Find all values of x such that [tex]\sqrt{4x^2} -\sqrt{x^2}= 6[/tex]

Answer:

The range of g(x) =  {-11,-9,-7,-5}.

Step-by-step explanation:

Given:

g(x) = x – 13 over the domain {2, 4, 6, 8).

Now, to evaluate:

Putting [tex]x=2[/tex]

[tex]g(2)=2-13=-11[/tex]

Putting [tex]x=4[/tex]

[tex]g(4)=4-13=-9[/tex]

Putting[tex]x=6[/tex]

[tex]g(6)=6-13=-7[/tex]

Putting [tex]x=8[/tex]

[tex]g(8)=8-13=-5[/tex]

So, the range is {-11,-9,-7,-5}.

Therefore, the range of g(x) =  {-11,-9,-7,-5}.

Answer:

[tex](2x)^2 + (x^2 - 1)^2 = (x^2 + 1)^2[/tex]  PROVED

Step-by-step explanation:

The sides of the given right triangle are : [tex]2x , (x^2 -1) , (x^2 +1)[/tex]

Now here, To show:  [tex](2x)^2 + (x^2 - 1)^2 = (x^2 + 1)^2[/tex]  .... (1)

Now, by ALGEBRAIC IDENTITY: [tex](a \pm b)^2  = a ^2 +b^2 \pm 2ab[/tex]

So here, similarly

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

Now, substituting the value on Left side of (1) , we get :

[tex](2x)^2 + (x^2 - 1)^2   = 4x^2 + (x^2)^2 + (1)^2 - 2 (x^2) = 4x^2 + (x^4) + 1 - 2 x^2  = x^4 + 1 + 2x^2[/tex]  ...... (a)

Also, the right side of (1) is:

[tex](x^2 + 1)^2 = (x^2)^2 + (1)^2+ 2 (x^2)  = x^4 + 1 + 2x^2[/tex]  ... (b)

from(a) and (b) we see that

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

HENCE PROVED.

Answer:

The last two, 250+25t and 25(10+t)

Step-by-step explanation:

Answer: 250+25t and 25(10+t)

Step-by-step explanation: trust me i just got it right on ixl.

Answer:

could you please take a screen shot please?

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

if there are 5 tanks and 65 fish in all the tanks together, you take 65 and divide it by 5 to get 13 fish in each tank

Answer: 24 people are in the class

I am sorry I don’t know the equation but I hope this helps.

Step-by-step explanation:

3. 18. 18

- =. —. =. —-

4. ? 24

Given information

ZW is parallel to XY

ZW is congruent to XY

---------------------

What we want to prove: ZY parallel to WX

==============================================

Proof:

Statement 1: ZW is parallel to XY

Reason 1: Given

--------------------

Statement 2: ZW = XY

Reason 2: Given

--------------------

Statement 3: Angle 3 = angle 4

Reason 3: Alternate interior angle theorem

note: it might help to erase or cover up the horizontal lines of the parallelogram temporarily to help see that angles 3 and 4 are alternate interior angles.

--------------------

Statement 4: ZX = ZX

Reason 4: Reflexive property of congruence

--------------------

Statement 5: Triangle WZX = Triangle YXZ

Reason 5: SAS congruence postulate

--------------------

Statement 6: Angle 1 = Angle 2

Reason 6: CPCTC

note: CPCTC stands for "corresponding parts of congruent triangles are congruent"

--------------------

Statement 7: ZY is parallel to WX

Reason 7: Converse of alternate interior angle theorem

--------------------

This concludes the proof.

ZY is parallel to WX.

To prove that line segment ZY is parallel to WX, given that ZW is parallel to YZ and ZW is congruent to MY, you can use the following properties and definitions:

If ZW is parallel to YZ, and ZW is congruent to MY, it means that angle ZWM is congruent to angle YZM (corresponding angles) and angle ZMW is congruent to angle MYZ (corresponding angles).

If two lines are cut by a transversal such that corresponding angles are congruent, then the lines are parallel.

So, using the above properties, you can conclude that ZY is parallel to WX. This is because the corresponding angles ZWM and YZM are congruent, and ZMW and MYZ are congruent, which is sufficient to establish that the lines ZY and WX are parallel.

for such more question on line segment

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Answer:40100 feet

Step-by-step explanation:26400 +13700 = 40100

The total height of Mauna Loa is by summation 26400 +13700 = 40100 feet.

A summation, abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There could be only two terms, but there could be one hundred, a thousand, or a million.

As per the given,

Initial height = 13700 feet

Height add on = 26400 feet

Total height = 13700 feet + 26400 feet = 40100 feet

Hence "The total height of Mauna Loa is by summation 26400 +13700 = 40100 feet".

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Answer:

10657.5

Step-by-step explanation:

We can start by finding the area of the larger triangle. Using the Pythagorean theorem, we can say that 251²-105²=the bottom side², and  251²-105²=51976, so the bottom side of the larger triangle is √51976 , or approximately 228. Then, the area of the larger triangle is √51976 * 105/2 = 11969 (approximately). Then, the area of the smallest triangle (the largest triangle - the one that we're trying to find the area of) is 105*(√51976-203)/2 = approximately 1312. Then, subtracting that from the total area, we get (√51976 * 105 -  105*(√51976-203))/2 = 105*203/2 = 10657.5

ALTERNATIVELY, upon further review, we can just see that the height is 105 and the base is 203, so we multiply those two and divide by 2, as is the formula for the area of a triangle, to get 10657.5

If it's Pythagorean Theorem, then use the following:

[tex]A^2 + B^2 = C^2[/tex]

You have to multiply the 2 values by themselves if you are trying to find the Hypotenuse, then you need to add those together, and then find the square root.

10 x 10 = 100

15 x 15 = 225

100 + 225 = 325.

[tex]\sqrt{325} = 18.0277564[/tex]

Answer: 18

Step-by-step explanation:

So this is referencing the Pythagorean theorem. It states that the two shorter sides squared, in your case 10 and 15, is equal to the longest side, or hypotenuse squared.

Step by step

1. Calculate both the shorter sides squared: 10*10= 100 and 15*15= 225

2. Add the 2 shorter sides: 100 + 225 = 325

3. Find the square root of 335: √(325) = 18.0277563773

4. Round to the nearest integer: 18

Answer:

The value of function (g o f) (2)  is 24  . option D

Step-by-step explanation:

Given function as :

f(x) = [tex]\frac{10}{x}[/tex] - 1

And g(x) = 7 x - 4

So ,

(g o f) (x) =  7 ( [tex]\frac{10}{x}[/tex] - 1 ) - 4

Or, (g o f) (x) =   [tex]\frac{70}{x}[/tex] - 7 - 4

Or,  (g o f) (x) =  [tex]\frac{70}{x}[/tex] - 11

So, For x = 2

I,e  (g o f) (2) =  [tex]\frac{70}{2}[/tex] - 11

Or,  (g o f) (2) = 35 - 11

∴ (g o f) (2) = 24

Hence The value of function (g o f) (2)  is 24  . Answer  ( option D )

Answer:

10 pounds of tilapias and 36 pounds of salmon,

15 pounds of tilapias and 33 pounds of salmon,

20 pounds of tilapias and 30 pounds of salmon,

25 pounds of tilapias and 27 pounds of salmon,

30 pounds of tilapias and 24 pounds of salmon.

Step-by-step explanation:

Let's call the amount of pounds of tilapia X and the amount of pounds of salmon Y.

If each pound of tilapia costs $3 and each pound of salmon costs $5, we can write the following equation:

210 = 3X + 5Y

To find five different combinations to solve this equation, we can choose values for X and then calculate values of Y.

So, for X = 10, we have that:

210 = 30 + 5Y -> Y = 36

For X = 15, we have that:

210 = 45 + 5Y -> Y = 33

For X = 20, we have that:

210 = 60 + 5Y -> Y = 30

For X = 25, we have that:

210 = 75 + 5Y -> Y = 27

For X = 30, we have that:

210 = 90 + 5Y -> Y = 24

So the combinations are (10,36), (15,33), (20,30), (25,27) and (30,24)

Answer:Your answer is..

Step-by-step explanation:(10,36), (15,33), (20,30), (25,27) and (30,24)

They need to babysit for 10 hours to have same money each day.

Step-by-step explanation:

On Thursday;

Charges = $3 per hour

Initial fee = $40

let x be the number of hours.

T(x) = 3x+40

On Friday;

Charges = $4 per hour

Initial fee = $30

F(x)= 4x+30

The cost will be same when;

T(x) = F(x)

[tex]3x+40=4x+30\\40-30=4x-3x\\10=x\\x=10[/tex]

They need to babysit for 10 hours to have same money each day.

Keywords: functions, addition

Learn more about functions at:

#LearnwithBrainly

Answer:

x=6/31, y=147/31. (6/31, 147/31).

Step-by-step explanation:

y=-22x+9

y=40x-3

-----------------

-22x+9=40x-3

9=40x-(-22x)-3

9=40x+22x-3

9=62x-3

62x=9+3

62x=12

x=12/62

simplify,

x=6/31

-----------------

y=40(6/31)-3=240/31-3=240/31-93/31=147/31

x=6/31, y=147/31.

Answer: m = 4

Step-by-step explanation: To solve for m in this equation, we want to get m by itself on the left side of the equation.

Since m is being multiplied by 3.6, to get m by itself, we need to divide by 3.6 on the left side of the equation. Since we divided by 3.6 on the left side, we must also divide by 3.6 on the right side.

On the left side, notice that 3.6's cancel out so we're simply left with m. On the right side, we have 14.4 divided by 3.6 which is 4. So we now have m = 4.

Finally, remember to check your answer by substituting a 4 back into the original equation.

So we have 3.6 (4) = 14.4 which is a true statement.

This means that our answer, m = 4, is correct.

Remember to show all your work when solving equations.

Answer:

2) The height of the sunflower plant is 210 cm when it is 60 days old.

Step-by-step explanation:

Given:

The height of the sunflower plant is given by the value of the function [tex]f(x)[/tex] for a given value of 'x' and the age of the plant is given by [tex]x[/tex].

The expression is given as:

[tex]f(60)=210[/tex]

So, the 'x' value is 60 and the function value is 210.

So, the age of the plant is 60 days old. The height of the plant is 210 cm.

Thus, the above expression [tex]f(60)=210[/tex] means that the height of the sunflower plant is 210 cm when the plant is 60 days old.

So, from among all the choices given, only choice (2) defines it correctly.

Answer:

$2853.5

Step-by-step explanation:

Let us assume that the interest rate of both the investments of Haley is simple interest.

So, $16820 amounts of investment in nine-year CD bearing 5.8% interest will get interest of [tex]16820 \times \frac{5.8}{100} \times 9 = 8780[/tex] dollars.

Again, $21950 amounts of investment in an online savings account giving 3% interest will give interest of [tex]21950 \times \frac{3}{100} \times 9 = 5926.5[/tex] dollars.

Therefore, the nine-year CD will give more interest by $(8780 - 5926.5) = $2853.5. (Answer)

Answer:

C. $2,853.54

Step-by-step explanation:

I just answered it correct

Answer:

Exact Form: 27/8

Decimal Form: 3.375

Mixed Number Form: 3 3/8

Step-by-step explanation:

3 + 5/8 - 1 + 3/4

I stared by making 5/8 a decimal

which is 0.625

then  added 3 to 0.625 which is 3.625 then subtracted 1 which is 2.625

then i turned 3/4 to a decimal which is 0.75

i added 2.625 and 0.75

which is 3.375

Answer: 0

Step-by-step explanation:

3 and 5 over 8 minus 1 and 3 over 4

= 3 +5/8 - 1+3/4

= 8/8 - 4/4

=1 - 1

=0

Answer: The answer is B.

Step-by-step explanation:

Final answer:

The correct transformation that carries the figure onto itself is Option B: reflecting across the line y=1 and rotating 1080° clockwise about the point (-7,1), as the 1080° rotation is a multiple of 360° and does not change the figure's orientation.

Explanation:

The question is asking to identify the transformation that can be applied to a figure such that the figure maps onto itself. We're given various options that involve a reflection and a rotation. Reflection across a line like y=1 would flip the figure over this horizontal line. A rotation of 1080° clockwise about a point is equivalent to a full 360° rotation three times (since 1080° = 360° × 3), which would bring the figure back to its original position, effectively leaving it unchanged.

The correct answer is Option B, which includes a reflection across the line y=1 and a 1080° clockwise rotation about the point (-7,1). This is because the 1080° rotation, being an integer multiple of full circles, results in no net rotation, so the figure looks exactly the same after this operation. The reflection flips the figure across the line y=1 but, when combined with the rotation, it results in the figure mapping onto itself.

Options A and C suggest a 990° rotation, which is not a multiple of 360° and therefore would not result in the figure mapping onto itself. Option D suggests reflecting across the line x=-6, which is not in the given options for the reflection, and a 1080° rotation about the point (-7,1), which would rotate the figure back onto itself after the reflection, but the reflection line is incorrect.

The adult weight in pounds is 185.39 lb

Solution:

Given that adult weighs 84.09 kilogram

To find : Adult’s weight in kilograms to pounds

We have the change the weight of the adult from kilogram to pound

The conversion between kilogram and pound is as follows:-

1 kilogram = 2.204623 lb

To find the adult weight in pound, we need to multiply the adult weight in kilogram by 2.204623

Converting 84.09 kg to pound:

[tex]\begin{array}{l}{84.09 \mathrm{kg}=84.09 \times 1 \mathrm{kg}} \\\\ {84.09 .09 \times 2.204623=185.39 \mathrm{lb}}\end{array}[/tex]

Therefore the weight of the person in pound = 185.39 lb

Answer:

C

[tex]6\sqrt{x} 5-4\sqrt{x} 15[/tex]

Answer:

6√5 - 4√3

Step-by-step explanation:

The question ask us to simplify the square root of 5 times the quantity 6 minus 4 square root of 3 . The word expression can be represented mathematically as follows:

√5 × 6 - 4√3 . The expression forms a Surd.

√5 × 6 - 4√3

6√5 - 4√3

Answer:

The Explanation is below with attachment.

Step-by-step explanation:

For the line  y = 2x - 5

For Drawing a line on a graph we require minimum two points, but we will plot three points.

Here you can take any random value for X so that the corresponding Y value you will get.

So, put x = 0, in the equation we will get

[tex]y = 2(0) - 5\\\therefore y = -5\\\therefore Let\ A(0,-5)[/tex]

Similarly,

Put x = 1 we will get,

[tex]y= 2(1)-5\\\therefore y =-3\\\therefore Let\ B(1,-3)[/tex]

Again,

Put x = -1 we will get,

[tex]y= 2(-1)-5\\\therefore y =-7\\\therefore Let\ C(-1,-7)[/tex]

Now we have three points say point A (0,-5)), point B (1.-3) and point C (-1,-7)

See the graph below

Answer:

D

Step-by-step explanation:

Firstly, perpendicular line has a slope that is "negative reciprocal" of the given line's slope.

The equation of a line is  y = mx + b

Where m is the slope and b is the y-intercept

So, the given line has a slope of "-4", hence the perpendicular line would have a slope of "1/4". So immediately we can eliminate Answer Choice "A".

Now, let's see which of the other choices is our correct answer. Since we know this line has slope of "1/4", we can write:

y = (1/4)x + b

Given the point (4,5), we can replace "x" with "4" and "y" with 5 and find b:

[tex]y=\frac{1}{4}x+b\\5=\frac{1}{4}(4)+b\\5=1+b\\b=5-1\\b=4[/tex]

So, the equation is:

[tex]y=\frac{1}{4}x+4[/tex]

Correct answer is D

Answer:

A=(5/2x+10)(5/2x+5)

Step-by-step explanation:

A=LW

A=(5/2x+10)(5/2x+5)

The molar mass of dinitrogen monoxide?

Is=N2O=(14×2)+16

=44g/mol

Final answer:

The molar mass of dinitrogen monoxide (N₂O) is 44.02 g/mol, calculated by adding the atomic masses of two nitrogen atoms (14.01 g/mol each) and one oxygen atom (16.00 g/mol).

Explanation:

The molar mass of dinitrogen monoxide, which is chemically denoted as N₂O, can be calculated by adding together the atomic mass of nitrogen with the atomic mass of oxygen. Nitrogen (N) has an atomic mass of approximately 14.01 g/mol, and since we have two nitrogen atoms, we multiply this by 2. Oxygen (O) has an atomic mass of about 16.00 g/mol. Therefore, the molar mass of dinitrogen monoxide is:

(14.01 g/mol × 2) + (16.00 g/mol × 1) = 28.02 g/mol + 16.00 g/mol = 44.02 g/mol.

This value represents the weight of one mole of dinitrogen monoxide molecules. The importance of knowing the molar mass of a compound like dinitrogen monoxide relates to the calculations involved in chemical reactions and stoichiometry, specifically when dealing with gases under various conditions of temperature and pressure.

Answer:

8 correct, 6 wrong : 14 problems tried!

Step-by-step explanation:

If she gets 8 points by every question correctly answered and she got 13 points in total, she must have answered at least two questions (if she answers only 1 she gets at maximum 8 points, not reaching 13 never).

So lets try to find the solution.

If she answered 2 and mistaken 1 she would get:

2*8 - 1*5 = 16 - 5 = 11 -> So this is not correct.

If she answered 3 correct she would get 24 points, with 2 mistaken  answers she would have:

8*3 - 5*2 = 24 -10 = 14

We need to see something important in this patterns:

As the wrong questions always subtract a multiple of 5, and we need a result of 13, we CAN'T have an even number of wrong questions, because this would imply a subtract of numbers like 10, 20, 30, etc; and as the correct answers only give us even numbers (8, 16, 32, 64, etc), the result of subtracting 2 even numbers would never be 13. And as we will be subtracting a number with a 5 in the units, the points for correct answers MUST have an 8 in the units, as 8-5=13.

So, lets go to the first posible number that ends in 8 and is multiple of 8 and greater than 16. This is 48. 48 = 6*8, this is, lets think about 6 correct answers that sum 48 points.

We now need to subtract a number to 48 that gives us 13. Which is?

48 - x = 13 <----> x = 35

So, we need a number of incorrect answers that sum 35. As every wrong answer sums 5 points, we need 7 wring answers (7*5 = 35):

8*6 - 5*7 = 48 - 35 = 13 points!!

There were 14 problems tried to solve

Answer:

B. y = 6x – 1

Step-by-step explanation:

where:

m is the slope of the line

b is the y-intercept of the line

The slope m of the line through any two points (x1, y1) and (x2, y2) is given by:

Slope Formula

The y-intercept b of the line is the value of y at the point where the line crosses the y axis. Since for point (x1, y1) we have y1 = mx1 + b, the y-intercept b can be calculated by: b = y1 - mx1

Answer:

The answer is A

Step-by-step explanation:

y - 5 = 6(x+1)

y - 5 = 6x + 6

y = 6x + 6 + 5

y = 6x + 11

Answer:

36.10, 36, 36.01,37

Step-by-step explanatoion:

Answer:

36 , 36.01 , 36.1 , 37

Step-by-step explanation:

Answer:

see the explanation

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

In this problem

If the perimeter of triangle is equal to 36 cm

The longest side can't be equal to 18 cm

The student is incorrect

Because if the longest side is equal to 18 cm, and the perimeter is equal to 36 cm, then the sum of the other two sides is equal to 18 cm

and

Applying the triangle inequality theorem

Let

c  -----> the longest side

a and b the other two sides

we have that

if c=18 cm

a+b > c

a+b > 18 cm

therefore

If the longest side is 18 cm, the sum of the other two sides must be greater than 18 cm and the perimeter will be greater than 36 cm

Answer:

y = [tex]\frac{25}{6}[/tex]

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 5 when x = 6

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{5}{6}[/tex], thus

y = [tex]\frac{5}{6}[/tex] x ← equation of variation

When x = 5, then

y = [tex]\frac{5}{6}[/tex] × 5 = [tex]\frac{25}{6}[/tex]