Answer:
23 is the answer
4√2/9+√2+√1/18. 1/√3-1-1/√3+1
Answer:
Exact form: 78√2 - 17√3 / 54
Decimal form: 1.49747766
Step-by-step explanation:
Rationalize and simplify the expression.
The graph below shows the speed of a car that is driven through a town and then on a major highway. During which of the following time intervals was the car stopped at a traffic light?
Considering the graph of the velocity of the car, it is found that the interval in which it was stopped at a traffic light was:
Between 3 and 4 minutes.
When is a car stopped at a traffic light?When a car is stopped at a traffic light, the car is not moving, that is, it's velocity is of zero.
In this problem, the graph gives the velocity as a function of time, and it is at zero between 3 and 4 minutes, hence the interval in which it was stopped at a traffic light was:
Between 3 and 4 minutes.
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I need help with this
Example 1 Find 6 – 9. 6 – 9 = 6 + ( – 9) To subtract 9, add – 9. = – 3 Simplify
Answer:
Step-by-step explanation: This example is saying that adding a negative number is the same as subtracting a positive number. For example 2-3 = 2 + (-3).
Jenny packaged 108 eggs in 9 cartons. Write this statement as a ratio
Answer:
12:1
Step-by-step explanation:
each pack contains 12 eggs
108/9 = 12
Hope this helps
find the square roots of each of the following number
1: 81
2: 100
Multiply 9 with 9, and we get:
9 × 9 = 81
Multiply 10 with 10, and we get:
10 × 10 = 100
We get the final result as:
9²10²Hope this helps :)
4. Emily's house has a chimney. What is the volume of her chimney?
4 in.
9 in.
12 in.
3 in.
4 in.
6 in. step by step pls i give brainliest and 80 points
Answer:
[tex] {216 \: in}^{3} [/tex]
Step-by-step explanation:
Split the chimney into 2 rectangular prisms. One is the short one, and the other is the tall one.
The dimensions of the short prism are 4 x 3 x 2. The volume of that prism is found by multiplying those numbers together, which is 24.
The dimensions of the tall prism are 4 x 4 x 12. The volume of that prism is 192.
Adding those 2 volumes together, you will get the volume of the composite figure. 192 + 24 = 216
Volume is always in cubic units
Use the recursive formula to find the first five terms in the arithmetic sequence.
The first five terms of the sequence are 1/5, 2/5, 3/5,4/5, 1
Recursive functionsRecursive functions are functions that is used to determine the next term of a given sequence giving the common difference.
Given the recursive function shown below;
f(1) = 1/5
f(n) = f(n-1) + 1/5
For the second term;
f(2) = f(1) + 1/5
f(2) = 1/5 + 1/5
f(2) = 2/5
For the third term;
f(3) = f(2) + 1/5
f(3) = 2/5 + 1/5
f(3) = 3/5
For the fourth term;
f(4) = f(3) + 1/5
f(4) = 3/5 + 1/5
f(4) = 4/5
For the fifth term;
f(5) = f(4) + 1/5
f(5) = 4/5 + 1/5
f(5) = 5/5 = 1
Hence the first five terms of the sequence are 1/5, 2/5, 3/5,4/5, 1
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How many lbs of peanuts must mike add to 9 lbs of mixed nuts containing 40% peanuts to make a mixture with 73% peanuts
The new mixture exists 56.5% peanuts.
How to estimate the total number of peanuts required for the mixture?The first batch of 9 lb of mixed nuts possesses 40% peanuts.
This means the quantity of peanuts exists:
9 [tex]*[/tex] 40/100 = 3.6 lb
The second batch of 9 lb of mixed nuts possesses 73% peanuts.
This means the quantity of peanuts exists:
9 [tex]*[/tex] 73/100 = 6.57 lb
The total quantity of peanuts in the mix exists
3.6 lb + 6.57 lb = 10.17 lb
There exist 9 lb + 9 lb = 18 lb of mix.
Therefore, the percent of peanuts in the mix exists:
10.17 / 18 [tex]*[/tex] 100 = 56.5%
The new mixture exists 56.5% peanuts.
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NEED HELP SOLVING
has to be simplified
State the converses of the following statements. In each case, also decide whether the converse is true or false.
(1) If n is an even integer, then 2n + 1 is an odd integer.
(2) If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.
(3) If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.
(4) If the decimal expansion of a real number is terminating, then the number is rational.
Help!
Answer:
See below.
Step-by-step explanation:
Converse
The converse of a statement is formed by switching the hypothesis and the conclusion.
Hypothesis: The part after the "if".Conclusion: The part after the "then".Question 1Given statement: If n is an even integer, then 2n + 1 is an odd integer.
Hypothesis: "n is an even integer"Conclusion: "2n + 1 is an odd integer"Converse: If 2n + 1 is an odd integer, then n is an even integer.
Question 2Given statement: If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.
Hypothesis: "a transversal intersects two parallel lines"Conclusion: "each pair of corresponding angles is equal"Converse: If a transversal intersects two lines such that each pair of corresponding angles is equal, then the two lines are parallel to each other.
Question 3Given statement: If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.
Hypothesis: "each pair of opposite sides of a quadrilateral is equal"Conclusion: "the quadrilateral is a parallelogram"Converse: If a quadrilateral is a parallelogram, then each pair of opposite sides of the quadrilateral is equal.
Question 4Given statement: If the decimal expansion of a real number is terminating, then the number is rational.
Hypothesis: "the decimal expansion of a real number is terminating"Conclusion: "the number is rational"Converse: If a real number is rational, then the decimal expansion of the number is terminating.
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Answer:
9/41
Step-by-step explanation:
Cosine represents adjacent / hypotenuse.
When A is the reference angle, AB is the adjacent side (9) and AC is the hypotenuse (41).
9/41 is already simplified.
HELP!!!!QUICK!!!!!!!!!!!
Answer:
= – 5 – 7
Step-by-step explanation:
3 – 8 = – 5 + 4 – 5 = – 1 –1 – 6 = –7= –5 – 7
Find the area of this parallelogram. D(-3,4) c(3,4) a(-6,-4) b(0,-4)
If the vertices of parallelogram ABCD is A(-6,-4),B(0,-4),C(3,4),D(-3,4) ,then the area of parallelogram ABCD will be 48 square units.
Given that the vertices of parallelogram ABCD is A(-6,-4),B(0,-4)
,C(3,4),D(-3,4).
We are required to find the area of parallelogram ABCD.
Let the point of intersection of height of parallelogram from point A is point E.
When we see the graph on which the parallelogram then we will be able to know that point E has coordinates of (-3,-4).
Area of parallelogram=Base*Height
=AB*DE
DE=[tex]\sqrt{(-4-4)^{2} +(-3+3)^{2} }[/tex]
=[tex]\sqrt{64}[/tex]
=8 units
AB=[tex]\sqrt{(-4+4)^{2} +(0+6)^{2} }[/tex]
=[tex]\sqrt{36}[/tex]
=6 units
Area=6*8
=48 square units.
Hence if the vertices of parallelogram ABCD is A(-6,-4),B(0,-4),C(3,4),D(-3,4) ,then the area of parallelogram ABCD will be 48 square units.
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please help if u can! greatly appreciated
don't answer if u dont know PLEASE
a. log₈8 = 1
b. log₇6/5
c. log₉3¹
The solution to the problem are1. log₈ 2 * 4 would produce an integer
= log₈8 = 1
The output is an integer
2. log₇6/5 would give us an irrational number
= log₇1.2
This would give us an irrational number
3. log₉3¹ would give us a rational number
= log₉9^[tex]^\frac{1}{2}[/tex] = 1/2 log⁹9
= 1/2
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What is the quotient of the given values to the correct level of precision? 16.017 in. ÷ 0.370 in. 43 43.289 43.29 43.3
Answer:43.289
Step-by-step explana
Solve the given initial-value problem. y'' 4y' 5y = 35e−4x, y(0) = −5, y'(0) = 1
The solution for the initial value problem is [tex]y_{g} = e^{-2x} (-12cos(x) + 5sin(x)) + 7e^{-4x}[/tex]
Given,
y" + 4y' + 5y = 35[tex]e^{-4x}[/tex]
y(0) = -5
y'(0) = 1
Solve this homogenous equation to get [tex]y_{h}[/tex]
According to differential operator theorem,
[tex]y_{h}[/tex] = [tex]e^{ax}[/tex]( A cos (bx) + B sin (bx)), where A and B are constants.
Therefore,
y" + 4y' + 5y = 0
([tex]D^{2}[/tex] + 4D + 5)y = 0
D = -2± i
[tex]y_{h} = e^{-2x} ( A cos (x) + B sin (x))[/tex]
Now, solve for [tex]y_{p}[/tex]
A function of the kind [tex]ce^{-4x}[/tex] is the function on the right, we are trying a solution of the form [tex]y_{p} =ce^{-4x}[/tex], here c is a constant.
[tex]y_{p} " + 4y_{p} ' + 5y_{p} = 35e^{-4x} \\=16ce^{-4x} -16ce^{-4x} +5ce^{-4x} = 35e^{-4x} \\= 5ce^{-4x} =35e^{-4x} \\c=\frac{35}{5} =7\\y_{p} =7e^{-4x}[/tex]
Then the general solution will be like:
[tex]y_{g} =y_{h} +y_{p} \\[/tex]
= [tex]e^{-2x} (Acos(x)+Bsin(x))+7e^{-4x}[/tex]
[tex]y_{g}(0)=-5=A+7=-12\\y_{g} '(0)=e^{-2x} (-Asin(x)+Bcos(x))-2e^{-2x} (Acos(x)+Bsin(x))-28e^{-4x} \\y'_{g} (0)=1=B-2A-28\\[/tex]
B = 1 - 24 + 28 = 5
Then the solution for the given initial value problem is
[tex]y_{g} =e^{-2x} (-12cos(x)+5sin(x))+7e^{-4x}[/tex]
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Consider the quadratic function f(x)=x²-5x+12. Which statements are true about the function and its
graph? Select three options.
A. The value of f(-10) = 82
B. The graph of the function is a parabola.
C. The graph of the function opens down.
D. The graph contains the point (20,-8).
E. The graph contains the point (0, 0).
There is only one statement that is true: B. The graph of the function is a parabola.
How to study and interpret the characteristics of quadratic equations
In this question we have a quadratic equation, whose characteristics have to be inferred and analyzed. We need to prove each of the five choices presented in the statement:
Choice A:
If we know that x = - 10, then we evaluated it at the function:
f(- 10) = (- 10)² - 5 · (- 10) + 12
f(- 10) = 162
False
Choice B:
By analytical geometry we know that all functions of the form y = a · x² + b · x + c always represent parabolae.
True
Choice C:
The quadratic function opens up as its leading coefficient is greater that 0.
False
Choice D:
If we know that x = 20, then we evaluate it at the function:
f(20) = 20² - 5 · (20) + 12
f(20) = 312
False
Choice E:
If we know that x = 0, then we evaluate it at the function:
f(0) = 0² - 5 · (0) + 12
f(0) = 12
There is only one statement that is true: B. The graph of the function is a parabola.
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5. Find the arc length on a circle with radius of 19 feet created by
an angle of 2(pie)/3radians.
19T
O
38
38T
O 19
O None of the above
**Disclaimer** Hi there! I am not fully sure what [ T ] represents. From the answer that I got [ 38π / 3 ], it does not match any one of them, so I choose none of the above. If there's a specific meaning of [ T ] and I am incorrect, please let me know and I will modify my answer.
Answer: None of above
Step-by-step explanation:
Given formula
S = r θ
S = arc lengthr = radiusθ = angle in radiansGiven information
radius = 19 ft
Angle = 2π / 3
Substitute values into the formula
S = r θ
S = (19) (2π / 3)
Simplify by multiplication
[tex]\Large\boxed{S=\frac{38\pi}{3} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
what is the decimal representation of 3/40
Answer:
0.075
Step-by-step explanation:
to convert a fraction to a decimal fraction
divide the numerator by the denominator, that is
[tex]\frac{3}{40}[/tex] = 3 ÷ 40 = 0.075
1.) You go skiing on one route with an equation = 2 + 4 and then
immediately go to a route with an equation = 4 + 1. Which of the
following responses best describes your routes?
A: Your second route was steeper than your first, and the second route was higher up
the mountain.
B: Your first route was positive (uphill), but your second route was negative (downhill).
C: Your first route was steeper than your second, and both were positive (uphill).
D: Your first route was flatter than your second, and your first route began at a higher
point than your second
The best information that describes your routes is the second route was steeper than your first, and the second route was higher up the mountain.
What is the slope of a linear equation?The slope of a linear equation is the change in the rise over the run. So, the slope of a linear equation shows that the larger the slope, the steeper the line becomes.
From the given information:
y = 2x + 4 --- (1)
y = 4x + 1 --- (2)
Using the slope-intercept formula:
y = mx + b
m = slopeb = y-interceptFrom the first equation, the slope is 2 and in the second equation, the slope is 4.
Therefore, we can conclude that the second route was steeper than your first, and the second route was higher up the mountain.
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Determine the slope of the line.
Answer:
2
Step-by-step explanation:
→ Find 2 points from the line
( 0 , 6 ) and ( - 3 , 0 )
→ Find the change in y coordinates
0 - 6 = -6
→ Find the change in x coordinates
-3 - 0 = -3
→ Divide the 2 results
-6 ÷ -3 = 2
Which value is a solution for the equation tan/2=-1
The value of the solution is 3π/2.
What is a trigonometric equation?
An equation involving one or more trigonometric ratios of unknown angles is called a trigonometric equation.
tan x/2 = -1
tanx/2 = tan(-π/4)
tanx=tanФ
⇒ The general equation of tanx=tanФ is
⇒ x=nπ+Ф
x/2=nπ+(-π/4)
at n=0
x/2=-π/4
x=-π/2
at n=1
x/2=π-π/4
x/2=3π/4
x=3π/2
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Questions: Which value is a solution for the equation tan x/2 = -1?
A. 5pi/4
B. 7pi/4
C. 3pi/4
D. 3pi/2
Find the general solution of the given second-order differential equation. 12y'' − 5y' − 3y = 0
The general soultion of the given differential equation 12y'' − 5y' − 3y = 0 is
y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].
According to the given question.
We have a differential equation
[tex]12y^{"} -5y^{'} -3y = 0[/tex]
The above equation can be written as
[tex](12D^{2} -5D -3)y = 0[/tex]
The auxillary equation for the above differential equation is
[tex]12m^{2} -5m-3 = 0[/tex]
[tex]\implies 12m^{2} -9m+4m -3 = 0[/tex]
⇒ 3m(4m - 3) +1(4m - 3) = 0
⇒ (3m + 1)(4m -3) = 0
⇒ m = -1/3 or 3/4
Therefore,
[tex]C.f = c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex]
Here, P.I = 0
As we know that the general solution of the differential equation is given by
y = PI + CF
Thereofre, the general soultion of the given differential equation 12y'' − 5y' − 3y = 0 is
y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].
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Profit is the difference between revenue and cost. the revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial 2x3 30x – 130. the cost, in dollars, of producing the skateboards can be modeled by 2x3 – 3x – 520. the variable x represents the number of skateboards sold.
Profit function in terms of x = 33x + 390.
What is a profit in business?
In its simplest form, it's the amount left after subtracting your total expenses from your total revenue. The money remaining, your profits, can either be kept in the business and re-invested to finance future growth, or distributed as a draw or dividends to stakeholders.Given that revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial
[tex]2x^{3} + 30x - 130[/tex]
The cost, in dollars, of producing the skateboards can be modeled by
[tex]2x^{3} -3x - 520[/tex]
Profit function = Revenue - cost
= [tex]2x^{3} + 30x - 130 - ( 2x^{3} - 3x - 520)[/tex]
= 33x + 390
Therefore, profit function in terms of x = 33x + 390
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20 PTS! Please Help!!!! Will Give Brainliest!! This is a Khan Academy Problem!!!
Find the approximate perimeter of pentagon ABCDE plotted below. A(0,7) B(6,0) C(3,-4) D(-3,-4) E(-6,0)
Using it's concept, the approximate perimeter of pentagon ABCDE is given as follows:
34.4 units.
What is the perimeter of a figure?The perimeter of a figure is given by the sum of the lengths of it's outside dimensions.
In this problem, the vertices are in a coordinate-plane, hence the distances are found using the formula for the distance between two points.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The length of segment AB is:
[tex]AB = \sqrt{(6 - 0)^2+(0 - 7)^2} = 9.2[/tex]
The length of segment BC is:
[tex]BC = \sqrt{(6 - 3)^2+(0 + 4)^2} = 5[/tex]
The length of segment CD is:
[tex]CD = \sqrt{(-3 -3)^2+(-4 + 4)^2} = 6[/tex]
The length of segment DE is:
[tex]DE = \sqrt{(-6 + 3)^2+(0 + 4)^2} = 5[/tex]
The length of segment EA is:
[tex]EA = \sqrt{(-6 +0)^2+(0 - 7)^2} = 9.2[/tex]
Hence the perimeter is:
P = AB + BC + CD + DE + EA = 9.2 + 5 + 6 + 5 + 9.2 = 34.4 units.
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Which of the following expressions is equivalent to ab² + 6ab + 7a3-14a?
(b + 7)(b + 6)(a²-2)
Ob(b + 6)+7(a²-2)
Oa[b(b + 6) +7(a²-2)]
a[(b + 7)(b + 6) (a²-2)]
Answer:
"a[b(b + 6) +7(a²-2)]" (the third one)
Step-by-step explanation:
Quick algebra 1 question for 50 points!
Only answer if you know the answer, Tysm!
Answer:
x=1
Step-by-step explanation:
2/3(9x-6) = 1/4(12-4x)
We want to solve for x
Distribute
6x-4=3-x
Add x to each side
6x-4+x = 3-x+x
7x-4 = 3
Add 4 to each side
7x-4+4 = 3+4
7x=7
Divide by 7
7x/7 = 7/7
x=1
Answer:
x = 1
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] (9x - 6) = [tex]\frac{1}{4}[/tex] (12 - 4x) ← distribute parenthesis on both sides
6x - 4 = 3 - x ( add x to both sides )
7x - 4 = 3 ( add 4 to both sides )
7x = 7 ( divide both sides by 7 )
x = 1
Lucy started the proof of the law of cosines using triangle WXY as shown.
W
Z
X
Given: XZ WY, AWXZand AYXZare right triangles
z; y cos (W) = WZ
Step 1: cos (W) =
Step 2: sin (W) =
Step 3: ZY = x - y cos (W)
Step 4: w²= (z-y cos (W))² + XZ²
Which step contains the first error in calculation?
z; XZ sin (W) = y
OA Step 1- the cosine ratio was applied incorrectly
OB. Step 2 - the sine ratio was applied incorrectly
OC. Step 3- the incorrect value was subtracted
OD. Step 4- the area formula should have been used instead.
4
The step which contains the first error in calculation is: B. Step 2 - the sine ratio was applied incorrectly.
What is the law of sines?The law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.
Mathematically, the law of sines is given by this equation:
[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]
For any right-angled triangle, the ratio of the length of its opposite sides to the length of its hypotenuse is generally referred to as sine ratio. Thus, sine ratio is given by this formula:
cos(θ) = Opp/Hyp
Where:
Opp is the opposite side of a right-angled triangle.Hyp is the hypotenuse of a right-angled triangle.θ is the angle.In this context, we can infer and logically deduce that the step which contains the first error in calculation is step 2:
sin(W) = y/XZ; XZsin(W) = y.
In conclusion, the correct step should have been written as follows:
sin(W) = XZ/y; ysin(W) = XZ.
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Answer:
step 2 is incorrect
Step-by-step explanation:
B. Step 2 - the sine ratio was applied incorrectly
One day, thirteen babies are born at a hospital. assuming each baby has an equal chance of being a boy or girl, what is the probability that at most eleven of the thirteen babies are girls? a. 29/128 b. 743/1024 c. 4089/4096 d. 11/64
Using the binomial distribution, there exists a 0.9983 = 99.83% probability that at most eleven of the thirteen babies exists girls.
What is the binomial distribution formula?The formula exists:
[tex]$&P(X=x)=C_{n, x} \cdot p^{x} \cdot(1-p)^{n-x} \\[/tex]
The parameters exists:
x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.
The values of the parameters are: p = 0.5 and n = 13
The probability that at most eleven of the thirteen babies are girls is:
[tex]$P(X \leq 11)=1-P(X > 11)$$[/tex] then
[tex]$P(X > 11)=P(X=12)+P(X=13)$$[/tex]
By using the binomial distribution formula
[tex]$&P(X=x)=C_{n, x} \cdot p^{x} \cdot(1-p)^{n-x} \\[/tex]
substitute the values in the above equation, we get
[tex]$&P(X=12)=C_{13,12} \cdot(0.5)^{12} \cdot(0.5)^{1}=0.0016 \\[/tex]
[tex]$&P(X=13)=C_{13,13} \cdot(0.5)^{13} \cdot(0.5)^{0}=0.0001[/tex]
So, [tex]$&P(X > 11)=P(X=12)+P(X=13)[/tex]
[tex]=0.0016+0.0001=0.0017 \\[/tex]
[tex]$&P(X \leq 11)=1-P(X > 11)[/tex]
[tex]=1-0.0017=0.9983[/tex]
0.9983 = 99.83% probability that at most eleven of the thirteen babies exists girls.
Therefore, the correct answer is option c. 4089/4096
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prove that if all the altitude lengths are different in a triangle, then the triangle is scalene. (use indirect proof or contrapositive)
The term "altitude" is the same as "height of a triangle". It is perpendicular to the base. Since we can rotate the triangle to have any side be horizontal, there are effectively 3 possible bases. Hence, there are 3 heights. It all depends how you look at it.
Let h1, h2, and h3 be the three altitudes or heights.
Without loss of generality, we'll focus on the first two heights h1 and h2. Their respective bases are b1 and b2.
If we use b1 as the base, then the area is...
area = 0.5*base*height = 0.5*b1*h1
Similarly, the other base gives the area of:
area = 0.5*b2*h2
------------------------
Since both formulas refer to the same area (because we're working with the same triangle), we can set the expressions equal to one another
0.5*b1*h1 = 0.5*b2*h2
b1*h1 = b2*h2
Let's see what happens when b1 = b2, so,
b1*h1 = b2*h2
b1*h1 = b1*h2
b1h1 - b1h2 = 0
b1(h1 - h2) = 0
b1 = 0 or h1 - h2 = 0
b1 = 0 or h1 = h2
If the bases b1 and b2 were equal, then either those bases must be 0 which isn't possible, or the altitudes must be equal. However, the initial premise is that the heights must be different from one another.
Therefore, the bases b1 and b2 can't be the same length.
We could follow the same steps and logic to conclude that if the altitudes h1 and h3 were different, then the bases b1 and b3 can't be the same. Similarly, we would conclude that b2 and b3 can't be the same. This is where the "without loss of generality" kicks in.
In other words, we only need to focus on one subcase to extend the logic to the other cases, without having to actually do every single step. That would be a bit tedious busywork.
In conclusion, we've shown that if the heights are different, then their respective bases must be different. This leads to wrapping up the proof that we have a scalene triangle.
Side note: I used an indirect proof or proof by contradiction. I assumed that a non-scalene triangle was possible and it led to a contradiction of h1 = h2.
