The dimension of the rectangle of the largest area in an equilateral triangle is √3/4L.
Here we have to find the dimension of the rectangle of the largest area.
Let the distance from the tip of the base of the triangle to the point that the top of the rectangle meets the triangle be x.
The width of the rectangle is √3/2 x.
By this, we can find the area of the rectangle
Area = √3/2x ( L -x) = √3/2 xL - √3/2x²
To find the maximum area we have:
dA/ dx = 0
dA / dx = √3/2L - √3x = 0
From we have to find the value of x,
√3 x = √3/2L
x = L/2
The dimension of rectangle is √3/2x = √3/2(L/2)
= √3/4 L
Therefore the dimension of the rectangle is √3/4 L.
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carter has 24 posters in his room. if he arranges them into 6 equal rows, how many posters will be in each row?
If he arranges them into 6 equal rows, 4 posters will be in each row.
Define division.One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal pieces. Every day, we might employ the division approach in various situations. Fraction division differs significantly from natural number division. We must change the division operator into a multiplication operator when dividing fractions. Therefore, the dividend should be multiplied by the inverted divisor.
Given,
Total posters = 24
Arranging them into 6 equal rows,
Dividing:
24÷ 6
Reciprocating,
24 × 1/6
4
If he arranges them into 6 equal rows, 4 posters will be in each row.
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Given l||m and m∠1 = 60°, select all angles that are also equal to 60°. 8 2 6 7 5 4 3
Answer:
2 , 3 , 4
Step-by-step explanation:
Corresponding angles: When two parallel lines are intersected by a transversal, the angles on the same side and same position of the transversal are same.
∠3 = ∠1
Vertically opposite angles: When two lines intersect, the opposite angles are congruent.
∠2 = ∠1
∠4 = ∠3
So, ∠1 = ∠2 = ∠3 = ∠4 = 60°
the initial number of views for a reader board was 25. the number of views is growing exponentially at a rate of 18% per week. what is the number of views expected to be four weeks from now? round to the nearest whole number.
The number of views in the four weeks round to the whole number is 48.
Here it is given that the initial number of views for a reader board was 25 and it gets increased at the rate of 18% per week.
We have to find the number of views in the fourth week.
On the first week the increase = 25 + 25× 18%
= 25 + 25 × 18/100
= 25 + 4.5
= 29.5
The second week increase = 29.5 + 29.5 × 18%
= 29.5 + 5.31
= 34.81
The third week increase = 34.81 + 34.81 × 18%
= 34.81 + 6.2658
= 41.0758
The fourth week increase = 41.0758 + 41.0758 × 18%
= 41.0758 + 7.393644
= 48.469444
Therefore the number of views in the four weeks is 48.
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you have $4000 with which to build a rectangular enclosure with fencing. the fencing material costs $30 per meter. you also want to have two partitions across the width of the enclosure, so that there will be three separated spaces in the enclosure. the material for the partitions costs $25 per meter. what is the maximum area you can achieve for the enclosure? (round your answer to the nearest whole number.) incorrect: your answer is incorrect. m2
The enclosure can be as large as 606 m2 in total.
Given that,
Let x be length of y be width of enclosure
fencing material cost $ 30 / m
Partition material cost $25/m
Total cost = (x+x+y+y)x 30+(y + y) x 25
c= 60(x+y) + 50y = 60 x + 110 y
4000 = 60 x + 110y
y = ( 400 - 6x / 11)
Now,Area of enclosure = x*y
A = x*(400 - 6x / 11)
A'(x)= 400-12x/11
for maximum area A'(x) = 0
400 - 12x/11 = 0,12x = 400,x = 100/3
A " ( x) = - 12/11 < 0 i.e., maximum
y = 400 - 6( 400/12 ) = 200/11 m
Maximum area = xy = 100/3 * 200/11 = 20000/33
=606.0606
A max = 606m²
Hence, the maximum area you can achieve for the enclosure is 606m²
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If y varies directly as x and y=8 when x=2 find when x=6
The equation is y = 4x. And the value of the function at x = 6 will be 24.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
If y varies directly to x. Then the relationship between them is written as,
y ∝ x
y = kx
When y = 8 and x = 2, then the value of the constant k is given as,
8 = k (2)
k = 8 / 2
k = 4
Then the equation is written as,
y = 4x
Then the value of the function at x = 6 will be given as,
y = 4 (6)
y = 24
The equation is y = 4x. And the value of the function at x = 6 will be 24.
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Find the slope of the line between the given points.
