Answer:
https://wb-qb-sg-oss.bytededu.com/mars_api/516070e015af3cbddbf0c9527d422fd6/1624892212752.jpeg!content
Step-by-step explanation:
If the section is created by slicing the equation 2x² + 2xy + 5y² + 6x - 4y = 40 at 45°. Then the conic will be an ellipse.
What is a conic section?A figure made up of a surface and a round cone intersecting. A conic section can be a circle, an ellipse, a parabola, or a hyperbola, based on the direction of the plane with regard to the cone.
The angle θ is 45° and the equation is 2x² + 2xy + 5y² + 6x - 4y = 40.
Then x will be
[tex]\rm x = x' \cos \theta - y' \sin \theta\\\\x = x' \cos 45- y' \sin 45\\\\x = \dfrac{x' - y'}{\sqrt2}[/tex]
Then y will be
[tex]\rm y = x' \sin \theta + y' \cos \theta\\\\y= x' \sin 45 + y' \cos 45\\\\y = \dfrac{x' + y'}{\sqrt2}[/tex]
Put these in the equation we have
[tex]\rm 2\left ( \dfrac{x' - y'}{\sqrt2} \right )^2 + 2\left ( \dfrac{x' - y'}{\sqrt2} \right )\left ( \dfrac{x' + y'}{\sqrt2} \right ) + 5 \left ( \dfrac{x' + y'}{\sqrt2} \right )^2+ 6\left ( \dfrac{x' - y'}{\sqrt2} \right ) - 4\left ( \dfrac{x' + y'}{\sqrt2} \right ) = 40[/tex]
On simplifying, we have
[tex]\rm 9x'^2 + 6x'y' + 5y'^2 + 10\sqrt2x' - 10 \sqrt2 y' - 80=0[/tex]
Then the value of a, b, and c will be
a = 2, b = 2, and c = 5
Then we have
[tex]\rm b^2 - 4ac = 2^2 - 4\times 2 \times 5 = 4 - 20 = -16[/tex]
Then b² - 4ac < 0, then the conic is ellipse.
More about the conic section link is given below.
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Use the graph of the function. To answer the question
Write the domain of the function given in the graph in set builder notation
A. {x|x>_10}
B. {x|x>_0}
C. {x|x>10}
D. {x|x>0}
Answer:
A. {x| x ≥ 10}
Step-by-step explanation:
in x-axis, the graph starts from 10 toward right.
it means x ≥ 10
Fraction:
Decimal:
Word Form:
Answer:
Fraction:
Decimal:
Word Form:
Step-by-step explanation:
Fill in the blank to make the number divisible by 3: 6178_9
Answer:
2, 5, or 8
Step-by-step explanation:
ccalculator go brr
Answer:
617829/3=205,943
617859/3=205,953
617889/3=205,963
Step-by-step explanation:
617819/3=205,939.666
617829/3=205,943
617839/3=205,946.333
617849/3=205,949.666
617859/3=205,953
617869/3=205,956.333
617879/3=205,959.666
617889/3=205,963
617899/3=205,966.333
Write the perimeter of the rectangle as a simplified expression
The simplified expression for the perimeter of the rectangle is 16x - 4. The perimeter of a rectangle is given by the formula: P = 2 * (length + width).In this case, the length of the rectangle is given as 7x + 1, and the width is given as x - 3.
So, the perimeter can be expressed as: P = 2 * (7x + 1 + x - 3)
Now, let's simplify this expression: P = 2 * (8x - 2)
P = 16x - 4
Therefore, the simplified expression for the perimeter of the rectangle is 16x - 4.
A rectangle is a type of quadrilateral with specific properties that distinguish it from other shapes. Here are some key properties of a rectangle:
Opposite Sides are Equal in Length: In a rectangle, the opposite sides are always equal in length. This means that the length of one pair of parallel sides is the same as the length of the other pair.
Opposite Angles are Equal: The opposite angles in a rectangle are equal in measure. This property makes all angles in a rectangle right angles (90 degrees).
Consecutive Angles are Supplementary: Consecutive angles in a rectangle are supplementary, meaning that the sum of any two consecutive angles is 180 degrees. This property is a consequence of the fact that opposite angles are equal, making each pair of consecutive angles form a linear pair.
To know more about perimeter:
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How much water should be added to 12mL of 11% alcohol solution to reduce the concentration to 6%
Answer:
We have 12 mL of 11% alcohol.
How much water do we add to make it a 6% solution?
We have 1.32 mL alcohol and 10.68 mL water
x is the water to add
(1.32) / (12 + x) = .06
1.32 = .72 + .06x
.6 = .06x
x = 10 mL
Step-by-step explanation:
Consider the expression
square root a^3 - 7 + b
When a = 2 and b = -4, the value of the expression is
Answer:
5
Step-by-step explanation:
substitute for the the given variables.
a=2
b=-4
sqrt 2^3-7=sqrt 8-7=sqrt1=1
1+absolute value of -4 = 1+4=5
answer 5
3. Amelia is at the mall buying more
school clothes. She purchases one pair
of jeans for $32.00 and 2 tops for
$23.99 each. If sales tax is $5.80, what
was the final cost of her clothes
What is the answer?
