A rectangle is constructed on a semicircle so that the length equals the diameter. The width of the rectangle is approximately 10.65 inches.
What are the approximate dimensions of the rectangle.?Generally, Let the width of the rectangle be x. Then the length of the rectangle is 3x.
The diameter of the semicircle is also the length of the rectangle, so it is 3x.
The area of the rectangle is x*(3x) = 3x^2. The area of the semicircle is (1/2)πr^2, where r is the radius of the semicircle. Since the diameter of the semicircle is 3x, the radius is (3x)/2. The area of the semicircle is (1/2)π((3x)/2)^2 = (9/8)πx^2.
The total area of the figure is the sum of the area of the rectangle and the area of the semicircle. We can set up the equation:
3x^2 + (9/8)πx^2 = 750
(21/8)πx^2 = 750
x^2 = 750/(21/8)*π
x = √(750/(21/8)*π)
To find the approximate dimensions of the rectangle, we can use the fact that pi is approximately 3.14. This gives us:
x = √(750/(21/8)*3.14)
= √(750/6.71)
= √(112.64)
= approximately 10.65 inches.
The width of the rectangle is approximately 10.65 inches. The length of the rectangle is 3 times the width, so it is approximately 31.95 inches.
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The ratio of the angles in a triangle is 3:5:8 what is the measure of the largest angle
The measure of the largest angle is 96 degrees.
What is a ratio?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3
The measure of the largest angle in the triangle is 96 degrees.
To find the measure of the largest angle, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.
Let's call the measures of the three angles x, y, and z, where x is the measure of the smallest angle, y is the measure of the middle angle, and z is the measure of the largest angle.
We are given that the ratio of the angles is 3:5:8, which means that x:y:z = 3:5:8.
We can set up the following equation to represent the sum of the measures of the angles in the triangle:
x + y + z = 180
We can also set up the following equation to represent the ratio of the angles:
x : y : z = 3 : 5 : 8
We can use these two equations to find the measure of the largest angle.
First, let's multiply the second equation by 3, 5, and 8 to get:
3x = 15y = 24z
Then, we can substitute these equations into the first equation to get:
15y + 24z = 180
Solving for z, we get:
z = 180 / (15+24) = 180 / 39 = 96
Therefore, the measure of the largest angle is 96 degrees.
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Help me please unit plsss
The possible elevation of Salton city will be;
⇒ x < - 2 feet
Where, x is the elevation of Salton city.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
New Orleans is 2 feet below sea level.
And, Salton City has an elevation that is lower than New Orleans.
Now,
New Orleans is 2 feet below sea level.
And, Salton City has an elevation that is lower than New Orleans.
Let the elevation of Salton city = x feet
Thus, We get;
The possible elevation of Salton city will be;
⇒ x < - 2 feet
Where, x is the elevation of Salton city.
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what happens if there are 36 members and you use more then 6 members per row
Answer:
6
Step-by-step explanation:
Joe is responsible for reserving hotel rooms for a company trip. His company changes plans and increases how many people are going on the trip, so they need at least 505050 total rooms. Joe had already reserved and paid for 161616 rooms, so he needs to reserve additional rooms. He can only reserve rooms in blocks, and each block contains 888 rooms and costs \$900$900dollar sign, 900. Let bbb represent the number of additional blocks that joe reserves. 1) which inequality describes this scenario? choose 1 answer:.
The inequality expression is :16 + 8B ≥ 50
Least amount that could be spent = $4500
What is inequality expression?
An algebraic inequality is a mathematical statement that uses the inequality sign to relate an expression to a value, a variable, or another expression. "Greater than" and "greater than or equal to" are two verbs that can be translated as inequalities.
need at least 50 total rooms.
Room already booked = 16
Number of Blocks booked = B
Each Block = 8
8B - Addition room Booked
Total room booked = 8B + 16
Total room booked ≥ need at least 50 total rooms
8B + 16 ≥ 50
=> 16 + 8B ≥ 50 , option B is correct
=> 8B ≥ 34
=> 4B ≥ 17
minimum B = 5
Cost = 900 * 5 = 4500 $
least amount of additional money Joe can spend to get the rooms they need in dollars = 4500
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Part A
MANUFACTURING A fashion company spends $10 to produce a pair of jeans and $2 to produce a shirt. During a
typical month, they spend $3500 on the production of jeans and shirts. During months in autumn, though, they
double the pairs of jeans produced and spend a total of $6000. How many pairs of jeans and t-shirts does the
company make during a typical month?
Letj= number of pairs of jeans and k = number of shirts.
Part A
Write the system of equations.
Select Choice vj+ Select Choice k= 3500
Select Choice v + Select Choice
k=6000
Answer: When you solve the equations and work them out, you get the answer of $4000.
Can someone help me with this
Answer:
y=-3/1x-2
y=9/3x+8
Step-by-step explanation:
Slope is -3/1 using rise over run, it's just negative because the graph is slanted down. The slope is 9/3 using rise over run. Then the y-intercepts are -2 and 8.
-Hope this helped & Happy Holidays!
1. Which expression is equivalent to 10x – 5 + 8x - 7?
Answer: 18x-12
Step-by-step explanation:
Add 10x +8x (because they both have x at the end so its fine to add them
then do -5-7= -12
2X-3Y=4
X+Y=6
please explain each step
Answer:
Step-by-step explanation:
Rewrite equations: x+y=6;2x−3y=4
Solve x+y=6 for x: x+y+−y=6+−y (Add -y to both sides)
x=−y+6
Substitute −y+6 for x in2x−3y=4: 2x−3y=4
2(−y+6)−3y=4
−5y+12=4 (Simplify both sides of the equation)
−5y+12+−12=4+−12 (Add -12 to both sides)
−5y=−8
−5y/−5=−8/−5 (Divide both sides by -5)
y=8/5
Substitute 8/5 for y in x=−y+6:
x=−y+6
x=−8/5 +6
x=22/5 (Simplify both sides of the equation)
Answer: x=22/5 and y=8/5
-35+12=
Could someone help me pls
Answer: -23
Step-by-step explanation:
When you're adding to a negative the negative number decreases, so if you're adding 12 from negative 35, you're taking away 12 negative numbers, hence why the answer is -23
hope that helped :)
Jasmine made fancy red costume decorations for each of the dancers in her year-end dance performance. She used 1/4 of a meter of ribbon for each decoration, which she got by cutting 1/2 of a meter of ribbon into equal pieces. How many decorations did Jasmine make?
There are 2 decorations that Jasmine makes.
What are word problems?
A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
You can tackle any word problem by following these five steps:
Read through the problem carefully, and figure out what it's about.Represent unknown numbers with variables.Translate the rest of the problem into a mathematical expression.Solve the problem.Check your work.Since we have given that
Length of a meter of ribbon used = 1/4
[tex]\frac{1}{4} = \frac{1}{4}.100 = 25[/tex]
Length of a meter cut into equal pieces = 1/2
[tex]\frac{1}{2} =\frac{1}{2}.100= 50[/tex]
So, Number of decorations that Eli make is given by
Length of total ribbon / Length of ribbon used
= 50 / 25
= 2
Hence, there are 2 decorations that Jasmine makes.
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Help please math question show answer of how you solved solve ASAP
The solution of the system of equations is (x, y) = (9/2, -7/10).
What is the system of linear equations?
A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
To solve a system of equations, we can use any of the following methods:
Substitution method,
Elimination method,
Matrix method.
Let's use the substitution method to solve the given system of equations.
We can solve the first equation for z:
z = 7 - 3x - 2y
Substituting this expression into the third equation, we get:
3x + 2y + 3(7 - 3x - 2y) = 1
This simplifies to:
-5x - 3y + 21 = 1
Adding 5x and 3y to both sides, we get:
21 = 5x + 3y + 1
Subtracting 1 from both sides, we get:
20 = 5x + 3y
Dividing both sides by 5, we get:
4 = x + 3/5 y
Substituting this expression into the first equation, we get:
3(x + 3/5 y) + 2y + 7 = 7
This simplifies to:
2y = -7/5
Dividing both sides by 2, we get:
y = -7/10
Substituting this value into the expression for x, we get:
x = 4 - 3/5(-7/10)
This simplifies to:
x = 4 + 21/10
x = 9/2
Hence, the solution of the system of equations is (x, y) = (9/2, -7/10).
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Find the equation of the line in tandard form that pae through the point (1, -3) and (-2, -1)
The equation of line in standard form that pass through the point (1, -3) and (-2, -1) is (-2x/3)-y=7/3 where -2/3 is x-intercept and -1 is the y-intercept.
What does the straight line equation mean?A straight line's equation is given by y=mx+c, where c is the height at which the line intersects the y-axis (often referred to as the y-intercept) and m is the gradient.
Why is there an equation of a line?The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y.
we are given with;
x1=1, y1=-3
x2=-2, y2=-1
equation of line in standard form:
Ax+By=C
so using formula:
(y−y1)=(y2−y1)(x−x1)/(x2−x1)
(y−(-3))=((-1)−(-3))(x-1)/(-2−1)
(y+3)=(2)(x−1)/(-3)
(y+3)=(2x−2)/(-3)
y+3=(-2x/3)+(2/3)
y=(-2x/3)+(2/3)-3
y=(-2x+2-9)/3
y=(-2x-7)/3
(2x/3)+y=-7/3
rearranging;
(-2x/3)-y=7/3
This is our required answer.
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Review the following derivation of the tangent double angle identity. The steps are not listed in the correct order
After reviewing the derivative of the tangent double , the correct order of the derivative is (a) .
In the question ,
the derivative of the double tangent is given ,
we have to select the correct order of the derivative .
the function is tan(2x) .
Step 4: tan(2x) = Sin(2x)/cos(2x)
Step 3 :
expanding sin(2x) and cos(2x) using identity ,
we get ,
= 2sinxcosx/(cos²x - sin²x)
Step 5 :
dividing the numerator and denominator by cos²x .
= [2sinxcosx/cos²x]/[cos²x/cos²x - sin²x/cos²x]
Step 1 : simplifying further,
we get ,
= [2sinx/cosx]/[1 - sin²x/cos²x]
Step 2 : writing sinx/cosx = tanx
we get ,
tan2x = 2tanx/(1 - tanx)
Therefore , the correct order for the given derivative is (a) 4, 3, 5, 1, 2 .
The given question is incomplete , the complete question is
Review the following derivation of the tangent double angle identity. The steps are not listed in the correct order
(a) 4, 3, 5, 1, 2
(b) 4, 5, 3, 1, 2
(c) 3, 4, 5, 1, 2
(d) 3, 4, 1, 5, 2
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(04.04 LC)
The functions f(x) = −2x + 30 and g(x) = 3x + 10 are shown in the graph.
graph of f of x equals negative 2 times x plus 30 and g of x equals 3 times x plus 10
Determine the approximate ordered pair for f(x) = g(x).
a
(4, 22)
b
(22, 4)
c
(4, 18)
d
(18, 4)
The approximate ordered pair for f(x) = g(x) is given as; (4, 22) from the graph. Option A
At what points are the solutions equal?We know that there are two equations that can be shown from the set of equations that have been written here and the set of equations that we have are;
f(x) = −2x + 30
g(x) = 3x + 10
We are now trying to see the points at which the equation can be said to be equal. This refers to the point where f(x) = g(x). How can we be able to obtain this point? If we are to get this point then we must go back and look at the graph very well.
As we are looking at the graph very well we should fix our eyes on any point where the line of two functions can be seen to intersect. Once that happens, we can say that we have reached the point where the two functions can be said to be equal. This point is read from the graph as (4, 22)
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Someone please help me
Answer: You are correct
Step-by-step explanation: You are correct with both answers because 9x + 7 and 7 + 9x will equal the same thing. Here's an example
X=3
9(3) + 7
27+ 7
34
7 + 9(3)
7+27
34
34=34
It only equals 34, no matter the order. So, it has one solution.
I hope this helps!
Answer:
Equivalent
Step-by-step explanation:
The expressions 9x+7 and 7+9x are equivalent .The equation has infinite many solutions
Workers are loading boxes onto a truck. So far, they have loaded 48 boxes onto the truck. According to their inventory, they still need to load 96% of the boxes on the truck. What is the total number of boxes the workers are loading on the truck?
The total number of boxes of inventory which is loading on the truck by the workers are 1,200 boxes.
What is percentage of a number?
Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.
Workers are loading boxes onto a truck . So far, they have loaded 48 boxes onto the truck.
According to their inventory, they still need to load 96% of boxes on the truck. There must be 100% box at the start of the loading. Thus, the percentage of boxes they have load,
p=100-96 = 4%
Thus the percentage of boxes they have load in the truck is 4%. This is equal to the 48 boxes they have loaded.
Let suppose there is x number of total boxes. Thus the 4 percent of x will be equal to the 48.
(4/100)x=48
x = 4800/4 = 1200
Thus, the total number of boxes of inventory which is loading on the truck by the workers are 1,200 boxes.
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I NEED THIS ASAP!!
f(x)=x^2. what is g(x)?
Answer:
A
Step-by-step explanation:
4. Jim paid £70 for a bike.
Then pays £10 per month.
a) Write down an expression
for the total amount paid after
m months.
b) Factorise the expression.
Step-by-step explanation:
Jim paid £70 for a bike. Then pays £10 per month.
a) Write down an expression for the total amount paid after m months.
cost = 10m + 70
_______________________________________
b) Factor the expression.
10m + 70
common factor is 10 so:
10(m + 7)
Answer:
Step-by-step explanation:
100
What is the slope of a line perpendicular to the line whose equation is 6x+y=-5.Fully simplify your answer.
Answer:
The slope is 1/6.
Step-by-step explanation:
The slope of the given equation is -6. Perpendicular lines have negative reciprocal slopes.
(35 POINTS!!)
The height of a hot air balloon over time is given in the following table.
The height of a blimp over time is given by y = 250x, where y represents the height in feet and a represents the time in minutes.
How fast is the hot air balloon rising? How fast is the blimp rising?
Hot air balloon: (?) feet per minute.
Blimp: (?) feet per minute.
The hot air balloon is rising at 600 feet per minute and the blimp are rising at 250 feet per minute
How to determine how fast the hot air balloon and the blimp are rising?How fast is the hot air balloon rising?
From the question, we have the following parameters that can be used in our computation:
The height of a balloon over time is represented by the graph
On the graph, we have the following points
(x, y) = (0, 0) and (2, 1200)
The rate is calculated as
Rate = (1200 - 0)/(2 - 0)
Evaluate
Rate = 600
Hence, the rate of rising is 600 feet per minute
How fast is the blimp rising?
From the question, we have the following parameters that can be used in our computation:
The height of a blimp over time is given by y = 250x
The above equation is a linear equation
A linear equation can be represented as
y = mx + c
Where
slope = m
This means that the slope of y = 250x is 250
The slope represents the rate
Hence, the rate of rising is 250 feet per minute
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Need help with this question
The value of the angle m∠BDC is 105°.
What is third angle theorem?If the other two sets are both congruent, then the third angles are equal.The third pair of angles must be congruent if two angles in one triangle are congruent with two angles in another triangle. The Third Angle Theorem refers to this.The Triangle Sum Theorem can be thought of as an extension of the Third Angle Theorem. The Triangle Sum Theorem states that once two angles in a triangle are known, you automatically know the third. This indicates that if you have two triangles with two pairs of congruent angles between them, you will receive the same result both times when you apply the Triangle Sum Theorem to each triangle to determine the third angle. The third pair of angles must therefore likewise be similar.Let separate the triangles and find missing angle in triangle with given angles.
CAD = 45°
CDA = 30°
Then, CAD+CDA+ACD = 180°
45°+30°+ACD=180°
ACD=180°-75°
=105°
by applying third angle theorem,
∠CAD=∠DBC=45°
∠ADC=∠BCD=30°
Then, ∠DBC+∠BCD+∠BDC=180°
45°+30°+BCD=180°
BCD=180°-75°
=105°
Hence, The value of the angle m∠BDC is 105°.
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Which statement is true?
O A.
B.
C.
D.
the other acute angle.
In any right triangle, the sine of one acute angle is equal to the cosine of
In any right triangle, the sine of one acute angle is equal to the sine of its complementary angle.
In any right triangle, the cosine of one acute angle is equal to the cosine of
angle.
its complementary
and the cosine of the other acute angle is 1.
In any right triangle, the sum of the sine of one acute angle
Answer:
In any right triangle, the sine of one acute angle is equal to the cosine of the other angle.
Step-by-step explanation:
Emma grew 6 plants with 3 seed packets. How many seed packets does Emma need to have a total of 16 plants in her backyard? Solve using unit rates.
8 seed packets
Step-by-step explanation:First, we need to figure out how many plants Emma can grow with each seed packet. To do this, divide 6 plants (the number of plants Emma currently has) by 3 seed packets (the number Emma had to begin with). This will give us a unit rate of "2 plants per seed packet".
Now that we know the unit rate, we can use it to figure out how many seed packets Emma needs to have 16 plants in her backyard. Divide 16 plants (the number of plants Emma wants to have) by 2 plants per seed packet (the unit rate). This will give us 8 seed packets.
Therefore, Emma needs 8 seed packets to have a total of 16 plants in her backyard.
If you have any additional questions or need further assistance, please let me know.
The Yellow Taxicab Co. charges a $2.75 flat rate and $.65 for each additional mile. Emma has no more than $14 to spend on a ride. Carefully set up an inequality, how many miles can Emma ride without exceeding her spending limit?
The maximum miles that Emma can ride without exceeding her spending limit is 17.3 miles
What are Linear Inequalities?
A linear inequality is a mathematical inequality that incorporates a linear function. A linear inequality contains one of the inequality symbols. It depicts the data which is not equal in graph form.
The linear expression formed using the given description will be 2.75 + 0.65x
where x is the total number of miles
and the linear inequality formed will be 2.75 + 0.65x < 14
Refer to the graph below
So, the maximum miles that Emma can ride without exceeding her spending limit is 17.3 miles
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There were 35 bunche of roe and tulip. Each bunch had 12 of the ame flower. There 7 more bunche of tulip than roe. How many tulip were there?
As per the unitary method, the number of tulip were 21.
Unitary method:
In algebra, unitary method defines how to find the value of a unit from the value of a multiple and the value of a multiple from the value of a unit.
Given,
Here we have There were 35 bunches of rose and tulip. Each bunch had 12 of the roe flower. There 7 more bunches of tulip than rose.
Now we need to find how many tulip were there.
Let number of bunches of roses be x.
And then the number of bunches of tulips will be x + 7
The total number of bunches of flowers = 35
So, it can be written as,
=> x + x + 7 = 35
When we simplify this one then we get,
=> 2x + 7 = 35
Now, we have to subtracting both sides by 7
=> 2x = 28
Then dividing both sides by 2
=> x = 14
So, the number of bunches of roses = 14
Then the number of bunches of tulips = 14 + 7 = 21
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Sinx+1 =cos x
Hint: square both sides
Answer:
1 – cos²x = Sin²x
Step-by-step explanation:
Sinx + 1 = cos x
by squaring both sides
(Sinx + 1)² = (cos x )²
Sin²x + 1 = cos²x
1 – cos²x = Sin²x
i hope this helped
What is an angle this is supplementary to CFE
I think you're answer is right angle
The line L has equation 3x + 4y -12 =0
The gradient of line L is: ?
The line crosses the y axis at the point P with coordinates: ?
The line crosses the x axis at the point Q with coordinates: ?
The triangle formed by the line and the x and y axes has area =
square units
For non-integer solutions, express the answer as a proper or an improper fraction using the notation a/b
Answer:
1 -3/4
2. P(00,3)
3. Q(4,0)
4. 6
Step-by-step explanation:
1. 3x+4y=12
4y= -3x+12
y= -(3/4)x+ 3 , so gradient = -3/4
2. Y intercept is P (0,3)
3. X intercept is Q(4,0)
4. Area = 3×4÷2=6
Evelyn need to add 3 1/3 cup of ugar to her cookie dough. She only ha a 2/3-cup meaure. How many coop of ugar doe Evelyn need to add?
The required fraction cup of sugar do Evelyn need to add is 8/3.
How to deal with fraction?Multiply the numerators and denominators independently to track down the item. At the point when you need to duplicate divisions, increase the 2 numerators together first and compose it on top. Then increase the denominators together and compose it on the lower part of the portion. Improve on your response on the off chance that you would be able so it is in the least terms.
According to question:As question says Evelyn need 3(1/3) cup og sugar
To find many cup of sugar do Evelyn need to add.
Let the required sugar be x
Then,
2/3 + x = 3(1/3)
x = 10/3 - 2/3
x = 8/3 cup of sugar need.
Thus, required cup of sugar is 8/3.
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Log base 28 of 7 plus log base 28 of 4
Answer:
log base 28 of (7x4)
log base 28 of (28)
which equals 1