The circumference of the circle is 18.84 cm and the area is 28.26 cm².
Explanation:To find the circumference of a circle, we use the formula C = πd, where d is the diameter. In this case, the diameter is 6 cm, so the circumference is:
C = 3.14 × 6 = 18.84 cm
To find the area of a circle, we use the formula A = πr², where r is the radius. Since the radius is half the diameter, the radius in this case is 6/2 = 3 cm. So the area is:
A = 3.14 × 3² = 28.26 cm²
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Triangle ABC has points A(2, -1), B(3, 4), C(-7, 2), and is dilated by a factor of 5 to create the triangle A'B'C'. What are the coordinates of triangle A'B'C'?
Answer:
[tex]A'(10,-5)\\\\B'(15,20)\\\\C'(-35,10)[/tex]
Step-by-step explanation:
You know that the triangle ABC has these points:
A(2, -1), B(3, 4), C(-7, 2)
If the triangle ABC is dilated by a factor of 5 to create the triangle A'B'C', you can find the coordinates of this new triangle by multiplying by 5 the coordinates of the triangle ABC given.
Therefore, the coordinates of the triangle A'B'C' are:
[tex]A'=(2(5),\ -1(5))=(10,-5)\\\\B'=(3(5),\ 4(5))=(15,20)\\\\C'=(-7(5),\ 2(5))=(-35,10)[/tex]
Given the ordered pair P(1, -3), determine the requested secant, cosecant, or cotangent of angle ?. Cot ? = _____
[tex]\bf P(\stackrel{x}{1},\stackrel{y}{-3})\qquad \qquad cot(\theta )=\cfrac{\stackrel{\stackrel{adjacent}{x}}{1}}{\stackrel{\stackrel{opposite}{y}}{-3}}[/tex]
The value of Cotangent or cot is: [tex]cot \;\theta= \frac{1}{-3}[/tex]
What are Trigonometric ratios?Trigonometric ratios are the ratios of the length of sides of a triangle.
In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent.
Given ordered pair P(1, -3).
As we know that Cotangent is ratio of base : perpendicular i.e.,
adjacent of x: opposite y
So, [tex]cot \;\theta= \frac{1}{-3}[/tex]
Now, Hypotenuse = [tex]\sqrt{base^{2}+perpendicular^{2} }[/tex]
= [tex]\sqrt{1^{2} + (-3)^{2}} =\sqrt{10}[/tex]
and,
[tex]sec\;\theta= \frac{\sqrt{10} }{1} \\cosec\;\theta =\frac{\sqrt{10} }{(-3)}[/tex]
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f(x)=2x^2-3x+9
what is f(3)
Answer:
when x=3, the answer is
f(3)=36
Step-by-step explanation:
You need to plug in 3 for x and then solve. :)
Hope this helps! If possible, could you please mark as brainliest? Thanks!
Answer:
18
Step-by-step explanation:
Wherever you put a 3 in for the x's that are on the right.
f(x) = 2x^2 - 3x + 9
f(3) = 2*3^2 - 3(3) + 9
f(3) = 2*9 - 9 + 9
f(3) = 18
Use the divergence theorem to evaluate the integral i = z z ∂w f · ds when f(x, y, z) = y i − 4yz j + 3z 2 k and ∂w is the boundary of the solid w enclosed by the upper half of the sphere
[tex]\vec f(x,y,z)=y\,\vec\imath-4yz\,\vec\jmath+3z^2\,\vec k[/tex]
[tex]\implies\nabla\cdot\vec f(x,y,z)=0-4z+6z=2z[/tex]
By the divergence theorem,
[tex]\displaystyle\iint_{\partial W}\vec f\cdot\mathrm d\vec S=\iiint_W2z\,\mathrm dV[/tex]
I'll assume a sphere of radius [tex]r[/tex] centered at the origin, and that [tex]W[/tex] is bounded below by the plane [tex]z=0[/tex]. Convert to spherical coordinates, taking
[tex]x=\rho\cos\theta\sin\varphi[/tex]
[tex]y=\rho\sin\theta\sin\varphi[/tex]
[tex]z=\rho\cos\varphi[/tex]
Then
[tex]\displaystyle\iiint_W2z\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^r2\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\pi r^4[/tex]
Final answer:
The given question involves using the divergence theorem to evaluate an integral involving a vector field and a surface. The vector field is given as f(x, y, z) = y i - 4yz j + 3z^2 k and the surface of interest is the upper half of a sphere.
Explanation:
The given question involves using the divergence theorem to evaluate an integral involving a vector field and a surface. The vector field is given as f(x, y, z) = y i - 4yz j + 3z^2 k and the surface of interest is the upper half of a sphere.
To solve this, we need to apply the divergence theorem, which states that the integral of the divergence of a vector field over a closed surface is equal to the triple integral of the divergence of the vector field over the volume enclosed by that surface. In this case, the volume is the upper half of the sphere and the divergence of the vector field is div(f) = ∂f/∂x + ∂f/∂y + ∂f/∂z.
By evaluating the divergence of the vector field and simplifying the expression, we can then use the divergence theorem to convert the surface integral into a volume integral, which can be evaluated using appropriate coordinates.
You can work no more than 60 hours each week at your two jobs. Dog walking pays $7 per hour and your sales job at Computers & More, Inc. pays $12 per hour. You need to earn at least $450 each week to pay your bills. Your friend solves the system of inequalities and tells you that a possible solution is (-3, 50). Is this a possible solution, why or why not?
Answer:
No
Step-by-step explanation:
You cannot work negative 3 hours, it's impossible. One possible solution would be to work 50 hours a week at dog walking for 7 dollars an hour, and 10 hours a week at Computers & More, Inc. for 12 dollars a week. This would give you 350 dollars from dog walking, and 120 dollars from Computers & More, Inc. This would be a total of 470 dollars.
Answer:
No, this is not a possible solution because it does not satisfy all inequalities of the system.
Step-by-step explanation:
Let x represents the number of hours spent on dog walking and y represents the number of hours spent on sales job at Computers & More Inc.,
Given,
Total hours can not be no more than 60 hours,
⇒ x + y ≤ 60
Dog walking pays $7 per hour and your sales job at Computers & More, Inc. pays $12 per hour.
Thus, the total earning = 7x + 12y
According to the question,
Total earning ≥ $ 450
⇒ 7x + 12y ≥ 450
Also, hours can not be negative,
⇒ x ≥ 0; y ≥ 0
Hence, the system of inequalities that shows the given situation is,
7x + 12y ≥ 450;
x + y ≤ 60;
x ≥ 0; y ≥ 0
Since, -3 ≥ 0 ( False ),
Thus, the point is not satisfying all inequalities of the system,
Hence, it can not be the solution.
What is the 6th value in the sequence with the explicit formula
an= −2n−14?
Answer:
a6 = -26
Step-by-step explanation:
Fill in n=6 and do the arithmetic.
a6 = -2·6 -14 = -12-14 = -26
Solution:
Given, Tn = -2n - 14
To Find : What is the 6th value in the sequence
Solution: Simply Substitute the value of n as 6 .
Tn = -2n-14
Tn = -2(6) -14
Tn = -12 - 14
Tn = -14 - 12
Tn = -26
Therefore -10 is the 6th value in the sequence.
Which of the following is csc(-166°) equal to?
csc(14°)
-csc(14°)
-csc(-14°)
csc(166°)
Answer:
-csc(14°)
Step-by-step explanation:
The given trigonometric expression is csc(-166°)
-166° is in the third quadrant.
It makes an angle of 14° with the x-axis.
Hence the principal angle for -166° is 14°
In the third quadrant the cosecant function is negative.
This implies that;
csc(-166°) =-csc(14°)
The correct choice is the second option.
Emanuel surveyed a random sample of 50 subscribers to Auto Wheel magazine about the number of cars that they own. Of the subscribers surveyed, 15 own fewer than 2 vehicles. There are 340 subscribers to Auto Wheel magazine. Based on the data, what is the most reasonable estimate for the number of Auto Wheel magazine subscribers who own fewer than 2 vehicles?
PLEASE
Answer:
The most reasonable estimate for the number of Auto Wheel magazine subscribers who own fewer than 2 vehicles is 102.
Step-by-step explanation:
Consider the provided information.
A random sample of 50 subscribers to Auto Wheel magazine about the number of cars that they own. Of the subscribers surveyed, 15 own fewer than 2 vehicles.
We need to find the most reasonable estimate for the number of Auto Wheel magazine subscribers who own fewer than 2 vehicles if there are 340 subscribers.
Here, the sample used is 50 and the population size is 340.
Now use the formula to find the reasonable estimate.
[tex]\frac{Part}{Sample}=\frac{x}{Population}[/tex]
Substitute the respective values in the above formula as shown;
[tex]\frac{15}{50}=\frac{x}{340}[/tex]
[tex]\frac{15}{50}\times 340=x[/tex]
[tex]x=3\times 34[/tex]
[tex]x=102[/tex]
Hence, the most reasonable estimate for the number of Auto Wheel magazine subscribers who own fewer than 2 vehicles is 102.
Please help me out with this
Answer:
76.9 in²
Step-by-step explanation:
The area (A) of any sector in a circle is
A = area of circle × fraction of circle
= πr² × [tex]\frac{77}{360}[/tex]
= π × 10.7² × [tex]\frac{77}{360}[/tex]
= [tex]\frac{10.7^2(77)\pi }{360}[/tex] ≈ 76.9 in²
A circle has center O(5, −1) and radius 5. Which of the following points is on the circle?
V(2, 3)
X(−3, −2)
Y(5, −4)
Z(6, 9)
Answer:
The correct answer is the first one listed.
Step-by-step explanation:
First you have to determine what the equation for that circle is. The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex] where h and k are the coordinates of the center and the radius is squared. Using the given info, our equation will look like this:
[tex](x-5)^2+(y+1)^2=25[/tex]
Now we use the coordinates given and plug in 2 for x and 3 for y and do the math and see if the 2 sides are equal.
[tex](2-5)^2+(3+1)^2=25[/tex]
and 9 + 16 = 25, right? So that's how you can check the other coordinate pairs to verify that they DON'T work out!
The point Y(5, -4) lies on the circle with center O(5, -1) and radius 5, as per the distance formula and the equation of a circle.
To determine which point lies on the circle with center O(5, -1) and radius 5, we can use the distance formula to check if any of the given points are exactly radius 5 units away from center O. The distance formula, which is derived from the Pythagorean theorem, states that the distance between two points (x₁, y₁) and (x₂, y₂) in a 2-dimensional plane is given by √[(x₂ - x₁)² + (y₂ - y₁)²].
Thus, if a point (x, y) is on the circle, the following must be true: (x - 5)² + (y + 1)² = 52.
Checking for each point:
For point V(2, 3), we find (√[(2 - 5)² + (3 + 1)²]) which does not equal 5.
For point X(-3, -2), we calculate (√[(-3 - 5)² + (-2 + 1)²]) which does not equal 5.
For point Y(5, -4), we get (√[(5 - 5)² + (-4 + 1)²]) which equals to 5, hence Y lies on the circle.
For point Z(6, 9), we determine (√[(6 - 5)² + (9 + 1)²]) which does not equal 5.
Therefore, the point Y(5, -4) is on the circle.
The probability that Carmen will get an A on her math test is 80%, and the probability that she will get an A on her science test is 60%.
What is the probability that she will get an A on both tests? Express your answer as a decimal rounded to the nearest hundredth.
Answer:
70%
Step-by-step explanation:
60+80=140
140/2=70
The surface areas of two similar pyramids are 48 m2 and 108 m2 Find the scale factor.
A.1/3 B.2/3 C. 3/4 D. 3/3
Answer:
[tex]\boxed{ \text{B. }\frac{2}{ 3}}[/tex]
Step-by-step explanation:
The scale factor (C) is the ratio of corresponding sides of the two pyramids.
The ratio of the areas is the square of the scale factor.
[tex]\frac{A_{1}}{ A_{2}} =C^{2}\\ \\\frac{48 }{108} = C^{2}\\\\ \frac{4}{9} = C^{2}\\\\ C = \frac{2}{3}\\\\[/tex]
The scale factor is [tex]\boxed {\frac{2}{3}}[/tex].
The amount of an ordinary $9000.00 annuity for 3 years at 12 percent compounded quarterly is _______? Show Work
Answer:
A = $12831.8
Step-by-step explanation:
We know that the formula for compound interest is given by:
[tex]A=P(\frac{1+r}{n} )^{nt}[/tex]
where [tex]A[/tex] is unknown which is the amount of investment with interest,
[tex]P=9000[/tex] which is the initial amount,
[tex]r=12/100=0.12[/tex] is the interest rate,
[tex]n=4[/tex] which is the number of compoundings a year; and
[tex]t=3[/tex] which is the number of times that interest is compounded per unit t.
So substituting these values in the above formula to find A:
[tex]A=P(\frac{1+r}{n} )^{nt}[/tex]
[tex]A=9000(\frac{1+0.12}{4} )^{(4.3)}[/tex]
[tex]A = 9000(1 + 0.03)^{12}[/tex]
A = $12831.8
Answer:
The amount after 3 years = $12381.85
Step-by-step explanation:
Points to remember
Compound interest
A = P[1 +R/n]^nt
Where A - amount
P - principle amount
R = rate of interest
t - number of times compounded yearly
n number of years
To find the amount
Here,
P = $9000.00, n = 3 years, t = 4, n = 3 and R = 12% = 0.12
A = P[1 +R/n]^nt
= 9000[1 + 0.12/4]^(3 * 4)
= 9000[1 + 0.03]^12
= 12831.85
Therefore the amount after 3 years = $12381.85
please answer fast!!! will give brainliest!!!
given: m arc KJ = 124°, m arc IC =38° Find: m∠CQJ, m∠LIJ
Answer:
First question C
C) after drawing the shape
Second question C
C). Solved the equation and then put 6 in place of X
x+17=3x+5. 3x-x= 17-5. 2x=12. 2x/2=12/2. x=6
NM=6+17= 23. OL=3(6)+5=23
Step-by-step explanation:
hope this helps and mark me as brainliest
I need to find the surface area and volume of all three figures. If you could provide what equations you used to I will be grateful :)
Thank you <3
Answer:
Part 1) Sphere The surface area is equal to [tex]SA=196\pi\ m^{2}[/tex] and the volume is equal to [tex]V=\frac{1,372}{3}\pi\ m^{3}[/tex]
Part 2) Cone The surface area is equal to [tex]SA=(16+4\sqrt{65})\pi\ units^{2}[/tex] and the volume is equal to [tex]V=\frac{112}{3}\pi\ units^{3}[/tex]
Part 3) Triangular Prism The surface area is equal to [tex]SA=51.57\ mm^{2}[/tex] and the volume is equal to [tex]V=17.388\ mm^{3}[/tex]
Step-by-step explanation:
Part 1) The figure is a sphere
a) Find the surface area
The surface area of the sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
we have
[tex]r=14/2=7\ m[/tex] ----> the radius is half the diameter
substitute
[tex]SA=4\pi (7)^{2}[/tex]
[tex]SA=196\pi\ m^{2}[/tex]
b) Find the volume
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=14/2=7\ m[/tex] ----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}\pi (7)^{3}[/tex]
[tex]V=\frac{1,372}{3}\pi\ m^{3}[/tex]
Part 2) The figure is a cone
a) Find the surface area
The surface area of a cone is equal to
[tex]SA=\pi r^{2} +\pi rl[/tex]
we have
[tex]r=4\ units[/tex]
[tex]h=7\ units[/tex]
Applying Pythagoras Theorem find the value of l (slant height)
[tex]l^{2}=r^{2} +h^{2}[/tex]
substitute the values
[tex]l^{2}=4^{2} +7^{2}[/tex]
[tex]l^{2}=65[/tex]
[tex]l=\sqrt{65}\ units[/tex]
so
[tex]SA=\pi (4)^{2} +\pi (4)(\sqrt{65})[/tex]
[tex]SA=16\pi +4\sqrt{65}\pi[/tex]
[tex]SA=(16+4\sqrt{65})\pi\ units^{2}[/tex]
b) Find the volume
The volume of a cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we have
[tex]r=4\ units[/tex]
[tex]h=7\ units[/tex]
substitute
[tex]V=\frac{1}{3}\pi (4)^{2}(7)[/tex]
[tex]V=\frac{112}{3}\pi\ units^{3}[/tex]
Part 3) The figure is a triangular prism
a) The surface area of the triangular prism is equal to
[tex]SA=2B+PL[/tex]
where
B is the area of the triangular base
P is the perimeter of the triangular base
L is the length of the prism
Find the area of the base B
[tex]B=\frac{1}{2} (2.7)(2.3)=3.105\ mm^{2}[/tex]
Find the perimeter of the base P
[tex]P=2.7*3=8.1\ mm[/tex]
we have
[tex]L=5.6\ mm[/tex]
substitute the values
[tex]SA=2(3.105)+(8.1)(5.6)=51.57\ mm^{2}[/tex]
b) Find the volume
The volume of the triangular prism is equal to
[tex]V=BL[/tex]
where
B is the area of the triangular base
L is the length of the prism
we have
[tex]B=3.105\ mm^{2}[/tex]
[tex]L=5.6\ mm[/tex]
substitute
[tex]V=(3.105)(5.6)=17.388\ mm^{3}[/tex]
If set A = {3, 4, 7, 9}, set B = {8, 9, 10, 11}, and set C = {4, 9, 11, 13, 15}, then A∩(B∪C) =
{}
{4, 9}
{3, 4, 7, 9, 11}
A = {3, 4, 7, 9}
B = {8, 9, 10, 11}
C = {4, 9, 11, 13, 15}
A∩(B∪C)
First let's solve parentheses, we want the union between B and C.
B∪C = {4, 8, 9, 10, 11, 13, 15}
Now we want the interception between A and this, which means we want just the value which appears in both.
A∩{4, 8, 9, 10, 11, 13, 15} = {4, 9}
Final answer:
To determine A∩(B∪C), first calculate the union of B and C which is {4, 8, 9, 10, 11, 13, 15}. Then find the intersection of this union with set A, which results in {4, 9}.
Explanation:
To find the intersection of set A with the union of sets B and C, denoted as A∩(B∪C), we first identify the union of sets B and C. The union of two sets contains all elements that are members of either set, without duplicates. Therefore, the union of set B = {8, 9, 10, 11} and set C = {4, 9, 11, 13, 15} is the set that contains all distinct elements from both, which is {4, 8, 9, 10, 11, 13, 15}.
Next, we identify the intersection of set A with this union. The intersection of two sets contains only the elements that are members of both sets. Set A = {3, 4, 7, 9}. We check which elements in set A are also in the union of B and C. The elements 4 and 9 appear in both set A and the union of B and C. Consequently, the intersection A∩(B∪C) is {4, 9}.
(05.06)
Choose the graph below that represents the following system of inequalities: (1 point)
y ≥ −3x + 1
y ≤ 1 over 2 x + 3
Answer:
The second graph represents the system of inequalities
[tex]y\geq-3x + 1\\\\y\leq\frac{1}{2}x + 3\\[/tex]
Step-by-step explanation:
Let us first consider how the graphs of the inequalities will look like.
For the inequality [tex]y\geq-3x + 1[/tex] all the values "above" the line [tex]y=-3x + 1[/tex] are its solutions (because of the [tex]\geq[/tex] sign).
And for the inequality [tex]y\leq\frac{1}{2}x + 3[/tex] all the values the "below" the line [tex]y=\frac{1}{2}x + 3[/tex] are its solutions (because of the [tex]\leq[/tex] sign).
Together these system of inequalities have the solutions as shown in the second figure.
Answer:
The second graph.
Yr Welcome
Step-by-step explanation:
which graph represents viable values for y=5.5x, where x is the number of cans of tomato paste abd y is the total weight of the sealed cans in ounces?
Answer:
The second graph.
Step-by-step explanation:
The second dotted graph represents viable values because the weights of cans are discrete data. We deal with a whole number of cans ( not parts of a can) so a continuous graph like the first one is not appropriate here.
Answer:
The second graph.Step-by-step explanation:
The second graph represents viable values to these variables, because the independent variable, which it's the horizontal axis, represents cans of tomato past, and that it's only represented by a discrete variables, this means that cans can be counted only in natural numbers 1, 2, 3, 4, 5, ... and the second graph represent these discrete values, because it shows points for each can.
On the other hand, the first graph represents a continuous variable, which admits decimal numbers that cannot represent cans, because we cannot say "I have 2.345 cans", it's not possible, because each can is a whole, 1 can, 2 cans, and so on.
Therefore, the second graph is the viable.
Please help me out..(:
Let's call the left side of this tirangle y and downside z.
3² + 6² = y²
y² = 45
y² + z² = (3 + x)²
45 + z² = 9 + 6x + x²
x² + 6² = z²
45 + x² + 6² = 9 + 6x + x²
45 + x² + 36 = 9 + 6x + x²
45 + 36 - 9 = 6x
72 = 6x
x = 12
if $6,000 is invested at an annual interest rate of 1.83%, compounded daily, what will the investment be worth after 10 years?
Answer:
[tex]\$7,204.85[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ P=\$6,000\\ r=0.0183\\n=365[/tex]
substitute in the formula above
[tex]A=\$6,000(1+\frac{0.0183}{365})^{365*10}=\$7,204.85[/tex]
The investment will be worth approximately $6,960.47 after 10 years.
To solve this problem, we can use the formula for compound interest, which is:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
Given:
[tex]- \( P = $6,000 \) \\-( r = 1.83\% = 0.0183 \) (as a decimal) \\- \( n = 365 \) (since the interest is compounded daily) \\- \( t = 10 \) years[/tex]
Plugging these values into the compound interest formula, we get:
[tex]\[ A = 6000 \left(1 + \frac{0.0183}{365}\right)^{365 \times 10} \][/tex]
Now, we calculate the value inside the parentheses first:
[tex]\[ \frac{r}{n} = \frac{0.0183}{365} \approx 0.000050137 \][/tex]
[tex]\[ 1 + \frac{r}{n} = 1 + 0.000050137 \approx 1.000050137 \][/tex]
[tex]\[ (1.000050137)^{365 \times 10} \] \[ = (1.000050137)^{3650} \][/tex]
Using a calculator or a software tool to compute this value, we find:
[tex]\[ (1.000050137)^{3650} \approx 1.1600785 \] \[ A = 6000 \times 1.1600785 \approx 6960.47 \][/tex]
Therefore, the investment will be worth approximately $6,960.47 after 10 years.
Find the volume of the pyramid below
Answer: OPTION B
Step-by-step explanation:
Since the base is a square, you need to use the following formula:
[tex]V=\frac{s^2h}{3}[/tex]
Where "s" is the lenght of any side of the base and "h" is the height of the pyramid.
You can identify in the figure that:
[tex]s=12units\\h=8units[/tex]
Then you can substitute these values into the formula to calculte the volume of this pyramid. Therefore, the result is:
[tex]V=\frac{(12units)^2(8units)}{3}=384units^3[/tex]
Answer:
The correct answer is option B. 384 units³
Step-by-step explanation:
Formula:-
Volume of pyramid = (a²h)/3
Where a - side of base
h - height of pyramid
To find the volume of given pyramid
Here a = 12 units and h = 8 units
Volume = (a²h)/3
= (12² * 8)/3
= (12 * 12 * 8)/3
= (4 * 12 * 8) = 384 units³
Therefore the correct answer is option B. 384 units³
If a(x) = 3x + 1 and 5(x)=1/x-4, what is the domain of (ba)(x)?
For this case we have the following fusions:
[tex]a (x) = 3x + 1\\b (x) = \frac {1} {x} -4[/tex]
We must find [tex](a * b) (x):[/tex]
By definition:
[tex](a * b) (x) = a (x) * b (x)\\(a * b) (x) = (3x + 1) * (\frac {1} {x} -4)\\(a * b) (x) = \frac {3x} {x} -12x + \frac {1} {x} -4\\(a * b) (x) = 3-12x + \frac {1} {x} -4\\(a * b) (x) = - 12x + \frac {1} {x} -1[/tex]
The domain of the function will be given by all the values for which the function is defined, that is, all real numbers except zero.
Answer:
(-∞, 0) U (0,∞)
Blueberry bushes are planted in a field in the year 2009. The blueberry bushes start to grow and cover the field in such a way that the area covered by the bushes doubles every year. If they continue to grow in this way, the field will be entirely covered with blueberry bushes by the year 2016.
When will the field be covered 25% of the way?
A.
The field will be covered 25% of the way in 2013.
B.
The field will be covered 25% of the way in 2015.
C.
The field will be covered 25% of the way in 2014.
D.
The field will be covered 25% of the way in 2012.
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Answer:
C. The field will be covered 25% of the way in 2014.
Step-by-step explanation:
Since the field was completely covered in 2016, and the blueberries doubled in size in one year to do that, the field was half-covered in 2015. Similar reasoning tells you the field was 1/4 covered in 2014.
(25 points to correct answer)
Find the area of sector GHJ given that θ=65°. Use 3.14 for π and round to the nearest tenth. Show your work and do not forget to include units in your final answer.
Answer:
The area of a sector GHJ is [tex]36.3\ cm^{2}[/tex]
Step-by-step explanation:
step 1
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=8\ cm[/tex]
substitute
[tex]A=\pi (8)^{2}[/tex]
[tex]A=64\pi\ cm^{2}[/tex]
step 2
Remember that the area of a complete circle subtends a central angle of 360 degrees
so
by proportion find the area of a sector by a central angle of 65 degrees
[tex]\frac{64\pi}{360}=\frac{x}{65}\\ \\x=64\pi (65)/360[/tex]
Use [tex]\pi =3.14[/tex]
[tex]x=64(3.14)(65)/360=36.3\ cm^{2}[/tex]
To rent a carpet cleaner at the hardware store, there is a set fee and an hourly rate. The rental cost, c, can be determined using this equation
when the carpet cleaner is rented for h hours
c = 25 + 3h
Which of these is the hourly rate?
A.3
B.3h
C.25
D.25h
3h
The set cost is 25, because c=25 when h=0. So, this leaves 3h as the hourly rate.
The hourly rate of the carpet cleaning is specified correctly by: Option A: 3
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
c = rental cost of a carpet cleaner
h = number of hours the carpet cleaner is rented.
c = 25 + 3h can be written as:
c = 25 + (3+3+3+...+3) (h times)
That shows that 3 is added h times, which is the number of hours, so for each 1 of h hours, there is one 3 added in the final rental cost. (assuming nothing complex is going to happen)
That shows that the hourly rate is 3.
Thus, the hourly rate of the carpet cleaning is specified correctly by: Option A: 3
Learn more about forming equations here:
https://brainly.com/question/11938672
wich is a better buy?4 cans for $6 or 8 cans for $10
Answer:
Step-by-step explanation:
6/4=1.5 (price per can)
10/8=1.25 (price per can)
1.25 is cheaper than 1.5
the second one is the better buy
The better buying option is 8 cans for $10 and this can be determined by using the unitary method and the given data.
Given :
4 cans for $6 or 8 cans for $10.
The following steps can be used in order to determine the correct buying option:
Step 1 - The unitary method can be used in order to determine the better buying option.
Step 2 - If the value of 4 cans is $6 then the value of 1 can is:
4 cans = $6
1 can = [tex]\rm \dfrac{6}{4}[/tex]
= $1.5
Step 3 - If the value of 8 cans is $10 then the value of 1 can is:
= $1.25
So, the best buying option is 8 cans for $10.
For more information, refer to the link given below:
https://brainly.com/question/12116123
if f(x)=8x+7 and g(x)=x+2 what is (f*g)(2)
Answer:
92
Step-by-step explanation:
Assuming your (f*g)(2) is the product f(2)*g(2), you have ...
f(2) = 8*2 +7 = 23
g(2) = 2+2 = 4
(f*g)(2) = f(2)*g(2) = 23*4 = 92
Answer:
Step-by-step explanation:23
What are the values of w and x in the triangle below? Round the answers to the nearest tenth.
w = 13.3; x = 10.3
w = 10.8; x = 6.1
w = 13.3; x = 23.6
w = 10.8; x = 16.9
Answer:
w = 13.3, x= 10.3
First option is correct.
Step-by-step explanation:
In triangle ABC, we have
[tex]\tan42^{\circ}=\frac{AB}{BC}\\\\\tan42^{\circ}=\frac{12}{w}\\\\w=\frac{12}{\tan42^{\circ}}\\\\w=13.3[/tex]
Now, in triangle ABD
[tex]\tan27^{\circ}=\frac{AB}{BD}\\\\\tan27^{\circ}=\frac{12}{w+x}\\\\13.3+x=\frac{12}{\tan27^{\circ}}\\\\13.3+x=23.6\\\\x=10.3[/tex]
Thus, we have
w = 13.3, x= 10.3
First option is correct.
Jason and Beth are married and don’t have any kids yet. They are out of debt except for their house, and they have a full emergency fund. But Beth’s car has sputtered its last breath. Fortunately, she’s found a new one for hundreds less than invoice. The payments will be less than a fourth of their combined take- home pay. This fits Dave’s formula, and the payments can be squeezed into their budget. She’ll take $2,000 out of their emergency fund for the down payment. Jason thinks it’s a really bad idea. Why?
Final answer:
Jason thinks it's a bad idea to use the emergency fund for a car down payment as it should be reserved for unforeseen financial emergencies, not planned expenses like a vehicle purchase.
Explanation:
Jason may consider it a bad idea for Beth to use the emergency fund for a down payment on a car because the emergency fund is supposed to be a safety net for unforeseen and critical financial needs, such as sudden medical expenses, job loss, or urgent home repairs.
Depleting the emergency fund for a car purchase, despite the fact that car payments are affordable, puts them at risk should multiple unplanned expenses arise simultaneously.
Financial advisers often recommend keeping 3-6 months of expenses saved for emergencies to maintain financial security. Therefore, it might be better to save up for the down payment separately or consider a less expensive car.
Final answer:
Jason may be concerned about using the emergency fund for a car downpayment since emergency funds are meant for unforeseen and urgent financial needs. Adding new debt could make them vulnerable to financial strain.
Explanation:
The concern Jason may have with Beth taking $2,000 out of their emergency fund for a down payment on a new car is that the emergency fund should be reserved for unforeseen circumstances, such as medical expenses, unexpected home repairs, or job loss. Using it for a car down payment, even if it seems manageable within their budget, could leave them vulnerable if a real emergency arises. Additionally, even though the car payments fit within Dave Ramsey's guidelines of being less than a quarter of their take-home pay, it introduces new debt—which they have worked hard to eliminate, except for their mortgage—and could potentially add financial strain if their income situation changes.
Malia is placing a barrier around the edge of a circular path with a diameter of 13 meters. The barriers are in lengths of 2.5 meters. What is the best approximation of how many pieces of barrier Malia will need? Use 3.14 to approximate for ? .
Answer:
64
Step-by-step explanation: