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
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.
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
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?
Answer:
2*12
3*8
4*6
6*4
8*3
Step-by-step explanation:
Please help!! I've attached a picture of the problem
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 :/
Find the value of b. Then find the angle measures of the pentagon.
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°
4x + (-3) = 5x + 3?????
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!
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
Answer:
4 - 7x = 15
Step-by-step explanation:
6 - 3x -10 + 8 - 4x = 15
4 - 7x = 15
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
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.
Kayla bought 2 books for $8.95 each, how much change would she get from a $20 bill?
Answer:
8.95 + 8.95 = 17.9
20 - 17.9
= $2.1
PLS HELP 100 POINTS The x-coordinate is ____
The y-coordinate is ___
The point is in quadrant ___
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:
what does congruent mean in geomatry?
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;)
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?
Answer:
its B
Step-by-step explanation:
the second graph
Answer: B
Step-by-step explanation:
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)}
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.
If DE KL, then M _____ F. Choose the relationship symbol to make a true statement.
Answer:
If DE KL, then M > F. Choose the relationship symbol to make a true statement.
Step-by-step explanation:
HELP PLZZZSS EASYYYY 10 POINTS *easy*
Answer:
A. 3:30.
Step-by-step explanation:
180 is 90+90 so that would put it in 3:30.
PLEASE HELP I'M GETTING GRADED ON THIS!!!!
Is this function even, odd, or neither and why?
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
Find the perimeter of the given figure, round to the nearest tenth
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
Determine whether the lines with the given slopes are parallel, perpendicular, or neither.
m1=−4 & m2=14
Answer:
Parallel
Step-by-step explanation:
Answer:
NeitherStep-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
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
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
4/11 + 3/4 also 8/9 - 2/5 and 2 1/4 + 3 3/8 what is the answer
Answer:
1 5/44, 22/45, 5 5/8
Step-by-step explanation:
Pls give brainliest
A line passes through (-1, 3) and (p, 7) and has a slope of -4/3 Find the value of p.
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
I need some help plz
Answer:
i can't see the equation because of light pleas take again another pic
Answer:
B
Step-by-step explanation:
gabe's party will cost $12 if he invites six friends how many friends can Gabe invite if you spend $18
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:
IM GIVING BRAINLIEST!!
What two integers between -100 and -20 could be divided to equal a number close to 0?
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
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
Help me solve this problem please
Answer:
the answer is x= -3
y = -14
Solve for x
-.02x = 1.6
Answer:
-8
Step-by-step explanation:
2/9 • 2/3 what is the answer
Answer:
4/27
Step-by-step explanation:
how does the percent equation relate to proportional quantities?
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).
which of the following relations or graphs are functions
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
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?
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