Answers
5[tex]\sqrt{3}[/tex]
Step-by-step explanation:Special right triangles, such as the one shown, have unique equations that can be used to find missing sides.
30-60-90 Triangles
The angle measurements show us that this is a 30-60-90 triangle. This name refers to the 3 angle measurement. There are 2 types of special right triangles, 45-45-90 and 30-60-90. For most triangles, it would take the law of sine or cosine to find a missing side with only 1 side given. But, with special right triangles, we can use shortcuts to find a.
Formulas
For all 30-60-90 triangles, there are 3 sides: the hypotenuse (c), the long leg (a), and the short leg (b). The shortcuts for 30-60-90 triangles are based on the length of the short leg.
The formulas are as follows (the variables match the variable given in the figure):
c = 2bb = 0.5ca = b[tex]\sqrt{3}[/tex]Solving for a
So, to find a, we must first find b. Since b is equal to half of c, we can divide the value of c by 2.
10/2 = 5Thus, b = 5
Next, plug this value into the formula for b
a = 5[tex]\sqrt{3}[/tex]Answer:
Last option
Step-by-step explanation:
cos30° = a/10
a = 10cos30°
[tex]cos30=0.8660=\frac{\sqrt{3} }{2}[/tex]
[tex]a=10(\frac{\sqrt{3} }{2} )=5\sqrt{3}[/tex]
Hope this helps
Related Questions
PLEASE HELP GEOMOTRY"the ratio of the angles of a pentagon is 1:2:2:3:4 find the largest angle"
Answers
The largest angle of the pentagon with the given ratio of angles is: 180°.
What is a Pentagon?A pentagon is a 5-sided polygon with 5 interior angles that have a sum of 540 degrees.
If the ratio of the angles are: 1:2:2:3:4, then the largest angle would be calculated as shown below:
4/(1+2+2+3+4) × 540
4/12 × 540 = 180°
The largest angle is: 180°.
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In the Kite ABCD, AB = 5√2mm AP= 5mm, PD = 7mm, find the area to the nearest mm2.
Answers
The area of the kite ABCD will be 60 square millimeters.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
In the Kite ABCD, AB = 5√2mm = 7.07 mm, AP= 5mm, PD = 7mm
Then the area of the kite ABCD will be
Area = 2(area of triangle APB and area of triangle APD)
The side length of PB will be
AB² = AP² + PB²
PB² = AB² – AP²
PB² = 7.07² – 5²
PB² = 50 – 25
PB² = 25
PB = 5 mm
Then the area will be
Area = 2[(1/2 × 7 × 5) + (1/2 × 5 × 5)]
Area = 60 square mm
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Type the correct answer in the box. Round off your answer to the nearest integer.
Angle A and Angle C are right angles. m
Answers
Answer:
59
Step-by-step explanation:
[tex] \sqrt{ {6}^{2} + {5}^{2} } = \sqrt{36 + 25} = \sqrt{61} [/tex]
[tex] \cos(p) = \frac{4}{ \sqrt{61} } [/tex]
[tex]p = {cos}^{ - 1} \frac{4}{ \sqrt{61} } = 59[/tex]
Make sure your calculator is in degree mode.
Jocelyn is training for a race by running several miles each day. she tracks her progress by recording her average speed in minutes per mile for each day since she started training. based on the information given, what could jocelyn expect to have for her average speed on the 9th day?
Answers
Finding the regression equation, her average speed on the 9th day should be expected to be of 6.92 minutes per mile.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
Researching the problem on the internet, the values of x and y are given as follows:
Values of x: 1, 2, 3, 4, 5, 6.Values of y: 8.2, 8.1, 7.5, 7.8, 7.4, 7.5.Hence, using a calculator, the equation for the average minutes per mile after t days is given by:
V(t) = -0.15143t + 8.28
Hence, for the 9th day, t = 9, hence the estimate is:
V(9) = -0.15143(9) + 8.28 = 6.92 minutes per mile.
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which choice is equivalent to the the expression
square root of -64
Answers
The equivalent expression of square root of -64 is 8i
How to determine the equivalent expression?We have:
square root of -64
Rewrite as:
√-64
Expand
√64 * √-1
Take the square root of 64
8√-1
In complex numbers
√-1 = i
So, we have:
8i
Hence, the equivalent expression of square root of -64 is 8i
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PLEASE ANSWER ASAP!!!!!! WILL GIVE BRAINLIEST!!!
Answers
Answer ya so 1 is the answer
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
Given expression:
[tex]\sf \left(\dfrac{3a^{-2}b^6}{2a^{-1}b^5} \right)^2[/tex]
To find the value of the expression when a = 3 and b = -2, substitute these values into the expression:
[tex]\implies \sf \left(\dfrac{3(3)^{-2}(-2)^6}{2(3)^{-1}(-2)^5} \right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}[/tex]
[tex]\sf \implies \left(\dfrac{3\left(\dfrac{1}{3^2}\right)(-2)^6}{2\left(\dfrac{1}{3^1} \right)(-2)^5} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{3\left(\dfrac{1}{9}\right)(-2)^6}{2\left(\dfrac{1}{3} \right)(-2)^5} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{3}{9}\right)(-2)^6}{\left(\dfrac{2}{3} \right)(-2)^5} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right)(-2)^6}{\left(\dfrac{2}{3} \right)(-2)^5} \right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad (-a)^n=a^n,\:\: \textsf{ if }n \textsf{ is even}[/tex]
[tex]\textsf{Apply exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right) (2^6)}{\left(\dfrac{2}{3} \right) (-(2^5))} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right) (64)}{\left(\dfrac{2}{3} \right) (-32)} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\left(\dfrac{1 \times 64}{3}\right)}{\left(\dfrac{2 \times -32}{3} \right)} \right)^2[/tex]
[tex]\sf \implies \left(\dfrac{\dfrac{64}{3}}{\dfrac{-64}{3}} \right)^2[/tex]
When dividing fractions, flip the second fraction and multiply it by the first:
[tex]\implies \sf \left( \dfrac{64}{3} \times \dfrac {3}{-64} \right)^2[/tex]
[tex]\implies \sf \left( \dfrac{64 \times 3}{3 \times (-64)}\right)^2[/tex]
[tex]\implies \sf \left( \dfrac{192}{-192}\right)^2[/tex]
[tex]\implies \sf \left(-1\right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad (-a)^n=a^n,\:\: \textsf{ if }n \textsf{ is even}[/tex]
[tex]\sf \implies 1^2=1[/tex]
how many nonisomorphic spanning trees does each of these simple graphs have
Answers
The characteristics of a nonisomorphic spanning tree are:
One would have 3 vertices of degree 2 and 2 of degree 1, Another spanning tree would have one vertex of degree three, The third spanning tree would have one vertex of degree four.4What is Nonisomorphic?This refers to the quality of a group of things not having the same form and is popularly used in mathematics to show and make identifications of maths objects that are structurally well-defined.
Hence, we can see that your question is incomplete so I gave you a general overview of the topic for better understanding.
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A university conducted a survey of 383 undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank. If a survey participant is selected at random, what is the probability that he or she is satisfied or a junior? *Round to 3 decimal places* ( I only need part d.)
Answers
Answer:
62/235 +95/383
Step-by-step explanation:
P(satisfied or junior)= P(satisfied participant that are junior) + P(junior participant)
P(satisfied or junior)= 62/235 + 95/383
P(satisfied or junior)= 46071/90005
the scale on a map is 1 cm to 2 cm what is the actual distance between two town if the distance on the map is 5.5
Answers
If the distance on the map is 5.5 cm. Then the actual distance between two town will be 11 miles.
The complete question is given below.
The scale on a map is 1 cm to 2 miles. What is the actual distance between two town if the distance on the map is 5.5 cm.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
The scale on a map is 1 cm to 2 miles.
If the distance on the map is 5.5 cm.
Then the actual distance between two town will be
⇒ 5.5 cm = 5.5 × 2 miles
⇒ 5.5 cm = 11 miles
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What is -8/15 of 21/12
Answers
Answer:
-14/15
Step-by-step explanation:
"of" means multiply, thus:
-8/15 * 21/12
-8 * 21 / 15 * 12
-2 * 7 / 15
-14/15
Answer:
-14/15
Step-by-step explanation:
So first you need to get rid of the negative sign. Don't worry you will add it back later!
So, you will do
-8/15×21/12
Once you cross cancel, you will have
-2/5x7/3
That would be equivalent to
-14/15
That's your answer!
Hope this helped :)
How do I solve the following system of inequalities graphically on the set of axes below?
y> x-3 y≥− 6/1 x+4
Answers
Thank you!!
Solve |x| > -9.
1. no solution
2. all reals
3. {x | x < -9 or x > 9}
Answers
Answer:
2. All reals
Step-by-step explanation:
It covers everything as absolute value (distance from 0)
If you graph it you will see
Reason:
Absolute value represents distance on a number line. Specifically it's the distance from x to 0.
For example, |-2| = 2 means -2 is 2 units away from 0.
Since |x| represents a distance, we cannot have negative distance. So |x| is either 0 or positive. Furthermore, it means |x| is larger than any negative value you pick.
Therefore, |x| > -9 is true for any x value and it's why we go for "all reals" (aka "all real numbers")
The graph of quadratic function f has zeros of -8 and 4 and a maximum at (-2,18). What is the value of a in the function’s equation?
Answers
To find the equation of a parabola given the vertex and the zeroes, we can use the intercept form equation to help us:
[tex]y=a(x-r)(x-s)[/tex]
r and s = intercepts/zeros of the graphSolving the QuestionWe're given:
Zeros: -8, 4Maximum: (-2, 18)[tex]y=a(x-r)(x-s)[/tex]
⇒ Plug in the given information:
[tex]y=a(x-(-8))(x-4)\\18=a(-2-(-8))(-2-4)\\18=a(-2+8)(-2-4)\\18=a(6)(-6)\\18=a(-36)\\1=-2a\\\\a=-\dfrac{1}{2}[/tex]
Answer[tex]a=-\dfrac{1}{2}[/tex]
Find the perimeter.
15 ft
25 ft
if the 25ft is diagonal in a rectangle
Answers
Let c=25 & b=15.
Therefore a=20
Perimeter is 2l+2w, and since a=20&b=15 are the length and width, we can plug that into the formula to get
70 ft
Hope this helped :)
Answer:
P=70ft
Step-by-step explanation:
25^2-15^2=400
Sqrt400=20
2l+2w=P
40+30=70
-5/7 x 1/5
please help
Answers
-5/7 x 1/5
-5 x 1 = -5
7 x 5 = 35
-5/35 = -1/7
Happy to help :P
what is 1,000,000,000 divided by -1,000
Answers
-1000000 that is the answer
hope this helps!
The vertical walls of two buildings are 50 m and 30 m tall. A vertical flagpole [XY] stands between the buildings such that B, Y, and C are collinear, and A, Y, and D are collinear. The vertical walls of two buildings are 50 m and 30 m tall . A vertical flagpole [ XY ] stands between the buildings such that B , Y , and C are collinear , and A , Y , and D are collinear . find the height of the flagpole
Answers
Answer:
which class of this exam
A trader mixes 2 kg
of butter which costs $8 per kg
with 3 kg of butter which costs $6 per kg. He sells the mixture at $2.55 per 250g. Express his profit as a percentage of his selling price.
Answers
Answer:
33.3333%
Step-by-step explanation:
Total number of kg- 2+3=5
Total money- (2×8)=16
(3×6)=18
16+18=34
$34=5000g
=250g
(250×$34)÷5000=$1.7
profit-2.55-1.7=0.85
(0.85/2.55)×100=33.333%
2.
(07.02 LC)
Which statement is true for the equation 4x − 4x − 5 = −5? (5 points)
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
Answers
Brian ordered 3 large cheese pizzas and a salad. The salad cost $4.95. If he spent a total of $47.60 including the $5 tip, how much did each pizza cost? (Considering there's no tax) Please I really need help
Answers
Answer:
Each pizza was $12.55.
Step-by-step explanation:
et's take it piece by piece.
Salad and the tip together is 4.95 + 5 = 9.95, right?
47.60 - 9.95 = 37.65 spent on pizza
37.65/3 = 12.55
Help me please and thxx
Answers
Option C).
If F= {(1,5), (4, 1), (2, 7)}and g= {(3, 1), (5 4) (-6,2)} represent fog in mapping of agram and to find fog in ordered pair form
Answers
From the given mappings, we have
[tex]f(1) = 5, f(4) = 1, f(2) = 7[/tex]
and
[tex]g(3) = 1, g(5) = 4, g(-6) = 2[/tex]
Then the composition of [tex]f[/tex] with [tex]g[/tex], or [tex]f\circ g[/tex], is
[tex]\boxed{f\circ g = \{(3,5), (5,1), (-6, 7)\}}[/tex]
since
[tex]g(3) = 1 \implies (f\circ g)(3) = f(g(3)) = f(1) = 5[/tex]
[tex]g(5) = 4 \implies (f\circ g)(5) = f(4) = 1[/tex]
[tex]g(-6) = 2 \implies (f\circ g)(-6) = f(2) = 7[/tex]
You are working in a lab and you need a solution of 22% acid. In the cupboard, you find a 10% and a 30% solution, but not a 22% solution. You will have to make your own 22% solution. You will need liters of the 10% and liters of the 30% to make 15 liters of a 22% solution?
Answers
The volume of 10% solution will be 6 l and 9 litre of the 30 % solution will be taken.
What is Volume ?Volume is the space occupied by a three dimensional object .
The concentration of solution required is 22% acid
The concentration of solution available is 10% and 30%
The total volume required is 15 liters
The formula for making a mixture is
Concentration = ( m₁x₁ +m₂x₂) / (x₁+x₂)
22 = (10 * x + 30 *(15 -x))/( 15)
10 x + 450 - 30x =330
-20x = -120
x = 6
The volume of 10% solution will be 6 l
and 9 litre of the 30 % solution will be taken.
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experimental verification
Answers
See below for the verification of ∠ACD = ∠ABC + ∠BAC
How to verify the angles?The following proof works for both triangles.
The sum of angles in a triangle is 180 degrees.
So, we have:
∠ABC + ∠BAC + ∠ACB = 180
Make ∠ACB the subject
∠ACB = 180 - ∠ABC - ∠BAC
The sum of angles on a straight line is 180 degrees.
So, we have:
∠ACD + ∠ACB = 180
Make ∠ACB the subject
∠ACB = 180 - ∠ACD
Substitute ∠ACB = 180 - ∠ACD in ∠ACB = 180 - ∠ABC - ∠BAC
180 - ∠ACD = 180 - ∠ABC - ∠BAC
Subtract 180 from both sides
- ∠ACD = - ∠ABC - ∠BAC
Multiply both sides by -1
∠ACD = ∠ABC + ∠BAC
Hence, ∠ACD = ∠ABC + ∠BAC has been verified
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A man 1.8 m tall observes the angle of elevation of a tree to be 26 degrees, if he is standing bf 16 m from the tree find the height of the tree
Answers
The height of the tree is the man's height plus x.
[tex]\tan 26^{\circ}=\frac{x}{16}\\x = 16 \tan 26^{\circ}[/tex]
So, the height of the tree is [tex]\boxed{(16 \tan 26^{\circ}+1.8) \text{ m}}[/tex]
(-3, 1)
-5-4-3
(-2,-4)
k
4
4
ob
1
2-
3+
(2/2)
What is the equation, in point-slope form, of the line
that is parallel to the given line and passes through the
point (-3, 1)?
Oy-1= -2(x+3)
Oy-1=-(x+3)
Oy - 1 =
Oy-1 =
(x+3)
(x+3)
Answers
Answer:
What is the slope of the line represented by the equation y = y equals StartFraction 4 Over 5 EndFraction x minus 3.x – 3?
Step-by-step explanation:
The equation of line that is parallel to the given line having slope m = -1 and passes through the point ( -3 , 1 ) is y = -x - 2
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -3 , 1 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
The slope of the line m = -1
Now , the line is parallel to the line passing through P
So , the slopes of the lines are equal
And , the equation of line is y - y₁ = m ( x - x₁ )
On simplifying , we get
y - 1 = -1 ( x - ( -3 ) )
y - 1 = -1 ( x + 3 )
Adding 1 on both sides , we get
y = -x - 3 + 1
y = -x - 2
Hence , the equation of line is y - 1 = -1 ( x + 3 )
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Part 1 of 3
the accompanying data are 45 commute times to work in minutes for workers of age 16 or older in chicago. construct a frequency distribution. use a
the data amounts appear to have a normal distribution? examine the data and identify anything appearing to be unique.
click the icon to view the commute times.
construct the frequency distribution.
commute time
(minutes)
frequency
(type whole numbers.)
Answers
The frequency distribution has been illustrated based on the information given.
What is frequency distribution?It should be noted that frequency distribution is the representation that displays the number of observations that are in a given interval.
From the data distribution, the frequency distribution will be:
Class. Frequency
0 - 14. 5
15 - 29. 15
30 - 44. 13
45 - 59. 6
60 - 74. 5
75 - 89. 1
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Which expression has a value of 16 when n = 5?
StartFraction 25 Over n EndFraction + 7
30 minus 3 n
7 + StartFraction 45 Over n EndFraction
n cubed minus 114
Answers
The expression that has a value of 16 when n = 5 is [tex]\rm 7+ \dfrac{45}{n}[/tex] , Option C is the correct answer.
What is an Expression ?An expression is mathematical statement consisting of variables , constant and mathematical operators.
The expression given in the question is
[tex]\rm \dfrac{ 25}{n} + 7 \\\\30-3n\\\\7+\dfrac{45}{n}\\\\n^3 -114[/tex]
On solving it can be seen that
The value of 16 when n= 5 is given by
7 +45/5 = 7+9 = 16
Therefore Option C is the right answer.
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in an enlargement PQ P1Q1|PQ|=3cm and|P1Q1|=15cm.Calculate the scale of the enlargement.
Answers
Answer:
374795-57770
Step-by-step explanation:
Abby uses
HELP 100 POINTS!
Step 1- Select three sites to review:
Tombs of Buganda Kings, Aksum, &
Step 2- Create your public service announcement.
Site # 1- Name of Site, and Picture
Paragraph that includes how it relates to the African city or kingdom, and why the site is worth preserving.
Site # 2- Name of Site, and Picture
Paragraph that includes how it relates to the African city or kingdom, and why the site is worth preserving.
Site # 3- Name of Site, and Picture
Paragraph that includes how it relates to the African city or kingdom, and why the site is worth preserving.
Answers
The tomb are worth preserving as they are important to the legacy of the people.
What is a tomb?It should be noted that a tomb simply means a repository of the remains of the dead. The Tombs of Buganda Kings can be found in Uganda.
It's a royal tomb and represents the heart of the Baganda people.
In this case, the tomb are worth preserving as they are important to the legacy of the people.
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