Answer:
The parabola [tex]y=x^{2}[/tex] at the points [tex](-2+\sqrt{17},21-4\sqrt{17})[/tex] and [tex](-2-\sqrt{17},21+4\sqrt{17})[/tex] when [tex]t=t_{1}=-4+\sqrt{17}[/tex] and [tex]t=t_{2}=-4-\sqrt{17}[/tex]
Step-by-step explanation:
We have the following line written in parametric form :
[tex]L(t)=(2+t,5-4t)[/tex] with [tex]t[/tex] ∈ IR.
In order to find the intersection between [tex]L(t)[/tex] and the parabola [tex]y=x^{2}[/tex] we know that ''[tex]2+t[/tex]'' is the x-coordinate of the line and ''[tex]5-4t[/tex]'' is the y-coordinate of the line. Now, to solve this problem we need to find the values of ''[tex]t[/tex]'' in which the intersection occurs. We can do this by replacing the components ''[tex]x[/tex]'' and ''[tex]y[/tex]'' of [tex]L(t)[/tex] in the equation of the parabola ⇒
[tex]L(t)=(2+t,5-4t)[/tex] = ( x component , y component ) = ( x , y ) ⇒
In the parabola : [tex]y=x^{2}[/tex] ⇒ [tex]5-4t=(2+t)^{2}[/tex]
Solving the equation we find that :
[tex]t^{2}+8t-1=0[/tex]
Using the quadratic formula with
[tex]a=1[/tex] , [tex]b=8[/tex] and [tex]c=-1[/tex]
We find that the two possible values for t :
[tex]t_{1}=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex] and [tex]t_{2}=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
are [tex]t_{1}=-4+\sqrt{17}[/tex] and [tex]t_{2}=-4-\sqrt{17}[/tex]
This values [tex]t_{1}[/tex] and [tex]t_{2}[/tex] are the values of the parameter t where the line intersects the parabola so we can find the points by replacing the values of the parameter in the equation [tex]L(t)[/tex] :
[tex]L(t_{1})=(-2+\sqrt{17},21-4\sqrt{17})[/tex] and
[tex]L(t_{2})=(-2-\sqrt{17},21+4\sqrt{17})[/tex]
The final answer is
The parabola [tex]y=x^{2}[/tex] at the points [tex](-2+\sqrt{17},21-4\sqrt{17})[/tex] and [tex](-2-\sqrt{17},21+4\sqrt{17})[/tex] when [tex]t=t_{1}=-4+\sqrt{17}[/tex] and [tex]t=t_{2}=-4-\sqrt{17}[/tex]
Can you solve 2g - 13 = 3.
g=
Steps to solve:
2g - 13 = 3
~Add 13 to both sides
2g = 16
~Divide 2 to both sides
g = 8
Best of Luck!
The solution to the equation 2g - 13 = 3 is g = 8.
To solve the equation 2g - 13 = 3 for g, we'll perform the necessary steps to isolate the variable g on one side of the equation.
Starting with the given equation:
2g - 13 = 3
First, we'll add 13 to both sides to eliminate the -13 term on the left side:
2g - 13 + 13 = 3 + 13
2g = 16
Next, to isolate the variable g, we divide both sides by 2:
(2g)/2 = 16/2
g = 8
Therefore, the solution to the equation 2g - 13 = 3 is g = 8.
In this equation, we initially have a linear expression involving the variable g and a constant term. By performing algebraic operations, we rearrange the equation to have g on one side and the constant value on the other side. This isolates the variable and provides us with a specific value for g that satisfies the equation. In this case, the value of g is determined to be 8, which can be verified by substituting it back into the original equation to see if it holds true.
