The value of cos of angle x of the dilated triangle would be exactly the same as in the first triangle cos (8/17).
How does dilation work?Dilation of a figure will leave its sides get scaled (multiplied) by same number. That number is called the scale factor of that dilation.
Its also called scaling of a figure, but due the involvement of coordinates, it involves a center of a dilation, which is like a pinned point which stays at same place after dilation.
Its like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1)
The cosine ratio is a ratio of the two sides.
We have been given If the cos of angle x is 8/17 and the triangle was displayed to be two times big as the original.
In the first triangle, the ratio is 8/17.
In the second triangle, the ratio is 16/34.
The second triangle could be reduced back to 8/17 which produces the same cosine value.
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Choose an equation for the relationship between the measures of the segments, angles, and arcs.
The correct equation for the relationship between the measures of the segments, angles, and arcs is [tex]PR^2[/tex] = PS * PT. The last option is the right choice.
Power of a Tangent: We know that the power of a point from an external point P to a circle is equal to the product of the lengths of the two tangents drawn from P to the circle (PQ * PR = PS * PT).
Identify the Tangents and Secant: In the given diagram, PR is the secant intersecting the circle at points T and S, and PQ and PS are the tangents drawn from P to points Q and S, respectively.
Apply the Power of a Tangent Theorem: Since PS and PT are tangents from P, we can apply the power of a tangent theorem to get:
PS * PT = PQ * PR.
Substitute PQ with PR: Since PQ and PR are both tangents drawn from the same point P, they have the same length (PQ = PR). Substituting PQ with PR in the equation, we get:
PS * PT = PR * PR.
Simplify the Equation: Simplifying the equation PR * PR = PS * PT, we get the final equation:
[tex]PR^2[/tex] = PS * PT.
Therefore, the equation [tex]PR^2[/tex] = PS * PT correctly represents the relationship between the measures of the segments, angles, and arcs in the given diagram.
The last option is the right choice.
What is the radian measure of the central angle of an arc that has an arc length of 3 units and a radius of 4 units?
Find the arc length intercepted by a central angle of pi/2 radians in a circle whose radius is 24 inches.
Find the measure of a central angle that intercepts an arc of 27 inches in a circle whose radius is 10 inches.
Answer:
Step-by-step explanation:
What is the measure of the central angle?
Answer : 140°
What ratio represents the measure of the central angle compared to the measure of the entire circle?
Answer7/18
If s = , what is the length of minor arc AB?
Answer : 14π
The equation below describes a parabola. If a is negative, which way does the parabola open?
y=ax^2
a. down
b. left
c. up
d. right
When [tex]\( a \)[/tex] is negative in the equation [tex]\( y = ax^2 \)[/tex], the parabola opens downwards. So, the answer is (a).
To determine the direction in which the parabola described by the equation [tex]\( y = ax^2 \)[/tex] opens, we need to understand the properties of the quadratic function. Let's analyze this step by step:
1. Identify the general form of the equation:
The given equation is [tex]\( y = ax^2 \)[/tex].
2. Determine the effect of the coefficient [tex]\( a \)[/tex] on the parabola:
- If [tex]\( a \)[/tex] is positive, the parabola opens upwards.
- If [tex]\( a \)[/tex] is negative, the parabola opens downwards.
3. Evaluate the given condition:
The problem states that [tex]\( a \)[/tex] is negative.
4. Apply the condition to the quadratic equation:
Since [tex]\( a \)[/tex] is negative, the coefficient of [tex]\( x^2 \)[/tex] in the equation [tex]\( y = ax^2 \)[/tex] is negative.
5. Conclusion:
When [tex]\( a \)[/tex] is negative, the parabola opens downwards.
Therefore, the correct answer is:
a. down
Will give brainliest.
What is the constant of proportionality for the graph? (Graph attached)
A- 0.5
B- 1
C- 2
D- 6
The strength of the force of gravity depends ona.the masses of the objects and their speeds.
b.the masses of the objects and the distance between them.
c.the weight of the objects and their speeds.
d.the masses of the objects and their weights.
Which decimal shows eighteen and eight hundredths?
Select the correct answer.
Question 3 options:
18.08
.1808
18.80
The correct decimal that represents eighteen and eight hundredths is 18.08, with the '8' in the hundredths place following the whole number 18.
The decimal that shows eighteen and eight hundredths is 18.08. This is because the number 18 represents the whole part, and the decimal part .08 represents the hundredths place. To express this, we place a decimal point after the whole number 18, followed by two digits: the first digit after the decimal point for tenths (which is 0 in this case), and the second digit for hundredths, which is 8. Thus, the correct decimal representation would be 18.08, as opposed to 18.80 which shows eighty hundredths, or .1808 which implies a number less than one with eight hundredths and eight ten-thousandths.
cole grew 2 3/4 inches last year kelly grew the same amount which fraction below represent the number of inches that kelly grew last year
What number is 35% of 22?
In how many different orders can you line up 8 cards on a table? I'll FAN AND MEDAL!!!
In the figure, TR−→− and TV−→− are secants to circle A. mRV=99∘ mSU=45∘ What is the measure of ∠RTV ? Enter your answer in the box.
The difference between 3.6 and a number is 2.95, as shown below. What number should go in the box to complete the subtraction problem?
Numerical Answers Expected!
Each week, Joey gets paid $10 plus $2 for each chore he does. His sister Julie gets paid $5 plus $3 per chore.
A. Write an expression for how much their parents pay Joey and Julie each week if they do the same amount of chores.
B. If Joey and Julie each do 5 chores, how much do they get paid individually? How much do their parents pay altogether?
If you rewrite the problem 14(22) as 14(20+2) so that you can use mental math, which of the following properties will you use?
*nevermind I got it*
Does anybody have the answer, please?
Jason knows that the equation to calculate the period of a simple pendulum is , where T is the period, L is the length of the rod, and g is the acceleration due to gravity. He also knows that the frequency (f) of the pendulum is the reciprocal of its period. How can he express L in terms of g and f?
Answer-
[tex]\boxed{\boxed{L=\dfrac{g}{4\pi^2 f^2}}}[/tex]
Solution-
The equation for time period of a simple pendulum is given by,
[tex]T=2\pi \sqrt{\dfrac{L}{g}}[/tex]
Where,
T = Time period,
L = Length of the rod,
g = Acceleration due to gravity.
Frequency (f) of the pendulum is the reciprocal of its period, i.e
[tex]f=\dfrac{1}{T}\ \Rightarrow T=\dfrac{1}{f}[/tex]
Putting the values,
[tex]\Rightarrow \dfrac{1}{f}=2\pi \sqrt{\dfrac{L}{g}}[/tex]
[tex]\Rightarrow (\dfrac{1}{f})^2=(2\pi \sqrt{\dfrac{L}{g}})^2[/tex]
[tex]\Rightarrow \dfrac{1}{f^2}=4\pi^2 \dfrac{L}{g}[/tex]
[tex]\Rightarrow L=\dfrac{g}{4\pi^2 f^2}[/tex]
PLEASE PLEEAASE HELP!! You have a 5-question multiple-choice test. Each question has four choices. You don’t know any of the answers. What is the experimental probability that you will guess exactly three out of five questions correctly? Type your answer below using complete sentences,
In the slope intercept equation for a line the coefficient of the _______-term gives the slope
The coefficient of the x-term in the slope-intercept equation of a line represents the slope. The slope indicates how the y-value changes with each one-unit increase of the x-value. The constant term 'b' is the y-intercept, the point where the line crosses the y-axis.
In the slope-intercept equation of a line, typically written as y = mx + b, the coefficient of the x-term gives the slope of the line. The slope, represented by the letter 'm', defines the steepness of the line, or how much the y-value changes for every one-unit increase in x. The y-intercept is given by the constant term 'b', which indicates the point where the line crosses the y-axis, occurring when x equals zero.
Slope is especially important in fields like economics as it measures the relationship between two variables. A positive slope means that as x increases, y also increases, and vice versa for a negative slope. Therefore, knowing the slope allows us to predict how one variable will change in response to the other.
What would the total bill be of painting the costs $44.80 with the tax rate of 6%?
1. Based on the information given, can you determine that the quadrilateral must be a
parallelogram? Explain.
Given: (BE) ̅ (ED) ̅ and (AE) ̅ (EC) ̅
2. The parallelogram has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain.
Solving Q1: Given BE = ED and AE = EC.
Considering triangles ΔAED and ΔCEB;
1. AE = EC (given)
2. ∠AED = ∠CEB (vertical angles)
3. ED = EB (given)
ΔAED ≡ ΔCEB (Side-Angle-Side congruency of triangles)
∠DAE = ∠BCE and AD = BC (using CPCTC)
⇒ AD║BC (Converse of Alternate Interior angles theorem)
Similarly consider triangles ΔABE and ΔCDE;
1. AE = CE (given)
2. ∠BEA = ∠DEC (vertical angles)
3. BE = DE (given)
ΔABE ≡ ΔCDE (Side-Angle-Side congruency of triangles)
∠ABE = ∠CDE and AB = CD (using CPCTC)
⇒ AB║CD (Converse of Alternate Interior angles theorem)
Since we have AB║CD, AB = CD and AD║BC, AD = BC.
Therefore, quadrilateral ABCD is a parallelogram.
****************************************************************************************************
Solving Q2: The parallelogram has the angle measures shown in the diagram.
It is clearly visible that both the triangles are Isosceles triangles, so opposite sides in each triangle are equal.
Consider two triangles given in the problem, we have two sets of congruent angles and one included side is common in both triangles.
Using Angle-Side-Angle congruence of triangles, both the triangles would be congruent too.
Using CPCTC, we can say opposite sides of quadrilateral would be congruent.
Therefore, all sides in given quadrilateral are equal.
Hence, Given quadrilateral is a Rhombus.
MAJOR HELP NEEDED!
Lea knows the following information about the 50 days where she tracked whether she wore a tie and whether she received a compliment on her outfit:
-There were 11 days where she neither wore a tie nor received a compliment.
-There were 30 days in total where she received a compliment.
-There were 16 days in total where she did not wear a tie.
Can you help Lea organize the results into a two-way frequency table?
We know that a two-way frequency table is constructed when we have to deal with two variables ( which is also known as a bivariate data)
Here we have two variables as wore a tie or not and the second variable is: Received compliment or not.
Hence, on the basis of the information provided to us in the question we see that the two-way frequency table is obtained as follows:
Wore tie Do not wore tie Total
Receive compliment 25 5 30
Do not receive compliment 9 11 20
Total 34 16 50
The considered data given about the frequencies of events can be used to fill the two-way frequency table. The values will be 25 and 5 in first row, and 9 and 11 in second row.
How to form two-way frequency table?Suppose two dimensions are there, viz X and Y. Some values of X are there as [tex]X_1, X_2, ... , X_n[/tex] and some values of Y are there as [tex]Y_1, Y_2, ... , Y_n[/tex]
List them in title of the rows and left to the columns. There will be [tex]n \times k[/tex] table of values will be formed(excluding titles and totals), such that:
Value(ith row, jth column) = Frequency for intersection of [tex]X_i[/tex] and [tex]Y_j[/tex] (assuming X values are going in rows, and Y values are listed in columns).
Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.
For n = 2, and k = 2, the table would look like:
[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]
where S denotes total of totals, also called total frequency.
n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.
We're given that:
There were 11 days where she neither wore a tie nor received a compliment.There were 30 days in total where she received a compliment.There were 16 days in total where she did not wear a tie.If we take:
A = event of Lea wearing a tie on a day
A' = event of Lea not wearing a tie on a day
B = event of Lea getting a compliment on a day
B' = event of Lea not getting a compliment on a day
then, we're given that:
[tex]n(A' \cap B') = 11\\n(B) = 30\\n(A') = 16[/tex]
Also, total number of days = S = 50
On each of those 50 days, she either wore a tie or not.
If she didn't put on a tie on 16 out of 50 days, then she wore tie for 50-16=34 days.
Thus, we get n(A) = 34
Similarly, we get n(B') = 50 - n(B) = 50 - 30 = 20
[tex]\begin{array}{cccc}&A&A'&\rm Total\\B&n(B\cap A)&n(B\cap A')&n(B)=30\\B'&n(B' \cap A)&n(B' \cap A')=11&n(B')=20\\\rm Total & n(A)=34 & n(A')=16 & S=50 \end{array}[/tex]
Using the total of the third row, we get:
[tex]n(B' \cap A) + 11 = 20\\n(B' \cap A) = 9[/tex]
Similarly, now using second column's total, we get:
[tex]n(B \cap A) + n(B' \cap A) = 34\\n(B \cap A) + 9 = 34\\n(B \cap A) = 25[/tex]
Now using second row's total, we get:
[tex]25 + n(B \cap A') = 30\\n(B\cap A') = 5[/tex]
Thus, we get:
[tex]\begin{array}{cccc}&A&A'&\rm Total\\B&n(B\cap A)=25&n(B\cap A')=5&n(B)=30\\B'&n(B' \cap A)=9&n(B' \cap A')=11&n(B')=20\\\rm Total & n(A)=34 & n(A')=16 & S=50 \end{array}[/tex]
Thus, finally, we can say that:
Wore a tie, Didn't wore a tie
Got a compliment 25 5
Didn't got a compliment 9 11
Thus, the values will be 25 and 5 in first row, and 9 and 11 in second row.
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The graph shown below is a scatter plot:
Which point on the scatter plot is an outlier?
Point S
Point T
Point U
Point V
Answer:
the answer is point S
~batmans wife dun dun dun...aka ~serenitybella
help no one is on biology
Fossils of a species of bear are found in layer 5. Which layer is most likely to have organisms that lived at the same time as the bear species?
A. Layer 4
B. Layer 2
C. Layer 1
D. Layer 8,
A = Layer 4..................................................
Kenny has $1,400 in the bank. He earns $150 every week at his afterschool job. What is the rate of change for the scenario described?
2
150
300
1,400
@tylermcmullen23,
Answer:
150
Step-by-step explanation:
a horse trots in a circle at the end of a 4m rope. About how far does the horse trotted after completing ten circles?
1. Astronomers measure large distances in light-years. One light year is the distance that light can travel in one year, or approximately 5.88 x 10^12 miles. Suppose a star is 9.8 x 10^1 light years from Earth. In scientific notation, approximately how many miles is it?
A. 5.88 x 10^13 miles
B. 5.76 x 10^14 miles
C. 5.88 x 10^12 miles
D. 9.8 x 10^12 miles
2. A 1,600.00 principal earns 7% annual interest, compounded semiannually (twice per year). After 33 years, what is the balance in the account?
A. $4,979.11
B. $14,920.54
C. $112,992.00
D. $15,494.70
Final Answer:
The answers are:
1. B. 5.76 x 10¹⁴ miles
2. D. $15,494.70
Explanation:
Let's solve each of these questions step by step.
Question 1:
First, we'll calculate the distance to the star in miles, given its distance in light years.
One light year is approximately 5.88 x 10¹² miles.
The star is 9.8 x 10¹ light years from Earth.
To find the distance in miles, we multiply the distance in light years by the length of one light year in miles:
Distance in miles = (5.88 x 10¹² miles/light year) * (9.8 x 10¹ light years)
To multiply these numbers in scientific notation, we multiply the coefficients (5.88 and 9.8) and then add the exponents of 10 (12 and 1).
Coefficient multiplication: 5.88 * 9.8
Using a calculator or doing the multiplication by hand, we find that 5.88 * 9.8 is approximately 57.624.
Exponent addition: 12 + 1 = 13
So the distance in miles is approximately 57.624 x 10¹³ miles.
However, in scientific notation, the coefficient should be between 1 and 10. Therefore, we need to adjust the coefficient from 57.624 to 5.7624 and increase the exponent by 1 to keep the same value.
Distance in miles = 5.7624 x 10¹⁴ miles
To make it approximately and match the answer choices, we can round the coefficient to 5.76.
Distance in miles ≈ 5.76 x 10¹⁴ miles
The closest answer to our computed value is:
B. 5.76 x 10¹⁴ miles
Question 2:
Next, let's use the compound interest formula to find the balance in the account after 33 years.
The compound interest formula is:
[tex]A = P (1 + r/n)^{(nt)[/tex]
where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
We're given:
P = $1,600.00
r = 7% annual interest = 0.07 (as a decimal)
n = 2 (since interest is compounded semiannually)
t = 33 years
Plugging these values into the formula gives us:
[tex]A = 1600.00 * (1 + 0.07/2)^{(2*33)[/tex]
Let's break it down:
Interest rate per compounding period: 0.07/2 = 0.035
Number of compounding periods: 2*33 = 66
Now substitute these values:
A = 1600 * (1 + 0.035)⁶⁶
We calculate (1 + 0.035)^66 using a calculator:
(1 + 0.035)⁶⁶ ≈ (1.035)⁶⁶ ≈ 9.682
So the final balance is:
A ≈ 1600 * 9.682 ≈ 15491.2
The closest answer to our computed value is:
D. $15,494.70
Hence, the answers are:
1. B. 5.76 x 10¹⁴ miles
2. D. $15,494.70
The sum of three consecutive even integers is 222. find the three integers.
Solve 4e^2x-3=12 please help
[tex] 4*e^{2x} -3 = 12 [/tex]
Step 1:
Here we have -3 in subtraction on the left side, so when we take it to the right we apply opposite operation of subtraction that is addition.
[tex] 4*e^{2x} = 12+3 [/tex]
[tex] 4*e^{2x} = 15 [/tex]
Step 2:
Next we have 4 in multiplication on left side, so dividing right side by 4,
[tex] e^{2x} = 15/4 [/tex]
[tex] e^{2x} = 3.75 [/tex]
Step 3:
taking log on both sides
[tex] ln ( e^{2x}) = ln(3.75) [/tex]
[tex] {2x} =ln 3.75 [/tex]
Step 4:
Dividing right side by 2,
x= ln (3.75) /2 = 0.66088
Answer : x = 0.66088..
2.5 = n
3.5 2
What is the variable?
Which of the following is equal to thirty-four and four hundred fifty-eight thousandths? A. 3,445.008 B. 34.0458 C. 34.58 D. 34.458
All the events for the volunteer committee need to be finished;____, parents' day needs to be completed.
Choose the transitional word or phrase that best fits the blank.
A. In essence
B. Similarly
C. Finally
D. In particular