The curve with equation y = x³ +3 has two tangents parallel to the line with equation
y = 12x-1. Find the co-ordinates of the two points.
Answers
Answer:
(-2, -5), (2, 11)
Step-by-step explanation:
You want the coordinates of the points on the curve y = x³ +3 where the tangent lines are parallel to y = 12x -1.
SlopeThe slope of the tangent line is the x-coefficient in its equation: 12.
The slope of the curve is given by its derivative:
y' = 3x²
We want the x-values where the slope is 12. These are the solutions to ...
12 = 3x²
4 = x² . . . . . . . . . . divide by 3
x = ±√4 = ±2 . . . . . take the square root
CoordinatesThe coordinates of the points with x = ±2 are ...
y = (±2)³ +3 = ±8 +3 = {-5, 11}
The tangent points are (-2, -5) and (5, 11).
__
Additional comment
The attached graphs and table show the solutions to y'=0 and the corresponding point locations. It also shows the tangent line equations (in point-slope form).
Related Questions
Identify the rate of change in each equation.
Answers
Answer:
7.
[tex] \frac{1}{4} [/tex]
8.
[tex]2[/tex]
9.
[tex] - \frac {5}{4} [/tex]
10.
[tex]3[/tex]
Step-by-step explanation:
rate of change is slop
Solve by factoring.
6^2 − − 12 = 0
Answers
Answer:
48
Step-by-step explanation:
1 ) Simplify...
[tex]6^2-\left(-12\right)[/tex]
[tex]=6^2+12[/tex]
[tex]6^2=36[/tex]
[tex]=36+12[/tex]
2 ) Add the numbers...
[tex]36+12 =[/tex]
[tex]48[/tex]
Hope this helps! :)
Levi has $0.74 worth of pennies and nickels. He has 2 more pennies than nickels.
Determine the number of pennies and the number of nickels that Levi has.
Answers
If he has 2 more pennies than nickels. the number of pennies is 10.6 and the number of nickels that Levi has is 12.6.
How to find the pennies and nickels?n = number of nickels
n-2 = number of pennies
Hence,
5n +1(n -2) = 74
Collect like terms
6n = 76
Divide both side by 6n
n = 76/6
n = 12.6 ( nickels)
Pennies
n-2
= 12.6 -2
= 10.6
Therefore Levi has 10.6 pennies and 12.6 nickels.
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Answer:
Step-by-step explanation:
Jb
In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers (1, 2, 3, 4, 5, 6, and 7). Among all the cards of each color, there is exactly one card labeled with each number. The cards in Ms. Q's deck are shown below.
Yunseol draws 5 cards from Ms. Q's deck. What is the probability that three cards have the same number?
Answers
The probability that three cards have the same number, using the hypergeometric distribution, is of:
0.0448 = 4.48%.
What is the hypergeometric distribution formula?The probability mass function for the hypergeometric distribution is defined as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters of the function are listed below:
x is the number of successes in the sample.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes in the population.In the context of this problem, the values of these parameters are given as follows:
N = 28, k = 4, n = 5, x = 3.
Hence for one color, the probability that three cards have the same number is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,28,5,4) = \frac{C_{4,3}C_{24,2}}{C_{28,5}} = 0.0112[/tex]
There are four colors, hence the probability is:
p = 4 x 0.0112 = 0.0448 = 4.48%.
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Please help me!!!! WILL GIVE BRAINLIEST!!!!
Answers
Answer: C & E
Step-by-step explanation: A is a lie, function 1 is pos
B is a lie function 1 is pos
C is true
D is a lie
E is true
What is the measure of angle ABC
Answers
Answer:
D
Step-by-step explanation:
[tex]m\angle EBD=33^{\circ} \implies m\angle EBC=33^{\circ} \\ \\ \therefore m\angle DBC=m\angle EBD+m\angle EBC=66^{\circ} \\ \\ m\angle DBC=66^{\circ} \implies m\angle ABD=66^{\circ} \\ \\ \therefore m\angle ABC=m\angle ABD+m\angle DBC=132^{\circ}[/tex]
Select the correct answer. Which inequality can this number line represent? A. 7 − x ≥ 1 or 4x + 9 < 13 B. 3x + 2 < 5 or 2x − 1 ≥ 11 C. 7 − x ≥ 1 and 4x + 9 < 13 D. 3x + 2 < 5 and 2x − 1 ≥ 11
Answers
Answer: A
Step-by-step explanation: A
A
K
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 59 tablets, then accept the whole batch if there is
only one or none that doesn't meet the required specifications. If one shipment of 3000 aspirin tablets actually has a 2% rate of defects, what is the probability that this whole
shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
The probability that this whole shipment will be accepted is
(Round to four decimal places as needed.)
4
Answers
Answer:
The probability that this whole shipment will be accepted is 72.39%.Step-by-step explanation:
The probability of no defects with 2% rate of defects:
P(no defects) = 59*0.02⁰*(1 - 0.02)⁵⁹ = 0.3583 (rounded) = 35.83%Probability of exactly one defect:
P(1 defect) = 59*0.02¹*(1 - 0.02)⁵⁸ = 0.3656 (rounded) = 36.56%Probability of one or no defects:
P(1 or none) = 35.83% + 36.56% = 72.39%This indicates that:
100% - 72.39% = 27.61% of shipments will be rejected, it is a lot, so many shipments will be rejectedThe probability that this whole shipment will be accepted is 72.39%.
A manager at SUBWAY wants to find the total cost of 24.8 pounds of sliced turkey at $1.89 a pound and 38.2 pounds of provolone cheese at $2.05 a pound. Find the final
cost. [1.4 and 1.5]
Answers
The final cost of the sliced turkey and provolone cheese is $31.84
How to calculate the final cost of both products?The first step is to calculate the cost of the sliced turkey
The pounds of turkey is 24.8
The amount of the turkey is $1.89
The cost is = 24.8/1.89
= 13.21
The next step is to calculate the cost of the provolone cheese
The pounds of the provolone cheese 38.2
The amount of provolone cheese is $2.05
The cost is = 38.2/2.05
= 18.63
Therefore the final cost can be calculated as follows
= 13.21 + 18.63
= 31.84
Hence the final cost is $31.84
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One factor of f (x ) = 4 x cubed minus 4 x squared minus 16 x + 16 is (x – 2). What are all the roots of the function? Use the Remainder Theorem.
A factor of f(x) is (x – 1).
A factor of f(x) is (x + 1).
Both (x – 1) and (x + 1) are factors of f(x).
Neither (x – 1) nor (x + 1) is a factor of f(x).
Answers
The answer is option A) A factor of f(x) is (x – 1).
What is the remaining theorem?
Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that when a polynomial P(x) is divided by a factor (x - a), which isn't really an element of the polynomial, a smaller polynomial is produced along with a remainder.
f(x) = 4x3 - 4x2 - 16x + 16 [Given]
One aspect is (x - 2)
The remaining theorem is used to:
Where q(x) is the quotient polynomial and r(x) is the remainder polynomial, f(x) = (x-2)q(x) + r(x).
As (x-2) is a factor of f, r(x) equals 0. (x)
f(x) = (x-2)·q(x) (x)
q(x) = f(x)/ (x-2) (x-2)
[4x3 - 4x2 - 16x + 16]/ (x - 2) (x - 2)
= [4x2 (x - 1) - 16 (x - 1)]
/ (x - 2) (x - 2)
By even more simplifying
= [(x - 1) (4x2 - 16)]
/ (x - 2) (x - 2)
excluding 4 as common
= [(x - 1) 4 (x2 - 4)]
/ (x - 2) (x - 2)
With the use of the algebraic formula a2 - b2 = (a + b) (a - b)
= [(x - 1) 4 (x + 2) (x - 2)]
/ (x - 2) (x - 2)
= [4 (x - 1) (x - 2) (x + 2)]
/ (x - 2) (x - 2)
The roots are therefore 2, -2, and 1.
there the ans is A) A factor of f(x) is (x – 1).
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A 17 inch candle burns down in 10 hours. At what rate does the candle burn, in inches per hour?
Answers
Answer:
1.7
Step-by-step explanation:
[tex]\frac{17 \text{ in}}{10 \text{ hr}}=1.7[/tex] in/hr
Evaluate 5 + x − 6 ∙ 8 for x = 8.
Answers
5 + 8 - 6 • 8
5 + 8 - 48
13 - 48
-35
*use pemdas!!*
What is the equation of a line that is perpendicular to y=0.25x−7 and passes through the point (-6,8)
Answers
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]0.\underline{25}\implies \cfrac{25}{1\underline{00}}\implies \cfrac{1}{4} \\\\[-0.35em] ~\dotfill\\\\ y=0.25x-7\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{4}}x-7\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{4}} ~\hfill \stackrel{reciprocal}{\cfrac{4}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{4}{1}\implies -4}}[/tex]
so we're really looking for the equation of a line whose slope is -4 and it passes through (-6 , 8)
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ - 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{- 4}(x-\stackrel{x_1}{(-6)}) \implies y -8= -4 (x +6) \\\\\\ y-8=-4x-24\implies {\Large \begin{array}{llll} y=-4x-16 \end{array}}[/tex]
Show that f(x)= 2x-3/2 & g(x)= 2x+3/2 are inverse fractions. Must show fog=x and gof=x. I really don’t understand this and it’s frustrating me. I must show work
Answers
Hence its proven that f and g are inverse of one another
What is a Function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Given,
f(x)= 2x-3/2
g(x)= 2x+3/2
Step 1: show that fog=x
f(g(x))
[2((2x + 3) / 2) - 3]/2
[(2x + 3) - 3] / 2
(2x + 3 - 3) / 2
2x / 2
x , which is equals to x
Now, for Step 2: gof = x
g(f(x))
g((2x - 3)/2)
[2((2x - 3)/2) + 3]/2
[(2x - 3) + 3]/2
(2x - 3 + 3)/2
2x/2
x , which is equals to x
Since, both fog(x) and gof(x) equals to x
Hence, its proven that f and g are inverse of one another
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what is -3/4x - 1/3 + 7/8x - 1/2 written in siplest form?
help me pls
Answers
Answer: 1/8x - 5/6
Step-by-step explanation:
Let's move the similar terms of the problem together.
So first we have:
-3/4x + 7/8x
And then we have:
-1/3 - 1/2
So to add/subtract fractions, the denominators have to be equal. We can change the -3/4 into -6/8 by just multiplying by 2/2 which is just 1. (Anything multiplied by 1 is just itself). So then we have:
-6/8x + 7/8x ---> 1/8x
Next, the second part.
Since neither denominators (3 or 2) can turn into one another by multiplying them with a number, we'll just multiply them with the opposite denominator.
So then we have:
-1/3 * (2/2) = -2/6
-1/2 * (3/3) = -3/6
-2/6 - 3/6 = -5/6
So finally we have:
1/8x - 5/6
Make the subject of
6x = t
Answers
The subject of the equation is x and it can be written as x = t/6.
What do you mean by solving an equation?Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. The equation's solution is the value of the variable for which the equation is true. An equation remains the same even when the LHS and RHS are flipped. The solution is discovered after isolating the variable for which the value must be determined. Depending on the kind of equation we are dealing with, we can solve it. There are various types of equations, including linear, quadratic, rational, and radical ones.
The given equation is
6x = t
Divide both sides by 6
6x/ 6 = t/ 6
x = t/ 6
So, the subject of the equation is x - t/6.
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Jillian sells handmade t- Shirts and large purses; each tea shirt costs $15. Each Large purse goes for $59 and the cost of small purses is $32 each. In the first week she sold 4 t-shirts and 3 large purses and 9 small. In the second week she sold another 5 t-shirts, 7 large bags and 4 small ones. Last week she sold 8 t-Shirts and also sold 3 large purses and 5 small purses. What was the exact amount she made in 3 weeks?
Answers
Answer:
$1598
Step-by-step explanation:
1st week
4*15=60
32*9=288
59*3=177
60+177+288=525
2nd week
5*15=75
59*7=413
32*4=128
75+413+128=616
3rd week
8*15=120
3*59=177
5*32=160
120+177+160=457
525+616+457=$1598
The function f(x) is graphed below. What is true about the graph on the interval from point a to point b?
Answers
Answer:
Option 1. It is positive and increasing.
Step-by-step explanation:
(7/4x - 5) - (2y - 3.5) - (-1/4x + 5)
Answers
The value of the expression given as (7/4x - 5) - (2y - 3.5) - (-1/4x + 5) is 2x - 2y - 6.5
How to determine the solution of the expression?In this question, the representation of the expression is given as
(7/4x - 5) - (2y - 3.5) - (-1/4x + 5)
Start by removing the brackets in the expression
So, we have
7/4x - 5 - 2y + 3.5 + 1/4x - 5
Evaluate the fractions in the expression
The expression becomes
1.75x - 5 - 2y + 3.5 + 0.25x - 5
Collect the like terms
1.75x + 0.25x - 2y - 5 + 3.5 - 5
Evaluate the like terms
2x - 2y - 6.5
Hence, the solution is 2x - 2y - 6.5
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Prime factorization of 216. Will give 10 points and 5 star if correct answer
Answers
Answer: The prime factorization of 216 is 2 × 2 × 2 × 3 × 3 × 3 or 23 × 33.
Step-by-step explanation:
PLEASE MARK BRAINLIEST
A rectangular room, / m long and b m wide,
has a perimeter p, where p = 2l+2b.
a Find the perimeter of a room which is
3.5 m long and 2 m wide.
b Find the length of a room of perimeter
20 m and width 3 m.
Answers
The perimeter of the given rectangular room is found as -
Part a: p = 11 m.
Part b: p = 46 m.
Explain the term perimeter of rectangle?A rectangle's perimeter (P) is the sum of the lengths of its four sides.A rectangle has equal size lengths plus two equal widths since its opposite sides are equal.As, given in the question-
The rectangular room has-
l m long and b m wide,
perimeter p, where p = 2l+2b ...eq 1
Part a: perimeter of a room for, 3.5 m long and 2 m wide.
Put l = 3.5 and b = 2 in eq 1.
p = 2l+2b
p = 2(3.5) +2(2)
p = 7 + 4
p = 11 m.
Part b: perimeter of a room for, 20 m long and 3 m wide.
Put l = 20 and b = 3 in eq 1.
p = 2(20) +2(3)
p = 40 + 6
p = 46 m.
Thus, the perimeter of the given rectangular room is found as 46m.
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Triangle ABC is shown with exterior ∠z.
triangle ABC with angle A labeled 77 degrees, angle B labeled 57 degrees, and side AC extended with angle z labeled as exterior angle to angle C
Determine m∠z.
46°
77°
123°
134°
Answers
Answer:
[tex]134^{\circ}[/tex]
Step-by-step explanation:
Using the exterior angle theorem,
[tex]m\angle z=m\angle A+m\angle B=134^{\circ}[/tex]
Using the exterior angle theorem, angle z is measured as 134°.which is the correct answer that would be an option (D).
What is the Exterior Angle Theorem?The exterior angle theorem is a triangle theorem that asserts that the measure of the external angle created by an extended side of a triangle is equal to the sum of the measures of the triangle's remote interior angles.
The given data will be the following as:
Exterior angle to angle C of triangle ABC = z
The remote interior angle of triangle ABC are angled A = 58° and angle B = 44°.
Therefore:
The measure of angle z = measure of angle A + measure of angle B [according to the exterior angle theorem]
Substitute the values and we get
Measure of ∠z = 77 + 57
Measure of ∠z = 134°
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The vertices of a rectangle are located at the coordinates (1, 4), (1, 5), (6, 5), and (6, 4). Find the length of the sides of the rectangle and its perimeter.
Answers
Answer: This is a 1 by 5 rectangle
perimeter = 12 units
========================================================
Work Shown:
Label the vertices A,B,C,D
A = (1, 4)
B = (1, 5)
C = (6, 5)
D = (6, 4)
The x coordinates of points A and B are the same (x = 1). The difference in y values of these points is 5-4 = 1 unit. This is the height of the rectangle. In other words, it's the length of segment AB.
Points B and C have the same y coordinate (y = 5). The difference in x value is 6-1 = 5 which is the horizontal length of the rectangle. This is the length of segment BC.
In short, this is a 1 by 5 rectangle. It's one unit tall and five units across.
--------
Perimeter = 2*(length+width)
Perimeter = 2*(5+1)
Perimeter = 2*6
Perimeter = 12 units
Or you can add up the four sides (1,5,1 and 5) to get the same result.
Intercept and slope?
Answers
Answer:
Slope = -2
Y-intercept = -8
Step-by-step explanation:
Hello!
Slope-Intercept Form: y = mx + b
m = slopeb = y-interceptThe m variable in this equation would be -2, and it is also the slope of the equation.
The b variable in this equation is -8, which is the y-intercept of the equation.
Answer:
y intercept -8
slope -2
Step-by-step explanation:
y = -2x-8
This is written in slope intercept form
y = mx+b
The slope is m which is -2
The y intercept is b which is -8
Race times for a recent 5k
run are normally distributed with a mean
time of 38 minutes and standard devia-
tion of 3.5 minutes.
(a) What is the median race time for this
event?
Answers
The median race time for this event is 38 minutes.
Given:
Race times for a recent 5k run are normally distributed with a mean time of 38 minutes and standard deviation of 3.5 minutes.
a.
X is normally distributed in (38,3.5).
so here the mean and the median are equal to each other.
Mean = 38
Median = mean
Median = 38 minutes.
Therefore the median race time for this event is 38 minutes.
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1x(3x6)=18 create a equivalent multiplication sentence that illustrates the associative property of multiplication
Answers
The equivalent multiplication sentence that shows associative property is 3x(1×6)
What is associative property?Associative property is defined as, when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped.
This means that if a,b,c are real numbers then a×(b×c)=b×(a×c)
using the associative property,1×(3×6)= 3×(1×6)
To verify the statement,let's find out
solving the parentheses first
1×(3×6)=1×18= 18
3×(1×6)= 3×6= 18
this means that 1×(3×6) and 3×(1×6) are associative
therefore 1×(3×6)=3×(1×6)
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c. Sandra sleeps for one-third of the day.
How many hours is that?
d. Sandra visits her family and friends for one-eighth of the day.
How many hours is that?
Answers
D) One eighth of the day is 3 hours. Sandra visits her family and friends for 3 hours.
Answer:
8 hours
3 hours
Step-by-step explanation:
24/3=8
24/8=3
PLEASE HELPP! ORDER THE NUMBERS FROM LEAST TO GREATEST
Answers
Answer:
least
- 1/4 ft
- 14 3/4 ft
- 15 1/2 ft
- 20 3/5 ft
greatest
Answer:
- 20 3/5 ft
- 15 1/2 ft
- 14 3/4 ft
- 1/4 ft
I the number is larger looking but have a negative symbol, then it is smaller.
For example, -1 is greater than -6. Also -1/4 is greater than -20 3/5.
Trust me, I am a year ahead in school, so trust me.
I hope this helped.
A hospital would like to determine the mean length of stay for its patients having abdominal surgery. A sample of 17 patients revealed a sample mean of 6.6 days and a sample standard deviation of 1.5 days. Assume that the lengths of stay are approximately normally distributed. Find a 99% confidence interval for the mean length of stay for patients with abdominal surgery. Round the endpoints to two decimal places, if necessary.
Answers
The 99% confidence interval for the mean length of stay for patients with abdominal surgery is 5.54, 7.66
How to solve for confidence intervalWe have the following data to solve the question with
sample size = 17
standard deviation s = 1.5
Confidence interval = 99%
mean = 6.6 days
α = 1 - 0.99
= 0.01
df = degree of freedom = n -1
17 - 1 = 16
tα/2 = 0.01 / 2
= t 0.005, 16
t critical value = 2.9208
99 % confidence interval =
X ± t critical * s/√n
[tex]6.6 +-2.9208 * \frac{1.5}{\sqrt{17} }[/tex]
6.6 ± 1.0626
6.6 - 1.0626, 6.6 + 1.0626
= 5.54, 7.66
The 99% confidence interval for the mean length of stay for patients with abdominal surgery is 5.54, 7.66
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A Mrs. Sharpe’s Starbucks card has a balance of $37.45 remaining. If each visit she spends$5.35, which equation represents the number of visits, v, she may make using the card?
Answers
Answer:
the equation is 37.45-5.35v=0
Step-by-step explanation:
37.45-5.35v=0
minus 37.45 to both sides
-5.35v=-37.45
divide -5.35 from both sides
v=7
after 7 days she will finish the card