The population of Collin County, which follows the exponential growth model, increased from 491,675 in 2000 to 782,341 in 2010. Find the exponential growth rate, k.

Answer: c

Step-by-step explanation:

The solution in slope-intercept form for:

y + 7 = -3(x - 1) is y = -3x - 4

3x + y = -4 is y = -3x - 4

We have been given two equations  

y + 7 = -3(x - 1) and 3x + y = -4

we have been asked to simplify these equations in slope intercept form.

The slope intercept form can be written as follows:

y = mx + b

Where, m is the slope of the line and b is the y-intercept.

The y-intercept of this line is the value of y at the point where the line crosses the y axis

Now, let us write the first equation in slope intercept form as follows:

y + 7 = -3(x - 1)

y + 7 = -3x + 3

y = -3x + 3 - 7

y = -3x - 4

The slope intercept form for the first equation is y = -3x - 4

Now, let us write the second equation in slope intercept form.

This can be done as follows:

3x + y = -4

y = -3x - 4

Therefore, the slope intercept form for the second line is y = -3x - 4

Answer:

The length of the original rectangle is 73.4 mm.

The breadth of the original rectangle is 86.6 mm.

Step-by-step explanation:

Given : The perimeter of a rectangle is 320 mm. If its length increases by 10 mm and its breadth decreases by 10 mm then it its area will be 32 less.

To find : Calculate the length and breadth of the original rectangle ?

Solution :

The area of the rectangle is [tex]A=L\times B[/tex]

Let the length of the rectangle be 'x'

The breadth of the rectangle be 'y'

The area is [tex]A=xy[/tex]

Now, length increases by 10 mm i.e. L=x+10

breadth decreases by 10 mm i.e. B=y-10

The new area is [tex]A_n=(x+10)(y-10)[/tex]

According to question,

[tex]A-A_n=32[/tex]

[tex]xy-(x+10)(y-10)=32[/tex] ......(1)

The perimeter of a rectangle is 320 mm.

i.e. [tex]P=2(L+B)[/tex]

[tex]320=2(x+y)[/tex]

[tex]x+y=160[/tex]

[tex]x=160-y[/tex] .....(2)

Substitute the value of y from eqn (2) in (1),

[tex]y(160-y)-(160-y+10)(y-10)=32[/tex]

[tex]160y-y^2-(170-y)(y-10)=32[/tex]

[tex]160y-y^2-(180y-1700-y^2)=32[/tex]

[tex]160y-y^2-180y+1700+y^2=32[/tex]

[tex]1700-20y=32[/tex]

[tex]20y=1732[/tex]

[tex]y=\frac{1732}{20}[/tex]

[tex]y=86.6[/tex]

Substitute in (2),

[tex]x=160-86.6[/tex]

[tex]x=73.4[/tex]

The length of the original rectangle is 73.4 mm.

The breadth of the original rectangle is 86.6 mm.

Answer:

The  number of adults visiting the zoo =  51

The number of children visiting the zoo =  134

Step-by-step explanation:

Let us assume the number of adults  going to the zoo = m

Total number of people visiting the zoo = 185

SO, the number of children visiting the zoo = 185 - m

Now, the cost of 1 adult ticket = $15

So, the total cost of m adult tickets = m x ( cost of 1 adult ticket)

= m  x ( $15)  = 1 5 m

And, the cost of 1 children ticket = $6

So, the total cost of ( 185 - m) adult tickets

= ( 185 - m) x ( cost of 1 children ticket)   = (185 - m )  x ( $6)  = 6( 185 - m)

Also, the combined cost of all tickets  = $ 1569

⇒ The cost of ( Adult's tickets  + Children's Tickets)  = $1569

or,  15 m + 6( 185 - m)  = $1569

or, 15 m + 1110 - 6 m = 1569

or, 9 m =  459

⇒ m = 459/9 =  51 , or m = 51

Hence the  number of adults visiting the zoo = m = 51

The number of children visiting the zoo = 185 -m =  134

Answer: 14

Step-by-step explanation: hope this helps u :)

Answer:

14 tons

Step-by-step explanation:

divide the mass value by 32000

448,000 divided by 32000 = 14 tons

Answer:

8:50 A.M

Step-by-step explanation:

You have to add all the numbers.

Example:

5+15+25=45

45 Minutes + 5 Minutes= 50 Minutes=

8:50 A.M

Answer: 8:55AM

Step-by-step explanation:

8:05 AM - 8:10 AM : gather the ingredients

8:10 AM - 8:25 AM: mix the ingredients

8:25 AM - 8:50 AM: bake the cake

5+15+25=45 minutes + 8:05 AM = 8:50 AM

Answer:

See explanation

Step-by-step explanation:

Which situation can be modeled by the inequality [tex]65-8x\ge 9?[/tex]

Suppose you have $65.

Each day you spend $8.

You want to have at least $9 left.

If x is the number of days you are spending money, what is the maximum number of days you can spend money?

Solution:

Let x be the number of days you are spending money, each day you spend $8, so in x days you spend $8x. Initially, you have $65, so after x days, $(65 - 8x). This amount of money must be no less than $9, so

[tex]65-8x\ge 9[/tex]

For this case we have a factorized quadratic equation. We equal each factor to zero and thus find the roots:

[tex]x + 5 = 0[/tex]

Subtracting 5 from both sides we have:

[tex]x = -5[/tex]

Thus, the first solution of the equation is:

[tex]x_ {1} = - 5[/tex]

On the other hand we have:

[tex]x-3 = 0[/tex]

Adding 3 to both sides:

[tex]x = 3[/tex]

Thus, the second solution of the equation is:

[tex]x_ {2} = 3[/tex]

Answer:

The solutions of the equation are:

[tex]x_ {1} = - 5\\x_ {2} = 3[/tex]

Answer:

[tex]\large\boxed{(x-3)^2+(y+7)^2=200\to(x-3)^2+(y+7)^2=(10\sqrt2)^2}[/tex]

Step-by-step explanation:

The standard form of an equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the equation:

[tex]x^2+y^2-6x+14y=142[/tex]

We must use

[tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]

[tex]x^2-6x+y^2+14y=142\\\\x^2-2(x)(3)+y^2+2(y)(7)=142\qquad\text{add}\ 3^2\ \text{and}\ 7^2\ \text{to both sides}\\\\\underbrace{x^2-2(x)(3)+3^2}_{(a-b)^2=a^2-2ab+b^2}+\underbrace{y^2+2(y)(7)+7^2}_{(a+b)^2=a^2+2ab+b^2}=142+3^2+7^2\\\\(x-3)^2+(y+7)^2=142+9+49\\\\(x-3)^2+(y+7)^2=200\\\\(x-3)^2+(y+7)^2=(\sqrt{200})^2\\\\(x-3)^2+(y+7)^2=(\sqrt{100\cdot2})^2\\\\(x-3)^2+(y+7)^2=(10\sqrt2)^2[/tex]

[tex]center:(3,\ -7)\\radius:10\sqrt2[/tex]

Answer:

7+7+7+6+4+2=33

Each friend will have to pay $11

Step-by-step explanation:

Answer:

111.15754585272 or 2√3089

Step-by-step explanation:

Here I will show you two methods that you can use to simplify the square root of 12356. In other words, I will show you how to find the square root of 12356 in its simplest radical form using two different methods.

To be more specific, I have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√12356 = A√B

Greatest Perfect Square Factor Method

The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12356 to simplify the square root of 12356. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 12356. The factors of 12356 are 1, 2, 4, 3089, 6178, and 12356. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 12356 divided by the greatest perfect square from the list of all factors of 12356. We determined above that the greatest perfect square from the list of all factors of 12356 is 4. Furthermore, 12356 divided by 4 is 3089, therefore B equals 3089.

Now we have A and B and can get our answer to 12356 in its simplest radical form as follows:

√12356 = A√B

√12356 = 2√3089

Double Prime Factor Method

The Double Prime Factor Method uses the prime factors of 12356 to simplify the square root of 12356 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 12356 and then take the square root of that product. The prime factors that multiply together to make 12356 are 2 x 2 x 3089. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 12356 by the number (A) squared. 2 squared is 4 and 12356 divided by 4 is 3089. Therefore, B equals 3089.

Once again we have A and B and can get our answer to 12356 in its simplest radical form as follows:

√12356 = A√B

√12356 = 2√3089

Answer:

144

Step-by-step explanation:

x^2+24x=17

b=24

(b/2)^2=(24/2)^2=12^2=144

Answer:

42

Step-by-step explanation:

Because she is moving from a 65 degree pool into a 107 degree hot tub so there is a 42 degree difference when she moves to the hot tub from the pool.

Answer:

Associative property of addition

Step-by-step explanation:

Answer:

The associative property of addition

Step-by-step explanation:

In an equation with 3 or more number numbers being added the placement of parentheses does not change the answer.

Answer:

f(a)=2a

Step-by-step explanation:

The formula of the expression -3a + 6b= a + 4b in terms of a will be f(a) = 2a.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given expression will be solved as below:-

-3a + 6b= a + 4b

-3a -a = -6b + 4b

-4a = -2b

b = 2a

f(a) = 2a

Therefore, the formula of the expression -3a + 6b= a + 4b in terms of a will be f(a) = 2a.

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Answer:

[tex]76\frac{7}{8}\ lb[/tex]

Step-by-step explanation:

we know that

One box of 12'' weighs 3 3/4 lb

so

To find out the weight of 20 1/2 boxes, multiply the weight of one box by the total number of boxes

[tex]3\frac{3}{4}(20\frac{1}{2})[/tex]

Convert mixed number to an improper fraction

[tex]3\frac{3}{4}\ lb=\frac{3*4+3}{4}=\frac{15}{4}\ lb[/tex]

[tex]20\frac{1}{2}\ boxes=\frac{20*2+1}{2}=\frac{41}{2}\ boxes[/tex]

substitute

[tex]\frac{15}{4}(\frac{41}{2})=\frac{615}{8}\ lb[/tex]

Convert to mixed number

[tex]\frac{615}{8}\ lb=\frac{608}{8}+\frac{7}{8}=76\frac{7}{8}\ lb[/tex]

Answer:

The correct answer is D. 15 squared centimeters.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Base one = 10 centimeters

Base two = 5 centimeters

Height = 2 centimeters

2. Let's find out the area of the trapezoid, using the following formula:

Area = 1/2 (Base one + Base two) * Height

Replacing with real values:

Area = 1/2 (10 + 5) * 2

Area = 1/2 (15 * 2) = 1/2 (30)

Area = 15 centimeters ²

The correct answer is D. 15 squared centimeters.

Note: Same answer provided to question 14021584, answered by me.

Answer:

Part a) [tex]-16t^{2}+35t+1.5=0[/tex]

Part b)

[tex]a=-16\\b=35\\c=1.5[/tex]

Part c) The soccer ball will take 2.23 seconds to reach the ground

Step-by-step explanation:

we have

[tex]h(t)=-16t^{2}+35t+1.5[/tex]

where

t  is the time the ball has been in the air, in seconds

h(t) is the height, in feet, of the  soccer ball

Part a) Write an equation that could be used to determine the time the ball traveled before it hit the ground

we know that

When the ball hit the ground, the value of h(t) is equal to zero

so

For h(t)=0

[tex]-16t^{2}+35t+1.5=0[/tex]

This equation can be used to determine the time the ball traveled before it hit the ground

Part b) Determine the values of a, b, and c

we know that

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]-16t^{2}+35t+1.5=0[/tex]

so

[tex]a=-16\\b=35\\c=1.5[/tex]

Part c)  How long will it take for the soccer ball to reach the ground after it was kicked?

Solve the quadratic equation by the formula

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

we have

[tex]a=-16\\b=35\\c=1.5[/tex]

substitute the values

[tex]x=\frac{-35(+/-)\sqrt{35^{2}-4(-16)(1.5)}} {2(-16)}[/tex]

[tex]x=\frac{-35(+/-)\sqrt{1,321}} {-32}[/tex]

[tex]x_1=\frac{-35(+)\sqrt{1,321}} {-32}=-0.04[/tex]  ---> cannot be a solution (is negative)

[tex]x_2=\frac{-35(-)\sqrt{1,321}} {-32}=2.23[/tex]

therefore

The soccer ball will take 2.23 seconds to reach the ground

Answer:

A) Irrational

Step-by-step explanation:

The square root of 27 is an irrational number since it's not a rational number. We identify rational numbers because they can be expressed as fractions

If we take the value of [tex]\sqrt{27}[/tex] we get

5.1961524227066318805823390245176...

There is no way to transform that number into a fraction because

* It has no decimal limit

* It has no decimal pattern (or period)

Examples of rationals are

5.44444...

[tex]0.\overline{32}[/tex]

2.375

The last one has limited decimals, the first two have repetitive patterns or a period.

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

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

Where:

m: It's the slope

b: It is the cut-off point with the y axis

We have the following equation:

[tex]6x + 5y = -5\\5y = -6x-5\\y = - \frac {6} {5} x- \frac {5} {5}\\y = - \frac {6} {5} -1[/tex]

Thus, the slope is: [tex]m = - \frac {6} {5}[/tex]

By definition, if two lines are parallel then their slopes are equal.

Thus, a line parallel to the given line will have a slope: [tex]m = - \frac {6} {5}.[/tex]Therefore, the equation will be of the form:

[tex]y = - \frac {6} {5} x + b[/tex]

We substitute the given point and find "b":

[tex]-4 = - \frac {6} {5} (5) + b\\-4 = -6 + b\\-4 + 6 = b\\b = 2[/tex]

Finally, the equation is:

[tex]y = - \frac {6} {5} x + 2[/tex]

Answer:

[tex]y = - \frac {6} {5} x + 2[/tex]

Answer:

The rate of interest for compounded daily is 2.1 6

Step-by-step explanation:

Given as :

The principal investment = $ 98,000

The Time period for investment = 7 years

Let The rate of interest compounded daily = R %

The Amount at the end up = $ 114,000

From compounded method

Amount = Principal × [tex](1+\dfrac{rate}{365\times 100})^{365\times Time}[/tex]

Or, $ 114,000 = $ 98,000  × [tex](1+\dfrac{R}{365\times 100})^{365\times 7}[/tex]

Or, [tex]\frac{114000}{98000}[/tex] = [tex](1+\dfrac{R}{36500})^{2555}[/tex]

or, 1.16326 = [tex](1+\dfrac{R}{36500})^{2555}[/tex]

or, [tex](1.16326)^{\frac{1}{2555}}[/tex] = 1 + [tex]\frac{R}{36500}[/tex]

1.00005919 - 1 =  [tex]\frac{R}{36500}[/tex]

or, 0.00005919 =  [tex]\frac{R}{36500}[/tex]

∴ R =  0.00005919 × 365000 = 2.16

Hence the rate of interest for compounded daily is 2.1 6   Answer

Slope intercept form: y = mx + b

m = slope

b = y-intercept

Solve for the y-intercept.

9 = 2(7) + b

9 = 14 + b

9 - 14 = 14 + b - 14

-5 = b

y = 2x - 5

______

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Final answer:

The equation of the line with a slope of 2 that passes through the point (7,9) in slope-intercept form is y = 2x - 5, where 2 is the slope and -5 is the y-intercept.

Explanation:

To find the equation of a line with a slope of 2 that passes through the point (7,9), we can use the point-slope form of a line equation, which is:

[tex]y - y_1 = m(x - x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is the point the line passes through. Plugging in our values we get: y - 9 = 2(x - 7).

To convert this to slope-intercept form (y = mx + b), expand the right side to get y - 9 = 2x - 14 and then add 9 to both sides to isolate y, resulting in y = 2x - 5. Here, the m value is 2 (the slope) and the b value is -5 (the y-intercept).

Answer:

Option C: 0.04 is the correct answer.

Step-by-step explanation:

Given that:

cups of sugar used = 7.5

cookies = 14 dozen

As we know that 1 dozen cookies equal 12 cookies so,

14 dozen cookies = 14* 12 = 168 cookies

Now,

we have to find the rate of cups of sugar per cookie, So:

Rate = cups of sugar / total cookies

By putting values:

Rate = 7.5/ 168

By simplifying we get

Rate = 0.04464

By rounding it off to nearest hundred:

Rate = 0.04

Hence the rate of cups of sugar per cookie is 0.04

i hope it will help you!

The question is incomplete. The complete question is attached below.

Answer:

(a). AB = 16.4 in

(b) BC = 11.5 in

Step-by-step explanation:

From the rectangle ABCD shown below,

AB is the base of rectangle and CB is the altitude of the rectangle.

Given:

AC = 20 in

(a)

From triangle ABC,

Applying cosine ratio for angle 35°, we get:

[tex]\cos(35)=\frac{AB}{AC}\\AB=AC\times \cos(35)\\AB=20\times \cos(35)=16.38\approx 16.4\ in[/tex]

Therefore, AB = 16.4 in

(b)

Applying sine ratio for angle 35°, we get:

[tex]\sin(35)=\frac{CB}{AC}\\CB=AC\times \sin(35)\\AB=20\times \sin(35)=11.47\approx 11.5\ in[/tex]

Therefore, CB = 11.5 in

Final answer:

Using the cosine function, the base AB of the rectangle is approximately 16.4 inches. Using the sine function, the altitude CB is approximately 11.5 inches, both rounded to the nearest tenth of an inch.

Explanation:

To find the base AB and the altitude CB of rectangle ABCD with a given diagonal AC of 20 inches and an angle of 35° with base AB, we can use trigonometric ratios.

First, we will use the cosine function, which relates the base of a right-angled triangle to the hypotenuse:

Next, we use the sine function, which relates the altitude to the hypotenuse:

The statement H(30) = H(25) + 5 means that when Amelia was 30 months old, she was 5 centimeters taller than when she was 25 months old.

The function H(t) tells us Amelia's height in centimeters when she was t months old. So H(30) tells us Amelia's height when she was 30 months old, and H(25) tells us Amelia's height when she was 25 months old.

The equation H(30) = H(25) + 5 tells us that these two values are equal, which means that Amelia was 5 centimeters taller when she was 30 months old than when she was 25 months old.

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Answer:

 What we are going to do for this case is find the cost for each case:

 Cost to run the car before the mechanic worked on it:

 Cost to run the car after the mechanic worked on it:

 The difference between both cases is:

 Answer:

 It cost to run the car after the mechanic worked on it 0.01 $ / mile less than before the mechanic worked on it.

Read more on Brainly.com - https://brainly.com/question/2528459#readmoreStep-by-step explanation:

Answer:

The value of x is 6 and The value of y is - 4

Step-by-step explanation:

Given as :

The Two linear equation is

- 3 x - 9 y = 18

4 x + 3 y = 12

Now,

4 × ( - 3 x - 9 y ) = 4 × 18

Or, - 12 x - 36 y = 72      ......1

And 3 × ( 4 x + 3 y ) =  3 × 12

or, 12 x + 9 y = 36        .....2

Solving eq 1 and 2

( 12 x + 9 y ) + (  - 12 x - 36 y ) = 72 + 36

Or, 9 y - 36 y = 108

or , 27 y = - 108

∴ y = - [tex]\frac{108}{27}[/tex]

I.e y = - 4

Put the value of y to get x value

So, 12 x + 9 (-4) = 36

Or, 12 x = 36 + 36

or, 12 x = 72

∴  x = [tex]\frac{72}{12}[/tex]

I.e x = 6

Hence The value of x is 6 and The value of y is - 4    Answer

Answer:

x = (-4/3)

y = (-5)

Step-by-step explanation:

there ya go, I think this was the answer you were looking for. :)