estimate the product 8.1 times 4.2

Answer:

[tex]\displaystyle \large{x=\pm \sqrt{y}}[/tex]

Step-by-step explanation:

We are given the equation:

[tex]\displaystyle \large{y=x^2}[/tex]

Make ‘x’ the subject of the formula by square root both sides:

[tex]\displaystyle \large{\sqrt{y}=\sqrt{x^2}}[/tex]

Cancel the square root and square in RHS and write plus-minus in LHS:

[tex]\displaystyle \large{\pm \sqrt{y}= x}\\\displaystyle \large{x=\pm \sqrt{y}}[/tex]

Therefore, the solution is [tex]\displaystyle \large{x=\pm \sqrt{y}}[/tex]

__________________________________________________________

Summary

To make a variable as the subject of equation means to isolate that variable. For an example, if you want to make y as the subject, you’ll have to isolate y-term.

You may also be curious why do you have to add plus-minus on another side when cancelling [tex]\displaystyle \large{\sqrt{x^2}}[/tex] because [tex]\displaystyle \large{\sqrt{x^2}=|x|}[/tex] and [tex]\displaystyle \large{|x|}[/tex] for their positive and their counterparts (opposite/negative) will always give same y-value.

From an example:

[tex]\displaystyle \large{\sqrt{x^2}=4}[/tex] can be rewritten as [tex]\displaystyle \large{|x|=4}[/tex], cancel absolute sign/square root then write plus-minus which the solution is [tex]\displaystyle \large{x=\pm 4}[/tex] and if you substitute x = 4 or -4, the equation will be true for both values.

__________________________________________________________

Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

Answer:

at aircraft(at z) sported by

Answer:

48% chance to be female and 52% chance to be male.

Step-by-step explanation:

14 female + 15 males =  29 total people

a) 14 females/29 total = 0.48... * 100 = 48%

b) 15 males/29 total = 0.57.... * 100 = 52%

Answer:

[D]

Step-by-step explanation:

Graph using the end point and a few selected points.

x            y

0           2

1            3

2        3.41

Graph is below:

[RevyBreeze]

Answer:

y=3x+1

Step-by-step explanation:

Answer: 3/8

Step-by-step explanation: 6/8 x 2/4 = 3/8

The fraction of attendees of legal age who are women are 3/8

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have in a stadium, 6/8 of the attendees are older and of these 2/4 are women.

The fraction of attendees of legal age who are women are -

2/4 of 6/8

2/4 x 6/8

12/32

3/8

Therefore, the fraction of attendees of legal age who are women are 3/8

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English translation of question -

In a stadium, 6/8 of the attendees are older and of these 2/4 are women, what fraction of the attendees of legal age are women?

Spanish translation of answer -

Tenemos en un estadio, 6/8 de los asistentes son mayores y de estos 2/4 son mujeres.

La fracción de asistentes mayores de edad que son mujeres son:

2/4 de 6/8

2/4 x 6/8

32/12

3/8

Por tanto, la fracción de asistentes mayores de edad que son mujeres son 3/8

Answer:

[tex]\displaystyle [-2, 7][/tex]

Step-by-step explanation:

You want to eradicate one pair of variables so they are set to zero. It does not matter which pair is selected:

[tex]\displaystyle \left \{ {{4x + 2y = 6} \atop {-2x + 2y = 18}} \right.[/tex]

{½[4x + 2y = 6]

{−2x + 2y = 18

>> [tex]\displaystyle \left \{ {{2x + y = 3} \atop {-2x + 2y = 18}} \right. \\ \\ \frac{3y}{3} = \frac{21}{3} \\ \\ \\ y = 7[/tex]

Plug this back into the system to get the x-value of [tex]\displaystyle -2.[/tex]

I am joyous to assist you at any time.

Answer:

$5.40

Step-by-step explanation:

First, find Dave's purchase. To do this, you multiply 15 by the tax percent and add that to the original.

So:

15 x 8% = 15 x 0.08 = 1.2

15 + 1.2 = 16.2

Next, do the same for Mel's purchase:

20 x 8% = 20 x 0.08 = 1.6

20 + 1.6 = 21.6

Then, you subtract Dave's purchase from Mel's:

21.6 - 16.2 = 5.4

This comes out to $5.40

Answer:

Part A: 512 ft²

Part B: 3 cans

Step-by-step explanation:

Part A:

We can divide the shape into 2 areas or rectangles.

The top rectangle's area: 20 x 12 =240

The bottom: 34 x 8 = 272

add these 2 up, 240 +272, and you get 512, the area of this figure.

Part B:

We have to divide the number of feet covered by the area:

512/200 = 2.56

However, we half to round up, cause we cant buy part of a can, we have to buy a whole one.

So, we get 3 cans.

Answer:

[tex]x = -5 \pm \sqrt{26}[/tex]

Step-by-step explanation:

[tex]x^2+10x-1=0\\\\\implies x^2+2\cdot 5 x +5^2-5^2-1=0\\\\\implies (x+5)^2-25-1=0\\\\\implies (x+5)^2 -26=0\\\\\implies (x+5)^2 = 26\\\\\implies x +5 = \pm\sqrt{26}\\\\\implies x = -5 \pm \sqrt{26}[/tex]

Answer:

100°

Step-by-step explanation:

the total of all angles around O on one side of AD is 180° (as that would represent a half-circle).

and the sum of the arc angles AB + BC + CD covers the whole 180°.

so, we have

180 = 55 + BC + 25

180 = 80 + BC

BC = 100°

Answer:

5/5 out of the 7/5 make ONE whole while 2/5 is left over.

The ONE whole is added to nine to make 10 and the remaining 2/5 is also added to the 10 hence 9 7/5 = 10 2/5

Step-by-step explanation:

5/5 out of the 7/5 make ONE whole while 2/5 is left over.

The ONE whole is added to nine to make 10 and the remaining 2/5 is also added to the 10 hence 9 7/5 = 10 2/5

Answer:

3

Step-by-step explanation:

Select an ordered pair: (2, 7)

Select another ordered pair: (6, 19)

slope = (difference in y)/(difference in x)

slope = (19 - 7)(6 - 2)

slope = 12/4

slope = 3

Answer:

Step-by-step explanation:

Pick any two points.

(2 ,7)  & (4, 13)

x₁  = 2  ; y₁ = 7    & x₂ = 4  ; y₂ = 13

[tex]Slope =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

         [tex]=\dfrac{13-7}{4-2}\\\\\\=\dfrac{6}{2}\\\\\\= 3[/tex]

Hello!

Let's use the Distributive Property & simplify:

6(8x+1)

distribute 6 by multiplying it times 8x and 1:

48x+6

Hope everything is clear.

Let me know if you have any questions!

#KeepLearning

:-)

Answer:

[tex]\displaystyle 6 + 48x[/tex]

Step-by-step explanation:

[tex]\displaystyle 6[8x + 1] \hookrightarrow \boxed{48x + 6}[/tex]

I am joyous to assist you at any time.

Answer:

what is your question??????

Step-by-step explanation:

Answer:

32x^7y^15

Step-by-step explanation:

x^2(2xy^3)^5

can be simplified by adding up the x and y values.

Answer:

220 millimeters

Step-by-step explanation:

If you take 22 cm * 10mm/1cm you get 220 mm

Please rate!

Answer:

− (45m+2084)/40

Step-by-step explanation:

I do not have one sorry,

Answer:

78°

Step-by-step explanation:

Angles on a straight line = 180°

AD is the straight line

Angle BFA = 48

Angle CFD = 54

54 + 48 = 102

180 - 102 = 78

Therefore, Angle BFC = 78°

The exponential function that passes through (0,2) and (3,54) is a growth function

The exponetial function is y = 2 * 3^x

The points are given as:

(x,y) = (0,2) and (3,54)

An exponential function is represented as:

y = ab^x

Substitute the points in the equation

2 = ab^0 and 54 = ab^3

Solve 2 = ab^0

a = 2

Substitute 2 for a in 54 = ab^3

54 = 2b^3

Divide by 2

27 = b^3

Take the cube roots of both sides

b = 3

So, we have:

y = ab^x

This becomes

y = 2 * 3^x

Hence, the exponetial function is y = 2 * 3^x

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Answer:

2

Step-by-step explanation:

gradient =y² -y¹ /x²-x¹

=9-1/2--2

=8/4

=2

Answer:

y = 2x + 5

Step-by-step explanation:

There are 2 ways to find this equation:

The first way:  We have: y = ax + b (this is the line, right?)

The line is through the point (-2, 1) so we have:

1 = (-2)a + b      (1)

The line is also through the point (2, 9) so we have:

9 = 2a + b.       (2)

From (1) and (2) we get a equals 2, b equals 5. Then:
y = 2x + 5

The second way:

Let A(-2, 1) and B(2, 9), then AB = (4, 8).

=> The normal vector of this line is n = (-2, 1).

The line that is through the points A(-2, 1) and B(2, 9), and has the normal vector n=(-2, 1) has the equation:

[tex]-2(x - 2) + 1(y - 9) = 0[/tex]

[tex]-2x + y - 5 =0\\ < = > y = 2x + 5[/tex]

Answer:

Here,

n(A)={0,1,3,5,6}

n(B)={1,2,3,7}

n(AUB)=?

we know that,

AUB={0,1,2,3,5,6,7}

Step-by-step explanation:

is it okay ?

hopefully it works <3 ❣️

Answer:

the answer is (0, 0) trust me

Answer:

25(m+3)

Step-by-step explanation:

25 is multiplied by (m+3)

'the sum of m and 3' is a quantity which must be indicated using parentheses

Hello!

The sum of means we add:

m+3

Multiply it times 25:

25(m+3)

The answer is Option C.

Now, the option you selected is wrong for the following reasons:

If you translate it into a verbal phrase, this is what it means:

25 plus the product of m and 3

Hence, Option C is correct.

Hope everything is clear.

Let me know if you have any questions!

Always remember: Knowledge is power! :-)

Answer:

x=2.16

Step-by-step explanation:

1. Cross multiply.  3.5x(5) = 9(4.2)

2. Simplify. 17.5x=37.8

3. Divide both sides by 17.5. x=2.16

Answer:

50°

Step-by-step explanation:

90-40= 50° ............

Answer:

To figure out the change, we subtract the original temperature by the following after temperature.

18°F - original

-9°F - subsequent time after original

So we set up the equation;

18°F - (-9°F)

(Two negatives combine to form a positive)

18°F + 9°F

= 27°F was the change in temperature.

The change in temperature from 2:00 PM to 10:00 PM is -27° F.

Temperature is a physical quantity that measures the coldness or hotness of an object in reference to some standard value.

Change in temperature can be defined by the difference of the final temperature with that of the initial temperature.

Temperature is usually measured in degree Celsius or degree Fahreheit.

Temperature at 2:00 PM = 18° F

Temperature at 10:00 PM = -9° F

Change in temperature = Final temperature - Initial temperature

                                       =  -9° F - 18° F

                                       = -27° F

Hence, the change in temperature can be calculated as -27° F.

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Answer: 7xy + 2x^2t

Step-by-step explanation:

The function (fg)(x) is a composite function

The value of the function (fg)(x) is 2x^3 + 7x^2 - 19x - 20

The functions are given as:

f(x) = 2x^2 - 3x - 4 and g(x) = x + 5.

To calculate (fg)(x), we make use of

(fg)(x) = f(x) * g(x)

So, we  have:

(fg)(x) = (2x^2 - 3x - 4) * (x + 5)

Expand

(fg)(x) = 2x^3 - 3x^2 - 4x + 10x^2 - 15x - 20

Collect like terms

(fg)(x) = 2x^3 - 3x^2 + 10x^2 - 4x - 15x - 20

Evaluate

(fg)(x) = 2x^3 + 7x^2 - 19x - 20

Hence, the function (fg)(x) is 2x^3 + 7x^2 - 19x - 20

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