Answers
1. 1
2. -1
3. 0
4. 1
5. 1 (x has been replaced by 1/x and the limiting value of x changed to 0)
Related Questions
A plane intersects a double-napped cone such that the plane intersects both nappes through the cone's vertex.
Which terms describe the degenerate conic section that is formed?
Select each correct answer.
pair of intersecting lines
degenerate ellipse
degenerate hyperbola
line
point
degenerate parabola
Answers
pair of intersecting lines
degenerate hyperbola
Answer:
degenerate hyperbola
pair of intersecting lines
Step-by-step explanation:
Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years. Five years after Brian's initial investment, Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years. Given that no additional deposits are made, compare the balances of the two accounts after the interest period ends for each account. (round to the nearest dollar)
Answers
Compound interest formula is [tex]A = P(1+r)^t[/tex]
Where P is the principal amount
r is the rate of interest
t is number of years
Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years
P = 10,000 , r= 4% = 0.04 , t =10
Plug in all the values
[tex]A = 10000(1+0.04)^{10}[/tex] = 14,802.44
Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.
P = 10,000 , r= 7% = 0.07 , t =5
Plug in all the values
[tex]A = 10000(1+0.07)^5[/tex] = 14,025.52
Brian balance after the interest period = $ 14,802.44
Chris balance after the interest period = $ 14,025.52
Balance in Brian's account is more than Chris account
Please help :)
Solve the system of equations and choose the correct answer from the list of options.
d + e = 1
−d + e = −5
Label the ordered pair as (d, e). (4 points)
(0, 0)
(3, −2)
(−2, 3)
(−3, 0)
Answers
(3, -2)
Given equations are
d+e=1
-d+e=-5
We need to find d and e.
What is system of equations?A system of equations is a set of one or more equations involving a number of variables
The system of equations are
d+e=1....(1)
-d+e=-5....(2)
d=1-e (from 1)
Substitute d in (2)
-(1-e)+e=-5
-1+e+e=-5
-1+2e=-5
2e=-5+1
2e=-4
e=-2
Now substitute value of e in (1)
d-2=1
d=1+2
d=3
Therefore the ordered pair for d + e = 1 and −d + e = −5 is (3, -2)
i.e value of d=3 and e=-2
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Help on both 13 and 14. Show work please
Answers
14. ST = 2×(XY)
8z +3 = 2(3z +2)
2z = 1
z = 1/2
What is the equation of the line that passes through (7, 4) and (4, -2)?
a) y = 2x - 10
b) y = -2x - 10
c) y = -2x + 18
d) y = 2x + 18
Answers
Solution:
we have been asked to find the equation of the line that passes through (7, 4) and (4, -2).
First we will find the slope of the line using the formula
[tex] m=\frac{y_2-y_1}{x_2-x_1} [/tex]
Plugin the given values we get
[tex] m=\frac{-2-4}{4-7}=\frac{-6}{-3}=2 [/tex]
Now using the point slope form of a straight line
[tex] (y-y_1)=m(x-x_1) [/tex]
Plugin the values
[tex] (y-4)=2(x-7)\\
\\
y=2x-14+4\\
\\
y=2x-10\\ [/tex]
Hence the correct option is a.
A cylindrical tank has a radius of 4.5 ft and an altitude of 14 ft. If a gallon of paint will cover 130 ft squared ft2 of surface, how much paint in gallons is needed to put two coats of paint on the entire surface of the tank? Aswer: To put two coats of paint on the entire surface of the tank, ______ full gallons of pain are needed.
Answers
circle area = pi * 4.5 * 4.5 = 63.585
circle circumference = 2*pi*4.5 = 28.26
lateral area = 28.26 * 14 =395.64
surface area = 63.585*2 + 395.64 = 522.81
522.81/130 = 4.02gallons
2*4.02= 8.04
To put two coats of paint on the entire surface of the tank, EIGHT full gallons of pain are needed.
What is the best first step in solving the equation 4 + squrt(6x) = 5?
Answers
Compare the exponential and logarithmic models of population growth
Answers
exponential is how much something increases by the way, tell me if this helps
Anna has leaned a ladder against the side of her house. The ladder forms a 72º angle with the ground and rests against the house at a spot that is 6 meters high. What length is the best approximation for the distance along the ground from the bottom of the ladder to the wall?
Answers
Answer:
The best approximation of AB is 2 meters.Step-by-step explanation:
Notice that this situation models a right triangle, when the height, which is a leg of the triangle, is 6 meters.
Also, we know the angle between the ladder and the ground, which is 72°.
To find the distance from A to B, which from the bottom of the ladder to the bottom of the wall, we just need to use trigonometric reasons.
[tex]tan(72\°)=\frac{opposite \ leg}{adjacent \ leg}[/tex]
Why we use tangent? Because it relates both legs where we just need to find the adjacent one.
[tex]tan(72\°)=\frac{6}{AB}\\AB=\frac{6}{tan(72\°)} \\AB \approx \frac{6}{3} \\AB \approx 2 \ m[/tex]
Therefore, the best approximation of AB is 2 meters.
The equation $1.50p + $5.00 = $14.00 shows the total cost of picking p pounds of blueberries at a local blueberry farm. how many pounds of blueberres were picked/
Answers
1.5p = 9
p = 6 pounds
Base your answer to the question on the diagrams shown below.
What is the probability of drawing a red card and then spinning a 1?
Answers
P(Red)×P(Spinning 1)
P(Red)=2/5
P(Spinning 1)=4/8=1/2
Thus:
P(Red)×P(Spinning 1)=1/2×2/5=1/5
Answer: [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
From the given picture, the total number of cards = 5
The number of red card = 2
Thus, the probability of drawing a red card P(red)=[tex]\frac{2}{5}[/tex]
Also, total number of digits on spinner = 8
Number of 1's=4
Thus, the probability of spinning a 1 P( spinning 1)=[tex]\frac{4}{8}=\frac{1}{2}[/tex]
Since both the events of drawing a red card and spinning a 1 are independent events, therefore, the probability of drawing a red card and then spinning a 1=[tex]\text{ P(red)}\times\text{P( spinning 1)}=\frac{2}{5}\times\frac{1}{2}=\frac{1}{5}[/tex]
Whats the distance between points C(0, 4), T(-6, -3)
a √(37)
b √(85)
c √(109)
Answers
[tex]\text{We have:}\\C(0;\ 4);\ T(-6;-3)\\\\\text{substitute coordinates of the points to the formula:}\\\\|CT|=\sqrt{(-6-0)^2+(-3-4)^2}=\sqrt{(-6)^2+(-7)^2}=\sqrt{36+49}=\sqrt{85}[/tex]
[tex]\text{Answer:}\ b.\ \sqrt{85}[/tex]
ABC Bookstore sells new books, n, for $12, and used books, u, for $8. The store earned $112 revenue last month. The store sold 4 more used books than new books. Using the substitution method, how many new and old books did ABC bookstore sell?
A.n = 4; u = 8
B.n = 8; u = 4
C.n = 8; u = 12
D.n = 12; u = 8
Answers
Revenue from new books = 12n
Revenue from old books = 8u
Last month, the store earned $112 as revenue, so we can write:
12n + 8u = 112
The store sold 4 more used books than new books, so we can write:
u = n + 4
Using the value of u, in above equation, we get:
12n + 8(n+4) = 112
12n +8n + 32 = 112
20n= 80
⇒
n=4
Since,
u = n + 4
u = 4 + 4 = 8
Thus, the store sold 4 new books and 8 old books last month. So the correct option is A
A line passes through the points (-6,4) and (-2,2). Which is the equation of the line?
Answers
Answer:
The equation of the line is [tex]y=\frac{-1}{2}x+1[/tex]
Step-by-step explanation:
1. The equation of the line that passes through two points can be expresed as:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex] (Eq.1)
where [tex]x_{1}[/tex], [tex]x_{2}[/tex], [tex]y_{1}[/tex] and [tex]y_{2}[/tex] are the given points.
