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dybincka [34]
3 years ago
9

Three consecutive numbers are such that when they are taken in increasing order and multiplied by 2,3and 4 respectively, they ad

d up to 74. Find these numbers.
Mathematics
1 answer:
Ivenika [448]3 years ago
3 0

Answer:

7 , 8 , 9

Step-by-step explanation:

Assume three consecutive number are,

x , (x+1) , (x+2)

Multiplied by 2 ,3 and 4 respectively

2x , 3(x + 1) , 4(x + 2)

Sum of all = 74

So,

2x + 3(x + 1) + 4(x + 2) = 74

2x + 3x + 3 + 4x + 8 = 74

9x + 11 = 74

9x = 63

x = 7

So,

x , (x+1) , (x+2)

7 , (7+1) , (7+2)

7 , 8 , 9

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Which of the following is not equal to sin⁡(-230°)?
xenn [34]

From trigonometry we know that:

if sin(\theta)=sin(\alpha)

then, \theta=n\pi+(-1)^n\alpha (where n is an integer)

This can be rewritten in degrees as:

\theta=n(180^{\circ})+(-1)^n\alpha.............(Equation 1)

Now, in our case, \alpha=-230^{\circ}

Therefore, (Equation 1) can be written as:

\theta=n(180^{\circ})+(-1)^n(-230^{\circ})..........(Equation 2)

Now, to find the correct options all that we have to do is replace n by relevant integers and find the values of \theta that match.

For n=2, (Equation 2) gives us: \theta=2\times 180^{\circ}+(-1)^2(-230^{\circ})=360^{\circ}-230^{\circ}=130^{\circ}.

Thus, sin(230^{\circ})=sin(130^{\circ})

Now, we know that: -sin(-50^{\circ})=sin(50^{\circ})

Let n=-1, then:

\theta=(-1)\times 180^{\circ}+(-1)^{-1}(-230^{\circ})=-180^{\circ}+230^{\circ}=50^{\circ}

Thus, sin(-230^{\circ})=-sin(-50^{\circ})

Likewise, sin(-230^{\circ})=sin(50^{\circ})

Only the last option sin(-50^{\circ}) will never match sin(-230^{\circ}) because no integral value of n will ever give \theta=-50^{\circ}

Thus the last option is the correct option.

3 0
3 years ago
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Help with inequalities
max2010maxim [7]

Answer:

2(b - 9) \geqslant 26

Step-by-step explanation:

difference of a number and 9 means to subtract

b - 9

twice that means multiply by 2

2(b - 9)

at least is greater than or equal to

2(b - 9) \geqslant 26

8 0
3 years ago
Please help and explain why you got it right please
gtnhenbr [62]

Answer:

y+7 = -3 ( x-4)

Step-by-step explanation:

First find two points on the graph to find the slope

( 1,2) and ( 3,-4)

The slope is given by

m = ( y2-y1)/(x2-x1)

m = ( -4-2)/(3-1)

    = -6/2

    =-3

We can use the point slope form

y - y1 = m(x-x1)  where m is the slope and x1,y1 is a point on the line

We have two choices with a slope of -3

We can either use and x coordinate of -2 or 4

for  -2, the y coordinate is not shown

for 4 , the y coordinate is -7

Using ( 4, -7) and m = -3

y--7 = -3( x- 4)

y+7 = -3 ( x-4)

4 0
3 years ago
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Juanita is 10 years old her father is 4 times older than her when Juanita is 30 how old will her father be explain how you got y
almond37 [142]

answer: 60

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40-10=30

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8 0
3 years ago
Teddy uses 2.5 gallons of ice to fill 4 buckets. He needs to 30 buckets.how many gallons of ice will teddy need
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Answer:

18.75 gallons of ice

Step-by-step explanation:

I divided the 2.5 gallons of ice by the number of buckets (4) it filled to determine how many gallons of ice are in each bucket.

2.5 / 4 = 0.625

I then multiplied the amount of ice it takes to fill a bucket (0.625) by 30 buckets to get 18.75 gallons of ice.

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