A plant is already 45 centimeters tall, and it will grow one centimeter every month.Let h be the plant's height (in centimeters) after m months.Write an equation relating h to m . Then use this equation to find the plant's height after 14 months.

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

As per the given information ~

The given triangles are similar, so their corresponding sides should be in same ratio :

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2x}{4} = \cfrac{5}{x - 3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{x}{2} = \cfrac{5}{x - 3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x(x - 3) = 10[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} - 3x = 10 [/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} - 3x - 10 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} - 5x + 2x - 10 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: x(x - 5) + 2(x - 5) = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: (x + 2)(x - 5) = 0[/tex]

so, x = 5 or -2

but since side length can't be negative, we will take x = 5 neglecting the negative value (-2)

So, side lengths of unknown sides are :

[tex] \qquad \sf  \dashrightarrow \: {2x = 2 × 5 = 10 units} [/tex]

and

[tex]\qquad \sf  \dashrightarrow \: x - 3 = 5 - 3 = 2 \: \: units[/tex]

Answer:

3x³ + 3x² - 30x - 48

Step-by-step explanation:

3(x + 2)(x² - x - 8) ← distribute (x + 2) by 3

= (3x + 6)(x² - x - 8)

each term in the second factor is multiplied by each term in the first factor

= 3x(x² - x - 8) + 6(x² - x - 8) ← distribute both parenthesis

= 3x³ - 3x² - 24x + 6x² - 6x - 48 ← collect like terms

= 3x³ + 3x² - 30x - 48

Answer:

7

Step-by-step explanation:

5x+3=38 subtract the 3 from the 38 leaving you with 35/5 getting you 7

The value of x in the given parallelogram is 7.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

So 5x+3=38

We need to find the value of x

Subtract 3 from both sides

5x=38-3

5x=35

Five times of x equal to thirty five

Divide both sides by 5

x=7

Hence, the value of x in the given parallelogram is 7.

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Answer:

1. Translate 5 units up (Fixed after a comment from subtomex0 - Thanks again!)

2. Vertical Compression by a scale factor of 3/8

3. Reflect across the y-axis, and shift 2 units to the left

4. Vertical stretch by a scale factor of 6, and shifting 1 unit up

5. Shifting 11 units to the left

6. Vertical stretch by a scale factor of 8

7. Vertical compression by a scale factor of 1/2, and reflection across the y-axis.

Answer:

( x-3) ^2 + ( y-1) ^2 = 4

Step-by-step explanation:

The equation for a circle is given by

( x-h)^2 + ( y-k) ^2 = r^2  where (h,k) is the center and r is the radius

( x-3) ^2 + ( y-1) ^2 = 2^2

( x-3) ^2 + ( y-1) ^2 = 4

The exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5

If an angle of measure 120 degrees intersects the unit circle at point (-1/2,√3/2), the measure of cos(120) can be expressed as;

Cos120 = cos(90 + 30)

Using the cosine rule of addition

cos(90 + 30) = cos90cos30 - sin90sin30

cos(90 + 30) = 0(√3/2) - 1(0.5)

cos(90 + 30) = 0 - 0.5

cos(90 + 30) = 0.5

Hence the exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5

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Answer:

It's -0.5

Explanation:
Answered it

Answer:

30

Step-by-step explanation:

18/60 =.3 x 100 = 30

The value of angle C in the triangle is 50°.

From the information given, the angle A = 60° while B is given as 70° and we are told to calculate the value of C.

