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3 years ago

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One serving of a certain brand of yogurt contains 7g of fat. The low-fat version contains 38.25% less fat per serving. How man

y grams of fat does one serving the low-fat yogurt contain?

1 answer:

Dafna1 [17]3 years ago

6 0

Answer:

7g-100%

x-38,25

38,25*7:100=2,6775g

7g-2,6775g=4,4325g

Step-by-step explanation:

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In a triangle ABC, measure of angle B is 90 degrees. AB is 3x-2 units and BC is x+3. If the area of the triangle is 17 sq cm, fo

Scorpion4ik [409]

Answer:

$x=\frac{8}{3}\ cm$

Step-by-step explanation:

we know that

The area of the right triangle ABC is equal to

$A=\frac{1}{2}(AB)(BC)$

we have

$A=17\ cm^2$

$AB=(3x-2)\ cm$

$BC=(x+3)\ cm$

substitute the values

$17=\frac{1}{2}(3x-2)(x+3)$

$34=(3x-2)(x+3)$

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$3x^2+7x-40=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$3x^2+7x-40=0$

so

$a=3\\b=7\\c=-40$

substitute in the formula

$x=\frac{-7(+/-)\sqrt{7^{2}-4(3)(-40)}} {2(3)}$

$x=\frac{-7(+/-)\sqrt{529}} {6}$

$x=\frac{-7(+/-)23} {6}$

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$x=\frac{-7(-)23} {6}=-5$

therefore

The solution is

$x=\frac{8}{3}\ cm$

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3 years ago

the graph shows the speed of a vehicle during the final 50 seconds of a journey at the start of the 50 seconds the speed is k me

Simora [160]

Answer:

a) 27 m/s

b) 30 m/s

c) i) 3

ii) Deceleration

Step-by-step explanation:

The question is not complete, the correct question is given as:

The graph shows information about the speed of a vehicle during the final 50 seconds of a journey. At the start of the 50 seconds the speed is k metres per second. The distance travelled during the 50 seconds is 1.35 kilometres.

(a) Work out the average speed of the vehicle during the 50 seconds

(b) Work out the value of k.

(c) (i) Calculate the gradient of the graph in the final 10 seconds of the journey

(ii) Describe what this gradient represents

Answer:

The graph is attached. The total time = 50 seconds, total distance = 1.35 km = 1350 m

a) The average speed is the ratio of the total distance traveled to the total time taken to cover this distance. The average speed is given by the formula:

$Average \ speed=\frac{total\ distance}{total\ time}\\ Substituting: \\ Average \ speed=\frac{1350\ m}{50\ s} = 27\ m/s$

b) From the graph, the total distance covered is the area of the graph. The graph is made up of a rectangle and triangle, the area of the graph is equal to the sum of area of rectangle and area of triangle.

$Total \ distance=Total\ area=Area\ of \ rectangle+Area\ of \ triangle\\Total \ distance=(length *breadth)+\frac{1}{2}base*height\\1350 \ m=(40*k)+0.5*10*k\\1350=40k+5k\\45k=1350\\k=1350/45\\k=30\ m/s$ c) i) The gradient in the last 10 seconds is the ratio of change in speed to change in time

$Gradient=\frac{change\ in\ speed }{change\ in\ time}=\frac{0-k}{50-40} \\ bt \ k=30\\Gradient=\frac{0-30}{50-40}= \frac{-30}{10} =-3$

ii) Since the gradient is negative it means it is deceleration. That is in the in the last 10 seconds the vehicle decelerates at a rate of 3 m/s²

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3 years ago