PLEASE HELP WILL GIVE BRAINLIEST
a boat would like to cross the river using the most direct route because of the current the boat must aim upriver as shown in the diagram to the nearest degree what is the angle the boat should head Upstream
19 degrees south of west
71 degrees south of west
19 degrees north of west
71 degrees north of west
Answers
The answer is:
According to the picture, the angle that the boat should head upstream is 19° north of west.
Why?From the figure, we can see that there is a right triangle formed, and since we know its hypothenuse and its opposite side, we can use the following trigonometric relation:
[tex]Sin(\alpha)=\frac{opposite}{hypothenuse}[/tex]
We are given that:
[tex]opposite=6\\hypothenuse=18[/tex]
So, substituting and calculating, we have:
[tex]Sin(\alpha)=\frac{6}{18}[/tex]
[tex]Arcosin(Sin(\alpha))=Arcsin(\frac{6}{18})\\\\\alpha =19.47\°[/tex]
Therefore the angle that the boat should head upstream is 19°, but since speeds and direction and involved, we need to look for the direction, we can see that the vertical speed is due to north, and the horizontal speed is due to west, knowing that, we can conclude that the resultant speed will be due to north of west.
Hence, according to the picture, the angle that the boat should head upstream is 19° north of west.
Have a nice day!
Related Questions
Find the radius of a sphere with a surface area of 1024π square inches
Answers
Answer:
R = 16 inStep-by-step explanation:
The formula of a Surface Area of a sphere:
[tex]S.A.=4\pi R^2[/tex]
R - radius
We have
[tex]S.A.=1024\pi\ in^2[/tex]
Substitute:
[tex]4\pi R^2=1024\pi[/tex] divide both sides by π
[tex]4R^2=1024[/tex] divide both sides by 4
[tex]R^2=256\to R=\sqrt{256}\\\\R=16\ in[/tex]
To find the radius of a sphere when you are given the surface area, you can use the formula for the surface area of a sphere, which is:
\[ \text{Surface area of a sphere} = 4 \pi r^2 \]
where \( r \) is the radius of the sphere. Now, let's solve for \( r \) using the surface area provided:
We are given that the surface area is \( 1024 \pi \) square inches, so we set that equal to the formula for the surface area:
\[ 1024 \pi = 4 \pi r^2 \]
To solve for \( r^2 \), we first divide both sides of the equation by \( 4 \pi \):
\[ \frac{1024 \pi}{4 \pi} = \frac{4 \pi r^2}{4 \pi} \]
On simplifying the left-hand side and cancelling \( 4 \pi \) from the right-hand side, we get:
\[ 256 = r^2 \]
Now, to solve for \( r \), we take the square root of both sides:
\[ r = \sqrt{256} \]
This results in:
\[ r = 16 \]
So, the radius of the sphere is 16 inches.
Solve x2 – 8x = 3 by completing the square. Which is the solution set of the equation?
Answers
Answer:
x = 4 ± [tex]\sqrt{19}[/tex]
Step-by-step explanation:
Given
x² - 8x = 3
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 4)x + 16 = 3 + 16
(x - 4)² = 19 ( take the square root of both sides )
x - 4 = ± [tex]\sqrt{19}[/tex] ( add 4 to both sides )
x = 4 ± [tex]\sqrt{19}[/tex]
Final answer:
To solve the equation x^2 - 8x = 3 by completing the square, we first rearrange the equation, add 16 to both sides to form a perfect square, and then take the square root of both sides resulting in the solution set {4 + √19, 4 - √19}.
Explanation:
Completing the Square Method
To solve the equation x2 − 8x = 3 by completing the square, follow these steps:
Move the constant term to the right side of the equation: x2 − 8x = 3 becomes x2 − 8x − 3 = 0.Add ½ of the coefficient of x, squared, to both sides to complete the square: The coefficient of x is -8, so ½ of -8 is -4, and (-4)2 is 16. Thus, add 16 to both sides: x2 − 8x + 16 = 3 + 16.Now the equation is (x − 4)2 = 19, which shows a perfect square on the left.To find the value of x, take the square root of both sides: x − 4 = ±√19.Add 4 to both sides to solve for x: x = 4 ±√19.
