WORD PROBLEMS INVOLVING SIMULTANEOUS EQUATIONS:
The cost of a bottle of water is Rsx.
The cost of a bottle ofjuice is Rsy.
The total cost of 9 bottles of water and 3 bottles of juice is Rs 153.
The total cost of 6 bottles of water and 5 bottles of juice is Rs 147.
Find the cost of a bottle of water and the cost of a bottle of juice.

Answer:

f(g(x))= log4(2(8x^6))

or log4(16x^6)

Step-by-step explanation:

Answer:

The number of books bought in each store would be 4 The amount spent will be the same in either store.

Step-by-step explanation:

Comment

The question has to make the assumption that no matter how many books are bought from store 1, the shipping charge is 8 dollars. Otherwise there is no solution.

Givens

Book1: 10 and  8 dollars total for shipping

Book2: 12 dollars, no shipping costs.

Equation

12x = 10x + 8         Subtract 10x from both sides

Solution

12x - 10x = 10x - 10x + 8      Combine

2x = 8                                   Divide both sides by 2

2x/2 = 8/2

x = 4

1 inch is the distance between Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given,

The community center is 3.1 miles away from Rodrigo's house.

We need to find how far apart are Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles

As given, 3 inches : 9.3 miles

1 mile = 3/9.3 inches

1 mile = 0.323 inches.

So let us multiply 3.1 with 0.323

3.1×0.323

1.0013 inches

Hence 1 inch is the distance between Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles

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The value of y which the slope formula  is 34.

Slope can be defined as the rate of change of a body.

To calculate the value of y, we use the formula below.

Formula:

Where:

From the question,

Substitute these values into equation 1 and solve for y

Hence, the value of y is 34.

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Answer:

A

Step-by-step explanation:

[tex]\huge\begin{array}{ccc}BT=21\\DC=10.2\end{array}[/tex]

If BT is the midsegment of ΔMAH and DC is the midsegment of ΔBTH, then MA, BT and DC are parallel.

Therefore the segments form the proportion:

[tex]\dfrac{HM}{MA}=\dfrac{HB}{BT}=\dfrac{HD}{DC}[/tex]

BT is the midsegment of ΔMAH, therefore

[tex]HB=\dfrac{1}{2}HM[/tex]

DC is the midsegment of ΔBTH, therefore

[tex]HD=\dfrac{1}{2}HB=\dfrac{1}{2}\cdot\dfrac{1}{2}HM=\dfrac{1}{4}HM[/tex]

[tex]\dfrac{HM}{42}=\dfrac{\frac{1}{2}HM}{BT}[/tex]

cross multiply

[tex]HM\cdot BT=42\cdot\dfrac{1}{2}HM[/tex]

divide both sides by HM

[tex]\boxed{BT=21}[/tex]

[tex]\dfrac{HM}{42}=\dfrac{\frac{1}{4}HM}{DC}[/tex]

cross multiply

[tex]HM\cdot DC=42\cdot\dfrac{1}{4}HM[/tex]

divide both sides by HM

[tex]\boxed{DC=10.5}[/tex]

The vertex form of the function g(x)= 2[tex]x^2[/tex]+16x+6 is g(x)= 2[tex](x+4)^2[/tex]-26.

What is vertex form of the function?

   The function's maximum or lowest possible output is represented by the vertex of the quadratic function's graph. When viewing a graph, the vertex is the highest or lowest point on the parabola. Utilizing the vertex formula is the simplest technique to discover the vertex. It is simple to locate the vertex of the parabola using the vertex form of a quadratic equation. Y=a(xh)2+k is the definition of the generic vertex form, where h is the x-coordinate and k is the y-coordinate of the vertex.

Here the given function is ,

=> g(x) = 2[tex]x^2[/tex]+16x+6

=> g(x) = 2([tex]x^2+[/tex]8x+3)

=> g(x) = 2([tex]x^2+[/tex]8x+16-16+3)

=>g(x) = 2 [[tex](x+4)^2[/tex]-13]

=> g(x)=  2[tex](x+4)^2[/tex]-26

Therefore vertex form of the function is g(x)= 2[tex](x+4)^2[/tex]-26 and vertex is (-4,-26).

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Answer:

g(x)=2(x+4)^2-26

Has a minimum value of -26

Step-by-step explanation:

i got it right!

The approximate percentage of sales tax is 1%

A gymnastics mat priced at $53.

A cost of mat after adding sales tax = $53.53

So, the tax amount would be,

53.53 - 53 = 0.53

We need to find the sales tax percentage.

Let x be the percentage of sales tax.

x = (0.53)/(53.53)  * 100

x = 0.0099 * 100

x = 0.99%

x ≈ 1%

Therefore, the approximate percentage of sales tax is 1%

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Answer:

It line splits the graph of a quadratic equation into two mirror image, or basically means every point on the parabola on one side of the axis will be a mirror image of the other side of the parabola.

np :d

The required value of "b" is 7, where the equation is y = -3x + 7.

As per the given table, we take the two points (9, 1) and (3,7).

y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = -3, y₁ = 16

x₂ = 1, y₂ = 4

y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute the values in the above equation,

y - 16 = [(4 - 16)/(1 - (-3))](x - (-3))

y - 16 = (-12/4)(x+3)

y - 16 = -3(x+3)

y - 16 = -3x - 9

y = -3x - 9 + 16

y = -3x + 7  ....(i)

Compare the given equation y = mx + b with the above equation, and we get

b = 7

Therefore, the required value of "b" is 7.

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The number of toy cars are in 1,000 boxes is 25000 and the place value of 25 increases by 4 places to the left.

It should be noted that place value is used to know the value of the numbers that are given in a data.

In this case, toy company puts 25 toy cars in each box, the number of toy cars that are in 1,000 boxes will be:

= 25 × 1000

= 25000

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Considering the figure < 4 ≅ < 5 alternate internal angles

Alternate internal angle theorem is a theorem that holds true when in the occurrence of parallel lines and a transversal line.

Some of the theorems occurring at this stage include

Using the figure.  alternate internal angle theorem proves that

This helps to complete the required proof that < 4 = < 5

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Mr. Fitzpatrick bought 9 adult tickets and 13 children's tickets.

It is given that Mr. Fitzpatrick bought 22 tickets

The tickets collectively cost him $265

The student tickets cost $10 while adult tickets cost $15

Let the no. of adult tickets sold be x

Let the no. of children's tickets sold be y

Therefore we get the equations

x + y = 22                      [1]

15x + 10y = 265                      [2]

or, 5x + 10x + 10y = 265

or, 5x + 10(x + y) = 265

from equation [1] we get

5x + 220 = 265

or, 5x = 265 - 220

or, 5x = 45

or, x = 9

Therefore,

y = 22 - 9

= 13

Therefore he bought 9 adult tickets and 13 children tickets.

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Answer:

119.5

Step-by-step explanation:

Since supplementary is 180 degrees, 180-60.5=119.5

Answer:

y = [tex]\frac{4}{3}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line

m = [tex]\frac{4-0}{0-(-3)}[/tex] = [tex]\frac{4}{0+3}[/tex] = [tex]\frac{4}{3}[/tex]

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = [tex]\frac{4}{3}[/tex] x + 4 ← equation of line

Answer:

175

how will convert it in mixes fraction when there is no division number

Step-by-step explanation:

when we say "a/b of c", we mean mathematically :

a/b × c

so,

a)

x = 1/5 × 15 = 15/5 = 3

b)

x = 3/4 × 48 = 3×48/4 = 3×12 = 36

Answer:

Step-by-step explanation:

a) 1/5 of 15 = ?

→ 1/5 of 15

→ (1/5) × 15

→ 15/5 = 3

So, answer is 3.

b) 3/4 of 48 = ?

→ 3/4 of 48

→ (3/4) × 48

→ 144/4 = 36

So, answer is 36.

Answer: 19

Step-by-step explanation:

The coordinates of x and y on the graph can not form a function.

x and y do not show any relationships.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates from the graph.

(2, 0)

(2, 1)

(-1, 2)

(1, 3)

(0, -1)

(2, -3)

(-1, -1)

(3, -2)

We can say that,

A function can not have one to many.

We have,

(2, 0), (2, 1), and (2, -3).

This means,

For x = 2, y = 0, 1, -3.

This is not possible.

Thus,

The coordinates of x and y on the graph can not form a function.

x and y do not show any relationships.

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Answer:

First simplify the ones that need dividing

Step-by-step explanation:

So i got

-0.4, -0.6, 0.5, 4.44, 66.2

Hope this helps!

The number 74.9963 would round down to 70

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

We need to round  74.9963 to the nearest 10

We can see that the 74.9963 is below 75 so it goes down, and it rounds down to 74.9963 instead of, 74.9 then that would round up to the decimal is higher than 70.

The answer would be 70

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i gotchu what do u want

The perimeter of the rug is 37.2

The first line says that the rug is twice as long as its width. If the width is taken as w and length is taken as l, we get an equation l= 2w. Since it is a rectangle, the area of the rectangle will be (length*width) which is equal to l*w.

Since l=2w, area = 2w*w = 2w^2. This is given equally to 76.88.

2w^2 = 76.88

w^2 = 38.44

w = 6.2

l = 2w = 2*6.2 = 12.4

Now, perimeter of rectangle is 2w+2l = 2*6.2 + 2*12.4 = 37.2

Hence the perimeter of the rug is 37.2

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Using the probability, the expected number of female children in a family with three children is 1.5. The option 2 is correct.

In the given question, we have to find the expected number of female children in a family with three children.

The possibility of having girls in family is 0,1,2 or 3.

From the 8 possible sequences, only one of them give the possibility of 0 girls.

So the probability of 0 girls is 1/8.

There are total 3 ways of having 1 girl.

That is: GBB, BGB, and BBG.

Thus, the probability of 1 girl is 3/8.

Similarly checking for having 2 girls with probability 3/8

Having 3 girls with probability 1/8.

The predicted number of girls is calculated as a weighted average of all potential numbers, where a number's weight is determined by its likelihood of occurring.

The anticipated number of girls is therefore

= 1/8⋅0+3/8⋅1+3/8⋅2+1/8⋅3

= 0+3/8+6/8+3/8

=(3+6+3)/8

=12/8

=1.5

Hence, the expected number of female children in a family with three children is 1.5.

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For all proportional relationships, the true statements are:

A, D, and E.

A proportional relationship between two variables x and y is written as:

y = k*x

Now let's analyze each of the given statements:

A) The origin is the point (0, 0).

If you evaluate the general equation in x = 0 you get:

y = k*0 = 0

So yes, this equation passes through the point (0, 0).

B) This is false, as we saw above.

C) The formula for the constant of proportionality is:

y = k*x

y/x = k

So we can see that k = rise/run

the statement is false.

D) Yes, this is true, a general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept, particularly if the y-intercept is zero, then we have a proportional relation.

E) Yes, slope, unit rate, constant of proportionality, are all equivalent terms for a proportional relation.

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Answer:

y=5 x= -2 z=1 the procedure Is in the picture

Answer:

the additive inverse of 16 5/7 IS 26/7

Is it possible to apply the conditional probability in its alternative form, P(R2|R1) is n(R1⋂R2) divided n(R1) Given that the product rule hasn't yet been taught, we have advocated this approach.

The probability of drawing a second red in the event that this red is not changed is 9/15,

hence the probability of A is 10/16 * 9/15, or 0.375.

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Using the concepts of weighting, we got that demographic groups helps in fixing  difference between the levels of different people if there are many or too few people in the sample from that group, compared to the population as a whole.

Demographic segmentation examples actually explain how researchers divide a market into the smaller groups according to age, gender, family income, race and ethnicity, qualification, marital status, nature of the  employment, etc.  

It is an extremely tedious task to the accommodate customers belonging to different demographics and develop the exhaustive marketing plan. Demographic examples ease creating the strategy for a marketer. Thus, they are one of  most commonly implemented marketing segmentation methods compared to the other techniques such as geographic segmentation, behavioral segmentation, or the psychographic segmentation.

Hence, certain demographic groups might end up being under or over-represented means that  there are too many or too few people in the sample from that group, compared to the population as a whole, in that case weighting can therefore potentially helps in fixing the difference in the levels of different people.

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