The length of the other leg is 9 units. Therefore, option B is the correct answer.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given that, one leg of a right triangle is 8 units long, and its hypotenuse is 12 units long.
Let the length of the other leg be x.
12²=8²+x²
144=64+x²
x²=144-64
x²=80
x=√80
x=8.94
x≈9 units
Therefore, option B is the correct answer.
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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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solve |x+3|<5
A. -8
B. -2
C. 3
D. -3
Answer: B
Step-by-step explanation:
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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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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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
The value in dollars of a $3,000 investment after n years is given by f(n) = 3,000(1.05)n. find the value of the investment (in dollars) after 4 years. (round your answer to the nearest cent.)
The value in dollars of a $3,000 investment after n years is given by f(n) = 3,000(1.05)n.
The value of the investment after 4 years is $12600.
A simple definition of an equation is a mathematical statement that depicts the relationship between two values. In an equation, the equal sign often equates the two values.
From this question we can assume that n = 4.
In the given equation,
F(n)= 3000(1.05)n
After putting the value of n which is 4, it will be:
F(4)= 3000(1.05) × 4 = 12600
Hence, the value of the investment after 4 years in $12600.
There are many different kinds of equations:
• Linear equation
o Equation with one variable
o Equation with two variables
o Equation with three variables
• Polynomial equation
o Monomial equation
o Binomial equation
o Polynomial equation
• Quadratic equation
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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
Jacob is going to invest $15,000 and leave it in an account for 6 years. Assuming the
interest is compounded quarterly, what interest rate, to the nearest hundredth of a
percent, would be required in order for Jacob to end up with $17,000?
The rate that Jacob would require to be able to end up with $17, 000 from $15, 000 after 6 years is 0.52%
How to find the rate?To find the rate, you can use a spreadsheet. The relevant function would be the rate function.
Nper = Number of periods = 6 years x 4 quarters per year = 24 quarters
Pv = $15, 000
Fv = $17, 000
The interest rate required by Jacob would be given as:
= 0.005228753
= 0.52%
In conclusion, Jacob would require a periodic interest rate of 0.52%.
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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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47°
131° 107°
X
X =
[?]°
Enter the number that goes in the green box.
How do you explain multiplying by 3?.
Answer:
a number x times by 3
Step-by-step explanation:
yw I hope that helps
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
Simplify 5(x-2)-3(x-2)+7x
Answer:
9x-4
Step-by-step explanation:
find the measure of the indicated angle to the nearest degree. GIVE EXPLANATION PLEASE
Answer:
1.90°
2.30°
3.60°
Step-by-step explanation:
calculate it using the distance and angle
which is division
determine the exponential generating function for the sequence of factorials: o!, i!, 2!, 3!, ... , n!, . ...
The exponential generating function for the sequence of factorials is x! = Γ(x+1) = [tex]\int\limits^{infinity}_0 {t}^{x}{e}^{-t} \, dt[/tex].
We are given a sequence. A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It has members, just like a set. The length of the sequence is defined by the number of elements. The given sequence consists of factorials. The product of all positive integers less than or equal to n, denoted by n!, is the factorial of a non-negative integer n. We need to find the exponential generating function for the given sequence. The sequence is 0!, 1!, 2!, …, n!. The exponential generating function for the sequence of factorials is given below.
x! = Γ(x+1) = [tex]\int\limits^{infinity}_0 {t}^{x}{e}^{-t} \, dt[/tex]
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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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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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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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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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Find the nth term of this quadratic sequence
3, 8, 15, 24, 35, …
The nth term of this quadratic sequence 3, 8, 15, 24, 35, … is 2n
What is Sequence?An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.
Confirm if the sequence is quadratic and this is done by finding the second difference
Sequence = 3, 8, 15, 24, 35, …
1st difference = 5, 7, 9, 11
2nd difference = 2, 2, 2
Divide the second difference by 2, and let the value be a
2 ÷ 2 = 1
So the first term of the terms is [tex]n^{2}[/tex]
subtract [tex]n^{2}[/tex] from the sequence gives 2, 4, 6 , 8, 10
the nth term is 2n
Therefore, the nth term is 2n
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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
Which pair of triangles can be used to show that the slope of line a is the same anywhere along the line?.
The pair of triangles that can be used to show that the slope of line a is same everywhere is upper half triangles
What is called a triangle?A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees
What is the geometry formula for a triangle?The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h.
The pair of triangles in choice C (shown in the figure below) demonstrates that line a has a constant slope throughout.
Let's investigate:
Rise/run = slope
Regarding the initial lower triangle:
Rise = 3.5
Run = 4.5
Slope = 3.5/4.5 ≈ 0.8
For the upper second traingle:
Rise = 4
Run = 5
Slope = 4/5 = 0.8
As a result, it demonstrates that the graph's line's slope is constant throughout.
The pair of triangles that can be used to show that the slope of line a is same everywhere is upper half triangles
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What does total change in math
mean ?
Answer: The integral of the rate of change of a function is equal to the total change in the function.
Step-by-step explanation:
The rate of change of the volume of a sphere with the radius is. DV.
[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...
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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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
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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-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
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
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]
