Answer:
The area of triangle ABC is 16 times larger than the area of triangle DEF
Step-by-step explanation:
Step 1: Re-state the input
Given two triangles ABC and DEF are similar with ratio k.
Step 2: Derive the information
Suppose that the triangle ABC is k times larger than triangle DEF.
=> It means that all sides and heights of triangle ABC are k times larger than corresponding sides and heights of triangle DEF.
For example:
AB = k x DE
AC = k x DF
BC = k x EF
=> AB + AC + BC = k x (DE + DF + EF)
=> Perimeter of triangle ABC is k times larger than perimeter of triangle DEF
Step 3: Solve the problem step-by-step
Suppose that AH is the height from vertex A to base BC of triangle ABC and DH' is the height from the vertex D to base EF of triangle DEF.
As the above assumption states:
AH = k x DH'
BC = k x EF
Multiply both sides of the two above equations:
=> AH x BC = DH x EF x k x k
Simplify k components:
=> AH x BC = DH x EF x k^2
Multiply (1/2) to both sides:
=> (1/2) x AH x BC = (1/2) x DH x EF x k^2
Apply the formula to calculate the area of a triangle:
=> Area of triangle ABC = Area of triangle DEF x k^2
In other words:
The area of triangle ABC is (k^2) times larger than area of triangle DEK.
Here, the perimeter of triangle ABC is 4 times larger than the perimeter of triangle DEF => k = 4
Step 4: Make the conclusion
=>The area of triangle ABC is (4^2 = 16) times larger than area of triangle DEK.
Hope this helps!
:)
What is unique about an equilateral triangle? *
Answer:
Option A
Step-by-step explanation:
An equilateral triangle's sides are equal to each other, and all their angles are equal.
The best option is A.
What makes the other answers wrong:All angles in a equilateral triangle are 60° each. They are not obtuse.
All three angles of a equilateral triangle are congruent. Again, they all measure 60° each.
All sides of a equilateral triangle are congruent.
Given the information in the diagram, which theorem best
justifies why lines e and f must be parallel?
alternate interior angles theorem
same side interior angles theorem
converse of the alternate interior angles theorem
converse of the same side interior angles theorem
Answer:
its D
Step-by-step explanation:
Just did the test. Goodluck
Answer:
d
Step-by-step explanation:
Solve.
-6x - 4y = -32
-2x + 7y = 6
A. (5, 3)
B. (5, 2)
C. (4, 3)
D. (4, 2)
Answer:
D
Step-by-step explanation:
-6x=4y-32
x=(2(2y-16))/-6
x=(2y-16)/-3
x=(-2/3)*y+16/3
solve for y:
-2((-2/3)*y+16/3)+7y=6
(4/3)y+21/3y+(-32/3)=18/3
(25/3)y=(18+32)/3
(25/3)y=50/3
25y=50
y = 2
solve for x:
-6x - 4y = -32
-6x - 8 = -32
-6x = -24
x = 4
answer: (4, 2)
How many roots does (x+10)^9 have. Please explain how u did it.
Answer:
This expression contains a one root (x= -10) of multiplicity 9
Step-by-step explanation:
Notice that this polynomial is given in factor form, since it is equivalent to 9 products of the same factor (x+10):
[tex](x+10)^9=(x+10)\,(x+10)\,(x+10)\,(x+10)\,(x+10)\,(x+10)\,(x+10)\,(x+10)\,(x+10)[/tex]
Therefore, there is a single root x = -10, since when x=-10 each of these binomial factors result in a zero.
In mathematical terms, such type of root is said to have multiplicity. And in this case, the multiplicity is "9" (the number of equal binomial factors of the polynomial form).
Answer:
9
Step-by-step explanation:
(x+10)^9 is the 9-degree polynomial so it has 9 roots
if it is equal to zero then it has 9 equal roots of x= -10
Given the speeds of each runner below, determine who runs the fastest.
Ron runs 8 feet per second.
Liz runs 104 feet in 7 seconds.
Katie runs 1 mile in 526 seconds.
Emily runs 835 feet in 1 minute.
Answer:
Liz
Step-by-step explanation:
lets make all speeds ft/1sec
Ron 8ft/1sec
Liz 104ft/7sec : 104/7=
14.8571428571 ft/1 sec
Katie
1 mile = 5280ft
5280ft/526sec
5280/526=
10.0380228137ft/1 sec
Emily,
1 min= 60 sec
835ft/60 sec
835/60=
13.9166666667 ft/sec
now, lets order from least to greatest
R:8ft/1sec, K:10.0380228137ft/1 sec,
E:13.9166666667 ft/sec, L:14.8571428571 ft/1 sec
Liz's speed is fastest
Christian created a model
of his truck using a scale of
1 inch : 36 inches. If the length
of his actual truck is 250.4
inches, how long is his model,
rounded to the nearest inch?
Answer:
7 inches
Step-by-step explanation:
250.4/36= 6.955555 rounded to nearest inch is 7
-7n2 + 5n + 2 = 0
Find the discriminant of each quadratic equation then state the number and type of solutions.
Answer:
Step-by-step explanation:
D=5^2-4*(-7)*2
D=25+56
D=81
two real rational solutions, since 81 is a perfect square
In the triangle below. 15 represents which ratio?
А
15
B
00
17
C
o tan
O tano
sin B
COS
Answer:
tanB
Step-by-step explanation:
In the picture attached, the question is shown.
By definition:
tan(β) = opposite/adjacent
From the picture, for angle B the opposite side measure 8 units and the adjacent side measures 15 units. Replacing into the equation:
tan(B) = 8/15
Determine the value of z in the figure answers: z = 40° z = 90° z = 20° z = 45°
Answer:
20 degreesStep-by-step explanation:
This is a linear pair, whose sum always equals 180 degrees,
hence, we can set up the equation:
2z+140=180
2z=180-140
2z=40
z=40/2
z=20
Thus, the answer is 20 degrees
Answer:
z = 20°
Step-by-step explanation:
The two angles form a straight line so they add to 180 degrees
2z+ 140 = 180
Subtract 140 from each side
2z+140-140 = 180-140
2z = 40
Divide by 2
2z/2 = 40/2
z = 20
What is the value of p?
Answer:
p = 50°.
Step-by-step explanation:
To find the value of 'p', we will need to solve for the measure of the other angles of the triangle using the Supplementary Angles theorem.
Notice 140° at the top of the figure. This angle is supplementary to the top angle of the triangle. We can find this angle by:
180 - 140 = 40°.
Repeat this same step for the other angle.
180 - 90 = 90°.
Since the sum of all 3 sides = 180, we must subtract these from 180 to get the measure of 'p'.
180 - 90 - 40 = 50°.
Therefore, p = 50°.
1a) What is the side length of the following square? *
Answer:
4 unit cubes
Step-by-step explanation:
Answer:
Exact: 2sqrt(5)
Approximate: 4.472
Step-by-step explanation:
The side of the square is the hypotenuse of a right triangle with legs of lengths 2 and 4.
c^2 = a^2 + b^2
c^2 = 2^2 + 4^2
c^2 = 4 + 16
c^2 = 20
c = sqrt(20)
c = sqrt(4 * 5)
c = 2sqrt(5) = 4.472
ABCD is a quadrilateral. Three of the angles of ABCD measure 100°, 87, and 106°, respectively. Find the measure of the
missing angle
A. 67
B. 74°
C. 80
D. 870
Answer:
A
Step-by-step explanation:
The angles in a quadrilateral add up to 360 degrees.
100 + 87 + 106= 293
360 - 293 = 67
The missing angle is 67°. (A)
EVERY quadrilateral has four inside angles that add up to 360°. It doesn't matter whether the quadrilateral is the size of a strep bacterium or the size of a galaxy. The inside angles always add up to 360°. It's a quadrilateral thing.
In this question, the first three angles add up to (100°+87°+106°) = 293°.
From there, it takes 67° more to get to 360°, so that's what the fourth angle has to be.
john gave brandon five dollars and 13 cents now he has 25 dollars how much did he have
I need help please!!!!!!!
Answer:
m = 1 and c = 3
Step-by-step explanation:
y = mx + c
so comparing with y = x + 3
m = 1 ( since there isn't any co-efficient of x) and c = 3
Isabella wants the distribution of money spent on advertising to match the distribution of profit gained from each product. If
Isabella has a budget of $22.5 million, how much should she allocate for ads for peripherals, to the nearest hundred thousand
dollars?
a. $9.7 million
b. $7.3 million
c. $4.1 million
d. $2.2 million
The company's profit in the year 2003 is $3.1 million
What is profit?Profit is stated as the amount of revenue generated after deduction of all the liabilities. Profit is the money you have left after paying for business expenses. There are three main types of profit: gross profit, operating and net profit.
Given that,
in the year 2000 profit = $2.2 million
Each year increase in profit = 13% =0.13
Total number of year = 2003-2000=3 years
Profit is denoted by
profit = initial profit ( 1 + each year increase)^years
Substituting the values we get
profit=2.2( 1 + 0.13)³
=2.2( 1.13)³
=3.174373
=3.1 million
Therefor , the company's profit in the year 2003 is $3.1 million
Learn more about Profit here
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Answer: Its C
Step-by-step explanation: I got it right
A restaurant has 75% of its tables being used. Which ratio compares the used tables with all the tables in the restaurant? A. 50:100 B. 25:75 C. 25:100 D. 15:20
Answer:
D
Step-by-step explanation:
It would 75:100
We then can simplify that by dividing by 5 so we get
15:20
Answer: 15:20
Step-by-step explanation:
75% tables are used out of 100%
The ratio will be 75:100 = 15:20
each ice cream cone cost $100. Students get 5 1/2 and seniors get 7 1/2. how much more does seniors get?
Answer:
2
Step-by-step explanation:
7 1/2 - 5 1/2
7.5 - 5.5
2
Prove that for any natural n the number 3^(n+4)−3n is divisible by 16.
Answer:
Step-by-step explanation:
Prove that for any natural number 3^(n+4)-3n is divisible by 16.
(I'm going to assume that you mean 3^(n+4)-3^n.)
1. We can break up 3^(n+4)-3n into 3^n * 3^4-3^n (by the rule a^b*a^c = a^b+c).
2. Solve to get 3^n * 81 - 3^n
3. Factor out the 3^n, and you'll get 3^n(81-1), and simplify: 3^n(80)
You may notice that 80 is divisible by 16.
4. Rewrite what we got from the last step as: 3^n*5(16).
Hope this helped you!
The proof that any natural number n in (3ⁿ⁺⁴ - 3ⁿ) is divisible by 16 is; it was simplified to 3ⁿ × 5
What is the proof that the number is divisible?
We want to show that show that 3ⁿ⁺⁴ - 3ⁿ is divisible by 16.
This is; (3ⁿ⁺⁴ - 3ⁿ)/16
From laws of indices, we know that;
aᵐ⁺ⁿ = aᵐ × aⁿ.
Thus; 3ⁿ⁺⁴ can be expressed as 3ⁿ × 3⁴.
Thus; (3ⁿ⁺⁴ - 3ⁿ)/16 is;
((3ⁿ × 3⁴) - 3ⁿ) = 3ⁿ((81 - 1)/16)
3ⁿ(80/16) = 3ⁿ × 5
The expression has been fully simplified to show that any natural number n in (3ⁿ⁺⁴ - 3ⁿ) is divisible by 16.
Read more about proof of numbers at; https://brainly.com/question/10657323
For every 4 hours of babysitting, Sam charges $30. If last month she earned $75, how many hours did she babysit ?
Answer:
10
Step-by-step explanation:
Simplify sqrt of 75x^6y^11 to the form a sqrt of b
Answer:
2121221
Step-by-step explanation:
−7/8 −(−5/6) in simplest form
Answer:
-1/24
Step-by-step explanation:
-7/8 - (-5/6)
Subtracting a negative is like adding
-7/8 + 5/6
Get a common denominator
-7/8 * 6/6 + 5/6 *8/8
-42/48 + 40/46
-2/48
-1/24
what are their means and extremes of the following proportion
Answer:
a and d are extremes b and c are meansStep-by-step explanation:
[tex]\frac{a}{b} =\frac{c}{d}[/tex]
another way to write the equality of the two ratios is :
a : b = c : d
as you can see in the equality a : b = c : d
a and d are extremes b and c are meansI put in 6.32 for A but it’s still saying it’s wrong and I need the √ , I only need to answer this right to pass my summer school class someone please help me !
Answer:
A = 2 (on the left). 10 (on the right)
Step-by-step explanation:
Use pythgaros therom
Do 7^2 - 3^2 = 40
Do square root of 40 which equals the answer
In the Metric System: As you move from a smaller unit to a larger unit, the number of larger units required will be LESS. Therefore the decimal point will always move to the LEFT when you want to make a number smaller because the unit is larger. is it true or false?
Answer:
True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Did it on edge2020
Can some text me and help me with all my e2020
Will be Marked brainliest and extra points
A. Yes
B. No do it your self
Answer:
idk what an e2020 is ....... education2020?????? and i cant give out my number bc ppl can see here on brainly
Solve the following equation. Then place the correct number in the box provided.
7x=84
x=?
Answer:
7x=84
divide by 7
12=x
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
We are looking for the value of x. To find this, we must isolate x on one side. To do this, we can divide by 7 on both sides, leaving us with x=12.
What is the common ratio for this geometric sequence? 64, 16, 4, 1, … A. B. 4 C. D. 8
Answer:
1/4
Step-by-step explanation:
Each term is a fourth of the term before.
So, each term is the previous term multiplied by 1/4
Answer:
1/4
Step-by-step explanation:
Determine the value of z in the figure answers: z = 50° z = 45° z = 10° z = 30°
Answer:
z = 10°
Step-by-step explanation:
Since the two sides are equal, the two base angles have to be equal
That means that 5z and 130 form a straight line and add to 180 degrees
5z+130 = 180
Subtract 130 from each side
5z = 50
Divide by 5
5z/5 = 50/5
z=10
Which set of data could have been used to create the stem-and-leaf plot shown below?
64, 79, 95, 83, 81, 90, 67, 86, 91, 84, 81, 69, 83, 92
6.4.7.9. 9.5, 8.3, 8.1, 9.0.6.7.8.6, 9.1, 8.4, 8.1,6.9, 8.3, 9.2
63,79,95, 83, 81, 90, 67, 86, 91, 84, 81, 69, 83, 92
6.3.7.9. 9.5, 8.3, 8.1, 9.0, 6.7.8.6, 9.1, 8.4, 8.1, 6.9. 8.3, 9.2
Human:
✧･ﾟ: *✧･ﾟ:* Answer: *:･ﾟ✧*:･ﾟ✧
✅ D.) 6.3.7.9. 9.5, 8.3, 8.1, 9.0, 6.7.8.6, 9.1, 8.4, 8.1, 6.9. 8.3, 9.2
I WOULD APPRECIATE BRAINLIEST!
~ ₕₒₚₑ ₜₕᵢₛ ₕₑₗₚₛ! :₎ ♡
~
I need help ASP on this
Answer:
2l + 2w is the formula for perimeter. l = 2w + 6 can be written as "the length is 6 feet more than two times its width."
The answer is B.
Answer:
B
Step-by-step explanation: