Answers
The answer to the given expression when [3(1/6) - 1(5/8)] divided by [8{3/4} - 1.35) will be equal to 0.00896.
Convert mixed numbers to fractions:
[tex]3(\frac{1}{6}) = \frac{(3 \times 6 + 1) }{6} = \frac{19 }{ 6}\\\\8(\frac{3}{4}) = \frac{(8 \times 4 + 3) }{ 4} = \frac{35 }{ 4}[/tex]
Substitute the fractions into the expression:
[tex]\frac{[ (\frac{19}{6}) - 1(\frac{5}{8}) ] }{ [ (\frac{35}{4}) - 1.35 ]}[/tex]
Simplify the expression:
Numerator:
Common denominator for (19/6) and (5/8) is 24
19/6 - 1(5/8) = (19/6) - (15/8) = (19*4 - 6*15)/24 = 1/24
Denominator:
Convert 1.35 to fraction: 1.35 = 135/100 = 27/20
Common denominator for (35/4) and (27/20) is 20
(35/4) - 1.35 = (35/4) - (27/20) = (35 * 5 - 27 * 1) / 20 = 123/20
Divide the numerator and denominator by their greatest common divisor (GCD):
GCD(1, 24) = 1
GCD(123, 20) = 1
Simplify the expression:
[tex]\frac{(\frac{1 }{ 24}) }{ (\frac{123 }{ 20})}\\\\ = \frac{1 }{ \frac{24 \times 123 }{ 20}}\\\\ = \frac{1 }{ 111.6}[/tex]
1 / 111.6 ≈ 0.00896
Related Questions
Find the coordinates when the parallel lines AB and PQ are reflected over the x-axis. The points are A(1, 1), B(1,4), and
P(3, 1). Q(3, 4).
Answers
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y )
Hence
A(1, 1 ) →A'(1, - 1 )
B(1, 4 ) → B'(1, - 4 )
P(3, 1 ) → P'(3, - 1 )
Q(3, 4 ) → Q'(3, - 4 )
When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 56 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 7000 batteries, and 1% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
Answers
Answer:
98.1% chance of being accepted
Step-by-step explanation:
Given:
sample size,n=56
acceptance condition= at most 2 batteries do not meet specifications
shipment size=7000
battery percentage in shipment that do not meet specification= 1%
Applying binomial distribution
P(x)=∑ᵇₐ=₀ (n!/a!(n-a)!)p^a (1-p)^(n-a)In this formula, a is the acceptable number of defectives;
n is the sample size;
p is the fraction of defectives in the population.
Now putting the value
a= 2
n=56
p=0.01
[tex]\frac{56!}{0!\left(56-0\right)!}\left(0.01\right)^0\:\left(1-0.01\right)^{\left(56-0\right)} + \frac{56!}{1!\left(56-1\right)!}\left(0.01\right)^1\:\left(1-0.01\right)^{\left(56-1\right)} +[/tex][tex]\:\frac{56!}{2!\left(56-2\right)!}\left(0.01\right)^2\:\left(1-0.01\right)^{\left(56-2\right)}[/tex]
=0.56960+0.32219+0.08949
After summation, we get 0.981 i.e. a 98.1% chance of being accepted. As this is such a high chance, we can expect many of the shipments like this to be accepted!
help me to do this question friends
Answers
Answer:
(1, 1 )
Step-by-step explanation:
Given the 2 equations
2x + 3y = 5 → (1)
3x + 2y = 5 → (2)
We can eliminate the term in x by multiplying (1) by 3 and (2) by - 2
6x + 9y = 15 → (3)
- 6x - 4y = - 10 → (4)
Add (3) and (4) term by term
(6x - 6x) + (9y - 4y) = (15 - 10), that is
5y = 5 ( divide both sides by 5 )
y = 1
Substitute y = 1 in either (1) or (2) and solve for x
Substituting in (1), then
2x + (3 × 1) = 5
2x + 3 = 5 ( subtract 3 from both sides )
2x = 2 ( divide both sides by 2 )
x = 1
Solution is (1, 1 )
In each function, x is the horizontal distance the ball travels in meters, and y
represents the height.
Whose soccer ball reaches a greater height?
