Answer:
Dimension of box:-
Side of square base = 10 in
Height of box = 5 in
Minimum Surface area, S = 300 in²
Step-by-step explanation:
An open box with a square base is to have a volume of 500 cubic inches.
Let side of the base be x and height of the box is y
Volume of box = area of base × height
[tex]500=x^2y[/tex]
Therefore, [tex]y=\dfrac{500}{x^2}[/tex]
It is open box. The surface area of box, S .
[tex]S=x^2+4xy[/tex]
Put [tex]y=\dfrac{500}{x^2}[/tex]
[tex]S(x)=x^2+\dfrac{2000}{x}[/tex]
This would be rational function of surface area.
For maximum/minimum to differentiate S(x)
[tex]S'(x)=2x-\dfrac{2000}{x^2}[/tex]
For critical point, S'(x)=0
[tex]2x-\dfrac{2000}{x^2}=0[/tex]
[tex]x^3=1000[/tex]
[tex]x=10[/tex]
Put x = 10 into [tex]y=\dfrac{500}{x^2}[/tex]
y = 5
Double derivative of S(x)
[tex]S''(x)=2+\dfrac{4000}{x^3}[/tex] at x = 10
[tex]S''(10) > 0[/tex]
Therefore, Surface is minimum at x = 10 inches
Minimum Surface area, S = 300 in²
A recipe uses 1 - cups of milk to make 10 servings. If the same amount of milk is used for
each serving, how many servings can be made using 1 gallon of milk?
Answer:
160 servings can be made using 1 gallon of milk.
Step-by-step explanation:
Since
1 cup = 10 servings
1 gallon of liquid is equivalent to 16 cups of the liquid
1 gallon = 16 cups
Therefore
1 gallon = (10 x 16) servings
1 gallon = 160 servings
160 servings can be made using 1 gallon of milk.
Write the equation of the line that is parallel to y=-0.75x and that passes through the point (8,0)
The equation of the line that is parallel to y=-0.75x and passes through the point (8,0) is y = -0.75x + 6.
Explanation:The equation of a line in the form y = mx + b represents a linear equation, where m is the slope of the line and b is the y-intercept. Since we are looking for a line parallel to y = -0.75x, we know that the new line will have the same slope. So, the equation of the new line is y = -0.75x + b. To find the value of b, we can substitute the coordinates of the point (8,0) into the equation and solve for b.
0 = -0.75(8) + b
0 = -6 + b
b = 6
Therefore, the equation of the line that is parallel to y = -0.75x and passes through the point (8,0) is y = -0.75x + 6.
A fireworks rocket is launched from a hill above a lake. The rocket will fall into the lake after exploding at its maximum height. The rocket's height above the surface of the lake is given by g(x)= -16x^2+64+80. What is the maximum height of the rocket?
A) 150 feet C) 120 feet
B) 80 feet D) 144 feet
Answer:
D
Step-by-step explanation:
At the maximum height, the value of the vertical velocity Vy equals zero. From the value of the equation, we can get the vertical velocity by its first differential.
Differentiating this, we get -32x + 64
We then equate this value to zero. This yield 32x = 64 and x = 2
We now plug the value of x back into the original expression for height.
-16(2)^2 + 64(2) + 80 = -64 + 128 + 80 = 144 feet
what is -21=-7x help
Answer:
x=3
Step-by-step explanation:
-21=-7x
-7x=-21
x=3
write a sentence explaining why all solutions of rational equation must be checked
Answer:
It is highly important for all solutions of rational equation to be checked to make sure you get the right answer.
In solving a rational equation, we always clear of fractions. When we clear of fractions we always multiply both sides by a variable quantity. When we multiply both sides of an equation by a variable expression, we may introduce an extraneous solution a zero of that expression we multiplied through by.
100% on edg
simplify: 3 1/2 + 1/8= 3 5/8 is that correct
Answer:
3.625
Step-by-step explanation:
I check on Google for yeah ;)
Whats 6x6+9-2-1=
(my mom will not let me use a calculator)
Answer:
42
Step-by-step explanation:
6*6+9-2-1
36+9-2-1
45-2-1
43-1
42
explain why you can have different values when evaluating an algebraic expression.
please help!
When evaluating an algebraic expression, the domain is typically all real numbers.
What are real numbers?
Every single number (irrational, rational, natural numbers) except imaginary ones.
When you evaluate an algebraic expression, you can choose from a range of values if it is restricted. If it is not you can only use real numbers.
You can use 1, 50, 1909893, 39309202, and many more. It goes on and on.
And since each number that is being inputted into the expression is different, you may end up with different outputs.
Thank you for posting your question on Brainly. Please feel free to ask more.
What is the simplified form of StartRoot StartFraction 48 Over 192 EndFraction EndRoot? One-fourth One-half 2 4
Answer:
1/2 or B on edge
Step-by-step explanation:
If one were to simplify the fraction 48 / 192, the result they would get is the fraction 1/4 or One-fourth
When taking a fraction to its simplest form, you divide both the numerator and the denominator by their greatest common factor.
The greatest common factor of both numbers is 48.
The simplest form is therefore:
= (48 ÷ 48) / (192 ÷ 48)
= 1 / 4
In conclusion, the fraction at its simplest form is 1/4.
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a box of cereal weighs 600 grams . how much is this weight in pounds ? explain or show your reasoning .
Answer:
600 Grams = 1.323 Pounds
Step-by-step explanation:
1 gram equals 0.0022 pounds
600 x 0.0022 = about 1.323
Answer:
the weight in pounds is 1.324 pounds
Step-by-step explanation:
Hello, i can help you with this, you can easily solve this by using a rule of three, also you need to know
1 pound = 453 grams
Step 1
establish the relation
1 pound ⇔ 453 grams
x pound ⇔ 600 grams
the relation is
[tex]\frac{1}{453} =\frac{x}{600}\\ solve\ for\ x\\x=\frac{1*600}{453}\\x=1.324\\[/tex]
so, the weight in pounds is 1.324 pounds
I really hope It helps , have a nice day.
Which expression is equivalent to (x^27y) ^1/3
Answer:
x^9*y^1/3
Step-by-step explanation:
Because x^(27*1/3)=x^9 and y^(1/3)=y^1/3.
What is the number place 2 in 582.091 rounded to
Answer:
582.091 Rounded to 2 places after the decimal point is 582.09
:)
Answer:
unit
Step-by-step explanation:
H. T. U.
5. 8. 2
5 is representing a hundred
8 is representing the tenth
2 is representing the units
How to solve : 16=2t + 0.25 t``squar
Answer:
The solutions of the equation are t = 4(√5 + 1) or 4(√5 - 1).
Step-by-step explanation:
We have to solve the given quadratic equation of single variable t.
The equation is 16 = 2t + 0.25t²
⇒ 0.25t² + 2t - 16 = 0
⇒ 25t² + 200t - 1600 = 0 {Multiplying both sides with 100}
⇒ 25t² + 200t + 400 - 400 - 1600 = 0
⇒ (5t + 20)² - 2000 = 0
⇒ (5t + 20)² - (20√5)² = 0
⇒ (5t + 20 + 20√5)(5t + 20 - 20√5) = 0
So, (5t + 20 + 20√5) = 0 or, (5t + 20 - 20√5) = 0
⇒ (t + 4 + 4√5) = 0 or, (t + 4 - 4√5) = 0
⇒ t = - 4(1 + √5) or, t = 4(√5 - 1) (Answer)
The scale of a map is 1:1000. The actual dimensions of a rectangle is 4cm by 3cm. What is the actual area in m²?
(hint: convert 1000cm -> m)
(ans: 1200m²)
BUT HOW TO DO....
Step-by-step explanation:
1cm:1000cm
multiply the dimensions by 1000cm
4cm--> 4000cm
3cm--> 3000cm
convert 4000cm and 3000cm to metres by dividing by 100
because 1m=100cm
4000/100=40m
3000/100=30m
40m x 30m= 1200m²
The average weight of a watermelon is 4.61 kg. The average weight of a coconut is 2.22 kg less than a watermelon. The total weight of an equal number of coconuts and watermelons is 140 kg. How many coconuts are there?
Since the average weight of a coconut is 2.22 kg less than a watermelon, its average weight is
[tex]4.61-2.22=2.39[/tex]Let n be the number of coconuts and watermelons. The total weight of n coconuts and n watermelons is
[tex]4.61n+2.39n = 7n[/tex]
If we want this total to be 140, we have
[tex]7n=140 \iff n=\dfrac{140}{7}=20[/tex]
So, you have 20 coconuts and 20 watermelons.
Final answer:
To find the number of coconuts, we can set up an equation using the given information. The average weight of a watermelon is 4.61 kg, and the average weight of a coconut is 2.22 kg less than a watermelon. By setting up the equation x(4.61 + 2.39) = 140 and solving for x, we find that there are 20 coconuts.
Explanation:
To solve this problem, we need to set up equations using the given information. Let's represent the number of coconuts as 'x'. The average weight of a watermelon is 4.61 kg, and the average weight of a coconut is 2.22 kg less than a watermelon, which means it is 4.61 - 2.22 = 2.39 kg. Since the number of coconuts and watermelons is equal, we can write the equation: x(4.61 + 2.39) = 140. Solving this equation, we get 7x = 140, which means x = 140/7 = 20.
Therefore, there are 20 coconuts.
Find the largest number. 16.3, 15.7, 16.9, 15.8
Answer:
16.9
Step-by-step explanation:
PLEASE HELPPPPPThe height of 200 adults were recorded and divided into two categories
Add the total males together: 13 + 85 = 98,
So the total male need to be 98,
the total adults is given as 200.
The total women would be 200 - 98 = 102
The table with those three totals is table D.
Answer: It's D
Step-by-step explanation:
First, look at the sum of both female and male adults. As it states in the question, they must add up to 200. Therefore, there are 98 males under 6 ft. So, graph that shows 98 females under 6ft is correct. Which is D in this case.
What is the effect on the graph of the function f(x) = 2x when f(x) is replaced with f(2/3x)?
A) vertical stretching
B) vertical compression
C) horizontal compression
D) horizontal stretching
Answer:
This will be an effect of vertical compression.
Step-by-step explanation:
We have to determine the change on the graph of the function f(x) = 2x when f(x) is replaced with [tex]f(\frac{2}{3}x )[/tex].
Therefore, [tex] f(\frac{2}{3} x) = 2(\frac{2}{3}x )= \frac{4}{3} x[/tex]
It is clear that for the same value of x the y-value decreased by the factor [tex]\frac{2}{3}[/tex].
Hence, this will be an effect of vertical compression. ( Answer )
Answer:it’s horizontal stretching
Step-by-step explanation:
if you’re in usa test prep, it is NOT vertical compression.
What is the slope of y = -4?
Answer:
The slope is 0 and the y-intercept is -4
Which of the following is a correct interpretation of the expression 4 - (-3)
Start at 4 on the number line and move 3 to the left.
Start at 4 on the number line and move 3 to the right.
Start at -3 on the number line and move 4 to the left.
Start at -3 on the number line and move 4 to the right.
4 - (- 3) = 4 + 3
Addition moves to the right.
Subtraction moves to the left.
Start at 4 on the number line and move 3 to the right.
Triangle A B C is shown with its exterior angles. Angle B A C is (p + 4) degrees and angle A C B is 84 degrees. Exterior angle X B C is (3 p minus 6 degrees).
What is the measure of ∠XBC?
m∠XBC = m∠BAC + m∠BCA
3p – 6 = p + 4 + 84
3p – 6 = p + 88
2p – 6 = 88
2p = 94
Answer:
The diagram of the question is attached here.
The measure of [tex]\angle XBC=135\ (deg)[/tex]
Step-by-step explanation:
All the options given here will be used to find the numeric value of [tex]\angle XBC[/tex]
Here it is shown systematically.
Exterior angle theorem: Sum of two interior angles are equal to the measure of opposite exterior angle in a triangle.
To find [tex]\angle XBC[/tex]
[tex]m\angle XBC = m\angle BAC + m\angle BCA[/tex]
Plugging the values.
[tex]3p-6 = p + 4 + (84)[/tex]
[tex]3p-6 = p + 88[/tex]
Subtracting [tex]p[/tex] both sides.
[tex]2p-6 = 88[/tex]
[tex]2p = 94[/tex]
Dividing [tex]2[/tex] both sides.
[tex]p=\frac{94}{2}=47[/tex]
So plugging the value of [tex]p=47[/tex] in [tex]3p-6[/tex] we will get the measure of [tex]\angle XBC[/tex].
So [tex]\angle XBC=(3p-6)=3(47)-6=135\ (deg)[/tex]
The measure of [tex]\angle XBC[/tex] is [tex]135\ degrees[/tex].
Based on the information, the measure of Angle XBC is 278 - 4p degrees.
What's the measurements?Given that Angle ACB is 84 degrees, Angle BAC is (p + 4) degrees, and Angle XBC is (3p - 6) degrees, you can plug in these values:
(p + 4) + 84 + (3p - 6) + Angle XBC = 360
Combine the like terms involving 'p':
4p + 82 + Angle XBC = 360
Subtract 82 from both sides:
4p + Angle XBC = 278
Now, isolate Angle XBC by subtracting 4p from both sides:
Angle XBC = 278 - 4p
So, the measure of Angle XBC is 278 - 4p degrees.
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Consider the following equations: f(x) = 2x – 2 and g(x) = 5 - x
a. The two equations represent lines on a graph, describe the difference in slope and y-intercept.
Answer:
The difference in slopes of [tex]f(x)\ and\ g(x)[/tex] is = 3
We can say slope of [tex]f(x)[/tex] is positive and 3 more than slope of [tex]g(x)[/tex] while slope of [tex]g(x)[/tex] is negative.
Difference of y-intercepts of [tex]f(x)\ and\ g(x)[/tex] is = -7
We can say the y-intercept of [tex]g(x)[/tex] is positive and 7 units above [tex]f(x)[/tex] while y-intercept of [tex]f(x)[/tex] is negative.
Step-by-step explanation:
Given equation:
[tex]f(x) =2x - 2[/tex]
[tex]g(x) =5-x[/tex]
We need to find the difference of slopes and y-intercepts of the given equations.
The standard form of a slope intercept equation of line is given by:
[tex]y=mx+b[/tex]
where [tex]m[/tex] represents slope and [tex]b[/tex] represents y-intercept of line.
Writing the given equations in standard form to find slope and y-intercept.
[tex]f(x) =2x +(-2)[/tex]
Slope = 2 and y-intercept =-2
[tex]g(x) =(-1)x+5[/tex]
Slope = -1 and y-intercept =5
The difference in slopes of [tex]f(x)\ and\ g(x)[/tex] is = [tex]2-(-1)=2+1=3[/tex]
We can say slope of [tex]f(x)[/tex] is positive and 3 more than slope of [tex]g(x)[/tex] while slope of [tex]g(x)[/tex] is negative.
Difference of y-intercepts of [tex]f(x)\ and\ g(x)[/tex] is = [tex]-2-5=-7[/tex]
We can say the y-intercept of [tex]g(x)[/tex] is positive and 7 units above [tex]f(x)[/tex] while y-intercept of [tex]f(x)[/tex] is negative.
Part of Eli’s job on the ranch is to feed the new calves. There are 5 new calves, and each calf eats 15 pounds of hay every day. Complete the area model to show the total number of pounds of hay Eli feeds the calves in 6 days. Then write the partial products and the total product.
Answer:
dfdssgfnfndfnfnb
Step-by-step explanation:
4
9
of students at a school are boys. If there are 2610 students at the school, how many are girls?
Answer:
There are 2561 girls in the school.
Step-by-step explanation:
2610-49=2561
There are 1331 girls in the school.
Define equation? What is Equation Modelling?
Equation is defined as a relation that equates two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given are 49% of students at a school are boys. There are 2610 students at the school.
Assume that there are [x] girls are there. Then, we can write -
x = 2610 - 49% of 2610
x = 2610 - (49/100) x 2610
x = 2610 - 1279
x = 1331
Therefore, there are 1331 girls in the school.
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Please show all work cuase I don’t understand thank you
Answer:
13a. 0.92 miles
13b. C
Step-by-step explanation:
13a. The first ride costs $2.75 more than the second ride. Each quarter mile after the first quarter mile costs $0.75, so the difference in distance is:
0.75 d = 2.75
d = 3.67
The difference is 3.67 quarter miles, or 0.92 miles.
13b. The total cost is the cost of the first quarter mile plus the cost of the rest of the quarter miles.
C(n) = 2.50 + 0.75 (n − 1)
A wooden plank is 19 feet long.Mrs Dambra cuts 3 feet off the wooden plank. She then cuts the remaining piece of wood into equal pieces,each 1/5 long. how many pieces does mrs.dambra cut
Answer:
80 pieces
Step-by-step explanation:
Answer:
80ft.
Step-by-step explanation:
Please mark brainliest and you will get a Dino Nuggie :)
One Morning in Atlanta, Tina observed that the temperature was 72 degrees. Later the temperature rose 21 degrees and then dropped 11 degrees. She then flew to New York where the temperature was 67 degrees. What was the change in temperature from when Tina left Atlanta and arrived in New York
answer: 72+21=93-11=82
The change in temperature from when Tina left Atlanta and arrived in New York will be 82° and 77°.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
One Morning in Atlanta, Tina observed that the temperature was 72 degrees.
Later the temperature rose 21 degrees and then dropped 11 degrees.
Then the final temperature in Atlanta will be
⇒ 72° + 21° - 11°
⇒ 82°
She then flew to New York where the temperature was 67 degrees.
Then the final temperature in New York will be
⇒ 67° + 21° - 11°
⇒ 77°
Then the change in temperature from when Tina left Atlanta and arrived in New York will be 82° and 77°.
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Which scenario can be modeled using the graph below
Answer:
Graph is not listed
Step-by-step explanation:
First, we need to know what graph. Then we can answer this.
after using six mushrooms to boost their speed. marcus racer has travelled 650 feet. hiw far did marcus racer travel after using three mishrooms?
Answer: 325 ft
Step-by-step explanation:
6 mushrooms = 650 ft
divide by 2 on both sides
3 mushrooms = 325 ft
5 mushrooms = 6-1 mushrooms
5 mushrooms = 650 - (boost distance for 1 mushroom)
1 mushroom = 650/6 = 108.3 repeating
so 5 mushrooms = 650 - 108.333333333 = 542.66666666
Which pair of ratios does
not form a true proportion?
A) 8:14 and 20:35
B) 6 to10 and 15 to 25
D) 12:15 and 30:50
Answer:
8:14
Step-by-step explanation:
just multiply