Answer:
12.16 milesStep-by-step explanation:
Speed - s, Distance - d, Time - t
Equation of time is:
t = d/sGiven,
s1 = 32 m/h, s2 = 38 m/h, t1 + t2 = 42 min = 42/60 h = 7/10 hTotal time is the sum of time values to and from the town:
d/32 + d/38 = 7/10d/16 + d/19 = 7/5d(1/16 + 1/19) = 7/5d(16 + 19) = 7(16*19)/535d = 425.6d = 425.6/35d = 12.16It is given that,
→ s1= 32 miles/h
→ s2 = 38 miles/h
Now t1 + t2 is,
→ 42 min
→ 42/60 hours
→ 7/10 hours
The formula we use,
→ Time = Distance/Speed
→ t = d/s
Then the total time is the,
Sum of time values to and from the town.
→ d/32 + d/38 = 7/10
→ d/16 + d/19 = 7/5
→ d{(1/16) + (1/19)} = 7/5
→ d(16 + 19) = (7/5) × (16 × 19)
→ 35d = 425.6
→ d = 425.6/35
→ d = 12.16
Hence, the distance is 12.16 miles.
Which of the following is result of using the remainder theorem to find F(3) for the polynomial function F(x) = x^3 - 9x^2 + 5x - 2
A. -32
B. 11
C. -59
D. -41
-41
Step-by-step explanation:The remainder theorem states that when a polynomial F(x) is divided by (x - k) the remainder is F(k). In other words, the remainder when f(x) is divided by (x-k) is calculated by simply calculating F(k).
Given:
F(x) = x³ - 9x² + 5x - 2 -----------------(i)
To calculate F(3), substitute x = 3 into equation (i) as follows;
F(3) = (3)³ - 9(3)² + 5(3) - 2
F(3) = 27 - 81 + 15 - 2
F(3) = -41
This means that if the polynomial F(x) = x³ - 9x² + 5x - 2 is divided by x - 3, the remainder will be -41.
Omgg please help right now
Answer:
64in^3
Step-by-step explanation:
6×3 = 18
18×2 = 36
4×7 = 28
36+28 = 64
Hope this helps! :)
2(5 – 9x) = -3(x - 2)
Answer:
[tex]x=\frac{4}{15}[/tex]
Step-by-step explanation:
1. Distributive Property[tex]10-18x=-3x+6[/tex]
2. Solving for x[tex]10-6=-3x+18x\\4=15x\\\frac{4}{15} =x[/tex]
Hope this helped! Please mark brainliest :)
The first five terms of an arithmetic sequence are shown below:
20, 17, 14, 11, 8, . . .
Let n represent the term number and f(n) the term in the sequence.
Choose a function that represents the sequence.
The answer to this question is f(n) = -3 + 23
Now my question is, how do you find the solution? I was taught the explicit formula is f(n) = m(n) + b, but no matter how many times I've tried to plug in the numbers I cannot seem to get the right answer. Please help me and do show the entire process and the steps.
Answer:
The function represents the sequence is - 3 n + 23.
Step-by-step explanation:
20. 17, 14, 11, 8,......
Here, the first term is
a = 20
Common difference, d = -3
Let the nth term is Tn.
Tn = a + (n -1) d
Tn = 20 + (n -1) x (-3)
Tn = 20 - 3 n + 3
Tn = 23 - 3 n = - 3 n + 23
So, the function represents the sequence is - 3 n + 23.
Answer:
Y'all know what it is already, but I want points, so: f(n) = -3n + 23
Factorize 5b2-11b+6=0
Answer:
5b^2-(5+6)b+6=0
5b^2-5b-6b+6=0
5b(b-1)-6(b-1)=0
(5b-6)(b-1)=0
either
(5b-1)=0
5b=1
b=1/5
or
b-1=0
b=1
Step-by-step explanation:
firstly find out the mid term factor i e in above qn 11 should be break down so that its multiple should be coefficient of b and constant and additiqn should be equals to 11 .so we find out 5 and 6
PLEASE HELP
Fill in the blanks. Then, choose the property of addition you used.
(a)3+_= 3
(Choose one)
(b)4 + 7) + _1 = 4 + (7 + 3)
(Choose one)
(c)9+8 = 8+_
(Choose one)
Fill in the blank and choose a property
Answer:
3+ 0 = 3
( 4+7) + 3.0 × 1 = 4 + (7+3)
9 + 8 = 8 + 9
XYZ ∆ where Angle Y =90° , XZ= 14 m , XY = 6 m . Find YZ ?
