This is a type of radioactive decay problem. Given an initial amount of N0, the amount at t years is given by
[tex]N(t)=N_0e^{-\lambda t}[/tex]The information "27 years is the half-life of the substance" means that if we replace t by 27, we will get exactly half of the initial amount we had. That is
[tex]N_0e^{-\lambda\cdot27}=\frac{N_0}{2}[/tex]We can cancell out N0 on both sides, so we get
[tex]e^{-\lambda\cdot27}=\frac{1}{2}[/tex]using the properties of exponentials, we have the equivalent equation
[tex]\frac{1}{2}=\frac{1}{e^{\lambda\cdot27}}[/tex]which is also equivalent to
[tex]e^{\lambda\cdot27}=2[/tex]If we apply natural logarithm on both sides, we get
[tex]\ln (e^{\lambda\cdot27})=\lambda\cdot27=\ln (2)[/tex]Finally, we can divide both sides by 27, to get
[tex]\lambda=\frac{\ln (2)}{27}[/tex]So, the function that describes the amount of the subtances at time t is given as
[tex]N(t)=N_0e^{\frac{-\ln (2)\cdot t}{27}}[/tex]Now, we want to calculate the value of t, for which the amount we have at year t is exactly 66% of what we have at t=0. That is
[tex]\frac{N_0e^{-\frac{\ln (2)\cdot t}{27}}}{N_0}=0.66[/tex]We can cancell out N0 and, by equivalence by using the properties of exponents, we get
[tex]\frac{1}{e^{\frac{\ln(2)}{27}\cdot t}}=0.66[/tex]which is also equivalent to
[tex]\frac{1}{0.66}=e^{\frac{\ln (2)t}{27}}[/tex]if we apply the natural logarithm on both sides, we get
[tex]\ln (\frac{1}{0.66})=\ln (e^{\frac{\ln(2)\cdot t}{27}})=\ln (2)\cdot\frac{t}{27}[/tex]Finally, we want to solve for t. To do so, we can multiply by 27 and then divide by ln(2). So we get
[tex]t=\frac{27}{\ln(2)}\cdot\ln (\frac{1}{0.66})[/tex]with help of a calculator, we have that t is approximately 16.185. That is, about after 16 years, we will have 66% of the initial amount.
Find the absolute value|9\5|
Absolute value simply means the number must be made positive. Since 9/5 is positive already the absolute value remains 9/5
I will add an additional picture with the answer options for the blank spaces
Given
[tex](y+5)^2=12(x+3)[/tex]Answer
The graph of the parabola is given as
The vertex of is (-3,-5). The parabola opens right. The focus is 3 units away from vertex. The directrix is 6 units away from focus. Focus is at (0,-5). The equation of the directix is x = - 6
In ∆OPQ, q =1.7cm, o=3.8 cm and < P=96°. Find < Q, to the nearest 10th of a degree.
To solve the exercise you can use the law of cosine, which applies to any triangle:
[tex]b^2=a^2+c^2-2ac\cdot\cos (B)[/tex]Where
So, in this case, you have
[tex]\begin{gathered} p^2=o^2+q^2-2oq\cdot\cos (P) \\ p^2=(3.8cm)^2+(1.7cm)^2-2(3.8cm)(1.7cm)\cdot\cos (96\text{\degree)} \\ p^2=14.44cm^2+2.89cm^2-12.92cm^2\cdot\cos (96\text{\degree)} \\ p^2=17.33\operatorname{cm}^2-(-1.35cm^2) \\ p^2=17.33\operatorname{cm}+1.35cm^2 \\ p^2=18.68\operatorname{cm}^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{p^2}=\sqrt[]{18.68\operatorname{cm}^2} \\ p=4.32\operatorname{cm} \end{gathered}[/tex]Now, you can use the law of sine, which applies to any triangle:
[tex]\frac{a}{\sin (A)}=\frac{b}{\sin (B)}=\frac{c}{\sin (C)}[/tex]In this case, you have
[tex]\begin{gathered} \frac{q}{\sin(Q)}=\frac{p}{\sin(P)} \\ \frac{1.7\operatorname{cm}}{\sin(Q)}=\frac{4.32\operatorname{cm}}{\sin(96\text{\degree})} \\ \text{ Apply cross product} \\ 1.7\operatorname{cm}\cdot\sin (96\text{\degree})=\sin (Q)\cdot4.32\operatorname{cm} \\ \text{ Divide by 4.32 cm from both sides of the equation} \\ \frac{1.7\operatorname{cm}\cdot\sin(96\text{\degree})}{4.32\operatorname{cm}}=\frac{\sin(Q)\cdot4.32\operatorname{cm}}{4.32\operatorname{cm}} \\ \frac{1.7\operatorname{cm}\cdot\sin(96\text{\degree})}{4.32\operatorname{cm}}=\sin (Q) \\ 0.39=\sin (Q) \\ \text{ Apply the inverse function }\sin ^{-1}(\theta)\text{ both sides of the equation} \\ \sin ^{-1}(0.39)=\sin ^{-1}(\sin (Q)) \\ 23.0\text{\degree}=Q \end{gathered}[/tex]Therefore, the measure of angle Q is 23 degrees.
Write the equation of the function in vertex form, then convert to standard form.
The equation of the parabola in vertex form is
[tex]y=a(x-h)^2+k[/tex]where the point (h,k) is the coordinate of the vertex. From our picture, we can note that (h,k)=(-6,-4).
By substituting these values into our first equation, we have
[tex]y=a(x-(-6))^2-4[/tex]which gives
[tex]y=a(x+6)^2-4[/tex]Now, we can find the constant a by substituting one of the other given point. If we choose point (0,-2) into this last equation, we get
[tex]-2=a(0+6)^2-4[/tex]which gives
[tex]\begin{gathered} -2=a(6^2)-4 \\ -2=36a-4 \end{gathered}[/tex]then, by moving -4 to the left hand side, we have
[tex]\begin{gathered} -2+4=36a \\ 2=36a \\ or\text{ equivalently,} \\ 36a=2 \end{gathered}[/tex]and finally, a is equal to
[tex]\begin{gathered} a=\frac{2}{36} \\ a=\frac{1}{18} \end{gathered}[/tex]hence, the equation of the parabola in vertex form is
[tex]y=\frac{1}{18}(x+6)^2-4[/tex]Now, lets convert this equation into a standrd form. This can be done by expanding the quadratic term and collecting similar term. That is, by expanding the quadratic terms, we obtain
[tex]y=\frac{1}{18}(x^2+12x+36)-4[/tex]now, by distributing 1/18, we have
[tex]y=\frac{1}{18}x^2+\frac{12}{18}x+\frac{36}{18}-4[/tex]which is equivalent to
[tex]y=\frac{1}{18}x^2+\frac{1}{3}x+2-4[/tex]and finally, the parabola equation in standard form is
[tex]y=\frac{1}{18}x^2+\frac{1}{3}x-2[/tex]With the points (8,4) (-6,-6) (-10, 12) (2,-4). What are the new points if thescale factor of dilation is 4?*
The transformation for a points using a dilation factor k follows the rule:
[tex](x,y)\Rightarrow k(x,y)\Rightarrow(kx,ky)[/tex]Applying this to the points given
[tex](8,4)\Rightarrow(8\cdot4,4\cdot4)\Rightarrow(32,16)[/tex][tex](-6,-6)\Rightarrow(4\cdot-6,4\cdot-6)\Rightarrow(-24,-24)[/tex][tex](-10,12)\Rightarrow(4\cdot-10,12\cdot4)\Rightarrow(-40,48)[/tex][tex](2,-4)\Rightarrow(4\cdot2,4\cdot-4)\Rightarrow(8,-16)[/tex]The volume of a cone with helght h and radius r can be found using the formula V1arth3Find the volume of a cone with radius 8 feet and height 10 feet.
ANSWER:
669.87 cubic feet
STEP-BY-STEP EXPLANATION:
The volume of the cone is given as follows:
[tex]V=\frac{\pi\cdot r^2\cdot h}{3}[/tex]We know the value of the radius and height, we replace and calculate the volume:
[tex]\begin{gathered} V=\frac{3.14\cdot8^2\cdot10}{3} \\ V=669.87ft^3 \end{gathered}[/tex]Therefore, the volume of the cone is 669.87 cubic feet.
Which of the following is a solution of 3x2 = 7x − 3?
negative 7 plus or minus the square root of 13 divided by 6
7 plus or minus the square root of 85 divided by 6
negative 7 plus or minus the square root of 85 divided by 6
7 plus or minus the square root of 13 divided by 6
By using Quadratic formula, the solutions are
[tex]x = \frac{7 + \sqrt{13}}{6}[/tex] or [tex]x = \frac{7 - \sqrt{13}}{6}[/tex]
Fourth option is correct.
What is Quadratic equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A two degree equation is known as Quadratic equation.
If [tex]ax^2+bx + c = 0 (a\neq 0)[/tex] be a quadratic equation,
[tex]x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
This is the quadratic formula
Here,
The given quadratic equation is
[tex]3x^2 = 7x - 3\\3x^2 - 7x + 3 = 0\\[/tex]
a = 3, b = -7, c = 3
x =
[tex]\frac{-(-7)\pm\sqrt{(-7)^2 - 4\times 3 \times 3}}{2\times 3}\\\frac{7 \pm \sqrt{49 - 36}}{6}\\\frac{7 \pm \sqrt{13}}{6}[/tex]
[tex]x = \frac{7 + \sqrt{13}}{6}[/tex] or [tex]x = \frac{7 - \sqrt{13}}{6}[/tex].
Fourth option is correct.
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What is the rate of change of the graph?a.1/32 gallons/mileb.1/64 gallons/milec.64 miles/gallond.32 miles/gallon
Taking two points on the graph
when miles = 160 , gallon = 5
when miles = 64 , gallon = 2
Joey’s sock drawer is unorganized and contains 3 black dress socks, 3 black ankle socks, 6 brown dress socks, and 4 brown ankle socks. What is the probability that Joey chooses a sock at random that is brown or is a dress sock?A) 1, or 100%B) 19/16C) 3/8D) 13/16
EXPLANATION:
Given;
We are told that Joey's drawer contains the following;
Black dress socks = 3
Black ankle socks = 3
Brown dress socks = 6
Brown ankle socks = 4
Required;
If a sock is chosen at random, find the probability that it is brown or is a dress sock.
Step-by-step solution;
The drawer contains a total of 16 socks.
Also, there is a total of 9 dress socks and 10 brown socks.
The probability of choosing a brown or dress sock will be determined by the following formula;
[tex]P[brown\text{ }sock\text{ }OR\text{ }dress\text{ }sock]=P[brown]+P[dress]-P[brown\text{ }and\text{ }dress][/tex]We can now substitute the values given for this experiment as follows;
[tex]P[brown\text{ }OR\text{ }dress]=\frac{10}{16}+\frac{9}{16}-\frac{6}{16}[/tex][tex]P[brownORdress]=\frac{19}{16}-\frac{6}{16}=\frac{13}{16}[/tex]ANSWER:
The probability that Joey would select a sock at random that is brown or is a dress sock is
[tex]\frac{13}{16}[/tex]Option D is the correct answer.
The matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system if it exists. Write an exact answer in simplified form. If there are infinitely many solutions, write an expression involving z for each coordinate where z represents all real numbers.
ANSWER:
[tex]\begin{gathered} x+2z=1 \\ y-5z=3 \end{gathered}[/tex]The solution is:
[tex]\begin{gathered} x=1-2z \\ y=3+5z \\ z=z \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We must convert the matrix into a system of linear equations.
Each vertical represents the letters x, y and z, the first the x, the second y and the third the z. The fourth value is the value of the independent term that would be equal to the other expression, just like this:
[tex]\begin{gathered} 1x+0y+2z=1 \\ 0x+1y-5z=3 \\ 0x+0y+0z=0 \end{gathered}[/tex]We operate and the system will finally be like this
[tex]\begin{gathered} x+2z=1 \\ y-5z=3 \end{gathered}[/tex]let's solve the system and we have:
[tex]\begin{gathered} x=1-2z \\ y=3+5z \\ z=z \end{gathered}[/tex]A dietitian at a hospital wants a patient to have a meal that has 113 grams of protein, 54 grams of carbohydrates, and 135.5 milligrams of vitamin A. The hospital foodservice tells the dietitian that the dinner for today is salmon steak, baked eggs, and acorn squash. Each serving of salmon steak has 30 grams of protein, 10 grams ofcarbohydrates, and 1 milligram of vitamin A. Each serving of baked eggs contains 20 grams of protein, 3 grams of carbohydrates, and 20 milligrams of vitamin A. Eachserving of acorn squash contains 4 grams of protein, 15 grams of carbohydrates, and 37 milligrams of vitamin A. How many servings of each food should the dietitian provide for the patient?__ salmon steak (x)__ baked eggs (y)__ acorn squash (z)
Hello there. To solve this question, we'll need to set up a system of equations with 3 equations and 3 variables.
In each equation, we'll have the amounts for protein, carbohydrates and vitamin A.
Talking about protein:
Each serving of salmon steak has 30 grams of protein, baked eggs contains 20 grams of protein and acorn squash contains 4 grams of protein.
Say the servings of salmon steak, baked eggs and acorn squash are the variables x, y and z, respectively. We multiply x, y and z by the respective values for the protein of each serving and add them up. It should be equal to the amount of protein the dietitian was thinking of.
30x + 20y + 4z = 113
Talking about carbohydrates:
The same thing will apply to carbs, we multiply the variables by how many carbs we can get for eachserving. A serving of salmon steak gives you 10 grams of carbs, baked eggs gives you 3 grams of carbs and acorn squash gives you 15 grams.
10x + 3y + 15z = 54
Talking about vitamin A:
Repeat the same process, this time using the values for the vitamin A you get form each serving.
x + 20y + 37z = 135.5
Then we have the following system of equations:
Solving this system of equations, you can use the method of your choice.
After you solved it, you find the values:
1.5 serving of salmon steak, 3 servings of baked eggs and 2 servings of acorn squash.
what is 3.33333333333 as a whole number?
1/3 = 0.333333333333
Then
3.33333333 is a whole number
= 3 + 1/3
a dog runs 12 miles per hour select animals that run faster than the doglion 100 miles 2 hrsbear 60 miles in 2 hrszebra 80 miles in 2 hrselk 90 miles in 2 hrs
We were told that a dog runs 12 miles per hour.
If a lion runs 100 miles in 2 hours, it means that the number of miles that the lion runs per hour is 100/2 = 50 miles per hour
If a bear runs 60 miles in 2 hours, it means that the number of miles that the bear runs per hour is 60/2 = 30 miles per hour
If a zebra runs 80 miles in 2 hours, it means that the number of miles that the zebra runs per hour is 80/2 = 40 miles per hour
If an elk runs 90 miles in 2 hours, it means that the number of miles that the bear runs per hour is 90/2 = 45 miles per hour
We can see that all the other animals cover more miles per hour than the dog. Thus,they all run faster than the dog
The arc length of the semicircle shown in green is 34. What is the radius of the circle? R=
Given:
[tex]\begin{gathered} \text{length of arc = 32}\pi \\ \theta=180^0(angle\text{ on a straight line or angle in semi circle)} \\ r=\text{?} \end{gathered}[/tex]To calculate the length of an arc, the formula is;
[tex]\begin{gathered} l=\frac{\theta}{360}\times2\pi r \\ \text{Substituting all the parameters into the formula;} \\ 32\pi=\frac{180}{360}\times2\pi r \\ 32\pi=\frac{360\pi\text{ r}}{360} \\ 32\pi=\pi r \\ r=\frac{32\pi}{\pi} \\ r=32 \end{gathered}[/tex]Therefore, the radius of the circle 32 units.
A marketing company takes a random sample of 700 men to get their opinion on a new style of car. The marketing company then reports the following: “Four out of five drivers surveyed prefer the new style over the old style.” Explain why this conclusion would be misleading. a. The company only surveyed men but made the claim about all drivers. b. The survey question was biased toward the new style. c. The people surveyed were not randomly selected. d. The sample size of drivers was too small.
According to the information given, the randome sample that was asked about their opinion was 700 men, however the results of the survey were given as "4 out of 5 drivers"
This information is misleading because the results should have been thrown for men and not for drivers since the sample does not give any information saying that all 700 men are drivers.
The correct answer is: A
Please help me on average rate of change!
The averge rate of change on the interval -1≤x≤5 for the given function f(x)= -3|x+2|-1 is -3.
In the given question we have to find the averge rate of change on the interval -1≤x≤5 for the given function.
Thegiven function is f(x)= -3|x+2|-1
The interval [a,b]=[-1,5]
As we know that the average rate of change of function f(x) on [a,b] is given by
R = {f(b)-f(a)}/(b-a)
As we know that a= -1 and b=5.
R = {f(5)-f(-1)}/(5-(-1))...........................(1)
Firstly we finding the f(-1) and f(5)
Now put x= -1 in the given function.
f(-1)= -3|-1+2|-1
f(-1)= -3|1|-1
f(-1)= -3-1
f(-1)= -4
As we know that b= 5.
Now put x= 5 in the given function.
f(5)= -3|5+2|-1
f(5)= -3|7|-1
f(5)= -3*7-1
f(5)= -21-1
f(5)= -22
Now putting the value in equation 1.
R = (-22-(-4))/(5+1)
R = (-22+4)/6
R = -18/6
R = -3
Hence, the averge rate of change on the interval -1≤x≤5 for the given function f(x)= -3|x+2|-1 is -3.
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Ivanna runs each lap in 4 minutes. She will run more than 11 laps today. What are the possible numbers of minutes she will runtoday?Use t for the number of minutes she will run today.Write your answer as an inequality solved for t.
So,
Let "t" be the number of minutes she will run today.
Given that she will run more than 11 laps today, then we can set up the inequality:
[tex]\begin{gathered} t>11\cdot4 \\ t>44 \end{gathered}[/tex]This is because 11 laps take 44 minutes to run, and if she will run more than 44 minutes, so t>44.
What is the slope of the line connecting the points (1,2) and (-2,1)?
For this type of problem we recall the formula for the slope (m) of a line passing through 2 points and substitute the given points:
[tex]m=\frac{y_1-y_2}{x_1-x_2}=\frac{2-1}{1-(-2)}=\frac{1}{3}[/tex]Answer: m= 1/3.
Find the value of z.7Xy3ZV[?]Z =Give your answer in simplest form.Enter
First, lets remember the property of right triangles as follows. Given a right triangle with the form:
The following formula is true:
[tex]Z^2=m\times(m+n)[/tex]So, in our case m=3 and m+n=7+3=10, if this we can find Z:
[tex]Z^2=3\times(7+3)\rightarrow Z^2=30\rightarrow Z=\sqrt[]{30}[/tex]What is the equation of the line through (-2, -3) with an undefined slope?a.y=-3b. -3x + 2y = 0c. -2x – 3y = 0d.x=-2
We have an undefined slope. It means that the line is parallel to the y-axis, that is, the slope could be "defined" as an infinite slope (in rough words).
Therefore, the equation of the line through the point (-2, -3) with an undefined slope is:
x = -2 (option d).
This line is represented as a parallel line to the y-axis (x = -2), and it passes through the point (-2, -3).
The coordinate plane is separated into four quadrants as shown.
Let p: x < 0
Let q: y < 0
What is represented by p ∨ q?
quadrant 1 because both x and y are positive coordinates
quadrant 3 because both x and y are negative coordinates
quadrants 1, 2, and 4 because in these quadrants x, y, or both are positive coordinates
quadrants 2, 3, and 4 because in these quadrants x, y, or both are negative coordinates
For the condition p: x < 0 and q: y < 0; p ∨ q represent quadrants 2, 3, and 4 is correct because in these quadrants x, y, or both are negative coordinates.
What is termed as the quadrants?The quadrant is the area confined by the X and Y axes interlinking. When the two axes, the X-axis and the Y-axis, intersect at 90o on the cartesian plane, four regions form around it, which are recognised as quadrants. As a consequence, each plane has four quadrants, each of which is bounded by half of a axes.We are told that p: x<0 and q: y<0.
Because the value of x is negative here, the graph of 'p' upon plotting will show quadrants 2 and 3.Also, because the value of y is negative here, the graph of 'q' after projecting will show quadrants 3 and 4.Now we must find 'pVq,' which means 'p or q' (where V is indeed the disjunction OR), i.e. satisfying either x<0 or y<0 or both x<0 and y<0.As a result, pVq = quadrants 2, 3, and 4, because both x and y are negative within those quadrants.
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Find the mZRPQ.25°RQ105
Given the figure in the attached image;
[tex]\begin{gathered} m\measuredangle\text{PRQ}=25^{\circ} \\ m\measuredangle QTU=105^{\circ} \end{gathered}[/tex]The angle PQS and QTU are corresponding angles so they are congruent.
[tex]m\measuredangle PQS=m\measuredangle QTU=105^{\circ}[/tex]Also, the angle PQS is an exterior angle to the angles PRQ and RPQ. So, the sum of angles PRQ and RPQ will give the angle PQS;
[tex]m\measuredangle PQS=m\measuredangle PRQ+m\measuredangle RPQ[/tex]substituting the given values;
[tex]\begin{gathered} m\measuredangle PQS=m\measuredangle PRQ+m\measuredangle RPQ \\ 105^{\circ}=25^{\circ}+m\measuredangle RPQ \\ m\measuredangle RPQ=105^{\circ}-25^{\circ} \\ m\measuredangle RPQ=80^{\circ} \end{gathered}[/tex]Therefore, the measure of angle RPQ is;
[tex]m\measuredangle RPQ=80^{\circ}[/tex]Two containers designed to hold water are side by side both in the shape of a cycle see. Container A has a radius of 4 feet and a height of 9 feet. Container B has a radius of 3 feet and height of 11 feet. Container A is full of water and the water is pumped into container B until container B is completely full. After the pumping is complete what is the volume of water remaining in container A to the nearest tenth of a cubic foot
We have to calculate the water remaining in A after B is complete.
This will be equal to the volume of A minus the volume of B.
The volume of each cylinder is equal to the area of the base times the height, so we can calculate this difference as:
[tex]\begin{gathered} V=V_A-V_B \\ V=\pi(r_A)^2h_A-\pi(r_B)^2h_B \\ V=\pi(4)^2(9)-\pi(3)^2(11) \\ V=\pi(16)(9)-\pi(9)(11) \\ V=144\pi-99\pi \\ V=45\pi \\ V\approx141.4 \end{gathered}[/tex]Answer: the remaining volume is approximately 141.4 cubic feet.
Find the perimeter of the rectangle. Be sure to write the correct unit in your answer. | cm 2 I Don't Know Submit
Answer:
Explanation:
(-19, -6) and (15, 16) find the slope?
Answer:
Explanation:
The slope is defined as the rise/ run. If a line passes through any two points (x0, y0) and (x1, y1) then the slope m is given by
[tex]m=\frac{y_1-y_0_{}_{}}{x_1-x_0}[/tex]Now, in our case (x0, y0) = ( -19, 6) and (x1, y1) = (15, 16); therefore, the slope is
[tex]m=\frac{16-6}{15--19_{}}[/tex]Simplifying the above gives
[tex]m=\frac{5}{17}[/tex]which is our answer!
how to do use excel formula.
The steps to use the excel formulas are:
Choose a blank cell.After entering the equal sign =, type function. Use =SUM, for instance, to calculate the total sales.Add a first parenthesis (.Type a closing parenthesis after choosing the cell range.To obtain the outcome, press Enter.What is an excel formula?A formula in Microsoft Excel is an expression that modifies values in a set of cells. Even if the result is incorrect, these formulas nonetheless return a result. You may execute calculations like addition, subtraction, multiplication, and division using Excel formulae.A formula in Excel is an expression that manipulates values in a cell or a range of cells. Consider the formula =A1+A2+A3, which calculates the sum of the values in cells A1 through A3.Simple Excel formulae include SUM, COUNT, COUNTA, COUNTBLANK, AVERAGE, MIN Excel, Excel MAX, and Excel LEN.Some steps to use the excel formulas are:
Choose a blank cell.After entering the equal sign =, type function. Use =SUM, for instance, to calculate the total sales.Add a first parenthesis (.Type a closing parenthesis after choosing the cell range.To obtain the outcome, press Enter.Therefore, the steps to use the excel formulas are:
Choose a blank cell.After entering the equal sign =, type function. Use =SUM, for instance, to calculate the total sales.Add a first parenthesis (.Type a closing parenthesis after choosing the cell range.To obtain the outcome, press Enter.Know more about an excel formula here:
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Solve each system of equations by GRAPHING. Clearly identify your solution.(2x+y=1) (x-2y=18)
Answer:
(x, y) = (4,-7)
Explanation:
To solve the system we need to graph the line that each equation represents, then the solution will be the point where the lines cross.
So, to graph the line for the first equation 2x + y = 1, we need to identify two points in the line.
Then, if x = 0, y is equal to:
2x + y = 1
2(0) + y = 1
y = 1
And if x = 1, y is equal to:
2(1) + y = 1
2 + y = 1
2 + y - 2 = 1 - 2
y = -1
So, for the first equation, we have the points (0, 1) and (1, -1)
In the same way, for the second equation x - 2y = 18, we get:
If x = 0, y is equal to:
0 - 2y = 18
-2y = 18
y = 18/(-2)
y = -9
If x = 2, y is equal to:
2 - 2y = 18
2 - 2y - 2 = 18 - 2
-2y = 16
y = 16/(-2)
y = -8
So, for the second equation, we have the points (0, -9) and (2, -8)
Therefore, the graph of both lines is:
So, the solution of the system is the point (x, y) = (4, -7)
Which of the equations below represent exponential decay? Select all that apply. • y= (6.35)^x• y= (0.01)^ x• y= (3/4) 2^x• y= 700 (1-0.35)^x • y= (4/3) ^x
The equation is that represent exponential decay is:
[tex]y=700(1-0.35)^x[/tex]Explanation:The rate in the equation of an exponential decay is negative, this would make it reduce expentially, rather than grow.
The best equation that demonstrate this is:
[tex]y=700(1-0.35)^x[/tex]Where the rate is 0.35
Find the term named in the problem,and the explicit formula. -32,-132,-232,-332,… find a40
We need to find the n term formula:
The given sequence represents an arithmetic sequence and it follows the next form:
[tex]a_n=a+(n-1)d[/tex]Where a represents the first term, in this case, a= -31
n is the term of the sequence
And d is the constant:
Let's find the constant
a1 to a2 =
-32 to -132, then, -32 needs -100 units bo equal to -132.
Now, -132 need -100 units to be equal to -232.
-232 needs -100 units to be equal to -332
Therefore, the constant d is equal to -100, d=-100
Replacing these values:
[tex]a_n=-32+(n-1)(-100)[/tex]Then:
[tex]a_n=-32-(n-1)(100)[/tex]With this n formula, we can replace n=40, then, we will find a40:
[tex]a_{40}=-32-(40-1)100[/tex]Therefore:
[tex]a_{40}=-3932[/tex]Flying Home A bird flies from the bottom of a canyon that is 70 5 feet below sea level to a nest 7. that is 652 feet above sea level. What is the difference in elevation between the bottom of the 10 canyon and the bird's nest?
If we refer the level 0 to the sea level.
Then, 10 feet belox the sea level is -10 and 10 above is 10 feet (positive).
Then, the bottom of the canyon is at level y=-70 4/5 (referred to the sea level) and the nest is y=652 feet.
Then, the distance is D=y2-y1=652-(-70)=652+70=772 feet.
The distance between canyon bottom and nest is 772 feet.
et