A flower 3 in. tall grows an average of 1.5 in. each month. Which equation models the flower’s height h after x months?


3 = x + 1.5


h = 3x + 1.5


h = 1.5x + 3


1.5 = x + 3

Answer:

[tex]y-\frac{3}{2}=\frac{-13}{3}(x-\frac{1}{2})[/tex] point-slope form

[tex]13x+3y=11[/tex] (standard form)

Let me know if you prefer another form.

Step-by-step explanation:

The slope of a line can be found using [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] provided you are given two points on the line.

We are.

Now you can use that formula.  But I really love to just line up the points vertically then subtract them vertically then put 2nd difference over 1st difference.

 (4/5  ,  1/5)

-( 1/2  ,  3/2)

-----------------

3/10          -13/10

2nd/1st = [tex]\frac{\frac{-13}{10}}{\frac{3}{10}}=\frac{-13}{3}[/tex] is our slope.

So the following is point-slope form for a linear equaiton:

[tex]y-y_1=m(x-x_1) \text{ where } m \text{ is slope and } (x_1,y_1) \text{ is a point on the line }[/tex]    

Plug in a point [tex](x_1,y_1)=(\frac{1}{2},\frac{3}{2}) \text{ and } m=\frac{-13}{3}[/tex].

This gives:

[tex]y-\frac{3}{2}=\frac{-13}{3}(x-\frac{1}{2})[/tex]

I'm going to distribute:

[tex]y-\frac{3}{2}=\frac{-13}{3}x-\frac{-13}{6}[/tex]

Now I don't like these fractions so I'm going to multiply both sides by the least common multiply of 2,3, and 6 which is 6:

[tex]6y-9=-26x+13[/tex]

Add 26x on both sides:

[tex]26x+6y-9=13[/tex]

Add 9 on both sides:

[tex]26x+6y=22[/tex] This is actually standard form of a line.

It can be simplified though.

Divide both sides by 2:

[tex]13x+3y=11[/tex] (standard form)

Answer:

[tex]\large\boxed{y=-\dfrac{13}{3}x+\dfrac{11}{3}}-\bold{slope\ intercept\ form}\\\boxed{13x+3y=11}-\bold{standard\ form}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

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

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points

[tex]\left(\dfrac{4}{5},\ \dfrac{1}{5}\right),\ \left(\dfrac{1}{2},\ \dfrac{3}{2}\right)[/tex]

Convert fractions to the decimals

(divide the numerator by the denominator) :

[tex]\dfrac{4}{5}=0.8,\ \dfrac{1}{5}=0.2,\ \dfrac{1}{2}=0.5,\ \dfrac{3}{2}=1.5[/tex]

[tex]\left(\dfrac{4}{5},\ \dfrac{1}{5}\right)=(0.8,\ 0.2)\\\\\left(\dfrac{1}{2},\ \dfrac{3}{2}\right)=(0.5,\ 1.5)[/tex]

Calculate the slope:

[tex]m=\dfrac{1.5-0.2}{0.5-0.8}=\dfrac{1.3}{-0.3}=-\dfrac{13}{3}[/tex]

Put the value of slope and the coordinates of the first point to the equation of a line:

[tex]0.2=-\dfrac{13}{3}(0.8)+b[/tex]      multiply both sides by 3

[tex]0.6=(-13)(0.8)+3b[/tex]

[tex]0.6=-10.4+3b[/tex]           add 10.4 to both sides

[tex]11=3b[/tex]           divide both sides by 3

[tex]\dfrac{11}{3}=b\to b=\dfrac{11}{3}[/tex]

Finally:

[tex]y=-\dfrac{13}{3}x+\dfrac{11}{3}[/tex] - slope-intercept form

Convert to the standard form (Ax + By = C):

[tex]y=-\dfrac{13}{3}x+\dfrac{11}{3}[/tex]      multiply both sides by 3

[tex]3y=-13x+11[/tex]          add 13x to both sides

[tex]13x+3y=11[/tex] - standard form

Answer:

32.49

Step-by-step explanation:

First you must set up the probably and plug in the variables into the formula. Sthe formula would turn into the equation: C=30.99 (c for cost) + .5 [r for tax] (30.99) c for cost. Then you will solve the equation:

1. C= 30.99+.5(30.99)

2. C= 30.99+ 1.50

3. C= 32.49

Answer:

The total cost of the shoes is $32.5395.

Step-by-step explanation:

The equation that you must use is [tex]C=p+p\times r[/tex]. Keep in mind that percentage number is the number divided by 100 in real numbers. For example, 5% equals 0.05. So, instead of using the term 5%, you must use 0.05.

Now, let's replace the variables in the equation with the data that the problem gives.

[tex]C=p+p\times r[/tex]

[tex]C=(30.99)+(30.99)\times (0.05)[/tex]

[tex]C=30.99+1.5495[/tex]

The term $1.5495 refers to the tax that must be paid for the shoes. The total cost is the sum of the price and the tax.

[tex]C=32.5395[/tex]

Thus, the total cost of the shoes is $32.5395.

Answer:

[tex]\large\boxed{\dfrac{5}{11}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ P(A\ \cup\ B)=P(A)+P(B)-P(A\ \cap\ B).\\\\\text{We have:}\\\\P(A)=\dfrac{4}{11},\ P(B)=\dfrac{3}{11},\ P(A\ \cup\ B)=\dfrac{2}{11}.\\\\\text{Substitute:}\\\\\dfrac{2}{11}=\dfrac{4}{11}+\dfrac{3}{11}-P(A\ \cap\ B)\\\\\dfrac{2}{11}=\dfrac{7}{11}-P(A\ \cap\ B)\qquad\text{subtract}\ \dfrac{7}{11}\ \text{from both sides}\\\\-\dfrac{5}{11}=-P(A\ \cap\ B)\qquad\text{change the signs}\\\\P(A\ \cap\ B)=\dfrac{5}{11}[/tex]

Answer:

See below in bold.

Step-by-step explanation:

(g + h)(x) = 4x - 4 + x - 5

= 5x - 9.

(g - h)(x) = 4x - 4 - (x - 5)  ( Note we put the x - 5 in parentheses)

= 4x - 4 - x + 5

=  3x + 1.

(g.h)(x) = (4x - 4)(x - 5)

so (g.h)(1) = (4(1) - 4)(1 - 5)

= 0 * -4

= 0.

The product of the functions will be (g·h)(x) = 4x² – 24x + 20. At x = 1, the product of the functions is zero.

A statement, principle, or policy that creates the link between two variables is known as a function.

The functions are given below.

g(x) = 4x – 4

h(x) = x – 5

Then the sum of the functions will be

(g + h)(x) = (4x – 4) + (x – 5)

(g + h)(x) = 4x – 4 + x – 5

(g + h)(x) = 5x – 9

Then the difference in the functions will be

(g – h)(x) = (4x – 4) – (x – 5)

(g – h)(x) = 4x – 4 – x + 5

(g – h)(x) = 3x + 1

Then the product of the functions will be

(g·h)(x) = (4x – 4)(x – 5)

(g·h)(x) = 4x² – 4x – 20x + 20

(g·h)(x) = 4x² – 24x + 20

At x = 1, then we have

(g·h)(x) = 4(1)² – 24(1) + 20

(g·h)(x) = 4 - 24 + 20

(g·h)(x) = 0

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The answer is A.75°

The sum of all the angles of a triangle is 180°

75+35+x = 180.

x = 180-75-35

x = 75

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle.

The sum of all three angles of the triangle is equal to 180 degrees.

The angles of a triangle always add up to 1800 degrees because one exterior angle of the triangle is equal to the sum of the other two angles in the triangle. When all the angles are added up, the sum obtained should be 180 degrees.

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Answer:

it is 11 degrees and i did the doom quiz and passt so yeah bye peace

For this case we have that the rug is rectangular.

By definition, the perimeter of a rectangle is given by:[tex]P = 2a + 2b = 2 (a + b)[/tex]

Where:

a, b: Represent the sides of the rectangle

Substituting according to the data we have:

[tex]P = 2 (5 + 3)[/tex]

Thus, the correct expression is option B.

