-2(y + 1) + 5y = 3(y + 1) - 2
solve for y

Answer:

The answer is true!

Step-by-step explanation

The car's displacement according to the description given is; 0 meters while it's distance travelled is; 90 meters.

It follows from definition that, displacement which is a vector quantity is a measure of the change in position of a body after undergoing motion while the distance travelled which is a measure of magnitude only (scalar) is a measure of the space covered over the course of time.

Hence, the displacement is zero as the start position is same as the end position.

Also, the distance is the space covered= 25 +20 +20 +25 = 90 meters.

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50 guests were there at the party

Total champagne available = 15 litres

1 litre = 1000 ml

15 litres = 15000 ml

Total = 15000 ml

Each guest had 2 glasses of 150 ml = 300 ml, which means each guest was served 300 ml of champagne

Total no of guests = Total champagne  / champagne served to each

= 15000 / 300

= 50

50 guests were there at the party

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Considering the expression of a line, they do not have the same value of m. So, the two lines are not parallel.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:

m= (y2 - y1)÷ (x2 - x1)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.

In this case, you can calculated the slope of the two lines as:

Being (x1,y1)= (-3,2) and (x2,y2)= (4, -1), the slope m can be calculated as:

m= (-1 -2)÷ (4 - (-3))

Solving:

m= (-3)÷ 7

m= -3/7

Being (x1,y1)= (1,3) and (x2,y2)= (-2,-4), the slope m can be calculated as:

m= (-4 -3)÷ (-2 -1)

Solving:

m= (-7)÷ (-3)

m= 7/3

You can observe that they do not have the same value of m. Finally, the two lines are not parallel.

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the graphed system of inequalities is:

y > − 2x − 4

y ≤ x + 1

Which is the first option.

On the image in the quesitonw e cans ee the graph of a system of inequalities. There we can see two lines.

One of the lines has a positive slope and we can see that it is a solid line, and we also can see that the region below that line is shaded, so one of the inequalities is of the form:

y ≤ line with positive slope.

The whole opposite happens for the other line, it has a negative slope, it is dashed (so this time we use the symbols > or <) and the region shaded is above the line, so this time we have an inequality of the form:

y > line with negative slope.

Then the system of inequalities is:

y ≤ line with positive slope.

y > line with negative slope.

By looking at the options, the only one with this form is:

y > − 2x − 4

y ≤ x + 1

Which is the first option

Finally, we conclude that the graphed system of inequalities is:

y > − 2x − 4

y ≤ x + 1

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Answer: 15. f(1)=3

16. g(3)=1

Step-by-step explanation:

15. (fog)(1)=

f(g(1))=

f(1)=3

16. (gof)(5)=

g(f(5))=

g(3)=1

Answer:

$350.00

Step-by-step explanation:

80 + 6(45) = ?

Answer:

8

Step-by-step explanation:

you first do operation in the brackets and then multiply and then divide:

2*2*2*2*2 / 4 = 8

Answer:

3 is the common factor

Step-by-step explanation:

3 x 3 =9

3 x 4= 12

3 x 5 =15

3 x 6 =18

hope it helps

Answer:

Factors for 9: 1, 3, and 9

Factors for 12: 1, 2, 3, 4, 6, and 12

Factors for 15: 1, 3, 5, and 15

Prime Factors for 9: 3 and 3

Prime Factors for 12: 2, 2, and 3

Prime Factors for 15: 3 and 5

GCF = 3

Answer:

(0, -3)

Step-by-step explanation:

.

The simplest form of the ratios are not the same, hence, the ratios 6:4 and 18:8 are not equivalent ratios

In order to show why the given ratios are not equivalent ratios, we need to express them in their simplest form as shown:

For the ratio of 6:4

6:4 = 6/4

simplify.

= 3/2

= 3×2/2×2

= 3/2

= 3:2

For the ratio of 18:8

18:8 = 18/8

simplify.

= 9/4

= 9×2/4×2

= 9/4

= 9:4

Since the simplest form of the ratios are not the same, hence, the ratios 6:4 and 18:8 are not equivalent ratios.

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The answer to the given question is 169.

13 * (((6 square) / (( 5 squared ) - (4 square))) + 9)

= 169

Therefore,  the correct value of the given question is 169

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The equation shows a slope of 5 for the line the equation represents of that given line will be y = 5x:

Given that

To find

So according the question

We have

We know that

Slope-intercept form of a line's equation is written as

Where

From question

so the equation of that given line will be

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Answer: look at the graph below

Step-by-step explanation:

Consider the given system of equation

x + y = -7     ........(1)

4x + y = 19   ..........(2)

Consider the equation (1)

x + y = -7

We first find different values of x and y that satisfies (1),

1) x = 1 , y = -7-1 = -8  

We get one point as (1,-8)

2) x= 2 , y = -7 -2 = -9

We get  point as (2 ,-9)

3) x = 0 , y = -7

We get point as (0 ,-7)

Similarly, find different values of x and y that satisfies (2),

4x + y = 19  

1) x = 2 , y = 19 -  8 = 11

We get  point as (0,11)

2)  x= 3 , y = 19 - 12 = 7

We get  point as (3 , 7)

3) x= 4 , y = 19 - 16 = 3

We get  point as (4 ,3)

Now , we plot these point on the graph paper,  we obtained graph as, (as attached below)

Answer:

12x + 9 = 4x + 7

Group likely terms

12x - 4x = 7 - 9

8x = -2

Now we need to isolate x

Therefore; Divide both side by the coefficient of x thus 8

Hence x = -1/4

Answer:

[tex]x = \bf -\frac{1}{4}[/tex]    

Step-by-step explanation:

We are given the following equation:

[tex]12x + 9 = 4x + 7[/tex]

In order to solve this equation, we have to rearrange it to make [tex]x[/tex] the subject of the equation:

[tex]12x + 9 = 4x + 7[/tex]

⇒ [tex]12x + 9 - 4x = 4x + 7 - 4x[/tex]       [Subtracting [tex]4x[/tex] from both sides]

⇒ [tex]8x + 9 = 7[/tex]

⇒ [tex]8x + 9 - 9 = 7 - 9[/tex]                     [Subtracting 9 from both sides]

⇒ [tex]8x = -2[/tex]

⇒ [tex]\frac{8}{8} x = -\frac{2}{8}[/tex]                                     [Dividing both sides by 8]

⇒ [tex]x = -\frac{2}{8}[/tex]

⇒ [tex]x = \bf -\frac{1}{4}[/tex]                                     [Simplifying the fraction]

If a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B', then the current coordinates of B' are (3, -2).

As per the question statement, a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B'.

We are required to calculate the coordinates of B'.

To solve this question, we need to know what Translation (a, b) to (x, y) and (-a, -b) to (x, y) means. Translation (a, b) to (x, y) means the abscissa "x" is to be shifted to the right by "a" units while the ordinate "y" is to be shifted to the right by "b" units, i.e., after translation, the new coordinates become [(a + x), (b + x)]. On the other hand, Translation (-a, -b) to (x, y) means the abscissa "x" is to be shifted to the left by "a" units while the ordinate "y" is to be shifted to the left by "b" units, i.e., after translation, the new coordinates become [(a - x), (b - x)].

Here, as per the above mentioned concept, a translation of T (2, -7) if applied to the point B (1, 5), the new point B' will be at [tex][(1+2), (5+(-7)]=[3, (-2)][/tex].

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Answer: D (3,-12)

Step-by-step explanation:

A population with 6 elements and mean 5 is given by:

4, 4, 5, 5, 6, 6

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

Hence, for this problem, we need 6 observations which add to 30, hence one possible population is:

4, 4, 5, 5, 6, 6

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Answer:

i the middle

Step-by-step explanation:

Answer:

2/100*40290

=805.8

40290 - 805.8

=$39484. 2

The graphs of the functions and relations gives;

4. The graph of y(x) = x² represents a function and the graph of y² = x represents a relation

5. In equation, y² = x, the value x = 9, gives two y–values y = 3 or -3, therefore y² = x is a relation rather than a function.

6. The domain and range are both [-8, 8]

7. From the equation,x = √(8 - y²), each x– value gives two y–values, therefore x² + y² = 8 is a relation not a function

The given equations of the graphs are;

Where;

x = The input or independent variable

y = The output or dependent variable

In a function each input or value of x can give only one output or value of y, such that a vertical line drawn from each x–value crosses the graph only once.

Therefore;

The graph of y(x) = x², represent a function, given the each x–value has only one y–value, or the value of x determines the y–value.

The graph of y² = x represents a relation given that one x–value can give two y–values (a vertical line drawn at a point, x > 0, crosses the graph twice.

5. Let 9 represent the value chosen from the domain of both y(x) = x² and y² = x, we have;

y(9) = 9² = 81

Therefore, the equation, y(x) = x² is a function

In the relation, y² = x, we have;

y² = 9

y = ±3

Therefore, when x = 9, y = 3, or y = -3, which are two outputs or y–value for one input or x–value.

Which makes y² = x a relation rather than a function.

6. The equation of the graph is the equation of a circle, x² + y² = 8

Where;

8 = The square of the radius of the circle

(h, k) = (0, 0), the center of the circle is at the origin.

Therefore;

The coordinates of the edges of the circle on the x–axis are;

(-√8, 0), and (√8, 0)

The domain is therefore [-8, 8]

Similarly, the range, which are the possible y–values is also [-8, 8]

7. The equation x² + y² = 8, and therefore, the graph is not a function given that we have;

Given that y²y(x) = x²is always positive, each x - value gives two y-values, which does not conform with the mapping relationship of a function

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The fraction that represents the parts shaded red (indicated by "R*) is 7/9

The figure is represented by the following list of characters

RRRRRWRRW

In the above list of characters, we have

n(R) = 7

Total = 9

The fraction that represents the parts shaded red (indicated by "R*) is then calculated as

Fraction = n(R)/Total

So, we have

Fraction = 7/9

Hence, the fraction that represents the parts shaded red (indicated by "R*) is 7/9

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Answer:

(-5, 5)

Step-by-step explanation:

The function increases from x = -11 to x = -5.

The function decreases from x = -5 to x = 5.

the function increases from x = 5 to x = 11.

Answer: (-5, 5)

The equation is 2.90 + 1.25m= 6.65

The number of miles in the taxi ride is 3 miles

The airport charged a pick up fee of $2.90

$1.24 was charged per mile

The total fare was $6.65

The equation can be expressed as

2.90 + 1.25m= 6.65

collect the like terms

1.25m= 6.65 - 2.90

1.25m= 3.75

divide by the coefficient of m which is 1.25

m= 3.75/1.25

m= 3

Hence the number of miles of the taxi ride is 3

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The circumference and area of the circular figure as given in the task content are; 31.4 and 78.5 respectively.

Since each unit on the graph measures one centimeter, it follows that the radius of the circle which is described by line PQ can be determined as; 5units = 5 centimetres.

On this note, the circumference of the figure; 2πr = 2 × 3.14 × 5

Circumference = 31.4 cm.

Also, the area of the circle in discuss can be determined from; πr² = 3.14 × 5²

Area = 3.14 × 25

Area = 78.5cm²

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Answer:

1.25

Step-by-step explanation:

Answer:1.25

Step-by-step explanation:

Answer:

[tex]5 { \\ }^{2} [/tex]

Step-by-step explanation:

exponents are ways to write multiplication powers 5

[tex]5 {}^{2} [/tex]

= 5×5 = 25

Answer:

Step-by-step explanation:

You want to know how multiplication and powers are related, and how powers can be evaluated.

You may be familiar with the fact that a coefficient is used to signify repeated addition:

  y + y + y + y = 4y

The coefficient of 4 in 4y signifies that y is in the sum that many times.

An exponent is used to signify repeated multiplication:

  y × y × y × y = y⁴ . . . . y to the fourth power

The exponent of 4 signifies that y is a factor in the product that many times.

In typeset text, the exponent is rendered in a superscript font. In plain text, the exponent (power) is identified using a caret (^):

  y⁴ = y^4

The rules of exponents derive from the idea of exponents signifying repeated multiplication:

  [tex](x\cdot x)=x^2\\(x\cdot x\cdot x)=x^3\\(x\cdot x)\cdot(x\cdot x\cdot x)=(x\cdot x\cdot x\cdot x\cdot x)\ \Longrightarrow\ x^2\cdot x^3=x^{2+3}=x^5[/tex]

Division has a similar rule.

  [tex]\dfrac{(x\cdot x\cdot x\cdot x\cdot x)}{(x\cdot x)}=(x\cdot x\cdot x)\ \Longrightarrow\ \dfrac{x^5}{x^2}=x^{5-2}=x^3[/tex]

This supports the idea that a positive exponent in the denominator is the same as a negative exponent in the numerator, and vice versa.

Powers can be evaluated in a straightforward way by carrying out the multiplications.

In general, the number of significant digits in the result will be the product of the exponent and the number of significant digits in the base.

For example, 9.2^5 could be expected to have 2×5 = 10 significant digits:

  9.2^5 = 9.2×9.2×9.2×9.2×9.2 = 65,908.15232

Most calculators are limited to 12 digits or less, and most spreadsheets are limited to 16 digits or less. Some special-purpose calculators have "variable" precision, so are able to properly render higher powers of numbers with more than 1 or 2 significant digits.

A calculator may use any of several techniques for evaluating powers. Among them might be ...

Logarithms turn a power problem into a multiplication problem:

  log(9.2^5) = 5·log(9.2)

Of course, once the logarithm is found, the issue of evaluating powers comes back:

  9.2^5 = 10^(5×log(9.2)) ≈ 10^(4.818939136727776)

Fortunately, there are methods of evaluating antilogs that simplify this part of raising to a power. The difficulty is that precision may be lost. Here, using the rounded value 10^(4.81893913673) gives the result 65,908.152320337..., which is in error after the 10th digit.

An integer power can be written as a sum of powers of 2. For example, ...

  37 = 32 +4 +1 = (8 +1)4 +1

Then ...

  9.2^37 = (((((9.2^2)^2)^2 · 9.2)^2)^2) · 9.2

This requires only 7 multiplications, not 36

__

Additional comment

Only the first token after the caret is considered to be the exponent:

  y^4x = (y^4)(x) . . . . . the first token is 4

  y^1/2 = (y^1)/2 = y/2 . . . . the first token is 1

If the exponent has multiple parts, they should be enclosed in parentheses:

  [tex]y^{3x+1}[/tex]

will be written in plain text as ...

  y^(3x+1)

and ...

  y^(1/2) = √y

You also need to be careful writing multiple exponents using the caret symbol. Parentheses are usually required. The Order of Operations has you evaluate multiple exponents right to left.

  3^4^5 = 3^(4^5) = 3^1024

  (3^4)^5 = 3^20