Answer:
[tex]Fourth \: option: y^2=9^2+19^2-2(9)(19) cos(41°)[/tex]
[tex]The \: law \: of \: cosines \: to \: solve \: for \: one \: side \: is:[/tex]
[tex]c^2=a^2+b^2-2ab \: cos \: C[/tex]
We must know the other two sides (a and b) and the angle between these sides (angle C, the opposite to the side that we want to determine)
In this case c=y, a=9, b=19, and C=41°, then:
[tex]y^2=9^2+19^2-2(9)(19) \: cos \: (41°)[/tex]
Roy used 1/4 of his money on 3 pens and 6 notebooks. The cost of each pen is 3 times the cost of each notebook. He bought some more pens with 2/3 of his remaining money. How many pens did Roy buy altogether?
=========================================================
Explanation:
Roy spends 1/4 of his money on 3 pens and 6 notebooks. That means 3/4 of it is leftover.
2/3 of 3/4 = (2/3)*(3/4) = 1/2 of his money is spent on buying some unknown number of additional pens. We'll come back to this later.
---------------
In terms of cost,
1 pen = 3 notebooks
which is another way of saying 1 pen is the same price as 3 notebooks.
Multiply both sides by 2 to get
2 pens = 6 notebooks
Therefore, saying "3 pens + 6 notebooks" is the same as "3 pens + 2 pens = 5 pens" when just thinking about costs.
---------------
In short, Roy buying 3 pens and 6 notebooks is the same as him buying 5 pens. He spends 1/4 = 25% of his money on getting these 5 pens.
Multiply those two values by 2 to find that 50% = 1/2 of his money would allow him to get 10 pens.
--------------
Recall that at the end of the first section, we concluded that Roy spent 1/2 of his money on buying those unknown additional number of pens. Then the previous section mentioned that 1/2 of his money gets him 10 pens. Therefore, he must have bought 10 additional pens on top of the original 3 mentioned in the instructions.
Overall, he purchased 3+10 = 13 pens
Answer:
13 pens
Step-by-step explanation:
If a pen costs 3 times the cost of a notebook, then the cost of 3 notebooks will equal the cost of a pen. The 6 notebooks that Roy bought are equivalent in cost to 2 pens, so 1/4 of Roy's money is the cost of 3+2 = 5 pens.
After the first purchase, Roy has (1 -1/4) = 3/4 of his money remaining. If he spends 2/3 of that on more pens, he will have spent ...
(2/3)(3/4) = 2/4
of his money on more pens. We've already seen that 1/4 of his money buys 5 pens, so 2/4 will buy 10 more pens.
Roy bought 3 +10 = 13 pens altogether.
Help help please …thanksss
Danielle earns a 7.75% commission on everything she sells at the electronics store where she works. She also earns a base salary of $800 per week. How much did she earn last week if she sold $4,700 in electronics merchandise? Round your intermediate calculations and answer to the nearest cent.
Answer:
1164.25
Step-by-step explanation:
90 is 95% of what number?
Answer:
94.74
Step-by-step explanation:
Hope this helps!
Answer:
94.74
Step-by-step explanation:
Please help me with this
Answer:
The measure of <Y = 85 degrees
Step-by-step explanation:
you can solve this problem algebraically if you know that the sum of the interior angles of a triangle is 180 degrees.
if you add all of these angles and set them equal to 180, you can find what "a" is.
a+2a+a+10=180 so 4a+10=180 so a is 42.5 (which is equal to angle x)
then looking at all of the options, it can be seen that the first two options are incorrect because angle x is equal to 42.5 degrees.
you know that angle y is equal to 2a, so multiplying "a" by two, you can find that angle y is 85 degrees.
Find the area for each of the given shapes below. If a shape has shading, find the area of the shaded region only.
Answer:
a. 39 ft²
c. 2x² +11x +12
e. 35 yd²
Step-by-step explanation:
a.The missing vertical dimension is 5-3 = 2'. The missing horizontal dimension is 11-8 = 3'. Then the figure can be decomposed into a rectangle 11'×3' and one that is 3'×2'. The sum of those areas is ...
total area = (11 ft)(3 ft) +(3 ft)(2 f) = (3 ft)(11 +2 ft) = (3 ft)(13 ft) = 39 ft²
__
c.We don't know what to make of the rectangles in each corner, so we'll assume they are distorted right-angle indicators. The area is the product of the dimensions shown:
A = LW
A = (2x +3)(x +4) = 2x² +11x +12 . . . area of figure
__
e.The shaded area is half the area of the rectangle. That is the same area you get if you use the triangle formula for the area of the shaded triangle.
A = 1/2(14 yd)(5 yd) = 35 yd²
Wite a numerical expression for the below problems. Simplify the expressions.
Multiply six times three then divide by lwo
The quotient of twelve and two subiracled from thirty-six
Answer:
1) 9
2) 34
Step-by-step explanation:
For the first one, it would be
= (6×3)/2
= 18/2
= 9
The second one is,
= 36- (12/6)
= 36 - 2
= 34
Help anyone?? Not that hardd
no links ! :(
Answer:
1.2
Step-by-step explanation:
First, you cancel out [tex]\frac{6}{20}[/tex] to become [tex]\frac{3}{10}[/tex]
Then that becomes [tex]-\frac{3}{10}+1.5[/tex]
Now, you convert the element to a decimal form to be [tex]-0.3+1.5[/tex]
Finally, you subtract them (because a negative plus a positive is subtraction) to get the final answer of 1.2
Hope this helps!
A U.S. citizen invested a $1200 government stimulus check they received on March 1, 2020,
into stocks that grew with an annual percentage rate of 20.2%, compounded continuously.
How much are these stocks worth 9 months later on December 1, 2020? Round to two
decimal place accuracy. (Hint: 9 months = 0.75 years)
The stocks are worth $ 1396.29 nine months later.
Using the continuous compounding formula,
[tex]A = Pe^{rt}[/tex] where
A = final amount of stocks P = initial amount of stocks = $1200, r = compounding rate = 20.2 % = 0.202 t = 9 months = 0.75 yearsSubstituting the values of the variables into the equation, we have
[tex]A = Pe^{rt}[/tex]
[tex]A = 1200e^{0.202 X 0.75}\\A = 1200e^{0.1515}\\A = 1200(1.1636)\\A = 1396.29[/tex]
So, the stocks are worth $ 1396.29 nine months later.
Learn more about continuous compounding here:
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Josh and Adelina are staff members for a political candidate. They are considering hiring callers who will call voters and ask for donations. (picture below)
a) only adelina's
b) only josh's
c) both statements are correct
d) neither statements are correct
Answer:
Adelina
Step-by-step explanation:
Amina recently moved and got a new job. The quickest way to get to work is to take a
freeway that charges a toll. There are two options for paying the tolls.
Option A: No monthly fee, each trip on the tollway is $2.80.
Option B: $30 monthly fee, each trip on the tollway is half-priced at $1.40.
a. Write a linear model for Option A showing the total cost, C, in dollars, for x trips on
the tollway.
b. Write a linear model for Option B showing the total cost, C, in dollars, for x trips on
the tollway.
c. How many trips on the tollway are needed for Option B to be cheaper? Show your
work or explain how you found this number.
d. If Amina plans to travel to and from work 5 times a week which option, should she
purchase? (assume a month has 4 weeks) Show your work and explain in words why
you choose the option that you choose.
22 trips on the tollway are needed for Option B to be cheaper. Thus, if Amina plans to travel to and from work 5 times a week (20 round trips per month, that is, 40 trips), she must choose Option B.
Since Amina recently moved and got a new job, and the quickest way to get to work is to take a freeway that charges a toll, and there are two options for paying the tolls:
Option A: No monthly fee, each trip on the tollway is $ 2.80.
Option B: $ 30 monthly fee, each trip on the tollway is half-priced at $ 1.40.
To determine how many trips on the tollway are needed for Option B to be cheaper; y, if Amina plans to travel to and from work 5 times a week, which option should she purchase; the following calculation must be performed:
Option A = 2.80X Option B = 30 + 1.40X 2.80 x 20 = 56 30 + 1.40 x 20 = 58 2.80 x 25 = 70 30 + 1.40 x 25 = 65 2.80 x 24 = 67.2 30 + 1.40 x 24 = 63.6 2.80 x 22 = 61.6 30 + 1.40 x 22 = 60.8
Therefore, 22 trips on the tollway are needed for Option B to be cheaper. Thus, if Amina plans to travel to and from work 5 times a week (20 round trips per month, that is, 40 trips), she must choose Option B.
Learn more about maths in https://brainly.com/question/25806839
1) A museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Let x represent the amount borrowed at 7%, y represent the amount borrowed at 8.5%, and z represent the amount borrowed at 9.5%. Set up a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $169,750 and the amount borrowed at 8.5% is four times the amount borrowed at 9.5%. Then write the system in matrix form. You do not have to solve the system.
Based on the information the amount borrowed at each rate is:
Z=9.5%=$350,000Y= 8.5%=$1,400,000X=7% =$250,000Let x=9.5%
Let 4x= 8.5%
Let 7% =$2,000,000 - 5x
Formulate
0.095x + 0.085(4x) + 0.07(2,000,000-5x) = 169,750
Collect like terms
0.095x + 0.34x + 140,000 - 0.35x = 169,750
Divide both side by 0.085x
0.085x = 29,750
x=29,750/0.085
x =$350,000
Amount borrowed at each rate:
Z=9.5% =$350,000
Y= 8.5% =$350,000×4
Y= 8.5% =$1,400,000
X=7% =$2,000,000 - 5($350,000)
X=7%=$2,000,000-$1,750,000
X=7% =$250,000
Matrix form
Z $350,000
Y $1,400,000
X $250,000
Inconclusion the amount borrowed at each rate is: $350,000; $1,400,000; $250,000.
Learn more about amount borrowed here:https://brainly.com/question/24576997
How do I solve this and what is the answer to this?! Number 14.
Answer:
You'll have to give more information about the question or about what you need solved.
Step-by-step explanation:
Dave and Kyle are 40 miles apart on a path when they start moving toward each other. Dave runs at a constant speed of 8 miles per hour, while Kyle walks at a constant speed of 5 miles per hour. How long does it take until they meet?
Answer:
About 3 hours
Step-by-step explanation:
together, they go 13 miles in one hour. 40/13 = 3 with remainder 1
sin(83)cos(7) + cos(83)sin(7)
Answer:
1
Step-by-step explanation:
correct on edge
sin(83 radians) * cos(7 radians)) + (cos(83 radians) * sin(7 radians)) =
0.893996664
Answer:
hope it helps
Yesterday, Carmen went surfing and was out for 5 hours. Today, she spent 60% more time
than yesterday riding waves. How long was Carmen out surfing today?
Answer:
Today, Carmen out surfing for 8 hours
Step-by-step explanation:
160/100 × 5 = 8
1. A stack of boards is 21 inches high. Each board is 1¾ inches thick. How many boards are there
Answer:
12
Step-by-step explanation:
We can solve this by setting up an equation with the variable x representing the number of boards. Since x number of 1.75 inches thick boards sum up to the height of 21 inches, the equation is 1.75x = 21, so x = 12. There are 12 boards.
At the end of the year, company A paid a dividend of 3,000 VND/share. Speed
constant annual dividend growth of 5%.
The current selling price of stock A is VND 60,000/share.
Definition of cost of common equity
Answer:
all u do is take 3000×5%=150
The graph of the function f is shown below
Find f(0)
Answer:
2
Step-by-step explanation:
Write that down before Katie deletes it. There is no work to show, only read the graph.
the IQR of the box plot is...
Answer:
IQR = 3
Step-by-step explanation:
Subtract your Q1 and Q3.
Q1 = 3
Q3 = 6
NO LINKS
A jaguar can run 40 miles per hour while a giraffe can run 32 per mile if they both run for 4 hours how much farther will the jaguar run? Show TWO ways to write the expression or equation and solve
Answer:
(40*4)-(32*4)=32
160-128=32
Step-by-step explanation:
The ratio of men to women working for a company is to 8 to 5 . If there are employees total 208 , how many women work for the company?
Answer:
130
ratio of woman to man is : 5/8
5/8×208=130
Answer:
130 women
Step-by-step explanation:
3 men to 5 women:
We can add the variable x:
3x + 5x = 208
8x = 208
x = 26
3 * 26 = 78 men,
5 * 26 = 130 women.
a man buys an article for $600 and sells it for $710/ what is the profit or loss
Answer:
110$ (profit)Step-by-step explanation:
a man buys an article for $600 and sells it for $710/ what is the profit or loss?
a financial gain, especially the difference between the amount earned and the amount spent in buying, operating, or producing something.
so
710 - 600 = 110$ (profit)
Answer:
Profit of 110
Step-by-step explanation:
As he sells it at a higher price, he makes a profit.
Which of the following are steps in practical problem solving?
Answer:
Assign an identifying variable to the quantity to be found. Write a sentence stating conditions placed on the quantity. Solve the sentence for the variable.
Step-by-step explanation:
can you mark me as brainlist
The answer is A but I couldn’t tell you why. If someone know, please let me know.
Answer:
a.0.311
Step-by-step explanation:
BRAINLIEST ANSWERWhat is the approximate surface area of the sphere? Round to the nearest hundredth and use 3.14 for Pi. Recall the formula S A = 4 pi r squared. A sphere with a radius of 9. 113.04 square units 226.08 square units 1,017.36 square units 4,069.44 square units
Answer:
Step-by-step explanation:
A = 4πr² = 4π9² = 324π units²
324(3.14) = 1,017.36 units²
3x2 - 4x – 7
factor
Answer:
3x2 = 6
6-4x-7
(6-4x) - 7
2x - 7 = messi ok no xd
3.5-
Step-by-step explanation:
Answer:
[tex](3x-7)(x+1)[/tex]
Step-by-step explanation:
Use the slide-and-divide method:
[tex]3x^2-4x-7[/tex]
[tex]x^2-4x-21[/tex] <-- Multiply last term by the leading coefficient 3
[tex](x-7)(x+3)[/tex] <-- Factor
[tex](3x-7)(x+1)[/tex]
An ice cream stand uses the expression to determine the cost (in dollars) of an ice cream cone that has scoops of ice cream.2 + 0.5x2+0. 5x2, plus, 0, dot, 5, xxxx
How much does an ice cream cone with scoops cost?55
Answer:
answer: 0
Step-by-step explanation:
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
(x+4)•(x-1)
——————————— • 2 = 0 • 2
2
Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
(x+4) • (x-1) = 0
7.2 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
simple form
x = 1
x = -4
Find the quotient: 7,308 divided by 18. A) 46 B) 406 C) 406 10/18. D) 408
Answer:
7308 / 18
= 406
B is the answer.
Help me with this plzzzzzzzzz
Answer:
B : x € (-∞, 1)
Step-by-step explanation:
we have 4x +9 -2 +3x < 14
7x +7 < 14
7(x+1) < 14
x + 1 < 2
x < 1
=> x € (-∞, 1)