Answer:
No, the triangle is not possible.
Step-by-step explanation:
Given,
A triangle ABC in which C = 38°, a = 19, c = 10,
Where, angles are A, B and C and the sides opposite to these angles are a, b and c respectively,
By the law Sines,
[tex]\frac{sin A}{a}=\frac{sin C}{c}[/tex]
[tex]\implies sin A = \frac{a sin C}{c}[/tex]
By substituting the values,
[tex]sin A = \frac{19\times sin 38^{\circ}}{10}[/tex]
[tex]=1.16975680312[/tex]
[tex]\implies A=sin^{-1}(1.16975680312)[/tex] = undefined
Hence, the triangle is not possible with the given measurement.
A family on a trip budgets $1,000 for meals and gasoline. If the price of a meal for the family is $50 and if gasoline costs $3.50 per gallon, then how many meals can the family buy if they buy 100 gallons of gasoline?
Answer:
They can buy 13meals if they buy 100 gallons of gasoline.
Step-by-step explanation:
3.50 PER gallon so 1 gallon is $3.50
if they buy 100 gallons you have to multiply 3.50 by 100 which gives you 350. you subtract 350 from 1000 so 1000-350 and get 650. now, you divide 650 by 50 because each meal is $50. And you get 13 so there you have it.
Final answer:
The family can buy 13 meals.
Explanation:
To find the number of meals the family can buy, we need to calculate the total cost of gasoline and subtract it from the total budget.
The family buys 100 gallons of gasoline at a cost of $3.50 per gallon, so the total cost of gasoline is 100 * $3.50 = $350.
The remaining budget for meals is $1,000 - $350 = $650.
The cost of each meal is $50, so the family can buy $650 / $50 = 13 meals.
Solve the problem.
The library is to be given 3 books as a gift. The books will be selected from a list of 16 titles. If each book selected must have a different title, how many possible selections are there?
48
560
3360
4096
Answer:
560Step-by-step explanation:
You must use a combination:
[tex]_nC_k=\dfrac{n!}{k!(n-k)!}[/tex]
We have n = 16, k = 3.
Substitute:
[tex]_{16}C_3=\dfrac{16!}{3!(16-3)!}=\dfrac{13!\cdot14\cdot15\cdot16}{2\cdot3\cdot13!}\qquad\text{cancel}\ 13!\\\\=\dfrac{14\cdot15\cdot16}{2\cdot3}=\dfrac{7\cdot5\cdot16}{1}=560[/tex]
The number of possible selections is 560.
Given information:The library is to be given 3 books as a gift. The books will be selected from a list of 16 titles.
Calculation of number of selections;Here we used the combination
[tex]= nC_n\\\\= 16C_3\\\\= \frac{16!}{3!(16-3)!}\\\\ = \frac{16!}{3!13!}\\\\ = \frac{16\times 15\times 14\times 13!}{13!3!}\\\\ = \frac{16\times 15\times 14}{3\times 2\times 1}\\[/tex]
= 560
learn more about the book here: https://brainly.com/question/19461476
A freight train is carrying goods across the country. The distance it has traveled varies directly with the number of gallons of fuel it has used. See the graph below.
Answer:
Step-by-step explanation:
The train uses
[tex]\frac{400gallons}{200miles}[/tex]
If you reduce that you get that the train uses
[tex]\frac{2gallons}{1mile}[/tex]
To find the slope of the line, we will use the 2 points on the coordinate plane where the graph goes through: (0, 0) and (400, 200)
Applying the slope formula:
[tex]m=\frac{200-0}{400-0}=\frac{1}{2}[/tex]
Answer:
6 miles per gallon
slope = 6
Step-by-step explanation:
Lola needs to sign 96 invitations. Using a stopwatch that measures time to tenths of a second, it takes Lola 5.3 seconds to sign her full name. Going by the accuracy of the stopwatch, which is the most accurate determination for the number of minutes Lola needs to sign all 96 invitations?3.3 minutes3.3125 minutes8.48 minutes8.5 minutes
Find the solution of the equation on graphically 7r-15= r+27
Answer:
r = 7
Step-by-step explanation:
let r = x
equation becomes
7x-15= x+27
Let the Left side AND Right side both equal y
y = 7x - 5
y = x + 27
graph these 2 equations. You should get 2 straight lines that intersect at x = 7, y = 34. (see attached)
recall at the start we let r = x, if we replace x with r again, we get r = 7
Cate solved an inequality to find c, the possible number of cats that a shelter can house. She found that c < 28. Which statement best describes a possible solution to Cate's problem?
Since the number of cats has to be less than 28, a statement could be "the shelter can house no more than 28 cats.
Answer:
Possible values of c are
[tex]c=0,1,2,3,4,...,26,27[/tex]
For example: The shelter can house 17 cats because 17 < 28.
Step-by-step explanation:
Let c be the number of cats.
The given inequality is
[tex]c<28[/tex]
We need to find the possible number of cats that a shelter can house.
The number number of cats can not be
1. A fraction value
2. A Decimal value
3. A negative value
Since c<28, therefore the number of cats must be greater that or equal to 0 and less that 28.
[tex]0\leq c<28[/tex]
The possible values of c are
[tex]c=0,1,2,3,4,...,26,27[/tex]
For example: The shelter can house 17 cats because 17 < 28.
The claim is that the proportion of peas with yellow pods is equal to 0.25 (or 25%). The sample statistics from one experiment include 520 peas with 140 of them having yellow pods. Find the value of the test statistic.
Answer:
Test statistic = z = 1.01264
Step-by-step explanation:
p = 0.25
q = 1 - p = 0.75
n = 520
x = 140
[tex]psample = \frac{x}{n} = \frac{140}{520} = 0.26923[/tex]
[tex]z = \frac{psample - p}{\sqrt{\frac{p*q}{n} } } =\frac{0.26923 - 0.25}{\sqrt{\frac{0.25 * 0.75 }{520} } } = \frac{0.01923}{\sqrt{\frac{0.1875}{520} } } = \frac{0.01923}{\ 0.01899} = 1.01264[/tex]
For safety reasons, four different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the four systems detects theft with a probability of .99 independently of the others. The bank, obviously, is interested in the probability that when a theft occurs, at least one of the four systems will detect it. This probability is equal to:
Answer:
Given is :
4 different alarm systems were installed in the vault.
Each of the four systems detects theft with a probability of .99 independently of the others.
For solving this question, we have to first find the probability that none works.
It will be given as:
As there is 0.01 probability that all four systems will fail to detect theft. As all are independent, we get probability as: [tex](0.01)^{4}[/tex]
Now, we have to find the probability that at least one system detects the theft, it is given by: [tex]1 -(0.01)^{4}[/tex]
In the figure below, segments AC and AB are tangent to circle E. If AC is equal to 10 cm, then segment AB is equal to 20 cm.
If tangents are drawn from the same spot, then they will be equal.
Since tangents AB and AC both start from point A, and go to the same circle, then:
AC = AB.
That means the statement:
'If AC is equal to 10cm, then segment AB is equal to 20cm'
is false
(if a AC = 10cm, then AB would = 20cm as well)
_____________________________________
Answer:
False
Answer:
The given statement is false.
Step-by-step explanation:
We have been given a statement. We are supposed to determine whether our given statement is true or not.
Segments AC and AB are tangent to circle E. If AC is equal to 10 cm, then segment AB is equal to 20 cm.
We know that tangents of circle from same external point are congruent.
We can see that both tangents AB and AC are drawn from same point A, so AB will be equal to AC.
Since [tex]AB=20[/tex] and [tex]AC=10[/tex], therefore, our given statement is false.
Christine has monthly loan payments of $1,857. Her loan is for $300,000 @ 6.3% interest. How much of her first payment goes towards interest?
Answer:
The interest paid is $1575.
Step-by-step explanation:
Given is:
Monthly loan payment = $1857
Loan amount = $300000
Rate = 6.3% annual
So, monthly rate will be = [tex]6.3/12/100=0.00525[/tex]
Hence, we will calculate the interest for month.
[tex]0.00525\times300000=1575[/tex] dollars
So, interest paid = $1575.
Principle paid = [tex]1857-1575=282[/tex] dollars
Please help as quickly as possible (20pts)
Find the solutions to the following linear-quadratic systems algebraically. Select the ordered pair that is one of the correct solutions from among the choices below
Y=x^2+3x+8
Y=2x+10
a)(2,14)
b)(0,10)
c)(-2,6)
d)(0,8)
Answer:
c) (-2, 6)
Step-by-step explanation:
Subtracting the second equation from the first gives ...
(y) -(y) = (x^2 +3x +8) -(2x +10)
0 = x^2 +x -2 . . . . . simplify
0 = (x -1)(x +2) . . . . factor
Solutions for x are 1 and -2. The corresponding y-values are ...
y = 2{1, -2} +10 = {2, -4} +10 = {12, 6}
The solutions are (1, 12) and (-2, 6). The only matching choice is (-2, 6).
What is the chromatic number for the map?
Answer:
The smallest number of colors needed to color the vertices of so that no two adjacent vertices share the same color.
the smallest value of possible to obtain a k-coloring.
Final answer:
The chromatic number for a map is the minimum number of colors needed to color the regions of the map such that no two adjacent regions have the same color.
Explanation:
The chromatic number for a map is the minimum number of colors needed to color the regions of the map such that no two adjacent regions have the same color.
The chromatic number can vary depending on the specific map and its regions. To determine the chromatic number, one approach is to use a graph-theoretic representation of the map, where each region corresponds to a vertex and adjacent regions are connected by edges. Then, a graph coloring algorithm can be used to find the minimum number of colors needed to properly color the regions of the map.
Using the value found in the previous question, find the measure of angle R and the measure of angle Q.
Answer:
∠R = 36.06°, ∠Q = 90.81°
Step-by-step explanation:
I used the Law of Cosines to find angle R first. If you use the Law of Sines, the main angle is the same, but it differs in the decimal value. Since you started the process with the Law of Cosines, I used it again. Setting up to find angle R:
[tex]36^2=48^2+60^2-2(48)(60)cosR[/tex] and
1296 = 2304 + 3600 - 5760cosR so
-4608 = -5700cosR and
.8084210526 = cosR
Taking the inverse cosine to find the angle,
R = 36.06
That means that Q = 180 - 36.06 - 53.13 so
Q = 90.81
In order to estimate the mean amount of time computer users spend on the internet each month, how many computer users must be surveyed in order to be 90% confident that your sample mean is within 13 minutes of the population mean? Assume that the standard deviation of the population of monthly time spent on the internet is 228 min
Answer:
832
Step-by-step explanation:
standard deviation =228 minute
error =13 minute given
confidence level =905% =0.90
α=1-0.90=0.1
[tex]z_\frac{\alpha }{2}=z_\frac{0.1}{2}=1.645[/tex]
we know that sample size should be greater than
[tex]n\geq \left ( z_\frac{\alpha }{2}\times \frac{\sigma }{E} \right )^2[/tex]
[tex]n\geq \left ( 1.645\times \frac{228}{13} \right )^{2}[/tex]
[tex]n\geq 28.850^2[/tex]
[tex]n\geq 832.3668[/tex]
n=832
please help!
Which rigid transformation(s) can map FGH onto VWX?
reflection, then rotation
reflection, then translation
rotation, then translation
rotation, then dilation
Answer:
reflection, then translationrotation, then translationStep-by-step explanation:
When the points designating each triangle are considered in order, they are seen to be in clockwise order. Segment FG is oriented to the west, while corresponding segment VW is oriented to the east. This means the figure could have been rotated 180° or reflected across a point. Either way, some translation may be necessary to align the figures as shown.
Possible transformations include ...
reflection across a point, then translation (depending on the location of the point)rotation 180° about a point, then translation (depending on the location of the point)___
If one of the triangles is reflected across the midpoint of GW, it will coincide with the other triangle. Hence only one reflection across a chosen point is required. Of course, reflection across a point is identical to rotation 180° about that point. For any other point of reflection or rotation, translation will be involved.
Answer:
rotation, then translation
Step-by-step explanation:
rotation, then translation
What are some terms that you use in your everyday life that are really hard to define, yet they're incredibly important and frequently used? How could you explain why undefined terms become so important when we start to write proofs in geometry?
Answer:
Step-by-step explanation:
Tough question.
Spiritual.
Love (if ever there was a misused word, it is love). I used to ask my classes what this sentence means "I love hunting." Try that one on. I don't know if you are dating someone, but how can you say "I love you." and "I love hunting." and not have something terribly wrong with the definition of the verb. One implies treasuring someone. The other means outfoxing a fox and murder.
Religion. Why are there so many different ones? The claim that there is only one true one makes the definition elusive to say the least. And it has caused a great deal of trouble.
==============================
Geometry: You have to know what a line segment is before you can say that one segment bears a relationship to another one.
You have to be able to define a point before you can calculate an intersection point of 2 lines or 2 curves or more.
You have to be able to define almost any term in geometry so that you can restrict enough to make it useful.
Select the correct answer.
Solve
Answer:
-44 4/9
Step-by-step explanation:
-36 4/9-(-10 2/9)-(18 2/9)
-36 4/9+10 2/9 = 26 6/9
26 6/9 - (18 2/9)= -44 4/9
The correct answer to the given fraction after simplification is equal to [tex]-44\frac{4}{9}[/tex] .
What is simplification?" Simplification is defined as the reduce the given expression, fraction or problem into the easiest form."
Convert mixed fraction to proper fraction
[tex]p\frac{q}{r} = \frac{(r\times p)+q}{r}[/tex]
According to the question,
Given fraction,
[tex]-36\frac{4}{9}- (-10\frac{2}{9})-(18\frac{2}{9})[/tex]
Simplify the given fraction using conversion mixed fraction to proper fraction we get,
[tex]\frac{-328}{9}+ \frac{92}{9}- \frac{164}{9}\\\\= \frac{-328+92-164}{9}\\ \\= \frac{-400}{9}\\ \\= -44\frac{4}{9}[/tex]
Hence, Option(A) is the correct answer.
Learn more about simplification here
https://brainly.com/question/17482308
#SPJ2
What refers to the quantity of goods and services that consumers are willing to buy at a given price?
Answer:
"demand"
Step-by-step explanation:
Vocabulary question.
"Demand" refers to the quantity of goods and services that consumers are willing to buy at a given price.
HELPP PPLEASEEE!!!
A ship moves through the water at 30 miles/hour at an angle of 30° south of east. The water is moving 5 miles/hour at an angle of 20° east of north. Identify the ship's vector, the water current's vector, and the vector representing the ship's actual motion.
Answer:
See below in bold.
Step-by-step explanation:
Ship's vector:
Horizontal component = 30 cos 30 = 25.98.
Vertical component = 30 sin(-30) = -15.
So it is <25.98, -15).
The current's vector:
Horizontal component = 5 sin 20 = 1.71.
Vertical component = 5 cos 20 = 4.7.
So it is <1.71, 4.7>.
The ship's vector representing its actual motion is 30.73 mph east of north.
Explanation:To solve this problem, we can break down the velocities of the ship and the water current into their horizontal and vertical components. The ship's vector can be represented as:
Ship's Vector: 30 mph at an angle of 30° south of east
Breaking this down into horizontal and vertical components:
Horizontal Component = 30 mph * cos(30°) = 25.98 mph east
Vertical Component = 30 mph * sin(30°) = 15 mph south
The water current's vector can be represented as:
Water Current's Vector: 5 mph at an angle of 20° east of north
Breaking this down into horizontal and vertical components:
Horizontal Component = 5 mph * cos(20°) = 4.75 mph north
Vertical Component = 5 mph * sin(20°) = 1.71 mph east
To find the ship's actual motion, we can add the horizontal and vertical components together:
Horizontal Component = 25.98 mph east + 4.75 mph north = 30.73 mph east of north
Vertical Component = 15 mph south + 1.71 mph east = 16.71 mph south of east
Therefore, the ship's vector representing its actual motion is 30.73 mph east of north.
Write an equation that could be used to find the value of a.
Answer:
see below
Step-by-step explanation:
The Law of Cosines tells you ...
a² = b² + c² -2bc·cos(A)
Substituting the given values gives you ...
a² = 4² +7² -2(4)(7)cos(52°)
Find the distance between the points (1, 5) and (1, -4).
Answer:
9
Step-by-step explanation:
[tex]\tt distance=\sqrt{(1-1)^2+(-4-5)^2}=\sqrt{0^2+9^{2}}=\sqrt{9^2} =9[/tex]
The formula for distance between two points is:
[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2}}[/tex]
In this case:
[tex]x_{2} =1\\x_{1} =1\\y_{2} =-4\\y_{1} =5[/tex]
^^^Plug these numbers into the formula for distance like so...
[tex]\sqrt{(1-1)^{2} + (-4-5)^{2}}[/tex]
To solve this you must use the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)
First we have parentheses. Remember that when solving you must go from left to right
[tex]\sqrt{(1-1)^{2} + (-4-5)^{2}}[/tex]
1 - 1 = 0
[tex]\sqrt{(0)^{2} + (-4-5)^{2}}[/tex]
-4 - 5 = -9
[tex]\sqrt{(0)^{2} + (-9)^{2}}[/tex]
Next solve the exponent. Again, you must do this from left to right
[tex]\sqrt{(0)^{2} + (-9)^{2}}[/tex]
0² = 0
[tex]\sqrt{0 + (-9)^{2}}[/tex]
(-9)² = 81
[tex]\sqrt{(0 + 81)}[/tex]
Now for the addition
[tex]\sqrt{(0 + 81)}[/tex]
81 + 0 = 81
√81
^^^This can be further simplified to...
9
***Remember that the above answers are in terms of units
Hope this helped!
~Just a girl in love with Shawn Mendes
PLS HELP ME !
The angle of depression of a point P on the ground, from the top T of the building is 23.6 degrees . If the distance from P to the foot of the building is 50m, calculate the height of the building, correct to the nearest meter.
Final answer:
To find the height of the building, we use the tangent function with the angle of depression and the horizontal distance from the point to the building's base, resulting in a building height of 22 meters when rounded to the nearest meter.
Explanation:
To calculate the height of the building when the angle of depression from the top of the building to a point P on the ground is 23.6 degrees and the distance from P to the foot of the building is 50 meters, we can use trigonometry.
Specifically, we use the tangent function which relates the angle of a right triangle to the ratio of the opposite side (height of the building in this case) over the adjacent side (distance from P to the foot of the building).
Let's denote the height of the building as H. Thus, we have:
tan(23.6°) = H / 50
From this, we can solve for H:
H = 50 × tan(23.6°)
Using a calculator, tan(23.6°) approximately equals 0.4364.Therefore, H = 50 × 0.4364 which equals 21.82 meters.Rounding to the nearest meter, the height of the building is 22 meters.
Drag the tiles to the correct boxes to complete the pairs.
Match the subtraction expressions to their correct answers.
Answer:
Part 1) [tex]-17\frac{8}{9}[/tex] -----> [tex]-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}[/tex]
Part 2) [tex]-15.11[/tex] ------> [tex]-12.48-(-2.99)-5.62[/tex]
Part 3) [tex]-19\frac{8}{9}[/tex] -----> [tex]-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})[/tex]
Part 4) [tex]-201.65[/tex] -----> [tex]-353.92-(-283.56)-131.29[/tex]
Part 5) [tex]74[/tex] ------> [tex]83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})[/tex]
Step-by-step explanation:
Part 1) we have
[tex]-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}[/tex]
To calculate the subtraction convert the mixed numbers to an improper fractions
[tex]6\frac{4}{9}=\frac{6*9+4}{9}=\frac{58}{9}[/tex]
[tex]3\frac{2}{9}=\frac{3*9+2}{9}=\frac{29}{9}[/tex]
[tex]8\frac{2}{9}=\frac{8*9+2}{9}=\frac{74}{9}[/tex]
substitute
[tex]-\frac{58}{9}-\frac{29}{9}-\frac{74}{9}=-\frac{(58+29+74)}{9}=-\frac{161}{9}[/tex]
Convert to mixed number
[tex]-\frac{161}{9}=-(\frac{153}{9}+\frac{8}{9})=-17\frac{8}{9}[/tex]
Part 2) we have
[tex]-12.48-(-2.99)-5.62[/tex]
To calculate the subtraction eliminate the parenthesis first
[tex]-12.48-(-2.99)-5.62=-12.48+2.99-5.62=-15.11[/tex]
Part 3) we have
[tex]-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})[/tex]
To calculate the subtraction convert the mixed numbers to an improper fractions
[tex]19\frac{2}{9}=\frac{19*9+2}{9}=\frac{173}{9}[/tex]
[tex]4\frac{1}{9}=\frac{4*9+1}{9}=\frac{37}{9}[/tex]
[tex]3\frac{4}{9}=\frac{3*9+4}{9}=\frac{31}{9}[/tex]
substitute
[tex]-\frac{173}{9}-\frac{37}{9}-(-\frac{31}{9})[/tex]
Eliminate the parenthesis
[tex]-\frac{173}{9}-\frac{37}{9}+\frac{31}{9}=\frac{(-173-37+31)}{9}=-\frac{179}{9}[/tex]
Convert to mixed number
[tex]-\frac{179}{9}=-(\frac{171}{9}+\frac{8}{9})=-19\frac{8}{9}[/tex]
Part 4) we have
[tex]-353.92-(-283.56)-131.29[/tex]
To calculate the subtraction eliminate the parenthesis first
[tex]-353.92+283.56-131.29=-201.65[/tex]
Part 5) we have
[tex]83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})[/tex]
To calculate the subtraction convert the mixed numbers to an improper fractions
[tex]83\frac{1}{5}=\frac{83*5+1}{5}=\frac{416}{5}[/tex]
[tex]108\frac{2}{5}=\frac{108*5+2}{5}=\frac{542}{5}[/tex]
[tex]99\frac{1}{5}=\frac{99*5+1}{5}=\frac{496}{5}[/tex]
substitute
[tex]\frac{416}{5}-\frac{542}{5}-(-\frac{496}{5})[/tex]
Eliminate the parenthesis
[tex]\frac{416}{5}-\frac{542}{5}+\frac{496}{5}=\frac{(416-542+496)}{5}=\frac{370}{5}=74[/tex]
What is 70% of 40,000.
Answer:
x = 28,000
Step-by-step explanation:
"What" is our unknown, x; "is" is an equals sign; 70% expressed as a decimal is .70; "of" means to muliply.
Our equation, then, is
x = .70(40,000) so
x = 28,000
Answer:
28000
Step-by-step explanation:
70% of 40,000 is 28000.
28,000/40,000 = 70%
40000=100%
x=70%
40000/x=100%/70%
Leo has b boxes of pencils. Each box contains 6 pencils. He has a total of 42 pencils. The equation that represents this situation is . The value of b that makes the equation true is .
The equation for this scenario is 6b= 42.
B= 42/6= 7
The value of b that makes the equation true is 7.
Hope this helps!
Answer:
6b = 42
b = 7 for the equation to be true.
Step-by-step explanation:
If Leo has b boxes of pencils with each containing 6 pencils, it means that the total number of pencils Leo has is dependent on the number of boxes given that the number in each box is known.
The product of the number of boxes with the number in each box gives the total number of pencils Leo has. This may be expressed mathematically as
= b × 6
= 6b
Given that Leo has 42 pencils, it means that
6b = 42
Dividing both sides by 6,
b = 42/6 = 7
It means he has 7 boxes.
HELPPPPPPP!!!!! Can someone help with this problem?? WILL MARK BRAINLIEST
Find an equation for the line below.
Answer:
[tex]y=\frac{-4}{3}x+\frac{-4}{3}[/tex] slope-intercept form
[tex]y+4=\frac{-4}{3}(x-2)[/tex] point-slope form
Step-by-step explanation:
Equation of a line in point-slope form is y-y_1=m(x-x_1) where m is the slope and b is the [tex](x_1,y_1)[/tex] is a point on the line.
So the m, slope, can be found by calculating the rise/run from one to another point on the line.
So let's start at (2,-4) and count to (-4,4).
So the rise is 8 and the run is -6.
The slope is therefore 8/-6=-8/6=-4/3.
Now if you didn't want to count because you can't count all the time.
You could line up the two points and subtract vertically, then put 2nd difference over 1st difference.
Like this:
( 2 , -4)
(-4 , 4)
---------------
6 -8
So the slope is -8/6=-4/3.
Anyways now using any point on the line as [tex](x_1,y_1)[/tex] along with the slope we found we can finally put into our equation for point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
with [tex](x_1,y_1)=(2,-4)[/tex] and [tex]m=\frac{-4}{3}[/tex].
This gives us:
[tex]y-(-4)=\frac{-4}{3}(x-2)[/tex]
[tex]y+4=\frac{-4}{3}(x-2)[/tex]
We probably want to put into y=mx+b form; not 100% sure so I will give you choices:
y=mx+b is called slope-intercept form because it tells us the slope is m and the y-intercept is b.
[tex]y+4=\frac{-4}{3}(x-2)[/tex]
Distribute the -4/3 to the terms inside the ( ):
[tex]y+4=\frac{-4}{3}x+\frac{8}{3}[/tex]
Subtract 4 on both sides:
[tex]y=\frac{-4}{3}x+\frac{8}{3}-4[/tex]
Simplify the (8/3)-4:
[tex]y=\frac{-4}{3}x+\frac{-4}{3}[/tex]
last one anyone that can help me out?
Answer:
Part a. t = 7.29 years.
Part b. t = 27.73 years.
Part c. p = $3894.00
Step-by-step explanation:
The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.
Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!
Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!
Part c. It is given that A = $5000, r = 2.5%, and t = 10 years. In this part, p is unknown. Therefore 5000 = p*e^(0.025*10). This implies 5000 = p*e^(0.25). Making p the subject gives p = 5000/e^0.25. This means that p = $3894.00(rounded to the nearest 2 decimal places)!!!
This is a Fractions as division word problems. NEED HELP!!
Answer:
The answer is between 2 to 3 scoops.
Answer:
The only logical answer would be between 2 and 3 scoops
Please help me with this question!
Answer:
h=2×6/8
x^2=h^2+4
x=5/2
Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and cot θ= -6/7 . Find the exact values of the five remaining trigonometric functions of θ. Show your work
Answer:
[tex]tan(\theta)=-\frac{7}{6}[/tex]
[tex]sec(\theta)=\frac{\sqrt{85} }{6}[/tex]
[tex]cos(\theta)=\frac{6\sqrt{85} }{85}[/tex]
[tex]sin(\theta)=-\frac{7\sqrt{85}}{85}[/tex]
[tex]cosec(\theta)=-\frac{\sqrt{85}}{7}[/tex]
Step-by-step explanation:
[tex]cot (\theta) = -\frac{6}{7}[/tex]
a) Since,
[tex]tan(\theta) = \frac{1}{cot(\theta)}[/tex]
[tex]tan(\theta) = \frac{1}{-\frac{6}{7} }=-\frac{7}{6}[/tex]
b) Also, according to the Pythagorean identity:
[tex]sec^{2}(\theta)=1+tan^{2}(\theta)[/tex]
Using the value of tan([tex]\theta[/tex]), we get:
[tex]sec^{2}(\theta)=1+(-\frac{7}{6} )^{2}\\\\ sec^{2}(\theta)=\frac{85}{36}\\\\ sec(\theta)=\pm \sqrt{\frac{85}{36} } \\\\ sec(\theta)=\pm \frac{\sqrt{85} }{6}[/tex]
Since, secant is positive in 4th quadrant, we will only consider the positive value. i.e.
[tex]sec(\theta)=\frac{\sqrt{85} }{6}[/tex]
c) Since,
[tex]cos(\theta)=\frac{1}{sec(\theta)}[/tex]
Using the value of secant, we get:
[tex]cos(\theta)=\frac{1}{\frac{\sqrt{85} }{6} } =\frac{6\sqrt{85} }{85}[/tex]
d) According to Pythagorean identity:
[tex]sin^{2}(\theta)=1-cos^{2}(\theta)\\sin(\theta)=\pm \sqrt{1-cos^{2}(\theta)}[/tex]
Since, sine is negative in fourth quadrant, we will consider the negative value. Using the value of cosine, we get:
[tex]sin(\theta)=-\sqrt{1-(\frac{6\sqrt{85} }{85})^{2}}=-\frac{7\sqrt{85}}{85}[/tex]
e) Since,
[tex]cosec(\theta)=\frac{1}{sin(\theta)}[/tex]
Using the value of sine, we get:
[tex]cosec(\theta)=\frac{1}{-\frac{7\sqrt{85} }{85}}=-\frac{\sqrt{85}}{7}[/tex]