Answer:
[tex]g(n) = \frac{11}{3} + \frac{5n}{3}[/tex] or g(n) = (11/3) + (5/3)n
Step-by-step explanation:
Equation: [tex]3m - 5n = 11[/tex]
To write a formula for g(n) in terms of n, we have to get m seperately.
[tex]3m - 5n = 11[/tex], add 5n in both sides
[tex]3m - 5n + 5n = 11 + 5n[/tex], now add
[tex]3m = 11 + 5n[/tex], now divide both sides by 3
[tex]\frac{3m}{3} = \frac{11 + 5n}{3}[/tex]
[tex]m = \frac{11}{3} + \frac{5n}{3}[/tex]
Now, replace m with g(n)
[tex]g(n) = m[/tex]
[tex]g(n) = \frac{11}{3} + \frac{5n}{3}[/tex]
A box without a top is to be made from a rectangular piece of cardboard, with dimensions 9 in. by 10 in., by cutting out square corners with side length x and folding up the sides.
What is the optimal volume of the box, and what is the optimal cut?
Answer:
The optimal volume is 63.1142 in3, with a cut of 1.5767 inches
Step-by-step explanation:
If we make a cut of x inches to create the box, the dimensions of the box will be:
Length = 10 - 2x
Width = 9 - 2x
Height = x
So the volume of the box would be:
Volume = (10 - 2x) * (9 - 2x) * x
Volume = 4x3 - 38x2 + 90x
To find the maximum volume, we need to take the derivative of the volume and find the values of x where it is equal to zero:
dV/dx = 12x2 - 76x + 90 = 0
6x2 - 38x + 45 = 0
Using Bhaskara's formula, we have:
Delta = 38^2 - 4*6*45 = 364
sqrt(Delta) = 19.08
x1 = (38 + 19.08) / 12 = 4.7567
x2 = (38 - 19.08) / 12 = 1.5767
Testing these values in the volume equation, we have:
Volume1 = 4*(4.7567)^3 - 38*(4.7567)^2 + 90*(4.7567) = -1.1883
(Negative value for the volume is not valid)
Volume1 = 4*(1.5767)^3 - 38*(1.5767)^2 + 90*(1.5767) = 63.1142
So the optimal volume is 63.1142 in3, with a cut of 1.5767 inches
Lupe is applying for a summer job. Six employees doing the same work earn $10.50, $10.50, $10.50, $10.50, $10.50 and $25.00 per hour. In the interview, the boss tells Lupe that the average hourly wage is about $13.00. Is the boss's statement misleading? Explain why or why not?
Answer:
Yes i think it is misleading because five employees get 10.50 wich is 2.50 less than the avrege and the sixth employee is getting 24 dollars. Wich is a lot more than the averege.
Step-by-step explanation:
Which is a graph for the inequality m<(or equal to)-2?
Answer:
cool
Step-by-step explanation:
help plz help plz help plz help plz find value of b
Answer:
9. x = 16
10. x = 18
Step-by-step explanation:
9. 2x + 9 + 3x + 1 = 90
5x + 10 = 90
5x + 80
x = 16
10. 90 - 53 = 47
2x + 11 = 47
2x = 36
x = 18
Find the missing length of the triangle. *
Answer:
50 ft
Step-by-step explanation:
This is the pythagorean theorem, so you should use the formula...
a squared + b squared = c squared
Then substitute in the numbers... (remember, a and b are the legs, and c is the hypotenuse)
14 squared + 48 squared = c squared
14 squared = 14 x 14 = 196
Now we have 196 + 48 squared = c squared
48 squared = 48 x 48 = 2,304
Now we have 196 + 2,304 = c squared
Add them together - 2,304 + 196 = 2,500
Now we have 2,500 = c squared
We find the square root of 2,500 which is 50
You should now have 50 = c
That is your answer. Don't forget to add units.
50 ft is your hypotenuse (c)
I hoped this helped
Answer: the missing length is 50
Step-by-step explanation:
in order to figure out the missing number, you have to do the pythagorean theorem, which is a²+b²=c². A is 14 ft, B is 48 ft, and C is the missing length. You have to square each number. 14 will be 196 and 48 would be 2304.
MARK AS BRAINLIEST!!!
Find the value of 1 and 2.
Do not answer unless you know the answer.
Translate the following phrase to a mathematical expression: a number times fifteen.
n15
15 n
15 ÷ n
15 + n
Answer:
it could either be n15
15n
because a number multiplied by 5 is
n15
but in mathematics a number comes before a letter when writing a mathematical expression
Answer:
The answer is n15
Hope this helps!!!
Please mark as brainliest
Step-by-step explanation:
Is the distance from Boston, Massachusetts, to Phoenix, Arizona,about 4,000 centimeters or 4,000 kilometers? Explain.
Answer:
it's most likely 4,000 kilometers because centimeters are a very small rate of measurement and the distance between the 2 landmarks are very far away
which situation is best represented by the equation 35p + 129.50 = 479.50
Answer:
p=10
Step-by-step explanation:
I don't know what you're asking with the situation, but p is equal to 10
Answer:
p = 10
Step-by-step explanation:
i hope this helps, can you please make me brainliest.
Determine the missing angle in a triangle.
Answer:
145
Step-by-step explanation:
The the that connects the outside line to the inside line will equal to 180 so you take 180 minus 137 to get 43 and you have two angles for the inside which is 43 and 102. You minus these two number to 180 to get the last missing angle in a triangle because the inside of a triangle is 180 and then minus 180 to 35(Last angle measure) to get the outside of the triangle and you get 145.
Answer:
?=145°
Step-by-step explanation:
The angle 137° is a supplementary angle. So subtract 137 from 180 to find the adjacent angle:
[tex]180-137=43[/tex]
The angle adjacent the angle 137° is 43°. Add this value to the angle measure in the triangle:
[tex]102+43=145[/tex]
Two angle measures within the triangle add up to 145°. The angle measures of a triangle should add up to 180°. Subtract:
[tex]180-145=35[/tex]
The third angle in the triangle is 35°. This angle is also a supplementary angle. Subtract this from 180 to find the measure of angle ?:
[tex]180-35=145[/tex]
The angle ? is 145°.
or
The outer angle of a triangle (angle ?) can be found by finding the sum of the two angles within a triangle, not including the adjacent angle (or ?'s supplementary angle). So find the measure adjacent 137°:
[tex]180-137=43[/tex]
Add the two inner angle measure together:
[tex]43+102=145[/tex]
So angle ? is 145°.
:Done
PLS HELP HURRY ASP HURRY BEST GETS BRAINLESST!
Answer:
25 mm < 3 cm
Step-by-step explanation:
Change cm to mm
1 cm = 10 mm
3 cm = 3*10 = 30 mm
25 mm < 30 mm
answer this asap for me and i will thank u if its correct
Answer:
B
Step-by-step explanation:
The 115° angle is adjacent to both unknown angles in the triangles, thus
unknown angles = 180° - 115° = 65°
The sum of the 3 angles in a triangle = 180°, thus
∠ 1 = 180° - (65 + 80)° = 180° - 145° = 35°
∠ 2 = 180° - (65 + 85)° = 180° - 150° = 30°
A registered dietitian is assisting a patient with hypertension to create a diet with a minimal amount of sodium. The recommended intake of sodium for patients with hypertension is to consume no more than 1,500 mg of sodium per day. The dietitian notes that 6 ounces of ham contains 550 mg of sodium.
How many mg of sodium does 1 pound of ham contain? (1 lb = 16 oz)
Answer:
1466 2/3 mg of sodium
Step-by-step explanation:
We can use a ratio to solve
550 mg x mg
------------- = --------------
6 ounces 16 ounces
Using cross products
550* 16 = 6x
Divide each side by 6
550*16 /6 = 6x/6
8800/6 =x
4400/3 =x
Change to a mixed number
1466 2/3 mg of sodium
Answer:
1466⅔ mg
Step-by-step explanation:
oz : mg
6 : 550
16 : X
X/16 = 550/6
X = 550/6 × 16
X = 4400/3
X = 1466⅔ mg
What is the image point of (2, 4) after a translation left 4 units and down 1 unit?
Answer:
-2,3
Step-by-step explanation:
because you are going to the left you would end up getting -2 for the x and since you are going one down you would have 3 for the y.
12x – 10 = 134
10
9
12
16
Answer:
shown below
explanation:
first off, you get the like terms which is 10 and 134
12x=134+10
12x=144
then you simplify which will look like this:
12x. 144
___ = ___
12. 12
144÷12=12
so the answer is option c.12
hope it helps!!17) A temperatura was -5 degrees on Monday. It increased 15 degrees on
Tuesday. What is the temperature on Tuesday? (NO LABEL) *
5 point
Answer:
10 degrees on Tuesday.
But only if the whole question states Monday was -5 degrees and it increases by 15 degrees.
Step-by-step explanation:
Solve this equation 5(y+2/5)= -13
Answer:
[tex]y = - 3[/tex]
Step-by-step explanation:
[tex]5(y + \frac{2}{5} ) = - 13 \\ 5y + \frac{10}{5} = - 13 \\ 5y + 2 = - 13 \\ 5y = - 13 - 2 \\ 5y = - 15 \\ \frac{5y}{5} = \frac{ - 15}{5} \\ y = - 3[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
need help ASAP!!!!!!
Answer:
c i think have a great day
Step-by-step explanation:
Answer:
[tex]5^{15}[/tex]
Step-by-step explanation:
You need to use PEMDAS for this.
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
[tex]( 5^{3})^{9}[/tex]÷[tex]5^{12} =\\[/tex]
[tex]125^{9}[/tex]÷[tex]5^{12} =[/tex]
7,450,580,596,923,828,125÷244140625=
30,517,578,125
[tex]5^{24} = 59,604,644,775,390,625[/tex]
[tex]5^{15} =30,517,578,125[/tex]
The correct answer is [tex]5^{15}[/tex]
(You don't actually have to multiply it all out, I just did it to make sure you understand)
Which equation results from adding the equations in this system? x + 6 y = 9. Negative x + 2 y = negative 15. 8 y = negative 6 8 y = 6 4 y = 24 4 y = negative 6Which equation results from adding the equations in this system? x + 6 y = 9. Negative x + 2 y = negative 15. 8 y = negative 6 8 y = 6 4 y = 24 4 y = negative 6
Answer:
8y = - 6
Step-by-step explanation:
Given the 2 equations
x + 6y = 9 → (1)
- x + 2y = - 15 → (2)
Adding the 2 equations term by term gives
(x - x) + (6y + 2y) = (9 - 15), that is
8y = - 6
Answer:
8y = -6
Step-by-step explanation:
I got it right on Edge 2020
Also: Plug in the slope 8 and the y-intercept -6 to check the answer. It is correct.
What is the purpose of the quadratic formula?
Answer:
In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others.
Step-by-step explanation:
hope that helps love!
Answer:
In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others.
That's what google says :)
Step-by-step explanation:
A chemist mixes different concentrations of
perfume using three scents the company already
produces. Scents A, B. and C have different
concentrations of rose oil. The results of three
different trials are listed in the table. The result is
the percent of rose oil by volume for each trial.
A
B
4 OZ
2 oz
4 OZ
1 oz
C
4 OZ
4 OZ
2oz
2 oz
7 oz
Result
2205
2706
23.50
How many total ounces of perfume are in the result
in each trial (each row?
Answer:
10 oz
Step-by-step explanation:
edge
The total ounces of perfume in trials 1, 2, and 3 are 7.8 oz, 7.3 oz, and 7.65 oz.
Given to us,
For Trial 1,
A = 2 oz
B = 4 oz
C = 4 oz
Percentage of rose oil = 22%
weight of trail 1 = A+ B+ C = 2+ 4+ 4 = 10 oz.
Weight of rose oil in trial 1 = weight of trail 1 x Percentage of rose oil in 1
= 10 oz x 22% = 2.2 oz
total ounces of perfume in trial 1
= weight of trail - Weight of rose oil in trial 1
= 10 - 2.2 = 7.8 oz
For Trial 2,
A = 4 oz
B = 2 oz
C = 4 oz
Percentage of rose oil = 27%
Total weight of trail 2 = A+ B+ C = 2+ 4+ 4 = 10 oz.
Weight of rose oil in trial2 = weight of trail 2 x Percentage of rose oil in 2
= 10 oz x 27% = 2.7 oz
total ounces of perfume in trial 2
= weight of trial 2 - Weight of rose oil in trial 2
= 10 - 2.7 = 7.3 oz
For Trial 3,
A = 1 oz
B = 7 oz
C = 2 oz
Percentage of rose oil = 23.50%
Total weight of trail 3 = A+ B+ C = 2+ 4+ 4 = 10 oz.
Weight of rose oil in trial 3= weight of trail 3 x Percentage of rose oil in 3
= 10 oz x 23.50% = 2.350 oz
total ounces of perfume in trial 3
= weight of trail - Weight of rose oil in trial 3
= 10 - 2.2 = 7.8 oz
Hence, The total ounces of perfume in trials 1, 2, and 3 are 7.8 oz, 7.3 oz, and 7.65 oz.
To know more visit:
https://brainly.com/question/801140
what is the mixed number form
of 33/8
The fraction 33/8 to a mixed number is 4 1/8
Changing 33/8 to a mixed numberFrom the question, we have the following parameters that can be used in our computation:
Number = 33/8
Divide 33 by 8
So, we have
Quotient = 4
Next, we have
Remainder = 33 - 4 * 8
Evaluate the products
Remainder = 1
Hence, the fraction to a mixed number is 4 1/8
Read more about fraction at
https://brainly.com/question/78672
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Cameron makes a blueprint for his game room to decide how to set up the room. He places the table in the center of the sketches room. How far away is each corner of the table from each closet corner of the room? Explain
[tex]\sqrt{5\\[/tex] is the correct answer. you use the Pythagorean Theorem with 2 as a and 1 as b. So the equation is [tex]c^{2}[/tex] = [tex]2^{2}[/tex] + [tex]1^{2}[/tex].
Find the missing length, when you know the perimeter. 9m + 9m + ? + ? = 42m
Answer:
MISSING LENGTH IS 12 M
Step-by-step explanation:
9+9+ ? + ? = 42m
18+ X + X = 42m
2X=42-18
2X=24
X=12
Answer:
The missing length is 12 meters.
Step-by-step explanation:
9+9+x+x=42
Subtract 9 from both sides
9+x+x=33
Subtract 9 from both sides
x+x=24
2x=24
Divide both sides by 2
x=12
The missing length is 12 meters.
HELP FIND THE SLOPE OFTHIS GRAPH
Answer:
-1.25
Step-by-step explanation:
Your points one the graph are (-4,4) and (0,-1)
Formula for slope is y1-y2/x1-x2
4--1/-4-0
5/-4
-1.25
What is the equation of the parabola that has its vertex at (7,6) and contains the point (6,8)?
Answer:
[tex]y = 2 (x-7)^{2} +6[/tex] is the equation of parabola.
Step-by-step explanation:
Vertex form of a parabola is given as :
[tex]y = a (x-h)^{2} +k ...... (1)[/tex]
(h,k) is the co-ordinate of vertex of parabola.
(x,y) are the points on parabola.
We are given that vertex is at (7,6) and a point on parabola is (6,8).
h = 7
k = 6
x = 6 and
y =8
Putting all the values in equation (1):
[tex]8 = a (6-7)^{2} +6\\\Rightarrow 8 = a + 6\\\Rightarrow a = 2[/tex]
Putting values of (h,k) and a in equation (1) to obtain the equation of parabola:
[tex]y = 2 (x-7)^{2} +6[/tex] is the equation of parabola with vertex at (7,6) and contains the point (6,8).
Answer:
Step-by-step explanation:
y = 2x2 – 28x + 52
wrong its not that
One more than the quotient of a number x and 4.
Answer:
Just write whatever it says so quotient means divide, more means add, and product means multiply
x/4+1
Make your the equation is in order by checking the words after, than, next to see if the equation is in order
Hope this helps
If you have any questions you can ask
Step-by-step explanation:
Please help me, will mark brainliest for correct answers.....
Answer questions 1-8
Please and ASAP....
Worth a lot of points
Answer:
1. B) 5.7
2. A) 12
3. A) 11.4
4. A) 5.7
5. A) 16.2
6. A) 11.2
7. No, they do not form a right triangle
8. Yes, they do form a right triangle
Step-by-step explanation:
Extra tip: The hypotenuse has to be less than both sides added together, but cannot be more than either of the sides alone.
1.
16² + b² = 17²
256 + b² = 289
256 - 256 + b² = 289 - 256
b² = 33
√b² = √33
b = 5.74 or 5.7
2.
16² + b² = 20²
256 + b² = 400
256 - 256 + b² = 400 - 256
b² = 144
√b² = √144
b = 12
3.
7² + 9² = c²
49 + 81 = c²
130 = c²
√130 = √c²
11.40 or 11.4 = c
4.
7² + b² = 9²
49 + b² = 81
49 - 49 + b² = 81 - 49
b² = 32
√b² = √32
b = 5.65 or 5.7
5.
a² + 5² = 17²
a² + 25 = 289
a² + 25 - 25 = 289 - 25
a² = 264
√a² = √264
a = 16.24 or 16.2
6.
10² + b² = 15²
100 + b² = 225
100 - 100 + b² = 225 - 100
b² = 125
√b² = √125
b = 11.18 or 11.2
7.
15² + 8² = 16²
225 + 64 = 256
289 ≠ 256
8.
5² + 12² = 13²
25 + 144 = 169
169 = 169
A six-sided number cube is labeled with the numbers 1-6, one number on each face. Each number is used exactly once. How
many possible outcomes exist when the cube is rolled two times?
6
8
12
36
I tried answering this question but got it wrong. Please ignore this message D:
PLS HELP ME. Use the opposite operation to undo the
process.
Examples(Please answer them also)
1. 2m = 24
2. y – 9 = 30
3. X = 12
4
4. k + 12.5 = 30
5. 3r = 15.3
Answer:
see below
Step-by-step explanation:
1. 2m = 24
Divide each side by 2
2m/2 = 24/2
m = 12
2. y – 9 = 30
Add 9 to each side
y-9+9 = 30+9
y = 39
3. X/4 = 12
Multiply each side by 4
x/4*4 = 12*4
x = 48
4. k + 12.5 = 30
Subtract 12.5 from each side
k+12.5-12.5 = 30-12.5
k =17.5
5. 3r = 15.3
Divide by 3
3r/3 = 15.3/3
r =5.1
Hey!!!!
Here's your answer:
1. 2m=24
or,m=24/2
m=12
2. y-9=30
or,y=30+9
y=39
3. 3x=12
or,X=12/3
x=4
4. k+12.5=30
or,k=30-12.5
k=17.5
5. 3r=15.3
or,r=15.3/3
r=5.1
Hope it helps....Good luck on your assignment