The value of x is 1/11.
The given statement is x times 11=1.
We need to find the value of x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, x times 11=11x
⇒11x=1
⇒x=1/11
Therefore, the value of x is 1/11.
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Need help on algebra please
Answer:
Step-by-step explanation:
A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
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A research firm conducted a study to determine the average amount of money that smokers spend on cigarettes during a week. The firm found that the population mean amount that all smokers spend on cigarettes is $20 and the population standard deviation is $5. What is the probability that a new sample this year of 100 steady smokers spends between $19 and $21 on average
Answer:
0.9544 = 95.44% probability that a new sample this year of 100 steady smokers spends between $19 and $21 on average
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The firm found that the population mean amount that all smokers spend on cigarettes is $20 and the population standard deviation is $5.
This means that \(\mu = 20, \sigma = 5\)
Sample of 100:
This means that \(n = 100, s = \frac{5}{\sqrt{100}} = 0.5\)
What is the probability that a new sample this year of 100 steady smokers spends between $19 and $21 on average?
This is the pvalue of Z when X = 21 subtracted by the pvalue of Z when X = 19. So
X = 21
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{21 - 20}{0.5}\)
\(Z = 2\)
\(Z = 2\) has a pvalue of 0.9772
X = 19
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{19 - 20}{0.5}\)
\(Z = -2\)
\(Z = -2\) has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% probability that a new sample this year of 100 steady smokers spends between $19 and $21 on average
Identify the correct graph of the system of equations.
3x + y = 12
x + 4y = 4
Sam and Liam raced each other up and then down the hill. Sam's average speed up the hill was 1 mph, and his average speed down the hill was 9 mph. Lian ran up the hill and down the hill with the same speed, 2 mph. if the path from the bottom to the top of the hill is 1 mile long, how much time did it take each of the boys to finish?
Answer:
\(\begin{gathered} \text{Lian - 1 hour} \\ \text{Sam - 1}\frac{1}{9}\text{ hours} \end{gathered}\)
Explanation:
Here, we want to calculate the time taken for each of the boys to finish the race
From what we have, the total distance traveled is 2 miles (1 mile up , 1 mile down)
The general formula to get time from speed and distance is:
\(\text{time = }\frac{dis\tan ce}{\text{speed}}\)Kindly understand that the journey is in two phases, the leg up and the leg down. The time spent on each will be summed to give the total time spent on the race
Let us start with Lian. We have it as:
\(\frac{1}{2}\text{ + }\frac{1}{2}\text{ = 1}\)Lian took one hour
For Sam, we have it that:
\(\frac{1}{9}+\text{ }\frac{1}{1}\text{ = }\frac{1\text{ + 9}}{9}\text{ = }\frac{10}{9}\text{ = 1}\frac{1}{9}\text{ hours}\)in the illustration below ,The two lights are designed tc pperate at 6 volts, 5 amps each,
5
f the power source is12 volts, what will be the value of the Resistor?
Round to the tenth position. (0.00)
The value of the resistor needed in this scenario is approximately 1.2 ohms.
To find the value of the resistor in the given scenario, we can apply Ohm's Law, which states that the current (I) flowing through a resistor is directly proportional to the voltage (V) across it, and inversely proportional to the resistance (R) of the resistor.
Using Ohm's Law, we have the formula:
V = I * R
Where:
V is the voltage across the resistor (12 volts in this case),
I is the current flowing through the resistor (5 amps for each light, so a total of 10 amps),
R is the resistance of the resistor (which we need to find).
Rearranging the formula, we have:
R = V / I
Plugging in the values:
R = 12 volts / 10 amps
R = 1.2 ohms
Therefore, the value of the resistor needed in this scenario is approximately 1.2 ohms.
It's worth noting that this calculation assumes the lights are connected in parallel, as the current remains the same for each light. If the lights were connected in series, the total resistance would be the sum of the individual resistances, and the calculation would be different.
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HELP ASAP!!! Question: Lisa wants to know how high a kite is flying. Her brother tells her that the string is 500 feet long which is nailed to the ground. Using a protractor she finds that the angle made by the string and the ground is 65 degrees. Explain in detail with step by step instructions of how Lisa can find the height, perpendicular to ground, that the kite is flying. Find the height.
Answer:
sin = opp/hyp
height = opp side
hyp = length of string
sin65 = height / 500
multiply both sides by 500
500 * sin 65 = height
use calculator
453.153893518324982 = height
~ 453 feet
Find m/ABC.
A. 81°
B. 86°
C. 47°
D. 49.5°
99°
B
D
94%
The value of m ∠ABC=86° ,because of the cyclic quadrilaterals.
Hence, Option (B) is correct.
Since, We know that,
A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.
The opposite angles of a cyclic quadrilateral have a total of 180°.
Hence, We can formulate;
m ∠ABC + m ∠ADC = 180°
m ∠ABC + 94° = 180°
m ∠ABC = 180° - 94°
m ∠ABC = 86°
Similarly, one can find m∠DCB
m∠DAB + m∠DCB = 180°
99° + m∠DCB = 180°
m∠DCB = 180° - 99°
m∠DCB = 81°
Hence, m∠ABC = 86°
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AB and AD are tangent to circle C. Find the length of AB, if AB = 8x and AD = x + 9. Round your answer to 2 decimal places.
Answer:
To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:
8x = x + 9
Solving for x, we get:
x = 1.5
Therefore, AB = 8x = 8(1.5) = 12.
To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:
AB^2 + BD^2 = AD^2
Substituting the values, we get:
12^2 + BD^2 = (1.5 + 9)^2
Simplifying, we get:
BD^2 = 56.25
Taking the square root of both sides, we get:
BD = 7.5
Hence, the length of AB is 12 and the length of BD is 7.5.
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Nina has 2 cups of flour. However, this is only 1/4 of the amount of flour that she needs for a bread recipe. How many cups of flour does the recipe call for?
Answer:
8 cups of flour
Step-by-step explanation:
if 2 is 1/4 then we would do 2 × 4 to get 4/4
Answer:
She needs 8 cups.
Step-by-step explanation:
Since 2 cups are only 1/4 of what she needs, you can also say that she needs 4 times that amount. Because of that, she needs 8 cups. To check, 2 divided by 8 is .25, which is equivalent to 1/4.
compute the surface integral over the given oriented surface: portion of the plane in the octant downward-pointing normal
Using the specified oriented surface, the surface integral is F=y³i+8j-xk is a downward-pointing normal is -53/60.
Given that,
We have to find using the specified oriented surface, calculate the surface integral: F=y³i+8j-xk is a downward-pointing normal that is a part of the plane x+y+z=1 in the octant x,y,z≥0.
We know that,
Finding the surface integral of \(\int {} \,\int\limits_s {F} \, ds\)
Here,
The surface of the plane's part is x+y+z=1;
In the 1st octant, x,y,z≥0, and the oriented surface F=y³i+8j-xk.
The plane x + y + z = 1
z=1-x-y
dz/dx=-1
dz/dy=-1
So, the surface is oriented downward
dS= (dz/dzi+dz/dyj-k)dxdy
dS=(-i-j-k)dxdy
So, we get
\(\int {} \,\int\limits_s {F} \, ds\)
\(\int {} \,\int\limits_s {F} \, (dz/dzi+dz/dyj-k)dxdy\)
-53/60
Therefore, Using the specified oriented surface, the surface integral is F=y³i+8j-xk is a downward-pointing normal is -53/60.
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Problem
Circles \(K\) and \(L\) touch externally at point \(P\). Line \(ABC\) cuts \(K\) at points \(A\) and \(B\) and is tangent to \(L\) at \(C\). The line through \(A\) and \(P\) meets \(L\) at a second point \(D\).
Prove that \(PC\) bisects angle \(BPD\).
Step-by-step explanation:
Using the various theorems relating inscribed and external angles to intercepted arcs, we can write the following relations:
angle A = 1/2(arc BP) . . . . . . . . . . . inscribed angle
angle A = 1/2(arc CD -arc CP) . . . external angle at tangent/secant
angle CPD = 1/2(arc CD) . . . . . . . inscribed angle
angle CPB = 1/2(arc CP) + 1/2(arc BP) . . . . . sum of angles at the mutual tangent
ProofEquating the expressions for angle A, we have ...
1/2(arc BP) = 1/2(arc CD -arc CP)
Adding arc CP gives ...
1/2(arc BP +arc CP) = 1/2(arc CD)
Substituting the last two equations for angles from above, this gives ...
angle CPB = angle CPD
Hence PC bisects angle BPD.
Which of the following best describes the number shown below?
0.898989...
A. Rational
B. Neither Rational nor Irrational
C. Both Rational and irrational
D. Irrational
Answer:
Step-by-step explanation:
0.898989..... is a rational number because it has a terminating decimals
Evaluate |x - y| + 4 if x = -1, y = 3, and z = -4.
Answer:
8
Step-by-step explanation:
Substitute the values in the expression, we have:
\(\displaystyle{|-1-3|+4}\)
Evaluate:
\(\displaystyle{|-4|+4}\)
Any real numbers in the absolute sign will always be evaluated as positive values. Thus:
\(\displaystyle{|-4|+4 = 4+4}\\\\\displaystyle{=8}\)
Hence, the answer is 8. A quick note that z-value is not used due to lack of z-term in the expression.
Question 1-6
Given parallelogram ABCD, which of the following statements about its angles must be correct?
O It has two pairs of complementary angles.
O It has two pairs of supplementary angles.
O
All of its angles are acute.
O The sum of the measures of its angles is 180°.
Answer:
the sum of the measures of it's angles is 180
pls solve...I will mark as BRAINLIST
Answer:
Here you go with your answer
Mark me as brainlist may your parents live long life
y=-6x-7 7x+y=-3 substitution
By substitution; x = 4 and y = -31
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. Equations can be solved to find the value of an unknown variable representing an unknown quantity.
y=-6x-7 --- 1
7x+y=-3 --- 2
Substituting y as 6x - 7 in equation 2
7x + (-6x - 7) = -3
7x - 6x - 7 = -3
x - 7 = -3
x = -3 + 7
x = 4
Substitute x as 4 in equation 1
y = -6x - 7
y = -6(4) - 7
y = -24 - 7
y = -31
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what is the difference of the fractions? 5/6 - 4/6
Answer
\(--------------------------------------------\)
\(\frac{5}{6}-\frac{4}{6}\) = \(\frac{1}{6}\)
\(0.8333333333\) - \(0.6666666667\) = \(0.1666666666\)
\(\frac{1}{6}\) = \(0.1666666666\)
\(It's\) \(\frac{1}{6}\) \(because\) \(5-4\) = \(1\)
\(and\) \(the\) \(denominator\) \(is\) \(the\) \(same.\)
\(So\), \(it's\) \(\frac{1}{6}\)
\(--------------------------------------------\)
Hope this helps! <3
\(--------------------------------------------\)
NEED HELP QUICK!!! Ron is trying to find the LCM of 4 and 6. His work is shown at the right. What is Ron's mistake? Explain how to find the correct LCM of 4 and 6.
The LCM of 4 and 6 is 12.
What is Least Common Multiple?Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.
For example, common multiples of 4 and 6 are 12, 24 and 36, but the lowest of those is 12; therefore, the lowest common multiple of 4 and 6 is 12.
Given:
4: 2 x 2
6: 2 x 3
Now, as there is one 2 common in both then it will be written for one time.
and the rest uncommon numbers are written as same as well.
So, LCM( 4, 6)= 2 x 2 x 3 = 12
Hence, the LCM of 4 and 6 is 12.
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Help ASAP fist correct answer get Brainly answer
Multiply -3 2/3• (-2 1/4)
Answer:
8 1/4.
Step-by-step explanation:
B 9.407
9.407
9.470
80
60
14. The number of hours in 80 minutes is
Select all that apply.
Which of these statements is true
The number of hours in decimal form is 1.3.
The amount of time is a full hour and į hour.
The number of hours is a terminating decimal.
The number of hours is between 1 and 1.35.
Dividing 6 by 8 will give the correct decimal value.
Answer:
The number of hours is between 1 and 1.35.The amount of time is a full hour and 1/3 hour.Step-by-step explanation:
14. The number of hours in 80 minutes is ...
(80 min)/(60 min/h) = 80/60 h = 4/3 h = 1.33333...(repeating) h
Of the offered statements, we know one is true. (Another may be, depending.)
The number of hours is between 1 and 1.35.__
Comment on other answer choices
We don't know what į is supposed to mean. If it means 1/3, then this statement is true, too.
The amount of time is a full hour and 1/3 hour.Find the value of x.
Answer:
x = 82
Step-by-step explanation:
The sum of the interior angles of a polygon with n sides = (n-2) x 180°
This polygon has 7 sides so the sum of its interior angles
= (7-2) x 180°
= 5 x 180°
= 900°
Adding up the given angles we get
x + 160 + 2x + 125 + 110 + 112 + 147 = 900
3x + 654 = 900
3x = 900 - 654
3x = 246
x = 246/3 = 82
Answer:
x = 82
Step-by-step explanation:
Sum of interior angles of a polygon
\(S=(n-2) \times 180^{\circ}\)
where n is the number of sides.
The given polygon has 7 sides:
n = 7To find the value of x, substitute the sum of the interior angles and the found value of n into the formula and solve for x:
\(\implies x+160+2x+125+110+112+145=(7-2)\times 180\)
\(\implies x+2x+160+125+110+112+145=5\times 180\)
\(\implies 3x+654=900\)
\(\implies 3x+654-654=900-654\)
\(\implies 3x=246\)
\(\implies \dfrac{3x}{3}=\dfrac{246}{3}\)
\(\implies x=82\)
Therefore, the value of x is 82.
jane needs $20 to buy a radio. she already saved $15. what percent of the cost of the radio has she already saved
Answer:
75%
Step-by-step explanation:
20x5=100 and 15x5=75 and 75/100 =75%
Answer:
75%
Step-by-step explanation:
1. Find extrema and intervals of increasing and decreasing the function
\(y = \frac{ {e }^ { - (x + 2)} }{x + 2} \)
2. Find inflection points and intervals of concavity and convexity of the function:
\(y = \frac{2x - 1}{(x - 1) ^{2} } \)
The function y = (e⁻⁽ˣ⁺²⁾) / x + 2 increases along intervals of (-∞, 3) and decreases along (-3, -2), (-2, ∞) and the function y = 2x - 1 / (x - 1)² has no inflection points but concave downwards along (-∞, 1) ∪ (1 ,∞)
Extrema and Intervals of a FunctionAn extremum (or extreme value) of a function is a point at which a maximum or minimum value of the function is obtained in some interval. A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.
The function given;
y = (e⁻⁽ˣ⁺²⁾) / x + 2
The extrema and intervals of increase or decrease of this function are
(-1, 1.63) and it increases along (-∞, 3) and decreases along (-3, -2), (-2, ∞)
2. The inflection points and intervals of concavity and convexity of the function
y = 2x - 1 / (x - 1)² are
The function has no inflection pointsIt's concave downwards along (-∞, 1) ∪ (1 ,∞)Learn more on intervals of a function here;
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store has m tanks of fish. Each tank has 39 fish. Using m, write an expression for the total number of fish in the store.
Answer:
39m is the expression as 39 x m = no of fish.
Step-by-step explanation:
If you was asked to turn it into a function
then you could call no of fish n
so that 6n( m + n) + 4 = no of fish.
Which is the graph of f(x) = 3/7?
Answer:
Rewrite the function as an equation. y= 3/7 Use the slope-intercept form to find the slope and y-intercept. Slope: 0 Y-intercept: 3/7 Hope this can help
Step-by-step explanation:
What is the Coefficient of 10x²
\(10 \: is \: the \: coefficient \: \)
How do i graph this?
x: 0,1 y: 8,6 slope-2 y intercept: (0,8)
There are 67 questions on an exam. If you miss 8 of these questions your grade is _______ %.
Answer:
88%
Step-by-step explanation:
There are 67 questions on an exam
You miss 8 questions
The first step is to calculate the number of correct questions
= 67-8
= 59
Therefore the grade can be calculated as follows
= 59/67 × 100
= 0.880 × 100
= 88%
Hence the grade is 88%
Show me how to work this out please
Answer:
it's A
Step-by-step explanation:
the reason why it's A is that X can not have to repeating numbers