What are a) the ratio of the perimeter’s b) and the ratio of areas of the larger figure to the smaller figure?
Answers
a) We have been given two similar figures and we have to find ratio of perimeters of these figures.
Let a be given side of larger figure and b be the given side of smaller figure. Let [tex]p_{1} \text{ and } p_{2}[/tex] be the perimeters of two figures and [tex]A_{1} \text{ and } A_{2}[/tex] be the areas of the two figures.
We know that perimeters of two similar figures are in the ratio of corresponding sides.
[tex]\frac{p_{1}}{p_{2}}=\frac{a}{b}[/tex]
We have been given, [tex]a=26\text{ and }b=6[/tex]
Therefore, upon substituting these values in the above equation, we get
[tex]\frac{p_{1}}{p_{2}}=\frac{26}{6}[/tex]
[tex]\frac{p_{1}}{p_{2}}=\frac{13}{3}[/tex]
(b)
Further we know that areas of two similar figures are in the ratio of squares of corresponding sides.
[tex]\frac{A_{1}}{A_{2}}=\frac{a^{2}}{b^{2}}\\ \frac{A_{1}}{A_{2}}=\frac{26^{2}}{6^{2}}\\ \frac{A_{1}}{A_{2}}=\frac{676}{36}\\ \frac{A_{1}}{A_{2}}=\frac{169}{9}\\[/tex]
Therefore, first option is the correct answer.
Related Questions
Find the missing numerators in each of the following problems. a. 10⁄15 = ⁄60 b. ⁄108 = 4⁄9 c. 7⁄11 = ⁄121 d. ⁄144 = 2⁄6
Answers
For 10/15 = x / 60
x = (10/15) * (60)
x = 40
For x / 108 = 4/9
x = (4/9) * (108)
x = 48
For 7/11 = x / 121
x = (7/11) * (121)
x = 77
For x / 144 = 2/6
x = (2/6) * (144)
x = 48
Final answer:
The missing numerators are found by creating equivalent fractions. By multiplying both the numerator and the denominator by the same factor that converts the original denominator to the new denominator, we find the missing numbers: 40, 48, 77, and 48 for each problem respectively.
Explanation:
To find the missing numerators, we need to use the concept of equivalent fractions. Equivalent fractions have different numerators and denominators but represent the same value.
a. 10⁄15 = ⁄60
We find the factor that converts 15 to 60, which is 4 (since 15 * 4 = 60), and multiply the numerator by the same factor (10 * 4 = 40). So, the missing numerator is 40.
b. ⁄108 = 4⁄9
To convert 9 into 108, multiply by 12 (since 9 * 12 = 108), and do the same with the numerator (4 * 12 = 48). Hence, the missing numerator is 48.
c. 7⁄11 = ⁄121
11 times 11 equals 121, so we multiply the numerator 7 by 11 as well (7 * 11 = 77), giving us 77 as the missing numerator.
d. ⁄144 = 2⁄6
To get from 6 to 144, multiply by 24 (since 6 * 24 = 144), so multiply the numerator 2 by 24 to get 48 as the missing numerator.
Which of the following is the graph of y=|x-1|-4y=∣x−1∣−4y, equals, vertical bar, x, minus, 1, vertical bar, minus, 4?
Answers
y = |x -1| -4
is show here.
Answer:
The graph of given function is shown below.
Step-by-step explanation:
The given function is
[tex]y=|x-1|-4[/tex] .... (1)
The vertex form of a absolute function is
[tex]y=a|x-h|+k[/tex] .... (2)
where, a is a constant and (h,k) is vertex.
On comparing (1) and (2), we get
[tex]a=1,h=1,k=-4[/tex]
The vertex of the function is (1,-4). The table of values is
x y
3 -2
2 -3
1 -4
0 -3
-1 -2
Plot these points on a coordinate plane. Draw a V-shaped curve by connecting these points with vertex at (1,-4).
Let ABCD be a cyclic quadrilateral. Let P be the intersection of AD and BC, and let Q be the intersection of AB and CD. Prove that the angle bisectors of angle DPC and angle AQD are perpendicular.
Answers
Cyclic quadrilateral ABCD.
Produce AD and BC to meet at P.
Produce AB and CD to meet at Q,
Angle bisector PJ of angle DPC divides angle DPC into two equal parts,x.
Angle bisector QI of angle AQD divides angle AQD into two equal parts,y.
Solution:
Construct segment PQ.
Name U= angle BPQ
Name V=angle BQP.
See attached figure.
Steps:
1. Consider triangle BPQ:
U+V=angle ABP (exterior angle)........................(1)
2. Consider triangle DPQ
U+2X+V+2Y = 180-angle PDQ (exterior angle)
= angle ABC (cyclic quad->opposite angles are supplementary)
=>
U+2X+V+2Y = angle ABC...................................(2)
3. Add (1) and (2)
U+V + U+2X+V+2Y = angle DPQ+angle ABC
=>
2(U+V+X+Y)=180 degrees (angles ABP and ABC lie on a straight lie)
=>
U+V+X+Y = 90 degrees = angle IKJ
4. angle bisectors PJ and QI are perpendicular.
What is the probability that a randomly thrown dart that lands within the rectangle lands within a shaded region? All of the circles are congruent, and the diameter of each circle is 100 cm. A. 39/200 B. 49/250 C. 98/125 D. 157/200
Answers
Need help on 1-6 please I need to solve for x and I need to get this done.
Answers
1. Sin = Opposite/Hypotenuse
x = 10*sin(40°) ≈ 6.428
2. Sin = Opposite/Hypotenuse
x = arcsin(7/12) ≈ 35.69°
3. Tan = Opposite/Adjacent
x = 18/tan(52°) ≈ 14.063
4. b^2 = a^2 +c^2 -2ac*cos(B)
B = arccos((a^2 +c^2 -b^2)/(2ac)) = arccos((7^2 +13^2 -8^2)/(2*7*13))
B = arccos(11/13) ≈32.20°
5. Same formula.
x = √(a^2 +c^2 -2ab*cos(B)) = √(157-132cos(42°)) ≈ 7.675
6. The ratio of side lengths is the same as the ratio of the sines of the opposite angles.
6/10 = sin(x)/sin(100°)
x = arcsin((6/10)*sin(100°)) ≈ 36.22°
Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(x) = x e2t2 − 4t dt 4
Answers
Using the Fundamental Theorem of Calculus Part 1, the derivative of the function g(x) = ∫ (x e2t2 - 4t) dt from x=4 is ex2 - 4x where 'x' is the variable 't' from the integral.
Explanation:The subject of this question is the use of part 1 of the Fundamental Theorem of Calculus to find the derivative of a complex function. This theorem states that if f is a function that is continuous over the interval [a, b] and F is an antiderivative of f on the interval [a, b], then the definite integral of f from a to b is equal to F(b) - F(a).
In your specific question, you are asked to find the derivative of the function g(x) = ∫ (x e2t2 - 4t) dt from x=4.
The derivative of a definite integral, from a constant to a variable, of a function is simply the original function evaluated at the upper limit.
Therefore, the derivative of the given function g(x) is simply ex2 - 4x, treating 'x' as the variable 't' from the integral.
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Hey can you please help me posted picture of question
Answers
So, now the expression graph will be - 3x²
Next, it is shifted to left by 4 units.
So, now the expression will be - 3(x - 4)²
Finally the graph is shifted up by 4 units,
So, now the graph will be: - 3(x - 4)² + 4
Thus, the answer is option D
Given rectangle PQRS with PQ=QR, PQ=SP, and SQ=6√2. Find SR. a)√2. b) 6. c) 5√2 d) not enough information
Answers
SQ is the diagonal of the square: [tex]SQ = 6 \sqrt{2} [/tex], but we know that in a square, the diagonal is equal to square root of 2 times the length of the side:
[tex]d = \sqrt{2} L [/tex]
where d is the diagonal and L the length of the side. Since in our square the length of the diagonal is [tex]d= 6 \sqrt{2} [/tex], the length of the side must be
[tex]L= \frac{d}{ \sqrt{2} } = \frac{6 \sqrt{2} }{ \sqrt{2} }=6 [/tex]
so, the correct answer is b) 6.
2-2*3+3. What is the correct answer
Answers
________________________________________________________
Note:
_________________________________________________________
2 - 2 * 3 + 3 =
2 - (2 * 3) + 3 =
(2 - 6) + 3 =
-4 + 3 = -1 .
_____________________________________________________
The correct answer is: " -1 " .
_____________________________________________________
(08.06 MC) Carly and Janiya put some money into their money boxes every week. The amounts of money (y), in dollars, in their money boxes after certain amounts of time (x), in weeks, are shown by the equations below: Carly y = 60x + 40 Janiya y = 50x + 80 After how many weeks will Carly and Janiya have the same amount of money in their money boxes and what will that amount be? (1 point) 5 weeks, $280 5 weeks, $340 4 weeks, $280 4 weeks, $340
Answers
y = 60x + 40
y = 50x + 80
Equaling both equations we have:
60x + 40 = 50x + 80
From here, we clear the value of x:
60x - 50x = 80 - 40
10x = 40
x = 40/10
x = 4 weeks
Substituting x = 4 in any of the equations we have:
y = 60 (4) + 40
y = 240 + 40
y = 280 $
Answer:
$ 280 4 weeks
Answer:
$ 280 4 weeks
Step-by-step explanation:
if I have 300 apples and eat 123 how many do I have left?
Answers
You have 177 apples left.
You will have 177 apples left.
X is a normally distributed random variable with a mean of 5 and a standard deviation of 2. the probability that x is greater than 10.52 is
Answers
A suitable calculator can help with this.
Final answer:
The probability that X is greater than 10.52 for a normal distribution with a mean of 5 and a standard deviation of 2 is found by calculating the z-score of 10.52. The z-score is 2.76, and the area to the right under the normal curve represents a very small probability, typically less than 0.003.
Explanation:
To find the probability that X is greater than 10.52, when X is a normally distributed random variable with a mean of 5 and a standard deviation of 2, we first need to calculate the z-score for 10.52. Using the formula:
Z = (X - mean) / standard deviation
Substitute the given values into the formula:
Z = (10.52 - 5) / 2 = 5.52 / 2 = 2.76
This z-score tells us how many standard deviations above the mean our value lies. In this case, X = 10.52 is 2.76 standard deviations above the mean.
The probability of X being greater than 10.52 corresponds to the area under the standard normal distribution curve to the right of the z-score 2.76. Using standard normal distribution tables or software, we can find this probability to be very small, typically less than 0.003.
Two quantities are related as shown in the table below:
x. y
2. 3
4. 4
6. 5
8. 6
Which equation best represents the relationship?
Answers
y-y
——
x-x
The y with the greatest value goes first and then the lowest. Same thing with x.
Choose two coordinates from the table
Ex: (4,4) & (2,3)
4-3=1
——-
4-2=2
The slop is 1/2 or 0.5
There is a y intercept which is 2. You get 2 when you divide 1 by 2
So the equation would be
y=1/2x+2 or y=0.5x+2
Hope this helped
A church has 10 bells in its bell tower. before each church service 3 bells are rung in sequence. no bell is rung more than once. how many sequences are there?
Answers
Answer:
720
Step-by-step explanation:
Given : A church has 10 bells in its bell tower.
Before each church service 3 bells are rung in sequence.
To Find: How many sequences are there?
Solution:
Since we are given that 3 bells are rung in sequence. no bell is rung more than once.
So, we will use permutation.
Formula :[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]
Since A church has 10 bells in its bell tower.
So, n =10
We are also given that Before each church service 3 bells are rung in sequence . So, r =3
So, the number of possible sequence = [tex]^{10}P_3[/tex]
= [tex]\frac{10!}{(10-3)!}[/tex]
= [tex]\frac{10!}{(7)!}[/tex]
= [tex]\frac{10 \times 9 \times 8 \times 7!}{(7)!}[/tex]
= [tex]10 \times 9 \times 8[/tex]
= [tex]720[/tex]
Hence there are 720 sequences.
There are 120 different sequences in which the 3 bells can be rung in sequence before each church service without any bell being rung more than once.
To find the number of sequences in which the 3 bells can be rung in sequence out of 10 bells without any bell being rung more than once, you can use the concept of combinations.
The number of ways to choose 3 distinct bells out of 10 is given by the binomial coefficient "10 choose 3," which is denoted as C(10, 3) and calculated as follows:
C(10, 3) = 10! / (3!(10 - 3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
So, there are 120 different sequences in which the 3 bells can be rung in sequence before each church service without any bell being rung more than once.
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Q9 Q4.) Write the augmented matrix for the system of equations to the right.
Answers
the first equation is x-y +8z = 7
so the first row in the matrix would be 1 ( there is 1x) -1 ( there is 1 negative y) 8 ( there are 8 z's) and then the answer is 7
then follow this step for the other 2 equations
see attached picture for answer:
A triangular traffic island has a base half as long as its height. The island has an area of 25 m2 . Find the base and the height.
Answers
What are the correct coefficients (reading from left to right) when the chemical equation is balanced?__pbr3(l)+__h2o(l)→__h3po3(aq)+__hbr(aq)what are the correct coefficients (reading from left to right) when the chemical equation is balanced?________1, 3, 1, 31, 3, 3, 13, 5, 1, 81, 2, 1, 2?
Answers
1,3,1,3
The correct coefficients (reading from left to right) are chemical equation is balanced as 1PBr₃(l) + 3H₂O(l) → H₃PO₃(aq) + 3HBr(aq). which is the correct answer would be an option (A).
What is the rule of conservation of mass?Mass, according to the rule of conservation of mass, cannot be generated or destroyed. As a result, the mass of products must match the mass of reactants. Each element's atom count must be identical on the reactant and product sides. As a result, chemical equations are balanced.
According to the given question,
We have to substitute the coefficients (reading from left to right) are 1,3,1,3 in the given chemical equation
Thus, the correct coefficients (reading from left to right) are balanced chemical equation as :
⇒ 1PBr₃(l) + 3H₂O(l) → H₃PO₃(aq) + 3HBr(aq).
Hence, the correct answer would be option (A).
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Q7 Q26.) Find the quotient of the complex numbers and leave your answer in polar form.
Answers
(Where [tex]\text{cis}(\theta) = \cos(\theta) + i\sin(\theta)[/tex])
Then [tex]\dfrac{c_1}{c_2} = \dfrac{r_1}{r_2}\text{cis}(\theta_1-\theta_2)[/tex]
So then for your problem, that would be
[tex]\dfrac{z_1}{z_2} = \dfrac37\text{cis}\left(\dfrac\pi8-\dfrac\pi9\right)=\boxed{\dfrac37\text{cis}\left(\dfrac\pi{72}\right)}[/tex]
So that would be [tex]\boxed{\dfrac37\left(\cos\left(\dfrac\pi{72}\right)+i\sin\left(\dfrac\pi{72}\right)\right)}[/tex]
Hope this helps.
A bank account earns interest at a rate of 3.5% per year ( in other words it increases in value by that percent) and starts with a balance of $350. Which of the following equations would give the account’s worth, W, as a function of the number of years, y, it has been gaining interest?
Answers
The account's worth, W, as a function of the number of years, y it has been gaining interest is given by the equation W = $350 + ($350 imes 0.035 imes y).
Explanation:The equation that gives the account's worth, W, as a function of the number of years, y, it has been gaining interest is:
W = $350 + ($350 imes 0.035 imes y)
Here's an example:
If the account has been gaining interest for 2 years, then W = $350 + ($350 imes 0.035 imes 2) = $364.70.
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Explain why a square is always a rectangle but a rectangle is not always a square.
Answers
therefore, because a square has 4 straight sides with 4 right angles, it is a rectangle.
and a rectangle can have unequal adjacent sides, so it is not always a square
Where does the graph of y=sin x from x=0 to x=2pie start.
A- at its minimum
B- at an x intercept
C- at its maximum
D- between an x intercept and its maximum
Answers
A- at its minimum
B- at an x intercept
C- at its maximum
D- between an x intercept and its maximum
The correct answer is;
A- at its minimum
When a function is graphed. it usually start at its minimum. Considering the plot for the sine function, the Sine Function has this beautiful up-down curve (which repeats every 2π radians, or 360°).
It starts at 0, heads up to 1 by π/2 radians (90°) and then heads down to -1.
Tim answered all the questions on his math test but got 101010 answers wrong. He received 444 points for every correct answer, and there was no penalty for wrong answers. His score was 767676 points.
Write an equation to determine the total number of questions (q)(q)left parenthesis, q, right parenthesis on Tim's math test.
Find the total number of questions on his math test.
questions
Answers
4(q -10) = 76 . . . . . Tim got 4 points for every right answer, for a score of 76. He answered correctly 10 fewer questions than were on the test.
b)
q = 10 +76/4
q = 29
The total number of questions on Tim's math test was 29.
Answers:
Equation: [tex]q=\frac{76}{4} +10[/tex]
Questions: [tex]29[/tex]
Also, the verified Tutor above is in fact correct, but this answer is way more simple and easier to understand, thank you for your time :D
Explanation:
First, we need to find out the questions, even though the first question is, "What is the equation?". So, to the find the answer to how many questions there are in total we need to grab the total points "[tex]76[/tex]" and divide that by "[tex]4[/tex]" because that'll tell us how many questions that he answered correct. Especially since the "[tex]10[/tex]" questions he got wrong didn't affect his points.
So [tex]\frac{76}{4} =19[/tex]. Now we must add 10 to 19. [tex]10+19=29[/tex]. And so [tex]29[/tex] is the total amount of questions. Now we must write down how we found out. We found out by dividing [tex]76[/tex] and [tex]4[/tex], then we added [tex]10[/tex]!
Conclusion:
As simple as that, we found out how many questions there were in total and how we found out! Thank you for sticking with me♥!
Turtle and vicent combine their coins to find they have all dimes and quarters .They have 8 more quarters them dimes and the coins are worth a total of 5.15 .How many dimes and quarters do they have?
Answers
There are 9 dimes and 17 quarters.
Isabel created the tree diagram to represent the different ways she could order a salad at her favorite restaurant.
According to the diagram, how many combinations of lettuce type, dressing, and topping are possible?
Answers
Answer: Option B
(B) 12
Step-by-step explanation:
What is the domain of this function?
{x| x > }
Answers
So the domain would be {x | x ≥ 0}
Hope this helps.
{x | x ≥ 0}
_____
The solid dot at (0, 9) indicates x=0 is part of the domain. The arrow at the right end of the line indicates the domain extends to +∞.
x·\sqrt[4]{x}
Rewrite simplest radical form
Answers
1. You have the following expression given in the problem above:
x√(4x)
2. You must simplify it as below:
(x)(4x)^1/2
3. By the exponents properties, you have:
4x^3/2
√(4x^3)
4. Finally, you obtain:
2√(x^3)
5. Therefore, as you can see, the answer is: 2√(x^3)
Answer:
b
Step-by-step explanation:
asdf
Kayla bought 9/4 pounds of apples. What is that weight as a mixed number?
Answers
Help!!!!!!!!!!!!!!!!
Answers
∠y + 56 + 51 = 180
To find y, simplify, isolate and simplify again to get y. Remember, what you do to one side, you do to the other.
∠y + 107 = 180
∠y + 107 (-107) = 180 (-107)
∠y = 180 - 107
∠y = 73°
A triangle is = 180°. With this knowledge, you can find ∠x (the last angle).
Plug in 73° for y
y = 73
73 + 72 + x = 180
Simplify.
x + 145 = 180
isolate the x, subtract 145 from both sides
x + 145 (-145) = 180 (-145)
x = 180 - 145
x = 35°
A) 35° is your answer
hope this helps
A particular hybrid car travels approximately 204 mi on 4 gal of gas. Find the amount of gas required for a 714-mi trip.
Answers
The car needs 14 gallons of gas for the 714 mile trip.
To determine the amount of gas required for a 714-mile trip, we can set up a proportion based on the given information:
We know that the car travels 204 miles on 4 gallons of gas. We need to find the amount of gas needed for 714 miles. Let the gas required for 714 miles be X gallons
First, let us set up the proportion:
204 mi / 4 gal = 714 mi / X galNext, we solve for x (the amount of gas required for 714 miles):
204 mi × X gal = 714 mi × 4 gal204X = 2856X = 2856 / 204X = 14Therefore, the car requires 14 gallons of gas for a 714-mile trip.
There is 3\8 of a pizza in one box and 1/8 of a pizza in another box. How much altogether
Answers
3/8 + 1/8 = 4/8
4/8 = 1/2
There is 1/2 of a pizza left
Hope this helps!
Hope this helps!