13.34 mi
from question,
perpendicular (p) = 3mi
base(b) = 13 mi
hypotenuse (h) = ?
from Pythagoras theorem,
h^2 = p^2 + b^2
h = √(3^2 + 13^2)
h = √(9+169)
h= √(178)
h= 13.34 mi
Answer:
≈ 13.3 miles
Step-by-step explanation:
a line due west and a line due south form a right triangle with the hypotenuse being the direct distance x from the house.
using Pythagoras' identity in the right triangle , then
x² = 13² + 3² = 169 + 9 = 178 ( take square root of both sides )
x = [tex]\sqrt{178}[/tex] ≈ 13.3
distance from house ≈ 13.3 miles ( to the nearest tenth )
Evaluate p2m−(np+r) if m=−32 , n=2 , p=−8 , and r=4 .
The value of the given expression will be equal to 2060.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using the signs like addition,substraction, multiplication and division.
It is given that:-
=p²(m)-(np+r)
=(-8)²(32)-(2x(-8)+4)
=(64x32)-(-16+4)
=2060
Hence value of the given expression will be equal to 2060.
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Please help me on this!
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Y=0, y= \cos(4 x), x = \frac{\pi}{8}, x = 0 about the axis y= -4f
The volume will be 3π + π²/16 if the solid obtained by rotating the region bounded by the given curves about the specified axis. y=0, y= cos(4 x), x = π/8, x = 0 about the axis y= -4f
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have curves,
[tex]\rm y=0, y= \cos(4 x), x = \frac{\pi}{8}, x = 0[/tex]
Here the axis is y = -4f, but not mentioned the value of f.
We are assuming the f = 3/2
So the axis will be y = -4(3/2) = -6
Inner radius = 6
Outer radius = 6 + cos4x
[tex]\rm A(x) = \pi((6+cos4x)^2-6^2)[/tex]
[tex]\rm A(x) = \pi (cos^24x+12cos4x)[/tex]
[tex]\rm A(x) = \pi( \dfrac{1+cos8x}{2}+12cos4x)[/tex]
For the volume;
[tex]\rm Volume = \int\limits^\dfrac{\pi}{8}}_0 {A(x)} \, dx[/tex]
Put the function A(x) in the above integration and solve we will get:
[tex]\rm Volume = 3\pi + \dfrac{\pi^2}{16}[/tex]
Thus, the volume will be 3π + π²/16 if the solid obtained by rotating the region bounded by the given curves about the specified axis. Y=0, y= \cos(4 x), x = π/8, x = 0 about the axis y= -4f
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Consider the quadratic function y = –16x
2 + 32x.
A. Does the parabola open upward or downward? Explain.
B. What are the roots, the x-intercepts of the
C. Calculate the x value of the vertex.
D. Use your answer for B to calculate the y value of the vertex.
The parabola y = -16x^2 + 32x opens downward and the y value of the vertex is 16
The direction of the parabolaThe equation of the function is given as:
y = -16x^2 + 32x
Factor out -16
y = -16(x^2 - 2x)
In the above equation, the factor -16 is negative,
This means that the parabola opens downward
The roots and the x-interceptsWe have:
y = -16(x^2 - 2x)
Set to 0
-16(x^2 - 2x) = 0
Divide by -16
x^2 - 2x = 0
Factor out x
x(x - 2) = 0
Split
x = 0 or x - 2 = 0
Solve for x
x = 0 or x = 2
Hence, the roots are 0 and 2, and the x-intercepts are (0,0) and (2,0)
The x value of the vertexWe have:
y = -16x^2 + 32x
Differentiate
y' = -32x + 32
Set to 0
-32x + 32= 0
Divide through by -32
x - 1 = 0
Add 1 to both sides
x = 1
Hence, the x value of the vertex is 1
The y value of the vertexIn (c), we have:
x = 1
Substitute x = 1 in y = -16x^2 + 32x
y = -16(1)^2 + 32(1)
Evaluate
y = 16
Hence, the y value of the vertex is 16
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The cost to produce a book is 1200 to get started plus 9 dollars per book. The book sells for 15 dollars each. How many books must be sold to make a profit?
720
Answer:
15/9 = 1200/x
15x/ 15 =10800/15
x= 720
Find the 5th term in the sequence an=3n - 5
Answer:
aₙ = 3n - 5
5th term = a₅ = 3.5 - 5 = 15 - 5 = 10
Answer:
a₅ = 10Step-by-step explanation:
aₙ = 3n - 5
Put n = 5:
a₅ = 3 · 5 - 5
a₅ = 15 - 5
a₅ = 10
Wanja bought fruits which were being sold at 3 fruits for sh 2.00. She then sold them at 3 fruits for sh 3.50. What profit did she make after selling 450 fruits? [1990 No. 25) sh 300.
Answer:
The answer is sh50......
A fair spinner has 12 equal sections: 4 red, 5 blue and 3 green.
It is spun twice.
What is the probability of getting 2 different colours?
Answer: 2/3 i beleive
Step-by-step explanation:
division equation where 13 is quotient with the dividend a whole number and a unit fraction is the divisor
The division equation that satisfies the required parameters where 13 is the quotient is 1/1/13 = 13
How to determine the equation?The given parameters are:
Quotient = 13Dividend = Whole numberDivisor = Unit fractionA division equation is represented as:
Dividend/Divisor = Quotient
Substitute Quotient = 13
Dividend/Divisor = 13
A unit fraction is represented as 1/n, where n is an integer.
So, the divisor can be represented as 1/13
Dividend/1/13 = 13
Divide both sides by 13
Dividend = 1
So, we have:
1/1/13 = 13
Hence, the division equation is 1/1/13 = 13
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What is angle 3
Help please
Answer:
a3 = 112
Step-by-step explanation:
a2 + a1 = a4
So
3x + 20 = 4x + 4
x = 16
a4 = 68
180 - 68 = 112
Maya used a total of 2 1/6 gallons of gas while driving her car. Each hour she was driving, she used 7/8 gallons of gas. What was the total number of hours she was driving?
Ans
2:47 mins
Step-by-step explanation:
2 1/6 ÷7/8 = 2 10/21
2 10/12 to decimal 2.47
what is 103 + 343 + 252
Answer:
its 698...............................
Parents donated fudge for the fund raiser for your classroom. 40 pounds of chocolate fudge sold for $2.15 per pound and vanilla fudge sold for $1.90 per pound. Your class made $158.20. How many pounds of fudge were sold?
Answer:
77 pounds of fudge were sold.
Write the expression in repeated multiplication form. Then write the expression as a power.
Answer:
The expression is repeated multiplication form is 5.
The expression as power is 9.
Step-by-step explanation:
Answer:
The expression as powers is 5^9
What is the length of the missing leg?
Answer:
[tex]a=12[/tex]
Step-by-step explanation:
Pythagorean Theorem: [tex]a^{2}+b^{2}=c^{2}[/tex]
In this case, a = 9, b = a, and c = 15.
[tex]9^{2}+a^{2}=15^{2}[/tex]
[tex]81+a^{2}=225[/tex]
The, we subtract 81 from both sides getting:
[tex]a^{2}=144[/tex],
Then, [tex]a=12[/tex]
Anyone know the answer to this
Answer:
The answer is A
Step-by-step explanation:
because the angle in the circle is a central angle the angle is the same value as the arc.
Hope this helps!!
joe received $375 for his graduation He put $205 into his savings account About what Percent of his graduation money did joe put into savings
I really need help with this. Please.
A chef has two dozen meatballs to add to a pot of sauce. Each meatball has a two-inch diameter. Before the meatballs are added, the sauce is 2 inches from the top of the 14-inch diameter pot. Will the sauce spill over when the chef adds the meatballs to the pot? Show all of your work to justify your answer.
Given the volume of the space in the pot and the volume of the meatballs, the sauce will not spill over.
Will the sauce spill over?
The first step is to determine the volume of the remaining space that the sauce is yet to fill. A pot usually has the shape of a cylinder, so the formula for the volume of a cylinder would be used.
Volume of a cylinder = πr²h
π x (14/2)³ x 2 = 98 in³
The second step is to determine the volume of the two dozen meatballs.
Volume of a sphere = 4/3πr³
24 x (4/3 x π x (2/2)³) = 32π in³
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The sauce will spill over if the volume of the pot is less than 146π in³ and it will not spill over if the volume of the pot is more than 146π in³.
Volume of the sauce in the potThe volume of sauce in the pot is calculated as follows;
V = πr²h
V = π x (7)² x (2)
V = 98π in³
Volume of the two dozen meatballsArea of 1 meatball = πr² = π x (1)² = π in²
Area of the 2 dozen = (2 x 12) x A
= 24 x π in² = 24π in²
the height of each meatball = 2 in,
Volume of the 2 dozens = 2 in x 24π in² = 48π in³
Total volume of the meatball and sauce in the pot = 98π + 48π = 146π in³
Thus, the sauce will spill over if the volume of the pot is less than 146π in³ and it will not spill over if the volume of the pot is more than 146π in³.
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In a sample of 30 men, the mean height was 177 cm. In a sample
of 16 women, the mean height was 164 cm. What was the mean
height for both groups put together?
Answer:
172.5
Step-by-step explanation:
mean of men=sum/no of men
177=sum/30
sum=177*30
= 5310
mean of women=sum/no of women
164=sum/16
sum=164*16
= 2624
mean height= (5310+2624)/30+16
=7934/46
=172.5
Answer:
172.48cm is the mean height for both groups put togther
Step-by-step explanation:
I've attached my work
- im red is the given information
- In pink is the formula used
- in green is the final answer
- In blue is what we need to find + the proccess
Please give me feedback on my repsomse by commenting,
any way i can improve showing my work?
Hope it helps, let me know if you have questions !
Have a nice rest of your day :)
A piece of wire 144 cm long is bent to form a semicircle as shown in the figure. Find the diameter of the semicircle, giving your answer in meters ( Take pi to be 22/7.)
Answer:
Circumference= 2πr
For a semi circle, C= 2πr/2
144= (2×22×r)÷(7×2)
144= (44r)÷(14)
cross multiply:
44r= 144×14
44r= 2016
divide both sides by 44
r= 2016÷44
r=45.8cm. But d=2r
d= 2×45.8
d=91.6cm approximately 92cm
Thus, diameter= 92cm
can i have help with this question
Answer:
y = 4 + 5x
Step-by-step explanation:
You can plug in numbers from the top row (the x's) and times and add to see if you get the corresponding number from the bottom row. This problem is a little mean and tricky because if you check with x=1, all of them work out right. But check with any other x and you will see that only one equation works, the first answer.
You can find "the rule" by looking for a pattern in the rows of numbers. The x goes up by 1, and the y goes up by 5 (if you go left to right on the table) With the 5 on top and 1 on the bottom, y/x, you get 5...that's the 5 that is beside the x in the answer. And if you imagine making one more column on the left side of the table, x=0 and y=4, that's the 4 that stands alone in the answer.
Solve the equation 28=[12-2x][15-2x]
Answer:
I got x=4
Step-by-step explanation:
Marina he spends one-third of his money on food and three-fifths of the rest on drinks If he had $120 left over,¿how much money did he have to start with?
Answer: $184
Step-by-step explanation:
Step (1)- 1/3 of 120= $40
Step (2)= 3/5 of 40= $24
Step (3)- 40+24+120= $184 (ToTaL)
Hope this helpss!
Nike, Ricky, and Danny competed in a go-cart race. Nike drove three times as fast as Ricky. Adding 2 to Nike's speed, and dividing by 4 gives the speed at which Danny drove. Danny drove at a speed of 26 mi/h. Identify the speed at which Ricky drove.
Answer:
Ricky drove at a speed of 34 mi/h.
Step-by-step explanation:
Danny = 26 mi/h
26 x 4 = 104
104 - 2 = 102
102/3 = 34
Find the sum of 100 and -100
Answer:
0
Step-by-step explanation:
-100+100 = 0
Answer:
the answer would be 0
because if you take 100 away from 100 you have 0 left
Determine the equation of the graph.
Answer: A
Step-by-step explanation:
Answer:
well its slop interform
Step-by-step explanation:
Its pretty easy i'm just being lazy
Answer:
Step-by-step explanation:
How does the slope of g(x) compare to the slope of f(x)? the slope of g(x) is the opposite of the slope of f(x). the slope of g(x) is less than the slope of f(x). the slope of g(x) is greater than the slope of f(x). the slope of g(x) is equal to the slope of f(x).
The statement that correctly compares the slopes of the linear functions is: the slope of g(x) is less than the slope of f(x).
How to Find Slope of a Linear Function?Slope of a linear function = change in y / change in x = rise/run
Given the linear functions, g(x) and f(x) as shown in the image attached:
Slope of g(x) = 1/2 = 0.5
Slope of f(x) = 2/1 = 2
Therefore, we can conclude that: the slope of g(x) is less than the slope of f(x).
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What’s the volume of the figure below
Answer:
41.89 cm3
Step-by-step explanation:
Given : Height = 10 cm
Given: Radius = 2 cm
Find the volume,
The formula for volume is,
V = π([tex]r^2[/tex])[tex]\frac{h}{3}[/tex]
Fill in the formula with the given values,
π · [tex]2^2[/tex] · [tex]\frac{10}{3}[/tex]
= 41.8879.....
Round answer to the nearest hundredth,
(The Rule For Rounding: the last digit is less than 5, keep the previous digit the same. If it's 5 or more then you should round the previous digit up.)
41.8879
7 is more than 5 so bring the 8 up to a 9,
41.89
Therefore the answer is 41.89 cm3.
Answer:
41.9 cm³ (nearest tenth)
Step-by-step explanation:
[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
r = 2 cmh = 10 cm[tex]\begin{aligned}\implies \textsf{Volume} &=\sf \dfrac{1}{3} \pi \cdot 2^2 \cdot 10\\\\ & = \sf \dfrac{1}{3}\pi \cdot 40\\\\& = \sf \dfrac{40}{3}\pi\\\\ & = \sf 41.88790205\:cm^3\end{aligned}[/tex]
Therefore, the volume is 41.9 cm³ (nearest tenth)
How can I solve (-2x-6x^2-4)+(5x^2-2x).
[tex] ( - 2x - 6x ^2 - 4) + (5 x^{2} - 2x)[/tex]
Step-by-step explanation:
we can only solve an equation.
but here we only have an expression, which we can simplify :
(-2x - 6x² - 4) + (5x² - 2x)
-2x - 2x - 6x² + 5x² - 4
-4x - x² - 4
