14. You bought shoes for $60. They were on sale for 40% off their original price.
a. Write a proportion to solve for the original price of the shoes.
ce to
b. Solve the proportion in part (a).

Answer:

Y = -4x + 1

Step-by-step explanation:

1. We know the equation of a line is y=mx+b.

2. using the slope formula, [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex], to find the slope. -12 / 3 = -4, so the slope is -4.

3. we need to find the Y intercept, or the Y coordinate at X=0. if at x=1 the Y is -3, and the slope is -4, then if we go down to x=0 then the Y would be 4 higher. therefore the Y intercept is 1.

4. now we can make the equation; Y = -4x + 1

Answer:

[tex]\boxed{r=3}[/tex]

Step-by-step explanation:

We can use SAS ≅ SAS congruence to validate that the triangles are similar (both share the same side, have another congruent side, and have a congruent angle).

Because the sides are congruent, set them equal to each other and solve for r.

18 - 2r = 4r

18 = 6r

3 = r ⇒ [tex]\boxed{\bold r = 3}[/tex]

Therefore, the answer is D.

Answer:

r = 3

Step-by-step explanation:

Here Triangle ALR is divided precisely in half by the vertical side LU.  The two triangles thus formed are therefore congruent.

Thus, 18 - 2r = 4r, and 6r = 18.  Then r = 3.

Answer:

18.3125

18.5635

18 13/16

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

1)

[tex]64=x^2\\x=\sqrt{64}\\x=8[/tex]

2)

[tex]64=x^3\\x=\sqrt[3]{64}\\ x=4[/tex]

[tex](4^3=64)[/tex]

3)

[tex]2^x=32\\2^x=2^5\\x=5[/tex]

4)

[tex]x=(\frac{2}{5})^3=\frac{2^3}{5^3}=8/125[/tex]

5)

[tex]\frac{16}{9} =x^2\\x=\sqrt{\frac{16}{9} }\\ x=\frac{\sqrt{16} }{\sqrt{9}} \\x=4/3[/tex]

6)

[tex]2\cdot2^5=2^x\\2^1\cdot2^5=2^x\\2^{(1+5)}=2^6=2^x\\x=6[/tex]

7)

[tex]2x=2^4\\2x=16\\x=8[/tex]

8)

[tex]4^3=8^x\\(2^2)^3=(2^3)^x\\2^6=2^{3x}\\3x=6\\x=2[/tex]

Answer:

1) 8

2) 4

3) 6

4) 6/15

5) 4/3

6) 6

7) 8

8) 2

Step-by-step explanation:

Im about to cook dinner just comment if you want work shown.

Answer:

∠2 ≅ ∠6

Step-by-step explanation:

Answer:

x=2,y=7

Step-by-step explanation:

Using elimination method:

Add both equations

8x=16

x=2

Put x=2 into equation 2

3•2+6y=48

6y=42

y=7

Answer: see proofs below

Step-by-step explanation:

Proofs are like a puzzle that you have to unravel.

You can manipulate the left side to get the right side (LHS → RHS)

                                                or

You can manipulate the right side to get the left side (RHS → LHS)

You will need to use Pythagorean Identities, Sum and Difference Identities, and/or Double Angle Identities when manipulating one of the sides.

Use the following Identities:

cos 2A = cos²A - sin²A

sin 2A = 2 cosA · sinA    Note that A can be substituted with 2A        

sin 3A = 3 sinA - 4sin³A

cos 3A = 4cos³A - 3cosA

***********************************************************************************

e) Prove: 4 sin A · cos³A - 4 cos A · sin³A = sin(4A)

LHS → RHS

Given:         4 sin A · cos³A - 4 cos A · sin³A

Factor:        4 sin A · cos x (cos²A - sin²A)

                  2(2 sin A · cos A)(cos²A - sin²A)

Double Angle Identity:  2(sin 2·A)(cos 2·A)

                                       2 sin (2A) · cos (2A)

Double Angle Identity:  sin (2·2A)

                                       sin 4A

Proven:  sin 4A = sin 4A   [tex]\checkmark[/tex]

*****************************************************************************************

f) Prove: 4 sin³A · cos 3A + 4 cos³A · sin 3A = 3 sin(4A)

LHS → RHS

Given:          4 sin³A · cos 3A + 4 cos³A · sin 3A

Triple Angle Identity:   4sin³A (4cos³A - 3 cosA) + 4cos³A (3sinA - 4sin³A)

Expand:      16sin³A · cos³A - 12sin³A · cosA + 12cos³A · sinA - 16sin³A · cos³A

Simplify:      12cos³A · sinA - 12sin³A · cosA

Expand:        6cos²A(2cosA · sinA) - 6sin²A(2cosA · sinA)

Double Angle Identity: 6cos²A(sin 2A) - 6sin²A(sin 2A)

Factor:       6sin 2A (cos²A - sin²A)

Double Angle Identity:  6sin 2A (cos 2A)

                                       3(2sin 2A · cos 2A)

Simplify:     3sin (2·2A)

                  3 sin 4A

Proven: 3sin 4A = 3sin4A   [tex]\checkmark[/tex]

Answer:

3/4 of the whole day(24 hours)

Step-by-step explanation:

1/3 of 24 hours equal to 8 hours. He slept for 8 hours. So his waking time equals 24-8=16

5/8 of his waking time (16 hours ) equal to 10 hours.

now total time spent in his house 10 + 8 = 18

in fraction 18/24 = 3/4

He slept 1/3 of the day, and is awake 2/3 of the day (note that 1/3 + 2/3 = 3/3 = 1)

2/3 of 5/8 = (2/3)*(5/8) = (2*5)/(3*8) = 10/24 = 5/12 of the day is spent at home when he is awake

Add 1/3 and 5/12 to get

1/3 + 5/12 = 4/12 + 5/12 = (4+5)/12 = 9/12 = 3/4

He spent 3/4 of a whole day at home (equivalent to 18 hours)

Answer:

using the equilateral formula of solution

Answer:

[tex]x^2-3\geq 12[/tex]

Step-by-step explanation:

[tex]x^{2} -3[/tex] is the difference of a number squared and three

is at least 12, means that is greater but not less

[tex]x^2-3\geq 12[/tex]

Answer:

27

Step-by-step explanation:

By the theorem of intersecting secant and tangent out side of a circle, we have:

[tex] {60}^{2} = 48 \times (48 + x) \\ 3600 = 48 \times (48 + x) \\ \frac{3600}{48} = 48 + x \\ 75 = 48 + x \\ 75 - 48 = x \\ x = 27 \\ [/tex]

Answer:

Step-by-step explanation:

Answer:

complex conjugates

Step-by-step explanation:

The factors (5 + i) and (5 – i) are called complex conjugates.

Answer:

complex conjugates

Step-by-step explanation:

Numbers of the form a+ bi and a - bi are complex conjugates.

Their product is real.

Answer:

16 cards

Step-by-step explanation:

We can use logic to find out how many cards were in the beginning.

If Ted took 6 cards, and Gina took half of what remained, then when Gina took cards, she had [tex]6\cdot2=12[/tex] to choose from.

Now, Anna took [tex]\frac{1}{4}[/tex] of the cards, meaning that 12 is [tex]\frac{3}{4}[/tex] of the amount of cards there originally were.

[tex]\frac{12}{x} = \frac{3}{4}\\\\12\cdot4=48\\\\48\div3=16[/tex]

Hope this helped!

Answer: g(1) is 1.

Step-by-step explanation:

If we are solving for g of 1  then the first equation can't be used to solve for g of 1 because it only works in x is equal to -2.

The same way the second function will not work because x has to equal to -1.

But in the last function which is written as a polynomial it will work for this situation because x is not equal to -2 or -1 so apart from those numbers every number will work the same way 1 will work.    

So plot 1 into the function and solve for it .

g(1) = 1^3 - 1^2 + 1  

g(1)=  1 - 1 + 1

g(1)= 1

Answer:

A. 17.5 in.

Step-by-step explanation:

The formula for the area of a triangle is 1/2 * (b * h), where h represents the height and b represents the base. We can solve from reverse using area/height = base*2

369.25/42.2 = 8.75

1/2base = 8.75

base = 8.75 * 2

base = 17.5

Answer:

369.25/42.2 = 8.75

1/2base = 8.75

base = 8.75 * 2

base = 17.5

hope I helped you

Answer:

it took him 3 hours to get to work

Step-by-step explanation:

For the first part of the trip, the executive covered a distance "d" in time 't" at 35 mph, therefore we can write that the time it took to get to the helicopter was:

[tex]t-\frac{d}{35}[/tex]

which if the distance is in miles, will render the time in hours.

We can write something similar for the second part of the trip", using the same "t" since it took the same time as for the first one, and using for distance 169.5 - d (since it is the distance to complete the total traveled distance :

[tex]t=\frac{169.5-d}{78}[/tex]

Now we equal those two equations because the time "t" is the same, and solve for "d":

[tex]\frac{d}{35} =\frac{169.5-d}{78} \\78\,d=35\,(169.5-d)\\78\,d=5932.5-35\,d\\(78+35)\,d=5932.5\\d=\frac{5932.5}{113} \\d=52.5[/tex]

Now, knowing the distance covered in the first trip, we can find the time of that first trip:

[tex]t=\frac{52.5}{35} =1.5\,\,hours[/tex]

Therefore, the time it took for thye total trip is: 1.5 h + 1.5 h = 3 hours

Answer:

Angle MON is equal to 130 degrees.

Step-by-step explanation:

We are told LON is 180 degrees.

Angles LOM and MON are supplementary meaning they add to 180 degrees.

Using this information we know 12x+120=180.

We can use the subtractive property of equality to subtract 120 from both sides.

Do thins we get 12x=60.

Using the division property of equality we can divide both sides by 12 to get x=5.

We can then use the substitution property of equality to get MNO=8(5)+90.

We can then simplify to get MNO=130.

Answer:

see explanation

Step-by-step explanation:

Given

x² - 6x = - 5

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3)x + 9 = - 5 + 9 [ part a, c = 9 ]

(x - 3)² = 4 [ part b ]

Take the square root of both sides

x - 3 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 3 to both sides )

x = 3 ± 2

Thus part c is

x = 3 - 2 = 1

x = 3 + 2 = 5

Answer:

5 is the answer

............

Answer:

5

Step-by-step explanation:

What number multiplied by itself gives you 25

5*5 = 25

sqrt(25) = 5

4cosec 0+cosec 0 + cosec 0 + 2 cosec 0

8 cosec 0

Answer:

I believe that the answer is F.

Step-by-step explanation:

The y coordinate is about the test score (per question is assume).  

It if is per question then 5 points will be handed out for every four questions or 1.25 per question.

Answer:

F

Step-by-step explanation:

Find the slope:

two points were given (1, 5/4) and (0, 0) because if you get zero question right you will recieve zero points.

Slope: 5/4

y= (5/4)x

Lets check F

You get 4 questions rights then you will get 5 points.

Answer:

x = a + 8

Step-by-step explanation:

x = The number that is 40% more than five more than a number a.

x = 40% more than 5 (plus a)

5 * 0.6 = 3

5+3 = 8

x = a + 8

Answer:

x = 1

Step-by-step explanation:

−31−4x=−5−5(1+5x)

First step is to simplify both sides

−31−4x=−5−5(1+5x)

−31+−4x=−5+(−5)(1)+(−5)(5x)

distribute

−31+−4x=−5+−5+−25x

−4x−31=(−25x)+(−5+−5)

and combine like terms

−4x−31=−25x+−10

−4x−31=−25x−10

Then add 25x to both sides

−4x−31+25x=−25x−10+25x

21x−31=−10

Add 31 to both sides

21x−31+31=−10+31

21x=21

And divide by 21!

21x/21 = 21/21

x=1

Answer:

X=1

Step-by-step explanation:

First this is you want to distribute the -5 to the 1 and 5x. Now you should have -31-4x=-5-5-25x. Next thing is to combine your like terms which would be -5 and -5 and you get -10. (-31-4x=-10-25x) Now add 31 to both sides and your new solution is -4x=21-25x. This time you add 25x to both sides and get 21x=21. Final step you divide both sides by 21 and get X=1. :)

Answer:

The y-intercept is 1/3.

Step-by-step explanation:

The equation given is in slope-intercept form. Recall that in slope-intercept form:

[tex]f(x)=mx+b[/tex]

m is the slope while b is the y-intercept.

Therefore, -2/9 would be the slope while 1/3 would be the y-intercept.

Answer:

Tessa has 3 ice-cream scoops

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]2ab(a-b)+3a^2(a+2b)+b^2(2a-b)\\\\=2a^2b-2ab^2+3a^3+6a^2b+2ab^2-b^3\\\\=\boxed{3a^3-b^3+8a^2b}[/tex]

For a = 2, b = 3 the total is

[tex]3\cdot 2^3-3^3+8\cdot 2^2 \cdot 3\\\\=3*8-27+96\\\\=24-27+96\\\\=\boxed{93}[/tex]

Thank you

Its very confusing so sry

Answer:

(5,5) and (5,-11)

Step-by-step explanation:

You can find this out by plotting a circle with the diameter of 10 on the point "(-1,-3)". Then find all the times the circle is on the x axis of 5.

Answer:

so when the mughal emperor humayun had died akbar his son was put as kind of india he was 10 yearls old when his father died and then Bairam Khan was elected as a regent for Akbar.

Step-by-step explanation:

Answer:

The net charge on the four atoms is 12

Step-by-step explanation:

The given parameters are;

The charge of each electron = -1

The charge of each proton = + 1

The charge of each neutron = neutral

Therefore, if 3 electrons are removed  from each of the three atoms, we have;

The quantity of net negative charge removed from the four atoms = 3 × -1 × 4 = -12

Given that the at the four atoms add equal  number of protons and electrons, we have;

Original charge on the four atoms = n×(-1) +  n×(+1) = 0

Therefore;

The net charge on the four atoms after removal of the 12 electrons  = Original charge - (-12)

The net charge on the four atoms = 0 - (-12) = +12

The net charge on the four atoms = +12.