To decompose 10 on basis of 8 it becomes 10 -2 =8
so 8 + 2 =10
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.
can you give me a step by step problem to this
Answer:
y = m x * b equation for a straight line
When x = 0 you have b = y = 4
y = m x + 4 revised equation
When y = 0, m = -4 / x = -4 / 2 = -2
y = -2 x + 4 or -2 x - y = -4
(a) is the correct answer
17 ohms to kilohms (Round answer to the nearest thousandth.)
In converting measurements, you must take note of the prefixes.
Note that a kilo is 1000 times the base measurement.
Example :
1 kilometer = 1000 meter
1 kilogram = 1000 gram
From the given problem :
1 kiloohm = 1000 ohm
17 ohms will be :
[tex]17\cancel{\text{ohms}}\times\frac{1\text{kiloohm}}{1000\cancel{\text{ohm}}}=\frac{17}{1000}=0.017\text{kiloohm}[/tex]The answer is 0.017 kiloohm
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]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
Find the vertical asymptotes of the graph of the rational function. y= x-15 / x + 6 The equation (s) of the vertical asymptotes is/are x= _____. (Use a comma to separate the answers as needed.)
Solution
The vertical asymptotes
[tex]\begin{gathered} y=\frac{x-15}{x+6}= \\ \end{gathered}[/tex]setting the denominator to 0
=> x + 6 = 0
=> x = - 6
The equation (s) of the vertical asymptotes is/are x = - 6
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 perimeter of a rectangular goat pen is 28 meters. The area is 45 square meters. Whatare the dimensions of the pen?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given information
[tex]\begin{gathered} Perimeter=2l+2b=28m \\ Area=lb=45m^2 \\ \\ where\text{ l is the length, b is the breadth} \end{gathered}[/tex]STEP 2: Label the two equations
[tex]\begin{gathered} 2l+2b=28------equation\text{ 1} \\ lb=45----equation\text{ 2} \end{gathered}[/tex]STEP 3: Solve for the missing values
Isolate l in equation 1
[tex]\begin{gathered} 2(l+b)=28 \\ l+b=\frac{28}{2}=14 \\ l=14-b-----equation\text{ 3} \end{gathered}[/tex]Substitute 14-b for l in equation 2
[tex]\begin{gathered} (14-b)\cdot b=45 \\ 14b-b^2=45 \\ We\text{ have the quadratic equation} \\ -b^2+14b-45=0 \end{gathered}[/tex]Solve the equation quadratically
[tex]\begin{gathered} -b^{2}+14b-45=0 \\ -b^2+9b+5b-45=0 \\ -b(b-9)+5(b-9)=0 \\ (-b+5)(b-9)=0 \\ -b+5=0,b=5 \\ b-9=0,b=9 \\ \\ b=5,b=9 \end{gathered}[/tex]Substitute the values into equation 3,
[tex]\begin{gathered} l=14-b \\ when\text{ b = 5} \\ l=14-5=9 \\ When\text{ b = 9} \\ l=14-9=5 \end{gathered}[/tex]Hence, the dimensions of the pen is given as:
[tex]9m\text{ }by\text{ }5m[/tex]The distance from Boston, Massachusetts to Little Rock, Arkansas is 1,452.8 miles. How many ft/min would you have to drive to get there in 20 hours and 45 minutes?
First we find the speed in mi/h.
We know that 20 h 45 min is equal to 20.75 hours, then the speed is
[tex]\frac{1452.8\text{ mi}}{20.75\text{ h}}=70.01\text{ mi/h}[/tex]Now we convert the speed to ft/min:
[tex]70.01\text{ mi/h}\cdot\frac{1\text{ h}}{60\text{ min}}\cdot\frac{5280\text{ ft}}{1\text{ mi}}=6161.27\text{ ft/min}[/tex]Therefore you would have to drive at a speed of 6161.27 ft/min
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.
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]Drag the tiles to the boxes to form correct pairs.
Match each addition operation to the correct sum.
Please look at the image below
Answer:
• -23.24 = 28.98 +(-52.22)
• 131.87 = 56.75 + 75.12
• 84 5/8 = 45 2/9 + 39 3/9
• 6 2/9 = -24 5/9 + 30 7/9
supposed that there are two types of tickets to a show: Advance and same-day. Advance tickets cost $25 and same-day tickets cost $40.For one performance, there were 60 tickets sold in all, and the total amount paid for them was $205. How many tickets of each type were sold?number of advanced tickets sold:number of same-day tickets sold:
For the show there are two types of tickets:
Advance tickets, that cost $25
Same-day tickets, that cost $40
We know that for one function there were 60 tickets sold for a total amount of $205.
Let "a" represent the number of advanced tickets sold and "s" represent the number of same-day tickets sold.
The total number of tickets sold for the function can be expressed as the sum of the number of advance tickets (a) sold and the number of same-day tickets sold (s)
[tex]60=a+s[/tex]If each advance ticket costs $25 and there were "a" advance tickets sold, the total earnings for advance tickets can be expressed as 25a
And if each same-day ticket costs $40 and there were "s" same-day tickets sold, the earnings for selling same-day tickets can be expressed as 40s
The total earnings for the performance can be expressed as the sum of the earnings for selling advance tickets and the earnings for selling same-day tickets:
[tex]205=25a+40s[/tex]Both equations established form an equation system and we can use them to determine the number of advance and same-day tickets sold:
-First, write the first equation for one of the variables, I will write it for "a"
[tex]\begin{gathered} 60=a+s \\ a=60-s \end{gathered}[/tex]-Second, replace the expression obtained for "a" into the second equation:
[tex]\begin{gathered} 205=25a+40s \\ 205=25(60-s)+40s \end{gathered}[/tex]From this expression, we can calculate the value of "s", first, you have to distribute the multiplication on the parentheses term, which means that you have to multiply both terms by 25:
[tex]\begin{gathered} 205=25\cdot60-25\cdot s+40s \\ 205=1500-25s+40s \end{gathered}[/tex]Next, simplify the like terms
[tex]205=1500+15s[/tex]Pass "1500" to the other side by applying the inverse operation to both sides of it, which means that you have to subtract 1500 to both sides of the equal sign:
[tex]\begin{gathered} 205-1500=1500-1500+15s \\ -1295=15s \end{gathered}[/tex]And finally divide both sides by 15 to reach the value of s
[tex]\begin{gathered} -\frac{1295}{15}=\frac{15s}{15} \\ -86.33=s \end{gathered}[/tex]With the value of s calculated, you can replace it into the expression obtained for a and calculate its value:
[tex]\begin{gathered} a=60-s \\ a=60-(-86.33) \\ a=146.33 \end{gathered}[/tex]So with the information given, the number of advanced and same-day tickets sold are:
a=146.33
s=-86.33
After graduating from college, Carlos receives two different job offers. Both pay a starting salary of $65000 per year, but one job promises a $3250 raise per year, while the other guarantees a 4% raise each year. Complete the tables below to determine what his salary will be after t years. Round your answers to the nearest dollar.
Given:
• Starting salary of each Job = $65000
,• Job 1 promises a $3250 raise per year
,• Job 2 promises a 4% raise each year.
Let's complete the given tables.
The equation to represent job 1 will be a linear equation:
y = 3250t + 65000
The equation which represents job 2 will be an exponential equation:
[tex]\begin{gathered} y=65000\mleft(1+0.04\mright)^t \\ \\ y=65000(1.04)^t \end{gathered}[/tex]Now, to complete the tables, input the different values of t into the equation and solve for y.
• For Job 1, we have the following:
• When t = 1:
y = 3250(1) + 65000 = 68250
• When t = 5:
y = 3250(5) + 65000
y = 16250 + 65000
y = 81250
• When t = 10:
y = 3250(10) + 65000
y = 32500 + 65000
y = 97500
• When t = 15:
y = 3250(15) + 65000
y =48750 + 65000
y = 113750
• When t = 20:
y = 3250(20) + 65000
y = 65000 + 65000
y = 130000
• For Job 2, we have the folllowing:
• When t = 1:
y = 65000(1.04)¹
y = 67600
• When t = 5
y = 65000(1.04)⁵
y = 65000(1.216652902)
y = 79082
• When t = 10:
y = 65000(1.04)¹⁰
y = 65000(1.480244285)
y = 96216
• When t = 15:
y = 65000(1.04)¹⁵
y = 65000(1.800943506)
y = 117061
• When t = 20
y = 65000(1.04)²⁰
y = 65000(2.191123143)
y = 142423
Therefore, we have the complete table below:
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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Please help on my question I have the graph part done, I need help on the other parts
the Here the equation of amount of salt in the barrel at time t is given by
[tex]Q(t)=21(1-e^{-0.06t})[/tex]a
At time t=7 minute the amount of salt will be
[tex]Q(7)=21(1-e^{-0.06\times7})\Rightarrow Q(7)=21\times0.342953\Rightarrow Q(7)=7.20[/tex]The amount of salt after 7 min will be 7.20lb.
b
At time t=14minute the amount of salt will be
[tex]Q(14)=21(1-e^{-0.06\times14})\Rightarrow Q(14)=11.93[/tex]Amount of salt will be 11.93 lb
d
From the graph, for large t the value Q(t) the amount of salt approaches to 21 lb.
Write an equation in slope-intercept form with aslope of 10 that passes through (0,6)A.x + y = 6B. y + 10x + 6C. 7x + y = 10D. y = 10x + 6
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.
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
4 gallons of water weigh 33.4 pounds how much do 7.5 gallons of water weigh
4 gallons of water weigh 33.4 pounds how much do 7.5 gallons of water weigh
Applying proportion
33.4/4=x/7.5
solve for x
x=(33.4/4)*7.5
x=62.625 poundsWhat is the amplitude and period of F(t) = sin 2t?a. amplitude: 1; period, pib. amplitude: -1; period: pic. amplitude: 1; period: 2pid. amplitude: -1; period: 2piPlease select the best answer from the choices provided
Answer:
[tex]\text{amplitude: 1, period: }\pi[/tex]Explanation:
Given the function in the attached image;
[tex]f(t)=\sin 2t[/tex]Comparing to the general form of periodic equations.
[tex]f(t)=A\sin B(t+C)+D[/tex][tex]\begin{gathered} A=\text{ Amplitude} \\ A=1 \end{gathered}[/tex][tex]\begin{gathered} \text{Period =}\frac{2\pi}{B} \\ \text{ from the equation B = 2;} \\ \text{ Period = }\frac{2\pi}{2}=\pi \end{gathered}[/tex]Therefore;
[tex]\text{amplitude: 1, period: }\pi[/tex]Rewrite the set G by listing its elements. Make sure to use the appropriate set notation.G = ( z l z is an integer and -3 < z <_ 0)
Given the set G = ( z l z is an integer and -3 < z <_ 0) , we are to write out all the elements in the set.
First you must take note of the inequality signs.
First aspect of the inequality-3 < z means that z is a value greater than -3 exclusive -3. The values are -2, and -1
The second part of the inequality z <_ 0 means that z is less than or equal to 0, this means that 0 is inclusive because of the equal to sign.
Hence the set of element G will be -2, -1 and 0. In set notataion, it is represented as:
G = {-2, -1, 0}
Note that -3 is not part of the element G
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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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.
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]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
Find the value of x that will make L||M.2x - 3MX + 4x = [?]
We can say that Line L and Line M are parallel to each other if, when cut by a transversal line, the corresponding angles, the alternate exterior angles, and the alternate interior angles are congruent.
In the figure shown, we have a pair of alternate exterior angles. Therefore, the two angles must be equal to each other. With that, we have the following equation:
[tex]2x-3=x+4[/tex]From that equation, we can solve x by joining like terms on either side of the equation.
[tex]\begin{gathered} 2x-x=4+3 \\ x=7 \end{gathered}[/tex]Therefore, x = 7. When asked, the measure of the two angles are 11 degrees.
I need help with number part a and bThank you very much
PART A
For our beautiful sun, we'll have that:
[tex]b=1.4\cdot10^3[/tex]This way,
[tex]\begin{gathered} M=-2.5\log (\frac{1.4\cdot10^3}{2.84\cdot10^{-8}}) \\ \\ \Rightarrow M=-9.74 \end{gathered}[/tex]PART B
We'll have the equation:
[tex]-0.27=-2.5\log (\frac{b}{2.84\cdot10^{-8}})[/tex]Solving for b,
[tex]\begin{gathered} -0.27=-2.5\log (\frac{b}{2.84\cdot10^{-8}})\rightarrow0.27=2.5\log (\frac{b}{2.84\cdot10^{-8}}) \\ \\ \rightarrow\frac{0.27}{2.5}=\log (\frac{b}{2.84\cdot10^{-8}})\rightarrow0.108=\log (\frac{b}{2.84\cdot10^{-8}}) \end{gathered}[/tex]Now we'll use the following property:
[tex]c=\log _a(b)\Leftrightarrow b=a^c[/tex]This way,
[tex]\begin{gathered} 0.108=\log (\frac{b}{2.84\cdot10^{-8}})\rightarrow e^{0.108}=\frac{b}{2.84\cdot10^{-8}} \\ \\ \Rightarrow b=2.84\cdot10^{-8}e^{0.108} \\ \\ \Rightarrow b=3.16\cdot10^{-8} \end{gathered}[/tex]