Mathematics College

the height of triangle is 8 meters less than its base. if the area of the triangle is 212.5 square meters, find the length of its bas and heiight.

Answers

Answer 1
If
b = length of base in meters, then
h = (b-8) m

Area of a triangle, A = (1/2)bh

Therefore,
212.5 = (1/2)(b)(b-8) = (1/2)(b^2-8b)
425 = b^2-8b
b^2 - 8b -425 =0
Solving the resulting quadratic equation;
b = [8+/- Sqrt [8^2 - 4(1)(-425)]]/2(1) = 4+/- 21 = 4+21 = 25 m (ignore negative value as it is not applicable)
Then,
h = b-8 = 25 - 8 = 17 m

Therefore,
Base = 25 m
Height = 17 m
Answer 2

Final answer:

The base of the triangle is 25 meters, and the height is 17 meters. This was calculated using the area formula for a triangle and by solving the resulting quadratic equation by using the quadratic formula.

Explanation:

The area of a triangle is given by the formula 1/2 × base × height. Given that the area is 212.5 square meters and the height is 8 meters less than the base, let's call the base 'b' and the height will then be 'b - 8'. Using the area formula:

Area = 1/2 × base × height

212.5 = 1/2 × b × (b - 8)

Multiplying both sides by 2 to get rid of the 1/2 gives:

425 = b × (b - 8)

Now we have a quadratic equation in the form of:

b² - 8b - 425 = 0

We can solve this equation by factoring or using the quadratic formula. In this case, the equation doesn't factor neatly, so we use the quadratic formula:

b = (-(-8) ± √((-8)² - 4 × 1 × (-425)))/(2 × 1)

b = (8 ± √(64 + 1700))/2

b = (8 ± √(1764))/2

b = (8 ± 42)/2

Since the base cannot be negative, we take the positive root:

b = (8 + 42)/2

b = 25 meters

Therefore, the base of the triangle is 25 meters and the height is b - 8 = 25 - 8 = 17 meters.

Related Questions

Find F'(x) for F(x) = [x^3,1] integral cos(t^4)dt

A. cos(1)-cos(x^12)
B. -3x^2cos(x^12)
C. cos(x^7)
D. -cos(x^12)

Answers

The upper limit is constant, so the derivative of the integral evaluated there is 0. The derivative of the integral evaluated at the lower limit is the product of the integrand evaluated at the lower limit and the derivative of the lower limit. 
  F'(x) = 0 -cos((x^3)^4)·3x^2
Simplifying, ...
  F'(x) = -3x^2·cos(x^12)

The appropriate choice is ...
  B. -3x^2cos(x^12)

I need help

Circle P is below

Answers

1. remember all of them add up equal to 360 degree.
2. add all of them up together
[tex](4y + 6) + (7y - 7) + (20y - 11) = 360[/tex]
3. combine like term then solve for Y
4. you will figure the arc measure of BC when you get answer for Y.
20y-11+4y+6+7y-7=360
31y-12=360
31y=360+12
31y=372
y=372/31=12

BC=BA+AC=4y+6+7y-7=11y-1
BC=11*12-1=131⁰

What is the y-intercept of the quadratic y=-2x^2-4x-5 ?
(-5,0)
(0,-2)
(-1,3)
(0,-5)

Answers

y - intercept is f(0) then (0; m)

We have:

[tex]y=-2x^2-4x-5\to f(0)=-2(0)^2-4(0)-5=-5[/tex]

Answer: (0; -5)

need help fast don't understand both A and B show work please

Answers

Problem A
Usually the number of bits in a byte is 8 or 16 or 32 and recently 64. You don't have to write a formula to restrict it to this number of bits. You are not asked to do so. The general formula is 2^n - 1 for the problem of Millie and her golden keys. Somehow the system can be made to choose the right number of bits. Apple IIe s for example, used 8 bits and there was a location that told the processor that fact.

2^n - 1 <<<<< Answer

Problem B
In this case n = 4
2^n - 1 = 2^4 - 1 = 16 - 1 = 15


Millie can collect 15 keys <<<<<< Answer

Q #15 Graph ARTS With vertices R(6, 6), S(3, -6),and T(0, 3) and its image. over the Y -axis

Answers

The rule of reflection over y-axis
(x,y) ⇒⇒⇒ (-x,y)
Note point T will not change
the solution is as shown in attached figure

205/1000 is less then are greater then 0.205

Answers

its equal to because 0.205 is 205/1000 as a fraction

giovanni justifies what is expression -4x - 8 is equivalent to -2( x + 1) - 2 ( x + 3 ) by letting x equal 3 in both expressions what is the value of each expression when x equals 3

Answers

Hello!

You put 3 in for x in both equations

Equation 1
-4(3) - 8 = 

Multiply

-12 - 8 = -20

The answer is one of the ones with -20
------------------------------------------------------------------------------------------------------
Equation 2
-2(3 + 1) - 2(3 + 3)

Do what is in paraenthesis

-2(4) - 2(6)

Multiply

-8 - 12 = -20
------------------------------------------------------------------------------------------------------
The answer is C) -20 and -20

Hope this helps!

Answer:

C. -20 & -20

Step-by-step explanation:

If you substitute x for 3 in the expressions, they will both evaluate to -20.

Thus, the answer is -20

show this fraction as a decimal 1 1/4

Answers

1 = 1

1/4 is the same as 25/100 (if you multiply 25 top and bottom). 25/100 = 0.25

1 + 0.25 = 1.25

1.25 is your answer

hope this helps
Fraction: 1 1/4
Decimal: 1.25
Think about like this: kinda like money
1/4: 25 (cents)
2/4 50 (cents)
3/4 75 (cents)
4/4 100 (cents) or 1 (a dollar bill)
Hope that could help out!

Pythagorean theorem to determine if a triangle with sides 2 ft,5ft,4ft is a right triangle

Answers

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

[tex] 2^2 + 4^2 = 5^2 [/tex]

[tex] 4 + 16 = 25 [/tex]

[tex] 20 = 25 [/tex]

Since 20 = 25 is clearly a false statement, the three side lengths 2 ft, 4 ft, and 5 ft do not form a right triangle.

MpRashawn recently spent $100 to open a store selling tee-shirts. At his business, he purchases plain tee-shirts for $11 each, prints graphics on them, and then sells them for $26 each. What is the minimum number of tee-shirts that Rashawn would need to sell in order to make a profit (total income minus total expenses) of at least $400?

Answers

26-11=15
400÷15=26,(6)
He would need to sell 27 T-shirts

Rashawn would need to sell 20 T-Shirts in order to make a profit of at least $400.

What is profit percentage?

SP-CP divided by CP multiplying with 100 we get profit percentage.

P= [(SP-CP)/CP ] × 100

Given the following details about Mr. Rashawn.

Mr. Rashawn recently spent = $100 to open a store selling tee-shirts

He purchases plain tee-shirts for = $11 each

Then sells them for = $26 each

Profit on each shirt = $26 - $11 = $15

Profit = $400 -$100= $ 300

Number of t- shirts= $300/15 = 20 T -shirts.

Thus, Rashawn would need to sell 20 T-Shirts in order to make a profit of at least $400.

Learn more Profit Percentage here:

https://brainly.com/question/11018349

#SPJ2

When multiplied, what is the simplified form of (5 − 2i)(1 − 2i)? Write the answer in standard form, a + bi, where a and b are real numbers.

Answers

(5 - 2i)(1 - 2i) You can solve this as though it was (x - 2)(x + 3): use foil

F: 5*1 = 5
O: 5 *(-2i) = - 10i
I : -2i * (1) = - 2i
L: (-2i)(-2i) This may take a bit. There's a few signs hanging around.
L: (-2 * -2)*(i * i)
L: 4 (i *i)
L: 4(-1)
L: - 4 So combine these results.

FOIL: 5 - 10i - 2i - 4 Group the like terms
FOIL: 5 - 4 - 10i - 2i Now collect them
FOIL: 1 - 12i <<<<<<< Answer

The American flag is customarily made with its width and length in the ratio of 10 to 19. Which of the following dimensions is in the correct ratio for the flag?

Answers

Final answer:

The given dimensions do not match the American flag's customary ratio of 10 to 19. To find the correct dimensions, the numbers must divide to equal approximately 0.5263. None of the provided options are correct.

Explanation:

The American flag is customarily made with its width and length in the ratio of 10 to 19. To ensure the dimensions are correct, we must find a pair of numbers that, when divided, are in the same proportion as 10/19 (approximately 0.5263). Looking at the listed dimensions:

51 H (Height is not a width or length measurement, so we cannot confirm the ratio)

53 x 38 (53/38 = 1.3947 which is not equal to 10/19)

55 x 0.025 (55/0.025 = 2200 which is not equal to 10/19)

57 x (2.93, 3.59) (This does not provide a pair of length and width measurements)

59 (This is not a dimension)

Since none of the provided options has numbers that mirror the 10 to 19 ratio of the flag, none of these dimensions would be correct for an American flag. If we want to find dimensions that are proportional, we have to look for any two numbers that, when divided, equal approximately 0.5263. Hence, an example of a correct dimension following the flag's ratio would be 10 inches by 19 inches or any multiple thereof.

of the pizzas sold last week at vondras pizzaria 7/12 were large pizzas and 1/4 were extra large pizzas, what fraction of the pizzas aild were either large or extra large? enter your answer simplified and as a proper fraction

Answers

7/12 + 1/4
7/12 + 3/12 = 10/12

10/12 of the pizzas sold were either large or extra large

I hope this helps :)

Answer:

Step-by-step explanation:

7/12 + 1/4

7/12 + 3/12 = 10/12

10/12 of the pizzas sold were either large or extra large

-845 degree coterminal angle

Answers

check the picture below.

with negative angles, we go "clockwise", the same direction a clock hands move.

so -360-360-125 = -845.

so as you see in the picture, you go around twice, and then a little bit more, an extra 125°, landing you at -125°, or its positive counterpart, 235°.

The Tigers’ first play when they had possession of the ball went for -3 yards. Did the Tigers gain or lose yards on that play? How many yards did they gain or lose?

Answers

On the first play the Tigers lost yards.  The number of yards they lost was 3 yards.  We know this because the integer that is shown is -3.  This negative value is move to the left or down on the number line.  It represents a negative change, and in football it is a loss of yards. 

Answer:

The correct answer is (The Tigers lost 3 yards on that play.)

A cross-section​ of a light reflector is a parabola. The bulb is located at the focus. Suppose the bulb is located 11 in from the vertex of the reflector.

Use this information to make the following determinations.
Model a cross section of the reflector by writing an equation of a parabola that opens upward and has its vertex at the origin.

Answers

An equation of a parabola that opens upward and has its vertex at the origin,

⇒ y² = - 8 x

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Now,

The equation of the parabola turned to the left is to the negative side of the coordinate system is:

⇒ y² = - 2 p x  

where, p is the parameter of the parabola

The relationship between the parameter and the focus is.

⇒ p = 2 f  

=> p = 2 × 2

⇒ p =  4 cm  

Then, the equation of the parabola is:

y² = - 2 p x

    = - 2 × 4 x

     = - 8 x

Therefore, An equation of a parabola that opens upward and has its vertex at the origin,

⇒ y² = - 8 x

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ3

Which statistic is used to test a global hypothesis about a multiple regression equation?

Answers

Answer:  an " F-statistic " .
_____________________________________________________

what is the answer to the problem above?

Answers

4 × 25 = 100
5 × 18 = 90
100/90 = 10/9 = 1 1/9

Over 4 hours, the temperature in Miami, Florida, rose 8ºF. How many degrees, on average, did the temperature rise per hour

Answers

2ºF is the answer you are looking for

Answer:

The correct answer is 2°F

Step-by-step explanation:

Your equation is 8÷4

8÷4=2

I hope this helps :)

please help me out i will reward brainliest

Answers

I can not see the picture so i caN NOT HELP SORRY

Evaluate 7i^4-12i^2
-5
19
19i

Answers

The answer is 19
Hope this helps

The powers of i repeat every four terms, so i⁴ equals 1 and i² equals -1. The result of the evaluation is 19.

To evaluate the expression 7i⁴-12i². In complex numbers, i is the imaginary unit with the property that i² = -1. The powers of i repeat every four terms:

i¹ = i

i² = -1

i³ = -i

i⁴ = 1

Using these properties, we can simplify the expression:

7i⁴ is 7 times 1, which equals 7.

-12i² is -12 times -1, which equals 12.

Adding these together, we get 7 + 12 = 19.

Therefore, the evaluated expression is 19.

What is the growth factor of the following example? Assume time is measured in the units given. A forest shrinks 80% per century.

Answers

1 -80% = 0.20

The growth factor is 0.20 per century.

What is the equation in slope-intercept form of the linear function represented by the table? x y –6 –18 –1 –8 4 2 9 12

Answers

Using the 2-point form of the equation for a line, you can write the equation as
  y = (y₂ -y₁)/(x₂ -x₁)×(x -x₁) +y₁
If we let (x₁, y₁) = (4, 2) and (x₂, y₂) = (9, 12) this becomes
  y = (12 -2)/(9 -4)×(x -4) +2
  y = (10/5)×(x -4) +2
  y = 2x -6

The equation in slope-intercept form of the given function is ...
  y = 2x -6

Answer: y=2x-6

Step-by-step explanation:

One side of a cube has an area of 25 centimeters squared. What is the surface area of the cube?

Answers

a cube has all equal sides, so every face in the cube is just a square, if the area of one of those square is 25 cm², that simple means,

[tex]\bf \textit{area of a square}\\\\ A=s^2~~ \begin{cases} s=length~of\\ \qquad a~side\\ ------\\ A=25 \end{cases}\implies 25=s^2\implies \sqrt{25}=s\implies 5=s[/tex]

now, look at the picture below, a cube is really just 6 squares stacked up to each other at the edges, in this case, all 6 squares are 5x5.

so, simply get the area of all of them, and sum them up, and that's the surface area of the cube.

(5*5)+(5*5)+(5*5)+(5*5)+(5*5)+(5*5).

What is 134,500 rounded to the nearest ten thousand

Answers

130,000 because when you round 1-4 is rounded down and 5-9 is rounded up. If you were to round to the nearest ten thousand then you would look at the 134 and round down
130,000 because it is lower than 5 grand so you would round down because it is less than halfway to 140,00. Hope this helps

Anyone have the answer?!!!

Answers

The appropriate choice is ...
  reflection across y = x.

Sergio runs 2 1/4 miles in 30 minutes. Write the ratio in fractional form and determine Sergio's speed in miles per hour.

Answers

[tex] \dfrac{ 2\dfrac{1}{4} }{ \dfrac{30}{60} } \\ \\ = \dfrac{9}{4} \div \dfrac{30}{60} \\ \\ = \dfrac{9}{4} \times \frac{60}{30} \\ \\ = 4.5[/tex]

4.5 miles per hour.

Hope this helps. - M
Final answer:

Sergio runs at a speed of 4.5 miles per hour. The ratio of his running distance to time is 9/2.

Explanation:

To determine Sergio's speed in miles per hour (mph), we use the equation: speed = distance/time. Sergio runs 2 1/4 miles in 30 minutes. First, we need to convert the fractional distance to a decimal and the time to hours. 2 1/4 miles is equal to 2.25 miles and 30 minutes is equal to 0.5 hours.

Substitute these values into the equation:

speed = 2.25 miles/0.5 hour = 4.5 mph.

Therefore, Sergio's running speed is 4.5 miles per hour. The ratio of distance to time in fractional form would be 9/2.

Learn more about Speed Calculation here:

https://brainly.com/question/19930939

#SPJ2

Emily got a newjob that guarantees her a 6% raise every year. If she started out making 25,000, how long will it be before she doubles her current salary

Answers

It would take about 17 years for her to double her salary, since the salary is increasing 1,500 dollars a year. This means we divide 25,000/1,500 to get 16.66666 which we can round to 17.

hey can you please help me posted picture of question

Answers

We have the following function:
 C (n) = 20n + 15
 Clearing t we have:
 20n = c - 15
 n = c / 20 - 15/20
 Rewriting:
 N (c) = (c-15) / 20
 Answer:
 The inverse function for this case is given by:
 N (c) = (c-15) / 20
 option B

Suppose you choose two families at random. what is the chance that family a owns exactly one car and family b owns exactly one car?

Answers

the chances or possibility would be 50/50
Other Questions
why is data organization important A police officer is investigating a sexual assault and recovered the underwear that was worn by the victim after the assault. how should the officer package the evidence so as not to damage potential dna evidence? Dewayne is a police officer. when he is off the job, he is an easygoing, fun-loving person who enjoys life. when he is on the job, he is a very stern, serious, and no-nonsense police officer. dewayne's professional behavior is an example of a: Ovulation typically occurs ________ days before the menstrual period begins. question 90 options: 7 10 20 14 Read the excerpt from Act I of The Importance of Being Earnest. Jack. My dear Algy, you talk exactly as if you were a dentist. It is very vulgar to talk like a dentist when one isnt a dentist. It produces a false impression. The main effect of the pun in the excerpt is that it confuses the reader. creates a funny moment. creates a serious moment. explains something to the reader. 1. Choose the vocabulary expression that could replace the underlined words in each sentence without significantly changing the meaning of the sentence. Do not use any of the underlined words again.Viste el artculo en el peridico sobre la actriz muy famosa que estuvo en un accidente de coche?a) la aficionadab) la estrella del cinec) el directord) el crtico2. Read each definition and write the corresponding word orexpression.una fruta grande y dulce, verde por fuera y roja o rosadapor dentro a) el duraznob) la piac) la cerezad) la sanda3. Read each definition and write the corresponding word orexpression.el opuesto (opposite)de seco a) frescob) dulcec) mojadod) congelado What is the best way to punctuate the bolded portion of the sentence? Some of the stories were originally published in magazines like The Atlantic Monthly. The Atlantic Monthly. The Atlantic Monthly. The Atlantic Monthly. The Atlantic Monthly. Which of the following reasons for European immigration would be considered pull factors?select all that apply* religious persecution *economic opportunity* chance at a better life* famine widespread poverty Which condition feeds a tropical storm as it develops into a hurricane? A. heat and moisture B. cool temperatures and rain C. high temperatures and freshwater D. wind and dry air An equation that is true for all allowed values of the variable A neighbor needs to put up a square fence around her garden to keep the deer out. If the area is 500 square feet, how much fence does she need to buy, rounded to the nearest tenth of a foot? Show your work. evaluate the following expressions 7/8 5/7 = Determine the length of the missing side in each of the right triangles below using the Pythagorean Theorem: a2 + b2 = c2. After a busy day of orders, a florist has 6 roses, 7 lilies, 3 carnations, 35 chrysanthemums, 27 sunflowers, 18 violets, and 9 tulips left in her inventory. parta.write a ratio that compares the number of roses to the number of violets. partb.describe what three other comparisons have the same ratio. partc.provide reasoning why more than one comparison can be made with the same ratio. I ate a slice of pepperoni pizza last night it upset my stomach.What type of sentence is this?sentence fragmentrun-on sentencecomma splicerambling sentence Which campaign pledge was president george h.w. bush forced to break in order to address the enormous federal budget deficit carried over from the reagan administration? Write the lewis structure for mgi2. draw the lewis dot structure for mgi2. include all lone pairs of electrons. how can x2+3x+1=2x2+2x+3 be set up as a system of equations An instructor makes $15 more per hour than an assistant. If the combined hourly wage of the instructor and assistant is $65, what is the hourly wage of the assistant? A. $15 B. $20 C. $25 D. $30 What is the molecular geometry around each carbon atom in a saturated hydrocarbon?