All categories

3 years ago

Each pair of polygons below is similar. Find the value of x. Some answers may be decimals.

Mathematics

2 answers:

sergiy2304 [10]3 years ago

7 0

Answer:

The answer to your question is below.

Step-by-step explanation:

14.- Use proportions to solve these problems.

$\frac{x + 6}{10} = \frac{x + 9}{14}$

14(x + 6) = 10(x + 9)

14x + 84 = 10x + 90

14x - 10x = 90 - 84

4x = 6

x = 6/4

x = 3/2

15.- $\frac{x - 1}{8} = \frac{x + 2}{10}$

10(x - 1) = 8(x + 2)

10x - 10 = 8x + 16

10x - 8x = 16 + 10

2x = 26

x = 26 / 2

x = 13

16.- $\frac{x + 1}{9} = \frac{10/3}{5}$

5(x + 1) = 9(10/3)

5x + 5 = 30

5x = 30 - 5

5x = 25

x = 25 / 5

x = 5

Elina [12.6K]3 years ago

5 0

Answer:

B C A D

Step-by-step explanation:

You might be interested in

Write an algebraic expression for the word expression. the sum of 1 and a number x The expression is

Anna11 [10]

Answer:

1+x

Step-by-step explanation:

sum means the answer for addition so I know I use an addition sign and add 1+x

3 0

3 years ago

Read 2 more answers

Which is an equation of the parabola that intersects the x-axis at points (-1, 0) and (3, 0)? Show your work or explain how you

hichkok12 [17]

Answer:

$\displaystyle \large{y=x^2-2x-3}$

Step-by-step explanation:

The given points are (-1,0) and (3,0) to find an equation of parabola. Notice that they say or the given points are x-intercepts, which means they make it easier for us to find an equation of parabola using these x-intercepts.

Quick Note:

x-intercepts are simply the roots or solutions of quadratic equation, so if our root is x = -2 then we can write as (-2,0) and write back to x+2=0.

So what we are going to do is to write the roots’ equation back as $\displaystyle \large{x+\alpha =0}$

Our points or roots are given, therefore:

If x = -1 then x+1=0

If x = 3 then x-3=0

Then multiply x+1 with x-3 because if (x-1)(x+3)=0 then x-1=0 or x+3=0:

$\displaystyle \large{(x+1)(x-3)=0}$

Convert 0 to y since we want to find a function:

$\displaystyle \large{(x+1)(x-3)=y}\\\displaystyle \large{y=(x+1)(x-3)}$

Expand the expressions in and simplify to standard form:

$\displaystyle \large{y=x^2-3x+x-3}\\\displaystyle \large{y=x^2-2x-3}$

Therefore, the equation is $\displaystyle \large{y=x^2-2x-3}$

__________________________________________________________

Summary

If we are given the points $\displaystyle \large{(\alpha ,0)}$ and $\displaystyle \large{(\beta ,0)}$ with wideness of the graph or a-value = 1 then the parabola equation is:

$\displaystyle \large{y=(x-\alpha )(x-\beta )}\\\displaystyle \large{y=x^2-\beta x-\alpha x+\alpha \beta }\\\displaystyle \large{y=x^2-(\beta +\alpha )x+\alpha \beta }$