12x2 = 18x
i need someone to explain this
Answers
12x² = 18x------> 12x²-18x=0-----> divided by 12----> x²-(3/2)*x=0
this is the equation of a vertical parabola
x²-(3/2)*x=0-----> x*(x-1.5)=0
the x-intercepts of the parabola are
x=0
x=1.5
using a graph tool
see the attached figure
Related Questions
A shell fits into a golden rectangle with a length of 8 in. What is the shell's width? write your answer is simplified radical form and rounded to the nearest tenth of an inch.
Select one:
a. About 4.9 inches
b. About 4.1 inches
c. About 5.3 inches
Answers
l / w = (1 + root (5)) / 2
Where,
l: length of the rectangle
w: width of the rectangle
Clearing the width we have:
w = (2 / (1 + root (5))) * (l)
Substituting values:
w = (2 / (1 + root (5))) * (8)
Rewriting:
w = 4.94427191 inches
Rounding off we have:
w = 4.9 inches
Answer:
the shell's width is:
w = 4.9 inches
a. About 4.9 inches
The correct answer is option(a) about 4.9 inches.
To find the width of a golden rectangle with a given length, we will use the golden ratio formula that is
l / w = (1 + √5) / 2
Where, l = length of rectangle & w = width of rectangle
By applying the above formula we get the golden ratio, which is ≈ 1.618.
The formula for a golden rectangle is length(l) = 1.618 × width.
Given that length is 8 inches, we set up the equation:
8 = 1.618 × width
Solving for width:
width = 8 / 1.618 = 4.948...
The simplified radical form of 4.948... is ≈ 4.9 inches.
Thus, the correct answer is about 4.9 inches or option (a).
Help Geometry!!
AC is tangent to circle O at A. If , m<BY= 24 , what is m<YAC?
a) 48
b) 156
c) 78
d) 132
Answers
The inscribed angle measures half of the arc it comprises.
so
∡BAY=BY/2------> 24/2------> 12°
angles YAC and BAY are complementary angles
∡YAC+∡BAY=90°
∡YAC=90-∡BAY-------> ∡YAC=90-12-----> 78°
the answer is
78°
Kenny is making creamy rice pudding his recipe requires 4 cups of milk he has a quart of milk in his fridge dose he have enough milk explain
Answers
Need help on this question
Answers
Area of the base: Ab=p*K
Semi-perimeter of the base: p
p=P/2
Perimeter of the base: P=20
p=P/2=20/2→p=10
Ab=p*k=10*K→Ab=10K
Lateral Area of the prism: Al
Al=P*h
Height of the prism: h=6
Al=P*h=20*6→
Al=120
T.A.=2*Ab+Al
T.A.=2*(10K)+120
T.A.=20K+120
T.A.=120+20K
Answer: (120+20K)
What is the linear function that best fits the data set?
Answers
Please, see the attached file.
Thanks.
suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. how high will the ball rebound after its third bounce? round to the nearest tenth
Answers
HELP!!!!!!NEED TO PASS!!!!WILL GIVE THE BRAIN!!!!!!!!!!!
Answers
So, x³ shifted 5 units to left will be (x + 5)³
Shifting 4 units upwards means adding 4 to the function value,
So, previous function shifted 4 units up will be (x + 5)³ + 4
Thus, g(x) = (x + 5)³ + 4
So, option b gives the correct answer
So, option b gives the correct answer
When he was 40 Keefer began investing $150 per month in various securities for his retirement savings. His investments averaged a 4.5% annual rate of return until he retired at age 70. What was the value of Keefer's retirement savings when he retired? Assume monthly compounding of interest.
Answers
Monthly saving, P = $150, Annual rate of return, R = 4.5% = 0.045.
Therefore, future value (FV) at the time of retirement will be;
FV = P*[1+(R/12)^12*30]/(R/12)
Substituting all the parameters;
FV = 150*[1+(1+0.045/12)^360]/(0.045/12) = $113.907.92
how do I solve (x-5)(x-1)=0
Answers
Next, you'd find the factors of 5, that when multiplied equal 5, and when added, equal -6. Being that 5 is a prime number (a number that is only divisible by 1 and itself) those numbers are 1 and 5. Both numbers have to be negative, in order to get -6.
-1*-5 = 5
-1 + -5 = -6
Finally you split up the X^2 to a single x with each of the factors and make it equal to zero (X - 1 = 0) and (X - 5 = 0). Then you solve each.
(X - 1 = 0) Add 1 to each side. X = 1
(X - 5 = 0) Add 5 to each side. X = 5
I hope this helps!
write an equation of an ellipse in standard form with the center at the origin and a height of 3 units and width of 1 unit
Answers
The equation of an ellipse with the specified attributes, using the center as the origin, is x2/0.25 + y2/2.25 = 1.
Explanation:The question asks for the equation of an ellipse with the center at the origin and a height of 3 units and width of 1 unit. In an ellipse, the center is the midpoint of both the major and minor axes. The major axis can be the horizontal (width) or vertical (height) axis, and the minor axis is the other one.
Given that the height of the ellipse is 3 units, this determines the major axis and its length of 2a=3, which means a=1.5. The width of the ellipse is 1 unit, this determines the minor axis and its length of 2b=1, which means b=0.5.
Using these values, the equation of such an ellipse, centered at the origin, in standard form is x2/0.25 + y2/2.25 = 1
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The equation of an ellipse in standard form with the center at the origin, a height of 3 units and width of 1 unit is [tex]\(4x^2 + (y^2/2.25) = 1\).[/tex]
Explanation:The equation of an ellipse in standard form with the center at the origin can be given by [tex]\(rac{{x^2}}{{a^2}} + rac{{y^2}}{{b^2}} = 1\)[/tex], where a is the semi-major axis and b is the semi-minor axis. Based on the information given in yourquestion, the height of the ellipse is 3 units which means the semi-major axis b is 1.5 units (since it's half the height). Similarly, the width of the ellipse is 1 unit which means the semi-minor axis a is 0.5 units (since its half the width). Substituting these values into the standard form of the ellipse we get: [tex]\(4x^2 + (y^2/2.25) = 1\)[/tex]
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What is the point-slope equation of the line with a slope 4/3 that goes through the point (-4,6)?
Answers
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})~\hspace{10em}slope = m\implies \cfrac{4}{3}\\\\\\\begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-6=\cfrac{4}{3}[x-(-4)]\implies y-6=\cfrac{4}{3}(x+4)[/tex]
Answer:
The point-slope form of the equation is y - 6 = 4/3(x + 4), which is answer B.
Step-by-step explanation:
In order to find the point-slope form of any equation, start with the base form of the equation.
y - y1 = m(x - x1)
Now input the slope given as m, and the point in for x1 and y1.
y - y1 = m(x - x1)
y - 6 = 4/3(x - -4)
y - 6 = 4/3(x + 4)
The difference of a number and 8 is the same as 34 less the number. find the number.
Answers
8 - x = x -34
2x = 8 + 34
2x = 42
x = 21
Answer: The number is 21.
PLEASE HELP 50 point will give brainlyest
Evaluate 81000−−−−√3 .
1/125
6/500
8/500
2/10
Answers
A car is traveling at a speed of 50 miles per hour. Each wheel of the car makes 770 revolutions per minute. To the nearest tenth of an inch, what is the diameter of each car wheel? (Note: 1 mile = 5,280 feet)
Answers
Answer: 21.8 inches
Given:
A car is traveling at a speed of 50 miles per hour. Each wheel of the car makes 770 revolutions per minute.
To get the diameter of each car wheel
Get first the length of revolution (circumference of the wheel) in inches.
Speed=50 miles/hr
=50miles/60 minutes
= 0.833333 miles/minute
=.833/5280=4400ft= 52,800 inches/minute
Since there are 770 revolutions per minute, per revolution (circumference of the wheel) =
=52,800/770
=68.57 inches
Formula of diameter given the circumference is:
D=C/π
D=68.57/3.14
D= 21.8 inches
Answer:
21.8
Step-by-step explanation:
just took test
A catapult is malfunctioning and not throwing objects in the intended manner. The builders have modeled the path of the objects thrown by using the following parametric equations. rewrite the parametric equations by eliminating the parameter.
x(t)=2t-1
y(t)= square root of t; t> or equal to 0
Answers
Answer:
The equation is [tex]y ^ 2 = \frac{x + 1}{2}[/tex]
Step-by-step explanation:
The parameter that we have is t. We want to eliminate this parameter in both equations, therefore in the first equation we solve for t and in the second equation we solve for the variable t.
We have:
[tex]x = 2t-1\\\\x + 1 = 2t\\\\t = \frac{x + 1}{2}[/tex]
Now we solve the other equation for t.
[tex]y= \sqrt{t}[/tex]
[tex]y ^ 2 = t[/tex] because [tex]t> 0[/tex]
As [tex]t = y ^ 2[/tex] and also [tex]t = \frac{x + 1}{2}[/tex]
Then:
[tex]y ^ 2 = \frac{x + 1}{2}[/tex]
The correct answer is:
D. [tex]x=2y^{2} -1, y\geq 0[/tex]
Help me solve this please!
Answers
a) The calculator shows 5 solutions:
{5π/23, 5π/17, 25π/23, 25π/17, 45π/23}
These have approximate decimal values of
{0.6830, 0.9240, 3.4148, 4.6200, 6.1466}
b) The calculator shows 2 solutions with approximate decimal values of
{1.2925, 4.4341}
c) The calculator shows 2 solutions with approximate decimal values of
{1.3694, 4.9137}
_____
This (desmos) calculator displays intercepts to 3 decimal places. Since you want 4 decimal places, some additional refinement of the answer was necessary. That was accomplished using Newton's method iteration. The details are not shown. A suitable graphing calculator (for example, a TI-84) will supply the intercept coordinates to full calculator accuracy.
Solve the quadratic equation. 8x2 + 16x + 8 = 0 A) 1 B) -1 C) 1 and 8 D) 1 and -1
Answers
Answer: B. -1
"the placement test for a college has scores that are normally distributed with a mean of 600 and a standard deviation of 60.if the college accepts only the top 1% of examinees, what is the cutoff score on the test for admission?"
Answers
let the cutoff be x
but
P(x>0.01)=1-P(x<0.01)=1-0.01=0.99
the z value corresponding to 0.99% is z=2.33
thus
2.33=(x-600)/60
solving for x we get:
139.8=x-600
x=739.8
Express answer in exact form.
A segment of a circle has a 120 arc and a chord of 8in. Find the area of the segment.
Answers
Please, see the attached file.
Thanks.
My brother owes me $10. I already have $10. My dads friend gave me and him $20 to split in half. He gave me the $20 and took my $10. Does he still owe me. Explain plz
Answers
your brother is supposed to give you $10
he gives you the money the friend told him to and you would have $20 PLUS the ten that he owes you. That would make you have $30. He took youre ten and gave you 20 but you were supposed to have 20 in the first place. He needs to give you the ten back he owes you.
on Sunday Mary pay $6 each on two tickets to a movie theater movies for $9.58 each Mary paid with 3 $20 bills how much changed
Answers
hjdjdjdjdbdhshssjdjdjdjdj
Simplify the square root of 864.
I cant remember this, please tell me how you got the answer.
Answers
[tex] \sqrt{864} [/tex]
[tex] \sqrt{4 \times 216} [/tex]
[tex] \sqrt{4 \times 4 \times 54} [/tex]
[tex] \sqrt{4 \times 4 \times 2 \times 27} [/tex]
[tex] \sqrt{4 \times 4 \times 2 \times 9 \times 3} [/tex]
now take out the pairs.
[tex]4 \sqrt{2 \times 9 \times 3} [/tex]
take out any of the square roots like 9
[tex]4 \times 3 \sqrt{2 \times 3} [/tex]
Now put it all back together.
[tex]12 \sqrt{6} [/tex]
I believe that is the answer.
How do you use properties of exponents and logarithms to rewrite functions in equivalent forms and solve equations?
Answers
1) log (a) ^ b = b * log (a)
2) log (a * b) = log (a) + log (b)
3) log (a / b) = log (a) - log (b)
These logarithmic properties can be used to solve equations.
For example:
2 ^ x = 56
If we apply to this equation the logarithm function on both sides that we have left
log (2) ^ x = log (56)
This function is equivalent to the first.
If we now apply the property 1) of the previous logarithms, we can reveal x of the equation.
x * log (2) = log (56)
x = log (56) / log (2)
x = 5,807
Thus, thanks to the properties of the logarithms, this exponential function could be solved
Final answer:
To use properties of exponents and logarithms effectively, one must apply specific rules such as the logarithm of a product being the sum of the logarithms and the logarithm of a number raised to an exponent being the product of the exponent and the logarithm. Log transformations help linearize and solve equations involving exponents.
Explanation:
To rewrite functions in equivalent forms and solve equations using the properties of exponents and logarithms, one must understand several key rules and relationships. For example, the common logarithm (log) indicates the power to which 10 must be raised to equal a given number.
Two essential properties we use are:
The logarithm of a product of two numbers is the sum of the logarithms of the two numbers (log xy = log x + log y).The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (log x^n = n log x).Exponential and logarithmic functions are inverses. This relationship allows us to simplify complex expressions and solve exponential equations by taking the logarithm of both sides. For instance, the natural logarithm (ln or loge) and the base e exponential are inverse functions, so ln (e^x) = x and e^(ln x) = x.
A log transformation can linearize functions that involve an exponent by taking the log of both sides of the equation. This technique is valuable in solving equations where the variable is an exponent.
peter put $8,000 into a savings account that pays 6% interest, compounded continuously. what will he have after 5 years?
Answers
[tex] Pe^{rt} [/tex]
P is Principal Amount
r is Rate
t is Time
P is 8000
r is 6%
t is 5
Therefore, you get $10,798.86.
giving brainliest please help, and give steps if possible. Im trying to learn this.
Answers
(fg)(x) = (6-5x)(6x^2+x = 36x^2 + 6x - 30x^3 - 5x^2
and then you must combine like terms: (fg)(x) = -30x^3 + 31x^2 + 6x
Answer:
[tex]f(x)g(x) = - 30x^{3} + 31 {x}^{2} + 6x[/tex]
Step-by-step explanation:
[tex](fg)(x) \\ (fx) = 6 - 5x \\ g(x) = {6x}^{2} + x \\ substitute \: and \: calculate: \\ f(x)g(x) = - 30x^{3} + 31 {x}^{2} + 6x[/tex]
The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency
Answers
A local movie theater charges $12 for an adult ticket and $10 for a child's ticket. a group of eight people spent a total of $86 on tickets to a movie. how many adults and how many children were in the group? write a system of linear equations based on the description. use x to represent the number of adults and y to represent the number of children.
Answers
You can get this by setting up the following system of equations.
x + y = 8 (number of people)
10x + 12y = 86 (cost)
someone help me please
Answers
f (x) = 3x + 1
g (x) = x ^ 2 - 6
Subtracting both functions we have:
(f-g) (x) = f (x) - g (x)
(f-g) (x) = (3x + 1) - (x ^ 2 - 6)
(f-g) (x) = 3x + 1 - x ^ 2 + 6
(f-g) (x) = - x ^ 2 + 3x + 7
Answer:
(f-g) (x) = - x ^ 2 + 3x + 7
option B
The angle of elevation to the top of a building in chicago is found to be 11◦ from the ground at a distance of 1000 feet from the base of the building. find the height of the building.
Answers
Alan is giving a basic math test in his class. One of the questions in the test is about finding two factors of the number 221. Which are the two factors of the given number? The two factors of the number 221 are ___ and ____.
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A factor refers to a whole number, which fits evenly into another whole number. Thus, factors are the numbers, which we multiply together to get another number. The two numbers that can be multiply together to get 221 are 13 and 17.