The length of the side CD is 5.195 cm and the Area of ΔABC is 31.17 cm²
How to use trigonometric ratios?
The basic trigonometric functions are;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the given triangle ABC, we can see that it is a right angle triangle where ∠ACD = 60°, and as such, ∠CAD = 30°.
Thus;
BC/AC = tan 30°
6/AC = 0.5774
AC = 10.39cm
Thus;
CD/AC = cos 60
CD = 10.39 * 0.5
CD = 5.195 cm
Formula for area of a triangle is;
Area = ¹/₂ * base * height
Area = ¹/₂ * 6 * 10.39
Area = 31.17 cm²
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“Find 3.4 x 2.6 by drawing an area diagram. Show your reason (I need help on this-
The area is 8.84 sq. units
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
To find the area we will find the product of 3.4 x 2.6, we can break each length into its base-ten units,
3.4 = 3+0.4
2.6 = 2+0.6
We can rewrite the product and solve it,
= (3+0.4) × (2+0.6)
= (3+0.4) × 2 + (3+0.4) × 0.6
= 3 × 2 + 0.4 × 2 + 3 × 0.6 + 0.4 × 0.6
This expression represents the partial product, each of the expression gives the area of sub rectangles (A, B, C and D). the sum of the partial product will give the area of the main rectangle.
Therefore,
3 × 2 + 0.4 × 2 + 3 × 0.6 + 0.4 × 0.6
= 6+0.8+1.8+0.24
= 8.84
Hence, the required area is 8.84 sq. units.
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Find the area and perimeter of the triangle
Answer: 25.2
Step-by-step explanation: hope the is helps :D
On Saturday, a local hamburger shop sold a combined total of 396 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Let x be the number of hamburgers sold, then the number of cheeseburgers sold can be represented as 2x. The total number of hamburgers and cheeseburgers sold is the sum of these two quantities, so we can write an equation:
x + 2x = 396
To solve for x, we can combine like terms on the left side of the equation:
3x = 396
Then we can divide both sides by 3 to get:
x = 132
So, the number of hamburgers sold on Saturday is 132.
f(x)=3^x+1 and g(x) = 2x-4, find f(2) - g(-1)
Answer:
16
Step-by-step explanation:
3^x +1 = f(X)
2x-4 = g(x)
find f(2)-g(-1)
we substitute in function f(X) by value (2), and in function g(X) by value (-1)
1. 3^x +1 becomes 3^2+1 =9+1=10
2. 2(-1)-4= -2-4=-6
then f(2)-g(-1)
= 10-(-6) =10+6=16
Please help (the value are 50 and 45
Answer:
85 degrees
Step-by-step explanation:
Angle DEC = 50 degrees (vertically opposite angles are equal).
So angle CDE= 180-45-50=85 degrees (angles in triangle sum to 180).
Because they are similar x = 85 degrees
In response to rising concerns about identity theft, the number of models of paper
shredders a company manufactures increased approximately steadily from 5 models
in 1993 to 34 models in 2005. Find the average rate of change of the number of
shredder models manufactured per year between 1993 and 2005.
The average rate of change of the number of paper shredders manufactured per year
between 1993 and 2005 was 0.41
(Type an integer or decimal rounded to two decimal places as needed.)
Customary American Units of Capacity
1 cup = 8 ounces
1 pint = 2 cups or 16 ounces
1 quart = 2 pints, 4 cups, or 32 ounces
1 gallon = 4 quarts, 8 pints, 16 cups, or 128 ounces
9 cups = ___ pints ____ cups
20.945649350649 c = 9 dry pt, Four pints equal nine cups. The metric system uses the litre and millilitre as the units of capacity. By dividing by 11000, we may convert millilitres into litres.
What is the US customary unit for capacity?In the United States, ounces, cups, pints, quarts, and gallons are the commonly used measurement units for capacity or volume. Cups, pints, quarts, and gallons are some of the volume or capacity measuring units used in the United States. 8 fluid ounces are the equivalent of 1 cup. There are 2 cups in a pint. 1 quart equals 2 pints.
The solution is clear cut and simple to remember when dealing with liquids. Eight fluid ounces make up one cup, which is the unit of measurement for liquids. Every liquid has this property. The solution is clear cut and simple to remember when dealing with liquids. Eight fluid ounces make up one cup, which is the unit of measurement for liquids. For all liquids, this is true. 4 pints are equal to 9 cups.
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Expand and simplify
(x-2)(2x+3)(x+1)
Answer:
2x³ + x² - 7x - 6
Step-by-step explanation:
(x-2)(2x+3)(x+1)
first: (x-2)(2x+3) = 2x² + 3x - 4x -6 = 2x² - x - 6
second: (2x² - x - 6)(x+1) = 2x³ + 2x² - x² - x - 6x - 6 = 2x³ + x² - 7x - 6
Answer:
(x-2) [(2x+3)(x+1)]
(x-2)[(2x²+2x+3x+3)]
(x-2)[(2x²+5x+3)]
(x-2) (2x²+5x+3)
2x³+5x²+3x-4x²-10x-6
Answer = 2x³+x²-7x-6
Please help me due today
Answer:
To find the answer consider that this is a right triangle and we can use the tangent function in order to find the value of x
remember the acronym soh cah toa.
to use the tangent function we divide the opposite and adjacent side that is what the oa stands for in toa
setting it up looks like this
tan 72° = [tex]\frac{x}{8\\}[/tex]
solving for x gives us x= 8×tan 72°
which is about 24.62
Step-by-step explanation:
Solve for x
answer needs to be fraction
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Answer:
9/8
Step-by-step explanation:
The triangles are similar, so corresponding sides are proportional.
AB/CB = AD/ED
x/1 = (x+9)/9
9x = x +9 . . . . . . multiply by 9
8x = 9 . . . . . . . . .subtract x
x = 9/8 . . . . . . . . divide by 8
Tracy puts $3,500 into an investment yielding 4.5% annual interest. She left the money in for 8 years and 3 months. How much interest does she get in that time
Tracy gets $1299.375 interest after 8 years and 3 months for an investment of $3,500 at a 4.5% annual interest rate.
What is Simple Interest?
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
The formula for calculating Simple Interest is -
S.I. = (P×R×T)/100
where, P = initial principal balance, R = annual interest rate and T = time (in years)
So, the principal rate, P = $3,500, the interest value, R = 4.5%, and the Time is T= 8.25 years.
Applying the formula for Simple Interest -
S.I. = (P×R×T)/100
S.I. = (3500×4.5×8.25)/100
S.I. = 1299.375
Therefore, the interest amount obtained is $1299.375.
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Which equation is equivalent 2^4x=8^x-3
a biking track has a length of 2376 feet. how long is this in miles
Answer:0.45 miles
Step-by-step explanation:
Conversion
A roller coaster begins at ground level, rises 63 feet, then falls 71 feet. What is the
elevation of the roller coaster, relative to the ground? *
134 feet
8 feet
- 8 feet
- 134 feet
Answer:
-8 feet
Step-by-step explanation:
63 - 71 = -8
A student takes a multiple choice exam with 10 questions, each with four possible selections for the answer. A passing grade is 60% or better. Suppose that the student was unable to find time to study for the exam and just guesses at each question. Identify the probability that the student gets exactly one question correct.
a. 0.00157
b. 0.00004
c. 0.0023
d. None of the given answers
Please solve the ques. below
The velocity of the train is given as follows:
900 m / min.
How to obtain the velocity of the train?To obtain the velocity of the train, we must understand the relation between velocity, distance and time, which is given as follows:
v = d/t.
In which the parameters are given as follows:
v is the velocity.d is the distance.t is the time.The train took a difference of 200 m in 15 seconds = 0.25 minutes, hence the difference in velocities is given as follows:
200/0.25 = 800 m / min.
(the difference in velocity is the distance covered divided by the time).
As Uncle Tony is walking at a rate of 100 m / min, the velocity of the train is calculated as follows:
800 + 100 = 900 m / min.
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50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
Correct answer is 8.2
I see 5 points instead of 50 pointssssss
Give 50, otherwise I will report u
Practice: Determining if a Relation is a Function the Siven is not a funcr...l
since the element in the domain is repeated!
1) {(-1, 8), (0, 15), (1,-4), (2, 0)}2) {(-5,2), (5, 2), (0, -3), (3, -8)} 3) {(-2,7), (6,2), (-2,-3), (0, 9)}
it is a function
because there is not any
Points which have the
X-Coordinate and differe
y-Coordinates.
4) {(7.2), (4,-6), (2,-2). (4,-9)} 5) {(2, 3), (2, 4), (2, 5), (2.6)}
6) {(1,-4), (2,-4), (3, 4), (4-4)}
On solving the provided question, we can say that - here in the function, every element has an unique image
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
every element has an unique image and,
this relation, is not a function, since it is not one-one and onto.
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1.1.2 Quiz: What Is Health?
Question 2 of 10
In order to maintain wellness, the parts of the health triangle always need to
be
Select two responses.
and
A. working together
B. apart from one another
C. independent of one another
D. in balance
Answer:
The World Health Organization (WHO) defines health as 'a state of complete physical, mental and social wellbeing and not merely the absence of disease or infirmity'
25x25=625 took the test
Answer: Correct
Step-by-step explanation:
Joe is building a fort for his little brother out of boxes. He is wondering how much room there will be inside the fort.
How much space is inside the fort?
Give an exact answer (do not round).
Find the midpoint and distance between (-3,10) and (15,-2)
The midpoint and distance between (-3,10) and (15,-2) are ( 6,4 ) and 6√13 respectively.
What is the midpoint and distance between the given coordinates?The midpoint formula is expressed as;
[ (x₁ + x₂)/2, (y₁ + y₂)/2 ]
The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
Given the data in the question;
Point 1(-3,10)
x₁ = -3y₁ = 10Point 2( 15,-2 )
x₂ = 15y₂ = -2Plug the given values into the midpoint formula and simplify.
[ (x₁ + x₂)/2, (y₁ + y₂)/2 ]
[ ( -3 + 15)/2, ( 10 + (-2) )/2 ]
[ ( 12)/2, ( 10 - 2 )/2 ]
[ ( 12)/2, ( 8 )/2 ]
( 12/2, 8/2 )
( 6,4 )
Therefore, the midpoint is (6,4).
Plug the given values into the distance formula and simplify.
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
D = √( ( 15 - (-3) )² + ( -2 - 10 )² )
D = √( ( 15 + 3 )² + ( -2 - 10 )² )
D = √( ( 18 )² + ( -12 )² )
D = √( 324 + 144 )
D = √( 468 )
D = 6√13
Therefore, the distance between the points is 6√13.
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Consider two stocks. Stock 1 always sells for $10 or $20. If stock 1 is selling for $10 today, there is a .80 chance that it will sell for $10 tomorrow. If it is selling for $20 today, there is a .90 chance that it will sell for $20 tomorrow. Stock 2 always sells for $10 or $25. If stock 2 sells today for $10, there is a .90 chance that it will sell tomorrow for $10. If it sells today for $25, there is a .85 chance that it will sell tomorrow for $25. On the average, which stock will sell for a higher price? Find and interpret all mean first passage times.
Answer:
On stock 2 will be has an average sell of $50 for higher price.
Step-by-step explanation:
stock 1 of $10 (today)+ $10 (80% chance tommorow)=$20 stock sell price and for $20(today)+$20(90% chance tommorow)= $40 this two final of price for stock 1.
Stock 2 of $10 (today)+$10(90% chance tommorow)= $20 and of $25(today)+$25(85% chance tomorrow)= $50 this two for final of it's price for stock 2.So as for Stock 2 has the average sell higher price.
Hope this helps you
PLEASE HELP!!
Angle three is the angle of elevation from the tree to the ship?
Angle three is the angle of depression from the tree to the ship?
Angle three is the angle of depression from the ship to the tree?
Angle three is the angle of elevation from the ship to the tree?
What is the expression?
Answer:
F=1.8C+32
113°F
Step-by-step explanation:
F=1.8C+32
F=1.8(45)+32
F=81+32
F=113
Answers:
The expression is 1.8C+32The given Celsius temperature converts to 113 degrees Fahrenheit==================================================
Explanation:
C = temperature in Celsius
1.8C = multiply C by 1.8
1.8C+32 = add on 32
The expression 1.8C+32 is the first part of the answer.
This represents the temperature in Fahrenheit.
----------
Now replace C with 45 and use the order of operations (PEMDAS) to simplify
1.8*C + 32
1.8*45 + 32
81 + 32
113
Therefore, 45 degrees Celsius converts to 113 degrees Fahrenheit.
(3x −5)^2 =(? + ?? +25)
Answer:
x = 3.556 or [tex]\frac{32}{9}[/tex]
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation:
(3*x-5)^2-((x+x+25))=0
Evaluate:
[tex](3x-5)^{2}[/tex] = [tex]9x^{2} -30x+25[/tex]
Pull like factors:
9x^2 - 32x = x • (9x - 32)
x • (9x - 32) = 0
Remember roots of a product:
A product of several terms equals zero. When a product of two or more terms equals zero, then at least one of the terms must be zero. We shall now solve each term = 0 separately. In other words, we are going to solve as many equations as there are terms in the product. Any solution of term = 0 solves product = 0 as well.
Solve : 9x - 32 = 0
Add 32 to both sides of the equation :
9x = 32
Divide both sides of the equation by 9:
x = 32/9 = 3.556
For the following geometric sequence, find the recursive formula.
(-80, 20, -5, ...)
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Answer:
a[1] = -80a[n] = -a[n-1]/4Step-by-step explanation:
The first term is -80, so the first part of the recursive definition is ...
a[1] = -80
The common ratio is 20/-80 = -1/4, so the recursive rule is ...
a[n] = (-1/4)a[n-1]
I need help with this
Answer:
im confusled
Step-by-step explanation:
1.an=5n+5
A1 A2 A3
2.An=6n²+3
A1 A2 A3
Answer:
a1=11
a2=15
a3=20
a1=9,a2=27,a3=57
Answer:
#1aₙ = 5n + 5
a₁ = 5*1 + 5 = 10a₂ = 5*2 + 5 = 15a₃ = 5*3 + 5 = 20#2aₙ = 6n² + 3
a₁ = 6(1²) + 3 = 9a₂ = 6(2²) + 3 = 27a₃ = 6(3²) + 3 = 57Find the length of the line segment shown below.
The line segment AB is d = [tex]\sqrt{106}[/tex] in length if (-5, 4) and (B), and A = (-5 , 0) . A line segment is hence a section or component of a line with two endpoints.
what is line segment ?A line segment in geometry is bordered by two separate points on a line. A line segment has two fixed or distinct endpoints, whereas a line has no endpoints and can stretch in both directions indefinitely. A line segment is hence a section or component of a line with two endpoints. A line segment, unlike a line, has a set length. Measuring the length of a line segment can be done using either metric measurements, such as millimeters or centimeters, or conventional measurements, such as feet or inches.
given
d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
(5 )2 + ( 9 ) 2 = d
d = 25 + 81
d = [tex]\sqrt{106}[/tex]
The line segment AB is d = [tex]\sqrt{106}[/tex] in length if (-5, 4) and (B), and A = (-5 , 0)
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