The two boundary curves y = √(6x + 4) and y = 2x meet at
√(6x + 4) = 2x
6x + 4 = 4x²
2x² - 3x - 2 = 0
(x - 2) (2x + 1) = 0
⇒ x = -1/2 and x = 2
R is bounded to the left by the y-axis (x = 0), so R is the set
R = {(x, y) : 0 ≤ x ≤ 2 and 2x ≤ y ≤ √(6x + 4)}
Using the shell method, the volume is made up of cylindrical shells of radius x and height √(6x + 4) - 2x. So each shell of thickness ∆x contributes a volume of
2π (radius) (height) ∆x = 2π x (√(6x + 4) - 2x) ∆x
and as we let ∆x approach zero, the total volume of the solid is given by the definite integral
[tex]\displaystyle \boxed{2\pi \int_0^2 x \left(\sqrt{6x + 4} - 2x\right) \, dx}[/tex]
A store sells almonds for $7 per pound, cashews for $10 per pound, and walnuts for $12 per pound. A customer buys 12 pounds of mixed nuts consisting of almonds, cashews, and walnuts for $118. The customer buys 2 more pounds of walnuts than cashews. The matrix below represents this situation.
If the reduced row echelon form of this matrix represents the amount of each type of nut the customer buys, which statement is a possible interpretation of the results?
One possible interpretation of the results is that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 2 pounds of walnuts to achieve a total cost of $118.
To determine the amount of each type of nut the customer buys, we can set up a system of equations based on the given information.
Let's use the variables:
A = pounds of almonds
C = pounds of cashews
W = pounds of walnuts
From the given information, we can create the following equations:
A + C + W = 12 (since the customer buys a total of 12 pounds of mixed nuts)
7A + 10C + 12W = 118 (since the total cost of the nuts is $118)
W = C + 2 (since the customer buys 2 more pounds of walnuts than cashews)
We can now represent this system of equations as a matrix:
[1 1 1 12]
[7 10 12 118]
[0 -1 1 2]
To find the reduced row echelon form of this matrix, we can use Gaussian elimination or a similar method. Solving the system of equations represented by the matrix, we obtain the following reduced row echelon form:
[1 0 2 6]
[0 1 -3 4]
[0 0 0 0]
Now, let's interpret the results:
From the reduced row echelon form, we can deduce that there are infinitely many solutions to this system of equations. This means that there are multiple possible combinations of almond, cashew, and walnut quantities that satisfy the given conditions.
One possible interpretation of the results could be that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 0 pounds of walnuts. This satisfies the equation A + C + W = 12, and the total cost of nuts is $7 * 6 + $10 * 4 + $12 * 0 = $42 + $40 + $0 = $82. However, since the given total cost is $118, this interpretation is not valid.
Another possible interpretation could be that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 2 pounds of walnuts. This satisfies all the given conditions. The equation A + C + W = 12 holds true, and the total cost is $7 * 6 + $10 * 4 + $12 * 2 = $42 + $40 + $24 = $106, which matches the given total cost of $118.
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justify whether the solution makes sense.
a. Are the two triangles similar?
b. How do you know? Justify.
Answer:
They are identical triangles.
Step-by-step explanation:
Angles in a triangle add up to 180 degrees.
The triangle with 39 and 90 has a missing angle of 51 degrees, and the triangle with 51 and 90 vice versa.
✎ let's answer it
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
it's ↓
( identical triangle)
by #galadohannadivine29What is the theoretical probability of drawing a blue marble from a bag containing 6 Green marbles, 9 yellow marbles and 5 blue marbles?
Answer:
1/20
Step-by-step explanation:
number of favourable outcomes/number of outcomes
Can you help me solve this equation I been trying to search a video explaining this but nothing and I gaved up studying for six days and now I am trying to get back to track anyways ... The equation is a linear equation : f(x)=-x-11 with the following
1.4f(-2)+5f(1)
2.-5f(12)-2f(-9)
3. 3f(5)x f(2)
4.f(9)/f(-6)
Answer:
4 I promise
jhjhhhhjjj bug check txt TC gym c rectify txt
What are the missing sides in the triangle written as integers or as decimals rounded to the
nearest tenth? The figure is not drawn to scale.
x= 18; y = 15.6
x= 12.7; y = 15.6
x= 12.7;y=9
x=9; y = 12.7
The value of x is 12.7 and the value of y is 9. The correct option is the third option x = 12.7; y = 9
TrigonometryFrom the question, we are to determine the values of the missing sides
From the diagram,
Opposite = 9
Adjacent = y
Hypotenuse = x
Included angle = 45°
Using SOH CAH TOA, we can write that
[tex]tan 45^\circ= \frac{9}{y}[/tex]
[tex]1 = \frac{9}{y}[/tex]
∴ y = 9
Since the triangle is a right triangle, we can write that
x² = y² + 9² (Pythagorean theorem)
x² = 9² + 9²
x² = 81 + 81
x² = 162
x = √162
x = 12.7
Hence, the value of x is 12.7 and the value of y is 9. The correct option is the third option x = 12.7; y = 9
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Evaluate l-x-2yl for x = -2 and y = 3.
Step-by-step explanation:
|...| means absolute value of "...". that means always the "+" value of "...", even if it is negative.
in other words
|-x| = x
|x| = x
|-x - 2y| for x = -2 and y = 3
|- -2 - 2×3| = |2 - 6| = |-4| = 4
evaluate f(x) = 3/6x+6 when x = -1
a) undefined
b) 0
c) 3
d) 3/36
Answer:
a) Undefined.
Step-by-step explanation:
[tex]f(x) = \dfrac 3{6x+6} = \dfrac{3}{6(x+1)} = \dfrac{1}{2(x+1)}\\\\\\f(-1) =\dfrac{1}{2(-1+1)}= \dfrac{1}{0}[/tex]
what is the awnser to this The Hernandez family orders 3 large pizzas. They cut the pizzas so that each pizza has the same number of slices, giving them a total of 24 slices.
The Wilson family also orders several large pizzas from the same pizza restaurant. They also cut the pizzas so that all their pizzas have the same number of slices. For the Wilson family, the equation y = 10x represents the relationship, where x represents the number of pizzas and y represents the number of total slices.
Which statements best describe the pizzas bought by the Hernandez and Wilson families? Select two options.
For the Hernandez family, the equation y = 3x represents the relationship between the number of slices and number of pizzas, where x represents the number of pizzas and y represents the number of total slices.
For each family, a graph of the relationship between number of pizzas, x, and number of slices, y, goes through the point (0, 0) and is a straight line.
The Hernandez family’s slices are smaller than the Wilson family’s slices.
If the Wilson family ordered 3 large pizzas from the same restaurant as the Hernandez family, they would have more slices than the Hernandez family after each family cut their pizzas into slices.
The constant of proportionality is 10 for the Wilson family, but cannot be determined for the Hernandez family.
The two true statements are the second statement (both lines contain the point (0,0)) and the fourth statement (If the Wilson family buys 3 pizzas, they will get more slices than the Hernandez family).
Which is the correct statement?
First, we know that the Hernandez family orders 3 large pizzas, such that they cut each pizza in the same number of slices, getting a total of 24 slices.
Then the number of slices that they get for each pizza is:
24/3 = 8
So from each large pizza, they get 8 slices.
So the relation between the number of pizzas bought (x) and the number of slices (y) is:
y = 8*x
In the other hand for the Wilson family we have the relation:
y = 10*x
Where y and x are the same ones as the defined above.
Then the true statements are:
"If the Wilson family ordered 3 large pizzas from the same restaurant as the Hernandez family, they would have more slices than the Hernandez family after each family cut their pizzas into slices."
This is true because Wilson family cuts each pizza in 10 slices, while the Hernandez family cuts each pizza in 8 slices.
"For each family, a graph of the relationship between number of pizzas, x, and number of slices, y, goes through the point (0, 0) and is a straight line."
The point (0, 0) means that if they buy 0 pizzas, they get 0 slices, which is true, so both relations contain this point.
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Product of square of x and cube of y
Since the square root of
x=√x
and the cube root of
x=3√x
and their product
=√x × 3√x
= x1/2 × x1/3 [Since, n√a =a 1/n]
=x1/2+1/3 [Since, a^m ×a^n =a^m+n]
=x^3+2 /6
= x 5/6
Therefore, required product is
=√6x5
Answer:
[tex]x^2y^3[/tex]
Step-by-step explanation:
[tex]\text{Square of}~ x =x^2\\\\\text{Cube of}~ y = y^3\\\\\text{Product} = x^2y^3[/tex]
2. What is the volume of this prism?
5
5
1.7
2
2
17 cubic units
28 cubic units
1.7
5
2
1.7
The volume of the rectangular prism is 17 cubic units
How to determine the volume?The given parameters are:
Length = 5 unitsWidth = 2 unitsHeight = 1.7 unitsThe volume is calculated as:
Volume = Length * Width * Height
Substitute known values
Volume = 5 * 2 * 1.7
Evaluate
Volume = 17
Hence, the volume of the prism is 17 cubic units
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In 9th grade Jade started a college fund with
$15,000 at a rate of 6.3% compounded bi-
annually. How much money will she have in 4
years?
Answer:
this is the answer I got hope it helps
Find the margin of error if p = 71% and n = 100. round to four decimal places.
0.2204
0.0041
0.0848
0.0908
Using the z-distribution, it is found that the margin of error for the 95% confidence interval is of 0.0889.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The estimate and the sample size are given as follows:
[tex]\pi = 0.71, n = 100[/tex]
Hence, the margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.71(0.29)}{100}}[/tex]
M = 0.0889.
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The archway of the main entrance of a university is modeled by the quadratic equation y = -x2 6x. the university is hanging a banner at the main entrance at an angle defined by the equation 4y = 21 − x. at what points should the banner be attached to the archway?
The banner attached to the archway will be at (1, 5) and (5.25, 3.938).
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The archway of the main entrance of a university is modeled by the quadratic equation
y = -x² + 6x ....1
The university is hanging a banner at the main entrance at an angle defined by the equation
4y = 21 − x ....2
Then the banner attached to the archway will be
From equations 1 and 2, we have
4(-x² + 6x) = 21 - x
-4x² + 24x = 21 - x
4x² - 25x + 21 = 0
4x² - 21x - 4x + 21 = 0
x(4x - 21) - 1(4x - 21) = 0
(4x - 21)(x - 1) = 0
x = 5.25, 1
Then the value of y will be
When x = 5.25, then we have
y = -(5.25)² + 6(5.25)
y = 3.938
When x = 1, then we have
y = -(1)² + 6(1)
y = 5
The banner attached to the archway will be at (1, 5) and (5.25, 3.938).
The graph is given below.
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Montraie has a coin collection. He keeps 10 of the coins in his box, which is 20% of the collection. How many total coins are in his collection?
By definition of percentages, we conclude that Montraie has 10 coins saved in his box that come from a collection with a total of 50 coins.
How to calculate the quantity of coins in a collection
In this question we know the quantity of coins in a box and such coins are part of the coin collection. By definition of percentage we have the total quantity of coins in the collection:
x = 10*(100/20)
x = 50
By definition of percentages, we conclude that Montraie has 10 coins saved in his box that come from a collection with a total of 50 coins.
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Is 0.2775 a rational number
Answer:
yes it is
Step-by-step explanation:
It is a rational number, as it can be written as a fraction.
Solve for g.
-15 + 3g = 2g
g =?
Answer:
g = 15
Step-by-step explanation:
Rearrange unknown terms to the left side of the equation: 3g - 2g = 15
Combine like terms: g = 15
Answer: g = 15
What is the area of the parallelogram?
A parallelogram has a base of 3 feet and height of 2 and one-half feet.
7 and one-half feet squared
9 feet squared
10 and one-half feet squared
12 feet squared
Answer:
7 and one-half feet squared
Step-by-step explanation:
3 x 2.5 = 7.5
8 9/10 x 1 4/5 = ? please answer soon and thanks
Answer:
16 1/50
Step-by-step explanation:
First, turn the fractions into improper fractions.
8 9/10 can be 89/10 and 1 4/5 can be 9/5.
Then you multiply them together:
89/10 * 9/5= 801/50
Now, since 801/50 is 16.02 turn that into a mixed fraction. It becomes 16 1/50.
That's your answer.
which of the following is a statement of the triangle inequality theorem
Answer:
A
Step-by-step explanation:
Pick any two sides....their sum must be greater than the third side....
a+b > c
a+c > b
c + b > a
What is the equation of the line that passes through the point (5,3) and has a slope of -1/5 ?
Answer: y=-1/5x+4
Step-by-step explanation: use the equation y=mx+b (x,y)->(5,3) 5 is an x value and 3 is a y value so you want to plug in these values into the equation. 3=-1/5(5)+b. We already know our slope so just plug it into m. Now multiply -1/5 and 5 which is -1. 3=-1+b you want to isolate b so you can find the intercept. Add one to both sides so it cancels out. 4=b we found our y-intercept so we can write the equation now. y=-1/5x+4
If f(x) = 3x² - 4 and g(x) = x+2, find (f - g)(x).
Answer:
for the x values: -2,-1,0,1,2
y-values: 13, 6, 5, 4, -3
Step-by-step explanation:
Write each of the following products in standard form. Show the work that
leads to your final answers.
(a) (x+8)(2x-3)
(b) (x-5)²
[tex]\textbf{a)}\\\\~~~(x+8)(2x-3)\\\\=2x^2 -3x + 16x - 24\\\\=2x^2 +13x -24\\\\\textbf{b)}\\\\~~~(x-5)^2\\\\=(x-5)(x-5)\\\\=x^2 -5x -5x+25\\\\=x^2 -10x +25[/tex]
Find the function to which the given series converges within its interval of convergence. Use exact values. 1 3 x 9 x 2 2 ! 27 x 3 3 ! 81 x 4 4 ! 243 x 5 5 !
It looks like the series could be
[tex]\displaystyle 1 + 3x + \frac{9x^2}{2!} + \frac{27x^3}{3!} + \cdots = \sum_{n=0}^\infty \frac{3^nx^n}{n!} = \sum_{n=0}^\infty \frac{(3x)^n}{n!}[/tex]
Recall that
[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{x^n}{n!}[/tex]
It follows that the given series is the power series expansion for [tex]\boxed{e^{3x}}[/tex].
David's phone battery level drops 6 percentage points each hour when he is not playing a game on it. When David does play a game on his phone, the phone battery level drops 18 percentage points each hour. On a particular day, the phone battery level was at 100 percentage points at 12:00 noon and at 22 percentage points at 6:00 P.M. If David did not charge his phone during this time, how many hours did he spend playing the game between 12:00 noon and 6:00 P.M. on that day
The number of hours he spent playing the game between 12:00 noon and 6:00 P.M. on that day will be 3.5 hours.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
David's phone battery level drops 6 percentage points each hour when he is not playing a game on it.
When David does play a game on his phone, the phone battery level drops 18 percentage points each hour.
On a particular day, the phone battery level was at 100 percentage points at 12:00 noon and at 22 percentage points at 6:00 P.M.
If David did not charge his phone during this time.
Then the number of hours he spent playing the game between 12:00 noon and 6:00 P.M. on that day will be
Let x be the number of no gaming hours and y be the number of gaming hours.
Then the equation will be
6x + 18y = 100 - 22
6x + 18y = 78
x + 3y = 13 ...1
x + y = 6 ...2
By solving the equations 1 and 2, we have
x = 2.5 hours and y = 3.5 hours
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What is the surface area in square inches of a basketball that has a diameter of 9 inches
if its diameter is 9, that means its radius is half that, or 4.5.
[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4.5 \end{cases}\implies \begin{array}{llll} SA=4\pi (4.5)^2\implies SA=81\pi \\\\\\ SA\approx 254.47~in^2 \end{array}[/tex]
The surface area of the basketball with diameter of 9 in will be 254.34 in².
What is surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Given that, a basketball has a diameter of 9 inches we need to find its surface area,
Since, the basketball is in the shape of the sphere and the surface area of the sphere = 4π×radius²
Therefore, the surface area of the basketball =
= 4×3.14×(9/2)²
= 4×3.14×4.5×4.5
= 254.34 in²
Hence the surface area of the basketball with diameter of 9 in will be 254.34 in².
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To convert a distance between miles and feet, you can use the equation f=5280m. In this equation, what is the role of f
For a two-tailed test with a sample size of 20 and a. 20 level of significance, the t value is _____.
Using a t-distribution calculator, it is found that the critical value for the hypothesis test is of t = 1.3277.
How to find the critical value of the t-distribution?The critical value is found considering three inputs:
The tail.The significance level.The amount of degrees of freedom, which is one less than the sample size.Hence, for a two-tailed test, with a 0.2 significance level and 19 df, the critical value is of t = 1.3277.
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When a number is halfway between two multiples of one hundred, round to _____.
A. zero
B. the smaller multiple
C. the nearest fifty
D. the larger multiple
Answer:
D. The larger multiple
Step-by-step explanation:
n7nj7j
True or false: f(x) represents a function.
A. True
B. False
Answer:
A.) True
Step-by-step explanation:
A set of outputs and inputs becomes a function when there is only one output per input. In this case, each "x" value only has one "y" value, making it a function.
The segment AC is?
A- the adjacent
B- the hypotenuse
C- The opposite
D- The tangent
Answer:
B
Step-by-step explanation:
the hypotenuse........
Answer:
B
Step-by-step explanation:
The hypotenus is always opposite to the right and angle and always the longest side