Answer:
f(g(2)) = 29
Step-by-step explanation:
First of all we write the new function defined as the composite function of f and g: f(g(x)) = 3(5x+1) - 2 = 15x + 3 - 2 = 15x -1
Now we can simply "plug in" 2 instead of the x in the function we just obtained: f(g(2)) = 15*2 - 1 = 29
A triangular prism is 18 centimeters long and has a triangular face with a base of 12 centimeters and a height of 8 centimeters. The other two sides of the triangle are each 10 centimeters.
What is the surface area of the triangular prism?
Answer:
672 sq cm
Step-by-step explanation:
Each triangular base is 1/2 (12 * 8) or 48, making them = 96.
One of the sides is 12 x 18 = 216
The other 2 sides are 10 x 18 = 180 x 2 = 360
Add them all together to get 672 sq cm
Define the following sequence recursively:
4, 15, 26, 37, ...
Answer:
a) f(n) = 11 + f(n - 1)
Step-by-step explanation:
f(2) = 11 + 4 = 15
f(3) = 11 + 15 = 26
f(4) = 11 + 26 = 37
f(5) = 11 + 37 = 48
Need some help in this please
Answer:
∠GHD is 85°
Step-by-step explanation:
180°-95°
85°
Omar needs at least $8 to buy lunch. Which number line represents this scenario?
Answer:
I'd say none, as we're missing something in this problem. Make sure you've included everything to solve this problem. Thanks.
Mary has 18 ounces of apple chips she evenly portions the apple chips between four containers how many ounces of apple chips are in one container
Answer:
4.5 ounces
Step-by-step explanation:
18/4=4.5
The area of the Mountain Island Educational State Forest in North Carolina is 3 square miles. What is the area, in square yards, of this forest
The area of the forest in square yards is [tex]9.3 \times 10^6[/tex]
The area of the forest in square miles is given as:
[tex]Area = 3mi^2[/tex]
To convert the area to square yards from square miles, we multiply the area by 3.098 * 10^6.
So, we have:
[tex]Area = 3 \times 3.098 \times 10^6yd^2[/tex]
Evaluate the product
[tex]Area = 9.294 \times 10^6yd^2[/tex]
Approximate
[tex]Area = 9.3 \times 10^6yd^2[/tex]
Hence, the area of the forest in square yards is [tex]9.3 \times 10^6[/tex]
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20 is 25% of what number?
Enter your answer in the box.
Answer:
80
Step-by-step explanation:
25 percent is equal to 1/4
1/4 of 80 is 20
Answer:
80
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPP
Answer: b
Step-by-step explanation: graph b is correct hope it helps
A line with a slope of 10 passes through the point (0,4). What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y=10x+4
Step-by-step explanation:
y-y1=m(x-x1)
y-4=10(x-0)
y-4=10(x)
y-4=10x
y=10x+4
I’ll give the crown thing
The band sold 456 pies in 2 weeks. Which proportion could be used to make the best estimate for the number of pies that will be sold in 12 weeks?
Answer:
i would say A. if its not a its B.
Step-by-step explanation:
Sammy's Chipmunk & Squirrel Observations
For a science project, Sammy observed a chipmunk and a squirrel stashing
acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The
squirrel hid 4 acorns in each of the holes it dug. They each hid the same number
of acorns, although the squirrel needed 4 fewer holes. How many acorns did the
chipmunk hide?
Answer:12 accorns
Step-by-step explanation:
If they each hid the same number of acorns, although the squirrel needed 4 fewer holes, the chipmunk hid 3 acorns in each hole
Let's assume the number of holes the chipmunk dug is 'c', and the number of acorns it hid in each hole is 'x'. Similarly, let's assume the number of holes the squirrel dug is 's', and the number of acorns it hid in each hole is 'y'.
According to the information provided, the chipmunk hid 3 acorns in each of the holes it dug, so x = 3. The squirrel hid 4 acorns in each of the holes it dug, so y = 4.
Both the chipmunk and squirrel hid the same number of acorns, so cx = sy.
Also, the squirrel needed 4 fewer holes, so s = c - 4.
Now, we can use the information to set up a system of equations:
cx = sy
c - 4 = s
Substitute the value of s from the second equation into the first equation:
c(c - 4) = 3(c - 4)
Expand the equation:
c² - 4c = 3c - 12
Now, bring all terms to one side of the equation:
c² - 4c - 3c + 12 = 0
Combine like terms:
c² - 7c + 12 = 0
Now, factor the quadratic equation:
(c - 3)(c - 4) = 0
Now, set each factor to zero and solve for 'c':
c - 3 = 0 => c = 3
c - 4 = 0 => c = 4
Since the chipmunk hid 3 acorns in each hole, the correct answer is The chipmunk hid 3 acorns.
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18. A glasscutter needs to cut rectangular pieces of
glass to make an aquarium. How can he make sure
that the glass pieces he is going to cut are
rectangular in shape? Justify your reasoning
For the cut glass pieces to be rectangular in shape, the glass cutter should ensure:
All four interior angles = 90° each.Opposite sides are parallel and equal to each other.Diagonals should be of the same length and should bisect each other.Properties of a RectangleAll four angles of a rectangle are 90° each.There are two pairs of parallel sides that are equal in length.The diagonals bisect each other and are of equal length.
Thus, to ensure the cut glass pieces are rectangular in shape, he should ensure the following:
Make the four interior angles 90° each.The opposite sides should be parallel and equal to each other.The diagonals should be of the same length and should bisect each other.Learn more about properties of rectangle on:
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20x^5 y^3 + 8x^6 y^3 - 4x^5 y^2
———————————————
4x^5 y^2
Answer:
1) 4x^{5} y^{2} (5y+2xy-1)
2) Implied to have no solution based on given context.
Step-by-step explanation:
Problem 1:
1) Find the Greatest Common Factor (GCF).
[tex]GCF=4x^{5} y^{2}[/tex]
2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
[tex]4x^{5}y^{2} (\frac{20x^{5} y^{3} }{4x^{5}y^{2} } +\frac{8x^{6}y^{3} }{4x^{5} y^{2} } +\frac{-4x^{5} y^{2} }{4x^{5} y^{2} } )[/tex]
3) Simplify each term in parentheses.
[tex]4x^{5} y^{2} (5y+2xy-1)[/tex]
Problem 2:
From the way the problem is given, there is no solution.
Jillian is making accessories for the soccer team. She uses 677.46 inches of fabric on headbands for 38 players and 4 coaches. She also uses 366.32 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
The amount of fabric used to make the headband is 16.13 inches. The amount of fabric used to make the wristband is 9.64 inches.
In order to determine the amount of fabric used to make the accessories, the total inches used would be divided by the total number of people the accessory was made for.
The amount of fabric used to make headband for a player = total quantity of fabrics used / total number of people
677.46 / (38 + 4)
677.46 / 42
= 16.13 inches
The amount of fabric used to make wristband for a player = total quantity of fabrics used / total number of players
366.32 / 38 = 9.64 inches
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Write and evaluate algebraic expressions
Answer:
9b+10s
Step-by-step explanation:
you are trying to find an expression for total cost after an unknown amount of hours. you need to multiply the number of hours (defined as b and s in this example) by the cost per hour given ($9/hr for the bike and $10/hr for the scooter).
this would result in the following expression: total cost=9b+10s
Max's parents bought $8,000 from the bank for a new car. The interest rate is 6% per year. How much simple interest will they pay if they take 3 years to repay the loan?
Answer:
1440
Step-by-step explanation:
Show that the equation y + 8 = 2(4x + 4) is linear and that it represents a proportional relationship between x and y.
Answer:
Step-by-step explanation:
A company manufactures and sells personalized stationery. The weekly fixed cost is $3850 and it cost $3.00 to produce each package of stationery. The selling price is $6.50 per package. How many packages of stationery must be produced and sold each week for the company to generate a profit?
The company will generate a profit if;
more than or equal to
more than
less than or equal to
less than
|blank|packages of stationery are produced and sold each week.
(sorry forgot to add that part in last question, hope this one is better)
Answer:
more than 1100
Step-by-step explanation:
The contribution margin for each package sold is ...
$6.50 -3.00 = $3.50
The number of packages that must be sold to cover fixed costs is ...
3.50n > 3850
n > 1100 . . . . . . . divide by 3.50
The company will generate a profit if more than 1100 packages are produced and sold each week.
_____
Additional comment
If exactly 1100 packages are sold, then costs are covered, but profit is 0. In order for profit to be positive, more than 1100 packages must be sold.
When solving negative one over five (x − 25) = 7, what is the correct sequence of operations?
Multiply each side by negative one over five, add 25 to each side
Multiply each side by 5, subtract 25 from each side
Multiply each side by negative one over five, subtract 25 from each side
Multiply each side by −5, add 25 to each side
Answer:
Multiply each side by −5, add 25 to each side.
Step-by-step explanation:
Match the description with the ratio. 1. There are four red bows out of ten bows. 6:10 2. There are three silver bows for every four red bows in a bag. 3:10 3. There are six blue bows and ten silver bows. 3:4 4. There are three black bows out of a bag of ten bows. 4:10 pls help daddy
Answer:
There are six blue bows and ten silver bows. = 6:10
There are four red bows out of ten bows. = 4:10
There are three black bows out of a bag of ten bows. = 3:10
There are three silver bows for every four red bows in a bag. 3:4
Jake has two dogs, Euclid and Pythagoras. Euclid is a smaller dog and Pythagoras is larger. Jake found that Pythagoras lost 13 pounds from January to June. If Pythagoras gains 1.2 times Euclid's weight, Pythagoras's weight would still be 1/4 pound less than he did in January. What is Euclid's weight? (a) Write an equation that represents the scenario. Begin by defining your variable (b) Solve the equation. Show your work. (c) What is Euclid's weight? (d) Jake adopts a third dog, Riemann. Riemann weighs exactly twice what Euclid weighs. The combined 1 pounds. What is Riemann's weight, and what is Pythagoras's weight? weight of the three dogs is Show your work.
The weight of Euclid is 10.625 pounds, and the weight of Riemann is 21.25 pounds.
Let the current weight of Euclid = xLet the current weight of Pythagoras = TLet the January weight of Pythagoras = yThe expression that represents the given scenario is written as;
when Pythagoras lost 13 pounds: T = y - 13when Pythagoras gains 1.2 times Euclid's weight: = T + 1.2xwhen Pythagoras weight is 1/4 pound less than weight in January:
T + 1.2x + 0.25 = y
y- 13 + 1.2x + 0.25 = y
1.2x - 12.75 = 0
Euclid's weight is calculated as follows;
1.2x = 12.75
[tex]x = \frac{12.75}{1.2} \\\\x = 10.625 \ pounds[/tex]
The weight of Riemann is calculated as follows;
[tex]= 2 (10.625)\\\\= 21.25 \ pounds[/tex]
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what is the solution to the system 3x+2y=-3 and 9x +4y=3
Answer:
x=3, y=-6
Step-by-step explanation:
As you know there are many ways to solve this question! First is Subsitutuion, Second is Elimination, and Third is Graphing!
Let’s begin with our detailed answer:
As you know subsitution is solving for a variable and then it can be used as a variable substitution to figure out x and y.
So in our system of equations:
[tex]\left \ {3x+2y=-3}} \atop {9x+4y=3}} \right.[/tex]
I will just take one equation and solve for x but it actually dosent matter which variable you subsitutue and solve for.
[tex]\left \ {3x+2y=-3}} \atop {9x+4y=3}} \right.[/tex]
To eliminate this question we can divide the top part by -3:
[tex]\left \ {-9x-6y=9}} \atop {9x+4y=3}} \right.[/tex]
Let‘s sum these system of equation and we get: [tex]y=-6[/tex]
We can now insert y as -6 and solve for x:
[tex]3x-12=-3[/tex]
[tex]x=3[/tex]
So, [tex]x=3, y = -6[/tex]
Answer:
(3, - 6 )
Step-by-step explanation:
3x + 2y = - 3 → (1)
9x + 4y = 3 → (2)
Multiplying (1) by - 3 and adding to (2) will eliminate the x- term
- 9x - 6y = 9 → (3)
Add (2) and (3) term by term to eliminate x
0 - 2y = 12
- 2y = 12 ( divide both sides by - 2 )
y = - 6
Substitute y = - 6 into either of the 2 equations and solve for x
Substituting into (1)
3x + 2(- 6) = - 3
3x - 12 = - 3 ( add 12 to both sides )
3x = 9 ( divide both sides by 3 )
x = 3
solution is (3, - 6 )
Write an equation of each sentence. Use n to represent the unknown number. You can use the back page for your solution. (2 points each) 11. Six increased by a number is twenty. 12. A number decreased by seven is four. 13. The sum of two consecutive numbers is thirty-one. 14. The sum of twice a number and two is thirteen. 15. One less than a number is eighteen. 16. The square of a number increased by four is twice the number. 17. Twice a number is one-half. 18. The product of a number and its half is eighteen. 19. The average of a number and ninety is seventy. 20. Two more than a number is twelve.
PLEASE HELP Me
Hoped this helped.
[tex]-BrainaicUser1357-[/tex]
Let the number be x
#11
[tex]\\ \sf\longmapsto x+6=20[/tex]
#12
[tex]\\ \sf\longmapsto x-7=4[/tex]
#13
[tex]\\ \sf\longmapsto x(x+1)=31[/tex]
#14
[tex]\\ \sf\longmapsto 2x+2=13[/tex]
#15
[tex]\\ \sf\longmapsto x-1=18[/tex]
#16
[tex]\\ \sf\longmapsto x^2+4=17[/tex]
#17
[tex]\\ \sf\longmapsto x^2/2=18[/tex]
#18
[tex]\\ \sf\longmapsto x+90/2=70[/tex]
Find the values of the variables.
isosceles trapezoid
Side measures are: 4, 2x, 2x + 2 and 4x +3
X=
Answer:
x=-1/2
Step-by-step explanation:
2x+2=4x+3
-1=2x
x=-1/2
I need help with this solve
Answer:
the answer is 64%
Step-by-step explanation:
80/125 = 64
Kevin and Randy Muise have a jar containing 80 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $11.80. How many of each type of coin do they have?
Answer:
39 quarters and 41 nickelsStep-by-step explanation:
Let the number of quarters be x and nickels be y.
Given:
Quarter is 25 centsNickel is 5 centsNumber of coins is 80Total amount is $11.80 = 1180 centsWe have equations:
x + y = 8025x + 5y = 1180Solve the system by elimination, subtract 5 times the first equation from the second one:
25x + 5y - 5x - 5y = 1180 - 80*520x = 780x = 780/20x = 39Find the value of y:
39 + y = 80y = 80 - 39y = 41Verify:
25*39 + 5*41 = 975 + 205 = 1180Given the function f(x)=X^2- 3x, find f(-4)
Help help help help help math math math
Answer:
∠4 = 135°
Step-by-step explanation:
∠4 = the sum of the two remote angles in the triangle. (remote angles are the angles not next to ∠4
∠4 = 80° + 55°
∠4 = 135°
Answer:
<4 = 135
Step-by-step explanation:
I took this test
Convert 65/36 radians to degree.
please help I'm stuck on this question.
See picture for solution.
14. What's the least common denominator of 3/4, 4/5, and 2/3?
A. 60
B. 20
C. 15
D. 12