2. Name the points:
[tex]x_{1}[/tex]=-6
[tex]x_{2}[/tex]=-2
[tex]y_{1}[/tex]=4
[tex]y_{2}[/tex]=2
3. Replace the points in the Eq.1:
[tex]\frac{y-4}{x-(-6)}=\frac{2-4}{-2-(-6)}[/tex]
[tex]\frac{y-4}{x+6}=\frac{2-4}{-2+6}[/tex]
[tex]\frac{y-4}{x+6}=\frac{-2}{4}[/tex]
[tex]\frac{4(y-4)}{x+6}=-2[/tex]
[tex]4(y-4)=-2(x+6)[/tex]
[tex]4y-16=-2x-12[/tex]
[tex]4y=-2x-12+16[/tex]
[tex]4y=-2x+4[/tex]
[tex]y=\frac{-2x+4}{4}[/tex]
[tex]y=\frac{-2x}{4}+\frac{4}{4}[/tex]
[tex]y=\frac{-1}{2}x+1[/tex]
Books spontaneously catch on fire in temperatures at or above 451, degree Fahrenheit. Write an inequality that is true only for temperatures (t)(t)left parenthesis, t, right parenthesis at which books spontaneously catch on fire.
Answers
We have then:
t: temperature (degree Fahrenheit).
We write then the inequation that adapts to the problem:
t> = 451
Answer:
an inequality that is true only for temperatures at which books spontaneously catch on fire is:
t> = 451
1. For which angle is secant undefined?
a. 30°
b. 45°
c. 180°
d. 270°
2. Which of the following is csc(-166°) equal to?
a. csc(14°)
b. -csc(14°)
c. -csc(-14°)
d. csc(166°)
Answers
2. stil looking
im in the same delima
1. The secant is defined as the inverse function of co-secant or cos function
Hence when the cosine is 0, the secant is 1/0 which is undefined. So, when cosine is 0, secant is undefined
Cos 30 = [tex] \sqrt{3} /2 [/tex]
Cos 45 = [tex] 1/\sqrt{2} [/tex]
Cos 180 = -1
cos 270 =0
Since cos 270 is 0, secant of 270 is undefined
Answer is d: 270
2. cosec (-x) = - cosec (180 -x)
We have cosec(-166) = - cosec (180-14) = -cosec (14)
Alternatively we can confirm this as csc (-166) = -4.133565 and -csc(14) = -4.133565; Hence, we can reconfirm that the answer arrived at is right
Therefore csc (-166) = -csc(14) (Option B) is the right answer
2. Which of the following is equivalent to 5455 cm3?
(
0.5455 L
5.455 L
54.55 L
5455 L
Answers
What is the 12th term of the sequence?
3, −9, 27, −81, 243, ...
Answers
The 12th term of the sequence 3, -9, 27, -81, 243, ... is 177,147.
Explanation:The given sequence is: 3, -9, 27, -81, 243, ...
To find the 12th term, we can observe that the sequence alternates between positive and negative, and each term is obtained by multiplying the previous term by -3. Starting with 3 as the first term, we can find the 12th term using the formula:
an = a1 * (-3)n-1
Substituting the values, we have:
a12 = 3 * (-3)12-1a12 = 3 * (-3)11a12 = 3 * (-32)5a12 = 3 * 95a12 = 3 * 59049a12 = 177,147Final answer:
The 12th term of the geometric sequence is -531441, found by using the formula for the nth term of a geometric series with a first term of 3 and a common ratio of -3.
Explanation:
The sequence given is geometric with each term being multiplied by -3 to obtain the next term. To find the 12th term of the sequence, we can use the formula for the nth term of a geometric sequence: Tn = a * rn-1, where a is the first term, r is the common ratio, and n is the term number.
For the given sequence, the first term a is 3 and the common ratio r is -3. The 12th term is found by placing these values into the formula:
T12 = 3 * (-3)12-1
T12 = 3 * (-3)11
T12 = 3 * (-177147)
T12 = -531441
Therefore, the 12th term of the sequence is -531441.
Randall bought a bond with a face value of $6000 and a coupon rate of 7.25%. the bond will mature in 5 years. how much interest will he receive semiannually?
Answers
Answer:
Face value of bond = $ 6000
Rate of interest =7.25 %
The Bond will mature in 5 years.
If the interest is semiannually , the rate of interest will reduce to half.
So, new rate of interest will be [tex]\frac{7.25}{2}=3.625[/tex]
Formula for simple interest
[tex]=\frac{\text{Principal}\times Rate \times time}{100}[/tex]
Interest after 6 months will be
[tex]=\frac{6000 \times 3.625 \times 1}{100}\\\\=60 \times 3.625\\\\=217.5[/tex]
So, interest that Randall will receive after six months = $ 217.50
order them from least to greatest, with the least at the top.
6\pi -6
\pi 3
\sqrt{99}
Answers
/sqrt{99} : 9.94
6/pi - 6 : 12.85
/pi 3 : 31
Sorry if it was incorrect, I am bored haha
Arranging the numbers in ascending order is: √99 < 6π - 6 < π³
How to arrange the numbers in ascending order?Arranging numbers in ascending order simply means arranging them from smallest to the biggest.
Now, the given numbers are:
6π - 6
π³
√99
Let us simplify the numbers to get:
6π - 6 = 6(3.14) - 6 = 12.85
π³ = 3.14³= 31
√99 = 9.95
Thus, arranging in ascending order is:
√99 < 6π - 6 < π³
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The day started at 48 degrees. by 3:00 p.m., the temperature has increased by 17 degrees. by nightfall, the temperature fell 17 degrees. what was the net change in temperature
Answers
Final answer:
The net change in temperature over the day is 0 degrees. After increasing by 17 degrees in the afternoon, the temperature fell by 17 degrees by nightfall, returning it to the starting temperature.
Explanation:
The student has asked about calculating the net change in temperature over the course of a day starting at 48 degrees. By 3:00 p.m., the temperature increased by 17 degrees, making it 65 degrees. But by nightfall, the temperature decreased by the same amount, falling back down to 48 degrees. The calculation of net change in this scenario is simple: subtract the starting temperature from the final temperature after all changes have occurred. In this case, the starting temperature was 48 degrees, it went up to 65 degrees, and then back to 48 degrees.
The net temperature change is therefore 48 degrees (final temperature) - 48 degrees (starting temperature), which equals 0 degrees. This means there was no net change in temperature over the course of the day. It is important to recognize that even though there was a temporary increase and subsequent decrease, the net effect cancels out, leaving the temperature the same as it started.
which graph shows the solution set of the compound inequality 1.5x-1>6.5 or 7x+3<-25
Answers
1.5x-1> 6.5
7x + 3 <-25
Clearing x from each one we have:
For 1.5x-1> 6.5:
1.5x> 6.5 + 1
1.5x> 7.5
x> 7.5 / 1.5
x> 5
For 7x + 3 <-25:
7x <-25-3
7x <-28
x <-28/7
x <-4
The solution set is:
(inf, -4) U (5, inf)
Answer:
See attached image
Answer:
It's B
Step-by-step explanation:
Find the first five terms of the sequence: an = 5an – 1 + 2; a1 = 3.
a) {3, 17, 87, 437, 2187}
b) {3, 15, 75, 375, 1875}
c) {3, 12, 17, 22, 27}
d) {3, 11, 27, 59, 123}
Answers
an=5an-1+2
where:
a1=3
then the other terms of the sequence will be:
a2=5a1+2
a2=5*3+2=17
a3=5a2+2
a3=5(17)+2
a3=87
a4=5a3+2
a4=5(87)+2
a4=437
a5=5a4+2
a5=(5*437+2)
a5=2187
hence the sequence will be:
3, 17, 87, 437, 2187
Answer: a) {3, 17, 87, 437, 2187}
How to find the sum of the squares of the lengths of the legs of a triangle of a=(-6,11) b=(2,8) c=(-1,0)?
Answers
To find the sum of the squares of the lengths of the legs of a triangle, use the distance formula to calculate the length of each leg and then square these lengths, summing the squares of the two legs that do not form the hypotenuse.
Explanation:To find the sum of the squares of the lengths of the legs of a triangle with vertices A=(-6,11), B=(2,8), and C=(-1,0), we first calculate the length of each leg using the distance formula, which is √((x2-x1)² + (y2-y1)²). For AB, AC, and BC we find distances:
AB = √((-6-2)² + (11-8)²)AC = √((-6+1)² + (11-0)²)BC = √((2+1)² + (8-0)²)Then, we square each leg's length:
AB² = ((-6-2)² + (11-8)²)AC² = ((-6+1)² + (11-0)²)BC² = ((2+1)² + (8-0)²)Finally, we sum up the squares of AB and AC because they represent the legs of the triangle:
Σ(leg squares) = AB² + AC²The sum of the squares of the lengths of the legs has now been found.
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What are the inputs of the function below?
Please help
Answers
Explanation:
The function declaration is f(x) where x represents the input. The input in the table given is the row labeled with x. Hence the inputs are -8 2 4 6 as shown in the table. So the correct option is Option (C) -8 2 4 6.
-i
Answer:
Input of the function are -8,2,4,6
Step-by-step explanation:
Input of a function are the domain .
Domain is the values of x. So inputs are the value of x in the table
Input of the table is x and output is f(x)
Input are the values that gives the output f(x)
From the table the x values are -8,2,4 and 6
Input of the function are -8,2,4,6
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Check all that apply.
A. y = –x + 1
B. 3x − 4y = −4
C. 4x − 3y = −3
D. y – 2 = –(x – 4)
E. y + 2 = (x + 4)
Answers
3x − 4y = 7
-4y = -3x + 7
y = (3/4)x - 7/4
The slope of the given line is 3/4.
The slope of the parallel line is also 3/4.
Now we need the equation of the line that has slope 3/4 and passes through point (-4, -2),
We use the point-slope form of the equation of a line.
y - y1 = m(x - x1)
y - (-2) = (3/4)(x - (-4))
y + 2 = (3/4)(x + 4) <---- check option E. Is the fraction 3/4 not there?
y + 2 = (3/4)x + 3
y = (3/4)x + 1
4y = 3x + 4
3x - 4y = -4 <------ this is choice B.
Due tomorrow help please
Answers
41 -39 = 2
43 -41 = 2
45 -43 = 2
These are all the same, so 2 is the common difference of the arithmetic sequence beginning with 39.
The Nth term is
[tex]a_{n}=a_{1}+(n-1)d\\a_{n}=39+2(n-1)\\a_{n}=37+2n[/tex]
The problem statement seems to ask for the 10th term and for a15. Here they are.
[tex]a_{10}=37+2\cdot 10=57\\a_{15}=37+2\cdot 15=67[/tex]
If the radius of a circle is 6 inches, how long is the arc subtended by an angle measuring 70°?
a. 3 7 π inches
b. 7 2 π inches
c. 7 3 π inches
d. 7 6 π inches
Answers
The correct answer to this problem C.)7/3
A student takes a 15 question
a. True
b. False quiz and guesses at every answer. what is the probability that the student gets exactly 10 questions right, given that the student got the first question right?
Answers
what is the height of the beach sign?
and what is the height of the beach umbrella?
I'm not sure if both images were attached, oops. but please help! I'll mark as brainliest! thank you!
Answers
[tex] tan 45 = \frac{8}{x} [/tex]
[tex](tan 45)(x) = 8 [/tex]
[tex]x = \frac{8}{tan 45} [/tex]
[tex]x = \frac{8}{1} [/tex]
[tex]x = 8[/tex]
The height of the umbrella is 8.
Hope this helps :)