Find the area of the triangle. Round the answer to the nearest tenth.
A.
7.8 square units
B.
8.9 square units
C.
19.3 square units
D.
38.5 square units
Answers
So the closest answer is C. 19.3
Hope this helps :)
Answer:
19.3 square units .
Step-by-step explanation:
∠D=∠F=52°
Opposite sides of equal angles are equal .
So, DE=EF =6.3
Now sum of all angles of triangle is 180°
So, ∠D+∠F+∠E = 180°
52°+52°+∠E =180°
104°+∠E =180°
∠E =180°-104°
∠E =76°
Now to find the length of DF we will use law of cosines
[tex]c^2=a^2+b^2+2(a)(b) Cos E[/tex]
[tex]DF^2=DE^2+EF^2+2(DE)(EF) Cos E[/tex]
[tex]DF^2=6.3^2+6.3^2+2(6.3)(6.3) Cos 76^{\circ}[/tex]
[tex]DF^2=79.38+79.38 (0.2419)[/tex]
[tex]DF^2=98.582[/tex]
[tex]DF=\sqrt{98.582}[/tex]
[tex]DF=9.9[/tex]
Now we are supposed to find the area of triangle
To calculate the area of given triangle we will use the heron's formula :
[tex]Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where [tex]s = \frac{a+b+c}{2}[/tex]
a,b,c are the side lengths of triangle
Now substitute the values :
[tex]s = \frac{6.3+6.3+9.9}{2}[/tex]
[tex]s =11.25[/tex]
[tex]Area = \sqrt{11.25(11.25-6.3)(11.25-6.3)(11.25-9.9)}[/tex]
[tex]Area = 19.2907[/tex]
Hence the area of the triangle is 19.2907 ≈19.3 square units .
Related Questions
I need help fast. Identify the apothem (a), the radius (r), and the perimeter (p) of the regular figure.
Answers
The apothem (a), radius (r), and perimeter (p) of a regular figure are defined as follows: the apothem is the perpendicular distance from the center of the figure to one of its sides, the radius is the distance from the center of the figure to any point on its circumference, and the perimeter is the total length of all its sides.
Explanation:The apothem (a) of a regular figure is the perpendicular distance from the center of the figure to one of its sides.
The radius (r) of a regular figure is the distance from the center of the figure to any point on its circumference.
The perimeter (p) of a regular figure is the total length of all its sides.
Consider the net of a triangular prism where each unit on the coordinate plane represents five feet. If a can of spray paint covers 25 square feet, how many cans of spray paint are needed to paint the outside of the prism blue?
Answers
Tetrahedron with vertices at
(0,0,0)
(5,0,0)
(0,5,0)
(0,0,5)
The surface area consists of 4 triangles, three of which each has an area
A1=bh/2=5*5/2=12.5
The slanted surface is an equilateral triangle of side
s=sqrt(5^2+5^2)=5sqrt(2).
The corresponding area is
A2=(sqrt(3)/4)s^2=sqrt(3)/4*(5sqrt(2))^2=sqrt(3)/4*50
=12.5sqrt(3)
So the overall surface area of the tetrahedron is
A=3A1+A2=3*12.5+12.5sqrt(3)
=12.5(3+sqrt(3)) ft ²
=59.15 ft ² to two decimal places.
Number of cans =A/25=2.366 cans, so three cans are needed.
If the circle x2 - 4x + y2 + 2y = 4 is translated 3 units to the right and 1 unit down, what is the center of the circle?
Answers
Answer:
(5,-2).
Step-by-step explanation:
First, let's find the original center of the circle, we have
[tex]x^2 - 4x + y^2 + 2y = 4[/tex]
we are going to complete square adding and subtracting 4 for the x terms and 1 for the y terms
[tex]x^2 - 4x+4-4 + y^2 + 2y+1-1 = 4[/tex]
[tex](x-2)^2 - 4 + (y+1)^2 - 1 = 4[/tex]
[tex](x-2)^2+ (y+1)^2 - 5 = 4[/tex]
[tex](x-2)^2+ (y+1)^2 = 4+5[/tex]
[tex](x-2)^2+ (y+1)^2 = 9.[/tex]
The canonical formula of a circumference is [tex](x-h)^2+(y-k)^2=r^2[/tex]
Then, we have a circle with [tex]r^2 =9[/tex] and center (h,k)=(2,-1).
Now, if we translate the circle 3 units to right and 1 unit down, then all the points in the circle will be translated including the center. Especifically, the x values will be added 3 units and the y-vaues will be subtracted 1 unit, then the new center will be
(2+3,-1-1) = (5,-2).
Elisa took out payday loan for $500 due in 2 weeks that charged an $80 fee. What is the periodic interest rate of the loan?
Answers
PLEASE FULL ANSWERS! need all the help I can get
Answers
The question is What happens at 4 -- exactly.
The function at x =4 is determined by 2 * x or 2*4 = 8
But look what happens to the top and bottom functions when you get infinitely close to x = 4. You could let x = 3.99999 to see what happens to the top function
g(x) = x - 2 when x is less than 4. So ...
Put in g(3.99999) = x - 2
g(3.99999) = 3.99999 - 2 = 1.99999 which rounds to 2. That's nowheres near 8.
We have already shown that at this point this is going to be discontinuous. 2 does not equal 8. But just for fun, we should try the bottom function
Suppose x = 3.99999 again.
then g(3.99999) = sqrt(3.99999) which is almost 2. there's no way that will work.
Which answer describes the function f(x) = x^6−x^4 ?
neither
even
odd
Answers
to determine if it is even replace x with -x and see if the answer is identical.
In this case, this function is even
Answer:
The function [tex]f(x)=x^6-x^4[/tex] is:
Even
Step-by-step explanation:
A function f(x) is even if:
f(-x)= f(x)
A function f(x) is odd if:
f(-x)= -f(x)
Here, we are given a function f(x) as:
[tex]f(x)=x^6-x^4[/tex]
[tex]f(-x)=(-x)^6-(-x)^4\\\\ =x^6-x^4\\\\=f(x)[/tex]
f(-x)=f(x)
Hence, the function [tex]f(x)=x^6-x^4[/tex] is:
Even
You buy a new laptop for
$299.99
$299.99
.
The sales tax is
6%
6%
.
What is the total cost for the laptop including the sales tax?
Answers
[tex]1 + \frac{tax}{100} [/tex]
So in this case we have to multiply by
[tex]1 + \frac{6}{100} = 1.06[/tex]
Therefore the price including tax is
[tex]299.99 \times 1.06 = 317.99[/tex]
Hence, $317.99
Lines p and q are perpendicular. If the slope of line p is 2, what is the slope of line q?
A. 1/2
B. -1/2
C. -2
D. 2
Answers
If the slope of line p is 2, then the slope of line q is -1/2.
The correct answer is letter B, -1/2.
Answer:
- 1/2
Step-by-step explanation:
I just did it
The graph of [tex]y= \sqrt[3]{x} [/tex] was shifted 5 units down and 4 units to the left. What is the equation of the resulting graph?
Please answer quickly!
Answers
Using translation concepts, it is found that the equation of the resulting graph is given by:
[tex]y = \sqrt[3]{x + 4} - 5[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the changes are given as follows:
Shift down of 5 units, hence y -> y - 5.Shift left of 4 units, hence x -> x + 4.Hence the equation of the resulting graph is given by:
[tex]y = \sqrt[3]{x + 4} - 5[/tex]
More can be learned about translation concepts at https://brainly.com/question/4521517
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The equation of the graph \\sqrt[3]{x} shifted down by 5 units and to the left by 4 units is \\sqrt[3]{x + 4} - 5.
Explanation:The transformation of the graph of y = \\sqrt[3]{x} down by 5 units and to the left by 4 units is represented by the function y = \\sqrt[3]{x + 4} - 5. When a graph is shifted to the left by 'a' units, we replace 'x' in the equation with (x + a). Similarly, when a graph is shifted down by 'b' units, we subtract 'b' from the function, resulting in f(x) - b. Therefore, incorporating both transformations into the original function, we get y = \\sqrt[3]{x + 4} - 5.
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A point P (x, y) is shown on the unit circle U corresponding to a real number t. Find the values of the trigonometric functions at t.
Answers
cos(t)=-15/17
tan(t)=-8/15
sec(t)=-17/15
csc(t)=17/8
cot(t)=-15/8
Point P is on the unit circle U. The values of trigonometric functions at t are [tex]sin\theta=\dfrac{8}{17},\;cos\theta=-\dfrac{15}{17}[/tex][tex],tan\theta=-\dfrac{8}{15},\;cot \theta=-\dfrac{15}{8},\;cosec\theta=\dfrac{17}{8},\;sec\theta=-\dfrac{17}{15}[/tex].
Given:
From the given figure, the coordinate of point P is [tex](-\dfrac{15}{17}, \dfrac{8}{17})[/tex].
The point P is present on a unit circle U. So, in general, the coordinates of a point on the circle will be [tex](x,y)\equiv (cos\theta, sin\theta)[/tex].
By comparing the given coordinate with the general expression, the value sine and cosine function will be,
[tex]sin\theta=\dfrac{8}{17}\\cos\theta=-\dfrac{15}{17}[/tex]
Now, the other trigonometric functions will be,
[tex]tan\theta=\dfrac{sin\theta}{cos\theta}\\tan\theta=-\dfrac{8}{15}\\cot \theta=-\dfrac{15}{8}\\cosec\theta=1/sin\theta=\dfrac{17}{8}\\sec\theta=1/cos\theta=-\dfrac{17}{15}[/tex]
Therefore, the values of trigonometric functions at t are [tex]sin\theta=\dfrac{8}{17},\;cos\theta=-\dfrac{15}{17}[/tex][tex],tan\theta=-\dfrac{8}{15},\;cot \theta=-\dfrac{15}{8},\;cosec\theta=\dfrac{17}{8},\;sec\theta=-\dfrac{17}{15}[/tex].
For more details, refer to the link:
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the greatest common factor of −27x2yz5 + 15x3z3
Answers
−27x2yz5 + 15x3z3
we know that
27-------------> 3³
15-------------> 3*5
z^5-----------> z² * z³
x³------------> x² * x
substituting in the original expression
−27x2yz5 + 15x3z3---------->[-3³*x²*y*z³*z²]+[3*5*x²*x*z³]
[-3³*x²*y*z³*z²]+[3*5*x²*x*z³]-------> [3*x² *z³]*{[-3² *y*z²]+[5*x]}
the greatest common factor is [3*x² *z³]
In the diagram below, m = 96 and m = 114. What is the measure of
JPM?
Answers
Angle Formed by Two Chords = 1/2(Sum of the Intercepted Arcs)
m<JPM = 1/2 (114 + 96) = 1/2 (210) = 105
Answer:
A ) 105
Answer:
C.Apex(105)
Step-by-step explanation:
Match each as a Compound (C) or Element (E)
Cu
HCI
CCI4
Co
HI
CH4
Answers
HCI compound?
CCI4 compound
Co compound ?
HI compound
CH4 compound
helppppppppppppppppppppppppppppppp
Answers
10√3 which is the last option
Explanation:
√30 * √10 = (30*10)^1/2
= 300^1/2
300 = 100 * 3
Therefore:
√300 = √100 * √3 = 10√3
Hope this helps :)
The point of intersection of the lines has an e-coordinate of?
Answers
.. y = k -x
.. 2x +3(k -x) = k +1
.. -x +3k = k +1 . . . . . collect terms
.. 2k -1 -x = 0 . . . . . . subtract k+1
.. 2k -1 = x . . . . . . . . .add x
The 3rd selection is appropriate.
A new softball dropped onto a hard surface from a height of 25 inches rebounds to about 2/5 the height on each successive bounce. (a) Write a function representing the rebound height for each bounce. (b) Graph the function. (c) After how many bounces would a new softball rebound less than 1 inch?
f(x) = 25(0.4)x; 6 bounces.
f(x) = 0.4(25)x; 6 bounces.
f(x) = 25(0.4)x; 4 bounces.
f(x) = 0.4(25)x; 4 bounces.
Answers
f(0) be the original height f(0)=25 in
then:
f(x)=f(0)(0.40)^x
since f(0)=25
f(x)=25(0.40)^x
the number of bounces that it will take for rebound to be less than 1 will be:
25(0.4)^x<1
this can be written as:
0.4^x<0.04
introducing natural logs we get:
xln0.4<ln0.04
x(-1.39794)<(-0.39794)
x>(-0.39794)/(-1.39794)
x>3.513~4
solve each equation 2/3 (m - 6)=3
Answers
2/3(m-6)= 3
2/3m-4=3
2/3m= 7
m= 10.5
We can check it.
2/3(10.5-6)= 3
7-4=3
3=3
I hope this helps!
~kaikers
multiply 2 by everything in fraction; keep same denominator for everything in parentheses
(2*m)/3 - (2*6)/3= 3
2m/3 - 12/3= 3
simplify 12/3= 4
2m/3 - 4= 3
Multiply everything by 3 to eliminate fraction
(3)(2m/3) - (3)(4)= (3)(3)
2m - 12= 9
add 12 to both sides
2m= 21
divide both sides by 2
m= 10.5
Check:
2/3(m-6)=3
2/3(10.5-6)= 3
2/3(4.5)= 3
(2*4.5)/3= 3
9/3= 3
3= 3
Hope this helps! :)
Corey spent 20% of his savings on a printer at Louie's ElectronisHow much did Corey have in his savings account before he bought the printer?
Answers
(printer cost)/0.20 = (savings)
savings = 5*(printer cost)
Whatever the cost of the printer was (information not supplied here), Corey's savings was 5 times that amount.
Answer:
5
Step-by-step explanation:
prove that root 7 is irrational by the method of contradiction
Answers
Let assume that [tex]\sqrt7[/tex] is a rational number. Therefore it can be expressed as a fraction [tex]\dfrac{a}{b}[/tex] where[tex]a,b\in\mathbb{Z}[/tex] and [tex]\text{gcd}(a,b)=1[/tex].
[tex]\sqrt7=\dfrac{a}{b}\\\\7=\dfrac{a^2}{b^2}\\\\a^2=7b^2[/tex]
This means that [tex]a^2[/tex] is divisible by 7, and therefore also [tex]a[/tex] is divisible by 7.
So, [tex]a=7k[/tex] where [tex]k\in\mathbb{Z}[/tex]
[tex](7k)^2=7b^2\\\\49k^2=7b^2\\\\7k^2=b^2[/tex]
Analogically to [tex]a^2=7b^2[/tex] ------- [tex]b^2[/tex] is divisible by 7 and therefore so is [tex]b[/tex].
But if both numbers [tex]a[/tex] and [tex]b[/tex] are divisible by 7, then [tex]\text{gcd}(a,b)=7[/tex] which contradicts our earlier assumption that [tex]\text{gcd}(a,b)=1[/tex].
Therefore [tex]\sqrt7[/tex] is an irrational number.
Final answer:
To prove that √7 is irrational, we assume the opposite and show that it leads to a contradiction. We start by assuming that √7 is rational and can be expressed as a fraction. By squaring both sides of the equation and simplifying, we get an equation that leads to p and q being divisible by 7, which contradicts our initial assumption. Therefore, √7 must be irrational.
Explanation:
To prove that √7 is irrational using the method of contradiction, we assume the opposite, which is that √7 is rational. This means that it can be expressed as a fraction p/q, where p and q are integers with no common factors other than 1. We can then square both sides of the equation (√7)² = (p/q)² and simplify to get the equation 7 = p²/q². Rearranging, we have p²= 7q².
From this equation, we can deduce that p² is divisible by 7, which means p must also be divisible by 7. Let's represent p as 7r, where r is another integer. Substituting back into the equation, we get (7r)² = 7q², which simplifies to 49r² = 7q². Dividing both sides by 7, we have 7r² = q². This implies that q² is also divisible by 7, so q must also be divisible by 7.
However, if both p and q are divisible by 7, this contradicts our initial assumption that p/q has no common factors other than 1. Therefore, our assumption that √7 is rational must be false, and hence √7 is irrational.
HELP PLEASE
Daniel, a 37-year-old male, bought a $160,000, 10-year life insurance policy. What is Daniel’s annual premium? Use the table. (table in attachment) $611.20 $728.00 $1268.80 $1652.80
Kara, a 25-year-old female, bought a $50,000, 10-year life insurance policy through her employer. Kara is paid semimonthly. How much is deducted from each of her paychecks for life insurance? Use the table below. $4.81 $5.21 $6.25 $6.77
Answers
Answer:
1) Option B- $728
2) Kara's annual premium is $62.5.
Step-by-step explanation:
1) Given : Daniel, a 37-year-old male, bought a $160,000, 10-year life insurance policy.
To find : What is Daniel's annual premium?
Solution :
In the table given,
Annual premium is per $1000 of coverage.
Daniel's life insurance policy buy is $160,000
Annual premium per $1000 coverage Daniel buy at $160
37 year old male 10 year cost is $4.55
(marked in the attached table below)
Daniel's annual premium is [tex]4.55\times 160[/tex]
[tex]=\frac{455}{100}\times 160[/tex]
[tex]=728[/tex]
Daniel's annual premium is $728
Therefore, Option B is correct.
2) Given : Kara, a 25-year-old female, bought a $50,000, 10-year life insurance policy through her employer. Kara is paid semimonthly.
To find : How much is deducted from each of her paychecks for life insurance?
Solution :
In the table given,
Annual premium is per $1000 of coverage.
Kara's life insurance policy buy is $50,000
Annual premium per $1000 coverage Kara buy at $50
25 year old female 10 year cost is $2.50
(marked in the attached table below)
Kara is paid semimonthly
So, cost is[tex]\frac{2.50}{2}=1.25[/tex]
Kara's annual premium is [tex]1.25\times 50[/tex]
[tex]=\frac{1.25}{100}\times 50[/tex]
[tex]=62.5[/tex]
Kara's annual premium is $62.5.
Jesse took out a 30-year loan for $85,000 at 7.2% interest, compounded monthly. If his monthly payment on the loan is $576.97, how much of his first payment went toward note reduction(reducing principal)? Show your work.
Answers
Answer:
$66.97 is his first payment went toward reduction.
Step-by-step explanation:
Given : Jesse took out a 30-year loan for $85,000 at 7.2% interest, compounded monthly. If his monthly payment on the loan is $576.97.
To find : How much of his first payment went toward note reduction(reducing principal)?
Solution :
First we find the interest of 1 month on a loan of $85,000 at 7.2% interest.
[tex]I=85000\times \frac{7.2}{12\times 100}[/tex]
[tex]I=85000\times 0.006[/tex]
[tex]I=510[/tex]
Interest of 1 month is $510.
Monthly payment = $576.97
Now, first payment or reducing principal is given by
F= monthly payment - interest of 1 month
F=$576.97- $510
F=$66.97
Therefore, $66.97 is his first payment went toward reduction.
PLEASE HELP!!!
The areas of a figure and its transformed image are the same. Which transformation could NOT have been applied to the original figure to create the image?
A. Rotation of 90
B. Reflection across a horizontal line
C. Dilation by a scale factor of 0.5
D. Translation down 4 and then right 1
Answers
The transformation that could NOT have been applied to the original figure to create an image with the same area is:
C. Dilation by a scale factor of 0.5.
To determine which transformation could NOT have been applied to the original figure to create the image with the same area, let's analyze each option:
A. Rotation of 90 degrees: When a figure is rotated by 90 degrees, the area remains the same.
This transformation is possible.
B. Reflection across a horizontal line: A reflection across a horizontal line (a horizontal flip) preserves the area of the figure.
This transformation is possible.
C. Dilation by a scale factor of 0.5: Dilation involves scaling a figure by a certain factor.
If a figure is dilated by a scale factor of 0.5, both its length and width are reduced to half, which means the area is reduced to one-fourth of the original area.
This transformation is not possible because it changes the area.
D. Translation down 4 and then right 1: A translation moves a figure without changing its size or shape. A translation down 4 and then right 1 would not change the area of the figure, as it simply shifts the figure's position.
This transformation is possible.
So, the transformation that could NOT have been applied to the original figure to create an image with the same area is:
C. Dilation by a scale factor of 0.5
Dilation by a scale factor of 0.5 would change the area, making it incompatible with the condition that the areas of the original figure and its image are the same.
For similar question on transformation.
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If carpet cost$5 per square yard, what would it cost to carpet a room that is 5 yards wide and 22 yards long?
Answers
So it’s 550
[7.07] Choose the correct product of (6x + 2)2.
36x2 − 4
36x2 + 4
36x2 − 24x + 4
36x2 + 24x + 4
Answers
36x^2 + 24x + 4
Explanation:
The perfect square has the following general formula:
(a + b)^2 = a^2 + 2ab + b^2
Now, we will expand the given perfect square based on the above general formula:
(6x + 2)^2 = (6x)^2 + 2(6x*2) + (2)^2
= 36x^2 + 24x + 4
Hope this helps :)
Draw the translation of LM along the vector (4, -5)
Answers
[tex] \binom{0}{ - 2} [/tex]
HELP!
Jeff volunteers his time by working at an animal shelter. Each year he works for a total of 240 hours. So far this year, he has worked 97 hours. Which equation will solve for how many more hours (h) Jeff will volunteer for?
A) 97 = 240 + h
B) 97 = 240h
C) 240 = 97 + h
D) 240 = 97 - h
A survey asked a group of students to choose their favorite type of sport from the choices of soccer, softball, basketball, and others. The results of the survey are shown in the graph.
Based on the graph, how many students in a class of 84 students would be expected to choose a sport other than soccer, softball, or basketball as their favorite type of sport?
A) 3
B) 12
C) 24
D) 72
You're the banker at HappyBank.com. Identify the two borrowers you would MOST likely offer a loan based on their credit scores.
A) F. Lutts and B. Parker
B) F. Lutts and K. Teller
C) A. Fulbright and K. Teller
D) A. Fulbright and B. Parker
What is the prime factorization of 240?
A) 23 · 3 · 5
B) 23 · 5 · 7
C) 24 · 3 · 5
D) 24 · 3 · 7
Answers
240 = 97 + h
For the second question, there is no graph so I cannot answer it.
3rd question: no image, can't answer.
4th question:
Use a factor tree:
240
/ \
10*24
/\ /\
5*2 *8*3
/ / /\ \
5 * 2 *4*2 *3
/ / /\ \ \
5 * 2 *2*2 * 2 * 3
Starting with the smallest factor and using exponents we have
[tex]2^4*3*5[/tex]
C is the correct choice.
Given that Jeff volunteers his time by working at an animal shelter, and each year he works for a total of 240 hours, and so far this year, he has worked 97 hours, to determine which equation will solve for how many more hours (h ) Jeff will volunteer for, the following calculation must be performed:
240 - 97 = h 240 = 97 + h
Therefore, C is the correct choice.
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The number of gallons of water,y, in a swimming pool is modeled by the equation y=7.5x+500,where x represents the time in minutes after the pump is turned on. How many gallons of water are in the pool if the pump is on for 200 minutes.
Answers
y = 1500 +500
y = 2000
2000 gallons are in the pool 200 minutes after the pump is turned on.
A histogram is being made for the following list of data. 78, 92, 98, 87, 86, 72, 92, 81, 86, 92 If the length of each interval is going to be 6, how many bars will there be on the histogram? 4 5 6 7
Answers
Therefore, the range is 98-72 = 26
The bars, 26/6
= 4.33
≈ 5 (to accommodate all the values)
Thus the number of bars will be 5.
Please help me out asap!!! Thanks :)
Answers
which of the binomials below is a factor of this trinomial
5x^2+14x-3
a. x-3
b. x+3
c. 5x+3
d. 5x-3
Answers
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
[tex]5x^2+14x-3[/tex]
As we know "Split the middle term":
[tex]5x^2+15x-x-3\\\\=5x(x+3)-1(x+3)\\\\=(5x-1)(x+3)[/tex]
Since it is quadratic equation so, it has 2 roots.
So, the roots are (x+3) and (5x-1).
Hence, Option 'B' is correct.