13. The length of a rectangle is 9 cm more than 2 times the width. If the perimeter of the rectangle is 60 cm,
what are its dimensions?
a. length = 7 cm; width = 23 cm
b. length = 5 cm; width = 16 cm
C. length = 23 cm; width = 7 cm
d. length = 23 cm; width = 16cm

Answer: 118.2

Step-by-step explanation:

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:

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

Answer:

-24

Step-by-step explanation:

[tex]x/4 + 8 = 2\\x/4 = 2 - 8\\x/4 = -6\\x = -6 *4\\x = -24[/tex]

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:

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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:

see explanation

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x )

The function that represents the rotation of coordination by 90° counterclockwise about the origin is R(x, y )= (- y, x ).

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

When the given coordinate (x,y) are rotated rotated 90° counterclockwise about the origin, then the coordinates become (- y, x ).

R(x, y )= (- y, x )

Therefore, the function that represents the rotation of coordination by 90° counterclockwise about the origin is R(x, y )= (- y, x ).

Learn more about Coordinates:

https://brainly.com/question/23450276

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Answer:

7) No

8) Yes

Step-by-step explanation:

7) 15 + 2y = -12 - 4y when y = -0.5

15 + (2*-0.5) = -12 - (4*-0.5)

15 + -1 = -12 - (-2)

15 - 1 = -12 + 2

14 = -10

The numbers are different on both sides so -0.5 is not a solution

8) 5 - 2( 3x + 5 ) = 3 - 10x when x = 2

5 - 2( (3*2) + 5 ) = 3 - (10*2)

5 - 2( 6 + 5 ) = 3 - 20

5 - 2*11 = 3 - 20

5 - 22 = 3 - 20

-17 = -17

The numbers are similar on both sides so 2 is a solution

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)

4 times 4 so your awnser is 12

Hope that helps :)

Answer:

16

Step-by-step explanation:

4+4+4+4

[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:

[tex]-342^{-7}[/tex]

Step-by-step explanation:

If we represent 343 as a power of (-7)

we get [tex]-342^{-7}[/tex]

the equation will be this

= -347 × -347 × -347 × -347 × -347 × -347 × -347

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:

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

More than means addition.

C is the correct option.

= (2x + 4) + 9 - 4y + 3x

= 2x + 4 + 9 - 4y + 3x

= 5x + 13 - 4y

= 5x - 4y + 13

Answer:

5x-4y+13 (c)

Step-by-step explanation:

9-(4y-3x)+(2x+4)

9-4y+3x+2x+4

3x+2x-4y+9+4

5x-4y+13

Answer:

50.37

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:

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

Given :-

To find :-

Solution :-

According to Question ,

As we know that ,

Answer:

2.93 repeating

Step-by-step explanation:

Answer:

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

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

Step-by-step explanation:

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:

look at the picture i have sent

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:

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

Answer:

a is 16 yards hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

Dozen = 12

Use the ratio:

Find x:

Answer:

7

Step-by-step explanation:

7x-6=43

    +6  +6

7x=49

/7   /7

x=7

Answer: x=7

is the answer