Apply the distributive property to factor out the greatest common factor.
30+42=

[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:

B) 8

Step-by-step explanation:

To count the number of possibilities on a tree diagram, all you need to do is count the total number of "branches" at the end of the "tree". Here, that is 8. Also, if the tree gets too big, you can multiply the number of combinations in the first sector, then the second, and so on. So, that will be 4 * 2 = 8.

Answer:

B). 8

Step-by-step explanation:

i go this right on my quiz if u want proof scroll down

I really hope this helps someone! have a great day!!

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:

y= 300 - 5/9x

Step-by-step explanation:

0.8y = 240 - 0.5x

divide both sides by 0.8,

y= 300 - 5/9x

-5/9 is your gradient

300 is your y-intercept

To graph 0.5x + 0.8y = 240, first arrange the equation into y = mx + b form, where m is the slope and b is the y-intercept. Finally, plot this equation on a graph using the slope and y-intercept.

To graph the equation 0.5x + 0.8y = 240, you need to first arrange it in the form of y = mx + b (slope-intercept form), where m is the slope and b is the y-intercept.

Solving for y, we get:

0.8y = -0.5x + 240

y = -0.625x + 300

Then you can plot this equation in the format y = mx + b on a graph. Place the y-intercept at 300 on the y-axis. From there, use the slope (-0.625) to find the second point: down 0.625 units and to the right 1 unit. Repeat this step to plot a few points and then draw a line passing through them.

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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.

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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:

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

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

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:

Step-by-step explanation:

The formula of an area of a rectangle:

[tex]A_r=lw[/tex]

l - length

w - width

We have l = 12 in and w = 8 in.

Substitute:

[tex]A_r=(12)(8)=96\ in^2[/tex]

The formula of an area of a triangle:

[tex]A_t=\dfrac{bh}{2}[/tex]

b - base

h - altitutde

We have b = 32 in and A - 96 in².

Substitute:

[tex]\dfrac{32h}{2}=96[/tex]

[tex]16h=96[/tex]          divide both sides by 16

[tex]h=6\ in[/tex]

Answer:

d = 3

Step-by-step explanation:

3.5d + 6.25 = 1 + 5.25d

5.25d - 3.5d = 6.25 - 1

1.75d = 5.25

d = 5.25 ÷ 1.75 = 3

Answer:

Step-by-step explanation:

If for x ≤ y < z

x² + y² = z²

then x, y and z form a right triangle.

1 .

15m, 20m, 25m

15² + 20² = 225 + 400 = 625

25² = 625

CORRECT :)

2.

3ft, 6ft, 5ft

3² + 5² = 9 + 25 = 34

6² = 36

34 ≠ 36

3.

10in, 41in, 40in

10² + 40² = 100 + 1600 = 1700

41² = 1681

1700 ≠ 1681

4.

7cm, 8cm, 10cm

7² + 8² = 49 + 64 = 113

10² = 100

113 ≠ 100

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

Answer:

50 is the change per week. And the starting total is 650.

Step-by-step explanation:

It is in the question.

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:

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

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.

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:

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}

The answers is A: 90 Degrees

Answer:  The correct option is (A) 90°.

Step-by-step explanation:  We are given to find the number of degrees by which the triangle ABC has been rotated counterclockwise about the origin.

From the graph, we note that

the co-ordinates of the vertices of triangle ABC are A(-8, 6), B(-5, 9) and C(-2, 6).

And, the co-ordinates of the vertices of the rotated triangle A'B'C' are (-6, -8), B(-9, -5) and C(-6, -2).

That is, the transformation is as follows :

(x, y)   ⇒    (-y, x).

Since this is the transformation rule for 90 degrees counterclockwise, so the required number of degrees is 90 degrees.

Option (A) is CORRECT.

Answer:

Step-by-step explanation:

Graph y = -3x.  Start at the origin (0, 0).  Place a dark dot there.  Now, starting with your pencil point on that dot, move 1 space to the right and from this new point move 3 spaces down.  Place a dark dot at this new point.

Now draw a straight line through both dark dots.  This is the desired graph.

Step-by-step explanation: Let's graph the equation y = -3x using its slope and y-intercept. The problem here is that our equation doesn't match up quite so well with the formula y = mx + b

Our slope or m which is represented by the coefficient of the x-term is clearly -3. However, you might be asking what is our y-intercept or b. Well, y = -3x can be thought of as y = -3x + 0. So you can now see that our b or y-intercept equals 0.

To graph the line, we start with the y-intercept. So our first point is a 0 on the y-axis and we call that point A. When the slope is a integer, you can change it to a fraction by putting it over 1. So our slope of -3 can be thought of as -3/1.

From point A, we would go down 3 units and over 1 unit to plot point B. Now we can connect points A and B like I did in the picture and we have our line.

Answer: The answer is d 10 times 2 squared-the last choise.

BECAUSE:a squared + b squared = c squared

10 squared + 10 squared = c squared

100+100=c squared

the square root of 200 = c squared

PUT ME AS BRAINLIESTTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer:

10√2 units

Step-by-step explanation:

Given : A right angles triangle QRS

           QS= SR = 10 units

To Find : Hypotenuse

Solution:

Perpendicular = 10 units

Base = 10 units

Hypotenuse = QR

Now we will use Pythagoras theorem

[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]

[tex]QR^2=QS^2+SR^2[/tex]

[tex]QR^2=10^2+10^2[/tex]

[tex]QR^2=100+100[/tex]

[tex]QR^2=200[/tex]

[tex]QR=\sqrt{200}[/tex]

[tex]QR=10\sqrt{2}[/tex]

Hence the length of the hypotenuse of the triangle is 10√2 units

So, Option D is correct.

[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

[tex]< \frac{1}{5} , - \frac{1}{3} \: >[/tex]

EXPLANATION

The given vector , u has the following components,

[tex]u = < \: - 5 , - 3 \: > [/tex]

If two vectors are orthogonal, then their dot product is zero.

[tex]< \: - 5 , - 3 \: > \bullet < \: \frac{1}{5} , - \frac{1}{3} \: > = - 5 \times \frac{1}{5} \times - 3 \times - \frac{1}{3} = - 1 + 1 = 0[/tex]

Hence,the vector

[tex] < \frac{1}{5} , - \frac{1}{3} \: >[/tex]

is orthogonal to vector u.

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:

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:

1, 2, 3, 5, 6, 10, 15, 30.

Answer:

Positive factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

Step-by-step explanation:

We are asked to list the positive factors of the number 30.

Factors are the whole numbers which when multiplied together produce another number. So positive factors only include the whole numbers that are greater than 0.

Positive factors of 30 include the following whole numbers:

[tex]1, 2, 3, 5, 6, 10, 15, 30[/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 surface area of the two triangles is 12 cm^2.

3*4=12

The surface area of the bottom rectangle is 8 cm^2.

4*2=8

The surface area of the rectangle that is on the left side of the figure is 6 cm^2.

3*2=6

The surface area of the rectangle that is on the top side of the figure is 10 cm^2.

To find the third side of the triangle, use the Pythagorean theorem.

3^2+4^2=h^2

9+16=25

The third side of the triangle is 5 cm.

The surface area of the whole figure is 36 cm^2.

12+8+6+10=36

Answer:

The correct answer is option A.   25°

Step-by-step explanation:

From the figure we can see an isosceles triangle. FGE

<G = 65° (given)

m<G = m<E = 65°

To find the value of m<HFE

Consider the triangle FHE in the figure we get,

m<E +  m<HFE + m<FHE  = 180

m<HFE = 180 - (m<E + m<FHE)

 = 180 - (65 + 90) = 25°

Therefore m<HFE = 25°

The correct answer is option A.   25°

The correct answer is option A. 25°