Step 1
Given; The area of a rectangle is given by a=6x^2y+4y^2x and the width of the rectangle is w=2xy. what is the length, l, of the rectangle if l=a/w?
Step 2
[tex]\begin{gathered} l=\frac{a}{w} \\ l=\frac{6x^2y+4y^2x}{2xy} \end{gathered}[/tex][tex]\begin{gathered} factorize \\ l=\frac{2xy\left(3x+2y\right)}{2xy} \end{gathered}[/tex]Thus;
[tex]l=3x+2y[/tex]Answer;
[tex]l=3x+2y[/tex]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
(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]Which of the following represents the slope of the line 2x - 5y = 10
find dy/
dx
Find where y = csc^-1(1/9x+5)
Answer:
csc(9x)
Step-by-step explanation:
Put the steps in order to find the distance between these
Answer:
See attachedStep-by-step explanation:
The distance between the points is found using the given coordinates and the distance formula.
The distance formula is based on right triangle and Pythagorean theorem and is the calculation of the hypotenuse provided the legs are known.
So the right order of operations is attached for you below.
You have found most of it, just small correction is needed.
Answer:
1., 2., 4., 5., 6., 3., 7.
Step-by-step explanation:
1. Draw a right triangle by dropping a vertical side and a horizontal side. (See attachment).
2. Determine the vertical side (2 units) and horizontal side (6 units) lengths by counting on the grid (be careful of the scale), or using the vertical coordinated (3 to 1) and horizontal coordinate (-2 to 4).
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Therefore:
a = 2b = 64. Use the Pythagorean Theorem for right triangles to determine the diagonal length:
[tex]\implies \sf 2^2+6^2=c^2[/tex]
[tex]\sf 5.\quad 4 + 36 = c^2[/tex]
[tex]\sf 6. \quad 40 = c^2[/tex]
[tex]\sf 3.\quad \sqrt{40}=\sqrt{c^2}[/tex]
7. √40 is between √36 and √49, so between 6 and 7 - closer to 6, so about 6.3 units.
I keep overthinking and confusing myself can you help me please
We are asked to prove that triangles △PQR and △TSR are congruent.
Let us write the statements and reasons to prove that the given triangles are congruent.
[tex]\begin{gathered} 1.\: Statement\colon\: \bar{PQ}\cong\bar{TS} \\ 1.Reason\colon Given \end{gathered}[/tex]We are given that R is the midpoint of QS and PT
This means that QR ≅ SR and also PR ≅ TR by the property of "Definition of midpoint"
[tex]\begin{gathered} 2.\: Statement\colon\: \bar{QR}\cong\bar{SR} \\ 2.\: Reason\colon\: \text{Definition of midpoint} \end{gathered}[/tex][tex]\begin{gathered} 3.\: Statement\colon\: \bar{PR}\cong\bar{TR} \\ 3.\: Reason\colon\: \text{Definition of midpoint} \end{gathered}[/tex]So, now we have 3 equal sides in both triangles
Therefore, by the property of "Side-Side-Side" (SSS) the given triangles are congruent.
[tex]\begin{gathered} 4.\: Statement\colon\: \triangle PQR\cong\triangle TSR \\ 4.\: Reason\colon\: \text{Side}-\text{Side}-\text{Side theorem of triangle congruence } \end{gathered}[/tex]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]Write 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 inequalityMatilda covers the interior faces of a kitchen drawer with shelf paper. The height of the drawer is 3/4 its width and the depth front to back is 7/4 its width. if the exact amount of shelf paper needed is 846 square inches what is the depth of the drawer? help me I need help
To know the depth of the drawer you need to know that the shelf paper is the area of the interior faces of the drawer, then:
A = 846sq in
the area is equal to:
[tex]A=A_b+A_l[/tex]Where:
Ab is the area of the base of the drawer
Al is the area of the laterals of the drawer
The Area of the base is:
[tex]A_b=\frac{7}{4}x\cdot x=\frac{7}{4}x^2[/tex]And the area of the laterals is the sum of the area of every lateral:
[tex]A_l=2\lbrack(\frac{3}{4}x)\cdot(\frac{7}{4}x)\rbrack+2\lbrack(\frac{3}{4}x)\cdot(x)\rbrack[/tex][tex]A_l=\frac{21}{8}x^2+\frac{3}{2}x^2=\frac{33}{8}x^2[/tex]Then:
[tex]846=\frac{7}{4}x^2+\frac{33}{8}x^2[/tex][tex]846=\frac{188}{32}x^2=\frac{47}{8}x^2=5.87x^2[/tex]The we clear the x:
[tex]\frac{846}{5.87}=x^2[/tex][tex]\sqrt[]{144.12}=x[/tex][tex]x=12.004in[/tex]The depth of the drawer is x= 12,004 inchesWhat 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
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
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]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?
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.
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.
Graph each pair of inequalities and indicate the solution set of the system with Cross hatching or shading. The cross hatching or shading, if extended would cover a set of three letters.
Given:
[tex]\begin{gathered} y4 \end{gathered}[/tex]To graph each pair of inequalities and indicate the solution set with cross hatching or shading
Solution
Determine the x and y intrcept of each of the given ineqiualities
[tex]\begin{gathered} y4 \\ 3x+2y=4 \\ y-intercept,make,x=0 \\ 3(0)+2y=4 \\ 2y=4 \\ y=\frac{4}{2}=2 \\ Coordinateof\text{ the y-intercept}:(0,2) \\ x-intercept,make,y=0 \\ 3x+2(0)=4 \\ 3x=4 \\ x=\frac{4}{3} \\ Coordinate\text{ of the x-intercept}:(\frac{4}{3},0) \end{gathered}[/tex]Plot the graph as shown below
It can be observed that the solution set is unbounded, as shown by the cross hatching
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.
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.
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.
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]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 =1/5Order 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
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
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]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
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]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%
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
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
What is y=3x2-1 linear or not linear
Answer:
it would be linear i gotcha bro