Joe is 68.4” tall. Set the ratio of 5/6=57/x, solve using the butterfly method (multiply 57 and 6, set equal to 5x) 57•6 is 342, so at this point it would be 342=5x. 342/5 is 68.4
what is the perimeter of a hexagon with an apothem of 10
Assuming that said hexagon is regular then triangles formed (split in half by the apothem) are 30-60-90 triangles. The side that you'd get would be 10√3/3. Multiplied by two, you'd get 20√3/3. The perimeter would be 120√3/3, which would be 40√3 as the answer.
The perimeter of the hexagon is 40√3 if the apothem is 10 after applying tan ratio.
What is hexagon?A hexagon is a six-sided polygon with six inner angles totalling 720° and six outside angles totalling 360° in geometry. Regular, irregular, concave, convex, and complicated hexagons are two-dimensional shapes.
From the figure, we can calculate the side length of the hexagon:
We know each interior angle of the hexagons = 120 degree
Half of the angle = 120/2 = 60 degree
From the tan ratio:
tan30 = (s/2)/10
1/√3 = s/20
s = 20/√3
Perimeter = 6×(20/√3) = 120/√3 = 40√3
Thus, the perimeter of the hexagon is 40√3 if the apothem is 10 after applying tan ratio.
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Consider the function f(x) = 3x. Which statement MUST be true?
A)
f(3)
f(1)
=
f(6)
f(4)
B) f(3)·f(1) = f(6)·f(4)
C) f(3) − f(1) = f(6) − f(4)
D) f(3) − f(1) = f(−3) − f(−1)
After substituting values of x into the function f(x) = 3x, statement 'f(3) − f(1) = f(6) − f(4)' is found to be correct.
Explanation:In order to determine which statement is accurate, we need to substitute the values of x into the function f(x) = 3x and perform the correct operations.
Let's examine the options:
A) This does not include any operation, so this is not a valid statement.
B) f(3)·f(1) = 9*3 = 27; f(6)·f(4) = 18*12 = 216. So this is not true.
C) f(3) − f(1) = 9 - 3 =6; f(6) − f(4) = 18 - 12 = 6. This statement is true.
D) f(3) − f(1) = 9 - 3 = 6; f(-3) − f(-1) = -9 - (-3) = -6. So this is not true.
Therefore, the statement that must be true is 'f(3) − f(1) = f(6) − f(4)'.
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Considering the function f(x) = 3x the correct Option is C: f(3) − f(1) = f(6) − f(4) .
Let's analyze each statement for the function f(x) = 3x to determine which one is true:
A) f(3)/f(1) = f(6)/f(4):
This statement suggests a proportional relationship. Computing the values, we get f(3) = 9, f(1) = 3, f(6) = 18, and f(4) = 12. Therefore, f(3)/f(1) = 9/3 = 3 and f(6)/f(4) = 18/12 = 1.5, so the statement is not true.B) f(3)·f(1) = f(6)·f(4):
This statement suggests a multiplicative relationship. Using the same computed values, f(3)·f(1) = 9·3 = 27 and f(6)·f(4) = 18·12 = 216, so this statement is not true.C) f(3) − f(1) = f(6) − f(4):
This implies an additive relationship. Using the computed values, f(3) − f(1) = 9 − 3 = 6 and f(6) − f(4) = 18 − 12 = 6. Both sides are equal, so this statement is true.D) f(3) − f(1) = f(−3) − f(−1):
This implies another additive relationship, but with negative inputs. Computing these values, f(−3) = −9 and f(−1) = −3, then f(3) − f(1) = 9 − 3 = 6 and f(−3) − f(−1) = −9 − (-3) = −6. Therefore, this statement is not true.Therefore, the correct answer is C.
I need to find the measure of each angle indicated and round to the nearest tenth.
45.2 (for question 1/#19)
To find the angle, you need to use the cosine because you have the adjacent and the hypotenuse.
Cosine 0 = 9.3/13.2
Cosine 0 = 9.3/13.2 = 0.705
Arccos 0.705
Angle 0 = 45.2
How is using the Pythagorean theorem in a rectangular prism similar to using it in a rectangle
The Pythagorean theorem is used in a similar manner to compute the diagonal of a rectangle and a rectangular prism. In both cases, the theorem is utilized to find the length of a line connecting two opposite corners across the shape or space.
Explanation:In the field of Mathematics, the Pythagorean theorem presents a fundamental relationship within a right triangle which expresses that the square of the hypotenuse (the side opposite the right angle) is equivalent to the sum of the squares of the other two sides. This theorem is represented mathematically as a² + b² = c².
When applying this theorem in a rectangle, consider a diagonal drawn from one corner to the opposite corner, which gives us a right triangle. To find the length of this diagonal (hypotenuse), we use the Pythagorean theorem, considering the two sides of the rectangle as the other two sides of the triangle.
In a rectangular prism, the same principle applies. However, instead of two sides (as in a rectangle), we now have three dimensions (length, width, and height) to consider. When one wishes to find the distance from one corner to the opposite corner (a diagonal cutting through the prism), the Pythagorean theorem can be employed. First, a right triangle is considered in the base of the prism, and the Pythagorean theorem is used to find the length of the diagonal of the base. Next, a second right triangle is constructed using the height of the prism and the diagonal of the base. Once again, the Pythagorean theorem can be implemented to calculate the length of the longest diagonal of the prism.
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The Pythagorean theorem applies similarly in both rectangular prisms and rectangles, using right triangles to calculate distances.
The Pythagorean theorem is fundamentally the same in both a rectangular prism and a rectangle, as it relies on the properties of right triangles. For a rectangle, the theorem states that the sum of the squares of the two shorter sides (a and b) equals the square of the hypotenuse (c), or a² + b² = c².
When applied to a rectangular prism, the theorem is used in three dimensions to find the length of the diagonal (d) stretching between opposite corners. In a rectangular prism, by applying the Pythagorean theorem successively across two-dimensional planes, we first calculate the diagonal of one face of the prism (b² = x² + y²).
Then, we incorporate the third dimension z to find the space diagonal: d² = x² + y² + z². This sequential application of the Pythagorean theorem leverages its two-dimensional principle to solve for three-dimensional distances.
Steps to Apply Pythagorean Theorem in a Rectangular Prism:
Identify the three side lengths of the prism: x, y, and z.Calculate the face diagonal using: b² = x² + y².Apply the theorem again to incorporate the third dimension: d² = x² + y² + z².This demonstrates how the Pythagorean theorem's consistent application in both two and three dimensions allows calculation of diagonals and distances in various geometric contexts.
Need help anyone please ?
ok well in this specific example you are multiplying by 1000 so the answer or you are moving the decimal to the right 3 places so the answer is 3240
Mean of the integers 10,-27,4,-9
Answer:
-5.5
Step-by-step explanation:
Add all numbers and divide by 4 (the total amount of numbers)
10+(-27)+4+(-9)=-22
-22/4 = -5.5
-5.5
In order to find the mean, you add up all numbers and then divide by the amount of numbers
g(t)=−9t−4
g ( ? ) = 23
Answer:
g(- 3) = 23
Step-by-step explanation:
We require to find the value of t so that g(t) = 23
Equate g(t) to 23 and solve for t, that is
- 9t - 4 = 23 ( add 4 to both sides )
- 9t = 27 ( divide both sides by - 9 )
t = - 3
Hence g(- 3) = 23
If the value of the function g(t) = -9t - 4 is 23. Then the value of t will be negative three.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
The function g(t) is given below.
g(t) = - 9t - 4
If the value of the function g(t) is 23. Then the value of t will be given as
23 = - 9t - 4
27 = - 9t
t = - 3
Then the value of t will be negative 3.
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The manager of an online news service received the report given in the table on the number of subscriptions sold by the service. The manager estimated that the percent increase from 2012 to 2013 would be half the percent increase from 2013 to 2014. How many subscriptions did the manager expect would be sold in 2014?
table:
2012: 5,600
2013: 5,880
Answer:
= 5880 +
= 5880 + (0.10 × 5880)
= 5880 + 588
= 6,468
In 2014 subscriptions would be sold 6,468.
Step-by-step explanation:
There are 5 white balls, 8 red balls, 7 yellow balls and 4 green balls in a container. A ball is chosen at random. What is the probability of picking a red
Answer:
8/24=1/3
There are 24 balls in total and 8 of them are red. So you get 8/24 but you need to simplify it to its simplest form which is 1/3
Final answer:
The probability of picking a red ball from a container with 5 white, 8 red, 7 yellow, and 4 green balls is 1/3, because you divide the number of red balls (8) by the total number of balls (24).
Explanation:
The subject of this question is probability, a branch of mathematics concerned with the likelihood of an event occurring. To find the probability of picking a red ball, we need to divide the number of red balls by the total number of balls in the container.
In the question, there are 5 white balls, 8 red balls, 7 yellow balls, and 4 green balls, which means there are a total of 24 balls. The probability of picking a red ball is calculated by taking the number of red balls and dividing it by the total number of balls:
Probability of picking a red ball = Number of red balls / Total number of balls = 8 / 24 = 1/3.
Using 3.14 for pie what is the area of the circle to the nearest tenth of an inch
[tex]area = \pi {r}^{2} \\ r = \frac{1}{2} \times 7.5 = 3.75 \\ 3.14 \times 3.75 {}^{2} \\ 3.75 {}^{2} = 14.06 \\ 3.14 \times 14.06 = 44.1484 \: inches {}^{2} [/tex]
hope that helped
[tex]A = \pi {r}^{2} \\ \\ r = \frac{7.5}{2} = 3.75[/tex]
So
[tex]A = (3.14)({3.75}^{2} ) \\ A = (3.14)(14.0625) \\ A = 44.15625 \\ A =44.16[/tex]
Find the correct value to fill in the space below.
cos 50° = 2 cos^2 ____° -1
Answer:
25.
Step-by-step explanation:
Use the identity cos 2x = 2 cos^2 x - 1
So cos 50 = 2 cos^2 25 - 1
So the space = 25.
Answer:
25°
Step-by-step explanation:
Using the double angle trigonometric identity for cosine
• cos2x = 2cos²x - 1
Here 2x = 50° ⇒ x = 25°, thus
cos50° = 2cos²25° - 1
This is a picture of a cube and the net for the cube.
What is the surface area of the cube?
a. 48mm
B. 64mm
c. 112mm
d. 384mm
B:64————————bc 8x8 is 64
Answer:it’s D
Step-by-step explanation:
Three neighbors plan to complete fencing projects this spring. As shown in the diagrams below, Neighbor A plans to fence in his rectangular backyard with a 6-foot tall wooden privacy fence. Neighbor B plans to construct a circular chain link fence around his pool. And, Neighbor C is putting a vinyl fence around three side of his front yard. Note: Diagrams are not drawn to scale. Intended fences are marked with a dashed line.
Wood fencing is sold in 8 foot sections for $111.50. Chain link fencing costs $9.75 per linear foot (in whole foot lengths). And, vinyl fencing can be purchased for $53.55 per linear yard (in whole yard lengths).
Which neighbor's fencing project will cost the most?
Which neighbor's fencing project will cost the least?
Answer:
- The neighbor's fencing project that will cost the most is: Neighbor A.
- The neighbor's fencing project that will cost the least is: Neighbor B.
Step-by-step explanation:
To calculate the amount of fence that Neighbor A has to put up, you need to add the following distances:
[tex]Fence_A=5yards+8yards+25yards+8yards\\Fence_A=46yards[/tex]
Convert yards to feet (Remember that [tex]1yard=3feet[/tex]:
[tex]Fence_A=(46yards)(\frac{3feet}{1yard})=138feet[/tex]
You know that wood fencing is sold in 8 foot sections for $111.50, then, the number of sections for this fence will be:
[tex]sections=\frac{138feet}{8feet}=17.25[/tex]≈18
Then, the cost for this fencing project will be:
[tex]Cost_A=\frac{(18sections)(\$111.50)}{1section}=\$2,007[/tex]
To calculate the amount of fence that Neighbor B has to put up, you need to use the formula for calculate the circumference of a circle:
[tex]C=2\pi r[/tex]
Where r is the radius.
In this case, the radius is:
[tex]r=\frac{30feet+10feet}{2}=20feet[/tex]
Substituting, you get:
[tex]C=Fence_B=2\pi (20feet)=125.66feet[/tex]≈126 feet
You know that the Chain link fencing costs $9.75 per linear foot, then, the cost for this fencing project will be:
[tex]Cost_B=(126)(\$9.75)=\$1,228.5[/tex]
To calculate the amount of fence that Neighbor C has to put up, you need to add the following distances:
[tex]Fence_C=16feet+58feet+16feet\\Fence_C=90feet[/tex]
Convert from feet to yards (Remember that [tex]1yard=3feet[/tex]:
[tex]Fence_A=(90feet)(\frac{1yard}{3feet})=30yards[/tex]
You know that the vinyl fencing can be purchased for $53.55 per linear yard , then, the cost for this fencing project will be:
[tex]Cost_C=(30)(\$53.55)=\$1,606.5[/tex]
Therefore, the neighbor's fencing project that will cost the most is: Neighbor A.
The neighbor's fencing project that will cost the least is: Neighbor B.
Answer:
Therefore, the neighbor's fencing project that will cost the most is: Neighbor A.
The neighbor's fencing project that will cost the least is: Neighbor B.
Step-by-step explanation:
AB has endpoints at (-1, -1) and (-2, -4). Its transformation A'B' has endpoints at (-2, -2) and (-4, -8). What type of transformation occurred? Are lengths of segments affected by this
A) rotation; no; The lengths of the two segments are the same.
B) reflection; yes; The length of segment A'B' is longer than the original segment AB.
C) dilation by a scale factor of 2; yes; The length of segment A'B' is longer than the original segment AB.
D) dilation by a scale factor of 1/2; The length of segment A'B' is shorter than the original segment AB.
type of transformation? Justify.
will mark brainliest if correct and give 50 pts.
The correct answer is C
Will mark brainliest if you show ur work
How many solutions does the equation 6z − 3z − 7 = −2 + 3 have?
Two
None
Infinitely many
One
Answer:
[tex]\boxed{\bold{One \ Solution}}[/tex]
Step-by-step explanation:
Solve equation to find answer(s)Combine: 6z - 3z = 3z
[tex]\bold{3z-7=-2+3}[/tex]
Add: -2 + 3 = 1
[tex]\bold{3z-7=1}[/tex]
Add 7 to both sides:
[tex]\bold{3z-7+7=1+7}[/tex]
Simplify:
[tex]\bold{3z=8}[/tex]
Divide both sides by 3:
[tex]\bold{\frac{3z}{3}=\frac{8}{3}}[/tex]
Simplify:
[tex]\bold{z=\frac{8}{3}}[/tex]
- M -
-5y = -5
7x + 6y = 7
Is (5,1) a solution of the system?
Choose 1 answer.
A. Yes
B. No
-5y = -5 = 1
7x + 6y = 7
=-1.167
your answer is B) no
The given coordinate (5,1) is not a solution to the system of equations -5y = -5 and 7x + 6y = 7. Both equations do not hold true when 5 and 1 are substituted for y and x respectively.
Explanation:In Mathematics, to confirm if the given set of numbers ((5,1)) are a solution to the system, we substitute these values back into both system equations. In this case, 5 for y and 1 for x. As a result, the equation -5y = -5 becomes -5*5= -25, which is not equal to -5. Therefore, 5 is not a solution for y. Similarly, solving 7x + 6y = 7 after substituting the values becomes 7*1 + 6*5= 37, which is not equal to 7. So, 1 is not a solution for x. Therefore, the provided answer (5,1) is not a solution for the given system of equations. Thus, the answer is B. No.
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Which of these are factors of 121?
11, 11 •11 equals 121 which makes it a factor
Please help!
Find the exact circumference of the circle.
The answer will be B
letter B is the answer
what is the surface of a cylinder that has a height of 8 and a radius of 10
Answer:
Surface area I'm guessing. 1,130.4
Step-by-step explanation:
The formula for the surface area of a cylinder is: 2*pi*r^2 + 2*pi*r*h.
Plug in the values given.
2*pi*10^2 + 2*pi*10*8
628 + 502.4 = 1,130.4
(If you want the most precise value, use a calculator for pi instead of just 3.14.)
ANSWER
[tex]S A = 1130.4[/tex]
square units.
EXPLANATION
The given cylinder has a height of 8 and a radius of 10.
The formula for calculating the surface area of a cylinder is
[tex]S A = 2\pi \: r(r + h)[/tex]
We substitute r=8 and h=10 into the formula to get:
[tex]S A = 2\pi \: 10(10+ 8)[/tex]
[tex]S A = 360\pi [/tex]
Or using π=3.14
[tex]S A = 1130.4[/tex]
units square.
Kenisha tried to subtract two polynomials her work is shown below. At which step did Kenisha make an error, If at all?
A. Step 1
B. Step 2
C. Step 3
D. Kenisha’s work is correct
Answer:
Step 1
Step-by-step explanation:
When you subtract a polynomial in parentheses, you have to remove them from the parentheses first, which Kenisha did right. The problem is that because the numbers are being subtracted, all of the signs switch, which they forgot to do. Step one should look like: 2b² + 3b + 11 - 7b² + 5b - 1
Solve -4/3x+1/6<7/9
< or >
A. -34/27
B. -17/24
C. -11/24
D. -22/27
EDIT THE ANSWER IS >-11/24 I TOOK THE TEST
Answer:
[tex]\large\boxed{x>-\dfrac{11}{24}}[/tex]
Step-by-step explanation:
[tex]-\dfrac{4}{3}x+\dfrac{1}{6}<\dfrac{7}{9}\qquad\text{multiply by common denominator}\to18\\\\18\!\!\!\!\!\diagup^6\left(-\dfrac{4}{3\!\!\!\!\diagup_1}x\right)+18\!\!\!\!\!\diagup^3\left(\dfrac{1}{6\!\!\!\!\diagup_1}\right)<18\!\!\!\!\!\diagup^2\left(\dfrac{7}{9\!\!\!\!\diagup_1}\right)\\\\(6)(-4x)+(3)(1)<(2)(7)\\\\-24x+3<14\qquad\text{subtract 3 from both sides}\\\\-24x<11\qquad\text{change the signs}\\\\24x>-11\qquad\text{divide both sides by 24}\\\\x>-\dfrac{11}{24}[/tex]
What is the answer??????
Answer:
D. G(x) = (x + 3)²Step-by-step explanation:
f(x) - n - shift the graph n units down
f(x) + n - shift the graph n units up
f(x - n) - shift the graph n units to the right
f(x + n) - shift the graph n units to the left
==========================================
From the graph:
G(x) - the graph F(x) has been shifted 3 units to the left (look at the vertex).
Therefore your answer is G(x) = F(x + 3) = (x + 3)²
The answer is D. D is the answer
A simplified algebraic expression for the expression, x decreased by 9
I think the answer is in the question itself
x-9
What is the quotient of -8x^6/4x^-3?
Answer: [tex]-2x^{9}[/tex]
Step-by-step explanation:
To find the quotient, you need to apply the Quotient of powers property. This is:
[tex]\frac{a^m}{a^n}=a^{(m-n)[/tex]
Then given the expression [tex]\frac{-8x^6}{4x^{-3}}[/tex] you can apply the property mentioned before. Then you get:
[tex]\frac{-8x^{(6-(-3))}}{4}[/tex]
You should remember the multiplication of signs:
[tex](-)(-)=+\\(+)(+)=+\\(-)(+)=-[/tex]
Therefore, simplifying the expression, you get that the quotient of [tex]\frac{-8x^6}{4x^{-3}}[/tex] is:
[tex]-2x^{9}[/tex]
Answer:
d
Step-by-step explanation:
d
pls help i need to finish all my khan academy work or else i fail my grade, plsssss help
Answer:
Start by dividing things up so that you know them. Use the dotted line to make a square a 2 triangles. Base and height for the square is 4 so that total is 16. Then the triangles have a base an height of 4 as well so that ((4•4)/2)= 8. Then add them together = 24
Hope this helps.
Answer:
Step-by-step explanation:
The Bulldogs, a baseball team, has nine starting players. The heights of the starting players are 72 in., 71 in ., 78 in., 70 in., 72 in., 72 in., 73 in., 70 in., and 72 in. Which term BEST describes the data value 78 in.?
A) mean
B) median
C) mode
D) outlier
By looking at this data, you can see that while most of the data is in between 70 and 73, the only number that isn't in that range is 78. Therefore, the term outlier describes 78in the best.
Answer:
D) Outlier
Step-by-step explanation:
A basketball player made 11 out 100 attempted free throws. What percent of free throws was made ?
Answer:11%
Step-by-step explanation:
A percent is always a number over 100, so 11/100 = 11%
Answer:
11%
Step-by-step explanation:
Line AB passes through A(-3, 0) and B(-6, 5). What is the equation of the line that passes through the origin and is parallel to ?
A.
5x − 3y = 0
B.
-x + 3y = 0
C.
-5x − 3y = 0
D.
3x + 5y = 0
E.
-3x + 5y = 0
Answer:
3y+5x=0
Step-by-step explanation:
The question is on equations of parallel lines
Finding the gradient m of line AB
m=change in y coordinates/change in x-co-ordinates
Given points A(-3,0) and B (-6,5)
m=Δy/Δx Δy=5-0=5 Δx=-6 - -3= -3 ⇒m= - 5/3
Equation
The line will have its gradient equal to - 5/3
m=-5/3
point is the origin (0,0)
m=Δy/Δx
y-0/x-0 = -5/3
3(y-0)=-5(x-0)
3y-0= -5x+0
3y=-5x
3y+5x=0
Answer:
c is the correct answer
Step-by-step explanation:
im lost . . .. . . ????????
Answer:
f(x) = 3x - 1
Step-by-step explanation:
The line can be represented in the form f(x) = mx + b, where m is the rate of change of the line and b is the value of the function when x = 0.
Looking at the graph, we can tell that when x = 0 the function = -1. (The point on the line and the y-axis).
We can also tell that when x increases by 1, y increases by 3. The points (0,-1) and (1, 2) are both on the line and their difference in x is 1 and their difference in y is 3.
The formula for slope (rate of change) is [tex]\frac{change\ in\ y}{change\ in\ x}[/tex], so m = [tex]\frac{3}{1}[/tex] or 3.
Now we have the equation for the line is f(x) = 3x - 1
What is the measure of angle C
Answer:
C = 77°
Step-by-step explanation:
From the intercepted arc theorem, we can say that Angle ABC (angle B) is HALF of the arc intercepted (which is 110).
Hence, angle ABC = 55.
Now, looking at triangle ABC, we know that sum of 3 angles of a triangle is 180. We already know Angle A to be 48 and Angle B to be 55, thus Angle C is:
A + B + C = 180
48 + 55 + C = 180
103 + C = 180
C = 180 - 103
C = 77