Which equation is equivalent to the following?
4x^2 + 4y^2 +16x – 24y = 34
Please answer it:(
Answers
Answer:
The correct answer is the third expression.
Step-by-step explanation:
We have the following equation:
[tex]4*x^2 + 4*y^2 + 16*x - 24*y = 34[/tex]
Let's organize it by variables, putting together the ones that have the same letter or no letter at all. We have:
[tex]4*x^2 + 16*x + 4*y^2 - 24*y = 34[/tex]
We can extract the common factor on the left side by dividing them by 4, we have:
[tex]4*(x^2 + 4*x) + 4*(y^2 - 6*y) = 34[/tex]
We need to complete the squares on the parenthesis without changing the value of the equation, to do that we will sum the proper values inside the parenthesis and those multiplied by four on the other side of the equation, we have:
[tex]4*(x^2 + 4*x + 4) + 4*(y^2 - 6*y + 9) = 34 + 16 + 36\\4*(x + 2)^2 + 4*(y - 3)^2 = 86[/tex]
The correct answer is the third expression.
Related Questions
A certain television is advertised as a 17-inch TV (the diagonal length). If the width of
the TV is 8 inches, how many inches tall is the TV?
Answers
Answer:
15 inches
Step-by-step explanation:
We can solve this problem using the Pythagorean theorem. The formula is:
[tex]a^{2} + b^{2} = c^{2}[/tex]
where 'c' is the hypotenuse (the longest side) and 'a' and 'b' are the legs (the other sides).
First, draw a diagram for the problem. (See the photo attached below)
We know the other leg is 8 and the hypotenuse is 17. 'a' is the missing side.
a = ?
b = 8
c = 17
Substitute the values into the equation.
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]a^{2} + 8^{2} = 17^{2}[/tex]
Rearrange to isolate 'a'
[tex]a^{2} = 17^{2} - 8^{2}\\[/tex] Square root both sides
[tex]a = \sqrt{17^{2} - 8^{2}}[/tex] Square each number
[tex]a = \sqrt{289-64}[/tex] Subtract under the root
[tex]a = \sqrt{225}[/tex] Find the square root
[tex]a =15[/tex] Final answer
Therefore, the TV is 15 inches tall.
You can work a maximum of 40 hours a week. You need to make $440 in order to cover your expenses. Your office job pays $12 an hour and your babysitting job pays $10 an hour. What is the least possible number of hours you can work at your office job and still meet the requirements?
Answers
Answer:
The least possible number of hours you can work at your office job is 20.
Step-by-step explanation:
$12/h ----> office
$10/h ----> babysitting
"o" -----> hours office job
"b" -----> hours babysitting job
[tex]12x + 10y = 440\\x + y \leq 40\\12x + 10y = 440 -----> 6x + 5y = 220 ----> y = \frac{220-6x}{5} \\\\x + y \leq 40\\x + \frac{220-6x}{5} \leq 40\\5x + 220 - 6x \leq 200\\x \geq 20[/tex]
Which choice is equivalent to the product below when x>0?
Answers
Answer: 1/3
Step-by-step explanation: Using Radical Properties, Whenever we have two or more radical terms which are multiplied with same index, then we can put only one radical and multiply the terms inside the radical.
[tex]\sqrt{ \frac{5}{x^2} }\times \sqrt{ \frac{x^2}{45} }=\sqrt{ \frac{5x^2}{45x^2} }=\sqrt{ \frac{1}{9} }=\frac{1}{3}[/tex]
The expression √(5/x²).√(x²/45) is equivalent to 1/3.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is √(5/x²).√(x²/45)
Square root of five by x square times square root of x square by forty five
√(5/x²).√(x²/45)
√(5x²/45x²)
Cancel out the x² in the numerator and denominator
√(5/45)
Divide numerator and denominator by 5
√(1/9)
1/3
Hence, the expression √(5/x²).√(x²/45) is equivalent to 1/3.
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From a point on the ground the angle of elevation of the top of a tower is x°. Moving 150 meters away from that point the angle of elevation was found to be y° .If tan x=3/4 and tan y=5/7 find the height of the tower.
Answers
Answer:
2250m
Step-by-step explanation:
Step 1
Since
Hence,
tan x = 3/4
tan y=5/7
tan x = BA/ CA where BA = height and CA = distance
3/4 = h/ d
4h = 3d
h = 3d/4.......... Equation 1
tan y = BA / DA + 150m
5/7 = h/d + 150
7 × h = 5(d + 150)
7h = 5d + 750............ Equation 2
Since h = 3d/4
7(3d/4) = 5d + 750
21d/4 = 5d + 750
Multiply both sides by 4
21d = 4(5d + 750)
21d = 20d + 3000
21d -20d = 3000
d = 3000
Distance (d) = 3000m
Substitute 3000m for d in equation 1
h = 3d/4
h = 3 × 3000/4
h = 2250m
Answer:
2250mStep-by-step explanation:
[tex]tangent=\dfrac{opposite}{adjacent}[/tex]
We have:
[tex]\tan x^o=\dfrac{3}{4}\\\\\tan y^o=\dfrac{5}{7}[/tex]
By definition of tangent, we have:
[tex]\tan x^o=\dfrac{AB}{AC}\\\\\tan y^o=\dfrac{AB}{AC+150}[/tex]
Therefore we have the system of equations:
[tex]\left\{\begin{array}{ccc}\dfrac{AB}{AC}=\dfrac{3}{4}&(1)\\\\\dfrac{AB}{AC+160}=\dfrac{5}{7}&(2)\end{array}\right[/tex]
From (1)
[tex]\dfrac{AB}{AC}=\dfrac{3}{4}[/tex] cross multiply
[tex]3AC=4AB[/tex] divide both sides by 3
[tex]AC=\dfrac{4AB}{3}[/tex]
Substitute it to (2):
[tex]\dfrac{AB}{\frac{4AB}{3}+150}=\dfrac{5}{7}\\\\\dfrac{AB}{\frac{4AB}{3}+\frac{3\cdot150}{3}}=\dfrac{5}{7}\\\\\dfrac{AB}{\frac{4AB}{3}+\frac{450}{3}}=\dfrac{5}{7}\\\\\dfrac{AB}{\frac{4AB+450}{3}}=\dfrac{5}{7}\\\\AB\cdot\dfrac{3}{4AB+450}=\dfrac{5}{7}[/tex]
[tex]\dfrac{3AB}{4AB+450}=\dfrac{5}{7}[/tex] cross multiply
[tex](3AB)(7)=(5)(4AB+450)\\\\21AB=(5)(4AB)+(5)(450)[/tex]
[tex]21AB=20AB+2250[/tex] subtract 20AB from both sides
[tex]AB=2250[/tex]
Such a tower height is rather impossible, but this is the solution.
En el videojuego "City Sweet" hay una ciudad sitiada en la que hay víveres para 2000 personas durante 15 días, un grupo de 500 habitantes decide rendirse. ¿Cuántos días podrán resistir los demás, si los que se rinden no se llevan víveres?
Answers
Answer:
20 days.
Step-by-step explanation:
In this case we must make an inverse proportionality rule, it is inverse because the fewer people there are, the more days must survive. In other words, we know that 2000 people can resist for 15 days, now, if there are no longer 2000 people, but 500 less, that is, 1500 (2000 - 500) how many days can they resist.
people days
2000 15
1500 x
x = 2000 * 15/1500
x = 20
That is, they could last 20 days.
(y+3)(x^2–3y+9) What is the product?
Answers
Answer:
yx
2
−3y
2
+3x
2
+27
Step-by-step explanation:
who can please help solve and explain
Answers
Answer:49882
when I put a number over a number it means I can't put the whole number inside the answer line so I toke out the last number and put it in
5 0 9
× 9 8
45810. this is from multiplying with the nine
+ 4062. this is from multiplying with the right
49882 this is the answer
u had to add the two answer and that's how I got 49882
Teena and Adil have a total of 560 counters. Adil has 2/5 of the number of counters that Teena has. How many more counters does Teena have then Adil?
A) 240
B) 336
C) 400
D) 224
Answers
ANSWER:
:2/5 * 560 = D) 224
PLEASE SEE PIC BELOW
Answers
Answer:
They have the same domain and range
Step-by-step explanation:
Although they are different equations, they both have a domain of
[0,∞)
and a range of
[0,∞)
What is the maximum number of possible extreme values for the function,
f(x) = x4+-7x2-x+6?
A. 3
B. 4
C. 2
D. 5
Answers
Answer:3
Step-by-step explanation:
Please answer correctly !!!!!!! Will mark brainliest !!!!!!!!!
Answers
Answer:
work is shown and pictured
Find the size of the final unknown interior angle in a polygon whose other interior angles are:
Answers
Answer:
Step-by-step explanation:(2ñ-4)90
(7×2-4)90
=900°
900-(162+125+148+105+98+115)
900-753
=147°
Which percent is equivalent to One-half? edgeunity
Answers
Answer:50%
Step-by-step explanation:
Answer:
The answer is 50%
Step-by-step explanation:
SOMEBODY PLEASE HELP:)
Answers
Answer:
A =12.92 cm^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
A = 1/2 ( 7.6) ( 3.4)
A =12.92 cm^2
Answer:
[tex] = 12.92 {cm}^{2} [/tex]
Step-by-step explanation:
[tex]area = \frac{1}{2} \times b \times h \\ = \frac{1}{2} \times 7.6 \times 3.4 \\ = \frac{25.84}{2} \\ = 12.92 {cm}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Kent is cutting a long tree into pieces. He cut the trunk into 3 pieces. Then he cut each of those pieces into 3 smaller pieces. Finally he cut each of those smaller pieces into 3 still smaller pieces. How many pieces did they have then?
Answers
Answer:
27
Step-by-step explanation:
he started by cutting one log into 3
1×3=3
then cutting each of those into 3
3×3=9
then again
9×3=27
what type of solutions does this equation have
Answers
Answer:
2 imaginary solutions
Step-by-step explanation:
A toy store marks down every toy by 15% in June .how much does a toy cost during June
Answers
Answer:
15% less than its regular price
Step-by-step explanation:
If the toy is marked down 15% in June, its cost during June is 15% less than its regular cost. (It will be 85% of its regular cost.)
Given: w ∥ x and y is a transversal. Prove: ∠3 and ∠5 are supplementary. Parallel and diagonal lines w and x are cut by horizontal transversal y. On line w where it intersects with line y, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 3, 4, 2. On line x where it intersects with line y, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 7, 8, 6. Use the drop-down menus to complete the proof. Given that w ∥ x and y is a transversal, we know that ∠1 ≅∠5 by the . Therefore, m∠1 = m ∠5 by the definition of congruent. We also know that, by definition, ∠3 and ∠1 are a linear pair so they are supplementary by the . By the , m∠3 + m ∠1 = 180. Now we can substitute m∠5 for m∠1 to get m∠3 + m∠5 = 180. Therefore, by the definition of supplementary angles, ∠3 and ∠5 are supplementary.
Answers
Answer:
1.Corresponding angles theorem
2.Linear postulate
3.By the definition of supplementary angles
Step-by-step explanation:
We are given that
[tex]w\parallel x \ and \ y[/tex] is a transversal.
We have to prove [tex]\angle 3[/tex] and [tex]\angle 5[/tex] are supplementary
Proof:
1.Given that [tex]w\parallel x \ and \ y[/tex] is a transversal.
We know that [tex]\angle 1\cong \angle 5[/tex]
Reason:Corresponding angles theorem
Therefore, [tex]m\angle 1=m\angle 5[/tex]
by the definition of congruent.We also know that, by definition, angle 3 and angle 1 are a linear pair.
Therefore, they are supplementary by linear pair postulate
By the definition of supplementary angles
[tex]m\angle 3+m\angle 1=180^{\circ}[/tex]
Now, we can substitute [tex]m\angle 5=m\angle 1[/tex]
Then, we get
[tex]\m\angle 3+m\angle 5=180^{\circ}[/tex]
Therefore, by the definition of supplementary angles,angle 3 and angle 5 are supplementary
Answer:
1. Corresponding angles theorem
2. Linear pair postulate
3. Definition of supplementary angles
Find the value of x in the given right triangle.
Answers
Answer:
cosine = adjacent / hypotenuse
cosine (62) = x / 12
x = 12 * 0.46947
x = 5.6
Step-by-step explanation:
Add
(2x^2 - 2x) + (6x - 4)
Answers
Answer:
2x^2 +4x -4
Step-by-step explanation:
(2x^2 - 2x) + (6x - 4)
Combine like terms
2x^2 +6x-2x -4
2x^2 +4x -4
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each division expression with the correct quotient.
6x - 8
5x - 8
2x + 6
8r - 2
6x + 5
2x + 5
50 + 6
5.1 – 2
A:(1812 + 150) - 3.1
B:(16x2 + 48x) - 81
C:(56x2 - 14x) = 7x
D:(20x2 – 32x) = 4x
Answers
Answer:
A. 6 x + 5
B. 2 x + 6
C. 8 x - 2
D. 5 x - 8
Step-by-step explanation:
Given: division expressions
To find: quotient of each of the division expressions
Solution:
Use formula: [tex]\left ( \frac{x^m}{x^n} \right )=x^{m-n}[/tex]
A.
[tex]\frac{18x^2+15x}{3x}=\frac{18x^2}{3x}+\frac{15x}{3x}=6x^{2-1}+5=6x+5[/tex]
B.
[tex]\frac{16x^2+48x}{8x}=\frac{16x^2}{8x}+\frac{48x}{8x}=2x^{2-1}+6=2x+6[/tex]
C.
[tex]\frac{56x^2-14x}{7x}=\frac{56x^2}{7x}-\frac{14x}{7x}=8x^{2-1}-2=8x-2[/tex]
D.
[tex]\frac{20x^2-32x}{4x}=\frac{20x^2}{4x}-\frac{32x}{4x}=5x^{2-1}-8=5x-8[/tex]
Answer:
A.[tex]\frac{18x^2+15x}{3x}=6x+5[/tex]
B.[tex]\frac{16x^2+48x}{8x}=2x+6[/tex]
C.[tex]\frac{56x^2-14x}{7x}=8x-2[/tex]
D.[tex]\frac{20x^2-32x}{4x}=5x-8[/tex]
Step-by-step explanation:
A.[tex]\frac{18x^2+15x}{3x}[/tex]
[tex]\frac{3x(6x+5)}{3x}[/tex]
=[tex]6x+5[/tex]
[tex]\frac{18x^2+15x}{3x}=6x+5[/tex]
B.[tex]\frac{16x^2+48x}{8x}[/tex]
=[tex]\frac{16x(x+3)}{8x}[/tex]
[tex]=2(x+3)[/tex]
[tex]=2x+6[/tex]
[tex]\frac{16x^2+48x}{8x}=2x+6[/tex]
C.[tex]\frac{56x^2-14x}{7x}[/tex]
[tex]=\frac{14x(4x-1)}{7x}=2(4x-1)=8x-2[/tex]
[tex]\frac{56x^2-14x}{7x}=8x-2[/tex]
D.[tex]\frac{20x^2-32x}{4x}[/tex]
=[tex]\frac{4x(5x-8)}{4x}=5x-8[/tex]
[tex]\frac{20x^2-32x}{4x}=5x-8[/tex]
Rafael ha comprado 185,8 kg. de manzanas y 300,2 kg. de naranjas. ¿Cuánto más pesan las naranjas que las manzanas? ¿Cuánto pesa su compra?
Answers
Answer:
a.114.4kg
b. 486kg
Step-by-step explanation:
Firstly , we want to know the value with which the apples weigh more than the oranges
To calculate this, we simply subtract the weight of the oranges from that of the apple
Mathematically, that would be ;
300.2-185.8 = 114.4kg
The total weight of the things bought is calculated by adding both weights together
That would be 185.8 + 300.2 = 486 kg
Find a coterminal angle to -180 degrees.
Answers
Answer:
540 degrees
Step-by-step explanation:
Hector draws a triangle with exactly two sides that have the same length. Which of the following are possible ways to classify the triangle by its angle measures and side lengths? Select all that apply. A. right and isosceles B. acute and isosceles C. obtuse and scalene D. acute and scalene E. obtuse and isosceles
Answers
Answer:
I think it's A but I'm not sure
Arrange the trigonometric functions in increasing order of their values
cos π/6 sin π/6 cos π/2 sin π/2 cos π/4
Answers
Answer: pretty sure it's this
Step-by-step explanation:
Factor 8d^2 - 18 ? HELP PLEASE!!!!
Answers
Answer:
2 ( 2d -3)(2d+3)
Step-by-step explanation:
8d^2 - 18
Factor out the greatest common factor 2
2(4d^2 -9)
Rewriting the terms in parentheses
2 (( 2d)^2 - 3^2)
We recognize that this is the difference of squares ( a^2 - b^2) = (a-b)(a+b)
2 ( 2d -3)(2d+3)
Answer:
[tex]2(2d-3)(2d+3)[/tex]
Step-by-step explanation:
[tex]8 {d}^{2} - 18 \\ 2(4 {d}^{2} - 9)
=2(2d-3)(2d+3) [/tex]
hope this helps
brainliest appreciated
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Pat walked around a circular track she knew that the distance across The center was 100 meters if she walked around the entire track how far did she walk
Answers
Answer:
314.16 m
Step-by-step explanation:
The distance across the track is 100 metres. This means that the diameter is 100 m.
The track is circular, so, we need the circumference.
The circumference of a circle is given as:
C = πD
where D = diameter
Therefore, the circumference of the track is:
C = π * 100 = 314.16 m
She walked a distance of 314.16 m
Which of the following exponential functions represents the graph below?
O A Rx) = 1 • 3*
O B. f(x) = 10
O c.
C. 12-23
OD. f(x) = 3.1
Answers
The exponential function represented on the graph is f(x) = (1/3)[tex].^x[/tex]. The correct option is B.
What is an exponential function?The mathematical expression f(x)=exp or e^x denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The given graph is representing the exponential function f(x) = (1/3)[tex].^x[/tex] The graph is attached with the answer below. The graph is showing the inverse fraction of ( 1/3).
Therefore, the exponential function represented on the graph is f(x) = (1/3)[tex].^x[/tex]. The correct option is B.
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What is the solution to the system of equations?
-2x + 3y = 13
3x + 4y = 6
Answers
Y=3
I guessed and checked, works for me most of the time
Answer:
x = -2
y = 3
Step-by-step explanation:
You are given a system of two linear equations:
-2x + 3y = 13
3x + 4y = 6
One of the good ways to solve this system is trying to eliminate one variable (x or y), calculate the remaining variable and substitute the calculated variable back into system to solve for eliminated variable.
Here, we will manipulate the original system, so that we can easily eliminate x.
Let's multiply both sides of the first equation by 3 and the second equation by 2 (this manipulating step does not change the original system of equations).
3*(-2)x + 3*3y = 3*13
2*3(x) + 2*4y = 2*6
<=>
-6x + 9y = 39
6x + 8y = 12
Now, we add up two equations, left side + left side, right side + right side, we obtain:
-6x + 9y + 6x + 8y = 39 + 12
or
17y = 51
We divide both sides of equation by 17, to get y.
=> y = 51/17 = 3
Substitute y = 3 back into the first equation of system (or the second equation, it doesn't matter, here we choose the first one).
=> -2x + 3*3 = 13
=> -2x + 9 = 13
=> -2x = 4
=> x = -2
=> The solution of this system is (x, y) = (-2, 3)
Hope this helps!
:)
if x
varies directly as y.
x=5 and y=10. find the
Value of a x when y=
3
Answers
Answer:
x = 1.5 when y = 3
Step-by-step explanation:
You can put this in a ratio:
x : y
5 : 10
1.5 : 3
x is 1.5 when y is 3.
