the height of a triangle is 4 meters less than the base. if the area of the triangle is 6 m^2 what is the height of the triangle. pls help. solve using applications of quadratics

Answers

Answer 1

Answer:

[tex]2m[/tex]

Step-by-step explanation:

Alrighty let's do this.

We know that formula for the Area of a triangle is:

[tex]A = \frac{1}{2}bh[/tex]

They give us the area as [tex]6m^2[/tex], so let's include it in the equation.

[tex]6 = \frac{1}{2}bh[/tex]

Now we reach a stage where we have 2 unknown variables! That means we can't solve it in its current state. So the idea you should have in cases like these where you have 2 or more unknown variables is, "Can I represent this one variable in terms of another variable?" In this case you can do exactly that. You can represent height in terms of length of the base. We are told the height of the triangle is 4 meters less than the base. That is telling us that [tex]h = b-4[/tex]

So replace [tex]h[/tex] in the equation with [tex]b-4[/tex].

You will now get:

[tex]6 = \frac{1}{2}b(b-4)[/tex]

Now we can work towards solving. Let's get simplifying.

[tex]12 = b(b-4)\\12 = b^2 - 4b\\[/tex]

bring everything to one side so we can make a quadratic and factor:

[tex]0 = b^2 - 4b - 12\\0 = (b-6)(b+2)\\\\b = 6\\b\neq -2[/tex]

We get that [tex]b=6[/tex].

Since we need the height of the triangle we'll need to call back on what h is. We found earlier that [tex]h = b - 4[/tex], so to find h, we just sub in our b value into that.

[tex]h = (6) - 4 = 2[/tex]

We find that [tex]h=2[/tex]


Related Questions

Donell compared the hours students spent each day on social networks to the hours they spent on homework. His data is shown below. Which statements are true?

Answers

It might have to be the amount he spent

What are the circumstances under which a person will feel disadvantage, if the parking ticket is lost​

Answers

The circumstances where an individual will feel disadvantaged if they misplace or lost a parking ticket is that:

The parking attendant will find it difficult and tasking to locate your car in an absence of a parking ticket.You'll also be charged an extra expensive fee for a lost ticket.

What is a parking ticket?

A parking ticket is a piece of paper informing someone that they have parked a car unlawfully or for an excessively lengthy period of time and must pay a fine.

It is also know to be a notice informing a driver of a fee levied for improperly parking, usually written by a traffic officer and placed to a vehicle windscreen.

However, an individual will feel disadvantaged if they misplace or lost the ticket because:

The parking attendant will find it difficult and tasking to locate your car in an absence of a parking ticket.You'll also be charged an extra expensive fee for a lost ticket.

Learn more about a parking ticket here:

https://brainly.com/question/26968718

Order Least to greatest
31/4 , 7.47, 7.706, 7 7/10

Answers

7.47, 7 7/10, 7.706, 31/4

Answer:

Okay ordering them from least to greatest would be  7.47, 7.70, 7.706, and then 7.75.

Step-by-step explanation:

31/4 can also be simplified into 7.75

7.47 stays the same

so does 7.706

and 7 7/10 can be simplified into 7.70

So the order would be 7.47, 7.70, 7.706, and then 7.75.

What's the difference between 2/8 and 5/8?

Answers

Answer:

-3/8

Step-by-step explanation:

3/8 ig ???? cuz 5-2=3 and its the same denominator

What are the solutions to the equation x^2 - 8x= 24

Answers

Answer:

Step-by-step explanation:

Try to get all the numbers and variables on one side of the =

X^2 - 8x - 24 = 0

I think solving this equation via factorisation would be difficult so you should use the quadratic formula which I have attached.

HELP PLEASE IT'S DUE IN AN HOUR, I also need to understand it for future qs

Answers

Answer:

a)5.83cm

Step-by-step explanation:

You have to do 3² × 5² to get the length of AC (the diagonal length of the base of the rectangle) which is √70 or 5.83 rounded to 2 d.p.

not sure about the 2nd bit, but you may have to use trigonometry

How to find the square root of complex numbers?? Find the square root of (6+8i) ??​

Answers

Answer: NaN

Step-by-step explanation: The square root of a complex number can be determined using a formula. Just like the square root of a natural number comes in pairs (Square root of x2 is x and -x), the square root of complex number a + ib is given by √(a + ib) = ±(x + iy), where x and y are real numbers.

http://www.math.com/students/calculators/source/square-root.htm

that's the website I used

You can also maybe do it on a scientific calculator?

Hope that's helpful

How many sides does a polygon have if the sum of the measures of the interior angles is 5940

Answers

Answer:

Sorry for my handwriting

The equation for the sum of interior angles is given by:

[tex]180(x - 2) = sum[/tex]

where x is the number of sides of the polygon.

[tex]180(x - 2) = 5940[/tex]

[tex]180x - 360 = 5940[/tex]

[tex]180x = 5940 + 360[/tex]

[tex]180x = 6300[/tex]

[tex]x = \frac{6300}{180} = 35 \: sides[/tex]

I have this equation that I tried to factor:

2m^2 +7m+6
I got (2m+1)(m+6) because 6*1=6 and 6+1=7
but after confirming it with an algebra solving site, the answer is (2m+3)(m+2)

How would you arrive to this answer? (It would be great if you could explain each step)

Answers

The first coefficient is 2 and the last term is 6. They multiply to 2*6 = 12.

Now we must find two factors of 12 that add to 7 (the middle coefficient).

Through trial and error, you should find that:

3*4 = 12

3+4 = 7

So 3 and 4 are the numbers we're after. We'll split the 7m into 3m+4m and use the factor by grouping method as shown in the steps below.

2m^2 + 7m + 6

2m^2 + 3m + 4m + 6

(2m^2 + 3m) + (4m + 6)

m(2m + 3) + 2(2m + 3)

(m + 2)(2m + 3)

(2m + 3)(m + 2)

The order of the factors doesn't matter since something like 2*3 is the same as 3*2.

------------------------------------------------

Verifying the answer:

You can use technology like you did to check the answer, but here's one way to do it without a calculator.

(2m + 3)(m + 2)

n(m + 2) ...... let n = 2m+3

mn + 2n .... distribute

m( n ) + 2( n )

m(2m+3) + 2(2m+3) .... plug in n = 2m+3

m*2m + m*3 + 2*2m + 2*3 .... distribute

2m^2 + 3m + 4m + 6

2m^2 + 7m + 6

We arrive back at the original trinomial, so we have confirmed the answer.

Pease help me

I will give BRAINLY
THANKS FIVE STARS

Answers

Answer:

23, 25, 27, 29

Step-by-step explanation:

14*2 = 28, 28-5=23

15*2=30, 30-5=25

16*2=32, 32-4=27

17*2=34, 34-5=29

[tex]14 \times 2 - 5[/tex]

[tex]28 - 5[/tex]

[tex]23[/tex]

[tex]15 \times 2 - 5[/tex]

[tex]30 - 5[/tex]

[tex]25[/tex]

[tex]16 \times 2 - 5[/tex]

[tex]32 - 5[/tex]

[tex]27[/tex]

[tex]17 \times 2 - 5[/tex]

[tex]34 - 5[/tex]

[tex]29[/tex]

We can denote these using the function defined by:

f(x)=2x-5

The steps to finding y, for each x are done above!!

hello people ~
factorise: x ^ 2 = 17x + 60​

Answers

Answer:

[tex]\rightarrow \sf x^2=\:17x\:+\:60[/tex]

change sides

[tex]\rightarrow \sf x^2 -17x -60 = 0[/tex]

breakdown, (60 : 20 * 3)

[tex]\rightarrow \sf x^2 -20x +3x-60 = 0[/tex]

factor the following

[tex]\rightarrow \sf x(x -20) +3(x-20) = 0[/tex]

collect into groups

[tex]\rightarrow \sf (x +3)(x-20) = 0[/tex]

final answer

[tex]\rightarrow \sf x=-3, \ 20[/tex]

Answer:

(x-20) (x+3) =0

Step-by-step explanation:

x ^ 2 = 17x + 60​

Subtract 17x from each side

x ^ 2 - 17x = 60​

Subtract 60 from each side

x ^ 2 - 17x - 60=0

What 2 numbers multiply by -60 and add to -17

-20 * 3 = -60

-20 +3 = -17

(x-20) (x+3) =0

Find the value of
(-3)
Show work
Must show work!!

Answers

Answer:

16/81

Step-by-step explanation:

(-2/3)^4

expand...

-2/3*-2/3*-2/3*-2/3

multiply

numerator: -2*-2*-2*-2=16

denominator: 3*3*3*3=81

Thus the fraction is 16/81

Hope this helps!!!


PLEASE LOOK AT PICTURE AND HELP!!!

Answers

Answer:

answer A

Step-by-step explanation:

nnnnmmmkkkkkkookl

PLS ANSWER THIS PLS PLS PLS

Answers

Answer:

20 shirts = $445.00

40 shirts = $541.00

60 shirts = $637.00

Step-by-step explanation:

multiply 20, 40 and 60 by 4.8 then add 349.

20*4.8 = 96

96+349 = 445

40*4.8 = 192

192+349 = 551

60*4.8 = 288

288+349 = 637

During taylor's experiment, which piece of data would be qualitative?

Answers

There isn't any piece of data during Taylor's experiment which can be taken as  qualitative. Thus, correct choice is: Option D: None are qualitative.

What is qualitative data?

Qualitative data tells about the quality or characteristic. It is tough to express it numerically or not at all expressible numerically. They are usually catagorical.

In contrast, there is quantitative data which can be expressed numerically.

The problem is missing its option, which are:

mass of the carsdegree of the ramp inclinetime in secondsnone are qualitative

Mass can be measured (in kgs, grams etc), degree of inclination can be measured (in radians, degree etc), time can be measured (in seconds, minutes etc).

Thus, there isn't any piece of data during Taylor's experiment which can be taken as  qualitative. Thus, correct choice is: Option D: None are qualitative.

Learn more about qualitative and quantitative data here:

https://brainly.com/question/12929865

helppppp
helpppppp helppp

Answers

Answer:

intersect at (-1,-3)

Step-by-step explanation:

y = 4x + 1. the points should be at (0,1) and (-0.25,0) and is an infinite line in both directions.

y = -2x - 5. the points should be at (-2.5,0) and (0,-5) and is an infinite line in both directions.

both the lines meet at (-1,-3) so make a point at that location

Zachary invested $130 in an account paying an interest
rate of 3.6% compounded daily. Assuming no deposits
or withdrawals are made, how much money would be
in the account after 11 years?

Answers

Answer:

i don't know lol

Step-by-step explanation:

it would be better to guess

Answer:193

Step-by-step explanation:

193.15923933 and then round to 193

Solve each pair of simulation equation.Giving both solutions. Multiply both equations by suitable numbers before adding/subtracting to elimination..
A) 6x-7y=9
3x+2y=54



B) 4x -5y =12
2x -3y =8


C)4x -2y=28
3x +3y=12


D)2x +5y =14
13x-11y=-83​

Answers

Answer:

Step-by-step explanation:

I haven't got time to do all these by I'll give you the method in each case.

You have to make the x or y term equal (or 1 term + and other -) in both equations before adding or subtracting.

A . Multiply  equation 2 by 2 and subtract (to eliminate x)

- don't forget to multiply EACH TERM by 2.

B. Multiply  equation 2 by -2 and add.

C.  Multiply  equation 1 by 3 and equation 2 by 2 ( this will give -6y and +6y in the resulting equations ) so  you then add to eliminate y.

D.  Multiply equation 1 by 13 and equation  and equation 2 by 2 to eliminate x then add.

Brainliest if correct

Answers

Answer:

The answer is D

Step-by-step explanation:

Mark brainliest

The perimeter of a quarter circle is 3.57
yards. What is the quarter circle's radius?
P = 3.57 yd

Answers

Given -

The perimeter of a quarter circle is 3.57yards. ie, P = 3.57 yd

To find -

the quarter circle's radius

Solution -

We know to find the perimeter of the quarter of a circle we use the formula,

1/4 × circumference of the circle

= 1/4 × 2πr

= 1/4 × 2×3.14×3.57

= 2.8 yards

And the cross-section perpendicular to the yaxis is a square. Set up a definite integral expressing the volume of the solid

Answers

The volume of the cross-section perpendicular to the solid is the amount of space in the cross-section

How to set up the integral?

The question is incomplete;

So, I will give a general explanation on how to set up a definite integral for volume of a solid

Assume the solid is a cone;

Using the disk method, the integral of the volume is:

[tex]V = \int\limits^a_b {\pi r(x)^2} \, dx[/tex]

Using the washer method, the integral of the volume is:

[tex]V = \int\limits^a_b {\pi [R(x)^2 -r(x)^2 ]} \, dx[/tex]

Read more about volume integrals at:

https://brainly.com/question/18371476

Ariana started a savings account with $240. She deposits $30 into her account at the end of each month. She wants to know how many months it will take for her account to have a balance greater than $500.

Answers

Answer:

9 months

Step-by-step explanation:

$500 - $240 = $260

$260/$30 = 8.67(3s.f.) ≈ 9 months

Recheck:

Balance after 9 months = 240 + (30×9) = 240 + 270 = $510

                                      ∴ $510 > $500

Mai's family is traveling in a car at a constant speed of 65 miles per hour.

a. At that speed, how long will it take them to travel 195 miles?


b. How far do they travel in 30 minutes?

Answers

Answer:

a) 3 hr    b  )  32.5 miles

Step-by-step explanation:

195 m / 65 m/hr = 3 hr

65 m/hr  *  1/2 hr = 32.5 miles

A irrational number less than 0

Answers

Answer:

Minus square root of 2, minus square root of 3, minus pi, minus e, etc. Or, to be a bit more fancy, 1 - pi, 2 - pi, 3 - pi, pi - 4, pi - 5, 2 - e, e - 3, square root of 2 minus 2, etc.

PLEASE, PLEASE LIKE ME AND FOLLOW ME IF YOU LIKE MY ANSWER PLEASE!!!

Gina has a bag of marbles with 5 different colors. She randomly selects a marble from
the bag and then returns the marble to the bag. She does this 300 times. The table
below shows her results.

Answers

Answer:

[tex] \frac{7}{20} [/tex]

Step-by-step explanation:

Red marbles = 33

Blue marbles = 72

Probability of selecting red or blue marbles:

[tex]33 + 72 = 105 \\ \frac{105}{300} = \frac{7}{20} [/tex]

I’m very confused I hate this

Answers

Answer:

12

Step-by-step explanation:

its as easy as this:
what is 4 times 3?

12

Answer: the answer is 12 .

Step-by-step explanation: multiply 4 shirts times 3 shorts will give you 12 . HOPE IT HELPS YOU .PLEASE GIVE BRAINLIEST

.THANKS .

I'd like someone to help me, please!
Julie has 9 rings in her jewelry box. Five are gold and four are silver. If she randomly
selects 3 rings to wear, find each probability:
a) P(exactly 2 silver)
b) P(at least 2 gold)
c) P(all 3 gold or all 3 silver)
d) P(at least 1 silver)

Answers

I think it’s c I’m not sure though

Simplify.
Cubed root of -128x^6y^5

Answers

Answer

-640x^6y

Step-by-step explanation:

Use the triangle to find each of the six trigonometric functions of _. Show all work

Answers

Answer:

you need to find that missing side... so (A squared) x (B squared) = (C squared)

A squared = 5

B squared is missing

C squared = 6

A=25

C=36

36-25= B squared....... B= (square root of 11)

now you need to plug in the numbers for the 6 trig equations...

sin0 = 5/6

cos0 = (square root of 11)/6

tan0 = 5/(square root of 11) which actually equals    5(square root of 11)/11

csc0 = 6/5

sec0= 6/ (square root of 11) which actually equals   6(square root of 11)/11

cot0 = (square root of 11/5

Step-by-step explanation:

A company just paid a dividend of $1.20 per share at the end of the year. It is expected to grow at 12% per year for three years, after that it grows constantly at 6%. The cost of equity is 9.5%. What is the current price of stock?

Answers

The current price of the stock given the dividend, cost of equity and growth rates is $46.90.

What is the current stock price?

Thw two-stage dividend growth model would be used to determine the value of the stock.

First stage:

dividend in Y1 = 1.20x 1.12 = 1.344dividend in Y2 = 1.20 x 1.12^2 = 1.505dividend in Y3 = 1.20 x 1.12^3 = 1.69

Second stage:

Y3 = (1.69 X 1.06) / (0.095 - 0.06) = 51.059

Find the present value of these cash flows

(1.344 / 1.095) + (1.505 / 1.095²) + (1.69 / 1.095³) + (51.059/1.095³) = $46.90

To learn more about the two stage dividend model, please check: https://brainly.com/question/26564273

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