Answer:
20b^3+12b^2
Step-by-step explanation:
v=(2b)^2 (5b+3) = 4b^2 (5b+3) = 20b3+12b^2
Helppppppp pleaseeee
Answer:
d 13
Step-by-step explanation:
Mrs Wong bought a rice cooker for $126 after a discount of 30%.
(a) What was the price of the rice cooker before discount? (b) She paid $40 for a toaster. The total discount for the rice cooker and the toaster was $64. What was the percentage discount given for the
toaster?
Answer:
(a) $180
(b) 25%
Step-by-step explanation:
(a) $126 = 30% of x; x is the total
so from this, you get an equation: 126 = 0.3x
solve the equation: x = 180; so the amount before
discount is $180
(b) You know the price of discount for the rice cooker is
180-126 which is $54
Then you subtract 54 from 64 to get the discount amount for the toaster
10/40 is 1/4 or 25%
? Question
A slingshot launches a water balloon into the air. Function f models the height of the balloon, where x is the horizontal
distance in feet:
f(x) = -0.05x2 +0.8x + 4.
From what height did the slingshot launch the balloon, and what was the balloon's maximum height? How far from the
slingshot did the balloon land?
The balloon's maximum height was____
The slingshot
launched the balloon from a height of _____
The balloon landed_____
from the slingshot.
Answer:
4 ft
7.2 ft
20 ft
Step-by-step explanation:
When the balloon is shot, x = 0.
y = -0.05(0)² + 0.8(0) + 4
y = 4
The balloon reaches the highest point at the vertex of the parabola.
x = -b / 2a
x = -0.8 / (2 × -0.05)
x = 8
y = -0.05(8)² + 0.8(8) + 4
y = 7.2
When the balloon lands, y = 0.
0 = -0.05x² + 0.8x + 4
0 = x² − 16x − 80
0 = (x + 4) (x − 20)
x = -4 or 20
Since x > 0, x = 20.
The slingshot launched the ballon from a height of 4 feet. The balloon's maximum height was 72 feet. The balloon landed 20 feet from the slingshot.
To determine the height from which the slingshot launched the balloon, we need to evaluate the function f(0) because when x is zero, it represents the starting point of the balloon's trajectory.
f(x) = -0.05x² + 0.8x + 4
f(0) = -0.05(0)² + 0.8(0) + 4
f(0) = 4
Therefore, the slingshot launched the balloon from a height of 4 feet.
To find the maximum height of the balloon, we can observe that the maximum point of the parabolic function occurs at the vertex.
The x-coordinate of the vertex can be calculated using the formula x = -b / (2a).
In our case, a = -0.05 and b = 0.8.
Let's calculate the x-coordinate of the vertex:
x = -0.8 / (2×(-0.05))
x = -0.8 / (-0.1)
x = 8
Now, substitute this x-coordinate into the function to find the maximum height:
f(x) = -0.05x² + 0.8x + 4
f(8) = -0.05(8)² + 0.8(8) + 4
f(8) = -0.05(64) + 6.4 + 4
f(8) = -3.2 + 6.4 + 4
f(8) = 7.2
Therefore, the balloon reached a maximum height of 7.2 feet.
To determine how far from the slingshot the balloon landed, we need to find the x-intercepts of the quadratic function.
These represent the points where the height is zero, indicating the balloon has landed.
Setting f(x) = 0, we can solve the quadratic equation:
-0.05x² + 0.8x + 4 = 0
x² - 16x - 80= 0
x=-4 or x=20
We take the positive value, so the balloon landed 20 feet from the slingshot.
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Dr. Gongol, a sleep specialist, predicts that the proportion of snoring events compared to other events during a sleep study is more than 35%. To test this prediction, he evaluates 200 random sleep studies and found that 140 studies showed that more than 35% events were snores. The following is the setup for this hypothesis test: H0:p=0.35 Ha:p>0.35 The p-value for this hypothesis test is 0.03. At the 5% significance level, should he reject or fail to reject the null hypothesis?
Answer:
Reject the null hypothesis
Step-by-step explanation:
The claim is H0:p=0.35 Ha:p>0.35
At a significance level of 0.05, if the p value observed is less than 0.05, then we reject the null hypothesis, but if the p value observed is greater than the null hypothesis, then we fail to reject the null hypothesis.
