b) The resale value of a piece of industrial equipment has been found to behave according to the function V=700,000e-0.02t.
i) What was the original value of the piece of equipment

The transformations are

The functions are given as:

f(x) = x

g(x)= x - 16

When a function is shifted right, the transformation rule is:

(x, y) = (x - h, y)

This means that the transformation is (d) A horizontal shift 16 units to the right

Since the parent function is a base linear function.

The transformation can also be represented as:

(x, y) = (x, k - h)

This gives

g(x)= x - 16

This means that the transformation is (b) A vertical shift 16 units downward.

Hence, the transformations are (b) and (d)

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Answer:

[tex]\tt x = 16[/tex]

Step-by-step explanation:

[tex]\tt 4x-64=0[/tex]

Add 64 to both sides.

[tex]\tt 4x - 64 + 64 = 0+ 64[/tex]

Simplify.

[tex]\tt 4x = 64[/tex]

Divide both sides by 4.

[tex] \tt \cfrac{4x}{4} = \cfrac{64}{4} [/tex]

Simplify.

[tex]\tt x = 16[/tex]

Done!!!

[tex]\Large\maltese\star\underline{\textbf{What is Asked}}\star\maltese[/tex]

[tex]\Large\maltese\star\underline{\textbf{The required answer is below -:}}\star\maltese[/tex]

First we need to add 64 to both sides. That way, we will be one step closer to solving this in terms of x.

[tex]\bf{4x-64+64=0+64}[/tex] | on the left side the 64's sum to zero

[tex]\bf{4x=0+64}[/tex] | the right side is now 64

[tex]\bf{4x=64}[/tex] | divide the equation by 4

[tex]\bf{x=16}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\gray\star\bf{Result / Required\;Answer:}[/tex]

                  [tex]\star\blacksquare\Large\boxed{\boxed{\bf{X=16.}}}\blacksquare\star[/tex]

When you're solving an equation in terms of x, or any other variable, use inverse operations to solve it. For instance, if something is added to x, use subtraction. If something is subtracted to x, use addition.

If x is multiplied by something, use division. If x is divided by something, use multiplication.

[tex]\infty\LARGE\boxed{\bf{\brace aesthetic\not1\theta\ell}}\infty[/tex]

Answer:

$17,500 was invested in the account that gained 10% and

$11,000 was invested in the account that lost 4%

Step-by-step explanation:

Define the variables:

Given information:

Percentages in decimal form:

Create a system of equations using the given information and defined variables:

[tex]\begin{cases}x + y = 28500\\0.1x - 0.04y = 1310 \end{cases}[/tex]

Rewrite Equation 1 to make y the subject:

[tex]\implies y=28500-x[/tex]

Substitute into Equation 2 and solve for x:

[tex]\implies 0.1x-0.04(28500-x)=1310[/tex]

[tex]\implies 0.1x-1140+0.04x=1310[/tex]

[tex]\implies 0.14x=2450[/tex]

[tex]\implies x=17500[/tex]

Substitute the found value of x into Equation 1 and solve for y:

[tex]\implies 17500+y=28500[/tex]

[tex]\implies y=11000[/tex]

Conclusion

$17,500 was invested in the account that gained 10% and

$11,000 was invested in the account that lost 4%

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Answer:

84π m^3

Step-by-step explanation:

1. The formula of a cone is: (1/3) · π · r^2 · h

2. The radius is 6m. (Diameter / 2)

3. (1/3) * π * (6^2) * 7

4. Multiply all numbers besides pi to get the answer in terms of pi

5. (36 / 3 ) = 12 * 7 = 84

6. 84π

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Given...}}}}} \: [/tex]

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{To \: Find ...}}}}} \: [/tex]

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Formula \: Using ...}}}}} \: [/tex]

[tex]\Large❏ \: \Large\begin{gathered} {\underline{\boxed{ \sf {{\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {r}^{2} h}}}}}\end{gathered}[/tex]

Where,

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Solution ...}}}}} \: [/tex]

Substituting the given values in formula.

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {r}^{2} h[/tex]

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {(6)}^{2} \: \times \: 7[/tex]

[tex] \large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{ \cancel3}\pi \: \times \: \cancel{ 36} \: \: ^{ \pink{12}} \: \times \: 7 \\ [/tex]

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \:\pi \: \times \: 12 \: \times \: 7 \\ [/tex]

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: 84 \pi \: {m}^{3} [/tex]

Hence , option b is the correct answer

The triangle is Obtuse and scalene , Option C is the correct answer.

A triangle is a polygon with three sides , three angles and three vertices.

A triangle can be classified as Acute , Right or Obtuse on the basis of the angle in a Triangle .

and it is classified as scalene , equilateral and isosceles on the basis of the length of the sides of a triangle.

The triangle given in the question has all the sides different , so it is a scalene triangle.

One of the angle is obtuse angle and so it can be classified as a Obtuse Angle Triangle.

Therefore , Option C is the correct answer.

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Answer:

right angle

Step-by-step explanation:

Answer: A, 6 cm

Step-by-step explanation:

Circumference is 2(radius) * pi.

A. 12pi   C. 24pi   B. 16pi   D. 32pi

Assuming pi is roughly 3,

A = 36

C = 72

B = 48

D = 96

A is the closest and if you actually used pi, it would be about 3.14159265 which would make the circumference slightly over 36, which 37.68 is.

Hope this helped.

The expression that is a sum of cubes is given as follows:

[tex]-27a^3b^6 + 8a^9b^12[/tex]

An expression that is a sum of cubes is given as follows:

a³ + b³.

For the sum, all numeric factors have to be powers of 3, while all exponents have to be multiples of 3. Hence the expression that is a sum of cubes is given as follows:

[tex]-27a^3b^6 + 8a^9b^12[/tex]

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The System of Equations 1, 2, 3, and 4 have solutions corresponding to the option B, A, C, and D.

A system of equations is a set of equations that have a common solution.

The first system of equations is

y+12 = x² +x

x+y = 3

To determine the solution, the equations are plotted on the graph and the intersection of the equations gives the solution.

The solution is (-5,8) (3,0)

The second system of equation is

y-15 = -x² +4x

x+y = 1

The solution to the system is (7,-6) (-2,3)

The third system of equation is

y+5 = x²-3x

2x+y = 1

The solution to the system is (3,-5) (-2,5)

The fourth system of equation is

y-17 = x²-9x

-x+y =1

The solution to the system is (2,3) , (8,9)

Therefore, the System of Equations 1, 2, 3, and 4 have solutions corresponding to the option B, A, C, and D.

The graphs are attached with the answer.

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The addition is one of the four fundamental mathematical operations. Jenny can have dinner at 7 pm and 7.5 mins.

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

The time can be calculated as,

Flight lands at 4 pm

Jenny has bought a 2.4kg chicken. It takes 35-45 minutes per kg plus an additional 30 minutes to cook the chicken. Time needed for cooking the chicken = (2.5×45 + 30) = 142.5 min

⇒ 15+25+5+142.5 min

Thus, the total time it takes for Jenny to cook the food starting when the flight lands are ⇒ 187.5 mins = 3 hours 7.5 mins

Since the flight lands at 4 pm

⇒ 4 pm + 3 hours 7.5 mins

⇒ 7 pm and 7.5 mins

Hence, Jenny can have dinner at 7 pm and 7.5 mins.

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Answer: 290.6

Step-by-step explanation:

The volume of the cone is [tex]\frac{1}{3}(\pi)(5.6^{2})(13.8-7)=\frac{26656}{375}\pi[/tex].

The volume of the cylinder is [tex](\pi)(5.6^2)(7)=219.52\pi[/tex].

Adding these together gives the exact volume to be [tex]\frac{108976}{375}\pi[/tex], which is 290.6 to the nearest tenth.

Answer:

x = 27°

Step-by-step explanation:

Hello!

Complementary angles add up to 90°.

Since angles A and B are complementary, we can sum up the equations to 90° and solve for x.

The value of x is 27°.

Answer:544/8.50=h

Step-by-step explanation:

544 divided by 8.50 = the number of hours

Answer:

35 585

Step-by-step explanation:

Each term is   the product of the previous two terms minus the term that is two before

3*5  - 3 = 12

5 x12 - 5   = 55

12 x 55 - 12 = 648

55 * 648  - 55 = 35 585

or each term is   term that is two before x  (term before -1)

3 (5-1) = 12

5 x (12-1) = 55

12 * (55-1) = 648

55 * ( 648-1) = 35 585

The required next term in the sequence is 35,185.

Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.

here,
Given sequence 3, 5, 12, 55, 648
The given sequence has the following pattern,
3 × 5 - 3 = 12
5 × 12 - 5 = 55
12 × 55 - 12 = 648

55 × 648 - 55 = 35,185

Thus, the required next term in the sequence is 35,185.

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Lakesha gave away 8/10 of her cookies.

We know that she gave away 3/10 of her cookies to Bailey and 5/10 of her cookies to Helen.

Then the fraction that she gave away is:

3/10 + 5/10

Notice that both fractions have the same denominator, then we can directly add the numerators:

3/10  + 5/10 = 8/10

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Answer:

4.23

Step-by-step explanation:

add 0.01

Problem 34

Answer: [tex]\boldsymbol{n(B) = 3}[/tex]

Reason:

We count the number of items inside set B. In this case there are 3 values, so that is why n(B) = 3

===========================================================

Problem 36

Answer:  [tex]\boldsymbol{n(A \cap C) = 1}[/tex]

Reason:

To be able to count the number of items inside set [tex]A \cap C[/tex], we first need to determine what this set looks like. In other words, we need to know the number(s) inside this set.

The upside down U symbol is the intersection symbol. It indicates we want to find what the sets A and C have in common. In this case, it's the value "4" and nothing else. This number is in both set A and set C at the same time. It might help to draw a venn diagram as you see below. I'm ignoring set B entirely since your teacher is not asking about the set in this problem.

We can then say [tex]A \cap C = \{4\}[/tex]

There's only one item inside this set, which is why [tex]n(A \cap C) = 1[/tex]

The distance between the ships is 26.65.

Based on the information given, after 3 hours, the distance of ship B will be:

= 20 + (17 × 3)

= 71.

A = 21 × 3 = 63

Well calculate the square root which will be:

A² + B² = 71² + 63²

= 5041 + 3969

= 9010

Therefore, ✓9010 = 94.92

Finally, the distance will be:

= (63 × 21) + (71 × 17) / 94.92

= (1323 + 1207)/94.92

= 26.65

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Answer:

[tex](x^2+y^2+xy)(x^2+y^2-xy)[/tex]

Step-by-step explanation:

Rewrite the middle term.

[tex]x^4+2x^2y^2-x^2y^2+y^4[/tex]

Rerrange terms.

[tex]x^4+2x^2y^2+y^4-x^2y^2[/tex]

Factor first three terms by perfect square rule.

[tex](x^2+y^2)^2-x^2y^2[/tex]

Rewrite [tex]x^2y^2[/tex] as [tex](xy)^2[/tex].

[tex](x^2+y^2)^2-(xy)^2[/tex]

Since both terms are perfect squares, factor using the difference of squares formula, [tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=x^2+y^2[/tex] and [tex]b=xy[/tex].

[tex](x^2+y^2+xy)(x^2+y^2-(xy))[/tex]

Remove parentheses.

[tex](x^2+y^2+xy)(x^2+y^2-xy)[/tex]

Answer...

32!!

Step-by-step explanation:

Subtract the numbers to see a pattern of decreasing odd numbers

167-118 = 49

118-82 = 36

82-57 = 25

57-41 = 16

The difference between is 13 then 11 then 9 so the next number should be x-7

Translating shape A by the vector [tex](^1_4)[/tex] means translating 1 unit right and 4 unit up to get A'(4, 7), B'(7, 7), C'(7, 5) and D'(4, 5)

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

Let us assume that the vertices of shape A is at A(3, 3), B(6, 3), C(6, 1) and D(3, 1)

Translating shape A by the vector [tex](^1_4)[/tex] means translating 1 unit right and 4 unit up to get A'(4, 7), B'(7, 7), C'(7, 5) and D'(4, 5)

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We can simplify the expression by using exponent properties, and we will see that the correct option is the fourth option.

Remember the exponent property:

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

Here we have the expression:

[tex]\frac{83.9*10^{12}*2.87*10^{-3}}{3.76*10^2}[/tex]

We can reorder this to get:

[tex]\frac{83.9*10^{12}*2.87*10^{-3}}{3.76*10^2} = \frac{83.9*2.87}{3.76}*\frac{10^{12}*10^{-3}}{10^2}[/tex]

The right side can be simplified to:

[tex]\frac{83.9*2.87}{3.76}*\frac{10^{12}*10^{-3}}{10^2} = 64.04*10{12 - 3 - 2} = 64.04*10^{7}[/tex]

Now, we can move the decimal point one time to the left and increase the exponent by one, so we get:

[tex]6.404*10^8[/tex]

Then we conclude that the correct option is the last one (where I rounded the expression to only 3 values after the decimal point).

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Answer:

14 inches

Step-by-step explanation:

If you think about it, if you were to shift the side DC to the left until it aligns with FE, you would get a straight line. This line would be parallel, and equal to AB, which can be determined by using the right angles, which are given. So AB = FE + DC, and the value of AB is given as well as the value of DC. So plugging in the known values you get 20 = FE + 6. Now subtract 6 from both sides and you get 14 = FE. So FE is 14 inches

Answer:

Step-by-step explanation:

Please help. I just need to know what the missing side is.

from the question you are looking for EF

EF + CD = 20 in (from AB misure)

so

20 - 6 = 14 = EF

The average rate of change in attendance from 2011-2021 is 1.132 per year

From the graph, we have:

The average rate of change is then calculated as:

Rate = (58.77 - 47.45)/(2021 - 2011)

Evaluate

Rate = 1.132

2022 is 11 years from 2011.

So, the predicted annual attendance for 2022 is;

Attendance = 47.45 + 1.132 * 11

Attendance = 59.90

The years with unusual growth are 2020 and 2021.

This is so because they have the same attendance.

The factor that might have contributed to the anomalous growth include

In (a), we have:

Attendance = 47.45 + 1.132 * 11

Express as a function

y(t) = 47.45 + 1.132(t)

2025 is 14 years from 2011.

So, we have:

y(14) = 47.45 + 1.132(14)

y(14) = 63.298

2030 is 19 years from 2011.

So, we have:

y(19) = 47.45 + 1.132(19)

y(19) = 68.958

The factors include:

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Answer:

a(a - b)

Step-by-step explanation:

given polynomial:  a²- ab - 8a + 8a

We can first simplify this answer by removing like terms,

- 8a + 8a = 0

so we have a²- ab in. the simplest form

we can take this one step further and factor out the a (not simplest form)

a time a = a²

a times b = ab

hence, a(a - b)

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Answer:

C ON EDGE

Step-by-step explanation:

Answer:

955,500,000,000,000,000,000,000,000,000,000,000,000

or 9.555 x 10^38

Step-by-step explanation:

multiply 245 x 39 first and then add all the zeros from both numbers after

Using proportions, the ratio that is not equivalent to the ones shown in the table is given by:

32 to 6.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In the table, the ratios is given as follows:

Hence the different ratio is:

32 to 6.

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