Tabitha has a DVD rack which can hold 42 DVDS. She can fit 8 more DVDS on the rack before the rack is full. How many DVDS are on the rack?

Answer:

b = [tex]\sqrt{45}[/tex]

Step-by-step explanation:

Using Pythagoras' identity in the right triangle on the left.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

b² + 6² = 9²

b² + 36 = 81 ( subtract 36 from both sides )

b² = 45 ( take the square root of both sides )

b = [tex]\sqrt{45}[/tex]

Answer:

[tex]b)\ Obtuse[/tex]

Step-by-step explanation:

[tex]We\ are\ given\ that:\\There\ are\ three\ rays.\\Lets\ mark\ them\ Ray\ OP, OQ,\ and\ OR\ with\ their\ common\ Vertex\ O.\\\\Now,\\We\ know\ that\ the\ sum\ of\ all\ angles\ around\ a\ point[or\ here\ Vertex\ O]\\ should\ be\ equal\ to\ 360.\\Here,\\\\Lets\ consider\ each\ case\ sepearately.\\If\ all\ the\ angles\ formed: \angle POR, \angle ROQ, \angle POQ,\ are\ acute\ then:\\\angle POR, \angle ROQ, \angle POQ<90\\If\ we\ add\ them\ together,[/tex]

[tex]\angle POR+ \angle ROQ+ \angle POQ<90+90+90<270[/tex]

[tex]But\ here\ the\ sum\ of\ the\ angles\ are\ less\ than\ 270,\ but\ the\ sum\ should\\ instead\ be\ 360.\\Hence,\ the\ angles\ formed\ by\ the\ rays\ are\ NOT\ acute.[/tex]

[tex]Similarly,\\If\ all\ the\ angles\ formed: \angle POR, \angle ROQ, \angle POQ,\ are\ right\ then:\\\angle POR, \angle ROQ, \angle POQ =90\\When\ we\ add\ them\ again:\\\angle POR+ \angle ROQ+ \angle POQ=90+90+90=270\\But\ again\ the\ sum\ here\ is\ equal\ to\ 270,\ but\ instead\ the\ sum\ had\ to\\ be\ equal\ to\ 360.\\Hence,\\The\ angles\ formed\ are\ NOT\ right.[/tex]

[tex]Lets\ consider\ the\ Last\ Case,\\If\ the\ angles\ formed: \angle POR, \angle ROQ, \angle POQ\ are\ obtuse,\\\angle POR, \angle ROQ, \angle POQ>90\\When\ we\ add\ them:\\\angle POR+ \angle ROQ+ \angle POQ>(90+90+90)>270\\Here,\\The\ angles\ formed\ are\ greater\ than\ 270.\ As\ 360>270,\ the\ angles\ ARE\\ obtuse.[/tex]

A and C is the answer

hope you'll learn from your teacher how?

Answer:

2<a<5

Step-by-step explanation:

Answer:

33/3  

55/5

77/7

When these are simplified, they are equal to 11/1

Answer:

6 and 2/5

Step-by-step explanation:

20% of 32 is 6.4

9514 1404 393

Answer:

  y = 2^x

Step-by-step explanation:

The x-values are sequential integers, which helps the discovery of the function. The y-values have a common ratio of 2 = 2/1 = 4/2 = 8/4. This is the base for the exponential function.

The initial value of y=1 at x=0 tells you the multiplier of the exponential factor is 1, and the exponent is x (with no additions or subtractions). Your function is ...

  y = 2^x

Answer:

y = 23

x = 28

Step-by-step explanation:

Find y first.

3y + 5y - 4 = 180                     The two angles are supplementary if the all the lines are parallel.  Combine the left side.

8y - 4 = 180                              Add 4 to both sides

8y - 4 + 4 = 180 + 4

8y = 184                                   Divide both sides by 8

y = 23

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

Now if the lines are parallel, then 3y = 2x + 13

But we already know y

3*23 = 2x + 13                         Do the multiplication

69 = 2x + 13                             Subtract 13

56 = 2x                                    Divide by 2

x = 56/2

x = 28

Answer:

y = 23

x = 28

Step-by-step explanation:

Shoooooot i am so late with this answer, so so sorry haha-

and i'm no gonna do the explanation because the guy above me did a fairly well explanation of how i solve them too.

uhm, have a good day!

Answer:

2sqrt5

Step-by-step explanation:

We know that the shortest distance would be with drawing a perpendicular line through BC and A.

BC is y = -2x+1

Therefore a perpendicular line should have slope 1/2

y = 1/2x + b

-3 = 1/2*-3 + b

b = -3/2

y = -2x+1

y = 1/2x - 3/2

-2x+1 = 1/2x - 3/2

-4x+2 = x - 3

5 = 5x

x = 1

y = 1

now of course the graph shows that already, but we're just proving that again

The x-difference is 4, the y difference is 2, so 16+4 = 18, sqrt20 = 2sqrt5

Answer:

Solution given:

AB=

[tex]AB = \sqrt{( - 3 +1 {)}^{2} + ( - 3 - 3 {)}^{2} } = 6.32units[/tex]

[tex]AC= \sqrt{( - 3 - 1) ^{2} + ( - 3 + 1) {}^{2} } = 4.5[/tex]units

[tex]AD= \sqrt{( - 3 - 0) {}^{2} + ( - 3 - 1) {}^{2} } = 5units[/tex]

so shortest distance=AC=4.5units

9514 1404 393

Answer:

  f(g(x)) = 50x² +140x +93

Step-by-step explanation:

Put the function argument in place of x and simplify.

  f(g(x)) = f(5x+7) = 2(5x+7)² -5

  = 2(25x² +70x +49) -5

  f(g(x)) = 50x² +140x +93

_____

We took advantage of the knowledge that ...

  (a + b)² = a² +2ab +b² . . . . . where a=5x and b=7

Answer: 6.7inch

Step-by-step explanation:

From the question, we are informed that Emma made a scale model of the Sam Houston's monument and that the monument's actual height is 67 ft tall but Emma is using a scale where 1 inch is 10 ft.

The height of Emma's model will therefore be 67ft divided by 10 since he's using a scale of 1:10. This will be:

= 67/10

= 6.7inch

Answer:

12.60.

Step-by-step explanation:

12.00 × 5%=.6

,6 + 12.00= 12.60

Answer:

Step-by-step explanation:

Answer:

a). m∠a = 62°

b). m∠b = 118°

Step-by-step explanation:

a). Since, an angle inscribed in a semicircle is a right angle,

  m∠ACB = 90°

  By triangle sum theorem in ΔABC,

  m∠CAB + m∠ACB + m∠ABC = 180°

  28° + 90° + m∠ABC = 180°

  118° + m∠ABC = 180°

  m∠ABC = 180°- 118°

  a = 62°

b). Since, quadrilateral ABCD is a cyclic quadrilateral,

   m∠ADC + m∠ABC = 180°

   b + a = 180°

   b + 62° = 180°

   b = 180° - 62°

   b = 118°

Answer:

[tex]\frac{a^3b^{-2}}{ab^{-4}} = a^{2}b^{2}[/tex]

Step-by-step explanation:

Given

[tex]\frac{a^3b^{-2}}{ab^{-4}}[/tex]

[tex]a\ne 0; b \ne 0[/tex]

Required

Evaluate

[tex]\frac{a^3b^{-2}}{ab^{-4}}[/tex]

Apply the following law of indices:

[tex]\frac{x^m}{x^n} = x^{m-n}[/tex]

So, the expression becomes:

[tex]\frac{a^3b^{-2}}{ab^{-4}} = a^{3-1}b^{-2-(-4)}[/tex]

Remove brackets

[tex]\frac{a^3b^{-2}}{ab^{-4}} = a^{3-1}b^{-2+4}[/tex]

[tex]\frac{a^3b^{-2}}{ab^{-4}} = a^{2}b^{2}[/tex]

Answer:

D. a^3 b^4 / ab^2

Step-by-step explanation:

Answer: Choice C.  [tex]y \ge -1[/tex]

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

Explanation:

The boundary line is a solid line and it's horizontal. Every point on the boundary line has y coordinate -1. So y = -1 is the equation of the boundary line. We can write it as y = 0x-1.

The shading is above the boundary line, so the inequality is [tex]y \ge -1[/tex]

Any point (x,y) in the shaded region has y coordinate that is y = -1 or greater.

For example, the point (0,2) in the shaded region has y coordinate y = 2, and it satisfies the inequality [tex]y \ge -1[/tex] because [tex]2 \ge -1[/tex] is a true statement.

Note: the boundary line is solid, so any point on the boundary line is part of the shaded solution set. This is due to the "or equal to" as part of the inequality sign.

Answer:

Step-by-step explanation:

Yes!

Answer: -8

Step-by-step explanation:

Solve for x  

5 (x − 2) = 3 (x − 4) − 14  

5x − 10 = 3 (x − 4) − 14

5x − 10 = 3x − 12 − 14

5x − 10 − 3x  = −26

2x  = −26 + 10

2x  = −16

x = −8

Answer:

answer of this equation is (-8)

:-))

Answer: he baked 69 muffins

Step-by-step explanation:

Answer:

Step-by-step explanation:

The "holes" are the x-es where function doesn't exist.

One must not divide by 0, so given function doesn't exis if the denominator is equal 0

x + 2 = 0  

x = - 2  

Answer:

[tex]3x ^{3} - {4}^{2} - 23x + 10[/tex]

Answer: c

Step-by-step explanation:

Answer:

The corresponding side length is 8 inches

Step-by-step explanation:

Similar Shapes

Two shapes are similar if all of their side lengths are in the same proportion. For example, triangle 1 has sides of 3-4-5 and another similar triangle has sides of 15-20-25. Note all their lengths are proportional with a scale factor of 5.

We are given the perimeter of figure A Pa=24 inches and the perimeter of figure B Pb=36 inches. The scale factor can be obtained as 36/24=3/2.

If one of the lengths of figure B is 12 inches, then the corresponding length for figure A is 12/(3/2) = 8 in.

The corresponding side length is 8 inches

Answer:

Step-by-step explanation:

first question is -1

and i think the sec option is  13/3+y/3 i think im wrong on the sec option

Answer:

f(-4) = 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = -3x - 8

f(-4) is x = -4

Step 2: Evaluate

Answer:

the correct answer is:

-3 × -4 -8 = 12 - 8 = 4