State what additional information is required in order to know the
triangles are congruent using the theorem or postulate listed.

For a triangle with base of 10 inches and altitude of 16 inches, its area will be 80 in² (third option).

Calculation For the Area of the Triangle:

It is given that,

The base of the triangle, B = 10 inches

The altitude from the base of the triangle or height, H = 16 inches

Now, the formula used for finding the area of a triangle is given as follows,

Area, A = (1/2) × B × H

Substituting the given values of B and H in the above formula for area, we get,

A = (1/2) × (10 inches) × (16 inches)

A = 5 × 16 inches²

A = 80 inches²

Thus, the area of the triangle have base 10 inches and altitude 16 inches is 80 square inches.

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Answer:

They are only equal on day 0, both having 10 population.

Step-by-step explanation:

Given the bacteria on the counter is initially measured at 5 and doubles every 3 days we can generate the following geometric equation:

[tex]f(x)=10*2^{\frac{x}{3} }[/tex]

Given the bacteria on the stove is measured at 10 and doubles every 4 days we can create another equation:

[tex]f(x)=10*2^{\frac{x}{4} }[/tex]

To find how many days it will take for the bacteria population to equal the same lets set both equations equal to eachother:

[tex]10*2^{x/3}=10*2^{x/4}[/tex]

Divide both sides by 10

[tex]2^{x/3}=2^{x/4}[/tex]

Since both exponents have the same base we can set the exponents equal to eachother and solve for x:

[tex]\frac{x}{3}=\frac{x}{4}[/tex]

Multiply both sides by 3 to isolate x on the left side

[tex]x=\frac{3x}{4}[/tex]

Multiply both sides by 4 to remove fraction

[tex]4x=3x[/tex]

Subtract 3x to isolate x on the left side

[tex]x=0[/tex]

Plug x into one of our original equations

[tex]f(0)=10*2^{0/3}[/tex]

Solve

[tex]f(0)=10[/tex]

The angles exist in the exact place in both triangles. So we will obtain the decision that they exist different.

Therefore, the the measure of their angles exists different.

No, because the measure of their angles exists different. If the angle measurements existed the exact, they would have been equivalent.

You see in the smaller triangle, the given angle exists at 55 degrees while in the bigger triangle the given angle exists at 30 degrees.

The angles exist in the exact place in both triangles. So we will obtain the decision that they exist different.

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Answer:

tanya 22

leah12

Step-by-step explanation:

i hope it

help ...

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

Explanation:

To go from gallons to fluid ounces (abbreviation fl oz), we multiply by 128

For example, 2 gallons becomes 2*128 = 256 fl oz as shown in the table.

Another example: 3 gallons = 3*128 = 384 fl oz.

Therefore, 6 gallons would be 6*128 = 768 fl oz.

To go in reverse, from fl oz to gallons, we divide by 128.

Answer:

The answer is 1. This table is an example of the principle of independence.

Step-by-step explanation:

This means any Trade activity is performed without reliance on another party.

He got the perfect answer to his question and he can get his answer without any other information.

Answer:

see explanation

Step-by-step explanation:

let x be the amount Kweku gets then Kofi gets 3x , so

x + 3x = 4800

4x = 4800 ( divide both sides by 4 )

x = 1200

that is

Kweku gets $1200

Kofi gets 3 × $1200 = $3600

Step-by-step explanation:

1.

how many glasses of 0.32 liter can she fill ?

that means, how often does 0.32 fit into 1.45 ?

that is solved by division :

1.45 / 0.32 = 4.53125

so, she will need at least 5 glasses to completely empty the bottle. the 5th glass will be filled only partly, but that does not matter in that regard.

2.

he has 5.6 kg and adds 2.5 kg. that is 5.6 + 2.5 = 8.1 kg.

1 dough (that means 1 portion of dough as described by his recipe) uses 0.48 kg flour.

how many doughs can he make

so, again, how often does 0.48 fit into 8.1 ?

8.1 / 0.48 = 16.875

he can therefore make 16 full portions of dough. he does not have enough flour for a full 17th.

so, he uses

16×0.48 = 7.68 kg of flour for the 16 doughs.

and he has

8.1 - 7.68 = 0.42 kg of flour left.

Answer:

  58.25

Step-by-step explanation:

A "moving average" is a "boxcar average," the unweighted average over the specified number of days.

The 4-day moving average ending on day 7 is ...

  4-day average = (day 4 +day 5 +day 6 +day 7)/4

  = (60 +59 +55 +59)/4 = 233/4

  4-day average = 58.25

The four-day moving average for the price of the stock for the end of day 7 is 56.00

What is moving average?

The moving average on a particular day  is the average of prices on the days prior to the pricing day.

In other words, four-day moving average on day 7 is the sum the prices of four days prior to day 7 divided by the number of days whose prices were considered.

In computing the four-day moving average for day 7, we would sum the prices for days 3-6, then divide the sum by 4 since prices of 4 days were made use of.

four-day moving average on day 7=(50.00+60.00+59.00+55.00)/4

four-day moving average on day 7= 56.00

Note, as the day of pricing changes, the input prices would also change

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Based on the dimensions of the support for the slides, the missing length and slide length is 15 yards.

The number of 3-yard straight pieces needed is 15 straight pieces.

The length of a single slide is the hypotenuse of the triangle which can be found using the Pythagoras theorem as:

Hypotenuse² = 9² + 12²

Hypotenuse = √(81 + 144)

= 15 yards

If a single slide is 15 yards, then 3 slides would be:

= 15 x 3

= 45 yards

The number of 3-yard straight pieces needed are:

= 45 / 3

= 15 pieces

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Answer: 39

Explain:

The length of each slanted area for each slide is 15 yards. The length of each straight piece is 3 yards. So, the number of straight pieces needed for 15 yards is 15 - 3, or 5. There are two slanted areas on each slide.

The number of straight pieces required for the flat area at the bottom of each slide is 3.

Adding them up, the total number of straight pieces required for one slide is 5 + 5 + 3, or 13. Because there are three slides, the total number of straight pieces needed is 13 • 3, or 39

Vince needs 39 straight pieces to build the three slides.

From ED

Answer:

52º, 128º

Step-by-step explanation:

8. Because ∠6 is an opposite angle to ∠5, ∠6=∠5=52º;

9. Because line a//line b, ∠6=∠4=52º, so ∠7=180º–52º=128º

Hello and Good Morning/Afternoon

Let's take this problem step-by-step:

What does this problem give us:

What does this problem want us to find:

Let's solve:

           ⇒ by the vertical angle theorem is equal in measure to ∠5

               ⇒ ∠6 = 52°

           ⇒ lines a and b are parallel

               ⇒ the corresponding angles on both lines formed by the

                    transversal are equal

                         i.e. m∠2 = m∠3, m∠7 = m∠8

           ⇒ ∠8 is on a straight line with ∠6

                      [tex]\hookrightarrow angle8 +angle6 = 180\\\hookrightarrow angle8 + 52 = 180\\\hookrightarrow angle8 =128[/tex]

           ⇒ since m∠8 is equal to m∠7

              ⇒ m∠7 = 128

Definitions

Answer:

Hope that helps!

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The volume of the cylinder and the cone is equal

The formula for calculating the volume of a cylinder is expressed as:

V = πr²h

where

r is the radius

h is the height

For the cylinder

r = 8/2 = 4 in

h = 5

Substitute

V = π(4)²*5
V = 80π cubic inches

For the cone

r = 4 in

h = 15in

Substitute

V = 1/3πr^2h

V = 1/3(π)(4)^2 * 15

V = 80π cubic inches

Hence the volume of the cylinder and the cone is equal

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Step-by-step explanation:

1500*.02*1=30

50*12*1=60

g(x)=50(12x) good

The range of the means is 0.5

Mean of S1

= 5 + 6+ 6+ 2

= 19/4

= 4.75

Mean of S2

= 4 + 8 + 4 + 3

= 19/4

= 4.75

Mean of s3

= 4 + 2 + 6+ 5

= 17/4

= 4.25

Range of sample means = 4.75 - 4.25

= 0.5

c. the true statements here is that

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Answer:

[tex]y=\frac{-x}{78} -\frac{220}{78}[/tex]

Step-by-step explanation:

Remember to create a line perpendicular to one another the slope has to be the reverse reciprocal of the first line.

Given the current slope is [tex]\frac{-78}{1}[/tex] the new slope would be [tex]\frac{1}{78}[/tex].

To find the line that passes through a point with a given slope we must use point slope form, remember the default equation of point slope form:

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

Where y1 is the y value of the point, m is the slope, and x1 is the x value of the point.

Lets substitute in our values

[tex]y-(-3)=\frac{-1}{78} (x-14)[/tex]

Simplify the equation

[tex]y+3=-\frac{1}{78}\left(x-14\right)\\y+3=\frac{-x}{78}+\frac{14}{78}\\y=\frac{-x}{78}-\frac{220}{78}\\[/tex]

Answer:

This is the answer of this question. Hope it helps.

Given that one can get 6 gems every 2 minutes and 30 seconds, one will have 144 gems after one hours.

Given that;

Hence 6 gems are gotten every  120sec and 30 seconds

Hence 6 gems are gotten every  150seconds

Next we convert 1 hour to seconds

1 hour = ( 60 × 60 × 1 )sec = 3600sec

Now,

6 gems can be gotten every  150seconds

x gems can be gotten every 3600 seconds

x = ( 6 × 3600 ) / 150

x = 21600 / 150

x = 144 gems

Given that one can get 6 gems every 2 minutes and 30 seconds, one will have 144 gems after one hours.

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Answer: 7 1/2 cups

Step-by-step explanation:

We first need to make both fractions have an equal denominator. Cross Multiply 3/4 and 1/10. You will end up with 30/40 and 4/40.

Next we divided 30 by 4, and we will end up with 7 1/2. 7 times 4 is 28, and half of 4 is 1/2, or in this case 2/10. John can fill 7 and 1/2 cups of orange juice.

Así, concluimos que la liebre da un total de 38 saltos.

Notar que solo se nos pregunta cuantos saltos da la Liebre, no importa en que dirección son dichos saltos.

Entonces solo debemos sumar todos los números de saltos que se nos dan, esto es:

18 saltos + 5 saltos + 9 saltos + 6 saltos = 38 saltos.

Así, concluimos que la liebre da un total de 38 saltos.

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The series and the sigma notations are[tex]\sum\limits^4_0 3(5)^n = 3 + 15 +75 + 375 +1875[/tex], [tex]\sum\limits^4_0 4(8)^n = 4 + 32 + 256+ 2048 + 16384[/tex], [tex]\sum\limits^4_0 2(3)^n = 2 + 6 + 18 + 54 + 162[/tex] and [tex]\sum\limits^4_0 5(3)^n = 5 + 15 + 45 + 135 + 405[/tex]

To do this, we simply expand each sigma notation.

So, we have:

[tex]\sum\limits^4_0 3(5)^n[/tex]

Next, we set n = 0 to 4.

So, we have:

3(5)^0 = 3

3(5)^1 = 15

3(5)^2 = 75

3(5)^3 = 375

3(5)^4 = 1875

So, we have:

[tex]\sum\limits^4_0 3(5)^n = 3 + 15 +75 + 375 +1875[/tex]

[tex]\sum\limits^4_0 4(8)^n[/tex]

Next, we set n = 0 to 4.

So, we have:

4(8)^0 = 4

4(8)^1 = 32

4(8)^2 = 256

4(8)^3 = 2048

4(8)^4 = 16384

So, we have:

[tex]\sum\limits^4_0 4(8)^n = 4 + 32 + 256+ 2048 + 16384[/tex]

[tex]\sum\limits^4_0 2(3)^n[/tex]

Next, we set n = 0 to 4.

So, we have:

2(3)^0 = 2

2(3)^1 = 6

2(3)^2 = 18

2(3)^3 = 54

2(3)^4 = 162

So, we have:

[tex]\sum\limits^4_0 2(3)^n = 2 + 6 + 18 + 54 + 162[/tex]

[tex]\sum\limits^4_0 5(3)^n[/tex]

Next, we set n = 0 to 4.

So, we have:

5(3)^0 = 5

5(3)^1 = 15

5(3)^2 = 45

5(3)^3 = 135

5(3)^4 = 405

[tex]\sum\limits^4_0 5(3)^n = 5 + 15 + 45 + 135 + 405[/tex]

Hence, the series and the sigma notations are[tex]\sum\limits^4_0 3(5)^n = 3 + 15 +75 + 375 +1875[/tex], [tex]\sum\limits^4_0 4(8)^n = 4 + 32 + 256+ 2048 + 16384[/tex], [tex]\sum\limits^4_0 2(3)^n = 2 + 6 + 18 + 54 + 162[/tex] and [tex]\sum\limits^4_0 5(3)^n = 5 + 15 + 45 + 135 + 405[/tex]

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Answer:

  5.09 years

Step-by-step explanation:

The formula for the future value of an investment can be filled with the given values and solved for time.

The future value of a one-time investment P earning interest at annual rate r compounded n times per year for t years is ...

  FV = P(1 +r/n)^(nt)

Using this formula with the given values, we have an expression for t:

  7300 = 5000(1 +0.075/4)^(4t)

Dividing by 5000, we have ...

  1.46 = 1.01875^(4t)

Taking logarithms gives the linear equation ...

  log(1.46) = 4t·log(1.01875)

Dividing by the coefficient of t, we find ...

  t = log(1.46)/(4·log(1.01875)) ≈ 5.0929

The time required for the value to reach $7300 is about 5.09 years.

__

Additional comment

The attachments show different calculator solutions. They give the same value for t.

The TVM Solver uses P/Y = 1 so the value of N is in years.

The graphical solution recasts the problem to f(x) = 0. It finds the value of t that makes the difference between the investment value and $7300 be zero.

The coordinate of P is (A) ( 40, 96).

To find What are the x- and y- coordinates of point p on the directed line segment from K to J:

It can be seen from the figure the coordinates of K and J:

The coordinates of P can be determined as:

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

So, as the P point divides the line into three-fifths of the length,

Which gives the ratio as 3: 2.

m:n = 3:2

Therefore, the coordinate of P is (A) ( 40, 96).

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The complete question is shown below:

What are the x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J?

x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1

y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1

(A) (40, 96)

(B) (85, 105)

(C) (80, 104)

(D) (96, 72)

Answer:

Infinite

Step-by-step explanation:

12x 8 = 12x 8

Infinitely many solutions, as left side = right side.

Truth statement exists statements or assertions that exist true yet of whether the constituent premises exist true or false.

There exist five Euclidean Postulates or axioms.

1. Any two ends can be bound by a straight line segment.

2. In a straight line, any straight line segment can be extended indefinitely.

3. A circle can be created utilizing any straight line segment as the radius and one endpoint as the center.

4. Right angles exist all the exact.

5. If two lines meet a third in a manner that the totality of the inner angles on one side exists smaller than two Right Angles, the two lines will inevitably collide on that side if they exist extended far enough.

1. The right angle on the first page of the book offered and the right angles on the last page of the book shown exist all the exact. (Axiom 4)

2. If the string from the Yoyo dangling from the hand in the picture exists circled for 360° such that the length of the string stays equivalent to all thought, and the point from where it exists attached stays fixed, it will trace a circular trajectory. (Axiom 3)

3. The swords held by the fighters can be extended into infinity because they exist in in straight lines. (Axiom 5)

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Answer:

$528
If not then it might be $385

The length of the longest piece of the cut rope is; 105 cm

We are given that;

Length of rope = 245 cm

We need to make the ratio of second piece equal in both the ratio to find the ratio of all three pieces.

2:3

4:5

Multiply 1st ratio by 4 and 2nd ratio by 3:

Now, the ratio becomes: 8:12 and 12:15

And the ratio of three pieces can be represented as:

8: 12: 15, this ratio is the first piece: second piece: third piece

Thus;

8x + 12x + 15x = 245

35x = 245

x = 245/35

So, the pieces lengths will be;

First piece = 8 * 7 = 56 cm

Second piece = 12 * 7 = 84 cm

Third piece = 15 * 7 = 105 cm

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Step-by-step explanation:

TSA of cylinder = 2πr (h + r)

according to the question

height = radius

then,

TSA = 2πr (r + r)

2464=2 × 3.1415×r ×2r

2464/4 ×3.1415 = r×r

196.08 = r^2

r = 14.00

r = 1 4 cm

We know,

volume = 2πr ^2 ×h

=2×3.1415×14×14×14 (h=r)

=17240.552 cm^3

Answer:

8620.5 cm³

Step-by-step explanation:

h = r

SA = 2πrh + 2πr²

Since h = r, we can substitute h with r.

SA = 2πr² + 2πr² = 4πr²

4πr² = 2464 cm²

r = 14 cm

V = πr²h

r = h = 14 cm

V = π(14 cm)²(14 cm)

V = 8620.5 cm³

The two numbers are 68 and 55.

Given that the sum of two numbers is 123. when the larger number is added to 5 times the smaller, the sum is 343.

We need to find the numbers,

Let's call the two numbers x and y. According to the given information, we have the following two equations:

x + y = 123 (The sum of the two numbers is 123)

x + 5y = 343 (When the larger number is added to 5 times the smaller, the sum is 343)

Now, we can solve these two equations simultaneously to find the values of x and y.

Let's rearrange equation 1 to express x in terms of y:

x = 123 - y

Substitute this value of x into equation 2:

(123 - y) + 5y = 343

Now, solve for y:

123 + 4y = 343

4y = 343 - 123

4y = 220

y = 220 / 4

y = 55

Now that we have the value of y, we can find the value of x using equation 1:

x = 123 - y

x = 123 - 55

x = 68

So, the two numbers are 68 and 55.

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