Answer:
population=300,000
population size per year=4.5%
population size for 8 years=8 × 4.5%
=0.36
=108000
Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
A. SAS theorem
B. SSS theorem
C. AA postulate
D. Similarity cannot be determined.
Answer:
C
Step-by-step explanation:
AA postulate because we are given 2 of the 3 angles of each triangle. They are both the same in each triangle. Also, we can find the 3rd angle in each triangle. Since both triangles have the exact same angles, they are similar.
The given triangles ΔABC and ΔLMN are similar by AA postulate.
What is a triangle?A triangle is a three sided polygon that consist of three edges and three vertices .
Here two given triangles are ΔABC and ΔLMN. In these two triangles ∠A=∠L=53° and ∠B=∠M= 72°.
Therefore, the two corresponding angles of triangles ΔABC and ΔLMN are equal . So the third angle of ΔABC is also equal to the corresponding angle of ΔLMN.
Hence two triangles are similar by AA postulate.
Thus two triangles are similar by AA postulate. So option (C) is correct.
To learn more about triagles click here:
https://brainly.com/question/24147586
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Can someone pls help me!
Answer: y =2x-5
Work:
2x-y=5
-y=-2x+5
-1y/-1 = -2x+5/-1
y =2x-5
A fishing trawler sails from port P in the direction 024o for 30 km, and then in the direction 114o for 20 km. Calculate: a) the distance and bearing of the trawler from P b) the direction in which the trawler must sail in order to return to P
Please use diagrams to explain.
Answer:
write these time in words 3:45
Divisibility rules for 2, 5, and 10
Which numbers are divisible by 5?
A)222
B)185
C)847
or none of these
Answer:
185 is divisible by 5.
Step-by-step explanation:
Anything that ends in a 0 or 5 can be divisible by 5.
Answer:
Hello There!!
Step-by-step explanation:
The answer is B)185 because a number divisible by 5 ends in 0 or 5.
hope this helps,have a great day!!
~Pinky~
The midpoint of two points is (5,4). If one of the points is (3,5), find the other point.
question is worth 4 marks The ble below show the food the number of calories per serving and the number of servis hained Open strict diet where he can only have a total of 1800 calories per day notion in the table have create a balanced meal of 3 items, one serving each he bave for Number of Se 15 2
Answer:
തത് httht bytbtybbybbtybbybyybyv6vyvyvtv5ct
The capacity of a CD-ROM is 800 MB (800 x 20 raised to 20 bytes). It stores information along a spiral track. If each byte uses a space of 9 microns, what is the length of the complete track in m? (Hint: 1 micron= 10 Raised to-6m)
Answer:
The length of the complete track= [tex]7.549\times 10^{23} m[/tex]
Step-by-step explanation:
We are given that
Capacity of CD-ROM=800MB=[tex]800\times 20^{20} bytes[/tex]
1 byte=9 microns
[tex]1micron=10^{-6}m[/tex]
We have to find the length of the complete track in m.
We change MB into micron
[tex]800\times 20^{20} bytes=800\times 20^{20}\times 9microns[/tex]
=[tex]7200\times 20^{20} microns[/tex]
Now, we change micron into m
[tex]7200\times 20^{20} microns=7200\times 10^{-6}\times 20^{20} m[/tex]
=[tex]7.549\times 10^{23} m[/tex]
Hence, the length of the complete track= [tex]7.549\times 10^{23} m[/tex]
Fill in the blanks using < or >. (a) -3 ...... -4 (b) 6 ....... -20 (c) -8 ...... -2 (d) 5 ...... -7
[tex]\sf \bf {\boxed {\mathbb {ANSWER:}}}[/tex]
(a) -3 [tex]\boxed{ > }[/tex] -4
(b) 6 [tex]\boxed{ >}[/tex] -20
(c) -8 [tex]\boxed{ < }[/tex] -2
(d) 5 [tex]\boxed{ > }[/tex] -7
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{☂}}}}}[/tex]
chung minh phan so sau toi gian : 21n+4/14n+3
Step-by-step explanation:
Cog, KY tj, kyzkysiyso6doydi6wkyx co70 kysu5, 5i
What are the measure of ∠1 and ∠ 2 ? Show your work or explain
Answer:
I need the picture.
The length of a rectangle is 5 less than
the width. Which polynomial describes
the area of the rectangle?
Answer:
Let length = x
Let width = x + 5
Let Area = A
A = x(x + 5)
A = x2 + 5x
Question 17 of 25
Imagine that you are given two linear equations in slope-intercept form. You
notice that both the slopes and the y-intercepts are the same. How many
solutions would you expect for this system of equations?
A. infinitely many
B. cannot be determined
C. O
D. 1
Answer:
A. infinitely many
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptSolving systems of equations
Step-by-step explanation:
If 2 lines are parallel (same slope, different y-intercept), they would have no solution.
If 2 lines were the same (same slope, same y-intercept), they would have infinite amount of solutions.
1) Mrs Tan is 43 years old and her daughter is 17 years old. How many years ago was Mrs Tan 3 times as old as her daughter?
2)Amy is 9 years old younger then her younger sister. if her younger sister is now 1 year old, how many years later will Amy be 4 times as old as her younger sister?
Answer:
No 1
Here,
Let X be age of daughter
and 3X be age of father
Now,x+17+3 = 20 age
and 3x+43-20 = 7point9x
Step-by-step explanation:
So,
20÷7point9 = 2point8 years ago
Hence,
age of father = 48÷2point8 = 21point5 years
age of daughter = 20÷2point8 = 10 years
so, before 2point8 years ago father was as old as his daughter
what is the gradient of line Y =-3×+5
find the volume of the following solid figures. show your solution
Answer:
37.68m^3
2143.57 m^3
Step-by-step explanation:
Volume of a cone 1/3(nr^2h)
n = 3.14
(1/3) x (3^2) x 4 x 3.14 = 37.68
Volume of a sphere = 4/3 x pi x r^3
4/3 x 8^3 x 3.14 =
pls tell me the correct option
Answer: I would go with C I hope i am right!!
Step-by-step explanation:
Answer:
b. [tex] \frac{1}{16} [/tex]
Step-by-step explanation:
A = {2, 3}
B = {4, 6}
C = set of all possible fractions where, the numerators are in set A and the denominators are found in Set B
The 4 possible fractions we can get for set C are as follows:
Set C: { [tex] \frac{2}{4} [/tex] , [tex] \frac{2}{6} [/tex] , [tex] \frac{3}{4} [/tex] , [tex] \frac{3}{6} [/tex] }
Multiply all to get the product of all elements in Set C:
[tex] \frac{2}{4}*\frac{2}{6}*\frac{3}{4}*\frac{3}{6} [/tex]
Simplify where necessary
[tex] \frac{1}{2}*\frac{1}{3}*\frac{3}{4}*\frac{1}{2} [/tex]
[tex] \frac{1*1*3*1}{2*3*4*2} [/tex]
[tex] \frac{3}{48} [/tex]
Simply further
[tex] \frac{1}{16} [/tex]
pls tell the answer by step by step
The point lies in 2nd quadrant.
Answer:
second quadrant
Step-by-step explanation:
here , -2 is x component and y component is 5
since x component is negative and y component is positive it lies on the second quadrant.
Note: if both x and y component are positive then the point lies on first quadrant.
id x component is negative and y component is positive then the point lies on second quadrant.
if x both x and y component are negative then the point lies on third quadrant.
if x component is positive and y component then the point lies on fourth quadrant.
i can't do this question can someone help me
Answer:
A=-3
Step-by-step explanation:
To begin, a parabola of form a(x-h)² +k opens upward when a is positive. Similarly, when a is negative, the parabola opens downward. Therefore, a must be negative here, as our expression for the parabola is a(x-0)²+0 = ax², with (0,0) being (h,k) and the vertex.
To determine whether a should be -3 or -0.6, we can think about the values on the graph that correspond to these values. A narrower graph would have a steeper slope. A narrower graph would have a large change in y with little change in x. Therefore, as ax² = y is our equation, and when a=-3, y changes more rapidly relative to when a = -0.6, A=-3 is our answer
plz anser this nathanmalhotra (if your not them dont anserw) From midnight to 7:00 am, the temperature rose 3/10 °C each hour. If the temperature at midnight was −1°C, what was the temperature at 7:00 am?
Answer:
11/10°C
Step-by-step explanation:
7 x 3/10 = 21/10
Temperature at midnight = -1°C
Temperature at 7.00 am = 21/10°C -1°C = 11/10°C
Answer:
1.1°C
Step-by-step explanation:
Assuming we are starting at midnight, we know that at midnight it is -1°C. We want to find the temperature at 7:00 AM. Or 7 hours later than midnight. The question says that every hour the temperature rises by 3/10°C. In 7 hours, we need to multiply 3/10*7=21/10=2.1 °C. So, it rises by 2.1 °C. Next add that to the -1 from midnight. Do 2.1+-1=1.1 °C.
Hope this helps!
deepak wrote out the steps to his solution of the equation 5/2-3x-5+4x=-7/4
Answer:
x = 3/4
Step-by-step explanation:
5/2-3x-5+4x=-7/4
Combine like terms
-10/2 + 5/2 +x = -7/4
-5/2+ x = -7/4
Add 5/2 to each side
-5/2+5/2 +x = -7/4 + 5/2
x = -7/4+5/2
Get a common denominator
x = -7/4 + 10/4
x = 3/4
A right triangle has a height of 22 centimeters and a base of 11 centimeters What is the area of the triangle ?
SOMEONE HELP ASAP !!!
Answer:
121 cm^2
Step-by-step explanation:
area of triangle = base*height/2
=11*22/2
=242/2
=121 cm^2
if α and β are the zeroes of the polynomial 3x^2 - 8x − 3 then find the value of i) α^2 + β^2 ii) α^-1 + β^-1
Step-by-step explanation:
the answer is in the above image
the figure below is a square . Find the length of side x in simplest radical form with a rational denominator.
Answer:
[tex]\sqrt{14}[/tex]
Step-by-step explanation:
In any square with side length [tex]s[/tex], the diagonal of the square is equal to [tex]s\sqrt{2}[/tex]. Since the side length of this square is [tex]\sqrt{7}[/tex], the diagonal is equal to [tex]\sqrt{7}\cdot \sqrt{2}=\boxed{\sqrt{14}}[/tex].
Alternatively, you can form two 45-45-90 triangles with the diagonal of the square. The diagonal acts as the hypotenuse for the both these triangles, and the legs of both triangles are equal to the side length of the square. To find the length of the diagonal, use the Pythagorean Theorem, which states [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle, and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.
In this question, both legs are equal to [tex]\sqrt{7}[/tex], and we're solving for the diagonal, which is the hypotenuse in this case:
[tex]\sqrt{7}^2+\sqrt{7}^2=c^2,\\c^2=14,\\c=\boxed{\sqrt{14}}[/tex]
Rachel loaned Adam $8510 at an interest rate of 13 % for 2 years. How much will Adam pay Rachel at the end of 2 years? Round your answer to the nearest cent, if necessary.
which statement about 0 is true ?
Answer:
❍ C. tan θ = 8 / 15
Step-by-step explanation:
Using trigonometry functions
sin θ = opposite side / hypotenuse
= 8 / 17
tan θ = opposite side / adjacent side
= 8 / 15
Hence, tan θ = 8 / 15 which is option C. is the correct statement.
Triangle NJK is similar to triangle LMK by
Answer:
B
Step-by-step explanation:
SAS cuz ML~NJ and K is common angle
The Eastminster Widget Company has an old machine that can produce 36
widgets in 9 hours, and a newer machine that can produce 40 widgets in 8
hours. Working together, how long would it take to produce 100 widgets?
Answer:
22 hours
Step-by-step explanation:
Old machine produces 36 widgets in 9 hours. The number of widgets produced in an hour can be determined as;
In 1 hour = [tex]\frac{36}{9}[/tex]
= 4 widgets
New machine can produce 40 widgets in 8 hours. The umber of widgets produced in an hour can be determined as;
In 1 hour = [tex]\frac{40}{5}[/tex]
= 5 widgets
Thus, let the time required by old machine be represented by s, and that of new machine by y. Working together we have;
4x + 5y = 100
(4 * 10) + (5 * 12) = 100
Thus the old machine would work for 10 hours, while the new machine would work for 12 hours to produce 100 widgets.
Working together, it would take both machines 22 hours.
7 th term and 14 th term of an Arithmetic sequence are 36 and 64 respectively , find the common difference and ,25th term
Answer:
(a) The common difference is 4
(b) The 25th term is 108
Step-by-step explanation:
Given
[tex]T_7 = 36[/tex]
[tex]T_{14} = 64[/tex]
Solving (a): The common difference
The nth term of an AP is:
[tex]T_n = a + (n -1)d[/tex]
For the 7th term, we have:
[tex]36 = a + (7 -1)d[/tex]
[tex]36 = a + 6d[/tex]
For the 14th term, we have:
[tex]64 =a + (14 -1)d[/tex]
[tex]64 =a + 13d[/tex]
Subtract both equations
[tex]64 - 36 = a - a +13d-6d[/tex]
[tex]28 = 7d[/tex]
Divide by 7
[tex]d = 4[/tex]
Solving (b): The 25th term
First, we calculate the first term (a)
The 7th term of the progression is:
[tex]36 = a + 6d[/tex]
Substitute [tex]d = 4[/tex]
[tex]36 = a + 6 * 4[/tex]
[tex]36 = a + 24[/tex]
Subtract 24
[tex]a = 36 -24[/tex]
[tex]a = 12[/tex]
The 25th term is:
[tex]T_{25} = a + (25 - 1)d[/tex]
[tex]T_{25} = 12 + (25 - 1)*4[/tex]
[tex]T_{25} = 12 + 24*4[/tex]
[tex]T_{25} = 108[/tex]
find the surface area of the composite figure. 6cm 5 cm 20cm 4cm 12cm 6cm
Answer:
644 cm²
Step-by-step explanation:
Surface area of the composite figure = surface area of the large rectangular prism + surface area of the small rectangular prism - 2(area of the surface of the small rectangular prism that joins the larger prism)
✔️Surface area of the large rectangular prism = 2(LW + LH + WH)
L = 6 cm
W = 5 cm
H = 20 cm
Surface area = 2(6*5 + 6*20 + 5*20)
= 500 cm²
✔️Surface area of the small rectangular prism = 2(LW + LH + WH)
L = 6 cm
W = 4 cm
H = 12 cm
Surface area = 2(6*4 + 6*12 + 4*12)
= 288 cm²
✔️area of the surface of the small rectangular prism that joins the larger prism = L*W
L = 12 cm
W = 6 cm
Area = 12*6
= 72 cm²
✅Surface area of the composite figure = 500 + 288 - 2(72)
= 644 cm²
Which is greater than 4?(show work)
(a) 5,
(b) -5,
(c) -1/2,
(d) -25.
Answer:
Letter A) 5
Step-by-step explanation:
all the other answers are negative so they are less than 4.
5 comes after 4 so 5 is greater than 4.
Hope this is helpful