Determine whether the triangles are congruent. Explain your reasoning .
SAS (Side, Angle, Side) or ASA (Angle, Side, Angle)

Answer:

4x² -4xy -4y -4

Step-by-step explanation:

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

In this case, a= 2x -y and b= y +2.

(2x -y)² -(y +2)²

= (2x -y +y +2)[2x -y -(y +2)]

= (2x +2)(2x -y -y -2)

= (2x +2)(2x -2y -2)

= 2x(2x) +2x(-2y) +2x(-2) +2(2x) +2(-2y) +2(-2) (expand)

= 4x² -4xy -4x +4x -4y -4

= 4x² -4xy -4y -4

Alternatively, start by expanding the brackets.

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

[tex]\boxed{(a + b)^{2} = {a}^{2} + 2ab \: + {b}^{2} }[/tex]

(2x -y)² -(y +2)²

= 4x² -4xy +y² -(y² +4y +4)

= 4x² -4xy +y² -y² -4y -4 (expand)

= 4x² -4xy -4y -4 (simplify)

Answer:

4. =3 ft

5. 2/1.25 lb

Answer:

4) 3 ft = 36in  ⇔   [tex]\frac{36in}{12in}[/tex]  = 3 inches

5) 2 lb = 32 oz  ⇔  [tex]\frac{32oz}{20oz}[/tex]  = 1.6 oz

Answer:

option E, C

Step-by-step explanation:

From the graph we will find the equation of g(x).

g(x) is a parabola with vertex ( h, k) = ( 0, 9)

Standard equation of parabola is ,  y = a (x - h)² + k

                                                     y = a (x - 0)² + 9

                                                     y = ax² + 9 ----------  ( 1 )

Now we have to find a .

To find a we will take another point through which the parabola passes .

Let it be ( 3, 0).

Substitute ( 3 , 0 ) in  ( 1 ) =>  0 = a (3 )² + 9

                                     => - 9 = 9a

                                     => a = - 1

Substitute a = - 1 in ( 1 ) => y = -1 x² + 9

                                  => y = - x² + 9

Therefore , g(x) = -x² + 9

Now using the table we will find h(x)

 [tex]h(x) = 4^{x}[/tex]

So g(x) = -x² + 9 and [tex]h(x) = 4^{x}[/tex]

Option A : both function increases on ( 0, ∞ ) - False

               [tex]\lim_{x \to \infty} g(x) = \lim_{x \to \infty} -x^2 + 9[/tex]

                                  [tex]= - \lim_{x\to \infty} x^2 + \lim_{x \to \infty} 9\\\\= - \infty + 9\\\\=- \infty[/tex]

g(x) decreases on ( 0 , ∞)

             [tex]\lim_{x\to \infty} h(x) = \lim_{x \to \infty} 4^{x}[/tex]

                                [tex]= \infty[/tex]

h(x) increases on ( 0, ∞)

option B : g(x) increasing on (- ∞, 0) - False

      g(x) = -x² + 9

       g( -2 ) = - (-2)² + 9

                 = - 4 + 9 = 5

       g ( -5) = - ( -5)² + 9

                =  - 25 + 9 = - 14

   As the value of x moves towards - ∞ , g(x) moves towards - ∞

   Therefore g(x) decreases on  (- ∞, 0)

Option C: y intercept of g(x) is greater than h(x) - True

         y intercept of g(x) = ( 0 , 9 )

         y intercept of h(x)  = ( 0 , 1 )

Option D : h(x) is a linear function - False

Option E : g(2) < h(2) - True

        g(x) =  -x² + 9

        g(2) = -(2)² + 9 = - 4 + 9 = 5

        h(x) = 4ˣ          

        h(2) = 4² = 16      

Answer:

Letter A) 5

Step-by-step explanation:

all the other answers are negative so they are less than 4.

5 comes after 4 so 5 is greater than 4.

Hope this is helpful

Answer:

nx12=p

Step-by-step explanation:

So every pack has 12 pencils. You multiply the packs of pencils that José bought with how much pencils per pack. Since José bought "n" packs of pencils, the equation is nx12. But the answer is also unknown since we don't know how much packs José bought, so the answer is "p", or the total number of pencils José bought.

Answer:

x = -10

Step-by-step explanation:

verticle angles are congruent

80 + x = 70

Subtract 80 from both sides

x = -10

Answer:

354 $ is correct

Step-by-step explanation:

your v id dead

Answer:

x = [tex]\sqrt{26}[/tex]

Step-by-step explanation:

using pythagoras theorem

here [tex]\sqrt{13}[/tex] and [tex]\sqrt{13}[/tex] are the legs of the right angled triangle and x is hypotenuse.

a^2 + b^2 = c^2

[tex](\sqrt{ 13 })^2 + (\sqrt{13})^2 = x^2[/tex]

13 + 13 = x^2

26 = x^2

[tex]\sqrt{26}[/tex] = x

Answer:

answer would be c

Step-by-step explanation:

hope this helps

Answer:

no

Step-by-step explanation:

no

Answer:

x <2

Step-by-step explanation:

2.5 – 1.2x < 6.5 – 3.2x

Add 3.2x to each side

2.5 – 1.2x+3.2x < 6.5 – 3.2x+3.2x

2.5 +2x < 6.5

Subtract 2.5 from each side

2.5+2x-2.5<6.5-2.5

2x<4

Divide by 2

2x/2 < 4/2

x <2

Answer:

d -x=y the awnssr may not be correct but I tried so

Answer:

x = 0

Step-by-step explanation:

-2(x-4)=4x+2x+8

Distribute

-2x +8 =4x+2x+8

Combine like terms

-2x+8 =6x+8

Add 2x to each side

-2x+2x+8 =6x+2x+8

8 = 8x+8

Subtract 8 from each side

8-8 = 8x+8-8

0 = 8x

Divide by 8

0=x

Answer:

x = 0

Step-by-step explanation:

-2(x-4) = 4x+2x+8

-2x+8 = 6x+8

8-8 = 6x+2x

0 = 8x

x = 0

Hope this will help and if so, then please mark me as brainliest.

1) 7/12= 0.58, 4/7= 0.57

they are about 1/2

2) 7/12 + 4/7 = 97/84= 1.15 approximately 1

which is 1m from the option

Answer:

Range: [-7, 8]

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

According to the graph, our y-values span from -7 to 8. Since both are closed dot, they are included in the range:

Range: [-7, 8]

Answer:

You didn't provide " the following" from which to choose.

Here are two solutions

y = 2x - 1

y - 1 = 2(x - 1)

Answer:

50 boys

Step-by-step explanation:

The number of groups = 24

The average number of children = 16

The new average number of children when one group is added = 18

The ratio of boys to girls in the group that just joined = 5:6

The initial number of boys = 220

Let the initial number of children

The initial total number of children = 24 × 16 = 384

The initial number of girls = 384 - 220 = 164

The final number of children = 25 × 18 = 450

The number of children in the group that joined in the game = 450 - 384 = 66

The ratio of boys to girls in the group = 5:6

Therefore, we get;

The number of boys = 66 × 5/11 = 30

The number of girls = 66 - 30 = 36

The number of boys at the end = 220 + 30 = 250

The number of girls at the end = 164 + 36 = 200

The number of more boys than girls at the end = 250 - 200 = 50

The number of more boys than girls at the end = 50 boys

Answer:

7 / 6

Step-by-step explanation:

Given the points:

points (0, 0) and (6, 7)

Point 1 : x1 = 0 ; y1 = 0

Point 2 : x2 = 6 ; y2 = 7

The rise = y2 - y1 = 7 - 0 = 7

The run = x2 - x1 = 6 - 0 = 6

Ratio of Rise to Run = Rise / Run = 7 / 6

Answer:

First Option

Step-by-step explanation:

Answer:

1 / 7

Step-by-step explanation:

Number of sections on spinner = 7

Section is numbered 1 to 7

Since the probability of landing on each section is the same:

Probability that spinner lands on 4 :

Probability, p = Required outcome / Total possible outcomes

Required outcome = landing on 4 = 1

Total possible outcomes = (1 to 7) = 7

P(landing on 4) = 1 /7

Answers:

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

Explanation:

Let's say that the letter k replaces the green box

We have the equation y = kx

Plug in (x,y) = (7,35) to get the equation 35 = k*7

Dividing both sides by 7 leads to k = 5

Therefore, the direct variation equation is y = 5x

We can check this by plugging in x = 7

y = 5x

y = 5*7

y = 35

So x = 7 leads to y = 35 as expected.

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

Do the same for x = 4

y = 5x

y = 5*4

y = 20 when x = 4

Side note: direct variation equations always go through the origin.

Answer:

20

Step-by-step explanation:

if y varies directly with x, then it takes the form y=mx

to find m, substitute in the values of x and y to get 35=m*7 and simplify to get that m=5

then the equation becomes y=5x

substitute in the value they gave for x which is 4 to get y=5*4

to get that y=20

Answer:

hey, i think it's the first alternative

Step-by-step explanation:

Answer:

the answer is 113.398 grams

Answer:

Option (1)

Step-by-step explanation:

From the graph of the piecewise function,

There are two pieces of the function,

1). Segment (1) having x < 0

2). Segment (2) having x ≥ 0

Segment (1),

Segment starts with a hollow circle at x = 0 and passes through two points (0, 1) and (-2, 2)

Slope of the segment = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                                     = [tex]\frac{2-1}{-2-0}[/tex]

                                     = [tex]-\frac{1}{2}[/tex]

Equation of the segment passing through (-2, 2) with slope = [tex]-\frac{1}{2}[/tex],

[tex]y-y'=m(x-x')[/tex]

[tex]y-2=-\frac{1}{2}(x+2)[/tex]

[tex]y=-\frac{1}{2}x-1+2[/tex]

[tex]y=-\frac{1}{2}x+1[/tex]

[tex]y=-0.5x+1[/tex] For x < 0

Segment (2),

Segment starts with a solid circle at x = 0 and passes through (0, -2) and (2,2)

Slope of the segment = [tex]\frac{2+2}{2-0}[/tex]

                                    = 2

Equation of the segment passing through (0, -2) and slope = 2,

y - y' = m(x - x')

y + 2 = 2(x - 0)

y = 2x - 2 For x ≥ 0

Therefore, Option (1) will be the correct option.

Answer:

for the firt one the patters is +6  +7   +8    +9  

Step-by-step explanation:

Answer:

(x - 2)^2 + (y + 2)^2 = 100

Step-by-step explanation:

We know that the equation for a circle with a center in the point (a, b) and a radius R is given by:

(x - a)^2 + (y - b)^2 = R^2

Here we know that the center of the circle is the point (2, - 2) and that the point (-4, 6) lies on the circle.

Then the radius of this circle will be the distance between (2, - 2) and  (-4, 6)

Remember that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:

[tex]D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

Then the distance between (2, - 2) and  (-4, 6) is:

[tex]D = \sqrt{(2 - (-4))^2 + (-2 - 6)^2} = \sqrt{6^2 + (-8)^2} = \sqrt{100} = 10[/tex]

Then the radius of the circle is R = 10

and we know that the center is (2, -2)

the equation for this circle is then:

(x - 2)^2 + (y - (-2))^2 = 10^2

(x - 2)^2 + (y + 2)^2 = 100