Answer:
x=5
Step-by-step explanation:
First you combine the like terms. next you add 7+23. After that you subtract 10 from both sides. You're left with 4x=20. divide the equation by 4 on each term. Then you're left with x=5.
A system of equations is made up of an ellipse and a hyperbola.
Part A: Create the equation of an ellipse centered at the origin, with a vertical major axis of 8 units and a minor axis of 6 units. Show your work. (3 points)
Part B: Create the equation of a hyperbola centered at the origin, with a horizontal transverse axis, vertex at (–4, 0), and asymptotes of y equals plus or minus seven fourths x period Show your work. (4 points)
Part C: Determine the domain of each conic section and use it to explain why there is no solution to the system. (3 points)
The equation of the ellipse and the equation of the hyperbola can be
derived from the given information and the general form of the equations.
[tex]Part \, A: The \ equation \ of \ the \ ellipse \ is; \displaystyle \frac{x^2}{3^2} + \frac{y^2}{4^2} = 1[/tex]
[tex]Part \, B: The \ equation \ of \ the \ hyperbola \ is; \displaystyle \frac{x^2}{(-4)^2} - \frac{y^2}{(-7)^2} = 1[/tex]
Part C: The domain of the ellipse is; [-3, 3]
The domain of the hyperbola is; (-∞, -4]
The domains of the ellipse and the hyperbola do not intersect, therefore, the system of equation has no solution.Reasons:
Part A: The center of the ellipse = At the origin;
The vertical major axis = 8 units
The minor axis = 6 units
The general equation for an ellipse is presented as follows;
[tex]\displaystyle \frac{x^2}{b^2} + \frac{y^2}{a^2} = 1[/tex]
Where;
[tex]\displaystyle a = The \ \mathbf{ semi \ major \ axis} = \frac{8}{2} = 4[/tex]
[tex]\displaystyle b = The \ semi \ \mathbf{ minor} \ axis = \frac{6}{2} = 3[/tex]
The equation of the ellipse is therefore;
[tex]\displaystyle \underline{\frac{x^2}{3^2} + \frac{y^2}{4^2} = 1}[/tex]Part B: center of the hyperbola = The origin
The transverse axis = Horizontal
The vertex of the hyperbola = (-4, 0)
[tex]\displaystyle The \ asymptote \ are; \ y = \mathbf{ \pm\frac{7}{4} \cdot x}[/tex]
The general equation of an hyperbola is presented as follows;
[tex]\displaystyle \mathbf{\frac{x^2}{a^2} - \frac{y^2}{b^2}} = 1[/tex]
[tex]\displaystyle The \ asymptote \ are; \ y = \mathbf{\pm\frac{b}{a} \cdot x}[/tex]
The vertices = (a, 0), (-a, 0)
Therefore, by comparison, we have;
a = -4
b = -7
Which gives the equation of the hyperbola as follows;
[tex]\displaystyle \underline{ \frac{x^2}{(-4)^2} - \frac{y^2}{(-7)^2} = 1}[/tex]The above equation can be written as follows;
[tex]\displaystyle \frac{x^2}{(4)^2} - \frac{y^2}{(7)^2} = 1[/tex]
Part C: Given that both equations are equal, we have;
The covertices of the ellipse are; (-3, 0) and (3, 0)
The domain of the ellipse = [-3, 3]
The domain of the hyperbola = x < The negative vertex
∴ The domain of the hyperbola = x < -4 = (-∞, -4]
The above domain of the ellipse does not extend to the hyperbola, therefore there is no solution to the system.Learn more about ellipse and hyperbola here:
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309,303,297 find the 33rd term
Answer:
111
Step-by-step explanation:
multiply 33 by 6 because 6 is being subtracted every time and then subtract 198 from 309
Answer:
117
Step-by-step explanation:
Hope this helps!
15(x + 3)2
Box the exponent (s)
please help
Answer:
"2" is the exponent
Step-by-step explanation:
There is no exponent in your expression.
__
When the expression is typeset, the superscript text is considered to be an exponent:
[tex]15(x+3){\boxed{^2}}[/tex]
When the expression is written in plain text, the exponent is indicated by a caret (^):
[tex]\textsf{15(x+3)\^\ \!\!\boxed{\textsf{2}}}[/tex]
Answer:
[tex] {15x}^{2} + 90x + 135 \\ [/tex]
Step-by-step explanation:
[tex]15 {(x + 3)}^{2} \\ 15(x + 3)(x + 3) \\ 15 |(x(x + 3) + 3(x + 3)| \\ 15( {x}^{2} + 3x + 3x + 9) \\ 15( {x}^{2} + 6x + 9) \\ {15x}^{2} + 90x + 135 \\ [/tex]
P = x y . Find P when: x = 8 and y = − 11
Answer:
P= -88
Step-by-step explanation:
Since P=xy (Or x times y)
We can solve it since we know that x and y is: 8 and -11
So 8 times -11
Which is -88
Thus P= -88
Hope this helps!
Simplify for x: 2/3 = x-1/5
Answer:
x=13/15
Step-by-step explanation:
2/3=x-1/5
find LCD=15
10/15=x-3/15
add 3/15 to both sides
13/15=x
PNC charges a monthly fee of $8 on checking accounts and an overdraft protection fee of $35. Neela's online banking showed she had a balance of $530 when she wrote a check for $375. Three days later a charge of $273 that she had forgot about appeared on the same day that the check cleared. How much money must she deposit to raise her balance to 0 ?
The amount of money Neela needs to deposit to raise her balance to 0 is; $163
Since Neela's online banking showed she's been charged a monthly fee of $8 on checking accounts and an overdraft protection fee of $35.
Total charges = $8 + $35 = $43.Subsequently, she wrote a check of $375 in which case; Three days later a charge of $273 that she had forgot about appeared on the same day that the check cleared.
Total debit amount = $375 + $275 = $650.Total debit = $650 + $43 = $693Since the account showed she had a balance of $530.
Her new account balance is; $530 - $693 = -$163
Therefore, Neela needs to deposit $163 to raise her balance to 0.
Read more on arithmetics:
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4. The original price of a pair of shoes is $80 and they are on sale for $48. What is the percent of discount?
O A 32%
O B. 40%
OC. 60%
O D. 66.7%
Answer:
c
Step-by-step explanation:
80 × percent = 48
percent = 48/80
= 0.6
= 60%
On Tuesday, it snowed 15 inches in 6 hours. On Friday, it snowed 30 inches in 8 hours. On which day did it snow at a greater rate each hour? How much more per hour? please answer asap
Answer: Friday, 1.25 more per hour
Step-by-step explanation: if we take the inches it snowed and divide it by the hours, we get the rate of snowfall for one hour. 15/6=2.5 and 30/8=3.75
To get how much more we take the bigger snowfall per hour minus the smaller snowfall per hour 3.75-2.5=1.25
what should I put?????
Classify the number -5
Integer
1. Whole Number
2. Irrational Number
3. Natural Number
Answer:
1. Whole number
Step-by-step explanation:
It's a negative number, but it is not a decimal, therefore it is a whole number.
20x+10x-8=0 solution set of equation
Answer:
0.2666666666Step-by-step explanation:
20x+10x-8=0
first of all, you will +8 on both sides so there are no negative numbers onany side
20x+10x=8
now gather everything up
30x=8
divide everything by 30 now to get the value of 1x
30x/30=x
8/30=0.2666666666
Each big square below represents one whole.
What percent is represented by the shaded area?
Answer:
the frist one
Step-by-step explanation:
hope it helps
simplify and factor if necessary
Hello there today we will solve your problem, we will need to factorize btw...
[tex]{\huge{\boxed{\mathfrak{Equation}}}[/tex]
[tex]{\big{\boxed{\frac{x^2-5x+4}{x^2-4x}}}}[/tex]
First we will factor [tex]x^2-5x+4[/tex], which gives us [tex]\left(x-1\right)\left(x-4\right)[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\left(x-1\right)\left(x-4\right)}{x^2-4x}\\[/tex]
factorize [tex]x^2-4x[/tex] giving us [tex]x\left(x-4\right)[/tex]
[tex]\frac{\left(x-1\right)\left(x-4\right)}{x\left(x-4\right)}[/tex]
cancel the common factor [tex]x-4[/tex]
and we get [tex]\frac{x-1}{x}[/tex]
jack predicted his car payment to be $300 each month. His actual car payment is $275 each month.what % was his prediction off by
Answer:
.91% he wa off by .91% because .91 of 300 is 25 and 300- 25 is 275
Step-by-step explanation:
Pls explain how to solve it!
Answer:
a = jd
Step-by-step explanation:
We want to solve for a given that a/d = j
To do so we want to isolate a (get a by itself )
We can do this by using inverse operations.
We would want to get rid of the d
A is being divided by d.
The inverse of division is multiplication so to get rid of the d we multiply a/d by d but whatever we do to one side we must do to the other so we multiply both sides by d
a/d * d = a
j * d = jd
we are then left with a = jd
And we are done!
Answer:
a = jd
Step-by-step explanation:
We have to solve the equation for a - in other words, we have to find a in terms of d and j. Another way to think about this is that we need a by itself on one side, equal to the other two values in some sort of relationship.
So, how can we accomplish this? Well, currently a is being divided by d, so we should probably multiply both sides by d to get that d away from a. The process is shown below:
[tex]\frac{a}{d} =j[/tex]
[tex]\frac{a}{d} *\frac{d}{1} =j*d[/tex]
[tex]\frac{ad}{d} =jd[/tex]
[tex]a=jd[/tex]
And look at that! We've solved for a in terms of the other two values. If you need any more help or everything I just did was confusing or overwhelming, let me know so I can clarify. :)
A shopkeeper bought 24 bottles of fruit juice for $63 dollars.
She sold them for $2.95 each.
Calculate her percentage profit or loss.
Answer:
0.325
Step-by-step explanation:
$63 divide by 24 you'll get 2.625
then $2.95 minus 2.625 you'll get 0.325
What is 2/5 divided by 2/3
Answer:
0.6
Step-by-step explanation:
Trust me
PLZ mark as brainliest
A teacher wants to give each student 2 pencils. A store is selling pencils in boxes of 24. If the teacher has a total of 125 students, how many boxes of pencils should he buy?
Answer:
10.41
Step-by-step explanation:
hehe
Answer:
11
Step-by-step explanation:
Total number of pencils needed = 125 × 2 = 250
Total number of boxes = [tex]\frac{250}{24}[/tex] = 10.416
the teacher need to buy 11 boxes
What angle would you use to represent 5 blue cars out of 20 cars in total on a pie chart?
Answer:
check online for more information
Helppppppppppp!!!!!!!!!!!
1)
Which of the following is not a linear equation in one variable?
(a) 32+5 = 0 (b) 3(x+y) = 0 (c) 3x+5 = 0 (d) 3y+5 = 0
Answer:
letter c is the answer
Step-by-step explanation:
hope it helps you
Answer:
The answer is Option C.) 3x+5 = 0
Step-by-step explanation:
Option A, can't be the answer. It doesn't show a linear graph. Therefore it's incorrect.
Option B, can't be the answer. It doesn't show a linear graph either. This one is also incorrect.
Option C, on the other hand, is correct because it's not a linear equation.
Option D, can't be the answer. It shows a graph, but with a squiggly line. Therefore, this one is also incorrect.
Hope this helps!
Have a nice day/night/afternoon.
(Can you mark me brainliest?)
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if p(x)=3x+1, what is the value of p(-2) ? *
Answer:
p(-1)= -5
p(2)= 19
Answer:
-5
Step-by-step explanation:
p(x)=3x+1
p(-2)=3(-2)+1
p(-2)=-6+1
p(-2)=-5
If you're satisfied with the answer, then please mark me as Brainliest. Thank you.
The temperature in Minnesota is 78 degrees at noon.
The temperature is 88 degrees by 4 pm. What is the
rate of change of the temperature from noon till 4?
Hello please answer everything carefully :)
Answer:
Line 3
Step-by-step explanation:
Line three should be
2*3*sqrt(5)-3sqrt(5)
HELP ME PLEASE I DONT KNOW HOW TO DO THIS
Answer:
Step-by-step explanation:
x = 1 - 1
A light post 5 1/5 metres long was set 1 1/2 metres into the ground. What was the length of the post above the ground? Write your answer in its simplest form *
Answer:
3.7 meters
Step-by-step explanation:
First, convert the fractions into decimals.
5 1/5 = 5.2
1 1/2 = 1.5
Then subtract them
5.2-1.5=3.7 meters!
can you help solve this?
Answer:
Step-by-step explanation:
By which angle measures can the regular pentagon be rotated so it maps onto itself?
Select each correct answer.
72°
90°
135°
144°
216°
300°
Answer:
hi there the answer is 72
Step-by-step explanation:
sorry but my work is on a piece of paper in front of me
To map the regular pentagon onto itself, rotate it at angles of 72, 144, 216, and 288 degrees.
What is a regular polygon?A polygon is a geometric form with a limited number of sides that exists in two dimensions. On the sides or edges of polygons, single-direction segments are joined end to end to form a closed shape. Vertices or corners are the points at which two line segments converge to form an angle.
It is given that:
There are five sides to the pentagon.
We are known that the typical pentagon has five vertices and interior angles of 72 degrees each. Rotational symmetry is also present in a regular pentagon.
Angles are 72°,144°,216°, and 288°
Thus, to map the regular pentagon onto itself, rotate it at angles of 72, 144, 216, and 288 degrees.
Learn more about the regular polygon here:
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What is an equation of a line that passes through the point
(0,3) and is perpendicular to the line whose equation is
y = 2x - 1?
-
Answer: y = -(1/2)x + 3
Step-by-step explanation:
y = 2x - 1
This is in the format of y=mx + b, where m is the slope and b is the y-intercept (the value of y when x=0).
Perpendicular lines have a slope that is the negative inverse of the reference line. The slope of this reference line is 2, so the slope of a perpendicular kline will be -(1/2).
This yields the equation y = -(1/2)x + b
To find the value of b, we can use the given point, (0,3) and use these values of x and y to solve for b:
y = -(1/2)x + b
3 = -(1/2)(0) + b
b = 3
The equation of a line perpendicular to y = 2x - 1 and goes through point (0,3) is:
y = -(1/2)x + 3
solve for z. -z+7=6 and thank you
Answer:
z = 1
Step-by-step explanation:
-z+7 = 6
so
7-6 = z
1 = z
good luck
Answer:
[tex]\huge\boxed{\sf z = 1}[/tex]
Step-by-step explanation:
-z + 7 = 6
Subtract 7 to both sides
-z = 6 - 7
-z = -1
Divide both sides by -1
z = 1
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807