Answers
Answer:
[tex]\sqrt{a^2+b^2}[/tex]
Step-by-step explanation:
The blue line (or, more accurately, ray) r makes up the hypotenuse of a right triangle with legs (or sides) of lengths a and b. The relationship among the three values is given by the Pythagorean theorem, which states that for any right triangle, the sum of the squares of the lengths of the legs is always equal to the square of the length of the hypotenuse.
Thus, with a and b being the lengths of this right triangle and r being the hypotenuse, the length of the blue line r expressed in terms of a and b can be written as
[tex]r = \sqrt{a^2+b^2}[/tex]
However, since the left-hand side of the equation is already provided for you, what you would write in the box would be simply [tex]\sqrt{a^2 + b^2}[/tex].
Related Questions
once you have done the calculations above, answer the following questions: points 1. in several sentences, explain the right triangle drawings you need to model the shadow scenarios. make sure it answers the following: a. what does each side length signify? in particular explain what does the hypotenuse in your drawing signify in the real world? b. explain why the angle you choose is the angle of elevation of the sun. / 8 / 4 2. from your measurements, when was your shadow the longest? what was the angle of elevation of the sun at this time? / 4 3. from your measurements, when was your shadow the shortest? what was the angle of elevation of the sun at this time? / 4 4. during what time of day do you think the shadow will be longest? explain why using your knowledge of trigonometric ratios. make sure you mention the angle of elevation, your height and a trigonometric ratio that will help explain why the shadow is the longest at this time of day. / 10 5. during what time of day do you think the shadow you cast will be shortest? explain why using your knowledge of trigonometric ratios and hint in question
Answers
By following the above procedure and having done the calculations the following questions can be answered:
According to ground level, each triangle represents the elevation of the sun. The height, for instance, corresponds to my height. The length also depicts my shadow. The line of sight is represented by the other angle. The angle of elevation between the sun and the surface is the same as the angle of elevation between my shadow and my height.My longest measurement was at 9:10 am, when my shadow measured 3.77m and the angle of elevation was 26º.My shortest measurement was at 12:10 pm, when my shadow measured 1.86m and the angle of elevation was 44ºBetween 6 and 7 o'clock in the evening, when the sun is sinking, is the ideal time to measure a lengthy shadow. The sun is hitting you from a horizontal angle at this time, allowing your shadow to cast a longer shadow.When the sun is at its highest point in the sky, around 11 a.m., is the perfect moment to measure a short shadow. The light is shining on you directly now, shortening your shadow, making this the ideal time.Learn more about Shadow cast :
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How do you classify a triangle having the sides 3cm 4cm and 5cm?
Answers
It is possible to construct a triangle whose sides are 3 cm 4 cm and 5 cm because the sum of two sides are greater than three sides.
In the given question, we have to classify a triangle having the sides 3cm 4cm and 5cm.
The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.
To check this we firstly add the 10.2 and 5.8
3 + 4 > 5
7 > 5
Now we add 3 and 5
3 + 5 > 4
8 > 4
Now we add 4 and 5
4 + 5 > 3
9 > 3
It is possible to construct a triangle whose sides are 3 cm 4 cm and 5 cm because the sum of two sides are greater than three sides.
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Question: What are 3 things you notice about the parabola below?
Answers
The 3 things, I noticed about parabola is given below.
What is parabola?A parabola is a curve drawn in a plane.
Where any point is at an equal distance from a fixed point (the focus) and a fixed straight line (the directrix)
We have a parabola.
From the graph of parabola:
1). The vertex of the parabola = (2, -5)
2). And the y-intercept = (0, 7)
3). The curve passes through (1, 2) and (3, 2).
Therefore, all the three points are given above.
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6. On a map, the distances between three small
islands that form a triangle are 3, 7, and 9 inches.
The longest side has an actual length of 1,000
meters. Which of the following is closest to the
actual length, in meters, of the shortest side?
F. 300
G. 333
H. 556
J. 600
K. 1667
Answers
The closest answer to the actual length of the shortest side, in meters, is G. 333.
What is length?Length is a measurement of distance or size. It can refer to the physical size of an object, such as its height, width, or depth, or it can refer to the amount of time it takes to complete an activity. Length is measured in a variety of units including inches, feet, meters, and miles. Length is one of the three fundamental dimensions of physical space, along with width and height.
This is because the ratio of the actual length of the longest side (1,000 meters) to the longest side on the map (9 inches) is 111.11:1. Therefore, the ratio of the actual length of the shortest side to the shortest side on the map is 111.11:3, which is equal to 37.04:1. When we multiply 3 inches (the length of the shortest side on the map) by 37.04, we get 111.12, which is closest to 333 meters (G).
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What is acute angle triangle example?
Answers
Acute angle triangle examples are Equilateral Acute Triangle, Isosceles Acute Triangle, and Scalene Acute Triangle.
The definition of an acute triangle states that it is a type of triangle in which all three interior angles are acute angles or less than 90°. The sides of an acute-angled triangle can be similar or unequal depending on whether the triangle is equilateral, isosceles, or scalene.
As we know that triangles can be categorised on the basis of sides and angles, an acute triangle can also be further categorised as:
Equilateral Acute Triangle: In an equilateral acute triangle, all three angles are equal to 60° and all sides are equal.
Isosceles Acute Triangle: In an isosceles acute triangle, two sides and two angles are equal, and all interior angles are less than 90°.
Scalene Acute Triangle: In a scalene acute triangle, all the 3 sides are of dissimilar lengths and the 3 interior angles are of dissimilar measures but all the interior angles measure less than 90°.
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consider the two functions given below.
f(x)=-3x-5
g(x)=f(x)+9
what is the y-intercept of g?
Answers
Reason:
Plug x = 0 into f(x)
f(x) = -3x-5
f(0) = -3*0-5
f(0) = 0-5
f(0) = -5
This then means,
g(x) = f(x)+9
g(0) = f(0)+9
g(0) = -5+9
g(0) = 4
The y intercept of g(x) is 4; meaning it is located at (0,4).
someone please help mee
Answers
Option B and option C are correct, RT is the altitude of triangle PQR and RS is the median of triangle PQR
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
A median of a triangle is a line segment that joins a vertex to the mid-point of the side that is opposite to that vertex
The altitude of a triangle is the perpendicular drawn from the vertex of the triangle to the opposite side.
RT is the perpendicular to the triangle PQR
RT is the altitude of triangle PQR.
RS is the median of triangle PQR
Hence, option B and option C are correct, RT is the altitude of triangle PQR and RS is the median of triangle PQR
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travels at 5) A will it take to an cover average speed of distance of 65 km 1h How 300km. Long
Answers
The Train to travel that distance =60kmh300km=5h.
How much time will be taken to cover a distance of 300km at a speed of 60km per hour?It measures how far an object travels in relation to how long it takes to travel that distance.
Due to its scalar nature, speed lacks direction.
It represents the rate of an object's motion.
Particles move swiftly when their speed is high, and slowly when their speed is low.
Example
The average speed of a train while it travels 300 kilometres per hour is 60 km/h. Approximately how long does it take to travel that distance?
Speed = 60 km/h 1.
300 kilometres were travelled;
∵ Speed = Distance covered / time taken
∵ Time taken = Distance covered / Speed
= 60kmh −1 / 300km =5h.
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Here is a table classifying 116 thousand US households (in thousands) in 2013 by tenure and insurance
status. Khan academy
Answers
The marginal distribution of tenure in counts for those who own a home is 76, while for those who rent a home is 40.
The marginal distribution of a subset of a group of random variables is the probability distribution of the variables included in the subset. It shows the probabilities of various values of the variables in the subset without reference to the values of the other variables.
Marginal variables are those variables in the subset of variables being included. These concepts are "marginal" because they can be encountered by summing values in a table along rows or columns, and writing the sum in the margins of the table.
For the given data. The marginal distribution of tenure can be calculated as,
Owns home = 71 + 5 = 76
Rents home = 13 + 27 = 40
--The given question is incomplete, the complete question is
"Here is a table classifying 116 thousand US households (in thousands) in 2013 by tenure and insurance. Here is a table giving the number of US households (in thousands) in 2013 by tenure and insurance status:
Insurance status
Owns home
Rents home
Insured
71
13
Uninsured
5
27
Find the marginal distribution of tenure in counts.
Owns home:
Rents home:"
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You have a function that take in an X value and produce a Y value. The y value equal 5 time the x value, plu 2 more. What' the y value when the x value equal 3?
Answers
Answer:
x = 3 is 17
Step-by-step explanation:
Given the function y = 5x + 2, the y-value when x = 3 is calculated as follows:
y = 5x + 2
y = 5 * 3 + 2
y = 15 + 2
y = 17
So the y-value when x = 3 is 17.
PLSS HELP
what’s the solution for the following equation
7x + 6y = 60
3x - 6y = 40
Answers
Answer:
x=10, y= [tex]-\frac{10}{6}[/tex]
Step-by-step explanation:
Add the two equations together
10x + 0y = 100 (+6y + (-6y) =0)
10x = 100
x = 10
substitute x=10 into 3x-6y=40 (either equation is fine)
3(10) - 6y=40
30-6y=40
-6y=10
y= [tex]-\frac{10}{6}[/tex]
A bowling ball has 3 circular holes drilled into it-1 large hole and 2 small holes of equal size. The combined length of the circumferences of the 3 holes is 38m millimeters. The large hole has a diameter of 14 millimeters.
Select whether each statement is true or false. 7.G.4
True False
The small holes each have a radius of 12 millimeters.
The large hole has an area of approximately 615.5 square millimeters.
The combined length of the circumferences of the small holes is 24m millimeters.
The diameter of the large hole is 2 millimeters longer than that of each small hole.
Answers
The statements that are true is A,C,D
What is the area of the circle?The area of the circle is defined as the product of the pie and the square of the radius.
The area of the circle = [tex]\pi r^{2}[/tex]
[tex]\pi[/tex]= 3.14
Given;
The length of the circumferences of the 3 holes is 38m millimeters. The large hole has a diameter of 14 millimeters
2[tex]\pi[/tex]R+2[tex]\pi[/tex]r+2[tex]\pi[/tex]r=38
R+2r=19/3.14...1
Radius of large hole=14/2=7mm
Substituting the value of R in equation 1
7+2r=19/3.14
2r=19*7/3.14
r=21.178
Therefore;
The small holes each have a radius of 12 millimeters.- True
The large hole has an area of approximately 615.5 square millimeters.-false
The combined length of the circumferences of the small holes is 24m millimeters.-True
The diameter of the large hole is 2 millimeters longer than that of each small hole.- True
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if f(x)=6x^2+12x-6 and g(x)=x^2-3 find (f+g)(x).
Answers
Value of (f+g)(x) = 7x² + 12x - 9
What is function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given function
f(x) = 6x² + 12x - 6
g(x) = x² - 3
(f+g)x = f(x) + g(x)
= 6x² + 12x - 6 + x² -3
adding like terms
= 7x² + 12x - 9
Hence, 7x² + 12x - 9 is the value of (f+g)(x) .
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Which given value, if any, is a solution of the equation 42 ÷ j = 6 for j: {7, 36, 48, 252}?
Answers
Answer: j = 7
Step-by-step explanation:
if we do 42 divided by 6 we would have a quotient, 7 so j would be equal to 7. Hope this helped ^^
Answer:
j = 7
Step-by-step explanation:
WILL GIVE BRAINLIEST FOR SOLVE: To write 4^-4 with a positive exponent, ______________.
A. Use the reciprocal of the base, then change the exponent to a positive number and
place it with the number in the denominator.
B. Simply change the exponent to a positive number.
C. Write it as 4/4
D. Change the base to a negative number and make the exponent positive.
Answers
Writing 4⁻⁴ to have a positive exponent should be of the form 1/4⁴
What is exponent?In math, the term exponent refers to the number of times a certain number multiplies it self.
The number that is being multiplies is referred to as the base number while the number of times it multiplies itself is the exponents.
In the law of exponents, numbers with negative exponents will have positive when written in reciprocal form.
Because of this law, the number as in the problem is 4⁻⁴ the reciprocal form of this number is 1/4⁴ and the negative exponent vanishes
The positive exponent of the number is 4⁻⁴
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Answer:
1/(4^4)
Step-by-step explanation:
A. Use the reciprocal of the base, then change the exponent to a positive number and place it with the number in the denominator.
find the equation of the line that is parellel to the line y=2x+6 and passes through the line (-9,-5)
Answers
Answer:
2x -y+13=0
Step-by-step explanation:
the given equation of the line is ,
[tex]\implies \rm y = 2x + 6 [/tex]
as we know that the slope of parallel lines are same so the line parallel to the given line will have the same slope as the given line . Comparing it to slope intercept form of the line we have ,
[tex]\implies \rm m = 2 \ (slope)[/tex]
Now we may use the point slope form of the line to find out the equation of the line as ,
[tex]\implies \rm y - y_1 = m(x-x_1)\\[/tex]
[tex]\implies \rm y -(-5) =2\{ x -(-9)\}\\[/tex]
[tex]\implies \rm y +5 = 2(x+9)\\ [/tex]
[tex]\implies \rm y +5 = 2x +18\\[/tex]
[tex]\implies \rm 2x -y+18-5=0\\[/tex]
[tex]\implies \rm 2x - y +13=0[/tex]
And we are done!
-Rishabh
Find the Average Rate of Change on the table from 2 < x < 5:
Answers
The Average Rate of Change on the table from 2 ≤ x ≤ 5 is 3
How to find the average rate from the table?The average rate of change of a function is a measure of how the output value of the function (y) changes with respect to the input value (x) as x changes. Mathematically:
Average rate of change = Δy/Δx
To find the Average Rate of Change on the table from 2 ≤ x ≤ 5:
when x =2, h(x) = 0 and when x = 5, h(x) = 9
Average rate of change = Δh/Δx
Average rate of change = (9 - 0) / (5 - 2)
Average rate of change = 9/3
Average rate of change = 3
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Do the segments connecting points A, B, and C form a right triangle? Show work that leads to your answer. Round to the nearest tenths place if necessary.
Show your work!
Answers
No, the segments connecting points A, B, and C does not to form a right-angled triangle.
What is Pythagorean theorem?Mathematically, Pythagorean's theorem is given by this mathematical expression:
a² + b² = c²
Where:
a, b, and c represents the length of sides of a right-angled triangle.
In order for the segments connecting points A, B, and C to form a right-angled triangle, its side lengths must satisfy the Pythagorean's theorem:
AB² = (xB - xA)² + (yB - yA)²
AB² = (6 - (-2))² + (2 - 2)²
AB² = 8² + 0²
AB² = 8²
AB = 8
AC² = (xC - xA)² + (yC - A)²
AC² = (0 - (-2))² + (6 - 2)²
AC² = 2² + 4²
AC² = 4 + 16
AC = √20
BC² = (0 - 6)² + (6 - 2)²
BC² = (-6)² + 4²
BC² = 36 + 16
BC = √52
From Pythagorean's theorem, we have:
a² + b² = c²
√20² + √52² = 8²
20 + 52 = 64
72 ≠ 64 (False, not a right-angled triangle).
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What is 12x^3-4x^2 while being fully factorised?
Answers
Answer:187
Step-by-step explanation:
Write y=-1/2|x+2|+5 as a piecewise function
Answers
The piecewise function of the given function is
y= -x/2+4 if x ≥ -2
y= x/2+6 if x < -2
The solution is obtained using the modulus function.
What is modulus function?
The magnitude of a given number is indicated by the modulus of the number. By definition, a modulus function is a real-valued function, such as f: R -> R, where y = |x| for any x R OR f(x) = |x|.
F(x) is equal to the positive value of x for every non-negative value of x. However, f(x) is equal to the negative value of x for negative x values.
We are given y=-1/2|x+2|+5
So, first we need to solve for x+2≥0
We get x≥-2
Now, we get two equations,
y=-1/2(x+2)+5 if x ≥ -2
y= 1/2(x+2)+5 if x < -2
On solving the equations, we get
y=-1/2(x+2)+5 if x ≥ -2
y= -x/2-1+5
y= -x/2+4
y= 1/2(x+2)+5 if x < -2
y= x/2+1+5
y= x/2+6
Hence, the final answer as a piecewise function is
y= -x/2+4 if x ≥ -2
y= x/2+6 if x < -2
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Let θ be an angle in quadrant II such that cos θ = −7/10
.
Find the exact values of csc θ and tan θ
Answers
Exact values of csc θ=10/[tex]\sqrt{51}[/tex] and tan θ= [tex]-\sqrt{5}/7[/tex]
Let θ be an angle in quadrant II such that cos θ = −7/10.
[tex](sinx^)^2 +(cosx)^2=1[/tex]
sin θ =[tex]\sqrt{51/100}[/tex]
cscθ=1/sinθ
cscθ=10/[tex]\sqrt{51}[/tex]
tanθ=sinθ/cosθ
tanθ= [tex]-\sqrt{5}/7[/tex]
Exact values of csc θ=10/[tex]\sqrt{51}[/tex] and tan θ= [tex]-\sqrt{5}/7[/tex].
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What is the equation of a horizontal line passing through the point (- 3 8?
Answers
The equation of a horizontal line passing through the point (- 3 8) is y = 8
How to determine the equation of the lineFrom the question, we have the following parameters that can be used in our computation:
Point = (-3, 8)
This means that
(x, y) = (-3, 8)
Horizontal lines that do not pass through the origin do not intersect with the x-axis
This means that
Line = y
So, we have
y = 8
Hence, the equation is y = 8
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For the school play, 205 students buy tickets and 232 adults buy tickets. All tickets cost $16. How much did the school make in ticket revenue
Answers
Answer: $6,992
Step-by-step explanation:
First you add 205 and 232 then multiply your answer by 16
Solve the following system of equations
5x+2y=-6
3x-2y=22
Answers
Answer:
y = 8
Step-by-step explanation:
5x + 2y = -6 .... 5x = -6 - 2y ...... x = -6/5 -2y/5
3 × ( -6/5 -2y/5 ) - 2y = 22
-18/5 - 6y/5 - 2y = 22 ... (×5)
-18 - 6y - 10y = 110
-16y = 128 .... (× -1)
16y = -128 .... (÷16)
y = 8
Raymond took 10 hours to build a small wall and Gideon took 8 hours to build the same size wall. How long would it take them working together? Express you answer as a common fraction.
I would really appreciate a quick response.
Answers
The time taken by them when working together is 40 / 9 hours.
What is unit rate?A unit rate means a rate for one of something.
Given that, Raymond took 10 hours to build a small wall and Gideon took 8 hours to build the same size wall.
Calculating their unit rates,
Work done by Raymond in 1 hour = 1 / 10 units
Work done by Gideon in 1 hour = 1 / 8 units
Therefore,
Wok done by them in 1 hour when working together =
= 1 / 10 + 1 / 8
= (5+4) / 40
= 9 / 40 units
Since, they are doing the 9 / 40 units of the work in 1 hour,
Therefore, whole work will be done in 40 / 9 hours by them.
Hence, the time taken by them when working together is 40 / 9 hours.
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A newspaper advertisement offers a $10 000 used car for nothing down and 36 monthly payments of $450. What is the interest rate used? How much interest will you have to pay if you purchase this car?
Answers
The interest paid if you purchase this car is $4,860.
What exactly is a monthly payment?A monthly payment is a payment made every month to pay off loans or advances. It's similar to EMI.
The interest rate used can be found using the formula: Interest rate = (monthly payment x number of payments) / principal.
Interest rate = (450 x 36) / 10000 = 16.2%
The interest rate used is 16.2%
The interest paid can be calculated using the formula: Interest = Principal x Interest rate x Number of payments / 12
Interest = 10000 x 0.162 x 36/12
Apply the multiplication operation, and we get
Interest = 4,860
Thus, the interest paid if you buy this car is $4,860
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Your friend wants to mark her favorite campsite on the map. She knows that the campsite is 65 miles north of her town. what distance on the map (in inches) represents the actual distance of 65 miles? show your work and explain your reasoning.
Using the scale 1/2 in. : 10 mi.
Answers
If your friend wants to mark her favorite campsite on the map. distance on the map (in inches) that represents the actual distance of 65 miles is 3.25.
How to find the distance?Scaling drawing 1/2 in = 10 miles
Scaling drawing 1 in = 20 miles
So,
Actual distance = 65 miles
Drawing distance = x inches
1 in /20 mi = x in /65 mi
Cross multiply
20x =65
Divide both side by 20x
x = 65/20
x = 3.25 inches
Therefore the distance is 3.25inches.
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1 out of 8 students wants pancakes and the rest want waffles. What is the ratio of the number of students who want waffles to the total number of students?
Answers
The ratio of students who want waffles to the total number of students is 7/8.
What is the ratio?
The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Out of 8 students, 1 student wants pancakes and 8 - 1 = 7 students want waffles.
To find the ratio of the number of students who want waffles to the total number of students, we can divide the number of students who want waffles by the total number of students and express the result as a fraction.
So the ratio is:
(Number of students who want waffles) / (Total number of students) = 7/8
This fraction can be simplified by dividing both the numerator and denominator by the greatest common factor, which in this case is 1, so it remains the same.
Hence, the ratio of students who want waffles to the total number of students is 7/8.
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A solution containing 32 % insecticide is to be mixed with a solution containing
55% insecticide to make 100 L of a solution containing 44% insecticide. How much
of each solution should be used?
Answers
40L of each solution should be used
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let x=amount of 32% insecticide needed
Then 100-x=amount of 55% insecticide needed
Now we know that the amount of pure insecticide in the 32% solution(0.32x) plus the amount of pure insecticide in the 55% solution(0.55(100-x)) has to equal the amount of pure insecticide in the final mixture (0.44×100).
So our equation to solve is:
0.32x+0.52(100-x)=0.44×100 get rid of parens
0.32x+52-0.52x=44
52-44-0.2x=0
8=0.2x
x=40L
Hence, 40L of each solution should be used
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What are the measures of â X and â Y?
Answers
The measure of angle x and angle y is x = 75° and y = 135°, respectively.
We know that,
If the angles of a triangle are θ₁, θ₂ and θ₃, respectively. Then the sum of θ₁, θ₂ and θ₃ is equal to 180°.
In triangle ABC,
⇒ 45° + 60° + x = 180°
⇒x = 180° − 105°
⇒x = 75°
Now, If the exterior angle of a triangle is θ and the two opposite interior angles are θ₁ and θ₂, then the sum of θ₁ and θ₂ will be equal to the θ.
⇒y = 60° + x
⇒y = 60° + 75°
⇒y = 135°
Therefore, x =75° and y = 135°
--The given question is incorrect, the correct question is
"What are the measures of angle x and angle y?"--
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