To learn more about the linear equation;
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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = 5√49 − x2
y = 0
x = 2
x = 4
Answer:
V = 4316.75 π
Step-by-step explanation:
Given that:
[tex]y = 5 \sqrt{49 -x^2}[/tex] y = 0, x = 2, x = 4
[tex]V = \pi \int \limits ^{x=4}_{x=2} y^2 \ dx[/tex]
where;
y² = 25 (49 - x²)
[tex]V = 25 \pi \int \limits ^4_2 (49-x^2) dx[/tex]
[tex]V = 25 \pi [ (49x-\dfrac{x^3}{3}]^4_2[/tex]
[tex]V = 25 \pi [ 49\times 4 -\dfrac{4^3}{3} - 2][/tex]
[tex]V = 25 \pi [ 196-21.33 - 2][/tex]
[tex]V = 25 \pi [ 172.67][/tex]
V = 4316.75 π
Use the simple interest formula to determine the missing value. p =$1325, r =?t=2 years I=$37.10 r=?% (Do not round until the final answer. Then round to one decimal place as needed.)
Answer:
r = 1.4 %
Step-by-step explanation:
given p(principle) is 1,375$, r(interest rate) is unknown, t(time in years) is 2, and I(Interest / final balance) is 37.10$. The simple interest formula: I = prt can be rewritten as: r = I/pt to solve for r. 37.1 / ( 1325 × 2 ) = 37.1 / 2650 = 0.014 = ( 0.014 * 100 ) % = 1.4 %
7. a. Use the distributive property to rewrite the equation.
Enter the new equation as your answer.
2 (x - 1) - 3 = 5
Enter your answer
8.b. Combine any like terms to rewrite the equation that you entered as an answer in part a.
Enter the new equation as your answer.
Enter your answer
9.c Use addition or subtraction to rewrite the equation that you entered as an answer in part b.
Enter the new equation as your answer.
Enter your answer
10.d. Use multiplication or division to rewrite the equation that you entered as an answer in part c.
Enter the new equation as your answer."
Answer:
Hey there!
a.
2(x-1)-3=5
2x-2-3=5
b.
2x-5=5
c.
2x=10
d.
x=5
Let me know if this helps :)
What is the perimeter of the rectangle with length of 2x + 3 and width of 5x – 5? Explain your process to find the perimeter.
Answer:
14x-4
Step-by-step explanation:
length:2x+3
width:5x-5
perimeter of rectangle:2(l+b)
:2(2x+3+5x-5)
:2(7x-2)
:14x-4
•••The perimeter of rectangle(p)=14x-4
In a box plot, if there is an outlier shown in the picture below, what is considered the min? The outlier or 59?
Step-by-step explanation:
The outlier is excluded, so the minimum is 59.
Lauren has dimes and nickels in her purse. The number of dimes is three more than seven times the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.
Answer:
X = 7n + 3
Step-by-step explanation:
x= dimes
n=nickels
X = 7n + 3
is y+2=8 an expression
Answer:
no
Step-by-step explanation:
hope this helps
24x - 22 = -4 (1 - 6x)
Answer:
ffdfssss
Step-by-step explanation:
fdfdfdfd
Answer:
x is invalid.
Step-by-step explanation:
Note the equal sign, what you do to one side, you do to the other. Remember to follow PEMDAS.
PEMDAS is the order of operation, and =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
First, distribute -4 to all terms within the parenthesis:
-4(1 - 6x) = (-4 * 1) + (-4 * -6x) = -4 + 24x
24x - 22 = -4 + 24x
Isolate the variable, x. Subtract 24x from both sides:
24x (-24x) - 22 = -4 + 24x (-24x)
0 - 22 = -4 + 0
-22 ≠ -4, therefore, this question is invalid.
~
Joshua is going kayaking with a group during one of his vacation days. In his vacation planning, he budgeted $50 for a kayak rental. How can Joshua determine the number of hours he can rent a kayak for himself?
Answer: Divide Kayak budget by rental rate
Step-by-step Explanation:
As Joshua is renting for himself alone, the two available options would be the Single Kayak and the Single Sea Kayak.
He can determine the number of hours to rent a Kayak for by dividing his Kayak Budget by the rental rate per hour of the 2 options available to him.
Single KayakBudget available = $50
Rental rate = $15 per hour
Hours he can rent = 50/15
= 3.33 hours
Single Sea KayakBudget available = $50
Rental rate = $18 per hour
Hours he can rent = 50/18
= 2.78 hours
-2times(3+8divided4)2
Answer:
20
Step-by-step explanation:
Answer:-20
Step-by-step explanation: 8/4+3=5 then -2*5 =-10*2 =-20
Which features describe the graph? Select all that apply
Answer:
- Decreasing
Step-by-step explanation:
im not sure of the last two but the others are for sure a no
the number in each block is the sum of the numbers in the two blocks beneath it. Some of the numbers are hidden. What is the value of y - x
Answer:
y - x = 69
Step-by-step explanation:
From the figure attached,
Number in each block is the sum of the numbers in the block beneath it.
Therefore, A + 21 = 32 ⇒ A = 11
A + 5 = B ⇒ B = 16
C = 5 + x
D = 32 + B ⇒ D = 32 + 16 = 48
E = B + C ⇒ E = 16 + (5 + x)
⇒ E = 21 + x
y = D + E ⇒ y = 48 + (21 + x)
y = 48 + 21 + x
y = 69 + x
y - x = 69
Therefore, y - x = 69 will be the answer.
What is the sum of 9+10 (;
Answer:
19 or 21.
Step-by-step explanation:
I swear.
5 + 5 = 10
10 + 5 = 15
15 + 4 = 19
________________
9 + 9 = 18
18 + 10 = 28
28 - 5 = 23
There are two nines so
23 - 2 = 21
2a+4b-a+2b=???
Where do I start
Jade had $520 to spend on extra items this month. She spent .15 on art supplies, 1 10 was spent at the book store, 3 5 was spent at Chicka-fila. How much did she have left of her extra money?
Answer:
515.25 is what she got left
Step-by-step explanation:
6+4m-1=21
PLEASE HELP! I’m stuck on this question :/
Answer:
m=4
best of luck!
Step-by-step explanation:
Answer:
m=4
Step-by-step explanation:
6+4m-1=21
(6-1=) 5+4m=21
21-5=16
16÷4m = 4
What is the angle between the given vector and the positive direction of the x-axis?8i + 6j.
Answer:
The between the given vector and the positive direction of the x-axis is approximately 41.186º.
Step-by-step explanation:
Let be [tex]\vec u = 8\,i + 7\,j[/tex] and [tex]\vec v = i[/tex] (Positive direction of the x-axis), the angle between both vectors can be determined from definition of dot product:
[tex]\vec u \bullet \vec v = \|\vec u\|\cdot \|\vec v\| \cdot \cos \theta[/tex]
Angle is cleared:
[tex]\cos \theta = \frac{\vec u\bullet \vec v}{\|\vec u\|\cdot \|\vec v\|}[/tex]
[tex]\theta = \cos^{-1}\left(\frac{\vec u \bullet \vec v}{\|\vec u\|\cdot \|\vec v\|} \right)[/tex]
The norms of [tex]\vec u[/tex] and [tex]\vec v[/tex] are found by Pythagorean Theorem:
[tex]\|\vec u\| = \sqrt{8^{2}+7^{2}}[/tex]
[tex]\|\vec u\| \approx \sqrt{113}[/tex]
[tex]\|\vec v\| = 1[/tex]
The dot product between both vectors is:
[tex]\vec u \bullet \vec v = (8)\cdot (1) + (6)\cdot (0)[/tex]
[tex]\vec u \bullet \vec v = 8[/tex]
The angle is now calculated:
[tex]\theta = \cos^{-1}\left(\frac{8}{\sqrt{113}} \right)[/tex]
[tex]\theta \approx 41.186^{\circ}[/tex]
The between the given vector and the positive direction of the x-axis is approximately 41.186º.
What is expression is equivalent to 210,704? Is it 20,000+10,000+700+4. 200,000+10,000+700+4. Or 200,000+10,000+700+40??
Answer:
200,000+10,000+700+4
Step-by-step explanation:
How much is 5 divided by 3/10?
Answer:
16.6666666667
Step-by-step explanation:
Answer:
16 2/3
Step-by-step explanation:
Step 1:
5/1 ÷ 3/10
Step 2:
5/1 × 10/3
Step 3:
50/3
Answer:
16 2/3
Hope This Helps :)
If g(x) = x^2 – 2x – 6 and h(x) = 2x^2 – 5x + 2 find (h – 9) (-2)
Answer: (h-g)(-2)=18
Step-by-step explanation:
(h – g) (-2) means the same as subtracting h(-2) and g(-2). Since we are given h(x) and g(x), we can use them to solve. There are two ways to solve. One is to find h(-2) and g(-2), and then subtract them. Another way is to do (h-g)(x), then plug in x=-2. I will show both methods.
Method 1
h(-2)=2(-2)²-5(-2)+2 [exponent]
h(-2)=2(4)-5(-2)+2 [multiply]
h(-2)=8+10+2 [add]
h(-2)=20
g(-2)=(-2)²-2(-2)-6 [exponent]
g(-2)=4-2(-2)-6 [multiply]
g(-2)=4+4-6 [add then subtract]
g(-2)=2
(h-g)(-2)=20-2 [subtract h(-2) and g(-2)]
(h-g)(-2)=18
--------------------------------------------------------------------------------------------------------
Method 2
(h-g)(x)=2x²-5x+2-(x²-2x-6) [distribute -1]
(h-g)(x)=2x²-5x+2-x²+2x+6 [combine like terms]
(h-g)(x)=x²-3x+8
(h-g)(-2)=(-2)²-3(-2)+8 [plug in x=-2, exponent]
(h-g)(-2)=4-3(-2)+8 [multiply]
(h-g)(-2)=4+6+8 [add]
(h-g)(-2)=18
--------------------------------------------------------------------------------------------------------
Now, we know that (h-g)(-2)=18. We confirmed this with both methods.
identify the method that will be used to solve for x for each equation. 4x = 20 5x + 6x = 22
Step-by-step explanation:
Identify the method that will be used to solve for x for each equation.
4x=20 division property fo equality
x-11=9 addition property of eqaulity
5x+6x=22 Combining Like terms
5(x-2)=30 distibute property
Answer:
ello
Step-by-step explanation:
Identify the method that will be used to solve for x for each equation.
4x=20 division property fo equality
x-11=9 addition property of eqaulity
5x+6x=22 Combining Like terms
5(x-2)=30 distibute property
14 + 3c = 35 la respuesta de esta también porfa se los agradezco que sea con el trabajo completo gracias oh
A cell phone weighs about 2.8x 10pounds. Which value of n is most reasonable?
-3
-1
0
1
Answer:0
Step-by-step explanation: took the quiz
2/3+1/3x=2x
x=1/2
x=5/2
x=2
x=2/5
Answer:
x = 2/5
Step-by-step explanation:
Solve for x:
x/3 + 2/3 = 2 x
Hint: | Combine x/3 + 2/3 into a single fraction.
x/3 + 2/3 = (x + 2)/3:
(x + 2)/3 = 2 x
Hint: | Make (x + 2)/3 = 2 x simpler by multiplying both sides by a constant.
Multiply both sides by 3:
(3 (x + 2))/3 = 3×2 x
Hint: | Cancel common terms in the numerator and denominator of (3 (x + 2))/3.
(3 (x + 2))/3 = 3/3×(x + 2) = x + 2:
x + 2 = 3×2 x
Hint: | Multiply 3 and 2 together.
3×2 = 6:
x + 2 = 6 x
Hint: | Move terms with x to the left hand side.
Subtract 6 x from both sides:
(x - 6 x) + 2 = 6 x - 6 x
Hint: | Combine like terms in x - 6 x.
x - 6 x = -5 x:
-5 x + 2 = 6 x - 6 x
Hint: | Look for the difference of two identical terms.
6 x - 6 x = 0:
2 - 5 x = 0
Hint: | Isolate terms with x to the left hand side.
Subtract 2 from both sides:
(2 - 2) - 5 x = -2
Hint: | Look for the difference of two identical terms.
2 - 2 = 0:
-5 x = -2
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of -5 x = -2 by -5:
(-5 x)/(-5) = (-2)/(-5)
Hint: | Any nonzero number divided by itself is one.
(-5)/(-5) = 1:
x = (-2)/(-5)
Hint: | Simplify the sign of (-2)/(-5).
Multiply numerator and denominator of (-2)/(-5) by -1:
Answer: x = 2/5
Answer: [tex]x=2/5[/tex]
Simplify both sides of the equation
[tex]1/3x+2/3=2x[/tex]
Subtract 2x from both sides
[tex]1/3x+2/3-2x=2x-2x\\-5/3x+2/3=0[/tex]
Subtract 2/3 from both sides
[tex]-5/3x=2/3-2/3=0-2/3\\-5/3x=-2/3[/tex]
Multiply both sides by 3/-5
[tex](3/-5)*(-5/3x)=(3/-5)*(-2/3)\\x=2/5[/tex]
Give the next three terms in each Arithmetic Sequence and the common difference
Answer:
A) Sequence: -5, -10, -15, -20, -25, -30, -35, -40 cd = -5
B) Sequence: -1, 2, 5, 8, 11, 14, 17, 20 cd = 3
C) Sequence: 17, 19, 21, 23, 25, 27, 29, 31 cd = 2
D) Sequence: 11, 16, 21, 26, 31 , 36, 41, 46 cd = 5
E) Sequence: -9, -6, -3, 0, 3, 6, 9, 12 cd = 3
Step-by-step explanation:
A) Sequence: -5, -10, -15, -20, -25
The common difference (cd) - which is the number that we need to add to each term in order to get the next - is -5
and the next three terms are: -30, -35, -40.
B) Sequence: -1, 2, 5, 8, 11,
The common difference is 3, cd = 3
so the next three terms in the sequence are; 14, 17, 20
C) Sequence: 17, 19, 21, 23, 25,
the common difference is 2, cd = 2
so the next three terms in the sequence are: 27, 29, 31
D) Sequence: 11, 16, 21, 26, 31
the common difference is 5, cd = 5
so the next three terms of the sequence are: 36, 41, 46
E) Sequence: -9, -6, -3, 0, 3,
the common difference is 3, cd = 3
so the next three terms in the sequence are: 6, 9, 12
Hello, please help with this question. Thanks.
Answer:
x = 17
Step-by-step explanation:
4x +22 = 90
4x = 68
x = 68/4
x = 17
Translate and solve: 24.67 is what percent of 129? Rounded to the nearest tenth of a percent.
Answer:
31.8
Step-by-step explanation:
24.67x129
=>31.82
=>31.8
Michael earns $10 per hour. He regularly works 40 hours per week.
How many overtime hours would he have to work in a week for his
overtime pay to be greater than his regular gross pay?
5. Tania earns $13.50 per hour at the Glendale Florist. She regularly works 40 hours per week. She is paid time-and-a-half for each hour of overtime work. Last week she worked. 43 hours. What was her gross pay for the ...
Missing: michael | Must include: michael
Mark used the money from his saving account for a down payment for a car. Money in his savings account is an example of a
3
Personal finance
Answer:
Personal finance
Step-by-step explanation:
Personal finance is a technical term in which a person or group of persons pool resources together for the purpose of budgeting, saving, or spending as they deem fit.
Money in Mark's saving account that he used as a down payment for his car is an example of personal finance.