Given:
Speed[tex]= \bold{9.2 \ \frac{miles}{hour}}[/tex]
[tex]\therefore \\\\[/tex]
1-hour= 60 minutes
1-minutes=60 second
So
1-hour= 3600 second
Converting the given time into seconds:
Time= 6 minutes and 30 second
[tex]=\bold{6\times 60 \ second + 30 \ second }\\\\=\bold{360\ second+30\ second}\\\\=\bold{390\ second}\\\\[/tex]
When 3600 seconds covers=9.2 miles
Then equation:
[tex]=\bold{\frac{9.2}{3600}}\\\\[/tex]
390 seconds covers:
[tex]=\bold{\frac{9.2}{3600}\times 390 \ miles} \\\\[/tex]
Let
[tex]\bold{1 \ miles= 1760\ yard}\\\\[/tex]
Convert the traveling value into yards:
[tex]=\bold{ \frac{9.2}{3600}\times 390\times 1760}\\\\=\bold{ \frac{9.2}{36}\times 39\times 176}\\\\=\bold{ \frac{9.2}{12}\times 13\times 176}\\\\=\bold{ \frac{9.2}{12}\times 2288}\\\\=\bold{ 9.2\times 190.66}\\\\=\bold{ 1754.072\ yards}\\\\[/tex]
Therefore, total traveling yards are"1754.072".
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Speed of the person has been given as 9.2 miles per hour.
Therefore, speed of the person in miles per minute = [tex]\frac{9.2}{60}[/tex]
Duration for which the person is running = 6 minutes and 30 seconds
= 6 minutes and [tex]\frac{30}{60}[/tex] minutes
= 6.5 minutes
Since, Distance = Speed × Time
By substituting the values in the expression we can get the distance traveled.
Distance = [tex]\frac{9.2}{60}\times 6.5[/tex]
= 0.9967 miles
Since, 1 mile = 1760 yards
Therefore, 0.99667 miles = 1760 × 0.99667
= 1754.13 yards
Total distance traveled by the person is 1754.13 yards.
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A submarine is 1000 feet below sea level and then rises 450 feet. Where is the submarine now?
Sea level is 0
1000 feet below sea level would be -1000. It rises 450 feet. Add 450 to -1000:
-1000 + 450 = -550
The submarine is at -550 feet ( 550 feet below sea level).
round 6.7 to the nearest whole number.
Please help me solve that question
Step-by-step explanation:
steps are in picture above.
if you need to ask questions I'll give you answers gladly.
Let the (x; y) coordinates represent locations on the ground. The height h of
a particle is governed by the function described below. Classify all the critical
points of height and find the value(s) of height h at those points.
h(x; y) = 8x + 10y - 4xy - 4x^2 - 4y^3
The critical points of h(x,y) occur wherever its partial derivatives [tex]h_x[/tex] and [tex]h_y[/tex] vanish simultaneously. We have
[tex]h_x = 8-4y-8x = 0 \implies y=2-2x \\\\ h_y = 10-4x-12y^2 = 0 \implies 2x+6y^2=5[/tex]
Substitute y in the second equation and solve for x, then for y :
[tex]2x+6(2-2x)^2=5 \\\\ 24x^2-46x+19=0 \\\\ \implies x=\dfrac{23\pm\sqrt{73}}{24}\text{ and }y=\dfrac{1\mp\sqrt{73}}{12}[/tex]
This is to say there are two critical points,
[tex](x,y)=\left(\dfrac{23+\sqrt{73}}{24},\dfrac{1-\sqrt{73}}{12}\right)\text{ and }(x,y)=\left(\dfrac{23-\sqrt{73}}{24},\dfrac{1+\sqrt{73}}{12}\right)[/tex]
To classify these critical points, we carry out the second partial derivative test. h(x,y) has Hessian
[tex]H(x,y) = \begin{bmatrix}h_{xx}&h_{xy}\\h_{yx}&h_{yy}\end{bmatrix} = \begin{bmatrix}-8&-4\\-4&-24y\end{bmatrix}[/tex]
whose determinant is [tex]192y-16[/tex]. Now,
• if the Hessian determinant is negative at a given critical point, then you have a saddle point
• if both the determinant and [tex]h_{xx}[/tex] are positive at the point, then it's a local minimum
• if the determinant is positive and [tex]h_{xx}[/tex] is negative, then it's a local maximum
• otherwise the test fails
We have
[tex]\det\left(H\left(\dfrac{23+\sqrt{73}}{24},\dfrac{1-\sqrt{73}}{12}\right)\right) = -16\sqrt{73} < 0[/tex]
while
[tex]\det\left(H\left(\dfrac{23-\sqrt{73}}{24},\dfrac{1+\sqrt{73}}{12}\right)\right) = 16\sqrt{73}>0 \\\\ \text{ and } \\\\ h_{xx}\left(\dfrac{23+\sqrt{73}}{24},\dfrac{1-\sqrt{73}}{12}\right)=-8 < 0[/tex]
So, we end up with
[tex]h\left(\dfrac{23+\sqrt{73}}{24},\dfrac{1-\sqrt{73}}{12}\right)=-\dfrac{4247+37\sqrt{73}}{72} \text{ (saddle point)}\\\\\text{ and }\\\\h\left(\dfrac{23-\sqrt{73}}{24},\dfrac{1+\sqrt{73}}{12}\right)=-\dfrac{4247-37\sqrt{73}}{72} \text{ (local max)}[/tex]
What is the range with steps? f(x)=x^2+8x+8
Answer:
[-8, ∞)Step-by-step explanation:
Given function:
f(x)=x² + 8x + 8This is a quadratic function with positive leading coefficient, therefore it is an increasing function with its minimum at vertex. It has no maximum value.
The vertex is at x = -b/2a:
x = -8/2 = -4The minimum value is:
f(-4) = (-4)² + 8(-4) + 8 = 16 - 32 + 8 = -8The range of the function is:
[-8, ∞)f(x)=x^2+8x+8
Find vertex to x[tex]\\ \sf\longmapsto \dfrac{-b}{2a}[/tex]
[tex]\\ \sf\longmapsto \dfrac{-8}{2(1)}[/tex]
[tex]\\ \sf\longmapsto \dfrac{-8}{2}[/tex]
[tex]\\ \sf\longmapsto -4[/tex]
Find value of function at -4[tex]\\ \sf\longmapsto f(-4)[/tex]
[tex]\\ \sf\longmapsto (-4)^2+8(-4)+8[/tex]
[tex]\\ \sf\longmapsto 16-32+8[/tex]
[tex]\\ \sf\longmapsto -16+8[/tex]
[tex]\\ \sf\longmapsto -8[/tex]
The range is
[tex]\\ \sf\longmapsto (8,\infty)[/tex]
2. The product of 7 and a number
I think the answer you are looking for is 7n, which also means 7 times n.
Answer:
7x
Step-by-step explanation:
Product refers to multiplication. "A number" refers to an unknown number otherwise known as a variable. In this case, I use x.
What is the solution to the system of equations below?
4x-2y=10
y=-2x-5
show your work! :)
Answer:
(0,-5)
Step-by-step explanation:
4x-2(-2x-5)+10
x=0
y=-2*0-5
y=-5
Please help me It’s my birthday!
2. Janyce conjectured that in the visual pattern below, there would be 3n – 1 small
squares in the nth figure
Can you disprove Janyce’s conjecture?
Step-by-step explanation:
Janyce's rule doesn't work. In the case where n = 3 her rule predicts that there will be 3(3) - 1 = 8 squares but instead, there are 10 squares. Likewise, for n = 4, there are 17 squares instead of 11 that she predicted. Instead, I propose the rule [tex]n^2 + 1.[/tex] It works for all the figures shown and mostly likely, for all other values of n.
2. Part A;
Given that the number of squares obtained using Janyce conjecture for
figures 3 and 4 which are 8 and 11 squares respectively and the number of
squares in the diagram for figures 3 and 4 which are 10 and 17 squares
respectively are not the same, disproves Janyce conjecture
Part B:
The rule for the number of squares in the nth squares is n² + 1
The reasons the above conclusion and rule are correct is as follows:
2. Part A
The given number of squares in each figure are;
[tex]\begin{array}{|c|c|c|}\mathbf{Figure \ number}&\mathbf{Number \ of \ squares} &\mathbf{Janyce \ conjecture \ (3\cdot n - 1)}\\&&\\1&2 \ squares &(3 \times 1 - 1 = 2) \ squares \\2&5 \ squares&(3 \times 2 - 1 = 5) \ squares\\3&10 \ squares &(3 \times 3 - 1 = 8) \ squares\\4&17 \ squares&(3 \times 4 - 1 = 11) \ squares\end{array}[/tex]
Given that the number squares in figure 3, and 4 are;
Figure 3 = 10 squares
Figure 4 = 17 squares
Janyce conjectured number of squares are;
Figure 3 = 8 squares
Figure 4 = 11 squares
The values for the number of squares in the diagram in figures 3 and 4 are different from Janyce conjecture which disproves Janyce's conjecture for the number of squares in the nth figure
Part B
From the diagrams, we have;
The number of squares on the each figure is given by a square shape with a side length equal to the figure number of squares plus one extra square at the top right end corner, we have;
The area of the square part of the shape = n² = The number of squares in the square shape
The number of squares in the nth figure = n² + 1
Verifying, we have;
Figure 1 = (1² + 1) squares = 2 squares (Same as in diagram)
Figure 2 = (2² + 1) squares = 5 squares (Same as in diagram)
Figure 3 = (3² + 1) squares = 10 squares (Same as in diagram)
Figure 4 = (4² + 1) squares = 17 squares (Same as in diagram)
Therefore;
The correct formula for the number of squares in the nth figure = n² + 1
Learn more about the nth term of a sequence here:
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P- 24000 R-10% T-2 years find the sum
Answer:
here
I =p×t×r/100
= 24000×2×10/100
= 4800
again,
sum = p+I
= 24000+4800
= 28800
In the number 6.253
(a) What is the place value of 2 ...................................................................