Answer:
The final cost of Amelia's clothes will be $79.98 without sales tax and $85.78 with sales tax.
Step-by-step explanation:
To find the final cost of Amelia's clothes without sales tax, start by writing an equation for the problem, and the equation will look like $[tex]32.00+2([/tex]$[tex]23.99)=x[/tex]. Next, simplify the equation, which will look like $[tex]32.00+[/tex]$[tex]47.98=x[/tex]. Then, solve the equation, which will look like $[tex]79.98=x[/tex]. The final cost of Amelia's clothes without sales tax will be $79.98.
To find the final cost of Amelia's clothes with sales tax, start by writing another equation for the problem, and this equation will look like $[tex]32.00+2([/tex]$[tex]23.99)+[/tex]$[tex]5.80=x[/tex]. Next, simplify the equation, which will look like $[tex]32.00+[/tex]$[tex]47.98+[/tex]$[tex]5.80=x[/tex]. Then, solve the equation, which will look like $[tex]85.78=x[/tex]. The final cost of Amelia's clothes with sales tax will be $85.78.
12.5 x 0.8
(without rounding and pls help me)
Answer:
That’s simple 10
Step-by-step explanation
Let me know if I’m correct
hope this helps
Last question of the day I need help with this.
The answer is 64.5 in2
[tex]7w+2=3w+94[/tex]
Answer:
7w+2=3w+94
Subtract 3w from both sides.
7w+2−3w=94
Combine 7w and −3w to get 4w.
4w+2=94
Subtract 2 from both sides.
4w=94−2
Subtract 2 from 94 to get 92.
4w=92
Divide both sides by 4.
w=492
Divide 92 by 4 to get 23.
w=23
Answer:
23
Step-by-step explanation:
7w + 2 = 3w + 94 Subtract 2 from both sides
7w = 3w + 94 - 2
7w = 3w + 92 Subtract 3w from both sides
4w = 92 Divide by 4
w = 92/4
w = 23
Help please! Find the perimeter and area of figure 1
Figure 1,
When 1 unit = 1 cm
Perimeter = Boundary of the figure
= 3+3+6
= 12 cm
Area of one square = side * side
= 1*1
No. of squares in the figure = 6 squares
Area = Space occupied inside the figure
= 6 cm^2
Hope it helped :)
18- 3 (2) = ?
show your work
help pls lol thanks
Answer:
12 is the answer
Step-by-step explanation:
18- 3×2= 18- 6 = 12
Akilometer is approximately 1094 yards . Toby runs a 6 km race. About how many yards does he run?
The length of a rectangle of area 45 sq cm is 9 cm. What is its breadth ?
Answer:
breadth = 5 cm
Step-by-step explanation:
Area of a rectangle = length × breadth
breadth = Area of a rectangle / length
breadth = 45 cm²/ 9cm
breadth = 5 cm
For the following set of sample data: {10, 50, 60, 70, 75 79, 85, 90, 91, 95, 100, 110} Find the sample mean.
Answer:
76.25
Step-by-step explanation:
Pls pls pls help me, im begging youuuk
Answer:
angle f = 147 degree and angle e = 33degree
Step-by-step explanation:
here,
angle d= 147 degree
angle f = ?
angle e= ?
we know that,
angle d= angle f (Being alternate angle always be equal.)
or, 147 degree = angle f
Hence, angle f is 147 degree.
And,
angle d sum angle e= 180 degree(being cointerior angle)
or, 147 degree add angle e=180 degree
or, angle e= (180-147) degree
or, angle e= 33 degree
Hence, angle e is 33 degree.
so, angle f=147 degree
angle e= 33 degree
ANS
angle e= 33 degree
Answer:
angle f=147 degrees (alternate angles)
angle e= 33 degrees
Step-by-step explanation:
angle d =147 degrees
angle f=147 degrees (alternate angles)
angle e +angle d=180 (allied angles)
e+ 147 =180
e =180-147
e = 33 degrees
what??? I need help urgent :( i didn’t focus in math
Answer: g(x) = (x+1)-3
Step-by-step explanation: Assuming you are moving from expression f to expression g, the plus one in the equation moves the vertex to the right one. subtracting three outside of the parenthesis moves the vertex down three, giving you a vertex of (1,-3). hope this helps!
In how many ways 4 books can be chosen from 8 different books and be arranged in 4 spaces on a bookshelf?
Answer:
hope this helps
Step-by-step explanation:
3*2 * 1 = 24 ways . It is called arrangement or permutations, while if you need to group some objects it is called combination and there we need to consider unique groups only.
(b) In the figure alongside, AB I BC and a - b= 10° then find the values of a and b.
Same side interiors(vertical) have sum 180°
a+b=180--(2)From both equations
2a=190a=95And
a-b=10b=95-10b=85the bill for dinner came to $75.48. The four Freinds decided to leave a $15.00 tip. If thwy share the bill equally, how much will each friend pay?
4. Factor: x2 – 36
Help please and show me the work on how to do it
Step-by-step explanation:
(X)^2 - (6)^2
= (x-6)(X+6)
Answer:
[tex](x - 6) \times (x + 6)[/tex]
Step-by-step explanation:
[tex] {x}^{2} - 36[/tex]
write in exponential form.
[tex] {x}^{2} - {6}^{2} [/tex]
factor:
[tex](x - 6) \times (x + 6)[/tex]
Write (2x)^4 without exponents
Answer:
16x^4
Step-by-step explanation:
Hi there!
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I believe your answer is:
[see below]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Simplifying the Expression:}}\\\\(2x)^4\\----------------\\\rightarrow (2x)^4 \text{ is 2x multiplied 4 times.}\\\\\rightarrow (2x)^4 = \boxed{2x * 2x * 2x * 2x}\\\\\rightarrow 2x * 2x * 2x * 2x = \boxed{16*x^4}\\\\\rightarrow 16*x^4 = \boxed{16 * x * x * x * x}\\\\\text{The boxed answers with exception to the second one could be possible answers.}[/tex]
»»————- ★ ————-««
⸻⸻⸻⸻
Hope this helps you. I apologize if it’s incorrect.
What number will make this statement true?
Help due today!
No links
Answer:
8
Step-by-step explanation:
0-(-8) = 8 ///////////
Answer:
8
Step-by-step explanation:
Let the number be x.
Then,
- 8 + x = 0
=> x = 0 + 8
=> x = 8
Which group of number shows the values of the 4s in 44,492?
Answer:
The values of the 4s in 244 is, 4 and 40
Explanation:
A place value is used to understand the value of each digit based on the place or position.
Given number is 244.
Since, there are 2 fours in 244 ;
The last digit i.e, 4 on the right is in the ones' place with value= 4, and
Answer:
The values of the 4s in 244 is, 4 and 40
Explanation:
A place value is used to understand the value of each digit based on the place or position.
Given number is 244.
Since, there are 2 fours in 244 ;
The last digit i.e, 4 on the right is in the ones' place with value= 4, and
Value of a number in the tens' place is ten times the value of the same number in the one's place.
then, the second one at ten's place with value,= 40.
Step-by-step explanation:
The linear function f with values f(-6) = 8 and f(5) = 3 is f(x) =
You can compute the slope given that you have two points [tex](-6,8)[/tex] and [tex](5,3)[/tex].
[tex]m=\frac{3-8}{5-(-6)}=\frac{-5}{11}=-\frac{5}{11}[/tex]
Your function has a form of,
[tex]f(x)=mx+n[/tex]
So we also need to find n. To do that, substitute y and x for some point we already know, I will pick point [tex](5,3)[/tex] then solve for n,
[tex]3=-\frac{5}{11}\cdot5+n[/tex]
[tex]n=3+\frac{5}{11}\cdot5[/tex]
[tex]n=3+\frac{25}{11}[/tex]
[tex]n=\frac{33+25}{11}=\frac{58}{11}[/tex]
So the function is,
[tex]f(x)=-\frac{5}{11}x+\frac{58}{11}[/tex]
Hope this helps :)
6 let A= (1,4,9,16) and B=(2,3,5,7). Find AS
Prove that A-B=( )
zip file, and phrase, angle of applicable. where are u doing now I need to make a sentence, but it was not the same time for changing the full range. uses the nation, angle and phrase, angle. uses a
A.38°
B.136°
C.112°
D.92°
Answer:
Step-by-step explanation:
( C ). 112°
Francisco Typed a 36-word paragraph in minute. What is his typing speed, in
words per minute?
Answer:36
Step-by-step explanation:
It says he typed 36 words in a paragraph in a minute which means he types 36 per minute
-1/3 - (-1/2) plz help I am confused
Answer:
[tex] \frac{ - 1}{3} - ( - \frac{1}{2} ) \\ \frac{ - 1}{3} + \frac{1}{2} ( - \times - = + ) \\ = \frac{ - 2 + 3}{6} \\ = \frac{1}{6} \\ thank \: you[/tex]
Answer:
[tex] \frac{1}{6} [/tex]
Step-by-step explanation:
[tex] - \frac{1}{3} - ( - \frac{1}{2} )[/tex]
[tex] - \frac{1}{3} + \frac{1}{2} [/tex]
[tex] \frac{ - 2 + 3}{ 6} [/tex]
[tex] = \frac{1}{6} [/tex]
Jason surveyed the student athletes at his school as they left the locker rooms for
practice. When selecting from a list of questions, he determined that he could survey
the athletes to determine which sport students in the school most liked to watch.Which
of the following statements is true?
A. Jason is not correct. Since the students are in a small age group, he should go to a baseball game
and survey the spectators there to find the most popular sport to watch.
B. Jason is correct. This population is best for his question.
C. Jason is not correct. Since sports are played during different seasons, he would have to conduct
his survey over the entire school year to get more accurate results.
D. Jason is not correct. Since there are other students in the school that watch sports but do not play them, he should expand his population.
Answer: D
Step-by-step explanation: