A car has a maximum speed of 341.7 feet/second. Convert this speed to miles/hours.

Answers

Answer 1
Answer: 341.7 feet per second = 232.98 miles per hour (rounded)
Answer 2
Answer: Just multiply measure in ft/s by 0.6818 to get mi/h

341.7 x 0.6818 = 232.97 mi/h

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Marshall solved an equation using the process below.Use the multiplication property of equality twice, by first multiplying both sides of the equation by x and then dividing both sides by 3.25.Which equation is the one Marshall solved?
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Peaches are being sold for $2 per pound. If x represents the number of pounds of peaches bought and y represents the total cost of the peaches, which best describes the values of x and y?

Answers

Answer with explanation:

Cost of Peaches per pound = $ 2

If x, is the total number of pound of peaches bought = x

→Total cost of pound of peaches bought = Cost of Peaches per pound × Total number of pound of peaches bought

It is given that,y is the total cost of peaches.

→→y=$ 2 × x

→→y=2 x→→Relationship between value of x and y

Total Cost of peaches=price of 1 pound x number of pounds bought
y=2x

Given the equation Square root of 8x plus 1 = 5, solve for x and identify if it is an extraneous solution.

Answers

It depends if you mean √(8x) +1=5 or √(8x+1) = 5 

√(8x) +1=5

Subtract 1 from both sides. 

√(8x) =4

Take the square root of both sides. 

8x = sqrt(4) 
8x = 2
x = 1/4.

Plugging it back in: 
sqrt(8*0.25) + 1 = 5 
sqrt(2) = 4

This is not true because the square root of 2 is about 1.41, which does not equal 4. 
So it is an extraneous solution.
__________________________________________
√(8x+1) = 5 
Square both sides. 
8x + 1 = 25 
8x = 24
x = 3

Not extraneous because equation works out when you plug x back in.

A map has a scale of 1 cm : 15.5 km. Two cities are 2.3 cm apart on the map. To the nearest tenth of a kilometer, what is the actual distance corresponding to the map distance?

Answers

The proportion
1 cm                    15.5 km
2.3 cm                 x km

1/2.3=15.5/x
x=2.3*15.5
x=35.65≈35.7 km
35.65 kilometers
15.5 times 2.3


The center of a cricle ids (h,7) and the radius is 10. The circle passes through (3,-1). Find all possible values of h.

Answers

center\ of\ a\ circle:(a;\ b)\n\nradius:r\n\n(x-a)^2+(y-b)^2=r^2\n\n========================\n\n(h;\ 7);\ r=10\n\n(x-h)^2+(y-7)^2=10^2\n\n========================

The\ circle\ passes\ throught\ (3;-1).\n\nSubstitute\ x=3\ and\ y=-1:\n\n(3-h)^2+(-1-7)^2=100\n\n(3-h)^2+(-8)^2=100\n\n(3-h)^2+64=100\ \ \ /-64\n\n(3-h)^2=36\iff3-h=\pm√(36)\n\n3-h=-6\ or\ 3-h=6\n-h=-6-3\ or\ -h=6-3\n-h=-9\ or\ -h=3\nh=9\ or\ h=-3\n\nAnswer:h=9\ or\ h=-3
equation\ of\ a\ circle:\n\n(x-h)^2+(y-7)^2=10^2\n\nif\ \ (x;y)=(3;-1),\ then\ \ (3-h)^2+(-1-7)^2=100\n\n(3-h)^2+64=100\n\n (3-h)^2=36\ \ \ \Leftrightarrow\ \ \ (3-h=6\ \ \ or\ \ \ 3-h=-6)\n\n3-h=6\ \ \ \ \ \Rightarrow\ \ \ h=-3\n3-h=-6\ \ \ \Rightarrow\ \ \ h=9\n\nAns.\ h=-3\ \ or\ \ h=9

The long division below shows the first term of the quotient. Which polynomial should be subtracted from the dividend first?x^2
-----------------------------------
x + 2 ) x^3 + 3x^2 + x


A. x + 3
B. x^2 + x + 2
C. x^3 + 2x^2
D. x2 + 3x

Answers

Answer:

Option C. x³ + 2x²

Step-by-step explanation:

In this long division x + 2 ) x³ + 3x² + x

when we divide the polynomial by (x + 2) then first quotient will be x². By the multiplication of (x + 2) and x² we get a polynomial which will be subtracted from the dividend.

(x + 2)×(x²) = x³ + 2x²

This is the polynomial to be subtracted.

Therefore option C is the correct answer.

Option C: x^3 + 2x^2

This is the result of the multiplication of the first term of the quotient (x^2) times the divisor (x + 2).

Factor completely, the expression: 2x^3-2x^2-12x

Answers

2x^3-2x^2-12x=2x(x^2-x-6)=(*)\n\n------------------------------\nx^2-x-6\n\na=1;\ b=-1;\ c=-6\n\n\Delta=(-1)^2-4\cdot1\cdot(-6)=1+24=25\n\n\sqrt\Delta=√(25)=5\n\nx_1=(1-5)/(2\cdot1)=(-4)/(2)=-2;\ x_2=(1+5)/(2\cdot1)=(6)/(2)=3\n\nx^2-x-6=(x+2)(x-3)\n\n------------------------------\n\n(*)=2x(x+2)(x-3)