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2 years ago

A side of the triangle below has been extended to form an exterior angle of 132 degrees. Find the value of x.

Mathematics

1 answer:

Lemur [1.5K]2 years ago

6 0

Answer:

48°

Step-by-step explanation:

m∠x plus 132° equals 180°, so x equals 180 minus 132, or 48°.

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The rectangle shown is dilated by a scale factor of 1/5

Harrizon [31]

Answer:

A'B'= 3 cm and B'D' = 1.6 cm

Step-by-step explanation:

First of all, we are told that the scale factor = 1/5

Now,we know that If the scale factor is less than 1, then the dilation is a reduction.

Thus, in this question the dilation is a reduction.

For us to calculate the dimensions of the dilated rectangle, we'll multiply the original dimensions by the scale factor

Thus;

A'B' = AB(1/5)

A'B' = 15(1/5) = 3 cm

B'D' = BD(1/5) = 8(1/5) = 1.6 cm

Thus, The length of each side of the dilated rectangle are;

A'B'= 3 cm and B'D' = 1.6 cm

5 0

3 years ago

Each year for 4 years, a farmer increased the number of trees in a certain orchard by of the number of trees in the orchard the

Neko [114]

Answer:

The number of trees at the begging of the 4-year period was 2560.

Step-by-step explanation:

Let’s say that x is number of trees at the begging of the first year, we know that for four years the number of trees were incised by 1/4 of the number of trees of the preceding year, so at the end of the first year the number of trees was $x+\frac{1}{4} x=\frac{5}{4} x$ , and for the next three years we have that

Start End

Second year $\frac{5}{4}x$ -------------- $\frac{5}{4}x+\frac{1}{4}(\frac{5}{4}x) =\frac{5}{4}x+ \frac{5}{16}x=\frac{25}{16}x=(\frac{5}{4} )^{2}x$

Third year $(\frac{5}{4} )^{2}x$ ------------- $(\frac{5}{4})^{2}x+\frac{1}{4}((\frac{5}{4})^{2}x) =(\frac{5}{4})^{2}x+\frac{5^{2} }{4^{3} } x=(\frac{5}{4})^{3}x$

Fourth year $(\frac{5}{4})^{3}x$ -------------- $(\frac{5}{4})^{3}x+\frac{1}{4}((\frac{5}{4})^{3}x) =(\frac{5}{4})^{3}x+\frac{5^{3} }{4^{4} } x=(\frac{5}{4})^{4}x.$

So the formula to calculate the number of trees in the fourth year is

$(\frac{5}{4} )^{4} x,$ we know that all of the trees thrived and there were 6250 at the end of 4 year period, then

$6250=(\frac{5}{4} )^{4}x$ ⇒ $x=\frac{6250*4^{4} }{5^{4} }= \frac{10*5^{4}*4^{4} }{5^{4} }=2560.$

Therefore the number of trees at the begging of the 4-year period was 2560.

7 0

3 years ago

What is FC in the figure?

Harlamova29_29 [7]

FC is median..

Median is a line from a vertex that equally divides the opposite side...
here FC divides DB therefore it is a median.....

HOPE IT HELPS YOU '_'

8 0

2 years ago

Read 2 more answers

If you were to plot a graph of the profit generated by this book, what would the slope and the y-intercept represent?

mojhsa [17]

What is the book? Show an image please.. I would love to help!

7 0

3 years ago

Read 2 more answers

X-y=6<br> 2x-3z=16<br> 2y+z=4<br><br> Solve the systems of equations.

Neko [114]

Answer:

Given System of equation:

x-y =6 .....,[1]

2x-3z = 16 ......[2]

2y+z = 4 .......[3]

Rewrite the equation [1] as

y = x - 6 .......[4]

Substitute the value of [4] in [3], we get

$2(x-6)+z = 4$

Using distributive property on LHS ( i.e, $a \cdot (b+c) =a \cdot b+ b \cdot c$ )

then, we have

2x - 12 +z =4

Add 12 to both sides of an equation:

2x-12+z+12=4+12

Simplify:

2x +z = 16 .......[5]

On substituting equation [2] in [5] we get;

2x+z=2x -3z

z = -3z

Add 3z both sides of an equation:

z+3z = -3z+3z

4z = 0

Simplify:

z = 0

Substitute the value of z = 0 in [2] to solve for x;

$2x-3(0) = 16$

2x = 16

Divide by 2 both sides of an equation:

$\frac{2x}{2} =\frac{16}{2}$

Simplify:

x= 8

Substitute the value of x =8 in equation [4] to solve for y;

y = 8-6 = 2

y = 2

Therefore, the solution for the given system of equation is; x = 8 , y = 2 and z =0

5 0

3 years ago