Answer:
189.14 miles.
Step-by-step explanation:
This is a vector problem.
A boat sails on a bearing of 73°. This means it is going north, forming a 90° triangle.
The sum of angles in a triangle = 180°
We need to find the third angle.
180° = 90° + 73° + x°
x° = 180° - (90 + 73) °
x = 180° - 163°
x = 17°
The boat then turns and sails 209 miles on a bearing of 190 degrees.
Since it is sailing 190°, it is sailing more than 180°
= 190° - 180° = 10°
This would lead to the formation of another triangle let us call it ABC
Hence, we would have:
90° - ( 10 + 17)°
90° - 27° = 63°
To find the distance of the boat, we would use Cosine rule.
a² = b² + c² - 2bc × Cos A
a = √(b² + c² - 2bc × Cos A
b = 128 miles
c = 209 miles
A = 63°
a = √(128² + 209² -2 × 128 × 209 × Cos 63°)
a = 189.14199miles
Approximately 189.14 miles.
Therefore, the distance of the boat from it's starting point is 189.14 miles.
The sum of a number and its square is 42. Which equation can be used to find the two numbers for which this is
true?
x2 + x = 42
x2 + 2x = 42
x²+x+42=0
x² + 2x + 42=0
Answer:
x2 + x = 42
Step-by-step explanation:
x = nhmber
x² = its square
then:
The sum of a number and its square is 42 is:
x² + x = 42
how do you find the area of a circle and what is the formula for it
Answer:
Read Exp:
Step-by-step explanation:
Area = 3.14 x r^2
I've Included a picture to tell you how to get the diameter as well as the circumference.
Answer:
formula is πr² ( pi x radius squared)
Step-by-step explanation:
the value of π is 3.142...
multiply this value with the squared radius of the circle and you'll get your answer.
For example:
we have a circle with diameter 5
so, π x 5² = 3.142 x 25 = 78.5
Each table below lists the squared residuals for a line of fit for a certain set of data points. Find the sum of the squared residuals for each potential line of fit, and then determine which potential line is the true line of best fit.
c.) Square of Residual
.200
.116
.16
D) Square of Residual
.0036
.0016
.009
Answer:
c
Step-by-step explanation:
7p − p = 18 2) −5n − 4n = −9
Answer:
[tex] \boxed{ \bold{ \sf{ \boxed{ p = 3}}}} [/tex][tex] \boxed{ \bold{ \sf{ \boxed{n = 1}}}}[/tex]
Step-by-step explanation:
1. [tex] \sf{7p - p = 18}[/tex]
Collect like terms
⇒[tex] \sf{6p = 18}[/tex]
Divide both sides of the equation by 6
⇒[tex] \sf{ \frac{6p}{6} = \frac{18}{6} }[/tex]
Calculate
⇒[tex] \sf{p = 3}[/tex]
2. [tex] \sf{ - 5n - 4n = - 9}[/tex]
Collect like terms
⇒[tex] \sf{ - 9n = - 9}[/tex]
Divide both sides of the equation by -9
⇒[tex] \sf{ \frac{ - 9n}{ - 9} = \frac{ - 9}{ - 9} }[/tex]
Calculate
⇒[tex] \sf{n = 1}[/tex]
Hope I helped!
Best regards!!
Marisha walks 8 miles in 5 days. If she walks at the same rate, how far
does Marisha walk in 40 days?
Answer:
56 miles
Step-by-step explanation:
0.07 is 10 times as great as ? A.0.1 B.0.7 C.0.001 D.0.007
Answer:
D. 0.007
Step-by-step Explanation:
0.07= 10 x
= 0.07/ 10
= 0.007
Which of the following represents a constant from the expression given? 15x^2 + 2x + 9
A. 9
B. 15
C. 2
D. 24
Answer:
A) 9
Step-by-step explanation:
Hello!
A constant is a fixed and defined number.
A constant is any number that does not have a variable next to it
The only number in the equation that follows this is 9
Hope this Helps!
The constant from the expression is 9. option A
What are algebraic expressions?
Algebraic expressions are defined as expressions that are made up of variables, constants, factors and coefficients.
Also, these algebraic expressions are made up of arithmetic operations, such as;
AdditionMultiplicationDivisionBracketParenthesesSubtractionFrom the information, we have that the expression is given as;
[tex]15x^2 + 2x + 9[/tex]
We have then that;
The terms are; 15x , 2x and 9
The coefficient of x is 2
The coefficient of x² is 15
The constant is 9
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you are building a new house and need to pour 1200 cubic feet of concrete for the foundation. the concrete truck delivers concrete by the cubic yard. how much concrete do you need to buy from the concrete company?
Answer:
400 cubic yards
Step-by-step explanation:
There are three cubic feet in each cubic yard
Homer Simpson entered a pie eating contest at the county fair. Homer was determined to win and went into training for 6 days. Each
day, he ate 4 more pies than the day before. Homer ate 150 pies while in training. How many pies did he eat each day?
Day 1: type your answer...
Day 2: type your answer....
Day 4: type your answer....
Day 3: type your answer....
type your answer...
Day 5: type your answer...
Day 6: type your answer...
Answer:
151923273135Step-by-step explanation:
He ate 15, 19, 23, 27, 31, 35 pies for each day.
What is addition?Addition in math is a process of combining two or more numbers.
Given that, Homer Simpson entered a pie eating contest at the county fair. Homer was determined to win and went into training for 6 days, each day, he ate 4 more pies than the day before. Homer ate 150 pies while in training.
Let he ate x pie for 1st day, then according to question,
1st day = x
2nd day = x+4
3rd day = x+8
4th day = x+12
5th day = x+16
6th day = x+20
He ate 150 pies for 6 days
Therefore, x+x+4+x+8+x+12+x+16+x+20 = 6x + 60 = 150
6x = 90
x = 15
Hence, he ate 15, 19, 23, 27, 31, 35 pies for each consecutive day.
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Classify the numbers as rational or irrational.
6
√2.6
√2+6
Step-by-step explanation:
[tex] \sqrt 2, \: \sqrt 2. 6 \: \& \: \sqrt 2 + 6[/tex] are irrational and 6 is the only rational number.
Factoring Polynomials, please help.
Answer:
(x²)² + 2(9)x² + 9²
(x² + 9)²
Step-by-step explanation:
Given expression in the question is,
(x⁴ + 18x²+ 81)
We have to factorize this expression.
We know the formula of (a + b)² = a² + 2ab + b²
Comparing this formula with the given expression,
a = x²
b = 9²
By substituting these values in the given formula,
Therefore, (x⁴ + 18x²+ 81) = (x²)² + 2(9)x² + 9²
= (x² + 9)²
Clarence set his watch 16 seconds behind , and it falls behind 2 seconds every day . How many days behind has it been since Clarence last set his watch if the watch is 46 seconds behind
Answer:
15 days.
Step-by-step explanation:
46 - 16 = 30.
It falls 2 seconds behind each day so the number of required days
= 30 / 2 = 15.
Answer:
Step-by-step explanation:
15 days 16-40=30 the take 30/2= 15
In a photograph, Alison stands next to her brother Caleb. Alison is 4 cm tall in the photograph. Her actual height is 60 in. Caleb is 3.2 cm tall in the photograph.
What is his actual height?
(Show your work)
Answer:
Caleb's actual height is 48 inches
Step-by-step explanation:
Alison's height in the photograph= 4 cm
Caleb's height in the photograph= 3.2 cm
Alison's actual height= 60 in
Caleb's actual height=x in
60 in= 152.4 cm
Alison's height in photograph : Her actual height = Caleb's height in photograph : his actual height
4cm : 152.4cm = 3.2cm : xcm
4 / 152.4 = 3.2 / x
Cross product
4 * x = 152.4 * 3.2
4x = 487.68
Divide both sides by 4
x= 121.92 cm
121.92 cm = 48 in
Caleb's actual height is 48 in
A parent rewards a child with 50 cents for each correctly solved mathematics problem and fines the child 30 cents for each incorrectly solved problem. If the child nets $22.00 after 100 problems. How many problems were solved correctly?
Answer:
65
Step-by-step explanation:
Let c = number of correct answer.
Let i = number of incorrect answers.
There are 100 questions, so
c + i = 100
The correct answers are worth 0.5c.
The incorrect answers are worth -0.3i (a negative value because 30 cents is taken away for each incorrect answer)
The total worth of the answers is 0.5c - 0.3i. The total worth of the answers is $22.00, so the second equation is
0.5c - 0.3i = 22
We have a system of two equations in 2 unknowns:
c + i = 100
0.5c - 0.3i = 22
We'll use the substitution method to solve the system of equations.
Solve the firt equation for c:
c = 100 - i
Now substitute 100 - i for c in the second equation.
0.5(100 - i) - 0.3i = 22
50 - 0.5i - 0.3i = 22
-0.8i = -28
i = 35
c = 100 - i
c = 100 - 35
c = 65
Answer: 65 problems were solved correctly.
40 ➗ [24 - 4 x (2 + 3) ]
What is the value of this expression?
Answer: this is your answer
10
_____
6-5x
Answer:
1.7-20x OR 10/6-5x
Step-by-step explanation:
40÷(24-4x(2+3))
first you add the last set of ()
40÷(24-4x(5))
then you multiply by 4x
40÷(24-20x)
since you can't subtract those two you do this
40÷24-20x
divide 40 and 24
you get 1.66666667 then you round up
1.7-20x
ORyou put 40/24-20x
divide the top and the bottom by 4
(40÷4)/(24÷4) -(20x÷4)
and your answer will be
10/6-5x
When the solution of x2 + 9x - 9 is expressed as
9&
2
what is the value of r?
X
-btvb2 - 4ac
2a
117
O 54
045
09
answer
r = b²-4ac
= 81 + 36
= 117
how do you break down 213 in times
Answer:2 hundred+1 tens+3 ones
Step-by-step explanation:
The calorie count of a serving of food can be computed based on its composition of carbohydrate, fat, and protein. The calorie count C for a serving of food can be computed using the formula C = 6h + 11f + 7p, where h is the number of grams of carbohydrate contained in the serving, f is the number of grams of fat contained in the serving, and p is the number of grams of protein contained in the serving. Solve this formula for f, the number of grams of fat contained in a serving of food.
Answer:
see below (I hope this helps!)
Step-by-step explanation:
C = 6h + 11f + 7p
Get all non-f terms on one side:
C - 6h - 7p = 11f
Divide by 11:
f = [tex]\frac{C - 6h - 7p}{11}[/tex]
26.9 microgram/milliliter to hectograms/deciliter
Answer:
.0000269 hectograms/ deciliter
2.69 * 10^e-5 hectograms/ deciliter
Step-by-step explanation:
micro grams to hectograms
10^8 micrograms = 1 hectogram
milliliters to deciliter
100 milliliters = 1 deciliter
Using conversion factors
26.9 microgram 1 hectogram 100 milliliters
----------------------- * --------------------------- * ---------------------
milliliter 10^8 micrograms 1 deciliter
2690 hectograms
---------------------------
10^8 deciliters
.0000269 hectograms/ deciliter
2.69 * 10^e-5 hectograms/ deciliter
In the accompanying diagram, a right circular cone is carved out of a solid foam cylinder and discarded. What is the volume of the foam remaining in the cylinder?
A. 150π cubic units
B. 125π cubic units
C. 100π cubic units
D. 50π cubic units
Answer:
100π cubic units is left
Step-by-step explanation:
πr²h - 1/3πr²h
π(5)²(6) - 1/3π(5)²(6)
150π - 50π = 100π
The volume of the foam is 100π cubic units remaining in the cylinder.
Given,
Radius of cone (r) = 5
Height of cone (h) = 6
What is the volume of a cone?The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.
∵ The volume of the cone (V )= 1/3πhr²
To determine the volume of the foam remaining in the cylinder
Subtract the volume of the cone into the volume of the cylinder
⇒ πr²h - 1/3πr²h
Substitute the values of h and r,
⇒ π(5)²(6) - 1/3π(5)²(6)
⇒ 150π - 50π
⇒ 100π
Hence, The volume of the foam is 100π cubic units remaining in the cylinder.
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Coleman uses his graphing calculator to find all of the solutions to the equation shown below.
23 + 3 = -24 + 4
What are ALL of the solutions to the equation, rounded to the nearest hundredth?
A.
x = 0.82 and 3.55
B. O x = -1.38 and 0.37
C.
x = 0.37 and 3.55
D.Ox=-1.38 and 0.82
Answer:
The correct option is;
D. x = -1.38 and 0.82
Please find attached the combined function chart
Step-by-step explanation:
The given equation is x³ + 3 = -x⁴ + 4
Plotting the equation using Excel, we have;
f(x) = x³ + 3, h(x) = -x⁴ + 4
x f(x) h(x)
-1.4 0.256 0.1584
-1.39 0.314381 0.26699
-1.38 0.371928 0.373261
-1.37 0.428647 0.477246
-1.36 0.484544 0.57898
Which shows an intersection at the point around -1.38
x f(x) h(x)
0.77 3.456533 3.64847
0.78 3.474552 3.629849
0.79 3.493039 3.610499
0.8 3.512 3.5904
0.81 3.531441 3.569533
0.82 3.551368 3.547878
0.83 3.571787 3.525417
Which shows the intersection point around 0.82
Therefore, the correct option is x = -1.38 and 0.82
From the graphing calculator the intersection point is given as
x = -1.3802775691 and 0.81917251339.
Only two four and eight
Answer:
2. -6
4. 0
8. 2
Step-by-step explanation:
Order of Operations: BPEMDAS
2
Step 1: Write out expression
-(8 - 2)
Step 2: Parenthesis (Subtract)
-(6)
Step 3: Multiply
-6
4
Step 1: Write out expression
-(0 + 0)
Step 2: Parenthesis (Add)
-(0)
Step 3: Multiply
0
8
Step 1: Write out expression
3 - [-(-1)]
Step 2: Brackets (Multiply)
3 - 1
Step 3: Subtract
2
area of a triangle two sides of which are 18 cm and 12 cm
and the perimeter is 44 cm.
Answer:
≈ 83.9 cm²
Step-by-step explanation:
Given:
P = a+b+c = 44 cma = 18 cmb = 12 cmThen:
c= P -(a+b) = 44 -(18+12) = 14 cmArea of the triangle is found by using Herons formula:
A = √s(s-a)(s-b)(s-c),where s = P/2 = 44/2 = 22 cm
A = √22(22-18)(22-12)(22-14) = √22*4*10*8= √7040 ≈ 83.9 cm²Answer:
[tex]\huge \boxed{\mathrm{83.9 \ cm^2}}[/tex]
Step-by-step explanation:
Two sides of the triangle are given.
The perimeter is given.
We need to solve for the third side.
[tex]P=a+b+c[/tex]
[tex]P= \sf perimeter[/tex]
[tex]a,b,c= \sf side \ lengths[/tex]
[tex]44=18+12+c[/tex]
[tex]c=14[/tex]
The measure of the third side is 14 cm.
When three sides of the triangle are given, we can solve for the area using Heron’s formula.
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]s=\sf semi \ perimeter[/tex]
[tex]\displaystyle s=\frac{P}{2} =\frac{44}{2} =22[/tex]
Plugging in the values and evaluating.
[tex]A=\sqrt{22(22-18)(22-12)(22-14)}[/tex]
[tex]A = 83.904708...[/tex]
The area of the triangle is approximately 83.9 cm².
A store reduces the price of a jacket by 40%. The sale price of the jacket is marked as $30. What percent of the original price is the sale price? What was the original price of a jacket?
Answer:
-60%
-$50
Step-by-step explanation:
As the statement says that the price of the jacket was reduced by 40%, to determine the percent that the sale price represents from the original price, you have to subtract 40% from 100% that represents the original price:
100%-40%= 60%
This means that $30 represents 60% of the original price.
-To determine the original price of the jacket, you can use the rule of three:
$30 → 60%
x ← 100%
x=(100*30)/60= 50
According to this, the original price of a jacket was $50.
Hello I was wondering if you can help me list these from least to greatest
Answer:
See below.
Step-by-step explanation:
Convert to decimal form
7 3/5 = 7.6
7 7/10 = 7.7
10 2/5 = 10.4
8 1/2 = 8.5
So the answer is
7 3/5 , 7 7/10, 8.3, 8.1/2, 10.2 10 2/5, 11.1.
Which choice shows the product of 22 and 39?
(22)(39) = 858
22 x 39 = 748
22 + 39 = 61
22. 39 = 648
Answer: (22)(39) = 858.
Step-by-step explanation:
Product of a number simply means that one has to multiply the numbers that are given. For example, if a student is told to find the product of 2 and 5, it simply means that 2 × 5 = 10.
Regarding the above question, the product of 22 and 39 is represented by: (22)(39) = 858. It should be noted that 22 × 39 = 858
Jacob spent $35.40 to fill up 15 gallons of gas in his pick-up truck. How much does 6 gallons cost?
Answer:
$14.16 for 6 gallons.
Step-by-step explanation:
35.40/15 = 2.36
2.36*6 = 14.16
is -7 a rational number
Quick please -4 (-2x - 4)
Answer:
-10x
Step-by-step explanation:
-2x-4=-6x
-4-6x = -10x
Answer:
x = -2
Step-by-step explanation:
To solve for x:
Equation: -4(-2x - 4) = -8x - -16-8x - -16 = -8x + 16Divide each side by -8 so it now looks like this: x = -2Therefore, x equals -2.
To simplify the equation:
-2x - 4 = -6x-4(-6x) = 24xNeed help! With both, please please help!