Answer:
85.71
Step-by-step explanation:
slant ht, half of base and perpendicular ht form a right triangle
here slant ht is hypotenuse.
so (89.7)^2 = 25.4^2 + h^2
85.71
how to evaluate 3n, if n = 17
Answer:
51
Step-by-step explanation:
3n means 3 × n
substitute n = 17 into the expression
3n = 3 × 17 = 51
Help me what is 6x-2=20
Answer: 3.33
Step-by-step explanation:
6x-2= 20
+2= +2
Add two to both sides
6x=22
÷ 6= ÷6
Divide both sides by 6
x= 3.33 OR x= 22/6 simplified = 11/3
What you do to one side you do to the other to make the equation balanced.
Answer:
Step-by-step explanation:
6x - 2 = 20
Add 2 to both sides
6x - 2 + 2 = 20 + 2
6x = 22
Divide both sides by 6
[tex]\dfrac{6x}{6}=\dfrac{22}{6}\\\\\\x =\dfrac{11}{3}\\\\\\x = 3\dfrac{2}{3}[/tex]
1 pint= 1/8 gallon. How many pints are there in 2/3 gallon.
gallon = pint *0.125
gallon = pint / 8
0.125+0.125+0.125+0.125+0.125+0.125+0.125+0.125+0.125+0.125+0.125+
0.125+0.125+0.125+0.125+0.125 = 2
16 would be the answer I believe, maybe I'm wrong, double check.
Answer:
5 1/3 pints
Step-by-step explanation:
1 pint is 1/8gal and u need to find how many pints in 2/3 gal so it'll be 2/3 ÷ 1/8 which is 5 1/3
WILL GIVE BRAINLIEST Chang deposited $5000 into an account with a 4.8% annual interest rate, compounded monthly. Assuming that no withdrawals are made, how long will it take for the investment to grow to $7850 ?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
Answer:
9.42 years (= 113 months)
Step-by-step explanation:
Use the compound rate interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where:
A = amountP = principal r = interest rate (in decimal format)n = number of times interest is compounded per unit tt = timeGiven:
A = $7850P = $5000r = 4.8% = 0.048n = 12t = years[tex]\implies 7850=5000(1+\frac{0.048}{12})^{12t}[/tex]
[tex]\implies 7850=5000(1.004)^{12t}[/tex]
[tex]\implies \dfrac{7850}{5000}=(1.004)^{12t}[/tex]
[tex]\implies 1.57=(1.004)^{12t}[/tex]
Take natural logs:
[tex]\implies \ln1.57=\ln(1.004)^{12t}[/tex]
[tex]\implies \ln1.57=12t\ln(1.004)[/tex]
[tex]\implies t=\dfrac{\ln 1.57}{12 \ln1.004}[/tex]
[tex]\implies t=9.42\textsf{ years (nearest hundredth)}[/tex]
[tex]\implies t=113 \textsf{ months}[/tex]
a man is 24 years older than son.in two years time, his age will be twice the age of his son. find the persent age of the son.
Answer:
22 years
Step-by-step explanation:
suppose his present age is x years
After 2 years, father's age (x+24+2) years and son will be (x+2). now x = 22 years is the answer if u solve it.
The present age of the son is 22 years .
Ⲋⲟⳑⳙⲧⳕⲟⲛ :Let us assume that the present age of the son is x years . Therefore according to question, we can say that the present age of his father will be x + 24 years. Then after two years, the age of the man will be twice the age of his son , i.e:
[tex] \quad\dashrightarrow\quad \sf {(x + 24) + 2 = 2 ( x + 2 ) }[/tex]
[tex] \quad\dashrightarrow\quad \sf { x + 26 = 2x + 4}[/tex]
[tex] \quad\dashrightarrow\quad \sf {2x -x = 26 - 4 }[/tex]
[tex] \quad\dashrightarrow\quad \underline{\sf {x = 22 }}[/tex]
Hence, the present age of the son is 22 years.
Evaluate the limit
[tex]\rm\displaystyle\lim_{\rm x\to 4}\left(\frac{\sqrt{\rm x}-\sqrt{3\sqrt{\rm x}-2}}{\rm x^2-16}\right)=\ldots[/tex]
We are given with a limit and we need to find it's value so let's start !!!!
[tex]{\quad \qquad \blacktriangleright \blacktriangleright \displaystyle \sf \lim_{x\to 4}\dfrac{\sqrt{x}-\sqrt{3\sqrt{x}-2}}{x^{2}-16}}[/tex]
But , before starting , let's recall an identity which is the main key to answer this question
[tex]{\boxed{\bf{a^{2}-b^{2}=(a+b)(a-b)}}}[/tex]Consider The limit ;
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{\sqrt{x}-\sqrt{3\sqrt{x}-2}}{x^{2}-16}}[/tex]
Now as directly putting the limit will lead to indeterminate form 0/0. So , Rationalizing the numerator i.e multiplying both numerator and denominator by the conjugate of numerator
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{\sqrt{x}-\sqrt{3\sqrt{x}-2}}{x^{2}-16}\times \dfrac{\sqrt{x}+\sqrt{3\sqrt{x}-2}}{\sqrt{x}+\sqrt{3\sqrt{x}-2}}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-\sqrt{3\sqrt{x}-2})(\sqrt{x}+\sqrt{3\sqrt{x}-2})}{(x^{2}-4^{2})(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]
Using the above algebraic identity ;
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x})^{2}-(\sqrt{3\sqrt{x}-2})^{2}}{(x-4)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{x-(3\sqrt{x}-2)}{(x-4)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{x-3\sqrt{x}+2}{\{(\sqrt{x})^{2}-2^{2}\}(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{x-3\sqrt{x}-2}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]
Now , here we need to eliminate (√x-2) from the denominator somehow , or the limit will again be indeterminate ,so if you think carefully as I thought after seeing the question i.e what if we add 4 and subtract 4 in numerator ? So let's try !
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{x-3\sqrt{x}-2+4-4}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(x-4)+2+4-3\sqrt{x}}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]
Now , using the same above identity ;
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-2)(\sqrt{x}+2)+6-3\sqrt{x}}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-2)(\sqrt{x}+2)+3(2-\sqrt{x})}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]
Now , take minus sign common in numerator from 2nd term , so that we can take (√x-2) common from both terms
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-2)(\sqrt{x}+2)-3(\sqrt{x}-2)}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]
Now , take (√x-2) common in numerator ;
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-2)\{(\sqrt{x}+2)-3\}}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]
Cancelling the radical that makes our limit again and again indeterminate ;
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{\cancel{(\sqrt{x}-2)}\{(\sqrt{x}+2)-3\}}{\cancel{(\sqrt{x}-2)}(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}+2-3)}{(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-1)}{(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]
Now , putting the limit ;
[tex]{:\implies \quad \sf \dfrac{\sqrt{4}-1}{(\sqrt{4}+2)(4+4)(\sqrt{4}+\sqrt{3\sqrt{4}-2})}}[/tex]
[tex]{:\implies \quad \sf \dfrac{2-1}{(2+2)(4+4)(2+\sqrt{3\times 2-2})}}[/tex]
[tex]{:\implies \quad \sf \dfrac{1}{(4)(8)(2+\sqrt{6-2})}}[/tex]
[tex]{:\implies \quad \sf \dfrac{1}{(4)(8)(2+\sqrt{4})}}[/tex]
[tex]{:\implies \quad \sf \dfrac{1}{(4)(8)(2+2)}}[/tex]
[tex]{:\implies \quad \sf \dfrac{1}{(4)(8)(4)}}[/tex]
[tex]{:\implies \quad \sf \dfrac{1}{128}}[/tex]
[tex]{:\implies \quad \bf \therefore \underline{\underline{\displaystyle \bf \lim_{x\to 4}\dfrac{\sqrt{x}-\sqrt{3\sqrt{x}-2}}{x^{2}-16}=\dfrac{1}{128}}}}[/tex]
We can transform the limand into a proper rational expression by substitution.
Let y = √x. Then as x approaches 4, y will approach √4 = 2. So
[tex]\displaystyle \lim_{x\to4}\frac{\sqrt x - \sqrt{3 \sqrt x - 2}}{x^2 - 16} = \lim_{y\to2} \frac{y - \sqrt{3y-2}}{y^4 - 16}[/tex]
Now let z = √(3y - 2). Then as y approaches 2, z will approach √(3•2 - 2) = 2 as well. It follows that y = (z² + 2)/3, so that
[tex]\displaystyle \lim_{y\to2} \frac{y - \sqrt{3y-2}}{y^4-16} = \lim_{z\to2} \frac{\frac{z^2+2}3 - z}{\frac{(z^2+2)^4}{81}-16} \\\\ = \lim_{z\to2} \frac{27(z^2+2)-81z}{(z^2+2)^4 - 1296} \\\\ = 27 \lim_{z\to2} \frac{z^2 - 3z + 2}{z^8 + 8z^6 + 24z^4 + 32z^2 - 1280}[/tex]
Plugging z = 2 into the denominator returns a value of 0, which means z - 2 divides z⁸ + 8z⁶ + 24z⁴ + 32z² - 1280 exactly. Polynomial division shows that
[tex]\dfrac{z^8 + 8z^6 + 24z^4 + 32z^2 - 1280}{z-2} \\\\ = z^7+2z^6+12z^5+24z^4+72z^3+144z^2+320z+640[/tex]
and it's easy to see that the numerator is also divisible by z - 2, since
[tex]z^2 - 3z + 2 = (z - 1) (z - 2)[/tex]
So, we can eliminate the factor of z - 2 and we're left with
[tex]\displaystyle 27 \lim_{z\to2} \frac{z^2 - 3z + 2}{z^8 + 8z^6 + 24z^4 + 32z^2 - 1280} = 27 \lim_{z\to2}\frac{z-1}{z^7+\cdots+640}[/tex]
The remaining limand is continuous at z = 2, so we can evaluate the limit by direct substitution:
[tex]\displaystyle 27 \lim_{z\to2}\frac{z-1}{z^7+\cdots+640} = \frac{27}{3456} = \boxed{\frac1{128}}[/tex]
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
C. 22/5
Step-by-step explanation:
4x5=20
20+2=22
Answer:
C. 22/5
When making an improper fraction you must first multiply the denominator with the whole number in this case that would be 4 and 5
4*5=20
Then just add the numerator
20+2=22
And bring it back over the denominator
22/5
There you go your improper fraction.
Step-by-step explanation:
i need help please thanks
Answer:
60 degrees
Step-by-step explanation:
It measures 60 degrees
Tip: the wider the angle, the bigger the degree.
Hope this helps!
How many people are ten percent of the world's population?.
60% of what number is 51?
Answer:
Set up an equation using the key terms:
60%Of a _ numberResults in 51We can consider 60% in our equation to be 60/100 which we later on simplify.
We contemplate that "-Of a blank number(of what number)" means the multiplication of an unknown value, "x".
The resulting of 51 will be what the equation will equal.
Form the equation;
60/100 · x = 51Solve for x:-
60/100x = 51
60/100 can simplify to 0.6 so it will now be,
0.6x = 51
Isolate x by dividing by 0.6 from both sides because the inverse operation of multiplication is division(since 0.6 is being multiplied by x).
÷0.6 ÷0.6
x = 85, therefore 60% of 85 is 51.
Write the sum using summation notation, assuming the suggested pattern continues. -9 - 3 3 9. 81.
The sum of the terms of the given sequence will be 648.
What is the arithmetic sequence?
An arithmetic sequence or arithmetic progression is a sequence in which each term is created or obtained by adding or subtracting a common number to its preceding term or value.
The given sequence is representing an arithmetic sequence.
Because every successive term of the sequence is having a common difference d = -3 - (-9) = -3 + 9 = 6
3 - (-3) = 3 + 3 = 6
Since last term of the sequence is 81.
By the explicit formula of an arithmetic sequence, we can find the number of terms of this sequence.
[tex]\rm T_n= a+(n-1)d\\\\[/tex]
Where a = first term of the sequence, d = common difference.
Substitute all the values in the formula
[tex]\rm T_n= a+(n-1)d\\\\ 81 = -9 + 6(n - 1)\\\\ 81+9 =6(n-1)\\\\90=6(n-1)\\\\ n-1=\dfrac{90}{6}\\\\n-1=15\\\\n = 15+1\\\\n=16[/tex]
Now we know the sum of an arithmetic sequence is represented by
[tex]\rm S_{16}=\dfrac{16}{2}[-9+(16-1)6]\\\\S_{16}=8 [-9+15\times 6]\\\\S_{16}=8 [-9+90}\\\\S_{16} = 8 \times 81\\\\S_{16}=648[/tex]
Hence, the sum of the terms of the given sequence will be 648.
To know more about arithmetic sequence click the link given below.
https://brainly.com/question/4199153
10,560 yards or 3 miles which one is bigger
Answer:
There are 10,560 yards in 3 mile or miles in 3 yard. Both yards and miles are units of length in the US customary and imperial systems of measurement.
how to find slope and writting a equation with tables
Answer:The equation of a line is written as y=mx+b, where the constant m is the slope of the line, and the b is the y-intercept.
Step-by-step explanation:
I do not know this answer
i need the u answer
In a survey of 600 people, 54% said they ate at a resaurant the previous week. How many people said they ate at a restaurant the previous week?
20 points for this
Answer:
324 people
Step-by-step explanation:
We can take 54% of 600 to find the answer to our problem.
54% becomes 0.54
600 * 0.54 = 324 people
DUE IN 10 MINSSSS ILL GIVE BRAINLYEST!!!!
Which description best describes the graph?
1. Linear increasing
2. Linear decreasing
3. Nonlinear increasing
4. Nonlinear decreasing
Answer:
nonlinear increasing
Step-by-step explanation:
Negative 32 to the power of 3 over 5
Answer:
-8
Step-by-step explanation:
-32^3/5
Fifth root of 32 is 2.
Thus, 2^3 is 8, but -8 instead due to making 32 positive
Hope this helps!
4 questions last ones thxxx
Answer:
(For the first two questions I do believe that you will need a protractor to calculate the angles.)
15) [tex]-(\frac{7\pi }{18} )\\[/tex] measures out to -70° in order to display that the angle would be in quadrant IV (the bottom right quadrant.)
The first image attached shows where the angle should be located.
16) [tex]\frac{\pi }{3}[/tex] is equal to 60° (the line you draw will be in quadrant 1 (the top right quadrant))
17) 350° is [tex]\frac{35\pi }{18}[/tex] or 6.11 (the answer depends on the format the professor wants.)
18) 240° is [tex]-(\frac{4\pi }{3})[/tex] radians or -4.19 (I am rounding to the nearest hundredths place the unsimplified answer is −4.18879020...)
I need help with this one
Answer: 3.5 ft cubed.
Step-by-step explanation:
width*length*height Multiply all the numbers to find the volume.
It will be easier to change the fractions to decimals first.
Find the perimeter 15in 8in 9in 14in 12in
Answer:
the perimeter is 58 inches
Step-by-step explanation:
15+8+9+14+12= 58
Prove that cos3A=sin2A
Answer:
Step-by-step explanation:
[tex]Cos3A= Sin2A ........ (i)\\\\Cos3A= Cos (90-2A)\\\\3A= 90-2A\\\\5A= 90\\\\A= 18\\\\[/tex]
Now,
Putting the value of A to find the value,
[tex]From (i)\\Cos(3x18) = Sin (2x18)\\Cos54= Sin36\\0.5877= 0.5877 \\LHS=RHSProved .[/tex]
Answer:
Cos3A= Sin2A ........ (i)
Cos3A= Cos (90-2A)
3A= 90-2A
5A= 90
A= 18
from (i)
Cos(3×18) = Sin (2×18)
Cos54= Sin36
0.5877= 0.5877 proved .
Step-by-step explanation:
what way is y-axis on the graph
Answer:
The y axis is a vertical line
Step-by-step explanation:
Y axis is up
Solve the equation:
10 In(100) – 3 = 117
Answer:
x = e^12/100
Step-by-step explanation:
Solve for x over the real numbers:
10 ln(100 x) - 3 = 117
Add 3 to both sides:
10 ln(100 x) = 120
Divide both sides by 10:
ln(100 x) = 12
Cancel logarithms by taking exp of both sides:
100 x = e^12
Divide both sides by 100:
Answer: x = e^12/100
Which statements are true about rhombuses? Select all that apply.
Answer:
A, C D
Step-by-step explanation:
sorry if wrong
4. A line has a slope of - 4. Which of the follow-
ing could describe two points on the line?
A. (2,5) and (1,9)
B. (9,7) and (4,-6)
C. (1,4) and (2,8)
D. None of the above
Mason claims that he can cut a parallelogram into two right scalene triangle. Which diagram best supports his claim
The solution is Option B.
The two right scalene triangles can be formed from the parallelogram B
What is a Scalene Triangle?A scalene triangle is a type of triangle with three different length sides and three interior angles that add up to 180 degrees. Scalene triangles have no equal of parallel sides , hence there is no line of symmetry. The interior angles of a scalene triangle can be acute , right or obtuse angles.
Given data ,
Let the parallelogram be represented as ABCD
Now , the figure ABCD represents a rectangle
So , the measures of angles ∠ABC = measure of angle ∠DCB = 90°
Let the diagonal of the rectangle be AC
The base of the rectangle = BC
The height of the rectangle = AB
So , the diagonal cuts the rectangle into two triangles each having different lengths and angles
And , the two triangles are ΔABC and ΔADC
Now , the triangles ΔABC and ΔADC are right scalene triangles
Hence , the triangles are scalene triangles
To learn more about scalene triangles click :
https://brainly.com/question/10651823
#SPJ2
I need help with this
Answer:
prop they're constant inchangeb
Step-by-step explanation:
At this weekend’s soccer game, 20 out of the first 50 people who entered the field were not wearing hats. If this sample is representative of the 250 people attending the game, about how many of them will probably NOT be wearing hats
Answer:
150 people
Step-by-step explanation:
20/50 = 40%
So 40% are wearing hats and 60% aren't
0.6=60%
250x0.6= 150
Rowan opens a savings account with $25 and saves $75 per month. Reem opens a savings account with $225 and saves $25 per month.
a) Write an equation for Rowan’s savings account balance. $225 and saves $25 per month
b) Write an equation for Reem’s savings account balance?
c) When will their account balances be the same? How much will they have? Justify your answer either through graphs and/or solving the equations.
Answer:
a.) y= 75x+25
b.) y= 25x+225
c.) Their account balances will be the same in 4 months and they'll have $325.
Step-by-step explanation:
For A and B: The variable is x which is the amount of months then add the initial amounts without a variable and equal it to y which is the amount in all.
For Rowan, they are saving $75 per month. This is where our variable goes and then we add the intial $25 dollars. The equation is y= 75x+25.
For Reem, they are saving $25 per month. This is where our variable goes and then we add the intial $225 dollars. The equation is y= 25x+225
C. You have to set the equations equal to each other and then solve for x.
75x+25 = 25x+225
Subtract 25 from each side
75x=25x+200
Subtract 25x from each side
50x=200
Divide each side by 50
X=4
For the amount they'll have, just plug 4 into one of the equations.
Rowan : y=75(4)+25
y=325
Reem: y=25(4)+225
y=325
Please help! 20 points thanks :)
Answer:
B
Step-by-step explanation:
(4 , 9) and (0, 5)
4 is x1, 9 is y1, 0 is x2, 5 is y2
formula:
slope = y2 - y1/ (underline is fraction line btw ;) )
x2 - x1
5 - 9
0 - 4
So the answer is B