Identify the equation without applying a rotation of axes.x squared +10xy+25y squared-2x-4y+10=0a. parabolab. ellipsec. hyperbolad. circle
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Solution
We are given the equation
[tex]x^2+10xy+25y^2-2x-4y+10=0[/tex]We will first simplify the equation
[tex]\begin{gathered} x^{2}+10xy+25y^{2}-2x-4y+10=0 \\ \left(x+5y\right)^2-2\left(x+y\right)+10=0 \\ (x+5y)^2=2(x+y)-10 \end{gathered}[/tex]We draw the graph
From the graph, one can see that this is a rotated parabola
Correct answer is a Parabola
Option A
Related Questions
Name
1.
Write an expression showing the sum of 8 and a number f.
How do I write this as an expression
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The sum of 8 and a number of f can be written as follow:
8 + f
Solve this system of equations by graphing. First graph the equations, and then type the solution.y=x+7y= –7/3x-3
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Solution
For this case we have the following system of equations:
y= x+7
y= -7/3 x -3
We can create the plot and we got:
Then the answer for this case should be:
x= -3 and y= 4
word problem using a two-step near inequallyPablo wants to rent a boat and spend less than $47. The boat costs $6 per hour, and Pablo has a discount coupon for $7 off. What are the possible numbers ofhours Pablo could rent the boat?Use t for the number of hours.Write your answer as an inequality solved fort
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Answer:
Pablo could rent the boat for less than 9 hours.
t < 9
Explanation:
Since Pablo wants to spend less than $47 to rent a boat and we're told that the boat costs $6 per hour and Pablo has a discount of $7 off, we can go ahead and represent this as an inequality as shown below using t to represent the number of hours;
[tex]6t-7<47[/tex]To solve for t, let's add 7 to both sides;
[tex]6t<54[/tex]Let's divide both sides by 6;
[tex]\begin{gathered} \frac{6t}{6}<\frac{54}{6} \\ t<9 \end{gathered}[/tex]From the above, we can see that Pablo could rent the boat for less than 9 hours in order to spend less than $47.
x + 7y = -3 and y = 7x + 25. Are these parallel, perpendicular, or neither.
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In order to know if those lines are parallel, perpendicular or neither we need to compare the slopes.
When two lines are parallel they have the same slope, when they are perpendicular their slopes are negative reciprocal, which means:
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ \text{Then} \\ m_1\cdot m_2=-1 \end{gathered}[/tex]Now, we need to arrange both equations into the slope-intercept form y=mx+b
Where m is the slope and b is the y-intercept.
The second line is already in slope-intercept form:
[tex]y=7x+25[/tex]Thus, its slope is 7.
The first line in slope-intercept form is:
[tex]\begin{gathered} x+7y=-3 \\ 7y=-3-x \\ y=\frac{-3-x}{7} \\ y=\frac{-3}{7}-\frac{x}{7} \\ \text{ By reordering terms} \\ y=-\frac{x}{7}-\frac{3}{7} \end{gathered}[/tex]Then it slope is -1/7.
Their slopes are not the same, then they aren't parallel, but let's check if they are perpendicular:
[tex]\begin{gathered} m1\cdot m2=-1 \\ -\frac{1}{7}\cdot7=-1 \\ -1=-1 \end{gathered}[/tex]They are negative reciprocal, then they are perpendicular lines.
Use the graph and the translation (x,y) → (x+2, y + 5) to answer parts a and b below.
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A → A' (-7, 10)
B → B' (1, 5)
C → C' ( -3, 3)
Explanations:The translation rule is:
(x+2, y+5)
We are going to get the coordinates of the vertices A, B, and C.
We will also get the coordinates of the vertices A', B', and C' after translation.
A (-9, 5)
B (-1, 0)
C (-5, -2)
After the translation (x+2, y+5)
A' (-9+2, 5+5)
A' (-7, 10)
B' (-1+2, 0+5)
B' (1, 5)
C' (-5+2, -2+5)
C' (-3, 3)
Therefore:
A → A' (-7, 10)
B → B' (1, 5)
C → C' ( -3, 3)
Suppose that 73% of the residents in a particular community speak English as their primary language.a. What is the probability that exactly seven out of eight random residents in this community will speak English as their primary language?
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Explanation
The question can be solved using the probability distribution formula, which can be seen below.
[tex]P_x=nCxp^xq^{n-r}[/tex]Part A
From the image we can see that n=8 and p=0.73 while q= 1-0.73 = 0.27
Therefore for;
[tex]\begin{gathered} P(7)=8C7(0.73)^7(0.27)^1 \\ =\frac{8!}{7!1!}\times(0.73)^7(0.27)^1 \\ =0.23862 \end{gathered}[/tex]Answer: 0.2386
Part B
[tex]\begin{gathered} Pr(x\ge7)=Pr(7)+Pr(8)=8C7(0.73)^7(0.27)^1+8C8(0.73)^8(0.27)^0 \\ =\frac{8!}{7!1!}\times(0.73)^7(0.27)^1+\frac{8!}{8!0!}\times(0.73)^8(0.27)^0 \\ =0.23862+0.08064 \\ =0.31926 \end{gathered}[/tex]Answer: 0.3193
Part C: Out of a random number of 40 people in the community, the expected number of people that speak English as a lnaguage will be;
[tex]\frac{73}{100}\times40=29.20[/tex]Answer: 29.20
Dr. Jordan is a veterinarian. The table shows the weights of 5 kittens at her office. What is the mean weight of the kittens? Kitten Weight (ounces) Kitten 1 6 Kitten 2 11 Kitten 3 6 Kitten 4 10 Kitten5 7
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Recall that the mean of a given set of values is given as
[tex]\begin{gathered} \text{Mean = }\frac{sum\text{ of all the items or values}}{total\text{ number of item or values}} \\ =\text{ }\frac{6+11+6+10+7}{5} \\ =\frac{40}{5} \\ =8 \end{gathered}[/tex]At State College last term, 61 of the students in a Physics course earned As, 89 earned Bs, 119 got Cs, 79 were issued Ds, and 70 failed the course. If this grade distribution was graphed on a pie chart, how many degrees would be used to indicate the A region? Round your answer to the nearest whole degree.
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The number of degrees that would be used to indicate region A is 53°
EXPLANATION
Number of students with As = 61
Number of students with Bs = 89
Number of students with Cs =119
Number of students with Ds = 79
Number of students with F = 70
To find the number degrees that would be used to indicate A region, we will use the formula below:
[tex]\text{ Region A in degre}e=\frac{Number\text{ of As}}{\text{Total number of student}}\times360^o[/tex]Number of As = 61
Total number of students = 61 + 89 + 119 + 79 + 70 = 418
Substitute the values into the formula and evaluate.
[tex]A\text{ region in degre}e=\frac{61}{418}\times360^o[/tex][tex]=52.55885[/tex][tex]\approx53^o\text{ to the nearest degre}e[/tex]Therefore, the number of degrees ithat would be used to indicate region A is 53°
From the time Ryan wakes up, he spends To hour to get ready and 1 hour to travelfrom home to school..How much time does he take to get to school from the time he wakes up?
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Hi I am having trouble with solving and finding the answers to this problem Find the perimeter of the figure. Use 3.14 for ππ and round to at least 1 decimal place.
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Given:-
An reatacngle with a half sphere at one side.
To find:-
The perimeter of the given image.
Now we are going to find the perimeter of the half sphere. The formula to find half sphere is,
[tex]\pi r+d[/tex]Where r is radius and d is diameter.
The radius of the sphere is 2.5 and the diameter is 5. Substituing the values we get,
[tex]\begin{gathered} \pi r+d=3.14\times2.5+5 \\ \text{ =12.85} \\ \text{ =12.9} \end{gathered}[/tex]Now we find the perimeter of the rectangle below. we get,
[tex]5+5+5=15_{}[/tex]Now to get the total perimeter we need to add both the values. so we get,
[tex]12.9+15=27.9[/tex]So the required perimeter is 27.9
Line L passes through point (10,−1) and line P is the graph of 5x−7y=8.
If L⊥P , what is the equation of L?
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The equation of line L is [tex]7x+5y=70[/tex].
Given,
Line L passes through point (10,-1)
Equation of line P = [tex]5x-7y=8[/tex]
Line L is perpendicular to line P
First find the slope of line P, for that convert the equation into the general form [tex]y=mx+c[/tex]
Where, m=slope
[tex]5x-7y=8\\\\5x-8=7y\\\\y=\frac{5}{7}x-\frac{8}{7}[/tex]
Comparing with general form,
[tex]m=\frac{5}{7}[/tex]
Any line perpendicular to it should have slope in the form [tex]-\frac{1}{m}[/tex]
So, the slope of line L becomes [tex]-\frac{7}{5}[/tex]
Equation of line L can be written as [tex]y-y1=m(x-x1)[/tex]
Where, (x1,y1) is the point through which line passes and 'm' is the slope of line L
[tex]y-(-1)=-\frac{7}{5}(x-10)\\\\5(y+1)=-7x+70\\\\5y+5=-7x+70\\\\7x+5y=70[/tex]
Thus, the equation of line L is [tex]7x+5y=70[/tex]
To learn more about equation of line refer here
https://brainly.com/question/10915693
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Find the slope of the line that passes thru the points (1,2) & (7,7)
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Determine the slope of line passing through points (1,2) and (7,7).
[tex]\begin{gathered} m=\frac{7-2}{7-1} \\ =\frac{5}{6} \end{gathered}[/tex]So slope of the line is 5/6.
Replace * with a digit that allows you to reduce the fraction. If there are two * in thesame fraction, replace them with the same digit. Find all possible values of * in eachfraction.6*2/1*0
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There are 10 possible digits that we can replace. These are from 0 - 9.
Let's start replacing with 0 first. The fraction will be 602/100 and can be reduced to 301/50.
If we replace * with 1, the fraction will be 612/110 and be reduced to 306/55.
If we replace * with 2, the fraction will be 622/120 and be reduced to 311/60.
If we replace * with 3, the fraction will be 632/130 and be reduced to 316/65.
We can use all the digits from 0 - 9 to replace * and it will allow us to reduce the fraction because the numerator and denominator ends in 2 and 0 respectively.
1. Lines p and q are intersected by line r, such that line p is parallel to line q. If m<1=7x - 36 and m<2 = 5x+12, what is the m<1
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We are given a figure in which line r intersects two parallel lines p and q.
The angles labeled as ∠1 and ∠2 are known as same-side interior angles.
Same-side interior angles are supplementary meaning that their sum is equal to 180°.
So we can write,
[tex]\begin{gathered} \angle1+\angle2=180\degree \\ (7x-36)+(5x+12)=180\degree \end{gathered}[/tex]Now let us solve this equation for x.
[tex]\begin{gathered} 7x+5x-36+12=180 \\ 12x-24=180 \\ 12x=180+24 \\ 12x=204 \\ x=\frac{204}{12} \\ x=17\degree \end{gathered}[/tex]Now we can find the exact value of the angle ∠1
[tex]\angle1=7x-36=7(17)-36=119-36=83\degree[/tex]Therefore, angle ∠1 = 83°
I’m confused the other answer is QUANTITATIVE sorry that it’s in capital but I don’t really get it
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answer is
discrete and quantitative
Gina was working in the laboratory on an experiment involving the population of bacteria. If her initial starting amount in a petri dish was 125 bacteria, how many would be in the petri dish after 24 hours?
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Answer:
It would be a lot of bavgeria
Answer:
450000
Step-by-step explanation:
125×(60×60)
=125×3600
=450000
Firestone tires cost $50.20 each. A set of four Lemans tires costs $197.99. How much can a person save by buying the set of four Lemans tires compared to four Firestone tires?
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Answer:
591.16
Step-by-step explanation:
im pretty sure this is right
Prescription 1: According to the eScience Lab Manual for Lab 1, Experiment 3, you need to prepare 65 mL of a 60% soda/syrup “prescription”.To do this, you can use the 80% soda solution and the syrup solution (0% strength) that you have in inventory.How many mLs of soda solution do you need to create this final solution?
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Let:
x = mL of soda solution
y = mL of syrup solution
The soda solution is 80% strength and the syrup solution is 0% strength, thus the combination of x and y of each solution gives strength of:
80x + 0y
This combination must be 60% strength, thus:
80x + 0y = 60(x + y) [1]
The total amount of solution is 65 mL, thus:
x + y = 65
Substituting in [1]
80x + 0y = 60*65
Operating and simpliifying:
80x = 3900
Dividing by 80:
x = 48.75
I need 48.75 mL of soda solution
drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters.{{x|x\geq7}}AnswerAnswer,AnswerAnswer
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In order to write this set in interval notation, first let's understand what the set represents.
This set includes all numbers that are greater than or equal to 7.
That is, the smaller number in the set is 7, and the greater value doesn't exist, so we can use positive infinity to represent that the set only grows.
Since number 7 is included in the set, we use square brackets, and since positive infinity is not included in the set (because it's not a number that is in the set), we use parenthesis, so the interval notation is:
[tex]\lbrack7,\text{inf)}[/tex]A larger pipe fills a water tank twice as fast as a smaller pipe. When both pipes are used, they fill the tank in 55 hours. If the larger pipe is left off, then how long would it take the smaller pipe to fill the tank?
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For this exercise you need to use the Work-rate formula. This is:
[tex]\frac{t}{t_A}+\frac{t}{t_B}=1[/tex]Where:
- "t" is the time for the objects A and B together.
- The individual time for object A is:
[tex]t_A[/tex]- The individual time for object B is:
[tex]t_B[/tex]In this case, you can idenfity that:
[tex]\begin{gathered} t=55 \\ t_A=2t_B \\ _{} \end{gathered}[/tex]Substitute them into the formula:
[tex]\frac{55}{2t_B_{}_{}}+\frac{55}{t_B}=1[/tex]Now you must solve for:
[tex]t_B[/tex]You get that this is:
[tex]\begin{gathered} \frac{55+2(55)}{2t_B}=1 \\ \\ \frac{55+110}{2t_B}=1 \\ 165=(1)(2t_B) \\ \\ \frac{165}{2}=t_B_{} \\ \\ t_B=82.5 \end{gathered}[/tex]The answer is: It takes the smaller pipe 82.5 hours to fill the tank.
A line segment, ST, has endpoints S(-7,-3) and T(-1,-1). Which of the following equations represents the perpendicular bisector of the line segment? A. y = 2x - 15 B. y = -3x - 14 C. y = 6x - 14 D. y = -3x - 20
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SOLUTION
The given points are: (-7,-3) and (-1,-1)
The slope of the line segment is:
[tex]\begin{gathered} m=\frac{-1-(-3)}{-1-(-7)} \\ m=\frac{-1+3}{-1+7} \\ m=\frac{2}{6} \\ m=\frac{1}{3} \end{gathered}[/tex]Recall that the product if solpes of perpendicular line give -1.
The the slope of the perpendicula bisector is:
[tex]\begin{gathered} m_1=\frac{1}{\frac{1}{3}} \\ m=3 \end{gathered}[/tex]Therefore the slope of the perpendicular bisector is -3.
Recall that the perpendicular bisector passes through the center of a line segment.
Hence the perpendicular bisector will pass through:
[tex]\begin{gathered} (\frac{-7-1}{2},\frac{-3-1}{2}) \\ =(\frac{-8}{2},\frac{-4}{2}) \\ =(-4,-2) \end{gathered}[/tex]Using the point slope form, the equation of the perpendicular bisector is:
[tex]\begin{gathered} y-(-2)=-3(x-(-4)) \\ y+2=-3x-12 \\ y=-3x-12-2 \\ y=-3x-14 \end{gathered}[/tex]Therefore the required equation is:
[tex]y=-3x-14[/tex]Want an extra challenge? This screen is **optional**: 30° If you want more practice to really level up your Right Triangle Trig skills, see if you can solve for the missing sides of the Right Triangle pictured to the left. C a You can enter your results and check your work in the table below. 7 HINT: The side that is 7 units long is OPPOSITE the 30° angle. Length of Hypotenuse (c) Length of Other Leg (a) Did I Get Them Right?!
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Answer:
c = 14
a = 7√3
Explanation:
To find the value of c, we will use the sin(30) because sin(30) is equal to the opposite side over the hypothenuse. So:
[tex]\sin (30)=\frac{7}{c}[/tex]Additionally, sin(30) is also equal to 0.5, so we can replace this value and solve for c:
[tex]\begin{gathered} 0.5=\frac{7}{c} \\ 0.5c=7 \\ c=\frac{7}{0.5} \\ c=14 \end{gathered}[/tex]Therefore, the length of the hypotenuse (c) is 7.
Now, we can calculate the length of the other leg using the Pythagorean theorem, where:
[tex]a=\sqrt[]{c^2-7^2}^{}[/tex]So, replacing the value of c by 14, we get:
[tex]\begin{gathered} a=\sqrt[]{14^2-7^2} \\ a=\sqrt[]{196-49} \\ a=\sqrt[]{147} \\ a=\sqrt[]{49\cdot3} \\ a=7\sqrt[]{3} \end{gathered}[/tex]Therefore, the length of the other leg (a) is 7√3
hi, I actually have this question not this one sorry
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we know that
If V is the midpoint of SU
then
SV=VU
substitute the given values
2x+18=8x-6
solve for x
8x-2x=18+6
6x=24
x=4Find SV
SV=2x+18
SV=2(4)+18
SV=26 unitsso
VU=26 unitsand
SU=2SV
SU=2(26)
SU=52 unitsHi! I need help with a couple math questions but heres this oneTriangle XYZ is located at X (−2, 1), Y (−4, −3), and Z (0, −2). The triangle is then transformed using the rule (x−1, y+3) to form the image X'Y'Z'. What are the new coordinates of X', Y', and Z'?
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Transformation rule:
[tex](x,y)\rightarrow(x-1,y+3)[/tex]Given triangle XYZ
To get X'Y'Z' coordinates of vertices, subtract 1 to the x coordinate and add 3 to the y-coordinate:
[tex]\begin{gathered} X(-2,1)\rightarrow X^{\prime}(-2-1,1+3) \\ X^{\prime}(-3,4) \end{gathered}[/tex][tex]\begin{gathered} Y(-4,-3)\rightarrow Y^{\prime}(-4-1,-3+3) \\ Y^{\prime}(-5,0) \end{gathered}[/tex][tex]\begin{gathered} Z(0,-2)\rightarrow Z^{\prime}(0-1,-2+3) \\ Z^{\prime}(-1,1) \end{gathered}[/tex]Then, the coordinates of vertices in triangle X'Y'Z' are: X'(-3,4), Y'(-5,0) and Z'(-1,1)A coach gives 2 water bottles to each player on a basketball team. There are p players on the team. which expression can be used to determine the total number of water bottles that the gives the player on the team?
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If there are p players and every player has 2 water bottles. The total number of water bottles is calculated as:
[tex]\text{Total}=2p[/tex]So, the expression that can be used to determine the total number of water bottles is:
[tex]2p[/tex]what digit is in the
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Given x = 7, we have:
[tex]6x=6(7)=42[/tex]Answer: 42
Cuts iy ucaly cal-VUMU Problem Sandy has a garden in her backyard. The drawing shows How many bags of fertilizer will Sandy need to cover the dimensions of her garden. A bag of fertilizer covers 3 her garden? square feet The area of the garden is feet Sandy will need garden bags of fertilizer to cover her 4 ft. 6 ft.
Answers
Determine the area of the garden by using the following formula for the area of a triangle:
A = b·h/2
where
b: base = 4 ft
h: height = 6 ft
replace the previous values of the parameters into the formula for A:
A = (4 ft)(6 ft)/2
A = 12 ft²
next, take into account that:
1 bag of fertilizer = 3 ft² of garden
then, you have:
number of bags of fertilizer = (12 ft²)/(3 ft²) = 4 bags
Answer:
Determine the area of the garden by using the following formula for the area of a triangle:
A = b·h/2
where
b: base = 4 ft
h: height = 6 ft
Replace the previous values of the parameters into the formula for A:
A = (4 ft)(6 ft)/2
A = 12 ft²
Next, take into account that:
1 bag of fertilizer = 3 ft² of garden
then, you have:
number of bags of fertilizer = (12 ft²)/(3 ft²) = 4 bags
Step-by-step explanation:
Tom is 26 years older than Paul. the product of his ages is 560. How old is Paul?
Answers
Given data:
The given age of Tom is T=P+26.
The expression for the product of their ages is TxP=560.
Substitute (P+26) for T in the second expression.
[tex]\begin{gathered} (P+26)P=560 \\ P^2+26P-560=0 \\ P^2+40P-14P-560=0 \\ P(P+40)-14(P+40)=0 \\ (P+40)(P-14)=0 \\ P=-40,\text{ 14} \\ P=14 \end{gathered}[/tex]Thus, the age of Paul is 14 years.
2. Lisa owns 40% of the stock in a private catering corporation.There are 1,200 shares in the entire corporation.How many shares does Lisa own?
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To find the umber of shares Lisa owns we need to calculate how many shares 40 % represents from the total 1,200 shares.
[tex]\begin{gathered} \frac{40}{100}\frac{\text{ \%}}{\text{ \%}}\text{ = }\frac{x}{1200}\text{ }\frac{shares}{shares} \\ 100\cdot x=40\cdot1200 \\ x\text{ = }\frac{48000}{100}=480\text{ shares} \end{gathered}[/tex]consider the line 4x+9y=-8find the equation of the line that is perpendicular to this line and passes through the point (-2, -2)find the equation of the line that is parallel of this line and passes through the point (-2, -2)