It should be noted that the sum of angles on a triangle is 180°. Therefore, the value of C will be:

= 180° - (60° + 70°)

= 180° - 130°

= 50°

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Answer: 30%

Step-by-step explanation:

The Number of teams is  mathematically given as

N= 30100

Generally, the equation for Number of teams is  mathematically given as

X items are selected from n items by [tex]^nC_x[/tex] ways

[tex]^nC_x = \frac{n!}{ [ (n-x)! * x! ]}[/tex]

Number of teams

N= n(1 child and 3 adults) + n(2 child and 2 adults) + n(3 child and 1 adults) + n(4 child)

N= 16C1 * 15C3 + 16C2 * 15C2 + 16C3 * 15C1 + 16C4 * 15C0

N= 16 * 455 + 120 * 105 + 560 * 15 + 1820

N= 30100

In conclusion, the Number of teams

N= 30100

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Answer:  0.0059   (choice C)

Explanation:

There are 4 jacks out of 52 cards total.

4/52 = 1/13 is the probability of getting a jack.

The same applies to an ace as well.

The probability of a jack followed by an ace is (1/13)*(1/13) = 0.0059 approximately, when we replace the first card. If the replacement wasn't done, then the second probability would be different from 1/13.

[tex]8 \: cars = 120 \: dollars \\ 1 \: car = \frac{120}{8} = 15 \: dollars[/tex]

[tex]m(c) = 15c[/tex]

Answer:

d: m=15c

Step-by-step explanation:

Usually (not always), variable y depends on variable x.

Since in this question, the amount of money Paul can earn changes based on the number of cars he washes, y is the amount of money, and x is the number of cars he washes.

This can be represented as: 120 = 8 times ___

___ is the amount of money Paul earns by cleaning 1 car.

___ is 120 divided by 8, which is 15.

--> Paul earns $15 by cleaning each car.

The new equation will be m = 15c

Answer:

the cat would take 13 steps

Answer:

12/5

Step-by-step explanation:

to find tan D you need the opposite and the adjacent sides.

12 is opposite D and 5 is adjacent to D

so using the equation tan=Opposite/adjacent

tanD=12/5

The probability you will roll a sum of 9 is 1/4.

Probability determines the chances that an event would happen. The probability the event occurs is one and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability you will roll a sum of 9 = total times a sum of 9 is derived / total sample spaces

The probability you will roll a sum of 9 = 4/36 = 1/9

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Answer:

x = 8

Step-by-step explanation:

complementary angles sum to 90°

sum the 2 angles and equate to 90

5x + 50 = 90 ( subtract 50 from both sides )

5x = 40 ( divide both sides by 5 )

x = 8

Triangles ABC and triangle PQR are congruent triangles based on angle-side-angle congruency theorem.

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent to each other. Also, their corresponding angles are congruent to each other.

Triangles ABC and triangle PQR are congruent triangles based on angle-side-angle congruency theorem.

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Health club members or were smokers is [tex]334[/tex] from a A survey of [tex]400[/tex] nurses yielded.

How can we find the health club members or were smokers ?

Events of health club members is [tex]P(M)=279[/tex]

Events of smokers is [tex]P(S)=215[/tex]

Probability of health club members and smokers is [tex]p(M and S)=160[/tex]

Probability of health club members or were smokers is =?

So we use the formula

[tex]p(M or S)=p(M)+p(S)-p(M and S)\\ = 279+215-160\\ = 334[/tex]

Probability of health club members or were smokers is [tex]334[/tex]

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The cost of delivering an item that weighs 4/5 of a pound?$21.60.  

Let x = the number of pounds

Thus, we can say that;

Cost = 25x * 1.08

Since we want to find the cost of delivering an item that weighs 4/5 of a pound, the we will put 4/5 for x to get;

Cost = (25 * 4/5) * 1.08

Cost = 20 * 1.08

Cost = 21.6

The delivery cost would be $21.60.  

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equation of a line is y=mx+ c

where m is that gradient and c is y intercept

so first we find the gradient (m)

M= change in y intercept ÷change in x

M=4-2÷5-1

M=2÷4=1/2(as a fraction)(you can also use o.5)

there 1/2is the gradient

then to find the equation of the line

y= 1/2x +c (from coordinates 1,2 we substitute)

2=1/2(1)+c

2-1/2=c

c=1.5

or

from the coordinates 5,4

4=1/2(5) +c

4=5/2+ c

c=4-5/2

c=1.5

equation of the line=y=0.5x + 1.5

or y=1/2x +1.5

hope it helps you^_^

Answer:

b

Step-by-step explanation:

edge

Answer:

volume = 3549.203

Step-by-step explanation:

you need to subtract the volume of the cylinder from the volume of the box

cylinder:

[tex]vol=\pi r^2h\\V=\pi (5)^2(20)\\V=\pi (25)(20)\\V=500\pi[/tex]

box:

[tex]vol=(length)(width)(height)\\V=(20)(16)(16)\\V=5120[/tex]

subtract:

[tex]5120-500\pi =3549.203[/tex]

[tex]3/ 5x^6*y^6[/tex] is the solution f the expression [tex](-9x^-1*y^-9) / (-15x^5*y^-3)[/tex]

Given expression:

(-9x^-1*y^-9) / (-15x^5*y^-3)

As we know, any number with negative power can be written in inverse form with positive power.

[tex]x^-a = 1/x^a[/tex]

Two number having same base their powers are added:

[tex]x^a + x^b = x^a+b[/tex]

[tex]= > (-9x^-1*y^-9) / (-15x^5*y^-3)= (-3x^-1*y^-9) / (-5x^5*y^-3)\\=3/(5x^6 y^6)[/tex]

Hence the solution would be [tex]3 (5x^6 y^6)[/tex].

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Answer:

b

Step-by-step explanation:

Answer:

  x = 7

Step-by-step explanation:

The integer values of x that satisfy |x| < 9 are ...

  {-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7. 8}

Of these values, the only one listed as an answer choice is ...

  x = 7

__

Additional comment

The expression |x| means "the absolute value of x". It is the value of x with the sign made positive. That is |-10| = 10, a number greater than 9. Of course, |13| = 13, also a number greater than 9.

The distance they finishes is 8.6 miles

Given that miles run by Joni is 5 miles and the miles ran by Lori is 7 miles

We need to find the distance they finished

To calculate the total distance along the diagonal line, the Distance Formula first squares the differences between the two x coordinates and the two y coordinates, then adds those squares, and finally calculates their square root.

We know that

According to the Distance formula

= [tex]\sqrt{(5)2+(7)^2}[/tex]

= [tex]\sqrt{25+49}[/tex]

= [tex]\sqrt{74}[/tex]

= 8.6 miles

Therefore the distance finished is 8.6 miles

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The instantaneous rate of change of the function is 5/π

The function is given as

[tex]f(x) =\cos(x - \pi) + 4[/tex]

Where

[tex]x = \pi[/tex]

Calculate f(π) as follows

[tex]f(\pi) =\cos(\pi - \pi) + 4[/tex]

This gives

[tex]f(\pi) =\cos(0) + 4[/tex]

Evaluate the expression

[tex]f(\pi) =5[/tex]

The instantaneous rate of change is then calculated as;

[tex]f'(x) = \frac{f(\pi)}{\pi}[/tex]

This gives

[tex]f'(x) = \frac{5}{\pi}[/tex]

Hence, the instantaneous rate of change of the function is 5/π

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The choice which best describes how to measure the center of these data is; both centers are best described by the median.

This is a measure of central tendency which helps determine the middle value in a data by rearranging the data either in an ascending order or a descending order.

Mean on the other hand, is used to find the best average of a data set.

Therefore, the mean cannot be used to find the center of the data.

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Answer:

118

Step-by-step explanation:

The total area is the area of the large rectangle in the middle plus the areas of the two triangles.

The length of the entire rectangle is 5 cm + 5 cm + 4 cm = 14 cm.

The width of the rectangle is 7 cm.

Each triangle has a base of 4 cm and a height of 5 cm.

A = LW + 2 × (1/2)bh

A = (14 cm)(7 cm) + (4 cm)(5 cm)

A = 98 cm² + 20 cm²

A = 118 cm²