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3 years ago

11

If ONE PAIR of opposite sides of a quadrilateral are BOTH parallel and congruent, the quadrilateral is a parallelogram. a TRUE b

FALSE

2 answers:

givi [52]3 years ago

8 0

Answer:

a. TRUE.

Step-by-step explanation:

If the pair of opposite sides are both parallel and congruent, the other two sides will have to fit in between the two lines. That will make the other two sides both parallel and congruent, so the quadrilateral is a parallelogram.

FrozenT [24]3 years ago

8 0

Answer:

a. True

Step-by-step explanation:

A parallelogram is a quadrilateral. A parallelogram has two pairs of opposite parallel sides. The opposite parallel sides are equal in length and are congruent.

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-5(6 +x)<br> Using distributed property

UkoKoshka [18]

Answer: -30 -5x

Step-by-step explanation:

(-5 times 6) = -30

(-5 times x)= -5x

you could write it as -30 + -5x or -30 -5x it’s the same thing

7 0

3 years ago

Read 2 more answers

Consider two functions f and g on [1, 8] such that integral^8_1 f(x) dx = 9, integral^8_1 g(x) dx = 5, integral^8_5 f(x) dx = 4,

Gelneren [198K]

I'll abbreviate the definite integral with the notation,

$I(f(x),a,b)=\int_a^bf(x)\,\mathrm dx$

We're given

$I(f,1,8)=9$
$I(g,1,8)=5$
$I(f,5,8)=4$
$I(g,1,5)=3$

Recall that the definite integral is additive on the interval $[a,b]$ , meaning for some $c\in[a,b]$ we have

$I(f,a,b)=I(f,a,c)+I(f,c,b)$

The definite integral is also linear in the sense that

$I(kf+\ell g,a,b)=kIf(a,b)+\ell I(g,a,b)$

for some constant scalars $k,\ell$ .

Also, if $a\ge b$ , then

$I(f,a,b)=-I(f,b,a)$

a. $I(2f,1,5)=2I(f,1,5)=2(I(f,1,8)-I(f,5,8))=2(9-4)=\boxed{10}$

b. $I(f-g,1,8)=I(f,1,8)-I(g,1,8)=9-5=\boxed{4}$

c. $I(f-g,1,5)=I(f,1,5)-I(g,1,5)=\dfrac{I(2f,1,5)}2-I(g,1,5)=10-3=\boxed{7}$

d. $I(g-f,5,8)=I(g,5,8)-I(f,5,8)=(I(g,1,8)-I(g,1,5))-I(f,5,8)=(5-3)-4=\boxed{-2}$

e. $I(7g,5,8)=7I(g,5,8)=7(5-3)=\boxed{14}$

f. $I(3f,5,1)=3I(f,5,1)=-3I(f,1,5)=-\dfrac32I(2f,1,5)=-\dfrac32(10)=\boxed{-15}$

4 0

3 years ago

What is the volume of the prism ?

galina1969 [7]

Answer:

Your answer is 150 units!

8 0

2 years ago

Read 2 more answers

Suppose that the IQs of university A's students can be described by a normal model with mean 150150 and standard deviation 77 p

NeX [460]

Answer:

The probability that the student's IQ is at least 140 points is of 55.17%.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

University A: $\mu = 150, \sigma = 77$

a) Select a student at random from university A. Find the probability that the student's IQ is at least 140 points.

This is 1 subtracted by the pvalue of Z when X = 140. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{140 - 150}{77}$

$Z = -0.13$

$Z = -0.13$ has a pvalue of 0.4483.

1 - 0.4483 = 0.5517

The probability that the student's IQ is at least 140 points is of 55.17%.

3 0

3 years ago

Urgent ASAP!! Imagine math

Paraphin [41]

Answer:

Graph A = 20miles/gallon

Graph B = 20

Step-by-step explanation:

For graph A, to find the change you will need to choose two points from the graph (the easier the better)

So for example, I've chosen 40miles-2gallons (2, 40) and point 0 (0, 0)

Now you will need to remember the slope formula which is:

$m=\frac{y_2-y_1}{x_1-x_2}$

so your point (x1, y1) will be (0, 0)

and point (x2, y2) will be (2, 40)

so $m=\frac{40-0}{2-0}$

which is $m=\frac {40}{2} = 20$

and so you get that the slope will be 20 miles/gallon

For graph B, what they want you to see is that change of y/change of x means the same as change of miles/change of gallons since x is the gallons and y is the miles.

8 0

3 years ago