Answers
The Solution:
Given the right-angled triangle below:
We are asked to find the cosine of angle R.
Using the Trigonometrical Ratio below:
[tex]\begin{gathered} \cos R=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{RT}{RS}=\frac{6}{10}=\frac{3}{5} \\ \end{gathered}[/tex]Thus, the cosine of angle R is 3/5.
Therefore, the correct answer is 3/5
Related Questions
Town A and Town B both currently have a population of 10, 000 people. If Town A increases by 500 people a year and Town B increases by 10% each year, when will the two towns have the same population again?
Answers
Let:
ya = Total population of town A
yb = Total population of town B
ya and yb are given by:
[tex]\begin{gathered} ya=10000+500x \\ yb=10000(1.1)^x \end{gathered}[/tex]We need to know when:
ya = yb
[tex]\begin{gathered} 10000+500x=10000(1.1)^x \\ \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} x=0 \\ 10000=10000 \end{gathered}[/tex]The only real solution is x = 0
Therefore, the towns will never have the same population again after the year 0
what else would need to be congruent tom show that ABC = XYZ by ASA
Answers
Given:
The two triangles ABC and XYZ are given:
To show both the triangles are congruent.
According to ASA ( angle-side-angle) property, If two angles and the side included between them
Use the graph below. How much money is earned in 5 weeks?
Pleaseeee hellppp
Answers
According to the given graph, in the 5th week, he earned $70.
Graph:
Graph refers the pictorial representation or a diagram that represents data or values in an organized manner. It contains two axis that are x an y axis.
Given,
The graph has been given in the questions, that contain the details about saving account of the person with the time and amount in the account.
Here we need to find the total amount of earning in the fifth week.
In the given graph the the x axis represents the time that is in weeks
And the y axis represents the Total savings.
So, here we have to look at the fifth place in the x axis and we have to identify the corresponding y value for that one.
Because that is the resulting amount of fifth week.
Here the points are gradually moves on the straight line,
So, in the fifth week the amount of saving is $70.
To know more about Graph here.
https://brainly.com/question/17267403
#SPJ1
Can I get some help with this problem?Graph the equations to determine the solution to the system.
Answers
Answer:
For the first equation;
The slope(m) is -3
The y-intercept(y) is 2
For the second equation;
The slope(m) is 2
The y-intercept(b) is -3
The solution of the system of equations is (-1, 1)
Explanation:
Given the below system of equations;
[tex]\begin{gathered} y=-3x+2\ldots\ldots\ldots\ldots\text{Equation 1} \\ y=2x-3\ldots\ldots.\ldots\ldots\text{.}\mathrm{}\text{Equation 2} \end{gathered}[/tex]Recall that the slope-intercept form of the equation of a line is generally given as;
[tex]y=mx+b[/tex]where m = slope of the line
b = y-intercept of the line
If we compare the slope-intercept equation with the given equations, we can deduce that for Equation 1;
The slope(m) is -3
The y-intercept(y) is 2
For the Equation 2;
The slope(m) is 2
The y-intercept(b) is -3
Below is the graph of the system of equations;
The point of intersection (-1, 1) of both lines is the solution of the system of equations
A rocket is thrown upward from the top of a tall building
Answers
The Solution:
The given function that describes the height of the rocket is
[tex]h=-16t^2+48t+160[/tex]a. We are asked to find the time (t) it takes for the rocket to reach a height of 160 feet.
We shall substitute 160 feet for h in the given function.
[tex]\begin{gathered} 160=-16t^2+48t+160 \\ 0=-16t^2+48t \end{gathered}[/tex]Factorizing, we get
[tex]\begin{gathered} 16t(-t+3)=0 \\ 16t=0\text{ or -t+3=0} \\ t=0\text{ or t=3} \end{gathered}[/tex]So, it took the object 3 seconds to reach a height of 160 feet.
b.
We are required to find the time(t) it will take the object to hit the ground.
For the object to hit the ground, the height has to be zero (0).
So, we shall substitute 0 for h in the given function.
[tex]0=-16t^2+48t+160[/tex]Solving the above quadratic equation by Factorization Method, we have
[tex]\begin{gathered} 16t^2-48t-160=0 \\ t^2-3t-10=0 \\ t^2-5t+2t-10=0_{} \end{gathered}[/tex][tex]\begin{gathered} t(t-5)+2(t-5)=0 \\ (t+2)(t_{}-5)=0 \\ t+2=0\text{ or t-5=0} \\ t=-2\text{ or t=5} \end{gathered}[/tex]Since, the time (t) cannot be negative, we discard -2.
So, the time it will take the object to reach the ground is 5 seconds.
solve the following nonlinear system algebraically. be sure to check for non-real solutions.
Answers
Use substitution method to and solve in terms of x using the first equation
[tex]\begin{gathered} x^2+y^2=8 \\ x^2=8-y^2 \end{gathered}[/tex]Next, substitute it to the second equation
[tex]\begin{gathered} 2x^2+4y^2=34 \\ 2(8-y^2)+4y^2=34 \\ 16-2y^2+4y^2=34 \\ 2y^2=34-16 \\ 2y^2=18 \\ \frac{2y^2}{2}=\frac{18}{2} \\ y^2=9 \end{gathered}[/tex]Then, substitute it back to first equation and solve for x
[tex]\begin{gathered} x^2+y^2=8 \\ x^2+9=8 \\ x^2=8-9 \\ x^2=-1 \end{gathered}[/tex]Now we have the following solutions
[tex]x^2=-1\text{ and }y^2=9[/tex]Get the square root of both x's and y's to get the solution
[tex]\begin{gathered} x^2=-1 \\ \sqrt{x^2}=\sqrt{-1} \\ x=\pm i \\ x=i\text{ and }x=-i \\ \\ y^{2}=9 \\ \sqrt{y^2}=\sqrt{9} \\ y=\operatorname{\pm}3 \\ y=3\text{ and }y=-3 \end{gathered}[/tex]Getting the combination of ordered pairs we have the following solutions
[tex]\begin{gathered} (i,3) \\ (i,-3) \\ (-i,3) \\ (-i,-3) \end{gathered}[/tex]Write the coordinates of the vertices after a translation 1 unit left and 7 units up.S (6, -10) -> S' (__,__)T (10, -10) -> T' (__,__)U (10, 0) -> U' (__,__)V (6, 0) -> V' (__,__)
Answers
To perform a horizontal translation of a point on the coordinate system you have to add/subtract the constant, k, from the x-coordinate of the point:
• If you add the constant, ,x+k,, the resulting translation will be, k units to the right,.
,• If you subtract the constant, ,x-k,, the resulting translation will be ,k units to the left,.
To perform a vertical translation of a point on the coordinate system, you have to add/subtract a constant, c, from the y-coordinate of the point.
• If you add the constant, ,y+c,, the resulting translation will be, ,c units up.
,• If you subtract the constant, ,y-c,, the resulting translation will be, c units down.
The points on the coordinate system were moved 1 unit to the left, which means that you have to subtract 1 unit from the x-coordinate of each point and 7 units up, which means that you have to add 7 units to the y-coordinate of each point.
You can express the translation rule as follows:
[tex](x,y)\to(x-1,y+7)[/tex][tex]S(6,-10)\to S^{\prime}(6-1,-10+7)=S^{\prime}(5,-3)[/tex][tex]T(10,-10)\to T^{\prime}(10-1,-10+7)=T^{\prime}(9,-3)[/tex][tex]U(10,0)\to U^{\prime}(10-1,0+7)=U^{\prime}(9,7)[/tex][tex]V(6,0)\to V^{\prime}(6-1,0+7)=V^{\prime}(5,7)[/tex]The resulting coordinates after the translation are:
S'(5,-3)
T'(9,-3)
U'(9,7)
V'(5,7)
Which expression is equivalent to 3 square root of x to the power of 10
Answers
The trick of the problem is to change the question into: Which expression is equivalent to x^10? Because the 3 square root is not changed in any sense. Now, we need to remember what could be with an expression like x^10. First, one can't add numbers without care (sloppily). For instance, if our x were 1,
[tex]x^{10}=(1)^{10}=1\ne3(1)=3\cdot x^{10}[/tex]Thus, we must discard the second option. We can discard the third option too, for sum and product are really different operations. Finally, without discard the first option, I want to say that we can "separate" the exponent of an expression through the product. This could sound strange, but it just means
[tex]x^{a+b}=x^a\cdot x^b[/tex]With this property in mind, we can say that
[tex]x^{10}=x^{9+1}=x^9\cdot x^1=x^9\cdot x[/tex]Thus, our answer is the last option.
Can you find 0.5% of a number by multiplying the number by 5/100?
Answers
No, to find the 0.5% of a number you multiply the number by 0.5/100 or 0.005
Example; the 0.5% of 200 is:
[tex]200*\frac{0.5}{100}=1[/tex](You multiply a number by 5/100 to find the 5%)
each person in a community was asked,what is your favorite type of pet? the pie below summarizes their responses
Answers
Given in the pie graph.
a.) Approximately one-fifth of the community chose Cats as their favorite pet.
b.) Approximately 50% of the community chose Cat or Dog.
c.) If 30% of the community chose Dog, approximately 15% chose Fish.
3. Write an equation of a quadratic function that has a vertex of (-2, 4) and is more narrow than the Parent function. Answers may vary. Carefully consider the best form to write your equation in.
Answers
Answer:
[tex]f(x)=3(x+2)^2\text{ + 4}[/tex]Explanation:
The general form of a quadratic equation in the vertex form is:
[tex]y=a(x-h)^2\text{ + k}[/tex]where the vertex would be (h,k)
Thus, we have the equation as:
[tex]f(x)=a(x+2)^2\text{ + 4}[/tex]The value of a will determine how narrow the function would look when plotted
Mathematically, we have the parent function as when a = 1
The higher the value of a, the narrower the plot would look
Putting this into consideration, we have the equation as:
[tex]f(x)=3(x+2)^2\text{ + 4}[/tex]Kindly note that if a is 4, we would have a narrower plot than the parent function where a is adjudged to be equal to 1
However, if a is 1/3 (a positive number less than 1), we would have a broader plot
If x=d +2 and d +2+x= y, then which of the following statements is true? A. p= 20 +4+x B. y = 2x C. 4d + 2 =) D. 60 = y A
Answers
We have the following equations:
[tex]\begin{gathered} x=d+2 \\ d+2+x=y \end{gathered}[/tex]notice that we can substitute d+2 on the second equation with x to get the following:
[tex]\begin{gathered} (d+2)+x=y \\ \Rightarrow x+x=y \\ \Rightarrow2x=y \end{gathered}[/tex]therefore, the statement that is true is y = 2x
if 2= (1+r)^7 then, solve the equation for what is"r" equal to.?
Answers
We need to solve the following expression.
[tex]2=(1+r)^7[/tex]The first step to do this is to remove the power of 7 from the parenthesis. To do this we need to apply the seventh root on both sides of the equation as shown below.
[tex]\sqrt[7]{2}=\sqrt[7]{\left(1+r\right)^7_{}}[/tex]The 7 root and the power of 7 cancel each other on the right side and with the help of a calculator we can find the 7 root of 2 from the left side.
[tex]1.104=1+r[/tex]We can now isolate the "r" variable on the left side to find its value.
[tex]\begin{gathered} r\text{ = 1.104-1} \\ r=0.104 \end{gathered}[/tex]The result is "r=0.104".
If you know how to properly solve the union and intersection of intervals, please help me.
Answers
I am going to write various equations, please give a moment as I do it
Lets notice that
[tex]F\subset\text{ H}[/tex]this because, if
[tex]w\text{ }\leq\text{ 2 }\Rightarrow\text{ w }<\text{ 5}[/tex]then,
[tex]\begin{gathered} F\cup H\text{ = H = (-}\infty,\text{ 5)} \\ F\cap\text{ H = F = (-}\infty,2\rbrack \end{gathered}[/tex]For the second question, now we consider that
[tex]\begin{gathered} B=\text{ (-}\infty,4) \\ C=\text{ \lbrack{}6,}\infty) \\ \text{then } \\ B\cap C=\text{ }\varnothing \\ B\cup C\text{ = (-}\infty,\text{ 4) }\cup\text{ \lbrack{}6,}\infty) \end{gathered}[/tex](a) How high is the ball when it was thrown?(b) What is the maximum height of the ball?
Answers
Given:
[tex]h(x)=-\frac{1}{20}x^2+8x+6[/tex]Where h(x) is the height of the ball that is thrown in the air
And (x) is the horizontal distance in feet from the point of throwing
We will find the following:
(a) How high is the ball when it was thrown?
So, substitute with x = 0
So, h(x) = 6
So, the answer to part (a) is 6 feet
(b) What is the maximum height of the ball?
So, as the function h(x) is a quadratic function, we will find the vertex point
We will complete the square of h(x):
[tex]\begin{gathered} h(x)=-\frac{1}{20}(x^2-160x)+6 \\ h(x)=-\frac{1}{20}(x^2-160x+6400-6400)+6 \\ \\ h(x)=-\frac{1}{20}(x^2-160x+80^2)+\frac{6400}{20}+6 \\ \\ h(x)=-\frac{1}{20}(x-80)^2+326 \end{gathered}[/tex]So, the vertex of h(x) will be = (80, 326)
So, the answer of part b) the maximum height = 326 feet
Evaluate f(x) = 4/5x - 6 for f(20)
Answers
f(x) = (4/5)x - 6
f(20) = (4/5)20 - 6 = 80/5 - 6 = 16 - 6 = 10
f(20) = 10
Answer: f(20) = 10
Given the following table with selected values of f (x) and g(x), evaluate f (g(3)).
Answers
The given functions are f(x) and g(x)
We want to evaluate f(g(3))
The first step is to find g(3). We would look at the row containing the values of x and select x = 3. We would trace it downwards to the row containging g(x). Where they meet is g(3)
therefore, g(3) = - 4
To get f(g(3)), we would locate x = - 4 on the first row. We would trace it downwards to the row containing f(x). Where they meet is f(g(3))
Thus,
f(g(3)) = - 1
Devante can shovel the driveway in 3.5 hours, but if his sister Naomi helps it would take 1.5 hours. How long would it take Naomi to shovel the driveway alone?
Answers
Answer: Naomi would take 2.625h to shovel the driveway.
Explanation
Given
• Devante (,d,) can shovel the driveway in 3.5 hours
,• If his sister Naomi (,n,) helps it would take 1.5 hours.
We can rewrite the information as one job done per 3.5 hours made by Devante:
[tex]d=\frac{1\text{ job done}}{3.5\text{ hours}}[/tex]We do not know how much time does Naomi takes, then:
[tex]n=\frac{1\text{ job done}}{x\text{ hours}}[/tex]At last, together (t) they make one job done per 1.5 hours:
[tex]t=\frac{1\text{ job done}}{1.5\text{ hours}}[/tex]Then, we can build the relation as follows:
[tex]\frac{1}{3.5}+\frac{1}{x}=\frac{1}{1.5}[/tex]Multiplying everything times x:
[tex]x\times(\frac{1}{3.5}+\frac{1}{x})=\frac{1}{1.5}\times x[/tex][tex]\frac{x}{3.5}+\frac{x}{x}=\frac{x}{1.5}[/tex][tex]\frac{x}{3.5}+1=\frac{x}{1.5}[/tex]Grouping common terms on one side and simplifying:
[tex]\frac{x}{1.5}-\frac{x}{3.5}=1[/tex][tex]x(\frac{1}{1.5}-\frac{1}{3.5})=1[/tex][tex]x(\frac{8}{21})=1[/tex]Solving for x:
[tex]x=\frac{1}{\frac{8}{21}}[/tex][tex]x=\frac{21}{8}=2.625[/tex]Solve this system of equations usingthe substitution method.y = 4x3x – 7 = y1
Answers
Given:
[tex]\begin{gathered} y=4x \\ 3x-7=y \end{gathered}[/tex]Required:
To solve the given equations by using substitution method.
Explanation:
Consider the given two equation
[tex]\begin{gathered} y=4x------(1) \\ 3x-7=y--------(2) \end{gathered}[/tex]Substitute equation (1) in (2), we get
[tex]\begin{gathered} 3x-7=4x \\ 3x-4x=7 \\ -x=7 \\ x=-7 \end{gathered}[/tex]Put x in (1), we get
[tex]\begin{gathered} y=4(-7) \\ \\ y=-28 \end{gathered}[/tex]Final Answer:
[tex](-7,-28)[/tex]What is the volume of the pyramid in mº? The pyramid has a square base and a height of 5 m. 12 m O A. 240 m 3 O B. 144 m 3 B O c120 O D. 60 m O E. 20 m
Answers
To be able to determine the volume of the Pyramid, we will be using the following formula:
[tex]\text{Volume = }\frac{1}{3}BH[/tex]Where,
B = Base area
H = Height
We get,
[tex]\text{Volume = }\frac{1}{3}BH[/tex][tex]\text{ = }\frac{1}{3}(12\text{ x 12)(5)}[/tex][tex]\text{ = }\frac{1}{3}(144)(5)[/tex][tex]\text{ = }\frac{1}{3}(720)[/tex][tex]\text{ Volume = 240 m}^3[/tex]Therefore, the volume of the Pyramid is 240 m^3
A town recently dismissed eight employees in order to meet their new budget reductions. The town had six employees over 50 years of age and 18 under 50. If the dismissed employees were selected at random what is the probability that exactly 6 employees were over 50? Express your answer as a fraction or decimal number rounded to four decimal places
Answers
Solution:
Given:
[tex]\begin{gathered} Total\text{ dismissed}=8 \\ \\ \\ Over\text{ 50}=6 \\ Under\text{ 50}=18 \\ Total\text{ employees}=24 \end{gathered}[/tex]If the dismissed employees were selected at random what is the probability that exactly 6 employees were over 50 will be;
[tex]\begin{gathered} \frac{^6C_6\times^{18}C_2}{^{24}C_8}=\frac{1\times153}{735471} \\ =\frac{153}{735471} \\ =\frac{1}{4807} \end{gathered}[/tex]Therefore, the probability that exactly 6 employees were over 50 will be;
[tex]\frac{1}{4807}[/tex]Find the functionFind the function that is finally graphed after the following transformations are applied to the graph of y=|x|. The graph is shifted right 3 units, stretched by a factor of 3, shifted vertically down 2 units, and finally reflected across the x-axis.Ay = -(3|x + 3| - 2)By = -(3|x - 3| - 2)Cy = 3|-x - 3| - 2Dy = -3|x - 3| - 2
Answers
When the graph of parent function above is shifted 3 units right, the equation becomes:
[tex]y=|x-3|[/tex]If it is stretch by a factor of 3, this means we will multiply the function by 3. The function becomes:
[tex]y=3|x-3|[/tex]Then, if we add another transformation, that is shifted vertically down by 2 units then, this means, we will subtract 2 on the function. The function becomes:
[tex]y=3|x-3|-2[/tex]Finally, if the function is reflected across the x-axis, then we will multiply -1 to the entire function. The function becomes:
[tex]y=-(3|x-3|-2)[/tex]The answer is found in Option B.
The oil in a lamp burns at a linear rate. The lamp contained 13 ounces of oil ten minutes after it was lit. It contained seven ounces of oil 38 minutes after it was lit. What was the original volume of oil before the lamp was lit?
Answers
Since the oil in the lamp burns at a linear rate, we can say that it follows an arithmetic progression. For an arithmetic progression, the formula for finding the nth term is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence(initial volume of oil)
n represents the number of terms(the time )
d represents the common difference(The constant amount by which the volume of oil is decreasing)
Tn represents the volume of oil left after n minutes
Looking at the information given, the following equations can be derived
For the first equation,
13 = a + (10 - 1)d
13 = a + 9d
For the second equation,
7 = a + (38 - 1)d
7 = a + 37d
subtracting the second equation from the first equation, it becomes
6d = 28
What is the y-intercept of 12x-4y=8
PLEASE EXPLAIN THE STEPS
Answers
Answer:
y-intercept = -2
Step-by-step explanation:
12x - 4y = 8
First, we want to put y on one side, so,
-4y = -12x + 8
Now we need to have y by itself without the -4, so,
y = [tex]\frac{-12x}{-4}[/tex] + [tex]\frac{8}{-4}[/tex]
Above the -12x and the -4 are both negative and are in a fraction, so, now we cross it out. This is because 2 negative signs make a positive.
y = [tex]\frac{12x}{4}[/tex] + [tex]\frac{8}{-4}[/tex]
Both the first and second fractions can now be simplified, so,
12 / 4 = 3 and 4 /4 = 1
8 / -4 = -2
The equation will now look like this
y = 3x - 2
The y-intercept of an equation is always at the end of the equation. In this case it is -2. This is because that is what we start with.
So, the y-intercept is -2.
a fair unbiased coin was flipped 10 times giving the results shown in the table where T=tails H=heads
Answers
Given that there are 2 possible outcomes (tails and heads), the theoretical probability of getting heads is 1/2 = 0.5
In the experiment, 2 heads were obtained in 10 times. Then the experimental probability is 2/10 = 0.2.
Therefore, the difference between theoretical and experimental probabilities is 0.5 - 0.2 = 0.3
Matt rolls an old inflated tire in his backyard. If the outer radius of the tire is 30 centimeters and the tire completes 20revolutions, what is the distance that the tire travels?
Answers
Given: Matt rolls an old inflated tire in his backyard. If the outer radius of the tire is 30 centimeters and the tire completes 20 revolution.
Find: the distance that the tire travels.
Explanation: the tire travel distance in 1 revolution is
[tex]\begin{gathered} 2\pi r \\ =2\pi\times30 \\ =60\pi\text{ cm} \end{gathered}[/tex]the tired travel distance in 20 revolution is
[tex]\begin{gathered} 60\pi\times20 \\ =1200\pi cm \end{gathered}[/tex]Final answer: the required answer is
[tex]1200\pi cm[/tex]I need help finding the answer. I don’t need a step-by-step explanation just the answer please. Thank you.
Answers
Answer: We have to find the composed functions, the answers are as follows:
[tex]\begin{gathered} p(x)=-2x \\ \\ \\ q(x)=x^2+2 \\ \\ -------------- \\ (q\ast p)(3)=q(p(3)) \\ \\ \\ q(p(x))=(-2x)^2+2=4x^2+2 \\ \\ \\ q(p(3))=4(3)^2+2=36+2=38 \\ \\ \\ (q\operatorname{\ast}p)(3)=38 \\ \\ ------------------- \\ (p\ast q)(3)=p(q(3)) \\ \\ \\ p(q(x))=-2(x^2+2)=-2x^2-4 \\ \\ \\ p(q(3))=-2(3)^2-4=-18-4=-22 \\ \\ \\ (p\ast q)(3)=-22 \end{gathered}[/tex]The answers are 38 and -22.
Employee A gets paid $150 weekly, plus $0.50 for each latte they sell. If he was paid $275,how many lattes did he sell this week?
Answers
Let x be the number of latter he sold this week
Let us first set the equation
y = 0.5x + 150 where y is the total pay
275 = 0.5x + 150
Let's go ahead and solve for x
substract 150 from both-side
275 - 150 = 0.50x
125 = 0.50x
Divide both-side by 0.50
250 =x
Hence, he sold 250 lattes
I see Q2, -1/2 220 degree and Q3, -1/2 on 210 degree..
Answers
In the given unit circle, the x coordinate gives the cos value of an angle and the y cooridnate gives the sine value of an angle.
The sine and cosine value of a particular angle is,
[tex]\frac{-\sqrt[]{2}}{2}[/tex]From the given unit circle
[tex]\begin{gathered} \cos \frac{3\pi}{4}=\frac{-\sqrt[]{2}}{2} \\ \sin \frac{5π}{4}=\frac{-\sqrt[]{2}}{2} \end{gathered}[/tex]A fully loaded Toyota Forerunner sells for $42,000. It depreciates 12% per year from the date of purchase. How many years will it take to be worth half its value?
Answers
Answer:
Explanation:
The formula for calculating exponential decay is expressed as
A = P(1 - r)^t
where
A is the price after t years
P is the initial price
r is the rate of decay
t is the number of years
From the information given
P = 42000
r - 12% = 12/100 = 0.12
By the time it is half of its initial price, A = 42000/2 = 21000
By substituting these values into the formula, we have
21000 = 42000(1 - 0.12)^t
21000/42000 = (0.88)^t
0.5 = (0.88)^t
Taking natural log of both sides,
ln 0.5 = tln0.88
t = ln0.5/ln0.88
t = 5.44
The closest option is 6
Thus,
time = 6 years
