Algebra Challenge
1. Simplifying Expressions
Demam
The elementary school is building a new triangular playground that they want to
fence in. Given the three side lengths of 2x-1, 4x and 12x + 5 find the value of x
when the perimeter of the playground is 112 ft.
The situation can be represented by
nswer:
(2x-1)+4x+(12x+5)=114

Answer:students are the independent because he will get a number of cards depending on how many students there are so its

s independent and c dependent

Step-by-step explanation:

Answer:

s = independent

c = dependent

The number of cards depends on the number of students in his class.

Hope this helps :)

The square of the equation 2[tex]x^{2}[/tex] – 12x – 20=0 is

What is a quadratic equation?

A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0.

a[tex]x^{2}[/tex]+bx+c , a, b, c are integers .

formula: −b±√b2−4ac/2a

Given equation ,

2[tex]x^{2}[/tex] -12x-20=0

By comparing with the quadratic equation

Here, a=2, b= -12, c= -20.

X=−b±[tex]\sqrt{b^2-4ac}[/tex]/2a

X= -(-12) + [tex]\sqrt{(-12)2-4(2)(20)}[/tex] /2(2)

X=12+-  [tex]\sqrt{144-160}[/tex]/4

X=12+- [tex]\sqrt{-16}[/tex]/4,

X=12+- (-4)/4

X=12+(-4)/4 and x=12-(-4)/4

X= 12-4/4 and x=12+4/4

X=8/4 and x= 16/4

X=2 and x= 4

Therefore, the square of the equation 2x2-12x-20=0 is x= 2 and x=4.

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Answer:

85%

Step-by-step explanation:

Total no. of matches played,

→ x = 20 matches

No. of matches they won,

→ y = 17 matches

Now the win percentage will be,

→ (y/x) × 100

→ (17/20) × 100

→ 0.85 × 100

→ 85%

Hence, the percentage is 85%.

Answer:

y=8,x=-3

Step-by-step explanation:

1/3×+1/4y=1

lcm=12

multiply through by lcm to get equation 1

4x+3y=12

equation 2

2×-3y=-30

equation 2 by 2

using the substitution method

y=8

x=-3

Answer:

There are 46,656 cubic inches in a cubic yard.

Explanation:      

for an approximate result, multiply the volume value by 46660

It is scale factor at 1/14.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, by increasing each side by, say, 2, we can expand the size of a rectangle with sides of 2 cm and 4 cm.

The fundamental equation to determine a figure's scale factor is written as, Scale factor is equal to the difference between the dimensions of the new and old shapes.

based on the information provided,

Scale Factor = Fish Model Length / Fish Length in Real Line

scale factor =10/140

                   =1/14

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The rectangle's width is 8m and the length is 4 times the width, so the length = 4 x 8 = 32m

To calculate the area of a rectangle, we take the width and multiply it with the length

A = 32 x 8 = 256m2

The translation of the function 2 | x | - 9 when translated 6 units up gives the function as 2 | x | - 3.

We are given a function:

2 | x | - 9.

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

We are asked to translate the function 6 units up.

This means that we have to add 6 units to the function.

A function has been “translated” when it has been moved in a way that does not change its shape or rotate it in any way.

So, we get that:

f(x) = 2 | x | - 9 + 6

f(x) = 2 | x | - 3

Therefore, the translation of the function 2 | x | - 9 when translated 6 units up gives the function as 2 | x | - 3.

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Answer: u = 80° v = 25°

Step-by-step explanation:

(a) angles on a straight line = 180° - 130° = 50°

In isosceles triangle, both angles on each side is equal, so

180° - 50° - 50° = 80°

u = 80°

(b) u = (2v + 30°) because opposite angles of a parallelogram are equal.

u = 80°

80° = 2v + 30°

80 - 30 = 50

50° = 2v

25° = v

A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is systematic sampling.

Therefore, a probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is systematic sampling.

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Answer:

WXZ, ZXW, 1

Step-by-step explanation:

The largest size of identical felt squares that can be used to cover the top of rectangle is 5 squares of side 24cm.

The rectangle is a 2-dimensional figure with length and breadth which may or may not be same. A square is also a 2-dimensional figure with equal length of its sides.

When the dimensions of rectangle are given, it's are is given as the product of the sides of the rectangle which is given as:

Area of rectangle = Length × Breadth = 60 × 48 = 2880 cm square

The length of the square that entirely covers up the top side i.e., rectangular top can be determined by hit and trial mechanism starting from the lowest whole number in order to determine the length of largest squares of equal dimensions. Then comparing the area of the rectangular top and product of number of squares needed and area of each square, we can find the largest size of the square.

Area of square = length × length = l²

Since, Area of rectangular top = No. of squares × Area of 1 square

Therefore, 2880 = N (l²)

Putting N =1, 2, 3, 4, 5 and so on, we find that when N = 5, the value of square root of l is a perfect whole number.

Hence, 2880 = 5 × (l²)

l = √576 = 24

Thus, 5 squares of side 24cm will be used to cover the rectangular top entirely.

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The cost of Robert purchase of books after the paid tax is $32.66.

For the given question;

The original cost of the book purchased by the Robet = $30.45.

The tax of 7.25% is applied on the original cost of the book.

