Congruency statements
ΔABC≅ΔDEF
List all pairings of congruent angles & sides for the above congruence statement.

f(x) + n - translate the graph n units up

f(x) - n - translate the graph n units down

f(x + n) - translate the graph n units left

f(x - n) - translate the graph n units right

|f(x)| - reflect over x-axis for x < 0.

[tex]f(x)=|x+2|-5[/tex]

Graph g(x) = x

g(x + 2) = x + 2 → translate 2 units left

|g(x + 2)| = |x + 2| → reflect over x-axis for x  < 0

|g(x + 2)| - 5 = |x + 2| - 5 → translate 5 units down

Answer:

B)3/8

Step-by-step explanation:

So there are 3 yellow or blue in total. So 3/8.

Answer:

3/8

Step-by-step explanation:

There are 8 pieces of equal size (and thus equal probability). 3 of them qualify as "success" (yellow or blue), so 3 out of 8 is the probability.

Answer:

the answer is x=5 for a fact

Step-by-step explanation:

Answer:

the answer would be x=5

Use the Pythagorean theorem two times:

[tex]NQ^2+NP^2=QP^2\\\\36^2+h^2=39^2\\\\1296+h^2=1521\qquad\text{subtract 1521 from both sides}\\\\h^2=225\to h=\sqrt{225}\\\\\boxed{h=15\ cm}[/tex]

second time:

[tex]PR^2=RN^2+NP^2\\\\x^2=8^2+15^2\\\\x^2=64+225\\\\x^2=289\to x=\sqrt{289}\\\\\boxed{x=17\ cm}[/tex]

Answer:

17 cm

Step-by-step explanation:

We must first find the length of the height, PN.  Since PN is an altitude, it makes a right angle with QR; this means that PNQ will be a right triangle, as will PNR.  This means we will use the Pythagorean theorem:

a²+b² = c²

Letting h represent PR (since it is the height),

h²+36² = 39²

h²+1296 = 1521

Subtract 1296 from each side:

h²+1296-1296 = 1521-1296

h² = 225

Take the square root of each side:

√(h²) = √(225)

h = 15

PN is 15 cm.

Now we will use it and the other "base," RN, to find PR:

15²+8² = x²

225+64 = x²

289 = x²

Take the square root of each side:

√(289) = √(x²)

17 = x

Answer: 23.13 lbs

Step-by-step explanation:

Weight in May + Weight gained = Weight in July

       4.5            +         18.63        =

                     23.13                      =

NOTE: Make sure to line up the decimal point when adding decimals:

    4.50

+  18.63

   23.13

Answer: 28.7 minutes

Step-by-step explanation:

Terrel: [tex]\dfrac{1}{69}[/tex] of job per minute

Wife: [tex]\dfrac{1}{49}[/tex] of job per minute

Together: [tex]\dfrac{1}{x}[/tex] of job per minute

Terrel + Wife = Together

 [tex]\dfrac{1}{69}+\dfrac{1}{49}=\dfrac{1}{x}[/tex]

 [tex]\dfrac{1}{69}(69*49*x)+\dfrac{1}{49}(69*49*x)=\dfrac{1}{x}(69*49*x)[/tex]

  49x + 69x = 69 * 49

        118x     =   3381

           x       =   28.7

Answer:

4

Step-by-step explanation:

Recall a linear function, is a line on a graph made up of an infinite amount of points which satisfy the relationship. That means at x=3 there is a specific point on the line with an output. The value of a function at x=3 asks, what is the output y value for the input x value?

To find it, we locate 3 on the x-axis. We draw a vertical line directly to the line following the grid line. We mark the point on the line. We then draw a horizontal line directly to the y-axis following the grid line. The point we hit on the y-axis is the value of the function.

Here it is 4.

Answer:

4

Step-by-step explanation:

i took the test

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-3-4}{0-0}\implies \cfrac{-7}{0}\impliedby und efined[/tex]

when the slope of the points is undefined, is a flag that is a vertical line.

Check the picture below.

Hi there! :)

Step-by-step explanation:

[tex]Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]

[tex]\frac{(-3)-4}{0-0}=\frac{-7}{0}=0[/tex]

Therefore, the slope is 0.

Undefined.

Final answer is 0.

I hope this helps you!

Have a nice day! :)

-Charlie

:D

Answer:-

[tex]11.4 + 0.5y = 9.9 + 0.6y[/tex] , then the two states have the same population.

Step-by-step explanation:

Let y represents the number of years

As per the statement:

In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year.

⇒ [tex]11.4 + 0.5y[/tex]

and

also, it is given that: Michigan's population was 9.9 million, increasing by 0.6 million each year.

⇒ [tex]9.9 + 0.6y[/tex]

When two states have the same population.

then the equation : [tex]11.4 + 0.5y = 9.9 + 0.6y[/tex].

Answer:

In 15 years the population will be same.

Step-by-step explanation:

Let y represent the number of years.

In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year.

[tex]x=11.4+0.5y[/tex]

Michigan's population was 9.9 million, increasing by 0.6 million each year.

[tex]x=9.9+0.6y[/tex]

We have to tell that when will the two years have the same population, so we will put both equations equal.

[tex]11.4+0.5y=9.9+0.6y[/tex]

=> [tex]11.4-9.9=0.6y-0.5y[/tex]

=> [tex]0.1y=1.5[/tex]

So, y = 15

Therefore, in 15 years the population will be same.

Answer:

No real solutions

129

Step-by-step explanation:

The quadratic formula is

-b ± sqrt(b^2 -4ac)

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

2a

3x^2 =2x-1

Lets get the equation in proper form

3x^2 -2x+1 = 2x-1-2x+1

3x^2 -2x+1 =0

a=3  b=-2 c=1

Lets substitute what we know

2 ± sqrt((-2)^2 -4(3)(1))

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

2(2)

-2 ± sqrt(4-12)

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

2(2)

-2 ± sqrt(-8)

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

4

No real solutions

The quadratic formula is

-b ± sqrt(b^2 -4ac)

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

2a

2x^2 -10= 7x

Lets get the equation in proper form

2x^2 -7x-10 = 7-7x

2x^2 -7x-10 =0

a=2  b=-7 c=-10

Lets substitute what we know, we are only looking for what is inside the radical

(b^2 -4ac)

((-7)^2 -4(2)(-10))

(49 +80)

129

Distribute

2x × 2x^4 + 2x × -6x^3 + 2x ×4x^2 + 2x × - 3x

Take out the constants

(2 × 2)xx^4 + 2x × -6x^3 + 2x × 4x^2 + 2x × -3x

Simplify 2 × 2 to 4

4xx^4 + 2x × -6x^3 + 2x × 4x^2 + 2x × -3x

Use Product Rule: x^a x^b = x^a + b

4x^1 + 4 + 2x × -6x^3 + 2x ×4x^2 + 2x × -3x

Simplify 1 + 4 to 5

4x^5 + 2x × -6x^3 + 2x × 4x^2 + 2x × -3x

Take out the constants

4x^5 + (2 × -6)xx^3 + 2x × 4x^2 + 2x × -3x

Simplify 2 × -6 to -12

4x^5 - 12xx^3 + 2x × 4x^2 + 2x × -3x

Use the Product Rule: x^a x^b = x^a + b

4x^5 - 12x^1 + 3 + 2x × 4x^2 + 2x -3x

Simplify 1 + 3 to 4

4x^4 - 12x^4 + 2x ×4x^2 + 2x × -3x

Take out the constants

4x^5 - 12x^4 + (2 × 4)xx^2 + 2x × -3x

Simplify 2 × 4 to 8

4x^5 - 12x^4 + 8xx^2 + 2x × -3x

Use the Product Rule: x^a x^b = x^a + b

4x^5 - 12x^4 + 8x^ 1 + 2 + 2x × -3x

Simplify 1 + 2 to 3

4x^5 - 12x^4 + 8x^3 + 2x × -3x

Take out the constants

4x^5 - 12x^4 + 8x^3 + (2 × -3)xx

Simplify 2 × -3 to -6

4x^5 - 12x^4 + 8x^3 - 6xx

Use the Product Rule: x^a x^b = x^a + b

4x^5 - 12x^4 + 8x^3 - 6x^2

Answer:

4x^5 - 12x^4 + 8x^3 - 6x^2

Step-by-step explanation:

Answer:

The midpoint of TS is (-1,-3)

The coordinates of M should be (8,18)

Step-by-step explanation:

Answer: x = 6

Step-by-step explanation:

[tex]\dfrac{3}{x}+\dfrac{1}{3}=\dfrac{5}{6}[/tex]

[tex](6x)\dfrac{3}{x}+(6x)\dfrac{1}{3}=(6x)\dfrac{5}{6}[/tex]  multiplied by common denominator

18 + 2x = 5x

      -2x   -2x

18         = 3x

÷3          ÷3

6          =  x

Since "x" is in the denominator, the restriction is that x ≠ 0.  If the solution was x = 0, then the solution would not be valid and would be eliminated as an answer.

Remember that "x" is just an unknown value.  It is possible to add two fractions together and have their sum be a fraction.

For example: [tex]\dfrac{1}{5} + \dfrac{2}{5} = \dfrac{3}{5}[/tex] could be written as [tex]\dfrac{1}{5} + \dfrac{2}{x} = \dfrac{3}{5}[/tex].  When we solve it, we will get x = 5.

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

Answer: Edward

Step-by-step explanation:

[tex]f(x)=\dfrac{(x-1)(x+2)(x+4)}{(x+1)(x-2)(x-4)}[/tex]

The denominator cannot equal zero, so:

Those x-values are the asymptotes, which is where the function is undefined.

Answer:

Yes, the side lengths of ΔABC forms a Pythagorean triple

Step-by-step explanation:

Given : A right angled triangle ABC

           Side lengths - 3,4 and 5

To Find: . Do the side lengths form a Pythagorean triple?

Solution :

Hypotenuse (longest side) = 5

To check we need to use Pythagoras theorem :

[tex]Hypotenuse^{2} =Perpendicular^{2} +Base^{2}[/tex]

[tex]5^{2} =3^{2} +4^{2}[/tex]

[tex]25 =9 +16[/tex]

[tex]25 =25[/tex]

Since Pythagoras theorem is verified . So, the side lengths form the Pythagorean triplet.

Hence  the side lengths of ΔABC forms a Pythagorean triple

Answer:

y=8

Step-by-step explanation:

We need to find the equation for the line.

The first step is to find the slope

We need 2 points  (0,2) (2,3)

slope = (y2-y1)/(x2-x1)

          = (3-2)/(2-0)

          = 1/2

We know the y intercept ( where it crosses the y axis)  at 2

Lets use the slope intercept form of the line

y= mx+b

y = 1/2 x+2

If we want to find the value of y when x =12 , substitute the value of x=12

y =1/2 * 12 +2

y = 6+2

y=8

Answer:

option A  :  graph is a function

Step-by-step explanation:

(a) option is given is a graph

For graph , the function should pass vertical line test

Draw vertical line for every value of x

The vertical lines cross only one red point at a time

So the graph is a function

(b) When each input has only one output then it is a function

in option B , input 3 has two output -5  and 0

so it is not a function

(c) in option C , input 3 has two output 14  and 19

so it is not a function

(d) in option d , input -1 has two output -11  and 5

so it is not a function

Answer:

The correct answer has already been given (twice). I'd like to present two solutions that expand on (and explain more completely) the reasoning of the ones already given.

One is using the hypergeometric distribution, which is meant exactly for the type of problem you describe (sampling without replacement):

P(X=k)=(Kk)(N−Kn−k)(Nn)

where N is the total number of cards in the deck, K is the total number of ace cards in the deck, k is the number of ace cards you intend to select, and n is the number of cards overall that you intend to select.

P(X=2)=(42)(480)(522)

P(X=2)=61326=1221

In essence, this would give you the number of possible combinations of drawing two of the four ace cards in the deck (6, already enumerated by Ravish) over the number of possible combinations of drawing any two cards out of the 52 in the deck (1326). This is the way Ravish chose to solve the problem.

Another way is using simple probabilities and combinations:

P(X=2)=(4C1∗152)∗(3C1∗151)

P(X=2)=452∗351=1221

The chance of picking an ace for the first time (same as the chance of picking any card for the first time) is 1/52, multiplied by the number of ways you can pick one of the four aces in the deck, 4C1. This probability is multiplied by the probability of picking a card for the second time (1/51) times the number of ways to get one of the three remaining aces (3C1). This is the way Larry chose to solve the this.

Step-by-step explanation:

Hi There!

Answer:

4/52 (With cards picked before put back.)

3/48 (With cards picked before not put back.)

Step-by-step explanation:

A standard deck of cards is made up of 52 cards.

There are 4 kings in a deck.

4/52

Bob has a 4/52 chance of picking a king.

I don't know if the cards he picked prior to this he put back or not. If he didn't then it's 3/48.

Hope This Helps :)

Answer:     73.55%

Step-by-step explanation:

p = (100-a) e^-b(0.07)

we have a = 20 and b =1.2

  = (100-20) e^-(1.2)(0.07)

=    80(e^-0.084)

= 80(0.919431)

= 73.55%

Answer:

The correct answer is 93.6%

Step-by-step explanation:

Got it right on Edge 2020

Answer:

38 = FH

Step-by-step explanation:

Because this is a rectangle, IG = FH

We know that IE + EG = FH

We also know that IE = EG   (perpendicular bisectors)

IE = EG

3x+4 = 5x-6

Subtract 3x from each side

3x-3x+4 = 5x-3x-6

4 = 2x-6

Add 6 to each side

4+6 =2x

10 =2x

Divide by 2

10/2 =2x/2

5=x

Now lets find FH

IE + EG = FH

3x+4 + 5x-6  = FH

Combine like terms

8x-2 = FH

Substitute in x =5

8*5-2

40-2

38 = FH

Answer:

40-2

38 = FH

Step-by-step explanation:

As per the given values, the opponent received 686 votes.

Total votes received by Mayor = 2058.

To find out how many votes the opponent received, we need to determine the ratio of votes received between the new mayor and her opponent. Given that the new mayor received three votes for every vote received by her opponent, we can set up the equation:

3x = 2058

where x represents the number of votes received by the opponent. To solve for x, we divide both sides of the equation by 3:

x = 2058 ÷ 3

= 686

Therefore, the opponent received a total of 686 votes.

https://brainly.com/question/30701353

#SPJ2

Answer:

2.5 rad ( to the nearest tenth )

Step-by-step explanation:

the time difference between the given times is 24 minutes

In 1 hour the hand moves 2π radians, hence in 1 minute moves

[tex]\frac{2\pi }{60}[/tex], thus in 24 minutes moves

[tex]\frac{2\pi }{60}[/tex] × 24 ≈ 2.5 radians

Answer:

B

Step-by-step explanation:

The square root of 131 is 11.445 and so it lies between 11 and 12 on a number line.

See where it goes on a number line below:-

Answer: 1) 9 days

2) a)37.5%

b)50%

c) 33.33%

Step-by-step explanation:

1) - Let's call:

x: number of days the company supposed to finish the order.

- You know that the company had to produce 40 items daily, but it produced 20 items more daily and finished the order 3 days ahead of time. Therefore, you can express this as following:

[tex]40x=(40+20)(x-3)\\40x=60(x-3)[/tex]

- Solve for [tex]x[/tex]:

[tex]40x=60x-180\\-20x=-180\\x=9[/tex]

(The answer is 9 days)

2) a) The percent that belongs to three people if eight eight people share equally in an inheritance, can be calculated as following:

[tex]\frac{3}{8}*100=37.5[/tex]%

b) The percent that belongs to three people if six people share equally in an inheritance (because two of the people are disinherited) can be calculated as following:

[tex]\frac{3}{6}*100=50[/tex]%

c) - The increase goes from 1/8 to 1/6, therefore, you must subtract them:

[tex]\frac{1}{6}-\frac{1}{8}=\frac{1}{24}=0.04167[/tex]

- Divide the result by 1/8 and multiply by 100 to obtain the percent:

[tex]\frac{0.04167}{\frac{1}{8}}*100=33.33[/tex]%

Answer:

x = - 1

x1 = - 3

x2 = 3

Step-by-step explanation:

x^2(x + 1) - 9(x + 1)    = f(x)                  x + 1 is a common factor

(x + 1) [ x^2 - 9]          = f(x)                 factor x^2 - 9

(x + 1)(x - 3)(x + 3)

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

x + 1 = 0

x = - 1

x - 3 = 0

x = 3

x + 3 = 0

x = - 3

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

Answer

x = - 1

x1 = - 3

x2 = 3

Question:

What are the zeros of the polynomial function?

Step-by-step explanation:

Hope this helps!

Answer: 25% of the ice cream must be eaten to insure it does not overflow the cone when it melts.

Step-by-step explanation:

1. You must calculate the area of spherical scoop of ice cream  with the following formula for calculate the volume of  a sphere:

[tex]Vs=\frac{4}{3}r^{3}\pi[/tex]

Where [tex]r[/tex] is the radius ([tex]r=\frac{8cm}{2}=4cm[/tex])

[tex]Vs=\frac{4}{3}(4cm)^{3}\pi=268.08cm^{3}[/tex]

2. Now, you need to calculate the volume of the sugar cone with the following formula:

[tex]Vc=\frac{1}{3}r^{2}h\pi[/tex]

Where [tex]r[/tex] is the radius ([tex]r=\frac{8cm}{2}=4cm[/tex]) and [tex]h[/tex] is the height ([tex]h=12cm[/tex]):

[tex]Vc=\frac{1}{3}(4cm)^{2}(12cm)\pi=201.06cm^{3}[/tex]

3. When the ice cream melt, the percent of the cone that will be filled is:

[tex]P_f=(\frac{201.06cm^{3}}{268.08cm^{3}})100=75[/tex]%

4. Therefore, the percent of the ice cream that must be eaten to insure it does not overflow the cone when it melts, is:

[tex]P_e=100[/tex]%[tex]-75[/tex]%

[tex]P_e=25[/tex]%

Final answer:

To ensure the melted ice cream does not overflow the cone, 75% of the ice cream must be eaten. This is calculated by finding the volumes of the ice cream sphere and the cone and comparing them to get the percentage that can fit into the cone without overflowing.

Explanation:

The student's question involves determining what percent of a spherical scoop of ice cream (with a diameter of 8 cm) must be eaten to ensure it does not overflow a sugar cone (also with a diameter of 8 cm and 12 cm deep) when the ice cream melts. The ice cream and the cone have the same diameter, so they have the same base area. To prevent overflow, the volume of the melted ice cream must be less than or equal to the volume of the cone.

To solve this, we must first calculate the volume of the spherical scoop of ice cream, which can be determined using the formula for the volume of a sphere: V = (4/3)πr³. Subsequently, we need to calculate the volume of the cone using the formula for the volume of a cone: V = (1/3)πr²h. We shall compare these volumes to find out the percentage of ice cream that must be eaten.

Let's calculate the volume of the sphere (ice cream):
V_s = (4/3)π(4 cm)³ = (4/3)π(64 cm³) = 256π/3 cm³

Now let's calculate the volume of the cone:
V_c = (1/3)π(4 cm)²(12 cm) = (1/3)π(16 cm²)(12 cm) = 64π cm³

To prevent overflow, the volume of melted ice cream should be the same or less than the volume of the cone. Therefore, the portion which would fit into the cone without overflowing when melted is:
percent = (V_c / V_s) × 100 = (64π / 256π/3) × 100 = 75%

This means that 75% of the ice cream must be eaten to ensure it does not overflow the cone when it melts.

You have 10 numbers to choose from, and you're choosing 4 from that pool. Order of the numbers matters, because having 1234 as a PIN is not the same having it be 1324, so we're counting the number of permutations of 10 digits taken 4 at a time. So there are

[tex]4!\dbinom{10}4=4!C(10,4)=4!C^{10}_4=\dfrac{10!}{(10-4)!}=5040[/tex]

possible PINs that can be made.

Answer:

5,040 PINs

Step-by-step explanation:

From the vast numbers from 1 to 10, the numbers can amount to over 5,040 PINs. Having to use the following equation in the attachment below (also found in the other question), the vast amount of numbers can either amount to 5,040 PINs, or possibly over that amount.

You need to have 10 numbers to choose from.

I hope this helps!