Answer:
1 coat: 256π cm² ≈ 804.25 cm²2 coats: 512π cm² ≈ 1608.50 cm² (rounds to 1608 cm²)Step-by-step explanation:
The radius of the ball is ...
r = C/(2π) = (16π cm)/(2π) = 8 cm
The formula for the area of a sphere is ...
A = 4πr²
Filling in the value of the radius, we find the area of the ball to be ...
A = 4π(8 cm)² = 256π cm² ≈ 804.25 cm²
Then 256π or 804.25 is the number of square centimeters needed to cover the given ball with one coat of latex.
If the ball is only considered to be covered when it has two coats of latex, then twice that amount, 512π or 1608.50 square centimeters of latex are required.
The amount of latex needed to cover a rubber ball with two coats, when the circumference of the ball is 16π cm, is 512π cm².
Explanation:To calculate the amount of latex needed to paint a rubber ball, we first need to calculate the surface area of the ball. The formula for the surface area of a sphere is 4πr², where r is the radius of the sphere. Given that the circumference of the sphere (rubber ball) is 16π cm, we can substitute this into the formula 2πr to find the radius, which equals 8 cm.
Substituting the radius into the surface area formula, we get 4π(8 cm)² = 4π(64 cm²) = 256π cm². This is the surface area for one layer of latex. But as the toy factory paints their balls with two coats of latex, we need to double this surface area, which gives us 512π cm² as the total area to be covered with latex.
Learn more about Surface Area Calculation here:https://brainly.com/question/32037353
#SPJ11
Need help with this math question
Answer:
[tex]x =7\sqrt{3}[/tex]
Step-by-step explanation:
By definition, the tangent of a z-angle is defined as
[tex]tan(z) =\frac{opposite}{adjacent}[/tex]
For this case
[tex]opposite = 7[/tex]
[tex]adjacent = x[/tex]
[tex]z=30\°[/tex]
So
[tex]tan(30) =\frac{7}{x}[/tex]
[tex]x =\frac{7}{tan(30)}[/tex]
[tex]x =7\sqrt{3}[/tex]
Answer:
7√3 = x
Step-by-step explanation:
Arbitrarily choose to focus on the 30 degree angle. Then the side opposite this angle is 7 and the side adjacent to it is x.
tan 30 degrees = (opp side) / (adj side), or (1√3) = 7 / x.
Inverting this equation, we get √3 = x/7.
Multiplying both sides by 7 results in 7√3 = x
A right rectangular prism has these dimensions: Length ? Fraction 1 and 1 over 2 units Width ? Fraction 1 over 2 unit Height ? Fraction 3 over 4 unit How many cubes of side length Fraction 1 over 4 unit are required to completely pack the prism without any gap or overlap? 36 45 51 60
The volume of the rectangular prism is length x width x height:
Volume = 1 1/2 x 1/2 x 3/4 = 9/16 cubic units.
The volume of cube is length^3 = 1/4^3 = 1/64
Divide the volume of the rectangular prism by the volume of the cube:
Number of cubes = 9/16 / 1/64 = 36
The answer is 36
Your fish tank holds 35 liters of water. How much is that in milliliter
Answer:
1 litre = 1000 millilitres (ml)
35 litres = 35×1000 => 35000 ml
So your fish tank holds 35000 ml of water
. Evaluate –x + 3.9 for x = –7.2.
Given.
-x + 3.9
Plug in.
-7.2 + 3.9 = -3.3
Answer.
-3.3
Answer:
11.1
Step-by-step explanation:
−(−7.2)+3.9
=7.2+3.9
=11.1
Ethan goes to a store an buys an item that costs x dollars. He has a coupon for 5% off, and then a 9% tax is added to the discounted price. Write an expression in terms of x that represents the total amount that Ethan paid at the register.
Final answer:
Ethan pays a total of 1.0355x dollars at the register for an item with an original price of x dollars, after applying a 5% discount and adding a 9% sales tax to the discounted price.
Explanation:
To calculate the total amount Ethan paid at the register, we need to take into account both the discount and the tax applied to the item's original price. First, we calculate the discounted price by subtracting the 5% off. Then, we add a 9% sales tax to that discounted price.
The original price is x dollars. The discount of 5% is 0.05x, so the discounted price is x - 0.05x, which simplifies to 0.95x. Next, we need to calculate the sales tax on the discounted price. The 9% tax on the discounted price is 0.09 * 0.95x, which is 0.0855x. Finally, to find the total amount paid, we add the sales tax to the discounted price:
Total Amount Paid = (0.95x) + (0.09 * 0.95x) = 0.95x + 0.0855x = 1.0355x
Which quadratic equation models the situation
correctly?
y = 27(x – 7)2 + 105
y = 27(x - 105)2 +7
y = 0.0018(x – 7)2 + 105
y = 0.0018(x - 105)2 + 7
Answer:
y = 0.0018(x -105)² +7
Step-by-step explanation:
The vertex of the function is at (x, y) = (105, 7), so the equation will be of the form ...
y = a(x -105)² +7
We can use x=0 to find the value of "a". At x=0, y=27, so ...
27 = a(0 -105)² +7
20 = 11025a
20/11025 = a ≈ 0.0018
So, the model is ...
y = 0.0018(x -105)² +7
Answer:
d
Step-by-step explanation:
Which of the following parabolas opens up?
ANSWER
A. Directrix y=-5, focus; (-2,6)
EXPLANATION
In other to figure out the parabola that opens up we need to know the relation between the directrix and focus.The focus is always inside the parabola and the directrix is always outside.If the directrix is above the focus,the parabola opens downwards.If the directrix is below the focus, the parabola opens upwards.How do you determine whether the directrix is above or below.You just have to compare the y-value of the focus to the directrix because the orientation is parallel to the y-axisFor the first option, the directrix y=-5 is below the focus (-2,6).Since the focus must lie inside the parabola, this parabola must open up.For the second option, the directrix, y=-5 is above the focus (2,-6). This parabola opens downwards.For the third option, the directrix, y=5 is above the focus (-6,-2). This parabola opens downwards.For the second option, the directrix, y=5 is above the focus (6,2). This parabola opens downwards.If two polynomial equations have real solutions, then will the equation that is the result of adding, subtracting, or multiplying the two polynomial equations also have real solutions?
No, there are polynomials that have real solutions but when combined would be possible to have no real solutions.
Answer:
No.
Step-by-step explanation:
No, one easy way to see it is with quadratic formulas. There exists quadratic polynomials with no real solutions, then if you add, subtract or multiply two polynomials and obtain a quadratic formula, possibly this polynomial won't have real solutions.
I am going to give one counterexample:
We have the two polynomials [tex]p(x) = x^2+2x+3[/tex] and [tex]q(x)= 2x^2+3x+4[/tex], then is we subtract q(x)-p(x) we obtain
[tex]2x^2+3x+4-(x^2+2x+3) = 2x^2+3x+4-x^2-2x-3 = x^2+x+1.[/tex]
The resulting polynomial is a quadratic polynomial of the form [tex]ax^2+bx+c[/tex] with a=1, b=1 and c=1. This polynomial has no real solutions, you can check it with the discriminating [tex]b^2-4ac = 1^2-4(1)(1) = 1-4 = -3.[/tex] As the discriminating is negative, the polynomial has no real solutions.
Suppose you invest $100 a month in an annuity that
earns 4% APR compounded monthly. How much money
will you have in this account after 2 years?
A. $2400.18
B. $2518.59
C. $1004.48
D. $3908.26
Answer:
$2502.60
Step-by-step explanation:
The formula for the amount of an annuity due is ...
A = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)
where P is the monthly payment (100), r is the annual interest rate (.04), n is the number of compoundings per year (12), and t is the number of years (2). Given these numbers, the formula evaluates to ...
A = $100(1.00333333)(1.00333333^24 -1)/0.00333333
= $100(301)(0.08314296)
= $2502.60
_____
This value is confirmed by a financial calculator. The given answer choices all appear to be incorrect. The closest one corresponds to an annual interest rate (APR) of 4.286%, not 4%.
What is the domain of y=sqrt x+5?
Answer:
interval notation: [-5,infinity)
or answer X=> -5
Step-by-step explanation:
For this case we must find the domain of the following function:
[tex]f (x) = \sqrt {x + 5}[/tex]
By definition, the domain of a function is given by all the values for which the function is defined.
The given function stops being defined when the argument of the root is negative. Thus, the domain is given by all values of "x" greater than or equal to -5.
Answer:
Domain: [tex]x\geq-5[/tex]
The parabola y = x² - 4 opens:
A.) up
B.) down
C.) right
D.) left
Answer:
Up
Step-by-step explanation:
Here the easy rules to remember the orientation of the parabolas are
a) If x is squared it opens up or down. And its coefficient of {[tex]x^{2}[tex] is negative it opens down.
b) If y is squared it opens side ways right or left. It its coefficient of [tex]y^{2}[/tex]
Hence in our equation of parabola
[tex]y = x^ 2-4[/tex]
x is squared and its coefficient is positive , hence it opens up towards positive y axis.
Triangle $ABC$ has side lengths $AB = 9$, $AC = 10$, and $BC = 17$. Let $X$ be the intersection of the angle bisector of $\angle A$ with side $\overline{BC}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{AC}$. Compute the length of $\overline{XY}$.
Answer:
[tex]\dfrac{72}{19}[/tex]
Step-by-step explanation:
Consider triangle ABC. Segment AX is angle A bisector. Its length can be calculated using formula
[tex]AX^2=\dfrac{AB\cdot AC}{(AB+AC)^2}\cdot ((AB+AC)^2-BC^2)[/tex]
Hence,
[tex]AX^2=\dfrac{9\cdot 10}{(9+10)^2}\cdot ((9+10)^2-17^2)=\dfrac{90}{361}\cdot (361-289)=\dfrac{90}{361}\cdot 72=\dfrac{6480}{361}[/tex]
By the angle bisector theorem,
[tex]\dfrac{AB}{AC}=\dfrac{BX}{XC}[/tex]
So,
[tex]\dfrac{9}{10}=\dfrac{BX}{17-BX}\Rightarrow 153-9BX=10BX\\ \\19BX=153\\ \\BX=\dfrac{153}{19}[/tex]
and
[tex]XC=17-\dfrac{153}{19}=\dfrac{170}{19}[/tex]
By the Pythagorean theorem for the right triangles AXY and CXY:
[tex]AX^2=AY^2+XY^2\\ \\XC^2=XY^2+CY^2[/tex]
Thus,
[tex]\dfrac{6480}{361}=XY^2+AY^2\\ \\\left(\dfrac{170}{19}\right)^2=XY^2+(10-AY)^2[/tex]
Subtract from the second equation the first one:
[tex]\dfrac{28900}{361}-\dfrac{6480}{361}=(10-AY)^2-AY^2\\ \\\dfrac{22420}{361}=100-20AY+AY^2-AY^2\\ \\\dfrac{1180}{19}=100-20AY\\ \\20AY=100-\dfrac{1180}{19}=\dfrac{1900-1180}{19}=\dfrac{720}{19}\\ \\AY=\dfrac{36}{19}[/tex]
Hence,
[tex]XY^2=\dfrac{6480}{361}-\left(\dfrac{36}{19}\right)^2=\dfrac{6480-1296}{361}=\dfrac{5184}{361}\\ \\XY=\dfrac{72}{19}[/tex]
Which expression is equivalent?
Answer:
Third choice from the top is the one you want
Step-by-step explanation:
This whole concept relies on the fact that if the index of a radical exactly matches the power under the radical, both the radical and the power cancel each other out. For example:
[tex]\sqrt[6]{x^6} =x[/tex] and another example:
[tex]\sqrt[12]{2^{12}}=2[/tex]
Let's take this step by step. First we will rewrite both the numerator and the denominator in rational exponential equivalencies:
[tex]\frac{\sqrt[4]{6} }{\sqrt[3]{2} }=\frac{6^{\frac{1}{4} }}{2^{\frac{1}{3} }}[/tex]
In order to do anything with this, we need to make the index (ie. the denominators of each of those rational exponents) the same number. The LCM of 3 and 4 is 12. So we rewrite as
[tex]\frac{6^{\frac{3}{12} }}{2^{\frac{4}{12} }}[/tex]
Now we will put it back into radical form so we can rationalize the denominator:
[tex]\frac{\sqrt[12]{6^3} }{\sqrt[12]{2^4} }[/tex]
In order to rationalize the denominator, we need the power on the 2 to be a 12. Right now it's a 4, so we are "missing" 8. The rule for multiplying like bases is that you add the exponents. Therefore,
[tex]2^4*2^8=2^{12}[/tex]
We will rationalize by multiplying in a unit multiplier equal to 1 in the form of
[tex]\frac{\sqrt[12]{2^8} }{\sqrt[12]{2^8} }[/tex]
That looks like this:
[tex]\frac{\sqrt[12]{6^3} }{\sqrt[12]{2^4} }*\frac{\sqrt[12]{2^8} }{\sqrt[12]{2^8} }[/tex]
This simplifies down to
[tex]\frac{\sqrt[12]{216*256} }{\sqrt[12]{2^{12}} }[/tex]
Since the index and the power on the 2 are both 12, they cancel each other out leaving us with just a 2! Doing the multiplication of those 2 numbers in the numerator gives us, as a final answer:
[tex]\frac{\sqrt[12]{55296} }{2}[/tex]
Phew!!!
9. If the diagonal of a square is 12 centimeters, the area of the square is
A. 102 cm2.
B. 36 cm2.
C. 144 cm2.
D. 72 cm2.
Answer:
D. 72 cm²
Step-by-step explanation:
The area of a square is given by ;
Area= l² where l = length
Given that the diagonal is 12 cm, let assume length of the square to be l
Apply the Pythagorean relationship where a=b=l
l² + l² = 12²
2 l² = 144
l²= 144/2
l²= 72
l =√72 =8.485 cm
⇒length of the square= l= 8.485 cm
⇒Area of the square= l² = 8.485² = 72 cm²
Answer:
36 cm2.
Step-by-step explanation:
The area of square A is 324 cm2. Since the dimensions of square A are three times larger than the dimensions of square B, the scale factor is 3.
To find the area of square B, first square the scale factor, 3.
3 squired =9
Next, divide the area of square A by 9.
324÷ cm2 ÷ 9 =36 cm2
Which statement is true about a skewed distribution?
A.) the mean lies to the right of the median for a positively skewed distribution.
B.) the mean lies to the left of the median for a positively skewed distribution.
C.) the mean lies to the left of the median for a symmetric distribution
D.) a distribution skewed to the left is said to be negatively skewed.
E.) a distribution skewed to the right is said to be positively skewed.
Answer:
B.) the mean lies to the left of the median for a positively skewed distribution.
Step-by-step explanation:
The blueprints for a new barn have a scale of 1/2 inch = 1 foot. A farmer wants to make sure she will have enough room for 12 new horse stalls to fit along one of the barn walls. Each stall has a width of five feet. If the blueprint of the barn is 20 inches by 30 inches, will there be enough room for the stalls?
Answer: yes
Step-by-step explanation: Wall would be 60 feet wide. 60 / 5 = 12.
Answer:
Yes
Step-by-step explanation:
Given :
1/2 in = 1 foot
re-written as : 1 in = 2 feet
THe blueprint is drawn to be 30 inches long
this is equivalent to 30 in x 2 feet/in = 60 feet long
With a minimum width of 5 feet per stall,
the number of stalls in 60 feet = 60 feet / 5 feet = 12 stalls
Hence there will be enough room for 12 stalls.
I don't understand how to do question c, d and f. Can someone please help me?
Answer:
Step-by-step explanation:
As with any equation involving fractions, you can multiply the equation by the least common denominator to eliminate fractions. Then solve in the usual way.
c) 1/a +b = c
1 +ab = ac . . . . multiply by a
1 = ac -ab . . . . subtract ab
1 = a(c -b) . . . . . factor out a
1/(c -b) = a . . . . divide by the coefficient of a
__
d) (a-b)/(b-a) = 1
a -b = b -a . . . . . multiply by b-a
2a = 2b . . . . . . . . add a+b
a = b . . . . . . . . . . divide by the coefficient of a
Please be aware that this makes the original equation become 0/0 = 1. This is why a=b is not an allowed condition for this equation. As written, it reduces to -1 = 1, which is false. One could say there is no solution.
__
f) bc +ac = ab . . . . . multiply by abc
bc = ab -ac . . . . . . subtract ac
bc = a(b -c) . . . . . . factor out a
bc/(b -c) = a . . . . . . divide by the coefficient of a
. Which of the following is a rational expression?
1/x
3x-4
x^2+x
x/2
Answer:
1/x
Step-by-step explanation:
1/x is rational because the x is in the denominator of the fraction. x/2 could be rewritten as (1/2)x, which is linear.
Easy Points!
Solve for x:
2x + 5 = 9
Happy Summer
Answer:
x = 2
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS = Parenthesis, Exponents (& roots), Multiplication, Division, Addition, Subtraction,
and is the order in which you follow for order of operation questions.
First, subtract 5 from both sides.
2x + 5 (-5) = 9 (-5)
2x = 9 - 5
2x = 4
Isolate the x, Divide 2 from both sides:
(2x)/2 = (4)/2
x = 4/2
x = 2
x = 2 is your answer.
~
Please help me. I need help asap!
Answer:
Step-by-step explanation:
They want you to translate N^3 into another form that would still be correct.
log N^3 = 3 * log N is the answer that I think you want. Try it it.
Suppose N = 6
Then N^3 = 6*6*6 = 216
log 216 = 2.3345
Now try it the other way.
3*log(6) = 3*0.7782
3*log(6) = 2.3345
Same answer as before.
Given x^4 − 4x^3 = 6x^2 − 12x, what are the approximate values of the non-integral roots of the polynomial equation?
Answer:
the values of the non-integral roots of the polynomial equation are:
4.73 and 1.27.
Step-by-step explanation:
To find the roots of the polynomial equation, we need to factorize the equation:
x^4 − 4x^3 = 6x^2 − 12x ⇒ x^4 − 4x^3 -6x^2 +12x = 0
⇒ x(x+2)(x -3 + sqrt(3))(x -3 - sqrt(3))
Then, the non integral roots are:
x1 = 3 - sqrt(3) = 1.26 ≈ 1.27
x2 = 3 + sqrt(3) = 4.73
Then, the values of the non-integral roots of the polynomial equation are:
4.73 and 1.27
The approximate values of the non-integral roots of the polynomial equation are:
1.27 and 4.73
Step-by-step explanation:We are given an algebraic equation as:
[tex]x^4-4x^3=6x^2-12x[/tex]
i.e. it could be written as:
[tex]x^4-4x^3-6x^2+12x=0\\\\i.e.\\\\x(x^3-4x^2-6x+12)=0[/tex]
Since, we pulled out the like term i.e. "x" from each term.
Now we know that [tex]x=-2[/tex] is a root of the term:
[tex]x^3-4x^2-6x+12[/tex]
Hence, we split the term into factors as:
[tex]x^3-4x^2-6x+12=(x-2)(x^2-6x+6)[/tex]
Now, finally the equation could be given by:
[tex]x(x-2)(x^2-6x+6)=0[/tex]
Hence, we see that:
[tex]x=0,\ x-2=0\ and\ x^2-6x+6=0\\\\i.e.\\\\x=0,\ x=2\ and\ x^2-6x+6=0[/tex]
[tex]x=0\ and\ x=2[/tex] are integers roots.
Now, we find the roots with the help of quadratic equation:
[tex]x^2-6x+6=0[/tex]
( We know that the solution of the quadratic equation:
[tex]ax^2+bx+c=0[/tex] is given by:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] )
Here we have:
[tex]a=1,\ b=-6\ and\ c=6[/tex]
Hence, the solution is:
[tex]x=\dfrac{-(-6)\pm \sqrt{(-b)^2-4\times 1\times 6}}{2\times 1}\\\\i.e.\\\\x=\dfrac{6\pm \sqrt{36-24}}{2}\\\\i.e.\\\\x=\dfrac{6\pm \sqrt{12}}{2}\\\\i.e.\\\\x=\dfrac{6}{2}\pm \dfrac{2\sqrt{3}}{2}\\\\i.e.\\\\x=3\pm 3\\\\i.e.\\\\x=3+\sqrt{3},\ x=3-\sqrt{3}[/tex]
Now, we put [tex]\sqrt{3}=1.732[/tex]
Hence, the approximate value of x is:
[tex]x=3+1.732,\ x=3-1.732\\\\i.e.\\\\x=4.732,\ x=1.268[/tex]
Shay works each day and earns more money per hour the longer she works. Write a function to represent a starting pay of $20 with an increase each hour by 4%. Determine the range of the amount Shay makes each hour if she can only work a total of 8 hours.
A.20 ≤ x ≤ 22.51
B.20 ≤ x ≤ 25.30
C.20 ≤ x ≤ 26.32
D.20 ≤ x ≤ 27.37
Answer:
Function: [tex]p(x)=20(1.04)^x[/tex]Range: option D. 20 ≤ x ≤ 27.37Explanation:
The function must meet the rule that the pay starts at $20 and it increases each hour by 4%.
A table will help you to visualize the rule or pattern that defines the function:
x (# hours) pay ($) = p(x)
0 20 . . . . . . . . [starting pay]
1 20 × 1.04 . . . [ increase of 4%]
2 20 × 1.04² . . . [increase of 4% over the previous pay]
x 20 × 1.04ˣ
Hence, the function is: [tex]p(x)=20(1.04)^x[/tex]
The range is the set of possible outputs of the function. To find the range, take into account that this is a growing exponential function, meaning that the least output is the starting point, and from there the output will incrase.
The choices name x this output. Hence, the starting point is x = 20 and the upper bound is when the number of hours is 8: 20(1.04)⁸ = 27.37.
Then the range is from 20 to 27.37 (dollars), which is represented by 20 ≤ x ≤ 27.37 (option D from the choices).
Answer:
its D for shure
Step-by-step explanation:
Mike is a salesperson in a retail carpet store. He is paid $500 base salary per month plus 5% commission on sales over $10,000. His sales this month were $23,750. His total deductions were $152.75. What is Mike’s net pay?
Answer:
$1034.75
Step-by-step explanation:
Mike's net pay is ...
base pay + commission - deductions
= $500 + 5%(23750 -10000) -152.75
= 347.25 + 0.05×13750
= $1034.75
Answer:
$1034.75
Step-by-step explanation:
Here we are given that the base salary of Mike is $500. He is also rewarded with some commission depending on sales. Hence we can bifurcate his gross pay as
Gross Pay = Base Pay + Commission
Commission = 5% of Sales over $10000
= 5% of (23750-10000)
= 5% of 13750
= 0.05*13750
= 687.50
Hence Gross pay = 500 + 687.50
= 1187.50
Also given that he has some deductions also i.e. $152.75 .
Therefor Net pay = Gross pay - Deductions
= 1187.50-152.75
= 1034.75
Hence Net Pay = $1034.75
The point A (3, 4) is reflected over the line x = 2, and then is reflected over the line x = -4. What are the coordinates of A'?
(1, 2)
(9, 4)
(-9, 4)
(1, 4)
Answer:
(- 9, 4)
Step-by-step explanation:
A(3, 4) is 1 unit to the right of x = 2
Thus it's reflection will be 1 unit to the left of x = 2, that is
A(3, 4 ) → A'(1, 4) ← y- coordinate remains unchanged
--------------------------------------------------------------------
A'(1, 4 ) is 5 units to the right of x = - 4
Thus it's reflection will be 5 units to the left of x = - 4
A'(1, 4) → A''(- 9, 4 )
Under the 2 parallel reflections
A(3, 4) → A''(- 9, 4 )
Match each item in Column A to an answer in Column B. 2. What is the distance between the two points on a number line? Column A Column B 1. X = –6, Y = 11 2. P = 8, Q = –15 3. U = –3, V = –20 4. J = 16, K = 7 A. 9 B. 17 C. 23
Answer:
17 (B)23 (C)17 (B)9 (A)Step-by-step explanation:
The distance between two points on a number line is the difference between the rightmost point and the leftmost point.
1. 11 -(-6) = 11+6 = 17
2. 8 -(-15) = 8+15 = 23
3. -3 -(-20) = -3+20 = 17
4. 16 -7 = 9
The measure of arc QR is _____
Answer:
132 degrees.
Step-by-step explanation:
SR and PQ are both 48 degrees. A circle is 360 degrees.
360-96 because 48+48 is 96, is 264. PS and QR are also the same so 264/2 is 132.
For the functions f(x) = 2x^2- 5x + 2 and g(x) = x– 2, find (f/g)(x) and (f/g)(4)
Answer:
[tex]\frac{f}{g}(x)=2x-1\\\\\frac{f}{g}(4)=7[/tex]
Step-by-step explanation:
[tex]\frac{f}{g}(x)=\dfrac{2x^2-5x+2}{x-2}=\dfrac{(x-2)(2x-1)}{(x-2)} =2x-1 \quad\text{x$\ne$2}\\\\\frac{f}{g}(4)=2\cdot 4-1=7 \qquad\text{fill in 4 for x and do the arithmetic}[/tex]
[tex]\left(\dfrac{f}{g}\right)(x)=\dfrac{2x^2-5x+2}{x-2}\\\\\left(\dfrac{f}{g}\right)(4)=\dfrac{2\cdot 4^2-5\cdot 4+2}{4-2}=\dfrac{32-20+2}{2}=7[/tex]
Find the circumference
[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =87\\ s=14 \end{cases}\implies 14=\cfrac{\pi (87)r}{180} \\\\\\ 2520=87\pi r \implies \cfrac{2520}{87\pi }=\boxed{r} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r\qquad \qquad \implies C=2~~\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \left(\boxed{\cfrac{2520}{87~~\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}} \right)\implies C = \cfrac{5040}{87} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill C\approx 57.93~\hfill[/tex]
let f(x)=3x+5 and g(x)=x^2.
find (f+g)(x)
i need the answer now plese and thack you
Answer: x² + 3x + 5
Step-by-step explanation:
f(x) = 3x + 5 g(x) = x²
(f + g)(x) = f(x) + g(x)
= 3x + 5 + x²
= x² + 3x + 5
The measure of angle θ is 7π/4. The measure of its reference angle is __°, and tan θ is __.
Answer:
Step-by-step explanation:
Even though I have been teaching calculus and precalc for several years now, my mind automatically wants to think in degrees as opposed to radians. So I converted the angle from radians to degrees to get 315. This angle lies in QIV. The reference angle is a 45 degree angle, since 360 - 315 = 45. This is a 45 degree angle, but if you consider direction, measuring clockwise gives you a negative angle. So it could be that the reference angle needs to be identified as -45 degrees. It depends upon what lesson you are dealing with. Regardless, because this is a 45-45-90 right triangle, both the legs measure the same length (because of the Isosceles Triangle Theorem), which is 1. Therefore, if the angle is 45 degrees, then the tangent of it is 1/1 = 1.