A triangle has side lengths of
(x-8) (4x2 – 3) and (4x2 + 4).
If the perimeter is 650 units, what is the value of x?​

Answers

Answer 1

Given:

The three sides of a triangle are:

[tex](x-8),(4x^2-3),(4x^2+4)[/tex]

The perimeter of the triangle 650 units.

To find:

The value of x.

Solution:

Perimeter of a triangle is the sum of all three sides of the triangle. So,

[tex]Perimeter=(x-8)+(4x^2-3)+(4x^2+4)[/tex]

[tex]Perimeter=8x^2+x-7[/tex]

The perimeter of the triangle 650 units.

[tex]8x^2+x-7=650[/tex]

[tex]8x^2+x-7-650=0[/tex]

[tex]8x^2+x-657=0[/tex]

Splitting the middle term, we get

[tex]8x^2+73x-72x-657=0[/tex]

[tex]x(8x+73)-9(8x+73)=0[/tex]

[tex](x-9)(8x+73)=0[/tex]

Using zero product property, we get

[tex](x-9)=0\text{ and }(8x+73)=0[/tex]

[tex]x=9\text{ and }x=-\dfrac{73}{8}[/tex]

For negative value of x, the side [tex](x-8)[/tex] will be negative, which is not possible because the side of a triangle cannot be negative.

Therefore, the only value of x is 9.


Related Questions

Suppose we want to choose 3 objects, without replacement, from the 4 objects pencil, eraser, desk, and chair.


(a) How many ways can this be done, if the order of the choices is relevant?


?


(b) How many ways can this be done, if the order of the choices is not relevant?

Answers

Answer:24 , 4

Step-by-step explanation:

Given

There are 4 objects

(a)When the order is relevant

We use permutation to get the no of ways, that is

Choosing 3 objects out of 4

[tex]^4P_3=\dfrac{4!}{(4-3)!}=\dfrac{4!}{1!}\\^4P_3=24[/tex]

(b) When the order is not important, the same thing can be done in

[tex]^4C_3\ \text{ways}\\\\\Rightarrow \dfrac{4!}{1!3!}=4\ \text{ways}[/tex]

Solve for x:
3x + 2 = 11
A.
11
5
B. 3
11
13
D.
13
3
E. 6

Answers

Answer:it is b

Step-by-step explanation:

The sum of 10 and twice a number
(an equation)

Answers

Answer:

10+2x= the sum (anything could be put here)

Step-by-step explanation:

Well sum is automatically addition

Doubleing a number is basically multiplying it by 2

so

10+2x= whatever youw ant to put here

I need help please!!

Answers

c, d, and e is the answer
c, d, and e are the answers

need help please hurry

Answers

i think it is 5ft sorry if i’m wrong
I’m pretty sure it’s five or 6 feet

Can someone help me solve this

Answers

Answer:

BC=15.01

Step-by-step explanation:

tan(65) = x/7

x = 7 x tan(65)

x = 15.01

 please help me ahhh im doing 8th grade math with pythagorean theorem

Answers

I think it isnt a right triangle, but im sorry if thats wrong

Step-by-step explanation:

The pythagorean theorem is the sum of the two legs squares equal the hypotenuse squared.

The hypotenuse is the longest side so 3.5 is our hypotenuse.

Apply formula to see of true.

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {2.5}^{2} + {3}^{2} = {3.5}^{2} [/tex]

[tex]6.25 + 9 = (3.5 {}^{2}) {?} [/tex]

[tex]15.25 = 12.25 {?}[/tex]

So it isn't a triangle since they aren't equal

Favorite Color
red
32.86 %
blue
24.36 %
yellow
15 %
green
27.78 %
1728 students were asked to name their favorite color.
The results are shown in this circle graph.
How many students gave green as their favorite?
O A 94
OB. 480
O c. 28
D. 432
O E. 568

Answers

Answer:

I say 28

Step-by-step explanation:

because its 27 and it's almost to 28

Answer:

E. 568

Step-by-step explanation:

A graph of a system of two equations is shown. HELP!!!!!

Answers

Answer:

8 and 2

Step-by-step explanation:

8 and 2 because y=5x +3 would be 5+3 which is 8 and y= 3x - 1 would be 3 - 1 which equals 2.

