Answer:
See below
Step-by-step explanation:
A vertical line is just x =
so if a = 1 b = 0 and c = 9 would be a vertical line through the point
so you wind up with x = 9
A rectangular storage container without a lid is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $20 per square meter. Material for the sides costs $12 per square meter. Find the cost (in dollars) of materials for the least expensive such container. (round your answer to the nearest cent. ).
The cost of materials for the least expensive such container is $327.081 .
In the question ,
it is given that
the volume of the container = 10 m³ .
let the width of the container = x
so , the length of the container = 2x
So , base area = 2x*x = 2x²
cost for base = $20
cost for the sides = $12
Since the volume is 10 m³
Volume = base area * height
10 = 2x² * h
h = 10/2x²
h = 5/x²
The cost of making the container
cost of base = 2x² * (20) = 40x²
cost of sides = [2*2x*(5/x²) + 2*x*(5/x²)](12)
= 360/x
the total cost of the container [tex]=[/tex] cost of base [tex]+[/tex] cost of sides
= 40x² + 360/x
= 40( x² + 9/x)
to get the minimum cost , we differentiate with respect to x and equate to 0
= 40 ( 2x - 9/x²)
2x - 9/x² = 0
2x³ = 9
x³ = 9/2
x³ = 4.5
x = 1.651
Substituting x in the cost equation ,
we get
Cost = 40x² + 360/x
= 40(1.651)² + 360/(1.651)
= 109.032 + 218.049
= 327.081
Therefore , The cost of materials for the least expensive such container is $327.081 .
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Fill out a table of equivalent ratios and plot the points on the coordinate axes provided
Box 1 = 8
Box 2 = 2
If he earned $64 in 8 hours then dividing by 64 by 8 will tell us how much he earned in 1 hour. That gives $8
Using that we can then divide the number of dollars by the amount he receives in 1 hour to see how many hours it was.
So $16 / $8 per hour gives 2 hours
tonnie divides a 2 liter bottle of iced tea among 8 people. how many millimeters does each person get?
please help asap tysm <3
The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers. x + (x + 1) + (x + 2) = 42 x + (x + 2) + (x + 4) = 42 (x minus 1) + x + (x + 1) = 42 (x minus 2) + x + (x + 2) = 42 x + 2 x + 3 x = 42
The equation representing the sum of three consecutive integers as 42 are x [tex]+[/tex] (x [tex]+[/tex] 1) [tex]+[/tex] (x + 2) [tex]=[/tex] 42 and (x - 1) [tex]+[/tex] x + (x [tex]+[/tex] 1) [tex]=[/tex] 42 , the correct option are (a) and (c) .
In the question ,
it is given that ,
the sum of the three consecutive integers = 42
the equations that shows the relationship is only option (a) and option(c) , because
option (a)
x [tex]+[/tex] (x [tex]+[/tex] 1) [tex]+[/tex] (x + 2) [tex]=[/tex] 42
3x + 3 = 42
3x = 39
x = 13
yes , the terms are consecutive and are 13 , 14 , 15 .
option(c)
(x - 1) [tex]+[/tex] x [tex]+[/tex] (x [tex]+[/tex] 1) [tex]=[/tex] 42
3x = 42
x = 14
putting in equation we get 14-1 = 13 , 14 , 14+1 = 15
yes , the terms are consecutive and are 13 , 14 , 15 .
Therefore , The equation representing the sum of three consecutive integers as 42 are x + (x + 1) + (x + 2) = 42 and (x - 1) + x + (x + 1) = 42 .
The given question is incomplete , the complete question is
The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers.
(a) x + (x + 1) + (x + 2) = 42
(b) x + (x + 2) + (x + 4) = 42
(c) (x - 1) + x + (x + 1) = 42
(d) (x - 2) + x + (x + 2) = 42
(e) x + 2 x + 3 x = 42
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The length and width of a rectangle are consecutive integers. The perimeter of the rectangle is 54 centimeters. Find the length and width of the rectangle.
Thank you!
Answer:
length = 13 cm and width = 14 cm
Step-by-step explanation:
let n be the length then n + 1 is the width
the perimeter (P) of a rectangle is calculated as
P 2(l + w) ← l is length and w is width
given P = 54 , then
2(n + n + 1) = 54 ( divide both sides by 2 )
2n + 1 = 27 ( subtract 1 from both sides )
2n = 26 ( divide both sides by 2 )
n = 13
n + 1 = 13 + 1 = 14
length = 13 cm and width = 14 cm
Write a recursive definition for sequence starting with 12, 6?
The recursive formula for sequence starting with 12, 6 is, [tex]a_1=a_0-\frac{a_0}{2}[/tex].
What is recursive formula?
Any term of a series can be defined by its preceding term in a recursive formula (s).
For instance: An arithmetic series has the recursive formula [tex]a=a_n_-_1+d[/tex] . [tex]a_n=a_n_-_1r[/tex] is the recursive formula for a geometric sequence.
Given two terms are, 12, 6.
The first term is 12, so [tex]a_0=12[/tex].
The second term is 6, which is half of the first term.
So, [tex]a_1=a_0-\frac{a_0}{2}[/tex]
Therefore, the recursive formula for the sequence starting with 12, 6 is
[tex]a_1=a_0-\frac{a_0}{2}[/tex].
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What is the coefficient in the algebraic expression: -x + 3
Answer:
- 1 is the coefficient-------------------------
Given expression- x + 3,It has a variable x and its coefficient (-1), the 3 is the constant.
[tex]\Large \boxed{\sf -1}\\\\\\\displaystyle \sf A\ coefficient\ in\ an\ expression\ is\ the\ integer\\ value\ multiplied\ by\ the\ variable.\\\\(-1) \times x + 3[/tex]
Help!
im very confused.
Answer:
458.7 cm
Step-by-step explanation:
to find circumference we multiply diameter by pi
146(pi)
458.673
And we round to 1 d.p.
458.7
Hopes this helps please mark brainliest
How do you explain multiplying by 3?.
Answer:
a number x times by 3
Step-by-step explanation:
yw I hope that helps
Simplify 5(x-2)-3(x-2)+7x
Answer:
9x-4
Step-by-step explanation:
47°
131° 107°
X
X =
[?]°
Enter the number that goes in the green box.
[tex]\frac{\sqrt{15} }{\sqrt[2]{3} }[/tex]
Step-by-step explanation:
both roots are square roots.
if we write the 2 or leave the base of the root blank, it both means square root.
so, we have
sqrt(15) / sqrt(3)
we can combine them into
sqrt(15/3) = sqrt(5) = 2.236067977...
Which expression is equivalent to
Expression equivalent to log 9⁵ is 5 log9.
Define equivalent.Equivalent is not the same as equal in mathematics. While equivalent indicates similar but not the same, equal means the same in all respects. For instance, 1 + 1 is equivalent to 2, even if 2 is said to be equal to 2. Equivalent value or dated value refers to the value of an original sum at any given moment. The original amount and interest accrued up to the dated value date are combined to create the comparable payment. Money amounts are not directly comparable if they are payable or due at separate times.
Given,
Expression equivalent to log 9⁵
a) 5 log9
Expression equivalent to log 9⁵ is 5 log9.
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2(x + 4) (x - 2) = 0
Answer:
x=-4 or x=2
Step-by-step explanation:
2(x+4)(x-2)=0
Subtract 4 from both sides:
(x+4)=0
Simplify:
x=-4
I NEED HELP Asap thank uu
Answer: 422.39
Step-by-step explanation:
To find the shaded region (I'm assuming it's the area inside the circle but outside the rectangle), subtract the area of the rectangle from the area of the circle.
The formula for circle area: πr^2
r is the radius, and it is given that r = 12, so the area of the circle is:
π * 12^2 ---> 144π is the area of the circle
Next, find the area of the rectangle: 3 * 10 = 30
Finally, find subtract the area of the rectangle from the area of the circle to find the shaded region:
144π - 30 ≈ 422.39
Find the area of a circle with diameter 14 in.
Use the value 3.14 for , and do not round your answer.
Be sure to include the correct unit in your answer.
The area of the circle is 153.86 inches square.
What is a circle?
Every point in a plane that is at a specific distance from the centre, or the circle's centre, forms a shape. To put it another way, it is the curve that a moving point in a plane draws to keep a constant distance from another point.
Main Body:
given:
diameter = 14 in
[tex]\pi[/tex] = 3.14
radius = diameter/ 2
= 14/2
r = 7 in
Area of circle is given by = [tex]\pi r^{2}[/tex]
Inserting the value of [tex]\pi[/tex] and r ,
area of circle = 3.14* [tex]7^{2}[/tex]
HENCE, Area of circle = 153.86 inches square
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Can you please help me with this one?
Thank u!
a) The bearing of Wellington from Gisborne is 232°
b) The bearing of Wellington from Auckland is 175.37°
How to solve bearing problems?We are given that AW = 410 km and GW = 400 km.
a) AG is a transversal intersecting two parallel lines N₁A and N₂B and ∠N₁AG = 115°.
Thus;
∠AGN₂ = 180 − 115 = 65°
since the sum of the interior angles on the same sides of the transversal intersecting two parallel lines are supplementary.
Thus;
∠N₂GW = 65 + 63 = 128°.
The reflex angle;
∠N₂GWW = 360 − 128° = 232°
b) In △AGW, we can say that by the sine rule;
(sin∠WAG)/WG = (sin∠AGW)/AG
Plugging in the relevant values;
(sin∠WAG)/400 = (sin∠63°)/410
Solving for ∠WAG gives; ∠WAG = 60.37°
Then;
∠N₁AW = 115 + 60.37
∠N₁AW = 175.37°
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a washer and a dryer cost combined. the cost of the washer is two times the cost of the dryer. what is the cost of the dryer?
If a washer and dryer cost $750 and the cost of the washer is two times the cost of the dryer, then the cost of the dryer $250
The total cost of a washer and dryer combined = $750
The cost of the dryer = x
The cost of the washer is two times the cost of the dryer.
The cost of the washer = 2x
Then the equation will be
x + 2x = 750
Add the like terms of the equation
3x = 750
Move 3 to the right hand side of the equation
x = 750/3
x = $250
Hence, if a washer and dryer cost $750 and the cost of the washer is two times the cost of the dryer, then the cost of the dryer $250
The complete question is:
A washer and dryer cost $750 combined the cost of the washer is two times the cost of the dryer what is the cost of the dryer?
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Two cell phone plans offer differing text packages. The two plans are outlined below:
Plan A: $5.00 per month charge along with a charge of $0.03 per text.
Plan B: No per month charge,but a charge of 0.10 per text. Is there a certain number of texts,when the two plans cost the same amount? Determine your answer by setting up a system of equations that model the two plans.
The system of equation for the given condition is: 5+0.03x = 0.10x, where x is the number of texts.
There is no certain number of texts for which two plans are equal.
Let the number of texts for which two plans amount to same number be = x
Plan A: $5.00 per month charge along with a charge of $0.03 per text.
So, Plan A: 5+0.03x
Plan B: No per month charge but a charge of 0.10 per text.
Plan B: 0.10x
Since the plans amounted to same for x texts. So, the suitable system of equation is,
5+0.03x = 0.10x
Solving the equation we get,
0.10x - 0.03x = 5
0.07x = 5
x = 5/0.07 = 71.42 (approximately)
Since the number of texts cannot be decimal number so there is no such number of texts for which plans are equal.
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-j + 0.8 = -0.9j + 0.76
What is the answer :D
Answer:
j = 0.4
Step-by-step explanation:
hope it helps
To answer this question, you should combine like terms:
Like terms are two or more terms that share the same variable.
J is the variable in this question so add 0.9j to both sides of the equation to get j on one side:
-0.1j + 0.8 = 0.76
Now subtract 0.8 from both sides to isolate j on one side of the equation:
-0.1j = -0.04
Divide both sides by -0.1 to isolate j and your answer should be:
Answer: j = 0.4
A tudent olve the following equation and determine that the olution i −2. I the tudent correct? Explain
a = -2 is the value of linear equation .
What are examples of linear equations?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.Step 1 - Write the equation.
3/a + 2 - 6a/a² - 4 = 1/a - 2
Step 2 - rewrite the equation.
3/a + 2 - 6a/a² - 4 = 1/a - 2
Step 3 - Take the LCM.
3(a- 2) - ( a + 2 )/a² - 2² = 6a/a²-4
Step 4 - Further simplify the above expression
3a - 6 - a - 2/a² - 4 = 6a/a² - 4
Step 5 - Cancel out the denominator of both sides and then further simplify.
2a - 8 = 6a
a = -2
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The complete question is -
A student solves the following equation and determines that the solution is −2. Is the student correct? Explain.
3/a + 2 − 6a/a2 − 4 = 1/a − 2
On a coordinate plane, the position of two friends can be defined by the points A(1, 3) and B(7,6). Their teacher is standing at point C, the
teacher's distance from point A is twice the distance from point B. What are the coordinates of point C?
(5,5)
(-5,5)
4, 9/2
8/3, 3
The coordinates of the point will be (5 , 5).
Section formula is used to find coordinates of a point when a point divides the line segment externally or internally.
For a line segment A ([tex]x_{1} , y_{1}[/tex]) and B ([tex]x_{2} , y_{2}[/tex]) getting divided by point C (x , y) in ratio m : n the formula is given as
x = [tex]\frac{mx_{2} + nx_{1} }{m + n}[/tex] y = [tex]\frac{my_{2} + ny_{1} }{m + n}[/tex]
Now in the question it is given that C from point A is twice the distance from point B which means ratio of A:B IS 2:1
A = (1 , 3)
B = (7 , 6)
by applying the formula
x = (2*7 + 1*1) / 2+1
x = 15/3
x = 5
y = (2*6 + 1*3) / 2+1
y = 15/3
y = 5
Therefore the coordinates of C will be (5 , 5)
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solve |x+3|<5
A. -8
B. -2
C. 3
D. -3
Answer: B
Step-by-step explanation:
each of cats has fleas. if two cats (and their fleas) are removed, and three fleas are removed from each remaining cat, the total number of fleas remaining would be half the original total number of fleas. what is the value of ?
1 is the value of cat in linear equation.
What is an explanation of a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.number of cats = n
number of fleas per cat = 2n
total number of fleas = (number of fleas per cat) * (number of cats) = 2n * n = 2n2
If we take the total number of fleas, subtract the fleas of two cats, then subtract 3 for every remaining cat, we get half the total number of fleas.
(total number of fleas) - 2(number of fleas per cat) - 3(n - 2) = (total number of fleas)/2
2n2 - 2(2n) - 3(n - 2) = (2n2)/2
2n2 - 4n - 3n + 6 = n2
Subtract n2 from both sides and combine like terms.
n2 - 7n + 6 = 0
Factor the left side
(n - 6)(n - 1) = 0
n = 6 or n = 1
n must be 6 because we can't remove 2 cats if there is only 1 cat to begin with.
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The complete question is -
Each of n cats has 2n fleas. If two cats (and their fleas) are removed, and three fleas are removed from each remaining cat, the total number of fleas remaining would be half the original total number of fleas. What is the value of n?
A new soup recipe contains 33\%33%33, percent less sodium per serving than the old soup recipe. The old soup recipe contained xxx milligrams of sodium per serving.
Which of the following expressions could represent the amount of sodium per serving, in milligrams, in the new soup recipe?
The expression that represents the amount of sodium per serving in the new soup is 0.67x milligrams.
How to find the expression that could represent the amount of sodium in the new soup?The new soup recipe contains 33%, percent less sodium per serving than the old soup recipe. The old soup recipe contained x milligrams of sodium per serving.
The expression that can be used to represent the amount of sodium per serving in milligrams in the new soup can be computed as follows;
Old soup amount of sodium = x milligram
The new soup contains 33% less sodium per serving than the old soup recipe.
Therefore,
amount of sodium per serving in the new soup = x - 33% of x
amount of sodium per serving in the new soup = x - 33 / 100 x
amount of sodium per serving in the new soup = x - 0.33x
Therefore,
amount of sodium per serving in the new soup = x(1 - 0.33)
amount of sodium per serving in the new soup = x(0.67)
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Please help me out! I don't get it.
Answer:
The perpendicular slope is the negative reciprocal of the original slope:
For example: the perpendicular slope for y/x is -x/y
In this case, we want the slope from x +4y = 28
x +4y = 28
4y = 28 - x
y = 7 -x/4
so the answer is: 4/x
Buying a car simple interest activity. Can you guys help me?
Answer:
BANK A
I=5700.825
T.P=25190.83
BANK B
I=3274.32
P=22764.32
Determine the unknown angle measures?
Answer:
Step-by-step explanation:
A certain data set has a line-of-best-fit that travels through these two points: (6, 275) and (8, 450) write the equation for that line-of-best-fit.
The equation of the line is - 175 x + 2 y = - 500
From the question, we have
Point 1 :
x-coordinate, x1 = 6
y-coordinate, y1 = 275
Point 2 :
x-coordinate, x2 = 8
y-coordinate, y2 = 450
We know that,
y-275 = (275-450)/(6-8)*(x-6)
y-275 = 175/2*(x-6)
- 175 x + 2 y = - 500
Slope of a Line :
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.
where "m" represents a line's slope.
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
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What is 5.37 divided by 3 equals explain your answer solve the question by using the paper.
The value of 5.37 divided by 3 will be 1.79.
How to do the division?The necessary steps include:
Take the first digit of the dividend from the left. Then divide it by the divisor and write the answer on top as the quotient.Subtract the result from the digit and write the difference below.It should be noted that it's important to bring down the next digit of the dividend. For long division problems, always follow the divide, multiply, subtract, and drop down process until each digit in the dividend has been divided.
Therefore, 5.37 ÷ 3 = 1.79.
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