1. Identify the graph that represents the system of
linear equations

Answer:

14 minutes below or 6 minutes above

Step-by-step explanation:

Let's say Sophia's time was 10 minutes WORSE

4 minutes below average- 10 minutes= 14 minutes below average

Let's say Sophia's time was ten minutes BETTER

4 minutes below average + 10 minutes= 6 minutes above average.

Hope this helps!

14 minutes below the average

6 minutes above the average

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

Let A = average running time

Jacob's time was 4 minutes under the average, so his time is A-4 minutes. Whatever A is, subtract off 4, and you'll get Jacob's time.

Sophia and Jacob have a difference of 10 minutes. If J = Jacob's time and S = sophia's time, then S-J = 10 or J-S = 10 depending on who has the larger time.

We can use absolute value to ensure that whatever we pick (S-J or J-S) will be positive. So |S-J| = 10. Recall that absolute value represents distance on a number line. Negative distance isn't possible.

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Let's plug in J = A-4 and solve for S

|S-J| = 10

|S - ( J )| = 10

|S - (A-4)|

|S-A+4| = 10

S-A+4 = 10  or  S-A+4 = -10

S-A = 10-4  or  S-A = -10-4

S-A = 6  or  S-A = -14

S = A+6 or S = A-14

The equation S = A+6 shows Sophia is 6 minutes above the average

The equation S = A-14 shows Sophia is 14 minutes below the average

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Let's pick some number for A that is over 14 minutes. Let's say the average running time is A = 20 minutes.

If A = 20, then Jacob's time is J = A-4 = 20-4 = 16

If the average running time is 20 minutes, then Jacob ran for 16 minutes.

If we subtract 10 from this, then J-10 = 16-10 = 6 is one possible time for Sophia. Notice how this is 14 minutes below the average (20-14 = 6)

If we add 10 to Jacob's time, then J+10 = 16+10 = 26, which is 6 minutes overage the average (20+6 = 26)

This is one numeric example, but you could use any value of A that you want as long as it's larger than 14. The reason A has to be larger than 14 is to ensure that Sophia's lower time value (A-14) is not negative. Having a time of zero is not feasible either.

Answer:

AMH = 32

Step-by-step explanation:

The angles are alternate exterior angles and when the lines are parallel, alternate exterior angles are equal

x+86 = 24+2x

Subtract x from each side

x+86 -x =24+ 2x+2x-x

86 = 24 +x

Subtract 24 from each side

86-24 = 24+x-24

62 =x

x+86 = 62+86 =148

AMH is supplementary since it forms a straight line

AMH + x+86 = 180

AMH + 148 = 180

AMH = 180-148

AMH = 32

Work Shown:

[tex]x = 3\sqrt{5}*3\sqrt{2}\\\\x = (3*3)(\sqrt{5}\sqrt{2})\\\\x = 9\sqrt{5*2}\\\\x = 9\sqrt{10}\\\\[/tex]

The rule used on line 3 is [tex]\sqrt{A}*\sqrt{B} = \sqrt{A*B}[/tex]

Answer:

Infinity

Step-by-step explanation:

It is equal to nothing.

2x+2=2x+2

-2x     -2x    

2=0x+2

-2      -2

0=0

Answer:

( − ∞ , ∞ )

Step-by-step explanation:

Distribute the 2 in 2 (x+1)

2 ⋅ x = 2 x

2 ⋅ 1 = 2

Combine:

2 x + 2

Equation is now:

2 x + 2 = 2 x + 2

Subtract 2 from both sides of the equation:

2 x = 2 x

Divide both sides by 2:

x=x

Both sides of the equation are the same:

x = x

Any real number or:

( − ∞ , ∞ )

Answer:

w=2r

r= w/2

r- w/2 = 0

w -2r= 0

Step-by-step explanation:

Let w be the number of weeks and r be the number of recipes learnt . So he will learn 2 recipes each week .Equating gives

w=2r

when w= 1

w= 2(1) = 2

For 1st week 2 recipes are learned

when w= 2

w= 2( 2) = 4

For 2nd week 4 recipes are learned.

or

when r= 2

r= w/2

r =2/2  = 1  one  recipe is learned in half of the week  

r- w/2 = 0

or

w -2r= 0

Answer:

16.1 mph is your rate

Step-by-step explanation:

Answer:

16.1 per hour

Step-by-step explanation:

just divide the mile by the hours.

64.4 / 4

Answer:

Literally take your f(x) and - your g(x)

(x^2+9x+18) - (x + 6)

Remember to distribute the negative sign.

Answer:

No.

Step-by-step explanation:

For functions, there can only be one y-value to every x value, and in this diagram x=0 has two y-values, therefore it is not a function      

Answer:Not a function

Step-by-step explanation:In a function, an input can only have one output. So the fact that 0 has two different outputs means it is not a function.

Answer:

$45

Step-by-step explanation:

ratio is 3:5

David gets 3x, Jack gets 5x

So, 3x+5x=120

8x=120

x=15

David got 3x = 3*15 = $45

Answer:

45$

Step-by-step explanation:

120/8=15

15*3=45

because it is 3:5 ratio

Answer:

It wouldn't.

Step-by-step explanation:

With the ratio, since Zeona has 36 cards, Kyle must have 54. If they each sold half, Kyle would have 27 and Zeona would have 18. So, the ratio would still be 3:2.

Answer:

Step-by-step explanation:

The first and last one

Answer:

answer is 5

Step-by-step explanation:

Answer:

you did not out the full equation so I am not able to solve your problem.

If you put the full problem I will try to solve and walk you through it.

Step-by-step explanation:

[tex]y = 16 {x}^{2} + 1 \\ \\ y - 1 = 16 {x}^{2} \\ \\ \frac{y - 1}{16} = {x}^{2} \\ \\ \pm \sqrt{ \frac{y - 1}{16} } = x \\ \\ x = \pm \frac{ \sqrt{y - 1} }{4} \\ \: this \: is \: the \: required \: inverse \: \\ equation \: of \: y = 16 {x}^{2} + 1[/tex]

The equation that represents the inverse of y = 16x² + 1 is y = ±√[(x - 1)/16]

Two or more expressions with an Equal sign is called as Equation.

Let us find the inverse of the equation y = 16x² + 1.

To find inverse we need to replace y with x and x with y in the original equation to obtain:

x = 16y² + 1

Now solve for y in terms of x by rearranging the terms

x - 1 = 16y²

Divide both sides by 16

y² = (x - 1)/16

Take square root on both sides.

y = ±√[(x - 1)/16]

Therefore, the equation that represents the inverse of y = 16x^2 + 1 is:

y = ±√[(x - 1)/16]

To learn more on Equation:

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Answer:

The slope is 7

Step-by-step explanation:

Choose any of the following points for example (0.5,3.5) and (1,7)

7-3.5=4.5/1-0.5=0.5

Divide 4.5/0.5 to get 7

Answer:

Charles Babbage, who was born in 1791, is regarded as the father of computing because of his research into machines that could calculate. Babbage's Difference Engine Number 1 was the first device ever devised that could calculate and print mathematical tables.

Answer:

35 minutes a day.

Step-by-step explanation:

4*7=28

980/28=35

Answer:

35

Step-by-step explanation:

980 divided by 28 (days in a month)

Answer:

The length of the bridge is 300 feet.

Step-by-step explanation:

Let A represent the length of one leg.

Let B represent the length of the other leg (i.e length of the bridge)

Let C represent the length of the Hypothenus.

From the question given above, the following data were obtained:

Length of Hypothenus (C) = 340 feet.

Length of one leg (A) = 160 feet.

Length of the bridge (B) =.?

The length of the bridge can be obtained by using the pythagoras theory as illustrated below:

C² = A² + B²

340² = 160² + B²

115600 = 25600 + B²

Collect like terms

115600 – 25600 = B²

90000 = B²

Take the square root of both side

B = √90000

B = 300 feet

Therefore, the length of the bridge is 300 feet

Answer:

I believe that the answer is number 2

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

got stuck on it too lol

The graph of an equation intersects the y-axis at some point. Therefore, the coordinates of the intersection indicate is B. the output when the input is zero.

Its the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).

Since sum of side lengths of the triangle of vertices: 3

Area: ½ × base × height

Number of edges: 3

Internal angle: 60° (for equilateral)

The Sum of interior angles is 180°

Therefore, the coordinates of the intersection indicate will be;

B. the output when the input is zero.

Learn more about perimeter here:

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Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

The angles 2 and 3 are corresponding angles. So it's choice C.

Tip: Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

Answer:

I believe that g=dc

Step-by-step explanation:

You swap positions with g and c along with their sign of operation.

Answer:

Step-by-step explanation:

p=15-4

p= 11

Answer:

D.) y=-x-2

Step-by-step explanation:

Answer:

D.) y=-x-2

Step-by-step explanation:

Trust me I just know

Answer:

2/3

Step-by-step explanation:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

25×53

Applying the fractions formula for multiplication,

=2×55×3

=10/15

Simplifying 10/15, the answer is

=2/3

Answer:

X > 7

Step-by-step explanation:

4(x + 3) < 6x – 2

4x + 12 < 6x -2

-6x            -6x

-2x + 12 < -2

-12           -12

-2x < -14

-----     -----

-2         -2

x > 7

The < change because it was divided by a negative number

Answer: go to Cymath

Step-by-step explanation: This helped me with like everything in math class! It gives you step by step answers

Answer:

84°

Step-by-step explanation:

I know that the other angle (not x) is 48 because the lengths are the same of 2 sides. Therefore I can use 180-48-48 to get 84, the correct answer.

Answer:

Atomic mass unit-

It is represented by ‘amu’. It is equal to the quantity 1/12th mass of an atom of C-12.

Actual mass of one atom of C-12 = 1.9924 x 10-23 gm. = 1.9924 x 10-26 Kg.

1 amu = 1.9924 x 10 -23/12 = 1.66 x 10 -24 gm. = 1.66 x 10 -27 Kg.

Atomic mass of an element = mass of one atom of the element / 1 amu

Actual mass of an element = atomic mass of an element in amu x 1.66 x 10 -24 gm.

For ex-

Actual mass of hydrogen atom = 1.008 x 1.66 x 10 -24 gm. = 1.6736 x 10-24 gm.

Actual mass of oxygen atom = 16.00 x 1.66 x 10 -24 gm. = 2.656 x 10-23 gm.

Average Atomic weight (Mass)-

“The Average Atomic Masses of many elements are determined by multiplying the atomic mass of each isotope by its fractional abundance and adding these values and then dividing it by 100.”

Ex.- Naturally occurring carbon contains three isotopes – C12 (98.892 % abundance), C13 (1.108 % abundance), C14 (2 x 10-10 % abundance).The relative atomic masses of these isotopes are 12.000, 13.00335 and 14.00317 amu respectively.

Average atomic mass = % of I isotope x its atomic mass + % of II isotope x its atomic mass +% of III isotope x its atomic mass/100

= 12 x 98.892 + 13.00335 x 1.108 + 14.00317 x 2 x10-10 /100

Average atomic mass= 12.011 amu

Molar volume –

Molar volume of a substance is volume occupied by 1 mole of that substance .

Molar volume of solid or liquid = molar mass / density

Molar volume of ideal gas at 00C or 273 K and 1 atmosphere pressure is 22.4 litre.

Gram atomic mass(weight) or gram atom –

“Gram atomic mass(weight) of an element is the mass of Avogadro number ( 6.023 x 1023 ) of atoms of that elements in grams.”

Ex –

mass of 1 atom of oxygen = 16 amu = 16 x 1.66 x 10-24 gm

Mass of 6.023 x 1023 atoms of oxygen= 16 x 6.023 x 1023 x 1.66 x 10-24 = 16 gm.

Hence, Gram atomic weight of oxygen = 16 gm.

No. of gram atoms = mass of element in gm / atomic mass of element in gm.