Andy and Jacob work as technicians in a laboratory where gemstones are tested and certified. Andy has already tested 30 gemstones and continues testing at a rate of 30 gemstones per hour. Jacob has already tested 40 gemstones and continues testing at a rate of 25 gemstones per hour. Which function can Andy and Jacob use to determine the total number of gemstones they have tested after x hours? How many gemstones will they have tested after 5 hours? A. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 55x + 10. Thus, they will have tested 285 gemstones in 5 hours. B. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 70x + 55. Thus, they will have tested 405 gemstones in 5 hours. C. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 55x + 70. Thus, they will have tested 345 gemstones in 5 hours. D. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 60x + 65. Thus, they will have tested 365 gemstones in 5 hours.

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:

[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:

50

Step-by-step explanation:

[tex]500 \div 100 \times 25 = 125[/tex]

[tex]500 \div 100 \times 15 = 75[/tex]

[tex]125 - 75 = 50[/tex]

50. From 500 people, 25% that prefer burger represent 125 people and 15% that prefer cheeseburger represent 75. This mean there are 50 more people that prefer burgers than cheeseburgers.

The key to solve this problem is by direct rule of three, we will place the 3 values (which we will call “a”, “b”, and “c”) and the unknown value that we want to figure out (“x”) to apply the formula:

a -----------> b

c -----------> x

[tex]x=\frac{b.c}{a}[/tex]

The circle graph represents the responses from 500 people in percentage.

To calculate the amount of people that prefer burgers:

If 100% ----------------> 500 people

    25% ----------------> x

[tex]x=\frac{(500)(25)}{100}= 125[/tex] which means 125 people prefer burgers

To calculate the amount of people that prefer cheeseburgers:

If 100% ----------------> 500 people

    15% ----------------> x

[tex]x=\frac{(500)(15)}{100}= 75[/tex] which means 75 people prefer cheeseburgers.

In order to know how many more people prefer burgers than cheeseburgers, let's apply the difference between people who prefer burgers and people who prefer cheeseburgers:

125 - 75 = 50 which mean 50 more people prefer burgers than cheeseburgers.

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!!

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:

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

[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:

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

Step-by-step explanation:

It is in the question.

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°

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

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: 2.0736 ft

Step-by-step explanation:

Bounce 1: 16*3/5=9.6

Bounce 2: 9.6*3/5=5.76

Bounce 3: 5.76*3/5=3.456

Bounce 4: 3.456*3/5=2.0736

Answer:

The ball will bounce to 2.07 feet after 4th drop.

Step-by-step explanation:

Bradley dropped a ball from a roof 16 feet high. So, its the initial height.

Each time the ball hits the ground it bounces 3/5 the previous height.

Means after 1st drop, the ball will again rise to [tex]\frac{3}{5}\times16= 9.6[/tex] feet.

Similarly after 2nd drop, it will bounce to  [tex]\frac{3}{5}\times9.6=5.76[/tex]

After 3rd drop, it will bounce to [tex]\frac{3}{5}\times5.76=3.456[/tex] feet

After 4th drop, it will bounce to [tex]\frac{3}{5}\times3.456=2.0736[/tex] feet

Hence, the ball will bounce to 2.07 feet after 4th drop.

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:

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:

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

[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:

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:

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

[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:

f(x) = 4^x

Step-by-step explanation:

In f(x) = (1/4)^x, 1/4 is equal to 0.25, which is less than 1, so its decreasing

In f(x) = 4^x, 4 is greater than 1, so its increasing

In f(x) = (0.4)^x, 0.4 is less than 1, so its decreasing

This is why f(x) = 4^x is the correct answer

I hope this helps!

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.

https://brainly.com/question/14240165

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Answer:

The definition of a circle uses the undefined term is plane then the undefined term can contain parallel lines is plane and. The definition of an angle uses the undefined term is point likewise there are 3 possible geometry will fall.

Hope I helped

Step-by-step explanation:

The slope would be the first one, 2/3. Hope this helps! Please mark brainliest! :) Thanks v much! :)

Answer:

2/3

Step-by-step explanation:

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}

Answer:

A = bh

A = 15(8)

A = 120 square centimeters

well then, the volume of the nose cone will just be the sum of the volume of the cylinder below and the cone above.

since the diameter for both is 8, then their radius is half that, or 4.

[tex]\bf \stackrel{\textit{volume of a cone}}{V=\cfrac{\pi r^2 h}{3}}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=6 \end{cases}\implies V=\cfrac{\pi (4)^2(6)}{3}\implies V=32\pi \\\\\\ \stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=6 \end{cases}\implies V=\pi (4)^2(6)\implies V=96\pi \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of the nose cone}}{32\pi +96\pi \implies 128\pi }\qquad \approx \qquad 402.12[/tex]

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: 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.

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]

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