Answer:
n E R
Step-by-step explanation:
Since 7n-8 is a linear equation with no restrictions, n's domain is real numbers.
Answer:
Step-by-step explanation:
with 1st term = -1. and common difference is 7
in this series we can say that 1st term is -1 , 2nd term is 6 , 3rd term is 13 , and so on
therefore in a series we cannot define a 0th term , so here n will be greater than or equal to 1.
what is the sum of the sequence 152,138,124, ... if there are 24 terms?
Answer: -216
Step-by-step explanation:
To solve the exercise you must use the formula shown below:
[tex]Sn=\frac{(a_1+a_n)n}{2}[/tex]
Where:
[tex]a_1=152\\a_n=a_{24}[/tex]
You should find [tex]a_{24}[/tex]
The formula to find it is:
[tex]a_n=a_1+(n-1)d[/tex]
Where d is the difference between two consecutive terms.
[tex]d=138-152=-14[/tex]
Then:
[tex]a_{24}=152+(24-1)(14)=-170[/tex]
Substitute it into the first formula. Therefore, you obtain:
[tex]S_{24}=\frac{(152-170)(24)}{2}=-216[/tex]
Answer:
Sn = -216
Step-by-step explanation:
We are given the following sequence and we are to find the sum of the given sequence if there are 24 terms in it:
[tex] 152, 138, 124, ... [/tex]
We know that the formula of sum for an arithmetic sequence is given by:
[tex]S_n =\frac{n(a_1+a_n)}{2}[/tex]
where [tex]a_1[/tex] is the first term (124)and [tex]a_n[/tex] is the last term [tex]a_{24}[/tex].
To find [tex]a_1[/tex], we will use the following formual:
[tex]a_n=a_1+(n-1)d[/tex]
[tex]a_24=152+(24-1)(-14)[/tex]
[tex]a_{24}=170[/tex]
Substituting the given values in the above formula to get the sum:
[tex]S_n =\frac{24(152-170)}{2}[/tex]
[tex]S_n=-216[/tex]
A radioactive substance has a decay rate of 0.073 per minute. How many grams of a 120 gram sample will remain radioactive after 30 minutes? Round the answer to the nearest tenth of a gram, and do not include the unit in your answer.
Answer:
13.4 grams of a 120 gram sample will remain radioactive after 30 minutes.
Step-by-step explanation:
Given : A radioactive substance has a decay rate of 0.073 per minute.
To find : How many grams of a 120 gram sample will remain radioactive after 30 minutes?
Solution :
Using decaying formula,
[tex]y(t)=y_o e^{-rt}[/tex]
Where, [tex]y_o=120[/tex] is the initial amount
r=0.073 is the decay rate
t=30 minute is the time
Substitute the value in the formula,
[tex]y(30)=120\times e^{-0.073\times 30}[/tex]
[tex]y(30)=120\times e^{-2.19}[/tex]
[tex]y(30)=120\times 0.1119[/tex]
[tex]y(30)=13.428[/tex]
[tex]y(30)=13.4[/tex]
Therefore, 13.4 grams of a 120 gram sample will remain radioactive after 30 minutes.
Answer:
13.4
Step-by-step explanation:
Substitute the given values into the formula: A(t)=Pert. Where P is the initial mass, r is the rate of decay, and t is time. Note, the rate is negative because we are finding the rate of decay.
A=120e−(0.073)(30)≈13.4
So, about 13.4 grams will remain after 30 minutes.
Zev is planting a garden. The garden is 10 1/3 yards long and 8 yards wide. What is the area of the garden?
Answer: 82 2/3 yards squared
Step-by-step explanation: The formula for area is l × w = A. Because of this, you need to multiply the two numbers.
1. Make 10 1/3 into an improper fraction.
10 1/3 = 31/3
2. Multiply!
31/3 × 8/1 = 248/3
3. Simplify
3 goes into 248 82 times with 2 left over (82 2/3)
What is the solution to the equation 5=2/5a
A.2
B.4 3/5
C.12 1/2
D.25
Answer:
C.12 1/2
Step-by-step explanation:
5=2/5a
Multiply each side by 5/2 to isolate a
5/2 * 5 = 5/2 * 2/5 a
25/2 = a
12 1/2 = a
Answer:
x=32
Step-by-step explanation:
(32-5)^(2/3)=9
A number from 1 to 100, inclusive, is selected at random. What is the probability that the
number selected—
a. is a prime number?
b. contains the digit 9?
c. is both prime and contains the digit 9?
Answer:i might be wrong but i believe its b
Step-by-step explanation:
Answer:
A : 1/4
B : 19/100
C : 3/50
Step-by-step explanation:
There are 25 prime numbers from 1 to 100.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
25/100 = 1/4
There are 19 numbers that contain 9.
9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, and 99.
19/100
There are 6 numbers that are prime and contain 9.
19, 29, 59, 79, 89, 97.
6/100 = 3/50
Javier has 30 year mortgage on his 120,000 home hid bank required a 20% down payment and initially offers him a rate of 5.75% but he chose to buy 2 points and lower his rate.His current mortgage is 55.698 Taken all this into consideration ,what is the total financed price he paid for his home ?
Answer:226,432.80
Step-by-step explanation:
Final answer:
Javier's total financed price for his home, excluding the longer-term interest but including the cost of buying points, is $97,920. This total includes the initial mortgage of $96,000 after a 20% down payment on a $120,000 home and the $1,920 spent on purchasing two points to reduce the interest rate.
Explanation:
Javier's home cost $120,000, and he was required to make a 20% down payment. Twenty percent of $120,000 is $24,000, which is the down payment amount. Therefore, the initial loan amount is $120,000 - $24,000 = $96,000.
Buying points typically costs 1% of the loan amount per point to lower the interest rate by a certain percentage. It is not specified how much the rate was lowered by purchasing 2 points, but we can calculate the cost. Two points on a $96,000 loan is 2% of $96,000, which equals $1,920.
Thus, the total financed price of the home, not counting interest payments over the term of the mortgage but including the cost of the points, is the initial loan amount plus the cost of the points: $96,000 initial loan + $1,920 for points = $97,920.
How many solutions does the system of linear equations have ? Y=3/4x+12
Answer:
1 solution
Step-by-step explanation:
Set it equal to 0
0=3/4x+12
Subtract 12
-12=3/4x
Multiply by 4
-48=3x
Divide by 3
X = -16
The equation has an infinite number of solutions
Given equation is,
[tex]y=\frac{3}{4}x+12[/tex]
We can write the given equation as,
[tex]3x-4y+12=0[/tex]
[tex]For x=1\\y=\frac{51}{4}\\For x=2\\y=\frac{27}{2}\\For x=3\\y=\frac{57}{4}[/tex]
In the above given equation for the different values of x gives the different solution of y.
Hence, the given equation has an infinite number of solutions.
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M angle r = 120 m angle s =110 find m angle t
For this equation I used the fact that S and U are congruent (because Line ur and rs are equal and lines UT and TS are equal. All the interior angles need to add to 360 degrees. U+R+S = 340 so T has to equal 20 degrees.
Two ramps are placed back to back as shown. What is the length of the ramp labeled x?
Answer:
16.6 ft
Step-by-step explanation:
Use Law Of Sines to solve this:
(Sin 7)/9 = (Sin 13)/x
Cross multiply...
x(Sin 7) = 9(Sin 13)
Divide both side by Sin 7
x = [9(Sin 13)]/(Sin 7)
x = 16.61254121
Answer:
16.6 ft
Step-by-step explanation:
If sinx=1/9, x in quadrant 1, then find (without finding x):
Sin(2x)=
Cos(2x)=
Tan(2x)=?
Answer:
Part 1) [tex]sin(2x)=8\frac{\sqrt{5}}{81}[/tex]
Part 2) [tex]cos(2x)=\frac{79}{81}[/tex]
Part 3) [tex]tan(2x)=8\frac{\sqrt{5}}{79}[/tex]
Step-by-step explanation:
Part 1) Find sin(2x)
we know that
[tex]sin(2x)=2sin(x)cos(x)[/tex]
we have
[tex]sin(x)=\frac{1}{9}[/tex]
Find cos(x)
Remember that
[tex]sin^{2}(x)+cos^{2}(x)=1[/tex]
substitute
[tex](\frac{1}{9})^{2}+cos^{2}(x)=1[/tex]
[tex]cos^{2}(x)=1-(\frac{1}{9})^{2}[/tex]
[tex]cos^{2}(x)=1-(\frac{1}{81})[/tex]
[tex]cos^{2}(x)=\frac{80}{81}[/tex]
[tex]cos(x)=\frac{\sqrt{80}}{9}[/tex]
[tex]cos(x)=4\frac{\sqrt{5}}{9}[/tex] -----> is positive because angle x belong to the I quadrant
Find sin(2x)
we have
[tex]sin(x)=\frac{1}{9}[/tex]
[tex]cos(x)=4\frac{\sqrt{5}}{9}[/tex]
so
[tex]sin(2x)=2sin(x)cos(x)[/tex]
[tex]sin(2x)=2(\frac{1}{9})(4\frac{\sqrt{5}}{9})[/tex]
[tex]sin(2x)=8\frac{\sqrt{5}}{81}[/tex]
Part 2) Find cos(2x)
we know that
[tex]cos(2x)=cos^{2}(x)-sin^{2}(x)[/tex]
we have
[tex]sin(x)=\frac{1}{9}[/tex]
[tex]cos(x)=4\frac{\sqrt{5}}{9}[/tex]
so
[tex]cos(2x)=(4\frac{\sqrt{5}}{9})^{2}-(\frac{1}{9})^{2}[/tex]
[tex]cos(2x)=\frac{80}{81}-\frac{1}{81}[/tex]
[tex]cos(2x)=\frac{79}{81}[/tex]
Part 3) Find tan(2x)
we know that
[tex]tan(2x)=\frac{sin(2x)}{cos(2x)}[/tex]
we have
[tex]sin(2x)=8\frac{\sqrt{5}}{81}[/tex]
[tex]cos(2x)=\frac{79}{81}[/tex]
so
[tex]tan(2x)=\frac{8\frac{\sqrt{5}}{81}}{\frac{79}{81}}[/tex]
[tex]tan(2x)=8\frac{\sqrt{5}}{79}[/tex]
Using trigonometric identity functions, when Sinx equals 1/9, Sin(2x) equals 2√80/729, Cos(2x) equals 79/81, and Tan(2x) equals 162√80/56831.
Explanation:The question asks for the values of Sin(2x), Cos(2x), and Tan(2x) when Sinx = 1/9 (x in Quadrant 1). To solve for these values, we can use the identity formulas. If given that sinx = 1/9, it follows that cosx = √(1 - sin²x) = √(1 - (1/81)) = √(80/81) because in quadrant 1, the cosine value is positive. Therefore:
Sin(2x) = 2sinxcosx = 2 * 1/9 * √80/81 = 2√80/729,Cos(2x) = cos²x - sin²x = (80/81 - 1/81) = 79/81,Tan(2x) = sin(2x)/cos(2x)= (2√80/729) / (79/81) = 162√80/56831Learn more about Trigonometry here:https://brainly.com/question/11016599
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SOMEONE PLEASE HELP ME! I have a few of the explanations but I'm not sure if I need more please suggest some thank you
Here are 3 different triangles with different missing side and/or angle measures (not to scale). For each triangle, explain what you can and cannot solve for.
For each thing you cannot find, explain whether or you think there is only one value it can be (but you just don't have a way to find it yet) or whether you think there isn't enough information for there to be just one right answer for the missing information.
For the things you do know how to find, explain which tool or fact about triangles you would use to solve it. (You do not need to find the missing values themselves.)
Answer:
For tingle #1
We can find angle C using the triangle sum theorem: the three interior angles of any triangle add up to 180 degrees. Since we know the measures of angles A and B, we can find C.
[tex]C=180-(A+B)[/tex]
[tex]C=180-(21.24+27.14)[/tex]
[tex]C=131.62[/tex]
We cannot find any of the sides. Since there is noting to show us size, there is simply just not enough information; we need at least one side to use the rule of sines and find the other ones. Also, since there is nothing showing us size, each side can have more than one value.
For triangle #2
In this one, we can find everything and there is one one value for each.
- We can find side c
Since we have a right triangle, we can find side c using the Pythagorean theorem
[tex]b^2=a^2+c^2[/tex]
[tex]4^2=2^2+c^2[/tex]
[tex]16=4+c^2[/tex]
[tex]12=c^2[/tex]
[tex]c=\sqrt{12}[/tex]
[tex]c=2\sqrt{3}[/tex]
- We can find angle C using the cosine trig identity
[tex]cos(C)=\frac{adjacent}{hypotenuse}[/tex]
[tex]cos(C)=\frac{2}{4}[/tex]
[tex]C=arccos(\frac{2}{4} )[/tex]
[tex]C=60[/tex]
- Now we can find angle A using the triangle sum theorem
[tex]A=180-(B+C)[/tex]
[tex]A=180-(90+60)[/tex]
[tex]A=30[/tex]
For triangle #3
Again, we can find everything and there is one one value for each.
- We can find angle A using the triangle sum theorem
[tex]A=180-(B+C)[/tex]
[tex]A=180-(90+34.88)[/tex]
[tex]A=55.12[/tex]
- We can find side a using the tangent trig identity
[tex]tan(C)=\frac{opposite-side}{adjacent-side}[/tex]
[tex]tan(34.88)=\frac{7}{a}[/tex]
[tex]a=\frac{7}{tan(34.88)}[/tex]
[tex]a=10.04[/tex]
- Now we can find side b using the Pythagorean theorem
[tex]b^2=a^2+c^2[/tex]
[tex]b^2=10.04^2+7^2[/tex]
[tex]b^2=149.8[/tex]
[tex]b=\sqrt{149.8}[/tex]
A modern equation involving positive and negative integers would be -3+4=1. How would Brahmagupta have represented this equation?
A. Three fortunes added to four debts will be one debt.
B. Three debts added to four debts will be one debt.
C. Three fortunes added to four fortunes will be one fortune.
D. Three debts added to 4 fortunes will be one fortune.
D. Three debts added to four fortunes will be one fortune.
Debts=negative, so -3
Fortunes= positive, so 4
-3+4=1
3debt+4fortune=1fortune
Or, 4fortune-3debt=1fortune
4-3=1
Answer:
D. Three debts added to 4 fortunes will be one fortune.
Step-by-step explanation:
Given : A modern equation involving positive and negative integers would be -3+4=1.
To find : How would Brahmagupta have represented this equation.
Solution : We have given that -3+4=1.
Here, - sing represent by debt and + sign represent by fortune .
In given statement 3 is with debt and 4 is with fortune and 1 with fortune.
Then we can see, Three debts added to 4 fortune will be one fortune.
Therefore, D. Three debts added to 4 fortunes will be one fortune.
how many solutions does 9x+3=9x+5 have?
There is No Absolute Solution
9x+3 = 9x+5 has zero solutions.
How to find the solution to an equation?The solution of an equation can be found by finding the value of the variable in the equation.
We can find the solution of the given equation as follows:9x+3 = 9x+5
⇒ 3 = 9x - 9x + 5
⇒ 3 = 5
But 3 ≠ 5
The variables canceled each other out and we found that the given equation doesn't have a solution. Thus the equation has no solution.
Therefore, we have determined that the given equation 9x+3=9x+5 has zero equations.
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What is the slope line y=5x+4
Answer:
The slope is 5
Step-by-step explanation:
This equation is in slope intercept form
y = mx +b
where m is the slope and b is the y intercept
y = 5x+4
where 5 is the slope and 4 is the y intercept
Answer:
The slope = 5Step-by-step explanation:
The slope-intercept form of the equation of a line:
y = mx + b
m - slope
b - y-intercept
We have the equation y = 5x + 4
Therefore the slope is m = 5
The table shows the mean daily temperature in Idaho during a week in January. Which statement about the data is true?
Math item stem image
The lowest mean temperature was on Tuesday.
The lowest mean temperature was on Thursday.
The highest mean temperature was on Sunday.
The highest mean temperature was on Tuesday.
Answer:
The correct option is 1.
Step-by-step explanation:
The given table shows the mean daily temperature in Idaho during a week in January.
Sunday = 0.7°F
Monday = -1.2°F
Tuesday = -1.8°F
Wednesday = 1.1°F
Thursday = 0°F
Friday = 0.2°F
Saturday = -0.4°F
Arrange the temperature in ascending order.
-1.8°F, -1.2°F, -0.4°F, 0°F, 0.2°F, 0.7°F, 1.1°F
It means the lowest mean temperature was on Tuesday and the highest mean temperature was on Wednesday.
Therefore the correct option is 1.
Answer:
The lowest mean temperature was on Tuesday.
THIS IS THE EXACT ANSWER ON TTM
Step-by-step explanation:
If a rectangular prism with a length of 12 feet and a width of 9 feet has a surface area of 930 square feet find its height
Answer:
The height is 17 ft
Step-by-step explanation:
The surface area of a rectangular prism is
SA = 2(LW +WH + LH)
where L = length, W = width, and H = height
We know SA = 930, L = 12, and W = 9
930 = 2(12*9 +9H + 12H)
Divide each side by 2
930/2 = 2/2(12*9 +9H + 12H)
465 = (12*9 +9H + 12H)
Combine like terms
465 = 84+21H
Subtract 84 from each side
465-84 = 84-84+21H
357 = 21H
Divide by 21
357/21=21H/21
17 = H
The height is 17 ft
Answer:
Height is 17 ft.
Step-by-step explanation:
Given: Rectangular Prism is also called cuboid
Length, L = 12 ft. and width, W = 9 ft.
Surface Area of cuboid, SA = 930 ft.²
To find: height , H
The surface area of a rectangular prism or cuboid
SA = 2(LW +WH + LH)
930 = 2(12×9 +9H + 12H)
[tex]\frac{930}{2}=108 +9H + 12H[/tex]
465 = 108 + 9H + 12H
108 + 9H + 12H = 465
21H + 108 = 465
21H = 465 - 108
21H = 357
[tex]H=\farc{357}{21}[/tex]
H = 17
therefore, Height is 17 ft.
A map is drawn with a scale of 1 inch= 15 miles. Nichol measured the distance to the next town as 3 inches. How many miles does she have to travel fo get to the next town? SHOW YOUR WORK!!!!
Answer:
45 miles
Step-by-step explanation:
if 1 in = 15 mi so put x=15
3 is 3 times 1 so x=3 and 3*15=45
Your answer is 45 miles.
In the following image, AB is parallel to DC, and BC is a transversal intersecting both parallel lines. The measure of angle ABC is 118°
Answer:
n° = 62°
p° = 62°
q° = 118°
v° = 84°
w° = 138°
Step-by-step explanation:
angle ABC is 118°
so
m° + 118° = 180
m° = 180° - 118°
m° = 62°
n° = m° = 62° (corresponding angles are equal since AB is parallel to DC, and BC)
p° = n° = 62° (vertical angles are equal)
q° + n° = 180° (linear pair angles)
q° + 62° = 180°
q° = 180° - 62°
q° = 118°
v° + 96° = 180° (linear pair angles)
v° = 180° - 96°
v° = 84°
w° + 42° = 180 (linear pair angles)
w° = 180° - 42°
w° = 138°
Answer:
n° = 62°
p° = 62°
q° = 118°
v° = 84°
w° = 138°
Step-by-step explanation:
angle ABC is 118°
so
m° + 118° = 180
m° = 180° - 118°
m° = 62°
n° = m° = 62° (corresponding angles are equal since AB is parallel to DC, and BC)
p° = n° = 62° (vertical angles are equal)
q° + n° = 180° (linear pair angles)
q° + 62° = 180°
q° = 180° - 62°
q° = 118°
v° + 96° = 180° (linear pair angles)
v° = 180° - 96°
v° = 84°
w° + 42° = 180 (linear pair angles)
w° = 180° - 42°
w° = 138°
What quadrant does the point (-10,9) lie?
Answer:
Quadrant II
Step-by-step explanation:
Quadrant II points are characterized by a negative X value but a positive Y value (-x,y).
Since -10 is negative and 9 is positive, this point lies on quadrant II.
Answer:
quadrant III
Step-by-step explanation:
A wire of length 7x is bent into the shape of a square. Express the area A of the square as a function of z.
The length of the wire is bent into a square, making each side equal to 7x/4. The area of a square is found by squaring the length of one side, so the area, as a function of , is (7x/4)^2 or 49x^2/16.
Explanation:The given information is that the length of the wire is 7x, and it is bent into a square. In a square, all sides are equal. Therefore, we can say that the length of each side of the square is 7x/4.
To find the area of a square, we simply square the length of one side. Thus, the area A of the square, expressed as a function of x, is (7x/4)^2 or 49x^2/16.
Therefore, the question's answer is that the area A of the square can be expressed as the function 49x^2/16.
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Final answer:
To express the area A of a square in terms of z, assuming the wire length is 7z, calculate the side length a as 7z/4 and then square it to get A = (7z/4)². If x is correct and unrelated to z, more information is needed.
Explanation:
To express the area A of a square as a function of z, given that a wire of length 7x is bent into the shape of a square, we follow these steps:
The perimeter of the square is equal to the length of the wire, which is 7x.
Since the perimeter P of a square is 4 times one of its sides a, we can write P = 4a. Therefore, 7x = 4a.
To find the side length a, we divide 7x by 4: a = 7x/4.
The area A of a square is the square of one of its sides, so A = a². By substituting a with 7x/4, we get A = (7x/4)².
Finally, we need to write the equation in terms of z. Here, it seems there might be an issue with the question, as there is no direct relationship provided between x and z. Assuming there's a typographical error and that the wire length is actually 7z, we can write a = 7z/4 and A = (7z/4)².
If x is indeed correct and unrelated to z, more information is required to express A as a function of z.
paul’s account balance is less than -$50. What is a possible balance for paul’s account? Explain.
Answer:
Step-by-step explanation:
-50 plus so above the number so like -51.5
If paul's account balance is less than - $50 the possible balance for Paul's account should be in the range of - $50.9 to - $50.1.
What is the range?Range defines possible values in between two values that are some distance apart on the number line. The range can also be defined as the possible values from the least value to the greatest value.
Given that Paul's account balance is less than - $50.
∴ The possible balance for Paul's account can be in the range of
- $50.9 to - $50.1 because if he had an amount which is less than - $51 then the given statement should have been mentioned.
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Which of the following xpressions is equivalent to -1/4 - 5/3? -1/4 + (-5/3) or - 1/4 + 5/3?
Mr. Gray's class is conducting an experiment to find the probability of pulling certain colors from a bag of 25 marbles. If 5 are purple, 2 are yellow, 4 are green, and the rest are black, what is the probability of drawing a green and black if the marbles are not replaced after they are picked?
The probability of drawing a green followed by a black marble from a bag containing 25 marbles without replacement is found by multiplying the individual probabilities of each event. These are 4/25 for the green marble and 7/12 for the black marble after the first draw.
Explanation:The subject of this question is probability within the field of Mathematics, suitable for a High School level student. The probability of drawing a green and black marble without replacement is a two-step probability problem. Given that there are 5 purple, 2 yellow, 4 green, and the rest black out of 25 marbles, we first need to calculate the total number of black marbles, which is 25 - (5 + 2 + 4) = 14. The probability of drawing a green marble first is 4 out of 25, which simplifies to 4/25. After a green marble is drawn, there are now 24 marbles left in the bag, with 14 being black. Therefore, the probability of then drawing a black marble is 14/24 or 7/12. To find the combined probability of both events occurring sequentially, we multiply the individual probabilities: (4/25) * (7/12). This calculation will give us the final probability of drawing a green and then a black marble without replacement.
Kalvin and 4 of his friends want
to share 4 pounds of nuts equally.
Write an expression to show
what fraction of the nuts each
friend should receive. Then write
2 equivalent fractions for this
amount.
Which of the following is the equation of a line that passes through the points (1,6) and (2,1)
A. Y=-5x+11
B. Y=-5x+1
C. Y=2x+1
D. Y=5x-1
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
To calculate m use the slope formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (2, 1)
m = [tex]\frac{1-6}{2-1}[/tex] = - 5, hence
y = - 5x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (1, 6), then
6 = - 5 + c ⇒ c = 6 + 5 = 11
y = - 5x + 11 → A
Answer:
[tex]y=-5x+11[/tex]
Step-by-step explanation:
Given : Points (1,6) and (2,1)
To Find : Which of the following is the equation of a line that passes through the points (1,6) and (2,1) ?
Solution:
[tex](x_1,y_1)=(1,6)\\(x_2,y_2)=(2,1)[/tex]
Now to find the equation of a line that passes through the points (1,6) and (2,1) we will use two point slope form
Two point slope form : [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Substitute the values
[tex]y-6=\frac{1-6}{2-1}(x-1)[/tex]
[tex]y-6=-5(x-1)[/tex]
[tex]y-6=-5x+5[/tex]
[tex]y=-5x+11[/tex]
So, Option A is true.
Hence The equation of a line that passes through the points (1,6) and (2,1) is[tex]y=-5x+11[/tex]
What is the value of x? Enter your answer as a decimal.
Answer:
x = 67.5 ftStep-by-step explanation:
ΔNPM and ΔABM are similar. Therefore the sides are in proportion:
[tex]\dfrac{AM}{NM}=\dfrac{BM}{PM}[/tex]
We have
[tex]AM=71.5\ ft-22\ ft=49.5\ ft\\NM=71.5\ ft\\BM=x\\PM=97.5\ ft[/tex]
Substitute:
[tex]\dfrac{49.5}{71.5}=\dfrac{x}{97.5}[/tex] cross multiply
[tex]71.5x=(49.5)(97.5)[/tex]
[tex]71.5x=4826.25[/tex] divide both sides by 71.5
[tex]x=67.5[/tex]
What is Z^6y^3/z^6y^4
Answer:
The correct answer is
Z⁶Y³/Z⁶Y⁴ = 1/Y
Step-by-step explanation:
Points to remember
1). xᵃ * xᵇ = xᵃ⁺ᵇ
2). xᵃ/xᵇ = xᵃ⁻ᵇ
3). x° = 1
4). x⁻ᵃ = 1/xᵃ
The given expression is Z⁶Y³/Z⁶Y⁴
To find the simplification of expression
Z⁶Y³/Z⁶Y⁴ = Z⁶⁻⁶ * Y³⁻⁴
= Z° * Y⁻¹ = 1 * 1/Y = 1/Y
Therefore the value of given expression Z⁶Y³/Z⁶Y⁴ is 1/Y
determine whether the question is a statistical question. If it is a statistical question, identify the units for the answer. “How tall is sam?”
Answer:
No
Step-by-step explanation:
Here we are taking only one measurement: the height of one person. Strictly speaking, this is NOT a statistical question.
"List the heights of a sample of 50 first-graders" would definitely be a stat. question.
The question 'How tall is Sam?' is not a statistical question. Statistical questions expect a variety of responses, not a singular answer. Height is typically measured in feet or centimeters.
Explanation:The question 'How tall is Sam?' is not considered a statistical question. A statistical question is one in which the answer varies and requires data collection for multiple items or individuals to answer. It is one for which you don't expect to get a single answer. Instead, you expect to get a variety of different answers, and you're interested in the distribution and tendency of those answers. For instance, 'How tall are the students in a class?' is a statistical question because it would result in a variety of answers and we could analyze that data set.
The unit for height in this context typically is measured in feet or centimeters.
Learn more about Statistical Question here:https://brainly.com/question/14877725
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Find an equation in standard form for the hyperbola with vertices at (0, ±6) and foci at (0, ±9).
Answer:
[tex]\dfrac{y^2}{36}-\dfrac{x^2}{45}=1.[/tex]
Step-by-step explanation:
Since vertices and foci lie on the y-axis, the equation of the hyperbola is
[tex]\dfrac{y^2}{b^2}-\dfrac{x^2}{a^2}=1.[/tex]
If the vertices are at points (0,±6), then [tex]b=6.[/tex]
If the foci are at points (0,±9), then [tex]c=9.[/tex]
Note that
[tex]c^2=b^2+a^2,[/tex]
then
[tex]9^2=6^2+a^2,\\ \\a^2=81-36,\\ \\a^2=45.[/tex]
The equation of the hyperbola is
[tex]\dfrac{y^2}{36}-\dfrac{x^2}{45}=1.[/tex]
What is the length of segment LM
Answer:
LM = 23 units
Step-by-step explanation:
triangle KLN and triangle MLN are congruent.
The segment LM is equal to segment LK.
Also, MN is same as KN, thus we can write:
[tex]MN=KN\\25=14x-3\\25+3=14x\\28=14x\\x=2[/tex]
Since, x = 2, we can get the side length LM:
[tex]LM=LK=9x+5\\LM=LK=9(2)+5\\LM=23[/tex]
Hence, LM = 23 units
Answer:
LM = 23 units
Step-by-step explanation:
From figure we can see an isosceles triangle KNM
KN = NM
NL is the perpendicular from N to KM,
Therefore KL = LM
To find the value of x
From figure we can write,
14x - 3 = 25
14x = 25 + 3 = 28
x = 28/14 = 2
To find LM
LM = KL
we have KL = 9x + 5
Therefore LM = 9x + 5 = (9 * 2) + 5 = 23 units