( Show all your workings )
[tex]4 \sqrt{10} [/tex]
Step-by-step explanation:
Use Pythagoras
A^2 + b^2 = c^2
(6)^2 + b^2 = (14)^2
36 + b^2 = 196
B^2 =160
[tex]b = \sqrt{160} [/tex]
[tex]b = 4 \sqrt{10} [/tex]
The function f is defined by f(x)=2x+5/x+4 find f (3x)
Answer:
[tex]\displaystyle f(3x) = \frac{6x + 5}{3x + 4}[/tex]
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \frac{2x + 5}{x + 4}[/tex]
Step 2: Find
Substitute in x [Function f(x)]: [tex]\displaystyle f(3x) = \frac{2(3x) + 5}{3x + 4}[/tex]Simplify: [tex]\displaystyle f(3x) = \frac{6x + 5}{3x + 4}[/tex]You want to buy a $203,000 home. You plan to pay 10% as a down payment, and take out a 30 year loan for the rest. or a) How much is the loan amount going to be? $ b) What will your monthly payments be if the interest rate is 6%? $ c) What will your monthly payments be if the interest rate is 7%?
Answer:
The amount of the loan is going to be $ 182,700, and the monthly payments, if the interest is 6%, are going to be $ 537.95, while if the interest is 7%, are going to be $ 543.02.
Step-by-step explanation:
Given that you want to buy a $ 203,000 home, and you plan to pay 10% as a down payment, and take out a 30 year loan for the rest, for A) determine how much is the loan amount going to be, B) determine what will your monthly payments be if the interest rate is 6%, and C) determine what will your monthly payments be if the interest rate is 7%, the following calculations must be made:
A) 100 - 10 = 90
203,000 x 0.90 = X
182,700 = X
B) (182,700 x 1.06) / (30 x 12) = X
193,662 / 360 = X
537.95 = X
C) (182,700 x 1.07) / (30 x 12) = X
195,489 / 360 = X
543.025 = X
Therefore, the amount of the loan is going to be $ 182,700, and the monthly payments, if the interest is 6%, are going to be $ 537.95, while if the interest is 7%, are going to be $ 543.02.
What is the slope of the line that passes through (17, −13) and (17, 8)?
(also can you try to explain ive been having trouble with these types of question)
Answer:
Slope is undefined. Line parallel to y-axis.
Step-by-step explanation:
By Analytic Geometry, we can determine the slope of a line by knowing two distinct lines and using the definition of secant line:
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] (1)
Where:
[tex](x_{1}, y_{1})[/tex] - Coordinates of the initial point.
[tex](x_{2}, y_{2})[/tex] - Coordinates of the final point.
[tex]m[/tex] - Slope.
If we know that [tex](x_{1}, y_{1}) = (17, -13)[/tex] and [tex](x_{2}, y_{2}) = (17, 8)[/tex], then the slope of the line is:
[tex]m = \frac{8-(-13)}{17-17}[/tex]
[tex]m = \frac{21}{0}[/tex]
The slope is undefined, which means that line is parallel to y-axis.
She uses a scale of 1 centimeter to 6 inches
the scale drawing of the front face is
Answer:
change inches into centimeter and then divide it
hope this help
Mathematics I need help
PLEASE HELP!!!! WILL GIVE BRAINLIEST!!!!
Answer:
9
[tex]3^{\frac{4}{2} }[/tex] = [tex]3^{2} =9[/tex]
Step-by-step explanation:
Please Help NO LINKS
Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by
y
=
x
2
,
y
=
0
, and
x
=
9
,
about the
y
-axis.
V
=
Answer:
[tex]\displaystyle V = \frac{6561 \pi}{2}[/tex]
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationGraphingCalculus
Integrals
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Shell Method: [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]
[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is volumeStep-by-step explanation:
Step 1: Define
y = x²
y = 0
x = 9
Step 2: Identify
Find other information from graph.
See attachment.
Bounds of Integration: [0, 9]
Step 3: Find Volume
Substitute in variables [Shell Method]: [tex]\displaystyle V = 2\pi \int\limits^9_0 {x(x^2)} \, dx[/tex][Integrand] Multiply: [tex]\displaystyle V = 2\pi \int\limits^9_0 {x^3} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle V = 2\pi \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^9_0[/tex]Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle V = 2\pi \bigg( \frac{6561}{4} \bigg)[/tex]Multiply: [tex]\displaystyle V = \frac{6561 \pi}{2}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e
If 2x^2 + 3x + 3 = Kx - K has real roots, find the possible values of k.
Answer:
Step-by-step explanation:
Dd
All I need is number two
A confided aquifer has a piezometric height of 30 feet before being pumped. The well is then pumped at 250 gallons/day for a very long time and results in a drawdown of 10 feet at the well. If the transmissivity in the aquifer is 10.0 ft2/day and the radius of the well is 0.5 feet, estimate the drawdown in feet for a well 50 feet away
Answer:
[tex]d_2=-8.32ft[/tex]
Step-by-step explanation:
From the question we are told that:
Height of first draw down [tex]h=30[/tex]
Pump Discharge [tex]Q=250gallons/day[/tex]
Well 1 depth [tex]d_1=10ft[/tex]
Transmissivity[tex]\=T 10.0 ft2/day[/tex]
Radius[tex]r=0.5[/tex]
Well 2 depth [tex]d_2=50ft[/tex]
Generally the Thiem's equation for Discharge is mathematically given by
[tex]Q=\frac{2\piT(h_2-h_1)}{ln(\frac{r_2}{r_1})}[/tex]
[tex]250=\frac{2*\pi 10 (10-d_2)}{ln(\frac{50}{0.5})}[/tex]
[tex]1151.293=2*\pi 10 (10-d_2)[/tex]
[tex]d_2=-8.32ft[/tex]
Find a vector equation and parametric equations for the line The line through the point (2, 2.4, 3.5) and parallel to the vector 3i 1 2j 2 k
Answer:
The vector equation
[tex]r = (2 + 3t)i+ (2.4 + 2t)j+ (3.5 - t)k[/tex]
The parametric equation
[tex]x = 2 + 3t\\y = 2.4 + 2t\\z = 3.5-t[/tex]
Step-by-step explanation:
Given
[tex]Point = (2,2.4,3.5)[/tex]
[tex]Vector = 3i + 2j - k[/tex]
Required
The vector equation
First, we calculate the position vector of the point.
This is represented as:
[tex]r_0 = 2i + 2.4j + 3.5k[/tex]
The vector equation is then calculated as:
[tex]r = r_o + t * Vector[/tex]
[tex]r = 2i + 2.4j + 3.5k + t * (3i + 2j - k)[/tex]
Open bracket
[tex]r = 2i + 2.4j + 3.5k + 3ti + 2tj - tk[/tex]
Collect like terms
[tex]r = 2i + 3ti+ 2.4j + 2tj+ 3.5k - tk[/tex]
Factorize
[tex]r = (2 + 3t)i+ (2.4 + 2t)j+ (3.5 - t)k[/tex]
The parametric equation is represented as:
[tex]x = x_0 + at\\y = y_0 + bt\\z = z_0 + ct[/tex]
Where
[tex]r = (x_0 + at)i +(y_0 + bt)j+(z_0 + ct)k[/tex]
By comparison:
[tex]x = 2 + 3t\\y = 2.4 + 2t\\z = 3.5-t[/tex]
Which line is parallel to the line that passes through the points (1,7) and (-3, 4)? A. y=--x-5 B. y=+*+1 y=-x-8 O c. D. 11 v==x+3 4
Answer:
B
Step-by-step explanation:
because
Given the following numbers: a = 12500000 b = 0.00125 c = 1120000
Calculate (ab)÷ (c) and write the answer in standard form. (2.5 marks)
d) Express the interval (-1.5, 4] as an inequality and then graph the interval.
Answer:
Answer to the following question is as follows.
Step-by-step explanation:
Given:
a = 12500000
b = 0.00125
c = 1120000
Calculate (ab) ÷ (c)
Given:
d) Express the interval [-1.5, 4] as an inequality and then graph
Computation:
(ab) ÷ (c) = (a)(b) / c
(ab) ÷ (c) = (12500000)(0.00125) / (1120000)
(ab) ÷ (c) = 25 / 1,792
Express the interval [-1.5, 4]
{x : -1.5 < x ≤ 4}
Graph.
._________._________.
-1.5 0 4
Test 21,753 for divisibility by 2,3,5,9 and 10
Answer:
Step-by-step explanation:
21,753
at unit place=3 not an even number,not equal to 5 and not equal to 0
so 21,753 is not divisible by 2,5 and 10
again
2+1+7+5+3=18 divisible by 3 and 9.
so 21,753 is divisible by 3 and 9.
A die is rolled 5 times and a 5 or 6 is considered a success. Find the peobability of no success
Answer:
0.1317 = 13.17% probability of no successes.
Step-by-step explanation:
For each toss, there are only two possible outcomes. Either there is a success, or there is not. The probability of a success on a toss is independent of any other toss, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A die is rolled 5 times.
This means that [tex]n = 5[/tex]
5 or 6 is considered a success.
2 out of 6 sides are successes, so:
[tex]p = \frac{2}{6} = 0.3333[/tex]
Find the probability of no success:
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.3333)^{0}.(0.6667)^{5} = 0.1317[/tex]
0.1317 = 13.17% probability of no successes.
Write an equation that expresses the following relationship.
d varies directly with w and inversely with p.
In your equation, use k as the constant of proportionality.
9514 1404 393
Answer:
d = kw/p
Step-by-step explanation:
When d varies directly with w, the equation is ...
d = kw
When d varies inversely with p, the equation is ...
d = k/p
When d does both, the equation is ...
d = kw/p
find the angle between following linesroot 3x-y=2,x-root 3y=7
Answer:
where I find? where is the directions
what is equivalent to x-2(3x-1)=3x
Answer:
1/4 = x
Step-by-step explanation:
x - 2( 3x - 1 ) = 3x
Step 1 :- Distribute 2
x - 2 × 3x - 2 × 1 = 3x
x - 6x + 2 = 3x
Step 2:- Combine like terms
-5x + 2 = 3x
Step 3 :- Add 5x to both sides
-5x + 5x + 2 = 3x + 5x
2 = 8x
Step 4 :- Divide both side by 8
2/8 = 8x / 8
1/4 = x
Lisa bought a house The value of the house increased by 1.5% each year for 2 years. At the end of 2 years, the value of the house was £123,627. Work out the value of the house when Lisa bought it.
Answer:
$370,881
Step-by-step explanation:
firstly we we multiply 1,5% by 2yrs. the answer we get is 3,0%. we then multiply 3 % by $123,627 and get $370,881
If Lisa bought a house The value of the house increased by 1.5% each year for 2 years. The value of the house was £123,627. The initial amount of the house is 95120.7.
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given,
Lisa bought a house The value of the house increased by 1.5% each year for 2 years
By the end of 2 years, the value of the house was £123,627.
A=P(1+rt)
A is the final amount,
r is rate of interest
t is the time
P is principle amount.
123,627=P(1+1.5/100 (2))
123657=P(1+0.15(2))
123657=P(1+0.3)
123657=1.3P
Divide both sides by 1.3
P=95120.7
The initial amount of the house when Lisa bought is 95120.7
To learn more on Percentage click:
https://brainly.com/question/28269290
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find the HCF by prime factorization method 60 and 75
HCF=15
Hope it helps you...
The function c(r)=2r+12.5 represents the cost c, in dollars, of riding r rides
at a carnival. How much does it cost to get into the carnival? *
1 point
A.$2
B. $12.50
C. $14.50
D.r
Find the value of z, the measure of the subtended arc.
86°
47°
188°
94°
Answer:
188 degrees
Step-by-step explanation:
The measure of the arc is the center angle, that is double of the circumference one
94 * 2 = 188 degrees
A pizza dough recipe calls for 6 1/2 cups of flour. The recipe makes 37 1/2 ounces of dough. How many ounces of dough does 1 cup of flour make?
Answer:
[tex]n = 5\frac{10}{13}[/tex]
Step-by-step explanation:
Given
[tex]Call = 6\frac{1}{2}[/tex] cups
[tex]Recipe = 37\frac{1}{2}[/tex] ounce
Required
Number of ounces per cup (n)
To do this, we simply divide the Recipe by the call
So, we have:
[tex]n = \frac{Recipe}{Call}[/tex]
[tex]n = 37\frac{1}{2} \div 6\frac{1}{2}[/tex]
Express as improper fraction
[tex]n = \frac{75}{2} \div \frac{13}{2}[/tex]
Rewrite as:
[tex]n = \frac{75}{2} * \frac{2}{13}[/tex]
[tex]n = \frac{75}{13}[/tex]
[tex]n = 5\frac{10}{13}[/tex]