Answers
In the given equation, [tex]\frac{(a^x)^{2}}{b^{5-x}} \times \frac{b^{y - 4}}{a^{y}} = a^2b^4[/tex], the value of x and y is x = 5 and y = 8
Simultaneous equations: Calculating the value of x and yFrom the question, we are to determine the value of x and y in the given equation.
The given equation is
[tex]\frac{(a^x)^{2}}{b^{5-x}} \times \frac{b^{y - 4}}{a^{y}} = a^2b^4[/tex]
To determine the value of x and y, we will simplify the left hand side of the equation and then compare to the right hand side of the equation
The equation can written as
[tex]\frac{(a^x)^2}{a^{y}} \times \frac{b^{y - 4}}{b^{5-x}} = a^2b^4[/tex]
[tex]\frac{(a^{2x})}{a^{y}} \times \frac{b^{y - 4}}{b^{5-x}} = a^2b^4[/tex]
[tex]a^{2x - y}\times b^{y - 4 -(5-x) = a^2b^4[/tex]
Simplify
[tex]a^{2x - y}\times b^{y - 4 -5+x = a^2b^4[/tex]
[tex]a^{2x - y}\times b^{x+y - 9} = a^2b^4[/tex]
By comparison
[tex]2x - y = 2\\x + y - 9 =4[/tex]
Thus,
2x - y = 2
x + y = 4 + 9
and
2x - y = 2
x + y = 13
Solve the equations simultaneously
2x - y = 2
x + y = 13
Adding the two equations, we get:
3x = 15
Dividing both sides by 3, we get:
x = 5
Substituting this value of x into the second equation, we get:
5 + y = 13
Subtracting 5 from both sides, we get:
y = 8
Hence, the solution is:
x = 5, y = 8
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Related Questions
my baby sitting service charges an initial $5.00 fee plus an additional 6.50 per hour. write an equation for the situation below
Answers
The equation for the situation is C = (f + 6.5)h + 5.00.
We have,
Let C be the total cost charged by the babysitting service.
h = the number of hours of service
f = the initial fee charged by the service.
Now,
The initial fee is $5.00 and the additional cost per hour is $6.50.
The equation for the situation can be written as:
C = f h + 6.5h
We can simplify this equation by combining like terms:
C = (f + 6.5)h + 5.00
This means,
So, the total cost charged by the babysitting service is equal to the sum of the initial fee and the additional cost per hour multiplied by the number of hours of service.
Thus,
The equation for the situation is C = (f + 6.5)h + 5.00.
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Find the length of the missing side
Answers
Answer:
1. 13 KM. 2. 3.43 KM
Step-by-step explanation:
For these questions, use A^2 + B^2 = C^2, with C being the hypotenuse.
12^2 + 5^2 = c^2
9.5^2 + b^2 = c^2
13 KM,
3.43 KM
A spring table arrangement of 30 flowers contains only two kinds of flowers,
daffodils and tulips. The number of tulips, t, is one-fourth the number of
daffodils. Write an equation that represents the relationship between the
number of tulips and the number of daffodils in the arrangement.
Answers
Answer:
t = (1/4)d
or
t/d = 1/4
Step-by-step explanation:
t = number of tulips
d = number of daffodils
t = (1/4)d
or
t/d = 1/4
t + d = 30
so, when using the first equation in the second we get
(1/4)d + d = 30
multiplying both sides by 4 to get rid of the fraction :
d + 4d = 120
5d = 120
d = 24
t = (1/4)d = 1/4 × 24 = 6
Consider the function
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(
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=
(
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(
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−
5
)
f(x)=(x+3)(x−5)
What is the axis of symmetry?
To find the axis of symmetry in factored form, use:
�
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1
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2
2
x=
2
r
1
+r
2
Answers
The calculated value of the axis of symmetry for the function f(x) = (x+3)(x-5) is x = 1.
Calculating the axis of symmetryTo find the axis of symmetry for the given function, we need to use the formula:
x = -b/2a
where a and b are the coefficients of the quadratic term and the linear term in the function, respectively.
For the given function f(x) = (x+3)(x-5), we can expand it as:
f(x) = x^2 - 2x - 15
Here, a = 1 and b = -2.
Substituting these values into the formula, we get:
x = -(-2)/(2*1) = 1
Therefore, the axis of symmetry for the function f(x) = (x+3)(x-5) is x = 1.
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Compostie surface area. Please and thank you.
Answers
Therefore surface area of given is 331.63square yards.
Define surface area of cuboid?A cuboid's total surface area is equal to the sum of all of its faces' surface areas. Given that a cuboid has six faces, the formula for its total surface area is as follows:
Cuboid's total surface area is equal to 2(lb + bh + hl).
where the cuboid's length (l), width (b), and height (h) are all integers.
Surface area of the given picture = Total surface area of cuboid - Curved surface area of base of hemisphere + curved surface area of hemisphere
= 2(lb+bh+hl) - πr²+ 2πr²
= 2(lb+bh+hl) + πr²
= 2 (36+60+60) + 3.14(2.5)²
= 2 (36+60+60) + 3.14(2.5)²
= 312 + 19.625
= 331.63 square yards.
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I NEED HELP ON THIS ASAPP!!!!!
Answers
a. The transformation for C > 0, f(x) is h(x) shifted C units to the right.
b. The transformation for C < 0, f(x) is h(x) shifted C units to the left.
What is a transformation?Transformation is a mathematical operation performed to change the shape, size or orientation of a graph or object.
Since we have the basic function h(x) = 2ˣ, we want to describe the functions. We proceed as folllows.
a. To compare f(x) = h(x - C) to the basic function for C > 0, we see that
f(x) = h(x - C)
[tex]f(x) = 2^{x - C}[/tex]
Now, for C > 0, f(x) is h(x) shifted C units to the right.
So, f(x) is h(x) shifted C units to the right.
b. To compare f(x) = h(x - C) to the basic function for C > 0, we see that
f(x) = h(x - C)
[tex]f(x) = 2^{x - C}[/tex]
Now, for C < 0,
[tex]f(x) = 2^{x - (-C)}\\f(x) = 2^{x + C}[/tex]
So, for C < 0, f(x) is h(x) shifted C units to the left.
So, f(x) is h(x) shifted C units to the left.
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17. The perimeter of a rectangle is 86 centimeters. The length is 2 centimeters longer than the
width, w. What is the width?
White an equation that could be used to find the width of the rectangle.
Answers
According to the problem, the length is 2 centimetres longer than the width, so the length can be expressed as:
l = w + 2
length = width + 2
The perimeter of a rectangle is twice the sum of its length and width, so we can set up an equation to represent the perimeter given in the problem:
P = 2(l + w)
Substituting the expression for l in terms of w, we get:
P = 2((w + 2) + w)
Simplifying this expression, we get:
P = 2(2w + 2)
P = 4w + 4
We know that the perimeter of the rectangle is 86 centimetres, so we can substitute this value into the equation:
86 = 4w + 4
Subtracting 4 from both sides:
82 = 4w
Dividing both sides by 4:
w = 20.5
Therefore, the width of the rectangle is 20.5 centimetres.
The equation that could be used to find the width of the rectangle is:
4w + 4 = 86
where w represents the width of the rectangle in centimetres.
perimeter = 2L + 2w
so 86 = 2L + 2w
if the length is 2cm longer than the width, that means w+2=L
plug this back into our original equation to get 2(w+2) + 2w = 86
distribute terms to get 4w + 4 = 86
4w = 82
w = 20.5cm
Complete the square to re-write the quadratic function in vertex form
Answers
Answer:
to express the quadratic equetion in to factor form
you must use completing squere method
[tex] y= {x}^{2} - 10x - 5[/tex]
y + 5 = x2 - 10x
y + 5 = x2 - 10xy + 5 + 25 = x2 - 10x + 25
y + 5 = x2 - 10xy + 5 + 25 = x2 - 10x + 25y + 30 = (x - 5)2
y + 5 = x2 - 10xy + 5 + 25 = x2 - 10x + 25y + 30 = (x - 5)2 y = ( x - 5)2 - 30 so we get the factor form of the quadratic equetion.
In other way :
if you need to get vertex (5, -30)
or simply by (x, f(x)) which is (-b/2a,f(-b/2a)) form
a=1
a=1b=-10
a=1b=-10c=-5
so when u substitute and you will get (5, f(5))
then for the y-coordinate you substitute 5 in place of x and you will get -30 so vertex = (5, -30)
what is 3(2/5) Witten in as column vector
Answers
The column vector of the expression is 6/5.
What is a column vector?
A column vector is an entity or matric with single column of entries.
Column vectors can be added and subtracted from each other, multiplied by a scalar, and transformed by matrices. They are also used to represent systems of linear equations.
The column vector of the expression is calculated as follows;
3 ( 2/5 ) = ( 3 x 2 )/ 5
= 6/5
Thus, by multiplying the fraction by 3 we have successfully converted the expression into a single vector.
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Do singles and families have the same distribution of cars? The results are shown in the table below. 10 65 Car Family Single Sport 45 Sedan 40 Hatchback 36 37 Truck 20 45 Van/SUV 22 8 For the data do the following: (a) Calculate the conditional distribution of the type of car given it is owned by families or singles. (b) Make an appropriate graph for comparing the conditional distributions in part (a). (c) Do singles and families have the same distribution of cars? Test at significance level of 0.01.
Answers
(a) The conditional distribution of car types differs between families and singles.
(b) An appropriate graph for comparing the conditional distributions could be a stacked or clustered bar chart.
(c) A chi-squared test at a significance level of 0.01 can be used to determine if singles and families have the same distribution of cars.
Do singles and families have the same distribution of cars?(a) The conditional distribution of the type of car given it is owned by families or singles can be calculated by dividing the count of each type of car for families or singles by the total count for families or singles, respectively.
For families:
Sport: 10
Sedan: 45
Hatchback: 40
Truck: 20
Van/SUV: 22
Total count for families = 10 + 45 + 40 + 20 + 22 = 137
Conditional distribution for families:
Sport: 10/137 ≈ 0.073
Sedan: 45/137 ≈ 0.328
Hatchback: 40/137 ≈ 0.292
Truck: 20/137 ≈ 0.146
Van/SUV: 22/137 ≈ 0.161
For singles:
Sport: 65
Sedan: 36
Hatchback: 37
Truck: 45
Van/SUV: 8
Total count for singles = 65 + 36 + 37 + 45 + 8 = 191
Conditional distribution for singles:
Sport: 65/191 ≈ 0.340
Sedan: 36/191 ≈ 0.188
Hatchback: 37/191 ≈ 0.194
Truck: 45/191 ≈ 0.236
Van/SUV: 8/191 ≈ 0.042
(b) An appropriate graph for comparing the conditional distributions in part (a) could be a stacked bar chart or a clustered bar chart, with the types of cars on the x-axis and the proportions on the y-axis. This would visually represent the differences in conditional distributions between families and singles.
(b) A chi-squared test for independence at a significance level of 0.01 can determine if there is a significant association between the type of car and ownership status (family or single), allowing for conclusions about whether singles and families have the same distribution of cars based on observed data.
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I NEED HELP ON THIS ASAP!!!!
Answers
In the two functions as the value of V(x) increases, the value of W(x) also increases.
What is the value of the functions?The value of functions, V(x) and W(x) is determined as follows;
for h(-2, 1/4); the value of the functions is calculated as follows;
v(x) = 2ˣ ⁺ ³ = 2⁻²⁺³ = 2¹ = 2
w(x) = 2ˣ ⁻ ³ = 2⁻²⁻³ = 2⁻⁵ = 1/32
for h(-1, 1/2); the value of the functions is calculated as follows;
v(x) = 2ˣ ⁺ ³ = 2² = 4
w(x) = 2ˣ ⁻ ³ = 2⁻⁴ = 1/16
for h(0, 1); the value of the functions is calculated as follows;
v(x) = 2ˣ ⁺ ³ = 2³ = 8
w(x) = 2ˣ ⁻ ³ = 2⁻³ = 1/8
for h(1, 2); the value of the functions is calculated as follows;
v(x) = 2ˣ ⁺ ³ = 2⁴ = 16
w(x) = 2ˣ ⁻ ³ = 2⁻² = 1/4
for h(2, 4); the value of the functions is calculated as follows;
v(x) = 2ˣ ⁺ ³ = 2⁵ = 32
w(x) = 2ˣ ⁻ ³ = 2⁻¹ = 1/2
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