Answer:
a=[tex]\frac{3}{x^{2} }[/tex]
b=5
Step-by-step explanation:
we are given
[tex]\frac{3}{x} }[/tex]+[tex]\frac{5}{x^{2} }[/tex]=ax+[tex]\frac{b}{x^{2} }[/tex]
we will compare both sides of equaion
[tex]\frac{b}{x^{2} }[/tex]=[tex]\frac{5}{x^{2} }[/tex]
comparing both sides we get
b=5
and
[tex]\frac{3}{x} }[/tex]=ax
a=[tex]\frac{3}{x^{2} }[/tex]
hence
a=[tex]\frac{3}{x^{2} }[/tex]
and b=5
Answer:
a=3
b=5
Step-by-step explanation:
answers on edge
352 ft is ____ % of 2 mi; 2 mi is ____ % of 352 ft
Answer:
352 ft is 3.34% of mi ;
2 mi is 3000% of 352 ft
Step-by-step explanation:
To calculate : 352 ft is ___% of 2 mi and 2 mi is ___% of 352 ft.
We can calculate first:
352 is x% of 2 mi.
Solve for x;
Use conversion:
1 mi = 5280 ft
2 mi = 10560 ft
x% of 10560 ft means [tex]\frac{x}{100} \times 10560 = 105.60 x[/tex]
then, our equation become;
352 = 105.6 x
Divide both sides by 105.6 we get;
x = 3.333333...
or
x ≈3.34
Similarly, for
2 mi is y% of 352 ft
Solve for y;
2 mi = 10560 ft
y% of 352 = [tex]\frac{y}{100} \times 352 = 3.52y[/tex]
then;
10560 = 3.52 y
Divide both sides by 3.52 we get;
[tex]y = \frac{10560}{3.52}[/tex]
y = 3000
Therefore; 352 ft is 3.34% of mi ; 2 mi is 3000% of 352 ft
what is the area of a square with a diagonals of the length of 6?
Answer:
Area = 18
Step-by-step explanation:
We know that a square has side lengths of s
We can use the Pythagorean theorem to find s
a^2 + b^2 = c^2
We know that the hypotenuse or c = the length of the diagonal or 6
Substituting in what we know
s^2 + s^2 = 6^2
2s^2 = 36
Divide each side by 2
2s^2/2 = 36/2
s^2 = 18
Take the square root of each side
sqrt(s^2) = sqrt(18)
We only have to take the positive square root since it is a length
s = sqrt(9) sqrt(2)
s= 3sqrt(2)
The side length of the square is 3sqrt(2)
To find the area, we multiply the side by the side or s^2
s^2 = (3sqrt(2))^2
From above
s^2 = 18
Jason is selling video games. To earn his monthly bonus, he must sell a minimum of 5 games. He has 30 he can sell. The video games cost $20 each. The function f(x) = 20x can be used to represent this situation. What is the practical range of the function? Question 16 options:
1. All whole numbers from 5 to 30, inclusive.
2. All whole numbers from 100 to 600, inclusive.
3. All real numbers.
4. All multiples of 20 between 100 and 600, inclusive.
Answer:
Correct choice is B
Step-by-step explanation:
The function [tex]f(x)=20x[/tex] represents the situation, where x is the number of sold video games and f(x) is the total cost of sold games.
Jason must sell a minimum of 5 games, this means that [tex]x\ge 5.[/tex] He has 30 video games he can sell, then [tex]x\le 30.[/tex]. Thus, the domain of the function is [tex]5\le x\le 30.[/tex]
The range of the function f(x) is
[tex]20\cdot 5\le f(x)\le 20\cdot 30,\\ \\100\le f(x)\le 600.[/tex]
Pat listed all the multiples for 15. Write the numbers in pats list
Answer: Answer : Answer : 15,30,45,60,75,90,105,120,135,150,165,180,195,210,225,240,255,270,285,300,315,330,345,360,375,390,405,420,435,450,465,480,495,510,525,540,555,570,585,600,615,630,645,660,675,690,705,720,735,
Step-by-step explanation:
Evaluate the following.
Click on "Not a real number" if applicable.
Answer:
1) [tex]\sqrt{-64}[/tex] is not a real number.
2) [tex]-\sqrt{25} =-5[/tex]
Step-by-step explanation:
1) The square root of a number is defined for real numbers if and only if the number under the square root sign is greater than or equal to zero.
This implies that [tex]\sqrt{-64}[/tex] is not a real number because [tex]-64\:<\:0[/tex]
2) [tex]-\sqrt{25} =-\sqrt{5^2} =-5[/tex].
The number under the square root sign is [tex]25[/tex], which is greater than zero. Note that the negative sign is not inside the square root sign, it is outside it.
The value √-64 is not a real number, and -√25 is a real number.
√-64 and -√25 involve taking the square root of negative numbers, which results in complex numbers because real numbers do not have square roots of negative values.
Let's evaluate both:
√-64:
The square root of -64 is denoted as √(-64). In the realm of complex numbers, it's represented as 8i, where 'i' stands for the imaginary unit. So, √-64 = 8i.
-√25:
The square root of 25 is 5, and when you add a negative sign in front of it, you get -5. So, -√25 = -5.
In summary, √-64 is not a real number, and it is equal to 8i in the realm of complex numbers, while -√25 is a real number and equal to -5.
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Use the Polygon tool to draw the image of the given quadrilateral under a dilation with a scale factor of 3/4 and center of dilation (0, 0) .
If you could tell me the point that the new quad will be at that would be great!
Answer:
Given : scale factor(k) = [tex]\frac{3}{4}[/tex]
Labelled the given diagram as A, B , C and D
Also, From the given quadrilateral figure:
The coordinates are;
A=(-8, 4).
B=(-4, -4),
C=(0, -8) and
D=(4, -4)
The rule of dilation with scale factor k and centered at origin is given by;
[tex](x, y) \rightarrow (kx, ky)[/tex]
or
[tex](x, y) \rightarrow (\frac{3}{4}x, \frac{3}{4}y)[/tex]
Then, the coordinates of the dilated given figures are;
[tex]A(-8, 4) \rightarrow (\frac{3}{4}(-8), \frac{3}{4}(4)) = A'(-6, 3)[/tex]
[tex]B(-4, -4) \rightarrow (\frac{3}{4}(-4), \frac{3}{4}(-4)) = B'(-3, -3)[/tex]
[tex]C(0, -8) \rightarrow (\frac{3}{4}(0), \frac{3}{4}(-8))=C' (0 , -6)[/tex]
[tex]D(4, -4) \rightarrow (\frac{3}{4}(4), \frac{3}{4}(-4)) = D'(3, -3)[/tex]
You can see the graph given below in the attachment
What is the surface area of the cylinder? 14ft length 9ft height
A.) 126πft²
B.) 273πft²
C.) 224πft²
D.) 175πft²
Answer:
C
Step-by-step explanation:
I am assuming the top and bottom are closed.
Surface are = area of the curved side + 2 * area of the top
= 9* 14 * π + 2 * π * 7^2
= 126π + 98π
= 224π ft^2
Answer:
224
Step-by-step explanation:
What is the first step when solving the equation below for x 4x - 0.3 = 1.9
A. Add 1.9 to both sides of the equation
B. Subtract 0.3 from both sides of the equation
C. Divide each side of the equation by 4
D. Add 0.3 to both sides of the equation
Answer:
The answer my frind is D
Step-by-step explanation:
When you divide,
you must
blablabla
The first step in solving the equation 4x - 0.3 = 1.9 is to D) add 0.3 to both sides of equation, isolating the term with the variable 'x'.
Explanation:The question is asking how to begin solving the equation 4x - 0.3 = 1.9 for the variable x.
The first step in solving this equation would be to eliminate the subtraction part of the equation. In other words, we want to isolate the term with the variable, which is '4x' in this case. So our best course of action is to add 0.3 to both sides of the equation.This balances the equation and moves us closer to discovering what x is, so the correct option would be 'D. Add 0.3 to both sides of the equation'.
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Which values of P and Q result in an equation with exactly one solution? 2x+Q=Px−31 Choose all answers that apply: Choose all answers that apply: A -Q=−31 and P=−2 B- Q=31 andP=2 C - Q=−31 and P=2 D - Q=-2Q=−2 and P=2
Answer:
Option A is correct
Values of P = -2 and Q = -31
Step-by-step explanation:
Given the equation: [tex]2x+Q= Px-31[/tex]
Now, we put the given values
A.
Q = -31 and P = -2
2x + (-31) = -2x - 31
2x - 31 = -2x -31
4x = -31 + 31
4x = 0
x = 0 [one solution]
B.
Q = 31 and P = 2
2x + Q = Px -31
2x + 31 = 2x -31
Subtract 2x from both sides we get
31 = -31 False.
C.
Q = -31 and P = 2
2x + (-31) = 2x - 31
2x - 31 = 2x - 31 [More than one solutions, for any x]
D.
Q = -2 and P = 2
2x + Q = Px -31
2x + (-2) = 2x -31
2x -2 = 2x -31
2x - 2x = -31 + 2
Combine like term;
0 = -29 False.
Therefore, the values of P and Q results in an equation with exactly one solution is; P = -2 and Q = -31
the eauation of the line has the points (0,-1) and (2,5) is:
Answer:
y = 3x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 5)
m = [tex]\frac{5+1}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3
the line crosses the y-axis at (0, - 1) ⇒ c = - 1
y = 3x - 1 ← equation of the line
You Start At (1,9) You Move Left 1 Unit And Up 1 Unit.Where Do You End?
Answer:
(0, 10)
Step-by-step explanation:
x=1 y=9
Up 1 means add 1 to the y coordinate
Left 1 means subtract 1 from the x coordinate
(1-1, 9+1)
(0, 10)
You and your friends play a game of miniature golf. On the first hole, the scores of your group are 6, 2, 3, 2, 4, and 1. What is the range of the scores?
Answer: Hello mate!
our set of numbers is 6, 2, 3, 2, 4, and 1.
the two extremes of the set are the lower and bigger numbers, so in this case are 1 and 6, so the range of the values in the set is {1,6} and the distance between these points is 6 - 1 = 5.
this means that all the numbers in our set are in the range between 1 and 6.
sal is making bracalets for a fundraser he uses 6 inches of yarn per bracalet how many bracalets can sal make with 5 ft of yarn
Answer:
10 bracelets
Step-by-step explanation:
we need to convert 5 ft to inches
1 ft = 12 inches
multiply by 5
5 ft = 60 inches
60 inches of yarn, 6 inches per bracelet
60/6 = 10
10 bracelets
Which portion would you use to solve this problem?
Nine is 4% of what number?
A. 9/x = 40/100
B. 9/x = 4/100
C. 4/9 = x/100
D. X/9 = 4/100
[tex]p\%=\dfrac{p}{100}\\\\4\%=\dfrac{4}{100}\\\\\dfrac{9}{x}=\dfrac{4}{100}\to\boxed{B.}[/tex]
Need help I’m really dumb
Answer: 83485
=====================
Explanation:
The formula we will use is
A = P*(1+r)^t
with
A = final amount = unknown (what we want to find)
P = starting amount = 24000
r = growth rate in decimal form = 0.12
t = number of years elapsed = 11 (since we go from 2014 to 2025)
Plug those values mentioned into the formula. Then use a calculator to simplify
A = P*(1+r)^t
A = 24000*(1+0.12)^11
A = 24000*(1.12)^11
A = 24000*3.47854999334551
A = 83485.199840292
A = 83485
The investment will be worth about 83485 dollars
A house on the market was valued at 34,000 . After several years, the value decreased by 16%. By how much did the house's value decrease in dollars? What is the current value of the house?
plug in the number of years for where x is
34,000(.84)ˣ
and then do
.84ˣ
and then when you get that answer, multiply by 34,000
How many complex zeros does the polynomial function have?
F(x)=2x^4 +5x^3 - x^2 +6x-1
Answer:
Two complex roots.
Step-by-step explanation:
F(x)=2x^4 +5x^3 - x^2 +6x-1
is a polynomial in x of degree 4.
Hence F(x) has 4 roots. There can be 0 or 2 or 4 complex roots to this polynomial since complex roots occur in conjugate pairs.
Use remainder theorem to find the roots of the polynomial.
F(0) = -1 and F(1) = 2+5-1+6-1 = 11>0
There is a change of sign in F from 0 to 1
Thus there is a real root between 0 and 1.
Similarly by trial and error let us find other real root.
F(-3) = -1 and F(-4) = 94
SInce there is a change of sign, from -4 to -3 there exists a real root between -3 and -4.
Other two roots are complex roots since no other place F changes its sign
Final answer:
The polynomial function has 4 complex zeros.
Explanation:
A polynomial function is a function of the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_1, a_0 are constants and n is a non-negative integer. The number of complex zeros of a polynomial function is equal to its degree.
The given polynomial function is f(x) = 2x^4 + 5x^3 - x^2 + 6x - 1. The highest power of x in the function is 4, so the degree of the function is 4. Therefore, the function has 4 complex zeros.
A line passes through the point (8,7) and has a slope of negative 3/4 Write an equation in slope-intercept form for this line.
The slope-intercept form for the line that passes through the point (8,7) and has a slope of -3/4 is y = -3/4x + 13. We found this by substituting the given slope and point into the slope-intercept equation and solving for b, the y-intercept.
Explanation:We're working on a mathematics problem here that involves the slope-intercept form of a line, which is usually written as y = mx + b. Here, m represents the slope of the line and b is the y-intercept, the point where the line intercepts the y-axis.
To write an equation for this line, we're given that the line passes through the point (8,7) and has a slope (rise over run) of negative 3/4, a negative value indicating the line decreases as it moves to the right.
We can substitute the slope and the given point into the slope-intercept equation to solve for the y-intercept: 7=(-3/4)*8+b, this simplifies to: 7=-6+b, and finally b=7+6 which gives us 13.
Therefore, the slope-intercept equation for this line with a slope of -3/4 and passing through the point (8,7) is y = -3/4x + 13.
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Final answer:
The equation of the line passing through the point (8,7) with a slope of negative 3/4 is y = -3/4x + 13 in slope-intercept form.
Explanation:
To write an equation for a line in slope-intercept form given a point and a slope, we use the formula y = mx + b, where m is the slope and b is the y-intercept. For a line that passes through the point (8,7) with a slope of negative 3/4, we first input the slope into the equation, getting y = -3/4x + b. We then substitute the x and y values from the point (8,7) into the equation and solve for b: 7 = -3/4(8) + b. This simplifies to 7 = -6 + b, and adding 6 to both sides gives us b = 13. Thus, the equation of the line in slope-intercept form is y = -3/4x + 13.
*NEED MAJOR HELP!*
Drag each equation to show if it could be a correct first step to solving the equation 2(x + 7) = 36.
A 2x + 14 = 36
B (2 • x) + (2 • 7) = 36
C 2x + 7 = 36
D 2(x + 7) = 72
E x + 14 = 36
F x + 7 = 18
Yes No Not Enough Information
Answer:
I believe a) is your answer
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
2(x+7)=36
Simplify: (Show steps)
2x+14=36
A snail moves 9feet in 3days at this rate how long will it take for the snail to move 15feet
A 60 by 80-foot rectangular walk in a park surrounds a flower bed. If the walk is of uniform width and its area is equal to the area of the flower bed, how wide is the walk?
Answer: 17.14 ft
Step-by-step explanation:
The area of the flower bed is 60 ft x 80 ft = 4800 ft²
The perimeter of the sidewalk that surrounds the flower bed is:
2(60 ft) + 2(80 ft) = 120 ft + 160 ft = 280 ftThe area of the sidewalk is:
perimeter x width= 280warea of sidewalk = area of flower bed
280w = 4800
[tex]\text{w}=\dfrac{4800}{280}[/tex]
[tex]=\dfrac{120}{7}[/tex]
≈ 17.14
find the distance between the points (-3,-4) and (5,4)
find the distance between the points (-3,5) and (0,1 )
The distance between the points (-3,-4) and (5,4) is approximately 11.31 units, and the distance between the points (-3,5) and (0,1) is exactly 5 units.
To find the distance between two points in a plane, you can use the distance formula derived from the Pythagorean Theorem, which is
d² = (x2 - x1)² + (y2 - y1)²
Let's calculate the distances for the given pairs of points.
Distance between (-3,-4) and (5,4)
d² = (5 - (-3))² + (4 - (-4))²
d² = (8)² + (8)²
d = 64 + 64 = 128
d = √128
≈ 11.31
Distance between (-3,5) and (0,1)
d² = (0 - (-3))² + (1 - 5)²
d² = (3)² + (-4)²
d = 9 + 16 = 25
d = √25
d = 5
Mr. Smith has a maximum of $50 to spend at a museum. A ticket costs $7. he can spend x dollars to buy other things at the museum. Write an inequality to find the possible values for x.
Answer:
The correct answer is D.
Step-by-step explanation:
p + 7 = ≤ 50
because I did it for the ECA 3 Exam. :>
The inequality which helps to find the possible values for x will be x + 7 ≤ 50.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
Total budget = $50
Ticket cost = $7
Total spent ≤ total budget
x + 7 ≤ 50
x ≤ 43
Hence "The inequality which helps to find the possible values for x will be x + 7 ≤ 50".
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A house valued at $100000 gains 6%in value. Which expression shows the current value of the house in dollars
Answer:
Current value of house is $106000
Step-by-step explanation:
We are given
A house valued at $100000
gains 6%in value
so,
current value = past house value + gain(%) * (past house value)
past house value =100000
gain(%)=6%
so, we can plug value
Current value is
[tex]=100000+\frac{6}{100}\times 100000[/tex]
[tex]=106000[/tex]
5b2-10b-15 factor this
Answer:
5(b - 3)(b + 1)
Step-by-step explanation:
take out a common factor of 5
= 5(b² - 2b - 3)
to factor the quadratic consider the factors of - 3 which sum to - 2
These are - 3 and + 1, thus
= 5(b - 3)(b + 1)
Find the value of y when x = 4 in the equation 3x - 7/y = 1/3 Show your work help
Answer:
y = ⅗
Step-by-step explanation:
3x – 7/y = 1/3 Substitute the value of x
3×4 – 7/y = 1/3
12 – 7/y = 1/3 Multiply each side by 3
36 – 21/y = 1 Subtract 36 from each side
-21/y = -35 Multiply each side by y
-21 = -35y Divide each side by -35
y = 21/35 Divide numerator and denominator by 7
y = ⅗
=====
Check:
3×4 – 7/(⅗) = 1/3
12 -7×5/3 = 1/3
12 – 35/3 = 1/3
(36 – 35)/3 = 1/3
1/3 = 1/3
What is the solution of this linear system? 2x + y = -4 y = -3x + 2
The equation below represents Function A and the graph represents Function B: Function A f(x) = 6x - 1 Function B graph of line going through ordered pairs 1, 4 and negative 1, negative 2 and negative 2, negative 5 Which equation best compares the slopes of the two functions?
Answer:
Slope of function A is 6 and slope of function B is 3. Slope of A is twice of slope of function B. The relationship between slopes is
[tex]\text{Slope of Function A}=2\times \text{Slope of Function B}[/tex]
Step-by-step explanation:
The function A is,
[tex]f(x)=6x-1[/tex]
It can be written as,
[tex]y=6x-1[/tex]
It is the slope intercept form like [tex]y=mx+c[/tex], where m is the slope. On comparing the function A with the slope intercept form, we get the value of slope of function A is 6.
[tex]m_{A}=6[/tex]
The graph of function B passing through the point (1,4), (-1,-2) and (-2,-5).
If a line passing through the points and , then the slope of line is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Choose any two points of function B. Let the function B is passing through the points (1,4) and (-1,-2).
[tex]m_{B}=\frac{-2-4}{-1-1}[/tex]
[tex]m_{B}=\frac{-6}{-2}[/tex]
[tex]m_{B}=3[/tex]
The slope of function B is 3.
Since slope of function A is 6 and the slope of function B is 3, so we can say that the slope of function A is twice of slope of function B.
[tex]\text{Slope of Function A}=2\times \text{Slope of Function B}[/tex]
The slope of Function A is 6 and the slope of Function B is 3. Therefore, the slopes of the two functions are not equal.
The equation representing Function A is f(x) = 6x - 1.
The graph representing Function B is a line passing through the ordered pairs (1, 4), (-1, -2), and (-2, -5).
To compare the slopes of the two functions, we can calculate the slope of each function and see if they are equal.
The slope of Function A is 6, and the slope of Function B can be found using the formula (y2 - y1)/(x2 - x1) by choosing any two pairs of ordered points.
For example, using (1, 4) and (-1, -2).
The slope of Function B is (4 - (-2))/(1 - (-1)) = 6/2 = 3.
Since the slope of Function A is 6 and the slope of Function B is 3, we can conclude that the slopes of the two functions are not equal.
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hope everyone can help me I'll really need your help
Answer:
See below. The solutions are x=-1/3 and y=-4/3
Step-by-step explanation:
[tex]\frac{1}{2}\log_2 y-\log_4 x = 1\\\frac{1}{2}\log_2 y = \log_4 x+1=\log_4x+\log_4 4=\log_4 4x\\\frac{1}{2}\log_2y = log_44x\\\frac{1}{2}\frac{\log_4y}{\log_4 2}=\log_4 4x\\\log_4y=\log_44x\\4^{\log_4y}=4^{\log_44x}\\y = 4x\\\\x-y = 1\\4x -y = 0\\\rightarrow\\3x=-1\implies x = -\frac{1}{3}, y=-\frac{4}{3}[/tex]
your company manufactures dolls each doll requires
2 feet of ribbon for bows how many yards of ribbons will be required to make 600 dolls
Answer:
400 yd
Step-by-step explanation:
There are 2 ft of ribbon for 1 doll.
For 600 dolls,
Ribbon = 600 × 2/1
Ribbon = 1200 ft
=====
Convert feet to yards
1 yd = 3 ft
Ribbon = 1200 × 1/3
Ribbon = 400 yd