Two ships leave the same port in different directions, forming a 120° angle between them. One ship travels 70 mi. and the other 52 mi. before they each drop their anchors. What is the distance between the ships to the nearest mile?
Answer : Distance between the ships to the nearest miles = 106.03 ≈ 106 mi.
Explanation :
Since we have shown in the figure below :
a=70 mi.
b=52 mi.
c=x mi.
[tex]\text{Since two ships leaves the same port in different directions forming a }120\textdegree\text{angle between them.}[/tex]
So, we use the cosine rule , which states that
[tex]c^2=a^2+b^2-2ab.cosC\\\\x^2=70^2+52^2-2\times 70\times 52\times cos(120\textdegree)\\\\x^2=4900+2704-7280\times (-0.5)\\\\x^2=7604+3640\\\\x^2=11244\\\\x=\sqrt{11244}\\\\x=106.03[/tex]
So, c = x= 106.03 mi.
Hence, distance between the ships to the nearest miles = 106.03 ≈ 106 mi.
10 Points Here come get them
If an object is projected upward with an initial velocity of 125 125 ft per sec, its height h after t seconds is h equals negative 16 t squared plus 125 t h=−16t2+125t. Find the height of the object after 5 5 seconds.
Does 3pi/5 have a supplementary angle?
What is decomposing fractions
Explanation:
"Decomposing fractions" means breaking them into a sum of fractions, often unit fractions (fractions with a numerator of 1). Here are a few examples:
3/8 = 1/8 + 1/8 + 1/8
5/6 = 1/2 + 1/3
3/4 = 1/2 + 1/4
What is the value of the leading coefficient a if the polynomial function P(x) = a(x + b)2(x − c) has multiplicity of 2 at the point (−3, 0) and also passes through the points (2, 0) and (0, 36)?
answers:
−2−3336
How do you solve 7.2>0.9(n+8.6)
After solving the given equation, the value obtained for n will be equal to n < -0.6.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the equation given in the question,
7.2 > 0.9(n + 8.6)
Solve the equation for n,
7.2 > 0.9n + 7.74
7.2 - 7.74 > 0.9n
-0.54/0.9 > n
-0.6 > n or,
n < -0.6
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How to find the x intercepts of f(x)=-2x^2+x+5
what is the product of (2p+7)(3p^2+4p-3)
Chris has $100 in his savings account and he adds $20 a month to the account. The total amount can be represented by the linear function T = 20x + 100. His goal is to have a total of $300 in four more months. What should he change in the function to reach this goal? A) Change the amount he adds each month to $50. B) Change the amount he adds each month to $40. C) Change the y-intercept of the linear function to $20. D) Change the y-intercept of the linear function to $50.
Answer:
Its A i did USAtestprep
Step-by-step explanation:
A
For which set of lines is it reasonable to state that The two lines are ALMOST perpendicular to each other? A) y = 2.1x + 3, y = 2.1x + 5 B) y = 0.9x + 5, y = -1.26x + 8 C) y = 5x + 1.25, y = -5x + 1.25 D) y = 3 4 x + 0.28, y = 4 3 x + 0.29
What is the beat estimate for the quotient? 591.3 device by 29
Two mechanics can assemble 10 bicycles in 8 hours. How many bicycles could one mechanic assemble in 8 hours?
Answer:
5 bicycles
Step-by-step explanation:
In the same time period (8 hours), half as many mechanics can assemble half as many bicyles: 10/2 = 5.
Algebra Functions and Data Analysis
×
[tex] \frac{x}{4} = \frac{6}{12} [/tex] solve the proportions
Mario buys 2 pounds of hamburger and 1 pound of sausage. Sausage costs 10 cents more per pound than hamburger. If the total cost of the meat is $5.50, what is the cost of the hamburger per pound?
PLEASEEEEE HEEEEEELPPPPPPPPPPPPPPP
Suppose ABCD is a rhombus such that the angle bisector of ∠ABD meets AD at point K. Prove that m∠AKB = 3m∠ABK.
1. Let m∠ABK=x°. Since line BK bisects ∠ABD, then
m∠ABK=m∠KBD=x°.
Also m∠ABD=m∠ABK+m∠KBD=2x°.
2. The diagonal BD of rhombus ABCD bisects ∠ABC, then
m∠ABD=m∠DBC=2x°.
This gives you that
m∠ABC=4x°.
3. Angles A and B are supplementary, so
m∠A+m∠B=180°,
m∠A=180°-4x°.
4. Consider triangle ABK. The sum of the measures of interior angles in triangle is always 180°, thus
m∠A+m∠ABK+m∠AKB=180°,
m∠AKB=180°-x°-(180°-4x°),
m∠AKB=3x°=3m∠ABK.
Answer:
Given information: ABCD is a rhombus, angle bisector of ∠ABD meets AD at point K.
[tex]\angle ABK\cong \angle DBK[/tex] (Definition of angle bisector)
[tex]m\angle ABK=m\angle DBK[/tex] (Definition of concurrency)
Let as assume the measure of angle ABK is x.
[tex]m\angle ABK=x[/tex]
[tex]m\angle ABD=m\angle ABK+m\angle DBK[/tex]
[tex]m\angle ABD=x+x[/tex]
[tex]m\angle ABD=2x[/tex]
All sides of a rhombus are same.
Since AB=AD, therefore ABD is an isosceles triangle and two angles of an isosceles triangle are congruent.
[tex]m\angle ADB=m\angle ABD[/tex]
[tex]m\angle ADB=2x[/tex]
According to exterior angle theorem, sum of two interior angles of a triangle is equal to third exterior angle.
Using exterior angle theorem, we get
[tex]m\angle AKB=m\angle ADB+m\angle DBK[/tex]
[tex]m\angle AKB=2x+x[/tex]
[tex]m\angle AKB=3x[/tex]
[tex]m\angle AKB=3(m\angle ABK)[/tex]
Hence proved.
The sum of the reciprocals of two consecutive even integers is 7/24. Write an equation that can be used to find the two integers. Find the two integers.
Can I have help with this please?
Try this:
2. 2.5/5=16/32; 2/4=16/34.
3. one - 6;6;6; two - 6;8;10; three - 5;10;12.
What is the equation for the vertical asymptote of f(x)= (x+2)/(4x+4)
Which of the following is equivalent to the expression below?
(8x + 10) + (13 - 8x)
A.
3
B.
8x + 23
C.
16x + 23
D.
23
f(x)=x^2-2x-1 and g(x)=5x-1/7x-3
find f(x+7) and g(x/2)
What is the value of h?
Answer:
Step-by-step explanation:
H=9 is the answer
what fraction would you add to 29/6 to make 4
152.5225 to two decimal places
There are 1,505 fruits for sale at at farmer’s market. 39% of them are apples, 28% are oranges, 13% are honeydrew melons, and the rest are watermelons. How many watermelons are there ?
Answer:
13
Step-by-step explanation:
In a local survey, 100 citizens indicated their opinions on a revision to a local land use plan. of the 62 favorable responses, there were 40 males. of the 38 unfavorable responses, there were 15 males. if one citizen is randomly selected find the probability a male and has a favorable opinion
The probability that a male and has a favorable opinion is selected is 2/5
Further explanationThe probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
Permutation ( Arrangement )Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
Combination ( Selection )Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
Let us tackle the problem.
This problem is about Probability.
Given:
Of the 62 favorable responses, there were 40 males and 22 females.
Of the 38 unfavorable responses, there were 15 males and 23 females.
There were total (40+15) males = 55 males
Let P(M) = probability a male is selected
[tex]P(M) = \frac{\texttt{Number of Male Citizens}}{\texttt{Total Number of Citizens}}[/tex]
[tex]P(M) = \boxed{\frac{55}{100}}[/tex]
There were 62 favorable responses
Let P(F) = probability citizens has a favorable opinion is selected
[tex]P(F) = \frac{\texttt{Number of Favorable Opinion Citizens}}{\texttt{Total Number of Citizens}}[/tex]
[tex]P(F) = \boxed{\frac{62}{100}}[/tex]
Let P(M ∪ F) = probability a male or citizens has a favorable opinion is selected
[tex]P(M \cup F) = \frac{\texttt{Number of Favorable Opinion Citizens or Male Citizens}}{\texttt{Total Number of Citizens}}[/tex]
[tex]P(M \cup F) = \frac{40 + 15 + 22}{100}[/tex]
[tex]P(M \cup F) = \boxed{\frac{77}{100}}[/tex]
At last , the probability a male and has a favorable opinion could be calculated as follows:
[tex]P(M \cap F) = P(M) + P(F) - P(M \cup F)[/tex]
[tex]P(M \cap F) = \frac{55}{100} + \frac{62}{100} - \frac{77}{100}[/tex]
[tex]P(M \cap F) = \frac{40}{100}[/tex]
[tex]P(M \cap F) = \large{\boxed {\frac{2}{5}} }[/tex]
Learn moreDifferent Birthdays : https://brainly.com/question/7567074Dependent or Independent Events : https://brainly.com/question/12029535Mutually exclusive : https://brainly.com/question/3464581Answer detailsGrade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
Solve for x: x^4 = 3^x
Which term is the perfect square of 3x4 ?
Answer:
just took the test answer is D
Step-by-step explanation:
What value is equivalent to ∣ −14 ∣?