7x2 + 7y2 − 28x + 42y − 35 = 0. in standard form
Answer:
[tex](x-2)^2+(y+3)^2=18[/tex]
Step-by-step explanation:
This is a circle. It already is in standard form, so maybe you mean work form? I'll go with that, since there's nowhere else to go!
Let's group the x terms together and the y terms together and move the constant to the other side of the equals sign first.
[tex]7x^2-28x+7y^2+42y=35[/tex]
In the world of conics, this is a circle because the leading coefficients on the x-squared term and y-squared term are the same, namely 7.
But if we are going to get this into its graphing form, or work form, we need that 7 to be a 1. We are going to complete the square on both the x terms and the y terms. First we factor out the 7 from both x and y:
[tex]7(x^2-4x)+7(y^2+6y)=35[/tex]
The rules for completing the square are as follows:
Take half the linear term, square it, and add it to both sides, keeping in mind the 7 you factored out as a multiplier.
Our linear term in the first set of parenthesis is 4 (from the -4x). Half of 4 is 2, and 2 squared is 4. We add a 4 into the parenthesis, but multiplying in the 7 has us actually adding in a 28.
Our linear term in the second set of parenthesis is a (from 6y). Half of 6 is 3, and 3 squared is 9. We add a 9 into the parenthesis, but multiplying in the 7 has us actually adding in a 63. Now here is what we have done thus far:
[tex]7(x^2-4x+4)+7(y^2+6y+9)=35+28+63[/tex]
We have, in the process of completing the square, created 2 perfect square binomials on the left. That's why we do this...to get those perfect square binomials. Stating those on the left and adding on the right breaks down our equation into work form. Well, almost.
[tex]7(x-2)^2+7(y+3)^2=126[/tex]
Actual work form has us divide both sides by 7 to get the final answer of
[tex](x-2)^2+(y+3)^2=18[/tex]
And there you are!
what adds to be the bottom number but also multiplies to the top
A class of 144 students voted for a class president. Three fourths of the students voted for you. Of the students who voted for you, 5/9 are female. How many female students voted for you?
What is 0.81 as a fraction when the 81 is repeating?
find the reciprocal 8
What is the domain of f(x) = 3x?
Answer:
C. All real numbers.
Step-by-step explanation:
We have been given a function [tex]f(x)=3^x[/tex]. We are asked to find the domain of our given function.
We know that domain of a function is all values of x for which a function is real and defined.
We know that the domain of an exponential function is all real values of x that is [tex](-\infty,\infty)[/tex].
Since our given function is an exponential function, therefore, domain of our given function is all real numbers.
The domain of a function is the set of input values the function can take.
The domain of f(x) = 3x is (c) all real numbers
The function is given as:
[tex]f(x)=3x[/tex]
The above function is not restricted to any input value.
This means that, x can assume any real number as its value, and the function will still be defined.
Hence, the domain of f(x) = 3x is (c) all real numbers
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Emily brought $35 to the fair. at the fair, she spent $16 on ride tickets and she also bought lunch. she had $7 when she left the fair. how much did emily spend on lunch?
A. 23 + x =35
x=12
B. 16 + x =35
x = 19
C. x - 23 = 35
x = 58
D. x + 9 = 35
x= 26
Answer:
the answer is A
Step-by-step explanation:
first you have to add 16+7 which is 23, then subtract 23 from 35 and you get 12, she spent 12 dollars on lunch.
A single six-sided die is rolled. find the probability of rolling a number less than 3
a 25-foot wire is to be cut so that the longer piece is one foot longer than 5 times the shorter peice . find the length of each peice
short piece = x
long piece = 5x +1
x +5x +1 = 25
6x = 24
x = 24/6 = 4
short piece = 4 feet
long piece = 21 feet
Harlen has a wooden board that is 2 and one-fourth feet long. He needs to cut the board into one half-foot piece. How many can one half-foot piece of the board Harlen cut? These are the answer choices
Answer Options with 4 options
A.
1 and one eighth
B.
1 and one fourth
C.
3 and one half
D.
4 and one half
I will rate you five stars and say thank you if right I will even recommend you to someone else
Dr. Hong prescribed 0.019 liter more medicine than Dr. Tannenbaum. Dr. Evans prescribed 0.02 less than Dr. Hong. Who prescribed the most medicine. Who prescribed the least
Who prescribed the
most medicine?
It would be Dr. Hong. This is because Dr. Hong has prescribed more than Dr.Tannenbaum and Dr.Evans.
Who prescribed the least?
It would be Dr.Evans. Because he has prescribed 0.02
less than Dr.Hong and 0.01 less than Dr.Tannenbaum.
Dr. Hong prescribed most medicine and Dr. Evan prescribed less medicine among all other doctors.
Further explanation:
Given:
Dr. Hong prescribed 0.019 liter more medicine than Dr. Tannenbaum.
Dr. Evans prescribed 0.02 liter less than Dr. Hong.
Calculation:
Consider Dr. Tannenbaum prescribed x liter medicine.
It is given that the Dr. Hong prescribed 0.019 liter more than the Dr. Tannenbaum.
Therefore Dr. Hong prescribed [tex]x+0.019{\text{liter}}[/tex] medicine.
It is also given that the Dr. Evans prescribed 0.02 liter less than Dr. Hong.
Therefore, Dr. Evans prescribed [tex]\left({x+0.019-0.02}\right){\text{liter}}[/tex] medicine.
So the Dr. Evans prescribed exactly [tex]\left({x-0.001}\right){\text{liter}}[/tex].
Therefore the medicine prescribed by Dr. Hong is [tex]\left({x+0.019}\right){\text{liter}}\\[/tex].
The medicine prescribed by Dr. Tannenbaum is x liters.
The medicine prescribed by Dr. Evans is [tex]\left({x-0.001}\right){\text{liter}}[/tex].
Arrange all doctors in ascending order with their prescribed medicine.
Dr. Hong > Dr. Tannenbaum > Dr. Evans
So it is obtained from the above expression that the Dr. Evans prescribed less medicine and Dr. Hong prescribed most medicine than other doctor.
Thus, Dr. Hong prescribed most medicine and Dr. Evans prescribed less medicine among all other doctors.
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Algebraic expression
Keywords:
Dr. Hong, Dr. Tannenbaum, Dr. Evans, medicine, Doctor, prescribed, less, more, liter.
The line 3x+4y=24 cuts the x-axis at point A and the y-axis at B. Find
The coordinate of A and B
The length of AB
Point C is on the line such that C is equidistant from x and y-axis.find coordinate of C.
The coordinates of A and B are (8,0) and (0,6) respectively. The length of AB is 10 units. The coordinates of point C, which is equidistant from both axes, are (3,3).
Explanation:To find the coordinates of points A and B, you should find the points where the line intersects the x and y-axes. For the x-axis (y=0), the equation 3x + 4(0) = 24 simplifies to 3x = 24, or x = 8. Therefore, the coordinates of A are (8,0). Similarly, for the y-axis (x=0), the equation 3(0) + 4y = 24 simplifies to 4y = 24, or y = 6. Therefore, the coordinates of B are (0,6).
To find the length of AB, we use the distance formula, √[(x2−x1)²+(y2−y1)²], which results in √[(0-8)²+(6-0)²] = √[64+36] = √100 = 10.
For point C to be equidistant from the x-axis and the y-axis, its coordinates must be the same. Substituting y=x into the equation of the line gives 3x + 4x = 24, or x=3. So the coordinates of C are (3,3).
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select two answers please!!!!!
evaluate -x+y+6 for x=-3 and y=-1
Circle D is shown with the measures of the minor arcs. Which segments are congruent? EH and EF GH and FE FG and EH EF and GF
Answer:
The answer is D or "EF and GF"
Step-by-step explanation:
Compute, in centimeters and in meters, the height of a basketball player who is 6 ft 6 in. tall.
Answer:
Height in cm =198.12 cm
Height in m =1.9812 m
Step-by-step explanation:
To make this conversion we have to get the conversion rate from feet and inches to centimeters.
Each feet is 30.48 cm. And each inch is 2.54 cm This is the rate of conversion.
So, to get the height of the basketball player we have to multiply the height in feet and inches by the rate.
6 ft x 30.48 cm= 182.88 cm
6 in x 2.54 cm= 15.24 cm
Adding both, height in cm =198.12 cm
Rate of conversion cm to m= 100 cm are a meter
We divide the height in cm by 100 to get the height in m
Height in m =1.9812 m
in a frog hopping contest,leaping louie finished one Leap ahead of able Mable able Mable was not in last place muddy buddy finish 7 Leaves ahead of hopping Henry hopping Henry finish three leaves behind leapin Louie's leapin Louie finished five leaves behind Dynamite Dixie who won the contest
Let’s assume that one drop is equal to 50 µl. a total of 2366 drops will fill how many tablespoons?
If 3x - 1 = 11, what is the value of x2 + x?
The value of x² + x will be 20 when 3x - 1 = 11 .
Given, equation : 3x - 1 = 11
Firstly find the value of x from the equation .
Equation : 3x - 1 = 11
3x = 11 + 1
3x = 12
x = 4
Substitute x in x² + x .
= (4)² + 4
= 20
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If m angle abf=7b-24 and m angle abe=2b find m angle ebf
angle ABE is equivalent
to the whole angle, and it measures 2b.
while the angle ABF is only a portion of angle ABE, and it
measure 7b - 24.
since we know the measure of the whole angle and a part of
the angle, we can then subtract to find the left over angle (angle EBF), so
Angle EBF = Angle ABE - Angle ABF
Angle EBF = 2b – (7b – 24)
Angle EBF = 24 – 5b
How do you solve for this show steps for it
Determine the number(s), x, between 0 and 2π where the line tangent to the function f(x)=2sin(x)+2cos(x) is horizontal.
An apartment has 918 square feet of carpeting. How much is this in square meters? Use the following conversion: 1 square meter is 10.8 square feet.
The area of the apartment in square meters will be 85 square meters.
Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
Given that an apartment has 918 square feet of carpeting. The area of the apartment in square meters will be calculated as:-
As we know that 1 square meter is equal to 10.8 square feet.
10.8 square feet = 1 square meter
918 square feet = 918÷10.8
918 square feet = 85 square meters
Therefore, the apartment will have an area of 85 square meters.
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The speed limit on a highway is 70 miles per hour. About how fast is this in miles per minute?
What is the place value of the2 in 324 and 0.324
Klara bought a dozen bags of bird food for $27. Use compatible numbers to find the approximate cost of six dozen bags of bird food
Answer:
The cost of six dozen bags of bird food is $162.
Step-by-step explanation:
Consider the provided information.
Klara bought a dozen bags of bird food for $27.
The above information can be written as:
1 dozen = $27
Multiply both the sides by 6.
1×6 dozen = $27×6
6 dozen = $162
Hence, the cost of six dozen bags of bird food is $162.
Suppose that a subset of 4 balls will be randomly selected from a collection of 4 amber balls, 4 blue balls,4 copper balls, and 4 green balls (so 16 balls in all). what is the probability that exactly two of the colorswill be present (and exactly two of the colors will be absent) in the set of randomly selected balls
16% can be fonud..............................................................
Im not sure
A fireman, 57.6 m away from a burning building, directs a stream of water from a fire hose at an angle of 35.2° above the horizontal. if the initial speed of the stream is 42.7 m/s, at what height will the stream of water strike the building?
First calculate the time it takes to reach the building using the x-component of the velocity.
t = 57.6 m / (42.7 m/s * cos35.2) = 1.65 s
Then we calculate the height y using the y-component of the velocity:
y = (42.7 m/s * sin35.2) * 1.65 s – 0.5 (9.81 m/s^2) (1.65 s)^2
y = 11.26 m
Final answer:
Using principles of projectile motion and given the initial speed, angle of projection, and horizontal distance, the stream of water from the fire hose will strike the building at a height of approximately 20.3 meters.
Explanation:
To determine at what height the stream of water will strike the building, we need to apply the principles of projectile motion. We are given the initial speed of the water stream (42.7 m/s), the angle of projection (35.2 degrees), and the horizontal distance from the fireman to the building (57.6 meters).
First, we separate the initial velocity into horizontal (ux) and vertical (uy) components:
ux = u * cos(θ) = 42.7 m/s * cos(35.2°) = 42.7 m/s * 0.8192 ≈ 35.0 m/s
uy = u * sin(θ) = 42.7 m/s * sin(35.2°) = 42.7 m/s * 0.5759 ≈ 24.6 m/s
Next, we use the formula for the horizontal motion to find the time (t) it takes for the water to reach the building:
x = ux* t => 57.6 m = 35.0 m/s * t => t ≈ 1.65 s
Finally, we can calculate the vertical distance (y) using the time and the vertical component of the velocity:
y = uy*t - (1/2) * g * t2 = 24.6 m/s * 1.65 s - (0.5 * 9.81 m/s2 * (1.65 s)2) ≈ 20.3 m
Therefore, the stream of water will strike the building at a height of approximately 20.3 meters above the ground.
The cost of two mopeds is the same as the cost of seven bicycles. The cost of one bicycle is $152. Therefore, the cost of one moped is
7 x 152 = 1064 for 7 bikes
since 2 mopeds cost that amount divide by 2 for the price of 1 moped
1064/2 = $532
Given the functions, f(x)=x^3+2 and g(x)=x-9, perform the indicated operation. When applicable, state the domain restriction. (f/g)(x)
Final answer:
To divide f(x) by g(x), we get [tex](f/g)(x) = (x^3 + 2) / (x - 9)[/tex] with a domain restriction where x cannot equal 9 because division by zero is undefined.
Explanation:
To perform the indicated operation (f/g)(x), we divide the function f(x) by the function g(x). Given[tex]f(x)=x^3+2[/tex] and g(x)=x-9, we have:
[tex](f/g)(x) = (x^3 + 2) / (x - 9).[/tex]
There is a domain restriction for the function g(x) because we cannot divide by zero. Therefore, the value that makes g(x) = 0 must be excluded from the domain of (f/g)(x). In this case, the domain restriction is x ≠ 9, as 9 would make the denominator zero.