need help with this ASAP
!!!!!!!!!!!!!!!!!!!!!!!!

Need Help With This ASAP!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer 1

The fence in dead center is about 399 feet from the third base.

What is the Pythagorean Theorem?

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

c > a and c > b is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.

For the triangle in this problem, we have that:

The sides are d ft and 90 ft.The hypotenuse is of 409 ft.

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Related Questions

If you draw a card from a standard deck of 52 playing cards, what is the probability that it is a heart or a diamond?

Answers

Answer:

1/2

Step-by-step explanation:

In a deck of cards, there are 13 hearts and 13 diamonds

13+13 = 26 hearts or diamonds

P( hearts or diamonds) = numbers of hearts or diamonds / total

                                       =26/52

                                       = 1/2

Review the Monthly Principal & Interest Factor chart to answer the question:


FICO Score APR 30-Year Term 20-Year Term 15-Year Term
770–789 5.5 $5.68 $6.88 $8.17
750–769 6.0 $6.00 $7.16 $8.44
730–749 6.5 $6.32 $7.46 $8.71
710–729 7.0 $6.65 $7.75 $8.99
690–709 7.5 $6.99 $8.06 $9.27


Determine the percent decrease in total principal and interest paid between a 30-year term mortgage and a 15-year mortgage with a principal balance of $484,500.00 and a 6.5% APR. Round the final answer to the nearest tenth.
31.0%
31.1%
59.0%
68.5%

Answers

The percent decrease in total principal and interest paid between a 30-year term mortgage and a 15-year mortgage with a principal balance of $484,500.00 and a 6.5% APR is 31.0%. (Option A)

How is this so ?

To calculate the  percent decrease, we can use the following formula.

Percent decrease = ( (30-year factor -   15-year factor) / 30-year factor) x 100

Substituting the values from the chart.  

= (($ 6.65 - $8.71) / $6.65) x 100

= ( -$ 2.06 / $6.65) * 100

= -0.309 *  100

Percent decrease ≈ - 30.9 %

Since the question asks for the percent decrease as a positive value, we take the absolute value of the result which is

Percent decrease ≈ 31%

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Point A is located at (2,-2) on the coordinate plane. Point A is reflected over the Y-
axis to create point A'. Point A' is then reflected over the x-axis to create point A".
What ordered pair describes the location of A"?

Answers

Answer: A''=(-2, 2)

Step-by-step explanation:

A' = (2, -(-2)) = (2,2)   ==> the y-coordinate is negated when A reflects over the y-axis

A''=(-(2), 2) = (-2, 2).  ==> the x-coordinate is negated when A reflects over the x-axis

A''=(-2, 2)

Please help really urgent

Please help really urgent

Answers

Answer:

0.0909

Step-by-step explanation:

4 blue + 5 red + 3 black = 12 chips in total.

p=probability

1st draw:

p (blue) = 4/12

there are now 11 chips in the bag, 4-1 =3 are blue.

2nd draw?

p (blue) = 3/11

probability of pulling one blue chip followed by another blue chip is:

(4/12) X (3/11) = (4X3)/12X11)

= (12)/(132)

= 1/11

0.0909

If the image is rotated about the x-axis, which of the following images best represents the result?
A. Y
B. Z
C. X
D. W

If the image is rotated about the x-axis, which of the following images best represents the result? A.
If the image is rotated about the x-axis, which of the following images best represents the result? A.

Answers

The images best represents the result is image W.

We have, the image is rotated about the x-axis.

Now, rotating around x axis can give the other half of the image.

Also, rotating about x axis gives the mirror image of the figure.

So, the rotation leads to a circle.

and, In three dimensional we can say that Sphere.

Thus, the required image is W.

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10 x 4 thousands in unit form

Answers

Answer:

Step-by-step explanation:

Simplify.

10 x 4000

40000

Unit form.

forty-thousand = four thousands

I'm sorry if I misunderstood.

Please add Brainliest if you'd like, not that it matters.

Multiplication is the process of multiplying. The value of the expression 10 × 4,000 is 40,000.

What is multiplication?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

In the given expression 10×4000, the symbol of '×' represents that the two digits should be multiplied. Therefore, the value of the multiplication of 10 and 4,000 is,

10 × 4,000 = 40,000

Hence, the value of the expression 10 × 4,000 is 40,000.

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How can you check if a line belongs to a plane (Cartesian equation of the line and the equation of the plane is given)?

Answers

To check whether a line belongs to a plane, you can substitute the coordinates of a point on the line into the equation of the plane. If the equation is satisfied, then the point lies on the plane and the line belongs to the plane.

For example, suppose you have the Cartesian equation of a line in the form:

y = mx + b

and the equation of a plane in the form:

ax + by + cz + d = 0

To check if the line belongs to the plane, you can substitute a point (x, y) on the line into the equation of the plane and solve for z. If the resulting value of z satisfies the equation of the plane, then the line belongs to the plane.

Here's an example:

Suppose the Cartesian equation of the line is y = 2x + 1, and the equation of the plane is 2x + 3y + 4z + 5 = 0.

If we substitute a point on the line, such as (1, 3), into the equation of the plane, we get:

2(1) + 3(3) + 4z + 5 = 0

Solving for z, we find that z = -1.5.

Since the resulting value of z satisfies the equation of the plane, the line belongs to the plane.

If the resulting value of z does not satisfy the equation of the plane, then the line does not belong to the plane.

Write an equivalent expression for 3x + 21

Answers

3(x + 7)
hope this helps

55 POINTS QUICK PLS Your friend is able to invest $120 a month in a 401(k) with a predicted growth rate of 3%. Your friend's company will match 50% of your friend's contributions.

55 POINTS QUICK PLS Your friend is able to invest $120 a month in a 401(k) with a predicted growth rate

Answers

a. The monthly contribution from a friend's company is $120 minus 0.5, or $60.

b. The total monthly contribution to the fund is $180.

The computation of FV in Excel is shown in the attachment below:

What is meant by growth rate?

Using the current number as a starting point, subtract the prior value to determine the growth rate. To calculate the growth rate in percentage terms, divide the difference by the previous amount and multiply the result by 100. Growth Rate equals (Ending Value - Beginning Value) - 1. The year-over-year (YoY) growth rate of a business, for instance, would be 20% if its revenue increased from $100 million in 2020 to $120 million in 2021.

GDP, turnover, wages, etc., all have growth rates that reflect how much they have changed over time (month, quarter, year). Percentages are a pretty common way to communicate it.

20 years is the age.

20 times 12 periods equals 240.

3% growth rate

The computation of FV in Excel is shown in the attachment below:

So, FV= $7,223,115.77

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55 POINTS QUICK PLS Your friend is able to invest $120 a month in a 401(k) with a predicted growth rate

PLEASE HURRY DUE TODAY WILL MARK BRAINLESTIS RIGHT

what is  √29 Place a dot on the number line at the BEST approximation​

PLEASE HURRY DUE TODAY WILL MARK BRAINLESTIS RIGHT what is 29 Place a dot on the number line at the BEST

Answers

Answer:

5.4

Step-by-step explanation:

square of 29 = 5.385164807

5.385164807 estimated is 5.4

PLEASE HURRY DUE TODAY WILL MARK BRAINLESTIS RIGHT what is 29 Place a dot on the number line at the BEST

A movie theater can seat a maximum of 25 people. Let p represent the total number of people. Which inequality represents p, the number of people the theater can seat?

Answers

The inequality that represents p, the number of people the theater can seat is p ≤ 25

Which inequality represents p, the number of people the theater can seat?

From the question, we have the following parameters that can be used in our computation:

A movie theater can seat a maximum of 25 people

This means that

Maximum =  25 people

In other words, the movie theatre can allow 25 or less people to attend a movie

In inequality, 25 or less means less than or equal to 25

When represented as an inequality expression, we have

≤ 25

Using the variable p, we have

p ≤ 25

Hence, the inequality is p ≤ 25

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how do i prove similarities of 2D shapes through sides

Answers

Answer:

i dont know hshshshsuojvw

Help ASAP!
Question 1:
Check attached file for question 1

Question 2:
A new lake was populated with a small number of trout. The number of trout in the lake can be modeled by the function: P(t)=740 / 1+73e^−0.07 where t is the number of months since the population of trout was first introduced. Round all answers to the nearest whole number

A. what is P(0)= I got 10

B. What does the answer from part A tell us about the trout population?

C. How many trout were in the lake after 1 year?

D. How many trout were in the lake after 10 years?

E. lim t→∞P(t)= I got 740

F. What does the answer from part E tell us about the trout population?

Help ASAP!Question 1:Check attached file for question 1Question 2:A new lake was populated with a small

Answers

The answer from part A tells us that the trout population was 10 in the first month after it was introduced.

How solve the problem?

A. P(0) = 740 / (1 + 73e^-0) = 740 / (1 + 73) = 740 / 74 = 10, so the answer is 10.

B. The answer from part A tells us that the trout population was 10 in the first month after it was introduced.

C. To find the number of trout in the lake after 1 year, we need to find P(12): P(12) = 740 / (1 + 73e^-0.07*12) = 740 / (1 + 73e^-0.84) ≈ 490, so the answer is 490.

D. To find the number of trout in the lake after 10 years, we need to find P(120): P(120) = 740 / (1 + 73e^-0.07*120) = 740 / (1 + 73e^-8.4) ≈ 740, so the answer is 740.

E. lim t→∞ P(t) = 740, so the answer is 740.

F. The answer from part E tells us that as the number of months t approaches infinity, the trout population will approach 740. This means that the trout population will eventually stabilize at 740 if no other factors such as predators, disease, or lack of food affect the population.

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7. The Taylor Rule states that the central bank should set the short-term nominal interest rate (i)
based on the inflation gap [the difference between inflation (3.14) and desired inflation (3.14*)] and the
output gap (the percentage difference between real GDP (Y) and potential GDP (Y*) An
example of a Taylor Rule would be the formula
i - 3.14 = 1.5 +0.5(3.14-3.14*) +0.5 (Y-Y*/Y*)
The term on the left-hand side is the real interest rate. Consider the following table

Inflation rate (3.14), %
Target inflation rate (3.14*), %
Output gap, %
Real interest rate
Nominal interest rate
Base Scenario Scenario B Scenario C
4.0
20
2.0
20
0.0
20
20
20
00
a. Fill in the real and nominal interest rates chosen by the policy maker in the base scenano
b. How does scenario B differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move the inflation rate toward its target?
c. How does scenario C differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move output toward the potential level?
d. Suppose a new chair of the central bank is appointed and she switches to a new policy rule of
the form given in the next equation. Recalculate the real and nominal interest rates for the
three scenarios. What has been the effect of the change in weights?
i-3.14=1.5 +0.75(3.14-3.14*) +0.25(Y-Y*/Y*)

Answers

The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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Mrs moth picked 24 flowers.Six of them each had 9 petals,7 of them had 8 petals, 5 of them each had 3 petals, and the rest had 10 petals.How many flowers had 10 petals?

Answers

Using the subtraction operation, the number of flowers with 10 petals that Mrs. Moth picked was 6.

What is a subtraction operation?

A subtraction operation is one of the four basic mathematical operations, including addition, division, and multiplication.

The subtraction operation involves the minuend, the subtrahend, and the difference.

The minuend is the number or value being subtracted from by the subtrahend.  The result of a subtraction operation is known as the difference.

The total number of picked flowers = 24

The number of flowers with 9 petals = 6

The number of flowers with 8 petals = 7

The number of flowers with 3 petals = 5

The total number of flowers identified = 18 (6 + 7 + 5)

The number of flowers with 10 petals = x

x = 24 - 18

= 6

Thus, 6 flowers had 10 petals out of the 24 Mrs. Moth picked.

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For data at the interval level you cannot calculate meaningful differences between data entries.
a. True
b. False

Answers

Answer: A. FALSE

Step-by-step explanation: The interval scale presents a measurement level for representing numerical variables in an ordered and fixed manner. Measurement are represented on the scale at equal intervals with each difference between consecutive intervals being the same. With this attribute, data represented on an interval scale gives meaningful difference between the data entries also allowing the US to know the size of the interval. Interval scales allows us to make subtraction and addition on data it's data. Examples of data represented on interval scale include, Temperature, ph and other numeric data with arbitrary zero levels

The solutions to the given equation can be written in the form m+-squre root K/2, where m and k are integers. What is the value of m + k ?
x^2-4x-9=0

Answers

With the given equation, the value of m + k is equal to 656 as K is 648 and the value of is 8

We have been given the equation: x² - 4x - 9 = 0

For finding the root, we need to, x = 8² ± 4AC/2A

When we solve for the following equation, we get: x = -10, 26

now we have been given root (m + √K/2) = 26

= (m/2) + (√K/2) = 26

= √2m + √K = 26√2 ......(1)

= m - √K/√2 = -10

= √2m - √K = -10√2 ......(2)

From equation (1) and (2), we get:

2√2m = 16√2

m = 8

therefore, √K = 26√2 - √2m

√K = 18√2

K = 2 × 18² = 648

Now, m + K = 648 + 8 = 656

Therefore, with the given equation, the value of m + k is equal to 656 as K is 648 and the value of is 8

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The equation Y= X^2/2 - 8 and Y= 2X -2 are graphed below what are the solutions to the equation X^2/2 - 8 = 2X -2 

Answers

The equation X^2/2 - 8 = 2X - 2 has two solutions, X = 6 and X = -2. These are the values of X that satisfy the equation and make both equations Y = X^2/2 - 8 and Y = 2X - 2 intersect on the graph.

To find the solutions to the equation X^2/2 - 8 = 2X - 2, we need to set the two equations equal to each other and solve for X.

The equation is:

X^2/2 - 8 = 2X - 2

To simplify the equation, let's multiply both sides by 2 to eliminate the fraction:

X^2 - 16 = 4X - 4

Next, we rearrange the equation to have all terms on one side:

X^2 - 4X - 12 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case:

(X - 6)(X + 2) = 0

Setting each factor equal to zero gives us two possible solutions:

X - 6 = 0 --> X = 6

X + 2 = 0 --> X = -2

So the solutions to the equation X^2/2 - 8 = 2X - 2 are X = 6 and X = -2.

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Which of the following demonstrates how the 70 is calculated using the
combination pattern?

Which of the following demonstrates how the 70 is calculated using thecombination pattern?

Answers

The correct answer is A.

Find the area of a semicircle whose diameter is 28cm​

Answers

Answer:

The area of a semicircle with diameter 28 cm is 98π cm², or 307.88 cm² to the nearest tenth.

Step-by-step explanation:

A semicircle is a two-dimensional shape that is exactly half of a circle.

The area of a circle is given by the formula:

\(\sf A=\pi r^2\)

where A is the area of the circle, and r is the radius of the circle.

The diameter of a circle is twice its radius.

Given the diameter of the semicircle is 28 cm, the radius is:

\(\sf r = \dfrac{28}{2} = 14 \; cm\)

Substituting this into the formula for the area of a circle, we get:

\(\sf A = \pi(14)^2\)

\(\sf A = 196 \pi\)

Finally, divide this by two to get the area of the semicircle:

\(\sf Area\;of\;semicircle = \dfrac{1}{2} \cdot 196 \pi\)

\(\sf Area\;of\;semicircle = 98 \pi\; cm^2\)

So the area of a semicircle with diameter 28 cm is 98π cm², or 307.88 cm² to the nearest tenth.

Warm-Up
Jug
Use the diagram below to answer the questions.
Intro
K
P
M
Which are shown on the diagram? Check all that apply.
O
OKM
Ojk
OPK
OLJK
COM
Dong

Warm-UpJugUse the diagram below to answer the questions.IntroKPMWhich are shown on the diagram? Check

Answers

KM, JK, PK, and MJ are shown on the diagram.

Then the correct options are B, C, D, and F.

Since, Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

A line segment in mathematics has two different points on it that define its boundaries.

All the line segments will be

JK, JM, KM, MP, PK, and KL

The triangle KPM.

And the angle will be ∠LKJ, ∠PKM. ∠KMP. and ∠MPK.

Then the correct options are B, C, D, and F.

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Warm-UpJugUse the diagram below to answer the questions.IntroKPMWhich are shown on the diagram? Check

If an ant can walk 7 inches per minute and the road is 28 feet wide, how many seconds will it take him to cross ?

Answers

Answer:

48 minutes

Step-by-step explanation:

Why did the ant cross the road?

Speed of ant = 7 inches per minute
Width of road = 28 feet

28 feet = 28 x 12 inches = 336 inches

At 7 inches per minute, to cross 336 inches , it would take 336/7 or 48 minutes

t
At a local movie theater, the price for tickets is $10.00 for adults and $5.50 for students. The price of adult tickets increases by $0.20 each year, and the price of student tickets increase
$0.50 each year. The equations y = 0.20z+10 and y=0.5z +5.5 represent the situation, where x represents the number of years since the first year, and y represents the price of
tickets. After how many years will the ticket prices be the same? after how many years.

Answers

Answer:

So ticket prices will be the same after 15 years

Step-by-step explanation:

Set the two equations right side equal to each other and solve for x

0.5x +5.5 = 0.20x + 10  

Subtract 0.2x from both sides

0.5x - 0.2x + 5.5 = 0.2x - 0.2x + 10

0.3x + 5.5 = 10

Subtract 5.5 from both sides:
0.3x + 5.5 - 5.5 = 10 - 5.5

0.3x = 4.5

Multiply by 10 for easier computation
10 x 0.3x = 10 x 4.5

3x = 45

Divide by 3 to get

3x/3 = 45/3

x = 15

So ticket prices will be the same after 15 years

What would the value of a equal so the linear function ay - 2x = 9 is parallel to a line with a slope of 2/3?

Answers

Answer:

y = \(\frac{2}{3} x + 9\)

Step-by-step explanation:

I. If y = mx + b

  when y is output, x is input , m is slope and b is addition

 so y - 2x = 9

      y = 9 + 2x

      y = 2x + 9

Replace 2 with \(\frac{2}{3}\)

     y = \(\frac{2}{3} x\) + 9

Answer:

a is 3

Step-by-step explanation:

\(ay - 2x = 9 \\ ay = 2x + 9 \\ y = \frac{2}{a} x + \frac{9}{a} \)

General equation:

\({ \bf{y = mx + c}}\)

m is slope; m = ⅔

by comparison:

\( \frac{2}{3} = \frac{2}{a} \\ \\ 2a = 6 \\ a = 3\)

please help! find the surface area of the prism

please help! find the surface area of the prism

Answers

Answer:

1. 172 cm²

2. 226.56 cm²

3. 336 cm²

4. 284 cm²

Step-by-step explanation:

which one ? all ?

a surface area of an object is always the sum of the individual shapes areas on its surface.

1. 6 rectangles (length×width)

2 rectangles of 2×8 = 16 cm²

32 cm²

2 rectangles of 2×7 = 14 cm²

28 cm²

2 rectangles of 7×8 = 56 cm²

112 cm²

total : 32+28+112 = 172 cm²

2. 2 triangles and 3 rectangles

2 triangles (baseline × height / 2) = 7.2×4.8/2 = 17.28 cm²

34.56 cm²

2 rectangles 10×6 = 60 cm²

120 cm²

1 rectangle 10×7.2 = 72 cm²

72 cm²

total : 34.56+120+72 = 226.56 cm²

3. 2 triangles (right-angled) and 3 rectangles

2 triangles (a×b/2) = 8×6/2 = 24 cm²

48 cm²

1 rectangle 6×12 = 72 cm²

72 cm²

1 rectangle 8×12 = 96 cm²

96 cm²

1 rectangle 10×12 = 120 cm²

120 cm²

total : 48+72+96+120 = 336 cm²

4. 6 rectangles

2 rectangles of 3×10 = 30 cm²

60 cm²

2 rectangles of 3×9 = 27 cm²

54 cm²

2 rectangles of 10×9 = 90 cm²

180 cm²

total : 60+54+180 = 294 cm²

Drag each expression to show if it is equivalent to 25, 52, 2 × 5, or none

Answers

Answer:

rag each expression to show whether it is equivalent to 36x + 9, ... 3.2/5. 20. AthenaSinclair. Ambitious. 467 answers. 151.9K people helped ... Lastly,, we will look at the final expression given which is 4(9x + 2). ... (25 votes).

Step-by-step explanation:

Rewriting 3x^2=6x and solving with rewritten

Answers

Answer:

x = 0 , x = 2

Step-by-step explanation:

3x² = 6x ( subtract 6x from both sides )

3x² - 6x = 0 ← factor out 3x from each term

3x(x - 2) = 0

equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 2 = 0 ( add 2 to both sides )

x = 2

solutions are x = 0 , x = 2

Given a quadratic function in vertex form:

Given a quadratic function in vertex form:

Answers

a) A vertical stretch happens for values of a such that |a| > 1.

b) A vertical compression happens for values of a such that |a| > 0.

c) For a vertical stretch, the graph increases vertically, and for a vertical compression, the graph increases horizontally.

d) A reflection across the x-axis takes place when a < 0.

How to obtain the transformations?

The definition of the quadratic function is given as follows:

f(x) = a(x - h)² + k.

The transformations to the function are given as follows:

Vertical stretch: multiplication of the function by a value with absolute value greater than 1, hence |a| > 1, increasing the graph vertically.Vertical compression: multiplication of the function by a value with absolute value less than 1, hence |a| < 1, increasing the graph horizontally.

Additionally, for a reflection over the x-axis, the function is multiplied by a negative number, hence:

a < 0.

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what is 7/9 x 5 2/5 please!

Answers

Answer:

\(4\frac{1}{5}\)

Step-by-step explanation:

=>\(\frac{7}{9} * 5 \frac{2}{5}\)

=> \(\frac{7}{9} * \frac{27}{5}\)

=> \(\frac{7*3}{5}\)

=> \(\frac{21}{5}\)

=> \(4\frac{1}{5}\)

Answer:

\(4\frac{1}{5}\)

Step-by-step explanation:

\(\frac{7}{9} \times 5 \frac{2}{5}\)

\(\frac{7}{9} \times \frac{27}{5}\)

\(\frac{7 \times 27}{9 \times 5 }\)

\(\frac{189}{45}\)

\(\frac{21}{5}\)

\(=4\frac{1}{5}\)

Tienes un triángulo equilátero con lados de 10cm, lo divides en dos partes de manera horizontal tal que el área de ambos figuras resultantes es igual, ¿cuánto vale la distancia del lado x?

Tienes un tringulo equiltero con lados de 10cm, lo divides en dos partes de manera horizontal tal que

Answers

Answer:

x = 10/√2 ≈ 7.07

Step-by-step explanation:

Comenzaremos por dividir el triángulo en dos partes y definir H, como en la figura adjunta.

Aplicando el teorema de Tales, sabemos que:

\(\dfrac{l/2}{H}=\dfrac{x/2}{h}\\\\\\\dfrac{l}{H}=\dfrac{x}{h}\)

También sabemos que, dado que el tirángulo menor es la mitad que el triángulo mayor, la relación entre áreas es:

\(\dfrac{A}{A_x}=\dfrac{lH/2}{xh/2}=\dfrac{lH}{xh}=2\)

Dado que formamos dos triángulos rectángulos, podemos despejar el valor de H como:

\((l/2)^2+H^2=l^2\\\\H^2=l^2-(l/2)^2=10^2-5^2=100-25=75\\\\H^2=\sqrt{75}\)

Podemos entonces despejar x de la siguiente manera:

\(h=\dfrac{H}{l}\cdot x=\dfrac{lH}{2x}\\\\\\2x^2\dfrac{H}{l}=lH\\\\\\2x^2=l^2\\\\\\x=\dfrac{l}{\sqrt{2}}=\dfrac{10}{\sqrt{2}}\approx7.07\)

Tienes un tringulo equiltero con lados de 10cm, lo divides en dos partes de manera horizontal tal que
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