Convert to a mixed number and simplify: 83/6
6
83​

Answers

Answer:

13 5/6

Step-by-step explanation:

83/6 = ?

6 can go into 83, only 13 times. Which would make 83/6 turn into:

13 5/6

Hopefully this helps :3 sorry if wrong :( Plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3

-Bee~

A map of the Orchid Hill Neighborhood is shown. The population of Orchid Hill Neighborhood is 360 people.

Answers

Answer:

(a) The area is 0.03 square miles

(b) The population density is 12000 people per square miles

Step-by-step explanation:

Given

See attachment for complete question

Solving (a): Area of Orchid Hill (in square miles)

The dimension of the neighborhood is 4 blocks by 3 blocks

Since each block are of the same dimensions

The area is calculated as:

[tex]Area = 4blocks * 3 blocks[/tex]

If [tex]20\ blocks = 1\ mile[/tex] then:

[tex]1\ block = \frac{1}{20} mile[/tex]

[tex]1\ block = 0.05mile[/tex]

So, we have:

[tex]Area = 4blocks * 3 blocks[/tex]

[tex]Area = 4 * 0.05 * 3 * 0.05[/tex]

[tex]Area = 0.03mi^2[/tex]

Solving (b): The population density of the neighborhood as people per square mile

From the question, we have:

[tex]People = 360[/tex]

[tex]Area = 0.03mi^2[/tex] --- calculated

So, the population density is:

[tex]Density = \frac{People}{Density}[/tex]

[tex]Density = \frac{360}{0.03}[/tex]

[tex]Density = 12000[/tex]

What is the surface area of the victory podium shown here? Include all surfaces of the podium, including the bottom. A. 61.5 square feet B. 61.75 square feet C. 65.25 square feet D. 69 square feet

Answers

Answer:

69

Step-by-step explanation:

the formula is 2( base x height) + 2 (base x width) + 2( height x width)

do that for top rectangle and bottom and add them together

Answer:

65.25 square feet.

The area of a rectangle is 38.5 square inches. The base of the rectangle is 4 inches. What is the height of rectangle?

Pls help me on this one. PLSSS :(

Answers

Answer:

The answer is 9.625

Step-by-step explanation:

So what you have is the area and the base of the rectangle. To find the height, just divide 4 into 38.5

38.5 / 4 = 9.625

To double check just multiple 9.625 by 4

9.625 x 4 = 38.5

Hope this helps

What's the circumference of a circle with a radius of 10 inches

Answers

Answer:

5

Step-by-step explanation:

5

find the perimeter of the figure

Answers

Answer:

the perimeter is 97 cm

Step-by-step explanation:

we find this by adding the lengths of all the sides

Answer:

10+3+3+33+33+15=97

Step-by-step explanation:

Can you maybe put up the explanation too and not just the answer? Thank you

Answers

Hope it helps you! .........

Consider the quadratic equation 3x^2-6=2x. (a) What is the value of the discriminant? (b) What does the discriminant of the quadractic equation tell about the solutions to 3x^2-6=2x?

Answers

Answer:

(a) discriminant is positive, 76

(b) the above tells you there are two real roots

Step-by-step explanation:

the discriminant is 'b² - 4ac'

3x² - 2x - 6 = 0  ∴ a = 3, b = -2, c = -6

(-2)² - 4(3)(-6) = 4 + 72

(a) The discriminant of the quadratic equation is positive, 76.

(b) The quadratic equation tells you there are two real roots.

What is a quadratic equation?

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

The discriminant of a polynomial in mathematics is a quantity that depends on the coefficients and enables inference of some root features without computing them.

Given that the quadratic equation 3x²-6=2x.

The discriminant Of the quadratic equation is calculated by the formula below:-

D = b² - 4ac

3x² - 2x - 6 = 0  ∴

a = 3, b = -2, c = -6

Put the value of the coefficient to get the value of the discriminant.

D = (-2)² - 4(3)(-6) = 4 + 72 = 76

Therefore, the discriminant of the quadratic equation is positive, 76, and the quadratic equation tells you there are two real roots

To know more about a quadratic equation follow

https://brainly.com/question/1214333

#SPJ2

621.72 round to the nearest whole number

Answers

Answer:

622

Step-by-step explanation:

Please mark brainliest

Answer:

Hi! The answer to your question is 622

Step-by-step explanation:

☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆

☆Brainliest is greatly appreciated!☆

Hope this helps!!

- Brooklynn Deka

Hannah has an offer from a credit card issuer for 0% APR for the first 30 days
and 12.22% APR afterwards, compounded daily. What effective interest rate
is Hannah being offered?
A. 11.87%
B. 13.00%
C. 12.93%
D. 12.22%

Answers

i believe the answer is A.11.87% because interest rates tend to be lower than APR

If the first 30 days and 12.22% APR afterwards, compounded daily. The effective interest rate is: A. 11.87%

Effective interest rate

After 1 year the daily percentage rate is compounded for:

(365 days - 30 dyas) = 335 days

Hence:

Effective interest rate=(1+0.1222/365)^335-1

Effective interest rate=(1+0.1222/365)^335-1

Effective interest rate=(1+0.00033479)^335-1

Effective interest rate=(1.00033479)^335-1

Effective interest rate=(1.11866-1)

Effective interest rate=0.11866×100

Effective interest rate=11.87% (Approximately)

Therefore the effective interest rate is: A. 11.87%.

Learn morer about effective interest rate here:https://brainly.com/question/8098678

#SPJ2

I need help with this and the first person who can answer this correctly gets a BRANLIST​

Answers

Answer:

c

Step-by-step explanation:

c because no x values repeat

Lines a and b are parallel. The slope of line b is 1/3 . What is the slope of line a?

Answers

Answer:

1/3

Step-by-step explanation:

Used to coordinate gird plane to find a distance between the points round to the nearest hundred

Answers

Answer:

8.94

Step-by-step explanation:

Distance formula:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

[tex]d = \sqrt{(3 - (-5))^2 + (2-6)^2}[/tex]

[tex]d = \sqrt{(64 + 16)}[/tex]

[tex]d= \sqrt{80}[/tex]

[tex]d= 8.94[/tex]

Please I need help ASAP 40. Points

Answers

Total owed = starting amount x( 1 + interest rate) ^ time

The equation would be total = 550(1.12)^x where x is the number of months.

Replace total with 550x2 = 1100 and solve for x

It will double in 6.11 months. Round to 6 months

iPaddle charges $15 for paddleboard rentals plus $5 per hour. Write an equation in slope- intercept form to represent this situation where y represents the total cost, for x hours.

Answers

Answer:

Y=5/1x+15

Step-by-step explanation:

I know this is old, but no one answered it so I thought I would

i think what the person above of me said is right

What the answer. ? Please no links

Answers

Answer:

would not be able to use 3 1/2 ft

Step-by-step explanation:

8.5 + 4.5 > 3rd side   ∴ 3rd side must be less than 13 feet

4.5 + 3rd side > 8.5   ∴ 3rd side must be greater than 4 feet

What is the best estimate for the quotient of the problem below? Round your answer to the nearest whole number

Answers

Answer:13

Step-by-step explanation: turn 6 1/4 into an improper fraction. Then, proceed to do the reciprocal of 1/2 which is 2/1 since this is division. You should get 12.5 and round from there to 13.

Help please. Question below.

Answers

The answer is to your question is x^2 - 8x

Please help help me please ASAP I am begging someone please
No links or files

Answers

Answer:

1. b

2. e

3. a

4. f

5. g

Step-by-step explanation:

hope this helps

HELPP ME PLEASE!!!!!

Answers

Answer:

-6×-4 and -2×-12 are pairs

-3×4 and 6×-2 are pairs

-8×-2 and 4×4 are pairs

the rest are left overs

When Ben does his math homework, he finishes 10 problems every 7 minutes. At this rate, how long will
it take him to complete 35 problems?lols please help.

Answers

Answer:

in 7 minutes he solve 10 problems

he solve one problem in = 7/10= 0.7 minute

he solve 35 problem in = 0.7x35= 24.5 minute

Step-by-step explanation:

hope it helps ❤️

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