Answers
Answer:
x = 45°
Step-by-step explanation:
We know that (2x + 45)° and x° are adjacent angles, so they add up to 180°.
(2x + 45) + x = 180
3x + 45 = 180
3x = 180 - 45
3x = 135
x = [tex]\frac{135}{3}[/tex]
x = 45°
Related Questions
if tan theta =3, find the value of tan theta + tan (theta+pi) + tan (theta +2pi)
Answers
Answer:
[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 9[/tex]
Step-by-step explanation:
Given
[tex]tan\theta = 3[/tex]
Required
Find
[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi)[/tex]
Calculate [tex]tan(\theta + \pi) \ and\ tan(\theta+2\pi)[/tex]
Using tan rule
[tex]tan(\theta + \pi) = \frac{tan\theta + tan\pi}{1 - tan\theta tan\pi}[/tex]
So:
[tex]tan(\theta + \pi) = \frac{tan\theta + 0}{1 - tan\theta *0}[/tex]
[tex]tan(\theta + \pi) = \frac{tan\theta}{1 }[/tex]
[tex]tan(\theta + \pi) = \tan\theta[/tex]
[tex]tan(\theta+2\pi)[/tex]
[tex]tan(\theta + 2\pi) = \frac{tan\theta + tan2\pi}{1 - tan\theta tan2\pi}[/tex]
[tex]tan(\theta + 2\pi) = \frac{tan\theta + 0}{1 - tan\theta *0}[/tex]
[tex]tan(\theta + 2\pi) = \tan\theta[/tex]'
'So:
[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi)[/tex] [tex]= tan\theta +tan\theta +tan\theta[/tex]
[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 3+3+3[/tex]
[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 9[/tex]
What number is 73 1/4th of
Answers
Step-by-step explanation:
70x4=280
12x4=48
48+280=328
HELP SOON PLEASE!!!!!
Answers
An arctic cold front is moving through an area. It is 37F when the temperature begins to drop. The scatter plot suggests a linear relationship between the temperature and the number of hours since the cold front arrived. Use the scatter plot to answer parts ac.
Answers
Answer: The slope describes the change in temperature for every hour after the cold front arrives.
Step-by-step explanation:
A manufacturing company produces 3 different products A, B, and C. Three types of components, i.e., X, Y, and Z, are used in the production of these products. One unit of product A requires 2 units of X, 2 units of Y, and 2 units of Z. One unit of product B requires 1 unit of X, 3 units of Y, and 2 units of Z. One unit of product C requires 1 unit of X, 2 units of Y, and 3 units of Z.Currently, the company has no existing inventory of the components. The company can purchase X at the price of $20 per unit but no more than 300 units due to the supplier's limited capacity constraint. The company can purchase Y at the price of $30 per unit without any upper limit. The company can purchase Z at the full price of $25 per unit for the first 100 units but the per unit price drops to $20 for the remaining units if any i.e., the purchase quantity in excess of 100 units). The market prices of the three products are $200 for A, $240 for B and $220 for C. The company knows that the demand for products A, B, and Care equal to 100, 80, and 90 units, respectively. Therefore, the company should not produce more than the demand for each product. However, the company incurs a per unit penalty of $40 for any unsatisfied demand. The company needs to decide the component płarchase plan and the production mix decisions to maximize its profits subject to all the business constraints described above. Formulate the company's problem as an optimization problem, i.e., providing the mathematical expressions for the decision variables, the objective function, and the constraints.
Answers
Answer:
Step-by-step explanation:
Using the Excel Formula:
Decision Variable Constraint Constraint
A 65 65 100
B 80 80 80
C 90 90 90
14100 300 300
= (150 *B3)+(80*B4) +(65*B5)-(100-B3+80-B4+90-B5)*90
Now, we have:
Suppose A, B, C represent the number of units for production A, B, C which is being manufactured
A B C Unit price
Need of X 2 1 1 $20
Need of Y 2 3 2 $30
Need of Z 2 2 3 $25
Price of
manufac - $200 $240 $220
turing
Now, for manufacturing one unit of A, we require 2 units of X, 2 units of Y, 2 units of Z are required.
Thus, the cost or unit of manufacturing of A is:
$20 (2) + $30(2) + $25(2)
$(40 + 60 + 50)
= $150
Also, the market price of A = $200
So, profit = $200 - $150 = $50/ unit of A
Again;
For manufacturing one unit of B, we require 1 unit of X, 3 units of Y, and 2 units of Z are needed and they are purchased at $20, $30, and 425 each.
So, total cost of manufacturing a unit of B is:
= $20(1) + $30(3) + $25(2)
= $(20 + 90+50)
= $160
And the market price of B = $240
Thus, profit = $240- $160
profit = $80
For manufacturing one unit of C, we have to use 1 unit of X, 2 unit of Y, 3 units of Z are required:
SO, the total cost of manufacturing a unit of C is:
= $20 (1) + $30(2) + $25(3)
= $20 + $60 + $25
= $155
This, the profit = $220 - $155 = $65
However; In manufacturing A units of product A, B unit of product B & C units of product C.
Profit --> 50A + 80B + 65C
This should be provided there is no penalty for under supply of there is under supply penalty for A, B, C is $40
The current demand is:
100 - A
80 - B
90 - C respectively
So, the total penalty
[tex]{(100 - A) + (80 - B) +(90 - C) } + \$40[/tex]
This should be subtracted from profit.
So, we have to maximize the profit
[tex]Z = 50A + 80B + 65C = {(100 -A) + (80 - B) + (90 - C)};[/tex]
Subject to constraints;
we have the total units of X purchased can only be less than or equal to 300 due to supplies capacity
Then;
[tex]2A + B +C \le 300[/tex] due to 2A, B, C units of X are used in manufacturing A, B, C units of products A, B, C respectively.
Next; demand for A, B, C will not exceed 100, 80, 90 units.
Hence;
[tex]A \le 100[/tex]
[tex]B \le 80[/tex]
[tex]C \le 90[/tex]
and [tex]A, B, C \ge 0[/tex] because they are positive quantities
The objective is:
[tex]\mathbf{Z = 50A + 80B + 65 C - (100 - A + 80 - B + 90 - C) * 40}[/tex]
A, B, C [tex]\to[/tex] Decision Varaibles;
Constraint are:
[tex]A \le 100 \\ \\ B \le 100 \\ \\ C \le 90 \\ \\2A + B + C \le 300 \\ \\ A,B,C \ge 0[/tex]
5. Which of the following rules could represent a transformation that mapped one shape onto another
to establish their congruence?
A) K(x,y) ---->(x-3,3y)
C) K(x, y) ---->(-y,x+2)
B) K(x, y)
--->(2x, y)
D) K(x, y) - - - - > (5x, 5y)
Answers
Answer:
i think it’s C
Step-by-step explanation:
1.1.
A quadratic pattern has a second term equal to 1, a third term equal to -6 and a fifth term equal to
- 14.
1.1.1. Calculate the second difference of this quadratic pattern.
(5)
Answers
The second difference of this quadratic pattern is 2.
The first term of this quadratic pattern is 10.
Quadratic patternA sequence of numbers has a quadratic pattern when its sequence of second differences is constant. Therefore,
let the first and fourth term be a and b.
Therefore,
first difference:
1 - a; - 6 - 1 = -7; b + 6; -14 - b;
Second difference:
The second difference is constant . Therefore,
-7 - (1 - a) = -8 + a; b + 6 + 7 = b + 13; -14 - b - b - 6 = -2b - 20;
Therefore,
b + 13 = -8 + a
b - a = -21
Then,
-2b - 20 = b + 13
-3b = 33
b = 33 / -3
b = - 11
Therefore,
- 11 - a = - 21
-a = -21 + 11
-a = -10
a = 10
Hence, the second difference = b + 13 = -11 + 13 = 2
First term = a
Therefore,
a = 10
learn more on quadratic pattern here:https://brainly.com/question/21517782
Given f ( x ) = 7 x + 5 Solve f ( x ) = 19
Answers
Answer:
2
Step-by-step explanation:
Given
f ( x ) = 7 x + 5
f ( x ) = 19
Now
f(x) = 7x + 5
19 = 7x + 5
7x = 19 - 5
7x = 14
x = 14 / 7
x = 2
Hope it will help :)❤
Answer:
Step-by-step explanation:
7x + 5 = 19
7x = 14
x = 2
Answer this question: -5x - 10y + 7x + 15y
Please try to explain it as best as possible <3
Answers
There’s also this app called Cymath where you type in your math equation and it gives you the answer
Answer:
2x + 5y
Step-by-step explanation:
-5x - 10y + 7x + 15y
add the ones with the same variables
-5x + 7x - 10y + 15 y
2x + 5y
and there you have the answer "2x + 5y"
what is the slope of the line through the points (-2,-1) and (4,3)
Answers
Answer:
2/3
Step-by-step explanation:
the slope is change of y divided by change of x
[tex]m = \frac{2}{3} [/tex]
Step-by-step explanation:-
[tex]( - 2, - 1) = (x {1} ,y {1}) [/tex]
[tex](4,3) = (x{2} ,y{2} )[/tex]
BY USING SLOPE OF LINE FORMULA
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]m = \frac{(3 - ( - 1))}{(4 - ( - 2))} [/tex]
[tex]m = \frac{(3 + 1)}{(4 + 2)} [/tex]
[tex]m = \frac{4}{6} [/tex]
[tex]m = \frac{2}{3} [/tex]
f(x)=x^(2)-13x+34, find x when f(x)=-2
Answers
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Answer:
Let's simplify step-by-step.
−2^2 − 13x + 34
= −4 + −13x + 34
Combine Like Terms:
= −4 + −13x + 34
= ( −13x ) + ( −4 + 34 )
= −13x + 30
Answer:
= −13x + 30
55 is 22% of what number?
Answers
Answer:
250
Step-by-step explanation:
100 / 22 = 4.54545455
4.54545455 x 55 = 250
Answer: 250
Step-by-step explanation:
Ur welcome
(55x100)/22
help
The formula for the volume of the circular cylinder show is v= r^2h. If r= 2b and h= 5b+3, what is the volume of the cylinder in terms of b?
Answers
Answer:
Step-by-step explanation:
The equation for volume is incorrect. The volume of a cylinder with radius r and height h is πr²h.
volume = π(2b)²(5b+3)
= π(4b²)(5b+3)
= π(20b³+12b²)
The formula for the volume of the given circular cylinder in terms of b is [tex]V = 20b^3 + 12b^2[/tex]
The given expression:
volume of circular cylinder, V = r²h
r = 2b
h = 5b + 3
To find:
the volume of the cylinder in terms of bTo find the volume of the cylinder in terms of b, we will substitute the given values of r and h as follows;
[tex]V = r^2 h\\\\V = (2b)^2 (5b + 3)\\\\simplify \ the \ expression;\\\\V = 4b^2 (5b + 3)\\\\remove \ the \ bracket \ by \ multiplying \ through \ by \ 4b^2\\\\V = 20b^3 + 12b^2[/tex]
Thus, the volume of the cylinder in terms of b is [tex]V = 20b^3 + 12b^2[/tex]
Learn more here: https://brainly.com/question/16142311
Point A is at (3,5). After being translated 10 units down, what are the coordinates of Point A?
Answers
Answer: The required co-ordinates of the new point are (6, 5).
Step-by-step explanation: Given that the point (-3, 15) undergoes a translation of 9 units right and 10 units down.
We are to find the coordinates of the new point.
We know that
if the point (x, y) undergoes a translation of 9 units right and 10 units down, then its translation rule is given by
(x, y) ⇒ (x+9, y-10).
Therefore, the co-ordinates of he new point are given by
(-3, 15) ⇒ (-3+9, 15-10) = (6, 5).
Thus, the required coordinates of the new point are (6, 5).
How would the following triangle be classified?
A triangle has three unequal sides. One of the angles formed is 90 degrees; the other two angles are less than 90 degrees.
Answers
Answer:
Scalene. A scalene triangle has three different angles and none of its sides are equal in length
What is the sum?
8+(-12)
-20
-4
4
20
Answers
Answer:
-4
Step-by-step explanation:
un comerciante vende un artículo en $196 y obtiene como telera con tanto porciento igual al precio del costo del artículo Hallar el costo del artículo
Answers
Answer:
$196 es el precio del articulo
Select all numbers that are solutions to the inequality w < 1.
Answers
Answer:
-5, -1.3, 0, and 0.9
Step-by-step explanation:
Answer:
2)-5
3)0
4)0.9
5)-1.3
Step-by-step explanation:
the given inequality tells us that every numbers which are less than 1 are the solution for w
there're only 3 numbers which are less than 1 i.e
2)-53)04)0.95)-1.3Using numbers 12,4,5,17,12 make 24.
Helllpppp
Answers
Answer: To get 24
Step-by-step explanation
What you would need to do is first multiply 12 x 5 would come out as 60.
Then from 60 you subtract 17 and 12 to get 5. Divide by the 5 that you just got from 17 and 12 and to get 20. Using the 4 add it to the 20 to get 24.
somebody help me with math:
Which situation would not be represented by the integer -10?
options:
1.A 10 yard penalty
2.You owe $10.
3.A hole 10 feet deep.
4.temperature of 10°.
Answers
Answer:
D
Step-by-step explanation:
Just stating the temperature, hope this helps
Answer:
temperature of 10 degrees
Step-by-step explanation:
every other option is negative, like owing $10 means you will have 10 less dollars, a hole 10 feet deep is 10 feet under the ground's surface, so they would be represented by -10. A temperature of 10 degrees is the only positive option :)
The circle graph shows how a family spends its annual income. If $37,800 is used for Housing and Clothing combined, what is the total annual
income?
Answers
Answer:
$90000
Step-by-step explanation:
From the pie chart,
Let the total annual income = $y
The percentage of housing = 28 %
The percentage of clothing = 14 %
The combined percentage of housing and clothing = 28+14 = 42 %
If the amount spent on both housing and clothing combined = $ 37800
Therefore,
y(42/100) = 37800
Solve for y
42y = 37800×100
42y = 3780000
y = 3780000/42
y = $90000
Hence, the total annual income is $90000
Declan's goal is to score 90% on the upcoming science test. If there are 50 questions on the test, how many does he need to answer correctly?
Answers
Answer:
45
Step-by-step explanation:
Does this graph represent a function? Why or why not?
• A. No, because it is not a straight line.
C B. No,
because it fails the vertical line test.
C. Yes, because it is curved line.
D. Yes, because it passes the vertical line test.
Answers
Answer:
Option D is the correct answer
Step-by-step explanation:
D. Yes, because it passes the vertical line test.
Circle the value of 25
10
25
32
Answers
Answer:
10
Step-by-step explanation:
(15x-7)-(23x-2)
use foil
Answers
Answer:
=15x-7-23+2
=-8x-7+2
=-8x-5
Step-by-step explanation:
How many integers satisfy each inequality?
-2 < x < 5
Answers
Answer:
all the numbers from -3 to 4
Step-by-step explanation:
so it would be,, 8 integers in total.
-3,,-2,,-1,,0,,1,,2,,3,,4
Answer:
6
Step-by-step explanation:
-2 , to 5 on a number line would be 6 apart
-1,1,2,3,4,5
cindy paid $2.58 for a 2/3 pounds of sunflower seeds. how much does each pound of sunflower cost?
Answers
Answer:
3.87
Step-by-step explanation:
2.58/2=1.29=1/3 pounds
1.29*3=3.87
21 divided by 4 equals 5 1/4
Answers
Answer:
yes
Step-by-step explanation:
5th grade math. Correct answer will be marked brainliest.
Answers
Answer: The answer would be (0,3)
Answer:
(0,3)
Step-by-step explanation:
The horizontal line is always x, and the vertical line is always y. You can see that D is 0 to the right and 3 up, so the answer will be (0,3)
A pack of 4 rolls of Charmin cost $3.64. A pack of 32 rolls of Charmin cost $20.80. How much cheaper per roll is it to purchase the bigger pack?
Answers
Answer:
.26 cents cheaper a roll
Step-by-step explanation:
to find this you would do 3.64/4 to get the price a roll which is .91
and then you would do 20.80/32 to get the price per roll which is .65
then to get the difference you would do .91-.65 to get .26