1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m². 2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm. 3. Find the area of the equilateral triangle whose each side is 8 cm. 4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
Answers
1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m².
a = 51 m, b = 37 m, c = 20 m
semiperimeter: p = (51+37+20):2 = 54 m
Area of triangle:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}\\\\A=\sqrt{54(54-51)(54-37)(54-20)}\\\\A=\sqrt{54\cdot3\cdot17\cdot34}\\\\A=\sqrt{9\cdot2\cdot3\cdot3\cdot17\cdot17\cdot2}\\\\A=3\cdot2\cdot3\cdot17\\\\A=306\,m^2[/tex]
Rate: ₹ 3 per m².
Cost: ₹ 3•306 = ₹ 918
2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm.
a = 5 cm
a+2b = 11 cm ⇒ 2b = 6 cm ⇒ b = 3 cm
p = 11:2 = 5.5
[tex]A=\sqrt{5.5(5.5-3)^2(5.5-5)}\\\\ A=\sqrt{5.5\cdot(2.5)^2\cdot0.5}\\\\ A=\sqrt{11\cdot0.5\cdot(2.5)^2\cdot0.5}\\\\A=0.5\cdot2.5\cdot\sqrt{11}\\\\A=1.25\sqrt{11}\,cm^2\approx4.146\,cm^2[/tex]
3. Find the area of the equilateral triangle whose each side is 8 cm.
a = b = c = 8 cm
p = (8•3):2 = 12 cm
[tex]A=\sqrt{12(12-8)^3}\\\\ A=\sqrt{12\cdot4^3}\\\\ A=\sqrt{3\cdot4\cdot4\cdot4^2}\\\\A=4\cdot4\cdot\sqrt{3}\\\\A=16\sqrt3\ cm^2\approx27.713\ cm^2[/tex]
4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
a = 2x
b = 3x
2x + 2•3x = 32 cm ⇒ 8x = 32 cm ⇒ x = 4 cm ⇒ a = 8 cm, b = 12 cm
p = 32:2 = 16 cm
[tex]A=\sqrt{16(16-8)(16-12)^2}\\\\ A=\sqrt{16\cdot8\cdot4^2}\\\\ A=\sqrt{2\cdot8\cdot8\cdot4^2}\\\\ A=8\cdot4\cdot\sqrt2\\\\ A=32\sqrt2\ cm^2\approx45.2548\ cm^2[/tex]
Related Questions
Find the value of x. Round your answer to the nearest tenth.
x
10
Blank 1:
Answers
Answer:
12.2
Step-by-step explanation:
By Pythagoras theorem:
[tex] {x}^{2} = {10}^{2} + {7}^{2} \\ {x}^{2} = 100 + 49 \\ {x}^{2} = 149 \\ x = \sqrt{149} \\ x = 12.2065556 \\ x \approx \: 12.2[/tex]
5x + 7 is a algebraic expression. it is a mathematical phrase that includes at least one variable and one operation. what is the variable
Answers
Answer:
x is the variable
Step-by-step explanation:
The variable is the letter in the expression
x is the variable
5 is the coefficient of the variable
7 is the constant
Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→1 3x x − 1 − 3 ln(x)
Answers
Answer:
3/2Step-by-step explanation:
Given the limit of a function expressed as [tex]\lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})[/tex], we are to evaluate it. To evaluate it, we will simply substitute x = 1 into the function since the variable x tends to 1.
[tex]\lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})\\\\= (\dfrac{3(1)}{1-1} - \dfrac{3}{ln1})\\\\= \dfrac{3}{0} - \dfrac{3}{0}\\\\= \infty - \infty (ind)[/tex]
Since we got an indeterminate function, we will find the LCM of the function and solve again.
[tex]= \lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})\\\\= \lim_{x \to 1} \dfrac{3xlnx-3(x-1)}{(x-1)lnx}\\\\\\= \dfrac{3(1)ln(1)-3(1-1)}{(1-1)ln1}\\\\= \frac{3(0)-3(0)}{0(0)} \\\\= \frac{0}{0} (ind)[/tex]
Applying L'hospital rule;
[tex]\frac{x}{y} = \lim_{x \to 1} \dfrac{d/dx(3xlnx-3(x-1))}{d/dx((x-1)lnx)}\\\\= \lim_{x \to 1} \dfrac{3x(\frac{1}{x})+ 3lnx-3)}{(x-1)\frac{1}{x} +lnx}\\\\= \lim_{x \to 1} \dfrac{3 + 3lnx-3}{(x-1)\frac{1}{x} +lnx}\\\\= \frac{3ln1}{(1-1)\frac{1}{1} +ln1}\\\\= \frac{0}{0} (ind)[/tex]
Applying L'hospital rule again;
[tex]= \lim_{x \to 1} \dfrac{\frac{d}{dx} (3lnx)}{\frac{d}{dx} ((x-1)\frac{1}{x} +lnx)}\\\\= \lim_{x \to 1} \dfrac{\frac{3}{x} }{(x-1)\frac{-1}{x^2} + \frac{1}{x} +\frac{1}{x} }\\\\= \dfrac{\frac{3}{1} }{(1-1)\frac{-1}{1^2} + \frac{1}{1} +\frac{1}{1} }\\\\= \frac{3}{0(-1)+2}\\ \\= \frac{3}{2-0}\\ \\= 3/2[/tex]
Hence the limit of the function is 3/2.
six times a number x squared
Answers
Answer:
6x^2
Step-by-step explanation:
Because we are multiplying 6 and a number x squared, we know that x will have an exponent of 2. Then, multiplying that by 6 and using conventional algebraic techniques, we can combine the two terms together.
6 * x^2
6x^2
Answer:
[tex]\displaystyle \rm \longmapsto 6 \times x {}^{2} [/tex]
[tex]\displaystyle \rm \longmapsto {6x}^{2} [/tex]
-5, 4, -26, -48, 12 least to greatest
Answers
Answer:
hey!
Your answer is ...
-48 , -26 , -5 , 4 , `12
Step-by-step explanation:
HOPE THIS HELPED!
:)
HELP HURRY!!!! Simplify. 15÷(2+3) Enter your answer in the box.
Answers
Answer:
It's equal =3
15/(2+3)
=15/5
=3
Round to the nearest eurocent per kilo
Answers
Answer:
2 eurocent per kilo
Step-by-step explanation:
Since we are already given the conversion units, we only simply need to divide/multiply and cancel out units.
Dollars and dollars cancel out.
We are left with eurocent.
Pounds and pounds cancel out.
We are left with kilograms.
We do want eurocent over kilograms.
0.89(0.93) = 0.8277/0.4536 = 1.82474
Since we want to round it to the nearest cent, we round up because 8 ≥ 5:
1.82474 ≈ 2
Find the equation of the line parallel to y= -5x-3 that passes through the point ( -5, -4). If possible, write the equation in slope-intercept form.
Answers
Answer:
y = -5x - 29
Step-by-step explanation:
y-intercept form is y = mx +b,
m is slope, for parallel line slope is the same, so m= -5
y = -5x + b
To find b, we need to use the point (-5, - 4).
- 4 = -5*(-5) + b
- 4 = 25 + b
b = - 29
y = -5x - 29
Find slope of the line (-3, -2) ((5, 4)
Answers
Answer:
4+2/5+3=3/4 slope
Step-by-step explanation:
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please help me. Brainiest to the first answer person
Answers
Explanation:
The probability of getting a blue is 1/10
I suppose it tells you that the total amount of balls are 10 because the denominator is 10 and the number of blue ball is 1.
But red ball is twice the white.
2W = R
Thus
2W + W = 9
3W = 9
W = 9/3
W = 3
So then there would be 3 white ball in the bag.
We can write the probability:
P(W) = 3/10
Answer:
0.3 or 30%
Step-by-step explanation:
Blue = 1/10
Red = 2 white
**************
White + red = 1 - 1/10
White +2white= 9/10
White = 3/10
Red = 6/10
So probability of white ball is 3/10 or 30%
Graph the equation.
y= 1/8(x-6)(x+2)
Answers
Answer:
see below
Step-by-step explanation:
See the attachment.
The graph will have x-intercepts where the factors are zero, at x=6 and x=-2. The y-intercept will be the value when x=0: (1/8)(-6)(2) = -1.5.
The axis of symmetry is halfway between the zeros, so is x = (6-2)/2 = 2.
The minimum value of the function is at x=2, so is ...
y = (1/8)(2 -6)(2 +2) = 1/8(-16) = -2
Other y-values can be found by substituting other x-values in the equation and evaluating it. Rather than go to that trouble, I prefer to use a graphing calculator.
