Answers
Answer:
24
Step-by-step explanation:
STEP 1. Write the given function
\(p(t) = - 1707t {}^{2} + 81000t + 10000\)
STEP 2. Find the maximum of the function
\( \frac{13500}{569} = 23.726 = 24\)
Related Questions
please answer me I will f0ll0w u
Answers
Step-by-step explanation:
1. let n=2, then, n+2= 2+2=4 so 2^2= 4 and 4^2=16 then 16-4=12 which is an even number
2. let n=4, the. n+3=4+3=7, and 4^2=16 and 7^2=49 then 49-16 =33 which is an odd number
please follow me
1) Let ‘n’ be 5
Therefore, (n + 2) = 5 + 2 = 7
=> 5^2 = 25
=> 7^2 = 49
Difference of Squares
= 49 - 25
=> 24
24 is an Even Number.
Hence, proved.
1) Let ‘n’ be 5
Therefore, (n + 3) = 5 + 3 = 8
=> 5^2 = 25
=> 8^2 = 64
Difference of Squares
= 64 - 25
=> 39
39 is an Odd Number.
Hence, proved.
How can you find the side length of the square of Kendra wants exactly 1,000 feet
Answers
Latonya works in a factory where she makes crispy snacks. first, she uses a machine that forms large 100 lb blocks of crispy. she cuts one block evenly into bars that each weigh 8oz. these bars are then pressed into a mold that creates 2 flat square wafers that each weigh 3oz. the left over waste material is put into recycle bins to be used elsewhere. these flat squares are then packed into bags of 5 which are sealed and finally packed into boxes, each containing 14 bags ready to be sent out to the stores. how much weight out of the original 100 lb block as a % is contained in the completely filled boxes (i.e. those containing a full 14 bags)?
Answers
The percentage of the original block cookie that is packaged and ready to be distributed to stores is: 12.6%.
How to calculate the biscuit percentage of the original biscuit that is packaged?
To calculate the percentage of the original 100lb cookie that is packaged and ready to be distributed, we must perform the following operations:
We must calculate how much each package of 5 cookies weighs, for this we multiply the weight of each cookie (3 ounces) 0.18 pounds by the number of cookies in each package (5).
0.18lb × 5 = 0.9 lbNext, we need to calculate how much the box containing 14 packages of cookies weighs by multiplying the weight of each package (0.9 lb) by the number of packages in each box (14).
0.9lb × 14 = 12.6 lbLastly, we need to calculate how much percentage the weight of each box is equal to the weight of the original 100 lb cookie that Latonya made. For that we divide 100 lbs. by 100 and multiply the result by the final weight of the box (12.6lbs).
100lbs ÷ 100 = 11 × 12.6 = 12.6%Based on the above, each box contains 12.6% of the first 100-lb cookie Latonya made.
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This is what I need help with!!!!
Answers
Step-by-step explanation:
Area of a triangle = 1/2 base * height
for these triangles area = 1/2 14 * 12.12 = 84.84 cm^2
and there are four of these four * 84.84 = 339.36 cm^2
The lines represented by the equations 5y+30x=-155y+30x=−15 and y+\frac{1}{6}x=3y+
6
1
x=3 are
Answers
Based on the graph below, f(x) and g(x) where g(x) =f(x)+h are shown
Answers
Answer:
The value of h is 5
Step-by-step explanation:
Remember the if two lines are parallel and one is taller than the other and is asking for what that is the difference it is the y-intercept or what you call in this problem "h" since h is 5 digits above the answer is 5
Predict what the products would be in the following double displacement reaction:
KBr + AgNO3---->____ + ____
Answers
KBr + AgNO3 --------> KNO3 + AgBr
It is Double displacement reactions ( means ions exchange take place)When potassium bromide react with silver nitrate then,products came out are potassium nitrate and silver bromide.The function:
V(x) = x(10-2x)(16-2x), 0
a) Find the extreme values of V.
b) Interpret any valuse found in part (a) in terms of volumeof the box.
Answers
The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.
To find the extreme values of V, we need to take the derivative of V and set it equal to zero. So, let's begin:
\(V(x) = x(10-2x)(16-2x)\)
Taking the derivative with respect to x:
\(V'(x) = 10x - 4x^2 - 32x + 12x^2 + 320 - 48x\)
Setting V'(x) = 0 and solving for x:
\(10x - 4x^2 - 32x + 12x^2 + 320 - 48x = 0\\8x^2 - 30x + 320 = 0\)
Solving for x using the quadratic formula:
\(x = (30 ± \sqrt{(30^2 - 4(8)(320))) / (2(8))\\x = (30 ± \sqrt{(1680)) / 16\\x = 0.93 or x =5.07\)
So, the extreme values of V occur at x ≈ 0.93 and x ≈ 5.07. To determine whether these are maximum or minimum values, we need to examine the second derivative of V. If the second derivative is positive, then the function has a minimum at that point. If the second derivative is negative, then the function has a maximum at that point. If the second derivative is zero, then we need to use a different method to determine whether it's a maximum or minimum.
Taking the second derivative of V:
V''(x) = 10 - 8x - 24x + 24x + 96
V''(x) = -8x + 106
Plugging in x = 0.93 and x = 5.07:
V''(0.93) ≈ 98.36 > 0, so V has a minimum at x ≈ 0.93.
V''(5.07) ≈ -56.56 < 0, so V has a maximum at x ≈ 5.07.
Now, to interpret these values in terms of the volume of the box, we need to remember that V(x) represents the volume of a box with length 2x, width 2x, and height x. So, the maximum value of V occurs at x ≈ 5.07, which means that the volume of the box is greatest when the height is about 5.07 units. The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.
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a) The extreme values of V are:
Minimum value: V(0) = 0
Relative maximum value: V(3) = 216
Absolute maximum value: V(4) = 128
b) The absolute maximum value of V at x = 4 represents the case where the box has a square base of side length 4 units, height 2 units, and width 8 units, which has a volume of 128 cubic units.
a) To find the extreme values of V, we first need to find the critical points of the function. This means we need to find where the derivative of the function equals zero or is undefined.
Taking the derivative of V(x), we get:
\(V'(x) = 48x - 36x^2 - 4x^3\)
Setting this equal to zero and solving for x, we get:
\(48x - 36x^2 - 4x^3 = 0\)
4x(4-x)(3-x) = 0
So the critical points are x = 0, x = 4, and x = 3.
We now need to test these critical points to see which ones correspond to maximum or minimum values of V.
We can use the second derivative test to do this. Taking the derivative of V'(x), we get:
\(V''(x) = 48 - 72x - 12x^2\)
Plugging in the critical points, we get:
V''(0) = 48 > 0 (so x = 0 corresponds to a minimum value of V)
V''(4) = -48 < 0 (so x = 4 corresponds to a maximum value of V)
V''(3) = 0 (so we need to do further testing to see what this critical point corresponds to)
To test the critical point x = 3, we can simply plug it into V(x) and compare it to the values at x = 0 and x = 4:
V(0) = 0
V(3) = 216
V(4) = 128
So x = 3 corresponds to a relative maximum value of V.
b) In terms of the volume of the box, the function V(x) represents the volume of a rectangular box with a square base of side length x and height (10-2x) and width (16-2x).
The minimum value of V at x = 0 represents the case where the box has no dimensions (i.e. it's a point), so the volume is zero.
The relative maximum value of V at x = 3 represents the case where the box is a cube with side length 3 units, which has a volume of 216 cubic units.
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The point (3, 4) lies on a circle centered at (0, 0). At what two points does the circle intersect the x-axis?
Answers
The circle intersects the x-axis at the points (-5, 0) and (5, 0).
We have,
Using the Pythagorean theorem to find the radius of the circle.
So,
r = √(0-3)² + (0-4)²
r = √(9+16)
= √25
= 5
The equation of the circle is x² + y² = 5² = 25.
To find the points where the circle intersects the x-axis,
We substitute y = 0 in the equation of the circle and solve for x:
x² + 0² = 25
x² = 25
x = ±5
Therefore,
The circle intersects the x-axis at the points (-5, 0) and (5, 0).
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What is 11x - 3 = 5x + 11
Answers
11x - 5x = 11+3
6x = 14
x = 14/6 =7/3
Which of the following rules describes the function graphed below? On a coordinate plane, points are at (negative 1, 1), (1, 2), (3, 3), (5, 4). a. Output = Input c. Output = (0.5)(Input) + 1.5 b. Output = (2)(Input) – 3 d. Output = (1.5)(Input) + 3 Please select the best answer from the choices provided A B C D
Answers
Answer:
B. Output = (2)(Input) – 3.
Step-by-step explanation:
The correct answer is B. Output = (2)(Input) – 3.
This is because the function is a linear function, and the slope is 2 and the y-intercept is -3.
You can see this by considering the difference in y for each pair of points and the difference in x for each pair of points.
For example, from (negative 1, 1) to (1, 2) the difference in y is 1 and the difference in x is 2.
This means the slope is 1/2 which is the same as 2, and the y-intercept is -3
I’m not sure how to find Area.
Answers
Answer:
B) 99
I see the eraser marks, thanks for actually giving it a try before asking
Step-by-step explanation:
split it into 3 parts
one is 4x12
the nest is 5x(12-5-4)
the last is 3x12
48
5x3=15
36
15+48+36
Solution:
Area = (base)x(height)
1st method:
—pretend you are finding the area of a big parallelogram where height is given 12m. The base is 4m+5m+3m=12m
—Area=(base)x(height)=(12)(12)=144square meters
—Find the area of the small dimensions or rectangles;
area=(base)x(height)=(4)(5)=20square meters
area=(base)x(height)=(5)(5)=25square meters
—Subtract the area of small dimensions from the total dimension which is 144 square meters; 144-20-25= 99 square meters
2nd method:
—Split the two dimensional figures to three rectangles and determine the area of each rectangles;
area=(base)x(height)=(12)(4)=48square meters
area=(base)x(height)=(12)(3)=36square meters
12m-4m-5m=3m
area=(base)x(height)=(3)(5)=15 square meters
—Add up the areas of the three rectangles;
(48+36+15) = 99 square meters
Hong runs 3 miles in 25 minutes. At the same rate, how many miles would he run in 20 minutes?
Answers
For the given values he covered 12/5 miles in 20 minutes.
what is relation between speed and distance?
Speed, time, and distance are all related. The rate at which a distance is travelled over time is the definition of speed. If my friend is driving at 55 mph, for instance, it simply means that she will cover 55 miles in an hour, 110 miles in two hours, 165 miles in three hours, and so on. This is predicated on the idea that the speed remains constant or that the speed being reported is the average of all speeds recorded for an hour, two hours, or three hours.
Given,
Hong runs 3 miles in 25 minutes
he runs at rate =
speed = distance / time
speed = 3/25 miles/minutes
He took 20 minutes to travel distance =
distance = speed * time
distance = 3/25 * 20
= 12/5 miles
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completed the chart for ordered pairs .Using the equation12x-8y=16x tea chart : __,0,2,__y tea chart: 0,__,__,3fil in the blanks
Answers
Given
Equation
\(12x-8y=16\)x tea chart __, 0, 2, __
y tea chart 0,__, __, 3
Procedure
y = 0
12x = 16
x = 16/12
x = 4/3
x = 0
-8y = 16
y = 16/-8
y = -2
x = 2
12(2) - 8y = 16
24 - 8y = 16
-8y = 16-24
-8y = -8
y = 1
y = 3
12x - 8(3) = 16
12x - 24 = 16
12x = 16+24
12x = 40
x = 40/12
x = 20/6
x tea chart 4/3, 0, 2, 20/6
y tea chart 0, -2, 1, 3
Southeastern College began the year with endowment investments of $1,210,000 and $710,000 of restricted cash designated by a donor for capital additions. 1. During the year an additional $502,000 donation was received for capital additions. These funds together with those contributed in the prior year were used to purchase 150 acres of land adjacent to the university. 2. An alum contributed $210,000 to the permanent endowment and pledged to provide an additional $420,000 early next year. The cash was immediately invested. 3. By terms of the endowment agreement, interest and dividends received on the investments are restricted for scholarships. Gains or losses from changes in the fair value of the investments, however, are not distributed but remain in the endowment. During the year $50,000 of interest and dividend were received on endowment investments. 4 . At year-end, the fair value of the investments had increased by $7,100. Required: Prepare journal entries to record the above transactions assuming: a. Southeastern College is a public university. b. Southeastern College is a private university. Required: Prepare journal entries to record the above transactions assuming: a. Southeastern College is a public university. b. Southeastern College is a private university. Complete this question by entering your answers in the tabs below. Prepare journal entries to record the above transactions assuming Southeastern College is a public university. a transaction/event, select "No Journal Entry Required" in the first account field.) Journal entry worksheet 456 Record the donation received for capital addition. Note: Enter debits before credits.
Answers
Journal entries for Southeastern College as a public university:
1. Donation received for capital addition:
Restricted Cash - Capital Additions Dr. $502,000
Donation Revenue Cr. $502,000
2. Contribution to the permanent endowment:
Cash Dr. $210,000
Permanently Restricted Net Assets Cr. $210,000
3. Interest and dividends received on endowment investments:
Restricted Cash - Scholarships Dr. $50,000
Investment Income Cr. $50,000
4. Increase in fair value of investments:
Investment Gain Dr. $7,100
Unrestricted Net Assets Cr. $7,100
To record the transactions for Southeastern College as a public university, the following journal entries are made:
1. Recording the donation received for capital addition:
Restricted Cash - Capital Additions Dr. $502,000
Donation Revenue Cr. $502,000
The restricted cash is increased by $502,000, representing the additional donation received for capital additions. The corresponding revenue account is credited.
2. Recording the contribution to the permanent endowment:
Cash Dr. $210,000
Permanently Restricted Net Assets Cr. $210,000
The cash received from the alum is debited, and the permanently restricted net assets (part of the endowment) are credited.
3. Recording interest and dividends received on endowment investments:
Restricted Cash - Scholarships Dr. $50,000
Investment Income Cr. $50,000
The interest and dividends received on the endowment investments are debited to restricted cash for scholarships, and the investment income account is credited.
4. Recording the increase in fair value of investments:
Investment Gain Dr. $7,100
Unrestricted Net Assets Cr. $7,100
The increase in the fair value of the investments is recorded as an investment gain. The unrestricted net assets account is credited, as gains or losses from changes in fair value are not distributed and remain in the endowment.
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a radiator contains 6 liters of a 48% antifreeze mixture. how much pure antifreeze should be added to make a mixture that is 74% antifreeze
Answers
The amount of pure antifreeze to be added to make a mixture that is 74% antifreeze is; 3 liters
How to solve linear equation word problems?A linear equation of one variable is defined as an equation in terms of only one variable of degree 1. A multi-step linear equation is defined as a linear equation that can be solved using multiple algebraic operations on both sides of the equation.
This seems like starting with 6 and ending up with 6.
Let x represent the amount to be drained and replaced
The % antifreeze equation:
0.48(6) - 0.48(x) + 1(x) = 0.74(6)
2.88 - 0.48x + x = 4.44
0.52x = 4.44 - 2.88
0.52x = 1.56
divide both sides by 0.52 gives us;
x = 1.56/0.52
x = 3 liters of pure antifreeze to be added to make a mixture that is 74% antifreeze
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Please answer in detail Determine whether the following statement is True, False, or Uncertain, and explain your answer. Statement: Flexible exchange rates ...
Answers
The statement "Flexible exchange rates ..." is incomplete, and without further clarification, it is uncertain to determine whether it is true or false. A complete statement is required to provide a clear context for discussing the nature and implications of flexible exchange rates.
Flexible exchange rates refer to a system in which currency exchange rates are determined by market forces, such as supply and demand. Under this system, exchange rates fluctuate freely based on various economic factors, including inflation rates, interest rates, trade balances, and investor sentiment.
Flexible exchange rates offer advantages such as the ability to adjust to changing economic conditions and promote trade balance adjustments. They can also help absorb external shocks and enhance monetary policy autonomy. However, they may also introduce volatility and uncertainty in international trade and investment. To assess the accuracy of the statement, additional information or context is needed.
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How many sides does a rectangular pyramid
Answers
Answer:
Step-by-step explanation:
A rectangular pyramid has five sides. It consists of a rectangular base and four triangular faces that meet at a common vertex or apex.
≧◉◡◉≦
I need help with this
Answers
The length of side x is equal to 14.57 units.
How to determine the length of x?In order to determine the length of x, we would apply the basic sine trigonometric ratio because the given side lengths represent the opposite side and hypotenuse of a right-angled triangle;
sin(θ) = Opp/Hyp
Where:
Opp represent the opposite side of a right-angled triangle.Hyp represent the hypotenuse of a right-angled triangle.θ represent the angle.For the sine trigonometric ratio, we have the following:
sin(θ) = Opp/Hyp
sin(59) = x/17
0.8572 = x/17
x = 17 × 0.8572
x = 14.57 units.
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if u had 76 lessons to do before summer and its march 5th how many would u need to do per week before June?
Answers
Answer:
Step-by-step explanation:
From March 5th to May 31st, that is 88 days.
So, you need to do 76 lessons in 88 days = 12.6 weeks.
You need to do 76 : 12.6 = 6.03174603.... (round to 6) lessons per week.
Help please I don’t get it
Answers
a) The expected number of people to die before their 71st birthday is given as follows: 128.
b) The probability that a 67 year old woman will live to her 68th birthday is given as follows: 0.8876 = 88.76%.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
0.025679 of the 70 year old men die, hence the expected number out of 5000 is given as follows:
0.025679 x 5000 = 128.
The probability for item b is given as follows:
0.016798/0.018925 = 0.8876 = 88.76%.
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Dans un repère du plan, on donne les points (−2 ; 3), (6 ; 2) (−1 ; 0).
1. Faire une figure
2. Conjecturer où l’on doit placer le point D pour que le quadrilatère ABDC soit un
parallélogramme.
Answers
Answer:
faut-il faire les ponits avec le pallergrom de (−2 ; 3), (6 ; 2) (−1 ; 0) ?
Step-by-step explanation:
veronica gets stuck at an intersection with road construction on her way to work and is running late. she has 25 minutes to travel 40 miles. how fast would she need to drive if she wanted to get to work on time?
Answers
Answer:
V=96 mi/h
Step-by-step explanation:
We know that the velocity is equal to displacement over the time.
So V=S/T
We change the minutes to hours.
V= 40/(25/60)
V=96 mi/h
Harper, inc., acquires 40 percent of the outstanding voting stock of kinman company on january 1, 2020, for $334,900 in cash. the book value of kinman's net assets on that date was $625,000, although one of the company's buildings, with a $70,800 carrying amount, was actually worth $135,550. this building had a 10-year remaining life. kinman owned a royalty agreement with a 20-year remaining life that was undervalued by $147,500. kinman sold inventory with an original cost of $77,700 to harper during 2020 at a price of $111,000. harper still held $18,750 (transfer price) of this amount in inventory as of december 31, 2020. these goods are to be sold to outside parties during 2021. kinman reported a $51,800 net loss and a $26,600 other comprehensive loss for 2020. the company still manages to declare and pay a $15,000 cash dividend during the year. during 2021, kinman reported a $57,200 net income and declared and paid a cash dividend of $17,000. it made additional inventory sales of $120,000 to harper during the period. the original cost of the merchandise was $75,000. all but 30 percent of this inventory had been resold to outside parties by the end of the 2021 fiscal year. prepare all journal entries for harper for 2020 and 2021 in connection with this investment. assume that the equity method is applied. (if no entry is required for a transaction/event, select "no journal entry required" in the first account field. do not round intermediate calculations.)
Answers
In 2020, Harper, Inc. acquired 40% of the outstanding voting stock of Kinman Company for $334,900 in cash.
The book value of Kinman's net assets was $625,000, but there were certain adjustments needed. One of Kinman's buildings was undervalued by $64,750 ($135,550 - $70,800), and there was an undervaluation of $147,500 for the royalty agreement. Harper also purchased inventory from Kinman for $111,000, out of which $18,750 was still held in inventory by the end of the year. Kinman reported a net loss of $51,800 and other comprehensive loss of $26,600 in 2020, but it still paid a $15,000 cash dividend.
To record these transactions, Harper would make the following journal entries in 2020:
1. To record the investment in Kinman's stock:
Investment in Kinman Company Stock 334,900
Cash 334,900
2. To adjust the building's carrying amount and recognize the related depreciation:
Investment in Kinman Company Stock 64,750
Depreciation Expense 6,475
Accumulated Depreciation 6,475
3. To adjust the undervalued royalty agreement:
Investment in Kinman Company Stock 147,500
Royalty Agreement 147,500
4. To record the purchase of inventory from Kinman:
Inventory 111,000
Investment in Kinman Company Stock 111,000
5. To recognize the equity in Kinman's net loss and comprehensive loss:
Equity in Net Loss 20,720
Equity in Other Comprehensive Loss 10,640
Investment in Kinman Company Stock 31,360
6. To record the receipt of the cash dividend:
Cash 15,000
Dividend Income 15,000
In 2021, Kinman reported a net income of $57,200 and paid a cash dividend of $17,000. Harper purchased additional inventory worth $120,000 from Kinman, out of which 70% ($84,000) was sold to outside parties by year-end. Harper would make the following journal entries in 2021:
1. To recognize the equity in Kinman's net income:
Equity in Net Income 22,880
Investment in Kinman Company Stock 22,880
2. To record the receipt of the cash dividend:
Cash 17,000
Dividend Income 17,000
3. To record the purchase of additional inventory from Kinman:
Inventory 120,000
Investment in Kinman Company Stock 120,000
4. To eliminate the unrealized profit in inventory:
Investment in Kinman Company Stock 8,400
Equity in Net Income 8,400
Overall, these journal entries reflect the investment in Kinman Company, adjustments for undervalued assets, recognition of income or loss, and dividend payments. The equity method is used to account for the investment, where Harper recognizes its share of Kinman's net income or loss and adjusts the investment account accordingly.
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Tracy picks a random shape. 7 pentagons 3 triangles 8 trapezoids. what is the probability that she picks a 4 sided shape?
Answers
Answer:
5/6
Step-by-step explanation:
Step 1: Determine the total number of four-sided shapes:
We know that pentagons are five-sided, triangles are three sides and trapezoids are four-sided. However, pentagons have at least five sides and therefore we include them since they have at least four sides. Thus, there are 15 four-sided shapes present among all the shapes Tracy has as 7 + 8 = 15.
Step 2: Determine the total number of shapes present:
Now we must add up the total number of shapes Tracy has:
7 + 3 + 8
10 + 8
18
Thus, Tracy has a total of 18 shapes.
Step 3: Divide the total number of four-sided shapes by the total number of shapes to determine probability of picking a four-sided shapes:
15/18
5/6
Thus, the probability that Tracy picks a shape with at least four sides is 5/6.
If this answer is wrong, it is possible that your teacher wants to know the probability of picking a shape with only four sides. Then you'd write 4/9 as you'd only include the trapezoids since only they have just four sides while the pentagons also have four sides but also an additional side:
Which of the following is the correct sequence of project phases? O A. Concept - Planning - Definition O B. Definition - Planning - Performance O C. Postcompletion - Performance - Planning OD. Performance - Concept - Planning
Answers
The correct sequence of project phases is Definition - Planning - Performance. The correct answer is B.
This is the typical order of project phases in a traditional project management approach. It starts with the definition phase, where the project's goals, the scope, and the requirements are established.
Then comes the planning phase, where the project plan is developed, including the allocation of resources, scheduling, and budgeting.
Finally, the performance phase begins, during which the project activities are executed, monitored, and controlled to ensure the successful project completion.
Therefore the sequence of project phase is Definition - Planning - Performance The correct answer is B.
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A right triangle has legs measuring 16 in. And 28 in. What is the length of the hypotenuse? Round your answer to the nearest tenth. 23. 0 in. 32. 2 in. 44. 0 in. 1040. 0 in.
Answers
In a right-angled triangle, the Pythagoras theorem is used to find the hypotenuse. Then the hypotenuse is 32.2 inches.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
Given
A right triangle has legs measuring 16 inches And 28 inches.
We know the Pythagoras theorem
\(\rm Hypotenuse ^2 = Base ^2 + Perpendicular^2\)
Then the hypotenuse will be.
\(\rm Hypotenuse ^2 = Base ^2 + Perpendicular^2\\\\\rm Hypotenuse ^2 = 16^2 + 28^2\\\\ \rm Hypotenuse ^2 = 256 + 784\\\\\rm Hypotenuse ^2 = 1040\\\\\rm Hypotenuse \ = 32.2\)
Thus, the hypotenuse is 32.2 inches.
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The diagram shows two right-angled triangles that share a common side. 6 10. Show that x is between 11 and 12.
Answers
We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:
Triangle 1:
Side adjacent to the right angle: 6 (let's call it 'a')
Side opposite to the right angle: x (let's call it 'b')
Triangle 2:
Side adjacent to the right angle: x (let's call it 'c')
Side opposite to the right angle: 10 (let's call it 'd')
Using the Pythagorean theorem, we can write the following equations for each triangle:
Triangle 1:\(a^2 + b^2 = 6^2\)
Triangle 2: \(c^2 + d^2 = 10^2\)
Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:
\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)
Substituting b = c, we get:
\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)
Now, let's add these two equations together:
\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)
Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12
For more such questions on right angled triangle.
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Factor 12w + 21 ????????
Answers
Answer:
12w + 21 =3(4w+7)
Step-by-step explanation:
12 and 21 are multiples of 3 so factor out 3
12w + 21 =3(4w+7)
Answer:
\( = 3(4w + 7)\)
Step-by-step explanation:
\(12w + 21 \\ = 3(4w + 7)\)
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The amount Troy charges to mow lawn is proportional to the time it takes him to mow the lawn. Troy charges $30 to mow a lawn that took him 1.5 hours to mow.
Which equation models the amount in dollars, d, Troy charges when it takes him h hours to mow a lawn?
Answers
Answer:
dez nuts
Step-by-step explanation:
ha gotem