A rectangular park 60 yards long and 50 yards wide. Plans call for increasing both the length and the width by x yards.
a. Write a function to find the new length of the park.
b. Write a function to find the new width of the park.
c. Write a function to find the area of the park after increasing both the length and width.

The quadratic equation with the given conditions is:

[tex]f(x) = \frac{3}{16}(x^2 + 2x - 24)[/tex]

The standard form of a quadratic equation with roots [tex](x_1,0)[/tex] and [tex](x_2,0)[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2)[/tex]

In which a is the leading coefficient.

In this problem, the roots are [tex]x_1 = -6, x_2 = 4[/tex], thus:

[tex]f(x) = a(x - (-6))(x - 4)[/tex]

[tex]f(x) = a(x + 6)(x - 4)[/tex]

[tex]f(x) = a(x^2 + 2x - 24)[/tex]

It passes through point (2,-3), which means that when [tex]x = 2, f(x) = -3[/tex], and this is used to find a.

[tex]a(2^2 + (2)(2) - 24) = -3[/tex]

[tex]-16a = -3[/tex]

[tex]a = \frac{3}{16}[/tex]

Thus, the equation is:

[tex]f(x) = \frac{3}{16}(x^2 + 2x - 24)[/tex]

A similar problem is given at https://brainly.com/question/17987697

7kg=$5

represent the unknown with an x.

Therefore,

7kg=$5

x=$2

5÷2 is 2.5

7kg÷2.5=2.8

2.8kg of nuts for $2.8

Answer:

Suzy needs to work 62.5 hours, or 62 hours and 30 minutes.

Hope it helps!

Answer:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtract

Step-by-step explanation:

[6-4]+16

[2]+16

18

The final answer is 18

Answer:

[tex]15t+10[/tex]

Step-by-step explanation:

We can plug in for [tex]5t[/tex] into [tex]f(x)[/tex]!

[tex]f(5t)=3(5t)+10=\boxed{15t+10}[/tex]

Answer: Its B 8:20

Step-by-step explanation:

U get this by adding the 15 minutes to the 7:10 and then u get 7:25 then you add the 10 and u get 7:35 then you add the 45 and you get 8:20

The time at which Javeria gets off the train is 8:20 thus option (b) is correct.

Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.

Another example of work is that if you have done your food by 1 hour it means your work duration is 1 hour so work is basically the time duration of any task which you have done.

As per the given,

Javeria left home at 7:10.

Add 15 + 10 + 45 = 70 minutes.

70 minutes = 1 hour + 10 minutes or 1:10

Add into 7:10 as

7 + 1:10 + 10

8:20

Hence "The time at which Javeria gets off the train is 8:20".

For more information about the work and time relation,

brainly.com/question/6912604

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Answer:

[tex]2x = 126 \\ x = 126 \div 2 = 63 \\ \\ z = y = x = 63[/tex]

Answer:

-3

Step-by-step explanation:

Answer: No

Step-by-step explanation: Tell Maria to do the problem again.

If Maria added 45,273 and 35,687 and got a sum of 70,960 : Yes, Maria's answer is reasonable.

When we add 45,273 and 35,687 we have:

45,273 + 35,687 = 80,960

Maria's response, however, is 70,960, which is 10,000 below the accurate total. This indicates that Maria most likely added incorrectly.

The rationality of the response is demonstrated by the fact that Maria's answer is considerably less than the right answer. This 10,000-difference discrepancy is not a trivial error and suggests that an addition error most likely occurred.

Learn more about sum here:https://brainly.com/question/25734188

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Answer:

-5, -9

Step-by-step explanation:

This point is located in the fourth quadrant. When rotated at 270 degrees, it'll end up in the third quadrant. The rules for this quadrant is that both the x and y value will be negative.

Answer: I think is -9(5,)

Step-by-step explanation:

The answer would be B and D because the slope stays consistent throughout the entire table unlike all of the other options.

Answer:

[tex]x = \frac{27}{10}[/tex]

Step-by-step explanation:

Hope this helps! :D

Answer:

c

Step-by-step explanation:

20/100 can be simplified to 2/10, which can be simplified further to 1/5

Answer:

[tex]6^{2}[/tex]

Step-by-step explanation:

Use power rules.

[tex]\frac{6^{7} }{6^{5} }[/tex]

[tex]6^{7-5}[/tex]

[tex]6^{2}[/tex]

Another way of solving in which the 6s on the numerator cancel with the 6s on the denominator:

[tex]\frac{6*6*6*6*6*6*6}{6*6*6*6*6}[/tex]

[tex]\frac{6*6}{1}[/tex]

6*6

[tex]6^{2}[/tex]

Answer:

The correct answer is 19 pencils.

Step-by-step explanation:

First, we have to multiply

57 x 4 = 228

Second, we have to divide

228 ÷ 19 = 12

Lastly, we write the answer in a complete sentence.

Each student got 19 pencils if there were no pencils left over.

Hope This Helps!

Answer:

Each student got 12 pencils

Step-by-step explanation:

57 times 4 = 228

228 divided by 19 =12

hope this helps :)

Answer:

She used a tool that's meant to draw a circle to draw 2 stragith lines

Step-by-step explanation:

Answer:

It is commutative property   (in my opinion)

Step-by-step explanation:

-1 + 5= 4       5 - 1 =4

Both give you the same answer, thus the arrangement of the INTEGERS does not matter.

Note that I mentioned integers since this is not possible for natural numbers alone. They are not closed under subtraction. Here you -1 and 5 both of  which are integers, their SUM  give you an integer as well.

Hope this explanation helps!!

-3x + 6 = 2x - 24

Value of 'x' term

[tex] -3x + 6 = 2x - 24 [/tex]

[Bringing 2x to left side and 6 to right side]

[tex] = > - 3x - 2x = - 24 - 6 \\ \\ = > - 5x = - 30 \\ \\ = > x = \cancel \frac{ - 30}{ - 5} \\ \\ = > x = 6[/tex]

[tex] \fbox \red{Hope This Helps}[/tex]

Answer:

(1 , 2) and  (3 , 6)

Step-by-step explanation:

the point P : (x , y) -> (x , 2x)    ... ordinate of P point is twice its abscissa, y = 2x

√10 = √(x-4)² + (2x-3)²

5x² - 20x + 25 = 10

x² - 4x + 3 = 0

(x-1)(x-3) = 0

x = 1    or    x = 3

y = 2    or   y = 6

Answer:

6/7 = 36/42

12/8 = 30/20

Step-by-step explanation:

(6*?) / (7*6) = ?/42

(6*6) / (7*6) = 36/42

(12*2.5) / (8*?) = 30/?

(12*2.5) / (8*2.5) = 30/20

Hope this helps!

Answer:

The answer to this expression would be 15

Step-by-step explanation:

(7) - 4(-2) = 7 + 8 = 15

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\mathsf{c - 4x}}\\\huge\boxed{\mathsf{\rightarrow 7 - 4(-2)}}\\\huge\boxed{\mathsf{\rightarrow 7 -(-8)}}\\\huge\boxed{\rightarrow{\mathsf{7 + 8}}}\\\huge\boxed{\mathsf{\rightarrow 15}}\\\\\\\\\\\huge\text{Therefore, your answer is: \textsf{15}}\huge\checkmark\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

Answer:

below

Step-by-step explanation:

I didn't see the picture you try to post... but, the formula for rotation counterclockwise 90° is (x,y) original -> (-y,x) rotated

For rotation clockwise 90°: (x,y) -> (y,-x)

In the given expression :

rate of change = 1

Initial condition = - 21

Answer:

Step-by-step explanation:

Given relationship:

It could be shown as:

The rate of change is 1 and the initial condition is -21.

Correct choice is B

Answer:

3(4)^2+7(4)(3)-6(3)^2

= 78

Answer:

i like to use desmos

it’s my fav calculator to use

or calculator soup

hope this help good luck on your SAT!!!!

Answer:

angle 1 = 61°

angle 2 = 119°

angle 3 = 61°

angle 4 = 119°

angle 5 = 119°

angle 6 = 61°

angle 7 = 119°

Step-by-step explanation:

angle 1 = 61° (corresponding angles are always equal)

angle 1 + angle 2 = 180° (linear pair)

=> 61° + angle 2 = 180°

=> angle 2 = 180° - 61° = 119°

angle 2 = 119

angle 1 = angle 3 = 61° (vertically opposite angles are equal)

angle 2 = angle 4 = 119° (vertically opposite angle are equal)

angle 4 = angle 5 = 119° (interior opposite angles are equal)

angle 6 = 61° (vertically opposite angles are equal)

angle 5 = angle 7 = 119° (vertically opposite angles are equal)

Hope it helps :)

Answer:

yes

Step-by-step explanation:yes

2.29 divided by 3.5

= 0.6542857143

and

rounded to the nearest tenth

= 0.7

Hope this helped you- have a good day bro cya)

Answer:

60 cm

Step-by-step explanation: