In the figure below, there are three right trangles. Complete the following.
A
C
D
B
(a) Write a similiarity statement relating the three right triangles.
ACDA~A~A
(b) Complete each proportion.
BD
BC
BC
DA
DC
=
0
BD
X
5

When the state of an object is changed from one to another it is known as translation in mathematics and they are of three types.

The three types of translation in math are

When the object moves either from left to right or from right to left it is known as vertical translation.

The movement in up or downward direction of the graph is known as  horizontal translation.

The domain of the function remains same in both the cases.

A translation in which the size of the object decreases or is compressed is known as the compression translation.

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To change logarithmic form to exponential form, spot the logarithmic equation's base and move the base to another side to the equal sign. Moving the base will make the current number or variable into the exponent.

Do not move something but the base: the other numbers or value will not change sides, and the word "log" will be release.

Log Rules:

1. the first rule is logb(mn) = logb(m) + logb(n)

2. the second rule is logb(m/n) = logb(m) – logb(n)

3. the third rule is: log b (mn) = n · logb(m)

1. Multiplication can be turned outside the log into addition and vice versa can be turned.

2. Division can be spin outside the log into a subtraction, and vice versa.

3. An exponent can be proceeded as a multiplier outward on all within a log, and vice versa.

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Answer:

See below.

Step-by-step explanation:

I'm assuming these questions are about the Midline Theorem (segment AL joins the midpoints of the non-parallel sides.

♦  The midline's length is the average of the lengths of the top and bottom parallel sides.

[tex]AL=\frac{OR+CE}{2}[/tex]

Use this equation and substitute values given in each problem, then solve for the missing information.

1. AL = x, CE = 9, OR = 5

[tex]x=\frac{9+5}{2}=7[/tex]

2. AL = m - 4, CE = 15, OR = 17

[tex]m-4=\frac{15+17}{2}=16\\\\m-4=16\\\\\\m=20\\\\AL=20-4=16[/tex]

3. OR = y + 5, AL = 15, CE = 18

[tex]15=\frac{(y+5)+18}{2}\\\\15=\frac{y+23}{2}\\\\30=y+23\\\\7=y\\\\OR = 7+5=12[/tex]

Answer:

5n

Step-by-step explanation:

(7^5 * 7^n) ^ 4   = (7^11/7^n)^3

7^(20 + 4n)   =  4.7^15 / n^3

= 20/4 = 5n   and  15/3 = 5n

Answer 5n

The standard form of linear function y = - (1 / 2) · x + 6 is (1 / 12) · x + (1 / 6) · y = 1.

In this question we find a linear function in slope-intercept form:

y = m · x + b

Where:

From which we must obtain the linear function in standard form:

a · x + b · y = c

Where:

We can derive the standard form of the linear equation by algebra properties:

y = m · x + b

(1 / b) · y = (m / b) · x + 1

- (m / b) · x + (1 / b) · y = 1

If we know that m = - 1 / 2 and b = 6, then the equation of the line in standard form is:

- [(- 1 / 2) / 6] · x + (1 / 6) · y = 1

(1 / 12) · x + (1 / 6) · y = 1

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Answer:

a = 14.9; b = 11.1

Step-by-step explanation:

SOHCAHTOA:

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

[tex]cos48[/tex]° : adjacent is 10, and hypotenuse is a

    [tex]cos48=10/a; a*cos48=10;a=10/cos48[/tex]

    type 10/cos48 into calculator to get a = 14.9

[tex]sin48[/tex]° : opposite is b, and hypotenuse is a

    [tex]sin48=b/a; sin48=b/14.9; b=14.9*sin48[/tex]

    type 14.9*sin48 into calculator to get b = 11.1

The equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

What is a linear equation?

A linear equation is an equation that can be written in the form of

y = mx + b

Where x and y are variables and m and b are constants. This is also known as the slope-intercept form of a linear equation. The slope of the line (m) represents the steepness of the line and the y-intercept (b) represents the point where the line crosses the y-axis.

Luciana is adding water to the pool at a constant rate of 9 gallons per minute. So, for every minute that passes, the number of gallons in the pool increases by 9. This relationship can be represented by the equation W = 12,000 + 9m, where W is the total number of gallons in the pool and m is the number of minutes that have passed.

Hence, the equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

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The equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

Option (D) is correct.

What is a linear equation?

A linear equation is an equation that can be written in the form of

y = mx + b

Where x and y are variables and m and b are constants. This is also known as the slope-intercept form of a linear equation. The slope of the line (m) represents the steepness of the line and the y-intercept (b) represents the point where the line crosses the y-axis.

Luciana is adding water to the pool at a constant rate of 9 gallons per minute. So, for every minute that passes, the number of gallons in the pool increases by 9. This relationship can be represented by the equation W = 12,000 + 9m, where W is the total number of gallons in the pool and m is the number of minutes that have passed.

Hence, the equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

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Answer:

(820 ; 980)

Step-by-step explanation:

Given :

Sample size, n = 80

Number of bilingual from sample = 36

Sample proportion, phat = x / n = 36 / 80 = 0.45

Margin of Error = 4% = 0.04

Interval = sample proportion ± margin of error

0.45 ± 0.04

(0.41 ; 0.49)

(0.41 * 2000 ; 0.49 * 2000)

(820 ; 980)

Answer:

I think this is how....

Step-by-step explanation:

4x + y = 12

4x + y -y = 12 - y

4x = 12

*divide by 4 on each side*

x = 3

Answer:

D)

Step-by-step explanation:

we know that,

Parallel lines have the same slope

given equation is in the form given by

[tex] \displaystyle y = mx + b[/tex]

where m is know

as [tex]m_{parallel}=m[/tex], the answer is -⅔

Answer:10 ft

Step-by-step explanation:

Answer:

x = 10, ∠ EHF = 110°

Step-by-step explanation:

7x and 11x are adjacent angles and sum to 180° , then

7x + 11x = 180

18x = 180 ( divide both sides by 18 )

x = 10

∠ EHF = 11x = 11(10) = 110°

Answer:

EHF = 110 deg

Step-by-step explanation:

From what it looks like 7x and 11x are being used as units of measurment. I can asssume a full circle adds up to 36x because 180deg adds up to 18deg.

If there were a number that was supposed to fill in for x it could be 0 because if the angles in this problem were 110 deg and 70 deg they would make 180 deg which is the straight line that the problem has.

Answer:

3p^3 (-p^4 + 1)

Step-by-step explanation:

The common factor of both -3p^7 and 3p^3 is 3p^3

Divide -3p^7 by 3p^3 and get -p^4

Divide 3p^3 by 3p^3 and get 1

So the factorisation is 3p^3 (-p^4 + 1)

Answer:

The ratio 9 to 12 is greater than 4 to 6.

9/12 = 3/4.

4/6 = 2/3.

3/4 is more.

Answer:

3/4 x

Step-by-step explanation:

The rise is 3 and the run is 4, making the slope 3/4 x

Answer:

C. Ferris wheel

Step-by-step explanation:

Circumference = pi x diameter

Take each of the entries from the diameter column and multiply by 3.14. They are all correct except for the Ferris wheel.

70.5 x 3.14 = 221.37

The x-intercept and the y intercept of the graph of 6x - 3y = 36 are x = 6 and y = -12

How to determine the x-intercept and the y intercept of the graph?

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

6x - 3y = 36

Set y to 0 to determine the x-intercept

So, we have the following representation

6x = 36

Divide by 6

x = 6

Set x to 0 to determine the y-intercept

-3y = 36

Divide by -3

y = -12

hence, the intercepts are x = 6 and y = -12

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Answer:

maximum height is 80 feet

8 seconds until it hits ground

Step-by-step explanation:

-5t(t - 8) = 0

-5t= 0;  t = 0  (this represents the beginning of the throw)

t-8=0;  t = 8   (this represents the end of the throw)

To find maximum height, find the vertex of the graph,

you can use -b/2a to find 't' and then substitute that value back into the function to find h(t)

x = -40÷2(-5)

x = -40/-10

x = 4

h(4) = -5(4²)+40(4)

h(4) = -5(16) + 160 which is 160 - 80 = 80

The number of calories Jina is burning per minute is 0.1 and the slope is 0.1

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

Points, (x, y) = (0, 0) and (150, 15)

The burning rate per minute can then be calculated as

Burning rate per minute = (y₂ - y₁)/(x₂ - x₁)

Substitute the known values in the above equation, so, we have the following representation

Burning rate per minute = (15 - 0)/(150 - 0)

Evaluate the quotient

Burning rate per minute = 0.1

In (a), we have

Burning rate per minute = 0.1

This rate is the same as the slope

Hence, the slope is 0.1

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Answer:

0.243 g/mL

Step-by-step explanation:

Density is grams divided by mL. All you need to do for this is take your values and use them for the equation. Divide 5.7 grams by 23.5 mL

Answer: 8 products in 1 minute

Step-by-step explanation:

6 min=48 products

48/6=8

1 min= 8 products

Answer:

25%

Step-by-step explanation:

Here is my punnett square:

                    D             d           <---parent 1

     D          DD           Dd

     d          Dd           dd

    ^

    |

    |  parent 2

The results: DD, Dd, Dd, dd

DD, Dd: will have dimples because they have a dominant allele in their genotype. So in their phenotype, they will have dimples.

dd: will not have dimples because they do not have the dominant allele for dimples in their genotype. So in their phenotype, they will NOT have dimples.

3 cases (25% chance for DD, 50% chance for Dd, 25% chance for dd)

1/4 is DD is 25%

2/4 is Dd is 50%

and 1/4 is dd is 25%

answer: 25%

Have a nice day!

After solving, the possible domain in interval notation is (0, 7).

In the given question, a researcher is following the growth of a particular type of flower.

The equation to show the height of the plant f(n), in cm, after days (n) = 8(1.05)^n

According to the given information,

The height of the plant is modeled by the function= f(n)

The height of the plant is approximately 11.04cm when the number of days = 7

The days are started from n > 0 and n<=7

Hence the possible domain in interval notation = (0, 7)

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The complete question is:

A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after days (n) = 8(1.05)^n

Part A: When the scientist concluded his study, the height of the plant was approximately 11.26 cm What is a reasonable domain toplot the growth function?

Part B: What does the y-intercept of the graph of the function () represent?

Part C: What is the average rate of change of the function f(n) from n = 2 ton, and what does it represent?

Given:

Dimensions of a block are [tex]\dfrac{1}{3}\times 1\times 1[/tex].

To find:

The number of block that can be fit in a unit cube.

Solution:

Volume of a cuboid is:

[tex]V=l\times b\times h[/tex]

Where, l is length, b is breadth or width and h is the height of the cuboid.

So, the volume of the given block is:

[tex]V_1=\dfrac{1}{3}\times 1\times 1[/tex]

[tex]V_1=\dfrac{1}{3}[/tex]

Dimensions of a unit cube are [tex]1\times 1\times 1[/tex]. So, the volume of the unit cube is:

[tex]V_2=1\times 1\times 1[/tex]

[tex]V_2=1[/tex]

We need to divide the volume of unit cube by the volume of a block to find the number of block that can be fit in a unit cube.

So, the number of blocks that fit in a unit cube is:

[tex]n=\dfrac{V_2}{V_1}[/tex]

[tex]n=\dfrac{1}{\dfrac{1}{3}}[/tex]

[tex]n=3[/tex]

Therefore, the correct option is B.

Answer:

the answer would be "b" 3 because its in 1/3 and the block is 1/3