(2,5) and (3,8)
Answer: m (slope) = 3
Step-by-step explanation: Slope Solution
m=rise run=ΔyΔx
m=y2−y1x2−x1
m=8−53−2
m=31
m = 3
Point Slope Form
y−y1=m(x−x1)
y−5=3(x−2)
Slope Intercept Form
Find the Equation of the Line:
y=mx+b
by solving for y using the Point Slope Equation.
y−y1=m(x−x1)
y−5=3(x−2)
y−5=3x−(3×2)
y−5=3x−6
y=3x−6+5
y=3x−1
m=3
b=−1
Hope this helps :)
What is the mathematical name of the shape
Answer:
Triangular prism
Step-by-step explanation:
If you were to fold all the creases and glue it together you would get a tent shape which is a triangular prism
HELP ME PLEASE.
f(x) = √2x
g(x) = √50x
Find (f g)(x). Assume x ≥ 0.
A. (f.g)(x) = 10√
B. (f.g)(x) = √52x
C. (f.g)(x) = 10x
D. (f g)(x) = 50x
The representation of the composite function (fg)(x) is (fg)(x) = 10x
How to determine the possible value of the composite function?From the question, we have the following function definitions
f(x) = √2x
g(x) = √50x
The function to calculate is given as (fg)x
This can be calculated using
(fg)(x) = f(x) * g(x)
Substitute √2x for f(x) and √50x for g(x) in the above equation
So, we have
(fg)(x) = √2x * √50x
Evaluate the products
(fg)(x) = √100x²
Evaluate the exponents
(fg)(x) = 10x
Hence, the possible equation is (fg)(x) = 10x
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3. Is this graph a function?
This is a function.
This is not a function.
This cannot be determined from this graph.
Answer:
that is a quadratic function so yes it is a function
Step-by-step explanation:
it is a function becausr you can write an equation with it. Hope I could help!
HELP ASAP!!! THANK YOU
To balanced hanger, adding a circle to the left and a square to the right. To both sides, add two triangles. The option 1, 2, and 5 are correct.
What is balanced hanger?
Because each side of the hanger is evenly spaced from the center and has a same amount of overall weight, they are balanced against one another. During the warm-up, students come across two real hangers—one is balanced and the other is slanted—and they observe and consider what might have caused the hangers' appearance.Adding two circles to the left side and a square to the right would adjust the hanger's balance in accordance with the lesson's emphasis on maintaining the equation in balance.
adding a circle to the left and a square to the right. To both sides, add two triangles.
Hence the option 1, 2, and 5 are correct.
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which statement is not a step used when constructing an inscribed equilateral triangle ?
Use the compass to join the two circles together, this statement is not a step used when constructing an inscribed equilateral triangle.
What is known as a triangle?A polygon having three vertices and three sides are called a triangle. The triangle's angles are created by joining its three sides end to end at a single point.
The triangle's construction does not include claim D, which is the case. Use the compass to join the two circles together.
It is necessary to keep the compass at a width equal to the circle's radius and to position it at the point where the circle and radius connect while building an inscribed equilateral triangle.
Additionally, it's crucial to pivot an arc the radius's length away from the circle's point. It is not a part of the steps to join the two circles using the compass.
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N is an integer. Work out:
a. the smallest possible value of N if N >= 6.5
b. the largest possible of N if N < -3
c. the possible values of N if N >= -2 and N <2.
According to the integer N,
a) The smallest possible value of N is 6.5 if N >= 6.5
b) The largest possible value of N is -2 if N < - 3
c) The possible value of N is {-2, -1, 0, 1} if N >= -2 and N < 2.
Integer
Integer refers a collection of whole numbers and negative numbers.
Given,
Here we have the integer N.
And we need to find the following:
a. the smallest possible value of N if N >= 6.5
b. the largest possible of N if N < -3
c. the possible values of N if N >= -2 and N <2.
Part a). smallest possible value of N if N >= 6.5
Here the smallest number is 6.5 because other value are greater than this one.
Part b). the largest possible of N if N < -3
The largest possible number is -2, because the other values on N are less than -2.
Part c). the possible values of N if N >= -2 and N <2.
Here the possible values between these are {-2, -1, 0, 1}.
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Select the ordered pair that is NOT marked on the coordinate plane.
An ordered pair that is not marked on the coordinate plane of this graph is (8, 0).
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which represent the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.
What is an ordered pair?An ordered pair can be defined as a pair of two (2) data points that are commonly written in a fixed order within parentheses as (x, y), in order to represent the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.
By critically observing the given graph, we can reasonably and logically deduce that data point (8, 0) is the missing ordered pair on the coordinate plane.
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Here is a correlation, does it also represent causation? Explain you answer.
The number of additional calories consumed and the amount of weight gained.
Yes, there is causation between the two given variables, as the weight is related at some point with the amount of calories consumed.
What does correlation and causation mean?
For two variables x and y, we say that there is causation when, if we modify one of the variables, the other changes in response.
Correlation just means that the variables are related in some way (maybe both have a causation relationship with the same other variable)
So causation implies correlation.
Correlation does not imply causation.
In this case, we have the example:
x = The number of additional calories consumed
y = amount of weight gained.
Clearly, we have causation between x and y as larger is the value of x, larger will be the value of x.-
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There is no prior information about the proportion of Americans who support free
trade in 2019. If we want to estimate a 98% confidence interval for the true
proportion of Americans who support free trade in 2019 with a 0.21 margin of error,
how many randomly selected Americans must be surveyed? Answer: (Round up your
answer to nearest whole number, do not include any decimals)
31 Americans should be surveyed by Z mean.
What does critical value of Z mean?
The Z-score will show you how far a specific data point is from your sample's mean. This kind of critical value will inform you of the amount of standard deviations above or below the population mean for your sample.If the prior population proportion is unavailable then the formula to find the sample size is given by
n = 0.25[tex](\frac{z^{*} }{E} )^{2}[/tex]
where z* = Critical z-value
E = margin of error
Given, Confidence level = 98%
The critical z-value for 98% confidence interval is 2.326 ( BY z-table)
Margin of error : E= 0.21
n = 0.25 [tex](\frac{2.326}{0.21})^{2}[/tex]
n = 0.25 * ( 11 .07)²
n = 0.25 * 122.5449
n = 30.363225 ≈ 31
Hence, 31 Americans should be surveyed.
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Carol buys a house for £234,900
she pays a 10% deposit
work out the amount of deposit paid by carol
Answer:
£23, 490
Step-by-step explanation:
10% deposit by Carol of £234,900
10/100 *£234,900
0.1*£234,900=£23,490
After 3 new kids came to the park, a total of 18 kids played at the park. Write an equation that could be used to find x, the number of kids at the park before the 3 new kids came.
Please help, please
Answer:
x + 3 = 18
Step-by-step explanation:
original number of kids: x
additional kids: 3
new total number of kids: x + 3
actual total number of kids: 18
Equation: x + 3 = 18
a music store buys instruments and then sells them for more than they paid. during a off sale, the store offers a clarinet for . how much did the store pay for the clarinet?
The current price of the clarinet and the various discounts and markups illustrate that the amount the store paid was $90.
How to calculate the price?First find out the selling price of the clarinet:
= Discounted price / ( 1 - discount rate)
= 93.60 / ( 1 - 20%)
= $117
This selling price is 30% more than what the store paid so the price the store paid was:
= Selling price / ( 1 + rate of increase)
= 117 / ( 1 + 30%)
= $90
In conclusion, the amount the store paid was $90.
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Complete question
A music store buys instruments and then sells them for 30% more than they paid. During a 20% off sale, the store offers a clarinet for $93.60.
How much did the store pay for the clarinet?
express -58 in the form of bi where b is a real number. TIME SENSITIVE!!
The number -58 is a real number and it cannot be represented as a complex number
How to determine the complex representation of the number?From the question, we have the following expression that can be used in our computation:
Expression = -58
The given expression above is a number
And also, it is a negative number
Negative numbers of this form are real numbers
This means that the such numbers cannot be represented as a complex number
Hence, the number -58 does not have a complex equivalent
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Plot the locus points for x = y
The the locus of the equation y = x is a straight line. The slope of the linear function → y = x is [m] = 1 and the [y] intercept is at [c] = 0.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
Given is the function -
x = y
We have the function -
y = x
Now, we can define locus as -
A curve or other figure formed by all the points satisfying a particular equation of the relation between coordinates, or by a point, line, or surface moving according to mathematically defined conditions.
This equation -
y = x
is a straight line.
Refer to the graph attached.
The slope of the line is [m] = 1
The [y] intercept is at [c] = 0
Therefore, the the locus of the equation y = x is a straight line. The slope of the linear function → y = x is [m] = 1 and the [y] intercept is at [c] = 0.
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How can 33 over 9 be expressed as a decimal?
Answer:
3.6
................................
please help asap will give brainliest
1. The angles measures are larger than the original angle measures is a false statement.
2. If two sides parallel in the original figure, then those sides are parallel in the final figure is true statement.
3. The final angle measure are the same as the original angle measure is false statement.
4. The original figure and the final figure may not be congruent is true statement.
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monique and tara each make an ice-cream sundae. monique gets 3 scoops of cherry ice-cream and 1 scoop of mint chocolate chunk ice-cream for a total of 84g of fat. tara has 1 scoop of cherry and 3 scoops of mint chocolate chunk for a total of 60g of fat. how many grams of fat does 1 scoop of each type of ice cream have?
The amount of fat in Cherry ice-cream is 24 grams.
The amount of fat in the Mint Chocolate Chunk ice-cream is 12 grams.
Writing data into equations using Algebra,3C + M = 84...(1)C + 3M = 60...(2)
Multiplying equation (2) by 3 and then subtracting equation (1) from
the result gives, 3 * (C +3M) = 3 × 603C + 9M = 180...(3)(3C + 9M = 180) - (3C + M = 84) = 8M =96M= 12
The amount of fat in the Mint Chocolate Chunk ice-cream, M = 12
grams C + 12*3 = 60C = 60-36 = 24
The amount of fat in Cherry ice-cream C = 24 grams As a result, Cherry ice cream contains 24 grams of fat and Mint Chocolate Chunk ice cream contains 12 grams of fat.
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The map above is being reduced by a scale factor of 1/9 and printed for the subway
station. How many square inches will the new map take up?
O 315 square inches
O 72 square inches
24 square inches
O 35 square inches
Answer:
35 square inches
Step-by-step explanation:
21x15=315
315/9=35
Therefore, the answer is 35 square inches
It cost Hassan $5.31 to send 59 text messages. How much does each text cost to send?
Each text will cost Hassan $0.09
What is rate ?A rate is a special ratio in which the two terms are in different units. It can also be defined as the amount of money that is charged for goods or services. For example, if a 12 malt can of costs 69¢, the rate is 69¢ for 12 malt. Then 1 malt will cost ¢69/12.
Similarly $5.31 is the cost of 59 text messages
Therefore a text message will cost $5.31/12=$0.09
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What is the solution to this inequality? x - 1 . 5 > 2 . 5 Question 1 options: x < 4 x < 1 x > 1 x > 4
The solution to the inequality is X > 4
InequalityInequality is a set of mathematical expression which the individual side is not equal to other side
To solve for x in the inequality x - 1 . 5 > 2, we followed the step;
Step 1: Add 1.5 to both sides
x - 1.5 + 1.5 > 2 . 5 + 1.5
X > 4
Therefore, the solution to the inequality is X > 4
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A line passes through the point (-8,-3) and has a slope of -3/4
The equation of the line that passes through the point (-8,-3) and has a slope of -3/4 is y = -3/4x - 9
How to determine the equation of the line?From the question, we have the following parameters that can be used in our computation:
Slope, m = -3/4
Points, (x₁, y₁) = (-8, -3)
A linear equation can be represented as
y = slope * x + y-intercept i.e. y = m(x - x₁) + y₁
Substitute the known values in the above equation
So, we have the following equation
y = -3/4(x + 8) - 3
Open the brackets
So, we have the following equation
y = -3/4x - 6 - 3
Evaluate the like terms in the above equation
So, we have the following representation
y = -3/4x - 9
The above equation cannot be further simplified
Hence. the linear equation is y = -3/4x - 9
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What is the image of the point (-7,9) after a rotation of 90 counterclockwise?
The point (9,7) is the image of the point after a rotation of 90° counterclockwise.
Given that,
The points (-7,9).
We have to find the image of the point after a rotation of 90° counterclockwise.
Because the hands of a clock move in a clockwise manner, we can rotate a point either in that direction or in the opposite direction when we rotate it. In mathematics, clockwise is defined as a negative rotation and counterclockwise as a positive rotation.
Consider the point on the coordinate plane (x,y). You may always swap the x- and y-coordinates and then multiply the new x-coordinate by -1 to rotate this point by 90 degrees around the origin in a clockwise orientation.
(x,y)→(y,-x)
(-7,9)→(9,7)
Therefore, The point (9,7) is the image of the point after a rotation of 90° counterclockwise.
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the ratio of drummers to guitar players who tried out for a band is 10:45 .
How many times the number of drummers is the number of guitar players?
Answer:
4.5
Step-by-step explanation:
45/10=4.5
What is the slope of the line that passes through the points (1, -9) and (4, -7)? Write your answer in the simplest form.
The slope of the line from the given points will be equal to 3/2 in the simplest form.
What is slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the given points in the question,
(1, -9) and (4, -7).
x1 = 1 and x2 = 4
y1 = -9 and y2= -7
Slope = (x2- x1)/(y2- y1)
= (4 - 1)/(-7 - (-9))
Slope = 3/2
Therefore, the slope of the line will be 3/2.
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