(b) What is the value represented by 5 ...................................................................
Answer:
place value of 2 is 100
Step-by-step explanation:
please brainleist my answer
Answer:
The place value of 2 in 6.253 is 200
Step-by-step explanation:
Place value of 2 is occurring in hundreds
Write an equation in slope-intercept form of the line passing through (0, 3) and (2, -1).
y=2x+3y=2x+3
y=-2x+3y=−2x+3
y=-2xy=−2x
y=-x+3y=−x+3
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]y = -2x + 3[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Slope-Intercept Form Is:}}\\\\y=mx + b\\---------------\\\boxed{\text{Key:}}\\\\m - slope\\b - y-intercept\\---------------\\\boxed{\text{\underline{Known Information:}}}\\\\\rightarrow \text{We are given the points: } (0,3) \text{ and } (2, -1)\\---------------\\\boxed[/tex]
[tex]\boxed{\text{\underline{Y-Intercept:}}}\\\\\rightarrow \text{Since the line passes at point (0, 3), the y-intercept would be 3.}\\---------------\\\boxed{\text{\underline{Slope:}}}\\\\\rightarrow m =\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1} \\\\\rightarrow m = \frac{-1-3}{2-0}=\frac{-4}{2}=\boxed{-2}\\\\\text{The slope is: } \boxed{-2}\\---------------[/tex]
[tex]\boxed{\text{\underline{Equation:}}}\\\\\text{Our equation should be:}\\\\y = -2x + 3[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Solve the equation 12v+10v+14=80
Answer:V=3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
12v+10v+14=80
(12v+10v)+(14)=80
(Combine Like Terms)
22v+14=80
22v+14=80
Step 2: Subtract 14 from both sides.
22v+14−14=80−14
22v=66
Step 3: Divide both sides by 22.
22v/22=66/22
V=3
:)
Factor x^2+x+6
Plz help
Answer:
2
Step-by-step explanation:
A motorboat travels 116 kilometers in 4 hours going upstream. It travels 164 kilometers going downstream in the same amount of time. What is the rate of the
boat in still water and what is the rate of the current?
Rate of the boat in still water:
Rate of the current:
9514 1404 393
Answer:
boat: 35 km/hcurrent: 6 km/hStep-by-step explanation:
Let b and c represent the rates of the boat and current, respectively. Then the upstream rate is ...
speed = distance/time
b -c = (116 km)/(4 h) = 29 km/h
b +c = (164 km)/(4 h) = 41 km/h
Adding these equations gives ...
2b = 70 km/h
b = 35 km/h
Substituting into the first equation, we have ...
35 -c = 29
c = 6
Rate of the boat: 35 km/h.
Rate of the current: 6 km/h
create a improper fraction with the number 10 as the denominator
Answer:
Decimal Fraction Percentage
0.101 101/1000 10.1%
0.1 100/1000 10%
0.1013 101/997 10.13%
0.1012 101/998 10.12%
Step-by-step explanation:
9(y-4) -3y = 2(3y-2 need solved as fast as possible
Step-by-step explanation:
did you give us all the information ? the equating looks cut off.
so, from what I can see we have
9(y-4) - 3y = 2(3y-2)
let's try :
9y - 36 - 3y = 6y - 4
0 = 32
so, no, this can't be it. this does not have a solution. you must have cut off some additional information.
99. Savings Bronwyn wants to buy a house, so she has decided
to save one quarter of her salary. Bronwyn earns $47.00 per hour
and receives an extra $28.00 a week because she declined
company benefits. She wants to save at least $550.00 each week.
How many hours must she work each week to achieve her goal?
Answer:
46.5 hours per week
Step-by-step explanation:
At least 550 a week.
Which is 1\4 of Bronwyn salary.
550 x 4 = 2200
To find minimum work hours
2200-28 = 2172
2172 \ 47 = 46.212 hours per week
So, bronwyn needs to work at least 46.5 hours per week
Answer:
Bronwyn must work nearly 47 hours each week to achieve her goal.
Step-by-step explanation:
Let x be the number of hours Bronwyn works per week.
If Bronwyn earns $47 per hour, if x is the number of hours she works per week and if Bronwyn earns $28 per week because she declined company benefits, lets assume that the left hand side of the equation is:
[tex]47x + 28[/tex]
Now onto the salary. Since Bronwyn wants to save $550 each week and since she also wants to save one quarter of her salary, her salary becomes $2200 for each week she works
Making the equation...
[tex]47x + 28 = 2200[/tex]
Time to solve for x
[tex]47x = -28 + 2200\\47x = 2172\\x = 46.2[/tex]
Since its at least, you can round it up to 47 making 47 the number of hours she must work each week to achieve her goal.
pls help im a little bit sтuрid
Step-by-step explanation:
a⁴+16a²b-2ab-a²+64b²-b²we can also write them as,
a⁴+16a²b+64b²-a²-2ab-b²Now, from -a²-2ab-b² if we take - as common term then we get,
a⁴+16a²b+64b²-(a²+2ab+b²)Now, by using the concept of a²+2ab+b²=(a+b)²
(a²)²+2×a²×8b+(8b)²-{(a)²+2×a×b+(b)²}(a²+8b)²-(a+b)²I hope it helped U
stay safe stay happy
x=-9 y=-8 evaluate the expression 8 x^2 - 6 y^2
Answer:
264Step-by-step explanation:
Let x= -9 y= -88x² - 6y² = ?8(-9)² - 6(-8)² = ?8(81) - 6(64) = ?648 - 384 = ?264[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
For the two numbers listed, find two factors of the first number such that their product is the first number and their sum is the second number.
- 10,9
9514 1404 393
Answer:
10, -1
Step-by-step explanation:
If you assume the numbers are integers, you can look at the factor pairs that make -10:
-10 = 10(-1) = 5(-2) = 2(-5) = 1(-10)
The sums of these pairs are 9, 3, -3, -9, so the pair of interest is the first one:
10, -1
8x – 3 = 11 + 6x
What is x
Answer:
x = 7
Step-by-step explanation:
[tex]8x-3=11+6x\\\\2x-3=11\\\\2x=14\\\\x=7[/tex]
Answer:
x = 7
Step-by-step explanation:
8x - 3 = 11 + 6x
8x - 3 + 3 = 11 + 6x +3
8x = 6x + 14
8x - 6x = 6x + 14 - 6x
2x = 14
2x/2 = 14/2
x = 7
helpppppppppppppopnanannsnsnnsnakaknfnsn
Step-by-step explanation:
y=107(vertically opposite angles)
x=180-107=73(angles on a straight line)
z=73(vertically opposite angles)
Answer:
[tex]{ \sf{y = 107 \degree}} \: \{ \sf{alternate \: angles} \}[/tex]
[tex]{ \sf{z + 107 \degree = 180 \degree}} \: \{ \sf{straight \: line \: angles \}} \\ z = 180\degree - 107\degree \\ z = 73\degree[/tex]
[tex]{ \sf{x = z}} \: \{ \sf{alternate \: angle \}} \\ x = 73\degree[/tex]
Evaluate: 24 - ( 5 - 3)^ 4
______________
4
24 - (5 - 3)⁴ = 24 - 2⁴ = 24 - 16 = 8
8 : 4 = 2 ← the end solution
if M ABD =75 and M abc =40 then m CBD =
help me plz branniest to whoever right
how many feet is 2160 yards?
The quotient c and -19 is 38
Answer:
c = 722
Step-by-step explanation:
-19/c = 38
c = 38 x 19 (positive)
c = 722
hope it helped !
two numbers are at ratio of 5:9 find the larger number if the smaller number 35
9514 1404 393
Answer:
63
Step-by-step explanation:
We observe that multiply the smaller number in the ratio by 7 we get 35. Then the ratio is ...
5 : 9 = 35 : 63 . . . . . . multiply both numbers by 7
The larger number is 63.
Two trains leave towns 1285 kilometers apart at the same time and traveled towards each other. One train travels 17 km/h faster than the other. If they meet in 5 hours what is the rate of each train
Distance = (Rate)(Time)
Let x = speed of slower train
x + 17 = speed of faster train
The trains meet when the sum of the distances = 1285
5x + 5(x+17) = 1285
(5 came from 5 hours)
10x + 85 = 1285
10x = 1200
x = 120 mph
The speeds are 120 mph and 137 mph
wyzant
a bakery sells 17 cups of coffee for every 3 cups of hot chocolate they sell. At the end of the day the bakery sold 406 more coffee than hot chocolates. How many of the two drinks did they sell in all?
Answer:
Step-by-step explanation: