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3 years ago

A quadrilateral has all sides congruent, opposite sides are parallel, and opposite angles are congruent.

Mathematics

1 answer:

VashaNatasha [74]3 years ago

4 0

Answer:

B: A square

Step-by-step explanation:

Let's use the process of elimination:

We know that each shape here has opposite parallel sides so there's not much we can do about that one.

All sides congruent automatically gets rid of A.) Rectangle and C.) Parallelogram because they do not always have congruent sides

Opposite angles are congruent gets rid of D.) Rhombus. Although a rhombus can have all congruent angles, it isn't always congruent the way a square is. The definition of a rhombus is a quadrilateral with equal side lengths. Not angles.

So the only shape that meets each criteria all the time is a square.

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Three years hence a father will four times as old as his son will be. Before two years he was seven times as old as his son was.

myrzilka [38]

Answer: The father is 37 years and the son is 7 years

Step-by-step explanation:

Let x represent the present age of the father.

Let y represent the present age of the son.

Three years hence a father will four times as old as his son will be. This means that

x + 3 = 4(y + 3)

x + 3 = 4y + 12

x - 4y = 12 - 3

x - 4y = 9- - - - - - - - - - - - - - - -1

Before two years he was seven times as old as his son was. This means that

(x - 2) = 7(y - 2)

x - 2 = 7y - 14

x - 7y = - 14 + 2

x - 7y = - 12- - - - - - - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

3y = 21

y = 21.3 = 7

Substituting y = 7 into equation 1, it becomes

x - 4 × 7 = 9

x - 28 = 9

x = 9 + 28

x = 37

7 0

3 years ago

Read 2 more answers

-6(1+7x)+7(1+6x)=-2

-BARSIC- [3]

-6(1+7x)+7(1+6x)=-2

This is False.

Use distributive property:

-6 -42x + 7 +42x = -2

Combine like terms to get:

1 = -2

Since 1 is not -2, it is false.

8 0

4 years ago

Find x. 300 043 00. 083 08 00 02 V3

____ [38]

Answer:

Therefore the value of x is 8 unit.

Step-by-step explanation:

Given:

In Right Angle Triangle ABC

angle B = 90°

angle C = 30°

AB = 4

To Find:

AC = Hypotenuse = ?

Solution:

In Right Angle Triangle ABC Sine Identity we have

$\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\$

Substituting the given values we get

$\sin 30 = \frac{AB}{AC}$

$\dfrac{1}{2} =\dfrac{4}{x}\\\\\therefore x=4\times 2=8\\\\\therefore x =8$

Therefore the value of x is 8 unit.

3 0

3 years ago

A researcher wants to estimate the true proportion of people who would buy items they know are slightly defective from thrift sh

belka [17]

Answer: 0.283

Step-by-step explanation:

Formula to find the lower limit of the confidence interval for population proportion is given by :-

$\hat{p}- z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

, where $\hat{p}$ = sample proportion.

z* = Critical value

n= Sample size.

Let p be the true proportion of people who would purchase a defective item.

Given : Sample size = 993

Number of individuals would buy a slightly defective item if it cost less than a dollar = 305

Then, sample proportion of people who would purchase a defective item:

$\hat{p}=\dfrac{305}{993}\approx0.307$

Critical value for 90% confidence interval = z*=1.645 (By z-table)

The lower bound of a 90% confidence interval for the true proportion of people who would purchase a defective item will become

$0.307-(1.645)\sqrt{\dfrac{0.307(1-0.307)}{993}}$

$0.307- (1.645)\sqrt{0.000214250755287}$

$0.307- 0.024078369963=0.282921630037\approx0.283$ [rounded to the nearest three decimal places.]

Hence, the lower bound of a 90% confidence interval for the true proportion of people who would purchase a defective item.= 0.283

8 0

3 years ago

Help me pleaseeee this is due at 8 am

Yuliya22 [10]

Answer:

Area = B x H + L (sum of sides of triangle)

= 9 x 12 + 10 (12 + 15 + 9)

= 108 + 360

= $468in^2$

Either your options are wrong or question is to find lateral surface.

Lateral Surface area = ( a + b + c) x H , where a, b , c are sides of the triangle.

Lateral Surface Area = (12 + 15 + 9) x 10

= $360in^2$

8 0

3 years ago