Answer:
leg 1= 36 feet
leg2 = 15 feet
Step-by-step explanation:
Hi, we have to apply the Pythagorean Theorem:
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (in this case the distance between Doreen’s house and the tower) and a and b are the other legs.
leg1 = x
leg2 = x-21 (21 feet less than the other leg)
Replacing with the values given:
39^2 = x^2 + (x-21)^2
1,521 = x^2 + x^2 -42x +441
0 = 2x^2 -42x +441-1,521
0= 2x^2 -42x -1,080
For: ax2+ bx + c
x =[ -b ± √b²-4ac] /2a (quadratic formula)
Replacing with the values given:
x=-(-42)± √(-42)²-4(2)-1080] /2(2)
x= 42± √10,404] /4
x = 42± 102 /4
Positive:
x = 42+102 /4 = 36
leg 1= 36
leg2 = 36-21 =15
Feel free to ask for more if needed or if you did not understand something.
The length of shorter leg is 15 feet and other leg is 36 feet.
Pythagoras theorem:Let us consider that, length of shorter leg is x feet.
So that, length of other leg is [tex](x+21)[/tex] feet.
It is given that, the hypotenuse is 39 feet.
Apply Pythagoras theorem,
[tex]x^{2} +(x+21)^{2} =(39)^{2}\\ \\x^{2} +x^{2} +441+42x=1521\\\\2x^{2} +42x-1080=0\\\\x=15 ,-36[/tex]
Since, side can not be negative.
So that, we have to consider x=15 feet.
Length of other leg[tex]=x+21=15+21=36feet[/tex]
Learn more about the Pythagoras theorem here:
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Differentiate the function.
y = (4x − 1)^2 (4 -x^5)^4
dy/dx=
Answer:
[tex]\displaystyle y' = -4(4x - 1)(4 - x^5)^3(22x^5 - 5x^4 - 8)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (4x - 1)²(4 - x⁵)⁴
Step 2: Differentiate
Product Rule: [tex]\displaystyle y' = \frac{d}{dx}[(4x - 1)^2](4 - x^5)^4 + (4x - 1)^2\frac{d}{dx}[(4 - x^5)^4][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = [2(4x - 1)^{2 - 1} \cdot \frac{d}{dx}[(4x - 1)]](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^{4 - 1} \cdot \frac{d}{dx}[(4 - x^5)]][/tex]Simplify: [tex]\displaystyle y' = [2(4x - 1) \cdot \frac{d}{dx}[(4x - 1)]](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^3 \cdot \frac{d}{dx}[(4 - x^5)]][/tex]Basic Power Rule: [tex]\displaystyle y' = [2(4x - 1) \cdot 4x^{1 - 1}](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^3 \cdot -5x^{5 - 1}][/tex]Simplify: [tex]\displaystyle y' = [2(4x - 1) \cdot 4](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^3 \cdot -5x^4][/tex]Multiply: [tex]\displaystyle y' = 8(4x - 1)(4 - x^5)^4 - 20x^4(4x - 1)^2(4 - x^5)^3[/tex]Factor: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3 \bigg[ 2(4 - x^5) - 5x^4(4x - 1) \bigg][/tex][Distributive Property] Distribute 2: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3 \bigg[ 8 - 2x^5 - 5x^4(4x - 1) \bigg][/tex][Distributive Property] Distribute -5x⁴: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3 \bigg[ 8 - 2x^5 - 20x^5 + 5x^4 \bigg][/tex][Brackets] Combine like terms: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3(-22x^5 + 5x^4 + 8)[/tex]Factor: [tex]\displaystyle y' = -4(4x - 1)(4 - x^5)^3(22x^5 - 5x^4 - 8)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
What is 40% of 160?
A. 20
B. 40
C.
32
D. 64
E.
75
it's 64
AnswerD. 64
Step-by-step explanation:
Answer:
D.) 64
Step-by-step explanation:
Rod has to read a book which has p pages. He plans to read r pages each day for d days.
Write an equation for the number of pages left, b, in the book, after d days.
Answer:
Look at the attachment
The equation is an illustration of a linear function.
The equation for the number of pages left in the book is [tex]b =p- rd[/tex]
The total number of pages is:
[tex]Total = p[/tex]
The daily rate is:
[tex]Rate = r[/tex]
So, the number of pages read in d days is:
[tex]Pages = Rate \times Days[/tex]
This gives
[tex]Pages = r \times d[/tex]
Multiply
[tex]Pages = rd[/tex]
The number of pages left (b) is then calculated as:
[tex]b =Total - Pages[/tex]
So, we have:
[tex]b =p- rd[/tex]
Hence, the equation for the number of pages left in the book is [tex]b =p- rd[/tex]
Read more about linear equations at:
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PLEASE I NEED A LOT OF HELP
Answer:
x = 45°
Step-by-step explanation:
Look at the picture*
Find the areas of the trapezoids.
Answer:
30 square units
Step-by-step explanation:
i did this problem before.
An initial population of 895 quail increases at an annual rate of 7%. Write an exponential function to model the quail population.
The age of father is three times the age of son. If the age of son is 15 years old, then the age of father is:
50 years
55 years
45 years
40 years
Which of the lines below is a line of symmetry?
A. Neither
B. Red
C. Yellow
D. Both
Answer:
d, both
Step-by-step explanation:
both separe two identical halves :)
Both yellow and red lines are lines of symmetry to the given figure, Option D is correct.
What is Coordinate System?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
A line of symmetry is the line that divides a shape or an object into two equal and symmetrical parts.
We know that the diameter of a circle is a line passing through its center. So, the diameter acts as a line of symmetry dividing the circle into two parts with equal area.
In the given figure both the lines represents symmetry as both the lines are dividing the figure to two equal parts.
Hence, both yellow and red lines are lines of symmetry to the given figure, Option D is correct.
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#SPJ5
John received 3 detentions in the fourth quarter. He received 4 other
detentions for 1st and 2nd quarters combined. He received 12 for the
whole school year so how many detentions did he receive in the 3rd
quarter?
Answer:
5
Step-by-step explanation:
12 - (3+4)
12 - 7
12 - 7 = 5
5
Answer:
5
Step-by-step explanation:
12 - (3 + 4)
12 - 7
12 - 7 = 5
In your own words, explain the steps you would need to take to find slope from data in a table.
Answer:
Sample Answer: Start by choosing two data points. Calculate the difference between the second y value and the first y value. Then divide that by the difference between the second x value and the first x value.
Solve this inequality.
7x + 2 > 30
A.x 224
B.x > 196
C.x 4
D.x > 3
Answer:
x > 4
Step-by-step explanation:
7x + 2 > 30
Subtract 2 from each side
7x + 2-2 > 30-2
7x > 28
Divide each side by 7
7x/7 > 28/7
x > 4
Answer:
it is c
Step-by-step explanation:
Find the coordinates of a point that divides the directed line segment XY in the ratio 2:6. answers: A) (3, 5) B) (–1, –3) C) (0, –1) D) (–2, –5)
Answer:
Option D.
Step-by-step explanation:
Let the coordinates of a point which divides the segment XY in the ratio of m : n is (x, y).
Segment X(-4, -9) and Y(4, 7) has been divided in the ratio of 2 : 6.
Therefore, x = [tex]\frac{[4m+n(-4)]}{m+n}=\frac{8-24}{2+6}[/tex]
= -[tex]\frac{16}{8}[/tex]
= -2
and y = [tex]\frac{[7m+n(-9)]}{m+n}=\frac{14-54}{2+6}[/tex]
= [tex]-\frac{40}{8}[/tex]
= -5
Therefore, the point (x, y) is (-2, -5).
Option D. will be the answer.
These are my last points. I just wanted to give them away so the first one to answer correctly get the last points.
Answer:
x=-3
Step-by-step explanation:
\left(5^3\right)^2\cdot 5^{x+4}=5^7
Apply\:exponent\:rule
x+10=7
x=-3
Answer:
x = -3
Step-by-step explanation:
(5^3)^2 · 5^(x+4) = 5^7
First of all, we simplify (5^3)^2. When you have an exponent in parentheses that is raised to another exponent that is outside the parentheses, you multiply the exponents.
(5^3)^2 = 5^(3·2) = 5^6
We cannot simplify 5^(x+4) or 5^7 any further, so our equation is now:
5^6 · 5^(x+4) = 5^7
We can divide 5^6 from both sides to get:
5^(x+4) = (5^7)/(5^6)
When exponents of like terms are divided we can subtract the exponents.
5^(x+4) = 5^(7-6)
5^(x+4) = 5^1
This last part is a bit trickier. When exponents of like terms are multiplied we add the exponents. We can use this knowledge to determine that 5^(x+4) is made up of 5^x · 5^4. Now we have:
5^x · 5^4 = 5^1
We can divide both sides by 5^4.
5^x = (5^1)/(5^4)
We simplify the right side by the same way we did earlier when we divided exponents:
5^x = 5^(1-4)
5^x = 5^-3
We can see that x = -3, but using logarithms, we can finish isolating x. Taking the log base 5 of both sides, we get:
x = log₅(5^-3)
If you don't already know, log₅(5^-3) means what exponent do you raise 5 to in order to get 5^-3. After stating it like this, we can clearly see that log₅(5^-3) equals -3.
So x = -3
Another way we could have solved the logarithm is by using one of the laws of exponents. In this case, we would use logₐ(x^y) = y(logₐm). This would give us:
x = -3(log₅5)
x = -3(1)
x = -3
Either way works.
8 - n = -4 what does N equal
Answer:
Make N alone
There is an 8 so we subtract 8 from both sides so the equation is still equal
-4 - 8 = -12
Because we are subtracting N it is positive
N = 12
8 - 12 = -4
Hope this helps
Step-by-step explanation:
If you awnser this correctly I will give you more points
Answer:
1) 5m-10
Parts, 5m, -10
Operation, Subtraction
Word Expression, 10 less than the product of 5 and m.
Step-by-step explanation:
1) 5m-10
Parts, 5m, -10
Operation, Subtraction
Word Expression, 10 less than the product of 5 and m.
2) 12/2+7
6+7
13
3) 8y-(22)
Terms, 8y, 22
Operation, Subtraction
Word Expression, 22 less than the product of 8 and y.
Answer:
number 2 is 13 and number 3 is-2.75
Step-by-step explanation:
-2.75
What similarity property, if any, can be used to show that the following two triangles are similar
A. Not enough information given
B. AA
C. SAS
D. SSS
Please answer this
Which expression is equivalent to 3x + 6y?
Answer:
3x+6y =0
-6y
3x=-6y
x=-2y
Step-by-step explanation:
HELP ASAP!
A health insurance provider had net incomes of $356 million, $460 million and -$166 million in 3 consecutive years. What was the health provider's total net income for these three years?
Step-by-step explanation:
The total income would be $650 million.
The fuel efficiency of passenger cars has increased significantly since the 1970s. A linear model of this situation is given below, where x represents the number of years after 1970, and y represents the average miles per gallon. Interpret the slope.
A. For each year since 1970, passenger car fuel efficiency has increased by 0.29 gallons per mile.
B. For each year since 1970, passenger car fuel efficiency has increased by 13 gallons per mile.
C. For each year since 1970, passenger car fuel efficiency has increased by 0.29 miles per gallon.
D. For each year since 1970, passenger car fuel efficiency has increased by 13 miles per gallon.
its C not A because
For each year since 1970, passenger car fuel efficiency has increased by 0.29 miles per gallon.
Answer: The answer is C. For each year since 1970, passenger car fuel efficiency has increased by 0.29 miles per gallon.
Step-by-step explanation:
In a linear model of the form y = mx + b, m is the slope and b represents the y-intercept.
In this situation, 0.29 is the slope.
The slope is the ratio of the change in y to the change in x.
In context, the slope indicates an increase of 0.29 miles per gallon per year after 1970.
Therefore, the slope means that for each year since 1970, passenger car fuel efficiency has increased by 0.29 miles per gallon.
What reason allows the following statement to be true?
Given AB + CD = JK and CD = 5, then AB + 5 = JK
Answer: Subtituting CD =5 in AB + CD = JK
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
• AB + CD = JK (equation 1 )
• CD = 5 (equation 2)
So, we simply have to combine the equations.
Substituting CD =5 in equation 1:
AB + CD = JK
AB+(5) =JK
Feel free to ask for more if needed or if you did not understand something.
multiply: (sqrt10 +2 sqrt8)(sqrt10-2 sqrt8)
Answer:
(√10 +2√8)(√10 -2√8)=
(10 -8√5 + 8√5 -32)
10+0-32
10-32
= -22
Hope this helps.
Answer:
The other person is right, A. -22
Step-by-step explanation:
How many solutions does the equation 4x + 8 = − 2 − 2 + 5x have?
Answer:
12 =x
There is one solution
Step-by-step explanation:
4x + 8 = − 2 − 2 + 5x
Combine like terms
4x+8 = -4+5x
Subtract 4x from each side
4x-4x+8 = -4+5x-4x
8 = -4+x
Add 4 to each side
8+4 = -4+4+x
12 =x
Answer: only one 4x+8=-4+5x
4x-5x=8+4
-1x=12
x=-12
Step-by-step explanation:
True or False?
When multiplying powers with the same base, you subtract the exponents. When dividing powers with the same base, you multiply the exponents. When raising a power to a power, you divide the exponents? EXPLAIN YOUR REASONING
Answer:
False
Step-by-step explanation:
(x^3)(x^4) = (xxx)(xxxx) = x^7 when multiplying you add the exponents
(x^5)÷(x^2) = (xxxxx)÷(xx) = xxx or x^3 because two of the x's reduce therefore when dividing you subtract the exponents
(x^2)^3 = (x^2)(x^2)(x^2) = (xx)(xx)(xx) = x^6 when raising a power to a power you multiply the exponents
what does it mean that the fan data are numerical and univariate?
Answer:
The fact that the data is univariate means that there is only one variable – age, and the fact the data is numerical means it involves numbers – age.
I'm doing the test and this is what I put for my answer
Plz Help!
Hank has cards that are 4 inches by 2 inches. A stack of these cards fits inside the box shown and uses up 8 cubic inches of volume.
L 4 in.
W 2 in.
H 2 in.
Part 1 out of 2
How tall is the stack of cards?
The stack is ___ inch(es) tall.
What is the missing number that will complete the
factorization?
6
8
12
24
Answer:
6
Step-by-step explanation:
6xa is 6a, just like how 2xa is 2a as shown
Please help me with my Algebra. :)
Answer:
[tex]\mathrm{D}[/tex]
Step-by-step explanation:
[tex]6x+5y=-2[/tex]
[tex]6(-2)+5(2)=-2[/tex]
[tex]-12+10=-2[/tex]
[tex]-2=-2[/tex]
[tex]\mathrm{Hence,\:it\:is\:true.}[/tex]
Answer:
A
Step-by-step explanation:
When the two crews start working together, what part of all
the garbage bins will the first garbage truck empty?
The crew of a garbage truck takes 5 hours to empty all the
bins in one neighborhood on pickup day. The city assigned
a second garbage truck to this neighborhood. During their
training, it took the crew from the second truck 8 hours to
empty all the bins.
0.6
0.5
0.7
Time
(hours)
t
Part of Bins
Emptied
Rate
(part/hour)
1
5
0.4
First Truck
500
(9
1
t
Second
Truck
1
8
8
This question is not properly written
Complete Question
When the two crews start working together, what part of all
the garbage bins will the first garbage truck empty?
The crew of a garbage truck takes 5 hours to empty all the bins in one neighborhood on pickup day. The city assigned a second garbage truck to this neighborhood. During their training, it took the crew from the second truck 8 hours to empty all the bins.
Options
• 0.6
• 0.5
• 0.7
Answer:
0.6
Step-by-step explanation:
Let us say that the total hours worked by both trucks = t hours
Number of hours worked by first truck = 5 hours
Number of hours worked by second truck = 8 hours
Let 1 = total number of bins.
For the 1st truck the rate at which work was carried out is
(1 ) ÷ (5 ) = 1/5
For the 1st truck the rate at which work was carried out is
( 1 ) ÷ (8 ) = 1/8
Then,
(1/5 + 1/8) × t =1
(1/5 + 1/8) × t= 1
(13/40)t = 1
t = 1÷ 13/40
t = 1× 40/13
t = 40/13 hours.
Hence, the total hours worked by both trucks = 40/13 hours
the part of all
the garbage bins that the first garbage truck will empty is calculated as:
1/5 × 40/13 hr
1/5 × 40/13
= 0.6153846154
Approximately = 0.6
Therefore, when the two crews start working together, the part of all
the garbage bins that the first garbage truck will empty is 0.6 of the total work done.
Answer:
A) 0.6
Step-by-step explanation:
Which expression is equal to (−3x2−2)(4x2+1)? −12x4−11x2−2 −12x4−5x2−2 −12x2−11x−2 12x4−11x2−2
Answer:
[tex]-12x^4-11x^2-2[/tex]
Explanation:
Step 1 - Expand
[tex](-3x^2-2)(4x^2+1)[/tex]
[tex]-12x^4-3x^2-8x^2-2[/tex]
Step 2 - Combine like terms
[tex]-12x^4-3x^2-8x^2-2[/tex]
[tex]-12x^4-11x^2-2[/tex]
Therefore, the expression that is equal to [tex](-3x^2-2)(4x^2+1)[/tex] is [tex]-12x^4-11x^2-2[/tex].
Answer:
On Edge, the answer is D. 31x2 – 2.
Find distance of each
Answer:
4
Step-by-step explanation:
Since the y value is the same, we only have to look at the x value
-1 - -5
-1 +5
4
The distance is 4
Answer: The distance of this segment is 4 units
Step-by-step explanation:
Obviously, you could count the number of units in this graph, but for the sake of math, let’s use the distance formula, which is:
d = √([tex]x_{2}[/tex] - [tex]x_{1}[/tex])² + ([tex]y_{2}[/tex] - [tex]y_{1}[/tex])²
We know that the two endpoints of our line segment are (-1, -4) and (-5, -4). So we will use these coordinates and substitute them into the equation. The -4s will be our y coordinates, and our -1 and -5 will be our x coordinates.
d = √((-5) - (-1))² + ((-4) - (-4))²
d = √(-4)² + (0)²
d = √16 + 0
d = √16
d = 4
This furthermore proves that the distance between the two segments is 4.
Hope this helps! :)
