PLEASE HELP IMAGE ATTACHED! These triangles are similar. Find the area of the smaller triangle to the nearest whole number.
Answers
The area of smaller triangle is 59 square feet
What are the similar triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
What is the formula for the area of triangle?The formula for the area of triangle is
[tex]Area = \frac{1}{2} \times base \times \ height[/tex]
According to the given question.
The area of the larger triangle is 105 square feet.
And the one side of the larger triangle and the smaller traingle is 16 and 12 feet respectively.
Suppose the height of thesmaller triangle be x feet and the height of the larger triangle be y feet.
Since, the corresponding edges of similar triangles are proportional.
Therefore,
[tex]\frac{y}{x} = \frac{16}{12}[/tex]
[tex]\implies y = \frac{4}{3} x[/tex]
Also, the area of larger triangle is 105 square feet.
[tex]\implies \frac{1}{2} \times \frac{4}{3} x \times 16 = 105[/tex]
The above euqtaion can be written as
[tex]\implies \frac{1}{2}\times \frac{4}{3} x \times \frac{4}{3} \times 12 = 105[/tex]
[tex]\implies \frac{1}{2} \times (\frac{4}{3} )^{2} \times x \times 12 = 105[/tex]
[tex]\implies \frac{1}{2} \times x \times 12 = 105 \times \frac{9}{16}[/tex]
[tex]\implies \frac{1}{2} \times x \times 12 = 59[/tex]
⇒ Area of smaller triangle = 59 square feet
Hence, the area of smaller triangle is 59 square feet.
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Related Questions
A restaurant offers a choice of 2 soups, 3 entrees, and 5 desserts. how many different meals consisting of a soup, an entree, and a dessert are possible?
Answers
The sum of two numbers is 61.61. if three times three times the smaller number is subtracted from the larger? number, the result is 5.5. find the two numbers.
Answers
y - 3x = 5...y = 3x + 5
x + (3x + 5) = 61
4x + 5 = 61
4x = 61 - 5
4x = 56
x = 56/4
x = 14
y - 3x = 5
y - 3(14) = 5
y - 42 = 5
y = 42 + 5
y = 47
ur 2 numbers are 14 and 47
Am I doing this right?
Answers
What would a monthly payment be on a purchase of a $10,000 car at a 5.9% for 4 years?
Answers
A=p(1/r/100)^n
A=10000
r=5.9/12=0.5%
10000=p(1+0.5/100)^(4*12)
10000=p(1.005)^48
p=10000/(1.005)^48
p=7,871
the monthly payment will be:
7871/12
=$655.92
Answer:
$234.39
Step-by-step explanation:
(15 POINTS) A student is chosen at random from a school. Why are the events "choosing a student of age group 5−10" and "choosing a student of age group 11−15" mutually exclusive?
a) They are independent.
b) They are dependent.
c) A student can belong to only one age group.
d) A student can belong to both the age groups.
Answers
Hence, the answer to this question is letter C.
Simplify the expression 3^5*6^-6/3^3*6^-4
A. 180
B. 5/2
C. 1/4
D. 3/20
Answers
= 3^(5-3) 6^(-6+4)
=3^2 6^-2
= 9/36
= 1/4
answer
C. 1/4
The value of the cumulative standardized normal distribution at z is 0.8770. the value of z is
Answers
Final answer:
To find the z-score corresponding to a cumulative area of 0.8770 in a standard normal distribution, one can look up this area in a z-table or use statistical software, yielding a z-score of approximately 1.15.
Explanation:
The question involves finding the value of z in a standard normal distribution given that the cumulative area to the left of z is 0.8770.
The z-score is a measure that describes the position of a raw score in terms of its distance from the mean, measured in standard deviations.
To find the value of z corresponding to an area of 0.8770, one would typically use a z-table or statistical software. The z-table lists areas to the left (cumulative probabilities) for different z-values.
For an area of 0.8770, the z-score is approximately 1.15. This calculation is based on the standard normal distribution, where the mean is 0 and the standard deviation is 1.
Solve each proportion. Show your work
Answers
2x/7 = 12/14
x=6
I don't know b i am sorry
cross multiply
(2x)(14) = (7)(12)
28x = 84
x = 84/28
x = 3
3 / (x - 1) = 5/7
cross multiply
5(x-1) = (7)(3)
5x - 5 = 21
5x = 21 + 5
5x = 26
x = 26/5 or 5.2
What is the following sum in simplest form? sqrt 8 + 3 sqrt2 + sqrt 32
\
Answers
Answer:-[tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}[/tex] in the simplest form.
Explanation:-
Given sum :- [tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}[/tex]
To simplify, rewrite the numbers inside the root in the product of primes, we get
[tex]\Rightarrow\sqrt{2\times2\times2}+3 \sqrt{2}+ \sqrt{2\times2\times2\times2\times2}\\\\\Rightarrow\sqrt{2^2\times2}+3 \sqrt{2}+ \sqrt{4\times4\times2}\\\\\Rightarrow\sqrt{2^2}\sqrt{2}+3 \sqrt{2}+ \sqrt{4^2\times2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+\sqrt{4^2}\sqrt{2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+4\sqrt{2}=9\sqrt{2}[/tex]
Thus [tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}[/tex] in the simplest form.
What is the 7th term of the geometric sequence where a1 = -5 and a5 = -1,280?
Answers
a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number.
Here we are give the initial term so we have to solve to solve for the common ratio...
a(5)=-1280 and a(1)=-5 so
-1280=-5r^(5-1)
-1280=-5r^4
256=r^4
256^(1/4)=r
4=r, so our sequence is:
a(n)=-5(4^(n-1)), so the 7th term is:
a(7)=-5(4^6)
a(7)= -20480
If x varies directly with y and x = 3.5 when y = 14, find x when y = 18.
Answers
x = 3.5 when y = 14
so
14 = 3.5k
k = 14/3.5
k = 4
when y = 18.
y = kx
18 = 4x
x = 18/4
x = 4.5
answer
when y = 18, x = 4.5
Answer:
the value of x= 4.5
Step-by-step explanation:
If x varies directly with y and x = 3.5 when y = 14
x varies directly with y , so equation is x= ky
where k is the constant of proportionality
x = 3.5 when y = 14, use the given values and find out k
Plug in the given values in x=k y
3.5= k * 14
Divide by 14 on both sides
0.25= k
So the value of k = 0.25
Now find out x when y= 18
x= ky
x= 0.25 * 18= 4.5
Your Cell Phone plane cost 55 dollars a month, plus 35 cents per minute. Write an equation to represent the monthly bill of the cell phone plan
Answers
T= total
55+35m=t
Hope this helps!
Answer:
F( x) = 0.35 x + 55
PLEASE HELP
Probability allows a person to effectively measure the risks in selecting one alternative over others.
True
False
Answers
solve for b, then find the value of b when a = 3.
4a=2b-7
a. -9/2
b. 5/2
c. 19/2
d. 17
Answers
4(3) = 2b - 7
12 = 2b - 7
2b = 12 + 7
2b = 19
b = 19/2
answer
c. 19/2
A catering service offers 12 appetizers, 6 main courses, and 7 desserts. A banquet chairperson is to select 6 appetizers, 2 main courses, and 5 desserts for a banquet. In how many ways can this be done?
Answers
= 291060
Which answer correctly describes the relationship between two of the lines in the figure?
Answers
Slope (12,-18),(11,12)
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x2-x1. You will get the fraction -30/1 or -30 which is your slope. Hope that made sense!
The slope of the line passing through the points (12, -18) and (11, 12) is calculated using the formula for slope (y2 - y1) / (x2 - x1). The result is -30.
Explanation:The subject of this question is Mathematics, more specifically the topic of 'Slope of a Line'. The grade level appears to be High School.
To answer the question 'Find the slope for the given coordinates (12,-18) and (11,12)', we use the formula to calculate the slope between two points which is (y2 - y1) / (x2 - x1). Let's take (12, -18) as (x1, y1) and (11, 12) as (x2, y2). Now we just input the values into the formula:
Slope (m) = (12 - (-18)) / (11 - 12).
This simplifies to Slope (m) = 30 / -1 = -30.
So, the slope of the line passing through the points (12, -18) and (11, 12) is -30.
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Joshua is 25 years old and has a high risk job making $72,000 a year. The insurance company charges him an extra 20% on top of his premium rate because of his job. If Joshua wants a policy that will replace five years of his salary, what is the annual premium for the cheapest policy?
Answers
What is the common difference of a 43-term arithmetic sequence where the first term is -13 and the sum is 9,374?
Answers
so.. .we know the first term is -13, and the 43rd term's value is 449...so...this is an arithmetic sequence, thus, in order for us to get from -13 to 449 in 43 hops, we had to add "d" the common difference, 42 times.
so -13, -13 + d, (-13+d)+d, (-13+d+d)+d, ..... and so on.
but in short d + d + d + ... 42 times is just 42d
so, we know that
[tex]\bf \begin{array}{llll} -13+42d=&449\\ \ \uparrow &\ \uparrow\\ a_1&a_{43} \end{array}\implies 42d=462\implies d=\cfrac{462}{42}\implies \boxed{d=11}[/tex]
PLEASE HELP!!!
The first two steps in determining the solution set of the system of equations, y = –x2 + 4x + 12 and y = –3x + 24, algebraically are shown in the table. Which represents the solution(s) of this system of equations? (3, 15) (–4, 36) (3, 15) and (4, 12) (–3, 33) and (–4, 36)
Answers
y = –3x + 24
so
–x2 + 4x + 12 = –3x + 24
x^2 -7x + 12 = 0
(x - 4)(x - 3) = 0
x - 4 =0; x =4
x - 3 = 0; x= 3
y = –3x + 24 = -3(3) + 24 = -9+24 = 15 (when x = 3)
y = –3x + 24 = -3(4) + 24 = -12+24 = 12 (when x = 4)
answer
(3, 15) and (4, 12)
Answer:
C
Step-by-step explanation:
or (3, 15) and (4, 12)
3. what is the simplified form of x+4/7 - x+3/x+5
Answers
------- * ----- - ----------- * --- = --------------------
7 (x+5) (x + 5) 7 7( x + 5)
The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]
Simplify the expression, then we have
⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]
⇒ [(x + 4)(x + 5) - 7(x + 3)] / [7(x + 5)]
⇒ [x² + 9x + 20 - 7x - 21] / [7(x + 5)]
⇒ (x² + 2x - 1) / 7(x + 5)
The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.
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If you start with a number divide it by 4 then multiply it by two you end up with 8 squared
Answers
8 squared = 64
so
(x/4)*2 = 64
divide x/4 by 2 to get x/2=64
now multiply both sides by 2 to get x=128
x = 128
identify the graph of the equation. What is the angle of rotation for the equation? 13x^2+6sprt3xy+7y^2-16=0
Answers
13x^2 + 6√3 xy + 7y^2 - 16 = 0
Based on the general equation of conic sections:
Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0,
A = 13
B = 6√3
C = 7
D = 0
E = 0
F = -16
So we can find the graph of the equation by solving for the discriminate B^2 - 4AC
B^2 - 4AC, substitute given:
(6^2 * 3) - 4 (13 * 7) = -256
since the discriminate is less than zero, the graph could be a circle or a parabola. In this case, the values of A and C are not equal, then our graph is a parabola.
Answer:
The answer is ellipse; 30° ⇒ answer (d)
A randomly generated list of numbers from 0 to 4 is being used to simulate an event, with the number 4 representing a success. What is the estimated probability of a success?
A.75%
B.60
C.25%
D.40%
Answers
The solution would be like this for this specific problem:
Given:
{0, 1, 2, 3, 4}
Success = 2, 3, and 4
Solution:
Success = 3 numbers
Sample = 5
= 3 / 5
= .6
= .6 * 100%
= 60%
So, the estimated probability of a success based from the randomly generated list of numbers being used to simulate an event is 60%.
To add, the measure of the likelihood that an event will occur is called probability and it is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty.
Sam scored 43 48 and 42 points on 3 test how many points should he get on the fourth test to get in average score of 50
Answers
(133+x)/4=50
133+x=200
x=67
House is 50.0 ft long and 26 ft wide and has 8.0-ft- m high ceilings. what is the volume of the interior of the house in cubic meters and in cubic centimeters?
Answers
Aiden calculated the area of triangle QRS below by finding half the product of 1.5 and 1.1.
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Aiden should have calculated
area = (1.1 * 5.4) / 2
because triangle area = half the base times the altitude.
Answer: The correct option is
(B) Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.
Step-by-step explanation: Given that Aiden calculated the area of triangle QRS by finding half the product of 1.5 and 1.1.
We are to select the correct option which states the error made by Aiden.
The AREA of a triangle is given by
[tex]A=\dfrac{1}{2}\times \textup{base}\times \textup{altitude},[/tex]
where the altitude is perpendicular to the base.
In ΔQRS, the length of the base is given by
b = QS = 0.9 + 4.5 = 5.4 units
and
the length of the altitude is given by
h = 1.1 units.
So, the area of the triangle QRS will be
[tex]A=\dfrac{1}{2}\times b\times h=\dfrac{1}{2}\times 5.4\times 1.1[/tex]
Therefore, the area of ΔQRS will be calculated by finding half the product of 1.1 and 5.4.
So, Aiden made the error by finding half the product of 1.5 and 1.1, because 1.5 line is not perpendicular to 1.1 line.
Thus, Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.
Option (B) is correct.
Corrugated Specialties produces boxes of all kinds, and they manufacture an average of 67,000 shirt-size boxes per month. In November, they were told to increase production by 35%. How many shirt-size boxes will they produce in November? Hint: This question requires two calculations. A. 91,125 B. 23,625 C. 23,450 D. 90,450
Answers
67,000×0.35=23,450
So they will produce in November
67,000+23,450=90,450....answer
I won tickets to a trip for four to the Super Bowl. I have eight friends but I can only bring three of them. In how many ways can I form my Super Bowl party?
Answers
Answer:
56
Step-by-step explanation:
Given the equation 2x + 4 = 4x − 2, select the reasoning that correctly solves for x.
Add 2, subtract 2x, then divide by 2.
Add 2, subtract 4x, then divide by −2.
Subtract 4, subtract 2x, then divide by −2.
Subtract 4, subtract 4x, then divide by 2.
Answers
Answer:
Number One / Letter A
Step-by-step explanation:
Add 2, subtract 2x, then divide by 2.
Hope This Helps!