Which of the following is one of the specific perspectives of organizational behavior? a. People as financial expenditures b. People as technology users c. People as task environments d. People as resources e. People as consumers
Answers
Answer:
d. People as resources
Step-by-step explanation:
organisational behavior is the study of human behavior in an organization, the interface between human behavior and the organization, and the organization itself. It studies layers of organisational behavior in the level of individual players in an organisation, work group of individual players in an organization, and the nature of interaction between organizations on the larger scale. One of the perspective of study of organizational behavior is to study people as resources.
Prove the following using a direct proof:
The sum of the squares of 4 consecutive integers is an even integer.
Answers
It is proven that "the sum of the squares of four consecutive integers is an even integer" is the solution part.
To prove that the sum of the squares of four consecutive integers is an even integer, we need to show that it can be expressed as twice another integer.
Let's assume the four consecutive integers are n, n+1, n+2, and n+3.
The sum of their squares can be expressed as:
[tex]n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2[/tex]
Expanding the squares, we have:
[tex]n^2 + (n^2 + 2n + 1) + (n^2 + 4n + 4) + (n^2 + 6n + 9)[/tex]
Combining like terms, we simplify this expression to:
[tex]4n^2 + 12n + 14[/tex]
Now, let's consider this expression [tex]4n^2 + 12n + 14[/tex].
We can factor out 2 from each term, resulting in:
[tex]2(2n^2 + 6n + 7)[/tex]
Since [tex]2n^2 + 6n + 7[/tex] is an integer, let's denote it as k, where k is an integer.
Therefore, the expression becomes:
2k.
We have successfully expressed the sum of the squares of four consecutive integers as twice another integer (2k), which proves that it is an even integer.
Hence, the sum of the squares of four consecutive integers is an even integer.
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WILL MARK BRAINLIEST TO FIRST CORRECT ANSWER!!!
Math the the sentence with an appropriate variable expression. The number of miles a plane can travel on 50 gallons of fuel.
a. x + 50
b. 50x
c. 50 ÷ x
d. 50 - x
Answers
Answer:
C.
Step-by-step explanation:
You will need to divide the miles in order to understand how much fuel
Triangle RST has the vertices R(2, 3), S(-2, 1), and T(-1, 5). What are the coordinates after the two transformations: Reflection over the y-axis and rotation at 180 degrees around the origin
Answers
Answer:
R''(2,-3), S''(-2,-1) and T'(-1,-5).
Step-by-step explanation:
The given vertices of triangle are R(2, 3), S(-2, 1), and T(-1, 5).
Reflection over the y-axis:
[tex](x,y)\to (-x,y)[/tex]
Using this rule, the vertices after reflection are
[tex]R(2,3)\to R'(-2,3)[/tex]
[tex]S(-2,1)\to S'(2,1)[/tex]
[tex]T(-1,5)\to T'(1,5)[/tex]
Rotation at 180 degrees around the origin.
[tex](x,y)\to (-x,-y)[/tex]
Using this rule, the vertices after reflection are
[tex]R'(-2,3)\to R''(2,-3)[/tex]
[tex]S'(2,1)\to S''(-2,-1)[/tex]
[tex]T'(1,5)\to T''(-1,-5)[/tex]
Therefore, the coordinates of vertices after the two transformations are R''(2,-3), S''(-2,-1) and T'(-1,-5).
In a behavioral field study, my colleagues and I found that teams of three
students exercised more than everyone else in the study.
True
False
Answers
Answer:
False
Step-by-step explanation:
The given statement is false because behavioral field study deals with the cognitive processes during field study or task.
In the given statement only the physical strength of the students is measured while behavioral field study measures or explores human behavior and how or what techniques are students using to perform the field task.
Hence, the correct option is "False".
What's ∣x−2∣=∣4+x∣????
Answers
Answer:
in the chapter 7 in class 9 Ex 7.3
one time - and second time +
Step-by-step explanation:
x-2=4+x
1) x-2=-(4+x)
x-2=-4-x
x+x=-4+2
2x=-2
x=-2/2
x=-1
2) x-2=4+x
=0
Use the diagram to find the angle measures of the triangle. Recall that the sum of the angle measures of a triangle is 180°
x°=
(x+5)°=
5X°=
Answers
Answer:
[tex] \boxed{ \bold{ \sf{x = 25°}}}[/tex]
[tex] \boxed{ \bold{ \sf{(x + 5) = 30°}}}[/tex]
[tex] \boxed{ \bold{ \sf{5x = 125°}}}[/tex]
Step-by-step explanation:
We know that sum of angle of triangle adds up to 180°
Finding the value of x
[tex] \sf{5x + x + x + 5 = 180°}[/tex]
Collect like terms
⇒[tex] \sf{7x + 5 = 180}[/tex]
Move 5 to right hand side and change its sign
⇒[tex] \sf{7x = 180 - 5}[/tex]
Subtract 5 from 180
⇒[tex] \sf{7x = 175}[/tex]
Divide both sides of the equation by 7
⇒[tex] \sf{ \frac{7x}{7} = \frac{175}{7} }[/tex]
Calculate
⇒[tex] \sf{x = 25°}[/tex]
Finding the value of ( x + 5 )°
[tex] \sf{x + 5}[/tex]
plug the value of x
⇒[tex] \sf{25 + 5}[/tex]
Add the numbers
⇒[tex] \sf{30°}[/tex]
Finding the value of 5x
[tex] \sf{5 \times 25}[/tex]
Multiply the numbers
⇒[tex] \sf{125°}[/tex]
Hope I helped!
Best regards!!
Answer:
x° = 25°
(x + 5)° = 30°
5x° = 125°
Step-by-step explanation:
total angle inside the triangle = 180 = x + (x+5) + 5x
180 = x + x + 5 + 5x
group like terms
7x + 5 = 180
subtract 5 each sides
7x = 175
x = 175/7
x = 25°
solve for : (x + 5)°
(x + 5)° = 25 + 5
(x + 5)° = 30°
solve for 5x°
5x° = 5 * 25
5x° = 125
check
180 = x + (x+5) + 5x
180 = 25 + (25+5) + (5*25)
180 = 25 + 30 + 125
180 = 180
Type the correct answer in the box. The motion of a clock pendulum is modeled by this graph. The function describing this graph is a transformation of the parent cosine function, y = cos x . Find the range, period, and maximum of the transformed function, D(t).
Answers
Answer:
The range of the function is -10, 10.
The period of the function is 1.2 seconds.
The maximum of the function is 10 centimeters.
Step-by-step explanation:
The range of a cosine function is the set of output values. In this situation, the range is the distance the pendulum covers, which is represented on the D(t) axis. The graph shows that the range of the function D(t) is [-10, 10].
The period is the length of a cycle. The graph shows that the cycle repeats every 1.2 seconds.
The maximum is the y-value of the highest point on the graph. The graph shows the maximum of the function is 10 centimeters.
In 25 years, a bond that paid 4.75% simple interest earned $4,750 interest. What was the principal of the bond in dollars?
Answers
Answer:
$ 4000Step-by-step explanation:
Given,
Rate ( R ) = 4.75 %
Time ( T ) = 25 years
Simple Interest ( I ) = $ 4,750
Principal ( P ) = ?
Finding the principal
We know that,
[tex] \boxed{ \sf{principal = \frac{interest \: \times 100}{ \: time \: \times \: rate} }}[/tex]
plug the values
⇒[tex] \sf{ \frac{4750 \times 100}{4.75 \times 25} }[/tex]
Calculate
⇒[tex] \sf{\frac{475000}{118.75} }[/tex]
⇒$ [tex] \sf{4000}[/tex]
Hope I helped!
Best regards!!
Answer:
2000
Step-by-step explanation:
in which number does the digit 7 have a value that is 10 times as great as the digit 7 in the number 0.975
a. 676 9
b. 7.99
c. 0.73
d. 8.457
Answers
The answer is 0.73 because in 0.975 the value of digit 7 is 7/100 ,10 times of 7/100 is 7/10 and the value of 7 in 0.73 is 7/10 ;.tenth value.
The value of each digit in a number is known as the place value. The number is 0.73. The correct option is C.
What is the place value of a digit in a number?The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.
Identification of the place value of a digit in a number:
The place values on the left of the decimal point start as ones, tens, hundreds, and so on.The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths and so onThe tens mean multiply by 10The tenth means the tenth part of that digit which is that digit divided by 10The value of digit 7 in the number 0.975 is hundredth. Therefore, the digit 7 in the number 0.975 is equal to 7/100.
Now, if the number is 10 times as great as digit 7 in 0.975. Therefore,
7/100 x 10 = 7/10 = 0.7
Thus, the number in which digit 7 have a value that is 10 times as great as the digit 7 in the number 0.975 is the number that is at the first place after the decimal.
Hence, the number is 0.73.
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solve for x
pleaseee answer and explain <333
Answers
Hello! :)
Answer:
[tex]\huge\boxed{x = (\frac{b}{a})(P+c)}[/tex]
[tex]\frac{a}{b}x - c = P[/tex]
Solve for x:
Begin isolating the variable by adding "c" to both sides:
[tex]\frac{a}{b}x - c + c= P + c[/tex]
[tex]\frac{a}{b}x = P+ c[/tex]
Divide both sides by a/b, or multiply by the reciprocal (b/a)
[tex](\frac{b}{a}) \frac{a}{b}x = (\frac{b}{a})(P + c)[/tex]
Therefore:
[tex]x = (\frac{b}{a})(P + c)[/tex]
A ladder is leaning against the side of a 10 m house. If the base of the ladder is 3 m away
from the house, how long is the ladder? Please draw a diagram.
Answers
Answer: It depends on how you round but about 10.44 m.
Step-by-step explanation:
Seven less than the product of 8 and a number is equal to 5.
Answers
Answer:
8n - 7 = 5
Step-by-step explanation:
number - n
product of 8 and a number - 8n
Seven less than the product of 8 and a number - 8n - 7.
Seven less than the product of 8 and a number is equal to 5.
8n - 7 = 5
Answer:
8n-7=5
you can do this
i cand do explaination
If 5 tickets cost $3.75 how much does 1 ticket cost
Answers
Answer:
0.75
Step-by-step explanation:
Answer:
$1.33 per ticket cost
Step-by-step explanation:
5 / $3.75 = $1.33 per 1 ticket cost
If cde is a straight angle, de bisects gdh, m gde = (8x-1), m edh = (6x+15), and m cdf= 43, find each measure.
Answers
Answer:
GDE = 63
EDH = 63
GDH = 126
FDG = 74
FDH = 200
FDE = 137
Step-by-step explanation:
It is stated that DE bisects <GDH. Since bisecting means halving into equal parts, <GDE = <EDH
from the question,
<GDE = (8x-1)
<EDH = (6x+15)
Since <GDE = <EDH,
(8x-1) = (6x+15), if we collect like terms
8x - 6x = 15 + 1
2x = 16
x = 8°
Again, from the diagram, we see that
<GDH = <GDE + <EDH, thus
<GDH = (8x-1) + (6x+15)
<GDH = 8x -1 + 6x + 15
<GDH = 14x + 14, substitute for x
<GDH = 14*7 + 14
<GDH = 112 + 14
<GDH = 126°
<FDG = 180 - <CDF - <GDE
<FDG = 180 - 43 - 63
<FDG = 74°
<FDH = <FDG + <GDE + <EDH
<FDH = <FDG + <GDH
<FDH = 74 + 126
<FDH = 200°
<FDE = <FDG + <GDE
<FDE = 74 + 63
<FDE = 137°
The measure of angle m∠GDE is 71.4° and the measure of angle m∠EDH is 65.6° on straight angle ∠CDE.
The straight angle ∠CDE, DE bisects GDH, m∠GDE=(8x-1)°, m∠EDH=(6x+15)° and m∠CDF=43°.
Here, m∠GDE+m∠EDH+m∠CDF = 180°
So, (8x-1)°+(6x+15)°+43°=180°
14x+57°=180°
14x=180°-57°
14x=123
x=123/14
x=8.8°
m∠GDE=8x-1
= 71.4°
m∠EDH= 65.6°
Hence, the measure of angle m∠GDE is 71.4° and the measure of angle m∠EDH is 65.6° on straight angle ∠CDE.
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set up a skeletal profit and loss statement in boss dollars and percentage if your year-end profit is 7800, the profit percentage is 3.9%, and the yearly cost of your goods sold is 120000
Answers
ne s o
Step-by-step explanation:
The tallest man in medical history was Robert Wadlow. He was 12 4/5times as tall as he appears in a Book of Reords photograph. He is 7 1/2 inches tall in the photograph. How tall was Robert Wadlow?
Answers
please help// geometry question pt.3
Answers
Answer:
Last one - CD with a line over it with arrowheads.
Step-by-step explanation:
Last one - CD with a line over it with arrowheads.
is 0.007 and 7 over 100 equal
Answers
Answer:
No it's not equal
Step-by-step explanation: