The length of a rectangle measures 5/8 of a foot. The width of the rectangle measures 2 1/2 feet. What is the area of the rectangle?

Using quadratic function concepts, it is found that:

1) The equation is [tex]y = -0.08x^2 + 4x[/tex]

2) The minimum distance is of 2.64 yards, and the maximum is of 47.36 yards.

A quadratic equation has the following format:

[tex]y = ax^2 + bx + c[/tex]

In this problem:

Item 1:

The vertex is: [tex]V(x_v,y_v)[/tex], in which:

[tex]x_v = -\frac{b}{2a}[/tex]

[tex]y_v = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]

In this problem, it is (25,50). Thus:

[tex]-\frac{b}{2a} = 25[/tex]

[tex]-b = 50a[/tex]

[tex]b = -50a[/tex]

[tex]-\frac{b^2 - 4ac}{4a} = 50[/tex]

[tex]-b^2 = 200a[/tex]

[tex]-(50a)^2 = 200a[/tex]

[tex]-2500a^2 - 200a = 0[/tex]

[tex]200a(-12.5a - 1) = 0[/tex]

Then, as [tex]a \neq 0[/tex]

[tex]a = -\frac{1}{12.5} = -0.08[/tex]

[tex]b = -50a = -50(-0.08) = 4[/tex]

Thus, the equation, in standard form, is:

[tex]y = -0.08x^2 + 4x[/tex]

Item 2:

The distances are the values of x for which:

[tex]y = 10[/tex]

Then

[tex]-0.08x^2 + 4x = 10[/tex]

[tex]-0.08x^2 + 4x - 10 = 0[/tex]

Which is a quadratic equation with [tex]a = -0.08, b = 4, c = -10[/tex]. Then:

[tex]\Delta = 4^2 - 4(-0.08)(-10) = 12.8[/tex]

[tex]x_{1} = \frac{-4 + \sqrt{12.8}}{2(-0.08)} = 2.64[/tex]

[tex]x_{2} = \frac{-4 - \sqrt{12.8}}{2(-0.08)} = 47.36[/tex]  

The minimum distance is of 2.64 yards, and the maximum is of 47.36 yards.

A similar problem is given at https://brainly.com/question/24713268

Answer:

Step-by-step explanation:

Nina's debt = 3 * 9 = $ 27

Debt is represented using negative sign.This represents (-27) on the number line.

Answer:(-27)

Step-by-step explanation:

i got it right on edge 2022

Step-by-step explanation:

the third option is the correct one

Answer:

I would answer it correctly but only 5 points -_-

Step-by-step explanation:

Answer:

No solutions.

Step-by-step explanation:

-10 = 7

No solutions

Answer:

2^-2

Step-by-step explanation:

When multiplying indices or exponents with the same base number, you can add the powers:

2^4 x 2³ = 2^7 (4 + 3 = 7)

2^5 x 2^4 = 2^9 (5 + 4 = 9)

When dividing indices or exponents with the same base number, you can subtract the powers:

2^7 ÷ 2^9 = 2^-2 (7 - 9 = -2)

The function that can be used to find t, the total number of gallons of water in the tank after w weeks will be t = -15w + 275

The initial volume of water in the tank is 275 gallons

The amount of water in the tank decreases at a constant rate of 15 gallons per week.

t = total number of gallons water in the tank after weeks

w = number of weeks

Therefore, the following equation/theory can be establish

The equation will be

t = 275 - 15w

or

t = -15w + 275

Check here for more details on how to find linear equations: https://brainly.com/question/17846793?referrer=searchResults

The measure of angle QRS is 35 degrees and the measure of angle Q is 116 degrees.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

As we know in the triangle the sum of the two interior angles is equal to the exterior angle.

Angle RQS + Angle RSQ = Angle TRQ

4y + y = 145

5y = 145

y = 29

The measure of angle QRS = 180 - Angle RQS - Angle RSQ

= 180 - 4(29) - 29

Angle QRS = 35 degree

The measure of angle Q = 4y = 4(29) = 116 degree

Thus, the measure of angle QRS is 35 degrees and the measure of angle Q is 116 degrees.

Learn more about the triangle here:

brainly.com/question/25813512

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Answer:

4500 gr

Step-by-step explanation:

4.5 kg equals some number (n) times one gram.  Solve this for n:

4.5 kg = n(1 gr)

Recall that 1 kg = 1000 gr.  Because of this, the equation above becomes

        4.5 kg          (4.5)(1000 gr)

n = --------------- or ------------------- or 4500 gr

       1000 gr                     1 gr

Hello there!

If a line has a slope of 3 and a y-intercept of 4, its equation looks like this:

[tex]y=3x+4[/tex]

Hope this helps you! Mark Brainliest, please! :)

~Just a joyful teen

[tex]SilentNature[/tex]

Answer:

y = 3x + 4

Step-by-step explanation:

Answer: $3.79 for 12.5 oz. is cheaper per ounce than $1.00 for 3oz.

Step-by-step explanation: Without much effort we can see that $ 1.00 for 3 oz $4.00 for 12 oz. but you can get more (12.5 oz.) for less than $4.00 (for $3.79) if you buy 12.5 oz. for $3.79

Answer:

128 divided by 2 for 5 times is your answer enjoy my.kiddo

Answer:

look at the picture i have sent

Given :-

To find :-

Solution :-

According to Question ,

As we know that ,

Answer:

2.93 repeating

Step-by-step explanation:

Answer:

a: 36

b: 10

c: 3.2

d: a

Step-by-step explanation:

Answer:

A = 36

B = 10

C = 3.2

D = a

Step-by-step explanation:

The square roots and power of 2s zero each other out.

Answer:

a) 168

b) 3

Step-by-step explanation:

a) 56÷4=14 14×12=168

b) 56÷4=14 56-14=42 42÷14=3

[tex]\large\underline{\sf{Solution-}}[/tex]

We have to find out the value of the fraction.

Let us assume that:

[tex] \sf \longmapsto x =2 + \dfrac{1}{2 + \dfrac{1}{2 + \dfrac{1}{2 + ... \infty} } } [/tex]

We can also write it as:

[tex] \sf \longmapsto x =2 + \dfrac{1}{x} [/tex]

[tex] \sf \longmapsto x =\dfrac{2x + 1}{x} [/tex]

[tex] \sf \longmapsto {x}^{2} =2x + 1[/tex]

[tex] \sf \longmapsto {x}^{2} - 2x - 1 = 0[/tex]

Comparing the given equation with ax² + bx + c = 0, we get:

[tex] \sf \longmapsto\begin{cases} \sf a =1 \\ \sf b = - 2 \\ \sf c = - 1 \end{cases}[/tex]

By quadratic formula:

[tex] \sf \longmapsto x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

[tex] \sf \longmapsto x = \dfrac{2 \pm \sqrt{ {( - 2)}^{2} - 4(1)( - 1)} }{2 \times 1} [/tex]

[tex] \sf \longmapsto x = \dfrac{2 \pm \sqrt{4 + 4} }{2 \times 1} [/tex]

[tex] \sf \longmapsto x = \dfrac{2 \pm \sqrt{8} }{2} [/tex]

[tex] \sf \longmapsto x = \dfrac{2 \pm2 \sqrt{2} }{2} [/tex]

[tex] \sf \longmapsto x = 1 \pm\sqrt{2}[/tex]

[tex] \sf \longmapsto x = \begin{cases} \sf 1 + \sqrt{2} \\ \sf 1 - \sqrt{2} \end{cases}[/tex]

But "x" cannot be negative. Therefore:

[tex] \sf :\implies x = 1 + \sqrt{2}[/tex]

So, the value of the fraction is 1 + √2.

Answer:

sorry I don't know pls ask someone else

Answer:

124.3

Step-by-step explanation:

42.15+20.00=1/2x

62.15=1/2x

62.15*2

124.3 is the total of her paycheck.

42.1<20.00+x

Answer: 118.2

Step-by-step explanation:

Answer: In 4 minutes he will make 5 portraits

Step-by-step explanation:

[tex]\large \boldsymbol{} 600p-8h=480 min \\\\ x \ p-4 min \\\\ x=\dfrac{600\cdot 4}{480} =\dfrac{2400}{480} =5 \ portraits \\\\ \rm Answer : 5[/tex]

Answer: (Read Explanation)

Step-by-step explanation:

I have attached a picture of the matching plot.

Answer:

a is 16 yards hope this helps

Step-by-step explanation:

Answer:

Correct answer is A

Step-by-step explanation:

In pic

Credits: Symbolab)

(Hope this helps can I pls have brainlist (crown)☺️)

Answer:

0.333...

Step-by-step explanation:

3 out of 9 can be written as 3/9 which reduces to 1/3.

1/3 = 0.333...

Answer:

56 adults and 35 children

Step-by-step explanation:

sum the parts of the ratio 16 + 10 = 26

Divide 91 by 26 to find one part of the ratio

91/26 = 3.5 ← 1 part of the ratio

16 parts = 16 × 3.5 = 56 ← number of adults

10 parts = 10 × 3.5 = 35 ← number of children

Therefore it 56 adults and 35 children.

To Check the Answer:  56 + 35 = 91

4 times 4 so your awnser is 12

Hope that helps :)

Answer:

16

Step-by-step explanation:

4+4+4+4

Answer: I’m pretty sure they are similar because they have the same interior degree.

Step-by-step explanation: