Answers
Answer:
≈ 50.7 cm²
Step-by-step explanation:
The area (A) of Δ XYZ is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height ), that is
A = [tex]\frac{1}{2}[/tex] × XY × YZ
Calculate YZ using the tangent ratio in the right triangle
tan40° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{YZ}{XY}[/tex] = [tex]\frac{x}{11}[/tex] ( multiply both sides by 11 )
11 × tan40° = x , that is
YZ ≈ 9.23 cm
Thus
A = [tex]\frac{1}{2}[/tex] × 11 × 9.23 = 5.5 × 9.23 ≈ 50.7 cm² ( to 3 significant figures )
Related Questions
Five times of a positive integer is less than twice its square by 3.
Find the integer.
Answers
Answer:
The positive integer is 3.
Step-by-step explanation:
Let 'x' be the integer
Given that five times of a positive integer is less than twice its square by 3.
so
5 times of x = [tex]5x[/tex]
3 less than twice of the square of x = [tex]2x^{2} - 3[/tex]
so the equation becomes
[tex]5x = 2x^{2} - 3[/tex]
[tex]2x^2-5x-3=0[/tex]
Factorise
[tex]\left(2x+1\right)\left(x-3\right)=0[/tex]
Using the zero factor principle
if ab=0, then a=0 or b=0 (or both a=0 and b=0)
[tex]2x+1=0\quad \mathrm{or}\quad \:x-3=0[/tex]
solving
[tex]2x+1=0[/tex]
Subtract 1 from both sides
[tex]2x+1-1=0-1[/tex]
Simplify
[tex]2x=-1[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{-1}{2}[/tex]
Simplify
[tex]x=-\frac{1}{2}[/tex]
Also solving
[tex]x-3=0[/tex]
Add 3 to both sides
[tex]x-3+3=0+3[/tex]
simplify
[tex]x=3[/tex]
Thus, we got integers:
x = 3 or x = -1/2
As x can not be a negative integer according to the question.Therefore, the positive integer is 3.
Investors buy a studio apartment for $240,000. Of this amount, they have a down payment of
$36,000. Their down payment is what percent of the purchase price? What percent of the purchase
price would a $12,000 down payment be?
Answers
Answer:
The down payment of $36000 is 15% of price.The down payment of $12000 is 5% of price.Step-by-step explanation:
Given that
Price of studio apartment = P = $240000
Down payment =d = $36000
Down payment is the amount that is initially given at the time of buying something.
Part A: For down payment of $36000
We will simply divide the down payment by total price.
[tex]= \frac{36000}{240000}\\=0.15[/tex]
Converting into percentage, multiplying by 100
[tex]= 0.15*100 = 15\%[/tex]
Part B: For down payment of $12000
We will simply divide the down payment by total price.
[tex]=\frac{12000}{240000}\\=0.05[/tex]
Converting into percentage, multiplying by 100
[tex]=0.05*100 = 5\%[/tex]
Hence,
The down payment of $36000 is 15% of price.The down payment of $12000 is 5% of price.16. Find the value of y.
Answers
y + (2x -12) = 180 (since they are supplementary angles)
(2x-12) = 96 ( since they are alternate exterior angle)
2x = 96 + 12
2x = 108
x = 108/2
x = 54.
y+( 2x-12)=180
y+(2× 54 -12) = 180
y + (108-12) = 180
y + 96 = 180
y= 180-96
y = 84.
i need help with this and all ppl is doing is just stealing it...
Answers
HELPPPPP
This table models a linear function.
x −12 −8 −4 4
y 4 2 0 −4
Enter the coordinates of the y-intercept in the boxes.
Answers
Answer:
(0,-2) is the correct answer.
Step-by-step explanation:
What is the domain and range of the graph
Answers
-6x+35/15=15-14x
Please help!
Answers
Answer:
x=13/8
Step-by-step explanation:
group like terms together
15*\sqrt(72) (15 times root 72. I can't seem to enter a square root symbol)
Answers
Answer:
Step-by-step explanation:ok so if you want too do the the root symbl on what
Kennedy needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 3.75 hours and charged her $58 for parts. The total was $226.75. Write and solve an equation which can be used to determine 2, the cost of the labor per hour.
Answers
Answer:
12.056
Step-by-step explanation:
Answer:12.056
Step-by-step explanation:
6-2x=y 14+3x=y plzzz helllllllllllllllp
Answers
Answer:
(- [tex]\frac{8}{5}[/tex], [tex]\frac{46}{5}[/tex] )
Step-by-step explanation:
Given the2 equations
6 - 2x = y → (1)
14 + 3x = y → (2)
Substitute y = 14 + 3x into (1)
6 - 2x = 14 + 3x ( subtract 3x from both sides )
6 - 5x = 14 ( subtract 6 from both sides )
- 5x = 8 ( divide both sides by - 5 )
x = - [tex]\frac{8}{5}[/tex]
Substitute x = - [tex]\frac{8}{5}[/tex] into either of the 2 equations for the corresponding value of y
Substituting into (1)
y = 6 - 2(- [tex]\frac{8}{5}[/tex] ) = [tex]\frac{30}{5}[/tex] + [tex]\frac{16}{5}[/tex] = [tex]\frac{46}{5}[/tex]
solution is ( - [tex]\frac{8}{5}[/tex], [tex]\frac{46}{5}[/tex] )
Each hexagon tile has an area of LaTeX: 18\sqrt{3} 18 3 in.2 . Solve for x. Then find the exact length of each side of the hexagon. (Hint: Six equilateral triangles make one hexagon.)
Answers
Answer:
The length of the side of the hexagon is [tex]2\sqrt{3}[/tex] inches.
Step-by-step explanation:
According to this question, we have a regular hexagon with a surface area of [tex]18\sqrt{3}\,in^{2}[/tex]. From Geometry, we know that all regular hexagons can be formed by six regular triangles, since the angle of one complete revolution (360º) divided by the number of triangles is equal to the internal angle of each triangle (60º). Then, the area of each triangle is found after dividing the complete area by the number of regular triangles:
[tex]A_{\triangle} = \frac{18\sqrt{3}\,in^{2}}{6}[/tex]
[tex]A_{\triangle} = 3\sqrt{3}\,in^{2}[/tex]
The area of the triangle as a function of the length of the side of the hexagon ([tex]l[/tex]), measured in inches, is determined by this equation:
[tex]A_{\triangle} = \frac{\sqrt{3}}{4} \cdot l^{2}[/tex] (1)
If we know that [tex]A_{\triangle} = 3\sqrt{3}\,in^{2}[/tex], then the length of the side of the hexagon is:
[tex]\frac{4}{\sqrt{3}}\cdot A_{\triangle} = l^{2}[/tex]
[tex]l^{2} = \frac{4\cdot \sqrt{3}}{3} \cdot A_{\triangle}[/tex]
[tex]l = 2\sqrt{\frac{\sqrt{3}}{3}\cdot A_{\triangle} }[/tex]
[tex]l = 2\sqrt{3}\,in[/tex]
The length of the side of the hexagon is [tex]2\sqrt{3}[/tex] inches.
Write in slope-intercept form an equation of the line that passes through the given points. (1, 2), (−2, −1)
Answers
Answer:
4 blocks down, 2 left
Step-by-step explanation:
blocks down
asap help please!!!! What's the volume of this figure?
Answers
Answer:
108 cubic feet
Step-by-step explanation:
V=w·h·l
fill in
V=3·9·4
V=108
Answer:
108 cubic feet is the answer
Explanation
volume = 9*4*3
= 108 cubic feet
WILL MARK BRAINIEST!! ...
suppose a city with population 600,000 has been growing at a rate of 8% per year. if this rate continues, fund the population of this city in 11 years
Answers
Answer:
1,398.983
Step-by-step explanation:
What is the area, in square feet, of the shaded part of the rectangle below?
Answers
Line q passes through the point (4,6)and (0,6).
Answers
Answer:
The equation of the line passing through the points (4, 6) and (0, 6) will be:
y = 6The graph of the equation y = 6 is also attached.
Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
m is the slopeb is the y-interceptGiven the points
(4, 6)(0, 6)Finding the slope between (4, 6)and (0, 6).
Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [6 - 6] / [0 - 4]
= 0 / -4
= 0
Thus, the slope of the line = m = 0
The slope m = 0 means the line is horizontal. Because the slope of the horizontal line is 0.
As the y-values are not changing with respect to the x-values.
Therefore,
The equation of the line passing through the points (4, 6) and (0, 6) will be:
y = 6The graph of the equation y = 6 is also attached.
what is the slope of the line -9x + 7y = 63
Answers
Answer: I think its x = 38
Step-by-step explanation:
Answer:
9/7
Step-by-step explanation:
ZABC is a straight angle. Which equation can be used to find the measure of
the unknown angle?
Answers
Answer:
180-45
Step-by-step explanation:
That is, supplementary angles
Does anyone else have to do i-Ready
Answers
Answer:
No
Step-by-step explanation:
Does anyone have to do DELTA-MATH
Answer: Can you send the question that you have.
Step-by-step explanation:
Please help this is due in ten minutes!!!
Use the figure to find measures of the numbered angles.
Answers
Answer:
angles 1 and 4: 113
angles 2 and 3: 67
Answer:
the angle should be 124° but I'm not sure so I'm sry If i get it wrong
Find the measurement of angle A & B
Answers
Answer:
Angle A = 65
Angle B = 78
Step-by-step explanation:
This is a triangle, and the total angles in a triangle is 180 degrees. What you can do is make all of the angles equal 180 and then solve for x.
180 = (2x +4) + (2x - 9) + x
180 = 2x +4 + 2x - 9 + x
180 = 4x -5 +x
180 = 5x - 5
185 = 5x
37 = x
Now, plug in x to solve for the angles.
Angle A = 2(37) - 9 = 65 Angle B = 2(37) + 4 = 78Angle C = x = 37I really need help if somebody could explain this into detail and show me how would really appreciate it please
Answers
Answer: y = (5x)^2
Step-by-step explanation: You're finding the inverse.
f(x) = [tex]\sqrt{x}[/tex]/5 --> y = [tex]\sqrt{x}[/tex]/5 (they mean the same thing)x = [tex]\sqrt{y}[/tex]/5 (switch x and y)5x = [tex]\sqrt{y}[/tex] (multiple both sides by 5)(5x)^2 = y (square both sides) --> the first answer choiceI'm thinking it's either a or d but I'm not sure.
Answers
Answer:
i think its d
Step-by-step explanation:
You are offered two jobs that you like. One job pays an hourly rate of $15.00 per hour for a 40-hour work week. Employees can take a two-week paid vacation. The employer says you will work about 5 hours of overtime per week at time-and-a-half pay. The other job pays $38,000 per year. You will be expected to work at least 55 hours per week, and you will have two weeks vacation and sick leave. Which job would you choose? Why?
Answers
Answer:
Second Job
Step-by-step explanation:
I would take the second job because you will make more. And it has sick time in addition to vacation.
First job:
$15x40=$600 then add in overtime which will be paid at $22.50 (time and half) so $22.50x5=$112.50. Add the two together $600+112.50=$712.50 weekly.
Second job:
$38,000/52=$730.77 weekly
7+(-11) =
Please help!
Answers
Answer:
-4
Step-by-step explanation:
7 + (-11) basically translates to 7 - 11. Since the bigger number has the negative sign here, you just have to subtract 11-7 and then add the negative onto the answer.
Answer:
-4
Step-by-step explanation:
7-11
-4
if it is a number + a negative number you remove the +and just subtract
factories:
x(x+1)-y(y+1)
Answers
Answer:
[tex](x - y)(x + y + 1)[/tex]
Step-by-step explanation:
[tex]x(x + 1) - y(y + 1)[/tex]
[tex]=> x^{2} + x - y^{2} - y[/tex]
Lets re-arrange it.
[tex]=> x^{2} - y^{2} + x - y[/tex]
Now , lets expand x² - y².
[tex]=> (x + y)(x - y) + (x - y)[/tex]
Taking ( x - y ) common ,
[tex]=> (x - y)(x + y + 1)[/tex]
Answer:
[tex]x(x + 1) - y(y + 1) \\ → {x}^{2} + x - {y}^{2} - y \\→( {x}^{2}- {y}^{2}) + (x - y) \\→ (x - y)(x + y) + (x - y) \\→ \boxed{ (x - y)(x + y + 1)}✓[/tex]
(x-y)(x+y+1) is the right answer.is 315/18 a rational or irrational number
Answers
Answer:
yes because it is a terminating decimal
Step-by-step explanation:
You have a bag of 15 marbles. 8 are red. 5 are blue. 2 are green. You asked 15 people to pull a random marble and replace it. The outcome was that 10 got red, 4 got blue and 1 got green. Joe thinks if 15 more people try 8 will pull red. Jill thinks if 15 more people try 10 will pull red. Choose the most accurate statement.
a
Joe is right because the theoretical probability is better.
b
Jill is right because the experimental probability is better.
c
We don't know what will happen, but both Joe and Jane are making good, educated assumptions.
d
We don't know what will happen because anything is possible and there is not point in calculating probabilities. Whatever happens, happens.
e
6 people will pull red to average out to 8. The long term average must match the theoretical probability.
Answers
Answer:
C.
Step-by-step explanation:
We have 2 probabilities: Theoretical probability and Experimental probability.
We cant know what will happen as it's just probability but both joe and Jill are making educated guesses based on probabilities, just different kinds.
Explain how to determine if two line segments are parallel, perpendicular
or neither.
Answers
Answer:
nelther
Step-by-step explanation:
trust me
multiple choice please help