The given triangle is a right angle triangle. Considering angle 18 as the reference angle,
x = hypotenuse
29 = adjacent side
We would find the hypotenuse, x by applying the cosine trigonometric ratio which is expressed as
Cos# = adjacent side/hypotenuse
Thus, we have
Cos18 = 29/x
29 = xCos18
x = 29/Cos18 = 29/0.95
x = 30.53
what is the anss? btw this is just a practice assignment.
Anime, this is the solution:
Part A. This exponential is decay because the factor of the exponential is below one, and it decreases every year.
Part B.
5,100 * (0.95)^5 =
5,100 * 0.77378 =
3,946 (rounding to the nearest carbon atom)
A swimmer is 1 mile from the closest point on a straight shoreline. She needs to reach her house located 4miles down shore from the closest point. If she swims at 3 mph and runs at 6 mph, how far from her house should she come ashore so as to arrive at her house in the shortest time?
Let's draw a diagram of this problem.
ABC is the shore.
D to A is 1 miles (given).
A to C is 4 miles (given).
If we let AB = x, then BC would be "4 - x".
Now, using pythgorean theorem, let's find BD:
[tex]\begin{gathered} AB^2+AD^2=BD^2 \\ x^2+1^2=BD^2 \\ BD=\sqrt[]{1+x^2} \end{gathered}[/tex]We know
[tex]D=RT[/tex]Where
D is distance
R is rate
T is time
Swimmer needs to go from D to B at 3 miles per hour. Thus, we can say:
[tex]\begin{gathered} D=RT \\ T=\frac{D}{R} \\ T=\frac{\sqrt[]{1+x^2}}{3} \end{gathered}[/tex]Next part, swimmer needs to go from B to C at 6 miles per hour. Thus, we can say:
[tex]\begin{gathered} D=RT \\ T=\frac{D}{R} \\ T=\frac{4-x}{6} \end{gathered}[/tex]So, total time would be:
[tex]T=\frac{\sqrt[]{1+x^2}}{3}+\frac{4-x}{6}[/tex]We want to find the shortest possible time. From calculus we know that to find the shortest possible time, we need to differentiate the function T, set it equal to 0 to find the critical points and then use that point in the function T to find the shortest possible time.
Let's differentiate the function T:
[tex]\begin{gathered} T=\frac{\sqrt[]{1+x^2}}{3}+\frac{4-x}{6} \\ T=\frac{1}{3}(1+x^2)^{\frac{1}{2}}+\frac{4}{6}-\frac{1}{6}x \\ T=\frac{1}{3}(1+x^2)^{\frac{1}{2}}+\frac{2}{3}-\frac{1}{6}x \\ T^{\prime}=(\frac{1}{2})\frac{1}{3}(1+x^2)^{-\frac{1}{2}}\lbrack\frac{d}{dx}(1+x^2)\rbrack-\frac{1}{6} \\ T^{\prime}=\frac{1}{6}(1+x^2)^{-\frac{1}{2}}(2x)-\frac{1}{6} \\ T^{\prime}=\frac{2x}{6(1+x^2)^{\frac{1}{2}}}-\frac{1}{6} \\ T^{\prime}=\frac{x}{3\sqrt[]{1+x^2}}-\frac{1}{6} \end{gathered}[/tex]Now, we find the critical point:
[tex]\begin{gathered} T^{\prime}=\frac{x}{3\sqrt[]{1+x^2}}-\frac{1}{6} \\ T^{\prime}=0 \\ \frac{x}{3\sqrt[]{1+x^2}}-\frac{1}{6}=0 \\ \frac{x}{3\sqrt[]{1+x^2}}=\frac{1}{6} \\ \text{Cross Multiplying:} \\ 6x=3\sqrt[]{1+x^2} \\ \text{Square both sides:} \\ (6x)^2=(3\sqrt[]{1+x^2})^2 \\ 36x^2=9(1+x^2) \\ 36x^2=9+9x^2 \\ 36x^2-9x^2=9 \\ 27x^2=9 \\ x^2=\frac{9}{27} \\ x=\frac{\sqrt[]{9}}{\sqrt[]{27}} \\ x=\frac{3}{3\sqrt[]{3}} \\ x=\frac{1}{\sqrt[]{3}} \end{gathered}[/tex]Plugging this value into the equation of T, we get:
[tex]\begin{gathered} T=\frac{\sqrt[]{1+x^2}}{3}+\frac{4-x}{6} \\ T=\frac{\sqrt[]{1+(\frac{1}{\sqrt[]{3}})^2}}{3}+\frac{4-\frac{1}{\sqrt[]{3}}}{6} \\ T=\frac{\sqrt[]{1+\frac{1}{3}}}{3}+\frac{4-\frac{1}{\sqrt[]{3}}}{6} \\ T=\frac{\sqrt[]{\frac{4}{3}}}{3}+\frac{4-\frac{1}{\sqrt[]{3}}}{6} \\ T=\frac{\frac{2}{\sqrt[]{3}}}{3}+\frac{4-\frac{1}{\sqrt[]{3}}}{6} \\ T=\frac{2}{3\sqrt[]{3}}+\frac{4-\frac{1}{\sqrt[]{3}}}{6} \end{gathered}[/tex]Now, we can use the calculator to find the approximate value of T to be:
T = 0.9553 hours
This is the optimized time.
Converting to approximate minutes, it will be:
57.32 minutes
Answer:[tex]T=0.9553\text{ hours}[/tex]Can you please check number 4 and check parts a, b, and c to make sure it’s right please
if the scale in the drawing is 1 centimeter= 20 meters, then:
a) Playground 3 centimeters.
[tex]\begin{gathered} \frac{1cm}{20m}=\text{ }\frac{3cm}{x}= \\ \text{ x\lparen1cm\rparen=\lparen20m\rparen\lparen3cm\rparen} \\ x=\text{ 60 meters} \end{gathered}[/tex]b) Tennis courts= 5.2cm
[tex]\begin{gathered} \frac{1cm}{20m}=\text{ }\frac{5.2cm}{x} \\ x(1cm)=\text{ \lparen5.2cm\rparen\lparen20m\rparen} \\ x=\text{ 104 meters} \end{gathered}[/tex]c) Walking trail= 21.7 cm
[tex]\begin{gathered} \frac{1cm}{20m}=\frac{21.7cm}{x} \\ \\ x(1cm)=(21.7cm)(20m) \\ x=\text{ 434 meters} \end{gathered}[/tex]There are two types of tickets sold at the Canadian Formula One Grand Prix race. The price of 6 grandstand tickets and 4 general admission tickets is $3200. The price of 8 grandstand tickets and 8 general admission tickets is $4880. What is the price of each type of ticket?
Let:
x = price of the grandstand ticket
y = price of the general admission ticket
The price of 6 grandstand tickets and 4 general admission tickets is $3200, so:
[tex]6x+4y=3200[/tex]The price of 8 grandstand tickets and 8 general admission tickets is $4880, so:
[tex]8x+8y=4880[/tex]Let:
[tex]\begin{gathered} 6x+4y=3200_{\text{ }}(1) \\ 8x+8y=4880_{\text{ }}(2) \end{gathered}[/tex]Using elimination method:
[tex]\begin{gathered} 2(1)-(2)\colon_{} \\ 12x-8x+8y-8y=6400-4880 \\ 4x=1520 \\ x=\frac{1520}{4} \\ x=380 \end{gathered}[/tex]replace the value of x into (1):
[tex]\begin{gathered} 6(380)+4y=3200 \\ 2280+4y=3200 \\ 4y=3200-2280 \\ 4y=920 \\ y=\frac{920}{4} \\ y=230 \end{gathered}[/tex]The price of the grandstand ticket is $380 and the price of the general admission ticket is $230
If mQR = 80° and mQS = 150°, what is m
we have that
m
by exterior angle
so
substitute given values
m
mwhat is the value of 6 × 7 – 3^2 × 9 + 4^3
Starting with the given expression:
[tex]6\cdot7-3^2\cdot9+4^3[/tex]Follow the hierarchy of operations to find the value.
First, solve potencies and roots. Solve the powers 3^2 and 4^3:
[tex]6\cdot7-3^2\cdot9+4^3=6\cdot7-9\cdot9+64[/tex]Next, solve the multiplications and divisions:
[tex]6\cdot7-9\cdot9+64=42-81+64[/tex]Solve the sums and substractions:
[tex]42-81+64=-39+64=25[/tex]Therefore:
[tex]6\cdot7-3^2\cdot9+4^3=25[/tex]a right cone has a radius of 27 cm and a height of 36cm. find the slant height of the cone. find the surface area of the cone. find the volume of the cone
A right triangle is formed where the radius is one leg, the height is the other leg and the slant height is the hypotenuse. Applying the Pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ s^2=27^2+36^2 \\ s^2=729+1296 \\ s^2=2025 \\ s=\sqrt[]{2025} \\ s=45\operatorname{cm} \end{gathered}[/tex]The surface area of a right cone is calculated as follows:
[tex]SA=\pi rs+\pi r^2[/tex]where r is the radius and s is the slant height. Substituting with r = 27 cm and s = 45 cm, we get:
[tex]\begin{gathered} SA=\pi\cdot27\cdot45+\pi\cdot27^2 \\ SA=1215\pi+729\pi \\ SA=1215\pi+729\pi \\ SA=1944\pi\approx6107.25\operatorname{cm} \end{gathered}[/tex]The volume of a right cone is calculated as follows:
[tex]V=\pi\cdot r^2\cdot\frac{h}{3}[/tex]where h is the height. Substituting with r = 27 cm and h = 36 cm, we get:
[tex]\begin{gathered} V=\pi\cdot27^2\cdot\frac{36}{3} \\ V=\pi\cdot729\cdot12 \\ V=8748\pi\approx27482.65\operatorname{cm}^3 \end{gathered}[/tex]Graph the line parallel to x= -1 that passes through (8,4).could you also draw a picture
The line x = -1 is a vertical line, since it has a specific x-coordinate and no y-coordinate.
A line parallel to a vertical line is also a vetical line, so our line will have the equation x = b, where we need to find the value of b.
Since our line passes through the point (8, 4), we know that its x-coordinate will be 8, so our line is x = 8.
Drawing the lines (x = -1 in blue and x = 8 in green), we have:
The answer that should be graphed is just the green line.
Mrs.Gall orders 240 folders and divides them equally among 3 classes. How many folders does each class receive? What basic fact did you use?
Answer:
80
Step-by-step explanation:
240 folders divided by 3 class
find first four terms of an arithmetic series if last term is 10 times first term and sum to n terms is 121
Answer: 120
Step-by-step explanation:
S = n/2 (a(1) + a(n)), where n is the number of terms (10), a(1) is the first term (3), and a(n) is the last term (21).
By substitution, we have,
S = 10/2 (3 + 21)
S = 120
What is the equation of the parabola shown below, given a focus at F(1, 5) and a directrix of x = −3? In addition, identify the vertex and the equation of the axis of symmetry for the parabola.
EXPLANATION
First, let's find the vertex.
From the graph, the vertex is (-1, 5).
It is symmetric about y = 5
Length of the Latus rectom (a) =2 x 4 = 8
Therefore, the equation of the graph is;
[tex]y=\frac{1}{a}(y-5)^2-1[/tex]Substitute a = 8
[tex]x=\frac{1}{8}(y-5)^2-1[/tex]8 divided by 856 long division
Answer: look at the attachment bellow
2(4+-8)⁶+3 evaluate the Expression
The given expression is
2(4+-8)⁶+3
The first step is to evaluate the bracket.
4 + - 8 = 4 - 8 = - 4
The expression becomes
2(-4)^6 + 3
= 2(4096) + 3
= 8192 + 3
= 8195
seven more than the product of 22 and a number
Answer:
22n + 7
Step-by-step explanation:
We can let n represent the number being multiplied by 22 (products imply multiplication).
We put the seven after the multiplication since "seven more" means that we're adding the 7 to the product.
A company purchased 10,000 pairs of men's slacks for $18.86 per pair and marked them up $22.63. What was the selling price of each pair of slacks? Use the formula S=C+M
Problem:
A company purchased 10,000 pairs of men's slacks for $18.86 per pair and marked them up $22.63. What was the selling price of each pair of slacks? Use the formula S=C+M.
Solution:
Cost = $18.86
Markup = $22.63
Markup = Sell Price - Cost
Sell Price = Cost + Markup
Sell Price = 18.86+ 22.63
Sell Price = $41.49
The selling price of each pair of slacks was $41.49.
Find the value of x.
Answer
Option A is correct.
x = 5 units
Explanation
We can draw the triangle and divide it into two similar right angle triangles shown below
In a right angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
The Pythagorean Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For each of the triangles,
a = 4
b = 3
hyp = x
a² + b² = (hyp)²
4² + 3² = x²
x² = 16 + 9
x² = 25
x = √25
x = 5 units
Hope this Helps!!!
May I please get help with finding weather they are quadrilaterals, parallelograms, or rectangles
Given:
Three diagrams are given.
Diagram VWXY:
Quadrilateral, Parallelogram,Rectangle
Diagram IJGH:
Quadrilateral
Diagram ABCD:
Quadrilateral , Parallelogram
(−2) × 36 × (−5) = ______.
we have 3 terms, two of them are negative
when operating multiplications, minus by plus gives minus and minus byminus gives plus, so the final result will be positive.
[tex]\begin{gathered} (-2)\cdot36\cdot(-5)=\text{?} \\ (-2)\cdot36\cdot(-5)=360 \\ \end{gathered}[/tex]The anwer is 360
157 - 95x + 72 + 13x =
given equation
157-95x+72+13x
First arrange the variables terms together and constant terms together,
157+72-95x+13x
Now simplify constant terms together and variable terms together
229-82x
82x=229
x=229/82
x=2.79
Determine if the following side lengths could form a triangle. Prove your answer with an inequality 3,3,7
According to the definition of triangle, the sum of two sides of a triangle must be greater than the third one.
In this case, the sum of 3 and 3 is 6 which is not greater than 7, it means that these length can't form a triangle:
[tex]3+3<7[/tex]That is the inequality that explains why they can form a triangle.
8. An urn contains 3 red, 2 blue, and 5 green marbles. If we pick 4 marbles with replacement and
count the number of red marbles in the 4 picks, the probabilities associated with this experiment are
P(0) = 0.24, P(1) = 0.41, P(2)= 0.265, P(3) = 0.076, and P(4) = 0.009. The probability of less than
2 red marbles is:
a. 0.41.
b. 0.65.
c. 0.915.
d 0.991
The probability of less than 2 red marbles is B. 0.65.
What is probability?Probability is the likelihood that an event will occur.
In this case, the urn contains 3 red, 2 blue, and 5 green marbles. Also, the probabilities associated with this experiment are give as:
P(0) = 0.24, P(1) = 0.41, P(2)= 0.265, P(3) = 0.076,
Therefore, the probability of less than 2 red marbles will be:
P(0) + P(1)
= 0.24 + 0.41
= 0.65.
Learn more about probability on:
brainly.com/question/24756209
#SPJ1
Point 0 is the center of the circle, What is the value of X
Answer: x = 22
Explanation:
From the information given. O is the center of the circle. The distance from the center of the circle to the circumference is the radius. This means that
OQ = radius
O to the vertex where angle 56 is formed is also a radius
This means that two sides the triangle formed insides the circle are equal. This also means that this triangle is an isosceles triangle. The base angles of an isosceles triangle are equal. This means that
angle 56 = angle Q because they are the base angles of the isosceles triangle
Recall, the sum of the angles in a triangle is 180 degrees. This means that
angle O + 56 + 56 = 180
angle O + 112 = 180
angle O = 180 - 112
angle O = 68
Recall, the angle formed by a tangent with the radius of the circle is 90 degrees. This means that angle Q = 90 degrees
Considering triangle POQ,
angle P + angle O + angle Q = 180
x + 68 + 90 = 180
x + 158 = 180
x = 180 - 158
x = 22
Write a recursive formula for the sequence: 8, 4, 2, 1,...Tn + 1 = Tn × 12Tn + 1 = Tn × (2)Tn + 1 = Tn - 4(n - 1)Tn + 1 = Tn + 4(n - 1)
Given:
The sequence is:
8, 4, 2, 1,...
Required:
Find a recursive formula for the given sequence.
Explanation:
The given sequence is:
8, 4, 2, 1,...
The common ratio of the sequence is:
[tex]\begin{gathered} \frac{4}{8}=\frac{1}{2} \\ \frac{2}{4}=\frac{1}{2} \\ \frac{1}{2} \end{gathered}[/tex]Since the common ratio for the given series is 1/2.
[tex]\begin{gathered} \frac{T_{n+1}}{T_n}=\frac{1}{2} \\ T_{n+1}=\frac{1}{2}T_n \end{gathered}[/tex]Final Answer:
The recursive formula for the given sequence is
[tex]T_{n+1}=\frac{1}{2}T_{n}[/tex]Use a 30 - 60 - 90 triangle to find the tangent of 60 Degrees
Let's put more details in the given figure to better understand the solution:
Let's now determine the Tangent of 60 degrees:
[tex]\text{ Tangent (60}^{\circ})\text{ = }\frac{\text{ Opposite}}{\text{ Adjacent}}[/tex][tex]\text{ = }\frac{\text{ }\sqrt[]{3}}{1}[/tex][tex]\text{ Tangent (60}^{\circ})\text{ = }\sqrt[]{3}[/tex]Therefore, the tangent of 60 degrees is √3.
The answer is Option 1 : √3
Please help me im so stressed rnIS (-2, 6) a solution of -3y + 10= 4x?
Given the expression:
[tex]-3y+10=4x[/tex]Let's check if (x,y) = (-2,6) is a solution by substituting each value on the equation:
[tex]\begin{gathered} x=-2 \\ y=6 \\ -3y+10=4x \\ \Rightarrow-3(6)+10=4(-2) \\ \Rightarrow-18+10=-8 \\ \Rightarrow-8=-8 \end{gathered}[/tex]since we got on both sides -8, we can see that (-2,6) is a solution of -3y+10=4x
I need to make sure this is correct please graph.
We have the expression:
[tex]y=\frac{4}{5}x+8[/tex]In order to plot the function we replace two values for x and we will get two values for y [Respectively], that is:
x = 0 => y =(4/5)(0)+8 => y = 8
x = 1 => y = (4/5)(1)+8 => y = 8.8
We then have the two points:
(0, 8)
(1, 8.8)
By looking at the fucntion we can tell is a function that describes a line, now we graph:
It is reported that approximately 20 squaremiles of dry land and wetland were convertedto water along the Atlantic coast between 1996and 2011. A small unpopulated island in the AtlanticOcean is 2000 ft wide by 9,380 feet long. Atthis rate, how long before the island issubmerged?
2 months
1) Notice that the sinking rate is 20miles² per 5 years (2011-1996) so:
[tex]\frac{20}{5}=\frac{4m^2}{y}[/tex]So the rate is 4 square miles per year.
2) We need to convert those measures from feet to miles:
[tex]\begin{gathered} 1\text{ mile=5280ft} \\ 2000ft=\frac{2000}{5280}=0.378miles \\ 9380ft=\frac{9380}{5280}=1.7765miles \end{gathered}[/tex]So, now let's find the area multiplying the width by the height:
[tex]\begin{gathered} A=1.7765\cdot0.378 \\ A=0.671517m^2 \end{gathered}[/tex]Now, considering the sinking rate of 4miles²/year we can write the following pair of ratios:
[tex]\begin{gathered} 1year-------4miles^2 \\ x----------0.6715 \\ 4x=0.6715 \\ \frac{4x}{4}=\frac{0.6715}{4} \\ x=0.17 \\ \\ --- \\ 0.17\times12\approx2 \end{gathered}[/tex]Note that we found that approximately 0.17 year is necessary to submerge tat island, converting that to months, we can state that in approximately 2 months
In February of 2014, gas was about $3.37 per gallon. In February 2015, gas was about 2.25 per gallon. What is the percent decrease from 2014 to 2015?
According to the problem, the price decrease from $3.37 to $2.25. Let's find the difference
[tex]3.37-2.25=1.12[/tex]Then, we divide
[tex]\frac{1.12}{3.37}=0.33[/tex]Hence, the answer is 33%.Quadrilateral A'B'C'D'is the image of quadrilateral of ABCD under a rotation of about the origin (0,0)a. -90b. -30c. 30d. 90
In this problem we have a couterclockwise about the origin
sp
Verify
option D
rotation 90 degrees counterclockwise
(x,y) -----> (-y,x)
so
A(-2,3) ------> A'(-3,-2) ------> is not ok
therefore
answer is option Cuse the circle graph to answer the following questionhow many more pop/rock records than soul records were sold in the year shown?
We are given the record sales of varous types.
67 million records were sold.
We are asked to find out how many more Pop/Rock records than Soul records were sold in the year?
From the given information we see that
Pop/Rock records = 56%
Let's find out 56% of 67 million
[tex]67\times\frac{56}{100}=37.52\: \text{million}[/tex]Sour records = 17%
Let's find out 17% of 67 million
[tex]67\times\frac{17}{100}=11.39\: \text{million}[/tex]Now find the difference between Pop/Rock records and Soul records
[tex]difference=37.52-11.39=26.1\: \text{million}[/tex]Therefore, about 26.1 million more Pop/Rock rethan Soul records were sold in the year