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melamori03 [73]
3 years ago
14

Sharon is decreasing the size of a diagram of a leaf that is 30 centimeters long by 10 centimeters wide. If the reduced diagram

is 4 centimeters wide, how long will it be?
Mathematics
1 answer:
ivanzaharov [21]3 years ago
5 0
10 : 30
4: x [x is the length]
10/4=2.5
30/2.5=x=12
length of the diagram is 12cm

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identify an equation in the point-slope form for the line parallel to y=1/2 x -7 that passes through (-3,-2)
Mariulka [41]

Answer:

Step-by-step explanation:

hello :

note :

Use the point-slope formula.

y - y_1 = m(x - x_1)   when : x_1= -3      y_1= -2         m= 1/2(parallel means same slope)

an equation in the point-slope form is : y +2 = 1/2(x+3)

3 0
3 years ago
Twice the greater of two consecutive odd intergers is 13 less than three times the lesser. Find the intergers ​
erastova [34]

Answer:

\large\boxed{15, 16}

Step-by-step explanation:

2 consecutive integers represented as variables:

x, x + 1

Greater one: x + 1

Lesser one: x

Write as an equation

2(Greater) + 13 = 3(Lesser)

Substitute in known values

2(x + 1) + 13 = 3(x)

Multiply

2x + 2 + 13 = 3x

Subtract 2x from both sides of the equation

2 + 13 = x

Add 2 + 13 to simplify

x = 15

Lesser = x = 15

Greater = x + 1 = 15 + 1 = 16

\large\boxed{15, 16}

Hope this helps :)

3 0
3 years ago
The mode and median of the data set below have the same value. What is the missing number?
Maru [420]
10 ! (To find the median add the two middle numbers 7,13 = 20 divide 20 by two and you get 10 as your median. Mode means the most common number which means the mode is also 10)
5 0
3 years ago
One angle of a triangle measures <img src="https://tex.z-dn.net/?f=10degrees" id="TexFormula1" title="10degrees" alt="10degrees"
iVinArrow [24]

Answer:

One\ angle: 35^o\\Second\ angle: 25^o\\Third\ angle: 120^o

Step-by-step explanation:

Let

x ----> the measure of one angle of the triangle

y ---> the measure of the second angle

z ----> the measure of the third angle

we know that

The sum of the measure of the interior angles in any triangle must be equal to 180 degrees

x+y+z=180^o -----> equation A

One angle of a triangle measures  10 degrees more than the second

x=y+10 ----> equation B

The measure of the third angle is twice the sum of the first two angles

z=2(x+y) ---> equation C

substitute equation B in equation C

z=2(y+10+y)

z=4y+20 ----> equation D

substitute equation D and equation B in equation A

(y+10)+y+(4y+20)=180^o

solve for y

6y=180-30\\6y=150\\y=25^o

Find the value of x

x=25+10=35^o

Find the value of z

z=4(25)+20=120^o

therefore

One\ angle: 35^o\\Second\ angle: 25^o\\Third\ angle: 120^o

5 0
3 years ago
Find the equation of the directrix of the parabola x2=+/- 12y and y2=+/- 12x
PIT_PIT [208]

Answer:

  1. x^2 = 12 y equation of the directrix y=-3
  2. x^2 = -12 y equation of directrix y= 3
  3. y^2 = 12 x   equation of directrix x=-3
  4. y^2 = -12 x equation of directrix x= 3

Step-by-step explanation:

To find the equation of directrix of the parabola, we need to identify the axis of the parabola i.e, parabola lies in x-axis or y-axis.

We have 4 parts in this question i.e.

  1. x^2 = 12 y
  2. x^2 = -12 y
  3. y^2 = 12 x
  4. y^2 = -12 x

For each part the value of directrix will be different.

For x²  = 12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = -a

So, we need to find the value of a.

The general form of equation for y-axis parabola having positive co-efficient is:

x² = 4ay  eq(i)

and our equation in question is: x² = 12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

4ay = 12y

a= 12y/4y

a= 3

Putting value of a in equation of directrix: y = -a => y= -3

The equation of the directrix of the parabola x²= 12y is y = -3

For x²  = -12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = a

So, we need to find the value of a.

The general form of equation for y-axis parabola having negative co-efficient is:

x² = -4ay  eq(i)

and our equation in question is: x² = -12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

-4ay = -12y

a= -12y/-4y

a= 3

Putting value of a in equation of directrix: y = a => y= 3

The equation of the directrix of the parabola x²= -12y is y = 3

For y²  = 12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = -a

So, we need to find the value of a.

The general form of equation for x-axis parabola having positive co-efficient is:

y² = 4ax  eq(i)

and our equation in question is: y² = 12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

4ax = 12x

a= 12x/4x

a= 3

Putting value of a in equation of directrix: x = -a => x= -3

The equation of the directrix of the parabola y²= 12x is x = -3

For y²  = -12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = a

So, we need to find the value of a.

The general form of equation for x-axis parabola having negative co-efficient is:

y² = -4ax  eq(i)

and our equation in question is: y² = -12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

-4ax = -12x

a= -12x/-4x

a= 3

Putting value of a in equation of directrix: x = a => x= 3

The equation of the directrix of the parabola y²= -12x is x = 3

5 0
3 years ago
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