Answer:

Option B

Answer:

Step-by-step explanation:

length=sqare root of(12^2+12^2-2*12*12*cos(75))=14.6

The length of a chord whose central angle is 75° in a circle with a radius of 12 inches is 14.6 inches.

A circle is the set of all points in the plane that are a fixed distance (the radius) from a fixed point (the center)

A central angle is an angle with endpoints and located on a circle's circumference and vertex located at the circle's center

[tex]cos A = \frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex], where a, b ,c are the sides opposite to ∠A, ∠B, ∠C respectively.

In triangle, let ∠A = 75°.

∴ We can write, [tex]cos 75 = \frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex].

So,  we can write,

(cos 75)(2 x 12 x 12) = (12)² + (12)² - a²

⇒ a = 14.6

∴ the length of the chord is 14.6 inches.

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Answer:

y= -5x+12

Step-by-step explanation:

slope int form ; y=mx+b

that is the only option in that form.

Answer:

the equation is y = 5x + 12

Step-by-step explanation:

The equation of line is 10x - 2y=-2

Write this equation in slope intercept form of line y = mx + b

[tex]10x-2y=-2\\\\2y=10x+2\\\\y=5x+1[/tex]

Therefore, the slope of the line is m = 5

Now, we know that parallel lines have same slope.

Hence, slope of the required line is also 5.

Thus, the equation of line is in the form y = 5x + b

Now, use the point (0,12) to find b

12= 5(0) + b

b = 12

Hence, the equation is y = 5x + 12

Answer:

-6

Step-by-step explanation:

[tex]m^2-36=0[/tex]

Adding 36 on both sides gives:

[tex]m^2=36[/tex]

Square rooting both sides:

[tex]m=\pm \sqrt{36}[/tex]

[tex]m=\pm 6[/tex]

So if square -6 , you will get 36 just like when you square 6.

That is [tex](-6)^2=6^2=36[/tex]

Answer:

-6

Step-by-step explanation:

If one solution to the problem m²-36=0 is 6, the other solution is -6.

(m + 6) • (m - 6)  = 0

Any solution of term = 0 solves product = 0 as well.

m+6 = 0  

m = -6

m-6 = 0

m = 6

Answer:

The correct option is C

Step-by-step explanation:

81x²+72x+16

We have to break the middle term:

If we multiply 81 by 16 we get 1296:

The same answer we get when we multiply 36 by 36:

36*36=1296

And if we add 36+36 then we get the middle term which is 72.

So,

=81x²+72x+16

=81x²+36x+36x+16

=9x(9x+4)+4(9x+4)

=(9x+4)(9x+4)

Thus the correct option is C ....

Answer:

[tex]7\sqrt{2}[/tex]

Step-by-step explanation:

We start by factoring 98 and look for a perfect square:

98=7*7*2 = [tex]7^{2} *2[/tex]

This allow us to simplify the radical:

[tex]\sqrt{98} = \sqrt{7^{2}*2 }[/tex]

Finally we have:

[tex]\sqrt{7^{2}*2 } =7\sqrt{2}[/tex]

Answer:

[tex]\frac{3}{11}=\frac{21}{y}[/tex]

Step-by-step explanation:

3 boys     ->   8 girls     -> 11 students

21 boys   ->   _____     ->  y students

This information is lined up for you to solve for your number of students, y:

Looking vertically you could say the proportion is:

[tex]\frac{3}{21}=\frac{11}{y}[/tex]

Looking horizontally you could say the proportion is:

[tex]\frac{3}{11}=\frac{21}{y}[/tex]

There are other ways to write this but this last one I wrote answers your question.

Answer:

American Bison

Step-by-step explanation:

First find out how many feet the bison runs in an hour.

To find that out you have to multiply 3520 by 60 minutes because there are 60 minutes in an hour.

So 3520*60 = 211,200 feet

Then you have to convert 211,200 feet into miles and since there are 5,280 feet in an a mile you have to divide.

So 211,200 divided by 5,280 = 40

So the American Bison runs 40 miles per hour which is faster than the White Tailed Deer who only runs 30 miles per hour.

So the answer is the American Bison.

Answer:

The integers are -5 , -6 ⇒ answer C

Step-by-step explanation:

* Lets explain the meaning of consecutive numbers

- Consecutive numbers are numbers that follow each other in order.

-  They have a difference of 1 between every two numbers

- Consider that the smaller of two consecutive integer is n, then the

  larger one will be n + 1

* In the problem

∵ The larger of the two consecutive integers is 7 greater than twice

  the smaller

- That means the larger one is 7 plus twice the smaller

∵ The smaller one is n

∵ The larger one is n + 1

∴ n + 1 = 2(n) + 7

∴ n + 1 = 2n + 7

- Subtract n from both sides

∴ 1 = n + 7

- Subtract 7 from both sides

∴ -6 = n

∴ The smaller number is -6

∵ The greater number is n + 1

∴ The greater number = -6 + 1 = -5

* The integers are -6 , -5

Answer:

- 90

Step-by-step explanation:

These are the terms of an arithmetic sequence with n th term

[tex]a_{n}[/tex] = a + (n - 1)d

where a is the first term and d the common difference

d = 6 - 9 = 3 - 6 = - 3 and a = 9, hence

[tex]a_{34}[/tex] = 9 - 3 × 33 = 9 - 99 = - 90

The [tex]a_{34}[/tex] is -90 in the given sequence.

The given sequence is 9,6,3,......

We are asked to find the [tex]34^{th}[/tex] term in the sequence which is denoted by  [tex]a_{34}[/tex].

We first need to know what type of sequence is given in the question.

A sequence where the difference between the consecutive terms is always the same.

The formula used to find the value of the required term is given by:

[tex]a_n = a + (n-1)d[/tex]

Where a = first term, n = the term value and d = common difference.

The given sequence is 9,6,3,.....

We see that the given sequence is an arithmetic sequence.

6 - 9 = -3 and 3 - 6 = -3

so,

d = -3.

Here a = 9.

And we need to find the value in the sequence at n = 34.

substituting a,d, and n values in  [tex]a_n = a + (n-1)d[/tex].

We get,

[tex]a_{34} = 9 + ( 34 - 1 ) (-3)\\a_{34} = 9 + 33(-3)\\a_{34} = 9 - 99\\a_{34} = -90[/tex]

Thus, the [tex]a_{34}[/tex] is -90 in the given sequence.

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Answer:

A) 0.0194

B) 1.94%

C) $ 170,000

Step-by-step explanation:

Value of house in 1992 = P = $ 120,000

Value of house in 2007 = S = $ 160,000

Time difference from 1992 to 2007 = 15 years

Part A)

The formula of compound interest is:

[tex]S=P(1+r)^{t}[/tex]

P is the original amount i.e. $ 120,000

t is the time in years which is 15 years

S is the amount after t years which is $ 160,000

r is the annual growth rate

Using the values, we get:

[tex]160000=120000(1+r)^{15}\\\\\frac{160000}{120000}=(1+r)^{15}\\\\ \frac{4}{3}=(1+r)^{15}\\\\(\frac{4}{3} )^{\frac{1}{15}}=1+r\\\\ r=(\frac{4}{3} )^{\frac{1}{15}}-1\\\\ r=0.0194[/tex]

Thus, the annual growth rate is 0.0194

Part B)

In order to convert a decimal to percentage, simply multiply the decimal by 100.

So, 0.0194 in percentage would be 1.94%

Part C)

We have to find the value of house in 2010 i.e. after 18 years. So t =18

Using the values in the formula, we get:

[tex]S=120000(1+0.0194)^{18}\\\\ S=169584[/tex]

Rounded to nearest thousand dollars, the value of the house would be $ 170,000

[tex]g(f(x))=3x+2+5=3x+7[/tex]

Answer:

75 in^2

Step-by-step explanation:

L = 3W here.  Also, P = 2W + 2L = 40 in here.  Subbing 3W for L, we get

                                    2W + 2(3W) = 40, or

                                     2W + 6W = 40, or 8W = 40.  Thus, W = 5 in and L = 15 in

and the area is W*L, or 5(15) in^2, or 75 in^2

The width of the rectangle is 5 inches and the length is 15 inches. Therefore, the area of this rectangle is 75 square inches.

Let's indicate the width of the rectangle as 'w'. Given the length is three times the width, it would be represented as '3w'. The perimeter of any rectangle is calculated as 2*(length + width). Therefore, 2*(w + 3w) = 40. Solving this, we get 'w' as 5 inches and, therefore, the length as 15 inches.

The area of a rectangle is calculated by multiplying the length and width. Therefore, the area of this rectangle would be length * width = 15*5 = 75 square inches.

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Answer:

The area of the field = 19966.21 units²

Step-by-step explanation:

* Lets explain how to find area of a triangle by trigonometry rule

- In any triangle if you have the lengths of two sides and the measure

 of the including angle between these two sides, then the area of the

 triangle is A = [tex]\frac{1}{2}s_{1}s_{2}sin\alpha[/tex] , wher α is the

 including angle between them

* Lets solve the problem

∵ The field is shaped triangle

∵ The lengths of two sides of the field are 218.5 and 213.3

∴ s1 = 218.5

∴ s2 = 213.3

∵ The measure of the angle between the two sides is 58.96°

∴ α = 58.96°

- Lets find the area using the rule of trigonometry

∴ [tex]A=\frac{1}{2}(218.5)(213.3)sin(58.96)=19966.21[/tex]

∴ The area of the field = 19966.21 units²

Answer:

W (-1, 4) ---> W' (-4, -1)

X (-1, 2)  ---> X' (-2, -1)

Y (2, 2)  ---> Y' (-2, 2)

Z (2, 4)  ---> Z' (-4, 2)

Step-by-step explanation:

We are given the graph with a rectangular figure WXYZ and we are to find the coordinates of its vertices W'X'Y'Z' after the transformation of 90° rotation.

We know that, the rule for 90° rotation of a point (x, y) gives (-y, x).

So,

W (-1, 4) ---> W' (-4, -1)

X (-1, 2)  ---> X' (-2, -1)

Y (2, 2)  ---> Y' (-2, 2)

Z (2, 4)  ---> Z' (-4, 2)

Answer

W'

✔(-4,1)

X'

✔ (-2, -1)

Y'

✔ (-2, 2)

✔Z'(–4, 2)

Step-by-step explanation:

To solve for the amount of pure silver in the alloy mixture, use the alloy mixture equation in algebra. After setting up and solving the equation, we find that roughly 22.83 ounces of pure silver are used to produce the desired alloy,

This problem can be solved using the alloy mixture equation, which is used to determine how to create a desired mixture by blending two substances of different concentrations. Let's denote the amount of pure silver used as 'x'. So, the equation can be set up as follows:

($30.48 × x + $21.35 × 52) / (x + 52) = $24.76.

After multiplying through by (x + 52) and doing algebra, you will find that x (ounces of pure silver) equals approximately 22.83 ounces.

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Answer:

slope = - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 3 = - [tex]\frac{1}{2}[/tex](x - 2) ← is in point- slope form

with slope m = - [tex]\frac{1}{2}[/tex]

Answer:

10 cm

Step-by-step explanation:

If the length of a rectangle is equal to triple the width, the width of the rectangle is 10 cm if the perimeter is 80 centimeters.​

L = 3w

P = 80

Formula: a = l × w

8W = 80 cm

W = 80 / 8 = 10 cm

Therefore, the width of the rectangle is 10 centimeters.

The width of the rectangle is found to be 10 centimeters, obtained by solving the equation created based on the fact that the perimeter of a rectangle is 2(length + width) and the given data that length is thrice the width and perimeter is 80 cm.

To figure out the width of the rectangle, we first need to understand the relationship between the length and width, and how they relate to the perimeter. The length of the rectangle is triple the width. Let's define the width as 'w'. Therefore, the length would be '3w'.

The formula for the perimeter of a rectangle is 2(length + width).

Given that the perimeter is 80 centimeters, we can set up the equation 2(3w + w) = 80. Simplifying this gives 8w = 80. To find the width 'w', we divide both sides of the equation by 8, giving us w = 10 centimeters.

Therefore, the width of the rectangle is 10 centimeters.

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Answer: 123.5 in^2

Step-by-step explanation: The formula for the area of a trapezoid is a+b/2 x h. In other words, base 1 plus base 2 divided by 2, and multiplied by the height. Plug in the numbers. The equation is:

6+7/2 x 19 = 123.5.

Since you are finding the area, the answer would be in inches squared. The answer is 123.5 in^2.

Answer:

B and C

Step-by-step explanation:

There are 3 conditions for the difference of squares.

The correct answer is B and C

Final answer:

Binomials that are a difference of squares have the form a² - b² and can be factored into (a + b)(a - b), where both terms are perfect squares. Examples include x² - 9 and 4y² - 25.

Explanation:

To determine which binomials are a difference of squares, we look for expressions in the form of a2 - b2. A difference of squares can be factored into (a + b)(a - b), where a and b are any expressions. It is essential that both terms be perfect squares and that they are subtracted from one another.

For example, x2 - 9 is a difference of squares as it can be factored into (x + 3)(x - 3), where both x2 and 9 are perfect squares. Another example could be 4y2 - 25, which factors to (2y + 5)(2y - 5). Keep in mind that if the sign is not subtraction, or if either term is not a perfect square, the binomial does not represent a difference of squares. The correct choice of examples, factoring process, and the nature of perfect squares are essential to identify differences of squares accurately.

(gºf) means solve f(x) first, then use that for g(x)

In the equation for f(x) replace x with -3:

f(x) = x +4 = -3 +4 = 1

Now replace the x in the equation for g(x) with 1

g(x) = x = 1

In the system of equations, x represents the number of tickets of Level 1 seats while y represents the number of tickets of Level 2 seats.

Given to us,

system of equations,

Equation 1, 150x + 250y = 125,000,

Equation 2,  x + y = 50,000,

Total number of seats = 50,000 seats,

Total number of sales = $125,000,

Level 1 tickets price = $150,

Level 2 tickets price = $250,

Let us assume, Number of tickets of Level 1 is [tex]\bold x[/tex], and, Number of tickets of Level 2 is [tex]\bold y[/tex],

Total sales = (Number of tickets of Level 1 x Level 1 tickets price ) + (Number of  tickets of Level 2 x Level 2 tickets price )

125,000 = ([tex]\bold x[/tex] x 150) + ([tex]\bold y[/tex] x 250)

125,000 = 150x + 250y

Now,

Total number of seats = Number of tickets of Level 1 + Number of tickets of Level 2

50,000 = x + y

Therefore, In the system of equations, x represents the number of tickets of Level 1 seats while y represents the number of tickets of Level 2 seats.

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The variables x and y represent the number of Level 1 and Level 2 tickets sold, respectively. These variables show how many of each type of ticket were sold at their respective prices ($150 and $250) to achieve a total sale of $125,000.

The problem presents a linear system of equations that models the pricing of tickets sold at a concert.

The equations are:

In this system:

Therefore, these equations together show the total number of tickets sold and the total revenue from these tickets.

Answer:

Height of light post = 33 feet

Step-by-step explanation:

We will use the trigonometric ratios to find the height of light post

The given scenario forms a right angled triangle with the right angle with the light post.

The distance between light post and the person is the base.

So, base = b = 40 feet

The height of light post will be the perpendicular

So,

Perpendicular = p = x

Angle = 35°

So,

tan (angle) = p/b

tan 35° = p/40

0.7002 =p/40

0.7002*40 = p

p = 28 feet

Since the persons eye level is 5 feet from the ground, 5 feet will be added to perpendicular for actual height of light post.

Height of light post = 28+5 = 33 feet ..