Answers
Soccer ball reaches its highest position when its equation turns from positive slope to zero and then negative. Mathematically it is where the derivative of the its function equals to zero. so:
d(-3x^2 + 6x + 3) / dx = -6x + 6
-6x + 6 = 0 -> x = 1 ->
[tex]y = 6[/tex]
it seems Paige's ball reaches higher than Viaola's with only 6 meters height.
18 is what percent of 24?
Answers
The number 18 expressed as a percentage of 24 is; 75%
To determine what percentage of 24 is 18;
We must evaluate the percentage as follows;
(18/24) × 100%= 0.75 × 100%= 75%Read more;
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In the diagram of circle O, what is the measure of ∠ABC?
I WILL GIVE BRAINLIEST
Answers
Answer:
The measure of angle ABC is 34°
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
so
∠ABC=(1/2)[major arc AC-minor arc AC]
∠ABC=(1/2)[major arc AC-146°]
Find the measure of major arc AC
major arc AC=360°-146°=214°
substitute
∠ABC=(1/2)[214°-146°]=34°
Which is an exponential decay function?
Answers
Step-by-step explanation:
exponential decay functions are written in the form :
[tex]y=ab^{x}[/tex]
where b is less than 1
if we look at the 3rd choice and consider the term on the right.
[tex](8/7)^{-x}[/tex]
= [tex](7/8)^{x}[/tex]
If we compare this to the general form above,
b = 7/8 (which is less than 1)
hence the 3rd choice is correct.
The function which is an exponential decay function is:
[tex]f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}[/tex]
Step-by-step explanation:We know that an exponential function is in the form of:
[tex]f(x)=ab^x[/tex]
where a>0 and if 0<b<1 then the function is a exponential decay function.
and if b>1 then the function is a exponential growth function.
a)
[tex]f(x)=\dfrac{3}{4}(\dfrac{7}{4})^x[/tex]
Here
[tex]b=\dfrac{7}{4}>1[/tex]
Hence, the function is a exponential growth function.
b)
[tex]f(x)=\dfrac{2}{3}(\dfrac{4}{5})^{-x}[/tex]
We know that:
[tex]a^{-x}=(\dfrac{1}{a})^x[/tex]
Hence, we have the function f(x) as:
[tex]f(x)=\dfrac{2}{3}(\dfrac{5}{4})^x[/tex]
Here
[tex]b=\dfrac{5}{4}>1[/tex]
Hence, the function is a exponential growth function.
c)
[tex]f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}[/tex]
We know that:
[tex]a^{-x}=(\dfrac{1}{a})^x[/tex]
Hence, we have the function f(x) as:
[tex]f(x)=\dfrac{3}{2}(\dfrac{7}{8})^x[/tex]
Here
[tex]b=\dfrac{7}{8}<1[/tex]
Hence, the function is a exponential decay function.
d)
[tex]f(x)=\dfrac{1}{3}(\dfrac{9}{2})^x[/tex]
Here
[tex]b=\dfrac{9}{2}>1[/tex]
Hence, the function is a exponential growth function.
Factor by grouping 6v^3-14v^2+15v-35
Answers
Answer:
(3v-7)(2v^2+5)
Step-by-step explanation:
To factor 6v^3-14v^2+15v-35 by grouping we are going to try pair to up the pair two terms and also the last two terms. Like this:
(6v^3-14v^2)+(15v-35)
Now from each we factor what we can:
2v^2(3v-7)+5(3v-7)
Now there are two terms: 2v^2(3v-7) and 5(3v-7).
These terms contain a common factor and it is (3v-7).
We are going to factor (3v-7) out like so:
2v^2(3v-7)+5(3v-7)
(3v-7)(2v^2+5)
A rectangle has a base length of 14 inches and an unknown height, h. The area of the rectangle is less than 56 square inches.
Which inequality represents the possible values of h, the height of the rectangle?
on-14> 56
14-h <56
14h> 56
14h <56
Answers
Answer:
14h <56
Step-by-step explanation:
The area of a rectangle is given by
A =bh
We know the area is less the 56
bh <56
The base length is 14
14h <56
Answer:
D
Step-by-step explanation:
i got this question right on edgeinuity
Find the GCF of 52 and 84.
Answers
Answer:
4
Step-by-step explanation:
The GCF of 52 and 84 is 4.
52 = 2 × 2 × 13
84 = 2 × 2 × 3 × 7
Therefore, GCF = 2 × 2
GCF = 4
The GCF of 52 and 84 is found by finding the prime factors of each number and identifying the common factors. The GCF is 4.
Explanation:The GCF (Greatest Common Factor) of two numbers is the largest number that can evenly divide both numbers. To find the GCF of 52 and 84, we need to find the prime factors of each number and then find the highest common factor of these sets of prime factors.
Prime factors of 52: 2 x 2 x 13 Prime factors of 84: 2 x 2 x 3 x 7
The common factors are 2 and 2, so the GCF of 52 and 84 is 2 x 2, which equals 4.
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What is the vertex of the graph of f(x) = |x + 5| – 6? (–6, –5) (–6, 5) (–5, –6) (5, –6)
Answers
Answer:
(-5, -6)
Step-by-step explanation:
The general form of absolute function is, and
its vertex form is given by:
.....[1]
where, (h, k) is the vertex
As per the statement:
we have to find the vertex of the graph of f(x).
On comparing given equation with [1] we have;
we have;
h =-5 and k = -6
⇒Vertex = (-5, -6)
Therefore, the vertex of the graph of f(x) = |x + 5| – 6 is, (-5, -6)
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Answer:
The answer is (-5, -6)
The temperature was t degrees farenheight . It fell 8 degrees farenheight and is now 32 degrees farenheight.What was the orginal temperature?
Answers
Find two consecutive odd integers whose sum is 36
Which of the following equations could be used to solve the problem
2x=36
2x+1=36
2x+2=36
x^2+2=36
Answers
Answer:
2x + 2 = 36Step-by-step explanation:
Two consecutive odd intergers: x, x + 2.
The sum: 36
The equation:
x + (x + 2) = 36
x + x + 2 = 36
2x + 2 = 36 subtract 2 from both sides
2x = 34 divide both sides by 2
x = 17
x + 2 = 17 + 2 = 19
Misaka solved the radical equation x – 3 = square root of 4x-7 but did not check her solutions. (x – 3)2 = square root of 4x-7^2 x2 – 6x + 9 = 4x – 7 x2 – 10x + 16 = 0 (x – 2)(x – 8) = 0 x = 2 and x = 8 Which shows the true solution(s) to the radical equation x – 3 = square root of 4x-7 x = 2 x = 8 x = 2 and x = 8 There are no true solutions to the equation.
Answers
Answer:
x=8 is a true solution of the radical equation
Step-by-step explanation:
we have
[tex]x-3=\sqrt{4x-7}[/tex]
Solve for x
squared both sides
[tex](x-3)^{2}=4x-7\\\\x^{2}-6x+9=4x-7\\\\ x^{2}-10x+16=0[/tex]
Convert to factored form
[tex]x^{2}-10x+16=(x-2)(x-8)[/tex]
The solutions are x=2 and x=8
Verify the solutions
For x=2
Substitute in the original equation
[tex]2-3=\sqrt{4(2)-7}[/tex]
[tex]-1=1[/tex] ----> is not true
therefore
x=2 is not a true solution of the radical equation
For x=8
Substitute in the original equation
[tex]8-3=\sqrt{4(8)-7}[/tex]
[tex]5=5[/tex] ----> is true
therefore
x=8 is a true solution of the radical equation
The true solution to the radical equation is x = 8, after checking the potential solutions by substituting them back into the original equation.
Explanation:The student is asked to find the true solution(s) to the radical equation x – 3 = square root of 4x-7. The student has solved the equation, but it is essential to check the solutions by substituting them back into the original equation to ensure they are not extraneous. The student got x = 2 and x = 8 as potential solutions. We must substitute these values back into the original equation to determine their validity:
For x = 2: 2 – 3 does not equal the square root of (4(2) – 7), so x = 2 is not a solution.For x = 8: 8 – 3 does equal the square root of (4(8) – 7), so x = 8 is a solution.Hence, the only true solution to the radical equation x – 3 = square root of 4x-7 is x = 8.
Find the equation for the parabola that passes through the point (-2,-4), with vertex at (3,1) and a vertical axis
of symmetry.
Answers
Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (3, 1), hence
y = a(x - 3)² + 1
To find a substitute (- 2, - 4) into the equation
- 4 = a(- 2 - 3)² + 1
- 4 = 25a + 1 ( subtract 1 from both sides )
25a = - 5 ( divide both sides by 25 )
a = - [tex]\frac{5}{25}[/tex] = - [tex]\frac{1}{5}[/tex]
y = - [tex]\frac{1}{5}[/tex] (x - 3)² + 1 ← in vertex form
What is the vertex form of y=x^2-6x+6
Answers
[tex]y=x^2-6x+6\\y=x^2-6x+9-3\\y=(x-3)^2-3[/tex]
The vertex form of the quadratic equation is y = (x-3)^2 + 3.
Explanation:The vertex form of a quadratic function is given by y = a(x-h)^2 + k, where (h,k) represents the coordinates of the vertex. To convert the quadratic equation y = x^2-6x+6 into vertex form, we need to complete the square.
First, let's group the terms with x together: y = (x^2-6x) + 6.To complete the square, take half the coefficient of x (-6), square it (-6/2)^2 = 9, and add it inside the parentheses: y = (x^2-6x+9) - 9 + 6.Simplify the equation: y = (x-3)^2 + 3. This gives us the vertex form of the quadratic equation.Learn more about Vertex form of quadratic equation here:https://brainly.com/question/31546205
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When figures (including points) are rotated 270° counterclockwise about the origin, it is also the same rotating figures clockwise by what other degree amount? Please help!
Answers
Answer: 90 degrees.
Step-by-step explanation: since 360 degrees is a whole circle, subtract 360 from 270 to get 90 degrees.
which methods could you use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15). Check all that apply.
a. Divide 1 by 15
b. Count by hand
c. Add the endpoints
d. Divide 15 by 2
Answers
The methods that we can use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15) are: Option B: Count by hand, Option D: Dividie 15 by 2
What is the midpoint of a line segment?Midpoint of a line segment that lies in the mid of that line segment, as the name 'midpoint' suggests.
If the endpoints of the considered line segments are (a,b), and (c,d), then the coordinates of the midpoint would be:
[tex](x,y) = \left(\dfrac{c-a}{2}, \dfrac{d-b}{2}\right)[/tex]
We're specified here that:
The line segment in consideration is vertical.The endpoints of the line segment are (0,0) and (0,15).Since the line is vertical, we can easily find its midpoint by going up by half of the length of the line segment.
The y-coordinate starts from 0 and goes to 15 and x-coordinate is still all along the line as the line is vertical, so the length's half is (15-0)/2 =15/2 = 7.5 units. This gives the y-coordinate of the midpoint as visible in the formula specified above.
If we go this units up, we will reach the midpoint. Since x-coordinates of the points in the line segment are fixed to 0, so the midpoint's coordinates are (0, 7.5)
We can also count by hand as there is motion only in y-coordinates, so move half of the total motion upwards from (0,0) or half of the total length downwards from (0,15).
So we see, that the second method and the fourth method listed in the option can be used.
Thus, the methods that we can use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15) are: Option B: Count by hand, Option D: Dividie 15 by 2
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Final answer:
To find the y-coordinate of a vertical line segment midpoint between (0,0) and (0,15), you can count by hand to get an approximate location, add the y-coordinates of the endpoints and then divide by 2, or simply divide 15 by 2 to get the correct value of 7.5.
Explanation:
To calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15), you can use the following methods:
Count by hand, which means visually looking at the line and counting to the middle point between 0 and 15, which is 7.5.Using the formula for the midpoint of a segment, add the endpoints together and then divide by 2. For the y-coordinate, this means adding 0 and 15 and then dividing by 2: (0 + 15) / 2 = 7.5.Divide 15 by 2, as this is equivalent to the method above without including the initial step of adding 0 to 15 since 0 has no effect on the outcome.Option d is the most direct mathematical approach to finding the midpoint's y-coordinate. Option b is a valid but less precise method that relies on visual estimation. Option c is essentially part of the formula used in option d.
Show that the LHS = RHS.
Answers
Step-by-step explanation:
:
2-csc²A
▬▬▬▬▬▬▬
csc²A + 2cotgA
2 - 1/sin²A
= ▬▬▬▬▬▬▬▬▬▬
1/sin²A + 2cosA/sinA
2sin²A - 1
= ▬▬▬▬▬▬▬
1 - 2cosAsinA
sin²A + sin²A - 1
= ▬▬▬▬▬▬▬▬▬▬▬▬
sin²A - 2cosAsinA + cos²A
sin²A - cos²A
= ▬▬▬▬▬▬▬
(sinA - cosA)²
(sinA - cosA)(cosA + sinA)
= ▬▬▬▬▬▬▬▬▬▬▬▬
(sinA - cosA)²
sinA + cosA
= ▬▬▬▬▬▬ <-- Let check "+" and "-"
sinA - cosA
By taking a common Equation denominator and simplifying, we will see that LHS = RHS. To prove that the given equation is true, we can simplify both sides step by step and show that they are equal.
To show that the left-hand side (LHS) is equal to the right-hand side (RHS) of the given equation, let's simplify both sides step by step.
LHS = 2 - cosec²A / cosec²A + 2cotA
= 2 - (1/sin²A) / (1/sin²A) + 2cosA/sinA
= 2 - 1/sin²A / 1/sin²A + 2cosA/sinA
RHS = sinA - cosA / sinA + cosA
By taking a common denominator and simplifying, we will see that LHS = RHS.
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The probable questionShow that the LHS = RHS.
2-cosec^2A/cosec^2A+2cotA=sinA-cosA/sinA+cosA may be:
What is the conjugated expression?
Answers
Domain: x>5
what would N be in this problem 9=8n
Answers
Answer:
9/8 = n
Step-by-step explanation:
9=8n
Divide each side by 8
9/8 = 8n/8
9/8 = n
I Need The Answer Plz Geometry Is Hard!!!
Answers
Answer:
∠F = 106°
Step-by-step explanation:
The opposite angles of a parallelogram are congruent, hence
∠F = ∠J = 106°
The price of a car has been reduced from $19,500 to $16,770. What is the percentage decrease of the price of the car?
Answers
so the price difference is 19500 - 16770 = 2730.
if we take 19500 to be the 100%, what is 2730 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 19500&100\\ 2730&x \end{array}\implies \cfrac{19500}{2730}=\cfrac{100}{x}\implies \cfrac{50}{7}=\cfrac{100}{x}\implies 50x=700 \\\\\\ x=\cfrac{700}{50}\implies x=14[/tex]
Answer:
The answer is 14%
Step-by-step explanation:
1) Divide 19500 by 16770
16770/19500= 0.86
2) Multiply by 100 (this is the percentage between the original and find prices of the car)
0.86(100)= 86%
3) Subtract 86% from 100% to find the change in percentage
100-86= 14%
Therefore, the percentage decrease of the price of the car is 14%.
Hope this helps!
In triangle ΔABC, ∠C is a right angle and segment CD is the height to segment AB . Find the angles in ΔCBD and ΔCAD if m∠A = 20°
m∠CDB =
m∠CBD =
m∠BCD =
m∠CDA =
m∠ CAD=
m∠ACD =
Answers
Step-by-step explanation:
Draw a picture (like the image below).
Notice that triangles ABC and ACD both contain right angles, and both contain angle A (20°). Since angles of a triangle add up to 180°, that means their third angle must also be the same (70°).
Also notice that triangles ABC and CBD both contain right angles, and both contain angle B (70°). So their third angle must also be the same (20°).
Therefore:
m∠CDB = 90°
m∠CBD = 70°
m∠BCD = 20°
m∠CDA = 90°
m∠CAD = 20°
m∠ACD = 70°
Find the slope of the line graphed on the Cartesian plane in the figure.
A. –3⁄4
B. 3⁄4
C. –7⁄2
D. 7⁄2
Answers
Answer:
C
Step-by-step explanation:
Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping?
Answers
Step-by-step explanation:
[tex]4x^3+x^2-8x-2\qquad\text{distributive}\\\\=x^2(4x+1)-2(4x+1)\\\\=(4x+1)(x^2-2)[/tex]
Find the equation of the line through (2,9)(1,6)(-7,-6)
Answers
Answer:
y=(3/2)x+6
If your equation is in a different form, let me know.
Step-by-step explanation:
So the slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.
Parallel lines have the same slope, m (different y-intercept (b) though).
So we need to find the slope going through (1,6) and (-7,-6).
To do this you could use [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
Or, what I like to do is line the points up vertically and subtract vertically then put 2nd difference over first difference. Like so:
( 1 , 6)
-( -7, -6)
---------------
8 12
So the slope of our line is 12/8.
Let's reduce it! Both numerator and denominator are divisible by 4 so divide top and bottom by 4 giving 3/2.
Again parallel lines have the same slope.
So we know the line we are looking for is in the form y=(3/2)x+b where we don't know the y-intercept (b) yet.
But we do know a point (x,y)=(2,9) that should be on our line.
So let's plug it in to find b.
y=(3/2)x+b with (x,y)=(2,9)
9=(3/2)2+b
9=3 +b
Subtract 3 on both sides:
9-3=b
6=b
So the equation in slope intercept form is y=(3/2)x+6
[tex]( \sqrt{5x + 6} ) ^{2} [/tex]
multiply
Answers
[tex]\bf (\sqrt{5x+6})^2\implies \sqrt{(5x+6)^2}\implies 5x+6[/tex]
Drag the titles to the boxes to form correct pairs .not all titles will be used. Match the pairs of equation that represents concentric circles. Pleaseeeeeeee help
Answers
Answer:
The concentric circles are
[tex]3x^{2}+3y^{2}+12x-6y-21=0[/tex] and [tex]4x^{2}+4y^{2}+16x-8y-308=0[/tex]
[tex]5x^{2}+5y^{2}-30x+20y-10=0[/tex] and [tex]3x^{2}+3y^{2}-18x+12y-81=0[/tex]
[tex]4x^{2}+4y^{2}-16x+24y-28=0[/tex] and [tex]2x^{2}+2y^{2}-8x+12y-40=0[/tex]
[tex]x^{2}+y^{2}-2x+8y-13=0[/tex] and [tex]5x^{2}+5y^{2}-10x+40y-75=0[/tex]
Step-by-step explanation:
we know that
The equation of the circle in standard form is equal to
[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
where
(h,k) is the center and r is the radius
Remember that
Concentric circles, are circles that have the same center
so
Convert each equation in standard form and then compare the centers
The complete answer in the attached document
Part 1) we have
[tex]3x^{2}+3y^{2}+12x-6y-21=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](3x^{2}+12x)+(3y^{2}-6y)=21[/tex]
Factor the leading coefficient of each expression
[tex]3(x^{2}+4x)+3(y^{2}-2y)=21[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex]3(x^{2}+4x+4)+3(y^{2}-2y+1)=21+12+3[/tex]
[tex]3(x^{2}+4x+4)+3(y^{2}-2y+1)=36[/tex]
Rewrite as perfect squares
[tex]3(x+2)^{2}+3(y-1)^{2}=36[/tex]
[tex](x+2)^{2}+(y-1)^{2}=12[/tex]
therefore
The center is the point (-2,1)
Part 2) we have
[tex]5x^{2}+5y^{2}-30x+20y-10=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](5x^{2}-30x)+(5y^{2}+20y)=10[/tex]
Factor the leading coefficient of each expression
[tex]5(x^{2}-6x)+5(y^{2}+4y)=10[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex]5(x^{2}-6x+9)+5(y^{2}+4y+4)=10+45+20[/tex]
[tex]5(x^{2}-6x+9)+5(y^{2}+4y+4)=75[/tex]
Rewrite as perfect squares
[tex]5(x-3)^{2}+5(y+2)^{2}=75[/tex]
[tex](x-3)^{2}+(y+2)^{2}=15[/tex]
therefore
The center is the point (3,-2)
Part 3) we have
[tex]x^{2}+y^{2}-12x-8y-100=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](x^{2}-12x)+(y^{2}-8y)=100[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex](x^{2}-12x+36)+(y^{2}-8y+16)=100+36+16[/tex]
[tex](x^{2}-12x+36)+(y^{2}-8y+16)=152[/tex]
Rewrite as perfect squares
[tex](x-6)^{2}+(y-4)^{2}=152[/tex]
therefore
The center is the point (6,4)
Part 4) we have
[tex]4x^{2}+4y^{2}-16x+24y-28=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](4x^{2}-16x)+(4y^{2}+24y)=28[/tex]
Factor the leading coefficient of each expression
[tex]4(x^{2}-4x)+4(y^{2}+6y)=28[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex]4(x^{2}-4x+4)+4(y^{2}+6y+9)=28+16+36[/tex]
[tex]4(x^{2}-4x+4)+4(y^{2}+6y+9)=80[/tex]
Rewrite as perfect squares
[tex]4(x-2)^{2}+4(y+3)^{2}=80[/tex]
[tex](x-2)^{2}+(y+3)^{2}=20[/tex]
therefore
The center is the point (2,-3)
Part 5) we have
[tex]x^{2}+y^{2}-2x+8y-13=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](x^{2}-2x)+(y^{2}+8y)=13[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex](x^{2}-2x+1)+(y^{2}+8y+16)=13+1+16[/tex]
[tex](x^{2}-2x+1)+(y^{2}+8y+16)=30[/tex]
Rewrite as perfect squares
[tex](x-1)^{2}+(y+4)^{2}=30[/tex]
therefore
The center is the point (1,-4)
Part 6) we have
[tex]5x^{2}+5y^{2}-10x+40y-75=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](5x^{2}-10x)+(5y^{2}+40y)=75[/tex]
Factor the leading coefficient of each expression
[tex]5(x^{2}-2x)+5(y^{2}+8y)=75[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex]5(x^{2}-2x+1)+5(y^{2}+8y+16)=75+5+80[/tex]
[tex]5(x^{2}-2x+1)+5(y^{2}+8y+16)=160[/tex]
Rewrite as perfect squares
[tex]5(x-1)^{2}+5(y+4)^{2}=160[/tex]
[tex](x-1)^{2}+(y+4)^{2}=32[/tex]
therefore
The center is the point (1,-4)
Part 7) we have
[tex]4x^{2}+4y^{2}+16x-8y-308=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](4x^{2}+16x)+(4y^{2}-8y)=308[/tex]
Factor the leading coefficient of each expression
[tex]4(x^{2}+4x)+4(y^{2}-2y)=308[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex]4(x^{2}+4x+4)+4(y^{2}-2y+1)=308+16+4[/tex]
[tex]4(x^{2}+4x+4)+4(y^{2}-2y+1)=328[/tex]
Rewrite as perfect squares
[tex]4(x+2)^{2}+4(y-1)^{2}=328[/tex]
[tex](x+2)^{2}+(y-1)^{2}=82[/tex]
therefore
The center is the point (-2,1)
Part 8) Part 9) and Part 10) in the attached document
The admission fee at an amusement park is $3.50 for children and $7.00 for adults. On a certain day, 331 people entered the park, and the admission fees collected totaled $1,771.00 dollars. How many children and how many adults were admitted?
Answers
Let c be children and a adults.
3.5c + 7a = 1771 (the total revenue is equal to the amounts made off of people)
c + a = 331 (total number of people)
The second formula becomes a = 331 - c. This can be substituted into the first formula.
3.5c + 7(331 - c) = 1771 = 7*331 - 3.5c = 1771. 7*331 = 2317, so 3.5c = 2317 - 1771 = 546.
546/3.5 = 156 = c (number of children).
c + a = 156 + a = 331 => a = 331 - 156 = 175 (number of adults).
There are 156 children and 175 adults
Answer:
156 children
175 adults
Step-by-step explanation:
Let's call x the number of children admitted and call z the number of adults admitted.
Then we know that:
[tex]x + z = 331[/tex]
We also know that:
[tex]3.50x + 7z = 1,771.00[/tex]
We want to find the value of x and z. Then we solve the system of equations:
-Multiplay the first equation by -7 and add it to the second equation:
[tex]-7x - 7z = -2,317[/tex]
[tex]3.50x + 7z = 1,771[/tex]
----------------------------------
[tex]-3.5x = -546[/tex]
[tex]x =\frac{-546}{-3.5}\\\\x=156[/tex]
Now we substitute the value of x in the first equation and solve for the variable z
[tex]156 + z = 331[/tex]
[tex]z = 331-156[/tex]
[tex]z = 175[/tex]