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KATRIN_1 [288]
3 years ago
8

michael was driving at a constant speed of 60 mph when he crossed the sandy river .after 1 hour he passed a highway marker for m

ile 84 . write an equation in point slop form and find which highway marker he will pass 90 minutes after crossing the sandy river
Mathematics
2 answers:
Alik [6]3 years ago
5 0

speed of Michael = 60 mph

distance traveled in 1 hour = speed* time= 60 *1 = 60 miles

marker crossed after 1 hour = 84

so start point of Michael had marker = 84-60 =24

to write linear equation, lets consider a general linear equation y = mx + c

where m is slope and c is constant, y is marker and x is actual distance traveled from starting point

putting y = 84 x = 60 and y =24 and x = 0 in the equation we get

84 = m*60 + c

24 = m*0 + c

on  solving,

m = 1  c = 24

so the equation is y = x + 24

distance traveled in 90 minutes after crossing sandy river = 60*90/60 = 90 miles

total distance traveled from starting point = 90+60 = 150

putting  x = 150 in y =x+24

y = 174

highway marker he will pass 90 minutes after crossing the sandy river = 174

Klio2033 [76]3 years ago
4 0
Slope intercept form is y=mx+b so use your numbers  to fill in the blanks 

heres an example:
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Alliic
pochemuha
First, we need to solve the first equation in order to see what the options need to be equivalent to. our first step to solving this is to distribute -3 through the parenthesis 
y + 5 = -3x + 3
next, move the constant to the right side and change its sign
y = -3x + 3 - 5
calculate the difference
y = -3x - 2
since we cant find x, your final solution for y is y = -3x - 2, x ∈ R
now that we know the solution to that equation, we can now solve the options listed to see which ones are equivalent.
first is y = -3x - 2, which is very simple to solve because y has already been found. since we know y and there is no solution for x, our answer to this equation is y = -3x -2, x ∈ R. since this is the exact same answer as our first equation, we know that the A is equivalent to y + 5 = -3(x - 1)
the next equation is also already solved for y and has no x, so the answer to this equation is y = -4x - 5, x ∈ R. since this is does not have the same answer that <span>y + 5 = -3(x - 1) had</span>, option B is not equivalent.
our next equation is 3x + y = -2 does not provide y for us, so we must solve it.
first, you need to move the variable to the right side and change its sign
3x = -2 - y
now divide both sides of the equation by 3
x = - 2/3 = y/3
write all the numerators above their common denominators
x = - 2 + y/3 
since we dont know what y is, our final solution is
x = - \frac{2+y}{3} , y ∈ R
since this answer does not match the answer we are looking for, option C is not equivalent.  
finally, we must solve -4x + y = -5
the first step to solving this is to move the variable to the right side and change its sign
-4x = -5 - y
divide both sides of the equation by -4
x = 5/4 + y/4
now, write all the numerators above their common denominators 
x = 5 + y/4
since we dont know what y is, our answer is x = \frac{5+y}{4} , y ∈ R
since this is also not equivalent to <span>y + 5 = -3(x - 1), our only answer is option A.
let me know if you have any further questions 
:)</span>
5 0
2 years ago
The weekly incomes of a large group of executives are normally distributed with a mean of $2,000 and a standard deviation of $10
cestrela7 [59]

Let X be the weekly incomes of a large group of executives. The weekly incomes of a large group of executives follows Normal distribution with mean $2000 and standard deviation $100.

μ =2000, σ =100

We have to find z score for income $2100 i.e x=2100

Z = \frac{x-mean}{standard deviation}

= \frac{2100 - 2000}{100}

Z = 100/100

Z = 1

The z score for income $2100 is 1

6 0
3 years ago
Write 21/4 as a decimal. Round to three decimal places
Nadusha1986 [10]

5.250

To change a fraction to a decimal fraction divide the numerator by the denominator.

that is 21 ÷ 4 = 5.250 ( to 3 decimal places )


5 0
3 years ago
Read 2 more answers
What is the value of x to the nearest tenth? A 14. B 14.4. C 13.5. D 13.2
Ivan

Answer:

x=13.5

Step-by-step explanation:

sin 48 = opposite/ hypotenuse

sin 48 = 10/x

multiply by x on each side

x sin 48 =10

divide by sin 48

x = 10/sin 48

x = 13.456

round to the nearest tenth

13.5

3 0
3 years ago
Read 2 more answers
Select the correct answer from the drop down menu. with references to the figure, sin x =
Lubov Fominskaja [6]

Answer:

.894

Step-by-step explanation:

First thing to do is to solve for the height of the triangle, BD.  That's easy.  We have the length of the hypotenuse and the base, so Pythagorean's Theorem gives us that the height is 8.003255588 which rounds nicely to 8.  Now you have to call on the fond memories you have of the geometric mean in right triangles to solve the rest.  For the sin of x you need the hypotenuse of that smaller right triangle on the left, side AB.  First let's use geometric mean to find AD.  The formula for that, now that we know the height, is

BD^2=(AD)(DC)

Filling that in with numbers we have

8^2=(AD)16 and

64 = 16(AD).  Solve for AD to get that AD has a length of 4.  Now we know two of the three sides in that smaller triangle on the left and can solve for the hypotenuse.

8^2+4^2=c^2 and

64+16=c^2 so

c=√80 which simplifies to 4√5.  That means that the sin ratio for x is

\frac{8}{4\sqrt{5} }

which divides out to .894

6 0
3 years ago
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