The base of a triangle is 5 meters greater than the height. If the area of the triangle is 102 m2, which are the dimensions of the base and the height?

Answers

Answer 1

Answer: The base is 17 meters long, and the height is 12 meters.

Step-by-step explanation:

The area of a triangle is:

A = b*h/2

where:

b = base

h = height.

For this particular triangle, we have that:

b = 5m + h

A = 102 m^2 = b*h/2

We can replace the first equation into the second one:

b*h/2 = 102 m^2

(5m + h)*h/2 = 102 m^2

(5m + h)*h = 2*102 m^2 = 204m^2

5m*h + h^2 = 204m^2

We can rewrite this as a quadratic equation:

h^2 + 5m*h - 204m^2 = 0

The solutions are given by the Bhaskara formula, the solutions are:

[tex]h = \frac{-5m +- \sqrt{(+5m)^2 -4*1*(-204m^2)} }{2*1} = \frac{-5m+-29m}{2}[/tex]

Then the two solutions are:

h = (-5m - 29m)/2 = -17 m

This is a negative height, that is not really defined, so this will be discarded.

The other solution is:

h = (-5m + 29m)/2 = 12m

This is positive, so this is the option we will use.

Knowing h, we can find the value of b.

b = 5m + h = 5m + 12m = 17m

Then the area is:

A = 12m*17m/2 = 102m^2


Related Questions

Find the perimeter of the given figure, round to the nearest tenth

Answers

Answer:

2√424 + 62 ≈ 103.1825205639 ≈ 103.2 units

Explanation:

Given the two baselengths, and the perpendicular height of the trapezoid, you can actually find the perimeter through the pythangorean theorem because the perpendicular height or height that forms a right or 90 degree angle makes a right triangle(2 be exact because this is an isoceles trapezoid which has two adjacent right triangles).

This is true of the trapezoid is icosceles.

Answer:

You cannot find the perimeter with numbers given.

Step-by-step explanation:

The top length, base length, and height are not sufficient to determine the perimeter of a trapezoid

If DE KL, then M _____ F. Choose the relationship symbol to make a true statement.

Answers

Answer:

If DE KL, then M > F. Choose the relationship symbol to make a true statement.

Step-by-step explanation:

what does congruent mean in geomatry?

Answers

Answer:

Congruent means same shape and same size. So congruent has to do with comparing two figures, and equivalent means two expressions are equal. So to say two line segments are congruent relates to the measures of the two lines are equal. Comment on David Severin's post “Congruent means same shape and same size.

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Your Welcome;)

Please help!! I've attached a picture of the problem

Answers

Answer: BC=8 units

Step-by-step explanation:

So in this figure, this triangle, that is a parallelogram named DFCE , and one of their property three yeti you add learn you learned is that a parallelogram has like rectangle two sides per two that are parallel and have the same measure ( but you can also use the little lines that show who is the same as who ) in this one you can write an equality: CE=FD=4. Then there is the same two lines on the EB segment so EB=4 . Then we can write that BC= BE + EC

BC= 4+4

BC= 8 units

I’m not English so I tried explaining as simple as possible sorry if you didn’t understand :/

IM GIVING BRAINLIEST!!
What two integers between -100 and -20 could be divided to equal a number close to 0?

Answers

-75 and -25, -75/-25=3
I hope this helps

Find the value of b. Then find the angle measures of the pentagon.

Answers

Answer:

b = 90

Step-by-step explanation:

Sum the interior angles of the pentagon and equate to 540

Starting from the top and going clockwise

b + b + 45 + 90 + 2b - 90 + [tex]\frac{3}{2}[/tex] b = 540 ← simplify left side

[tex]\frac{11}{2}[/tex] b + 45 = 540 ( multiply through by 2 to clear the fraction )

11b + 90 = 1080 ( subtract 90 from both sides )

11b = 990 ( divide both sides by 11 )

b = 90

Thus

b + 45 = 90 + 45 = 135

2b - 90 = 2(90) - 90 = 180 - 90 = 90

[tex]\frac{3}{2}[/tex] b = [tex]\frac{3}{2}[/tex] × 90 = 135

The angle measure from the top clockwise are

90°, 135°, 90°, 90°, 135°

PLS HELP 100 POINTS The x-coordinate is ____

The y-coordinate is ___

The point is in quadrant ___

Answers

Answer: A y-coordinate is the second element in an ordered pair. When an ordered pair is graphed as the coordinates of a point in the coordinate plane, the y-coordinate represents the directed distance of the point from the x-axis. (-1,-4).

Step-by-step explanation:

Answer:

The x-coordinate is –4 . The y-coordinate is  –1 . The point is in quadrant  III .

Step-by-step explanation:

can someone plz help me solve this equation :)
6 - (3x + 10) + 4(2 - x) = 15
a) 12 - 7x = 15
b) 4 - 4x = 15
c) 4 - 7x = 15

Answers

Answer:

4 - 7x = 15

Step-by-step explanation:

6 - 3x -10 + 8 - 4x = 15

4 - 7x = 15

Rock bands often stack their speakers in an array. One teen banda
has 24 speakers. They stack them at least 2 high, but no taller than
8 high. What are all the different arrays they can make?
8 high. What are all the different arrays they can make?

Answers

Answer:

2*12

3*8

4*6

6*4

8*3

Step-by-step explanation:

A painting is made from three different colors whose ratios are as follows: 4 parts blue, 3 parts red, and 3 parts green. The blue part of the painting took 12 gallons of paint. How many gallons of paint were needed for the green part of the painting

Answers

Answer: 9 gallons

Step-by-step explanation:

Given: Ratio of colors in painting:

4 parts blue, 3 parts red, and 3 parts green.

Total parts = 4+3+3 =10

Fraction of blue = [tex]\dfrac{\text{Number of parts of blue}}{\text{total parts}}=\dfrac{4}{10}[/tex]

Since, Quantity of blue color used = 12 gallons

Let total quantity of color be x,

[tex]\dfrac{4}{10}x=12\\\\\Rightarrow\ x=\dfrac{120}{4}=30\text{ gallons}[/tex]

Total color used = 30 gallons

Color used for green part only = [tex]\dfrac{3}{10}\times30 = \text{9 gallons}[/tex]

Hence, 9 gallons of paint were needed for the green part of the painting.

4x + (-3) = 5x + 3?????

Answers

Hi there! :)

[tex]\large\boxed{x = -6}[/tex]

Solve for x:

4x + (-3) = 5x + 3

Adding a negative number is simply subtracting, therefore:

4x - 3 = 5x + 3

Subtract 4x from both sides:

4x - 4x - 3 = 5x - 4x + 3

-3 = x + 3

Subtract 3 from both sides:

-3 - 3 = x + 3 - 3

-6 = x

Answer:

[tex]x=-6[/tex]

Step-by-step explanation:

Isolate the variable.

[tex]4x+(-3)=5x+3[/tex]

[tex]4x=5x+6[/tex]

[tex]0=x+6[/tex]

[tex]x=-6[/tex]

Hope this helps!

how does the percent equation relate to proportional quantities?

Answers

Answer:

Step-by-step explanation:

Use cross product to determine if the two ratios form a proportion. Here we can see that 2/16 and 5/40 are proportions since their cross products are equal. Percent means hundredths or per hundred and is written with the symbol, %. Percent is a ratio were we compare numbers to 100 which means that 1% is 1/100.

Answer:

The proportion is a general case of percentage.

Step-by-step explanation:

Proportion is a general case of percentage.

It describes how much of the total a particular sample is.

For example, if a pie contains eight slices and you have five, the proportion is 5/8.

You have a total of five out of eight.

A percent (the number of parts out of 100) is a special case of proportion where the denominator (“whole”) equals 100 parts.

I suspect that percentages were created to allow a normalized comparison of proportions when the total number of parts was not the same.

Imagine a small pizza with 6 slices and a large pizza with 8 slices.

If Tom got 4 from the first and Ram got 5 from the second, it is not immediately clear who got more from the second.

Converting 4/6 and 5/8 to percentages (66.7 and 62.5) allows you to see when the denominator equals who got relatively "more".

Furthermore, I suspect that 100 was used because we live in a 10-base world (we have 10 fingers, which makes it natural).

A line passes through (-1, 3) and (p, 7) and has a slope of -4/3 Find the value of p.

Answers

slope= (x2-xl)(y2-y1)

Answer:

Step-by-step explanation:

y - 3 = - [tex]\frac{4}{3}[/tex] ( x + 1 )

y = - [tex]\frac{4}{3}[/tex] x - [tex]\frac{4}{3}[/tex] + 3

y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{5}{3}[/tex]

7 = - [tex]\frac{4}{3}[/tex] p + [tex]\frac{5}{3}[/tex]

[tex]\frac{4}{3}[/tex] p = - 7 + [tex]\frac{5}{3}[/tex]

p = ( - [tex]\frac{16}{3}[/tex] ) × [tex]\frac{3}{4}[/tex] = - 4

Determine whether the lines with the given slopes are parallel, perpendicular, or neither.

m1=−4 & m2=14

Answers

Answer:

Parallel

Step-by-step explanation:

Answer:

Neither

Step-by-step explanation:

Parallel lines have same slope, perpendicular lines have negative reciprocal slopes

Given slopes of -4 and 14 are neither same not negative reciprocal, therefore the answer is neither

PLEASE HELP I'M GETTING GRADED ON THIS!!!!

Is this function even, odd, or neither and why?

Answers

Even, the ends of the lines are going in the same direction

Answer:

I'm reallly sorry if this is wrong, but I believe it is neither

Step-by-step explanation:

Odd and even functions need to exhibit some sort of reflection symmetry across the x axis (i think--we are learning this rn) and the graph does not seem to show this so i believe it is neither... i could be wrong thooughh

The equation y = 8.1x models the relationship between the number of hours Alexander works, x, and the dollar amount he earns, y. Which is the graph of the equation y = 8.1x?

Answers

Answer:

its B

Step-by-step explanation:

the second graph

Answer: B

Step-by-step explanation:

A person invests 3000 dollars in a bank. The bank pays 4% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 6500 dollars?

Answers

p=amount put in
t=amount of time in years
%=growth rate
f(t)=total

f(t)=p(1+%)^t
6500=3000(1+.04)^t
Solve for t
6500/3000=(1.04)^t
*Logs*
Log (13/6) = 19.7138...
1.04
Rounded to nearest 10th

t = 19.7

Answer:19.4

Step-by-step explanation:

A=P(1+\frac{r}{n})^{nt}

A=P(1+  

n

r

​  

)  

nt

 

A=6500 \hspace{15px} P=3000 \hspace{15px} r=0.04 \hspace{15px} t=?

A=6500P=3000r=0.04t=?

n=4\text{ (quarterly)}

n=4 (quarterly)

6500=3000(1+\frac{0.04}{4})^{4t}

6500=3000(1+  

4

0.04

​  

)  

4t

 

6500=3000(1.01)^{4t}

6500=3000(1.01)  

4t

 

\frac{6500}{3000}=\frac{3000(1.01)^{4t}}{3000}

3000

6500

​  

=  

3000

3000(1.01)  

4t

 

​  

 

2.1666667=(1.01)^{4t}

2.1666667=(1.01)  

4t

 

\log(2.1666667)=\log((1.01)^{4t})

log(2.1666667)=log((1.01)  

4t

)

\log(2.1666667)=4t\log(1.01)

log(2.1666667)=4tlog(1.01)

Power Rule.

\frac{\log(2.1666667)}{4\log(1.01)}=\frac{4t\log(1.01)}{4\log(1.01)}

4log(1.01)

log(2.1666667)

​  

=  

4log(1.01)

4tlog(1.01)

​  

 

t=\frac{0.3357921}{0.0172855}

t=  

0.0172855

0.3357921

​  

 

t=19.42624\approx 19.4 \text{ years}

t=19.42624≈19.4 years

Help me solve this problem please

Answers

Answer:

the answer is x= -3

y = -14

Classify the sequence {an) = {10,4,8/5,16/25,...} as arithmetic, geometric, or neither. If there is not enough information to classify the sequence, chose not enough information.
-
-
-
A. arithmetic
B. geometric
C. neither
D. not enough information

Answers

the answer is arithmetic

It is a geometric series.

The ratio of the second to first term is= [tex]\frac{4}{10}=\frac{2}{5}[/tex]

The ratio of the third to second term is= [tex]\frac{\left(\frac{8}{5}\right)}{4}=\frac{2}{5}[/tex]

The ratio of the fourth to third term is=[tex]\frac{\left(\frac{16}{25}\right)}{\left(\frac{8}{5}\right)}=\frac{2}{5}[/tex]

Since the common ratios are same so it is a geometric series.

Learn more: https://brainly.com/question/8806877

gabe's party will cost $12 if he invites six friends how many friends can Gabe invite if you spend $18​

Answers

Answer:

i dont like gabe, hes mean to me >:(

Step-by-step explanation:

so no, i wont go to his party :))

Answer:

7

Step-by-step explanation:

Of two consecutive integers, twice the smaller is four less than the greater. Find the integers. Provide and equation if you don't have a direct answer.

Answers

Answer:

The smaller integer is -3 and the greater integer is -2

Step-by-step explanation:

Equations

Let's call

x = the smaller integer

x + 1 = greater consecutive integer

The relationship between them is that twice the smaller is four less than the greater:

2x = x + 1 - 4

Subtracting x:

x = 1 - 4

Operating:

x = -3

x + 1 = -2

The smaller integer is -3 and the greater integer is -2

Kayla bought 2 books for $8.95 each, how much change would she get from a $20 bill?

Answers

Answer:

8.95 + 8.95 = 17.9

20 - 17.9

= $2.1

Solve for x

-.02x = 1.6

Answers

Answer:

-8

Step-by-step explanation:

which of the following relations or graphs are functions

Answers

Answer:

Step-by-step explanation:

The functions are:

(a), (c), (d), (e).

Relations may or may not represent a function.

The relations that are functions are (a), (c), (d), (e)

Graph (a) shows a linear relationship, and all linear relations are functions.

Graph (b) fails the vertical line test, because an x value corresponds to multiple y values; so graph (b) is not a function.

Similarly, ordered pair (f) is not a function because an x value corresponds to multiple y values

Other relations (c), (d) and (e) are functions

Read more about relations and functions at:

https://brainly.com/question/10889102

4/11 + 3/4 also 8/9 - 2/5 and 2 1/4 + 3 3/8 what is the answer ​

Answers

Answer:

1 5/44, 22/45, 5 5/8

Step-by-step explanation:

Pls give brainliest

HELP PLZZZSS EASYYYY 10 POINTS *easy*

Answers

Answer:

A. 3:30.

Step-by-step explanation:

180 is 90+90 so that would put it in 3:30.

Question 1

Which point could be removed in order to make the relation a function?
{(-4,3), (-5, 6), (1, 0),(-4,5), (9,5), (0, -7)}

Answers

Answer:

Either (-4, 3) or (-4, 5).

Step-by-step explanation:

A function is a relation when each input has exactly one output. The inputs must not repeat in a function.

In the relation given, the input '-4' repeats.

{(-4,3), (-5, 6), (1, 0),(-4,5), (9,5), (0, -7)}

If we remove either (-4, 3) or (-4, 5), it would make the relation a function.

Hope this helps.

2/9 • 2/3 what is the answer

Answers

It’s going to be 4/27.

Answer:

4/27

Step-by-step explanation:

The length, width, and height of a rectangular prism can be represented by the expression (x + 3), (x + 7) and (x - 1). write an expression to represent the surface area of the prism

Answers

Answer:

A=2wl+2lh+2hw

A=2(x+7)(x+3)+2(x+3)(x-1)+2(x-1)(x+7)

A=2(x^2+7x+3x+21)+2(x^2-x+3x-3)+2(x^2+7x-x-7)

A=2(x^2+10x+21)+2(x^2-2x-3)+2(x^2+6x-7)

Answer:

6x²+36x+22

Step-by-step explanation:

Surface Area = 2(wl + hl + wh)

Length = (x+3)

Width   = (x+7)

Height  = (x-1)

Surface Area = 2((x+7)(x+3) + (x-1)(x+3) + (x+7)(x-1))

Then simplify

2((x+7)(x+3)+(x−1)(x+3)+(x+7)(x−1))

=(2)((x+7)(x+3)+(x−1)(x+3)+(x+7)(x−1))

=(2)((x+7)(x+3))+(2)((x−1)(x+3))+(2)((x+7)(x−1))

=2x²+20x+42+2x²+4x−6+2x²+12x−14

=6x²+36x+22

I need some help plz

Answers

Answer:

i can't see the equation because of light pleas take again another pic

Answer:

B

Step-by-step explanation:

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