25 points!!
Can postulates always be proven true?

Answer:

True.

Step-by-step explanation:

If the sides of one triangle are lengths 2,4 and 6 and another triangle has sides of lengths 3,6 and 9 then the triangles are similar.

Answer:

624 people

(I put two ways to look at the problem.)

Step-by-step explanation:

What is describe here is an exponential function of the form:

[tex]P=P_0 e^{kt}[/tex]

[tex]t[/tex] is the number of years after 1761.

[tex]P_0[/tex] is the initial population.

So t=0 represents year 1761.

t=1 represents year 1762

t=2 represents year 1763

....

t=20 represents year 1781.

So we have the doubling time is 5 years.  This means the population will be twice what it was in 5 years.  Let's plug this into:

[tex]P=P_0e^{kt}[/tex]

[tex]2P_0=P_0e^{k\cdot 5}[/tex]

Divide both sides by [tex]P_0[/tex]:

[tex]2=e^{5k}[/tex]

Convert to logarithm form:

[tex]5k=\ln(2)[/tex]

Multiply both sides by 1/5:

[tex]k=\frac{1}{5}\ln(2)[/tex]

[tex]k=\ln(2^{\frac{1}{5}})[/tex] By power rule.

So in the next sentence they actually give us the initial population and we just found k so this is our function for P:

[tex]P=39e^{\ln(2^{\frac{1}{5}})t}[/tex]

So now we plug in 20 to find how many residents there were in 1761:

[tex]P=39e^{\ln(2^{\frac{1}{5}})(20)}[/tex]

This is surely going to the calculator:

[tex]P=624[/tex]

Now if you don't like that, let's try this:

Year 0 we have 39 people.

Year 5 we have 39(2)=78 people.

Year 10 we have 78(2)=156 people.

Year 15 we have 156(2)=312 people.

Year 20 we have 312(2)=624 people.

He afford 5 games at bowling alley C.

Comparing Numbers means identifying a number that is smaller or greater than the rest. We can compare numbers using different methods such as on a number line, by counting, or by counting the number of digits, using place values of the numbers, etc.

According to the topic , we know

4 games at bowling alley B need to speed [tex]4 \times 5.25 = 21 > 20[/tex]

5 games at bowling alley C need to speed [tex]5 \times 3.75 =18.75 < 20[/tex]

5 games at bowling alley A need to speed [tex]5 \times 4.25 = 21.25 > 20[/tex]

6 games at bowling alley D need to speed [tex]6 \times 3.50 = 21 > 20[/tex]

So, the answer is 5 games at bowling alley C.

Option B is correct.

He afford 5 games at bowling alley C.

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Answer:

A

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = x - 1 ( add 1 to both sides )

y + 1 = x

change y back into terms of x, hence

[tex]f^{-1}[/tex] (x ) = x + 1 → A

the correct (answer)

is A f1(x)=x+1

Answer:

The correct answer is second option  option

9¹/⁸ ˣ

Step-by-step explanation:

Points to remember

Identities

ᵃ√x = = x¹/ᵃ

√x = x¹/²

(xᵃ)ᵇ = xᵃᵇ

To find the correct option

It s given that,

(⁴√9)¹/² ˣ

By using the above identities we can write,

(⁴√9)¹/²ˣ = (9¹/⁴)¹/²ˣ     [ since ⁴√9 = 9¹/⁴]

 = 9⁽¹/⁴ * ¹/²⁾ ˣ

 = 9¹/⁸ ˣ

Therefore the correct answer is second option  option

9¹/⁸ ˣ

To solve for the distance from the base of the cliff, the time to hit the ground is calculated from the initial vertical velocity and the height of the cliff. The horizontal distance is then found by multiplying the time by the horizontal component of the initial velocity.

To determine how far from the base of the cliff a bullet strikes the ground, we use the concepts of projectile motion. The initial velocity components are [tex]v_{0x} = 800 \cos(30^{\circ}) m/s[/tex] (horizontal component) and v_{0y} = [tex]800 \sin(30^{\circ}) m/s[/tex](vertical component downwards). The time it takes for the bullet to hit the ground can be found using the equation for vertical motion: y =[tex]v_{0y}t + \frac{1}{2}gt^2[/tex], where y is the height of the cliff, g is the acceleration due to gravity [tex](-9.8 m/s^2[/tex] since the bullet is moving downwards), and t is the time. Solving for t we get two possible times, but we choose the positive one. Once we have t, we can find the horizontal distance using x = v_{0x}t. Using these calculations, the appropriate distance from the base of the cliff can be determined.

Answer:

3/6=1/2 so one half

Step-by-step explanation:

3/6 × 10 =30/60=3/6=1/2

Answer:

Average number of even number outcomes =5

Step-by-step explanation:

Probability = number of possible outcome / sample space

A fair die has sides labeled 1,2,3,4,5,6.

Therefore sample space = 6

Odd numbers = 1,3,5

Possible outcome of odd numbers = 3

Even numbers = 2,4,6

Possible outcome of even numbers = 3

Probability of even numbers = possible outcome of even numbers / sample space

Probability of even numbers = 3/6 = 1/2.

If the die is rolled 10times

Total number of outcome = 10

Average number of even number outcomes = probability of even numbers * total number of outcome

= 1/2 x 10

= 5

Average number of even number outcomes =5

Answer:

5

Step-by-step explanation:

The radius is a distance on a circle from the center to a point on the circle.

We have both of these points describe here in this definition.  Using the distance formula will give us the radius.

[tex]\sqrt{(x \text{ difference })^2+(y \text{ difference})^2[/tex]

The difference between 1 and -3 is 1-(-3)=4.

The difference between 5 and 2 is 5-2=3.

[tex]\sqrt{4^2+3^2}[/tex]

[tex]\sqrt{16+9}[/tex]

[tex]\sqrt{25}[/tex]

[tex]5[/tex]

Answer:

a. A parallelogram

Step-by-step explanation:

A trapezoid is a four-sided flat shape with a pair of parallel sides.

A parallelogram has two pairs of parallel sides.

b. can apply to a trapezoid. A polygon has three or more sides.

c. can apply to a trapezoid. A quadrilateral has four sides.

d. can apply to a trapezoid. A shape with four angles is also a quadrilateral.

The term that does not describe a trapezoid is A. a parallelogram.

The term that does not describe a trapezoid is A. a parallelogram. A trapezoid is indeed a polygon, which by definition is a plane figure with at least three straight sides and angles. Also, a trapezoid is a type of quadrilateral or quadrangle, meaning it has four sides. However, unlike a parallelogram, a trapezoid only has one pair of parallel sides, while a parallelogram has two pairs of parallel sides. The distinct characteristic of a parallelogram is that its opposite sides are not only parallel but also equal in length, which does not apply to a trapezoid.

Answer:

RS/VU=ST/UT and ∠S≅∠U

Step-by-step explanation:

we know that

The Side-Angle-Side Similarity Theorem states that: If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar

In this problem the included angle is

∠S≅∠U

therefore

side RS must be proportional to side VU  and side ST must be proportional to side UT

so

RS/VU=ST/UT

Verify

substitute the given values

12/6=16/8

2=2 -----> is true

therefore

The two sides are proportional

Answer:

[tex]\frac{1}{x+4}[/tex]

Step-by-step explanation:

because you want to do [tex]\frac{x}{x+4}[/tex] divided by 4 which would end up being [tex]\frac{x}{x(x+4)}[/tex] then you cancel out the x and you are left with [tex]\frac{1}{x+4}[/tex]

For this case we must find an expression equivalent to:

[tex]\frac {\frac {x} {x + 4}} {x}[/tex]

Applying double C we have:

[tex]\frac {x} {x (x + 4)} =[/tex]

We simplify common terms of the numerator and denominator:

[tex]\frac {1} {x + 4}[/tex]

Finally we have:

[tex]\frac {1} {x + 4}[/tex]

Answer:

[tex]\frac {1} {x + 4}[/tex]

Answer:

224 square centimeters

Step-by-step explanation:

If you slice this rectangular prism parallel to the face BFCG, you will get another cross section that is a rectangle with base 32 cm and height 7 cm.

We know area of rectangle = base * height

Thus, the area of the cross section is 7 * 32 = 224 square centimeters.

Answer:

The answer for K12 is 216

NOT 224 i got it wrong on the test

Have a great day guys! You can do it!

Step-by-step explanation:

Answer:

Estimate

Step-by-step explanation:

Estimation is the process by which we deduce a close value to the required value through the method of approximation.

A graph is one of the tools used for finding the exact value of a limit. It can help us to approximate a limit by allowing us to estimate the finite value we're approaching as we get closer asymptotically to some independent variable values.

When working with graphs, the best we can do is estimate the value of limits in an appropriate step or procedure.

Therefore, the great fall back plan hen working with graph is to estimate.

Answer: Create a t-chart to graph the coordinates

Answer:

the answer you picked is the right one.

Step-by-step explanation:

both are obtuse angles

and

angle 2 = angle 3

they are also alternative interior angles

Answer: Z=30.8 when X=14 and Z=16.7 when Y=7

Step-by-step explanation:

Z is directly proportional to X: Z=K*X, Where K is a constant

Z is inversely proportional to Y:[tex]Z=\frac{K_{1} }{Y}[/tex] where [tex]K_{1}[/tex] is another constant.

When Z=19.5 ,   X=9 , Using this condition we find K value  

19.5=K*9 so, K=[tex]K=\frac{19.5}{9}[/tex]=2,2

When Z=19.5 ,   Y=6 , Using this condition we find [tex]K_{1}[/tex] value  

19.5=[tex]\frac{K_{1} }{6}[/tex] so, [tex]K_{1}[/tex]=19.5*6=117

So, When X=14,  Z= 2.2*14=30.8

When Y=7  Z= [tex]\frac{117}{7}[/tex]=16.7

Answer: 11.18

Step-by-step explanation:

You’re substituting 5 for x in the equations...

Sqrt[x^2+4x^2]

Sqrt[5^2+4(5)^2]

Sqrt[25+4(25)]

Sqrt[25+100]

Sqrt[125]

In the provided equation, substituting x with 5 and simplifying gives us the square root of 425, which is approximately 20.6. Therefore, the estimated length of the ladder when the base is 5 ft from the wall is about 20.6 feet.

In this problem, the length of the ladder should be the square root of the sum (x)^2 and (4x)^2. In this equation, you're given that the base of the ladder is 5 feet from the wall, represented by 'x'. First substitute x with 5 into the equation: √[(5)^2 + (4*5)^2]. This simplifies to √[25 + 400] = √425. The square root of 425 is about 20.6. Therefore, if you round it to the nearest tenth, the desired length of the ladder when the base is positioned 5 ft from the wall is approximately 20.6 feet.

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Answer:

B. You had a math test on Thursday

Step-by-step explanation:

B is most likely the answer because you would have a math test regardless of the weather. Teachers do stuff like that. Also I just took this quiz on APEX.

Answer:

The correct option is B....

Step-by-step explanation:

The  given equation is:

x + 2y = 12  -----equation 1

- x= -y-6. -------equation 2

lets take equation 2:

-x=-y-6

Take minus as common on R.H.S

-x= -(y+6)

x=y+6  (Lets call it equation 3)

Substitute the value of x in the first equation:

x+2y=12

y+6+2y=12

Combine the like terms:

y+2y = 12-6

3y=6

Divide both the sides by 3

3y/3=6/3

y=2

Now substitute the value of y in equation 3:

x=y+6

x=2+6

x=8

Thus the solution set is (x,y){(8,2)}.

The correct option is B....

Answer:

B. (8,2)

Step-by-step explanation:

Apex

Hope this helps Have a nice day

Answer:

The linear equation that represent this problem is [tex]y=50x-2,500[/tex]

Step-by-step explanation:

Let

x -----> the number of people

y ----> the profit in dollars

we have

For x=100, y=2,500

and

For x=80, y=1,500

Find the slope m

we have

(80,1,500) and (100,2,500)

The slope is equal to

[tex]m=(2,500-1,500)/(100-80)\\ \\m=50\frac{\$}{people}[/tex]

Find the equation of the line into point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=50[/tex] and point (100,2,500)

substitute

[tex]y-2,500=50(x-100)[/tex] ----> equation in slope point form

Convert to slope intercept form

[tex]y=50x-5,000+2,500[/tex]

[tex]y=50x-2,500[/tex]

Answer:

Option 2

Step-by-step explanation:

Given

B = (-6,1)

B' = (-3,-2)

Step 1: Substitute the original and translated coordinates into (x,y) => (x+a,y+b)

B(-6,1) => B'(-6+a , 1+b) = B'(-3,-2)

Step 2: Write two equations

-6+a = -3 => a = -3+6 = 3

1+b=-2 => b = -2-1 = -3

Hence, we can conclude that Indira wrote the equations wrong which was her first error.

Therefore, Option 2 is correct ..

Answer:

y = - 9

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, - 6) and (x₂, y₂ ) = (4, 3)

m = [tex]\frac{3+6}{4-1}[/tex] = [tex]\frac{9}{3}[/tex] = 3

y = 3x + c ← is the partial equation

To find c substitute any of the 2 points into the partial equation

Using (4, 3), then

3 = 12 + c ⇒ c = 3 - 12 = - 9, hence

y- intercept c = - 9 ⇒ (0, - 9 )

Answer:

=-9 (the first choice)

Step-by-step explanation:

To find the y-intercept we must first find the equation of the line in the form y=mx + c where m is the gradient and c is the y- intercept.

m=Δy/Δx

=(3--6)/(4-1)

=9/3

=3

Let us write the equation using any of the given points, say (4,3)

(y-3)/(x-4)=3

y-3=3(x-4)

y-3=3x-12

y=3x-12+3

y=3x-9

Using the format y=mx+c, the y-intercept is -9

Answer: False

Step-by-step explanation:

Lets assume 15/33=22/46

15x46=22x33 (according to the cross multiply rule)

690=726

Here^^ clearly the answer is not equal thus, the answer is false, hope this was helpful :D

The given proportion is not correct.

We have to given that,

Expression for proportion is,

15/33 = 22/46

Now, WE can simplify each fraction as,

15/33 = 5/11

22/46 = 11/13

Clearly, 5/11 ≠ 11/13

Hence, The given proportion is not correct.

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Answer: a.) 3

Step-by-step explanation:

Using the common convention that the horizontal axis represents variable x and the vertical axis represents variable y, then x-intercept or horizontal intercept is a point where the graph of the function intersects the x-axis of the coordinate system. As such, these points satisfy y = 0 where the line crosses the x-axis.

Then replacing this value in the equation

2x-3y = 6

2x - 3*0 = 6

2x = 6

x = 6/2 = 3

The x-intercept is 3

Answer: a.) 3

[tex]\textit{\textbf{Spymore}}[/tex]

Answer:

a 3

Step-by-step explanation:

Given

2x - 3y = 6

To find the x- intercept substitute y = 0 into the equation and solve for x

2x - 3(0) = 6

2x = 6 ( divide both sides by 2 )

x = 3 ← x- intercept

Answer:

[tex](x-1)^2+(y-4)^2=4[/tex].

Step-by-step explanation:

So the standard form of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex] where (h,k) is the center and r is the radius.

You are given (h,k)=(1,4) and r=2.

So we are going to plug in 1 for h, 4 for k, and 2 for r:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

[tex](x-1)^2+(y-4)^2=2^2[/tex]

[tex](x-1)^2+(y-4)^2=4[/tex].

Answer:

(x-1)^2 + (y+4)^2 = 4

Step-by-step explanation:

APEXXXX

Answer:

the only answers are 8 and 5

Answer:

[tex]\large\boxed{(2,2)}[/tex]

Step-by-step explanation:

In this question, we're trying to find the midpoint of the line segment "ST"

In order to find the midpoint, we're going to need to sue the midpoint formula.

Mid point formula:

[tex]m=({\frac{x1+x2}{2}},\frac{y1+y2}{2})[/tex]

You would plug the numbers into the right spot. Plugging the first "x" coordinate to x1 and etc.

Your equation should look like this:

[tex]m=({\frac{-2+6}{2}},\frac{-4+8}{2})[/tex]

Now you will solve:

[tex]m=({\frac{-2+6}{2}},\frac{-4+8}{2})\\\\\text{Lets add all the numbers}\\\\m=({\frac{4}{2}},\frac{4}{2})\\\\\text{Now, you would simply divide the fractions}\\\\m=(2,2)[/tex]

When you're done solving, you should get (2,2)

This means that the midpoint of ST is (2,2)

The formula for midpoint is ([tex]\frac{x_{1}+x_{2}}{2}[/tex], [tex]\frac{y_{1}+y_{2}}{2}[/tex])

In this case:

[tex]x_{1} =-2\\x_{2} =6\\y_{1} =-4\\y_{2} =8[/tex]

^^^Plug in these number into the formula given above...

([tex]\frac{-2 + 6}{2}[/tex], [tex]\frac{-4 + 8}{2}[/tex])

([tex]\frac{4}{2}[/tex], [tex]\frac{4}{2}[/tex])

Simplify the fractions:

(2, 2)

^^^This is the coordinate of the midpoint

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Question 1

Part A: The total length of sides 1, 2, and 3 is (8y² + 8y - 10)

Part B: The length of the fourth side is 22y³ + 2y² + 2y - 7

Part C: Yes the answers for Part A and Part B show that the polynomials are closed under addition and subtraction

Question 2

Part A: The expression of the area of the square is 4x² - 20x + 25

Part B: The degree and classification of the expression obtained in part A

are second degree and trinomial

Part C: The polynomials are closed under multiplication

Question 3

Part A: The function of the area of the circle of spilled oil is 49 πt²

Part B: The area of the spilled oil after 8 minutes is 9847.04 units²

Step-by-step explanation:

* Lets explain how to solve the problems

# Question 1

∵ The length of the three sides of a quadrilateral are

- Side 1: 4y + 2y² - 3

- Side 2: -4 + 2y² + 2y

- Side 3: 4y² - 3 + 2y

- The perimeter of the quadrilateral is 22y³ + 10y² + 10y − 17

* Part A:

- To find the total length of sides 1, 2, and 3 of the quadrilateral

  add them

∴ s1 + s2 + s3 = (4y + 2y² - 3) + (-4 + 2y² + 2y) + (4y² - 3 + 2y)

- Collect the like terms

∴ S1 + S2 + S3 = (2y² + 2y² + 4y²) + (4y + 2y + 2y) + (-3 + -4 + -3)

∴ S1 + S2 + S3 = 8y² + 8y + (-10) = 8y² + 8y - 10

* The total length of sides 1, 2, and 3 is (8y² + 8y - 10)

* Part B:

∵ The perimeter of the quadrilateral is the sum of its 4 sides

∴ The length of its fourth side is the difference between its

   perimeter and the sum of the other 3 sides

∵ The perimeter of the quadrilateral is 22y³ + 10y² + 10y − 17

∵ The sum of the three sides is (8y² + 8y - 10)

∴ The length of the 4th side = (22y³ + 10y² + 10y − 17) - (8y² + 8y - 10)

- Remember that (-)(+) = (-) and (-)(-) = (+)

∴ S4 = 22y³ + 10y² + 10y - 17 - 8y² - 8y + 10

- Collect the like terms

∴ S4 = (22y³) + (10y² - 8y²) + (10y - 8y) + (-17 + 10)

∴ S4 = 22y³ + 2y² + 2y + (-7) = 22y³ + 2y² + 2y - 7

* The length of the fourth side is 22y³ + 2y² + 2y - 7

* Part C:

- Polynomials will be closed under an operation if the operation

 produces another polynomial

∵ In part A there are 3 polynomials add to each other and the answer

  is also polynomial

∴ The polynomials are closed under addition

∵ In part B there are 2 polynomial one subtracted from the other and

  the answer is also polynomial

∴ The polynomials are closed under subtraction

* Yes  the answers for Part A and Part B show that the polynomials

  are closed under addition and subtraction

# Question 2

∵ The side of a square measure (2x - 5) units

* Part A:

