Label the sides of the right triangle.*2 pointsCaptionless ImageA) Hypotenuse = 8 m, Adjacent = 15 m, Opposite = 17 mB) Hypotenuse = 17 m, Adjacent = 8 m, Opposite = 15 mC) Hypotenuse = 15 m, Adjacent = 17 m, Opposite = 8 mD) Hypotenuse = 17 m, Adjacent = 15 m, Opposite = 8 m
Answers
Given:
There are given that the right angle triangle, UVW.
Where,
[tex]\begin{gathered} UV=8m \\ VW=15m \\ UW=17m \end{gathered}[/tex]Explanation:
According to the concept:
The hypotenuse is defined as the longest side in the right-angle triangle.
The perpendicular side is defined by the perpendicular base angle.
And,
The adjacent side is defined by the leg of the right-angle triangle.
Final answer:
Hence, the correct option is D.
Related Questions
A group of workers can plant 334 acres in 118 days. What is the unit rate in acres per day? Write your answer as a fraction or a mixed number in simplest form.
Answers
Number of acres = 334
Number of days = 118 days
unit rate = Number of acres/Number of days
Unit rate = 334 acres/114 days
2 is common to both numerator and denominator
Divide both by 2:
Unit rate = 167/57
No other number asides 1 is common to both the numerator and denominator
Hence, the unit rate in acres per day is 167/57
In mixed fraction = 2 53/57
Write two numbers that multiply to the value on top and add to the value on bottom.-14Х5
Answers
Let the first number be m while the second num
Use long division to find the quotient. If there is a remainder do not include it in your answer. Recall:dividend\div divisor=quotient (4x^2-10x+6) \div(4x+2) Answer:
Answers
Let's do the division:
Answer: x-3
An ice cream shop offers 27 different flavors of ice cream and 11 different toppings.How many different sundaes can you create using one of the ice cream flavors and one of the toppings
Answers
297 different sundaes can you create using one of the ice cream flavors and one of the toppings.
Define multiplication.We can rapidly determine the total number of things by multiplying. In order to do this, we will consider the number of groups with equal sizes and the number of items in each group.
The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers. When we need to merge groups of similar sizes, we employ it.
Given,
An ice cream shop offers 27 different flavors of ice cream and 11 different toppings.
Multiplying,
27 × 11
297
297 different sundaes can you create using one of the ice cream flavors and one of the toppings.
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The figure below shows an upside-down pyramid with a square base.inverted pyramid with a square baseNote: figure not to scale.Which shape does the intersection of the horizontal plane with the pyramid look like?
Answers
ANSWER:
EXPLANATION:
Given:
Since the pyramid has a square base, therefore intersection of the horizontal plane will produce a shape that looks like a square.
2.Flight of a Model Rocket A model rocket is launched from the ground with veloc-ity 48 ft per sec at an angle of 60° with respect to the ground.(a) Determine the parametric equations that model the path of the projectile.(b) Determine the rectangular equation that models the path of the projectile.(c) Determine approximately how long the projectile is in flight and the horizontaldistance covered.
Answers
The parametric equation for the rocket is given by
x = 24 t and y = 24√3 t
Given velocity = 48 ft per sec
∅ = 60°
Distance = speed × time
d = 48t
Displacement along the x-axis
= v cos ∅
= 48× t ×cos60°
=24 t
displacement along the y axis
= v sin ∅
=48 t sin 60°
=24√3 t
In mathematics, a parametric equation represents a set of numbers as functions between one or maybe more independent variables, often known as parameters.
When equations are used to indicate the dimensions of the constituent parts of a geometric object, such as a curve or surface, they are collectively referred to as the parametric representation (alternatively written as parametrization) of the object.
b) now we will use the parametric equation to calculate the rectangular equation.
we know that x = 24t and y = 24√3 t
again, x/24 = y/24√3
or, √3x = y
c) Hence we can see that the parametric equation for the projectile is given by x = 24 t and y = 24√3 t and the rectangular equation is given by
√3x = y .
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Four times a number plus two is equal to 3 times the number.
Answers
We have to find the number that satisfies: "Four times a number plus two is equal to 3 times the number".
Four times a number is 4x.
Then, we can write and solve the expression as:
[tex]\begin{gathered} 4x+2=3x \\ 4x-3x=-2 \\ x=-2 \end{gathered}[/tex]The number is -2.
Find the range of the function for the given domain: {-4, 0, 4}
f(x)=x²-2
O {-14, 2)
O {-14, 2, 18)
O {-2, 14)
O (-18, -2, 14)
Answers
Answer:
{-2,14}
Step-by-step explanation:
f(-4) = f(4) = 14
f(0) = -2
Which would you use to compare 10 / 12 and 2 / 5 a common numerator or common denominator?
Answers
We can compare 2 fractions by means of the cross multiplication method. In our case, we have
since 50 is greater than 24 then 10/12 is greater than 2/5:
[tex]\frac{10}{12}>\frac{2}{5}[/tex]how do I do plus 4 with 928 times 90 equal to what plus 57 divided by 134
Answers
What to plus 57 divided by 134 is 83523.57
Approximate one of the solutions to the system of equations graphed below? 4 d 194 (0,5) O (4,-5) (3, 0) (-3, -3)
Answers
SOLUTION
Method:
The solution is gotten at the coordinates of the point of intersection.
The points of intersections are (-2, 0) and (4, -5)
Final answer:
(4, -5)
I need the answer for this question on math
Answers
Answer:
12.8 grams per 1 package
102.4 grams per 8 packages
128 grams per 10 packages
Step-by-step explanation:
we can take
25.6 ÷ 2
to get the unit rate (number of grams per 1 package)
25.6 ÷ 2 = 12.8
12.8 grams per 1 package
multiply 12.8 by 8 to get the amount of grams per 8 packages
12.8 * 8 = 102.4
102.4 grams per 8 packages
we can set up a proportion to find the number of packages for 128 grams
let p = number of packages
12.8/1 = 128/p
12.8 = 128/p
multiply by "p" on both sides to get rid of the "p" in the denominator
12.8*p = (128/p )* p
12.8p = 128
divide by 12.8 on both sides to isolate "p"
12.8p = 128
÷12.8 ÷12.8
p = 10
128 grams per 10 packages
Find the tangent of the larger acute angle in a right triangle with side lengths 3, 4, and 5.
Write your answer as a fraction.
The tangent of the larger acute angle is ______?______
Answers
The tangent should be in fraction is 4/3
Calculation of the tangent:
Since in a right triangle with side lengths 3, 4, and 5
Here there is the larger acute angle in the 3, 4 and 5 so it should be lies between 3 and 5
So, it should be like
= opposite side ÷ adjacent side
= 4/3
Hence, The tangent should be in fraction is 4/3
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301123233What Happened When the Crossword Puzzle Champion Died?Find the graph of the solution set of each inequality below in the corresponding column of graphs. Notice the letter next to it.Write this letter in each box containing the number of that exercise. Keep working and you will find out about this grave event.x<2(10 x<1 0 4x is less than 2-3 -2 -1 0 1 2 3-3 -2 -1 0 1 2X<2D++++-3 -2 -123-3 -2 -1 0 1 2 33 x>2+ 12 -3 2 A +++ +13 x>-3-3 -2 -1 0 1 2-3 -2 -1 0 1 2 3(5) x 114 #-1 ++++-3 -2 -10 1 2 3x < -1 A+++ 6 0 >-3 -2 -12-3 -2 -1 0 1 2 3x>-1 E+6 0 6 +++-3 -2 -1 0 1 2-3 -2 -1 0 1 2 318 0
Answers
I'm doing it on my notebook, hold on, it's easy
Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas.tan(u) = 13/5, 0 < u < /2
Answers
The first step to answer this question is to find tan(2u) by using the double angle formula:
[tex]\begin{gathered} tan(2u)=\frac{2tan(u)}{1-tan^2(u)} \\ tan(2u)=\frac{2(\frac{13}{5})}{1-(\frac{13}{5})^2} \\ tan(2u)=\frac{\frac{26}{5}}{1-\frac{169}{25}} \\ tan(2u)=\frac{\frac{26}{5}}{-\frac{144}{25}} \\ tan(2u)=-\frac{65}{72} \end{gathered}[/tex]It means that tan(2u) is -65/72.
The next step is to rewrite the equations for sin(2u) and cos(2u) to have them in terms of the least number of variables possible, this way:
[tex]\begin{gathered} sin(2u)=2sin(u)cos(u) \\ sin(2u)=2sin(u)\frac{sin(u)}{tan(u)} \\ sin(2u)=\frac{2sin^2(u)}{tan(u)} \end{gathered}[/tex][tex]\begin{gathered} cos(2u)=cos{}^2(u)-sin^2(u) \\ cos(2u)=1-sin^2(u)-s\imaginaryI n^2(u) \\ cos(2u)=1-2sin^2(u) \end{gathered}[/tex]If we rewrite tan(2u) in terms of sin(2u) and cos(2u) we will have:
[tex]\begin{gathered} tan(2u)=\frac{sin(2u)}{cos(2u)} \\ tan(2u)=\frac{\frac{2s\imaginaryI n^{2}(u)}{tan(u)}}{1-2sin^2(u)} \end{gathered}[/tex]We know the values of tan(2u) and tan(u), so we can solve the equation for sin^2(u).
[tex]\begin{gathered} tan(2u)=\frac{2sin^2(u)}{tan(u)(1-2sin^2(u))} \\ -\frac{65}{72}=\frac{2s\imaginaryI n^2(u)}{\frac{13}{5}(1-2s\imaginaryI n^2(u))} \\ -\frac{65}{72}\cdot\frac{13}{5}\cdot(1-2sin^2(u))=2sin^2(u) \\ -\frac{169}{72}(1-2sin^2(u))=2sin^2(u) \\ -1+2sin^2(u)=\frac{72}{169}\cdot2sin^2(u) \\ -1+2sin^2(u)=\frac{144}{169}sin^2(u) \\ 2sin^2(u)-\frac{144}{169}sin^2(u)=1 \\ \frac{194}{169}sin^2(u)=1 \\ sin^2(u)=\frac{169}{194} \end{gathered}[/tex]Using this value we can find the values of sin(2u) and cos(2u):
[tex]\begin{gathered} sin(2u)=\frac{2sin^2(u)}{tan(u)} \\ sin(2u)=\frac{2\cdot\frac{169}{194}}{\frac{13}{5}} \\ sin(2u)=\frac{65}{97} \end{gathered}[/tex][tex]\begin{gathered} cos(2u)=1-2sin^2(u) \\ cos(2u)=1-2\cdot\frac{169}{194} \\ cos(2u)=1-\frac{169}{97} \\ cos(2u)=-\frac{72}{97} \end{gathered}[/tex]It means that sin(2u)=65/97, cos(2u)=-72/97 and tan(2u)=-65/72.
When 7 times a number is decreased by 1, the result is 9 more than 5 times the number?So I got this below: 7x-1 = 9+5yHow do I find the number?
Answers
5
1) Translating that into a mathematical expression, we can write out the following. Let's call this number by "n":
[tex]\begin{gathered} I)7n-1 \\ II)9+5n \\ 7n-1=9+5n \\ 7n-5n=9+1 \\ 2n=10 \\ \frac{2n}{2}=\frac{10}{2} \\ n=5 \end{gathered}[/tex]Just one mistake: when we refer to the same number we use the same variable.
Both circles have the same center. What is the area of the shaded region?10.7 md=26.2 mUse 3.14 for a. Write your answer as a whole number or a decimal rounded to the nearesbundredth
Answers
To determine the area of the shaded region, we would subtract the area of the smaller or inner circle from the area of the bigger or outer circle.
From the information given,
diameter of inner circle = 26.2m
radius of inner circle = diameter/2 = 26.2/2 = 13.1m
B applying the formula for determining the area of a circle which is expressed as
Area = pie * r^2,
pie = 3.14
Area of inner circle = 3.14 * 13.1^2 = 538.86 m^2
Radius of outer circle = 10.7 + 13.1 = 23.8m
Area of outer circle = 3.14 * 23.8^2 = 1778.62m^2
Therefore,
Area of shaded region = 1778.62 - 538.86 = 1239.76m^2
4. An object is at rest if all forcesacting on the object have a netforce of zero. If an object has aforce of -5.5 Newtons applied toit, what force needs to be appliedin order for the object to be atrest?
Answers
The object will be at rest if the resultant forces = 0
For the given object, a force of -5.5 Newtons applied to it
So, to be at rest we will add another force equal in magnitude and opposite in direction
So, the answer will be the required force = +5.5 newtons
Select the correct answer from each drop-down menu. The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0. The equation of this circle in standard form is . The center of the circle is at the point , and its radius is units.
Answers
In the last three years, Franks basketball team won 20 more games than they lost. if they won 130 games, what was the ratio of wins to looses? Write in fraction form.
Red
2.) Green Beans are canned by 2 companies. The Del Monte Company sells
14.5 oz for $1.75 and the Green Giant company sells 15.5 oz for $1.95.
Who has the best deal?
3.)In the last three years, Frank's basket ball team won 20 more games than
they lost. If they won 130 games, what was the ratio of wins to losses?
Write in fraction form.
((. 3 questions into one pls answer !))
A professor had students keep track of the social relations for a week and a number of social directions over the weekend and following the distribution how many students had at least 75 social interactions in the week?
Answers
Answer: 12 students
Since we need to find how many students had at least 75 social interactions in the week, we will add up all the frequencies from at least 75 interactions. Looking at the given table, that would be 3, 6, 1, and 2.
Adding them up together and we will get:
[tex]3+6+1+2=12[/tex]Therefore, 12 students had at least 75 social interactions in the week.
5.True or False: The ordered pair (0, 3) is a solution to the equationy = -5x + 3.
Answers
You have the following equation:
y = -5x + 3
in order to determine if the point (0,3) is solution of the previous equation, replace the values of x = 0 and y = 3, and verify if the equation is consistent, as follow:
3 = -5(0) + 3
3 = 3
the equation is consistent for the given point, then, the point (0,3) is a olution of the given equation
The area of a new wctabfle is 28m^2 and the length of the rectangle is 1m more than double the width. Find the dimensions
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Represent the sides of the rectangle
Let the length be represented by l
Let the width be represented by w
STEP 2: Interpret the statements in the question.
[tex]\begin{gathered} length\text{ is 1m more than the double of the width:} \\ double\text{ of the width}\Rightarrow2w \\ 1m\text{ more than the double}\Rightarrow2w+1 \\ \therefore l=2w+1 \end{gathered}[/tex]STEP 3: Equate the area of the rectangle to given measure
[tex]\begin{gathered} Area=length\times width \\ length=2w+1,width=w \\ Area=(2w+1)\cdot w=28 \\ By\text{ simplification,} \\ w(2w+1)=28 \end{gathered}[/tex]STEP 4: Solve for the width
[tex]\begin{gathered} w(2w+1)=28 \\ By\text{ expansion,} \\ 2w^2+w=28 \\ Subtract\text{ 28 from both sides} \\ 2w^2+w-28=28-28 \\ 2w^2+w-8=0 \end{gathered}[/tex]STEP 5: Solve the equation using quadratic formula
[tex]quadratic\text{ formula}\Rightarrow\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]From the equation,
[tex]a=2,b=1,c=-28[/tex]By substitution,
[tex]\begin{gathered} w_{1,\:2}=\frac{-1\pm\sqrt{1^2-4\cdot\:2\left(-28\right)}}{2\cdot\:2} \\ \sqrt{1^2-4\times2(-28)}=15 \\ By\text{ substitution,} \\ w_{1,\:2}=\frac{-1\pm \:15}{2\cdot \:2} \\ \mathrm{Separate\:the\:solutions} \\ w_1=\frac{-1+15}{2\cdot \:2},\:w_2=\frac{-1-15}{2\cdot \:2} \\ w=\frac{-1+15}{2\times2}=\frac{14}{4}=\frac{7}{2}=3.5 \\ w=\frac{-1-15}{2\cdot\:2}=\frac{-16}{4}=-4 \end{gathered}[/tex]Since the width cannot be negative, this means that the value of the width is 3.5m
STEP 6: Solve for the length
By substitution into the formula in step 2, we have:
[tex]\begin{gathered} l=2w+1 \\ l=2(3.5)+1=8 \\ l=8 \end{gathered}[/tex]Hence,
length = 8m
width = 3.5m
n - 3 over 10 = 3 over 5
Answers
The given expression is
[tex]\frac{n-3}{10}=\frac{3}{5}[/tex]First, we multiply by 10 on each side.
[tex]\begin{gathered} 10\cdot\frac{n-3}{10}=\frac{3}{5}\cdot10 \\ n-3=6 \end{gathered}[/tex]Then, we sum 3 on each side.
[tex]\begin{gathered} n-3+3=6+3 \\ n=9 \end{gathered}[/tex]Therefore, the solution is 9.How much should be invested now at an interest rate of 6.5% per year, compounded continuously l, to have $3500 in four years.Round your answer to the nearest cent.
Answers
Okay, here we have this:
Considering the provided information we are going to replace in the formula of continuous compound interest:
[tex]\begin{gathered} A=Pe^{rt} \\ 3500=Pe^{(0.065\cdot4)} \end{gathered}[/tex]Now, let's solve for P:
[tex]\begin{gathered} P=\frac{3500}{e^{0.26}} \\ P=$2,698.68$ \end{gathered}[/tex]Finally we obtain that should be invested $2,698.68.
Logan made 5 1/4 pounds of trail mix. If he puts 3/4 pounds into each bag how many bags can Logan fill?
Answers
There are 25
students in an
Algebra class. 9 of
them got an A on
the test. What
percent of them
scored an A?
Answers
Answer:
36%
Step-by-step explanation:
First, you would write that as a fraction, which would be 9/25. Then, you'd convert the fraction to a percentage by getting the denominator to 100. Multiply the numerator and denominator by 4 to achieve this. The answer would be 36/100, which translates to 36%.
Evaluate the expression and leaving your answer in polar form.
Answers
Complex numbers z₁ = 6 · [tex]e^{i\,\frac{17\pi}{20} }[/tex] and z₂ = 6 · [tex]e^{i\,\frac{27\pi}{20} }[/tex] are the square roots of the complex number in polar form.
How to find the square root of a complex number in polar form
In this problem we find a complex number in polar form, that is, a complex number of the form:
z = r · [tex]e^{i\,\theta}[/tex]
Where:
r - Norm of the complex number.θ - Direction of the complex number, in radians.The square root of this number can be found by means of the De Moivre's theorem:
[tex]\sqrt{z} = \sqrt{z} \cdot e^{i\,\left(\frac{\theta + 2\pi\cdot k}{n} \right)}[/tex], for k = {0, 1}
If we know that z = 36 and θ = 17π / 10, then the roots of the complex number are:
z₁ = 6 · [tex]e^{i\,\frac{\frac{17\pi}{10}}{2} }[/tex]
z₁ = 6 · [tex]e^{i\,\frac{17\pi}{20} }[/tex]
z₂ = 6 · [tex]e^{\frac{\frac{17\pi}{10} + 2\pi }{2} }[/tex]
z₂ = 6 · [tex]e^{i\,\frac{27\pi}{20} }[/tex]
The solutions are z₁ = 6 · [tex]e^{i\,\frac{17\pi}{20} }[/tex] and z₂ = 6 · [tex]e^{i\,\frac{27\pi}{20} }[/tex].
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Paul has $50,000 to invest. His intent is to earn 13% interest on his investment. He can invest part of his money at 8% interest and part at 16% interest. How much does Paul need to invest in each option to make a total 13% return on his $50,000?8% interest $ 16% interest $
Answers
Let x be the amount invest at 8%
Let y be the amount invest at 16%
Paul has $50,000 to invest:
[tex]x+y=50,000[/tex]His intent is to earn 13% interest on his investment. He can invest part of his money at 8% interest and part at 16% interest.
[tex]\begin{gathered} 50,000(0.13)=x(0.08)+y(0.16) \\ \\ 6,500=0.08x+0.16y \end{gathered}[/tex]Use the next system of equations to find x and y:
[tex]\begin{gathered} x+y=50,000 \\ 6,500=0.08x+0.16y \end{gathered}[/tex]1. Solve x in the first equation:
[tex]x=50,000-y[/tex]2. Substitute the x in the second equation by the value you get in the previous step:
[tex]6,500=0.08(50,000-y)+0.16y[/tex]3. Solve y:
[tex]\begin{gathered} 6,500=4,000-0.08y+0.16y \\ 6,500=4,000+0.08y \\ 6,500-4,000=0.08y \\ 2,500=0.08y \\ \frac{2,500}{0.08}=y \\ \\ y=31,250 \end{gathered}[/tex]4. Use the value of y to solve x:
[tex]\begin{gathered} x=50,000-y \\ x=50,000-31,250 \\ x=18,750 \end{gathered}[/tex]Solution for the system:
x=18,750
y=31,250
Answer: Paul needs to invers8% interest $18,75016% interest $31,250Kyle throws a baseball straight up from a height of 5 feet with an initial speed of 41feet per second.What is the maximum height of the baseball?
Answers
We will determine the maximum height of the baseball as follows:
We will need the following formulas:
[tex]v=u+at[/tex][tex]s=ut+\frac{1}{2}at^2[/tex]Here "u" represents the original speed, "t" represents the time, "a" the acceleration of the body and "s" is the total discance moved. [We will find s to solve the problem].
So:
First we have that the acceleation that the body will experience is -9.8m/s^2 [Since the object is going upwards and gravity is pulling on it towards the ground]. [acceleration of gravity using feet over second squared is 32.17 ft/s^2].
[tex]v=(12.4968)+(-9.8)t[/tex]But the maximum height will be reached when the velocity after certain time has passed is 0 ft/s, so:
[tex]0=(12.4968)+(-9.8)t\Rightarrow9.8t=12.4968[/tex][tex]\Rightarrow t=1.275183673\ldots\Rightarrow t\approx1.3[/tex]So, at approximately 1.3 seconds the maximum heigth willl be reached.
Now, we solve for s:
[tex]s=(12.4968)(1.275183673)+\frac{1}{2}(-9.8)(1.275183673)^2\Rightarrow s=7.967857665[/tex][tex]\Rightarrow s\approx8[/tex]So, the maxumum altitude for the baseball will be 8 meters, but we have to add the initial 5 feet at which it was launched:
[tex]h\approx8+1.524\Rightarrow h\approx9.491857665[/tex]And taking that to feet we will have:
[tex]h\approx31.141265305118\ldots[/tex]So, the solution must be the last option. [The discrepanc
Jeff has 45 pounds of organic apples. He earns $4.50 for every 3/4of a pound of organicapples he sells. How much money will Jeff receive if he sells all his organic apples?
Answers
Given data:
The total weight of the apples Jeff have W=45 pounds.
The amount Jeff earned for every 3/4 pound of apple is A=$4.50.
The expression for the given statement is,
[tex]\begin{gathered} \frac{3}{4}\text{ pound =\$4.50} \\ 1\text{ pound =\$6} \end{gathered}[/tex]Multiple the above expression by 45 on both sides.
[tex]\begin{gathered} 45(\text{ 1 pound)=45(\$6)} \\ 45\text{ pounds =\$270} \end{gathered}[/tex]Thus, the amount Jeff earned is $270.