Any two figures in a plane can be proven congruent by:

A. the fact that they are the same shape.
B. the fact that all of their angles are the same measurement.
C. a series of rigid motions that takes one figure to the other.
D. having at least three corresponding parts.

Answer:

f(x)=x^2+3

[tex]f(x) = x^{2} + 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: x < 1 \\ \\ f(x) = - 2x + 5 \: \: \: \: \: \: \: \: \: \: \: \: \: x \geqslant 1[/tex]

Answer:

When you see f^-1(x), its asking for the inverse. In this case, you swap y with x and solve for y.

The inverse is 5 / x - 8

Answer:

A. 272 cm^2

Step-by-step explanation:

The area of the rectangle is 17cm * 7cm = 119 cm^2

The area of the right triangle is (25-7) * 17cm * 1/2 = 153cm^2

Answer: 119+153 = 272 cm^2

Answer:

30.7

Step-by-step explanation:

Recall: SOH CAH TOA

We are to solve for the missing side

First, label the sides:

Reference angle (θ) = 61°

x = Opposite (this is opposite to the reference angle)

17 = Adjacent

Hypotenuse = side opposite to right angle

Apply TOA, which is:

Tan θ = Opp/Adj

Plug in the values

Tan 61° = x/17

17*Tan 61° = x

30.6688118 = x

x ≈ 30.7 (approximated to nearest tenth)

Complete question is;

Do oddsmakers believe that teams who play at home will have home field advantage? Specifically, do oddsmakers give higher point spreads when the favored team plays home games as compared to when the favored team plays away games?

Two samples were randomly selected from three complete National Football League seasons (1989, 1990, and 1991). The first sample consisted of 50 games, where the favored team played in a home game, while the second sample consisted of 50 games, where the favored team played in an away game. The oddsmakers’ point spreads (which are the number of points by which the favored team is predicted to beat the weaker team) were then collected.

If µ1 and µ2 represent the mean point spread for home games and away games, respectively, which of the following is the appropriate.

A) H0: μ1 - μ2 = 0

Ha: μ1 - μ2 < 0

B) H0: μ1 - μ2 = 0

Ha: μ1 < μ2

C) H0: μ1 - μ2 > 0

Ha: μ1 - μ2 = 0

D) H0: μ1 - μ2 = 0

Ha: μ1 - μ2 > 0

E) None of the above

Answer:

D) H0: μ1 - μ2 = 0

Ha: μ1 - μ2 > 0

Step-by-step explanation:

We want to find out if oddsmakers give higher point spreads when the favored team plays home games as compared to when the favored team plays away games.

Now, since µ1 and µ2 represent the mean point spread for home games and away games, respectively;

It means we want to find out if µ1 > µ2 as the alternative hypothesis.

Thus, alternative hypothesis is;

Ha: µ1 - µ2 > 0

Meanwhile null hypothesis assumes that equal point spreads are given when the favored team plays home games as well as when the favored team plays away games.

Thus, null hypothesis is;

H0: μ1 - μ2 = 0

The only correct option is D.

Answer:

p < 0.24

Step-by-step explanation:

If earning is 24% less Than predicted, this means that the we can represent the predicted earning with a variable, p

If the predicted earning = p

Then, the actual earning can be represented by the inequality ; p < 24%

p < 0.24

Answer:

y - 5 = -1/6 (x - 4)

Step-by-step explanation:

y = 6x - 1          y = -1/6x + b

y - 5 = -1/6 (x - 4)

Answer:

1/9

Step-by-step explanation:

The vertex form is

y =a(x-h)^2 +k where (h,k) is the vertex

The vertex is (-2,-3)

y =a(x--2)^2 +-3

y =a(x+2)^2 -3

Substitute the point into the equation

-2 = a(-5+2)^2 -3

-2=a(-3)^2-3

Add 3 to each side

-2+3 = a(9)

1 = 9a

1/9 =a

y =1/9(x+2)^2 -3

The coefficient of the x^2 is 1/9

Answer:

[tex]\frac{1}{9}[/tex]

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (- 2, - 3) , then

y = a(x + 2)² - 3

To find a substitute (- 5, - 2 ) into the equation

- 2 = a(- 5 + 3)² - 3 ( add 3 to both sides )

1 = a(- 3)² = 9a ( divide both sides by 9 )

[tex]\frac{1}{9}[/tex] = a

y = [tex]\frac{1}{9}[/tex] (x + 2)² - 3

The coefficient of the x² term is therefore [tex]\frac{1}{9}[/tex]

Step-by-step explanation:

To evaluate such, the following must be comprehended, on the behalf of linear data:

Slope: Rise/Run.

Y-intercept: The peculiar point in which the observed linear data intersects the y-axis.

X-intercept: The peculiar point in which the observed linear data intersects the x-axis.

Recall:

Slope-Intercept Form is acknowledged and defined as the integration of the intersection point, in relation or in proportion to the distance between two points within the linear data presented on the Cartesian Plane.

Slope-Intercept Form:

Y = mx + b

Y = The line.

M = Slope.

B = y-intercept.

The following may be equated, as stated:

- Slope = 0

Y = b

- Y-intercept = 7

Y = 7

Thus, on the Cartesian Plane is identified as a horizontal line positioned within quadrants I and II, intersection (0, 7).

Answer:

The age of E is 40

Step-by-step explanation:

When E didn't join them, the average age was 30,that is six years ago. But present making 36.

But when E joined, the average age is now 40.

Answer:

E is 56 years old

Step-by-step explanation:

I assume E joined them now.

(A - 6 + B - 6 + C - 6 + D - 6)/4 = 30

(A + B + C + D + E)/5 = 40

(A + B + C + D - 24)/4 = 30

A + B + C + D - 24 = 120

A + B + C + D = 144

(A + B + C + D + E)/5 = 40

A + B + C + D + E = 200

144 + E = 200

E = 56

Answer:

hello,

answer A c=n+2

Step-by-step explanation:

if n=0 then c=2

if n=2 then c=4

slope=m=(4-2)/(2-0) =2/2=1

c-2=1*(n-0)

c=n+2

Answer:

Part A: One | Part B: x = 4

Step-by-step explanation:

[tex]3(2x-7)=3\\6x-21=3\\6x=24\\x=4[/tex]

Answer:

4

Step-by-step explanation:

3(2x _7)=3

multiply 3 by everything in the bracket

6x-21 = 3

move 21 to the other side of the equation,it becomes positive sine it crosses the = sign

6x = 3+21

6x =24

divide both sides by 6

6x/6=24/6

x = 4

Answer:

  (d) 10 cm, 15 cm, 23 cm

Step-by-step explanation:

21 cm, 7 cm, 11 cm — 7+11 < 21 . . . not a triangle

7 cm, 23 cm, 11 cm — 7+11 < 23 . . . not a triangle

12 cm, 7 cm, 19 cm — 7+12 = 19 . . . not a triangle

10 cm, 15 cm, 23 cm — 10+15 > 23 . . . can form a triangle

__

The sum of the two shortest sides must exceed the length of the longest.

Answer:

Step-by-step explanation:

Use Pythagorus to find the length of the unmarked length

c^2 = a^2 + b^2

a = 5

b = 17 -10 = 7

c = ?

c^2 = 5^2 + 7^2

c^2 = 25 + 49

c = sqrt(74)

c =8.602

P = 5 + 10 + 17 + 8.602

P = 40.602

Answer:

a = 64

Step-by-step explanation:

The geometric mean of 2 numbers a and b is [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{28a}[/tex] = 16[tex]\sqrt{7}[/tex] ( square both sides )

28a = (16[tex]\sqrt{7}[/tex] )² = 1792 ( divide both sides by 28 )

a = 64

Answer:

a = 64

Step-by-step explanation:

The geometric mean for two numbers is given by :

GM = sqrt(ab)

16 sqrt(7) = sqrt(a*28)

Square each side

(16 sqrt(7))^2 = (sqrt(a*28))^2

256*7 = 28a

1792 = 28a

Divide each side by 28

1792/28 = 28a/28

64 = a

Answer:

72

Step-by-step explanation:

The interior angles of a 6 sided figure add to (n-2) * 180

where n is the number of sides

(6-2) *180

4*180

720

2x+4x+4x+4x+4x+2x = 720

20x = 720

Divide by 20

20x/20 = 720/20

x =36

We want <F

<F = 2x = 2*36 = 72

hope it helps you............

Answer:

0.5 = 50% probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.

Step-by-step explanation:

La probabilidad condicional :

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

En el cual:

P(B|A) es la probabilidad de que ocurra el evento B, dado que A sucedió.  

[tex]P(A \cap B)[/tex] es la probabilidad de que ocurran tanto A como B.  

P(A) es la probabilidad de que ocurra A.

En esta pregunta :

Evento A: Estudiante A aprueba.

Evento B: Estudiante B aprueba.

La probabilidad de que el estudiante A apruebe un examen de MM-100 es 0.6

Entonces [tex]P(A) = 0.6[/tex]

La probabilidad de que ambos estudiantes aprueben es 0.3

Entonces [tex]P(A \cap B) = 0.3[/tex]

¿Cual es la probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3}{0.6} = 0.5[/tex]

0.5 = 50% probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.

Step-by-step explanation:

Because it is a 45-45-90 triangle (we know this because two legs are congruent) x witll be [tex]\sqrt{10} *\sqrt{2}[/tex]

Answer:

1.94 mm

Step-by-step explanation:

V = pi(r^2)h

V/pi(h) = r^2

r = sqrt(V/pi(h))

r = sqrt(200/pi(17))

r = 1.94 mm

Answer:

Carlos is 37 years old and Ella is 17.

Step-by-step explanation:

Let,

Carlos = c

Ella = e

If Carlos is 3 more than twice Ella's age, we get the equation:

2e + 3 = c (1)

Since the sum of their ages is 54, we get the equation:

c + e = 54 (2)

Now we have a system of equations.

Since equation number 1 already designated the value of c in terms of e, we can substitute it into the second equation.

(2e+3) + e = 54

Lets combine like terms and solve!

2e + e + 3 = 54

3e = 51

e = 17

Let's substitute e back into one of the equations to figure out the value of c. I'm going to use equation 1.

2e + 3 = c

2(17) + 3 = c

34 + 3 = c

37 = c

Let's substitute the values of c and e into the second equations to check our work! (We know c and e already fulfill the first equation as we substituted e into it to get c)

c + e = 54

37 + 17 = 54

54 = 54

Now that we've checked our work, we know our answer is correct! Carlos is 37 years old and Ella is 17.

Answer:

No

Step-by-step explanation:

From the information provided, we can say that he is not correct. This is because the depth of the water is the only measurement that he is using to make his estimate. Comparing the depth of the aquarium and the bucket is one measurement, but both the aquarium and bucket are most likely of different shapes and sizes. Therefore, this equates to more buckets for the same amount of depth in the aquarium. To get a proper estimate on how long it will take he needs to calculate the volume of water in the bucket and compare it to the volume of water needed to fill the aquarium.

Answer:

21cm2

Step-by-step explanation:

Area (A = BH)

B = 7cm

H = 3cm

Therefore we multiply Base(B) with height (H) to get the area.

Hence;

Area = (7 × 3) cm2

= 21cm2

Answer:

14

Step-by-step explanation:

3*4=12

3*7=21

Diff= 21-12

Diff= 9

Plus 5=9+5

The number is 14

Answer:

base = 13 in

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

Here A = 52 and h = 8 , then

[tex]\frac{1}{2}[/tex] b × 8 = 52

4b = 52 ( divide both sides by 4 )

b = 13

Answer:

96m³

Step-by-step explanation:

Base area = 8×6/2 = 24 m²

Height = 12 m

Volume of a pyramid = 1/3 × Base area × Height

= 1/3 × 24 × 12

= 288/3

= 96 m³

Answered by GAUTHMATH

Step-by-step explanation:

according to the graph,

the domain is : -2 ≤ x < 0 or 0 < x ≤ 5

=> [-2, 0) U (0, 5]

the range is : -2< y ≤ 0 or 2≤ y ≤ 4

=> (-2, 0] U [2, 4]

the answer is option 1

The domain and range of the function are,

Domain = [-2, 0) U (0, 5]

Range = (-2, 0] U [2, 4]

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The graph of the function is shown in figure.

Now, According to the graph, We get;

The domain is;

-2 ≤ x < 0

Or, 0 < x ≤ 5

Domain = [-2, 0) U (0, 5]

And, the range is;

-2< y ≤ 0

Or , 2≤ y ≤ 4

Range = (-2, 0] U [2, 4]

Thus, The domain and range of the function are,

Domain = [-2, 0) U (0, 5]

Range = (-2, 0] U [2, 4]

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ7

Answer:

Step-by-step explanation:

See the solution in steps: