I have to solve the equation:
[tex] |4 \sqrt{2} - 6 | + |2 \sqrt{10} - 6| [/tex]
The first thing I tried is simply removing the modules, it seemed like the most logical solution and this is the answer I got, but it wasn't any of the options:
[tex]4 \sqrt{2} + 2 \sqrt{10} + 12[/tex]
The second thing I tried is putting both equations in one module and sum the first one with the second one in parentheses like this:
[tex] |4 \sqrt{2} - 6 + (2 \sqrt{10} - 6 | = \\ = |4 \sqrt{2} - 6 + 2 \sqrt{10} + 6 | = \\ = 4 \sqrt{2} + 2 \sqrt{10}[/tex]
But this wasn't in the answers either.
After I checked, the correct answer was:
[tex]2 \sqrt{10} - 4 \sqrt{2} [/tex]
So I was wondering where does the minus come from?

It is in a module and between the modules, there's a plus and even if that plus somehow turns into a minus when it goes inside the modules, which I'm not aware of, it would still turn into a plus because it is in a module ;-; Or I'm just st*pid, I don't know. ​

Answers

Answer 1

Think back to the definition of absolute value:

• If x ≥ 0, then |x| = x.

• If x < 0, then |x| = -x.

In other words, the absolute value always returns a positive number. So if x is positive, leave it alone; but if it's negative, then you have to negate it to get a positive number back.

This means that you cannot simply reduce |x - y | to x - y because you need to consider the possibility that x - y may be negative, in which case |x - y | would reduce to -(x - y) = y - x.

In this case,

|4√2 - 6| = -(4√2 - 6) = 6 - 4√2

because 4√2 < 6, which you can determine by comparing both of these numbers as square roots:

4√2 = √16 √2 = √32

6 = √36

and √32 < √36 because 32 < 36.

Similarly,

|2√10 - 6| = 2√10 - 6

because

2√10 = √4 √10 = √40

6 = √36

So ultimately,

|4√2 - 6| + |2√10 - 6| = (6 - 4√2) + (2√10 - 6) = 2√10 - 4√2


Related Questions

Find the value of x. Around the length to the nearest tenth.

Answers

Answer:

x = 6 m

Step-by-step explanation:

x = 16sin22°

x = 6.0 m

Answer:

Step-by-step explanation:

Plzzz help me with thiss

Answers

Answer:

Step-by-step explanation:

rather than doing all of the sums, you should just learn the formula (for the pattern)

it is n(highest + lowest) where n is number of numbers

             2

for example 2+3+4+5+6 = 20

5(6+2) =  20

  2

~~~~~~~~~~~~~~~~~~~~

1+2+3+4+5+6+7+8 = 36

8(9) = 72/2= 36

2

A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = - 16t^2 + 48t where t equals the time in seconds and the h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent? Help please!!!

Answers

Answer:

x = 3/2

The axis of symmetry is located at the vertex,

which is the also the highest point in this problem...

the x component of the vertex can be calculated as -b/2a = -48/-32 = 24/16 = 6/4 = 3/2

x = 3/2

Step-by-step explanation:

In a right angle triangle , the two shorter sides are 6cm and 8cm in length . What is the length of the longest side

Answers

Answer:

10 cm

Step-by-step explanation:

In a right triangle, there are three sides, A, B, and C.

A and B are the short sides, while C is the long side.

So we know that A = 6 cm, and B = 8 cm.

We can then use the Pythagorean theorem which states that

[tex]C=\sqrt{(A^2)+(B^2)[/tex]

Once we plug in the numbers we get

[tex]C=\sqrt{6^2+8^2}[/tex]

[tex]C=\sqrt{36+64}[/tex]

[tex]C=\sqrt{100}[/tex]

C=10 cm

Determine f(a+h)-f(a)/h for f(x)=x^2+5x

Answers

Answer:

2x + 5

ok.. slightly silly question...

you will eventually learn that this formula is the

formula for the "derivative" in calculus....

A[tex]x^{b}[/tex] becomes (a*b)  [tex]x^{b-1}[/tex]

2x + 5

Step-by-step explanation:

solve it : -

[tex] \sqrt{8 \times 5 \times 10} [/tex]
______​

Answers

Answer:

20

Step-by-step explanation:

8 * 5 = 40

40 * 10 = 400

√400 = 20

Answer:

20

Step-by-step explanation:

sqrt(8*5*10)

sqrt(400)

sqrt(20*20)

20

Krystal got $10 from his father and $x from his mother. how much did he get altogether​

Answers

Answer:

16

Step-by-step explanation:

they got 16 all together in total

Answer:

$10x

Step-by-step explanation:

We know that Krystal got $10 from his father but we don't know how much Krystal got from his mother because there's just x for the amount. So, we can just write that Krystal got $10x altogether.

Hope this helps

La Base de un triangulo mide 28 cm y su altura es correspondiente, 3/7 cm de la base. calculen el area del triangulo

Answers

Answer:

168 cm²

Step-by-step explanation:

altura = 3/7 × 28 = 12 cm

area = ½×28×12 = 168 cm²

Find the mode of the data​

Answers

Answer:

[tex]mode = l _{1} + ( \frac{d _{1} }{d _{1} + d _{2}} ) \times c \\ \\ = 6.5 + (\frac{50}{50 + 88} ) \times 3 \\ = 7.59[/tex]

what fraction of 42 is 6​

Answers

The fraction of  42 that is 6 is mathematically given as

42*1/7

What fraction of 42 is 6?

Generally, the equation for the statement is mathematically given as

42/x=6

Therefore

x=42/5

x=7

In conclusion, The fraction of  42 that is 6  is

42*1/7

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HELPPP QUICK W THIS QUESTION
***
A
What is the value of x in the proportion
نانا اتيت |cr
X
2
CO
C
5
53
الIl F
10
3
12
20

Answers

Answer:

it's second option

[tex]5 \times \frac{2}{5} [/tex]

Step-by-step explanation:

for this change them to points so it be easier to solve

[tex] \frac{2.25}{x} = \frac{1.5}{3.6} \\ \\ x = \frac{3.6 \times 2.25}{1.5} = 5.4[/tex]

and then 5.4 equals 5(2/5)

2. Find the perimeter of a triangle with vertices A(–3, 5), B(–3, 2), and C(1, 2).

Answers

Answer:

12 units

Step-by-step explanation:

the perimeter = 3 + 4 + 5 = 12 units

The perimeter of a triangle is 12 cm.

To find the perimeter of the triangle.

What is triangle?

A triangle has three sides, three vertices, and three angles. The sum of the three interior angles of a triangle is always 180°.

Use the distance formula to find the length between point A and B, B and C, C and A. Then add all three lengths together to get the perimeter.

 Distance = √ ( (x2 - x1)2 + (y2 - y1)2 )

Points A and B:

d = √(-3 +3)2 + (2 - 5)2

d = √ 0 + 9

d = √9

d = 3

Points B and C:

d = √ (1+ 3)2 + (2 -2)2

d = √ 16 + 0

d = √ 16

d = 4

Points C and A:

d = √ (-3 - 1)2 + (2 -5)2

d = √ 16 + 9

d = √ 25

d = 5

Perimeter=  3 + 5 + 4 = 12

So,  the perimeter of a triangle is 12 cm.

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is (6,3) a solution to this system of equations y=3x - 3 3x - y =3

Answers

Answer:

It is not a solution

Step-by-step explanation:

Plug the point into the equations and check to see if they are true

y=3x - 3

3 = 3(6) -3

3 = 18-3

3 = 15

False

We do not need to check the other equation since this is false

20 PTS!! Which best describes the relationship between the line that passes through the points (1, -6) and (3,-2) and the line that
passes through the points (4, 8) and (6, 12)?

A. parallel
B. neither perpendicular nor parallel
C. same line
D. perpendicular

Answers

Answer:

A

Step-by-step explanation:

Lines are parallel...

The answer would be A. parallel because both lines have a slope of 2

someone please help me ASAP

Answers

Answer:

(x + (2), y - (4))

Step-by-step explanation:

An easy way to figure out how a shape has undergone a ridge transformation (meaning a transformation only in location and not size) is to compare corresponding points on the figure.

In this figure, use point (C) to describe the transformation. Point (C) is located at (-2, 4). However, its corresponding point (C') is located at (0,0). To go from (-2, 4) to (0,0) one has to add (2) units to the (x-coordinate) and subtract (4) units from the (y-coordinate). Therefore, the transformation can be described as the following,

(x + (2), y - (4))

I need help pls answer:

Express in simplest form:

4(X^2-1)-(X^2-8x-5)


Answers

Answer:

3x² + 8x + 1

Step-by-step explanation:

Given

4(x² - 1) - (x² - 8x - 5) ← distribute both parenthesis

= 4x² - 4 - x² + 8x + 5 ← collect like terms

= 3x² + 8x + 1

Solve for CD using the following image

Answers

Here,

BC = 12

CD+BD=12

2x-9+x-9 =12

3x-18 12

3x =12+18

x =30/3

x =10

Now,

CD = 2x-9

= 2×10-9

= 20-9

= 11

Therefore,CD = 11

Hope this solution may help you!!

The value of the segment CD is 11 units for the given line segment.

A line segment is a fundamental geometric object that represents a portion of a straight line with defined endpoints. It is a finite portion of a line that connects two distinct points. The endpoints of a line segment are specific points that mark its boundaries.

From the given image the value of x will be calculated as,

CD + DE = 12

(2x - 9 ) + ( x - 9 ) = 12

3x - 18 = 12

3x = 30

x = 10

The measure of the segment CD is,

CD = 2x - 9

CD = 2(10) - 9

CD = 20 - 19

CD = 11

Therefore, the value of the segment is 11.

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Will give branliest
Find l.
l= [?] in

Answers

L= Square Root of (h^2 + r^2)
h=15 and r= d/2= 12/2= 6
So, (15^2+6^2)=
225+36= 261
L= Square Root of [261] in
L= the square root of 261 in

Calculate the compound interest a saleswoman would have to pay if she borrows
$54 000 for 9 years at 12% per annum compound interest.​

Answers

Given:

Principal = $54,000

Time = 9 years

Rate of compound interest = 12% per annum.​

To find:

The compound interest.

Solution:

The formula for amount is:

[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]

Where, P is principal, r is the rate of interest in decimal, n is the number of time interest compounded and t is the number of years.

The interest is compounded annually, so [tex]n=1[/tex].

Substituting [tex]P=54000,\ t=9,\ n=1,\ r=0.12[/tex] in the above formula, we get

[tex]A=54000\left(1+\dfrac{0.12}{1}\right)^{1(9)}[/tex]

[tex]A=54000\left(1.12\right)^{9}[/tex]

[tex]A=149746.252902[/tex]

[tex]A\approx 149746.25[/tex]

The amount after 9 years is $149746.25.

Now, the compound interest is:

[tex]C.I.=A-P[/tex]

Where, C.I. is compound interest, A is amount and P is principal.

[tex]C.I.=149746.25-54000[/tex]

[tex]C.I.=95746.25[/tex]

Therefore, the compound interest is $95746.25.

find the slope of the line (-5,7) (-3,4)(-1,1)(1,-2)

Answers

Answer:

-3 is the gradient.

BONUS: y-interspet is -1

Step-by-step explanation:

The gradient is what you mean by slope I am guessing?

well, the line that contains those points will more or less look  like the one in the picture below, and we can use any two points from that set to get its slope, say hmmmmm let's use (-5,7) and (1,-2)

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}}\implies \cfrac{-9}{1+5}\implies \cfrac{-9}{6}\implies -\cfrac{3}{2}[/tex]

Zach bought a car for $20,000. He
paid a $5,000 down payment and
will pay $450 per month for 5
years. What type of liability is this
for Zach?
A. liquid
B. long-term
C. short term
D. budget

Answers

Answer:

The correct answer is B. Long-term.

Step-by-step explanation:

Since Zach has bought a car for $ 20,000 paying a down payment of $ 5,000 and monthly payments of $ 450 per month for 5 years, he will be paying a total of $ 32,000 for that car (5,000 + 450 x 12 x 5). Thus, the responsibility that Zach has incurred forces him to maintain his monthly payment obligation for 5 years, thus becoming a long term liability.

Work out m and c for the line:2y+6x=4​

Answers

Answer:

2y +6x=4

Step-by-step explanation:

2y=4-6x

y =(4-6x)÷2

Helena has five different flowers. She plans to give one flower to each of her five teachers in any order. She gives the first flower to one of her teachers in the morning.

In how many different ways can she give the four remaining flowers to the rest of the teachers in the afternoon?

1 combination
4 combinations
21 combinations
24 combinations

Answers

Answer:

24

Step-by-step explanation:

Based on the number of flowers and teachers left, the other ways Helena can distribute the other flowers is in 24 combinations.

How many combinations can Helana use?

This can be found as:

= (4 flowers left x 3 flowers after 4th teacher given x 2 flowers x 1 flower for last teacher)

Solving gives:

= 4 x 3 x 2 x 1

= 24 combinations

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Use the drawing tools to form the correct answer on the graph
Graph the line that represents this equation:
y +2 = 1/2 (x + 2)

Answers

Step-by-step explanation:

answer is in photo above

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

What is the equation of a line?

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is constant.

The graph of the line y +2 = 1/2 (x + 2), can be drawn as shown below. Therefore, the line will be a straight line passing through (0,-1) on the y-axis, and (2,0) on the x-axis.

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PLEASE HELP!!!!!!!!!!!!!

Answers

Answer:

[tex]\text{C. }\pm \frac{1}{2}[/tex]

Step-by-step explanation:

Start by moving the 2 to the right (so we can multiply both sides by the denominator):

[tex]\frac{1}{2x^2-1}=-2[/tex]

Multiply both sides by [tex]2x^2-1[/tex]:

[tex]1=-2(2x^2-1),\\1=-4x^2+2[/tex]

Move everything to one side:

[tex]4x^2-2+1=0,\\4x^2-1=0,\\4x^2=1,\\x^2=\frac{1}{4},\\x=\boxed{\pm\frac{1}{2}}[/tex]

Answer:

the answer for this is C.

A Galapagos tortoise can 1/5 mile in an hour. How many hours would it take the tortoise to walk 1/6?

Answers

Answer:

5/6 hours

Step-by-step explanation:

Create a proportion where x is the number of hours it will take to walk 1/6 of a mile:

[tex]\frac{1/5}{1}[/tex] = [tex]\frac{1/6}{x}[/tex]

Cross multiply and solve for x:

1/5x = 1/6

x = 5/6

So, it will take the tortoise 5/6 hours to walk 1/6 of a mile

What type of angel is 107 degrees

Answers

Answer:

[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]

⏩ 107° angle will be an obtuse angle because its measurement is more than 90° but less than 180°.

⁺˚*・༓☾✧.* ☽༓・*˚⁺‧

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Answer:

An obtuse angle

Step-by-step explanation:

Angles are classified by how large their degree measure is. Here is a list of the basic classifications of an angle,

acute: degree measure between (0) and (90) degrees

right: exactly (90) degrees,

obtuse: degree measure between (90) and (180) degrees

reflex: degree measure between (180) and (360) degrees

is it okay to eat 8 day used by bread that been left in the refrigherater

Answers

Bread is usually fine to eat if you don't see any mold.

Once refrigerated, it will retain its freshness for three to four days before becoming stale. If you want to extend its shelf life, packaged bread will stay fresh for at least three months in the freezer. If you do see mold, however, throw the bread out.

Someone found 100! And added up all its digits. Then, this person added up the digits of this sum. The process was continued until the sum was a one-digit number. What was that number?

Answers

1 because the digits of 100 is 1,0 and 0 so 1+0+0 =1

I’ll give brainliest to whoever gets it right. Find the surface area of this prism.
Round to the nearest tenth.
6.72 cm
5.78 cm
12.7 cm
[ ? ]cm

Answers

Answer:

493.29[tex]cm^2[/tex]

Step-by-step explanation:

Multiply all values (6.72, 5.78, and 12.7) together, then round to the nearest tenth.

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