∵ The are of the square = S × S, where S is the length of its side

∵ S = 2x - 5

∴ The area of the square = (2x - 5) × (2x - 5)

- Multiply the two brackets using the foil method

∵ (2x - 5)(2x - 5) = (2x)(2x) + (2x)(-5) + (-5)(2x) + (-5)(-5)

∴ (2x - 5)(2x - 5) = 4x² + (-10x) + (-10x) + 25

- Add the like terms

∴ (2x - 5)(2x - 5) = 4x² + (-20x) + 25 = 4x² - 20x + 25

∴ The area of the square = 4x² - 20x + 25

* The expression of the area of the square is 4x² - 20x + 25

* Part B:

∵ The greatest power in the expression obtained in Part A is 2

∴ Its degree is second

∵ The expression obtained in part A has three terms

∴ The expression obtained in Part A is trinomial

* The degree and classification of the expression obtained in Part A

  are second degree and trinomial

* Part C:

- Polynomials will be closed under an operation if the operation

 produces another polynomial

∵ (2x - 5) is polynomial

∵ (4x² - 20x + 25) is polynomial

∴ The product of two polynomials give a polynomial

∴ The polynomials are closed under multiplication

# Question 3

∵ n(t) = 7t, where t represents time in minutes and n represents how

  far the oil is spreading

∵ The area of the pattern can be expressed as A(n) = πn²

* Part A:

- To find the area of the circle of spilled oil as a function of time, then

  find the composite function A[n(t)]

- That means replace n in A(n) by the function n(t)

∵ n(t) = 7t

∴ A[n(t)] = A(7t)

∵ A(n) = πn²

- Replace n by 7t

∴ A(7t) = π (7t)² = 49 πt²

∴ A[n(t)] = 49 πt²

* The function of the area of the circle of spilled oil is 49 πt²

* Part B:

∵ The area of the circle of spilled oil in t minutes = 49 πt²

- To find the area of the circle of spilled oil after 8 minutes substitute

  t by 8

∴ Area of the spilled oil after 8 minutes = 49 π (8)²

∵ π = 3.14

∴ Area of the spilled oil after 8 minutes = 49(3.14)(64) = 9847.04

* The area of the spilled oil after 8 minutes is 9847.04 units²

Answer:

red, red, red, red, red, red, green, red, red, yellow

A. red, red, red, red, red, red, green, red, red, yellow

Frequency state to the number of times an event and the value occurs. A frequency table is a table that lists items or shows the number of times the items occur. We represent a frequency by the English alphabet ‘f’.

From the frequency table, there are 8 red lights, 1 green light and 1 yellow light for a total of 10 lights.

In option A, there are 8 red lights, 1 green light and 1 yellow light, with 10 total lights.  This is the correct option.

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Answer:

36

Step-by-step explanation:

We have to compute 4 distances and then add them up.

It may help to draw this first to see which distances to compute.

So I'm going to start with computing the distance from (0,0) to (5,12), then from (5,12) to (9,9), then from (9,9) to (12,5), and then finally from (12,5) to (0,0).

So distance from (0,0) to (5,12)

d=sqrt((5-0)^2+(12-0)^2)=sqrt(25+144)=sqrt(169)=13

Distance from (5,12) to (9,9)

d=sqrt((9-5)^2+(12-9)^2)=sqrt(4^2+3^2)=sqrt(16+9)=sqrt(25)=5

Distance from (9,9) to (12,5)

d=sqrt((12-9)^2+(9-5)^2)=sqrt(3^2+4^2)=sqrt(9+16)=sqrt(25)=5

Distance from (12,5) to (0,0)

d=sqrt((12-0)^2+(5-0)^2)=sqrt(12^2+5^2)=sqrt(144+25)=sqrt(169)=13.

Up all of our distances 13+5+5+13=(13+13)+(5+5)=26+10=36

Answer:

c. 36

Step-by-step explanation:

that is what that one says up there