Find the approximate side length of a square game board with an area of 160
in2.

The correct answer is option C that is on step 4 - 5 the right side should have been ± i.

A quadratic polynomial function is the one which can be written in the form ax² + bx + c = y where a, b and c are coefficients and x, and y are independent and dependent variables respectively. The quadratic polynomial function is solved using Completing the square method. In this method the quadratic polynomial is converted into the form (x + a)² in order to find the roots of the quadratic polynomial. Here, the steps 1, 2 and 3 are correct but in step 4 after taking square root on both the sides the value of √-1 is not taken as ± i and further it is solved. This becomes an error as we know that the value of √-1 = ± i and if not taken properly errors occur.

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The inequality x & lt; 4 is represented on a number line .

What is number line?
A number line is a representation of a graduated straight line in elementary mathematics that serves as a visual representation of the real numbers. It is assumed that every point on a number line corresponds to a real number, and that vice versa. Frequently, the integers are represented by specially marked, uniformly spaced points on a line. The line includes all real numbers, continuing indefinitely in both directions, as well as numbers that are in between the integers, even though the image only displays the integers from -3 to 3. It is frequently employed as a teaching tool, particularly when teaching simple addition and subtraction with negative numbers.

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The percentage change in the home sale price between the year 1970 and 2010 is 13.01%

It is a relative value used to denote hundredths of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. A number's percentage is its weight in relation to 100. For example in the case, there are 26 females and 24 boys in a class. 52% of the class is made up of girls, which means that out of 100 students, 52 are female.

Given Data

Average home sale

1980 = $18300

1990 - 2010= $2000

Percentage sale = [tex]\frac{20300}{156000}[/tex] × 100

Percentage sale = 13.01

The percentage change in the home sale price between the year 1970 and 2010 is 13.01%

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Answer: $3.55

Step-by-step explanation:

5 oranges * $2.84/4 oranges =

5 oranges * $0.71/1 orange=

5 oranges/1 orange * $0.71=

5/1 * 0.71=

5*0.71=$3.55

Answer:

4x - 5y = 30

4x - 5(0) = 30

x1 = 7.5 y1 = 0

Find y-intercept

The y-intercept is where the graph crosses the y-axis. To find the y-intercept, we set x2=0 and then solve for y.

4x - 5y = 30

4(0) - 5y = 30

y2 = -6 x2 = 0

(x1,y1) and (x2,y2)

(7.5,0) and (0,-6)

Solve for x

To solve for x, we solve the equation so the variable x is by itself on the left side:

4x - 5y = 30

x = 1.25y + 7.5

Solve for y

To solve for y, we solve the equation so the variable y is by itself on the left side:

4x - 5y = 30

y = 0.8x - 6

By using the equation for the line of best fit, the salary for an employee with 7 years of experience is: D. $55,573.

A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

In this scenario, the employee's years of experience would be plotted on the x-axis of the scatter plot while salary would be plotted on the y-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the data in the given table, we can reasonably and logically deduce that the equation for the line of best fit is given by:

y = 2233.3x + 39940

Next, we would use the equation for the line of best fit to predict the salary for an employee with 7 years of experience:

y = 2233.3(7) + 39940

y = 15,633.1 + 39940

y = 55,573.1 ≈ $55,573.

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Answer:

D

Step-by-step explanation:

$55,573

Answer:

Step-by-step explanation:

It could be

ax(x - 4)(x - 3)(x + 3)     where a is some constant ( a could be 1 of course)

For a = 1 the polynomial is

x(x - 4)(x - 3)(x + 3)

In expanded form this is

x^4 - 4x^3 - 9x^2 + 36x

Answer: 4b+6a+3c

Step-by-step explanation:

<B, <ABC, <CBA

based off the image

The cost of one ounce of cereal is $0.23

Given:

Amount of cereals a box contain = 24 ounces

Cost of one box = $5.52

Cost of cereal per ounce = Cost of cereal / Amount of cereals in  a box

Cost of cereal per ounce =  $5.52 / 24

Cost of cereal per ounce =  $0.23

An ounce is any of various units of mass, weight or volume derived almost invariably from the ancient Roman unit of measure, the ounce. an avoirdupois ounce is 1⁄16 avoirdupois pound; it is the US and British imperial ounce. 1 ounce is equal to 437.5 grains or 28.349 grams, A US customary fluid ounce is 1⁄16 of a US liquid pint and 1⁄128 of a US liquid gallon or exactly 29.5735295625 mL.

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The value of x based on the equation given as 3(4x + 6) = 9x + 12 is -2.

It should be noted that an equation shows that relationship between the variables that are given or illustrated in the data.

The value for x based on the equation will be:

3(4x + 6) = 9x + 12

Open bracket

12x + 18 = 9x + 12

Collect like terms

12x - 9x = 12 - 18

3x = -6

Divide

x = -6/3

x = -2

Therefore, x is -2.

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[tex]\displaystyle\\Answer:\ (0,-\frac{29}{13} )[/tex]

Step-by-step explanation:

[tex]\displaystyle\\A(-3,-5)\ \ \ \ \ B(10,7) \ \ \ \ \ \lambda=3/10=0.3\ \ \ \ \ C(x_C,y_C)=?\\\\\boxed {x_C=\frac{x_A+\lambda x_B}{1+\lambda} }\ \ \ \ \ \ \ \ \ \ \boxed {y_C=\frac{y_A+\lambda y_B}{1+\lambda} }\\\\x_C=\frac{-3+0.3(10)}{1+0.3} \\\\x_C=\frac{-3+3}{1.3} \\\\x_C=\frac{0}{1.3}\\\\x_C=0\\[/tex]

[tex]\displaystyle\\y_C=\frac{-5+0.3(7)}{1+0.3} \\\\y_C=\frac{-5+2.1}{1.3} \\\\y_C=\frac{-2.9}{1.3} \\\\y_C=-\frac{2.9(10)}{1.3(10)} \\\\y_C=-\frac{29}{13}[/tex]

[tex]\displaystyle\\Thus,\ C(0,-\frac{29}{13} )[/tex]

y = x + 6 and 3x - 3y = -18 will have no solution (parallel lines)

y = −4x + 11 and −6x + y = 11 will have unique solution (intersecting lines)

y = -2x + 5 and 2x + y = -7 will have no solutions (parallel lines)

taking first set of equations,

y = x + 6 and 3x - 3y = -18

rearranging it in the ax+by=c form we get,

x - y = 6

3x - 3y = -18

a1=1, b1= -1, c1= 6

a2=3, b2= -3, c2= -18

now comparing,

1/3 = 1/3 ≠ 6/(-18) 0r -1/3

thus, we get a1/a2=b1/b2≠c1/c2, which satisfies the condition for parallel lines, thus there will be no solution.

taking second set of equations,

y = −4x + 11 and −6x + y = 11

rearranging it in the ax+by=c form we get,

4x+y=11

-6x+y=11

a1=4, b1= 1, c1= 11

a2=-6, b2= 1, c2= 11

4/6 or 2/3≠1/1

thus, we get a1/a2≠b1/b2, which satisfies the condition for intersecting lines, so there will be a unique solution.

taking third set of equations,

y = -2x + 5 and 2x + y = -7

rearranging it in the ax+by=c form we get,

2x+y=5

2x+y=-7

a1=2, b1= 1, c1= 5

a2=2, b2= 1, c2= -7

2/2 or 1/1 =1/1≠ -5/7

thus, we get a1/a2=b1/b2≠c1/c2, which satisfies the condition for parallel lines, thus there will be no solution.

What are intersecting and parallel lines?

Parallel lines never cross, always have distinct ends, and are always spaced at the same distance from one another. Lines that intersect are lines that have a common point and do cross.

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Answer:

I believe cubic function

Step-by-step explanation:

the x^3 represents a cubic function

The numbers are  26.087, 2.6 x 10', 26.079, 2.6432x 10,26.295, 2.6803x10​. The order of the number from least to greatest is 26, 26.079, 26.087, 26.295, 26.432, 26.803.

Given that,

The numbers are  26.087, 2.6 x 10', 26.079, 2.6432x 10,26.295, 2.6803x10​.

We have to find the order of the numbers from least to greatest.

The order of the numbers from least to greatest is nothing but an ascending order.

Ascending order is nothing but ascending order refers to the grouping of information from the lowest to the highest value. Increasing order is another name for it.

Now, we take the numbers

1st number is 26.087.

2nd number is 2.6×10=26.

3rd number is 26.079.

4th number is 2.6432×10=26.432.

5th number is 26.295.

6th number is 2.6803×10=26.803.

Now, we write in ascending order

26, 26.079, 26.087, 26.295, 26.432, 26.803.

Therefore, the order of the number from least to greatest is 26, 26.079, 26.087, 26.295, 26.432, 26.803.

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Answer:

f= -g/3

Step-by-step explanation:

Using the sine rule we estimate the value of b to be approximately 4.6 units.

The sine law, often referred to as the sine formula, sine rule, or law of sines, is a trigonometrical equation that connects the lengths of any triangle's sides to its sines.

The sine rule states that [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex] , where A ,B and C are the three vertices of the triangle and a, b and c are the three side lengths.

Given A = 50° and B = 62 ° and a = 4 .

Now we use the given values to :

[tex]\frac{4}{sin50} =\frac{b}{sin62}[/tex]

or, b = 4.6104...

or , b ≈ 4.6

Hence the length of b is 4.6

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Answer:

Step-by-step explanation:

Solution of the given equation -3x =2x² -4,using quadratic formula is (-3 ±√41) /4.

As given in the question,

Given equation is:

-3x =2x² -4

Rearrange the terms in proper order:

2x² + 3x -4 =0

Solve it using quadratic formula

x = (-b ±√b²-4ac)/ 2a

Here compare the given equation with general quadratic equation:

a =2 , b=3 , c=-4

Substitute the values in the quadratic formula we get,

x = [ -3± √(3)² -4(2)(-4)]/2(2)

  = (-3 ± √9+32)/4

  = (-3 ±√41) /4

Therefore, Solution of the given equation -3x =2x² -4, using quadratic formula is (-3 ±√41) /4.

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Answer:

I think the answer is d..

Answer:

27/5

Step-by-step explanation:

x/3+x-1/4 = 2+x

4x+3x-3/12=2+x

7x-3=24+12x

7x-12x=24+3

5x=27

x=27/5

Answer:146,600,000

1.496*10^8

Step-by-step explanation:

As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.[tex]f(x)=x^2-2x-10[/tex]  general form to vertex form is y=[[tex](x-1)^{2}[/tex]-9]

The intersection of two or more curves, lines, or edges is known as a vertex in geometry (plural: vertices or vertexes), which is frequently represented by the letters S, P, Q, or R. As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.

The point where two rays start or meet, where two line segments join or meet, where two lines intersect (cross), or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location is the vertex of an angle.

[tex]f(x)=x^2-2x-10[/tex]

      = [[tex](x-1)^{2}[/tex]-9]

Use the form, [tex]ax^{2} + bx+c[/tex]

a=1

b=2

c=-10

Consider a vertex form of parabola,

[tex]a(x+d)^{2} + e[/tex]

find the value of d, using the formula d=[tex]\frac{b}{2a}[/tex]

d=[tex]\frac{2}{2*(-1)}[/tex]

simplify the right side,

d= -1

find the value of e, using e= [tex]c-\frac{b^{2} }{4a}[/tex]

e= [tex]-10\frac{2^{2} }{4*(-1)}[/tex]

simplify the right side,

e= -9

substitute the value of a, d and e into vertex form.

y=  [[tex](x-1)^{2}[/tex]-9]

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Answer:

Your answer would be the last one since that's the one that doesn't have a changed result when the numbers are moved around.

The area of a circle with the value of its circumference as 60cm is 286. 38cm²

The formula for determining the formula for circumference of  a circle is expressed as;

Circumference = 2 πr

Given that;

Now, we have to substitute the value of circumference of the circle as 60cm

We have;

60 = 2 πr

Now, substitute the value for π into the equation, we have;

60 = 2× 3.14r

Multiply the values, we get;

60 = 6.28r

Make 'r' the subject of formula in the equation

r = 60/6.28

r = 9.55cm

But we know that e formula for area of a circle is expressed as;

Area = πr²

Now, substitute the value of radius into the formula, we have;

Area = 3. 14(9.55)²

Find the squares

Area = 3.14(91.2025)

Multiply the values by expanding the bracket

Area = 286. 38cm²

Hence, the area is 286. 38cm²

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Answer:

0.7

Step-by-step explanation:

Answer:

4 2/3

Step-by-step explanation:

1 3/4 x 2 2/3

We need to change the mixed numbers to improper fractions

1 3/4 = ( 4*1+3) /4 = 7/4

2 2/3 = ( 3*2 +2) /3 = 8/3

7/4 * 8/3

Rewriting

7/3 * 8/4

Simplify

7/3 *2

14/3

Make this a mixed number

4 goes into 14 4 times with 2 left over

4 2/3

Answer:

[tex]4\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]1\frac{3}{4} *2\frac{2}{3}[/tex]

First, make fractions as improper fractions.

[tex]\frac{7}{4} *\frac{8}{3}[/tex]

Now multiply the answers.

[tex]\frac{56}{12}[/tex]

Now make the answer a mixed number.

[tex]4\frac{8}{12}[/tex]

To write the answer in its simplest form, divide the numerator and denominator by 4.

[tex]4\frac{2}{3}[/tex]

Answer:

i'm sure you would have a amount of 1,200 dollars because there are 12 months in a year and you just got to x times 100 x 12=1,200 Booyah

Step-by-step explanation:

Answer:

bottom right rectangle: 5x − y

bottom circle: 6x

Step-by-step explanation:

First, solve for the bottom right rectangle by finding the difference between the top right rectangle and the middle right circle:

(9x + 4y) − (4x + 5y)

= (9x − 4x) + (4y − 5y)

= 5x − y

Next, to find the bottom circle, add the bottom left rectangle with the bottom right rectangle (the one we just solved for):

(x + y) + (5x − y)

= (x + 5x) + (y − y)

= 6x