A rectangle has an area of k2 + 19k + 60 square inches. If the value of k and the dimensions of the rectangle are all natural numbers, which statement about the rectangle could be true? The length of the rectangle is k – 5 inches. The width of the rectangle is k + 4 inches. The length of the rectangle is k – 20 inches. The width of the rectangle is k + 10 inches.

Answers

Answer 1

Answer:

The width of the rectangle is k+4 inches

Step-by-step explanation:

you have [tex]k^{2}+19k+60[/tex] which can be factorized to (k+4)(k+15)

if the length of the rectangle is k-5 that would mean that we can write [tex]k^{2}+19k+60[/tex] as (k-5)n which we know is false, so the only one that applies is k+4

Answer 2

The true statement is:

"The width of the rectangle is k + 4"

Which statement is true?

Remember that for a rectangle of length L and width W, the area is given by:

A = L*W

So we want to factorize the area equation, which is a quadratic equation, into a product of two terms.

A = k^2 + 19k + 60

The two zeros are given by Bhaskara's formula:

[tex]k = \frac{-19 \pm \sqrt{19^2 - 4*1*60} }{2} \\\\k = \frac{-19 \pm 11 }{2}[/tex]

So we have two zeros, these are:

k = (-19 - 11)/2 = -15

k = (-19 +11)/2 = -4

So we can factorize the area as:

A = (k - (-15))*(k - (-4)) = (k + 15)*(k + 4).

From this, the only statement that can be true is:

"The width of the rectangle is k + 4"

If you want to learn more about quadratic equations, you can read:

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Related Questions

This formula v = u + at, links:

initial velocity (u)

final velocity (v)

acceleration (a)

time (t)

What is the value of v if u = 5, a = 10 and t = 2?

Answers

Answer:

[tex]v=u+at[/tex]

[tex]v= 5+(10)\times2\\v=25[/tex]

FAST ANSWER PLEASE THANKS

Answers

Answer: D

Step-by-step explanation:

When you are asked what is the domain, you are basically asked what x values work for the function.

Multiply the function to get [tex]xe^x + 6e^x[/tex]

[tex]e^n[/tex], n being any real number, is defined for every value you input for n. So its domain is all real numbers

Its range is also all real numbers because the domain is continous for every single value you plug in

y=-5y=−5 Evaluate this expression: 3y+6=3y+6=

Answers

Answer: 3y+6

Step-by-step explanation:

At Central Online High School, 45/100 of the students have a dog, 30/100 of the students have a cat, and 18/100 of the students have both a dog and a cat. What is the probability that students who have a cat also have a dog?

Answers

Answer:

6/15

Step-by-step explanation:

18/30 becuase 30 have a cat and 18 have both.

18/30 = 6/15

I'm always happy to help :)

*EASY GRADE 7 MATH*
BEST ANSWER WITH EXPLANATION WILL BE MARKED BRAINLIEST!

Evelyn wants to cover the top of a circular table with a price of cork board to protect it from spills. How much cork board will Evelyn need to completely cover the table if the diameter of the table is 48 inches?
Select ALL that apply. (possible answers on image)

Answers

Answer:

576π in² and 1,809 in².

Step-by-step explanation:

To find the answer, the formula for the area of a circle, or A = πr², will need to be used.

In this question, we are only given the diameter. Simply divide by 2 to calculate the radius:

48/2 = 24 inches.

Now, plugging this into the equation for the Area of a Circle, gets us:

A = π24²

A = 576π or 1808.64 in².

Looking at the answer choices, we can choose 576π in² and 1,809 in² (as 1808.64 ≈1809)

I’m kinda stuck on this, could anyone explain it ?

Answers

The slope of the given line is -3/4.

Any line perpendicular to this one will have slope -1/(-3/4) = 4/3.

Use the given point and the point-slope formula to get the equation of the particular line:

y - (-1) = 4/3 * (x - 0)

y + 1 = 4x/3

y = 4x/3 - 1

this question is my thing

Answers

Answer:

Below

Step-by-step explanation:

8 is classified as a rational number because it can be made into a fraction. 8.8 = 8 8/10 = 88/1

how is converting percentages to and from fractions and decimals used in daily life

Answers

Answer & Step-by-step explanation:

We use decimals every day while dealing with money, weight, length etc. Decimal numbers are used in situations where more precision is required than the whole numbers can provide. For example, when we calculate our weight on the weighing machine, we do not always find the weight equal to a whole number on the scale.

what are the values a b and c in the quadratic equation 0 equals 5x - 4x^2- 2​

Answers

Answer:

A: -4

B: 5

C: -2

Step-by-step explanation:

The equation we are given is 5x-4x²-2. We can rewrite this in order of standard form.

-4x²+5x-2

Now that we have the standard form, we can find a, b, and c. A, B, and C ar ethe coefficients of each term.

A: -4

B: 5

C: -2

Suppose that you placed $500 in a bank account at the end of each year for the next 10 years. How much would be in that account at the end of the tenth year if the deposits earned an annual rate of return of 8% each year?

Answers

Answer:

5400$

Step-by-step explanation:

First, you need to figure out 8% of 500$.

That is 40$.

Now, you need to multiply 500 by 10, because there are 10 years.

That is 5000$

Now, we need to add the 8% that was added each year. So we do 40$ times 10.  400$

Then we add the 5000 and 400.

The answer is 5400$

I really hope this helped you! So sorry if it doesn't!

how many servings are in 8 liters of honey if one serving is 1/4 of a liter?

Answers

Answer:

32 servings

Step-by-step explanation:

Take the amount of honey and divide by the size of a serving

8 ÷ (1/4)

Copy dot flip

8 * 4/1

32

There are 32 servings

Answer:

32 servings

Step-by-step explanation:

Find x in this proportion. x/3 = x+2/5 x =

Answers

[tex]x = 3 \\ solution \\ \frac{x}{3} = \frac{x + 2}{5} \\ or \: 5x = 3(x + 2)(cross \: multiplication) \\ or \: 5x = 3x + 6 \\or \: 5x - 3x = 6 \\ or \: 2x = 6 \\ or \: x = \frac{6}{2} \\ x = 3 \\ hope \: it \: helps[/tex]

7. A shopkeeper can buy 36 toys for $20.52. What will be
for 120 toys?​

Answers

Answer:

$68.40

Step-by-step explanation:

Let x represent the required cost.

Since the number of toys is directly proportional to the cost:

x : $20.52 = 120 : 36

i.e.  x/$20.52 = 120/36

      x = ([tex]\frac{120 * $20.52}[/tex])/36

      x = $2462.40/36

      x = $68.40

Hope this helps!!!

How many two-digit primes have both their digits non-prime?

Answers

Answer:

89

Step-by-step explanation:

8 is divisible by 4

And 9 is divisible by 3

PLEASE HELP IM STRUGGLING here is a rectangle all the measurements are in centimeters
The perimeter of the rectangle is 39cm
Work out the area of the rectangle

Answers

Answer:

Area of the rectangle = 95 cm²

Step-by-step explanation:

Perimeter of the rectangle = Sum of the measures of the sides of the rectangle

From the figure attached,

Perimeter of the rectangle = 2[(3x -1) + (2x + 3)]

                                       39 = 2(5x + 2)

                                       39 = 10x + 4

                                      10x = 39 - 4

                                      10x = 35

                                          x = 3.5

Therefore, measure of the given sides will be,

Length = (3x - 1) cm

3x - 1 = (3×3.5) - 1

        = 10.5 - 1

        = 9.5 cm

Width = (2x + 3) cm

2x + 3 = (2×3.5) + 3

          = 7 + 3

          = 10 cm

Area of the rectangle = Length × width

                                   = 9.5 × 10

                                   = 95 cm²

Therefore, area of the rectangle is 95 cm².

How do I post a picture

Answers

Answer:

Go to me. Click on your profile picture then click on your profile picture again to change it

factorise 6 x ^2 + 17 X + 5​

Answers

Answer:

( 3x + 1) (2x+5)

Step-by-step explanation:

6 x ^2 + 17 X + 5​

We break the 6 into 3 and 2

(3x    ) (2x   )

We need the middle term to be 17

( 3x + 1) (2x+5)

3*5+2 = 17 so it works

(3x+1)(2x+5)
So it works

Please answer (-3+4)2 and another one is -5(4-2) I need answers to both pleaseee

Answers

Answer:

Step-by-step explanation:

Think of the outside function as a scaling quantity. You are applying that outside term to each and every term on the inside, Thats the basis for the distributive property.

1.)3 x 2 + 3 x 8 = 24

Now that you got the steps down, ima do the rest in my head

2.) 2

3.) -10

4.) -50

Answer:

Step-by-step explanation:

Distributive property: a(b +c) = ab + ac

                                    a(b - c) = ab - ac

1) 3(2 + 8) = 3*2 + 3*8

                = 6 + 24

                = 30

2) (-3 + 4)2 = -3*2 + 4*2

                 = -6 + 8

                = 2

3) -5(4 - 2) = -5*4 - (-5)*2

                 = - 20 + 10

                = -10

4)(12 +13)(-2) = 12*(-2) + 13 *(-2)

                    = -24 - 26

                    = -50

What is the x-value of the vertex?

f(x)=(x+2)^2−1

x-value of the vertex:

Answers

Answer:

-2

Step-by-step explanation:

x-value of the vertex is -2.

What is vertex form of parabola?

The vertex formula helps to find the vertex coordinates of a parabola. The standard form of a parabola is [tex]y = ax^{2} + bx + c.[/tex] The vertex form of the parabola  [tex]y=a(x - h)^{2} + k.[/tex]

Given

[tex]f(x)=(x+2)^{2}- 1[/tex]............................(1)

The vertex formula helps to find the vertex coordinates of a parabola.

The standard form of a parabola is [tex]y = ax^{2} + bx + c.[/tex]

The vertex form of the parabola  [tex]y=a(x - h)^{2} + k.[/tex]

By comparing vertex form of parabola in equation 1

a = 1, h = -2 , k = -1

Hence, x-value of the vertex is -2

Learn more about vertex form of parabola here

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Determine the value of
f(2) when
f(x)=x² - 5x+2

Answers

Answer:

-4

Step-by-step explanation:

Substitute [tex]x = 2[/tex] in to the function

[tex]f(2) = 2^2 -5(2) + 2[/tex]

= -4

Urgent! Please help fast! Estimate using mental math: 903.6 ÷ 29.1. Show how you would estimate mentally, then show your estimated answer.

Answers

Answer:

31

Step-by-step explanation:

I would use my fingers mostly.

But, I just do it normally. I pretend I'm using a sheet of paper then I write on it for the equation.

903.6 divided by 29.1

Then I estimate it because I know that 29.1 can go into 903.6 about 31 times. Then I multiply 31 and 29.1 and i get around 903.6.

I hope this helps. I'm sorry if you get this wrong.

Answer:

30

Step-by-step explanation:

Round 903.6 to 900 and 29.1 to 30

So 900/30

= 30

This would be my estimated answer

Also 30^2

= 900

If x = 4 and y = 8 , evaluate the following expression: x/y Give your answer as a fraction in its simplest form.

Answers

Answer:

X/Y = 4/8= 1/2

Step-by-step explanation:

This is the answer of this question

What should be done first to simplify 11 – 2 + 7 + 5 – 8 + 13

Answers

Answer:

I think the first step is to group all the addition first and then you do the subtraction.

Answer:

Remember PEMDAS; parenthesis, exponents, multiplication, division, addition and subtraction.

Step-by-step explanation:

so ti will be;

2+7+5-8+13

27-8

21

Uma lousa digital possui uma forma retangular e tem sua largura expressa pelo polinômio b+2. Sendo sua área igual ao polinômio B ao quadrado + 5b+ 6, qual é o polinômio que expressa a altura dessa lousa?

Answers

Answer:

b+3

Step-by-step explanation:

Largura : b+2

Área: b² +5b +6

Sabe-se que a área de um retângulo é dada pela largura multiplicada pela altura.

A partir dos zeros da equação da área é possível encontrar o polinômio da altura:

[tex]b^2 +5b +6\\b=\frac{-5\pm \sqrt{25-4*1*6} }{2} \\b'=-2\\b''=-3[/tex]

Visto que o polinômio da largura é b+2, para que a equação da área seja válida, o polinômio da altura deve ser b+3.

A prova pode ser feita pela multiplicação dos polinômios:

[tex]A = L*H\\A=(b+2)*(b+3)\\A=b^2+5b+6[/tex]

The velocity of an object in meters per second varies directly with time in seconds since the object was dropped, as represented by the table. The acceleration due to gravity is the constant of variation. What is the acceleration due to gravity of a falling object?

Answers

Answer: 10.2

Step-by-step explanation:

What is the frequency of a wave with a period of 0.2 seconds?

Answers

Answer:  5 Hz

The frequency is the inverse of period... Them:

[tex]f=\frac{1}{T}=\frac{1}{0.2}=5 Hz[/tex]

HELP ANYONE PLEASE RIGHT ANSER ?!

Answers

Answer:

B.

Step-by-step explanation:

They all are alternating interior angles so they'll be congruent.

Answer:

B. Alternating interior angles are congruent

Step-by-step explanation:

The angles that are in the statements are all interior angles. When compared to each other, they lie on opposite sides of the transversal.

please answer asap! A couple plans to have 5 children. The gender of each child is equally likely. Design a simulation involving 125 trials that you can use to model the genders of the children. Write your answers as numbers.

Answers

Step-by-step explanation:

The gender of a child which is either a boy or a girl is determined by the XX-chromosomes, or XY-chromosomes.

Since the couple plan to have 5 children, the chance of a child being a boy is equal to the chance of it being a girl - the chances are 50/50.

What we do to achieve our aim is to run a simulation that would add an X or Y to an X for all 5 children.

Doing this 125 times, we obtain the number of trials we desire.

For each trial, we get for each child, C:

C1: X + (X or Y)

C2: X + (X or Y)

C3: X + (X or Y)

C4: X + (X or Y)

C5: X + (X or Y)

Since the chance of having an X is equal to the chance of having a Y, they equal probability, which is 0.5 for each.

what is the solution to the equation x-16=-8

Answers

Answer:

x = 8

Step-by-step explanation:

8 minus 16 equals to a negative answer, resulting to -8.

Answer:

x = 8

Step-by-step explanation:

Add 16 to both sides of the equation.

x = −8 + 16

Add − 8 and  16

 x = 8

Answer the following Questions
Which of the following points lie on the x-axis?
A(1, 1), B (1.0). c (0,1)D (0,0), E (-1,0), F (0-1), G (4,0), H (0,7)​

Answers

Answer:

B, D, E and G lies on X axis

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