- 3}} =[/tex]

By definition of power properties we have:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Rewriting the expression we have:

[tex]\frac{-8}{4}*x^6*x^3[/tex]

By definition of multiplication of powers of the same base we have to put the same base and add the exponents:

[tex]-2x^{6+3}[/tex]

Answer:

[tex]-2x ^ 9[/tex]

Answer:

[tex]30 < \frac{1}{2}x[/tex]

Step-by-step explanation:

we know that

The algebraic expression of the phrase " thirty less than one half the value of x" is equal to

[tex]30 < \frac{1}{2}x[/tex]

solve for x

Multiply by 2 both sides

[tex]2*30 < x[/tex]

[tex]60 < x[/tex]

Rewrite

[tex]x > 60[/tex]

The solution is the interval ----> (60,∞)

All real numbers greater than 60

The phrase 'thirty less than one half the value of x' can be interpreted as a mathematical statement and translated into the algebraic equation 0.5x - 30.

The question 'thirty less than one half the value of x' asks us to express a mathematical concept in an algebraic equation. We can do this by firstly taking half the value of x, represented as 0.5x. Following the phrase 'thirty less than', we subtract 30 from this half-value of x, giving the equation "0.5x - 30". So, when someone says 'thirty less than one half the value of x', they are referring to this mathematical equation.

https://brainly.com/question/28612373

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Answer:

Step-by-step explanation:

[tex]-7-i\\\\\text{complex conjugate:}\ -7+i\\\\(-7-i)(-7+i)\qquad\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=(-7)^2-(i)^2\qquad\ i=\sqrt{-1}\to i^2=-1\\\\=49-(-1)\\\\=49+1\\\\=50[/tex]

Answer:

It is 5 miles difference . GOOD JOB!!!!!!!!!!!!!!!

Step-by-step explanation:

Answer:

Yes, the distance is 5 miles

Step-by-step explanation:

Since the y-coordinates are the same, we can ignore the y-distance and treat the total distance like a number line.

So, the distance is |9 - 4| = 5 units

Since each unit is a mile, that translates the distance to 5 miles.