2. Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. It
turns out Clare's work has three mistakes!
8(2 + 7x)
10+56x
10+56x
10
12
3
16
3x - (2+5x)
3x - 2 + 5х
8r-2
642-2
64x

Answer:

Never

Because for example; 25(the multiple of 5) + 20(the multiple of 10) equals 45

Answer:

Step-by-step explanation:

never

Solution of the given equation x² -6x +10 =0 using quadratic formula or perfect square method is same in complex number and is equal to   3 + i or 3 - i.

As given in the question,

Given equation is:

x² -6x +10 = 0

Complex number i² = -1

Using perfect square method:

x² -6x + 9 +10 -9 =0

⇒x² -6x +9 =-1

⇒ (x - 3)² = (i)²

⇒x-3 = ± i

⇒ x= 3 ± i

Using quadratic formula,

x = [ -(-6) ±√ (-6)² -4(1)(10)] / 2(1)

  =( 6 ± √-4)/ 2

  = (6± √4i²) /2

  = (6 ± 2i) / 2

  = 3 ± i

Therefore, solution of the given equation x² -6x +10 =0 using quadratic formula or perfect square method is same in complex number and is equal to 3 + i or 3 - i.

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The solution for the given inequality has been graphed in detail.

A linear inequality can be gives the values for a variable in an interval of numbers.

Given inequalities are as below,

2x - 7 > 3 and 4 - x < -4

They can be simplified as,

2x - 7 > 3    

=> 2x > 10    

=> x > 5

And,  

4 - x < -4

=> x - 4 > 4

=> x > 8

The solution of the given inequality is the intersection of two solutions x > 5 and x > 8, which is x > 8.

This is graphed as follows,

Hence, the given inequality has solution x > 8 which has been graphed.

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The algebraic expression that correctly represents the cost of t tickets is 8t , the correct option is (a) .

In the question ,

it is given that

the cost of 1 ticket for the theater is = $8.00

let the number of ticket be = t

so , the cost for t tickets = (cost of 1 ticket ) × ( number of tickets )

Substituting the values of number of tickets and cost of 1 ticket ,

we get ,

cost for t tickets = 8 × t

= 8t

Therefore , The algebraic expression that correctly represents the cost of t tickets is 8t .

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The value of the function f(x) = [tex]x^3-2x^2+3[/tex] when x = 2 is f(2) = 3

The given function is

f(x) = [tex]x^3-2x^2+3[/tex]  

The function is the mathematical statement which represents the relationship between one variable and another variable. If one variable is dependent variable the other variable will be independent variable.

The given function is

f(x) = [tex]x^3-2x^2+3[/tex]

The value of x = 2

Then substitute the value of x in the function

f(x) = [tex]x^3-2x^2+3[/tex]  

f(2) = [tex]2^3-2(2)^2+3[/tex]

Solve the power of each terms

f(2) = 8 - 8 + 3

Do the arithmetic operations

f(2) = 3

Hence, the value of the function f(x) = [tex]x^3-2x^2+3[/tex] when x = 2 is f(2) = 3

The complete question is:

Find the value of f(x) = [tex]x^3-2x^2+3[/tex] , when x = 2

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The required number is 1 which represents "6 times as large as 9 minus 3".

The analysis of mathematical representations is algebra, and the handling of those symbols is reasoning.

We have to determine the number that is "6 times as large as 9 minus 3".

Let the required number would be x

Translate the phrase "6 times as large as 9 minus 3" into the algebraic form :

⇒ 6 × x = 9 - 3

⇒ 6x = 6

⇒ x = 6 / 6

⇒ x = 1

Thus, the required number is 1 which represents "6 times as large as 9 minus 3".

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Answer: x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]

Step-by-step explanation:

f(x) = x³ - 4x² - 5x + 14

-2    |    1    -4     -5     14

                -2      12   -14

           1    -6       7     0

x³ - 4x² - 5x + 14 = (x+2)(x²-6x+7)

x²-6x+7=0

x²-6x+9-2=0

(x²-6x+9)-2=0

x²-6x+9=2

x²-3x-3x+9=2

x(x-3)-3(x-3)=2

(x-3)²=2

x-3=[tex]\sqrt{2}[/tex], -[tex]\sqrt{2}[/tex]

x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]

Hence, zeroes are x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]

Step-by-step explanation:

our first "suspicion" for a factoring is an integer factor of the constant term : 14.

14 = 2 × 7 or -2 × -7

I started to try 2 or -2 and found that -2 is indeed a zero solution.

so, the first factors are

f(x) = (x + 2)(x² + ...)

let's divide (x³ - 4x² - 5x + 14) by (x + 2) to get the x² term.

x³ - 4x² - 5x + 14 ÷ x + 2 = x² - 6x + 7

- x³ + 2x²

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

0 -6x² - 5x

- -6x² - 12x

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

0 7x + 14

- 7x + 14

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

0 0

f(x) = (x + 2)(x² - 6x + 7)

the zeros for x² - 6x + 7 we get from the general solution for a quadratic equation

ax² + bx + c = 0

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (6 ± sqrt((-6)² - 4×1×7))/(2×1) =

= (6 ± sqrt(36 - 28))/2 = (6 ± sqrt(8))/2 =

= 3 ± sqrt(8/4) = 3 ± sqrt(2)

x1 = 3 + sqrt(2)

x2 = 3 - sqrt(2)

so, the zeros are

-2, 3 - sqrt(2), 3 + sqrt(2)

The equation to model the situation is given below. And the months will the populations of the towns be​ equal will be 12.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A town's populace is 43,200. Around 125 individuals move out of the town every month. Every month, 175 individuals on the normal move into town. A close by the town has a populace of 45,900. It has nobody moving in and a normal of 175 individuals moving away consistently.

Let y be the total population and x be the number of months. Then the equations are given as,

y = (175 - 125)x + 43200

y = 50x + 43200           ...1

y = -175x + 45900        ...2

From equations 1 and 2, then we have

50x + 43200 = - 175x + 45900

50x + 175x = 45900 - 43200

225x = 2700

x = 2700 / 225

x = 12

The months will the populations of the towns be​ equal will be 12.

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The linear pair theorem cannot be used to state ZAOP is complementary to ZPOB.

Complementary angles are two angles with a combined angle of 90 degrees, whereas supplementary angles have a combined angle of 180 degrees.

A good that adds value to another good or service is said to be complimentary. To put it another way, they are two items that the client uses in tandem with one another. For instance, cereal and milk or a DVD and a DVD player.

Because the three angles of a triangle sum up to 180° and the right angle has already taken up 90°, the two non-right angles in a right angled triangle are complimentary. We say two angles "Complement" one other when their sums equal 90 degrees. because a complete angle is what is considered to be the right angle.

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The number of ways to fill the tic-tac-toe grid, with at least 4 of each symbol in the grid, using the arrangements formula, is of:

252.

The number of possible arrangements that can be chosen from a set of n elements is given by the factorial of n, as follows:

[tex]A_n = n![/tex]

When the elements arranged can be repeated, the number of arrangements is presented as follows:

[tex]A_{n}^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1! \times n_2! \cdots n_3!}[/tex]

In which [tex]n_1, n_2, \cdots, n_n[/tex] represent the number of repetitions of each element.

For the tic-tac-toe grid, we have that the possible ways to organize the nine positions with at least four instances of each symbol is given as follows:

Hence the number of ways to fill up the grid is given as follows:

[tex]\frac{9!}{5!4!} + \frac{9!}{4!5!} = 2 \times 156 = 252[/tex]

Thus 252 ways to fill up the grid.

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Answer: : (4 – 5) – (13 – 18 + 2).

Step-by-step explanation:

hoped dat helped

Answer:A. (10 x 3) + 8

Answer:

A : ( 10 * 3 ) + 8

Hope this helps!

Step-by-step explanation:

10 friends, each donate 3 pieces of clothing, ( 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 ) or ( 10 * 3 ), plus the 8 pieces of clothing Emily is donating. ( 10 * 3 ) + 8.

Answer:

Step-by-step explanation:

Each exponent on the left side is a positive number and therefore their sum is positive too.

But we have a negative value on the right.

This is not possible, hence no solutions.

Using the percentage, Rapunzel participated in 9581/100 matches.

In the given question we have to find the fraction of the wrestling matches did Rapunzel participate in.

Rapunzel's team participated in a total of 143 wrestling matches.

Rapunzel participated in 67 percent of the wrestling matches.

Total matches = 143

Participated in = 67%

Total number of matches in which Rapunzel participated is

= 143*67%

= 143* 67/100

= 9581/100

Rapunzel participated in 9581/100 matches.

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The standard form of linear equation is 4x - y = 1.

What is the standard form of a linear equation?

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).

The slope intercepts form a linear equation is y = mx + c, where m is the slope and c is y-intercept of the line.

Given linear equation is:

4y=16x-4

Subtract 16x from both sides:

4y - 16x = -4

Divide both sides by -4

-y + 4x = 1

4x - y = 1

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a.

A gardener can afford to buy 125 vinca plants and 60 phlox plants. $1.20/plant Vinca $2.50/plant Phlox.

The equation in standard form that models the possible combinations of x vinca plants and y phlox plants the gardener can afford to buy is

⇒ $1.20*x + $2.50*y

b.

An equation that models the possible combinations is

⇒ $1.20*125 + $2.50*60 = 300

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Answer: A

Step-by-step explanation:

Answer:

9 units

Step-by-step explanation:

We see that on the x-axis, everything is equal.

On the y-axis, there are -2 and 7.

So we are finding the distance between -2 and 7

|-2|+|7|=9

So the distance between the points is 9 units.

The circumference of the circle is 25.1 inches.

The length of the arc ACB is 4.2 inches.

The circumference of a circle is the perimeter of the circle.

Therefore,

circumference of a circle = 2πr

where

Hence,

circumference of a circle = 2 × 3.14 × 4

circumference of a circle = 8 × 3.14

circumference of a circle = 25.1 inches

The length of the arc ACB can be found as follows:

length of arc = ∅/ 360 × 2πr

length of the arc = 60 / 360 ×  2 × 3.14 × 4

length of the arc = 60 / 360 ×  25.12

length of the arc = 1507.2 / 360

length of the arc = 4.18666666667

length of the arc = 4.2 inches

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Answer: Yes

Step-by-step explanation:,

The factors of 10 are 2 and 5 any number divisible by 10 will also be divisible by both 2 and 5.

Hope this helps! ^-^  Have a good day! :)

Answer:

Yes, Because factors of 10 are 1,2,5,10.

So all numbers divisible by 10 must be divisible by 2 and 5.

Step-by-step explanation:

Answer:

No, the point is on the x-axis, it is not a y-intercept.

The value of (-42n+28p)(-1/4) is 249n/4

A fraction represents a part of a whole or, more generally, any number of equal parts. A fraction describes how many parts of a certain size there are, for example, one-half, three-fifths, three-quarters.

A fraction has a denominator and numerator. There are three types of fraction. Proper, improper and mixed fraction

Opening the parentheses of the equation

(-42n+ 28p)(-1/4).

= -42n× -1/4+ 28× -1/4

= (42n×-7)/4

= -294n/4

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Considering the five number summary of the data-set, we have that:

a. None of the prices were outliers, as all the prices are within 1.5 IQR of the quartiles.

b. That is not a very low price, as it is above the first quartile, while very low prices have to be 1.5 IQR below the first quartile.

The outliers, considering the five number summary of a data-set, are the values that are more than 1.5 Interquartile Ranges from the quartiles, that is, either:

The interquartile range of a data-set is the difference between the third quartile and the first quartile, hence, for the given data-set:

IQR = Q3 - Q1 = 110 - 30 = 80.

Hence the bounds for outliers are given as follows:

Since the maximum value of 200 is less than 230, there are no outliers in the data-set.

The five number summary is given by the image at the end of the answer.

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The graph that beast describes the slope of -2/3 passing through points (-1, 0) is in option c

Information given in the question include

a linear function graph

The data is plotted as a linear function

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m = -2/3

negative slopes slants from top left to bottom right as in a and c

from the graph, option c has points (-1, 0) and (0, -2/3)

m = (-2/3 - 0) / (0 - -1)

m = (-2/3) / (0 + 1)

m = -2/3

This matches with option C

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For given equation, the constant of proportionality is 4

In this question, we have been given an equation m = 4b that represents the time in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b).

We need to determine the constant of proportionality.

We know that the the constant of proportionality is nothing but the ratio of two proportional values.

In this case the time a chef needs to cook depend on the number of bacon cheeseburgers (b).

So, m is directly proportional to the b

Therefore, the constant of proportionality is 4

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Answer:

The answer is 4

Step-by-step explanation:

I hope this helps!!

The values of the variables, x and y in the angles formed by the parallel lines that have a common transversal are;

x = 4°, y = 10°

11. x = 9°, y = 12°

12. x = 14°, y = 5°

13. x = 8°, y = 11°

14. x = 16°, y = 23°

15. x = 9°, y = 13°

Parallel lines are lines that maintain the same distance from each other along their lengths.

From the figure, we get;

(29·x - 3) and (15·x + 7) are linear pair angles, therefore;

(29·x - 3) + (15·x + 7) = 180°

44·x + 4 = 180

x = (180 - 4)/44 = 4

x = 4°

(15·x + 7) and (13·y - 17) are same side exterior angles between parallel lines, therefore;

(15·x + 7) + (13·y - 17) = 180°

(15×4 + 7) + (13·y - 17) = 180°

67 + 13·y - 17 = 180°

50 + 13·y = 180

13·y = 180 - 50 = 130

y = 130 ÷ 13 = 10

y = 10°

11. (18·x - 44)° and  (8·x - 10)° are same side exterior angles, therefore;

(18·x - 44)° +  (8·x - 10)° = 180°

26·x - 54 = 180

x = (180 + 54)/26 = 9

x = 9°

(8·x - 10)° and (13·y - 38)° are linear pair angles, therefore;

(8·x - 10)° + (13·y - 38)° = 180°

(8 × 9 - 10)° + (13·y - 38)° = 180°

62 - 38 + 13·y = 180

13·y = 180 - (62 - 38) = 156

y = 156 ÷ 13 = 12

y = 12°

12. (9·x - 2)° and (5·x + 54)° are corresponding angles, therefore;

(9·x - 2)° = (5·x + 54)°

(9·x - 2)° = (5·x + 54)°

9·x - 5·x = 54 + 2 = 56°

4·x = 56°

x = 56° ÷ 4 = 14°

x = 14°

(9·x - 2)° and (10·y + 6)° are linear pair angles, therefore;

(9·x - 2)° + (10·y + 6)° = 180°

(9 × 14 - 2)° + (10·y + 6)° = 180°

124 + 6 + 10·y = 180

10·y = 180 - 130 = 50

y = 50 ÷ 10 = 5

y = 5°

13. The angle to which the angle (8·x - 1)° is an alternate interior angle is a corresponding angle to the angle (11·x - 25)°, therefore;

(8·x - 1)° is congruent to angle (11·x - 25)°

(8·x - 1)° = (11·x - 25)°

11·x - 8·x = 25 - 1 = 24

3·x = 24

x = 24 ÷ 4 = 8

x = 8°

Angles (15·y - 48)° and (8·x - 1)° are linear pair angles, therefore;

(15·y - 48)° + (8·x - 1)° = 180°

(15·y - 48)° + (8 × 8 - 1)° = 180°

(15·y - 48)° + 63° = 180°

15·y + 15° = 180°

15·y = 180° - 15° = 165°

y = 165° ÷ 15 = 11°

y = 11°

14· The angle (4·x + 4)° and (7·x - 44)° are alternate exterior angles, therefore;

(4·x + 4)° = (7·x - 44)°

7·x - 4·x = 44° + 4° = 48°

3·x = 48°

x = 48° ÷ 3 = 16°

x = 16°

The vertical angle to angle 39° is a linear pair angle to the angle (8·y - 43)°

Therefore;

39 + 8·y - 43 = 180°

8·y  = 180 + 43 - 39 = 184

y = 184 ÷ 8 = 23

y = 23°

15. The diagram indicates that the angles (15·x - 26)° and (12·x + 1)° are congruent, therefore;

(15·x - 26) = (12·x + 1)

(15·x - 12·x) = (26 + 1)

3·x = 27

x = 27 ÷ 3 = 9

x = 9°

The vertical angle to (2·x + 1) is therefore;

12·x + 1 = 12 × 9 + 1 = 109

The angle sum property indicates that we have;

28° + 109° + (4·y - 9)° = 180°

(4·y - 9)° = 180° - (28° + 109°) = 43°

(4·y - 9)° = 43°

(4·y)° = 43° + 9° = 52°

y = 52°/4 = 13°

y = 13°

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Answer:5) gcf=6 lcm=42 | 6) gcf=2 lcm=270 | 7) gcf=2 lcm=224

Step-by-step explanation:

Answer:

1

2

[

x

2

2

−

x

3

3

]

2

0

=

1

2

[

(

4

2

−

8

3

)

−

(

0

)

]

=

1

2

(

−

2

3

)

=

−

1

3

Step-by-step explanation: