Explain Mathematical Ideas (1)(G) A classmate questions your solution to
the problem. Use precise mathematical language to explain why your solution
is correct.

Answer:

x = 4 + √3 and  x = 4 − √3

Step-by-step explanation:

(a−b)^2=a^2−2ab+b2

a^2−b^2=(a−b)(a+b)

−2x^2+16x−26

=−2(1x^2−8x+13)

=−2(x^2−8x+13+3−3)

=−2(x^2−8x+16−3)

=−2(x^2−2(4)x+4^2−3)

=−2((x−4)^2−3)

=−2((x−4)^2−(√3)^2)

=−2((x−4)−√3)((x−4)+√3)

=−2((x−(4+√3)((x−(4−√3))

The zeros of the given algebraic expression are:

−2x^2+16x−26=0

−2((x−(4+√3)((x−(4−√3))=0

x = 4 + √3 and  x = 4 − √3

I strongly suggest using the quadratic formula as this problem is much easier to solve using it.

x = (−b ± [tex]\sqrt{b^{2}-4ac }[/tex] ) / 2

Answer:

The elevation when the boiling point of water is [tex]190[/tex] °[tex]F[/tex] is 12790.70 feet

Step-by-step explanation:

Let every 1,000 feet of elevation be [tex]x[/tex]. Hence, we can write

[tex]T = 212[/tex] [tex]- 1.72x[/tex]

Where [tex]T[/tex] is the boiling temperature of water at different elevations

Now, to the determine the elevation when the boiling point of water is [tex]190[/tex] °[tex]F[/tex].

We will determine [tex]x[/tex] by putting [tex]T = 190[/tex] °[tex]F[/tex].

Hence,

[tex]T = 212[/tex] [tex]- 1.72x[/tex]

[tex]190[/tex]  [tex]= 212[/tex]  [tex]- 1.72x[/tex]

[tex]190 - 212[/tex]    [tex]= - 1.72x[/tex]

[tex]- 22[/tex]  [tex]= - 1.72x[/tex]

[tex]22 = 1.72x\\x = \frac{22}{1.72} \\x = 12.79070[/tex]

Since [tex]x[/tex] represents every 1,000 feet of elevation, then the elevation when the boiling point of water is [tex]190[/tex] °[tex]F[/tex]

[tex]12.79070[/tex] × [tex]1000\\[/tex] [tex]= 12790.70[/tex] feet

Hence,  the elevation when the boiling point of water is [tex]190[/tex] °[tex]F[/tex] is 12790.70 feet

[tex]\boxed{3:5}[/tex]

We need to first change the measurement of 2 feet to inches, and then find the most simplified version of the resulting ratio.

2 feet = 24 inches (1 foot = 12 inches)

Ratio: 24:40

Simplify ratio:

24/8 = 3

40/8 = 5

Ratio: 3:5

Therefore, the simplified ratio is 3:5 inches.

Answer:

a = - 1

Step-by-step explanation:

Given the points are equidistant from A then AP = AQ

Calculate the distance using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A(0, a) and (x₂, y₂ ) = P(3, - 3)

AP = [tex]\sqrt{3-0)^2+(-3-a)^2}[/tex] = [tex]\sqrt{3^2+(-3-a)^2}[/tex] = [tex]\sqrt{9+(-3-a)^2}[/tex]

Repeat with (x₁, y₁ ) = A(0, a) and (x₂, y₂ ) = Q(- 2, 2)

AQ = [tex]\sqrt{(-2-0)^2+(2-a)^2}[/tex] = [tex]\sqrt{(-2)^2+(2-a)^2}[/tex] = [tex]\sqrt{4+(2-a)^2}[/tex]

Equating AP and AQ

[tex]\sqrt{9+(-3-a)^2}[/tex] = [tex]\sqrt{4+(2-a)^2}[/tex] ( square both sides )

9 + (- 3 - a)² = 4 + (2 - a )² ← expand parenthesis on both sides

9 + 9 + 6a + a² = 4 + 4 - 4a + a² ( subtract a² - 4a from both sides )

18 + 10a = 8 ( subtract 18 from both sides )

10a = - 10 ( divide both sides by 10 )

a = - 1

The value of a is -1 if A(0,a) is equidistant from P(3,-3) and Q(-2,2) the answer is a = -1.

It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).

[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]

It is given that:

A(0,a) is equidistant from P(3,-3) and Q(-2,2).

It is required to find the value of a:

Using the distance formula:

The distance formula can be given as:

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

AP = AQ

[tex]\rm \sqrt{(3-0)^2+(-3-a)^2} = \sqrt{(-2-0)^2+(2-a)^2}[/tex]

After simplification:

9 + (3 + a)² = 4 + (2 - a)²

9 + 9 + 6a + a² = 4 + 4 - 4a + a²

18 + 10a = 8

10a = - 10

a = - 1

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division.

Thus, the value of a is -1 if A(0,a) is equidistant from P(3,-3) and Q(-2,2) the answer is a = -1

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Answer:

Step-by-step explanation:

[tex]8+9\div3\times6-5\\= 8+9\div \:3\times \left(6-5\right)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(6-5\right)\::\quad 1\\=8+9\div \:3\times \:1\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:9\div \:3\times \:1\::\quad 3\\=8+3\\\\= 11[/tex]

[tex]5+3-8\div \:4-2\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:8\div \:4\::\quad 2\\=5+3-2-2\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:5+3-2-2\::\quad 4\\=4[/tex]

[tex]\left(5+3\right)-8\div \:4-2\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(5+3\right)\::\quad 8\\=8-8\div \:4-2\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:8\div \:4\::\quad 2\\=8-2-2\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:8-2-2\::\quad 4\\=4[/tex]

Answer:

1) 85+(-96)=-11

2) 86+(-38)=48

3) 22+(-41)=-19

Step-by-step explanation:

1)

Here you are adding a negative to a positive. The if you were to take the absolute value of the negative number it would be greater than that of the positive.

Think about it like 96-85=11, but it was flipped so negative 11.

-11

2)

86+(-38) is the same as 86-38

48

3)

Here you are also adding a negative to a positive. The if you were to take the absolute value of the negative number it would be greater than that of the positive.

Think about it like 41-22=19, but it was flipped so negative 19.

-19

Hope this is helpful :-)

Answer:31

Step-by-step explanation:

Answer:

c.) 20%

Step-by-step explanation:

•1/3 chnace of picking Strawberry flavor

•2/3 chance of picking a milkshake or cone serving

(1/3)*(2/3)=2/9=0.222...(approx.)=0.20=20%

Edit for more clarification:

If you have a situation where multiple outcomes are favorable ("or" statements) then you add the odds together. The customer here wouldn't have minded a milkshake or a cone, so we add their odds together to get 2/3.

If you have a situation where a specific combination of outcomes is favorable ("and" statements) then we multiply the odds. The customer would be getting a flavor and a type of serving, so we multiply the odds of each combination together.

(Note that this is technically a simplified version of the general formulas/equations for probabilities so if you go look them up on the internet they might include some other ideas.)

Answer:C

Step-by-step explanation:

quiz says it was right

Answer:

1,582.25 kilogramos

Step-by-step explanation:

Para determinar los kilogramos de maíz que lleva el camión, se debe multiplicar el peso de los dos tipos de bultos que lleva por la cantidad de cada uno y sumar estos valores para obtener la respuesta:

(20.5*32)+(48.75*19)=656+926.25=1,582.25

De acuerdo a esto, el camión lleva 1,582.25 kilogramos de maíz.

Answer: x= 2, y= -1/2

Step-by-step explanation:

The value of x is 2 and y is -1/2

equations are  3x-2y=7 --1

                         7x+2y=13 --2

lets  consider  3x-2y=7 as equation 1,

       consider  7x+2y=13 as equation 2

by putting both the equations :-

              3x-2y=7

               7x+2y=13

we get  10x=20

           x=20/10

           x=2

Now by putting the value of x in equation 1;

3(2)-2y=7

6-2y=7

-2y=1

y=-1/2

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y. They are called simultaneous equations because the equations are solved at the same time. Each of these equations on its own could have infinite possible solutions.

algebraic equation, a statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root.

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answer:

A.7/5 is the correct answer because numerator is more than denominator.

thank me plz

Answer:

the answer is A

Step-by-step explanation:

Answer:

5.48

Step-by-step explanation:

Given length of three strings:

[tex]\text{Length of first string}, L_1=7.68\ inches\\\text{Length of second string}, L_2=3.9\ inches\\\text{Length of third string}, L_3=2.2\ inches[/tex]

To find:

The difference in length between the longest and the shortest string?

Solution:

First of all, let us compare the given three decimal numbers.

We check the number before decimal first of all.

We can see that the numbers are 7, 3, and 2.

7 being the largest [tex]L_1[/tex] is the longest string.

2 being the smallest [tex]L_3[/tex] is the shortest string.

So, the difference is:

[tex]L_1-L_3=7.68-2.2\\\Rightarrow \bold{L_1-L_3=5.48 }[/tex]

So, the answer is 5.48.

Answer:

Volume of a cylinder=1/2πr^2h.

1/2×3.142×10^2×5.

1/2×3.142×100×5.

1/2×1571

=785.5

Answer:

About 1570.8

Step-by-step explanation:

Start by looking at the equation for solving a cylinder, which is V = π x r² x h. Since r = radius (5) and h = height (10), you add those numbers into the equation. Now you have to solve V = π x 5² x 10, which will get you your repeating decimal of 1570.79633...which then can be rounded your answer of 1570.8.

Answer:

I think its rational

Step-by-step explanation:

Answer: 0.35 is rational! :D Hopefully this will help others as well!

Step-by-step explanation:

Answer:

100 minuets aka 1 hour and 40 minuets

Step-by-step explanation:

It would be 100 because 500÷5=100

Answer:

  13.2

Step-by-step explanation:

√175 ≈ 13.2 . . . units

The area of a square is the square of the edge length. Hence, the edge length is the square root of the area.

Answer:

Step-by-step explanation:

1). [tex]a^{3}\times a^5=a^8[/tex]

2). [tex](a^3)^3[/tex] = [tex]a^{9}[/tex]

3). [tex]\frac{a^{10}}{a^3}=a^{10-3}=a^7[/tex]

4). [tex]\frac{a^2}{a^7}=\frac{1}{a^{7-2}}=\frac{1}{a^5}[/tex]

5). [tex]\frac{a^5\times a^2}{a^7}=\frac{a^{5+2}}{a^7}=1[/tex]

6). [tex]\frac{16a^5b^3}{8a^2b}=(\frac{16\times 5}{8})(\frac{a^5}{a^2})(\frac{b^3}{b})[/tex]

              [tex]=\frac{80}{8}(a^{5-2})(b^{3-1})[/tex]

              = 10a³b²

7). [tex]\frac{2a^3b^3}{2b^2}=(\frac{2}{2})(a^3)(\frac{b^3}{b^2})[/tex]

             = a³b

8). [tex](\frac{a^{-8}}{b^{11}})^{-2}=(\frac{b^{11}}{a^{-8}})^2[/tex]

                 [tex]=(b^{11}a^8)^2[/tex]

                 = [tex]a^{16}b^{22}[/tex]

9). [tex]\frac{(2a^3)(a^4)^2}{8a^{11}}=(\frac{2}{8})(\frac{1}{a^{11-3}})(a^4)^2[/tex]

                   [tex]=\frac{1}{4}(\frac{a^8}{a^8})[/tex]

                   [tex]=\frac{1}{4}[/tex]

10). [tex]\frac{5a^7b^2}{15a^{10}b^{-3}}=(\frac{5}{15})(\frac{a^7}{a^{10}})(b^{2+3})[/tex]

                   [tex]=\frac{1}{3}(\frac{b^5}{a^3} )[/tex]

                   [tex]=\frac{b^5}{3a^2}[/tex]

11). 3a⁰ = 3(1) = 3

12). (a²b)⁴ = (a²)⁴(b)⁴

                = a⁸b⁴

Answer:

GCF-12

Step-by-step explanation:

Find the prime factorization of 84

84 = 2 × 2 × 3 × 7

Find the prime factorization of 120

120 = 2 × 2 × 2 × 3 × 5

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 2 × 2 × 3

GCF = 12

Answer: The GCF is 12

Step-by-step explanation:

84=2*2*3*7

120=2*2*2*3*5

So, the GCF is 2*2*3=12

Answer:

$28.50

Step-by-step explanation:

21 chicken wings= $39.90

1 chicken wing= 39.90÷21= $1.90

15 chicken wings= 15×1.90= $28.50

Answer:

hundred thousands

Step-by-step explanation:

You would move it to the left one place, so it would be the hundred thousands place.

Answer: The answer is hundred thousands place.

Step-by-step explanation: The question is wanting you to name the space the 8 is in. So 10's, 100's, 1000's and so on. But in this case an 8 in the hundred thousand's place has 10 times more value then an 8 in the ten thousand's place.

Answer:

The first one is a linear function with the slope of 3 with no shift. the second is a vertical line on the 2 of the x axis. the third is a horizontal line on the -3 of the y axis.

Answer:

53 and 54

Step-by-step explanation:

x + (x+1) = 107

2x+1 = 107

2x = 107

x = 53

x+1 = 54

Answer:

9 eazy

Step-by-step explanation:

Answer:

B.9

Step-by-step explanation:

3^4=81

3^2=9

81/9=9

Answer:

X = 5

Step-by-step explanation:

3x + 12 + 9x = 72

okay hopefully i can explain so when your doing this combine like terms so

3x + 9x = 12x

12x + 12 = 72

then you would subtract both sides by 12

+12 = subtract x+12=2

- 12 = add x-12=2

there just flipped so in this case i would subtract 12

12x + ( 12-12) = ( 72-12 )

so 12-12 = 0 and 72-12 is equal to 60

12x = 60

the divide on both sides l but leave the x alone so its just 60 divided by 12 wich is 5

so X = 5

hope this helps with ur homework a little btw go back and redo ur other awnsers with this new concept hope it helps

Answer:

We have this equation:

[tex]3(y+3)+7(2y-8)-(y-1)=0​[/tex]

First, we do the parenthesis:

[tex]3y+9+14y-56-(y-1)=0\\[/tex]

When there is a minus (-) in front of a parenthesis, all signs change inside it:

[tex]3y+9+14y-56-y+1)=0\\[/tex]

Now we operate:

[tex]16y-46=0[/tex]

We add 46 on both sides:

[tex]16y - 46 + 46 = 0 +46[/tex]

[tex]16y = 46[/tex]

And divide 16 on both sides:

[tex]\frac{16y}{16}=\frac{46}{16}[/tex]

[tex]\bol{x = \frac{46}{16}}[/tex] = [tex]\frac{23}{8}[/tex]

Answer:

Step-by-step explanation:

3(y+3)+7(2y-8)-(y-1)=0​

3y + 9 + 14y - 56 - y + 1 = 0

16y - 46 = 0

16y - 46 + 46 = 0 + 46

16y = 46

16y/16 = 46/16

y = 23/8

Answer: KE= 900,000t^2

Step-by-step explanation:

The geometric terms that best describes each part of the tennis court are Playing Surface ⇒ Plane and Corner of Serving Box ⇒ Vertex

There are several geometric terms; some of them are:

Using the above definitions, the geometric terms that best describes each part of the tennis court are

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Answer:

c

Step-by-step explanation: