WXYZ is a rectangle. XZ = 12 and ∠ ZXW = 30°. Find:
7). ZW
8). WX
9). The area of rectangle WXYZ
The side length ZW is 6 units and the side length WX is 10.392 units. Then the area of the rectangle is 62.352 square units.
Given that:
Diagonal, d = 12
Angle, α = 30°
The rectangle's area will be given as,
Area of the rectangle = L × W square units
The measure of the side length ZW is calculated as,
sin 30° = ZW / 12
ZW = 6 units
The measure of the side length WX is calculated as,
cos 30° = WX / 12
ZW = 10.392 units
The area of the rectangle is calculated as,
A = 6 x 10.392
A = 62.352 square units
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Help me please find EC
The length of segment EC is 24 in the given triangle
A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.
3x=2(x+4)
Apply distributive property on RHS
3x=2x+8
Subtract 2x from both sides
x=8
The segment EC =3x
=3(8)
=24
Hence, the length of EC is 24 in the given triangle
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Cousteau is building a cubed cage for a parrot at his local zoo. Since the the cage's side length is 12 feet, its volume will be 12³ cubic feet. Can you help Cousteau write out 12³ in expanded form?
The expanded form of 12³ is given as follows:
12³ = 12 x 12 x 12 = 1728 cubic feet.
How to obtain the volume of a cube?The volume of a cube of side length a is given by the cube of the side length, as follows:
V(a) = a³.
This expression is equivalent to multiplying the side length of the object by itself twice, as follows:
V(a) = a x a x a.
The side length for this problem is given as follows:
a = 12 feet.
Hence the volume of the cube is given as follows:
V = 12³ = 1728 feet³.
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please help me, quick and right answers only algebra :)
The slope of f(x) is less than the slope of g(x).
How to compare the slopes of the lines?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know two points on a line, then the slope is equal to the quotient between the difference of the y-values and the difference of the x-values.
So the slope of f(x) is:
a = (3 - 0)/(0 + 2) = 3/2
And g(x) = (4/5)*x - 2
So here the slope is 4/5
We can see that clearly the slope of g(x) is larger.
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(-35z^4x+32z^4 x^6) divided by (-4z^3 x^5)
(-35z⁴x + 32z⁴x⁶) divided by -4z³x⁵ gives {(35z - 32zx⁵)/ (4x⁴)} by applying simple rule of division of polynomials.
Let the given polynomial be written as,
f(z,x) = -35z⁴x + 32z⁴x⁶
g(z,x) = -4z³x⁵
Here the functions of the given polynomial are composed of two variables, namely x and z, so the functions are denotes likewise.
We can divide the polynomial f(x) by g(x) by the division method as,
[tex]\frac{f(z,x)}{g(z,x)}[/tex] = (-35z⁴x + 32z⁴x⁶) / ( -4z³x⁵)
= { (-35z⁴x)/ ( -4z³x⁵) } + {(32z⁴x⁶)/ ( -4z³x⁵)}
= [tex]\frac{35z}{4x^4}[/tex] + [tex]\frac{-8zx}{1}[/tex]
= [tex]\frac{35z - 32zx^5}{4x^4}[/tex]
or, = {(35z - 32zx⁵)/ (4x⁴)}
Thus the required value of (-35z⁴x + 32z⁴x⁶) divided by -4z³x⁵ is {(35z - 32zx⁵)/ (4x⁴)}
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Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts. What percent of the new mixture if peanuts?
A. 34%
B. 17%
C. 13%
D. 26%
The new mixture contains 34% peanuts. The correct option is A
To solve this problemThe idea of weighted averages can be applied.
First, let's determine the mixture's entire weight:
Total weight = 4 kg + 12 kg = 16 kg
We can now calculate how many peanuts there are overall in the mixture:
Total weight in kilograms is = (4 kg) (0.16) + (12 kg) (0.40)
= 0.64 kg + 4.80 kg
= 5.44 kg.
Finally, we can find the percentage of peanuts in the mixture:
Percent of peanuts = (Total amount of peanuts / Total weight) x 100%
= (5.44 kg / 16 kg) x 100
= 34%
Therefore, the new mixture contains 34% peanuts, which is option A.
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In a dice game you win $1 if you roll a 1,2,3, or 4. If you roll a 5 or 6 you lose $2. What is the expected value of the game?
Answer:
Step-by-step explanation:
no higher than 4
Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows. Ariadne's shadow is 6 feet long and Dixon's shadow is 9 feet long. If Dixon is 6 feet tall, how tall is Ariadne?
Answer: 4
Step-by-step explanation:
We can use the proportion. We already know that Dixon is 6 ft tall and that his shadow is 9 ft long. Also we know that the shadow of his sister is 6 ft long. 6 : x = 9 : 6, or 6 / x = 9 / 6. After that we will cross multiply : 9 * x = 6 * 6, 9 x = 36 , x = 36 : 9, x = 4. Answer: Ariadne is 4 feet tall.Hope I helped! :) Cheers!
Determine whether or not it defines a function. Pease shows steps so I understand the answer.
The requried, justification for the given function has been shown below.
(a) Yes, R₁ defines a function. Each element in the domain is mapped to a unique element in the codomain, which is 0 in this case.
(b) No, R₂ does not define a function. For some values of n, there may be multiple animals with n legs, so there is no unique output for each input.
(c) Yes, R₃ defines a function. Each element in the domain is mapped to a unique element in the codomain, which is the remainder of n divided by 5.
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Find the distance between the points (1,2) and (10,-10) round decimal to nearest tenth
The distance between the points (1, 2) and (10,-10) is 15 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given points into the distance formula, we have the following;
Distance = √[(10 - 1)² + (-10 - 2)²]
Distance = √[(9)² + (-12)²]
Distance = √[81 + 144]
Distance = √225
Distance = 15 units.
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Find the area of each figure. Round to the nearest hundredth where necessary.
Answer:
28(17) + π(7^2)
= 476 + 49π square meters
= 629.94 square meters
Town A and Town were located close to each other, and recently merged into one city. Town A had a population with 12% whites. Town B had a population with 10% whitesAfter the merge, the new city has a total of 5000 residents, with 10.56% whitesHow many residents Town A and Town used to have?
The number of residents Town A used to have is 1400, and the number of residents Town B used to have is 3600, as shown by the simple equation below.
How to find the number of residentsLet x be the number of residents Town A used to have. The number of residents in Town B is:
5000 - x
We know that Town A had 12% whites and Town B had 10% whites. After the merge, the percentage of whites is 10.56%. With that in mind:
12%x+10%(5000-x) = 10.56%(5000)
0,12x + 500 - 0,1x = 528
0.02x = 28
x = 1400
Therefore, the number of residents Town A used to have is 1400. Now, the number of residents town B used to have is:
5000 - 1400 = 3600
With that in mind, we can conclude our answer is correct.
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Given the point with Cartesian coordinates, (−7√3/2,7/2), find the polar coordinates of the point.
Select the correct answer below:
(7,4π/3)
(7,11π/6)
(3,4π/3)
(3,5π/6)
(3,11π/6)
(7,5π/6)
Answer: the last option is correct
Step-by-step explanation:Using the formulas for converting Cartesian coordinates to polar coordinates:
r = √(x^2 + y^2)
θ = atan2(y, x)
where x and y are the Cartesian coordinates, r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.
Given the Cartesian coordinates (x, y) = (-7√3/2, 7/2), we can substitute these values into the formulas:
r = √((-7√3/2)^2 + (7/2)^2)
θ = atan2(7/2, -7√3/2)
Simplifying the expressions:
r = √(147/4 + 49/4) = √(196/4) = √49 = 7
θ = atan2(7/2, -7√3/2)
Using a calculator or reference table to find the arctangent of 7/2 divided by -7√3/2, we get:
θ ≈ 5π/6
So the correct answer is: (7, 5π/6), which is option (6).
Help with this question.
The contrapositive statement is option D
What is contrapositive statement?If the hypothesis and conclusion of an earlier conditional statement are reversed, a contrapositive statement is produced.
Technically speaking, the contrapositive of a conditional statement that starts with "If p, then q" is "If not q, then not p." The initial assertion and its contrapositive, then, are both true because they are logically equivalent.
Thus the contrapositive statement as shown is the statement ~q ~p
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Please answer this as quick as possible, wrong answers or chatgpt will be reported:
Q3. A Ferris wheel reaches a maximum height of 60 m above the ground and takes twelve minutes to complete one revolution. Riders have to climb a 4 m staircase to board the ride at its lowest point.
(a) [4 marks] Write a sine function for the height of Emma, who is at the very top of the
ride when t = 0.
(b) [2 marks] Write a cosine function for Eva, who is just boarding the ride.
(c) [2 marks] Write a sine function for Matthew, who is on his way up, and is at the same height as the central axle of the wheel.
For Matthew, the height is given as [tex]52 + 8 sin (\pi/6t)[/tex]
What is a Sine Function?To express the characteristic repetition of certain actions or events, a sine function is often employed.
This mathematical function links a position on the edge of a unit circle with the height of its corresponding y-coordinates. Conveyed generally as sin(x), it represents angle measurement in radians.
This repeatable pattern attains values between -1 to 1 and reappears once per every 2π radians. There are numerous applications of this type of sinusoidal oscillation pattern, including signal processing, engineering, and physics among others.
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What is the smallest whole number that rounds to 2,560 to the nearest ten?
The requreid smallest whole number that rounds to 2,560 to the nearest ten is 2,565. When we round 2,565 to the nearest ten, we get 2,570, which is the desired result.
When rounding a number to the nearest ten, look at the digit in the tens place. If that digit is 5 or greater, we round up by adding 1 to the digit in the hundreds place. If that digit is less than 5, round down by keeping the digit in the hundreds place the same.
In the given question, 2,560 rounded to the nearest ten would be,
2,560 rounded up to 2,560 + 10 = 2,570.
Therefore, the smallest whole number that rounds to 2,560 to the nearest ten is 2,565. When we round 2,565 to the nearest ten, we get 2,570, which is the desired result.
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4. Expand these brackets:
a. 9(2q + 3)
Answer:
18q + 27
Step-by-step explanation:
9(2q + 3)
9 x 2q = 18q
9 x 3 = 27
18q + 27
: )
24. Brittany is making lemonade from
a mix. The instructions say to mix
8 scoops of powder per gallon, but
she is only making a quart. How
many scoops should Brittany use?
A. 1
B. 2
C. 4
D. 16
Answer:
B 2
Step-by-step explanation:because a quart is 0.25 of a gallon
On the 6th grade math test, twelve students had a score of 80 points. Eight students had a score of 88 points.
What was the class average?
The requried class average is 83.2 points.
To find the class average, we need to calculate the total number of points earned by all the students and divide by the total number of students.
The 12 students who scored 80 points earned a total of 12 × 80 = 960 points.
The 8 students who scored 88 points earned a total of 8 × 88 = 704 points.
The total number of points earned by all the students is 960 + 704 = 1664 points.
The total number of students is 12 + 8 = 20.
To find the class average, we divide the total number of points by the total number of students:
average = total points / total students
average = 1664 / 20
average = 83.2
Therefore, the class average is 83.2 points.
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is y=x-3 a function or an equation
Video D Find the distance between the points (-2, 2) and (-7, -10). Write your answer as a whole number or a fully simplified radical expression. Do not round.
The distance between the two points is 13.
We have,
The two points are (-2, 2) and (-7, -10)
Now,
Distance between two points.
= √(c - a)² + (d - b)²
Where (a, b) and (c, d) are the two points.
Now,
Distance between (-2, 2) and (-7, -10).
= = √(-7 + 2))² + (-10 - 2)²
= √(-5)² + (-12)²
= √(25 + 144)
= √169
= √13²
= 13
Thus,
The distance between the two points is 13.
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27. The side length of a cube is (b+7). What is its volume?
HELP WHICH INE IS IT CORRECTT ITS DUE TODAY
Answer:
Step-by-step explanation:
CRITICAL THINKING The total area of the polygon is 176 square feet. What is the value of $x$ ?
A drawing of a polygon. It consists of a rectangle with two triangles on either side. Length of the rectangle is 16 feet. The width of the rectangle is 8 feet and is same as the height of the triangles. Lengths of the base of each triangle is labeled as x.
$x=$
ft
The value of x is, x = 6 ft
Now, We can formulate;
Area of the polygon = area of the square + 2(area of the triangle)
Here, We have;
Area of the polygon = 176 ft²
So, Area of the square = length × width
= 16 × 8
= 128
And, Area of the two triangles = 2( 1/2 x base x height)
= 2(1/2 × x × 8)
= 8x
Now, Plug in the above values into the equation for area of the polygon.
Thus: We get;
176 = 128 + 8x
Subtract 128 from each side
176 - 128 = 8x
48 = 8x
Divide both sides by 8
6 = x
x = 6 ft
Thus, The value of x is, x = 6 ft
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Consider the function: ƒ(x) = 2/5 x- 5/2
The value of the function f(1/2) for the f(x) = 2 / 5 x- 5 / 2 is equal to -2.3.
Function is equal to,
f(x) = 2 / 5 x- 5 / 2
To get the value of f ( 1 / 2 ) .
Substitute the value of x equals to ( 1 / 2 ) we get,
f(x) = (2 / 5 ) x- ( 5 / 2 )
This implies,
f ( 1 / 2 ) = ( 2 /5 ) × ( 1 / 2 ) - ( 5 / 2 )
⇒ f ( 1 / 2 ) = ( 1 / 5 ) - ( 5 / 2 )
Take the least common multiple of 5 and 2 we get,
least common multiple of 5 and 2 is 10.
⇒ f ( 1 / 2 ) = ( 2 - 25 ) / 10
⇒ f ( 1 / 2 ) = -23 /10
⇒ f ( 1 / 2 ) = -2.3
Therefore, the value of f(1/2) for the given function is equal to -2.3.
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The above question is incomplete, the complete question is:
Consider the function: ƒ(x) = 2/5 x- 5/2 find the value of f( 1/2)?
The area of the triangle below is 1/8 square feet . What is the length of the base ? Express your answer as a fraction in simplest form.
The length of the base of the right-angle triangle will be 1 / 2 inches.
Since, We know that;
It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
So, The area of the right-angle triangle is given as
A = 1/2 x B x H
Where B is the base and H is the height of the right triangle.
The area of the triangle below is 1/8 square inches. And the length of the perpendicular will be 1/2 inches.
Then the length of the base will be;
A = 1/2 x B x H
1/8 = 1/2 x B x 1/2
1/8 = 1/4 x B
B = 1/2
Thus, The length of the base of the right-angle triangle will be 1/2 inches.
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Are the triangles similar? If so, complete the similarity statement and state how you know they are similar. Not Similar OA BST by SSS~ A BTS by SSS~ O A BTS by SAS~ OA BST by SAS~ 64 D 176 S ABCD~ B 44 121 C
The triangle triangle ∆BCD is not similar to the triangle ∆BTS since their sides and angle does not correspond in proportion.
What are similar trianglesSimilar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.
Triangle ∆BCD is not similar to the triangle ∆BTS, BT does not correspond to BC, and BS does not correspond to BD. Also, the angle m∠SBT does not correspond to m∠DBC.
Therefore, the triangle ∆BCD is not similar to the triangle ∆BTS since their sides and angle does not correspond in proportion.
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
rango de y=5/(x^2-25)
Answer: x = -5, 5 y= 0
Step-by-step explanation:
vertical asymptotes = x= -5, 5
horizontal asymptotes = y= 0
Which system of linear equations has no solutions?
a) y = 4x +1 y= -4x + 1
b) y= 2x + 7 y= 2x - 7
c) 3x + y =1 6x + 2y =2
d) 5x + y =3 x + 5y = 15
Answer:
b)
Step-by-step explanation:
a) y = 4x +1 y= -4x + 1
Different slopes; same y-intercept; lines intersect at 1 point; there is 1 solution.
b) y= 2x + 7 y= 2x - 7
Same slopes; different y-intercepts; parallel lines do not intersect; no solution.
c) 3x + y =1 6x + 2y =2
Equations are the same; infinite number of solutions.
d) 5x + y =3 x + 5y = 15
Different slopes; lines intersect at 1 point; there is 1 solution.
Answer: b)
Help with this please and thank you
The ordered pair that would best represent the location of point E' is (8z, 4z).
A graph of the vertices of the dilated image is shown in the image below.
The rule that best represent the dilation of quadrilateral WXYZ to quadrilateral W'X'Y'Z'.
What is a dilation?In Mathematics and Geometry, a dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 5/2 centered at the origin as follows:
Ordered pair W (-2, 1) → Ordered pair W' (-2 × 5/2, 1 × 5/2) = W' (-5, 5/2).
Ordered pair X (2, 2) → Ordered pair X' (2 × 5/2, 2 × 5/2) = X' (10, 10).
Ordered pair Y (1, -1) → Ordered pair Y' (1 × 5/2, -1 × 5/2) = Y' (5/2, -5/2).
Ordered pair Z (-2, -2) → Ordered pair Z' (-2 × 5/2, -2 × 5/2) = Z' (-5, -5).
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