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3 years ago

Which value of x would make NO || Kj?

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

6 0

Answer:

$x = 8$

Step-by-step explanation:

Given

The attached figure

Required

Find x

To find x, we make use of the following equivalent ratios:

$LN : LO = NK:OJ$

This gives:

$(x-3) : (x - 4) = (x +2) : (x)$

Convert to fractions

$\frac{x-3}{x-4} = \frac{x+2}{x}$

Cross Multiply

$x(x-3) = (x-4)(x+2)$

Open brackets

$x^2-3x = x^2 -4x +2x - 8$

Collect Like Terms

$x^2 - x^2-3x +4x -2x =- 8$

$-3x +4x -2x =- 8$

$-1x =- 8$

$-x =- 8$

Multiply through by -1

$-1 * -x =- 8*-1$

$x = 8$

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The triangles in the image are similar. Solve for x. A) 7 B) 6 C) 10 D) 5

Natalka [10]

ANSWER

A) 7

EXPLANATION

The given triangles are similar

Hence the corresponding sides are in the same proportion.

$\frac{3x + 4}{30} = \frac{30}{36}$

Simplify the right hand side:

$\frac{3x + 4}{30} = \frac{5}{6}$

Cross multiply;

6(3x+4)=5×30

Expand

18x+24=180

18x=150-24

18x=126

$x = \frac{126}{18} = 7$

4 0

3 years ago

Which products result in a difference of squares? Select three options. (x minus y)(y minus x) (6 minus y)(6 minus y) (3 + x z)(

ValentinkaMS [17]

Answer:

Third option: $(3 + xz)(-3 + xz)$

Fourth option: $(y^2 - xy)(y^2 + xy)$

Sixth option: $(64y^2 + x^2)(-x^2 + 64y^2)$

Step-by-step explanation:

By definition, we can factor the Difference between two squares:

$a^2 - b^2 = (a+b)(a-b)$

In order to find which products results in a difference of squares, we need to check each option:

$1.\ (x - y)(y - x)=(x)(y)+(x)(-x)-(y)(y)+(-y)(-x)=xy-x^2-y^2+xy=-x^2-y^2+2xy$

The product does not result in a difference of squares.

$2.\ (6 - y)(6 - y)$

Since the signs are equal ( $-$ ), the product will not result in a difference of squares.

Using Distributive Property for the other options, we get:

$3.\ (3 + xz)(-3 + xz)=(3)(-3)+(3)(xz)+(xz)(-3)+(xz)(xz)=\\\\=-9+3xz-3xz+x^2z^2=x^2z^2-9=(xz)^2-(3)^2$

The product results in a difference of squares.

$4.\ (y^2 - xy)(y^2 + xy)=(y^2)(y^2)+(y^2)(xy)-(xy)(y^2)-(xy)(xy)=\\\\=y^4+xy^3-xy^3-x^2y^2=y^4-x^2y^2=(y^2)^2-(xy)^2$

The product results in a difference of squares.

$5.\ (25x - 7y)(-7y + 25x)=(25x - 7y)(25x - 7y)$

Since the signs are equal ( $-$ ), the product will not result in a difference of squares.

$6.\ (64y^2 + x^2)(-x^2 + 64y^2)=(64y^2 + x^2)(64y^2 - x^2)=\\\\=(64y^2)(-x^2)+(64y^2)(64y^2)+(x^2)(-x^2)+(x^2)(64y^2)=\\\\=-64y^2x^2+4096y^4-x^4+64y^2x^2=\\\\=4096y^4-x^4=(64y^2)^2-(x^2)^2$

The product results in a difference of squares.

5 0

3 years ago

Read 2 more answers

Suppose that Y1, Y2,..., Yn denote a random sample of size n from a Poisson distribution with mean λ. Consider λˆ 1 = (Y1 + Y2)/

Burka [1]

Answer:

The answer is " $\bold{\frac{2}{n}}$ ".

Step-by-step explanation:

considering $Y_1, Y_2,........, Y_n$ signify a random Poisson distribution of the sample size of n which means is λ.

$E(Y_i)= \lambda \ \ \ \ \ and \ \ \ \ \ Var(Y_i)= \lambda$

Let assume that,

$\hat \lambda_i = \frac{Y_1+Y_2}{2}$

multiply the above value by Var on both sides:

$Var (\hat \lambda_1 )= Var(\frac{Y_1+Y_2}{2} )$

$=\frac{1}{4}(Var (Y_1)+Var (Y_2))\\\\=\frac{1}{4}(\lambda+\lambda)\\\\=\frac{1}{4}( 2\lambda)\\\\=\frac{\lambda}{2}\\$

now consider $\hat \lambda_2$ = $\bar Y$

$Var (\hat \lambda_2 )= Var(\bar Y )$

$=Var \{ \frac{\sum Y_i}{n}\}$

$=\frac{1}{n^2}\{\sum_{i}^{}Var(Y_i)\}\\\\=\frac{1}{n^2}\{ n \lambda \}\\\\=\frac{\lambda }{n}\\$

For calculating the efficiency divides the $\hat \lambda_1 \ \ \ and \ \ \ \hat \lambda_2$ value:

Formula:

$\bold{Efficiency = \frac{Var(\lambda_2)}{Var(\lambda_1)}}$

$=\frac{\frac{\lambda}{n}}{\frac{\lambda}{2}}\\\\= \frac{\lambda}{n} \times \frac {2} {\lambda}\\\\ \boxed{= \frac{2}{n}}$

8 0

3 years ago

[-3 1/4] greater or less than [-4]

Afina-wow [57]

Step-by-step explanation:

-3¼ is greater than -4

hope that helps you ;)

7 0

3 years ago

Read 2 more answers

The ratio 3:4:5:7 represents the ratio of apples to oranges to melons to grapefruit used to make a fruit salad. If you need 38 c

inessss [21]

Answer:

Step-by-step explanation:

3:4:5:7 added up is 19 so doubling it is-

6:8:10:14 =38

Hope this helps!

7 0

3 years ago