By evaluating the function in j = 1, we conclude that each bottle costs 80 cents.
We know that the total cost in dollars can be represented by the linear equation:
C(j) = 0.8*j
Where C is the cost, and j is the number of juice bottles bought.
Then to get the cost of each bottle, we can evaluate the function in 1, which means buying only one.
C(1) = 0.8*1 = 0.8
So each bottle costs $0.80 (or 80 cents).
In mathematics, a function is a relationship between a set of inputs and a set of possible outputs, such that each input is associated with a unique output. Functions are represented by mathematical expressions or equations that specify how the input values are transformed into output values. For example, the function f(x) = x^2 takes an input value x and produces an output value equal to x squared.
Functions play a crucial role in many areas of mathematics, science, and engineering. They can be used to model complex systems, analyze data, and solve problems. Functions are also used in computer programming, where they are used to encapsulate a specific set of operations that can be reused throughout a program.
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A grain silo has a cylindrical shape. Its diameter is 17 ft , and its height is 42 ft . What is the volume of the silo? will give brainliest
Answer:
Below
Step-by-step explanation:
Volume of a cylinder is given by the formula
V = pir^2 h SUbstitute in the values given for r , h
V = pi * (17/2)^2 * 42 = 9533 ft^3 = 353 yd^3
1) A 20 lb. BAG OF GRASS SEED WILL COVER AN AREA OF 10,000 ft2 . HOW MANY POUNDS WILL YOU NEED TO COVER AN AREA OF 140,000 ft2 . HOW MANY WHOLE BAGS OF SEED WILL YOU NEED TO BUY? WRITE THE EQUATION FOR A PROPORTION AND SOLVE IT.
2) SOLVE THE FORMULA FOR T2. ???????????????? ???????? = ???????????????? ????????
3) THE GILBERTS PURCHASED A CAR. IF THE TOTAL COST, INCLUDING A 5% SALES TAX, WAS $14,512, FIND THE COST OF THE CAR BEFORE TAX.
4) JIM MEYERS BOUGHT A NEW LAPTOP COMPUTER AT A 15% OFF SALE. IF THE SALE PRICE WAS $722.50, WHAT WAS THE LIST PRICE OF THE COMPUTER?
5) FIND THE x AND y INTERCEPTS FOR THE EQUATION 3x + 6y = 9.
1) 140
2) T2 = ?
3) $13,786.40
4) $835.88
5) x = 3, y=(0, 1.5)
1) To find the number of pounds of grass seed needed to cover an area of 140,000 ft2, you need to write a proportion and solve it. Set up the proportion using the given information:
20 lb/10,000 ft2 = x lb/140,000 ft2
To solve for x, multiply both sides of the equation by 140000:
20 lb * 140000/10,000 ft2 = x lb
x = 2800 lb
You will need 2800 lbs of grass seed to cover an area of 140,000 ft2. To find out how many whole bags of seed you will need to buy, divide the total number of pounds by the number of pounds in a bag, which is 20 lbs. You will need to buy 140 whole bags of seed.
2) To solve for T2 in the equation ???????????????? ???????? = ???????????????? ????????, divide both sides of the equation by ???????????????? :
T2 = ???????????????? ????????/????????????????
3) To find the cost of the car before the sales tax, subtract the 5% sales tax from the total cost. The formula is:
Cost before tax = Total Cost - (Total Cost * Sales Tax %)
Cost before tax = $14,512 - ($14,512 * 0.05) = $13,786.40
4) To find the list price of the laptop computer, add the 15% off sale to the sale price. The formula is:
List Price = Sale Price + (Sale Price * Discount %)
List Price = $722.50 + ($722.50 * 0.15) = $835.88
5) The x and y intercepts for the equation 3x + 6y = 9 can be found by setting x or y equal to 0 and solving for the other. To find the x intercept, set y = 0:
3x + 6(0) = 9
3x = 9
x = 3
The x intercept is (3, 0). To find the y intercept, set x = 0:
3(0) + 6y = 9
6y = 9
y = 1.5
The y intercept is (0, 1.5).
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5−8=State the property of real numbers being used. 5.3+2x=2x+36.(a+b)(a−b)=(a−b)(a+b)7.A(x+y)=Ax+Ay8.(A+1)(x+y)=(A+1)x+(A+1)y
The properties of real numbers being used in the equations you provided are as follows:
1. 5−8: This equation does not use any specific property of real numbers. It is simply subtraction of two real numbers.
2. 5.3+2x=2x+36: This equation uses the Commutative Property of Addition, which states that the order in which real numbers are added does not affect the sum. This is why 5.3+2x is equal to 2x+5.3.
3. (a+b)(a−b)=(a−b)(a+b): This equation also uses the Commutative Property of Multiplication, which states that the order in which real numbers are multiplied does not affect the product. This is why (a+b)(a−b) is equal to (a−b)(a+b).
4. 7.A(x+y)=Ax+Ay: This equation uses the Distributive Property, which states that multiplying a real number by a sum is the same as multiplying each term in the sum by the real number and then adding the products. This is why A(x+y) is equal to Ax+Ay.
5. (A+1)(x+y)=(A+1)x+(A+1)y: This equation also uses the Distributive Property, as explained in the previous example.
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What are the Big Ideas or Focal Points in the mathematics
curriculum in grades 4?
The Big Ideas or Focal Points in the mathematics curriculum in grades 4 are as follows:
Using data to analyze, interpret and represent relationshipsUnderstanding and applying relationships between operationsComputing and communicating solutions with understandingReasoning mathematically with understandingLearn more about focal points
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solve the equations in problems 31−46 by completing the square. 31. x^2-2x-8 = 0
32. x^2-4x-9 = 0
33. x^2+6x4 = 0
34. x^2+x-4 = 0
35. x^2-3x+1 =0
The solutions for the given equations are:
31. x = 4 or x = -2
32. x = 2+√13 or x = 2-√13
33. x = -3+√5 or x = -3-√5
34. x = -0.5+√4.25 or x = -0.5-√4.25
35. x = 1.5+√1.25 or x = 1.5-√1.25
To solve the equations by completing the square, we will use the following steps:
Step 1: Move the constant term to the right side of the equation.
Step 2: Take half of the coefficient of the x term and square it.
Step 3: Add this value to both sides of the equation.
Step 4: Factor the left side of the equation.
Step 5: Take the square root of both sides of the equation.
Step 6: Solve for x.
Let's apply these steps to the given equations:
31. x^2-2x-8 = 0
Step 1: x^2-2x = 8
Step 2: (-2/2)^2 = 1
Step 3: x^2-2x+1 = 9
Step 4: (x-1)^2 = 9
Step 5: x-1 = ±3
Step 6: x = 4 or x = -2
32. x^2-4x-9 = 0
Step 1: x^2-4x = 9
Step 2: (-4/2)^2 = 4
Step 3: x^2-4x+4 = 13
Step 4: (x-2)^2 = 13
Step 5: x-2 = ±√13
Step 6: x = 2+√13 or x = 2-√13
33. x^2+6x+4 = 0
Step 1: x^2+6x = -4
Step 2: (6/2)^2 = 9
Step 3: x^2+6x+9 = 5
Step 4: (x+3)^2 = 5
Step 5: x+3 = ±√5
Step 6: x = -3+√5 or x = -3-√5
34. x^2+x-4 = 0
Step 1: x^2+x = 4
Step 2: (1/2)^2 = 0.25
Step 3: x^2+x+0.25 = 4.25
Step 4: (x+0.5)^2 = 4.25
Step 5: x+0.5 = ±√4.25
Step 6: x = -0.5+√4.25 or x = -0.5-√4.25
35. x^2-3x+1 = 0
Step 1: x^2-3x = -1
Step 2: (-3/2)^2 = 2.25
Step 3: x^2-3x+2.25 = 1.25
Step 4: (x-1.5)^2 = 1.25
Step 5: x-1.5 = ±√1.25
Step 6: x = 1.5+√1.25 or x = 1.5-√1.25
Therefore, the solutions for the given equations are:
31. x = 4 or x = -2
32. x = 2+√13 or x = 2-√13
33. x = -3+√5 or x = -3-√5
34. x = -0.5+√4.25 or x = -0.5-√4.25
35. x = 1.5+√1.25 or x = 1.5-√1.25
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What does point J represent on the graph? Responses The cost of 2 ounces of orange juice is $3.00 . The cost of 2 ounces of orange juice is $ $ 3.00 . The cost of 2 ounces of orange juice is $6.00 . The cost of 2 ounces of orange juice is $ $ 6.00 . The cost of 6 ounces of orange juice is $2.00 . The cost of 6 ounces of orange juice is $ $ 2.00 . The cost of 6 ounces of orange juice is $4.00 .
The meaning of point J(2,6) on the graph is given as follows:
The cost of 2 ounces of orange juice is $6.00.
How to define the ordered pair?The general format of an ordered pair is given by the rule presented as follows:
(x,y).
In which:
x is the x-coordinate, representing the input variable.y is the y-coordinate, representing the output variable.The input and output variables for this problem are given as follows:
Input variable: number of ounces of orange juice.Output variable: Total cost.Hence the point (2,6) represents that the cost of 2 ounces of orange juice is $6.00, meaning that the second option is the correct option in the context of this problem.
Missing InformationThe coordinates of the point are (2,6).
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work out 4/5 0f 30 this is long
Answer:
[tex]\frac{4}{50fx^{30} } :[/tex][tex]\frac{2}{25f^{30} }[/tex]
Step-by-step explanation:
Factor thenumber:4=2\2
[tex]=\frac{2 . 2}{50fx^{30} }[/tex]
Factor the number 50= 2 x 25
[tex]=\frac{2.2}{2.25f^{30} }[/tex]
Cancel the common factor:2
[tex]=\frac{2}{25f^{30} }[/tex]
SYSTEMS OF EQUATIONS AND MATRICES Linear programming Find the maximum value of the function z=8x+3y subject to the following constraints y>=0 x>=4 y<=10 5x+2y<=60
The maximum value of the function z=8x+3y subject to the constraints is 94
The maximum value of the function z=8x+3y subject to the constraints y>=0, x>=4, y<=10, and 5x+2y<=60 can be found using the method of linear programming.
Graph the constraints on a coordinate plane. The constraints y>=0 and x>=4 are vertical and horizontal lines, respectively.
The constraint y<=10 is a horizontal line at y=10, and the constraint 5x+2y<=60 can be rewritten as y<=-5/2x+30 and graphed as a line with a slope of -5/2 and a y-intercept of 30.
Identify the feasible region, which is the area of the graph that satisfies all of the constraints.
In this case, the feasible region is the quadrilateral bounded by the lines x=4, y=0, y=10, and y=-5/2x+30.
Find the vertices of the feasible region. The vertices are the points (4,0), (4,10), (8,10), and (10,5).
Substitute the coordinates of the vertices into the function z=8x+3y to find the maximum value. The maximum value occurs at the vertex (8,10), where z=8(8)+3(10)=94.
Therefore, the maximum value of the function z=8x+3y subject to the constraints y>=0, x>=4, y<=10, and 5x+2y<=60 is 94.
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Help me Pleaseee it would mean a lot
Answer:
D is the answer trust me
50
45
36
35
27
44
43
32 Write next to these numbers if these numbers are composite or prime
Answer:
50: Composite
45: Composite
36: Composite
35: Composite
27: Composite
44: Composite
43: Prime
32: Composite
Find the zeros and find the multiplicity of each zero for the function f(x)=(3x+2)^(5)(x^(2)-10x+25)
The zeros and their multiplicities are x=-2/3, multiplicity 5 and x=5, multiplicity 1.
To find the zeros of the function f(x)=(3x+2)^(5)(x^(2)-10x+25), we need to set the function equal to zero and solve for x.
0=(3x+2)^(5)(x^(2)-10x+25)
Since the product of two factors is zero, one of the factors must be zero. We can set each factor equal to zero and solve for x.
(3x+2)^(5)=0
3x+2=0
3x=-2
x=-2/3
The other factor is:
x^(2)-10x+25=0
This is a quadratic equation, which we can solve using the quadratic formula:
x=(-b±√(b^(2)-4ac))/(2a)
x=(-(-10)±√((-10)^(2)-4(1)(25)))/(2(1))
x=(10±√(100-100))/2
x=(10±0)/2
x=10/2
x=5
So the zeros of the function are x=-2/3 and x=5.
To find the multiplicity of each zero, we need to look at the exponent of the factor that contains the zero. The zero -2/3 comes from the factor (3x+2)^(5), which has an exponent of 5, so the multiplicity of -2/3 is 5. The zero 5 comes from the factor (x^(2)-10x+25), which has an exponent of 1, so the multiplicity of 5 is 1.
Therefore, the zeros and their multiplicities are:
x=-2/3, multiplicity 5
x=5, multiplicity 1
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In the 2021 football season, the Riverside Red Dragon's manager gathered the points scored by the team during the regular season games. The following data set shows the values collected by the manager.
{17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3}
Which of the following stem-and-leaf plots correctly graphs the data set?
2021 Riverside Red Dragon Football Season Points
0 0 3
1 1 7 7 7 7
2 0 0 0 2 4 8 8
3 1 3
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
0 0 3
1 1 7
2 0 2 4 8
3 1 3
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 7
2 0 2 4 8
3 0 1 3
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 7 7 7 7
2 0 0 0 2 4 8 8
3 0 1 3
Key 1|1 = 11
The key shows that 1|1 represents the score 11.
The stem-and-leaf plot that depicts the data set accurately is as follows:
Season Points for the 2021 Riverside Red Dragon Football
0 | 0 3
1 | 0 1 7 7 7 7 7
2 | 0 0 2 4 8 8
3 | 1 3
Key: 1|1 = 11
The stems represent the tens digit and the leaves represent the ones digit in this stem-and-leaf plot, which accurately depicts the frequency of each score in the data set. For instance, the stem 2 and the leaves 0 and 0 indicate the two instances of the score 20, which appears twice. The score 11 is represented by the key as 1|1.
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Which ordinal numbers match the cardinal numbers below? Check all that
apply.
183, 201, 82
A. 183rd
B. 183st
C. 87th
☐ D. 82nd
E. 201th
OF. 201 st
The correct options are A, D, and E. Option B is not a valid ordinal number ending, and option C does not match any of the given cardinal numbers.
What is cardinal number ?
A cardinal number is a type of number used to represent the size or quantity of a set or collection of objects. It is a number that expresses how many objects are in a particular set or group, and is used to answer questions like "how many?"
For example, the cardinal number of the set {1, 2, 3} is 3, because there are three objects in the set. The cardinal number of a set can be finite or infinite, depending on whether the set has a definite number of elements or not.
The ordinal numbers corresponding to the cardinal numbers are:
183: 183rd
201: 201st
82: 82nd
Therefore, the correct options are A, D, and E. Option B is not a valid ordinal number ending, and option C does not match any of the given cardinal numbers.
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Lin's sister has a checking account. If the account balance ever falls below zero, the bank charges her a fee of $5.95 per day. Today, the balance in Lin's sister's account is −$2.67.
If she does not make any deposits or withdrawals, what will be the balance in her account after 22 days?
Type the answer in the box below.
If Lin's sister dοes nοt make any depοsits οr withdrawals, the balance in her accοunt after 22 days will be -$133.57.
What is meant by accοunt balance?The balance is the sum οwing οn an accοunt in banking and accοunting. The term "balance" in bοοkkeeping refers tο the difference between the tοtal οf debit entries and the tοtal οf credit entries made intο an accοunt οver the cοurse οf a certain financial periοd. The accοunt shοws a debit balance when tοtal debits exceed tοtal credits.
Net debt is represented by an accοunt balance that is less than zerο. An accοunt with a minus sign (-) at the end οf the amοunt typically has a negative balance οr is in debt.
Given,
The fee charged when the balance falls belοw zerο = $5.95/day
The current balance in Lin's sister's accοunt = −$2.67
We are asked tο find her accοunt balance after 22 days if nο transactiοns are made.
Since the current balance in her accοunt is belοw zerο, a fee will be charged.
The fee charged fοr 22 days = 5.95 × 22 = $130.9
Then the current balance = -2.67 - 130.9 = -$133.57
Therefοre if Lin's sister dοes nοt make any depοsits οr withdrawals, the balance in her accοunt after 22 days will be -$133.57.
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A car travels at 80 kmph for 4 hours. How far does it travel?
Answer:
Step-by-step explanation:
80*4=320km
Please help me!!! I need it very urgently
The angle LZW, given that angles Izw and Wzo are supplementary, would be an Obtuse angle.
How to find the angle type ?If the angles Izw and Wzo are supplementary, then their sum is equal to 180 degrees.
Since Wzo is an acute angle (meaning it measures less than 90 degrees), we know that Izw must be an obtuse angle, so that their sum is 180 degrees. An obtuse angle is an angle that measures greater than 90 degrees and less than 180 degrees. It is "obtuse" because it is more than a right angle (90 degrees), which is considered "sharp" or "acute".
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The value of x in the sequence notation is 27/4
How to determine the value of xFrom the question, we have the following sequence that can be used in our computation:
[tex]\sum\limits^4_{j=-2} {2x(-\frac{3}{2})^j = \frac{1389}{32}[/tex]
When the above expression is expanded, we have the following equation
2x[(-3/2)⁻² + (-3/2)⁻¹ + (-3/2)⁰ + (-3/2)¹ + (-3/2)² + (-3/2)³ + (-3/2)⁴] = 1389/32
Evaluate the exponents the expressions
So, we have
2x[4/9 - 2/3 + 1 - 3/2 + 9/4 - 27/8 + 81/16] = 1389/32
Evaluate the fractions
2x * 463/144 = 1389/32
Evaluate the products
x * 463/72 = 1389/32
Solve for x
x = 72/463 * 1389/32
Evaluate
x = 27/4
Hence, the value of x is 27/4
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Which function represents a horizontal dilation of the function y = log x ? Select all that apply.
The functions that represent a horizontal dilation of the function y = log x are A and C.
What is horizontal dilation?
Horizontal dilation, also known as horizontal stretching or compression, is a transformation of a function that changes the shape of its graph by scaling the independent variable (x-axis).
When a function is horizontally dilated, it is stretched or compressed horizontally without changing its vertical position. If the function is stretched horizontally, it becomes flatter and wider, while if it is compressed horizontally, it becomes steeper and narrower.
Horizontal dilation is achieved by multiplying the independent variable x in the function by a positive constant a. If a > 1, the function is horizontally compressed, and if 0 < a < 1, the function is horizontally stretched. If a = 1, the function is not affected by horizontal dilation.
The function that represents a horizontal dilation of the function y = log x is a function of the form y = log(ax), where a is a positive constant. This is because changing the value of a will stretch or compress the graph horizontally.
A. h(x) = log(2x) + 1 represents a horizontal compression by a factor of 2, followed by a vertical translation upward by 1 unit.
B. K(x) = log(x + 1) represents a horizontal translation to the left by 1 unit.
C. f(x) = log(0.3x) represents a horizontal compression by a factor of 1/0.3 = 3.33.
D. g(x) = 5 log(x) represents vertical stretching by a factor of 5.
Therefore, the functions that represent a horizontal dilation of the function y = log x are A and C.
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Please help!! Anything is fine
The missing angle is 90°. So, to obtain the values of the sides given the lengths we will have:
8. PT = 1
PV = 2
9. VT = 0.76
PV = 0.66
10. PT = 3
PV = 6
11. PV =0.58
PT =1.154
12. PT = 1.73
VT = 3
13. VT = 3
PV = 3.5
How to find the missing sidesThe given triangle is a scalene triangle because of the three different angles it has which sum up to 180 degrees. The sides will also be different.
For the first triangle whose known side is √3, the missing values can be obtained this way:
sin 60°/ √3 = sin 90/PV
PV = √3 Sin 90/ sin 60
PV = 1.732/0.866
= 2
PT = sin 60/ √3 = sin 30/ PT
PT = √3 sin 30/sin 60
PT = 1
Using this same pattern, the values for the other figures can be obtained.
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Given the area of the square factor to find the side length of 144x² - 24x + 1
144x² - 24x + 1 = 12²x² - 24x + 1 = (12x)² - 2(12x) + 1² = (12x - 1)²
I’ll give you brainly
Answer:
x = 1
y = 1
Step-by-step explanation:
A 6-foot person standing 18 feet from a streetlight casts a 10-foot shadow. Two similar triangles are formed. One triangle is formed by the person and the shadow that the person casts. A second triangle is formed by the streetlight and the ground from the base of the streetlight to the end of the shadow.
Due to the formation of two identical rectangles, the streetlight is consequently twice as large as the individual.
what is triangle ?A triangle is a polygon with three vertices and three angles that has three sides. It is one of the fundamental geometric shapes and has numerous uses in fields like engineering, physics, architecture, and more. The lengths of a triangle's sides and angles can be calculated using a variety of geometric formulas. Triangles come in a variety of shapes, including equilateral, isosceles, scalene, right-angled, acute-angled, and obtuse-angled triangles, each of which has unique attributes.
given
Let x represent the person's height.
Let x represent the streetlight's height.
Let d represent the distance between an individual and a streetlight.
Let s be the size of the shade cast by the subject.
According to the facts provided, x equals 6 feet (height of the person)
d Equals 15 feet (distance from the person to the streetlight)
The shadow's extent, s, is 15 feet.
Finding y's number, or the streetlight's height, is necessary.
The following ratios can be written using the comparable triangles property:
y / (d + s) Equals x / s
Inputting the numbers provided yields:
By condensing and figuring out x, we arrive at:
y = 12 feet
Consequently, the streetlight has a 12 foot height.
We can divide the streetlight's height by the person's height to determine how many times higher the streetlight is:
y / x = 12 / 6 = 2
Due to the formation of two identical rectangles, the streetlight is consequently twice as large as the individual.
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calculate the side of the unknown side of this right angled triangle 17cm 9cm
The side of the unknown side of this right angled triangle is 14cm
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given two sides of the triangle are 17cm and 9cm.
We have to find the unknow side of the triangle.
By Pythagoras theorem we find the length of unknown side.
The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
17²=9²+x²
289-81=x²
208=x²
Take square root on both sides
x=√208
x=14.42 cm
Hence, the side of the unknown side of this right angled triangle is 14cm
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Order the number from the least to greatest
-8,7,-10,0
The number from the least to the greatest is -10, -8, 0, 7.
To order numbers means to arrange them in a particular sequence based on their magnitudes or values. This can be done in ascending order (smallest to largest) or descending order (largest to smallest).
Ascending order refers to arranging a set of numbers or values from the smallest to the largest value. For example, if we have a set of numbers {3, 1, 7, 2, 8}, arranging them in ascending order would give us {1, 2, 3, 7, 8}.
Descending order refers to arranging a set of numbers from the largest value to the smallest value. For example, if we have the numbers 7, 2, 9, 4, and 1, the descending order would be: 9, 7, 4, 2, 1.
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In 8 years, Claire will be three times her current age. In how many years will she be 20 years old?
Claire will be 20 years old in 16 years. To solve this problem, we use algebra.
Let's represent Claire's current age with the variable x. According to the problem, in 8 years, Claire will be three times her current age. We can write this as an equation:
x + 8 = 3x
Next, we can rearrange the equation to solve for x:
8 = 2x
x = 4
This means that Claire is currently 4 years old. To find out when she will be 20 years old, we can subtract her current age from 20:
20 - 4 = 16
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"Given tan a = 3/4, and sin a = -3/5, find the exact value of:
(Remember to consider which sign is appropriate)
a) cos(2a)
b) sin a/2"
The exact value of cos(2a) is 7/25 and the exact value of sin a/2 is √10/10. Remember to consider which sign is appropriate when using the trigonometric identities.
Given tan a = 3/4, and sin a = -3/5, we can find the exact value of cos(2a) and sin a/2 by using the appropriate trigonometric identities.
a) cos(2a) = 1 - 2sin^2(a) = 1 - 2(-3/5)^2 = 1 - 18/25 = 7/25
b) sin a/2 = √[(1 - cos a)/2] = √[(1 - (4/5))/2] = √[(1/5)/2] = √(1/10) = 1/√10 = √10/10
Therefore, the exact value of cos(2a) is 7/25 and the exact value of sin a/2 is √10/10. Remember to consider which sign is appropriate when using the trigonometric identities.
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Find the values of the variables for the figure.
Using some rules for interior angles, we will see that:
x = 22.5
y = 22.5
How to find the values of x and y?Remember that the sum of the interior angles of any triangle is 180°.
Now, we can see that :
3x + k = 180°
Where k is the missing angle in the left triangle.
k = 180° - 3x
if we add the 3 interior angles, we will get:
2x + y + 180° - 3x = 180°
y - x = 0°
So x and y have the same value.
If now use the top triangle, we can write:
(90 - y) + 3x + 2x = 180
And we know that y = x
90 -x + 3x + 2x = 180
90 + 4x = 180
4x = 180 - 90 =90
x = 90/4 = 22.5
Then:
x = 22.5
y = 22.5
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Find m<DEC
a) 144°
b) 58°
c) 118°
d) 180°
Both circles have the same center. The circumference of the inner circle is 125.6 inches. What is the area of the shaded region?
Use 3.14 for pi. Write your answer as a whole number or decimal rounded to the nearest hundredth.
Using the circumference formula of the circle, we know that the area of the shaded region is 2,375 in.
The circumference of a circle is the distance encircling its edge.
The diameter of a circle is the distance measured through its center.
The radius of a circle is the distance from the center to any point on the edge.
The circumference of a circle or ellipse in geometry is its perimeter.
That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.
The curve length around any closed figure is more often referred to as the perimeter.
So, the circumference of the inner circle is 125.6 inches.
Then, the radius would be:
C = 2πr
125.6 = 2πr
125.6 = 6.28r
r = 125.6/6.28
r = 20 in
r for the outer circle: r will be 20 + 14 = 34 in
Area of the inner circle:
A = πr²
A = π20²
A = 1256.63706
A = 1257 in
Area of the outer circle:
A = πr²
A = π34²
A = 3631.68111
A = 3632 in
Area of the shaded region:
3632 in - 1257 in = 2,375 in
Therefore, using the circumference formula of the circle, we know that the area of the shaded region is 2,375 in.
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Shot Down A cruise missile is traveling straight across the desert at 548 mph at an altitude of 1 mile, as shown in the figure.
A gunner spots the missile coming in his direction and fires a projectile at the missile when the angle of elevation of the missile is 35°. If the speed of the projectile is 688 mph, then for what angle of elevation of the gun will the projectile hit the missile?
The elevation of the gun will the projectile hit the missile will be 62.18°.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
Let 't' be the time. And 'θ' be the angle. Then the measure of the angle is given as,
688t / sin 35° = 548 / sin θ
sin θ = 0.4568
θ = 27.18°
The angle from the base is calculated as,
⇒ 27.18° + 35°
⇒ 62.18°
The elevation of the gun will the projectile hit the missile will be 62.18°.
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The first step in the industrial recovery of zinc from zinc sulfide ore is roasting. That is the conversion of ZnS to ZnO by heating: 2ZnS (s)- 30₂(g) → 2ZnO(s) - 250, (g) AH=-879 kJ/mol Calculate the heat (in kJ) associated with roasting 6.00 grams of zinc sulfide. Round your answer to 3 significant digits.
The heat associated with roasting 6.00 g of zinc sulfide is 27.1 kJ.
How to solve thisThe molar mass of ZnS is 97.45 g/mol, which means that 6.00 g of ZnS is equal to:
6.00 g ZnS × (1 mol ZnS/97.45 g ZnS) = 0.0616 mol ZnS
According to the balanced equation, the roasting of 2 mol of ZnS releases 879 kJ of heat:
2 ZnS (s) + 3 O₂ (g) → 2 ZnO (s) + 2 SO₂ (g) ΔH = -879 kJ/mol
Therefore, the roasting of 0.0616 mol of ZnS releases:
(879 kJ/mol) × (0.0616 mol ZnS / 2 mol ZnS) = 27.1 kJ
Therefore, the heat associated with roasting 6.00 g of zinc sulfide is 27.1 kJ. Rounded to three significant digits, the answer is 27.1 kJ.
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