Given:
5x - y = 3(x + y)
To express x in terms of y means to make x the subject of the equation.
Let's take the following steps.
Step 1:
Expand the parenthesis
5x - y = 3x + 3y
Step 2:
Subtract 3x from both sides
5x - 3x - y = 3x - 3x + 3y
2x - y = 3y
Step 3:
Add y to both sides
2x - y + y = 3y + y
2x = 4y
Step 4:
Divide both sides by 2:
[tex]\begin{gathered} \frac{2x}{2}=\frac{4y}{2} \\ \\ x=2y \end{gathered}[/tex]Let's find the value of x when y = 5.
Substitute y for 5 in (x = 2y).
We have:
x = 2(5)
x = 10
ANSWER:
x = 2y
x = 10
can you please help me solve angle 1 and 2
Angle 2 is 45 degrees. because DB bisects angle ABC
Angle 1 is 90 degrees. because DB bisects
Mary wants to know the length of a tunnel built through a mountain. To do so, she makes the measurements shown in the figure below. Use these measurements to find the length of the tunnel.
Solution
Using cosine rule to solve for the length of the tunnel:
[tex]a^2=b^2+c^2-2bccosA[/tex]c=length of side c
a=length of side a
b=length of side b
A=angle opposite c
[tex]\begin{gathered} a^2=116^2+247^2-2(116)(247)cos78^0 \\ a^=\sqrt{116^2+247^2-57304cos78} \\ a=250.1016 \end{gathered}[/tex]Therefore the length of the tunnel = 250.1m
What is the end behavior of f(x) in the function f(x) = log(x - 2) as x approaches 2?
Step 1
Given; What is the end behavior of f(x) in the function f(x) = log(x - 2) as x approaches 2?
Step 2
Graph the function
[tex]\begin{gathered} \lim _{x\to \:2}\left(\ln \left(x-2\right)\right) \\ \mathrm{If\:}\lim _{x\to a-}f\left(x\right)\ne \lim _{x\to a+}f\left(x\right)\mathrm{\:then\:the\:limit\:does\:not\:exist} \\ \end{gathered}[/tex]Thus;
[tex]\lim _{x\to \:2}\left(\ln \left(x-2\right)\right)=\mathrm{Does\:not\:exist}[/tex]Therefore the answer is;
[tex]f(x)\rightarrow-\infty[/tex]wich expresion have a value of 180 when b=4? select all that apply. USE PEMDAS
So, to solve this we will have to Test by substituting the 4 into the equations given
[tex]\begin{gathered} 18b\text{ - 179 +957 }\frac{\cdot}{\cdot}\text{ 87} \\ 18(4)\text{- 179 +957 }\frac{\cdot}{\cdot}\text{ 87} \\ 72\text{- 179 +957 }\frac{\cdot}{\cdot}\text{ 87} \\ 72\text{- 179 +11} \\ -96\ne\text{ 180 (not equal to 180)} \end{gathered}[/tex][tex]\begin{gathered} (B)\frac{33b}{12}\text{ = }\frac{33\times4}{12}\text{ = }11\text{ } \\ \text{ 11}\ne180(not\text{ equivalent to 180)} \end{gathered}[/tex][tex]\begin{gathered} C)b^2\text{ + 120} \\ \text{ (4)}^2\text{ + 120 =136 } \\ \text{136 }\ne\text{ 180(Not equivalent to 180)} \end{gathered}[/tex][tex]\begin{gathered} D)\text{ 51b - 24} \\ \text{ 51(4) - 24 } \\ \text{ 204 -24 = 180 This question is correction} \end{gathered}[/tex]E) 11b + 187 -2756/13
11(4) + 187 - 212
44+187 - 212 = 19
19 is not equivalent to 180
Shamara has been tracking her credit score. In October, her credit score was 702 but by April of the following year, it was 679. What is the absolute and relative change in Shamara's credit score from October to April?
Step 1
Given; Shamara has been tracking her credit score. In October, her credit score was 702 but by April of the following year, it was 679. What is the absolute and relative change in Shamara's credit score from October to April?
Step 2
[tex]Absolute\text{ change= 679-902=-23}[/tex][tex]Relative\text{ change=-}\frac{23}{702}\times100=-\frac{1150}{351}\%[/tex]Answer;
[tex]\begin{gathered} Absolute\text{ change=-23} \\ Relative\text{ change=-3.28\%} \end{gathered}[/tex]what is the distance between (-7,2) and (1,-6)
The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 2 dimensional plane, the distance between points (X1, Y1) and (X2, Y2) is given by the Pythagorean theorem:
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex][tex]\begin{gathered} d=\sqrt[]{(1-(-7))^2+(-6-2)^2} \\ d=\sqrt[]{8^2+8^2} \\ d=\sqrt[]{64+64} \\ d=\sqrt[]{128} \\ d=11.31 \end{gathered}[/tex]The answer would be d = 11.31
tan (θ) cot (θ)=1Trig: use trigonometric identities to transform the left side of the equation into the right side
1) Let's prove this identity
Since tan (θ) = sin(θ)/cos((θ)
And cot((θ) = cos ((θ)/sin((θ)
2) Let's plug it into:
[tex]\begin{gathered} \tan \text{ (}\theta)\cot \text{ (}\theta)\text{ =1} \\ \frac{\sin (\theta)}{\cos (\theta)}\cdot\frac{\cos (\theta)}{\sin (\theta)}=1 \\ 1=1 \end{gathered}[/tex]Simplifying (dividing) sin(θ) on the numerator, with sin (θ) on the denominator and similarly cos (θ) with cos(θ) we'll get to 1 over 1 time 1 over 1 = 1
Then 1=1
Robert is paid $12.00 per hour to chop firewood he chops 40% of the pile of firewood in 3/4 of an hour at this rate how much will Robert be paid to chop the entire pile of firewood?
Robert chops 40% of the pile of firewood in 3/4 of an hour.
Then, we would chop 80% of the pile of firewood in 2*(3/4)=3/2 hours.
where 3/2 = 1.5 hours
Also, he would chop the missing 20% in (3/4)/2=3/8.
The full work is for 3/8+3/2 =15/8 hours
Now, if one hour is paid $12.00, we can use the rule of three to know how much is paid for 15/8 hours:
1h-----------$12.00
15/8 h -------- $x
where x=(12.00*5/8)/1
x=22.50
Hence, Robert will be paid $22.50 to chop the entire pile of firewood.
Using a graphing calculator to grab the support on an approximate square viewing window
For this problem, we are given the expression for a circle and we need to determine which graph represents it.
The expression for the circle is:
[tex]x^2+y^2=49[/tex]We can rewrite it as:
[tex]x^2+y^2=7^2[/tex]This means that the radius is equal to 7. So we need to find the circle that has a center in the origin and a radius equal to 7. The correct option is the bottom right option.
Events A and B are independent. Find the indicated Probability.P(A) = 0.4P(B) =P(A and B) = 0.2
From the statement, we know that:
• P(A) = 0.4,
,• P(A and B) = 0.2.
Because A and B are independent events, the probability of A and B is the product of the individual probabilities:
[tex]P(A\text{ and }B)=P(A)*P(B)\Rightarrow P(B)=\frac{P(A\text{ and }B)}{P(A)}.[/tex]Replacing the data of the problem, we get:
[tex]P(B)=\frac{0.2}{0.4}=0.5.[/tex]AnswerP(B) = 0.5
A regular 9 sided building is 814 ft along one side what is the distance from a Vertex to the center of the building
A regular 9 sided building is 814 ft along one side what is the distance from a Vertex to the center of the building
we know that
A regular 9 sided polygon, can be divided into 9 isosceles triangle
The equal distances of the isosceles triangle is equal to the radius or the distance from a Vertex to the center of the building
the base of the isosceles triangle is given and is equal to 814 ft
The measure of the interior angle of the vertex is equal to
360/9=40 degrees
that means
we have
Applying the law of sines
814/sin(40)=r/sin(70)
solve for r
r=(814/sin(40))*sin(70)
r=1,190 ft
therefore
the distance is 1,190 ftTest ContentQuestion 110 PointsA box is 36 inches long, 18 inches wide, and 6 inches deep. How many cubic feet are in the box?A 5 cubic feetB4.5 cubic feet© 3 cubic feetD2.25 cubic feet
The box is 2.25 cubic feet (option D)
Explanation:length of the box = 36 inches
width = 18 inches
depth = height = 6 inches
To get the volume of the box in cubic feet, we need to first convert the dimensions from iches to feet to make it easy to solve.
conversion from iches to ft:
12 inches = 1 ft
36 inches = 36/12
= 3 ft
18 inches = 18/12
width = 18 inches = 3/2 ft
6 inches = 6/12
height = 6 inches = 1/2 ft
The box is a rectangular prism
Volume of rectangular prism = length × width × height
[tex]\begin{gathered} \text{Volume of the rectangular prism = 3 ft }\times\text{ }\frac{3}{2}\text{ ft }\times\text{ }\frac{1}{2}\text{ ft} \\ \text{Volume of the rectangular prism = 9/4 ft}^3\text{ = }2.25ft^3 \\ \\ \\ Volume\text{ of the box = 2.25 cubic f}eet\text{ (option D)} \end{gathered}[/tex]The graph of the function y=f(x) is given. Find the domain of f(x).Using the graph given.
Given
Graph of the function y = f(x)
Find
domain of f(x)
Explanation
As we know domain of a function is all the values of x that makes the function defined.
here in the graph , the function is defines for x values 0 to 5
since , the point 0 and 5 is in open interval , so , the graph does not include the points 0 and 5
hence , the domain is (0 , 5)
Final Answer
Therefore , the domain of the given function is (0 , 5)
Using the following image, solve for UW. 7 2x + 3 U V 2x+3 W X + 10 UW
Answer
UW = 10
Explanation
From the image attached, we can see that
UV + VW = UW
But
UV = 2x + 3
VW = 7
UW = x + 10
UV + VW = UW
(2x + 3) + 7 = x + 10
2x + 3 + 7 = x + 10
2x + 10 = x + 10
2x - x = 10 - 10
x = 0
UW = UV + VW
UW = 2x + 3 + 7
UW = 2 (0) + 10
UW = 0 + 10
UW = 10
Hope this Helps!!!
Need help on homework
Answer:
The solution of the equation is;
[tex]x=-11[/tex]Explanation:
Given the equation;
[tex]6(x-6)+4=8x-10[/tex]Applying Distributive property of multiplication, we have;
[tex]\begin{gathered} 6(x)-6(6)+4=8x-10 \\ 6x-36+4=8x-10 \\ 6x-32=8x-10 \\ \text{collect the like terms, and solve;} \\ 8x-6x=+10-32 \\ 2x=-22 \\ x=\frac{-22}{2} \\ x=-11 \end{gathered}[/tex]Therefore, the solution of the equation is;
[tex]x=-11[/tex]The equation we used today to represent a line is called _______ formFor the equation y=mx+b, m is the ______For the equation y=mx+b, b is the _______
1) The equation we used today to represent a line is called :
The slope-intercept form
In this form, y=mx +b
2) For the equation y=mx+b, m is the slope
It measures how steep is the line.
3) For the equation y=mx+b, b is the line coefficient
This is the point where the line intercepts the y coordinate.
in the figure below , DGH was dilated and then rotated 180° about point G to create the other triangle .
We can eliminate some of these choices , knowing that if we dilate a triangle they are the same shape but not necessarily the same size. Thus , they are not congruent. Therefore, the last two choices are false since it denotes congruency.
It is also stated from the problem that the triangle is rotated by 180 degrees therefore the congurent pair of angle can be found on the opposite side in the figure. Therefore , we can eliminate the first choice since it states that the congruency among angles are at the same side.
Thus, CHOICE 2 is true.
In a class of 30 students, 19 have a cat and 12 have a dog. There are 6 students who do not have a cat or a dog. What is the probability that a student has a cat given that they have a dog?
We are asked to find the probability to find a student that has a cat when we know he/she has a dog. Then, we need to know how many students have a dog, and how many have a dog and a cat.
We already know that 12 students have a dog. However we do not know how many students have a cat and a dog.
Let's calculate that.
We know we have 30 students.
We know 6 do not have dogs nor cats.
[tex]19\text{ + 12 +6 = 37}[/tex]The sum of students having dogs, the students having cats and the students having none is 37, but we know that there are only 30 students. Then, we can say that 7 students have both a dog and a cat. That is just the information we needed.
Then, we can calculate the probability that a student has a cat given that they have a dog as follows:
Let's say P is that probability:
[tex]P=\frac{\text{Number of students having both}}{\text{Number of students having a dog}}=\frac{7}{12}[/tex][tex]P=\frac{7}{12}=0.5833=58.33\text{ \%}[/tex]5 6 3 4 13. Jose is 35 years old, and makes $40,000 per year. If he dies, how much would the beneficiaries of his life insurance policy receive if they can get by on 75% of his income? Muilples-of-Salary Chart PEET Շնոաս: Օրհi# ԵՆՔրցե 5.5 5.5 6.5 6.5 40 3.0 3.0 810 6.0 4.5 70 BD 85 6.5 75 5.5 2350 GO 5.0 1.5 70 00010 RO ED 70 7.5 60 65 5.5 75 50
We are told that jose is 35 years old and makes 40.000 per year. Also, we are told that they can get by 75% of his income. So, in the table, we look for the age column for 35 years and in the gross earnings we look for the 40000 row.
Inside the 35 years column, we take a look at the inner column that says 75%. Crossing all this information, we get that the table shows a multiplier of 8.0
This means that their beneficiaries would earn 8 times the salary of jose. That is
[tex]8\cdot40000=320000[/tex]Is -13, -6, 1, 8 arithmetic?
Given the following sequence
[tex]\lbrace-13,-6,1,8,\ldots\rbrace[/tex]We want to know if this sequence is arithmetic. The general term of an arithmetic sequence is given by
[tex]a_n=a_1+(n-1)d[/tex]Where d represents the common ratio. An arithmetic sequence increases by the same value every term(this value is the common ratio). If the difference between neighbor terms is the same for all of our terms, this sequence can be written as an arithmetic sequence.
Let's calculate the difference between the terms
[tex]\begin{gathered} a_2-a_1=-6-(-13)=-6+13=7 \\ a_3-a_2=1-(-6)=1+6=7 \\ a_4-a_3=8-1=7 \end{gathered}[/tex]Since the difference is the same, this sequence is Arithmetic.
Find the area of the sector. Round to the nearest tenth.459 m254.616.9O 31.8O 7.1
The area of the sector is 31.8m^2 ( nearest tenth)
1 plus 1 my little sister needs help
Answer:
[tex]1+1=2[/tex]Step-by-step explanation:
If you have one apple and you buy another one, you will have 2 apples. Therefore,
[tex]1+1=2[/tex]I need help with this practice Having troubleIf you can, use Desmos to graph the function
In general, given a function g(x)
[tex]undefined[/tex]identify the correct graph of the circle. (x + 3)² + (y + 1) = 16I have to send the graphs in message
The general form of a equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where:
r is the radius of the circle
(h,k) are the coordinates of the center of the circle
Then, the given equation:
[tex](x+3)^2+(y+1)^2=16[/tex]The radius and the coordinates of the center are:
[tex]\begin{gathered} r=4 \\ h=-3 \\ k=-1 \\ \\ \mleft(-3,-1\mright) \end{gathered}[/tex]Then, the graph for this circle is: Photo number 2
Determine weather each question is an example of statistical question. Drag each question to the correct classification in the table.What is Steve favorite sport?How many books are on the shelf in our math class?What is the height of each player on the basketball team ?what temperature outside the school at 6 o'clock this morning? What is the number of tickets sold at the movie theater each day this month
Find a linear equation satisfying the followingf(2)= 21 and f(-4) = -15f(x) =help (formulas)
Recall
f(x)=y
Given
f(2)= 21 and f(-4) = -15
f(x) =
Step 1
[tex]\begin{gathered} y=mx+b \\ \text{when} \\ f(2)=21_{} \\ 21=2m+b\ldots\text{Equation (i)} \end{gathered}[/tex][tex]\begin{gathered} y=mx+b \\ \text{when } \\ f(-4)=-15 \\ -15=-4m+b\ldots\text{Equation (i}i) \end{gathered}[/tex]Step 2
Let's solve equation (i) and Equation (ii) simultaneously
[tex]\begin{gathered} 21=2m+b\ldots(i) \\ -15=-4m+b\ldots(ii) \\ In\text{ equation (i) Let's make b the subject} \\ b=21-2m \end{gathered}[/tex][tex]\begin{gathered} we\text{ now substitute in equation (i}i) \\ -15=-4m+21-2m \\ \text{collect the like terms} \\ -15-21=-4m-2m \\ -36=-6m \\ \text{Divide both sides by -6} \\ -\frac{36}{6}=-\frac{6m}{-6} \\ \\ m=6 \end{gathered}[/tex]Step 3
[tex]We\text{ can substitute for m either in equation(i) or (i}i)[/tex]using Equation (ii)
[tex]\begin{gathered} -15m=-4m+b \\ -15=-4(6)+b \\ \text{collect the like terms} \\ -15=-24+b \\ \text{collect the like terms} \\ -15+24=b \\ b=9 \end{gathered}[/tex]Step 4
M= 6 and b= 9
[tex]\begin{gathered} We\text{ can substitute into y=mx+b} \\ y=6x+9 \end{gathered}[/tex]The linear equation is
[tex]y=6x+9[/tex]Julie asked 50 students in her school whether they do volunteer work. This table shows the results.The graph is in the pictureHow many more seventh graders than eighth graders did Julie survey?
Solution:
Given the table below:
From the table,
[tex]\begin{gathered} Number\text{ of seventh graders = 27} \\ Number\text{ of eighth graders = 23} \end{gathered}[/tex]Since there are more seventh-graders than eighth-graders, we can evaluate the number of more seventh-graders by subtracting the number of eighth-graders from the number of seventh-graders.
Thus, we have
[tex]\begin{gathered} 27-23 \\ =4 \end{gathered}[/tex]Hence, Julie surveyed 4 more seventh-graders than eighth-graders.
What is the first step in constructing this equilateral triangle?O A. Draw two circles with radius AB.B. Draw an angle with vertex A.C. Draw an angle with vertex C.D. Draw line segment AB.SUBMIT
The first step is draw line segment AB.
the sum of the first two terms of an arit
SOLUTION:
We are told that;
[tex]\begin{gathered} a+a+d=15 \\ a+2d+a+3d=43 \end{gathered}[/tex]Rewriting, we have;
[tex]\begin{gathered} 2a+d=15 \\ 2a+5d=43 \end{gathered}[/tex]Subtracting the first and second equations, we have;
[tex]\begin{gathered} 4d=28 \\ d=7 \end{gathered}[/tex]and;
[tex]\begin{gathered} 2a+7=15 \\ 2a=8 \\ a=4 \end{gathered}[/tex]Thus, the first four terms of the sequence are;
[tex]4,11,18,25[/tex]What diameter must a circular piece of stock be to mill a hexagonal shape with a side length of 2.7 in.?
Given:
A circular piece of stock be to mill a hexagonal shape with a side length of 2.7 in.
Required:
We need to find the diameter of hexagon.
Explanation:
now use the sin function
[tex]\begin{gathered} sin30=\frac{1.35}{r} \\ \\ \frac{1}{2}=\frac{1.35}{r} \\ \\ r=2.7 \end{gathered}[/tex]so by r
[tex]d=2r=5.4\text{ in}[/tex]Final answer:
Diameter of hexagon is 5.4 in