Answers
To find the length of the diagonal, we need to calculate the length of the base first and then use the value to calculate the diagonal since we are given the value of height of the triangle.
Pythagorean TheoremThis theorem is used to find the missing side of a right angle triangle given that we have the length of two sides.
To calculate the base of the triangle, let's use Pythagorean theorem here
[tex]x^2 = y^2 + z^2\\x^2 = 2^2 + 3^2\\x^2 = 4 + 9 \\x^2 = 13\\x = \sqrt{13} \\x = 3.61[/tex]
Having the length of the base, let's consider the height of the triangle which is 6 and substitute the values.
[tex]d^2 = 6^2 + 3.61^2\\d^2 = 36 + 13.0321\\d^2 = 49.0321\\d = \sqrt{49.0321} \\d = 7.00[/tex]
From the calculations above, the values of the triangle are
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Related Questions
To see why no one noticed time dilation until the twentieth century, consider the time dilation of a clock in an automobile moving past you at 30m / s (about 67mph for reference). What happens when you try to compute gamma for this problem? Write out the steps you take.
(PLLS)!!!
Answers
When we try to compute gamma, for this problem, the value of gamma is 1
To answer the question, we need to know what time dilation is.
What is time dilation?Time dilation is a phenomenon in special relativity in which there is an elongation of time due to the motion of an object.
Now, the time is given by t = γt₀ where
γ = gamma = 1/√[1 - (v/c)²] where v = speed of object c = speed of light and t₀ = proper timeThe value of gammaSince we need to compute gamma when the speed of the automobile moving past you is 30 m/s.
Given that
v = 30 m/s and c = 3 × 10⁸ m/sSubstiting these into γ, we have
γ = 1/√[1 - (v/c)²]
γ = 1/√[1 - (30 m/s/3 × 10⁸ m/s)²]
γ = 1/√[1 - (1/1 × 10⁷)²]
γ = 1/√[1 - (1 × 10⁻⁷)²]
γ = 1/√[1 - (1 × 10⁻¹⁴)]
γ = 1/√[1 - 0.00000000000001]
γ = 1/√0.99999999999999
γ = 1/1
γ = 1
So, when we try to compute gamma, the value of gamma is 1
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14 What are the solutions to the equation 3(x − 4)² = 27?
(1) 1 and 7
(3) 4 ± √24
(2) −1 and -7
(4) − 4 ± √24
Answers
Answer:
(1) 1 and 7
Step-by-step explanation:
Hello!
We can solve by isolating the variable.
Solve3(x - 4)² = 27(x - 4)² = 9
√(x - 4)² = √9
(x - 4) = ± 3
x = 4 ± 3
There are two solutions, 1 and 7.
The answer is option 1: x = 7, x = 1.
Alisha buys 200 books costing £3 each.
She sells 2/5 of the books at £8 each.
Alisha then reduces the price of the remaining books by a quarter.
She then sells some of the remaining books.
Alisha makes £490 profit.
Work out how many books Alisha did not sell?
Answers
The number of books Alisha did not sell after making a profit of £490 is 45 books
How to find how many book she sell base on the profit?
She buys 200 books costing £3 each.
Therefore,
cost = 3 × 200 = £600
Hence,
She sells 2/5 of the books at £8 each.
total amount = 2 / 5 of 200 × 8
total amount = 80 × 8
total amount = £640
Alisha then reduces the price of the remaining books by a quarter.
She then sells some of the remaining books.
Therefore,
the remaining book = 120
She sold some of the remaining books.
profit = selling price - cost price
490 = selling price - 600
selling price = 490 + 600
selling price = £1090
Therefore,
the cost of the remaining book she sold = 1090 - 640 = £450
Hence,
let
x = number of book sold
6(x) = 450
x = 450 / 6
x = 75
The number book she did not sell = 120 - 75 = 45
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y=-2/5x
a. direct
b. inverse
c. neither
Answers
Answer:
a. direct
Step-by-step explanation:
direct variation is y = kx and y = -2/5x is written in direct variation.
represent , the set of numbers between 10 to 50 when they are divided by 5 then the remainder is 2 by description method listing method and set builder method
Answers
The numbers between 10 and 50 when they are divided by 5 then the remainder is 2 is shown in the form of description method and in set-builder form is {12, 17, 22, 27, 32, 37, 42, 47}.
What is set?A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.
We have:
The set of numbers between 10 and 50 when they are divided by 5 then the remainder is 2
The numbers are:
12, 17, 22, 27, 32, 37, 42, 47
By description method:
1 2 3 4 5 6 7 8
12 17 22 27 32 37 42 47
By set builder form:
s = {12, 17, 22, 27, 32, 37, 42, 47}
Thus, the numbers between 10 and 50 when they are divided by 5 then the remainder is 2 is shown in the form of description method and in set-builder form is {12, 17, 22, 27, 32, 37, 42, 47}.
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The length of a rectangle is four times the width. The perimeter of the rectangle is 45 inches. Write a system of equations that represents this problem. What is the area of the rectangle
Answers
Step-by-step explanation:
2×length + 2×width = 45
length = 4×width
now, we are using the second equation (a variable identity) in the first equation
2×4×width + 2×width = 45
8×width + 2×width = 45
10×width = 45
width = 45/10 = 4.5 in
length = 4×width = 4×4.5 = 18 in
the area of the rectangle is
length × width = 18 × 4.5 = 81 in²
PLEASE HELP ASAP CANT MOVE ON
What is the scale factor of LaTeX: \triangle ABC\:to\:\triangle DEC? Be sure to simplify your answer!
answers:
2/7
10/21
3/14
5/14
Answers
Answer:
[tex]\frac{2}{7}[/tex]
Step-by-step explanation:
Triangle ABC is similar to triangle DEC, because all angles in one triangle are equal to angles in the other triangle.
That means that corresponding sides have the same ratio. Side AB and side DE are corresponding sides. Since there are no unknowns we can calculate the ratio (scale factor).
Since we are looking for scale factor of triangle DEC to triangle ABC, we put side AB (which is in triangle ABC) in the numerator.
[tex]\text{scale factor} = \frac{\text{AB}}{\text{DE}} = \frac{6}{21} = \frac{2}{7}[/tex]
I've marked corresponding sides and angles in the attached picture.
Marc is trying to determine how many blue marbles are in a bag of `100` marbles. he can only fit `10` marbles in his hand at a time. he takes `11` samples of `10` marbles, returning the marbles to the bag each time. based on these results, how many of the `100` marbles do you expect are blue
Answers
Based on the result from the box plot, the number of blue marbles is equal to the median of the data set and this is equal to 40.
What is a boxplot?A boxplot is a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread. Also, the five-number summary include the following:
MinimumFirst quartileMedianThird quartileMaximumFor this exercise, we would create a box plot (see attachment) for the marbles in a bag of 100 marbles. By critically observing the box plot, we can logically deduce that the number of blue marbles is equal to the median of the data set and this is given by:
Median = 4 × 10
Median = 40.
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A chandelier is suspended from the ceiling by two chains. one chain is 46cm long and forms an angle of 60o with the ceiling. the other chain 64cm long. what angle does the longer chain make with the ceiling?
Answers
The angle the longer chain makes with the ceiling is 38.5°
The two chains and ceiling form a triangle and with two sides and an angle, we use the sine rule to find the other angle
What is the sine rule?The sine rule states in any triangle with sides a, b, c and angles A, B and C, repsectively, we have that
a/sinA = b/sinB = c/sinC
Since one chain is 46cm long and forms an angle of 60° with the ceiling. the other chain 64cm long. So, we find the other angle.
So, a/sinA = b/sinB where
a = 46 cm, b = 64 cmA = other angleB = 60°The value of the other angleMaking A subject of the formula, we have
A = sin⁻¹(asinB/b)
So, substituting the values of the variables into the equation, we have
A = sin⁻¹(asinB/b)
A = sin⁻¹(46 cm × sin60/64 cm)
A = sin⁻¹(46 cm × 0.8660/64 cm)
A = sin⁻¹(39.84 cm/64 cm)
A = sin⁻¹(0.6225)
A = 38.49°
A ≅ 38.5°
So, the angle the longer chain makes with the ceiling is 38.5°
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there are 100 students in the 5th grade. of those 43 of them are in the school band.what percent of 5th grade are in the band
Answers
Answer:
43 percent
Step-by-step explanation:
When you divide 43 by 100 you get .43 which is 43%
Answer:
43%
Step-by-step explanation:
Because if you divide 43 by 100 you get, .43 and so there you have it, 43% Hope you understand <3
HELP!!!! THIS IS A MATRIX PROBLEM (WILL GIVE BRAINLIEST)
If T= 23 -38
17 -6
What is -10(T)
Answers
Answer:
hope you can understand
ΔDEF rotates 90° clockwise about point A to create ΔD 'E 'F. Therefore, which equation must be true?
Answers
The equation that must be true about the rotation is that m∠EAE ' = m∠FAF.
How to explain the rotation?Rotation is a type of transformation in which the shape of the original object is preserved and the angle of rotation is constant for all the parts of the body.
In this case, ΔDEF rotates 90° clockwise about point A to create ΔD 'E 'F, m∠EAE ' = m∠FAF.
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Which polar coordinates represent the same point as the rectangular coordinate (1,-3)?
The ANSWERS are (sqrt{10} , 288.4°) and (-sqrt{10} , 108.4°) ----- PLEASE EXPLAIN THANK YOU!!!
Answers
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the objects. The polar coordinate of the coordinate (1, -3) is (√10, 288.435).
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
The polar coordinate of the coordinate (1, -3) are,
r = √(x² + y²) = √[(1)²+(-3)²] = √10
θ = tan⁻¹(-3/1) = -71.565 = 288.435
Hence, The polar coordinate of the coordinate (1, -3) is (√10, 288.435).
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Abrianna sold 20, 23, 18, 4, 17, 21, 15, and 56 boxes of cookies after different football games. Which data value(s) are outliers? Select all that apply.
Answers
The data value that is an outlier in the data for boxes of cookies is: E. 56.
How to Determine Outliers in a Data?The simple rule is that values lower than Q1 - 1.5 × IQR and values greater than Q3 + 1.5 × IQR are outliers of a data distribution.
Given the data, 20, 23, 18, 4, 17, 21, 15, 56, find the Q1, Q3, and IQR of the data distribution:
First Quartile (Q1) = 15.5
Third Quartile (Q3) = 22.5
Interquartile Range (IQR) = 22.5 - 15.5 = 7
Q1 - 1.5 × IQR = 15.5 - 1.5 × 7 = 5
Q3 + 1.5 × IQR = 33
None of the values are lower than 5.
However, the only value that is greater than 33 is 56.
The outlier in the data is: E. 56.
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Carson is organizing textbooks on his bookshelf. he has a spanish textbook, a math textbook, a history textbook, and a writing textbook. how many different ways can he line the textbooks up on his bookshelf?
Answers
Answer:
16
Step-by-step explanation:
Answer:24
Step-by-step explanation:
Write the slope intercept form of each equation of the line. Use a fraction for slope if needed.
Parallel to y=−x+5, through (2, 4)
Answers
Answer:
y=-x+6
Step-by-step explanation:
Start by graphing y=-x+5. Then mark the point (2,4) for easier reference. A parallel line just has the same slope, so if you make another line with the same slope, and change the y-intercept until the line goes through (2,4), you will have the answer.
Find an angle with a positive measure and an angle with a negative measure that are coterminal with each angle. 175
Answers
Answer:
185 anle with the postive measure and a negative measure
The lengths of the diagonals of a parallelogram are 10 feet and 16 feet. If one side of the parallelogram measures 4 feet, to the nearest hundredth of a degree, find the measure of the acute angle formed by the intersection of the diagonals.
Answers
Answer: 24.15
Step-by-step explanation:
A new pizza restaurant uses paid advertisement to increase pizza sales on Mondays. The table below is a record of the restaurant’s sales each Monday for the first quarter (13 weeks) of the paid advertisement.
Part A: Create a scatter plot to represent the data in the table. Then, draw the line of best fit, going through the points representing weeks 5 and 13. Be sure to label each axis, as well as to include the proper titles for the scatter plot.
Part B: Use the total sales for weeks 5 and 13 to write an equation for the line of best fit. In your final answer, include all of your calculations.
Part C: In terms of the slope of the equation for the lines of best, fit explain whether or not you think the paid advertisement is responsible for the restaurant's increase or decrease in pizza sales during the first quarter. Use complete senteneces in your answer.
Part D: Assuming that the pizza restaurant wishes to continue the paid advertisement for an additional quater, use the equation for the line of best fit to predict the restaurant's sales for the Monday of the 20th week.
Answers
A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
What is a line of best fit?A line of best fit is also referred to as a trendline and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.
Part B.By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that an equation for the line of best fit is given by:
y = 22.214x + 291.27
Part C.Since the slope of the equation for the line of best fit is positive, the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.
Part D.Next, we would predict the restaurant's sales for the Monday of the 20th week as follows:
y = 22.214x + 291.27
y = 22.214(20) + 291.27
y = 444.28 + 291.27
y = $735.55.
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(TR)546 - (TR)540
pls help!
Answers
The computation of (TR)546 - (TR)540 will give a value of 3261.
How to compute the value?
TR(546) = 546(546 + 1)/2 = 273 * 547
TR (540) = 540(540 + 1)/2 = 270 * 541
273 * 547 = (270 + 3)(541 + 6)
= 270*541 + 270*6 + 541 *3 + 18
= 270*541 + 1620 + 1623 + 18
= 270*541 + 3261
TR(546) -TR (540) = 270*541 + 3261 - 270 * 541
= 3261
TR(546) -TR (540) = 3261
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find the value of "w" that makes this quadrilateral a parallelogram.
Answers
Answer:
w=7
Step-by-step explanation:
A parallelogram is defined as a four-sided plane rectilinear figure with opposite sides parallel. This means that GH and FE must be equivalent, and HE and GF must be equivalent. Now, we just use those equations to solve.
16w-63=7w
9w-63=0
9w=63
w=7!!!
and we can double check.
16w-81=15w-74
16w=15w+7
w=7
Indicate in standard form the equation of the line passing through the given points, writing the answer in the equation box below.
M(0,6), N(6,0)
Answers
The slope of the line is [tex]\frac{6-0}{0-6}=-1[/tex]. so in point-slope form, the equation of the line is [tex]y=-x+6[/tex].
In standard form, this is [tex]\boxed{x+y=6}[/tex]
The midpoint of AB = ([?], [])
M = (x¹+x², ¹2²)
PLS HELP I WILL MARK BRAINLIEST
Answers
Answer:
[tex]\sf M=\left(-\dfrac{1}{2},0\right)[/tex]
Step-by-step explanation:
Let (x₁, y₁) = Point A = (-2, 1)
Let (x₂, y₂) = Point B = (1, -1)
[tex]\sf Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]\implies \sf Midpoint=\left(\dfrac{-2+1}{2},\dfrac{1+(-1)}{2}\right)[/tex]
[tex]\implies \sf Midpoint=\left(-\dfrac{1}{2},0\right)[/tex]
25% of 80 help nowww
Answers
80 * 25 /100 = 20 .........
Answer:
20
Step-by-step explanation:
25% of 80
to turn 25% into a decimal, 25 / 100 = 0.25
multiply 80 by 0.25, 80 x 0.25 = 20
Question 17 of 25
Which is a correct expansion of (3x+2)(3x² + 4)?
OA. 3x 3x² + 3x • 4+2·3x²+2 • 4
OB. 3x. 3x² + 3x• 4+2·3x+2·4
O C. 3x. 3x²+2·3x² + 3x².4+2·4
Answers
Answer:
A is the answers for the question
Step-by-step explanation:
please mark me as brainlest
what is the formula for the nth term of the sequence (1x3),(2x4),(3x5)
Answers
Answer:
nth term = n(n + 2)
Step-by-step explanation:
Note that the first number in each parentheses is the sequence number n of the term. This value of n is then multiplied by (n + 2) - for example 3 x 5
( 3 x (3+2)).
So the nth term = n(n + 2).
This is an example of a Quadratic Sequence.
On the scale drawing of a car, the length from bumper to bumper is 6 inches. The car’s actual length, from bumper to bumper, is 16 feet. How many inches would be used to represent an actual length on the car of 10 feet? Explain or show your reasoning.
Answers
Answer: x = 3.75 inches
Step-by-step explanation:
We will set up a proportion to solve.
[tex]\displaystyle \frac{6 \text{ inches}}{16 \text{ feet}} =\frac{x \text{ inches}}{10 \text{ feet}}[/tex]
Now, we will cross multiply, simplify and isolate the variable to solve your math problem.
6 * 10 = 16 * x
60 = 16x
3.75 = x
x = 3.75 inches
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Find the axis of symmetry of the graph of the function. (5 points) f(x) = 3x2 + 12x + 9
Answers
Considering the definition of axis of symmetry, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.
Axis of symmetryAn axis of symmetry is an imaginary reference line that, when dividing any shape into two parts, its opposite points are equidistant from each other, that is, they are symmetrical.
In other words, the axis of symmetry is a vertical line that divides the parabola into two congruent halves.
The axis of symmetry is the line perpendicular to the "x" axis that contains the vertex of the function, that is, it always passes through the vertex of the parabola. So the x-coordinate of the vertex is the equation of the axis of symmetry.
That is, in a quadratic function that has the form:
f(x)= ax² + bx + c
the axis of symmetry is a vertical line and it is defined as [tex]x=\frac{-b}{2a}[/tex].
Axis of symmetry of f(x) = 3x² + 12x + 9In this case, you know:
a= 3b=12c=9Replacing in the definition of axis of symmetry:
[tex]x=\frac{-12}{2x3}[/tex]
Solving:
[tex]x=\frac{-12}{6}[/tex]
x= -2
Finally, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.
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a boat leaves at 4:25 a.m. and returns to port at 10:55a.m. How long was the boat out?
Answers
Answer:
6 hours 30 minutes
Step-by-step explanation:
10 subtract 4 is 6
55 subtract 25 is 30
What is the standard deviation of the data? Round to the nearest whole number.
65
75
100
130
Answers
Rounded to the nearest whole number, the standard deviation of the data is 29.
How do we calculate the standard deviation of data?The following notations and formulas will be used in these calculations:
Mean = (sum of the values) / n
Variance = ((Σ(x - mean)^2) / (n - 1)
Standard deviation = Variance^0.5
Where:
n = number of values = 4
x = each value
Therefore, we have:
Mean = (65 + 75 + 100 + 130) / 4 = 92.50
Variance = ((65-92.5-)^2 + (75-92.50)^2 + (100-92.50)^2 + (130-92.50)^2) / (4-1) = 2,525 / 3 = 841.666666666667
Standard deviation = Variance^0.50 = 841.666666666667^0.5 = 29.011491975882
Rounding to the nearest whole number, we have:
Standard deviation = 29
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Answer:
The answer is C. 100
Step-by-step explanation: