If abc is 1 degree and 25', the angle ACD is 178° 35'.
What is angle?An angle is a figure in Euclidean geometry formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are termed dihedral angles. An angle is generated when two straight lines or rays meet at a shared terminus. The common point of contact is called the vertex of an angle.
Here,
∠ACB and ∠ACD are supplementary, so they add up to 180°.
First, convert to degrees (there are 60 minutes in a degree).
∠ACB = 1°25' = 1° + (25/60)° = 1.4167°
Now find the supplementary:
∠ACD = 180° − 1.4167°
∠ACD = 178.5833°
∠ACD = 178° 35'
The value of angle ACD is 178° 35' if abc is 1 degree and 25' .
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a cook uses 1 3/4 teaspoons if salt to make 3 1/2 pounds of pasta. what is the unit rate in teaspoons per pound , at which the cook uses salt to make pasta?
The unit rate in teaspoons per pound would be 1/2 teaspoons per pound.
What is the unit rate?
A unit rate means a rate for one or something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
The number of teaspoons:
[tex]=1\frac{3}{4}\\\\=\frac{4+3}{4}\\\\=\frac{7}{4}[/tex]
Amount of pasta:
[tex]=3\frac{1}{2}\\\\=\frac{6+1}{2}\\\\=\frac{7}{2}[/tex]
Now the unit rate = number of teaspoons/ amount of pasta
[tex]=\frac{7/4}{7/2}\\\\=\frac{1}{2}\\[/tex]
Hence, the unit rate in teaspoons per pound would be 1/2 teaspoons per pound.
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Answer:
Step-by-step explanation:
1/2
An equation that pass through -4,-1 and perpendicular to the line y = 4/3x + 6
The equation of the perpendicular line is y = 3/4(x + 4) - 1
How to determine the perpendicular line equation?From the question, we have the following parameters that can be used in our computation:
y = 4/3x + 6
Also, from the question;
We have the following points
The point is given as
Point = (-4, -1) i.e. (x, y) = (-4, -1)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = -4/3
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is 3/4
The equation of the line is then calculated as
y = m(x - x₁) +y₁
Where
m = 3/4
(x₁, y₁) = (-4, -1)
So, we have
y = 3/4(x + 4) - 1
Hence, the line has an equation of y = 3/4(x + 4) - 1
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A middle school is having a fundraiser. Edwin wants to buy two candles for $5.95 each, three cans of candy for $2.50 each, and an ornament for $7.95.
Answer:
$27.35
Step-by-step explanation:
To solve this, we just set up an equation based on the situation given:
2 candles for 5.95 each would be (2 x 5.95)
3 cans of candy for 2.50 each would be (3 x 2.50)
1 ornament for 7.95 would just be 7.95
(2 x 5.95) + (3 x 2.50) + 7.95 = total cost
11.90 + 7.50 + 7.95 = total cost
$27.35 = total cost
if a fair coin is tossed 100 times. the distribution of the number of heads is b(100, 0.5). what is the probability that the obtained heads, x, is between 45 and 55? p (45 less or equal than x less or equal than 55 )
The probability that obtained heads, x, is between 45 and 55 is 0.6826.
The Binomial distribution provides the precise response. Wolfram Alpha is one of the software tools that may perform the computation for you. Using this method manually is painful.
Maybe you're supposed to use the binomial's normal approximation. If there are X heads, then X has a roughly normal distribution first we have to find what is the mean and standard deviation.
Given that n = 100 is a relatively large number, we will assume a normal distribution.
mean M = n*p 100*0.5 =50
Consequently, Sd = √(npq) = √1000.5*0.5 = 5.
The standard deviation is 5.
Z = x-µ/σ
Z = (x-50)/5
we have to find the probability in this range.
P(45<X<55) = P((45-50)/5<X<(55-50)/5
P(-1<X<1) = 0.8413 - 0.1587
0.6826
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Solve the inequality.
a-2>4
The solution is
Graph the solution.
-14 -12
-10
1
-8
-6
-4 -2 0
−2
AL
4
6
+8
8
10
12
14
The solution to the given inequality is; a > 6
How to solve Inequality problems?The given inequality is;
a - 2 > 4
Now, to start to solve this, we add 2 to both sides of the inequality using addition property of equality to get;
a - 2 + 2 > 4 + 2
a > 6
Now, the inequality when shown on a line plot is as attached and it shows that the arrow points to the right hand side.
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Is the converse of the statement valid?
If x is even, then x + 4 is even.
O Yes. If x + 4 is even, then x is even.
Yes. If x is even, then x + 4 is odd.
O
O
No. If x is even, then x + 4 is even.
O No. If x + 4 is even, then x is even.
The valid converse of the statement is, Yes. If x + 4 is even, then x is even. If x is even, then x + 4 is even.
Define converse.A conditional statement's opposite is produced when the hypothesis and conclusion are switched around. The converse statement is known as p⇒ q in geometry. In logic and mathematics, the reverse of a categorical or implicational statement is the outcome of reversing its two constituent statements, and it is denoted by the symbol q⇒ p. The opposite of the implication P ⇒ Q is Q P. The inverse of the categorical assertion All S are P is that All P are S.
Given,
If x is even, then x + 4 is even.
The valid converse of the statement is,
Yes. If x + 4 is even, then x is even.
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A toy is being constructed in the shape of a pyramid. The maximum amount of material to cover the sides and bottom of the pyramid is 250 square centimeters. The height of the toy is double the side length. What are the maximum dimensions to the nearest square centimeter for a square base and for a hexagonal base?.
The maximum dimensions (side length and height) of the pyramid for a given square base is equal to 6.99cm and 13.98cm respectively.
As given in the question,
Maximum amount of material used to cover sides of pyramid and its bottom = 250cm²
Surface area of the ( sides + bottom ) = 250cm²
Base is square :
Let 's' represent the the side length
Then height 'h' of the toy = 2 ( side length)
= 2s
Surface area of Pyramid = s² + 2s√(s²/4) + h²
⇒ 250 = s² + 2s√(s²/4) + (2s)²
⇒250 = s² + 2s√(s² + 16s²)/4
⇒250 = s² + 2s√17s²/4
⇒250 = s² + 2s(s/2)√17
⇒250 = s²+ s²√17
⇒250 = s² ( 1+ √17)
⇒250 = s²( 1 + 4.123 )
⇒ 250 = 5.123s²
⇒s² = 250/5.123
⇒ s= 6.99cm
Height 'h' = 2(6.99)
= 13.98cm
Therefore, the side-length and height of the pyramid with square base is equal to 6.99cm and 13.98cm respectively.
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The HA theom is a special case of the ____
The HA Theorem is a special case of proving that two triangles are congruent. The HA theorem is a special case of the AAS theorem.
What is HA Theorem?
The HA congruence theorem for right triangles says that if the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle then the two triangles are congruent.
It states that if both hypotenuses and a pair of acute angles of two right triangles are congruent, then the triangles are congruent.
The HA Theorem is a special case of proving that two triangles are congruent.
What is AAS theorem?AAS theorem says that if two angles and any side of a triangle are congruent to two angles and any side of another triangle, then the triangles are congruent.
AAS (Angle Angle Side) theorem states that in the two triangles, if two angles and one side of a triangle are congruent to two angles and one side of a second triangle, then the two triangles are congruent.
Hence, the HA theorem is a special case of the AAS theorem.
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g suppose a small library has five book shelves labeled a-e. in how many different ways can 30 books be placed on these shelves if the books are all different
There are 150 different ways can 30 books be placed on these shelves if the books are all different.
The number of shelves on a bookshelf is 5.
The number of books on one shelf is 30.
The number of books on 5 shelves= The number of books on one shelf *The number of shelves.
which implies that, the total number of books =30*5
By multiplying 30 by 5 we get 150
total number of books =150.
hence, bookshelves have 150 books if books are placed differently.
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PLEASE HELP
Write and solve the inequality that represents negative one third is greater than or equal to the product of negative two fifths and a number.
negative one third is greater than or equal to negative two fifths y where y is greater than or equal to negative five sixths
negative one third is greater than or equal to negative two fifths y where y is greater than or equal to five sixths
negative two fifths is greater than or equal to negative one third y where y is less than or equal to negative two fifteenths
negative two fifths is less than or equal to negative one third y where y is greater than or equal to two fifteenths
Negative one third is greater than or equal to negative four fifths y where y is greater than or equal to five twelfths
What is inequality?
A statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.
From the text given in this problem, we build the inequality, and then solve it. Also,
Negative one fifth is -1/5.The product of negative two thirds and a number is -2/3x, as the number is unknown, hence we call it x.Given:
-1/3≥ (-4/5) * y
-1/3*(-5/4) ≤ y
5/12≤y
Hence, negative one third is greater than or equal to negative four fifths y where y is greater than or equal to five twelfths.
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What is the equation of the line that is perpendicular to the linear graph of y=−23x+5 and passes through the point (0, –2)?
The equation of the Line that is perpendicular to the given number is
x - 23y - 4 = 0
When two lines cross at a straight angle or 90° then the pair of lines said to a pair of perpendicular lines. If the slopes of the two perpendicular lines are m₁, m₂, then the connection between the slopes of perpendicular lines will be represented by the following formula
m₁.m₂ = -1
Here we have
Given line y = −23x+5 ------ (1)
A line perpendicular to the line (1) passes through the point (0, –2).
Here given line is y = −23x+5 which is in the form of y = mx + c
On comparing both equations
=> Slope of line m = −23
Let (y - y₁) = m(x - x₁) be the required equation
=> (y - y₁) = m(x - x₁) ----- (2)
As we know product of slopes of line(1) and (2) is - 1
=> mm₁ = - 1
=> −23m₁ = -1
=> m₁ = 1/23
Substitute m₁ = 1/23 in line (2)
=> (y - y₁) = [1/23](x - x₁)
=> 23(y - y₁) = (x - x₁)
Given the line passes through the point (0, –2).
=> 23(y - (-2)) = (x - 0)
=> 23(y + 4) = x
=> 23y + 4 = x
=> x - 23y - 4 = 0
Therefore,
The equation of the Line that is perpendicular to the given number is
x - 23y - 4 = 0
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Beth bought 16 tickets to a movie, where adult tickets cost $8.00 and senior citizen
tickets cost $5.00. She spent a total of $120. Create a system of equations to determine
the number of adult tickets and the number of senior citizen tickets that Beth
purchased?
A system of equations that determines the number of adult tickets and the number of senior citizen tickets that Beth purchased is x + y = 16
8x + 5y = 120.
What is a system of an equation?
A set or group of equations that you solve all at once is referred to as a "system" of equations. The simplest linear system is one with two equations and two variables. Linear equations (those that graph as straight lines) are easier to understand than non-linear ones.
Here, we have
Given: Beth bought 16 tickets to a movie, where adult tickets cost $8.00 and senior citizen tickets cost $5.00. She spent a total of $120.
We let adult tickets be x and
let senior citizens' tickets be y.
x + y = 16....(1)
8x + 5y = 120...(2)
From equation(1)
x = 16 - y
we put the value of x in equation(2) and we get
= 8(16 - y) + 5y = 120
= 128 - 8y + 5y = 120
= 3y = 8
y = 8/3
Now, we put the value of y in equation(1) and we get
x = 16-8/3
x = 40/3
Hence, a system of equations that determines the number of adult tickets and the number of senior citizen tickets that Beth purchased is x + y = 16
8x + 5y = 120.
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Determine the measure of the indicated angle 53 106 127 307
Answer: 127
Step-by-step explanation: It must add up to 180 degrees
Interior consecutive = congruent
Corresponding = 180
Marcus has x songs downloaded on his phone. He downloads 20 more songs to his phone.
Enter an expression in the box to represent the number of songs Marcus now has on his phone.
Answer:
x + 20 = y
Step-by-step explanation:
x + 20 = y
where x= number of songs
y = total songs marcus has
a drawer contains 7 black socks, 3 brown socks, and 1 gray sock. a sock is chosen at random. what is the probability that the sock is black or gray? use the formula below to solve this problem. question 2 options: 7/11 1/11 6/11 8/11
The Probability that the sock is black or gray is
What is Probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Total number of socks in a bag = 7+3+1 =11
so total number of outcomes possible = 11
The chance that black or gray will occur, resulting in a greater number of favorable outcomes
Number of favourable outcome will be -
Number of Black sock + Number of gray sock
=7+1
=8
Therefore probability (P) will be 8/11
=0.7272
and individual probability of coming black and gray sock will be
Probability for black socks is 7/11
Probability for gray socks is 1/11
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how can we find vertex of degree 4 polynomials
Answer:
Below
Step-by-step explanation:
Everywhere there is a local max or minima, the slope = 0
IF you take the first derivative, set it = 0 and solve for the x values, you will get these local max/min points ....but you will not know if they are a max or a min....
so take the SECOND derivative and sub in each of the values that you got ......if you get a POSITIVE result it is a min.... a negative result is a max point...... when you find the min point(s) ...use that value of 'x' in the original equation to find the corresponding 'y' coordinate.....
OR: You can graph the function to SEE the min points .....
Quick my grade is down from this Exam, and I'm honestly so lost on this question
Which of the following expressions represents the simplified version of the expression below?
(5x3y2−3xy+2)+(2x3y2−3x2y2+4xy−7)
(Just tell me the color and explain if you want)
The equivalent expression of the given expression is 7x³y² -3x²y² + xy -5. Second option is the correct option.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator).
What are like terms?
Similar variables and powers are referred to as like words in algebra. It is not necessary for the coefficients to agree. When two or more terms do not share the same variables or powers, they are said to be unlike terms. Unless there is a power, the variables' order is irrelevant.
Given expression is
(5x³y²−3xy+2)+(2x³y²−3x²y²+4xy−7)
Now open the brackets:
= 5x³y²−3xy+2+2x³y²−3x²y²+4xy−7
Combine like terms:
= (5x³y²+2x³y²)+ (−3xy + 4xy )+(2−7)−3x²y²
= 7x³y² + xy -5 -3x²y²
= 7x³y² -3x²y² + xy -5
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For sheets of steel:
500 mm x 500 mm x 0.7 mm costs £6.00
1,000 mm x 1,000 mm x 0.7 mm costs £17.00
How much of a saving, in both pounds (£) and percentage (%), could you make by getting the larger sheets
cut into four pieces that are 500 mm x 500 mm?
The amount of saving in pounds is £7.00 and in percentage is 29.167%
What is percentage ?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
Cost of 500mm×500mm×0.7mm = £6.00
No. of sheets that can be cut will be = [tex]\frac{1000 * 1000 * 0.7}{500 *500 *0.7}[/tex]
= 4 sheets
Cost of 1 sheet of 1000mm x 1,000 mm x 0.7 mm = £17.00
Cost of 4 sheets of 500 mm x 500 mm x 0.7 mm = £6.00 × £4.00
= £ 24.00
Hence saving = £ 24.00 - £17.00
= £ 7.00
Hence percentage of savings = 7/24 × 100
= 175/6
= 29.167%
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Which of the following equations has no real roots
a. x² - 4x + 3√2 = 0
b. x² + 4x - 3√2 = 0
c. x² - 4x - 3√2 = 0
d. 3x² + 4√3x + 4 = 0
The equation (A) x² - 4x + 3√2 = 0 has no real roots.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
(A) x² - 4x + 3√2 = 0
b² - 4ac = (-4)² - 4(1)(3√2)
= 16 - 12√2
= 16 - 12(1.414)
= 16 - 16.968
= -0.968 < 0
There are no true roots to the equation.
(B) x² + 4x - 3√2 = 0
b² - 4ac = (4)² - 4(1)(-3√2)
= 16 + 12√2 > 0
There are 2 different real roots in the equation.
(C) x² - 4x - 3√2 = 0
b² - 4ac = (-4)² - 4(1)(-3√2)
= 16 + 12√2 > 0
There are 2 different real roots in the equation.
(D) 3x² + 4√3x + 4 = 0
b² - 4ac = (4√3)² - 4(3)(4)
= 48 - 48
= 0
The equation contains two equal roots.
Therefore, the equation (A) x² - 4x + 3√2 = 0 has no real roots.
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HELPPPP ASAPPPP PLEASEE!!!
Answer:
step 4 ,step 2, step 1 , step 3 , step 5
ASAPPPPPP!!!!! for each graph caculate the slope of each line
Answer:
[tex]m = -1[/tex]
Step-by-step explanation:
Use the slope formula:
slope [tex](m) = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Let:
[tex](x_1 , y_1) = (1 , 1)\\(x_2 , y_2) = (-5 , 7)[/tex]
Plug in the corresponding numbers to the corresponding variables:
[tex]m = \frac{7 - 1}{-5 - 1}[/tex]
Simplify. Combine:
[tex]m = \frac{(7 - 1)}{(-5 - 1)} \\[/tex]
[tex]m = \frac{6}{-6} = -\frac{6}{6} = -1[/tex]
[tex]m = -1[/tex] is your answer.
~
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Answer:
Slope (m) = -1
Step-by-step explanation:
Formula we use,
→ m = (y2 - y1)/(x2 - x1)
Now required slope will be,
→ (y2 - y1)/(x2 - x1)
→ (7 - 1)/(-5 - 1)
→ 6/(-6)
→ -1 => {Slope}
Therefore, the slope is -1.
this take over causes the cell to _____________ instead of makeing new cells
Meiosis causes the cell to divide instead of makeing new cells.
What are cells?Cells are the fundamental building blocks of all life. Trillions of cells make up the human body. They support the body's structure, absorb nutrients from food, convert those nutrients into energy, and perform specialized functions.
Meiosis is a type of cell division that occurs in sexually reproducing organisms and results in a reduction in the number of chromosomes in gametes; he sex cells, or egg and sperm. Body or somatic cells in humans are diploid, with two sets of chromosomes one from each parent.
It should be noted that meiosis is a type of cell division of germ cells that produces gametes such as sperm or egg cells in sexually reproducing organisms. It consists of two rounds of division that result in four cells with only one copy of each chromosome.
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What number is 12% of 45?
By solving a simple product we will see that 12% of 45 is equal to 5.4
What number is 12% of 45?
If we have a number N and we want to take a percentage P of that number, the operation we need to do is:
new number = N*(P/100%)
Here the original number is N = 45 and the percentage is 12%, then we need to solve:
new number = 45*(12%/100%) = 5.4
Then the 12% of 45 is equal to 5.4
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What is the input value for which g(x) = 3?
At the Input Value 9 the function g(x) will be 3.
What are Function?
A function in mathematics from a set X to the a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Al-Biruni as well as Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the earliest known treatment of the concept of function. Initially, functions represented the idealised relationship between two varying quantities. A planet's position, for instance, depends on time. In the past, the idea was developed with infinitesimal calculus just at end of the seventeenth century, and indeed the functions that were taken into consideration were differentiable until the 19th century.
Solution:
So, it can be observed from the graph that g(x) = 3
when the value of x is 9
So, the input value is 9.
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Use the following sample to estimate the population proportion of red automobiles in the United States.
A.19%
B.20%
C.21%
D.22%
The population proportion of red automobiles in the United States exists 22 %.
What is meant by proportion?An analysis of two numbers in terms of their proportion. A ratio is said to be directly proportional to another if two sets of given numbers are increasing or decreasing in the same ratio.
The proportion of red automobiles in the United States(P) is given by:
P = [Number of red automobiles / Number of automobiles in US ]× 100
According to the table
Number of red automobiles = 32 + 29 + 23
Number of red automobiles = 84
Number of automobiles
= 32 + 29 + 23 + 18 + 36 + 25 + 4 + 17 + 11 + 25 + 26 + 39 + 10 + 46 + 33
Number of automobiles = 374
put the values into the equation
P = [Number of red automobiles / Number of automobiles in US ] × 100
substitute the values in the above equation, we get
P = [84 Cars / 374 Cars] × 100
simplifying the above equation, we get
Proportional = 0.2245 × 100
Proportional = 22.45
Proportional = 22 percentage
Therefore, the correct answer is option D. 22 %.
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YOO need help with a short word problem :)
Using a system of linear equations the number of quarter and dime present are 1 and 8 respectively
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables.
Let:
q = quarterd = dime1 quarter = $0.25
1 dime = $0.1
A) An equation for the number of coins
q + d = 9 ...eq(i)
B) The amount of money can be represented as;
0.25q + 0.1d = 1.05 ..eq(ii)
C) The number of dimes; solving equation (i) and (ii)
q + d = 9 ..eq(i)
0.25q + 0.1d = 1.05 ...eq(ii)
q = 1, d = 8
There are 8 dimes
D) There is 1 quarter in the money
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Giselle wants to buy the newest book in her favorite series. She has some money saved but does not want to use all her savings on the book. Giselle's grandma offers to pay some of the cost of the book for every weed she pulls in her grandma's garden. The graph shows the cost to Giselle for the purchase of the book after pulling x weeds in her grandma's garden.
1. The book is $18.
2. Giselle can earn up to $18 pulling weeds for her grandma.
3. Giselle's grandma pays her $1 for every 5 weeds she pulls.
4. Giselle does not have to use any of her own money toward the purchase of the book when she pulls 90 weeds.
5. Giselle only needs to pull 18 weeds to not use any of her own money.
The correct statements regarding the linear function graphed are given as follows:
The book is $18.Giselle's grandma pays her $1 for every 5 weeds.Giselle does not have to use any of her money when she pulls 90 weeds.What are the correct statements?The correct statements are identified from the graph of the function.
The y-intercept of the function is of 18, which represents how much she has to pay when she does not pull any week, that is, the price of the book.
The x-intercept of the function is of 90, meaning that if she pulls 90 weeks, she earns $18 from her grandmother, which is the entire price of the book.
From the intercept, we get that when the input increases from 90, from 0 to 90, the output decays by 18, from 18 to 0, hence the slope of the function is given as follows:
m = -18/90 = -0.2.
Meaning that for each weed pulled, the amount her grandma pays is of $0.2, and thus for five weeds she is paid one dollar.
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A farm is rectangular with an area of 5/8 square miles. If the length
of the farm is 1/9 miles, what is its width? Answer with a fraction in
simplest form.
Answer:
45/8 or 5 5/8
Step-by-step explanation:
5/8 divided by 1/9 - 5/8 x 9/1
Answer:
5 5/8
Step-by-step explanation:
Math and stuff I dunno
you are selling tickets for a high school play. student tickets cost $4 and general admission tickets cost $6. you sell 31 tickets and collect $170. write the system of equations that could be used to determine the number of student tickets, s, and the number of general admission tickets, g, were sold for the high school play. how many student tickets did you sell?
As tickets are selling for a high school play. student tickets cost $4 and general admission tickets cost $6 and sell 31 tickets and collect $170.
Therefore, the system of equation is
8$4 + 23$6 = $32 + $138 = $170 total
A system of equations is a set of one or more equations with many variables. A solution to a system of equations is a variable map such that all component equations are satisfied. That is, the point where all those equations intersect.
Given that :
Ticket cost = $ 4 and $6
and collection = $170.
Now,
4S+6G = 170 ------------------------ (1)
S+G = 31 ----------------------- (2)
Therefore, subtract from 1st equation to eliminate one variable:
4S+ 4G = 124 ----------------------------- (3)
Now,
2G = 46
⇒ G = 23 tickets
putting G = 23 in equation(2)
S = 31-23
= 8 student tickets
The system of equation is:
8$4 + 23$6 = $32 + $138
= $170 total
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Complete the following equations with the correct values.
sin(____) = cos(75)
cos(x) = sin(____-x)
Answer:
first blank: 15
second blank: 90
Step-by-step explanation:
Obviously, sin and cos are related, but they are not the same thing. In order for them to be equal:
sin(____) = cos(75)
the angles have to add up to 90 (complementary)
What + 75 is 90?
Do a tiny calc:
90 - 75 is 15
The second question is stating the rule generically.
x + (90 - x) is 90
