Use special right triangle ratios to find the length of the hypotenuseA. 15 square root 3B. 30C. 15D. 15square root 2
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EXPLANATION
To find the length of the hypotenuse using the right triangle ratio
Since the angles are in the ratio
[tex]45^0,45^0,90^0[/tex]So the side ratio will be in the ratio
[tex]1\colon1\colon\sqrt[]{2}[/tex]Thus,
If x = 15 and the hypotenuse is y
Then
[tex]\begin{gathered} 45^0\colon45\colon90^0 \\ 15\colon x\colon y \\ 1\colon1\colon\sqrt[]{2} \end{gathered}[/tex]Thus, from the above relationship
[tex]\begin{gathered} x=15 \\ y=15\times\sqrt[]{2}=15\sqrt[]{2} \end{gathered}[/tex]Therefore, the hypotenuse is
[tex]15\sqrt[]{2}[/tex]
Related Questions
6500 is 7/10 of a number what is the number
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Given the expression
6500 is 7/10 of a number, let the number be k
The expression is
[tex]\frac{7}{10}\text{ of k}=6500[/tex]Solve for k by crossmultiplying
[tex]\begin{gathered} \frac{7}{10}\text{ of k}=6500 \\ \frac{7}{10}\times k=6500 \\ \frac{7k}{10}=6500 \\ \text{Crossmultiply} \\ 7k=6500\times10 \\ 7k=65000 \\ \text{Divide both sides by 7} \\ \frac{7k}{7}=\frac{65000}{7} \\ k=9285\frac{5}{7} \end{gathered}[/tex]Hence, the number, k, is
[tex]9285\frac{5}{7}[/tex]whats 2/7 dividee by 4/9?
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In division of fractions A/B divided by C/D = ( A•C)/(B•D)
if you vertically shift the square root parent function, F(x)=/x, up nine units, what is the equation of the new function?
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Answer:
The new function is;
[tex]G(x)=\sqrt[]{x}+9[/tex]Explanation:
Given the parent function;
[tex]f(x)=\sqrt[]{x}[/tex]To move it up 9 units.
Then we will need to add 9 units to the right-hand side of the equation;
[tex]\begin{gathered} G(x)=f(x)+9=\sqrt[]{x}+9 \\ G(x)=\sqrt[]{x}+9 \end{gathered}[/tex]Therefore, the new function is;
[tex]G(x)=\sqrt[]{x}+9[/tex]Which is the correct equation of the line for the following graph?
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ANSWER :
The equation of the line is y = -3x + 6
EXPLANATION :
Recall the two-point formula :
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]We need two points that lie on the line.
The points are (0, 6) and (2, 0)
Using the formula above :
[tex]\begin{gathered} y-6=\frac{0-6}{2-0}(x-0) \\ \\ y-6=-3x \\ y=-3x+6 \end{gathered}[/tex]The circumference of the circle is 9.42 inches, What is the diameter of the circle?
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EXPLANATION
Since the circumference of the circle is 9.42, we can get the diameter by applying the following relationship:
[tex]Circumference=2\pi r=2\pi\frac{d}{2}=\pi d[/tex]Isolating the diameter:
[tex]Diameter=\frac{Circumference}{\pi}[/tex]Plugging in the numbers:
[tex]Diameter=\frac{9.42}{3.14}=3[/tex]Therefore, the diameter is equal to 3 inches.
A movie-theater employee notes an inverse relationship between the theater's popcorn sales and its nacho sales. On a given night, the theater makes $2,254 from popcorn sales and $1,628 from nacho sales. If on the next night the employees sell $2,024 of popcorn, how much is earned from nachos?
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the employee earned $1813 from Nachos
Explanation:The theater's popcorn sales is inversely proportional to nacho sales
Let theater's popcorn = P
nacho sales = N
[tex]P\text{ }\alpha\text{ }\frac{1}{N}[/tex]Equating the relationship:
[tex]\begin{gathered} P\text{ = k(}\frac{1}{N}) \\ P\text{ = }\frac{k}{N} \\ \text{where k = constant of proportionality} \end{gathered}[/tex]when theater sales = $2,254
Nacho sales = $1,628
[tex]\begin{gathered} 2254\text{ =}\frac{k}{1628} \\ k\text{ = 2254(1628)} \\ k\text{ = 3}669512 \end{gathered}[/tex]The relationship becomes:
[tex]P\text{ = }\frac{3669512}{N}[/tex]When cost of the theater popcorn = $2,024
The cost from nachos = ?
We would use the relationship to get the above:
[tex]\begin{gathered} 2024\text{ = }\frac{3669512}{N} \\ 2024N\text{ = 3669512}18 \\ N\text{ = }\frac{\text{3669512}}{2024} \\ N\text{ = }1813 \end{gathered}[/tex]Hence, the employee earned $1813 from Nachos
Select the correct answer from the drop-down menu.A box contains shirts in two different colors and two different sizes. The numbers of shirts of each color and size are given in the table.SizeShirt ColorLarge Medium TotalRed424890Blue354075Total7788165From the data given in the table, we can infer thatResetNext
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First option
P(red shirt | large shirt) = P(large shirt)
From conditional probability: P(A | B) = n(A ∩ B) / n(B)
n is "the number of..."
So: P(red shirt | large shirt) = n(red shirt ∩ large shirt) / n(large shirt)
Where:
Huai takes out a 3100 student loan at 6.1% to help him with 2 years of community college. After finishing the 2 years, he transfers to a state university and borrows another 12,100 to defray expenses for the 5 semesters he needs to graduate. He graduates 4 years and 4 months after acquiring the first loan and payments are deferred for 3 months after graduation. The second loan was acquired 2 years after the first and had an interest rate 7.6% of . Find the total amount of interest that will accrue until payments begin. find the total amount of interest that will accrue for loan 1
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In linear equation, p = $65.47 per month is the total amount of interest .
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. As an illustration, the conventional form of the linear equation 2x+3y=5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y).Huai takes out a 3100 student loan at 6.1% to help him with 2 years of community college.
The monthly payment on loan1 can be finding as
3100 = p [ 1 - ( 1 + 0.066/12)⁻⁴/0.066/11
3100 = p[ 1 - ( 1.0055)⁻⁵⁵/0.0055
3100 = p [ 1 - 0.73958/0.0055 ]
3100 = p [ 0.26041/0.0055 ]
3100 = p [ 47.34886 ]
p = 3100/47.34886
p = 65.47148
p = $65.47 per month
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Wesley spent $34.60 at the grocery store. 15%of that was spent on fruit. How much didWesley spent on fruit?
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We determine what he spent as follows:
[tex]34.60(0.15)=5.19[/tex]So, he spent %5.19.
A circular fountain, 20 meters in diameter, has a 2 meters wide gravel walkway around it. What is the approximatearea of the walkway in square meters?a.100
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The area of the gravel walkway with a fountain of 20 meters is 263.76m².
What is the area of the circle?The area of a circle seems to be the region of a two-dimensional plane occupied by the circle. It is simple to calculate using the formula A = πr², (Pi x r-squared), where r seems to be the circle's radius. The square unit, like m2, cm2, and so on, is the unit of area.The area of a circle is:
Area = πr²Here given the circular fountain:
Diameter = 20mSo radius = diameter /2 = 20/2Radius = 10mGravel walkway has a radius of 2m, so diameter = 4m
The gravel walkway area = circular fountain area.
The gravel walkway area is equal to the area of the big circle less than the area of the inner circle:
(3.14 x 10²)-(3.14 x 4²)314 - 50.24= 263.76 m²Therefore, the area of the gravel walkway with a fountain of 20 meters is 263.76m².
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(d) Based on your analysis from part c, sketch a graph of what y=9^x could look like.
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Given the expression:
[tex]y=9^x[/tex]The graph of the function will be as shown in the following picture:
We will study the behaviour for the following conditions:
x < 0, the function tends to zero
x = 0, the function will be = 1, which represents y-intercept
0 < x < 1 , the function will be in the rangle 1 < y < 9
x = 1 , the function will be = 9
x > 1 , the function tends to infinity
how is the volume of a rectangular prism related to its dimensions
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We know that a rectangular prism has a length l, a width w and a height h.
The volume of this prism is given as:
[tex]V=lwh[/tex]That means that to find the volume we have to multiply its dimensions.
Which is a graph for the inequality x>=2
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The inequality is:
[tex]x\ge2[/tex]Graph:
What is the interquartile range of the number of days represented on Kelly's line plot? Be sure to show your work and explain your reasoning.
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The ordered list of the given plot is:
0, 0, 2, 2, 2, 3, 4, 4, 5, 5, 5, 7, 7
The first interquartile is given by:
IQ = Q3 - Q1
Where Q3 and Q1:
[tex]\begin{gathered} Q_1=\frac{1}{4}(n+1) \\ Q_3=\frac{3}{4}(n+1) \end{gathered}[/tex]where n = 8 is the total number of data.
[tex]\begin{gathered} Q_1=\frac{1}{4}(8+1)=\frac{1}{4}(9)=\frac{9}{4} \\ Q_3=\frac{3}{4}(8+1)=\frac{3}{4}(9)=\frac{27}{4} \end{gathered}[/tex]Then, the interquatile range:
IQ = 27/4 - 9/4 = 18/4
Hence, the interquartile range is 18/4
1. Graph the pre-image A(-1,0) B(2,5) C(-1,5) Do the following (x, y) = (x + 2, y - 1) Graph and give the coordinates for the image
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Graph the pre-image A(-1,0) B(2,5) C(-1,5) Do the following (x, y) = (x + 2, y - 1) Graph and give the coordinates for the image
________________________________-
A(-1,0) A' (-1 + 2, 0 - 1) = (1,-1)
B(2,5) B' (2 + 2, 5 - 1) = (4, 4)
C(-1,5) C' (-1 + 2, 5 - 1) = (1, 4)
________________________________
A company will need 1.8 million 5 years from now to replace some equipment. Currently, the firm has some extra cash and would like to establish a savings account for this purpose. The account pays 5.25 percent interest, compounded annually. How much money must the company deposit today to fully fund the equipment purchase?
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Given:
a.) A company will need 1.8 million 5 years from now to replace some equipment.
b.) The account pays 5.25 percent interest, compounded annually.
We will be applying the Compounded Interest Formula:
[tex]\text{ A = P\lparen1 + }\frac{r}{n})^{nt}[/tex]Where,
A=final amount
P=initial principal balance/money to initially deposit
r=interest rate (decimal)
n=number of times interest applied per time period
t=number of time periods elapsed (in years)
In this scenario, we are asked what is the amount of principal balance/initial deposit to make to get 1.8 million in 5 years.
Annually = n = 1
We get,
[tex]\text{ 1,800,000 = P\lparen1 + }\frac{\frac{5.25}{100}}{1})^{(1)(5)}[/tex][tex]1,800,000\text{ = P \lparen1 + 0.0525\rparen}^5\text{ = P \lparen1.0525\rparen}^5[/tex][tex]\text{ P = }\frac{1,800,000}{(1.0525)^5}[/tex][tex]\text{ P = 1,393,676.5175887556 }\approx\text{ 1,393,676.52}[/tex]Therefore, the answer is 1,393,676.52
Translate each problem into an algebraic expression & solve 1) The difference between four times a number and three is twenty-five. Find the number
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1) The difference between four times a number and three is twenty-five. Find the number
In order to write in an algebraic way the previous statement you take into account the stament part by part.
The difference between... (two term are going to be subctrated)
four times a number... 4x
and three... 3
is twenty-five = 25
4x and 3 are the number to be subtracted, and this subtraction is equal to 25. Then, you have:
4x - 3 = 25 "this is the algebraic expression"
Next, to solve the previous equation for x, you proceed as follow:
4x - 3 = 25 sum both sides by 3
4x = 25 + 3
4x = 28 divide both sides by 4
x = 28/4
x = 7
Then, the number is 7
Use a graphing calculator to solve the equation to the nearest tenth.2x^2 - 4x -10=0; x between 3 and 4
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Given the equation:
[tex]2x^2-4x-10=0;x\in(3,4)[/tex]We will use a graphing calculator to solve the equation
The graph of the equation will be as shown in the following figure:
As shown the intersection between the given equation and the x-axis is a point between 3 and 4 which = 3.4495
Rounding to the nearest tenth
So, the answer will be the solution to the equation:
[tex]x=3.4[/tex]The table below shows the probability distribution of a random variable X. X P(X) -20 0.53 -19 0.11 -18 0.26 -17 0.09 -16 0.01 What is the expected value of X? Write your answer as a decimal.
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ANSWER
[tex]E(X)=-19.06[/tex]EXPLANATION
We want to find the expected value of x.
To do this, we need to find the product of each value with its corresponding proabibilty and then find the sum.
That is:
[tex]E(x)=\Sigma\mleft\lbrace xP(x)\mright\rbrace[/tex]Therefore, we have:
[tex]\begin{gathered} E(X)=(-20\cdot0.53)+(-19\cdot0.11)+(-18\cdot0.26)+(-17\cdot0.09)+(-16\cdot0.01)_{} \\ E(X)=(-10.6)+(-2.09)+(-4.68)+(-1.53)+(-0.16) \\ E(X)=-19.06 \end{gathered}[/tex]That is the expected value.
in training for a swim meet Logan swim 750 m in 1/3 of an hour. His swimming partner Mila swim 2/3 of Logan's distance and in 1/4 of an hour. What is Logan's average swimming speed?
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Average speed
The average speed can be computed as the ratio of the distance over the time take to cover that distance. Being d the distance and t the time, we have:
[tex]v=\frac{d}{t}[/tex]Logan swims 750 m in 1/3 of an hour. Let's work in meters and in minutes to make calculations easier. The time taken by Logan is 1/3 of an hour. Since one hour has 60 minutes:
t = 1/3*60 = 20 minutes
The distance is 750 m. Let's calculate the average speed
[tex]v=\frac{750\text{ m}}{20\text{ min}}=37.5\text{ m/min}[/tex]Logan's average swimming speed is 37.5 m/min
Which equation is equivalent to log(base 2)y = x + 7?y=2^(x + 7)y=2^x +7y=(x + 7)
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Given the logarithmic equation
[tex]\log _2y=x+7[/tex]To determine an equivalent equation, we convert the equation from logarithm form to index form using the rule below.
[tex]\begin{gathered} If\; \log _ab=c,\text{ then:} \\ a^c=b \end{gathered}[/tex]Therefore:
[tex]\log _2y=x+7\equiv y=2^{x+7}[/tex]The equivalent form of the given equation is:
[tex]y=2^{x+7}[/tex]
Perform the following division and write the quotient in trigonometric form. Write the magnitude in exact form. Writethe argument in radians and round it to twodecimal places if necessary.-4 - 2i3 + 2iyea
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First step is to simplify the expression
-4-2i
------
3+2i
Multiply by the complex conjugate
-4-2i ( 3-2i)
------ * ----------------
3+2i ( 3-2i)
(-4-2i) (3-2i)
------------------
3^2 +2^2
-12 -6i +8i -4
----------------------
9+4
-16+2i
--------
13
Now we can find the magnitude
z = sqrt( a^2 + b^2) where a = real part and b = imaginary part
z = sqrt( 256/139 + 4/139) = sqrt(260/139) = 2 sqrt(65)/13
theta = tan^-1 ( b/a) = tan^-1 ( -2/16) = tan^-1 (-1/8) = .12
z = 2 sqrt(65)/13 ( cos .12 + i sin .12)
I need to know how to graph this function in a slope intercept form
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Answer:
Explanation:
Solve the Perfect Square Trinomial Expression.x2 – 16x + 64-
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we have the expression
[tex]x^2-16x+64[/tex]Complete the square
[tex]\begin{gathered} (x^2-16x)+64=0 \\ (x^2-16x+8^2-8^2)+64 \\ (x^2-16x+8^2)+64-8^2 \\ rewrite\text{ as perfect square} \\ (x-8)^2 \end{gathered}[/tex]using the table below find the probability express your answer as a percent to the nearest whole number sport. hikeing. reading phoningFemale 39. 48. 85. 62. male. 67. 58. 76. 54p(hiking I female)=???
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You have to calculate the probability of the person liking hiking, given that is a female.
This a conditional probability, there are two ways of calculating it, one is using the definition of the conditional probability that states that:
"Given two dependent events A and B, the probability of A given B is equal to the probability of A and B divided by the probability of B"
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]Using this option we will work using all the sampled people.
The second option, considering that we already know the person is "female" is to work directly with the group of females and calculate the probability of hiking.
Let "H" represent the event "hiking" and "F" represent the event "female"
1) Using the definition of conditional probability.
[tex]P(H|F)=\frac{P(H\cap F)}{P(F)}[/tex]First lets determine the probability of "female", to do so you have to divide the number of females by the total number of people on the sample:
Total females:
[tex]F=39+48+85+62=234[/tex]Total number of people
[tex]T=M+F=(67+58+76+54)+234=489[/tex]The probability of "female" is then:
[tex]\begin{gathered} P(F)=\frac{234}{489} \\ P(F)=\frac{78}{163} \end{gathered}[/tex]Second, calculate the probability of the intersection between "female" and "hiking". For this calculateion you have to divide the number of people that are females and like hiking, by the total number of people
[tex]\begin{gathered} P(H\cap F)=\frac{48}{489} \\ P(H\cap F)=\frac{16}{163} \end{gathered}[/tex]Now you can calculate the conditional probability as:
[tex]\begin{gathered} P(H|F)=\frac{P(H\cap F)}{P(F)} \\ P(H|F)=\frac{\frac{16}{163}}{\frac{78}{163}}=\frac{16}{163}\cdot\frac{163}{78} \\ P(H|F)=\frac{8}{39} \end{gathered}[/tex]2) The second option was to work only with the data of the "female" group.
To calculate the probability of the person liking hiking, given that she is female, you have to divide the total number of females that like hiking by the total number of females of the sample
[tex]\begin{gathered} P(H|F)=\frac{48}{234} \\ P(H|F)=\frac{8}{39} \end{gathered}[/tex]Using both ways, we reached the same result, the probability of P(H|F)=8/39
As a percentage is (8/39)*100=20.51%
Given the triangle below identify which trig function we must use, solve for the anglesTrig Function:
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Since we have a right triangle, we can solve the sides of the triangle using cos(x), sin(x), or tan(x).
To fin
Which is the graph of y = [x]-2?
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The given function is,
[tex]f(x)=\lfloor x\rfloor-2[/tex]⌊⌋ is the symbol representing a greatThe greatest integer less than or equal to x is represnted as ⌊x⌋.
Tina's savings account earns 4.3% simple interestyearly. Two and a half years ago, she opened heraccount with $18000. How much interest has sheearned so far?
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Notice that the interest is defined as yearly, then, we have to take the time period as 2 years (since the money was saved 2 and a half years ago), then, using the equation of simple interest we have:
[tex]\begin{gathered} I=P\cdot n\cdot i \\ P=18,000 \\ n=2 \\ i=4.3\%=0.043 \\ \Rightarrow I=18,000(2\cdot0.043)=18000(0.086)=1548 \\ I=\$1548 \end{gathered}[/tex]Therefore, Tina has earned $1548
find the percent markup. Cost of a microphone $99.50, selling price 124.38
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Let's begin by listing out the information given to us:
Percent markup (m) = ?, Cost (c) = $99.50, Selling price (p) = $124.38
The formula for percent markup is given by:
[tex]\begin{gathered} \text{\% }Markup=\frac{SellingPrice-Cost}{Cost}\cdot100\text{ \%} \\ m=\frac{p-c}{c}\cdot100\text{ \%}=\frac{124.38-99.50}{99.50}\cdot100\text{ \%} \\ m=25.005\text{\%}=\text{ }25\text{ \%} \\ m=25\text{ \%} \end{gathered}[/tex]The percent markup is 25%
Help me pls Match each expression with the type of factoring that applies
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3) Difference of Squares:
The difference of squares formula is
[tex]a^2-b^2=(a+b)(a-b)[/tex]We can identify that on the expression:
[tex]x^2-25[/tex]Applying the difference of square we have
[tex]x^2-25=(x+5)(x-5)[/tex]4) Difference of Cubes
Here the formula is quite different from what we have on the difference of squares.
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)^{}[/tex]Now we identify it on
[tex]x^3-1[/tex]The factoring will be
[tex]x^3-1=(x-1)(x^2+x+1)[/tex]5) Sum of Cubes
We have a very similar formula as 4), the difference will be
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)^{}[/tex]We just have to change some signals.
Then
[tex]x^3+27[/tex]We can write as a sum of cubes
[tex]x^3+27=(x+3)(x^2-3x+9)[/tex]6) Grouping
Here we have a quite different technique, we don't have the formula to apply, therefore, let's see the expression and how to group it
[tex]3x^3+15x^2+2x+10[/tex]Here we must factor and find two equal factors, that's the most difficult part, after that we just group them.
If we look at the expression we will see that we can group:
[tex](3x^3+15x^2)+(2x+10)[/tex]If the factor 3x² on the left ( ) and factor 2 on the right ( ) we get
[tex]3x^2(x+5)+2(x+5)[/tex]Look that now we have (x+5) on both terms, then we group them!
[tex](x+5)(3x^2+2)[/tex]That's the final form, hence
[tex]3x^3+15x^2+2x+10=(x+5)(3x^2+2)[/tex]1) GCF (greatest common factor)
Here we must identify one factor that appears on all terms, look at
[tex]2x^2+6x[/tex]See that "2x" appears on both terms, then it's the greatest common factor:
[tex]2x^2+6x=2x(x+3)[/tex]See that if we do the distribution we will get the other form again.
2) Unfoil
Here we must find two numbers that the sum is 6 and the product is 8, these two numbers are 4 and 2.
The generic formula is
[tex]x^2+bx+c=(x+x_1)(x+x_2)_{}[/tex]Where x₁ and x₂ are the numbers we find doing the sum and the product, in our case it's 4 and 2, then
[tex]x^2+6x+8=(x+4)(x+2)[/tex]Final answer:
2 - Unfoil - x² + 6x + 8
1 - GCF - 2x² + 6x
3 - Difference of Cubes - (x³ - 1)
4 - Sum of Cubes - (x³ + 27)
5 - Grouping - (3x³ + 15x² + 2x + 10)
6 - Difference of Squares - (x² - 25)