You are hiking and are trying to determine how far away the nearest cabin is, which happens to be due north from your current position. Your friend walks 245 yards due west from your position and takes a bearing on the cabin of N 22.6°
e. How far are you from the cabin?
Answer:
589 yards
Step-by-step explanation:
This is a question that requires the use of trigonometric functions.
The trigonometric function to be used here is the tangent function.
tan θ = Opposite side/ Adjacent side
In the question, we are told
Your friend walks 245 yards due west from your position = Opposite side
Your friend's takes a bearing on the cabin of N 22.6° = θ
Your distance from the cabin = Adjacent side
Hence,
tan 22.6 ° = 245/ Adjacent side
Cross Multiply
Adjacent side = 245/ tan 22.6°
Adjacent side = 588.57469726 yards.
Therefore, your distance from the cabin approximately to the nearest yard(whole number) = 589 yards
slope of (-2,2) and (3,4)
Answer:
2/5
Step-by-step explanation:
Good luck!
Find the odds in favor of rolling two even numbers when rolling a pair of dice.
Answer:
1/4 or 25%
Step-by-step explanation:
Each dice has six sides, meaning the numbers that are even are: 2,4, and 6, three even numbers per dice. Meaning the chance of rolling ONE dice is 50%. So if you were to get two even numbers on TWO dice, it would be 25% hope this helps.
The odds in favor of rolling two even numbers when rolling a pair of dice would be 25% or 1/4.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Each dice has six sides, means the numbers that are even are:
2,4, and 6, three even numbers per dice.
The total number of outcomes is 6 x 6 or 36.
Meaning the chance of rolling ONE dice is 50%.
The odds in favor of rolling two even numbers when rolling a pair of dice would be 25%.
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Hellllllllllppppppppppp please
Answer:
As x decreases in value.f(x) decreases in value.......
Five less than the product of a number and 6
A. 5-6n
B. 6(n-5)
C. 6n-5
D. 6(5-n)
Answer:
C. 6n - 5
Step-by-step explanation:
Hello!
A product of a number and 6 means we have to multiply a number by 6.
This can be shown by 6n.
Then 5 less means we subtract by 5.
We get the answer: 6n - 5
Hope this Helps!
Answer:
B) 6(n-5)
Step-by-step explanation:
Mark as Brainliest
How many three-digit positive integers [tex]x[/tex] satisfy [tex]3874x+481\equiv 1205 \pmod{23}[/tex]
Answer:
40
Step-by-step explanation:
Any solution x will mod 23 will also have x+23n as a solution, for some integer n. Since 900/23 = 39 3/23, we know there are 39 or 40 three-digit integers of this form.
As it happens, 100 is the smallest 3-digit solution. So, there are 40 three-digit numbers that are of the form 100 +23n, hence 40 solutions to the equation.
_____
The equation reduces, mod 23, to ...
10x = 11
Its solutions are x = 23n +8.
12. Explain why is (+5) + (-7) = -2.
Let's use a number line to help us visualize what's going on.
Starting at 0, +5 takes us 5 units to the right.
From there, -7 moves us 7 units back to the left and we end up at -2.
So (+5) + (-7) simplifies to -2.
Take a look at the image below.
A business made a profit of $44,000 in 1991. Then its profits decreased by 5% each year for 4
years. Find its profit in the year 1995.
Answer:
= profit in the year 1995 are $880,000
For the function F defined by F(x)=x2−2x+4, find F(5). For the function F defined by F ( x ) = x 2 − 2 x + 4 , find F ( 5 ) . A. 32 32 B. 39 39 C. 19 19 D. 4
Answer:
C. 19
Step-by-step explanation:
Given the function defined by F(x)=x²−2x+4, in order to get f(5), we will have to simply substitute x = 5 into the formula given as shown;
F(5) = 5²-2(5)+4
F(5) = 25 - 10 + 4
F(5) = 15 + 4
F(5) = 19
Hence, for the function F defined by F(x)=x²−2x+4, F(5) = 19
The polygons are regular polygons. Find the area of the shaded region to the nearest tenth.
The area of the shaded region in the regular polygon is 161.3 cm²
What is a regular polygon?
A regular polygon is a polygon in which all the sides are equal.
From the diagram, the regular polygon is a square which is composed of a small square and a large square. In a square, all the sides are equal.
For the small square, half of the diagonal is 4 cm, therefore the length of the diagonal is 8 cm (2 × 4 cm). Let the length of the side be a cm, using Pythagoras theorem:
a² + a² = 8²
2a² = 64
a² = 32
a = √32 = 5.7 cm
The area of the small square = length × length = 5.7 × 5.7 = 32.5 cm²
For the large square, half of the diagonal is 9 cm, therefore the length of the diagonal is 18 cm (2 × 9 cm). Let the length of the side be b cm, using Pythagoras theorem:
b² + b² = 18²
2b² = 324
b² = 162
b = √162 = 12.7 cm
The area of the large square = length × length = 12.7 × 12.7 = 161.3 cm²
The area of the shaded region = Area of large square - Area of small square = 161.3 cm² - 32.5 cm² = 128.8 cm²
The area of the shaded region in the regular polygon is 161.3 cm²
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Answer:
it’s actually 130 or 130.0
Step-by-step explanation:
The slope of the line below is -3. Which of the following is the point-slope
form of the line?
13
A. ¥+ 2 = -3(x-6)
© B. y-6--3(x + 2)
© C. y. 2 = -3(x + 6)
D) D. y + 6 = -3(x-2)
Answer:
[tex]\boxed{D. y + 6 = -3(x - 2)}[/tex]
Step-by-step explanation:
Hey there!
Well given point,
(2,-6)
Point slope form is,
y - y1 = m(x - x1)
Plug in the given point
y + 6 = m(x - 2)
Plug in slope
y + 6 = -3(x - 2)
So choice D. y + 6 = -3(x - 2) is correct.
Hope this helps :)
Use slope-intercept form to graph each system of equations and solve each system.
Answer:
(0,3), graph is attached.
Step-by-step explanation:
We know that the first equation will increase 2 points in y for every 1 x, since the constant next to x is 2. We also know it's y-intercept will be 3.
As for the second equation, we know it will have no y and instead run through the y=3 line, crossing every value of x.
Graphing this, we see that these lines intersect at (0,3) so that's the solution to this system.
Hope this helped!
find the exterior angle of a triangle whose interior opposite angles are 43 degree and 27 degree
Answer:
[tex]\huge\boxed{Exterior\ angle = 70\°}[/tex]
Step-by-step explanation:
The measure of exterior angle is equal to the sum of opposite interior angles.
So,
Exterior angle = 43+27
Exterior angle = 70°
help me pleasssseeeeeee
Answer:
[tex]{ \bf{b. \: \: {i}^{47} }}[/tex]
Step-by-step explanation:
[tex] {i}^{46} = ( {i}^{2} ) {}^{23} = - 1 \\ \\ {i}^{47} = (i)( {i}^{46} ) = ( - 1 \times i) = - i \\ \\ {i}^{48} = ( {i}^{2} ) {}^{24} = 1 \\ \\ {i}^{49} = (i)( {i}^{48}) = (1 \times i) = i[/tex]
Answer:
[tex]i^{46} = -i[/tex]
~~~~~~~~~~~~~~~~~~~
46/4 = 11 remainder 2 = [tex]-i[/tex]
47/4 = 11 remainder 3 = 1
48/4 = 11 remainder 0 = [tex]i[/tex]
49/4 = 11 remainder 1 = -1
Step-by-step explanation:
[tex]i = \sqrt{-1} = i[/tex] (remainder 0)
[tex]i^{2} = \sqrt{-1} * \sqrt{-1} = -1[/tex] (remainder 1)
[tex]i^{3} = \sqrt{-1} * \sqrt{-1} * \sqrt{-1}= -1 * \sqrt{-1} = -i[/tex] (remainder 2)
[tex]i^{4} = \sqrt{-1} * \sqrt{-1} * \sqrt{-1} * \sqrt{-1}= -1 * -1 = 1\\[/tex] (remainder 3)
[tex]i^{5} = \sqrt{-1} * \sqrt{-1} * \sqrt{-1} * \sqrt{-1}* \sqrt{-1}= 1 * \sqrt{-1} = i\\[/tex] (remainder 0)
The pattern repeats every FOUR in the exponent
when a number is divided by 37, the quotient is 57, and the remainder is 29. what is the number
Answer:
Step-by-step explanation:
Hello, it means that the number is
57 * 37 + 29 = 2138
Thank you
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Answer: y= 3+x
Step-by-step explanation:
Answer: y = x - 3
First, find two points on the graph:
(x₁, y₁) = (3, 0)(x₂, y₂) = (0, -3)Substitute in the points to the slope formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] to find the slope:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{-3-0}{0-3}=\frac{-3}{-3}=1[/tex]
Substitute in a point to the function [tex]y=1x+b[/tex] to find the y-intercept(b):
[tex]-3=1(0)+b\\b=-3[/tex]
Therefore, the function is:
[tex]y=x-3[/tex]
Find the value of the following (-42) + 15 + (-63) can someone say this and fast
[tex]\\ \sf\longmapsto (-42)+15+(-63)[/tex]
[tex]\\ \sf\longmapsto -42+15+(-63)[/tex]
[tex]\\ \sf\longmapsto -27+(-63)[/tex]
[tex]\\ \sf\longmapsto -27-63[/tex]
[tex]\\ \sf\longmapsto -90[/tex]
Answer:
42 + 15 + (-63) = -90
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Dr. Potter provides vaccinations against polio and measles. Each polio vaccination consists of 6 doses, and each measles vaccination consists of 3 doses. Last year, Dr. Potter gave a total of 60 vaccinations that consisted of a total of 225 doses. How many more measles vaccines did Mr. Potter give than polio? Show All Work !!
Answer:
The number of measles vaccines that Dr. Potter give than polio vaccines is 30
Step-by-step explanation:
The parameters given are;
The number of doses given in a polio vaccine = 6 doses
The number of doses given in a measles vaccine = 3 doses
The number of vaccinations given by Dr. Potter last year = 60 vaccinations
The number of doses given in the 60 vaccinations = 225 doses
Let the number of polio vaccine given last year by Dr. Potter = x
Let the number of measles vaccine given last year by Dr. Potter = y
Therefore, we have;
6 × x + 3 × y = 225.......................(1)
x + y = 60.......................................(2)
From equation (2), we have;
x = 60 - y
Substituting the derived value for x in equation (1), we get;
6 × x + 3 × y = 225
6 × (60 - y) + 3 × y = 225
360 - 6·y + 3·y = 225
360 - 225 = 6·y - 3·y
135 = 3·y
y = 45
x = 60 - y = 60 - 45 = 15
Therefore;
The number of polio vaccine given last year by Dr. Potter = 15
The number of measles vaccine given last year by Dr. Potter = 45
The number of measles vaccines that Dr. Potter give than polio vaccines = 45 - 15 = 30 vaccines.
The number of measles vaccines that Dr. Potter give than polio vaccines = 30 vaccines.
Find the quotient. (5x4 – 3x2 + 4) ÷ (x + 1)
Answer:
A
Step-by-step explanation:
The quotient is 5x³ -5x² + 2x -2.
What is Synthetic Division?Synthetic division is typically used to identify the zeroes of polynomials and is described as "a simplified method of dividing a polynomial with another polynomial equation of degree 1." This division method requires less human calculation effort than the lengthy division method.
Given:
(5[tex]x^4[/tex] – 3x² + 4) ÷ (x + 1)
So, the division is
(x+1) | (5[tex]x^4[/tex] – 3x² + 4) | 5x³ -5x² + 2x -2
5[tex]x^4[/tex] + 5x³
___________
-5x³ - 3x²
-5x³ - 5x²
____________
2x² + 4
2x² + 2x
____________
4 - 2x
-2 - 2x
_______
6
Hence, the quotient is 5x³ -5x² + 2x -2.
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In a math class of 28 students, 14 boys and 14 are girls. On a unit test, 5 boys and 9 girls made an A grade. A student is chosen at random from the class. What is the probability of choosing a girl or an A student?
A. 0.82
B. 0.68
C. 0.14
D. 0.50
Answer:
The probability of choosing a girl is 1/2.
The probability of choosing an A student who is a BOY is 5/28.
1/2 = 14/28, and 14/28 + 5/28 = 19/28. This can be simplified to 0.68
Thus, the answer is B. 0.68
Let me know if this helps!
The required probability of choosing a girl or an A student is 0.82. Option A is correct.
Given that,
In a math class of 28 students, 14 boys and 14 are girls. On a unit test, 5 boys and 9 girls made an A grade.
A student is chosen at random from the class. What is the probability of choosing a girl or an A student is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Total sample space = 28
Number of girls = 14
Number of boys = 14
Number of girls A grade student = 9
probability of a girl = 14/28 = 0.5
probability of A grader girl = 9 / 28 = 0.32
Now the probability of choosing a girl or an A grader girl student,
= 0.32 + 0.5
= 0.82
Thus, the required probability of choosing a girl or an A student is 0.82. Option A is correct.
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Which transformation can NOT be used to prove that ABC is congruent to
DEF?
O A. dilation
B. rotation
C. reflection
ОО
D. translation
Answer
A. dilation
Step-by-step explanation:
if we dilate the diagram it will be enlargedd so cannot be proved as congruent
The transformation that can not be used to prove that ABC is congruent will be dilation. The correct option is A.
What is transformation?Transformation a process by which one figure, expression, or function is converted into another one of similar value. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
When the triangle is rotated its original shape and size will not change it only changes its position then the triangle will remain congruent.
When the triangle is reflected it means that its mirror image is formed then the size and shape will again remain unchanged the triangle will be congruent.
When the triangle is translated then also its size will not change only it changes its position. The triangle will be congruent.
When the triangle is dilated it means that the shape of the triangle is increased or decreased then the triangle will not be congruent when it is dilated.
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When a number is decreased by 2.6%, the result is 83. What is the original number to the nearest tenth?
Answer:
85.2
Step-by-step explanation:
we can represent this in an equation where the initial value is going to be and to this we will subtract 2.6% of it
x - x * 2.6/100 = 83
x - 0.026x = 83
0.974x = 83
x = 83 / 0.974
x = 85.2156
we round to the nearest tenth and finally, we get that the result is 85.2
Help me solve seven pls pls
Answer:
B. 20
Step-by-step explanation:
First, 20% of 20 is 4.
36 decreased by 4 (36-4) is 32.
The equation is N (160%)=32 or 1.6n=32
160% because it was already 100%, and its increased by 60% (100+60)
Divide both sides by 1.6.
You get n=20
I hope this helps!
14. peggy had 4 times as many quarters as nickels, she had 2.10 in all how many buckles and quarters did she have?
Answer:
academic study or science that deals with human behavior in its social
Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589. You must show all of your work to receive credit.
PLSSS SHOW WORK <3
Answer:
x = 18
Step-by-step explanation:
First, let's find the ratios between the two triangles
We'll use AV and AC
372 ÷ 589 = 12/19
All of the sides of the smaller triangle are 12/19 of the bigger triangle
Now let's find x
We know that AU + UB = AB
So it's 20x + 108 + 273 = AB
12/19 of a bigger triangle side equals a small triangle side
(12/19)AB = AU
For this equation multiply both sides by 19/12 to isolate AB
(12/19)AB x 19/12 = AU x 19/12
AB = (19/12)AU
Now we have this
20x + 108 + 273 = (19/12)(20x + 108)
20x + 381 = (19/12)(20x + 108)
Distribute the 19/12
20x + 381 = 95/3x + 171
Move all like terms to one side
20x + 381 = 95/3x + 171
- 171 - 171
20x + 210 = 95/3x
- 20x - 20x
Don't forget about common denominators
210 = 95/3x - 60/3x
210 = 35/3x
Multiply both sides by 3
210 x 3 = 35/3x x 3
630 = 35x
Divide both sides by 35
630/35 = 35x/35
x = 18
Answer:
Step-by-step explanation:
[tex]\frac{20x+108}{20x+381}[/tex] = [tex]\frac{372}{589}[/tex]
589( 20x + 108 ) = 372( 20x + 381 )
11780x + 63612 = 7440x + 141732
4340x = 78120
x = 18
Find the distance between the two points in simplest radical form. (1, 5) and (9, 0)
Answer:
√89Step-by-step explanation:
[tex](1,5)=(x_1,y_1)\\(9,0) = (x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\d = \sqrt{(9-1)^2 +(0-5)^2}\\ \\d = \sqrt{(8)^2+(-5)^2}\\ \\d = \sqrt{64+25}\\ \\d = \sqrt{89}\\[/tex]
The distance between the points (1, 5) and (9, 0) is √89 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given end points (1, 5) and (9, 0) into the distance formula, we have the following;
Distance = √[(9 - 1)² + (0 - 5)²]
Distance = √[(8)² + (-5)²]
Distance = √[64 + 25]
Distance = √89 units.
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Elias made a polyhedron with 9 edges and 5 faces. Which solid could he have made?
The polyhedron that Elias could have made is a TRIANGULAR BASED PRISM.
Triangular based prism are as described below:
A triangular-based prism is known to consists of 9 edges and 5 faces as shown in the diagram below.
It is a three-sided prism and also a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sidesThe edges are made up of lines and these lines are the ones that intersect to form facesLearn more here: https://brainly.com/question/16682058
Answer: c
Step-by-step explanation:
Find the least number by which the following number must be multiplied so that the product are perfect cube one number 72 to number 128 number 288 phone number 675
Answer:
Well this question is actually a piece of cake. Just pick your favorite number. Multiply it by 10. Then do whatever operation you want with the 2,300. For the exponent part of this. Lets say we do it this way y times z equals 2,300. Exponents are letters used in mathematical terms. So any letter can be used to represent any number.
Step-by-step explanation:
PLEASE HELP URGENT AND EXPLAIN FOR 25 POINTS MUST BE CORRECT Brielle bought an apartment building for $202,444. The value of the real estate appreciated at a constant rate per year. The table shows the value of the apartment building after the first and second years: Year 1 2 Value (in dollars) $212,566.20 $223,194.51 Which function best represents the value of the apartment building after t years? f(t) = 202,444(0.05)t f(t) = 202,444(1.05)t f(t) = 212,566.20(1.05)t f(t) = 212,566.20(0.05)t
Answer:
f(t) = 202,444(1.05)^t
Step-by-step explanation:
Simple Interest Rate Formula: A = P(1 + r)^t
A = final amount
P = principle amount
r = interest rate
t = time
Step 1: Find rate r
212,566.20 = 202,444(1 + r)¹
1.05 = (1 + r)¹
1.05 = 1 + r
r = 0.05
Step 2: Define variables
P = 202,444
r = 0.05
Step 3: Plug in variables into formula
A = 202,444(1 + 0.05)^t
A = 202,444(1.05)^t
Factorise : x²-17x+ 60 Step by Step
Answer:
Step-by-step explanation:
x^2 - 17 x + 60
we should find two numbers such that their sum is equal to -17 and product is equal to 60
The two numbers are -12 and -5
now, x^2 - 12 x - 5 x + 60 { splitting the middle term }
x ( x- 12 ) - 5 ( x - 12 )
= ( x - 5 ) ( x - 12 )
hope this helps
plz mark as brainliest !!!!!!
Answer:
x² - 17x + 60 = (x - 12)(x - 5)Step-by-step explanation:
[tex]x^2-17x+60\quad \implies\quad a=1\,,\quad b=-17\,,\quad c=60\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-(-17)\pm\sqrt{(-17)^2-4\cdot1\cdot60}}{2\cdot1}=\dfrac{17\pm\sqrt{289-240}}{2}=\dfrac{17\pm\sqrt{49}}{2}\\\\x_1=\dfrac{17-7}{2}=5\quad,\qquad x_2=\dfrac{17+7}{2}=12\\\\\\x^2-17x+60=(x-5)(x-12)[/tex]
or:
x² - 17x + 60 =
= x² - 12x - 5x +60 =
= x(x - 12) - 5(x - 12) =
= (x - 12)(x - 5)