We have that in a right triangle, the larger side is the hypothenuse since the sum of the others angles must be equal to 90. Thus, we can apply the Pythagorean Theorem to solve this question.
The legs of the triangle are a = 18 ft, b = 24 ft, and c = ?.
Then, applying the Pythagorean Theorem, we have (without using units):
[tex]c^2=a^2+b^2\Rightarrow c^2=(18)^2+(24)^2\Rightarrow c^2=324+576\Rightarrow c^2=900[/tex]Then, taking the square root to both sides of the equation, we have:
[tex]\sqrt[]{c^2}=\sqrt[]{900}\Rightarrow c=30[/tex]Then, the measure of the third side (hypothenuse) is c = 30 ft.
if a rectangle with an area of 42 units^2 has a length of seven units what is the rectangles primeter?
EXPLANATION
Let's see the facts:
The area of the rectangle is equal to 42 squared units.
Length = 7 units
The perimeter is given by the following relationship:
[tex]\text{Perimeter}=2\cdot(\text{length}+\text{width)}[/tex]But i don't know the width, so i can find it by isolating from the area formula as follows:
[tex]\text{Area}=\text{length}\cdot\text{width}[/tex]Isolating the width:
[tex]\text{Width}=\frac{Area}{\text{length}}=\frac{42}{7}=6\text{ units}[/tex]So, width = 6 units
Finally the perimeter is:
[tex]\text{Perimeter = 2(7+6) = 2(13)=26 units}[/tex]The perimeter is 26 units
(6.6 x 10^8)÷(2.0 x 10^4)
Given:
[tex]\frac{6.6\times10^8}{2.0\times10^4}[/tex]Simplify the expression
[tex]\frac{6.6\times10^8}{2.0\times10^4}=\frac{6.6}{2.0}\times\frac{10^8}{10^4}[/tex]Solve the expression by applying the law of indices
[tex]\frac{6.6\times10^8}{2.0\times10^4}=\frac{6.6}{2.0}\times10^{8-4}[/tex]Simplify further
[tex]\begin{gathered} \frac{6.6\times10^8}{2.0\times10^4}=3.3\times10^{8-4} \\ \frac{6.6\times10^8}{2.0\times10^4}=3.3\times10^4 \end{gathered}[/tex]Therefore, the answer is
[tex]3.3\times10^4[/tex]Determine the point on the graph of the unit circle that corresponds to pi. Then find cos pi and sin pi, and state which functions are undefined for pi.
The entire unit circle measures 2pi, then, pi corresponds to the half of the unit circle. It is located at the point (-1,0).
The cosine of pi is equal to the x-coordinate, and the sin of pi is equal to the y-coordinate of the point pi.
Since it is located at (-1,0) thus the cos(pi)=-1 and sin(pi)=0.
The functions that are undefined for pi are those which have sin(pi) as denominator, let's check:
[tex]\begin{gathered} \csc (\pi)=\frac{1}{\sin(\pi)}=\frac{1}{0}=undef \\ \cot (\pi)=\frac{\cos (\pi)}{\sin (\pi)}=\frac{-1}{0}=undef \end{gathered}[/tex]1.5 part 1 question 18 Determine whether the table represents functions or not assume that the input is in the left column or top row (explain your answer)
A function is a relation in which each element of the input is associated with exactly one element of the output. For example:
In this case, we have:
As we can see, the table does not represent a function because there is a value in the input set that is associated with two values in the output set.
с C' B' A B D' D The distance from A to B is 10 and the distance from A to B'is 2. What is the scale factor? 1/5 4 5 1/4
In this problem, we have that
the center of the dilation is pointed A ----> because the intersection segments c
so
the scale factor is equal to
scale factor=AB'/AB
substitute given values
scale=2/10
scale =1/5Write an inequality for the word problem and answer the question about the inequality. The faculty team scored less than half as many points as the varsity team. A total of 100 points was scorered. If x represents the number of points that the varsity team scored Could x = 60
From the exercise we can indentify the following
• x, = number of points that the varsity team scored
,• y ,= number of points that the faculty team scored
[tex]\begin{gathered} x+y=100\to(1) \\ y<\frac{1}{2}x\to(2) \end{gathered}[/tex]Let's clear y in (1) to be able to replace in (2)
[tex]\begin{gathered} y=100-x\to(1) \\ 100-x<\frac{1}{2}x\to(1)\text{ in (2)} \\ \frac{1}{2}x+x>100 \\ \frac{3}{2}x>100 \\ x>\frac{100\cdot2}{3} \\ x>\frac{200}{3} \\ x>66.6666 \\ x>67 \end{gathered}[/tex]The answer is x cannot be equal to 60 because they have to be at least 67 points to comply with the inequalityWhat is y=3x2-1 linear or not linear
Answer:
it would be linear i gotcha bro
find the circumstance of each circle. use your calculator's value of pi. round your answer to the nearest tenth.
The area of the circle is given by:
[tex]\pi\cdot r^2[/tex]where r is the radius of the circle
Given area = 615.8 yd^2
so, we will calculate the radius of the circle as follows:
[tex]\begin{gathered} \pi\cdot r^2=615.8 \\ r^2=\frac{615.8}{\pi}=196.015 \\ \\ r=\sqrt[]{196.015}\approx14yd \end{gathered}[/tex]So, the radius of the circle = r = 14 yd
The circumference of the circle =
[tex]2\cdot\pi\cdot r=2\cdot\pi\cdot14=87.9646[/tex]rounding the answer to the nearest tenth
So, the circumference = 88 yd
Please help me with this timed practice problem.The first step have different options: substract, distribute, divide, add.
From the starting equation to the first step we can see that the only change was made on the left side of the equation.
We can see that the distributive property of multiplication is being applied to the parenthesis.
So, the "-2"is being distributed to the 5x and the 8.
So, the correct options in step 1 is distribute.
In step 2, we can see that the 6x on the left side are not there anymore and the -10x on the left turned into -16x. That is, we substracted 6x from both sides. Thus, the correct option on Step 2 is substract.
In Step 3, the -16 is not on the left side anymore and the 30 from the right side is in place of the 14. So, we added 16 to both sides in this step, and the correct alternative is add.
Now, on Step 4 we had -16x that turned into x and a denominator of -16 appeared on the right side, so we have divided both sides by -16. The correct alternative on Step 4 is divide.
What is the total cost for fixing a drain that takes 6 hours?If the plumber charged a total of 364$ how many hours did she spend fixing the drain?
a) Recall that to evaluate a function at a given value, we substitute the variable by the given value.
Therefore, evaluating C(h) at h=6 we get:
[tex]C(6)=76+24\cdot6.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} C(6)=76+144 \\ =220. \end{gathered}[/tex]b) Setting C(h)=364 we get:
[tex]76+24h=364.[/tex]Subtracting 76 from the above equation we get:
[tex]\begin{gathered} 76+24h-76=364-76, \\ 24h=288. \end{gathered}[/tex]Dividing the above equation by 24 we get:
[tex]\begin{gathered} \frac{24h}{24}=\frac{288}{24}, \\ h=12. \end{gathered}[/tex]Answer:
(a) $220.
(b) 12.
Write the given function as the composition of two functions.y=√15 + 6xChoose the correct answer below.OA. If f(x) = -√x and g(x) = 15+ 6x, then y = f(g(x)].1B. If f(x)=√x and g(x) = -OC. If f(x) =³√xCOD. If f(x) = -115+ 6x'then y = f[g(x)].and g(x)= 15+ 6x, then y = f[g(x)].and g(x) = 15+ 6x, then y = f[g(x)]....
Given:
[tex]y\text{ = -}\sqrt[3]{15+6x}[/tex]To find:
the functions that give the above composite function
f(g(x)): substitute x in f(x) with g(x)
This means g(x) will be 15 + 6x which will be substituted into function f(x)
[tex]\begin{gathered} f(x)\text{ = -}\sqrt[3]{x} \\ g(x)\text{ = 15 + 6x} \\ \\ Check: \\ f(g(x)):\text{ substitute x in g\lparen x\rparen with f\lparen x\rparen} \\ f(g(x))\text{ = -}\sqrt[3]{15\text{ + 6x}} \end{gathered}[/tex]What is the center of the data?Number of Green Candies in a Bag:O101112131415The center is0):tivity
Given:
10, 11, 12, 13, 14, 15
Find the center of the data.
To find the center of the data,
Twice a number, decreased by 4, is at least 12. Which of the following is a solution?8576
Answer:
8
Explanation:
Let the number = n
Twice the number decreased by 4:
[tex]2n-4[/tex]The phrase 'at least' means the expression above can either be equal to or greater than 12.
Thus, the given statement as inequality is:
[tex]2n-4\geq12[/tex]We then solve the inequality for n.
[tex]\begin{gathered} \text{ Add 4 to both sides} \\ 2n-4+4\geq12+4 \\ 2n\geq16 \\ \text{ Divide both sides by 2} \\ \frac{2n}{2}\geq\frac{16}{2} \\ n\geq8 \\ \implies n=(8,9,10,\cdots) \end{gathered}[/tex]The number that is a solution is 8.
5. What are the zeros of the polynomial function f(x) = x³ - 2x² - 4x + 8? (Select all that apply.)
□ (√2,0)
(2,0)
(0,0)
(-2,0)
Answer:
(2, 0), (-2, 0)
Step-by-step explanation:
f(x) = x³ - 2x² - 4x + 8
(x³ - 2x²) (-4x + 8)
x²(x - 2) - 4(x - 2)
(x² - 4) (x - 2)
(x + 2)(x - 2)(x - 2)
(x + 2) (x - 2)²
x = -2, 2 multiplicity of 2
I hope this helps!
find dy/
dx
Find where y = csc^-1(1/9x+5)
Answer:
csc(9x)
Step-by-step explanation:
What is the radius and diameter of the following circle?18 cmRadius =cmDiameter =cm
We are given the diameter of the circle = 18 cm
Radius = Diameter /2 = 18 /2 = 9 cm
is 0.56>0.056 yes or no
The question is asking you to compare to decimal numbers:
0.56 and 0.056 and decide which one
Answer each part. If necessary round to the nearest hundredth
If 85 pounds of seed are needed to plant a 10-acre field, then each pound can cover
[tex]\frac{10}{85}\text{acres per pound.}[/tex]Computing the above division, we get:
[tex]0.12\text{ acres per pound.}[/tex]Now, in the second problem, the rent for 3 hours is $10, therefore, the cost per hour is:
[tex]\frac{10}{3}\text{dollars per hour.}[/tex]The decimal form of the above solution is:
[tex]3.33\text{ dollars per hour.}[/tex]Answer:
a)
[tex]0.12\text{ acres.}[/tex]b)
[tex]3.33\text{ dollars per hour.}[/tex]tenemos $5000 en una cuenta. A final de cada mes se ingresa un 5% del dinero que hay en la cuenta en dicho momento. Calcular el dinero que habrá en la cuenta después de un trimestre¿ en que porcentaje ha subido la cantidad inicial?
Al final del primer mes tenemos:
5000 + 5000*0.05 = 5250
Al final del segundo mes:
5250 + 5250*0.05 = 5512.5
Y al final del tercer mes nos queda:
5512.5 + 5512.5*0.05 = 5788.125
El dinero que habra en la cuent despues de un trimestre es $5788.125
Para calcular en que porcentaje ha subido la cantidad inicial, dividimos la cantidad extra obtenida despues de un trimestre entre la cantidad inicial:
[tex]\begin{gathered} \frac{788.125}{5000}=0.157625 \\ \text{Expresado en porcentaje:} \\ 0.157625\cdot100=15.7625 \end{gathered}[/tex]Ha subido en un 15.7625%
Determine if the set of number of days in January, J, and the set B={6,9,15,10,1,0,8,4,11} is equivalent
equivalent sets are those that have the same cardinality, that is, the same number of elements
does this represents apolynomial?and if it does is it amonomial,binomial,trinonial,ornoneand what's the degree if it is
The algebriac expression is a polynomial, if all the exponents of expression is non negative.
The width of a rectangle is 5x-4. The perimeter is 14x+4. What is the length
Given:
The width of rectangle is w = 5x - 4.
The perimeter of rectangle P = 14x + 4.
Explanation:
The formula for the perimeter of rectangle is,
[tex]P=2(L+w)[/tex]Substitute the expression in formula to determine the length of rectangle.
[tex]\begin{gathered} 14x+4=2(L+5x-4) \\ L+5x-4=\frac{14x+4}{2} \\ L=7x+2-5x+4 \\ =2x+6 \end{gathered}[/tex]So length of rectangle is 2x + 6.
Answer: 2x + 6
Kelly bought a cup of coffee and drank 5/8 of it. Write an addition equation to represent how much coffee is remaining.Enter your answer as an addition equation, formatted like this: 42+(-53)=-11
Step 1
Given; Kelly bought a cup of coffee and drank 5/8 of it. Write an addition equation to represent how much coffee is remaining.
Step 2
[tex]\begin{gathered} The\text{ total fraction representing the cup=1} \\ Let\text{ the fraction left be x} \\ Thus; \\ x+\frac{5}{8}=1 \end{gathered}[/tex]The addition equation representing how much coffee is remaining is;
[tex]\begin{gathered} x=1+(-\frac{5}{8}) \\ x=\frac{3}{8} \\ Thus \\ 1+(-\frac{5}{8})=\frac{3}{8} \\ \end{gathered}[/tex]Answer;
[tex]1+(-\frac{5}{8})=\frac{3}{8}[/tex]Which of the following represents the slope of the line 2x - 5y = 10
Order of operations was it evaluated correctly? 10 - 2(5+11)= 10-2(16)= 10 -32= -22EXPLAIN your reasoning Please this is due today thank you
10 - 2(5+11)
Step 1
first, you need to eliminate the () by making the operation inside, it is an addition
10-2(5+11)
10-2(16)
then,
Step 2
do the operation related to the (), it is multiplication, rember a(b) = a*b = (a)b = (a)*(b), the meaning is the same.
10-2(16)
10-32
Step 3
finally, do the subtraction
You have 4929 songs in your computers music library. The songs have a mean duration of 246.3 seconds with a standard deviation of 111.42 seconds. One of the songs is 391 seconds long. What is its z-score?
All points from which of the following patterns would be contained on the given graph?321-6-5-4-3 -2 -1 0123 4 5 6-1-2-3OA. -1.-3.-5.-7....OB. -3, -7, -11, -15....OC. -2,-5.-8.-11.....OD. 3,5,7.9....Ht
To determine which pattern could represent points on the graph, we notice that the following points are on the graph:
[tex](1,-1),(2,-3),(3,-5).[/tex]We can infer that the point
[tex](4,-7)[/tex]is also on the line.
Therefore, the pattern that could be contained in the graph is:
[tex]-1,-3,-5,-7...[/tex]Answer: Option A.
How did the reporter state probability for rain last week compared to the actual results
Answer:
The probability of rain was less than the actual results
Explanation:
Given that it rained on Monday, Tuesday, Thursday, and Friday, the actual probability of rain is 4 out of 7 days.
If the reporter stated that the probability of rain was 3 out of days, we can see that the probability of rain the reporter stated was less than the actual result of 4 out of 7 days
How do you work the following problem:517 37/50 + 312 3/100? and I also need to turn in to a decimal
Calculate the following sum of mixed fractions:
[tex]517\frac{37}{50}+312\frac{3}{100}[/tex]Before adding the fractions, we should express them as improper fractions:
[tex]517+\frac{37}{50}+312+\frac{3}{100}[/tex]We can add the integers 517+312=829
And now the fractions:
[tex]\frac{37}{50}+\frac{3}{100}[/tex]Expand the first fraction to have a denominator 100:
[tex]\frac{2\cdot37}{2\cdot50}+\frac{3}{100}=\frac{74}{100}+\frac{3}{100}=\frac{77}{100}[/tex]Now we simply join the integer part with the proper fraction:
[tex]829\frac{77}{100}[/tex]It's the final answer
Let's elaborate on the sum:
[tex]\frac{37}{50}+\frac{3}{100}[/tex]We need to make both denominators equal and then add the numerators easily
For example:
[tex]\frac{3}{8}+\frac{4}{8}=\frac{7}{8}[/tex]Note the fraction 37/50 does not have the same denominator as 3/100
How can we make them equal?
Multiply by 2
both the 37 and 50
To express the result as decimal, we divide the fraction and add it to the integer:
[tex]829\frac{77}{100}=829+\frac{77}{100}=829+0.77=829.77[/tex]I don't understand problem like this : h >4
Solution
For this case we can assume that x = number of minutes that Ebony waited
Then the correct sequence is given by
Identify the variable as the number of minutes, x. Identify the inequality symbol as greater than. Identify the constant as 56 minutes. Write the inequality as x >56