Answer:
see below
Step-by-step explanation:
If you haven't memorized it so you know it already, it takes about 10 seconds with your calculator to discover that ...
arccos((√3)/2) = β = 30°
This fact matches only one answer choice.
Which of the following situations cannot be modeled with the equation 5x – 15y = 335? A. Randy earns $5 for each hour he works at his job, and spends $15 each time he goes out to dinner. He has $335 at the end of the week. B. A hamburger sells for $5 but costs $0.15 to make, giving a net income of $3.35. C. Ruby is paid for the 5 sales she made but docked for the 15 sales she missed for a net income of $335. D. Tommy earned points for 5 correct answers on a standardized test, but was docked for 15 incorrect answers for a point total of 335.
Answer:
B. A hamburger sells for $5 but costs $0.15 to make, giving a net income of $3.35.
Step-by-step explanation:
It's the right answer, for many wrong reasons:
- The units aren't the same... since the 5 is expressed in dollars and the the costs would be expressed in cents.
- There could only have one production cost per burger... so it's not a second variable.
- Of course, the calculation in the statement is also wrong ($5.00 - $0.15 doesn't equal $3.35)
So, for all these three reasons, that statement cannot be expressed in the given equation.
true or false: b) If a line contains a center of a circle, it is a secant of the circle. (c If 2 chords intersect a circle, they intercept equal arcs. d) If a line is perpendicular to a diameter at one of its endpoints, then it is tangent to the circle. e) Inscribed angle that intercept equal arcs are equal.
Answer:
b) true
c) false
d) true
e) true
Step-by-step explanation:
b) Any line that contains an interior point of a circle is a secant of the circle. The center is an interior point, so a line that contains the circle center is a secant.
__
c) Chords of different lengths intercept arcs of different measures
__
d) Any line perpendicular to a radius at the point where the radius meets the circle is a tangent to the circle. The endpoint of a diameter is the endpoint of a radius, so a line perpendicular there will be a tangent.
__
e) The measure of an inscribed angle is half the measure of the intercepted arc, so all inscribed angles that intercept equal arcs are equal.
The statement 'If a line contains the center of a circle, it is a secant of the circle.' is true. The statement 'If 2 chords intersect a circle, they intercept equal arcs.' is false. Statements 'If a line is perpendicular to a diameter at one of its endpoints, then it is tangent to the circle.' and 'Inscribed angle that intercept equal arcs are equal.' are both true.
Explanation:b) True. If a line contains the center of a circle, it does pass through the circle at two points, therefore it's a secant of the circle.
c) False. Two chords intersecting inside a circle do not always intercept equal arcs. The length of the arcs they intercept depends on their distance from the center of the circle, not on the mere fact that they intersect.
d) True. If a line is perpendicular to a diameter at one of its endpoints, it does indeed result in a tangent to the circle. This is because the line touches the circle at exactly one point (the endpoint), fulfilling the definition of a tangent line.
e) True. Inscribed angles that intercept (cut off) equal arcs are indeed equal. This is a basic theorem in circle geometry.
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Your new dresser will be 2/5ths larger than your old dresser. Your old dresser can hold 6.25 cubic feet, how much cubic feet will the new dresser hold ?
Answer:
8.75 cubic feet
Step-by-step explanation:
Your new dresser will be [tex]\frac{2}{5}^{ths}[/tex] larger than your old dresser.
This means that your new dresser wil be
[tex]1+\dfrac{2}{5}=\dfrac{5+2}{5}=\dfrac{7}{5}[/tex]
of your old dresser.
Your old dresser can hold 6.25 cubic feet, so your new dresser can hold
[tex]\dfrac{7}{5}\cdot 6.25=7\cdot 1.25=8.75\ ft^3[/tex]
Final answer:
To find the volume of the new dresser, find 2/5ths of the old dresser's volume (6.25 cubic feet) and add it to the original volume, resulting in a new dresser's volume of 8.75 cubic feet.
Explanation:
To calculate the volume of the new dresser, which will be 2/5ths larger than the old dresser, we will first determine what 2/5ths of the old dresser's volume is, and then add that to the original volume. The old dresser has a volume of 6.25 cubic feet.
Calculate 2/5ths of 6.25 cubic feet: (2/5) × 6.25 = 2.5 cubic feet
Add the additional volume to the original volume to get the new dresser's volume: 6.25 + 2.5 = 8.75 cubic feet
So, the new dresser will hold 8.75 cubic feet of items.
A bowl in the shape of a hemisphere has a volume of 18π cubic inches. What is the radius of the bowl
For this case we have by definition, that a hemisphere represents half of a sphere.
Its volume is given by:
[tex]V = \frac {2} {3} \pi * r ^ 3[/tex]
Where "r" represents the radius.
Substituting the data and clearing the radio we have:
[tex]\frac {2} {3} \pi * r ^ 3 = 18 \pi\\\frac {2} {3} * r ^ 3 = 18\\r ^ 3 = 18 * \frac {3} {2}\\r ^ 3 = 27\\r = \sqrt [3] {27}\\r = 3[/tex]
Thus, the radius of the hemisphere is 3 inches.
Answer:
[tex]3 \ in[/tex]
Answer: these nats
Step-by-step explanation:verry carefully
(9^3)^3 = ____
A) 9^0
B) 9^6
C) 9^9
D) 81
The answer is:
The correct option is:
C) [tex](9^{3})^{3}=9^{9}[/tex]
Why?To solve the problem, we need to remember the power of a power property, it's defined by the following way:
[tex](a^{m})^{n}=a^{m*n}[/tex]
When we have a power of a power, we need to keep the base and then, the new exponent will be the product between the two original exponents.
So, we are given the expression:
[tex](9^{3})^{3}[/tex]
Then, calculating we have:
[tex](9^{3})^{3}=9^{3*3}=9^{9}[/tex]
Hence, we have that the correct option is:
C) [tex](9^{3})^{3}=9^{9}[/tex]
Have a nice day!
Answer:
The correct answer is option C) 9^9
Step-by-step explanation:
Points to remember
Identities
(xᵃ)ᵇ = xᵃᵇ
xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾
xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾
It is given that (9^3)^3
To find the correct option
(9^3)^3 can be written as, (9³)³
By using above identities,
(9³)³ = 9³ ˣ³
= 9⁹
Therefore the correct answer is option C). 9^9
how do you find the area of a compound figure
Answer: It's easy and simple!
Step-by-step explanation: Split it into rectangles and multiply the height and length. Than add it together and Then you have your answer.
Answer:
It depends on the figure.
Step-by-step explanation:
The compound figures we're generally concerned with are combinations of rectangles, triangles, circles or parts of circles, with or without cutouts of those shapes. The area is the sum of the areas of the component shapes, less the areas of any cutouts.
__
Consider the attached examples:
7) This is half a circle together with two triangles. Or, the two triangles can be considered to be a rectangle with a triangular cutout.
The area is the sum of the areas of the semicircle and the rectangle, less the area of the triangular cutout.
__
8) This can be considered as a square with a square cutout. The area is the difference between the area of the larger square and the area of the smaller one. Alternatively, one can find the area by finding the length of the centerline of the shaded area and multiplying that by the width of the shaded area.
__
9) The area of this figure can be considered to be the total of the area of the bottom rectangle and the top triangle. Alternatively, one can cut the figure into two trapezoids (with a vertical line) and sum their areas.
Use the addition-subtraction method to solve each of the following systems of equations.
1. 4x + 3y = 17 and 5x – 3y = 1
2. –5m + 6n = –8 and –5m + 8n = 6
3. 2x – 7y = –9 and 6x + 7y = 57
4. 5p – 4q = 3 and –5p – 4q = 13
5. 6c + d = 12 and c – d = 2
The best answer will receive Brainliest .
Answer:
1. x=2, y=3
2. n=7, m=-6.8
3. x=6, y=3
4. q=-2, p=-1
5. c=2, d=0
Step-by-step explanation:
4x + 3y = 17
5x – 3y = 1
first make it so either x or y can cancel out in both equations, then combine the equations, giving you 9x=18. solve for x, x=2. substitute 2 for x in either equation, 4(2) + 3y = 17. solve for y, 8+3y=17, 3y=9, y=3
–5m + 6n = –8
–5m + 8n = 6
first make it so either m or n can cancel out in both equations, multiply –5m + 6n = –8 by -1, 5m - 6n = 8, then combine the equations, giving you 2n=14. solve for n, n=7. substitute 7 for n in either equation, 5m - 6(7) = 8. solve for m, 5m - 42 = 8, 5m = -34, m = -6.8
2x – 7y = –9
6x + 7y = 57
first make it so either x or y can cancel out in both equations, then combine the equations, giving you 8x=48. solve for x, x=6. substitute 6 for x in either equation, 2(6) – 7y = –9. solve for y, 12 – 7y = –9, –7y = –21, y = 3
5p – 4q = 3
–5p – 4q = 13
first make it so either p or q can cancel out in both equations, then combine the equations, giving you -8q=16. solve for q, q=-2. substitute -2 for q in either equation, 5p – 4(-2) = 3. solve for p, 5p + 8 = 3, 5p = -5, p = -1
6c + d = 12
c – d = 2
first make it so either c or d can cancel out in both equations, then combine the equations, giving you 7c=14. solve for c, c=2. substitute 2 for c in either equation, 6(2) + d = 12. solve for d, 12 + d = 12, d = 0
[EDIT] question 2 is impossible.
Please help me with this math problem on i-ready
Answer:
its the second one
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
the answer is B, is this a lesson or a quiz?
Please answer this multiple choice question CORRECTLY for 30 points and brainliest!!
Answer:
C. 6 kg
Step-by-step explanation:
Let m represent the mass of plates on one side of the barbell. Then the total weight of the barbell is ...
2m +24 = 60 . . . . . kilograms
m +12 = 30 . . . . . . . divide by 2
m = 18 . . . . . . . . . . . subtract 12
The mass of plates on one side of the barbell must total 18 kg. If they all have the same mass, then that must be a divisor of 18. In whole numbers, that would include plates of mass 1, 2, 3, 6, 9, 18 kg.
The only one of these on your list of answer choices is ...
6 kg
A vintage guitar is being auctioned. The graph below traces the prices quoted by bidders at different time intervals, measured in minutes, since the auction began.
Which statement is true about the graph?
A. The average rate of change is greater for interval D than for interval E because the line is increasing more quickly at interval D than at interval E.
B. The average rate of change is greater for interval C than for interval B because the line is increasing more slowly at interval C than at interval B.
C. The average rate of change is greater for interval A than for interval B because the line is increasing more slowly at interval A than at interval B.
D. The average rate of change is greater for interval D than for interval C because the line is increasing more quickly at interval D than at interval C.
Answer:
d. :)
Step-by-step explanation:
Answer:
D. The average rate of change is greater for interval D than for interval C because the line is increasing more quickly at interval D than at interval C.
Step-by-step explanation:
The difference between C and D interval is the lowest.
This means that line is increasing more quickly at interval D as compared to others.
Therefore, option D is the right answer.
Triangle DEF is congruent to D'EF' by the SSS theorem. Which single rigid transformation is required to map DEF onto D'EF'? dilation reflection rotation translation
Answer: rotation
Step-by-step explanation:
Rotation is required to map DEF onto D'EF'
What is Rotation?Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.
Rotation exists as the operation or act of turning or circling something.
Rotation exists in the circular movement of an object around an axis of rotation. A three-dimensional object may include an infinite numeral of rotation axes.
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Nadir saves $1 the first day of a month, $2 the second day, $4 the third day, and so on. He continues to double his savings each day. Find the amount that he will save on the fifteenth day.
$16,384
$29
$32,768
$8192
ANSWER
$16,384
EXPLANATION
From the question we have that,
Nadir saves $1 the first day of a month, $2 the second day, $4 the third day, and so on.
This forms a geometric sequence,
[tex]1,2,4,...[/tex]
The first term of this sequence is
[tex]a = 1[/tex]
The common ratio is
[tex]r = \frac{2}{1} = \frac{4}{2} = 2[/tex]
The general term of a geometric sequence is given by the formula:
[tex]f(n) = a {r}^{n - 1} [/tex]
To find the 15th term, we plug in a=1, r=2 and n=15.
[tex]f(15) = 1 {(2)}^{15 - 1} [/tex]
[tex]f(15) = {2}^{14} [/tex]
[tex]f(15) = 16384[/tex]
The amount he will save on the 15th day is $16,384
Solve the given initial-value problem. the de is of the form dy dx = f(ax + by + c), which is given in (5) of section 2.5. dy dx = cos(x + y), y(0) = π 2
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\cos(x+y)[/tex]
Let [tex]v=x+y[/tex], so that [tex]\dfrac{\mathrm dv}{\mathrm dx}-1=\dfrac{\mathrm dy}{\mathrm dx}[/tex]:
[tex]\dfrac{\mathrm dv}{\mathrm dx}=\cos v+1[/tex]
Now the ODE is separable, and we have
[tex]\dfrac{\mathrm dv}{1+\cos v}=\mathrm dx[/tex]
Integrating both sides gives
[tex]\displaystyle\int\frac{\mathrm dv}{1+\cos v}=\int\mathrm dx[/tex]
For the integral on the left, rewrite the integrand as
[tex]\dfrac1{1+\cos v}\cdot\dfrac{1-\cos v}{1-\cos v}=\dfrac{1-\cos v}{1-\cos^2v}=\csc^2v-\csc v\cot v[/tex]
Then
[tex]\displaystyle\int\frac{\mathrm dv}{1+\cos v}=-\cot v+\csc v+C[/tex]
and so
[tex]\csc v-\cot v=x+C[/tex]
[tex]\csc(x+y)-\cot(x+y)=x+C[/tex]
Given that [tex]y(0)=\dfrac\pi2[/tex], we find
[tex]\csc\left(0+\dfrac\pi2\right)-\cot\left(0+\dfrac\pi2\right)=0+C\implies C=1[/tex]
so that the particular solution to this IVP is
[tex]\csc(x+y)-\cot(x+y)=x+1[/tex]
For the inverse variation equation xy = k, what is the value of x when y = 4 and k = 7?
4/7
7/4
3
28
7,4 is the answer to the question
Answer:
[tex]x=7/4[/tex]
Step-by-step explanation:
the equation is:
[tex]xy=k[/tex]
To find the value of [tex]x[/tex], we need to substitute the values that we know for [tex]y[/tex] and [tex]k[/tex]:
[tex]y=4[/tex]
and
[tex]k=7[/tex]
so, we substitute this values into the equation
[tex]xy=k[/tex]
[tex]x(4)=7[/tex]
and we clear for [tex]x[/tex], for this we move the 4 to the right dividing:
[tex]x=7/4[/tex]
plz helpp FASTT
Find the area of triangle ABC with vertices A(2, 3), B(1, -3), and C(-3, 1).
a.
10 units2
c.
14 units2
b.
12 units2
d.
16 units2
The area of the triangle will be 14 square units. Then the correct option is C.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The triangle ABC with vertices A(2, 3), B(1, -3), and C(-3, 1).
Then the area of the triangle is given as,
A = 1/2 | {[2 x (-3) + 1 x 1 + (-3) x 3] - [3 x 1 + (-3) x (-3) + 2 x 1]} |
A = 1/2 | {[-6 + 1 - 9] - [3 + 9 + 2]} |
A = 1/2 | {-14 - 14} |
A = 1/2 x 28
A = 14 square units
The area of the triangle will be 14 square units. Then the correct option is C.
More about the triangle link is given below.
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christian is going to paint the wall underneath his staircase . how many square feet will he need to paint
To express the given information in a linear equation, the setup time and hourly rate per square foot should be considered in the equation y = 4 + (1/1000)x.
Explanation:To express the information in a linear equation:
Setup time is 4 hours, so it's a constant term.For the painting job, 1 hour per 1,000 square feet is required, so the coefficient of square feet is 1/1000.Therefore, the linear equation would be: y = 4 + (1/1000)x, where y is the total time in hours and x is the total square footage.Choose the TWO factored binominals for the expression: x2+6x – 27 Question 6 options: A) (x - 3) B) (x - 9) C) (x + 6) D) (x + 9) E) (x + 3)
Answer:
A) x-3 and D) x+9
Step-by-step explanation:
x^2 + 6x - 27
You need to find two numbers that multiply to -27 and add up to 6
Those two numbers are -3 and 9, because 9 * -3 = -27 and 9+ -3 = 6
So you add those to x and those are your two factored binomials
(x-3) and (x+9)
Please help me with this
Answer:
7, 5
Step-by-step explanation:
_________________________________________________
Answer:
7 and 5
Step-by-step explanation:
So we can start with 1 and 4. We can see they added 3 to 1. Ok, that's the first part.
Then, they took 4 and subtracted 2. We can see they subtracted 2. Ok, that's the second part.
We can see they keep doing this:
Add 3, subtract 2. Add 3, subtract 2. and so on, until we get to 4. They just subtracted 2, so we can add 3. So, our first unknown number would be 7. We can then subtract 2, making the second unknown number 5.
Hope I helped, soz if I'm wrong ouo.
~Potato.
Copyright Potato 2019.
Find the value of x to the nearest tenth
Check the picture below.
make sure your calculator is in Degree mode.
Answer:
The opposite side x is 7
Step-by-step explanation:
Step one
From the given expression in the picture
We can estimate x by applying the
SOH CAH TOA rule on the triangle
Since we have one side and one angle given
step two
From the given picture we have
We have θ and adjacent side given
Hence we need to apply
tan θ= opposite/adjacent =
Tan 35°=x/10
Step three
From 4 figure table or calculator
tan 35° is 0.7
0.7=x/10
x=0.7*10
x= 7
The center pole used to hold up a circus tent is supported by a guy wire 53 feet long. The guy wire is anchored to the ground 45 feet from the base of the pole. What is the height, h, of the center pole? Round your answer to the nearest foot if necessary.
A. h = 31 feet
B. h = 70 feet
C. h = 784 feet
D. h = 28 feet
Answer:
D. 28 feet
Step-by-step explanation:
a²+b²=c²
45²+b²=53²
2025+b²=2809
b²=784
[tex]\sqrt{784}[/tex]=[tex]\sqrt{b}[/tex]
b=28
Answer:
D. 28 feet
Step-by-step explanation:
The first figure of the Sierpinski triangle has one shaded triangle. The second figure of the Sierpinski triangle has three shaded triangles. The third figure of the Sierpinski triangle has nine shaded triangles. Which summation represents the total number of shaded triangles in the first 15 figures?
Answer:
[tex]\texttt{The summation form} = \sum\limits_{n=1}^{15} 3^{(n-1)}=7,174,453[/tex]
Step-by-step explanation:
We can find the total number of shaded triangles in the first 15 figures by first finding the pattern between the first, second, and the third triangles.
1st triangle (T₁) has 1 shaded triangle2nd triangle (T₂) has 3 shaded triangles3rd triangle (T₃) has 9 shaded trianglesWe can see that the number of shaded triangles of T₂ is 3 times more compared to T₁. Also, the number of shaded triangles of T₃ is 3 times more compared to T₂. Then we can conclude that the numbers of shaded triangles form a geometric sequence with:
1st term (U₁) = 1 (the number of T₁'s shaded triangle)ratio (r) = 3 (the number is 3 times more than the previous number)For the summation form, we can find each term using the geometric sequence formula:
[tex]\boxed{U_n=U_1\cdot r^{(n-1)}}[/tex]
[tex]U_n=1\cdot 3^{(n-1)}[/tex]
[tex]U_n=3^{(n-1)}[/tex]
Then, the summation form for the 1st 15 term =
[tex]\displaystyle\sum\limits_{n=1}^{15} 3^{(n-1)}[/tex]
We can also find the summation by using the geometric series formula:
[tex]\boxed{S_n=\frac{U_1(r^n-1)}{r-1} ,\ \texttt{for r > 1}}[/tex]
Then, for S₁₅:
[tex]\begin{aligned}S_{15}&=\frac{U_1(r^{15}-1)}{r-1}\\\\&=\frac{1(3^{15}-1)}{3-1} \\\\&=\bf 7,174,453\end{aligned}[/tex]
Please help me with this
Answer:
see explanation
Step-by-step explanation:
Corresponding angles are associated with parallel lines
L and M would have to be parallel but not so cannot name a corresponding angle.
If they were parallel then ∠7 would correspond to ∠3
19. Simplify 3√ 2 – √ 2 .
A. 4√ 2
B. 2√ 2
C. √ 2
D. 3√ 2
Answer: OPTION B
Step-by-step explanation:
You need to remember that, to subtract radicals, the indices and the radicands must be the same.
Given the expression [tex]3\sqrt{2}-\sqrt{2}[/tex], you can identify that both have index 2 and the radicands are 2 (The numbers that are inside of radicals), therefore, you can conclude that the subtraction can be made.
Then, you must subtract the terms in front of the radicals. Therefore, you get:
[tex]3\sqrt{2}-\sqrt{2}=2\sqrt{2}[/tex]
You can observe that this matches with the option B.
Answer:
The correct answer is option B. 2√ 2
Step-by-step explanation:
It is given that, 3√ 2 – √ 2
To find the correct option
3√ 2 – √ 2 can be written as,
3√ 2 – √ 2 = √ 2 (3 - 1) taking √ 2 as common
= √ 2 * 2
= 2√ 2
Therefore the correct answer is 2√ 2 .
The correct option is option b. 2√ 2
Please please help me
Answer:
(a + b, c )
Step-by-step explanation:
Using the midpoint formula
given 2 points (x₁, y₁ ) and (x₂, y₂ ) then midpoint is
[ [tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] ]
let (x₁, y₁ ) = P(0, 0) and (x₂, y₂ ) = R(2a+2b, 2c), then
midpoint = [ [tex]\frac{0+2a+2b}{2}[/tex], [tex]\frac{2c}{2}[/tex] ]
= [tex]\frac{2(a+b)}{2}[/tex], c ] = (a + b, c )
The value of an explanatory variable is 18, while the corresponding value of the response variable is 8. What would be the coordinates of this data point when plotted on a scatterplot?
A. (26, 8)
B. (8, 26)
C. (8, 18)
D. (18, 8)
D.(18.8) is the answer because the explanatory variable is the x-axis while the response variable is the y-axis.
Answer: The correct option is (D) (18, 8).
Step-by-step explanation: Given that the value of an explanatory variable is 18, while the corresponding value of the response variable is 8.
We are to find the co-ordinates of this data plot when plotted on a scatter plot.
Let y = f(x) be a function, where x is the independent variable and y is the dependent variable.
On a scatter plot, we plot any point satisfying this function as (x, y).
Explanatory variable = independent variable, x = 18
and
Response variable = dependent variable, y= 8
Therefore, the required coordinates of this data point when plotted on a scatter plot are (18, 8)
Option (D) is CORRECT.
question 65 true or false
Answer:
True
Step-by-step explanation:
we know that
sin(90°)=1
sin(270°)=-1
sin(-90°)=-sin(90°)=-1
sin(-90°)=sin(270°)
therefore
For sin(x)=-1
the values of x are x=-90° and x=270° ------> is true
Which of the following polynomials is the expansion of (x - y)4? x4 - x3y + x2y2 - 2xy3 + y4 x4 -2x3y3 + y4 x4 - 2x3y + x 2y 2 - xy3 - y4 x4 - xy + y4
Answer:
[tex](x-y)^4=x^4-x^3y+6x^2y^2-4xy^3+y^4[/tex].
Step-by-step explanation:
We want to find the polynomial that will result from expanding:
[tex](x-y)^4[/tex].
Recall that we can use the Pascal's triangle to obtain the coefficient as:
1 4 6 4 1
Also note how the negative sign is going to alternate.
The power of x will decrease from left to right while the power of y increases from left to right
The expansion then becomes:
[tex](x-y)^4=x^4-x^3y+6x^2y^2-4xy^3+y^4[/tex].
Answer:
The Answer is A!!!!
Step-by-step explanation:
Many areas of Northern California depend on the snowpack of the Sierra Nevada Mountains for their water supply. If 300 cubic centimeters of snow will melt to 33 cubic centimeters of water, how much water does 600 cubic centimeters of snow produce?
16.5 cubic centimeters
66 cubic centimeters
72.6 cubic centimeters
5454 cubic centimeters
Answer:
Option B is correct.
Step-by-step explanation:
300 cm^3 of snow melts into 33 cm^3 water. We need to find how much water is produced if 600 cm^3 of snow is melt.
Solving using unitary method:
300 cm^3 of snow melts into water = 33 cm^3
1 cm^3 of snow melts into water = 33/300
600 cm^3 of snow melts into water = 33/300 *600
= 66 cm^3
So, Option B is correct.
Help! If you know this can you tell me how to do it?
Answer:
c
Step-by-step explanation:
Here's how this works:
Get everything together into one fraction by finding the LCD and doing the math. The LCD is sin(x) cos(x). Multiplying that in to each term looks like this:
[tex][sin(x)cos(x)]\frac{sin(x)}{cos(x)}+[sin(x)cos(x)]\frac{cos(x)}{sin(x)} =?[/tex]
In the first term, the cos(x)'s cancel out, and in the second term the sin(x)'s cancel out, leaving:
[tex]\frac{sin^2(x)}{sin(x)cos(x)}+\frac{cos^2(x)}{sin(x)cos(x)}=?[/tex]
Put everything over the common denominator now:
[tex]\frac{sin^2(x)+cos^2(x)}{sin(x)cos(x)}=?[/tex]
Since [tex]sin^2(x)+cos^2(x)=1[/tex], we will make that substitution:
[tex]\frac{1}{sin(x)cos(x)}[/tex]
We could separate that fraction into 2:
[tex]\frac{1}{sin(x)}[/tex]×[tex]\frac{1}{cos(x)}[/tex]
[tex]\frac{1}{sin(x)}=csc(x)[/tex] and [tex]\frac{1}{cos(x)}=sec(x)[/tex]
Therefore, the simplification is
sec(x)csc(x)
Please help me out with this
Answer:
10.4 cm
Step-by-step explanation:
The volume (V) of a pyramid is calculated using
V = [tex]\frac{1}{3}[/tex] area of base × height (h)
area of square base = 6² = 36, thus
[tex]\frac{1}{3}[/tex] × 36h = 120
12h = 120 ( divide both sides by 12 )
h = 10 cm
To find the slant height (s) consider the right triangle from the vertex to the midpoint of the base and from the midpoint of base to the side.
That is a right triangle with hypotenuse s and legs 10(h) and 3 (midpoint of the base )
Using Pythagoras' identity then
s² = 10² + 3² = 100 + 9 = 109
Take the square root of both sides
s = [tex]\sqrt{109}[/tex] ≈ 10.4 cm