In this case study: the p value is 0.03 which is less than the significance level, this we will reject the null hypothesis and conclude that there is enough statistical evidence to prove that the proportion of snoring events compared to other events during a sleep study is more than 35%.
3. Use the Counting Principle to find the probability.
rolling a 1 on each of 4 number cubes
329
324
1
24
1
1, 296
Step-by-step explanation:
Each number cube has 6 possible values, so there are 6⁴ = 1296 possible permutations. Only 1 of those permutations is all ones. Therefore, the probability is 1/1296.
Find the slope of the line that passes through (1, 14) and (4,9)
Which two numbers in the points represent x values? Select both in the
list.
In any coordinate pair, the first number is the x-value and the second number is the y-value.
To find the slope, simply take the difference of the y values and divide by the difference in the x values: (14-9)/(1-4) is equal to -5/3.
The slope of the line that passes through (1, 14) and (4,9) is -5/3.
It is find the slope of the line.
what is slope?The slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).
The slope is always calculated from the rise divided by the run. Typically, the equation is presented as:
m = Rise/Run
If you have two points, the points should be [tex]P_{1} (x_{1} ,y_{1} )[/tex] and [tex]P_{2} (x_{2} ,y_{2} )[/tex] So, the equation would be:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
In any coordinate pair, the first number is the x-value and the second number is the y-value.
The difference of the y values and divide by the difference in the x values:
m=(14-9)/(1-4) is equal to -5/3.
The slope of the line that passes through (1, 14) and (4,9) is -5/3.
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Solve the formula for the perimeter of a rectangle, with width w and length I,
for the length.
P= 2W + 2/
Answer:
( P -2w) /2 = l
Step-by-step explanation:
P= 2W + 2l
Subtract 2W from each side
P= 2W -2W + 2l
P -2W = 2l
Divide by 2
( P -2w) /2 = l
Answer:
A. [tex]\frac{P - 2w}{2} = l[/tex]
Step-by-step explanation:
Well in,
P = 2w + 2l
to solve for l we need to single it out.
P = 2w + 2l
-2w
P - 2w = 2l
divide everything by 2
[tex]\frac{P - 2w}{2} = l[/tex]
Thus,
the answer is A.
Hope this helps :)
The measure of ∠1 is 150°. What are the measures of ∠4, ∠3 and ∠2?
Answer:
∠1 is 150°
∠2 is 30°
∠3 is 150°
∠4 is 30°
Step-by-step explanation:
∠1 is vertically opposite to ∠3 so they are equal
360° - (150° + 150°) = 360° - 300° = 60°
∠2 and ∠4 must sum to 60°
Step-by-step explanation:
From the question
∠1 is opposite to ∠ 3 and vertically opposite angles are equal
So
∠1 = ∠ 3
That's
∠ 3 = 150°∠ 3 and ∠ 4 are on a straight line and angles on a straight line add up to 180°
So to find ∠4, subtract ∠3 from 180°
That's
∠ 4 = 180 - ∠ 3
∠ 4 = 180 - 150
∠ 4 = 30°Since ∠ 4 and ∠ 2 are opposite they are also equal
That's
∠ 4 = ∠ 2
Therefore
∠ 2 = 30°Hope this helps you
The floor of a room is 8m 96cm long and 6m 72cm broad. Find the maximum dimension of a square tile
of the same size needed to cover the entire floor.
Bryan invests $500 in an account earning 3.5% interest that compounds annually. If he makes no additional deposits or withdraws, how much will be in the account:
After 10 years?
After 15 years?
After 20 years?
Answer:
$705.30, $837.67, $994.89 Respectively
Step-by-step explanation:
Given
P= $500
r= 3.5%= 3.5/100= 0.035
Applying the compound interest formula we have
[tex]A= P(1+r)^t[/tex]
where
A = final amount
P = initial principal balance
r = interest rate
t = number of time periods elapsed
1. for t= 10 years[tex]A= 500(1+0.035)^1^0\\\ A= 500(1.035)^1^0\\\\ A= 500*1.410598\\\ A=705.299[/tex]
A= $705.30
2. for t= 15 years[tex]A= 500(1+0.035)^1^5\\\ A= 500(1.035)^15\\\\ A= 500*1.67534\\\ A=837.67[/tex]
A= $837.67
3. for t= 20 years[tex]A= 500(1+0.035)^2^0\\\ A= 500(1.035)^2^0\\\\ A= 500*1.98978\\\ A=994.89[/tex]A= $994.89
For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate Lim Sn to obtain the value of the series or state that the series diverges.
n→[infinity]
[infinity]
Σ (4/√k+5 ) - 4/ √ k+6)
k=1
Looks like the series is
[tex]\displaystyle\sum_{k=1}^\infty\left(\frac4{\sqrt{k+5}}-\frac4{\sqrt{k+6}}\right)[/tex]
This series has n-th partial sum
[tex]S_n=\displaystyle\sum_{k=1}^n\bullet[/tex]
(where [tex]\bullet[/tex] is used as a placeholder for the summand)
[tex]S_n=\displaystyle\left(\frac4{\sqrt6}-\frac4{\sqrt7}\right)+\left(\frac4{\sqrt7}-\frac4{\sqrt8}\right)+\cdots+\left(\frac4{\sqrt{n+4}}-\frac4{\sqrt{n+5}}\right)+\left(\frac4{\sqrt{n+5}}-\frac4{\sqrt{n+6}}\right)[/tex]
In each grouped term, the last term is annihilated by the first term of the next group; that is, for instance,
[tex]\displaystyle\left(\frac4{\sqrt6}-\frac4{\sqrt7}\right)+\left(\frac4{\sqrt7}-\frac4{\sqrt8}\right)=\frac4{\sqrt6}-\frac4{\sqrt8}[/tex]
Ultimately, all the middle terms will vanish and we're left with
[tex]S_n=\dfrac4{\sqrt6}-\dfrac4{\sqrt{n+6}}[/tex]
As [tex]n\to\infty[/tex], the last term converges to 0 and we're left with
[tex]\displaystyle\sum_{k=1}^\infty\bullet=\lim_{n\to\infty}S_n=\frac4{\sqrt6}=\boxed{2\sqrt{\dfrac23}}[/tex]
State the slope of the line.
1
0
Undefined
-4
Answer:
Hey there!
The slope of a vertical line is undefined! The run is zero, and as we know, dividing by zero is undefined!
Hope this helps :)
Answer:
Undefined
Step-by-step explanation:
A vertical line has an undefined slope or there is no slope of the line.
Use partial fractions to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
∫x2/x1−20x2−125dx
Answer:
125/6(In(x-25)) - 5/6(In(x+5))+C
Step-by-step explanation:
∫x2/x1−20x2−125dx
Should be
∫x²/(x²−20x−125)dx
First of all let's factorize the denominator.
x²−20x−125= x²+5x-25x-125
x²−20x−125= x(x+5) -25(x+5)
x²−20x−125= (x-25)(x+5)
∫x²/(x²−20x−125)dx= ∫x²/((x-25)(x+5))dx
x²/(x²−20x−125) =x²/((x-25)(x+5))
x²/((x-25)(x+5))= a/(x-25) +b/(x+5)
x²/= a(x+5) + b(x-25)
Let x=25
625 = a30
a= 625/30
a= 125/6
Let x= -5
25 = -30b
b= 25/-30
b= -5/6
x²/((x-25)(x+5))= 125/6(x-25) -5/6(x+5)
∫x²/(x²−20x−125)dx
=∫125/6(x-25) -∫5/6(x+5) Dx
= 125/6(In(x-25)) - 5/6(In(x+5))+C
The amount of time to complete a physical activity in a PE class is approximately normally normally distributed with a mean of 32.9 seconds and a standard deviation of 6.4 seconds.
A) What is the probability that a randomly chosen student completes the activity in less than 33.2 seconds?
B) What is the probability that a randomly chosen student completes the activity in more than 46.6 seconds?
C) What proportion of students take between 35.5 and 42.8 seconds to complete the activity?
D) 75% of all students finish the activity in less than____seconds.
Answer:
The answer is below
Step-by-step explanation:
Given that mean (μ) of 32.9 seconds and a standard deviation (σ) of 6.4 seconds.
The z score is used to measure by how many standard deviation the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}\\[/tex]
a) For x < 33.2 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{33.2-32.9}{6.4} =0.05[/tex]
From the normal distribution table, the probability that a randomly chosen student completes the activity in less than 33.2 seconds = P(x < 33.2) = P(z < 0.05) = 0.5199 = 51.99%
b) For x > 46.6 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{46.6-32.9}{6.4} =2.14[/tex]
From the normal distribution table, the probability that a randomly chosen student completes the activity in more than 46.6 seconds = P(x > 46.6) = P(z > 2.14) = 1 - P(z < 2.14) = 1 - 0.9927 = 0.0073 = 0.73%
c) For x = 35.5 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{35.5-32.9}{6.4} =0.41[/tex]
For x = 42.8 seconds
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{42.8-32.9}{6.4} =1.55[/tex]
From the normal distribution table, the proportion of students take between 35.5 and 42.8 seconds to complete the activity = P(35.5 < x < 42.8) = P(0.41< z< 1.55) = P(z < 1.55) - P(z < 0.41) = 0.9332 - 0.6591 = 0.2741 = 27.41%
d) A probability of 75% = 0.75 corresponds to a z score of 0.68
[tex]z=\frac{x-\mu}{\sigma}\\\\0.68=\frac{x-32.9}{6.4} \\\\x-32.9=4.4\\x=4.4+32.9\\x=37.3[/tex]
75% of all students finish the activity in less than 37.3 seconds
You are looking to invest in several different real estate deals. You have received ceconomic reports that explain the probability of good economic conditions will be .6 and .4 for bad economic conditions. Below is the Payoff Table, and after calculating the expected value for each decision, you determine the best "payoff deal is:
Good Economic Bad Economic
Conditions Condition (.60) Conditions (.40)
Apartment Building 50,000 30,000
Office Building $100,000 $-40,000
Warehouse 30,000 $10,000
A. Apartment Building
B. Office Building
C. Warehouse
D. None of the above.
Answer:
Real Estate Deals
The best "payoff deal:"
B. Office Building
Step-by-step explanation:
A) Payoff Table
Good Economic Bad Economic
Conditions Conditions
Probability (.60) (.40)
Apartment Building $50,000 $30,000
Office Building $100,000 $-40,000
Warehouse $30,000 $10,000
B) Calculation of Expected Values:
Good Economic Bad Economic Expected Values
Conditions Conditions
Probability (.60) (.40)
Apartment Building $30,000 $12,000 $42,000
Office Building $60,000 $-16,000 $44,000
Warehouse $18,000 $4,000 $22,000
b) The expected value for these real estate deals can be derived as the sum of the payoffs under the two economic conditions after they have been weighed with their odds of occurrence. The office building, in this example, showed the best payoff deal as the expected payoff from it results to a payoff of $44,000, which is higher than the expected payoff from the Apartment and Warehouse. However, it is also the riskiest, especially when bad economic conditions occur. This also accords with the general economic risk-return pattern that higher risky investments attract higher returns.
A transformation of KLM results in K'L'M'. Which transformation maps the pre-image to the image?
a. dilation
b.translation
c. reflection
d. rotation
Answer:
a. dilation.
Step-by-step explanation:
In this problem, the triangle has been neither reflected nor rotated. Although you could say the triangle has been translated, translation will preserve the lengths of the legs of the triangle.
Since all the angles are still congruent, we can say that the triangle has been dilated. It has been enlarged.
Hope this helps!
The dilation is a transformation that transfers the pre-image to the final image. The correct answer is A.
What is a transformation?When a point is relocated from its original place to a new location, it is changed. Different transformations include translation, rotation, reflection, and dilation.
As per the given figure, ΔKLM is transformed into ΔK'L'M'.
Here, the triangle hasn't been reflected or rotated.
Although we cannot claim the triangle has been translated, translation maintains the lengths of the triangle's legs.
We conclude that the triangle has been dilated because all of the angles are still congruent. It has grown in size.
Therefore, dilation is a transformation that transfers the pre-image to the final image.
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In △ABC,a=11 , b=20 , and c=28 . Find m∠A .
Answer:
18.4°
Step-by-step explanation:
Use law of cosine.
a² = b² + c² − 2bc cos A
11² = 20² + 28² − 2(20)(28) cos A
121 = 1184 − 1120 cos A
cos A = 0.949
A = 18.4°
Tom compared 2/12 and 7/6 by first comparing each fraction to 1/2 and 1. In which step did Tom make his first mistake?
Answer:
2/12 is not 1/2 it is 1/6 and 7/6 is greater than 1
Step-by-step explanation:
His comparison to each fraction was incorrect, to simplify fractions you must do to the numerator what you do to the denominator. Find the common number between them and divide. In the case of 2/12 the number would be 2, divide each by that and you get 1/6, Toms comparisons are not proportionate
Am I right or wrong?
You are absolutely right.
Find the value of x.
Answer:
[tex]\huge\boxed{x=\sqrt{21}}[/tex]
Step-by-step explanation:
ΔABD and ΔBCD are similar (AAA).
Therefore the corresponding sides are in proportion:
[tex]\dfrac{BD}{CD}=\dfrac{AD}{BD}[/tex]
Substitute
[tex]BD=x;\ CD=3;\ AD=7[/tex]
[tex]\dfrac{x}{3}=\dfrac{7}{x}[/tex] cross multiply
[tex](x)(x)=(3)(7)\\\\x^2=21\to x=\sqrt{21}[/tex]
A landscaping company charges $50 per cubic yard of mulch plus a delivery charge of $24. Find a
linear function which computes the total cost C(in dollars) to deliver a cubic yards of mulch.
C(x) =
Answer: c(x) = $50*x + $24
Step-by-step explanation:
First, this situation can be modeled with a linear equation like:
c(x) = s*x + b
where c is the cost, s is the slope, x is the number of cubic yards of mulch bought, and b is the y-intercept ( a constant that no depends on the number x)
Then we know that:
The company charges $50 per cubic yard, so the slope is $50
A delivery charge of $24, this delivery charge does not depend on x, so this is the y-intercept.
Then our equation is:
c(x) = $50*x + $24
This is:
"The cost of buying x cubic yards of mulch"
Convert the measurement. Use unit fractions or the metric conv
38 L to mL
38 L =
mL. (Type a whole number or a decimal.)
Please answer this correctly without making mistakes
Answer:
The distance between the art gallery and the office supply store is 42 miles
Step-by-step explanation:
Notice that the segment that joins the office store with the art gallery, has a length that equal the distance between the art gallery and the bank, plus the distance between the bank and the office supply store. That is;
32.1 mi + 9.9 mi = 42 mi
What is 36/100 added with 4/10
Answer:
0.76 or 19/25
Step-by-step explanation:
Convert 4/10 so that it has a common denominator with 36/100.
4/10 x 10/10 = 40/100
Now that the denominator is the same, just add the top values.
40/100 + 36/100 = 76/100
We can also simplify the answer to be 19/25 by dividing the top and bottom by 4.
Answer:
19/25Step-by-step explanation:
[tex]\frac{36}{100}+\frac{4}{10}\\Let\: first\: deal\: with\: ;\frac{36}{100}\\\mathrm{Cancel\:the\:common\:factor:}\:4\\=\frac{9}{25}\\\\=\frac{9}{25}+\frac{4}{10}\\Now \:lets \:deal \:with ; \frac{4}{10}\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=\frac{2}{5}\\=\frac{9}{25}+\frac{2}{5}\\\mathrm{Prime\:factorization\:of\:}25:\quad 5\times\:5\\\mathrm{Prime\:factorization\:of\:}5:\quad 5\\\mathrm{Multiply\:each\:factor\:the\:greatest\:number\:of\:times\:it\:occurs\:in\:either\:}25\mathrm{\:or\:}5\\[/tex]
[tex]\lim_{n \to \infty} a_n =5\cdot \:5\\\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:5=25\\=25\\\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}\\\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:25\\\mathrm{For}\:\frac{2}{5}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}5\\\frac{2}{5}=\frac{2\times \:5}{5\times \:5}=\frac{10}{25}\\=\frac{9}{25}+\frac{10}{25}\\[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{9+10}{25}\\\\=\frac{19}{25}[/tex]
State the degrees of freedom error in each of the following tests. (a) A consultant measures job satisfaction in a sample of 14 supervisors, 14 managers, and 14 executives at a local firm. (b) A researcher tests how nervous public speakers get in front of a small, medium, or large audience. Ten participants are randomly assigned to each group. (c) A high school counselor has 8 students in each of five classes rate how much they like their teacher.
Answer:
.
Step-by-step explanation:
Please answer this correctly without making mistakes my work is due today
Answer:
24.24
Step-by-step explanation:
brainlist plzzzzzzzzzzz
What is 25÷5what is 25 / 5
Answer:
5
Step-by-step explanation:
25/5
=5✖️5=25
=5/1
Answer:
25÷5 = 5 and 25/5 = 125
Step-by-step explanation:
hope this helps!
An open box is made from a 10cm by 20cm Piece of Tin by cutting a square from each corner and folding the edges. The area of the resulting base is 96 cm2. What is the length of the sides of the squares?
Answer:
2 cm
Step-by-step explanation:
If x is the length of the sides of the squares, then the height of the box is also x. The length and width of the base are 10−2x and 20−2x. The area of the base is the length times the width.
96 = (10 − 2x) (20 − 2x)
96 = 200 − 20x − 40x + 4x²
0 = 4x² − 60x + 104
0 = x² − 15x + 26
0 = (x − 2) (x − 13)
x = 2 or 13
Since x < 5, x = 2.
So the length of the sides of the squares is 2 cm.
Help ASAP!!!!
1. Solve for x. Round to the nearest hundredth if necessary.
Answer:
The answer is option B
34.28Step-by-step explanation:
To solve for x we use tan
tan ∅ = opposite / adjacent
From the question
The adjacent is x
The opposite is 19
So we have
tan 29 = 19/ x
x = 19/ tan 29
x = 34.276
x = 34.28 to the nearest hundredthHope this helps
Answer:
x ≈ 34.28
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan29° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{19}{x}[/tex] ( multiply both sides by x )
x × tan29° = 19 ( divide both sides by tan29° )
x = [tex]\frac{19}{tan29}[/tex] ≈ 34.28 ( to the nearest hundredth )
see attached the question is in an image attached
37.62202 sq units
First, calculate the areas of the separate triangles:
ABD = 20.19968 sq units
ACD = 17.46234 sq units
then add them to get 37.62202 sq units
Answer:
30.51 units^2
Step-by-step explanation:
Well to find the area of a triangle without height we use the following formula,
[tex]A = \sqrt{S(S-a)(S-b)(S-c)}[/tex]
To find S we use the following formula,
[tex]S = \frac{1}{2} (a+b+c)[/tex]
So a b and c are the sides of a triangle, we'll start with the left triangle.
S = 1/2(7 + 5.22 + 7.4)
S = 1/2(19.62)
S = 9.81
Now we can plug in 9.81 for S,
[tex]A = \sqrt{9.81(9.81-a)(9.81-b)(9.81-c)}[/tex]
[tex]A = \sqrt{9.81(9.81-7)(9.81-5.22)(9.81-7.4)}[/tex]
[tex]A = \sqrt{9.81(2.81)(4.59)(2.41)}[/tex]
[tex]A = \sqrt{9.81(31.083939)}[/tex]
[tex]A = \sqrt{304.93344159}[/tex]
[tex]A = 17.46234353086664[/tex]
But we can just simplify that to the nearest hundredth place which is,
17.46.
Now for the next triangle,
[tex]S = \frac{1}{2} (6.36 + 6.85 + 7.4)[/tex]
[tex]S = \frac{1}{2} (20.61)[/tex]
[tex]S = 10.305[/tex]
Plug in 10.305 for S,
[tex]A = \sqrt{10.305(10.305-6.36)(10.305-6.85)(10.305-7.4)}[/tex]
[tex]A = \sqrt{10.305(3.945)(3.455)(2.905)}[/tex]
[tex]A = \sqrt{10.305(16.534975)}[/tex]
[tex]A = \sqrt{170.392917375}[/tex]
A = 13.053463807549
We can round it to the nearest hundredth,
A = 13.05
So we just add 17.46 + 13.05
= 30.51 units^2
Thus,
the area of the figure is 30.51 units^2.
Hope this helps :)
