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We have that the hypotenuse is 5.2 feet and we wish to find the angle Θ, therefore:
[tex]\begin{gathered} \cos \theta=\frac{BD}{AB} \\ \cos \theta=\frac{3}{5.2} \\ \theta=\cos ^{-1}(\frac{3}{5.2}) \\ \theta=54.77\approx54.8 \end{gathered}[/tex]Answer: 54.8°
Related Questions
Rewrite each expression of two powers or a quotient of two powers
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Expression:
[tex](\frac{8^4\cdot5^3}{8^5})^2[/tex]To solve this expression first we have to use the Power rule:
[tex](a^x)^y=a^{x\cdot y}[/tex]We can use this to simplify our expression as follows:
[tex]=\frac{(8^4)^2\cdot(5^3)^2}{(8^5)^2}[/tex][tex]=\frac{8^{4\cdot2}\cdot5^{3\cdot2}}{8^{5\cdot2}}[/tex][tex]=\frac{8^8\cdot5^6}{8^{10}}[/tex]Now we will use the Quotient rule:
[tex]\frac{a^x}{a^y}=a^{x-y}[/tex]To do that, we have to have the same number a, we cannot do this in the division of 5^6/8^10, but we can use it in 8^8/8^10:
[tex]=\frac{8^8}{8^{10}}\cdot5^6[/tex][tex]=8^{8-10}\cdot5^6[/tex][tex]=8^{-2}\cdot5^6[/tex]Answer:
[tex]=8^{-2}\cdot5^6[/tex]I have a few I just really do not understand..1) What is the term that describes translations?a. enlargementb. reductionc. slided. dilation2) describe with words the translation: (x,y) (x-4, y+2)3) describe with words the translation:(x,y) (x+2, y-6)4) describe with words ths dilation:(x,y) (2x, 2y)
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*For point 1: We have that a translation is an un-interrupted movement without transforming the shape, so the term that best describes it is "slide".
*For point 2: The translation that is shown is: four units to the left and two units up.
*For point 3: The translation that is shown is: two units right and six units down.
*For point 4: The dilation that is shown is: the shape increases by two times in the x-axis and increases by two times in the y-axis.
the answer to this question is 85. first solve the problem, then use conplete sentences, at least 5 sentences to describe the steps involved in solving the problem. What theorem did you use?
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Angle 1 and Angle 2 are vertical angles.
Vertical Angles are equal.
So, we can write:
[tex]x+50=3x-20[/tex]Lets solve this:
[tex]\begin{gathered} 3x-x=50+20 \\ 2x=70 \\ x=\frac{70}{2} \\ x=35 \end{gathered}[/tex]Angle A:
x + 50
x is 35, so
35 + 50 = 85
Angle A is 85 degrees
Malik earns $25 per hour at his old job. At his new job, he earns $32 per hour. What’s the percent increase in his earnings? Show your work.
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
Malik earnings:
old job:
$25 per hour
new job:
$32 per hour
Step 02:
percentage:
percent increase (per hour):
[tex]\text{ \% increase = }\frac{(\text{ \$ }32\text{ }-\text{ \$ 25\rparen}}{\text{ \$ }25}*100\text{ \% = 0.28 * 100 \% = 28\% }[/tex]The answer is:
the percent increase in his earnings is: 28%
19. The equation 7( − 11)^2 + 7( + 13)^2 = 343 is.a. A circle of radius 49 centered on (11,-13)b. A circle of radius 7 centered on (-11,-13)c. A circle of radius 7 centered on (11,-13)d. A circle of radius 343 centered on (11,-13)e. A circle of radius 49 centered on (-11,13)
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The equation of the circle looks like:
[tex](x-a)^2+(y-b)^2=r^2[/tex]where a, b and r are numbers.
The principal parts of the circle are its center and its radius:
(a, b) is the location of the center
r is the radius
We have the equation:
[tex]7(x-11)^2+7(y+13)^2=343[/tex]and we want to convert it into another aquation that looks like the circle formula. We want to remove the 7 outside the parenthesis. We do this by factoring it:
[tex]\begin{gathered} 7(x-11)^2+7(y+13)^2 \\ =7\lbrack(x-11)^2+(y+13)^2\rbrack \\ \downarrow \\ 7\lbrack(x-11)^2+(y+13)^2\rbrack=343 \end{gathered}[/tex]Now, we can take the 7 to the right side:
[tex]\begin{gathered} 7\lbrack(x-11)^2+(y+13)^2\rbrack=343 \\ \downarrow\text{ taking 7 to the right} \\ (x-11)^2+(y+13)^2=\frac{343}{7}=49 \end{gathered}[/tex]Then,
[tex]\begin{gathered} (x-11)^2+(y+13)^2=49 \\ \downarrow\text{ since }7^2=49 \\ (x-11)^2+(y+13)^2=7^2 \\ \downarrow\text{ since +}13=-(-13) \\ (x-11)^2+(y-(-13))^2=7^2 \end{gathered}[/tex]Now we have an equation that look like the original equation of the circle:
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \uparrow\downarrow \\ (x-11)^2+(y-(-13))^2=7^2 \end{gathered}[/tex]Comparing them, we have that:
a = 11
b = -13
and
r = 7
This means that this is a circle centered on
(a, b) = (11, -13)
and that has a radius of 7.
ANSWER: c. A circle of radius 7 centered on (11,-13).In the diagram of ABC, BC is extended to D, m
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Answer:
The measure of angle A is;
[tex]m\angle A=20^{\circ}[/tex]Explanation:
Given the triangle in the attached image;
[tex]m\angle ACB+m\angle ACD=180^{\circ}[/tex]sum of angles on a straight line;
[tex]\begin{gathered} m\angle ACB+m\angle ACD=180^{\circ} \\ 6y+3y=180 \\ 9y=180 \\ y=\frac{180}{9} \\ y=20 \end{gathered}[/tex]Also;
[tex]\begin{gathered} m\angle ACD=m\angle ABC+m\angle A \\ 3y=2y+m\angle A \\ m\angle A=3y-2y \\ m\angle A=y=20 \\ m\angle A=20^{\circ} \end{gathered}[/tex]Therefore, the measure of angle A is;
[tex]m\angle A=20^{\circ}[/tex]find all the zeros of polynomial functionsf(x)=x^6+6x^5-14x^4-208x^3-672x^2-928x-480
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Explanation:
Taking into account the graph of the function, we can identify zeros at x = 6 and x = -2. So, we can start the synthetic division with these numbers.
So, The synthetic division of f(x) = x⁶ + 6x⁵ -14x⁴-208x³ - 672x² -928x - 480 with x = 6 is:
Therefore, x = 6 is a zero of the equation.
If we make the synthetic division again with x = -2, we get:
Write an equation as part of solving the problem.The cost to replace a water pump in a Corvette was $255. This included $95 for the water pump plus $80/h for labor. How many hours of labor were required to replace the water pump?
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cost of replacing a water pump= C = $ 255
water pump cost = $95
Hour of labor = $80 per hour
Number of hours of labor = x
255 = 95 + 80x
Solve for x
255 - 95 = 80x
160 = 80x
160/80 = x
x = 2 hours
this is an example problem for me to learn so I can do similar ones, so please show me how to do this one. Thank you!
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The resultant force on the object = 16.65 N
Explanation:The first force is 10N acting in in the direction N 45 degrees E
F₁ = 10N in the direction N 45 degrees E
The second force is 8N acting due South
F₂ = 8N due South
The diagram below illustrates the description
Resolve F₁ in the x and y direction
[tex]\begin{gathered} F_{1x}=10\sin 45 \\ F_{1x}=\frac{10}{\sqrt[]{2}} \\ F_{1y}=10\cos 45 \\ F_{1y}=\frac{10}{\sqrt[]{2}} \\ F_1=F_{1x}i+F_{1y}j \\ F_1=\frac{10}{\sqrt[]{2}}i+\frac{10}{\sqrt[]{2}}j \end{gathered}[/tex][tex]\begin{gathered} F_{2x}=0 \\ F_{2y}=8j \end{gathered}[/tex][tex]\begin{gathered} R_x=\sum ^{}_{}F_x \\ R_x=F_1x+F_2x \\ R_x=\frac{10}{\sqrt[]{2}}+0 \\ R_x=\frac{10}{\sqrt[]{2}} \end{gathered}[/tex][tex]\begin{gathered} R_y=\sum ^{}_{}F_y \\ R_y=F_{1y}+F_{2y} \\ R_y=\frac{10}{\sqrt[]{2}}+8 \end{gathered}[/tex][tex]\begin{gathered} R=R_xi+R_yj \\ R=\frac{10}{\sqrt[]{2}}i+(\frac{10}{\sqrt[]{2}}+8)j \\ |R|=\sqrt[]{(\frac{10}{\sqrt[]{2}})^2+(\frac{10}{\sqrt[]{2}}+8)^2} \\ R=\sqrt[]{50+227.14} \\ R=\sqrt[]{277.14} \\ R=16.65N \end{gathered}[/tex]The resultant force on the object = 16.65 N 1
the lines are perpendicular if the slope of one line is -5 what is the slope of the other line
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At first we should know that :
The product of the slope of the perpendicular lines = -1
Which mean if the slope of one of them is m and the slope of the other is m'
So,
[tex]m\times m^{\prime}=-1[/tex]Given : the slope of one line is = m = -5
So, the slope of the perpendicular line will be m'
So,
[tex]\begin{gathered} -5\cdot m^{\prime}=-1 \\ \\ m^{\prime}=\frac{-1}{-5}=\frac{1}{5} \end{gathered}[/tex]So, the answer is : the slope of the other line = 1/5
1. Solve the problem.A person is watching a boat from the top of a lighthouse. The angle of depression from the person to the boat is 28°. The lighthouse is 200 feet tall. How far away is thelighthouse? Round to the nearest foot.
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Solution:
Given:
Description of a person's view from a lighthouse to a boat.
This can be sketched as shown below;
The sketch can be made as a right triangle;
To get the distance between the boat and the lighthouse, we use the trigonometrical ratio of tangent.
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{adjacent} \\ \text{where;} \\ \theta=28^0 \\ \text{opposite=200} \\ \text{adjacent}=x \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{adjacent} \\ \tan 28=\frac{200}{x} \\ \text{Cross multiplying;} \\ x\times\tan 28=200 \\ x=\frac{200}{\tan 28} \\ x=376.15 \\ To\text{ the nearest foot,} \\ x\approx376ft \end{gathered}[/tex]
Therefore, to the nearest foot, the lighthouse is 376 feet away from the lighthouse.
Solve the problem. Use what you learned from the model. Graph the functions y = 2x + 1 and y grid to determine whether they are linear or nonlinear. Describe the similarities and differences between the graphs, including their initial values and rates of change. Then graph the function y = 2x - 3 on the same grid. What are its similarities to the other two functions? Show your work. Use graphs, words, and numbers to 2x + 1 and y = 2x + 4 on the same explain your answer.
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Determine whether the given points are on the graph of Select all points that lie on the graph.
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Given the following equation of a graph:
[tex]\text{ y = 2x + 3}[/tex]For us to be able to determine which points lie on the graph, we will be plugging in each given coordinate to see if it will make the equation valid.
a.) x, y = 6, 15
y = 2x + 3
15 = 2(6) + 3
15 = 12 + 3
15 = 15 (The equation is valid)
Therefore, (6, 15) lies on the graph.
b.) x, y = 2, 2
y = 2x + 3
2 = 2(2) + 3
2 = 4 + 3
2 = 7 (The equation is invalid)
Therefore, (2,2) doesn't lie on the graph.
c.) x, y = -1, 1
y = 2x + 3
1 = 2(-1) + 3
1 = -2 + 3
1 = 1 (The equation is valid)
Therefore, (-1, 1) lies on the graph.
d.) x, y = -6, -10
y = 2x + 3
-10 = 2(-6) + 3
-10 = -12 + 3
-10 = -9 (The equation is invalid)
Therefore, (-6, -1) doesn't lie on the graph.
In summary, the points that lie on the graph are (6, 15) and (-1, 1).
I answered my homework problem, but I don’t think it’s correct
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the new standard deviation with the sample is equal to
[tex]\frac{2.2}{\sqrt[]{100}}=\frac{2.2}{10}=0.22[/tex]therefore
the answer is option C, because the mean is the same that the original graphthe number of cheeseburgers sold was 2 times the number of hamburger
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Answer:
137 hamburgers
Explanation:
Let us call h the number of hamburgers sold and c the number of cheeseburgers.
Now we are told that a combined 411 hamburgers and cheeseburgers were sold, meaning
[tex]h+c=411[/tex]Furthermore, we are also told that two times as many cheeseburgers were sold as hamburgers, meaning
[tex]c=2h[/tex]Now, the first step in finding the value of h is to substitute c = 2h in the first equation to get
[tex]2h+h=411[/tex][tex]3h=411[/tex]Dividing both sides by 3 gives
[tex]h=\frac{411}{3}[/tex][tex]h=137[/tex]which is our answer!
Hence, 137 hamburgers were sold.
Type the following inequality in the box below in standard form, do not use spaces.sion20+1091FRIENSAErrorK10
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When you have an inequality the correct form to write it in a standrad form is:
You have a dotted line it means that the result of the inequality doesn't include the value in the line just the values that are less than: (As you have the part below the line shaded)
[tex]yKnowin that we can know use the graph and determine the value of the slope (m) and b:We can find the m and the b by using the dotted line as a lineal function:
For the slope we use two points
X1= -3 Y1= 0
X2=0 Y2=-2
Then the slope willn be:
[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}=\frac{(-2-0)}{(0-(-3))}=\frac{-2}{3}==-\frac{2}{3}[/tex]Then so, the slope m= 12/3
The b is the point that takes y when x=0, we can see it is b=-2
Then the final standard form of this inequality is:[tex]y<-\frac{2}{3}x-2[/tex]the cube root is like the square root and should only be defined on the positive x-axis?
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Statement Problem: The cube root is like the square root and should only be defined on the positive x-axis?
Solution:
The cube is unlike the square root because the result of a cube root can be any real number, that is positive values, negative values and zero.
Also, the radicand of a cube root can be negative while still achieving a real result for the cube root. But when a radicand of a square root is negative, then the result is a complex number.
Area of a square or a rectangleFind the area of this rectangle.6 ydyd?11 yd
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The area of a rectangle can be calculated by the formula
Area = Length x Breadth
For this question,
Length = 11yd
Breadth = 6yd
[tex]\begin{gathered} \text{ Area = 11yd x 6yd = 66yd}^2 \\ \\ \text{ The answer is 66 yd}^2 \end{gathered}[/tex]Find the odds in favor of his character unlocking the treasure chest
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Solution
First, we are given the probability of unlocking the treasure chest
[tex]p=\frac{9}{20}[/tex]To find the odd, we
[tex]\begin{gathered} Favourable\text{ Event = 9} \\ \\ Unfavorable\text{ Event = }20-9 \\ \\ Unfavorable\text{ Event =}11 \end{gathered}[/tex]So the answer is
[tex]Odd=\frac{9}{11}[/tex]Pete bought pots for 5 dollars each and joe bought buckets for 7 dollars each. If they spent 1140 dollars for 192 items. How many of each item did they buy?
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It is given that the pots bought for 5 dollars each and the buckets bought for 7 dollars each.
It is also given that they spent 1140 dollars for 192 items.
Let the pot be x.
Let the bucket be y.
Then the equation formed is
x+y=192 .......................1
Another equation formed is
5x+7y=1140 ,.......................2
Solve both the equations for x and y by elimination method where multiply the equation 1 by 5 and subtract from 2.
[tex](5x+7y)-(5x+5y)=(1140)-(192\times5)[/tex][tex]2y=1140-960[/tex][tex]2y=180\Rightarrow y=90[/tex]Then the value of x is
[tex]x+90=192\Rightarrow x=102[/tex]Hence the pots they bought is 102 dollar and buckets they bought is 90 dollars.
A paddle board is originally priced at $80 The online retailer give a discount and the paddleboard is now $56 enter the percentage amount for the cost of the paddle board 
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Given:
A paddleboard is originally priced at $80
The online retailer gives a discount and the paddleboard is now $56
We need to find the percentage amount for the cost of the paddleboard
So, the percentage =
[tex]\frac{56}{80}\cdot100=\frac{7\cdot8}{10\cdot8}\cdot100=\frac{7}{10}\cdot100=70\%[/tex]So, the online price is 70% of the original price.
a woman can hike 2 miles faster down a trail to Archuletta Lake then she can on the return trip uphill. it takes her 2 hours to get to the lake and 4 hours to return. what is her speed hiking down to the lake?
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Assume that her speed down is x
Then her speed up is x - 2/h
Because she is faster by 2 miles down
Since D = S x T, where
D is the distance and S is the speed, T is the time
Her time up is 4 hours, and her time down is 2 hours
Her speed up = D/4
Her speed down = D/2
Since her speed down is faster by 2 miles, then
[tex]\begin{gathered} \frac{D}{2}-\frac{D}{4}=2 \\ \frac{2D}{4}-\frac{D}{4}=2 \\ \frac{D}{4}=2 \\ D=8 \end{gathered}[/tex]The distance between up and down is 8 miles
Her speed down = 8/2 = 4 miles per hour
Her speed hiking down to the lake is 4 miles/hour
the dimensions of a rectangle ABCD are shown below what is the area in square units of the Shaded region
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We get that shaded area is the difference between the complete rectangle and a triangle. So it's area is
[tex]A=9\cdot3-\frac{5\cdot3}{2}=27-7.5=19.5[/tex]A class consists of 1/3 freshmen, 1/6 sophomores, and 1/6 juniors; the rest are seniors. What fraction of the class is seniors?
Answers
1/3
Explanation
Step 1
let the entire class represents 1,so
class= freshmen +sophomores+junior+senior
replace
[tex]\begin{gathered} 1=\frac{1}{3}+\frac{1}{6}+\frac{1}{6}+\text{senior} \\ 1=\frac{2}{3}+\text{senior} \\ \end{gathered}[/tex]now, to solve the equaiton subtract 2/3 in both sides
[tex]\begin{gathered} 1=\frac{2}{3}+\text{senior} \\ 1-\frac{2}{3}=\frac{2}{3}+\text{senior-}\frac{2}{3} \\ \frac{1}{3}=\text{senior} \end{gathered}[/tex]it means 1/3 of the class is senior
I hope this helps you
Hi! I’ve missed some school and need help with my homework please. Thank you
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Rational function
A rational function is any function which can be written as the ratio of two polynomial functions.
Any function of one variable, x, is called a rational function if, and only if, it can be written in the form:
[tex]\begin{gathered} f(x)=\frac{P(x)}{Q(x)} \\ \end{gathered}[/tex]Yes, a rational function always have an aymptote.
It always have an asymptote because the denominator can never be zero.
Yes, It is possible to have holes in the graph of a rational function.
The main reason why there is a hole because if there is the same factor in the numerator and denominator, there is a hole.
Fill in the table using this function rule.y=3x-3х -4 -2 0 2y ? ? ? ?
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Given the function y = 3x - 3
When x = -4
y = 3x - 3 = 3 * (-4) - 3 = -12 - 3 = -15
When x = -2
So, y = 3 * -2 - 3 = -6 - 3 = -9
When x = 0
So, y = 3x - 3 = 3 * 0 - 3 = 0 - 3 = -3
When x = 2
y = 3x - 3 = 3 * 2 - 3 = 6 - 3 = 3
Write the equation that describes that function.Express it in slope-Intercept form.
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The equation of a line in slope-intercept form is expressed as:
[tex]y=mx+b[/tex]where:
• m is the ,slope
,• b is the ,y-intercept
From the graph, the y-intercept is the point where the line crosses the y-axis. The y-intercept is (0, -3)
Determine the slope using the coordinate point (0, -3) and (4, -2) on the line
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-2-(-3)}{4-0} \\ m=\frac{-2+3}{4} \\ m=\frac{1}{4} \end{gathered}[/tex]Substitute the slope and y-intercept into the equation to have:
[tex]\begin{gathered} y=mx+b \\ y=\frac{1}{4}x+(-3) \\ y=\frac{1}{4}x-3 \end{gathered}[/tex]Hence the equation of the line in slope-intercept form is y = 1/4 x - 3
Identify one possible combination of T-shirts and pairs of shorts that Ayonna could purchase. Use mathematics to justify your answer
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Let's use the variable x to represent the number of t-shirts and y to represent the number of pairs of shorts.
Since the total number of items needs to be more than 5 items, we can write our first inequality:
[tex]x+y>5_{}[/tex]Then, since the total cost needs to be no more than 160, we have our second inequality:
[tex]12x+25y\le160[/tex]One possible combination of values would be:
5 t-shirts and 4 pairs of shorts
(x = 5, y = 4)
This way, the number of items is 9 (greater than 5) and the total cost is $160 (no more than $160).
Which of the following measurement is more precise?0.9560.90.9090.1
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We have four measures and we have to identify which one is more precise.
We can define precision as the consistency in a group of measures.
It is not related to how exact is the value but more to how close are the measures from each other.
In this context, we can not give the precision of only one measure and without knowing the true actual value.
A SHADED REGION IS DESCRIBED BY THE FOLLOWING INEQUALITIES: X> OR EQUAL O , Y > OR EQUAL O , X+2Y< OR EQUAL 4 , X-Y < OR EQUAL 1 WHAT ARE THE CORNER POINTS?WHAT ARE THE CORNER POINTS- THESE ARE MY ANSWERS CAN YOU CONFIRM WHICH ONE IS RIGHT?(0,0) (1,0) (0,1) (0,2)(0,0) (2,1) (0,2) (1,0)
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Explanation:
The inequalities are given below as
[tex]\begin{gathered} x\ge0 \\ y\ge0 \\ x+2y\leq4 \\ x-y\leq1 \end{gathered}[/tex]Hence,
By using a graphing tool, we will have the corner points be
Hence,
The corner points are
[tex]\left(0,0\right),(2,1),(0,2),(1,0)[/tex]