The table shows the population of a small town over time. The function P = 10,550(1. 1)x models the population x years after the year 2000. A 2-column table with 5 rows. The first column is labeled years after 2000, x with entries 0, 3, 4, 7, 10. The second column is labeled population, P with entries 10,5000; 14,000; 15,500; 20,500; 27,000. For which year would this model most likely be sufficient to make a prediction of the population? 1950 2005 2025 2050.

Answer:

yes

Step-by-step explanation:

For the sides to form a triangle , then the sum of any 2 sides must be greater than the third side

9 + 11 = 20 > 15

9 + 15 = 24 > 11

11 + 15 = 24 > 9

The 3 sides given will form a triangle

Note that

The length of any two sides must be greater than the third side

So

Yes it's a triangle

[tex]\huge \tt༆ Answer ༄[/tex]

The respective terms used for the lines are ~

Step-by-step explanation:

a is tangent

b radius

c diameter

d chord

5x = 10 + 3x

5x - 3x = 10

2x = 10

x = 5

To check

5(5) = 10 + 3(5)

25 = 10 + 15

25 = 25

Answer:

x = 5

Step-by-step explanation:

Number = x

5x = 10 + 3x  

2x = 10

x = 5

Answer:

32

...when you subtract five from 37

It is a pattern that goes:

-13

-11

-9

-7

and now -5 = 32

Answer:

Step-by-step explanation:

The area of the square is 3 units by 3 units. because the area of a square is side length squared.

side length = 3

side length^2 = 3 * 3 = 9

The area of a circle is much harder to reason out. You could start with the area of a square and use the diameter is 3 units. But the corners are rounded and you don't know off hand what the area of one of them is, let alone all 4. You are given a formula for circles area, but you have no real idea what the formula actually means. Does it take the corner area into account? At the beginning levels, we don't know.

Answer:

The area of the square is 9 aka [tex]3^{2}[/tex]

You can find it easily by just counting the number of squares inside the square, or by counting the number of squares at its length then multiplying it by its width; so 3 x 3 = 9

It wouldn't be as easy to find the area of the circle because you don't have the radius, nor diameter, so basically, no quantitative values could be used to at least guess.

Answer:

V to X = 68mi

X to W = 50mi

V to W = will be 68mi too

Step-by-step explanation:

note ; it's a triangle*

Answer:

-2

Step-by-step explanation:

Answer:

Cost = 8 + 1.25x

Step-by-step explanation:

The base and altitude of the triangular plot are [tex]42m[/tex] and [tex]21m[/tex] respectively.

The perimeter of the square plot having the same area as the triangular plot is [tex]84m[/tex]

a) Calculate the base and altitude of the triangular plot

The relationship between the Total cost of leveling the triangular plot, the cost per unit area, and the area of the triangular plot is

[tex]\text{unit cost}=\frac{\text{total cost}}{\text{area}}\\\\\text{area}=\frac{\text{total cost}}{\text{unit cost}}\\\\=\frac{\text{11025Rs.}\rupee}{25Rs./m^2}=441m^2[/tex]

The formula for calculating the area of a triangle, given the base and altitude is

[tex]\text{area of triangle}=\frac{1}{2}\text{base}\times\text{altitude}[/tex]

From the question

[tex]\text{base}=2\times\text{altitude}[/tex]

so

[tex]\text{area of triangle}=\frac{1}{2}\times 2\times\text{altitude}\times\text{altitude}\\\\\text{area of triangle}=\text{altitude}^2\\441=\text{altitude}^2\\\text{altitude}=\sqrt{441}=21m[/tex]

from this we can get the base

[tex]\text{base}=2\times\text{altitude}\\=2\times21m=42m[/tex]

b) Calculate the perimeter of a square plot having the same area

Since we found the area of the triangular plot to be [tex]441m^2[/tex], we will use this value for the area of the square plot, so that we can obtain the side

[tex]\text{area of square plot}=side^2\\441=side^2\\\sqrt{441}=side=21m[/tex]

Hence, the perimeter is equal to

[tex]perimeter=4\times side\\=4\times21=84m[/tex]

Learn more about area here: https://brainly.com/question/1447350

Using the given roots, it is found that on the interval [tex]-\frac{3}{4} < x < 1[/tex], the function is positive.

The function is:

[tex]f(x) = (x - 1)(4x + 3)(3x - 8)[/tex]

The zeroes are:

[tex]x = -\frac{3}{4}, x = 1, x = \frac{8}{3}[/tex]

Between two zeroes, the function has the same sign, hence, to find the sign on the interval [tex]-\frac{3}{4} < x < 1[/tex], we find the numeric value of the function of a value of x on the interval, for example f(0), for x = 0.

Then:

[tex]f(0) = (0 - 1)[4(0) + 3][3(0) - 8] = (-1)(3)(-8) = 24[/tex]

Since f(0) is positive, the function is positive on the interval [tex]-\frac{3}{4} < x < 1[/tex].

A similar problem, in which it is desired to find the sign of the function, is given at https://brainly.com/question/4787253

Step-by-step explanation:

remember, the general formula to solve a quadratic equation ax² + bx + c = 0 is

x = (-b ± sqrt(b² - 4ac))/(2a)

a)

I think there is a typo, and this should be

5x² - 7x = 72

5x² -7x - 72 = 0

x = (7 ± sqrt(49 - -1440))/10 = (7 ± sqrt(1489))/10

x1 = (7 + sqrt(1489))/10

x2 = (7 - sqrt(1489))/10

b)

x(x + 2) = 5

x² + 2x - 5 = 0

x = (-2 ± sqrt(4 - -20))/2 = (-2 ± sqrt(24))/2 =

= (-2 ± sqrt(4×6))/2 = (-2 ± 2×sqrt(6))/2 =

= -1 ± sqrt(6)

x1 = -1 + sqrt(6)

x2 = -1 - sqrt(6)

c)

3x² + 2x - 4 = 0

x = (-2 ± sqrt(4 - -48))/6 = (-2 ± sqrt(52))/6 =

= (-2 ± sqrt(4×13))/6 = (-2 ± 2×sqrt(13))/6 =

= (-1 ± sqrt(13))/3

x1 = (-1 + sqrt(13))/3

x2 = (-1 - sqrt(13))/3

Step-by-step explanation:

f(-2)= -2^2-3= -7

f(4)= 4^2-3= 13

f(0)=0^2-3= -3

Answer:

Hallo, I will help you with the problem T^T

Step-by-step explanation:

3.75r + 2.75b = 22.25

3.75r = The amount a red can costs, MULTIPLIED BY the amount of red cans they bought!

2.75b = The amount a black can costs, MULTIPLIED BY the amount of black cans they bought!

So this means that they bought:

3 cans of red paint.

And 4 cans of black paint.

Now you may be thinking, how do you know?

If you multiply the COST 3.75, by 3 cans of red paint, you get 11.25

And then if you multiply the COST of the black paint (The cost for a can of black paint is 2.75) multiply that by 4, you get 11 :0

So add 11 + 11.25 and you get 22.25 :]

Comment if you have any questions, no matter how insignificant you think they may be, I will help you :]

Answer:

f=24km/h

Step-by-step explanation:

Alright, here's what we know.

He travels 2 hours at a fast speed, lets call that speed f km/h

He then travels 3 hours at (f-10) km/h

In these 5 hours, he travels 90km

So we have the formula velocity = distance/time. If you don't know where that formula comes from, let me know and I'll explain.

So we have:

[tex]v=\frac{d}{t}[/tex]

d and t are given to us as 90 and 5 respectively

v is going to be his average speed, so we take 2 times the fast speed plus 3 times the slower speed and divide it by 5. This gives us the average speed he traveled over the 5 hours.

[tex]\frac{2f+3(f-10)}{5} =\frac{90}{5}[/tex]

2f+3f−30=90  by cancelling the 5's in the denominator and expanding 3(f−10)

5f=120

f=24km/h

So his faster speed is 24 km/h. Let me know if this solution did not make sense to you at any point.

Answer:

65/13

650/130

Step-by-step explanation:

6.5/1.3

times 10: 65/13

times 100: 650/130

Answer:

Yup ur Right ;D

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

3m - 30

Hope you could get an idea from here.

Doubt clarification - use comment section.

So the expression till now

[tex]\\ \sf{:}\Rrightarrow m(3)[/tex]

[tex]\\ \sf{:}\Rrightarrow 3m[/tex]

But the required weight is 30pounds less than it

[tex]\\ \sf{:}\Rrightarrow 3m-30[/tex]

Answer:

x=15

Step-by-step explanation:

the basic property is: AB/AD=BC/CD, for more info see the attachment.

The percent of the purchase price that is the price of the warranty is: b. 19%.

Using this formula

Purchase price percent=Total cost-Purchase price/Purchase price

Where:

Total cost=$512

Purchase price=$430

Let plug in the formula

Purchase price percent=$512-$430/$430

Purchase price percent=$82/$430

Purchase price percent=0.19×100

Purchase price percent=19%

Inconclusion the percent of the purchase price that is the price of the warranty is: b. 19%.

Learn more about purchase price here:https://brainly.com/question/6076645

Answer:

The graph will be on the bottom:

Step-by-step explanation:

First find the slope intercept form:

y=mx+b

m is slope

b is y-intercept

since we already have slope we can replace that with m

y=-3/4x+b

Now substitute x and y with 2 and 3

3=-3/4 (2)+b

3=-3/2+b

Add on both sides:

9/2=b

Thus the Slope-intercept form is

y=-3/4x+9/2

Hope this helps!

Answer:

B and C

Step-by-step explanation:

look at comments

[tex]\underline{\bf{Given \:equation:-}}[/tex]

[tex]\\ \sf{:}\dashrightarrow ax^2+by+c=0[/tex]

[tex]\sf Let\:roots\;of\:the\: equation\:be\:\alpha\:and\beta.[/tex]

[tex]\sf We\:know,[/tex]

[tex]\boxed{\sf sum\:of\:roots=\alpha+\beta=\dfrac{-b}{a}}[/tex]

[tex]\boxed{\sf Product\:of\:roots=\alpha\beta=\dfrac{c}{a}}[/tex]

[tex]\underline{\large{\bf Identities\:used:-}}[/tex]

[tex]\boxed{\sf (a+b)^2=a^2+2ab+b^2}[/tex]

[tex]\boxed{\sf (√a)^2=a}[/tex]

[tex]\boxed{\sf \sqrt{a}\sqrt{b}=\sqrt{ab}}[/tex]

[tex]\boxed{\sf \sqrt{\sqrt{a}}=a}[/tex]

[tex]\underline{\bf Final\: Solution:-}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}[/tex]

[tex]\bull\sf Apply\: Squares[/tex]

[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2= (\sqrt{\alpha})^2+2\sqrt{\alpha}\sqrt{\beta}+(\sqrt{\beta})^2[/tex]

[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2 \alpha+\beta+2\sqrt{\alpha\beta}[/tex]

[tex]\bull\sf Put\:values[/tex]

[tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2=\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\sqrt{\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}}[/tex]

[tex]\bull\sf Simplify[/tex]

[tex]\\ \sf{:}\dashrightarrow \underline{\boxed{\bf {\sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\sqrt{\dfrac{-b}{a}}+\sqrt{2}\dfrac{c}{a}}}}[/tex]

[tex]\underline{\bf More\: simplification:-}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{-b}}{\sqrt{a}}+\dfrac{c\sqrt{2}}{a}[/tex]

[tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{a}\sqrt{-b}+c\sqrt{2}}{a}[/tex]

[tex]\underline{\Large{\bf Simplified\: Answer:-}}[/tex]

[tex]\\ \sf{:}\dashrightarrow\underline{\boxed{\bf{ \sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\dfrac{\sqrt{-ab}+c\sqrt{2}}{a}}}}[/tex]

The value  [tex]\sqrt{\alpha } +\sqrt{\beta }[/tex] in terms of a, b and c is [tex]\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]

Roots of a quadratic equation

Given the quadratic equation ax² + bx + c, the sum and product  of the roots are expressed as:

Get the value of the radical expression [tex]\sqrt{\alpha } +\sqrt{\beta } [/tex]

Taking the square of the expression will give:

Take the square root of both sides:

[tex]\sqrt{(\sqrt{\alpha } +\sqrt{\beta } )^2} =\sqrt{(\sqrt{\alpha } )^2+(\sqrt{\beta } )^2+2\sqrt{\alpha \beta} } \\ \sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(\alpha }+{\beta} )+2\sqrt{\alpha \beta} } \\[/tex]

Substitute the product and the sum values into the expression to have:

[tex]\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(-\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]

Hence the value  [tex]\sqrt{\alpha } +\sqrt{\beta }[/tex] in terms of a, b and c is [tex]\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]

Learn more on the roots of equation here: https://brainly.com/question/25841119

Answer: 64.80% not 100% positive if i did that math right but thats what i got

Step-by-step explanation:

38.8679

Step-by-step explanation:

Answer: plant 1 grows at a faster rate

Step-by-step explanation:

Answer:x<-3

Step-by-step explanation:

Answer:

x < -3

Step-by-step explanation:

[tex]-7x-4>17\\\\-7x-4+4>17+4\\\\-7x>21\\\\\frac{-7x}{-7}>\frac{21}{-7}\\\\x<-3[/tex]

Answer:

Use the table to complete the statements.

The x-intercepts shown in the table are  

(–2, 0)

and  

(2, 0

.

The y-intercept shown in the table is  

(0, –4)

.

Step-by-step explanation:

Answer:

3/4 of a bar.

Step-by-step explanation:

Each piece of the granola bar is 1/4 of the bar. She ate 3 portions, so she ate 3/4.