17. A bag contains 2x yellow counters, 4x + 6 red counters and 6x - 10 blue counters. a. Write an expression, in terms of x, for the total number of counters in the bag.
The total number of counters in the bag is 44.
b. Work out the number of blue counters in the bag.
c. How many more red counters are there than blue counters in the bag?​

Rounded to the nearest square units, the surface area of the cone, is: 524 square units.

The surface area of a cone = πr(r + l), where:

r is the radius of the cone

l is the length of the cone.

Given the following:

Radius of the cone (r) = 12/2 = 6 units

Slant height of the cone (l) = √(21² + 6²) [Pythagorean theorem]

Slant height of the cone (l) = 21.8 units.

Plug in the values into πr(r + l):

Surface area of the cone = π × 6(6 + 21.8)

Surface area of the cone = 3.14 × 6(27.8)

Surface area of the cone ≈ 525 square units

The surface area of the cone, approximated to the nearest square units, we have: 524 square units.

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Given the point U and point V, the midpoint between of the line segment UV is ( 0, -5/2 ).

The midpoint formula is used to find the midpoint of a line segment.

It is expressed as;

[ (x₁ + x₂ )/2 , (y₁ + y₂ )/2 ]

Given the data in the graph,

Point U = ( 3, -1 ) and Point V = ( -3, -4 )

We substitute into the formular above.

[ (x₁ + x₂ )/2 , (y₁ + y₂ )/2 ]

[ (3 + (-3) )/2 , ( (-1) + (-4) )/2 ]

[ 0/2, (-1-4)/2 ]

[ 0/2, -5 /2 ]

( 0, -5/2 )

Given the point U and point V, the midpoint between of the line segment UV is ( 0, -5/2 ).

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Answer:

Step-by-step explanation:

A chord is a straight line that connects two points on a curve. An arrangement of three or more notes that blend harmoniously when played together.

A section of a circle has both endpoints on the circle. Chords are the sections of a circle.

Therefore, the final answer is "chords".

I hope this helps, let me know if you have any questions.

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The system of the linear systems of equation using substitution is;

3x-y=4

x+2y=6

from (2)

x = 6 - 2y

substitute into (1)

3x-y=4

3(6 - 2y) - y = 4

18 - 6y - y = 4

- 6y - y = 4 - 18

-7y = -14

y = 2

Substitute into

x+2y=6

x + 2(2) = 6

x + 4 = 6

x = 6 - 4

x = 2

2. 2x-y= -39

x+y= -21

From (2)

x = -21 - y

substitute into

2x-y= -39

2(-21 - y) - y = -39

-42 - 2y - y = -39

- 2y - y = -39 + 42

- 3y = 3

y = 3/-3

y = -1

substitute into

x+y= -21

x + (-1) = -21

x - 1 = -21

x = -21 + 1

x = -20

3. 2x+y =11

6x-5y =9

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Answer:

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=-4^x+5\\g(x)=x^3+x^2-4x+5 \end{cases}[/tex]

This is an exponential function.

An exponential function includes a real number with an exponent containing a variable.

x-intercept (when y = 0):

[tex]\begin{aligned}f(x) & = 0\\\implies -4^x+5 & =0\\ 4^x &=5\\\ln 4^x &= \ln 5\\x \ln 4 &= \ln 5\\x&=\dfrac{ \ln 5}{\ln 4}\\x&=1.16\:\: \sf(2\:d.p.)\end{aligned}[/tex]

Therefore, the x-intercept of f(x) is (1.16, 0).

y-intercept (when x = 0):

[tex]\begin{aligned}f(0) & = -4^{0}+5\\& = 1+5\\& = 6\end{aligned}[/tex]

Therefore, the y-intercept of f(x) is (0, 6).

End behavior

[tex]\textsf{As }x \rightarrow \infty, \: f(x) \rightarrow \infty[/tex]

[tex]\textsf{As }x \rightarrow -\infty, \: f(x) \rightarrow 5[/tex]

Therefore, there is a horizontal asymptote at y = 5 which means the curve gets close to y = 5 but never touches it.  Therefore:

This is a polynomial function of degree 3 (since the greatest exponent of the function is 3).

A polynomial function is made up of variables, constants and exponents that are combined using mathematical operations.

x-intercept (when y = 0):

There is only one x-intercept of function g(x).  It can be found algebraically using the Newton Raphson numerical method, or by using a calculator.

From a calculator, the x-intercept of g(x) is (-2.94, 0) to 2 decimal places.

y-intercept (when x = 0):

[tex]\begin{aligned}g(0) & = (0)^3+(0)^2-4(0)+5\\& = 0+0+0+5\\& = 5 \end{aligned}[/tex]

Therefore, the y-intercept of g(x) is (0, 5).

End behavior

[tex]\textsf{As }x \rightarrow \infty, \: f(x) \rightarrow \infty[/tex]

[tex]\textsf{As }x \rightarrow -\infty, \: f(x) \rightarrow - \infty[/tex]

Therefore:

Conclusion

Key features both functions have in common:

Answer:

$613.04

Step-by-step explanation:

Compound Interest Formula:

   [tex]A = P(1+\frac{r}{n})^{nt}[/tex]

   n = number of compounds

   t = time

   r = interest rate

   P = principle amount (original amount)

   A = final amount

Since it's compounded quarterly, that means there will be 4 compounds per year, so n=4. The interest rate has to be converted to the decimal value, and this is done by simply dividing it by 100 to get r=0.06.

Plug Values into equation:

[tex]A = 300(1+\frac{0.06}{4})^{12*4}[/tex]

Simplify inside parenthesis

[tex]A = 300(1.015)^{48}[/tex]

Calculate exponent

[tex]A \approx 300(2.043478)[/tex]

Multiply values

[tex]A \approx 613.04348[/tex]

Round

[tex]A = 613.04[/tex]

[tex]1.2 \: degrees \: drop \: a \: day \\ 14 \: days \: in \: two \: weeks \\ net \: change = 14 \times 1.2 = 16.8 \: deg[/tex]

Answer:

A

Step-by-step explanation:

Based on the given table:

(x, y )  values  are

(-1, 0)

(0, 3)

(1, 6)

A.

y = 3x+3, substitute each x and y pair in the equation to see if it checks

(x= -1, y= 0)              (x= 0, y= 3)          (x= 1, y= 6)

0 = -1·3+3                 3 = 0·3 +3          6 = 1·3 + 3

0 = 0✅                    3 = 3✅               6 = 6✅

The company is considering the purchase of a new machine for $75,660 (based on the available data), and the payback period is 24 years.

The payback period is the time the company requires to recoup its investment for the new machine.

The payback period can be computed by dividing the investment cash outflows by the annual net cash inflows.

Initial investment in new machine = $75,660

Annual depreciation expense = $4,600

Investment period = 10 years

Annual sales revenue = $20,000

Annual expenses = $16,800

Ne annual cash inflow = $3,200 ($20,000 - $16,800)

Payback period = 24 years ($75,660/$3,200)

Thus, since the payback period is 24 years, while the investment period is 10 years, it sounds unwise for the company to continue the investment.

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Answer:

g = 4

Step-by-step explanation:

if 2 tangent segments are drawn to a circle from the same external point then they are congruent , that is

RJ = RW and MJ = MB and KB = KW

given MR = 6 , then

MJ = 6 - g = MB

given KM = 5 , then

KB = 5 - MB = 5 - (6 - g) = g - 1 = KW

given KR = 7 , then

RW = 7 - KW = 7 - (g - 1) = 8 - g

Then

RJ = RW , that is

g = 8 - g ( add g to both sides )

2g = 8 ( divide both sides by 2 )

g = 4

There are 66 ways Kim can put the 10 identical lamps on the 3 identical tables

The given parameters are:

The combination involving identical objects is calculated using:

(n + r - 1)C(r - 1)

So, we have:

n + r - 1 = 10 + 3 - 1

Evaluate the sum

n + r - 1 = 13 - 1

Evaluate the difference

n + r - 1 = 12

Also, we have:

r - 1 = 3 - 1

Evaluate the difference

r - 1 = 2

So, we have:

(n + r - 1)C(r - 1) = 12C2

Apply the following combination formula:

nCr = n!/((n - r)!r!)

So, we have:

12C2 = 12!/((12 - 2)! * 2!)

Evaluate the difference

12C2 = 12!/(10! * 2!)

Expand the numerator

12C2 = 12 * 11 * 10!/(10! * 2!)

Evaluate the quotient

12C2 = 12 * 11/2!

Expand the denominator

12C2 = 12 * 11/2 * 1

Evaluate the product

12C2 = 132/2

Evaluate the quotient

12C2 = 66

Hence, there are 66 ways Kim can put the 10 identical lamps on the 3 identical tables

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Answer: 6/23  mph

Step-by-step explanation: We change the 1/3 of an hour to 1 hour by multiplying 1/3 and 2/23 by 3. 1/3 times 3 is 1(hour) and 2/23 x 3 is 6/23(miles). So the unit rate the turtle is traveling at is 6/23 mph.

Answer:

c

Step-by-step explanation:

In geometry, an equilateral triangle is a triangle in which all three sides have the same length.

Answer:

Step-by-step explanation:

The standard form equation for a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where h and k are the coordinates of the center. Our center is given as (-6,7)  and the radius is given as 9, so that information fits into our standard form like this:

[tex](x-(-6))^2+(y-7)^2=9^2[/tex] and simplified, it looks like this:

[tex](x+6)^2+(y-7)^2=81[/tex]

That's choice C

Answer:

I think it's A (parallel)

Answer:

A. its parallel

Step-by-step explanation:

all angles are equal... two sides are perpendicular and two are parallel

Answer:

  (b)  x = 10.5

Step-by-step explanation:

The angle bisector divides the triangle line segments proportionally.

The proportion between corresponding line segments can be written several ways. One of them is ...

  long side/long side = short side/short side

  x/19.3 = 3.9/7.2

Multiplying by 19.3, we get ...

  x = 19.3×3.9/7.2 ≈ 10.5 . . . units

__

Additional comment

You can eliminate the incorrect answer choices simply by looking at the possible side lengths of x.

  19.3 -(3.9+7.2) < x < 19.3 +(3.9+7.2) . . . . . from triangle inequality

  8.2 < x < 30.4 . . . . . . . simplify

There is only one answer choice in this range: the correct one.

Answer:

{-2, -1, 1}

Step-by-step explanation:

Since we are given all the possible inputs {-8, -3, 7} we can use them one by one in the equation to find the outputs.

5y = x - 2 , if x is -8

5y = -8 - 2

5y = -10

y = -2

Next,

5y = x - 2, if x = -33

5y = -3 - 2

5y = -5

y = -1

Last,

5y = x - 2 when x =7

5y = 7 - 2

5y = 5

y = 1

So the set is {-2, -1, 1}

First of all, your question should be: Factor completely 2xy – 6mn – 3my + 4nx, and not Factorize completely 2xy – 6mn – 3m + 4nx. This noted, we proceed to the solution, which is:

2xy – 6mn – 3my + 4nx

→ y(2x – 3m) + 2n(–3m + 2x)

→ (2x – 3m) (y + 2n)

.: Final answer: (2x – 3m) (y + 2n)

(2x – 3m) (y + 2n) is the factorized form of  2xy -6mn - 3m + 4nx

Two or more expressions with an Equal sign is called as Equation.

Factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

The given expression is 2xy – 6mn – 3my + 4nx

Two times of xy minus six times of mn minus three times of m y plus four times of nx

2xy – 6mn – 3my + 4nx

By using commutative property arrange the terms

2xy –3my– 6mn+ 4nx

Take y as common from first two terms and 2n as common in last two terms

y(2x – 3m) + 2n(–3m + 2x)

(2x – 3m) (y + 2n)

Hence, (2x – 3m) (y + 2n) is the factorized form of  2xy -6mn - 3m + 4nx

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Answer:

Your answer is 7^2.

Step-by-step explanation:

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

Have a great day,

Nish

The equivalent expression is [tex]7^{2}[/tex].

We have the following expression -

[tex]\frac{7^{-3} }{7^{-5} }[/tex]

We have to find its equivalent value.

[tex]f(x, y) =\frac{A^{x} }{A^{y} }[/tex]

In order to divide two exponents with same base, we use the 'Quotient property of exponents.

The equivalent expression can be written as -

f(x, y) = [tex]A^{x} A^{-y} = A^{x-y}[/tex]

In the question given we have -

[tex]\frac{7^{-3} }{7^{-5} }[/tex]

Using the property discussed above -

[tex]7^{-3}\;7^{5}[/tex] = [tex]7^{-3+5}[/tex] = [tex]7^{2}[/tex]

Hence, the equivalent expression is [tex]7^{2}[/tex].

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1. Independent Variable (x) is the number of toys.

Dependent Variable (y) is the amount.

2. Graph A - Income Graph.

Graph B - Expense Graph.

3. Zandi won't make a profit while selling 5 toys.

4. Zandi must sell 10 toys to reach break-even.

5. Zandi's variable cost per toy is $15.

6. The total cost function is, total cost = 100 + 15x.

1. The independent variable will be the number number of toys marked on the x-axis, whereas the dependent variable will be the amount on the y-axis, as the cost and revenue both depend on the units.

2. Graph A will be Zandi's income as when the unit is 0, the income is 0, whereas graph B is the expense graph as when the unit is 0, still some fixed expenses are generated for example rent.

3. Zandi will make a loss while making and selling 5 toys as the amount on graph B corresponding to 5 toys, that is, the expenses, are greater than the amount on graph A corresponding to 5 toys, that is, the income.

4. The break-even is the point where the income = expense, which on the graph is at the point where the number of toys is 10.

Thus, Zandi must sell 10 boys to reach break even.

5. The variable cost per toy can be found as the slope of the expense graph, m = (400 - 100)/(20 - 0) = 300/20 = 15.

Thus, Zandi's variable cost is $15.

6. Total cost = Fixed cost + a number of units*variable costs.

Thus, the total cost = 100 + 15x.

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Answer:

The second option.
y > x^2 + 4x -2

y < 3x +4

Step-by-step explanation:

First off, we can eliminate the last option because the graph shows that both inequalities are greater than or less than, but not equal to. We come to this conclusion because both lines on the graph are dashed meaning not equal to. Look at the attached image below (1).

Next, we can input the point (0,0) and test to see if the inequality works. If we input the point (0,0) into the second equation in the second option, we end up with 0 < 4. This is factual meaning that this is your answer.
Hope this helps! If I wasn’t clear enough or you need more information, please let me know in the comments. Have an amazing day!

Answer:

Step-by-step explanation:

The expression is:

Find its value when n = 3, substitute n with 3 in the expression:

The matching answer choice is B.

Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.

Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.

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The solution of the equation is (2, 1).

x=2 and y=1

A mathematical assertion that two expressions are equal is known as equating. It can be expressed as either an identity, in which case the variables can take on any value, or a conditional equation, in which case the variables can only have specific values (roots).

We have two options for finding the answer. The first is to solve the equations via term elimination:

x + 3y = 5  ..............1

x - 3y = -1  ...............2

2x = 4 ..............3

With the equation, we can determine x. (3)

x = 4/2

x = 2

To determine y, we may now swap out x=2 in equation (1).

x + 3y = 5

2 + 3y = 5

3y = 3

y = 1

We've discovered x and y now.

x=2

y=1

The second method involves removing x from equation 1.

x + 3y = 5

x = 5 - 3y

In the equation right now, we may substitute x = 5 - 3y.........  (2)

x - 3y = -1

(5 - 3y) - 3y = -1

5 - 6y = -1

6y = -6

y = 1

Currently, we can change y=1 in equations (1), (2), or (4) to find x.

We'll apply the equation (1)

x + 3y = 5

x + 3(1) = 5

x + 3 = 5

x = 2

The two variants x = 2 and y = 1 have allowed us to confirm this.

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Answer:

Step-by-step explanation:

the ratio of the area of the triangle to the area of the rectangle is 1: 2

The formula for calculating the area of a triangle is;

Area of triangle = 1/ 2 base × height

The formula for area of a rectangle is;

Area of a rectangle = length ×  width

From the information given, we have;

Now, let's substitute the values;

Area of a triangle = 1/ 2 × 11 × 4

Area of a triangle = 44/ 2 = 22m²

Area of a rectangle = 11 × 4

Area of a rectangle = 44m²

The ratio of the area of the triangle to the area of the rectangle is

= 22: 44

= 1 : 2

Thus, the ratio of the area of the triangle to the area of the rectangle is 1: 2

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The interpretation of f(30) is the distance travelled after 30 minutes

The function is given as:

A function representing distance (feet) as a function of time (minutes),

This means that, the dependent variable is the distance and the time is the independent variable

This in other words means that:

x = time

f(x) = distance

So, the interpretation of f(30) is:

The distance travelled after 30 minutes

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Answer:

3 consecutive no.s are

5×6×7=210

sum of them is= 5+6+7

=18

So, I hope. it helps !!