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3 years ago

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One month, Ruby worked 6 hours more than isaac, and Svethlana worked 4 times as many hours as Ruby. Together they worked 126 hou

rs. How many hours did each person work?

1 answer:

stepladder [879]3 years ago

4 0

63.............................................

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On a coordinate plane, a line has points (negative 2, negative 4) and (4, 2). Point P is at (0, 4). Which points lie on the line

NikAS [45]

Answer:

the correct options are:

(–1, 3), (–2, 2) and (–5, –1)

Step-by-step explanation:

Given that a line passes through two points

A(-2, -4) and B(4, 2)

Another point P(0, 4)

To find:

Which points lie on the line that passes through P and is parallel to line AB ?

Solution:

First of all, let us the find the equation of the line which is parallel to AB and passes through point P.

Parallel lines have the same slope.

Slope of a line is given as:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{2-(-4)}{4-(-2)} = 1$

Now, using slope intercept form ( $y = mx+c$ ) of a line, we can write the equation of line parallel to AB:

$y =(1)x+c \Rightarrow y = x+c$

Now, putting the point P(0,4) to find c:

$4 = 0 +c \Rightarrow c = 4$

So, the equation is $\bold{y=x+4}$

So, the coordinates given in the options which have value of y coordinate equal to 4 greater than x coordinate will be true.

So, the correct options are:

(–1, 3), (–2, 2) and (–5, –1)

8 0

2 years ago

Read 2 more answers

Calculate the value of the exterior angle

aev [14]

What we know is that the sum of a triangle's internal angles are 180º, and a straight angle makes 180º.

first, we have to find the third internal angle(let's call it n) so that we can use it to find the exterior angle.

(3x + 20) + (4x + 5) + n = 180

simplify:

7x + 25 + n = 180

7x + n = 155

n = 155 - 7x

Now we can add it to the external angle to find x.

(155 - 7x) + (8x + 15) = 180

simplify:

170 + 8x - 7x = 180

170 + x = 180

x = 10

Now we can substitute it to the external angle.

8 x 10 + 15 = 95

the exterior angle is 95º.

8 0

3 years ago

there are six blades on each windmill. How many total blades are on seven windmills? Use a fives fact to solve.plzzz help me plz

astra-53 [7]

Well 6*7 = 42 .....//...

6 0

3 years ago

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State the solution to the equations f(x) and g(x).

Digiron [165]

Answer:

x = -1

Step-by-step explanation:

f(x) = g(x) when x = -1

3 0

2 years ago

Read 2 more answers

A standard oil drum is a cylinder with a volume of approximately 218.276 liters (or 0.218276 cubic meters). The cost of producin

Arte-miy333 [17]

Answer:

r = 2,85 feet

h = 8,56 feet

Step-by-step explanation:

Area of two circular caps (m ^(2)) : 2* pi* r^(2) (where r is the radius of circular cap) Area of wall (m ^(2)) is 2*pi*r*h (where h is the height of drum)

V= pi*r^(2)*h so h=V/pi*r^(2) (1)

Cost in $:

Cost of wall 25 $/m^(2) plus 10% for manufacturing so:

C(w) = 27,5*2*pi*r*h $/square feet

Cost of (both top and bottom cap) = 2*40,97*pi* r^(2) so:

C(caps) = 257,29* r^(2) $/squaer feet

Total cost of cylnder = cost of wall + cost of caps

Total cost f cylinder: F(c)= 55*pi*r*h+257,29* r^(2)

F(c) = 172,7*r*h + 257,29*r^(2) F(c) is F(r)

Since from (1) we have h=218,276/pi*r^(2)

F(r) = (172,7)*r*(69,514)/r^(2) +257,29*r^(2) F(c) = 12005/r + 257,29*r^(2)

Taken the first dervative

F´(r)= -12005*(1)/r^(2) +2*257,29*r F´(r) = -12005*(1)/r^(2) +514,58*r

f F´(r) = 0 -12005*(1)/r^(2) + 514,58*r =0

-120005 + 514,58*^(3) = 0 514,58*^(3) = 12005 r =cubic root (23,32)

r = 2,85 ft

if we replace this value en F(r) we can see F(r) tend to infinite both when r tend to 0 and when r tends to infnite so there is a minimun for the functon

r = 2,85 ft and h = 8,56 ft

5 0

3 years ago