Which answer choice shows a solution set in which all values, when input for x, will be true?
12−(x+2)>2

Answer:2 and 5

Step-by-step explanation:

The ratios that are equal to [tex]cos(B)[/tex] : [tex]\bold{\frac{BC}{AB}}[/tex] and [tex]\bold{\frac{EF}{DE}}[/tex]

"Two triangles are said to be similar

- if corresponding angles are equal and the sides

- if corresponding sides of the triangles are in proportion."

In a right triangle,

cos(Ф) = (adjacent side of angle Ф) ÷ hypotenuse

For given example,

Triangles ABC and DEF are similar triangles.

This means, ∠A = ∠D, ∠B = ∠E, ∠C = ∠F

And, [tex]\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}[/tex]               ..............(i)

For a right triangle ABC,

the cosine of angle B is,

[tex]cos(B)=\frac{BC}{AB}[/tex]

From (i),

[tex]\frac{BC}{AB}=\frac{EF}{DE}[/tex]

So, the cosine of angle B is,

[tex]cos(B)=\frac{EF}{DE}[/tex]

Therefore, the ratios that are equal to [tex]cos(B)[/tex] : [tex]\frac{BC}{AB}[/tex] and [tex]\frac{EF}{DE}[/tex]

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Answer:

a = 3

Step-by-step explanation:

If (x+3) is a factor of f(x) = x³+ax²+x+3,

From remainder theorem,

When we substitute -3 into the expression, we equate to zero

That is,

F(-3) = 0

(-3)³+a(-3)²+(-3)+3 = 0

-27+9a-3+3 = 0

9a = 27

divide both sides by the coefficient of a

a = 27/9

a = 3

Hence the value of a = 3

Step-by-step explanation:

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Answer:

r≈2.86

Step-by-step explanation:

Using the formula

C=2πr

Solving forr

r=C

2π=18

2·π≈2.86479

Answer:

a. P(x = 5) = 0.24

b. P(x ≥ 6) = 0.43

c. P(x < 4)= 0.14

Step-by-step explanation:

According to the Question,

⇒We use Binomial Probability Formula

[tex]P(X = x ) = \frac{n!}{x!((n-x)! } * p^{x} * (1-p)^{n-x}[/tex]

Where, p=0.52 & n=10

a. The probability that the number of U.S. adults who have very little confidence in newspapers is ​exactly​ five . So, (x=5)

Thus, [tex]P(X = 5 ) = \frac{10!}{5!((10-5)! } * 0.52^{5} * (1-0.52)^{10-5}[/tex]

On Solving Above Equation we get,

P(5)=0.2441 ≈ 0.24

b. The probability that the number of U.S. adults who have very little confidence in newspapers is at least 6 . So, (x≥6)

Then,

P(x≥6) = P(6)+P(7)+P(8)+P(9)+P(10)

P(x≥6) = [tex]\frac{10!}{6!((10-6)! } * 0.52^{6} * (1-0.52)^{10-6}[/tex] + [tex]\frac{10!}{7!((10-7)! } * 0.52^{7} * (1-0.52)^{10-7}[/tex] +[tex]\frac{10!}{8!((10-8)! } * 0.52^{8} * (1-0.52)^{10-8}[/tex] + [tex]\frac{10!}{9!((10-9)! } * 0.52^{9} * (1-0.52)^{10-9}[/tex]+[tex]\frac{10!}{10!((10-10)! } * 0.52^{10} * (1-0.52)^{10-10}[/tex]

On solving above equation we get,

P(x≥6) =  0.4270 ≈ 0.43

c. The probability that the number of U.S. adults who have very little confidence in newspapers is less than 4 . So, (x<4)

Then,

P(x < 4)=P(3) + P(2)+P(1)+P(0)

P(x<4) = [tex]\frac{10!}{3!((10-3)! } * 0.52^{3} * (1-0.52)^{10-3}[/tex] + [tex]\frac{10!}{2!((10-2)! } * 0.52^{2} * (1-0.52)^{10-2}[/tex]+ [tex]\frac{10!}{1!((10-1)! } * 0.52^{1} * (1-0.52)^{10-1}[/tex] + [tex]\frac{10!}{0!((10-0)! } * 0.52^{0} * (1-0.52)^{10-0}[/tex]

On solving we get,

P(x < 4)= 0.1410 ≈ 0.14  

There are (5 C 1) = 5! / (5 - 1)! = 5 ways of drawing a red marble, and (11 C 1) = 11! / (11 - 1)! = 11 ways of drawing any marble, so that the probability of drawing a red marble is 5/11.

After putting back the first marble, the probability of drawing another red is again 5/11.

So the probability of drawing 2 red marbles with replacement is (5/11)² = 25/121.

Answer:

(3, -6)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

y = 4x - 18

y = -5x + 9

Step 2: Solve for x

Substitution

Step 3: Solve for y

Answer:

x=3

y = -6

Step-by-step explanation:

y = 4x – 18

y = -5x +9

Set the two equations equal

4x – 18 = -5x +9

Add 5x to each side

4x – 18 +5x= -5x+5x +9

9x -18 = 9

Add 18 to each side

9x -18 +18 = 9+18

9x =27

Divide by 8

9x/9 = 27/9

x = 3

Now find y

y = 4x-18

y = 4*3 -18

y =12-18

y = -6

Answer:

I think C is the relation between the variables.

1 1/3 × 4

= 4/3 × 4

= 16/3

= 5 1/3

Answer:

5 1/3

Step-by-step explanation:

1 1/3 * 4

Change 1 1/3 to an improper fraction

1 1/3 = (3*1+1)/3 = 4/3

4/3 *4 = 16/3

Change to a mixed number

3 goes into 16 5 times with 1 left over

5 1/3

Answer:

[tex] \sqrt{x + 2} [/tex]

If you horizontally shift the square root parent function f(x)=√x left two units the equation of the new function is: g(x) = √(x + 2).

A horizontal shift is a function transformation that shifts a graph to the left or right without changing its shape.

If we want to shift the square root parent function f(x) = √x two units to the left, we must replace the argument x with (x + 2), because a positive value of x + 2 gives us the same x value two units to the left.

So the equation of the new function is:

g(x) = √(x + 2)

This new function is the square root function shifted two units to the left. For any given input value of x, we add 2 to it before taking the square root. This causes the graph to shift horizontally to the left by two units.

Thus, g(x) = √(x + 2) will be the new function.

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Answer:

$45.07

Step-by-step explanation:

46.91-1.84= 45.07

ANSWER

0.9

Step-by-step explanation:

no.of favourable outcome/no.of.possible outcome  

13+5=18 favourable outcome and 20 possible outcome 18/20=0.9

Answer:0.9

Step-by-step explanation: khan academy

Answer:

y = mx + by= mx+ b

Step-by-step explanation:

since we know the two points on the line. we use the two points formed to find its equation. the final equation.the slope intercept form ,y=mx+by = mx+b

Answer:

1. Terminating

2. 60

3. I don't know

Step-by-step explanation:

Answer:

x = 15

Step-by-step explanation:

Given that,

The length of the base of an isosceles triangle is x.

The length of a leg is 3x-4.

Perimeter, P = 97

An isosceles triangle has one base. The perimeter of a triangle is given by :

97=x+3x-4+3x-4

97 = 7x-8

97+8=7x

105 = 7x

x = 15

So, the value of x is 15.

Answer:

From Pythagoras Theorem

The square of the hypotenuse is equal to the sum of the squares of the other two sides

C² = 12² + 35²

C= √12²+35²

C= 37in

Answer:

side c = 37 in.

Step-by-step explanation:

side c is the hypotenuse as it is opposite of right angle (90 degree ).

12 and 35 are the two other smaller sides of the given right angles triangle.

using pythagoras theorem to find side c

a^2 + b^2 = c^2

12^2 + 35^2 = c^2

144 + 1225 = c^2

1369 = c^2

[tex]\sqrt{1369}[/tex] = c

37 = c

Answer:

88

Step-by-step explanation:

line AC is equal to line DB

The angle of x in the right angle triangle is 30.80 degrees

Right angle triangle have one of it angles as 90 degrees. The angles can be found using trigonometric ratios.

Let's find the angle x using trigonometric ratios;

tan x = opposite / adjacent

Therefore,

tan x = 3.1 / 5.2

x = tan⁻¹0.59615384615

x = 30.7991697243

x ≈ 30.80°

Therefore, the angle of x is 30.80 degrees

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Answer:

y=1/2 , x= -5/8

Step-by-step explanation:

⇒[tex]2y=1. -4x+y=3 : y=\frac{1}{2} \\\left \{ {{2y=1} \atop {-4x+y=3}} \right. \\ where: y=\frac{1}{2} \\-4x+\frac{1}{2}=3\\isolate for -4x+\frac{1}{2} =3: x=-\frac{5}{8} \\y=\frac{1}{2} : x=\frac{-5}{8}[/tex]

Answer:

Step-by-step explanation:

1 )  2 + 7t                        [ there are no like terms , so no further simplifying ]

2) 6r + ( - 16 r )

   =  6 r - 16 r                 [ both are like terms ]

   = - 10 r

3) (3x + 2 ) + ( 2x - 4 )

   = 3x + 2 + 2x - 4

   = 3x + 2x - 4 + 2               [ arranging like terms together ]

   = 5x - 2

4) (8 n² - 3 n + 6 ) + ( n - 2 )

   = 8n² - 3n  + 6 + n - 2

   = 8n² - 3n + n + 6 - 2             [ bringing like terms together ]

   = 8n² - 2n + 4

Answer:

1.) 2 + 7 t

2.) - 10 r

3.) 5 x - 2

4.) 8 n² - 2 n + 4

Step-by-step explanation:

1.) 2 + 7 t

No like terms, so no further simplifying.

2.) 6 r + ( - 16 r )

6 r - 16 r. ... ( combine like terms)

- 10 r

3.) ( 3 x + 2 ) + ( 2 x - 4 )

= 3 x + 2 + 2 x - 4

combine like terms

= 3 x + 2 x - 4 + 2

= 5 x - 2

4.) ( 8 n ² - 3 n + 6 ) + ( n - 2 )

= 8 n² - 3 n + 6 + n - 2

combine like terms

= 8n² - 3 n + n + 6 - 2

= 8 n² - 2 n + 4.

Answer

The answer is y= x-3

- - - - -

5

Explanation

Replace

f(x) with y.

y =5x+3

Swap x and y.

x =5y+3

Solve for y.

x - 3=5y

x-35=y

Answer:

2 days

Step-by-step explanation:

It takes four plumbers five days

total labor needed

4 * 5 = 20 days

How long would it take ten plumbers?

20 / 10 = 2 days

The function g(x) = x²/3

Given that graph of the function f(x) = x²,

Since, the graph of f(x) is transformed to form the g(x).

We see that g(x) is passing by (3, 3)

Here, the scale factor is 1/3,

So, we can say that the equation of the function g(x) is g(x) = x²/3

Therefore, the required function is g(x) = x²/3

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Answer:

A

Step-by-step explanation:

The line is parallel to y axis, so the equation is x = 5

Answer:

[tex]\displaystyle \theta \approx 36.4[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ

Opposite Leg = 31

Adjacent Leg = 42

Step 2: Find Angle

Answer: yes

Step-by-step explanation: because if you can draw a line through the graph and hit most of the dots it would be considered linear.

Answer:

Yes

Step-by-step explanation:

The correlation of the dots is very strong although it can't be a straight line.

Hope this helps

Step-by-step explanation:

Given that,

Hypotenuse, H = 13

Base, b = 12

Perpendicular, P = 5

[tex]\sin\theta=\dfrac{P}{H}\\\\\sin\theta=\dfrac{5}{13}[/tex]

[tex]\cos\theta=\dfrac{B}{H}\\\\\sin\theta=\dfrac{12}{13}[/tex]

and

[tex]\tan\theta=\dfrac{P}{B}\\\\=\dfrac{5}{12}[/tex]

Hence, this is the required solution.