Answer:
1 : 9
Step-by-step explanation:
Given 2 similar figures with sides in ratio a : b , then
ratio of areas = a² : b²
Here the ratio of sides = 1 : 3 , thus
ratio of areas = 1² : 3² = 1 : 9
The ratio of the areas of the similar triangles is 1 : 9
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔABC
Let the second triangle be represented as ΔDEF
And , they are similar triangles
Now , the sides of one are three times as long as the sides of the other
Let's call the sides of the smaller triangle a, b, and c, and the sides of the larger triangle 3a, 3b, and 3c. Then we know that:
a : 3a = b : 3b = c : 3c
Simplifying this, we get:
1 : 3 = 1 : 3 = 1 : 3
This means that the corresponding sides of the two triangles are in a ratio of 1:3
Now, let's use the formula for the area of a triangle:
A = ( 1/2 ) x base x height
The base and height of the two triangles are also in a ratio of 1:3, so the ratio of their areas is:
(1/2) x 1 x 1 : (1/2) x 3 x 3
So , the ratio is 1 : 9
Hence , the ratio of the areas of the smaller triangle to the larger triangle is given by 1 : 9
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What is the area of the given compound shape?
1. 19 sq cm
2. 25 sq cm
3. 34 sq cm
Answer:
(A)
Step-by-step explanation:
As you can see, the figure can be divided into a square of side 2cm and a rectangle of sides 5cm and 3cm so we find the area of both and add.
Area of the square
= 2x2 = 4cm^2
Area of the rectangle
= lxb
= 3x5
= 15 cm^2
Therefore the area of the entire figure
= Area of square + area of rectangle
= 15+4
= 19 cm^2
So the correct option is (a)
Hope this helps:)
Answer:
Option 1
Step-by-step explanation:
I broke the figure up into two shapes. One of them was a square and the other one was a big rectangle. I calculated the two areas and added them back together. My work is attached in the picture.
Area of a square is: s^2
's' -side length
Area of a rectangle is: b * w
'b' - base or length
'w' - width
The area of the figure should be 19cm².
Des buys a pack of starbursts that has 3 orange,6 pink , 1 yellow , and 5 red starbursts. She puts the candy in the bowl. If she reaches in and grabs two starbursts without putting one back , what is the probability that she will pick a pink and then a yellow?
Answer:
3/70
Step-by-step explanation:
3 orange,6 pink , 1 yellow , and 5 red = 15
P(pink) = number of pink/ total = 6/15 = 3/5
Then without putting it back
3 orange,5 pink , 1 yellow , and 5 red = 14
P(yellow) = number of yellow/ total = 1/14
P(pink, no replacement, yellow) = 3/5*1/14 = 3/70
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!
Answer:
-5x=-11
Step-by-step explanation:
[tex]-4x-2y=-2 \\\\x-2y=9[/tex]
Subtract the second equation from the first:
[tex]-4x-(x)-2y-(-2y)=-2-(9)\\\\-5x=-11[/tex]
Hope this helps!
BRAINLIEST 5 STARS AND THANKS
Answer:
8. 24+36+12= 72 in cubed
And yes it would fit because 72 is greater than 64
9. 2+21= 23 ft cubed
Maya spent her allowance on playing an arcade game a few times and riding the Ferris wheel more than once. Write about what additional information you would need to create a two-variable equation for the scenario. What kind of problem could you solve with your equation?
Answer:
You would need to know how much money she spent and how much she had left.
Step-by-step explanation:
With this, you could find out how much money she had in total.
Sample Response:
To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game.
Rania is riding the ferris wheel. Her vertical height H(t)H(t)H, left parenthesis, t, right parenthesis (in \text{m}mstart text, m, end text) off the ground as a function of time ttt (in seconds) can be modeled by a sinusoidal expression of the form a\cdot\cos(b\cdot t)+da⋅cos(b⋅t)+da, dot, cosine, left parenthesis, b, dot, t, right parenthesis, plus, d. At t=0t=0t, equals, 0, when she starts moving, she is at a height of 10\text{ m}10 m10, start text, space, m, end text off the ground, which is as low as she goes. After 20\pi20π20, pi seconds, she reaches her maximum height of 30\text{ m}30 m30, start text, space, m, end text. Find H(t)H(t)H, left parenthesis, t, right parenthesis.
Answer:
H(t) = -10·cos(t/20) +20
Step-by-step explanation:
The range of heights is ...
30 m - 10 m = 20 m
The amplitude of the cosine function is half that, or 10 m. Here, the function starts off at a minimum, whereas the parent cosine function starts at a maximum. That means the parent function is reflected vertically, so the amplitude coefficient in H(t) is negative.
The midline of the cosine function is the average of the extreme heights, so is ...
midline = (30 m +10 m)/2 = 20 m
The period of the function is double the time it takes to go from a minimum to a maximum, so is ...
p = 2(20π) = 40π . . . . seconds
In the given function form ...
H(t) = a·cos(bt) +d
the amplitude is a=-10; the coefficient b is 2π/p = 1/20; and the midline is d = 20. Then the function is ...
H(t) = -10·cos(t/20) +20
What’s c ? And I need explanation plz
Answer:
a
Step-by-step explanation:
the probablity of getting head when flipping a coin that hasn't been altered is 50/50, therefor it's a :) hope it helped
Answer:
A
Step-by-step explanation:
The probability scale shows how likely or unlikely something is going to happen. So when flipping an unbiased (fair) coin, the probability of getting a head is exactly 50%. Thus, A means "half" on the probability scale so A is the correct answer.
Find The equation of a circle that has it center at (-4,3) and has a radius of 5.
Answer:
A.
Step-by-step explanation:
Center = (a,b) = (-4,3)
So, a = -4, b = 3
Radius = 5
Equation of circle:
[tex](x-a)^2+(y-b)^2 = r^2[/tex]
Putting the givens
=> (x+4)²+(y-3)² = 25
[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \\
{(x - (4))}^{2} + {(y + 3))}^{3} = {5}^{2} \\ {(x - 4)}^{2} + {(y + 3)}^{2} = 25[/tex]
What is the answer for this question??
The correct answer is D: 10x = 1000, which simplifies to x = 100
What is the solution to the system of equations?
y=x+3
x=-2
Simply plug in x to the formula to y.
y = -2 + 3
y = 1
and
x = -2
I hope this is what you were looking for.
Answer:
y=1
Step-by-step explanation:
Plug x=-2 into the equation y=x+3:
y=(-2)+3
y=1
Marcus deposited his paycheck in the amount of $625.84. He’ll use the check register to record his transaction. What will be his new balance? A check register has a balance of 640 dollars and 31 cents.
Answer:
His new balance will be $1,266.15
Step-by-step explanation:
Solve for h.
–10 − 8h − 14h = –15h + 18
h =
Answer:
[tex] \boxed{h = -4} [/tex]
Step-by-step explanation:
[tex] = > - 10 - 8h - 14h = - 15h + 18 \\ \\ = > - 10 - 22h = - 15h + 18 \\ \\ = > - 22h + 15h - 10 = 18 \\ \\ = > - 7h - 10 = 18 \\ \\ = > - 7h = 18 + 10 \\ \\ = > - 7h = 28 \\ \\ = > 7h = - 28 \\ \\ = > h = - \frac{28}{7} \\ \\ = > h = -4[/tex]
What is the value of:
1/2f (c-d) +k-d
where f=5, d=114c, k=f-2 and c=8
The cost of 4 bear toys and a lion toy is $70. If the cost of a lion toy and 2 bear toys is
$41, what is the cost of a lion toy?
$36
$28
$14.50
$12
Answer:
14.50 because you need to divide the total amount by 2 and then you have the remaining
The cost of a lion toy is $12
What is a linear equation?An equation between two variables with a constant in the form of ax +by =c is called a linear equation.
Given the cost of 4 bear toys and a lion toy is $70.
And If the cost of a lion toy and 2 bear toys is $41,
Write a linear equation for the above equation
4B +1L =70
2B +1L =41
By solving the above equations we get B= $14.5 and L=12
Thus the cost of a bear is $14.5 and cost of a lion is $12.
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A counter recorded 254 revolutions of the bicycle wheel shown. How far did the bicycle travel? Use 22/7
[tex]C=\pi d[/tex]
[tex]22/7(5/4)[/tex]
[tex]=3.92857142857[/tex]
[tex]3.92857142857(254)[/tex]
[tex]=997.857142857[/tex]
In 254 revolutions , the bicycle will travel [tex]997.85m[/tex]
Circumference :The circumference of bicycle is given as,
[tex]C=\pi d[/tex]
Where [tex]d[/tex] is diameter of bicycle.
Given that,[tex]d=\frac{5}{4} ,\pi=22/7[/tex]
Substitute values in above equation.
[tex]C=\frac{22}{7}*\frac{5}{4}\\ \\ C=\frac{110}{28}=3.93[/tex]
In 254 revolutions of the bicycle wheel is,[tex]C=254*3.93=997.85m[/tex]
In 254 revolutions , the bicycle will travel [tex]997.85m[/tex]
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Your question was incomplete , Complete question is here :
"A counter recorded 254 revolutions of the bicycle wheel shown below how far did the bicycle travel. Use 22/7 as pi and the diameter of the wheel is 5/4."
Mason says that (12x+4)-(-3x+5) and 15x -1 are equivalent. Is he correct
Answer:
Yes.
Step-by-step explanation:
I have attached the work to your problem.
Please see the attachment below.
I hope this helps!
Answer:
yes he is correct
Step-by-step explanation:
(12x+4)-(-3x+5)
take out parenthesis,
12x+4--3x-5
simplify,
12x+4+3x-5
do the math,
15x-1
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!!!
Answer:
- [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ - 8, 2 ] , thus
f(b) = f(2) = - 4 ← read from graph
f(a) = f(- 8) = 1 ← read from graph, thus
average rate of change = [tex]\frac{-4-1}{2-(-8)}[/tex] = [tex]\frac{-5}{10}[/tex] = - [tex]\frac{1}{2}[/tex]
Tyron made 60 cakes. He gave 1/6 of the 60 cakes to Lilly. What fraction of the cakes does he have left?
Answer:
38/60 or 19/30
Step-by-step explanation:
The question isn't fully attached as stated by the person who submitted it.
The fraction of the cakes he has left is ( 5 / 6 ). The remaining number of cakes is 50.
What is a fraction?Expression in maths is defined as the collection of numbers, variables, and functions using signs like addition, subtraction, multiplication and division.
The fraction is calculated as:-
The remaining fraction = 1 - ( 1 / 6 )
= ( 6 - 1 ) / 6
= 5 / 6
The remaining number of cakes,
Remaining number = 60 x ( 5 / 6 )
Remaining number = 50
Hence, the remaining number of cakes is 50.
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What is the purpose and structure of a proof in Geometry?
Answer: A geometric proof involves writing reasoned, logical explanations that use definitions, axioms, postulates, and previously proved theorems to arrive at a conclusion about a geometric statement.
Please help im really confused
Answer:
A=235 cm 2
Step-by-step explanation:
A1=L x W
A1=9 x 20 180 + 55=235
A1=180cm 2
A2= L x W
A2=11 x 5
A2=55 cm2
Answer:
[tex]246 {cm}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
What is the equation of the line of best fit for the following data round the slope and Y intercept of the line to three dimensional places. Please help ASAP thank you so much.
Answer:
y = 1.56 x - 4.105
which agrees with answer "B" in your list of possible options.
Step-by-step explanation:
Notice that you are expected to use some type of regression tool for this problem. either a computer program or a handheld graphing calculator with such functionality.
I have entered the set of data points in two separate lists, one for the x-values,and another one for the y-values, and run the linear regression tool in order to get the best fitting line. See what I obtained using this tool in the screen capture I am attaching below.
Notice that the line of best fit reads:
y = 1.56015038 x - 4.10526316
showing clearly the slope and y-intercept of the line of best fit.
Rounding slope and y-intercept to the third decimal, we get:
y = 1.56 x - 4.105
which agrees with answer "B" in your list of possible options.
For an exponential regression equation in the form y=ab^x , a value of 1.101 for b will cause y to get smaller as x gets larger True or false
Answer:
False
Step-by-step explanation:
2. Find the value of V343 X V27
Answer:
De value of v is 12
Step-by-step explanation:
v343×v27
343×27÷27
=12red 7
What is the answer of the Fractions listed? Will give Brainliest 20 points
Answer:
- 6 1/2
Step-by-step explanation:
-4 - 2 1/2
Since the signs are the same, we add them together and take the signs
4+2 1/2 = 6 1/2
Take the sign
- 6 1/2
Answer:
(-4) - 2 1/2 = -6.5
Step-by-step explanation:
( −4 ) − 2 1/2 = -13/2
-13/2 = -6 1/2
Help! Stuck on this question (calculus)
If [tex]y=\frac{3}{x^2}[/tex]
work out [tex]\frac{dx}{dy}[/tex]
Answer:
[tex]\displaystyle \frac{dx}{dy} = \frac{3\sqrt{\frac{3}{y}}(y - 1)}{6y}[/tex]
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{3}{x^2}[/tex]
Step 2: Differentiate
Rewrite Function: [tex]\displaystyle yx^2 = 3[/tex][Implicit Differentiation] Basic Power Rule [Product Rule]: [tex]\displaystyle y^{1 - 1}x^2 + y(2x^{2 - 1})\frac{dx}{dy} = 3[/tex]Simplify: [tex]\displaystyle x^2 + y(2x)\frac{dx}{dy} = 3[/tex]Isolate [tex]\displaystyle \frac{dx}{dy}[/tex] term: [tex]\displaystyle y(2x)\frac{dx}{dy} = 3 - x^2[/tex]Isolate [tex]\displaystyle \frac{dx}{dy}[/tex]: [tex]\displaystyle \frac{dx}{dy} = \frac{3 - x^2}{2xy}[/tex]Substitute in x²: [tex]\displaystyle \frac{dx}{dy} = \frac{3 - \frac{3}{y}}{2xy}[/tex]Simplify: [tex]\displaystyle \frac{dx}{dy} = \frac{3(y - 1)}{2xy^2}[/tex]Substitute in x: [tex]\displaystyle \frac{dx}{dy} = \frac{3(y - 1)}{2y^2(\sqrt{\frac{3}{y}})}[/tex]Simplify: [tex]\displaystyle \frac{dx}{dy} = \frac{3\sqrt{\frac{3}{y}}(y - 1)}{6y}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Please help me this is pretty easy I’m just dumb . Tell me wheaten each of the following is a proper fraction(p), and improper fraction (I), or a mixed number (M)
Answer:
1. I,P,M,P
2. P,I,P,M
3. M,P,P,I
4. P,I,M,P
The weights of the cars passing over a bridge have a mean 3,550 pounds and standard deviation of 870 pounds. Assume that the weights of the cars passing over the bridge are normally distributed. Use the empirical rule to estimate the percentage of cars over the bridge whose weights are between 1810 and 4420 lbs.
a. 13.5%
b. 81.5%
c. 68%
d. 95%
Mean = 3550
SD = 870
Find P(1810 <x<4420)
z = x -mean / sd
= (1810 - 3550 / 870) < z< (4420 - 3550 / 870)
= -2 <z< 1
Using the -z table -2 = 0.0228 and 1 = 0.8413
Subtract: 0.8413 - 0.0228 = 0.8185 x 100 = 81.85%
Rounding everything may change answer slightly so
The closest one is B 81.5%
Mr. Nicholas invested $4,250 into an account that pays 3.5% interest, compounded annually. How much will Mr. Nicholas’s investment be worth after 8 years?
Answer:
$5596.44
Step-by-step explanation:
$4250*(1.035)^8= $5596.44
Isaac is constructing a circular pool that has a diameter of 20 ft and is 5 ft deep. Part A: Find the circumference of the pool to the nearest tenth of a foot. Use 3.14 for pi. Part B: Find the area of the circle formed by the pool to the nearest foot.
Answer:
The circumference of the pool is 62.8 foot long and the area of the circle formed by the pool is 314 ft².
Step-by-step explanation:
The circumference of the pool can be found by calculating the arc's length of the edges of the pool. This is done by using the following formula:
[tex]circumference = 2*\pi*r[/tex]
Where the radius is half the diameter, applying the data from the problem we have:
[tex]circumference = 2*3.14*10 = 62.8 \text{ ft}[/tex]
The area of the circle formed by the pool can be found using the following expression:
[tex]area = pi*r^2 = 3.14*(10)^2 = 314 \text{ ft}^2[/tex]
The circumference of the pool is 62.8 foot long and the area of the circle formed by the pool is 314 ft².
Evaluate 4 squared times 3 to the power of 3
Answer: 432
Step-by-step explanation:
Four squared = 16 since 4 times 4 = 16
3 to the power of 3 = 27 since 3 times 3 times 3 = 27
Finally, multiply them together, 16 times 27 = 432
Answer: 432
Step-by-step explanation:
(4^2)×(3^3)
4×4=16
16×3^3=16×(3×3×3)
16×27=432