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Related Questions
Find an equation of the normal line to the parabola y = x2 â 9x + 7 that is parallel to the line x â 7y = 2.
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I'm taking the liberty of correcting your input: "Find an equation of the normal line to the parabola y = x2 â 9x + 7 that is parallel to the line x â 7y = 2." may be:
Find an equation of the normal line to the parabola y = x^2 - 9x + 7 that is parallel to the line x - 7y = 2.
How do you find the slope of a normal line to the graph of a given quadratic? Differentiate y = x^2 - 9x + 7: dy/dx = 2x - 9
You can see that this slope varies with x. You have not named an x-value here, so I will have to stop at dy/dx = 2x - 9.
The slope of a line perpendicular to the tangent line is the negative reciprocal of the slope of the tangent line, or
-1
------- which obviously depends upon the x value you choose or are given.
(2x)
Now focus on the given line x - 7y = 2. Solving for y, 7y =x-2. The slope of this line is (1/7). Thus,
-1 1
--------- = ---------- Cross-multiplying, -7 = 2x; x = -3.5
2x 7
So it appears we DO have the x-value at the point of tangency on the curve.
Find the associated y-value by subst. x = -3.5 into the eq'n of the parabola.
Call it Y.
Then the eq'n of the normal line to the parabola that is parallel to x - 7y = 2
is y-Y = (1/7)(x-[-3.5])
The normal line to the parabola y = x^2 - 9x + 7 that is parallel to the line x - 7y = 2 is y = -7x + 65, which was determined by finding the normal slope and point of tangency using the derivative.
Explanation:In mathematics, the normal line to a curve at a particular point is the line that is perpendicular to the tangent of the curve at that point. First, it's important to establish that any line parallel to x - 7y = 2 would have the same slope, which in this case is 1/7. To find the normal line, we need a line that is perpendicular to this -- hence, it would have a slope of -7.
Now, to find the point of tangency, you must take the derivative of y = x^2 - 9x + 7, making it 2x - 9. Set this equal to -7 (the slope of the normal line) and solve for x, which comes out to be 8. Substituting x = 8 back into our parabola equation gives us y = -9. Therefore, our point of tangency is (8, -9).
Finally, using the point-slope form of a line formula, we can find our equation of the normal line, which is y - (-9) = -7*(x - 8), simplifying to y = -7x + 65.
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3/4xy What are the factors of the expression?
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The factors of the given expressions are [tex]\dfrac{3}{4},x,y[/tex].
Given:
The given expression is [tex]\dfrac{3}{4}xy[/tex].
To find:
The factors of the given expression.
Explanation:
Factors of an expression are the terms or expressions whose product is equal to that expression.
We have,
[tex]\dfrac{3}{4}xy[/tex]
Therefore, the factors of the given expressions are [tex]\dfrac{3}{4},x,y[/tex].
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Which of the following represents the zeros of the function
g(x) = x3 - 9x2 + 2x + 48 ?
A. x= -8, x= 2 , and x= -3
B. x = 8, x = -2 , and x = 3
C. x = 6, x = -4 , and x = 9
D. x = -6, x = 4 , and x = -9
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Probe some roots. When you use x = - 2
you will have: (-2)^3 - 9(-2)^2 + 2(-2) + 48 = -8 - 36 - 4 + 48 = 0
So, - 2 is a root
From that you can divide x^3 - 9x^2 + 2x + 48 by x + 2 and you will get
x^2 - 11x + 24
Then you can factor that: (x - 8)(x - 3)
So, the three roots are x = - 2, x = 3 and x = 8, which is the option B.
Answer: option B. x = 8, x = -2 , and x = 3
Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, two green ones, four white ones, and three purple ones. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.] She does not have all the green ones.
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Explanation of calculating the probability of choosing 3 green marbles out of 10 from a bag with 50 marbles.
Explanation:
The probability of choosing exactly 3 green marbles if a total of 10 marbles are selected from a bag filled with 50 marbles, 15 of which are green, can be calculated as follows:
Calculate the total number of ways to choose 3 green marbles out of 15: C(15, 3).Calculate the total number of ways to choose 7 non-green marbles out of 35: C(35, 7).Find the total number of ways to choose 10 marbles out of 50: C(50, 10).Calculate the probability by dividing the product of the above two calculations by the total ways to choose 10 marbles.what is the equation of the line graph shown? (-2,-3), (3, -3)
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Which of the following expressions is in simplified form?
1n + 2.9n
4w - 5
-2 + 1.4m + 0.5
9j - 3 - j
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I believe the answer is B. 4w - 5, because B is the most short (or simplified) of all the rest..
Hope this helps! ☺♥
Toby, a toy store buyer, ordered 2 gross rubber spiders, 60 teddy bears, and 5 dozen video games. The spiders cost 7 cents each, the bears cost 59.76 dollars per dozen, and the video games were on sale for a special price—12 for 156 dollars. What was the total cost of Toby’s order, in dollars?
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7 × 2 gross (1 gross = 144 units)
7 cents x 288 = 2016 cents = $20.16
Total cost of teddy bear:
59.76 x (60÷12) (1 dozen = 12 units)
59.76 x 5 = $298.80
Total cost of video games:
156 x 5 = $780.00
Total spent:
780 + 298.80 + 20.16 = $1098.96
If the equation were y=40x+70.What would the x-intercept be? Plz...Help!?!
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[tex]( - \frac{7}{4} .0)[/tex]
the period is a comma
brainleiest!!! What is the unit rate for 4543.08 km in 52.4 h? Enter your answer, as a decimal, in the box. km/h
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(4543.08) / (52.4) = 86.7 km per hour
Answer:
86.7
Step-by-step explanation:
you divide 4543.08 by 52.4
Assume that you select two 3-digit numbers at random from the set of consecutive integers from 000 through 999. The selections are made with replacement and are independent of one another. If the two numbers are the same, you make $700. If they are different, you lose $2. A random variable XX is defined as your gain or loss.
How many different values are possible for the random variable XX
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Answer:
the answer is: 2
Step-by-step explanation:
from 000 to 999 makes a total of 1000 numbers from which we are selecting two numbers with replacement. This means that the possible combinations will be double of 1000.
1000 * 1000 = 1000000
to have the same number twice means that the possible combinations will be only 1000. (As there are only 1000 numbers).
But whether they are same or not there will be only two possible values of XX , 2 dollars or 700 dollars which will be the loss or gain for one trial, as the numbers picked will either be same or different.
Owl can clean piglets house in 25 minutes. eeyore can clean piglets house in 40 minutes. how long will it take owl and eeyore to do the job if they work together?
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Let us say that the task of cleaning the house is equal to 1 job. Therefore the rates are:
rate of Owl = 1 job / 25 minutes
rate of eeyore = 1 job / 40 minutes
So working together, the time is:
(1 / 25) + (1 / 40) = 1 / t
0.065 = 1 / t
t = 15.38 minutes
So it takes about 15.38 minutes working together.
Tuiton at a certain college recently increased from $4000 to $5000. Find the ratio of the increase in price to the original price.
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$1000
-------- = 1/4 (no units of measurement here)
$4000
For homework, a student had to complete 54 problems total. If she finished 9 problems in class, what is the ratio of problems she still needs to complete the problems that she already finished?
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Answer:
29
Step-by-step explanation:
f(x) = x2 + 5x – 1 is shifted 3 units left. The result is g(x). What is g(x)?
A. g(x) = (x – 3)2 + 5(x – 3) – 1
B. g(x) = x2 + 5x + 2
C. g(x) = (x + 3)2 + 5x – 1
D. g(x) = (x + 3)2 + 5(x + 3) – 1
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Answer:
g(x) = (x+3)² + 5(x+3) – 1.
Step-by-step explanation:
Given : f(x) = x² + 5x – 1 is shifted 3 units left.
To find : The result is g(x). What is g(x).
Solution : We have given that
f(x) = x² + 5x – 1 is shifted 3 units left.
By the transformation rule : If f(x) →→ f(x +h) shifted by h unit left .
f(x) = x² + 5x – 1 is shifted 3 units left.
Here , h = 3
Then g(x) = (x+3)² + 5(x+3) – 1.
Therefore, g(x) = (x+3)² + 5(x+3) – 1.
Find the minimum and maximum values of the function subject to the given constraint. (if an answer does not exist, enter dne.) f(x, y) = x2y + x + y, xy = 5
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[tex]L(x,y,\lambd)=x^2y+x+y+\lambda(xy-5)[/tex]
[tex]L_x=2xy+1+\lambda y=0[/tex]
[tex]L_y=x^2+1+\lambda x=0[/tex]
[tex]L_\lambda=xy-5=0[/tex]
[tex]\underbrace{10}_{2xy}+1+\lambda y=0\implies \lambda=-\dfrac{11}y[/tex]
[tex]xy=5\implies y=\dfrac5x\implies\lambda=-\dfrac{11}5x[/tex]
[tex]\impliesx^2+1+\left(-\dfrac{11}5x\right)x=0\implies x^2=\dfrac56\implies x=\pm\sqrt{\dfrac56}[/tex]
[tex]xy=5\implies y=\pm\sqrt{30}[/tex]
At these points, we get local minima of [tex]f\left(\pm\sqrt{\dfrac56},\pm\sqrt{30}\right)=\pm2\sqrt{30}[/tex].
- - -
Another way to do this is to make [tex]f(x,y)[/tex] a function independent of [tex]y[/tex], which is made possible by the constraint.
[tex]xy=5\implies y=\dfrac5x[/tex]
[tex]\implies f(x,y)=f\left(x,\dfrac5x\right)=F(x)=6x+\dfrac5x[/tex]
[tex]\implies F'(x)=6-\dfrac5{x^2}=0\implies x=\pm\sqrt{\dfrac56}[/tex]
and so on.
what is scatterplot ?
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A scatter plot is a graph in which the data is plotted on a coordinate grid. The horizontal axis will be the x-axis and the vertical axis will be the y-axis.
A music school has budgeted to purchase 3 musical instruments. they plan to purchase a piano costing $4,000, a guitar costing $600, and a drum set costing $750. the mean cost for a piano is $5,000 with a standard deviation of $2,000. the mean cost for a guitar is $550 with a standard deviation of $250. the mean cost for drums is $950 with a standard deviation of $100. (enter your answers to two decimal places.) how many standard deviations above or below the average piano cost is the piano
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To solve this, we can use the z statistic. The formula for z score is given as:
z = (x – u) / s
where x is the actual cost = 4000, u is the mean cost = 5000, and s is the standard deviation = 2000
Solving for z:
z = (4000 – 5000) / 2000
z = - 0.5
Therefore the piano cost is only 0.5 standard deviations below the average cost.
An indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumping it on the people below. One buckets dumps water every 18 min. The other buckets dumps water every 21min. It is currently 1:15 p.m. and both buckets dumped water 5 minutes ago. Find the next two times that both buckets dump water at the same time
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126 minutes is equal to 2 hours and 6 minutes.
(1) Time 1:
1:10 pm + 2:06 = 3:16 pm
(2) Time 2:
3:16 pm + 2:06 = 5:22 pm
E xex2 + y2 + z2 dv, where e is the portion of the unit ball x2 + y2 + z2 ≤ 1 that lies in the first octant.
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[tex]=\displaystyle\int_{\varphi=0}^{\varphi=\pi/2}\int_{\theta=0}^{\theta=\pi/2}\int_{\rho=0}^{\rho=1}\rho\cos\theta\sin\varphi e^{\rho^2}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]
[tex]=\displaystyle\left(\int_{\rho=0}^{\rho=1}\rho^3e^{\rho^2}\,\mathrm d\rho\right)\left(\int_{\theta=0}^{\theta=\pi/2}\cos\theta\,\mathrm d\theta\right)\left(\int_{\varphi=0}^{\varphi=\pi/2}\sin^2\varphi\,\mathrm d\varphi\right)=\frac\pi8[/tex]
The question is asking to evaluate the triple integral of a function over a portion of the unit sphere lying in the first octant. It involves the use of multivariable calculus and spherical coordinates
Explanation:This question is asking to evaluate the triple integral of E xex2 + y2 + z2 dv over the region e, which is the section of the unit sphere x2 + y2 + z2 ≤ 1 within the first octant. Here, dV is the differential volume element, and x, y, and z are the Cartesian coordinates. As the first octant is defined by x ≥ 0, y ≥ 0, and z ≥ 0, we will only need to consider positive values for these variables.
To evaluate the integral, the formula for the volume of the unit sphere in three dimensions x2 + y2 + z2 should be used. Furthermore, as the integral is taken over the first octant, each variable would be bound between 0 and 1.
It is important to note that this is a multivariable calculus problem and involves the concept of integration in spherical coordinates. This topic is typically covered in a college-level calculus course.
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find the measure of each marked angle (2x-21) and (x+3)
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A recipe calls for 1 1/2 cups of flour, 3/4 cup of white sugar, and 1/3 cup of brown sugar. The recipe makes 6 servings.
How many cups of flour are there per serving? Show your work.
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How many total cups of sugar (white and brown) are there per serving? Show your work.
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Suppose you modify the recipe so that it makes 9 servings. How much more flour do you need for the modified recipe than you need for the original recipe? Show your work.
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Answer all 3 questions.
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How many cups of flour are there per serving? Show your work.
1 1/2 = 3/2
3/2 x 1/6 = 3/12 = 1/4
answer 1/4 cup of flour per serving
How many total cups of sugar (white and brown) are there per serving? Show your work.
sugar = 3/4 +1/3 = 9/12 + 4/12 = 13/12 (6 servings)
1 serving = 13/12 x 1/6 = 13/72
answer
13/72 sugar (white and brown) per serving
Suppose you modify the recipe so that it makes 9 servings.
1/4 cup of flour per serving
so
9 x 1/4 = 9/4 = 2 1/4
answer
2 1/4 cups of flour for 9 servings
Benny wants to put a rectangular fence in his yard, and he wants the length of the fence to be 5 less feet than twice its width. He also found that every foot of fencing will cost $3.16. The total cost of the fence is C = 3.16(6w - 10), where w is the width of the fence. What does 6w - 10 represent?
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At the corner store, Nico bought 5 pencils for $0.10 each and 3 pens for $0.50 each. He used t to represent the sales tax, in dollars, that he also paid. He paid a total of $2.12, including tax.
Nico wrote this equation to represent what he paid. What errors, if any, did he make?
5(0.10) + 3(0.50) - t = 2.12
He should have multiplied 0.10 by 3 instead of 5.
He should have multiplied 0.50 by 5 instead of 3.
He should have added t instead of subtracting t.
He should have multiplied by t instead of subtracting t.
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Answer:
C. He should have added t instead of subtracting t.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
A line has a slope of -2/3 and a y-intercept of (0, 3). What is the value of y when x = 4?
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ahemmm so, we know the slope, and we also know the y-intercept, thus the equation of that line is
[tex]\bf y=\stackrel{slope}{-\cfrac{2}{3}}x\stackrel{y-intercept}{+3} \\\\\\ \textit{when x = 4, what is \underline{y}?}\qquad y=-\cfrac{2}{3}(4)+3\implies y=-\cfrac{8}{3}+3 \\\\\\ y=\cfrac{-8+9}{3}\implies y=\cfrac{1}{3}[/tex]
What is 0.3 * 1.3 = ?
Please help me!
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Hope this helps!
Since the ratios for sides of triangles are the same, when the angles are the same, ? have been developed which show these ratios for every angle encountered in a triangle. select one:
a. cos tables
b. sin tables
c. tan tables
d. trigonometric tables
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Answer: d. trigonometric tables
Step-by-step explanation:
A trigonometric table would provide all of the ratios of the sides in respect to the angles. Sin, cos, and tan are parts of trigonometric table.
Trigonometry table, tabulated values for some or all of the six trigonometric functions for various angular values.
Since the ratios for sides of triangles are the same, when the angles are the same, trigonometric tables have been developed which show these ratios for every angle encountered in a triangle.
Each class at briarwood elementary collected at least 54 cans of food lduring the food drive.If tbere are 29 clases in the school what was the least numbet of cans collected?
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For each class → x ≥ 54
Full School → x ≥ 54(29)
If we simplify the second inequality, we get this:
x ≥ 1566
The answer to your query is x ≥ 1566. Hope this helps and have a fantastic day!
Evaluate 3 to the power of 3 + 6 (2 + 3/6)
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Thus, 3 + 6(2 + 3/6) = 3 + 6 (15/6)
= 3 + 15 = 18.
Then: 3^18 is the answer. You could expand this if you wanted, but what would be the point of that?
last week, several gas stations in a neighborhood all charged the same price for a gallon of gas.The table below shows how much gas prices have changed from last week to this week.
a. Order the numbers in the table from least to greatest.
b. Which gas station has the cheapest gas this week?
c. Critical Thinking. Which gas station changed their price the least this week?
Gas and Samson. Star
Go. Gas. Gas
-6.6. 5.8. -6 3/4
Corner store. tip top
27/5. shop
-5 5/8
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–6 3/4 = –6.75
27/5 = 5.4
–5 5/8 = –5.625
Now that the numbers are –6.6, 5.8, –6.75, 5.4 and –5.625.
a) A negative number is always less than a positive number. In addition, a negative with a larger magnitude would be less. Like –4 < –3. So the order from least to greatest is –6.75 < –6.6 < –5.625 < 5.4 < 5.8. In other words, –6 3/4 < –6.6 < –5 5/8 < 27/5 < 5.8.
b) A negative change means that the gas price decreased. The gas station that decreased the gas price the most is the Star gas since the –6 3/4 is the least number in the list.
c) The changes in prices can be compared in relation to each other based on their magnitude, which is the value without the sign. For example, the magnitude of –4 is 4. The magnitudes of the changes in prices are 6.6, 5.8, 6.75, 5.4 and 5.625. So the least change is 5.4, that is, 27/5. So the Corner Store changed the price the least.
Without the correctly formatted data, we cannot give direct answers. However, the answers would come from ordering the data from least to greatest, identifying the least positive or most negative change as the cheapest gas, and the smallest change as the least change in price.
Explanation:Unfortunately, the question you provided is a bit unclear because the table is not formatted correctly. However, it's clear that you're asked to analyze a set of data, which refers to changes in gas prices at several gas stations. Usually, to order the numbers from least to greatest, you would list them in ascending numerical order, taking into account whether they are positive or negative, with negative numbers being less than positive numbers. The gas station with the cheapest gas this week would be the one with the least positive change or the greatest negative change. The gas station that changed their price the least would be the gas station with the smallest change in price, whether positive or negative. However, without the correct formatting of data, I am unable to provide specific answers. It's always important to check your data for clarity in order to perform accurate mathematical analyses. These principles of data analysis and number order are crucial skills in your mathematical education.
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the volume of 10000 drops of liquid is 100 fluid ounces. what is the volume of 10 drops?
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Answer:
0.1 fluid ounces
Step-by-step explanation:
If 10000 drops lof liquid is 100 fluid ounces we can determine the drops of liquid per fluid ounces by dividing the two values:
[tex]100/10000=0.01[/tex]
Therefore 0.01 fluid ounces is equivalent to 1 drop. We have our conversion factor now we can determine the volume by multiplying the conversion factor by the number of drops:
[tex]0.01*10=0.1[/tex]
10 drops is 0.1 fluid ounces