7.25% of $30.45 = (7.25×30.45)/100

7.25% of $30.45 = $2.21

The final cost of the book = original cost + tax

The final cost of the book = $30.45 + %2.21

The final cost of the book = 32.66

Therefore, the total price paid by the Robert for the book after 7.5% of the tax is applied is $36.66.

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The complete question is-

Robert spends $30.45 before tax at the bookstore. If the sales tax rate in his city is 7.25%, what is the total cost of his purchase?

The length and width of the given rectangle is 10.77 and 5.385 respectively.

According to the question statement, The length of a rectangle is twice the width and the area of the rectangle is 58 square units.

We are supposed to find the length and width of the rectangle.

Before solving this we need to know that the area of the rectangle is the product of its length and width,

Let's assume the length be "l" and width be "w"

Therefore Area = l*w

Now as length is twice the width so [tex]l=2w[/tex]

Area = [tex]58 square units[/tex]

Therefore [tex]l*w=58\\[/tex]

but [tex]l=2w[/tex]

[tex]2w*w = 58\\2w^{2}=58\\w^{2} = \frac{58}{2} \\w^{2}= 29[/tex]

[tex]w=\sqrt{29} \\w=5.385[/tex]

as [tex]l=2w[/tex]

[tex]l=2*5.385\\l=10.77[/tex]

Hence length l = 10.77 unit and width w = 5.385 unit

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Ralph would most likely get more items correct than his Grandmother.

If both Ralph and his Grandmother took the Intelligence Quotient i.e., IQ test, then Ralph would most likely get more items correct than his Grandmother. This is due to Flynn Effect.

Flynn Effect refers to secular increase in population intelligence quotient observed throughout the 20th century. It demonstrates that the average of the IQ scores will change as varying generations have different thresholds for what intelligence is necessary.

Flynn Effect is documented by Flynn in a study on intelligence quotient. As Ralph's grandmother was born on 1925 and Ralph was born in 1990, so they have a generation gap of almost six decades. That is why Ralph will have a higher IQ than his grandmother.

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Answer:

82,337

Step-by-step explanation:

   76,749

      5565

+         23
   82,337

Hope it helps!!!

;}

Step-by-step explanation:

1

A: is a function since 2 different x values can have the same y value

B: not a function since the x value 0 gives different values which makes it not a function.

C: since 4 corresponds to 2 different y values it is not a function.

D and E are not function since there are different y values for the same x value.

2: all of the answers are determined by the vertical line test.

A NOT A FUNCTION

B NOT A FUNCTION

C A FUNCTION

D UNCLEAR

E NOT A FUNCTION

hope this helps and make sure to ask any qs if you doubt anything :)

The result are-

The values of x that correspond to the given quadratic equation ax² + bx + c = 0 are known as its roots.

For, the given expression;

x² + px + q = 0.      ....... (equation 1)

where p and q are constants, has roots -3 and 5.

Part 1: solve for p and q.

Put x = -3 in equation 1.

p(-3) = (-3)² + p(-3) + q = 0

9 - 3p + q = 0         .........(equation 2)

Now, put x = 5 in equation 1.

p(5) = (5)² + p(5) + q = 0

25 + 5p + q = 0     ..........(equation 2)

Solve equation 2 and 3 by elimination method.

p = -2 and q = -15.

Part 2: Estimate the constant r.

The equation is; x² + px + q + r = 0.

Substitute the values of p = -2 and q = -15.

x² + (-2)x + (-15) + r = 0.

As, the equation given real equal roots; then,

discriminant value: b² - 4ac = 0.

Substitute the values;

(-2)² - 4×1×(-15 + r) = 0

On simplification;

4 + 60 - r = 0

r = 64.

Therefore, the value of the constant r is estimated as 64.

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Answer:

y=1/4 -2

Step-by-step explanation:

y =mx + c

m= slope

c= y-intercept

putting the valves of x and y ( 0,-2)

-2 = 1/4(0) + c

solve for C

C = -2

substituting back to the general equation of

y= 1/4x + C

y = 1/4x - 2( ans).

Step-by-step explanation:

Just do the calculations at last by using the value of x

Answer:

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

Ivory's scaled counterpart has a 48-square-unit area.

Ivory's scale factor for producing their scaled replica is;

On the graph, one interval corresponds to four units of the rectangle. This ratio is 1:4.

We can see from the provided image that the rectangle's y-axis has three intervals and its x-axis has one interval.

Now, the picture informs us that the scaled copy's area is 48 square units.

This indicates that the triangle she is attempting to depict with that graph has an area of 48 square units.

Now, if one of the graph's intervals is in units of x, then it indicates;

Y-axis: length; 3x units

size; x-axis equals x units

A rectangle's area is

based on the formula Area = Length Width, 3x [tex]\times[/tex] x = 48.

1 interval on the graph corresponds to 4 units of the rectangle because 3x2 = 48 x2 = 48/3 x2 = 16 x = 16 x = 4.

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Answer:

Starting from the left, the points plotted are:

-√9, -1.75, -3/2, -5/3, √4

Answer:

Domain:

$%error%$

Range:

$%error%$

Explanation:

Both

x

and

y

belong to all the real numbers since there is no restriction on either the domain or the range.

Step-by-step explanation:

Answer:

Alright, 53 + 28 = 81

Answer:

81

Step-by-step explanation:

Answer:

adding decimals is different then subtracting because adding would be bigger subtracting means smaller