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3 years ago

Find the area of each trapezoid. Round to the nearest tenth if necessary.

Mathematics

1 answer:

Katarina [22]3 years ago

3 0

The equation to find the area of a trapezoid is, A=(base1+base2)xHeight/2

1) (5+23)x12/2= 168

2) (1.1+3.4)x2/2= 4.5

3)(17.75+10.25)x8/2= 112

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Solve for x given that QRST is a rhombus.

AVprozaik [17]

$\bold{\huge{\underline{ Solution }}}$

<h3>Given :-</h3>

We have given Rhombus QRST
The measurement of two sides of rhombus that is ( 6x - 5 ) and ( 4x + 13).

We have to find the value of x

<h3>Let's Begin :-</h3>

Here, We have 

Rhombus QRST

We know that,

All sides of rhombus are equal
Opposite sides of rhombus are parallel to each other

Therefore, 

From the figure, we can conclude that :-

$\bold{ 6x - 5 = 4x + 13 }$

$\sf{ 6x = 4x + 13 + 5 }$

$\sf{ 6x - 4x = 13 + 5 }$

$\sf{ 2x = 18 }$

$\sf{ x = }{\sf{\dfrac{18}{2}}}$

$\bold{ x = 9 }$

Hence, The value of x is 9 .

<h3>The measurement of the sides of rhombus QRST :- </h3>

Length of side QR

$\sf{ = 6x - 5 }$

$\sf{ = 6(9) - 5 }$

$\sf{ = 54 - 5 }$

$\bold{ = 49 }$

Length of side RS

$\sf{ = 4x + 13 }$

$\sf{ = 4(9) + 13 }$

$\sf{ = 36 + 13 }$

$\bold{ = 49 }$

From above we can say that,

All sides of rhombus are equal.

<h3>Some more properties of rhombus </h3>

Opposite angles of rhombus are equal
Diagonals of rhombus bisect each other at 90°
Diagonals of rhombus also bisect the side angles of rhombus
Rhombus is a quadrilateral, so the sum of interior angles of rhombus are 360°
Whereas, The sum of the adjacent angles of rhombus are 180°.
All rhombus are parallelogram but all parallelograms are not rhombus .

5 0

2 years ago

PLS HELP WILL MARK YOU BRAINLIEST!! No fake answers pls

aleksklad [387]

Answer:

so as a result b, d is an example of linear inequality

Step-by-step explanation:

a. cant be done so not a linear inequality

b. x<2/7

c.x=12/11 but it has "=", so not a linear inequality; it becomes a linear equation

d. x<(2-3y)/4

5 0

3 years ago

Read 2 more answers

If there are 3 parts to a circle one is 2/7 and the other is 1/3 what is the 3rd shaded area

harina [27]

So first we start off multiplying 3 • 7 to find a common denominator and you get 21. Then because you technically multiplied 3 by 7 you also have to multiply 1 by 7! you instead of 1/3 you have 7/21! do the similar thing to 2/7 but instead of multiplying it by 7 you use 3 so for this one instead of 2/7 it’s 6/21! add the two fractions together and get 13/21! subtract 13 from 21 to see what the remaining fraction is and your answer is 8/21! hope this helps!!

6 0

3 years ago

TEMA: 1.1 Multiplicación de monomio por binomio 1. Dibuja el rectángulo formado por las siguientes expresiones algebraicas y enc

azamat

Answer:

Step-by-step explanation:

isisisisisisisisisisid

8 0

3 years ago

Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

kondor19780726 [428]

Answer:

The equation of the regression line is:

$y~=~234.56158 ~-~ 2.95835 \cdot x$

Step-by-step explanation:

The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It’s called a “least squares” because the best line of fit is one that minimizes the variance.

We have the following data:

$\begin{array}{c|ccccccccc}X&50&55&50&79&44&37&70&45&49\\Y&152&48&22&35&43&171&13&185&25\end{array}$

To find the line of best fit for the points:

Step 1: Find $X\cdot X$ and $X\cdot Y$ as it was done in the table

Step 2: Find the sum of every column:

$\sum{X} = 479 ~,~ \sum{Y} = 694 ~,~ \sum{X \cdot Y} = 32784 ~,~ \sum{X^2} = 26897$

Step 3: Use the following equations to find a and b:

$\begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 694 \cdot 26897 - 479 \cdot 32784}{ 9 \cdot 26897 - 479^2} \approx 234.56158 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 9 \cdot 32784 - 479 \cdot 694 }{ 9 \cdot 26897 - \left( 479 \right)^2} \approx -2.95835\end{aligned}$

Step 4: Assemble the equation of a line

$\begin{aligned} y~&=~a ~+~ b \cdot x \\y~=~234.56158 ~-~ 2.95835\cdot x\end{aligned}$

The graph of the regression line is:

5 0

4 years ago