Answer:
0
Step-by-step explanation:
[tex]\sin(12\º) - \cos(78\º)[/tex]
Consider the cofunction identity:
[tex]$\boxed{\sin(\theta)=\cos \left(\frac{\pi}{2} - \theta \right)} $[/tex]
[tex]$\boxed{\sin(\theta)=\cos \left(90\º - \theta \right)} $[/tex]
[tex]\sin(12\º)=\cos(90\º - 12\º)=\cos(78\º)[/tex]
[tex]\therefore \cos(78\º) - \cos(78\º) = 0[/tex]
The value of Sin 12-cos 78 is 0
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: sin 12 - cos 78 = Sin(90-12)-cos78 but we know sine of any angle = the cosine of any complementary angle
Thus we have Sin78-Cos78=0
Hence, The value of Sin 12-cos 78 is 0
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Solve the following system of equations using the elimination method.
6x + 7y = 10
–8x – 14y = –4
Question 3 options:
A)
(3,–8)
B)
(4,–2)
C)
(–4,6)
D)
(7,–3)
Answer:
Step-by-step explanation:
12x + 14y = 20
-8x - 14y = -4
4x = 16
x = 4
6(4) + 7y = 10
24 + 7y = 10
7y = -14
y = -2
(4, -2)
the solution is B
Steven earns extra money babysitting. He charges $33.75 for 5 hours and $54.00 for 8
hours.
Enter an equation to represent the relationship. Let x represent the number of hours
Steven babysits and y represent the amount he charges.
The equation is y =
Answer:
y = 6.75x
Step-by-step explanation:
These 2 pieces of information can be used to create 2 points on the graph, where x is the number of hours and y is the amount he charges:
(5, 33.75) and (8, 54) are the 2 points
Use rise/run (y2 - y1) / (x2 - x1) to find the slope
(54 - 33.75) / (8 - 5)
20.25/3
= 6.75
Now, plug this and another point into y = mx + b to find b, the y intercept
54 = 6.75(8) + b
54 = 54 + b
0 = b
So, the equation is y = 6.75x
can you please help me
Answer:
12
Step-by-step explanation:
I need help with this geometry question.
Answer:
Step-by-step explanation:
a). There are 8 points in the figure attached.
b). There are 9 lines in the given figure.
c). There are 5 planes in the figure attached.
d). Three collinear points are D,G and F.
e). Four co-planar points are G, F, H and C.
f). Intersection of planes ABC and ABE is the common line AB.
g). Intersection of planes BCH and DEF is the common line EF.
h). Intersection of AD and DF is a point D.
43. Can you place ten lumps of sugar in three empty cups so that
there is an odd number of lumps in each cup?
Answer: No.
Step-by-step explanation:
We have 10 lumps of sugar, and we want to divide them into 3 cups, in such a way that there is an odd number of lumps in each cup.
This only can happen if we have 3 odd numbers such that the addition is equal to 10.
Now 10 is an even number, remember that even numbers can be written as:
2*k
where k is an integer number.
And odd numbers can be written as:
2*n + 1
where n is an integer.
Then we have 3 odd numbers, let's call them:
(2*n + 1), (2*k + 1) and (2*p + 1).
Now let's add them:
(2*n + 1) + (2*k + 1) + (2*p + 1).
2*(n + k + p) + 1 + 1+ 1
2*(n + k + p) + 2 + 1 =
2*(n + k + p + 1) + 1.
Now, the number n + k + p + 1 is an integer number, let's call it X, then we have that the addition of the 3 odd numbers is:
2*X + 1
This is an odd number
So for any 3 odd numbers that we add together, the result will always be an odd number.
Then is impossible to add 3 odd numbers and get 10 as the result (Again, 10 is an even number).
Then is not possible to have an odd number of lumps in each cup.
i need help with this math question please :)
Answer: 9/16
Step-by-step explanation:
Answer: 9/16
Step-by-step explanation: (1/4)^2 turns into 1/16. 5/8 - 1/16 so make them have the same denominator. 5/8 x 2 = 10/16 - 1/16 = 9/16
A man weighing 340 pounds is admitted into a hospital for a special diet to lose no more than 6 pounds per week. What is the shortest time in weeks it could take the man to reduce his weight to 243 pounds?
Answer:
Step-by-step explanation:
340-243 =97
97/6 = 16
16 weeks to lose 6 pounds per week.
Answer:
Let's think.
If we want the man to be in the best case scenario in which he loses the most pounds that his limit lets him, we should always make the man lose the highest he could go: 6 pounds.
This is just a simple multi step problem if you break it down.
If his goal is to get to 243 pounds, we firstly subtract 243 from 340 to see how much he needs to lose.
340 - 243 = 97
The man wants to lose 97 pounds.
Let's divide this number by 6 with remainder.
I'll let you think for a bit.
97 / 6 = 16 remainder 1.
This means that in 16 weeks, he needs to lose 6 pounds while on the 17th week, he needs to lose 1 pound.
I'm sorry if i misunderstood.
Good luck Mate :)
Don't forget to try everyday !
Charlie and Clare are playing a number-guessing game. Charlie picked two numbers between 1 and 5. To win the game, Clare must guess both his numbers in three tries. Her guesses, simulated using a random-number generator, are shown in the table. If Charlie’s numbers are 1 and 3, what is the experimental probability that Clare won?
The experimental probability is 3/10 that Clare won if Charlie's numbers were 1 and 3
What is probability?The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Charlie picked two numbers between 1 and 5
So the numbers should be 2, 3, and 4
There is the number of favorable outcomes is 3
To win the game, Clare must guess both his numbers in three tries
The experimental probability that Clare won if Charlie's numbers were 1 and 3 = P(E)
There are 10 trials given
There are total number of possible outcomes is 10
So the required experimental probability P(E) = favorable outcomes/total outcomes
⇒ P(E) = 3/10
Hence, the experimental probability is 3/10 that Clare won if Charlie's numbers were 1 and 3.
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Answer: 3/10
Step-by-step explanation:
A new electronic store opened recently. There are several sales associate positions that pay an hourly rate of $7.50 plus a 4.5% commission based on the sales associates total weeking sales. Sales assqqociates are guaranteed 30 hrs of work per week,but no more that 40 hrs. At the electronics store, sales associates average $7,000 in sales each week. USE THE AVERAGE WEEKLY SALES FIGURE OF $7,000 AND HOURLY RATE OF $7.50. WRITE AN EQUATION, CREATE A TABLE, AND CREATE A GRAPH FOR A SALES ASSOCIATE'S WEEKLY EARNINGS, f(x), where x represents the total number of hours the sales associate would work.
Answer: f(x) = 7.50x + 315
Step-by-step explanation:
Let x represent the number of hours
Given: rate = 7.50, commission = 4.5%(7,000) = 315
Equation: f(x) = 7.50x + 315
Table:
[tex]\boxed{\begin{array}{c||r|c||c}\underline{\text{Hours}}&\underline{\text{Wage}}&\underline{\text{Commission}}&\underline{\text{Weekly Earnings}}\\30&7.5(30)=225.00&315&540.00\\31&7.5(31)=232.50&315&547.50\\32&7.5(32)=240.00&315&555.00\\33&7.5(33)=247.50&315&562.50\\34&7.5(34)=255.00&315&570.00\\35&7.5(35)=262.50&315&577.50\\36&7.5(36)=270.00&315&585.00\\37&7.5(37)=277.50&315&592.50\\38&7.5(38)=285.00&315&600.00\\39&7.5(39)=292.50&315&607.50\\40&7.5(40)=300.00&315&615.00\end{array}}[/tex]
Graph: (see below)
h - 20/j = k solve for j
Answer: j = 20/k-h
Step-by-step explanation: Multiply to remove your variable from your denominator.
I hope this helps you out.
3. Find the midpoint between the following points. (-2,-5) and (-3,1)
Answer:
Step-by-step explanation:
(x₁, y₁) = (-2 , -5) & (x₂ , y₂) = (-3 , 1)
Midpoint = [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]
[tex]=(\frac{-2 + [-3]}{2} ,\frac{-5 + 1}{2})\\\\\\=(\frac{-5}{2} , \frac{-4}{2})\\\\=(-2.5, -2)[/tex]
The table shows the time Merrida spent driving and the number of miles she drove. She drove the same number of miles each hour. How many miles did she travel each hour? • 23 miles per hour • 35 miles per hour • 42 miles per hour • 53 miles per hour
Answer:
35 miles per hour
Step-by-step explanation:
175 -140 = 35
35/1 = 35
Answer:
35
Step-by-step explanation:
The width of a rectangle is 2 units shorter than half the length x write an expression that represents the perimeter of the rectangle
Answer:
3x-4
Step-by-step explanation:
Length = x
width = 2 units shorter than half the length x
width = x/2 - 2
For rectangle
perimeter = 2(length + width)
Perimeter for given rectangle = 2(length + width)
Perimeter for given rectangle = 2(x + x/2 - 2) = 2x + 2x/2 -4
Perimeter for given rectangle = 2x+x -4 = 3x -4
Expression that represents the perimeter of the rectangle is 3x-4.
How are operations with variables like operations with real numbers?
Answer:
The relation between inputs and outputs is given by an equation called the equation of function. Since the outputs are also real values, hence, reasoning by analogy, you may use the arithmetical operation between functions (addition, subtraction, multiplication, division) to produce new functions.
Justin wants to cover the top of a circular swimming pool to keep insects out of the pool. If the diameter of the pool is 20 feet, what will be the area of the top of the cover (the portion of the cover that covers the surface of the pool)?
Answer: The area is approximately 314 ft^2
Step-by-step explanation:
Well if the diameter is 20 feet then the radius will be 10 because the radius is half the diameter, and to find the area of a circle, you use the formula
A= [tex]\pi r^{2}[/tex] where A is the area and pi times the radius squared.
We will represent pi by 3.14
A= 3.14* 10^2
A= 3.14 * 100
A = 314
What is the speed of a train that travels 52 kilometers in 3 hours?
Answer:
17 km/h
Step-by-step explanation:
52:3=17.3≈17 km/hour
Answer:
17 km/hr
Step-by-step explanation:
Speed=
[tex] \frac{distance}{time} [/tex]
so, since the units are the same, kilometer per hour and hour, we simply divide
that's
[tex] \frac{52}{3} [/tex]
and that's 17.333 approximately 17km/hr
What’s the answer for number 9
a florist sells bouquets that use Rose's and carnations in a ratio of 2 to 7. she receives a shipment of 343 carnations. how many Rose's will the florist need?
Answer: 98 roses
Step-by-step explanation: 2:7 is like x:343
343 divided by 7 is 49, so that is what you multiply 2 by to get the roses. 49 x 2 = 98
Answer:
343÷7×2=98
98 roses
The ratio of flowers is 7 to 2. The answer is question 98
a town Pharmacy in hospital is doing it as a part of format of the town has a scale 18840.35 miles what is the distance between the pharmacy in the hospital on the map in inches pharmacy in hospital is doing it as a part it’s a map of the town has a scale where 1inch = 0.25 miles what is the distance between the pharmacy in the hospital on the map in inches
Answer:34344e4365655.6
Step-by-step explanation:
Write an algebraic expression for 1 more than the quotient of n and 2
Answer:
1 + n/2 or n/2 + 1
Answer:2/n
Explanation:
Quotient just means "divide", so this would just be equal to
2/n
Hope this helps!
The number that has the exponent over it is called the what?
Answer: An expression that represents repeated multiplication of the same factor is called a power .
I hope this is the answer you were looking for if it's not I'm really sorry:(
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 8% vinegar, and the second brand contains 13% vinegar. The chef wants to make 270 milliliters of a dressing that is 9% vinegar. How much of each brand should she use
Answer:
Amount of 8% vinegar = 216 mL
Amount of 13% vinegar = 54 mL
Step-by-step explanation:
First, of all, let x be the amount of 8% vinegar used
Since, the scientist needs 270 mL of vinegar, then;
Let 270 - x be the amount of 13% vinegar used
Now, we are told that she needs 270 mL of a 9% vinegar.
This means that;
8%x + 13%(270 - x) = 9%(270)
Simplifying this gives;
0.08x + 0.13(270 - x) = 0.09 × 270
Expanding the bracket gives;
0.08x + 35.1 - 0.13x = 24.3
0.13x - 0.08x = 35.1 - 24.3
0.05x = 10.8
x = 10.8/0.05
x = 216 mL
Thus, she will need to use 216 mL of the 8% vinegar.
Since 270 - x is the amount of 13% vinegar used , then;
the amount of 13% vinegar = 270 - 216 = 54 mL
If x-2=2^(2/3) + 2^(1/3), show that x3 - 6x3 + 6x-2=0
AC = 23. AB = 2x + 2, and BC = 3x + 6. Find BC
Answer:
21Step-by-step explanation:
Given AC = 23, AB = 2x + 2 and BC = 3x+6 then using vector notation;
BA+AC = BC
Since BA = -AB
The equation becomes -AB+AC = BC
Substituting the given equations;
-(2x+2)+23 = 3x+6
open the parenthesis
-2x-2+23 = 3x+6
-2x+21 = 3x+6
collect the like terms
-2x-3x = 6 - 21
-5x = -15
Divide both sides by -5
-5x/-5 = -15/-5
x = 3
TO get BC, we will substitute x = 3 into the expression BC = 3x+6
BC = 3(5)+6
BC = 15+6
BC = 21
Hence the length of BC is 21 units
a box shaped like a rectangular prism has a length of 8 inches and a width of 8 inches. its volume is 512 cubic inches. what is the height of the box
Answer:
8 inches
Step-by-step explanation:
the volume is length x width x height
so the equation would be 8 x 8 x (height) = 512
8x8 is 64, and you divide 512 by 64 which is 8
Answer:
16
Step-by-step explanation:
Simplify –56 ⋅ 25 ⋅ 4. State a property that you can use.
Answer: [tex]-56\cdot 25\cdot 4 = -5600[/tex] .
Step-by-step explanation:
Associative property of multiplication : We can group numbers to multiply in any order like
[tex]p\times (q \times r) = (p\times q )\times r = p\times q\times r[/tex], where p , q and r can be any expression.
The given expression : [tex]-56\cdot 25\cdot 4[/tex]
By using associative property of multiplication, we have
[tex]-56\cdot(25\cdot 4)\\\\= -56\cdot 100\\\\=-5600[/tex]
Hence, [tex]-56\cdot 25\cdot 4 = -5600[/tex] .
Suppose statement p is true but statement q is false. Which of these compound statements are true? Check all that
apply.
p ^ q
p V q
p -> q
q -> p
p<-> q
q <-> q
Answer:
b and d
Step-by-step explanation:
Answer:
Your answer would be p V q and q->p. Hope I helped :D
If G is a 3 x 4 matrix and H is a 4 x 3 matrix, what is the dimension of GH?
Given that 110ₓ = 40₅ , find the value of x.
Answer:
is therr more to that question
Step-by-step explanation:
Answer:
x = 4
Step-by-step explanation:
110ₓ = 40₅ --------- change all to base ten.
the system called binary
1x²+1x ¹+0x⁰ = 45¹+0*5⁰
x² + x + 0 = 20
x² + x – 20 = 0
solve x using Quadratic equation
-1 ± [tex]\sqrt{1^2 - 4 * 1 * (-20)}[/tex]
x = ------------------------------------
2 * 1
x = -5; x = 4
therefore, x = 4
Write the phrase as an algebraic expression. A number less than eight and two thirds HELP ME
The picture is the answer
The algebric expression of the given phrase will be x < 8 + 2/3.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given phrase,
A number less than eight and two thirds
Suppose that number is x then,
x < 8 + 2/3
Hence "The algebric expression of the given phrase will be x < 8 + 2/3".
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