The solution set for the equation is {4 + √19, 4 − √19}.
How do I count by twelfths
Answers
12, x 1 = 12
12 x 2 =24
12 x 3 = 36
12 x 4 =48
12 x 5= 60
12 x 6 =72
12 x 7 = 84
12 x 8= 96
12 x 9= 108
12 x 10 = 120
12 x 11=132
12x 12= 144
hope this helps
Please help ASAP my grade is so dependent on this and I need help I’m so lost
Answers
Answer:
see explanation
Step-by-step explanation:
Given
[tex]\frac{x}{4}[/tex] > - 16 ( multiply both sides by 4 )
x > - 64
To show the solution on a number line
Place an open circle ( indicating x ≠ - 64 ) at - 64
greater than - 64 is to the right of - 64 , hence the direction of the shaded line points to the right of - 64
Tell me if you have troubles understanding something!
Please Help Quickly!!
A box contains red, blue, green, purple, and yellow crayons such that the probability of drawing a purple crayon is 3/7.
Answers
Answer:
Option C.
Step-by-step explanation:
It is given that a box contains red, blue, green, purple, and yellow crayons such that the probability of drawing a purple crayon is 3/7.
We draw two crayons randomly such that both draws are independent.
Let X be a random variable that assigns the number of purple crayons to each outcome.
We need to find the range of X.
If no purple crayon is selected, then X=0
If 1 purple crayon is selected, then X=1
If 2 purple crayons are selected, then X=2
The range of X is {0,1,2}.
Therefore, the correct option is C.
Write a polynomial function in factored form with zeros at −2, 5, and 6.
Answers
Answer:
f(x) = (x + 2)(x - 5)(x - 6)
Step-by-step explanation:
given the zeros of f(x) are x = a, x= b and x = c, then the factors are
(x - a), (x - b) and (x - c)
The function is then the product of the factors
f(x) = (x - a)(x - b)(x - c)
Here zeros are x = - 2, x = 5 and x = 6, thus the factors are
(x + 2), (x - 5) and (x - 6), so
f(x) = (x + 2)(x - 5)(x - 6) ← in factored form
Final answer:
To create a polynomial with zeros at -2, 5, and 6, the factored form is (x + 2)(x - 5)(x - 6).
Explanation:
To write a polynomial function in factored form with zeros at −2, 5, and 6, we start by creating factors based on these zeros. Each zero corresponds to a factor of the polynomial where the variable x is set equal to the zero value. Therefore, the factors would be (x + 2), (x - 5), and (x - 6). We then multiply these factors together to get the polynomial.
The factored form of the polynomial is then (x + 2)(x - 5)(x - 6). If you wanted to write this polynomial in standard form, you would expand the factors to get x³ - 9x² + 4x + 60.
graph from liner standard form 3x+2y=12?
Answers
Answer:
See picture below.
Answer:
Graph??
Step-by-step explanation:
I can't really graph, but the answer to this is...
[tex]3x+2y=12\\\\2y=3x+12\\\\y=\frac{3}{2} x+6[/tex]
I divided all by 2 to get y
[tex]y=\frac{3}{2} +6\\\\(2,9) -- (x,y)[/tex]
how much interest is earned on a principal of $575 invested at an interest rate of 7% compounded annually for nine years?
Answers
Answer:
$482.11 in interest
Step-by-step explanation:
Use the compound amount formula. Calculate the compound amount and then subtract the principle to find the amount of interest earned.
A = P(1 + r)^t, where r is the interest rate as a decimal fraction
This becomes:
A = $575(1 + 0.07)^9, or A = $1057.11.
Subtracting the principal: A - P: $1057.11 - $575 = $402.11
The total interest earned is $482 on a principal of $575 invested at an interest rate of 7% compounded annually for nine years
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = P(1 + r/100)ⁿ.
Where, A = amount, P = principle, r = rate, and n = time in years.
Given, P = $575, n = 9 and r = 7%.
∴ A = 575(1 + 7/100)⁹.
A = 575(1.07)⁹.
A = 575(1.84).
A = 1057.
So, Interest earned is (A - P) = (1057 - 575) = $482.
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12 _ (7 - 4) +5 _ 3 = 19
Answers
The first blank is "division" and the second blank is "multiplying"
12 / (3) = 4
5 x 3 = 15
15 + 4 = 19
The student's equation 12 _ (7 - 4) + 5 _ 3 = 19 is solved by inserting addition after 12 and subtraction after 5, resulting in 12 + (7 - 4) + 5 - 3. Following correct order of operations, we get the desired result of 19.
Explanation:The student has presented a mathematical equation with missing operations that needs to be solved to equal 19. To find the correct operations, we can see that 12 with an addition operation followed by 5 minus 3 gives us 14. Adding this to the original 12 gives us the desired result of 19. Hence, the missing operations are addition after the 12 and subtraction after the 5.
The equation now looks like 12 + (7 - 4) + 5 - 3 = 19. Here, we first perform the operation inside the parentheses, which is 7 - 4 = 3. Then, we substitute this result into the expression and proceed with the operations: 12 + 3 + 5 - 3. Next, we add the numbers together, which gives us 12 + 3 + 5 = 20, and finally deduct 3 to get 20 - 3 = 19.
This kind of problem teaches us the significance of operation placement within equations, as seen in different examples provided. Understanding the properties of arithmetic operations and the correct application of the order of operations (parentheses, exponents, multiplication and division, addition and subtraction) is crucial for solving such mathematical puzzles.
Solve the equation x2 - 2x - 7= 0 by using
the quadratic formula.
Answers
B is the correct choice
We used the quadratic formula (-b ± √(b² - 4ac) / 2a) to solve the quadratic equation x² - 2x - 7 = 0. We identified a, b, and c from the equation, plugged them into the formula, and solved for x to find the roots of the equation.
Explanation:The subject of your question involves solving the equation
x2 - 2x - 7 = 0
using the
quadratic formula.
This is a task in Algebra, a branch of Mathematics. The quadratic formula is a tool for solving equations of the form
ax² + bx + c = 0
, also known as quadratic equations. If we apply the quadratic formula, which is -b ± √(b² - 4ac) / 2a, to solve for your equation, we start by identifying a = 1, b = -2, and c = -7 from your equation. Substituting these into the formula gives:
x = [2 ± √((-2)² - 4*1*(-7))] / 2*1
After simplifying the above, we will get the solutions for x which are the roots of the quadratic equation.
We used the quadratic formula to solve the algebraic equation x2 - 2x - 7 = 0.
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what is the value of t=1
Answers
Answer:
B. 7
Step-by-step explanation:
When you solve the series for each term, you get 4 + 2 + 1 = 7
Answer:
A
Step-by-step explanation:
cjvjfgxgxhzjxjcjgkfifjffifi
Answers
Answer:
∛x^4
Step-by-step explanation:
x^(4/3) = ∛x^4
Last option is the answer
Determine whether the two figures are similar if so give the similarity ratio of the smaller figure to the larger figure figures are not drawn to scale
Answers
[tex]\bf \cfrac{\textit{small prism}}{\textit{large prism}}\qquad \qquad \stackrel{~\hfill \textit{yes 1:4}}{\cfrac{18}{72}\implies \boxed{\cfrac{1}{4}}\qquad \cfrac{4}{16}\implies \boxed{\cfrac{1}{4}}\qquad \cfrac{3}{12}\implies \boxed{\cfrac{1}{4}}}[/tex]
The figures are same and the ratio of the adjacent sides of the small rectangular prism to big is 1:4 option first is correct.
What is a cuboid?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape.
As we can see in the figure two three-dimensional figures are given.
To know whether the two figures are similar or not we first find the ratio of the adjacent sides.
4/16 = 1/4
3/12 = 1/4
18/72 =1/4
The ratios are equal that's why the two figures are same, and the ratio is: 1:4
Thus, the figures are same and the ratio of the adjacent sides of the small rectangular prism to big is 1:4 option first is correct.
Learn more about the cuboid here:
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Please assist, thank you.
Answers
Answer:
392 ft²
Step-by-step explanation:
Break this area into two parts, that is, into two trapezoids. The first trapezoid, on the left, has length 8 ft and average length (30 ft + 27 ft)/2, so its area is (8 ft)(28.5 ft) = 228 ft ².
The second trapezoid has width 8 ft and average length (19 + 22)/2 ft, or 8 ft by 20.5 ft). The area of this part is 164 ft².
Thus, the total area is 164 ft² + 228 ft², or 392 ft²
flip your phone sideways to view the question
Answers
Answer:
- 160 I think
Step-by-step explanation
I think i'm right but there are
200 blocks and there are 40 left out so then i did 40 - 200 = -160
What is the value of x?
Answers
Check the picture below.
Help please on both please
Answers
On what I don’t see anything on here
Solve for m -3+m/9=10
Answers
-3+m/9=10
Add 3 to both sides:
m/9 = 13
Multiply both sides by 9:
m = 13 * 9
m = 117
Answer:
The proportional relationship between the number of pages (p) and the number of hours (h) is represented by the equation
. Write the equation in standard form with a constant of proportionality greater than 1.
Step-by-step explanation:
What is the reflection of point P(−1, 6) across the line y = x?
Answers
ANSWER
P'(6,-1)
EXPLANATION
The mapping for a reflection in the line y=x is
The line y=x is the mirror line for a function and it's inverse.
[tex](x,y)\to (y,x)[/tex]
The x and y coordinates swap position.
The reflection of point P(−1, 6) across the line y = x is
P'(6,-1)
If x= -3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?
A) The discriminant is negative.
B) The discriminant is -3.
C) The discriminant is 0.
D) The discriminant is positive.
Answers
Answer:
C) The discriminant is 0.
Step-by-step explanation:
Since the graph of the quadratic equation has only one x-intercept, we can conclude that the quadratic has only one real root.
If a quadratic equation has only one real root, then the discriminant is 0
1. Victoria is opening a pet store. She will start by making custom dog collars. If the collar cost her $3 each, the embellishments $2, and $0.15 per bag, what is her unit cost per collar?
Answers
Answer:
$5.15
Step-by-step explanation:
A dog collar usually consists of a base(collar), the embellishments and the bag in which it is packed.
As we are given,
Collar Price = c = $3
Embellishment price = e = $2
and
Bag price = b =$0.15
The cost of one collar will be the cost of all these combined.
So,
Cost of collar = c+e+b
=3+2+0.15
=5.15
So the price of one collar is $5.15 ..
Answer:
5.15
Step-by-step explanation:
Use the order of operations to simplify the expression
23 + 5 × 10 ÷ 2 – 33 + (11 – 8)
A. 9
B. 41
C. 10
D. 55
Answers
For this case according to the order PEMDAS we have:
P: Perform the parenthesis calculations
E: Simplify exponential expressions
MD: Multiplications and divisions from left to right
AS: Addition and subtraction from left to right.
We have:
23 + 5 * 10÷2-33 + (11-8) =
23 + 5 * 10÷2-33 + 3 =
23 + 50÷2-33 + 3 =
23 + 25-33 + 3 =
48-33 + 3 =
15 + 3 =
18
Thus, the value of the expression is 18
ANswer:
18
can somebody help me..... Please
Answers
Answer:
[tex]\large\boxed{B.\ \dfrac{7}{8}}[/tex]
Step-by-step explanation:
[tex]\text{Put the values}\ x=\dfrac{15}{8}\ \text{and}\ y=-3\ \text{to the expression}\ \dfrac{3}{8}y^2-\dfrac{4}{3}x:\\\\\dfrac{3}{8}(-3)^2-\dfrac{4}{3\!\!\!\!\diagup_1}}\cdot\dfrac{15\!\!\!\!\!\diagup^5}{8}=\dfrac{(3)(9)}{8}-\dfrac{(4)(5)}{8}=\dfrac{27}{8}-\dfrac{20}{8}=\dfrac{27-20}{8}=\dfrac{7}{8}[/tex]
Use the relation to answer the following questions. Graph the relation. State the domain of the relation. State the range of the relation. Is the relation a function? How do you know? Answer:
Answers
Answer:
All answers in the pic attached
REALLY NEED THIS PLZZ ANSWER ESY I JUST DON'T KNOW PLZZZZZZZZZZZWhich quadratic rule represents the data in the table? 20PTS AND BRAINLIEST !!!!!!!!!!!!!!!
x –1 0 1 2 3
y –4 –5 –4 –1 4
A.)y = –2x² + 5
B.) = –x² + 5
C.) y = x² – 5
D.y = x² + 5
Answers
Answer:
It is answer C
Step-by-step explanation:
Answer:
C.) y = x^2 -5
Step-by-step explanation:
The table pair (x, y) = (0, -5) tells you that the constant will be -5. Only answer choice C has that value for the constant.
___
You can check other (x, y) values in the rule to see that they work.
Three boys and four girls enter a contest at the local movie theater. A randomly chosen winner will be awarded a free movie ticket, a collectible poster, or free popcorn. What is the probability that a girl will win free popcorn?
Answers
Answer:
4/21
Step-by-step explanation:
⇒This question is on probability
⇒Number of boys=3
⇒Number of girls=4
⇒P(S)= 4+3=7
Probability for a girl to win is= 4/7
We have 3 awards a free movie ticket, a collectible poster, or a free popcorn
P(S)= 3
Probability of being awarded a free popcorn = 1/3
The probability that a girl will win free popcorn =
[tex]\frac{4}{7} * \frac{1}{3} = \frac{4}{21}[/tex]
Answer:
4/21
Step-by-step explanation:
Find Kara’s percent grade if she answered 94 questions correctly on the test that had 100 questions
Answers
Answer:
94%
Step-by-step explanation:
Since there are 100 questions, it's like 1% for each question. If she answers 94 questions right, then it is 94%.
Frank, Carl, and Vinny started a lawn mowing business over the summer. This table shows how many lawns each worker mowed during the summer months.
Display the data in matrix W with rows indicating workers. What is element w13?
a.22
b.29
c.21
d.19
Answers
Answer:
A.22
Step-by-step explanation:
Answer:
d. 19
Step-by-step explanation:
A matrix is an array of rectangular shape which consists of numbers, symbols, or expressions, arranged in rows and columns.
[tex]\begin{bmatrix}28&21&19\\17&24&15\\22&29&17\end{bmatrix}[/tex]
[tex]w_{1,3}[/tex] means element in first row third column. First row means Frank and third column means August.
So, the number of lawns mowed by Frank in August is
[tex]w_{1,3}=19[/tex]
Let f(x) = -4x - 2 and g(x) = 5x - 6. Find f×g and state its domain
Answers
Answer:
see explanation
Step-by-step explanation:
f(x) × g(x)
= (4x - 2)(5x - 6) ← expand factors
= 20x² - 24x - 10x + 12 ← collect like terms
= 20x² - 34x + 12
This is a polynomial of degree 2 and is defined for all real values of x
domain : x ∈ R
10 points which of the following describes the graph ? Help
Needed
Answers
ANSWER
First choice
EXPLANATION
The graph of f(x) and
[tex] {f}^{ - 1} (x)[/tex]
are symmetric about the line y=x.
This means that the graph of
[tex]{f}^{ - 1} (x)[/tex]
is the reflection of f(x) in the line y=x.
This explains why the composition of a function and its inverse yields x, as the result.
The first choice is correct.