Answers
Answer:
The perimeter is 28.13 cm
Step-by-step explanation:
We connect a line from A to C
we can use the cosine rule to find the length AC
let us call it x
AC^2 = AB^2 + BC^2 - 2(AB)(BC) cos B
we have this as;
x^2 = 6^2 + 8^2 - 2(6)(8) cos 95
x^2 = 36 + 64 + 8.37
x^2 = 108.37
x = √108.37
x = 10.4 cm
AC = 10.4 cm
now, let us look at triangle ADC Where we have AC as the hypotenuse as it is the side facing the right angle
We can use Pythagoras’ theorem to get the value of CD
We have it that the square of the hypotenuse AC is the sum of the squares of the two other sides
let DC be y
10.4^2 = 5^2 + y^2
y^2 = 108.37 - 25
y^2 = 83.37
y = √83.37
y = 9.13 cm
The perimeter of the shape is the sum of all its sides
so we have;
AB + BC + CD + AD
= 6 + 8 + 9.13 + 5
= 28.13 cm
Related Questions
solve the inequality and please show work !!
Answers
The solution to the inequality 2√(x-3) < √(x+3) is x ∈ (3, 7].
What is an inequality?
In mathematics, an inequality is a statement that compares two values or expressions and states that one is greater than, less than, or not equal to the other. An inequality is typically written using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to). Inequalities are used to represent a wide range of mathematical concepts, such as the relationships between two quantities, the constraints on a system, or the conditions for a particular outcome to occur. Solving inequalities involves finding the set of values that satisfy the inequality, which may be a single value, a range of values, or no values at all.
What are the key steps to solve this inequality?
To solve the inequality, we need to isolate the variable x on one side of the inequality and then square both sides to eliminate the square roots. However, we need to be careful when squaring both sides because this may introduce extraneous solutions. To avoid this, we need to check our solutions at the end to make sure they satisfy the original inequality.
Isolate the square root term on one side of the inequality
2√(x-3) < √(x+3)
Square both sides:
4(x-3) < x+3
Simplify and rearrange the inequality to get x on one side
4x - 15 < 0
x < 15/4
Check the solution by plugging it into the original inequality
2√(15/4 - 3) < √(15/4 + 3)
2√(3/4) < √27/4
2(√3/2) < 3/2
√3 < 3/2 (This is true)
Therefore, the solution to the inequality is x ∈ (3, 7].
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There are two bags of carrots on sale. The prices are shown below: Bag A: $1100 containing 10 carrots Bag B: $3500 containing 35 carrots Which one is the better buy?
Answers
Answer: Bag B
Step-by-step explanation:
1100 DIVIDED BY 10= 110 PER ONE
3500 DIVIDED BY 35= 100 PER ONE
OBVIOUSLY, BAG B IS THE BETTER BUY BECAUSE IT IS $10 LESS THAT BAG A
I need to know the steps to solve it
Answers
The value of x that makes both triangles congruent is x = -1 and x = 5
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Two triangles are congruent if their corresponding sides are equal to each other and their angles are also equal.
Since triangle ABC is congruent to DEF, hence:
BC = EF
Substituting:
4x - 2 = x² - 7
x² - 4x - 5 = 0
x² - 5x + x - 5 = 0
x(x - 5) + 1(x - 5) = 0
(x + 1)(x - 5) = 0
x = -1 and x = 5
The value of x is x = -1 and x = 5
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Right triangle ABC is shown.
A
3 m
с
50°
a
5
B
7 8
9
10
Which equation can be used to solve for c?
O sin(50%) = 3
C
O sin(50%) =
O cos(50%) = -
35
O cos(50%) ==
Save and Exit
~/w
Next
TIME REMAINI
53:24
Submit
Answers
Using relations in a right triangle, the equation that can be used to solve for c is:
sin(50º) = 3/c.
What does the right triangle shows?The question is incomplete, hence, researching it on a search engine, we get that:
The hypotenuse is of c.The side opposite to the angle of 50º has a length of 3.What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.We have the side opposite to the angle, hence we use the sine, and the equation to solve for c is:
sin(50º) = 3/c.
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vic's favorite cookie recipe uses 250 250250 grams of flour for every 170 170170 grams of butter. imani made cookies using 750 750750 grams of flour for every 630 630630 grams of butter. what will vic think of the amount of butter in imani's cookies? choose 1 answer:
Answers
Vic would think that the amount of butter in Imani's cookies is appropriate since the ratio of flour to butter used in Imani's recipe is the same as the ratio used in Vic's favorite cookie recipe, which is 250:170 grams of flour to butter.
Specifically, in Vic's recipe, there are approximately 1.47 grams of flour for every gram of butter (250/170), while in Imani's cookies, there are approximately ratio 1.19 grams of flour for every gram of butter (750/630). This means that there is relatively more butter in Imani's cookies compared to Vic's recipe. Based on this difference, Vic might expect Imani's cookies to have a richer, denser texture and a stronger buttery flavor than his favorite recipe.
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Where is the graph of f(x)=4[x-3]+2 discontinuos
Answers
Answer:
Below
Step-by-step explanation:
4 [x-3] + 2 = y is not discontinuous anywhere
However 4 / [x-3] + 2 DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!
y = 3x^2 – 6, minimum or maximum?
Answers
Answer:
Minimum
Step-by-step explanation:
Since the leading coefficient is positive, this means that the parabola will open upward in a U-shape, showing that its vertex will be a minimum.
That answers is maximum because it states the power of so it multiplies
Each histogram represents a set of data with a median of 29.5. Which set of data most likely has a mean that is closest to 29.5?
A graph shows the horizontal axis numbered 9 to 48. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 33 then a downward trend from 33 to 45.
A graph shows the horizontal axis numbered 15 to 48. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 30 then a downward trend from 30 to 45.
A graph shows the horizontal axis numbered 12 to 56. The vertical axis is numbered 2 to 8. The graph shows an upward trend from 1 to 32 then a downward trend from 32 to 56.
A graph shows the horizontal axis numbered 15 to 54. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 24, a downward trend from 24 to 27, an upward trend from 27 to 30, a downward trend from 30 to 39, an upward trend from 39 to 45, a downward trend from 45 to 48, then an upward trend from 48 to 51.
Answers
To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.
Looking at the histograms described:
The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.
The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.
The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.
The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.
Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.
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This exercise shows that if we bring the dual problem into stan- dord form and then apply the primal simplex method, the resulting algorithm is not identical to the dual simplex method. Consider the following standard form problem and its dual. minimize 21 +22 maximize Pi + P2 subject to x1 = 1 subject to P1 <1 22=1 P2 <1. 21,22 > 0 Here, there is only one possible basis and the dual simplex method must terminate immediately. Show that if the dual problem is converted into standard form and the primal simplex method is applied to it, one or more changes of basis may be required.
Answers
The exercise highlights that converting the dual problem into standard form and applying the primal simplex method does not yield the same algorithm as the dual simplex method. By considering a specific standard form problem and its dual, it is shown that the primal simplex method applied to the dual problem may require one or more changes of basis, unlike the dual simplex method where termination occurs immediately due to the specific structure of the problem.
In the given exercise, we have a standard form problem and its dual:
Primal Problem:
minimize 21x1 + 22x2
subject to x1 = 1
x1, x2 ≥ 0
Dual Problem:
maximize P1 + P2
subject to P1 < 1
P2 < 1
P1, P2 ≥ 0
Since there is only one possible basis in this case, the dual simplex method terminates immediately because of the specific structure of the problem.
However, if we convert the dual problem into standard form and apply the primal simplex method to it, one or more changes of basis may be required. This is because the primal simplex method operates differently from the dual simplex method and may encounter different pivot elements and entering/leaving variables during the iterations. These differences in the algorithm can lead to changes in the basis during the primal simplex method's execution.
Therefore, it is evident that converting the dual problem into standard form and applying the primal simplex method does not result in the same algorithm as the dual simplex method. The primal simplex method may require one or more changes of basis during its execution, unlike the dual simplex method, which terminates immediately in this specific problem due to the singular structure of the basis.
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if two samples a and b had the same mean and sample size, but sample b had a larger standard deviation, which sample would have the wider 95% confidence interval? g
Answers
If two samples have the same mean but different standard deviations, the sample with the larger standard deviation will have a wider 95% confidence interval.
This is because the standard deviation is a measure of the variability of the data, and a larger standard deviation indicates that the data points are more spread out from the mean.
The confidence interval is a range of values that we can be reasonably confident contains the true population mean. The width of the confidence interval depends on the standard error of the mean, which is calculated as the standard deviation of the sample divided by the square root of the sample size.
Since the larger standard deviation in sample b implies a larger standard error of the mean, the confidence interval for sample b will be wider than that of sample a, even though both samples have the same mean and sample size. We will be less precise in estimating the true population mean with sample b than with sample a.
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How many people are ten percent of the world's population?.
Answers
The Sun appears about 8.4 times as large as Deimos in the Martian sky. It takes Deimos approximately 550 of its diameters to transit the shadow of Mars during a lunar eclipse. Using these values, a radius for Mars of 3,000,000 m, a ratio of Sun-from-Mars distance to Deimos-from-Mars distance of 365,000, calculate the radius of Deimos to one significant digit in meters
Answers
The radius of Deimos to one significant digit in meters is approximately 9.4 m
.
Given the ratio of the Sun-from-Mars distance to Deimos-from-Mars distance is 365,000, the distance between Mars and Deimos can be found to bedeimos distance = Sun-Mars distance / 365,000
Next, we can find the diameter of Deimos by noting that 550 of its diameters is equal to the distance it takes to transit the shadow of Mars during a lunar eclipse.
Let's call the diameter of Deimos "d", so we can
diameter = 1/550 * deimos distance
Finally, the Sun appears about 8.4 times as large as Deimos in the Martian sky. If we call the radius of Deimos "r", then the radius of the Sun is 8.4r.
Using the information given, we can set up the following equation:
deimos distance / (3,000,000 + r) = 8.4r / (3,000,000)Simplifying and solving for r,
we get:r = 9.39 m (rounded to one significant digit)
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.Quadrilateral QRST is reflected across the y-axis and rotated 360° clockwise about the origin to create the quadrilateral Q'R'S'T', what arethe vertex coordinates of quadrilateral Q'R'S'T',y8642-8 ---6-6-4-20이 R₂46S-2Q-6-8
Answers
Coordinates of QRST:
\(\begin{gathered} Q(-1,-4) \\ R(2,-1) \\ S(5,-2) \\ T(4,-6) \end{gathered}\)Rule for a reflection accros the y-axis:
\((x,y)\rightarrow(-x,y)\)Find the coordiantes of the figure after the reflection across y-axis:
\(\begin{gathered} Q(-1,-4)\rightarrow(1,-4) \\ R(2,-1)\rightarrow(-2,-1) \\ S(5,-2)\rightarrow(-5,-2) \\ T(4,-6)\rightarrow(-4,-6) \end{gathered}\)A rotation 360º clockwise is a full rotation, the figure still in the same direction after the rotation (the coordinates of the points don't change)
Then, the coordiantes of Q'R'S'T are:Q'(1,-4)R'(-2,-1)S'(-5,-2)T'(-4,-6)let x and y be continuous random variables with joint probability density function fx,y (x, y) = 2e^−x e^−2y , 0 < x < [infinity], 0 < y < [infinity], 0, otherwise. find p(x/2 < y < x).
Answers
Let X and Y be jointly continuous random variables with joint density function f(x,y)=c(y2−x2)e−2y,−y≤x≤y,0<y<∞. c = 1/4 so that f is a density function.
Throughout the complete range of potential X and Y values, the joint density function must integrate to 1.
The interval [-y, y] for 0 < y < ∞ defines the range of potential values for X and Y. The joint density function integral over this region must therefore be equal to 1.
Integrating the given density function, we have:
∫∫c(y2−x2)e−2y dxdy
= c ∫∫(y2−x2)e−2y dxdy
= c ∫y2e−2y dy − c ∫∫x2e−2y dxdy
= c [−2ye−2y − (−2/2)e−2y]|y=0 to ∞
= c [2 − (−1)]
= c(3)
Therefore, c = 1/4 so that the joint density function integrates to 1.
Complete Question:
Let X and Y be jointly continuous random variables with joint density function f(x,y)=c(y2−x2)e−2y,−y≤x≤y,0<y<∞. Find c so that f is a density function.
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The school that Mei goes to is selling tickets to a spring musical. On the first day of ticket sales the school sold 6 adult tickets and 8 child tickets for a total of $96. The school took in $33 on the second day by selling 2 adult tickets and 3 child tickets. Find the price of an adult ticket and the price of a child ticket.
Answers
Answer:
The adult ticket is 11 and the child is 9
Step-by-step explanation:
TRUE OR FALSE
The product of a fraction and its multiplicative inverse is 1
(plus explain reasoning)
Answers
Step-by-step explanation:
a/b is a general fraction.
it's multiplicative inverse is b/a.
a/b × b/a = a×b / b×a = 1
A soccer team has different colored pinnies that are worn over their practice jerseys. A team member is going to randomly select a pinnie from the bag. Which of the following statements is not true?
Answers
What is the y-intercept (initial value) for the function shown in the graph?
Answers
Answer:
5 is the y-intercept
Step-by-step explanation:
A tent is in the form of a right circular cylinder and cone. The radius of the cone and cylinder is 4 meters. The height of the cylinder and cone are 4.5 meters and 3 meters respectively. Find the outer surface area of the tent. (Assume π = 22 /7)
Answers
Answer:
176m²
Step-by-step explanation:
When we are asked to find the outer surface area of a geometric shape, it means to find the Lateral or Curved Surface Area of the shape. We are given two shapes above.
Step 1
Find the Outer surface area of the cone
Outer / Lateral surface area of a cone =
πrl
Where l = √r² + h²
r = 4 m
h = 3m
Outer surface area = 22/7 ×√4² + 3²
= 22/7 × √16 + 9
= 22/7 × √25
= 22/7 × 5
= 62.83185m²
Step 2
Find the outer surface area of a cylinder
= 2πrh
π = 22/7
r = 4m
h = 4.5
π = 22/7
Outer surface area of a cylinder = 2 × 22/7 × 4 × 4.5
= 113.09734m²
Step 3
The Outer Surface Area of the Tent = Outer Surface Area of the cone + Outer Surface Area of the cylinder
= 62.83185m² + 113.09734m²
= 175.92919m²
Approximately ≈ 176m²
Therefore, the outer surface area of the tent = 176m²
for problems 7–21, verify that the given function is a solution to the given differential equation (c1 and c2 are arbitrary constants), and state the maximum interval over which the solution is valid. 8. y(x)
Answers
The function y(x) = c₁ cos 2x + c₂ sin 2x is a valid solution to the differential equation y'' + 4y = 0. The solution is valid for all values of x, unless specific initial conditions or constraints are given that limit its interval.
To verify if the given function y(x) = c₁ cos 2x + c₂ sin 2x is a solution to the differential equation y'' + 4y = 0, we need to substitute the function into the differential equation and check if it satisfies the equation for all values of x.
First, let's find the first and second derivatives of y(x):
y'(x) = -2c₁ sin 2x + 2c₂ cos 2x
y''(x) = -4c₁ cos 2x - 4c₂ sin 2x
Now, substitute y(x), y'(x), and y''(x) into the differential equation:
y''(x) + 4y(x) = (-4c₁ cos 2x - 4c₂ sin 2x) + 4(c₁ cos 2x + c₂ sin 2x)
= -4c₁ cos 2x - 4c₂ sin 2x + 4c₁ cos 2x + 4c₂ sin 2x
= 0
As we can see, the expression simplifies to zero, which means that y(x) = c₁ cos 2x + c₂ sin 2x is indeed a solution to the differential equation y'' + 4y = 0.
The maximum interval over which this solution is valid depends on the initial conditions or any other constraints provided in the problem. In general, since the given solution contains periodic functions (cosine and sine), it can be defined for all real values of x.
The complete question is:
For Problems 7-21, verify that the given function is a solu- tion to the given differential equation c₁ and c₂ are arbitrary constants), and state the maximum interval over which the solution is valid.
8. y(x) = c₁ cos 2x + c₂ sin 2x, y'' + 4y = 0
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I REALLY NEED HELP ILL MARk BRANLIEST AND IVE MADE IT EXTRA POINTS
Find the measure of the angle indicated.
A. 130∘
B. 142∘
C. 145∘
D. 38∘
Answers
Answer:
142 degrees
Step-by-step explanation:
Easy, 180 degrees in a triangle... so 180-73-69 is 38... now two angles combined on a staight line is also 180 degrees. So now 180 degrees minus 38 is 142 degrees.
Answer:
angle ? (or angle BAN) = 142 degrees Choice (B)
Step-by-step explanation:
all triangles contain 180 interior degrees
180-73-69 = 38 degrees = interior angle at A (or angle CAB)
angle CAN = 180 degrees
180 - 38 = 142 degrees
if 24x - 8 = ab + ac what is the value of a?
Answers
Therefore:
\(a=\frac{24x-8}{b+c}\)prove by induction that 7^2n+1 +1 is divisible by 8, for all nEN
Answers
Answer:
See below.
Step-by-step explanation:
Base case:
Replace n with 1.
7^(2×1+1)+1
7^3+1
343+1
344
8 is a factor of 344 since 344=8(43).
Induction hypothesis:
Assume there is some integer n such that 7^(2k+1)+1=8n for positive integer k.
7^(2[k+1]+1)+1
7^(2k+3)+1
7^(2k+1+2)+1
7^(2k+1)7^2+1
49×7^(2k+1)+1
Induction step:
49×(8n-1)+1
49(8n)-49+1
49(8n)-48
8[49n-6]
This means 8 is a factor of 7^(2(k+1)+1)+1.
Thus, this proves for all positive integer n that 8 is a factor of 7^(2n+1)+1.
helpp meeeeeeeeeeeeee
Answers
Answer:
Step-by-step explanation:
M. 1/6 or 0.16
U. 1/20 or 0.05
T. 1.8
R. 12.5
N. 2 9/13
identify all of the necessary assumptions for a significance test for comparing dependent means.
Answers
When performing a significance-test for comparing dependent means, several assumptions are necessary to make a valid inference- Normality, Equal variances, Independence,Random-sampling.
Some of these assumptions are:
Normality: The distribution of differences between the paired observations must be approximately normal.
This can be assessed using a normal probability plot or by conducting a normality test.
Equal variances: The variances of the paired differences should be approximately equal.
This can be assessed using the Levene's test.
Independence: The paired differences should be independent of each other.
This means that each observation in one sample should not influence the corresponding observation in the other sample.
Random sampling: The observations should be selected randomly from the population of interest.
This ensures that the sample is representative of the population.
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Please help what’s 6,7,8.
Answers
Answer: 7 is 1/8, 8 is 2/8 or 1/4
Step-by-step explanation:
will mark BRAINLIEST
Answers
Answer:
(2, - 1 )
Step-by-step explanation:
The solution to a system of equations given graphically is at the point of intersection of the 2 lines.
The lines intersect at (2, - 1 ) ← solution
Answer:
the answer is C
Step-by-step explanation:
I think pls dont come at me if i am wrong
A player in a board game rolls a six-sided
number cube labeled 1 through 6 once.
Determine the theoretical probability of
rolling a 1 or 2.
Answers
Answer:
A six sided number from 1 to 6 is rolled in a game.
Step-by-step explanation:
Theoretical probability of rolling a 1 or 2.
1) The cube has 6 faces so the total number of the outcome would be 6 only.
2) As per the question we need only 1 or 2 so the favorable outcome would be 2.
3) P(E) = favorable outcome/ total number of outcome
P(E) = 2/6
P(E) = 1/3
Theoretical probability of rolling a 1 or 2 is 1/3
Please help me on this and show the steps I really need help understanding this and I don’t know how to do it and im stressed so please help!
I will mark brainliest
Answers
For the given isosceles triangle LMK, the distance between the points L and K is found as 5 units.
What is defined as the distance formula?The Euclidean distance equation is another name for the distance formula used to calculate the distance between two in a two-dimensional plane.For the given question,
The coordinates of the points L and K taken from the graph are-
L = (-7, 4)
K = (-4, 8)
The distance between the points are found by the distance formula given as;
d = √(x₂ - x₁)² + (y₂ - y₁)²
Where x and y are the respective coordinates of two given points.
put the value;
LK = √(-4 + 7)² + (8 - 4)²
LK = √(3)² + (4)²
LK = √25
Taking square root both sides.
Lk = 5 units.
Thus, for the given isosceles triangle LMK, the distance between the points L and K is found as 5 units.
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Find the AM and GM for the numbers 18 and 2
Answers
Answer:
Step-by-step explanation:
Solution:
AM =( X_1 + X_2 )/2
=( 18 + 2 )/2
=20/2
=10
Find Geometric mean for data 18,2
Solution:
GM =sqrt( X_1 × X_2 )
=sqrt( 18 × 2 )
=sqrt(36)
=6