Find the equation of tangent and normal line to the given curves...
1.) y = x^3 - 7x + 6 at its points of intersection with the x-axis.
...?
In desperate need of help with long division with variables and exponents!!!
Write the expression as either the sine, cosine, or tangent of a single angle.
sin 48° cos 15° - cos 48° sin 15°
A. cos 33°
B. cos 63°
C. sin 63°
D. sin 33°
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
sin 48° cos 15° - cos 48° sin 15°
As we know that,
[tex]\sin A\cos B-\cos A\sin B=\sin(A-B)[/tex]
So, we get that
[tex]A=48\textdegree\\B=15\textdegree[/tex]
Now, put it in the above expression.
[tex]\sin (A-B)=\sin(48-15)=\sin 33\textdegree[/tex]
Hence, Option 'D' is correct.
What is the value of x in the equation 2(6x+4)-6+2x+3(4x+3)+1
Answer: the answer you will get is 4
Step-by-step explanation:
3x + 2y = 2
-2x + y = 8
Solve the system of equations.
Answer:
A: (-2,4)
Step-by-step explanation:
i did it on usatestprep
The domain of the following relation: R: {(−4, 3), (3, 6), (−2, 1), (3, 6)} is
1, 3, 6}.
{–4, 3, −2, 3}.
{–4, −2, 3}.
No domain exists.
...?
The domain of the given relation includes the set of all x-values in the relation, which is: {–4, −2, 3}.
What is the Domain of a Relation?The domain of a relation is the set of all possible x-values (input), while the y-values are the range.
Given the relation, {(−4, 3), (3, 6), (−2, 1), (3, 6)}:
Domain of the relation is: {–4, −2, 3}.
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What is the 12th term in the sequence?
Note: Use the explicit rule.
an=−16+2n
Enter your answer in the box.
What is the 12th term in the sequence?
an=−16+2n
n =term
n=12
Sub n=12
a(12)=-16+2(12)
a(12)=-16+24
a(12)=8
A local hamburger shop sold a combined total of 510 hamburgers and cheeseburgers on Saturday. There were 60 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?
On Saturday, 285 hamburgers were sold.
What is the system of equation?A simultaneous equation is anyone or more equations that can have the same number of unknowns and be solved concurrently. And an equation system is a simultaneous equation.
Given, a local hamburger shop sold a combined total of 510 hamburgers and cheeseburgers on Saturday.
Let x represents the number of hamburgers sold and y represents the number of cheeseburgers sold.
So, x + y = 510 {equation 1}
According to the question,
there were 60 more cheeseburgers sold than hamburgers.
x = y+ 60
We have a system of equations,
Substituting the value of x to the equation 1,
y+60+ y = 510
2y = 510 - 60
y = 450 / 2
y = 225
Then, x = 285
Therefore, 285 hamburgers were sold on Saturday.
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The list of a certain tool is x dollars. In store A the original selling price of the tool was $50 less than the list price, and the current selling price is 10% less than the original selling price. In store B the original selling price of the tool was 10% less than the list price, and the current selling price is $50 less than the original selling price.
A) Quality A is greater
B) Quality B is greater
C) The two quantities are equal
To compare the selling prices in store A and store B for the tool described:
Let's denote the list price of the tool as x dollars.
In Store A:
- Original selling price = List price - $50
- Current selling price = 90% of the original selling price
In Store B:
- Original selling price = 90% of the list price
- Current selling price = Original selling price - $50
Now, we can calculate the selling prices for both stores and compare:
For Store A:
Original selling price in Store A = x - 50
Current selling price in Store A = 0.9(x - 50)
For Store B:
Original selling price in Store B = 0.9x
Current selling price in Store B = 0.9x - 50
To determine which quantity is greater, we need to compare the expressions for the current selling prices in both stores. We will simplify the expressions to make the comparison easier.
Store A:
0.9(x - 50) = 0.9x - 45
Store B:
0.9x - 50
Comparing the simplified expressions, we see that:
0.9x - 45 is greater than 0.9x - 50
Therefore, Store A has a greater current selling price for the tool compared to Store B.
So, the correct answer is:
A) Quality A is greater.
Which expression is a factor of 2xy + 6x – 3y – 9?
2x – 3
2y + 3
x – 2
y – 3
...?
Answer:
(2x-3) is the answer.
Step-by-step explanation:
The given expression is :
[tex]2xy+6x-3y-9[/tex]
Grouping these terms we get-
[tex]2x(y+3)-3(y+3)[/tex]
So, the factors are :
[tex](2x-3)(y+3)[/tex]
Hence, out of the given options (2x-3) is the answer.
And he other factor is (y+3) that is not mentioned in the options.
Final answer:
The factor of the expression 2xy + 6x - 3y - 9 is 2x - 3, which is found by factoring the expression by grouping.
Explanation:
The expression given is 2xy + 6x − 3y − 9. To determine which expression is a factor of it, we can attempt factoring by grouping. Grouping the terms as (2xy + 6x) and (− 3y − 9) and factoring out the common factors from each group gives us:
2x(y + 3)−3(y + 3)We can see that (y + 3) is a common factor between the two groups. Factoring this out, we get:
(2x − 3)(y + 3)
This shows that 2x − 3 is a factor of the given expression.
x ^{sqrt{logx}}=10^{8} ...?
find the width, ans height and area of 26'' TV screen that has an aspect ratio of 4:3. round to the nearest whole number.
erform a simple calculation to match the screen size of a standard TV to that of a widescreen TV. If you currently have a 4:3 TV and you want to continue watching 4:3 on a widescreen TV, multiply the diagonal length of the older TV model by 1.22. The result would be the diagonal screen size that the widescreen TV would have to be to match the old model.
Say you have a 40 inch (102 cm) TV with a 4:3 aspect ratio, but you're thinking about upgrading and you don't want your screen size to get smaller. You'd need to get at least a 50 inch (127 cm) screen to view in 4:3 without your picture getting smaller. That's because 1.22 x 40 = 49. Since 49 inch TVs are generally not made, you'd need to go up to 50 inches (127 cm).A movie ticket costs $9.75. two years ago, a movie ticket cost $7.50. by how many dollars has the price of a movie ticket increased?
a. $17.25
b. $16.75
c. $2.75
d. $2.25
16 more than eight of a certain number is twenty four more than 6 times of thatnumber.
Vanessa has scored 45, 32, and 37 on her three math quizzes. She will take one more quiz and wants a quiz average of at least 40. What is the minimum score Vanessa needs to earn on her fourth quiz?
Answer:
46
Step-by-step explanation:
A right prism has a base in the shape of an octagon. The side length of the octagon is 4 inches. The length of the apothem is 4.83 inches. The height of the prism is 12 inches. What is the volume of the prism? Round your answer to the nearest whole number.
cubic inches
The volume of the prism is 927 cubic Inches.
What is Volume?This is defined as the measure of how much space there is within a three-dimensional object.
Area of Octagon A = 1/2 x apothem x perimeter
A= 1/2 x 4.83 x 4(8) = 77.28
Volume = Area of the base × height
= 77.28 x 12 = 927 cubic inches.
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Y=mx 6. can you solve for m
The value of 'm' in the equation y=mx represents the slope of the line. However, without specific 'x' or 'y' values or a complete equation like y=mx+b, it is impossible to determine the value of 'm'.
Explanation:The formula y=mx is the slope-intercept form of a linear equation where y is the dependent variable, m is the slope, and x is the independent variable. However, in this particular case, the equation provided is not complete in this form because there is no specific 'x' or 'y' value provided, and so it's not possible to calculate 'm' directly from this equation. Instead, in a more complete example, like y = 3x, you could identify 'm' as 3 by simply looking at the coefficient of 'x'. In order to clarify your equation, please provide either specific values of 'x' and 'y', or a complete equation in the format y = mx + b, where b is the y-intercept.
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Convert 1.835 × 10−4 to standard notation.
calculate the length of the line segment Round answer to the nearest tenth.
The graph shows the mass of a radioactive substance as a function of time.
Enter the initial mass of the substance in the box
?? = g
At 6:00 a.m., the outside temperature was –14.4⁰. By noon, the outside temperature had dropped 8.1⁰. What was the outside temperature at noon? 6.3⁰ –6.3⁰ 22.5⁰ –22.5⁰
Simplify: 4xy + 3x2y - 5xy - 8xy
The sum of two positive integers, a and b, is at least 30. The difference of the two integers is at least 10. If b is the greater integer, which system of inequalities could represent the values of a and b?
A. a + b ≥ 30 b ≥ a + 10
B.a + b ≥ 30 b ≤ a – 10
c. a + b ≤ 30 b ≥ a + 10
D. a + b ≤ 30 b ≤ a – 10
Option A, with inequalities a + b ≥ 30 and b ≥ a + 10, correctly describes these conditions.
We are given that the sum of two positive integers, a and b, where b is greater, is at least 30, which can be represented as a + b ≥ 30.
The difference between the two integers is also at least 10, and since b is the greater integer, this relationship is given by b - a ≥ 10.
The correct system of inequalities that represents these conditions is Option A:
a + b ≥ 30
b ≥ a + 10
Option B is incorrect because it suggests b is less than or equal to a - 10, which doesn't make sense in this context since b is the greater integer.
Options C and D are incorrect because they suggest that the sum of a and b is less than or equal to 30, which contradicts the given that the sum is at least 30.
If carmen ran 2 miles and melanie ran 4 miles, who ran farther?
Bonds issued by Raxin Accounting have a total yield of 11.4% annually, while Raxin Accounting stocks have a total yield of 14.4% annually. If you invest $2,600 in Raxin Accounting bonds and $2,000 in Raxin Accounting stocks, which investment will have a greater return after nine years, and how much greater will it be
Answer:
A. in edge
Step-by-step explanation:
$75.69
Final answer:
After nine years, investing $2,600 in Raxin Accounting bonds will yield a greater return than investing $2,000 in their stocks, specifically $579.30 more due to the effect of compound interest.
Explanation:
If you invest $2,600 in Raxin Accounting bonds with a total yield of 11.4% annually and $2,000 in Raxin Accounting stocks with a total yield of 14.4% annually, we can calculate the future value of both investments after nine years using the formula for compound interest: Future Value = Principal × (1 + rate)^time.
For bonds: Future Value = $2,600 × (1 + 0.114)^9 = $2,600 × 2.7845 = $7,239.70
For stocks: Future Value = $2,000 × (1 + 0.144)^9 = $2,000 × 3.3302 = $6,660.40
Comparing the future values, the investment in Raxin Accounting bonds will yield a greater return after nine years, specifically $579.30 more than the investment in stocks.
The function for the cost of materials to make a hat is f(x) = one half x + 1, where x is the number of hats. The function for the selling price of those hats is g(f(x)), where g(x) = x + 2. Find the selling price of 10 hats. A. 6 b. 8 c. 10 d. 12
The selling price for 10 hats, calculated by applying the cost function f(x) to find the cost and then the selling price function g(x), is $8.
Explanation:The selling price of 10 hats can be found by first calculating the cost of materials to make those hats using the function f(x) = 0.5x + 1, and then applying the g(f(x)) function to find the selling price, where g(x) = x + 2.
First, we calculate the cost for making 10 hats:
f(10) = 0.5 imes 10 + 1 = 5 + 1 = 6.
Now, we use the selling price function g to calculate the selling price for 10 hats:
g(f(10)) = g(6) = 6 + 2 = 8.
Therefore, the selling price for 10 hats is $8.
how was percent used to solve real-world problems
show that the following set of functions are subspaces of F(-infinity,infinity)
a) all everywhere differentiable function that satisfy f'+2f=0 ...?
To show that the set of functions satisfying f' + 2f = 0 is a subspace of F(-∞,∞), we prove closure under addition and scalar multiplication.
Differentiable functions: To prove that the set of functions satisfying f' + 2f = 0 is a subspace of F(-∞,∞), we need to show that the set is closed under addition and scalar multiplication. This involves demonstrating that if two functions f1 and f2 satisfy the given differential equation, then any linear combination c1f1 + c2f2 also satisfies it.
Proof:
Let f1, f2 be solutions of f' + 2f = 0, then (c1f1 + c2f2)' + 2(c1f1 + c2f2) = c1(f1' + 2f1) + c2(f2' + 2f2) = c1(0) + c2(0) = 0. Therefore, any linear combination of solutions is also a solution.
Whats the value of 6 5 x 22 - 9 ÷ 3?
I'm studying for a test, and I can't seem to remember how to find missing coordinates. Here's one example of the question,
Fill in the other coordinate for the line 3x-5y=2 (2,) I need to find Y. I thought that my answer was 4/5 (4over5) I did, 3 times 2, (6) -6 on both sides, so then I had -5y = -4. So I divided both by 5. . . But that doesn't sound right to me! Anyone know what I'm doing wrong? Or right? Thanks!
Here's another one by the way . . Y = 3x + 2 (1,)