Answer:
By using The Pythagorean Theorem:
[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \[/tex]
/Hypotenuse/ = [tex]\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}[/tex]
Step-by-step explanation:
The Pythagorean theorem states that: Given a Right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides ( Here, being the length of the altitude and length of leg). That is,
[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \[/tex] and hence,
/Hypotenuse/ = [tex]\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}[/tex]
For example, If the length of the altitude is 4m and the length of leg is 3m. Using The Pythagorean theorem, the length of the hypotenuse will be
[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \\\/Hypotenuse/ = \sqrt{/Length of altitude/^{2} + /Length of leg/^{2}} \\/Hypotenuse/ = \sqrt{4^{2} + 3^{2} }[/tex]
[tex]/Hypotenuse/ = \sqrt{16+9} \\/Hypotenuse/ = \sqrt{25} \\/Hypotenuse/ = 5m[/tex]
The length of the hypotenuse for the given example will be 5m.
This is how to find the length of an hypotenuse.
Consider the circle of radius 10 centered at the origin. Find an equation of the line tangent to the circle at the point (6, 8)
Answer:
y = -3/4 x + 25/2
Step-by-step explanation:
x² + y² = 100
Take derivative with respect to x.
2x + 2y dy/dx = 0
2y dy/dx = -2x
dy/dx = -x/y
Evaluate at (6, 8).
dy/dx = -6/8
dy/dx = -3/4
Use point-slope form to write equation:
y − 8 = -3/4 (x − 6)
Simplify.
y − 8 = -3/4 x + 9/2
y = -3/4 x + 25/2
Getaway Travel Agency surveyed a random sample of 45 4545 of their clients about their vacation plans. Of the clients surveyed, 21 2121 expected that they would go on 3 33 vacations in the next year. There are 516 516516 Getaway Travel Agency clients. Based on the data, what is the most reasonable estimate for the number of Getaway Travel Agency clients who expect to go on 3 33 vacations in the next year?
Answer:
241
Step-by-step explanation:
Given the following :
Number of random samples surveyed = 45
Of the random samples surveyed, 21 expected to go on 3 vacations in the next year:
Total number of clients = 516
Percentage of random sample surveyed who intend to go 3 vacations in the next year :
(21 / 45) * 100
0.4666667 * 100 = 46.7%
That is 46.7% of surveyed sample intend to go on 3 vacations in the next year.
Therefore using these to make inference about the number of total client who will go on 3 vacations in the next year:
46.7% of total clients
(46.7 / 100) * 516
= 240.8
= 241 ( to the nearest whole number)
Sasha is twice as old as Kapila. If Kapila is x years old, find their total age.
Answer:
3x
Step-by-step explanation:
If Kapila's age =x.
Then Sasha's age would be =2x.
Their total age would be 3x.
Because 2x+x adds up to be 3x.
What is the slope of the line below (1, -2) (4, -2)
Answer:
0
Step-by-step explanation:
We can use the slope formula to find the slope
m = (y2-y1)/(x2-x1)
= ( -2 - -2)/( 4 -1)
= (-2+2)/( 4-1)
= 0/3
= 0
Answer:
Slope =0Step-by-step explanation:
[tex](1, -2) , (4, -2)\\m = ?\\x_1 =1\\y_1 =-2\\x_2 =4\\y_2 =-2\\\\m = \frac{y_2-y_1}{x_2-x_1} \\\\m = \frac{-2-(-2)}{4-1} \\m = \frac{-2+2}{3}\\ m = \frac{0}{3}\\ m = 0[/tex]
Simplify
Help me please
Answer:
[tex]\frac{-27b^{6}}{c^{18}}[/tex]
Step-by-step explanation:
first distribute the ^3, -3^3=-27, for the variables, (x^y)^3=x^(3y) so (b^2)^3=b^6 and (c^-6)^3=c^-18. now we have [tex]-27b^{6}c^{-18}[/tex]. Next we have to get rid of the negative in c^-18. x^-y=1/x^y so c^-18=[tex]\frac{1}{c^{18}}[/tex], plug it in and you get [tex]\frac{-27b^{6}}{c^{18}}[/tex]
Solve for q. –17 − 12q = –17 + 10q
Step-by-step explanation:
–17–12q=–17+10q
–17+17=10q+12q
0/22=22q/22
q=0
HELLOOOPPPPPPPPOPPPP
Answer:
Below
Step-by-step explanation:
Sale price of each tire : $92.99 - $20 = 72.99. The cost of x tires is 72.99x
If the sales tax is 4% there is an additional (72.99x)(1.04)
Here is the equation
= (72.99)(1.04) t
If Patrick bought 8 tires.....
= (72.99)(1.04)(8)
= $607.2768
Hope this helps!
I need help ASAP!!
Can someone explain this? And answer it? I am so confused!!
Answer:
Step-by-step explanation: hope this helps
In how many ways can we put five identical fruits into three bowls? Note that the bowls may be empty.
So u have 5 fruits and 3 bowls
Divide 5 into 3 that would equal how many grams you would put in one bowl then measure that and then complete it by adding that amount into each bowl
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
Answer:
Astrid needs 280 tons of wood to build ships that can accommodate 2100 sailors
Step-by-step explanation:
Here, in this question, we want to know the amount of wood needed by Astrid to accommodate 2100 sailors.
From the question, we can see that 40 tons are needed to build a ship that can accommodate 300 sailors.
Now, we want to make a calculation for the amount of wood needed for 2100 sailors.
Let’s have it this way;
40 tons = 300 sailors
x tons = 2100 sailors
So mathematically,
x * 300 = 2100 * 40
x = (2100 * 40)/300
x = 280 tons of wood
We can see that 280 tons of wood are needed to build ships that can accommodate 2100 sailors
Answer:
280 tons of wood
Step-by-step explanation:
Khan
A bag has six balls labeled a,b,c,d.e and f . One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of choosing the letter a or c . If there is more than one element in the set, separate them with commas.
We simply list all of the letters mentioned as they are the possible outcomes. We can only pick one item from the sample space. The event space is the set of outcomes where we want to happen (picking either an 'a' or 'c').
Hey There!!
To this Question, This answer going to had A Explanation to this: Sample space--
A sample space is a set which contains the set of all the possible outcomes or results that could occur while performing an experiment.
i.e. the sample space while flipping a coin is: {H,T}
The sample space while tossing a six-sided die is: {1,2,3,4,5,6}
Here it is given that:
A bag has six balls labeled: A,B,C,D,E,F
One ball will be randomly picked, and its letter will be recorded as the outcome.
This means that the sample space is given by:
Sample space={ A,B,C,D,E,F}
Now, when the event is choosing a letter from D to F.
Then the sample space is:
Sample space= {D,E,F}
Hope It Helped!~ ♡
ItsNobody~ ☆
Population data from three towns is displayed in the tables below. Which
town has growth that follows an exponential model?
Answer:
Rushmont
Step-by-step explanation:
Trenton can be ruled out due to its constant increase rate of 1.5. Rushmont can be ruled out because it goes from an increase rate of ~1.8 to an increase rate of 1.4 to an increase rate of 1.3 (exponential decay, not growth, so possibly...). Springville has a rate of ~1.9, then 1.475, then 1.3, also exponential decay. However, y\ =\ x\frac{38}{10}-185 goes through all of springville's points (or close to it), so Rushmont must be the answer.
The town that has growth that follows an exponential model is Town B, Rushmont where the population increases or decreases at a consistent rate over time.
In this case, analyze the population data from the three towns to determine which one exhibits exponential growth.
Let's go through each option briefly:
A. Springville:
The population of Springville in 1960 is 42, and in 1990 it is 156.The difference in population over 30 years is 156 - 42 = 114.The average increase per year is 114 / 30 = 3.8.The growth in Springville does not follow a consistent exponential pattern, as the average increase is not constant over time.B. Rushmont:
The population of Rushmont in 1960 is 38, and in 1990 it is 131.The difference in population over 30 years is 131 - 38 = 93.The average increase per year is 93 / 30 = 3.1.The growth in Rushmont exhibits a consistent increase of approximately 3.1 per year, indicating a possible exponential model.C. Trenton:
The population of Trenton in 1960 is 32, and in 1990 it is 108.The difference in population over 30 years is 108 - 32 = 76.The average increase per year is 76 / 30 = 2.5.The growth in Trenton does not follow a consistent exponential pattern, as the average increase is not constant over time.Based on the analysis above, the town that shows growth following an exponential model is Rushmont (B). It exhibits a consistent increase in population over time, suggesting exponential growth.
Learn more about population models here:
https://brainly.com/question/32701660
#SPJ4
What is the length of BC?
Answer:
The answer is option B2.1Step-by-step explanation:
To find the length of a we use the cosine rule
That's
a² = b² + c² - 2bc cos A
We have
a² = AB ² + AC ² - 2(AB)(AC) cos A
From the question
AB = 6
AC = 5
A = 20°
Substituting the values into the above formula we have
a² = 6² + 5² - 2(6)(5) cos 20
a² = 36 + 25 - 60cos 20
a² = 61 - 56.38
a² = 4.62
Find square root of both sides
a = √4.62
We have the final answer as
a = 2.1Hope this helps you
Victoria is scuba diving off the coast of Hawaii. When she is ready to come back to the surface, she rises 40 yards at a safe speed. She climbs 1 foot every 2 seconds. How many minutes will it take her to reach the surface?
Answer:
it will take her 79.76 minutes to rise to the surface
Step-by-step explanation:
Total distance to the surface = 40 yards
speed of rising = 1 foot per seconds
1 foot = 1 second
since the total distance is in yards, let's convert from foot to yards:
1 yard = 3 feet
1 foot = 1/3 yards = 0.333 yards
0.33 yards = 1 second
Next, let's convert from seconds to minutes
60 seconds = 1 minute
∴ 1 second = 1/60 minute
1 second = 0.0167 minute
Therefore the speed at which she rose:
speed
0.333 yards = 0.0167 minutes
Now for a distance of 40 yards:
[tex]1\ yard = \frac{0.0333}{0.0167} minutes\\\therefore\ 40\ yards = \frac{0.0333}{0.0167} \ \times\ \frac{40}{1} \\= \frac{1.332}{0.0167} \\= 79.76\ minutes[/tex]
Answer:
4 minutes
Step-by-step explanation:
1/5 of a certain number is added to 5½ the same as when ⅙ of the number that is subtracted from 30⅖find the number
Step-by-step explanation:
1%2F5n + 51%2F5 = 302%2F5 - 1%2F6n
make the 3rd term an improper fraction
1%2F5n + 51%2F5 = 152%2F5 - 1%2F6n
multiply equation by 30, cancel the denominators, resulting in:
6n + 6(51) = 6(152) - 5n
6n + 306 = 912 - 5n
6n + 5n = 912 - 306
11n = 606 is the number
n = 606/11
n = 55 1/11
Answer:
68
Step-by-step explanation:
let unknown number be x
⅕x + 5½= 30⅖ - ⅙x
⅕x + 11/2= 152/5 - ⅙x
collect like terms
⅕x+⅙x= 152/5 - 11/2
[tex] \frac{11}{30}x = \frac{249}{10} [/tex]
cross multiply
30 * 249=(11 * 10)x
7470=110x
x=7470/110
x= 68
Given the trinomial, what is the value of the coefficient B in the factored form? 2x2 − 12xy − 32y2 = 2(x − 8y)(x + By) −4 −2 2 4
Answer:
B is related to the last term of trinomial
Last term on the left hand side of the equation = Last term on the right hand side of the equation.
The last term on the right hand side is gotten by multiplying all the terms on the right of the two expression.
-32y²= 2*-8y*By
-32y² = -16By² Compare both
32 = 16B
16B = 32
B = 32/16
B = 2.
Answer:
B = 2
Step-by-step explanation:
2x^2 − 12xy − 32y^2
Factor out a 2
2 ( x^2 -6xy -16y^2)
Factor inside the parentheses
What two numbers multiply to -16 and add to -6
-8 * 2 = -16
-8+2 = -6
2( x-8y) ( x+2y)
B = 2
I really need this answered. I need to find the area
Answer:
I think 5
Step-by-step explanation:
5u^2
just count the no. of squares
if they allocate sides or an area for the small square then:
sides
(side^2 • 5)
eg. the side is equal to 2cm, then
(2^2 • 5) = 4(5)
= 20 cm^2
allocated area for small square
square area • 5
eg. one square has an area of 4 cm^2
4 • 5 = 20 cm^2
In a bag there are red, green and purple counters. 3⁄8 of the counters are red, 1⁄6 of the counters are green. What fraction of the counters are purple?
find the product using formula (a+b) (a-b) = a square + b square a.61×59. Note: Solve by using formula.
Answer:
[tex]\huge\boxed{\sf 3599}[/tex]
Step-by-step explanation:
= 61 × 59
You can write 61 = 60 + 1 and 59 = 60 - 1
Hence,
= ( 60 + 1 ) ( 60 - 1 )
According to the formula:
[tex](a+b)(a-b) = a^2-b^2[/tex]
= (60)² - (1)²
= 3600 - 1
= 3599
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Peace!three decreased by the product of a number and two
Find all values of $x$ such that \[\frac{2x}{x + 2} = -\frac{6}{x + 4}.\]If you find more than one value, then list your solutions, separated by commas.
Greetings from Brasil...
2X/(X + 2) = 6/(X + 4)
2X(X + 4) = 6(X + 2)
2X² + 2X - 12 = 0 ÷2
2X²/2 + 2X/2 - 12/2 = 0/2
X² + X - 6 = 0Δ = 25
X' = 2X'' = - 3S = {-3, 2}
By using factorization, [tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex] , values of x are -2, 3.
What is factorization?Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number. These numbers are broken down into factors or divisors.
Given
[tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex]
⇒ 2x(x + 4) = 6(x + 2)
⇒ [tex]2x^{2} +8x = 6x + 12[/tex]
⇒ [tex]2x^{2} +8x-6x-12=0[/tex]
⇒ [tex]2x^{2} +2x -12=0[/tex]
Divide above equation by 2, we get
⇒ [tex]x^{2} +x -6=0[/tex]
⇒ [tex]x^{2} +2x-3x-6=0[/tex]
⇒ [tex]x(x+2)-3(x+2)=0[/tex]
⇒ [tex](x+2)(x-3)=0[/tex]
⇒ x = -2, 3
By using factorization, [tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex] , values of x are -2, 3.
Find out more information about factorization here
https://brainly.com/question/1863222
#SPJ2
Please answer this question now
Answer:
112°
Step-by-step explanation:
By inscribed angle theorem:
[tex] m\widehat {BCD} = 2\times m\angle BAD\\
\therefore m\widehat {BCD} = 2\times 129\degree \\
\therefore m\widehat {BCD} = 258\degree\\\\
\because m\widehat{CD} = m\widehat {BCD}-m\widehat{BC} \\
\therefore m\widehat{CD} = 258\degree - 146\degree \\
\huge \red {\boxed {\therefore m\widehat{CD} = 112\degree}} [/tex]
how many secods are in 24 hours
Express the following as decimals step by step. 3×10+4×1+7×1/10
Answer:
34.7
Step-by-step explanation:
First Step: Multiply.
3 × 10 = 30
4 × 1 = 4
7 × 1/10 = 7/10
Second step: Add.
30 + 4 + 7/10= 347/10
Final step: Make it a decimal.
347 ÷ 10 = 34.7
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]3\times 10+4\times 1+7\times 1/10[/tex]
[tex]= \frac{347}{10}[/tex] (Decimal: 34.7)
Step by Step Explanation.
[tex](3) (10) + (4) (1) + \frac{(7)(1)}{10} \\= 30 + (4) (1) + \frac{(7)(1)}{10} \\= 34 + \frac{(7)(1)}{10} \\= 34 + \frac{7}{10} \\= \frac{347}{10}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
If this helped you, could you maybe give brainliest..?
❀*May*❀
please please please help asap
Answer:
1,3,5
Step-by-step explanation:
81 is a perfect square so it can be written as an integer
11.8 is rational because it can be written as a fraction (107/9)
sqrt(6) isn't a perfect square so it is irrational
3/7 is a fraction so it is rational
8.57 is a terminating decimal so it is rational
Please help explanation if possible
Answer:
y = 4x + 12
Step-by-step explanation:
y = mx + b
4 = 4(-2) + b
4 = -8 + b
12 = b
m = 4 and b = 12
Therefore, the equation of your line is y = 4x + 12
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST!!!
Can someone please help me
Answer:
a = 84°
Step-by-step explanation:
∠ QPR and ∠ TPR are adjacent and supplementary, thus
∠TPR = 180° - 123° = 57°
Given there are parallel lines , then
∠ PTR = 27° ( alternate angle )
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ TRS is an external angle , thus
∠ TRS = a = 57° + 27° = 84°
Answer:
84 degrees.
Step-by-step explanation:
m < R + m < T = 123 (External angle of a triangle theorem)
m < T = 27 degrees (alternate angle to 27 degrees).
So m < R = 123 - 27 = 96 degrees.
Finally m < a = 180 - 96 = 84 degrees ( as it is adjacent to < R)
PLZ HELP NOW!
Geoffrey is trying to earn $50 to buy a video game. He has saved $14.25. He earns $3.75 per hour cleaning windows with his uncle and he earns $6.50 per hour working at the grocery store. Can Fred buy the video game if he works with his uncle for 3 hours and at the grocery store for 4 hours? Use the inequality 3.75y + 6.50z + 14.25 ≥ 50.
Yes, because the total will be $51.50.
Yes, because the total will be $60.25.
No, because the total will be $24.50.
No, because the total will be $37.25.
Answer:
yes the total will be 51.50
Step-by-step explanation:
3.75(3) + 6.50(4) + 14.25 [tex]\geq[/tex] 50.
11.25 + 26 + 14.25 = 51.50
Answer:
Yes, or A
Step-by-step explanation:
You can go onto a graphing calculator and input that inequality to find the solution, but you can multiply the 3.75 by 3 because he works with his uncle for 3 hours, and multiply the 6.5 by 4 to get 11.25 and 26. You add these together to get 37.25 and then add the 14.25 from his savings to get 51.50.
51.50 is how much he will have, and this is greater than 50.
2. A curve has equation y = x2 – 2x - 3. A point moves along the curve in such a way that at P
the y coordinate is increasing at 4 units per second and the x coordinate is increasing at 6
units per second. Find the x coordinate of P.
[3]
Answer:
The x coordinate of P is [tex]\frac{4}{3}[/tex].
Step-by-step explanation:
Let is find the rate of change of the equation in time, which consists in a composite differentiation. That is:
[tex]\frac{dy}{dt} = 2\cdot x \cdot \frac{dx}{dt} -2\cdot \frac{dx}{dt}[/tex]
According to the statement of the problem, these variables are known:
[tex]\frac{dx}{dt} = 6[/tex] and [tex]\frac{dy}{dt} = 4[/tex]
Hence, the x coordinate of P is found by direct substitution:
[tex]4 = 2\cdot x \cdot (6)-2\cdot (6)[/tex]
[tex]4 = 12\cdot x -12[/tex]
[tex]x = \frac{4}{3}[/tex]
The x coordinate of P is [tex]\frac{4}{3}[/tex].