Complete the equation of the line whose slope is -2 and y-intercept is (0,-8).
y =

Answer: Decrease a number by 25% is the same as increasing by 75%

Step-by-step explanation:

The value of the missing data point is 10. Option C

The data set has 8 data points, and the median is given as 12. The median is the middle value when the data points are arranged in ascending or descending order.

Let's arrange the data set in ascending order:

6, 8, ?, 8, 14, 15, 16, 18

Since the median is 12, it should be the fourth data point when arranged in ascending order. Therefore, the missing data point must be the fourth value in the sorted data set.

From the given options, the only whole number that could fit as the fourth value in the data set is 10.

Thus, the value of the missing data point is C. 10.

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Answer: We have f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

                        (f-g)(x)= 3x⁵-2x⁴-x²+x-21

Step-by-step explanation:

Here we have,

Given : f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

We know,

(f-g)(x)= f(x)-g(x)

= (3x⁵+6x²-5 ) - ( 2x⁴+7x²-x+16)

On subtracting g(x) from f(x) we get,

(f-g)(x)= (3x⁵+6x²-5  - 2x⁴-7x²+x-16)

On simplify,

 (f-g)(x) =3x⁵-2x⁴-x²+x-21

Hence,

(f-g)(x) = f(x) - g(x) = 3x⁵-2x⁴-x²+x-21

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Answer:1.53

Step-by-step explanation:

Answer:

10 years

Step-by-step explanation:

Given

Decline from (0,h) to (10,0)

See attachment for graph

Required

Determine the age when height = 0

The function of the graph is represented as: (age, height)

So, we need to read from the graph the corresponding value of age (on the x-axis) when height = 0 (i.e. the y-axis)

From the attached graph;

\(age = 10\) when \(height = 0\)

Hence, the age of the car is 10 years

Answer:

Step-by-step explanation:

Hello,

\((x-40)^2=36=6^2\\\\<=> \sqrt{(x-40)^2}=6\\\\<=> |x-40|=6\\\\<=> x-40 = 6 \ or \ x-40 = -6\\\\<=>x=46 \ or \ x = 34\)

Hope this helps

Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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Step-by-step explanation:

normally a simple expression in x has no natural limitations.

but for fractions we have to pay attention, because we have to avoid results like .../0, as they are undefined.

so, 4x + 1 has no limitations, but x² - 1 must never be 0.

the only "bad cases" are

x² - 1 = 0

x² = 1

x = ±1

therefore, the domain (the definition of the valid values for x) is

x € R, x <> -1 and x <> 1

the range (the definition of valid values for y) is then any value between -infinity and +infinity.

simply because around x=-1 and x=+1 the tendency goes against - and + infinity.

Answer: the first thing is your answer :)

thx for the points

Step-by-step explanation:

g

(

x

)

=

x

2

−

3

The parent function is the simplest form of the type of function given.

f

(

x

)

=

x

2

The transformation being described is from

f

(

x

)

=

x

2

to

g

(

x

)

=

x

2

−

3

.

f

(

x

)

=

x

2

→

g

(

x

)

=

x

2

−

3

The horizontal shift depends on the value of

h

. The horizontal shift is described as:

g

(

x

)

=

f

(

x

+

h

)

- The graph is shifted to the left

h

units.

g

(

x

)

=

f

(

x

−

h

)

- The graph is shifted to the right

h

units.

In this case,

h

=

0

which means that the graph is not shifted to the left or right.

Horizontal Shift: None

The vertical shift depends on the value of

k

. The vertical shift is described as:

g

(

x

)

=

f

(

x

)

+

k

- The graph is shifted up

k

units.

g

(

x

)

=

f

(

x

)

−

k

- The graph is shifted down

k

units.

Vertical Shift: Down

3

Units

The graph is reflected about the x-axis when

g

(

x

)

=

−

f

(

x

)

.

Reflection about the x-axis: None

The graph is reflected about the y-axis when

g

(

x

)

=

f

(

−

x

)

.

Reflection about the y-axis: None

Compressing and stretching depends on the value of

a

.

When

a

is greater than

1

: Vertically stretched

When

a

is between

0

and

1

: Vertically compressed

Vertical Compression or Stretch: None

Compare and list the transformations.

Parent Function:

f

(

x

)

=

x

2

Horizontal Shift: None

Vertical Shift: Down

3

Units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

image of graph

Answer: 5/12

Step-by-step explanation:

Our common denominator is 60.

25 * 27 = 675

675 / 45 = 15

40 - 15 = 25

Since our denominator is 60, 25/60 is our answer.

25 / 60 simplified is 5 / 12.

hope this helps

Answer:

ln 15 must be greater (larger than) if log 15 is common.

Step-by-step explanation:

log 15 [assumed to be a common logarithm]

‹–› 15 = 10 ^ log(15)

ln 15 [natural log which has a base of e] ‹–› 15 = e ^ ln(15).

10 > e

e ≈ 2.7218.

e is approximately 3 rounded to the nearest whole number.

Logically you would need to raise 3 to a greater power for 3ⁿ = 15. Than 10ⁿ = 15.

For example 3² < 10² → 3³ < 10³ → 3⁴ < 10⁴ → ... Thus 3ⁿ < 10ⁿ for n > 0.

Answer: hello! have a good day! :)))

P = 2

Answer:

Correct Answer

hope that will help you

Answer:

\( \boxed{ \sf{i. \: \: \: \: 0}}\)

\( \boxed{ \sf{ ii.\: \: \: curly}}\)

\( \boxed{ \sf{ \: iii. \: \: \: 3}}\)

\( \boxed{ \sf{ iv. \: \: \: \: \frac{3}{100} }}\)

\( \boxed{ \sf{v. \: \: \: ∅}}\)

\( \boxed{ \sf{vi. \: \: \: \frac{ - 3}{2} }}\)

\( \boxed{ \sf{vii. \: \: \: - 1}}\)

\( \boxed{ \sf{viii. \: \: \: 1}}\)

\( \boxed{ \sf{ix. \: \: \: 24}}\)

Step-by-step explanation:

\( \sf{ \: i. \: - 5 \times 0 = \underline{ \bold{ \sf{0}}}}\)

\( \text{Remember!} : \) Any number multiplied by zero is equal to zero.

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

\( \sf{ii. \: The \: sets \: are \: always \: represented \: in \: \underline{ \bold{ \sf{curly}}}} \: brackets.\)

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

\( \sf{iii. \: \frac{1}{2} + \frac{5}{2}}\)

While performing the addition and subtraction of like fractions , you just have to add or subtract the numerator respectively in which the denominator is retained same.

\( \mapsto{ \sf{ \frac{1 + 5}{2}}} \)

\( \mapsto{ \sf{ \frac{6}{2} }}\)

Divide 6 by 2

\( \mapsto{ \sf{3}}\)

\( \sf{ ∴ \: \: \frac{1}{2} + \frac{5}{2} = \: } \underline{ \sf{3}}\)

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

\( \sf{iv. \: Fraction \: form \: of \: 3\% : }\)

To convert the percent into a fraction, divide it by 100 and remove the % symbol.

\( \sf{ ∴ \: fraction \: form \: of \: 3\% \: = \underline{ \sf{ \frac{3}{100}}}} \)

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

\( \sf{ \: v. \: The \: symbol \: of \: null \: set \: is \: = \: \underline{ \sf{ ∅ }}}\)

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

\( \sf{ \: vi \: . \: \frac{ - 15}{6} \times \frac{3}{5}} \)

To multiply one fraction by another , multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the obtained after multiplication into lowest term.

\( \mapsto{ \sf{ \frac{ - 15 \times 3}{6 \times 5}}} \)

\( \mapsto{ \sf{ \frac{ - 45}{30} \: }}\)

\( \mapsto{ \sf{ \frac{ \cancel{ - 45} ^{ \: \: \: \: - 3} }{ \cancel{30 } ^{ \: \: \: \: \: \: \: 2} } } }\)

\( \mapsto{ \sf{ \frac{ - 3}{2} }}\)

\( \sf{∴ \: \frac{ - 15}{6} \times \frac{3}{5} = \underline{ \sf{ \frac{ - 3}{2} }}}\)

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

\( \sf{vii. \: \: ( - 1) \times ( - 1) \times ( - 1)}\)

First, multiply -1 by -1

\( \sf{ \text{Remember!}} : \) Multiplying a negative integer by a negative integers gives a positive integer.

\( \mapsto{ \sf{1 \times ( - 1)}}\)

Now, multiply 1 by -1

\( \text{Remember!} : \) Multiplying a positive integer by an negative integer gives a negative integer

\( \mapsto{ \sf{ - 1}}\)

\( \sf{∴ \: ( - 1) \times ( - 1) \times ( - 1) = \underline{ \sf{ - 1}}}\)

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

\( \sf viii \: . \: \sf{ \: the \: value \: of \: {3}^{0} \: is \: \underline 1}.\)

\( \text{Remember!} : \) The value of any term having the index 0 is 1.

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

\( \sf{ix. \: \: x \times ( - 1) = - 24}\)

\( \mapsto {\sf{ - 1x = - 24}}\)

Divide both sides by -1

\( \mapsto{ \sf{ \frac{ - 1x}{ - 1} = \frac{ - 24}{ - 1} }}\)

\( \text{Remember!} : \) Dividing a negative integer by a negative integer gives a positive integer

\( \mapsto{ \sf{x = 24}}\)

\( \sf{∴ \: The \: value \: of \: x \: = \underline{ \sf{24}}}\)

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

Hope I helped!

Best regards! :D

~\( \text{TheAnimeGirl}\)

Answer:

33 1/3

Step-by-step explanation:

1. First, you want to make 6 into a fraction with a bottom/denominator of 3 to make adding 6 and 2/3 easier.  So, to make 6 into a fraction with a denominator of 3 , you multiply 6 by 3 to get 18.  The 18 is the numerator (top of the fraction) and 3 is the denominator (the bottom).  So now you have 18/3+2/3 divided by 1/5.

2. Now, add the 18/3 and the 2/3 to get 20/3 divided by 1/5.

3. After this, you want to divide.  To divide fractions, you use Keep, Change, Flip (KCF).  To do this, keep the 20/3 the same, change the division sign to multiplication, and flip the 1/5 to 5/1.  So, now you have 20/3 multiplied by 5/1.

4. Simplify this by multiplying 20 by 5 and 3 by 1 to get 100/3.

5. Now we have to create 100/3 into a mixed number.  To do this, we know that 33 multiplied by 3 is 99, which is as close as we can get to 100 without going over.  This means that we can make 100/3 into 33 and 1/3.  

Hope this helps! :) If you could give me Brainliest that would be super helpful!

The mixed fraction is 33 1/3.

A fraction represented with its quotient and remainder is a mixed fraction.

Given:

​6 2/3÷1/5​

On further solving the given expression

=20/3 ÷1/5​

Now, division of fraction is not possible

so,

=20/3 * 5/1

=100/3

=33 /13

Hence, the mixed fraction is 33 1/3.

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Answer:

In technical terms, the slope of the line is the change in y over the change in x. But I just like to think of it as rise over run. To find the slope of the line, pick two points on the line.

Answer:

Uphill slopes are positive slopes.

The slope will be a positive number like 5 or 2/3.

Downhill slopes are negative slopes.

The slope will be a negative number like -7 or -1/3.

Step-by-step explanation:

To calculate Swornima's annual income and the amount of tax she should pay, let's break down the information provided:

Monthly basic salary: Rs 48,000

Social security tax rate: 1%

Income tax rate on income up to Rs 5,00,000: 0% (no tax)

Income tax rate on income from Rs 5,00,001 to Rs 7,00,000: 10%

Dashain allowance: 1 month's salary

Deposit in Citizen Investment Trust (CIT): 10%

Rebate on income tax: 10%

(i) Annual Income:

Swornima's monthly basic salary is Rs 48,000, so her annual basic salary would be:

Annual Basic Salary = Monthly Basic Salary x 12

= Rs 48,000 x 12

= Rs 5,76,000

Additionally, she receives 1 month's salary as the Dashain allowance, which we can add to her annual income:

Annual Income = Annual Basic Salary + Dashain Allowance

= Rs 5,76,000 + Rs 48,000

= Rs 6,24,000

Swornima's annual income is Rs 6,24,000.

(ii) Tax Rebate:

Swornima receives a 10% rebate on her income tax. To calculate the rebate, we need to determine her income tax first.

(iii) Annual Income Tax:

First, let's calculate the income tax for the range of income from Rs 5,00,001 to Rs 7,00,000. The tax rate for this range is 10%.

Taxable Income in this range = Rs 6,24,000 - Rs 5,00,000

= Rs 1,24,000

Income Tax in this range = Taxable Income x Tax Rate

= Rs 1,24,000 x 0.1

= Rs 12,400

Now, let's calculate the total annual income tax:

Total Annual Income Tax = Income Tax in the range Rs 5,00,001 to Rs 7,00,000

= Rs 12,400

Next, we calculate the rebate on income tax:

Tax Rebate = Total Annual Income Tax x Rebate Rate

= Rs 12,400 x 0.1

= Rs 1,240

Swornima's annual income tax is Rs 12,400, and she receives a tax rebate of Rs 1,240.

To summarize:

(i) Swornima's annual income is Rs 6,24,000.

(ii) Swornima's tax rebate is Rs 1,240.

(iii) Swornima should pay an annual income tax of R

The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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Answer

6.6

Explanation

In order to determine the number of gallons that Catherine put on the hot tub, calculate the absolute value of the difference between the two endpoints.

The two endpoints are -4.8 and 1.8

So, the distance between the two red points on the number line is

Hence, the number of gallons catherine put in the hot tub is 6.6 gallons

Answer:

See answers below

Step-by-step explanation:

T59 = a+58d = -61

T4 = a+3d = 64.

Subtract

58d-3d = -61-64

-55d = -125

d =125/55

d = 25/11

Get a;

From 2

a+3d = 64

a+3(25/11) = 64

a = 64-75/11

a = 704-75/11

a = 629/11

T23 = a+22d

T23 = 629/11+22(25/11)

T23 = 1179/11

The four rectangles can be painted with 7 different paints in 840 ways.

A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order. For example, the permutation of set A={1,6} is 2, such as {1,6}, {6,1}, there are no other ways to arrange the elements of set A.

The formula for permutattion is;

\(P_r_n = \frac{n!}{(n-r)!} \\\)

where r = 4

n = 7

Substituting the values for n and r

\(P = \frac{7!}{(7-4)!}\)

\(P = \frac{7!}{3!}\)

P = 840 ways.

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The proportional relationship that models the table is given as follows:

y = 14x.

Hence the quantities A, B and C are given as follows:

To model the proportional relationship, first we must obtain the constant, which is the ratio between the output and the input, as follows:

k = 42/3 = 28/2 = 14/1 = 14.

Hence the equation is given as follows:

y = 14x.

Then the quantities are given as follows:

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Orlando is approximately 1021.5 miles from Tucson.

a) Let's use the formula: distance = rate x time.

Let t be the time Zuri spent driving from Orlando to Tucson.

Then, the time she spent driving from Tucson to Orlando would be 49 - 10 - t = 39 - t (subtracting the time she stayed in Tucson and the time she already spent driving from Orlando to Tucson from the total time).

Using the formula, we can write two equations:

distance from Orlando to Tucson = 50t

distance from Tucson to Orlando = 55(39 - t)

The total distance traveled is the same in both directions, so we can set the two equations equal to each other and solve for t:

50t = 55(39 - t)

50t = 2145 - 55t

105t = 2145

t = 20.43

b) Now that we know the time it took for Zuri to travel from Orlando to Tucson, we can use one of the equations above to find the distance:

distance from Orlando to Tucson = 50t

distance from Orlando to Tucson = 50(20.43)

distance from Orlando to Tucson = 1021.5

Therefore, Orlando is approximately 1021.5 miles from Tucson.

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Orlando is approximately 1021.5 miles from Tucson.

What is the linear equation?

A linear equation is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

a) Let's use the formula: distance = rate x time.

Let t be the time Zuri spent driving from Orlando to Tucson.

Then, the time she spent driving from Tucson to Orlando would be 49 - 10 - t = 39 - t (subtracting the time she stayed in Tucson and the time she already spent driving from Orlando to Tucson from the total time).

Using the formula, we can write two equations:

distance from Orlando to Tucson = 50t

distance from Tucson to Orlando = 55(39 - t)

The total distance traveled is the same in both directions, so we can set the two equations equal to each other and solve for t:

50t = 55(39 - t)

50t = 2145 - 55t

105t = 2145

t = 20.43

b) Now that we know the time it took for Zuri to travel from Orlando to Tucson, we can use one of the equations above to find the distance:

distance from Orlando to Tucson = 50t

distance from Orlando to Tucson = 50(20.43)

distance from Orlando to Tucson = 1021.5

Therefore, Orlando is approximately 1021.5 miles from Tucson.

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Distributing the cubic root:

Rewriting the cubic roots:

The rate of the boat in still water and the rate of the current will be 25 miles per hour and 5 miles per hour.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

A boat travels upstream for 60 miles in 3 hours and returns in 2 hours traveling downstream in a river.

Then the speed upstream will be

v₁ = 60 / 3

v₁ = 20 miles per hour

Then the speed downstream will be

v₂ = 60 / 2

v₂ = 30 miles per hour

Then the rate of the boat in still water and the rate of the current will be

The rate of the boat in still water will be

⇒ (v₁ + v₂) / 2

⇒ (20 + 30) / 2

⇒ 50 / 2

⇒ 25 miles per hour

The rate of the current will be

⇒ |v₁ - v₂| / 2

⇒ |20 - 30| / 2

⇒ 10 / 2

⇒ 5 miles per hour

Then the rate of the boat in still water and the rate of the current will be 25 miles per hour and 5 miles per hour.

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Answer:

41.93 degrees

Step-by-step explanation:

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8.4\% of 16.83}}{\left( \cfrac{8.4}{100} \right)16.83} ~~ \approx ~~ 1.41~\hfill \underset{ Total~for~lunch }{\stackrel{ 16.83~~ + ~~1.41 }{\approx\text{\LARGE 18.24}}}\)

Answer:

Step-by-step explanation:

Find the diagram attached.

Given the scale factor of circle A to circle B as 3/4

A:B = 3:4

Total ratio = 3+4 = 7

Area of bigger square A = 45sq. units;

The Total area can be gotten using the expression;

\(\frac{4}{7} \times x = 45\) where;

x is the total area of both circles.

Get x;

\(\frac{4}{7} \times x = 45\\4x = 7 \times 45\\4x = 315\\x = \frac{315}{4}\\x = 78.75\)

Area of circle B = 78.75 - 45 = 33.75

Let the fraction required be y

45 * y = 33.75

y = 33.75/45

y = 3375/4500

y = 45/60

y = 3/4

Hence the area of circle B is 45 * 3/4 of circle A

b)The ratio of circle A to Circle B is expressed as;

Ratio = Area of circle A/Area of circle B

Ratio = 45/33.75

Ratio = 45 * 100/3375

ratio = 4500/3375

Ratio = 4:3

Hence the ratio of circle A to Circle B is 4:3