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3 years ago

Vertical angles must:Check all that apply. A.be complementary. B.be acute. C.have the same vertex. D.be congruent.

1 answer:

3 0

<span>Vertical angles must be C and D

A.be complementary. They are not always complementary, to be complementary means having a sum of 90 deg
B.be acute. - Vertical angles can be NOT acute depending on how they are positioned and intersected with the lines.

Answer
C.have the same vertex.
D.be congruent.</span>

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Five less than half of a number in a equation

Sholpan [36]

It would be .5x-5= because it says 5 less so it would be subtract 5 from half of x.

7 0

2 years ago

A rectangle has a length that is 7 inches less that twice it's width. The area of the rectangle is 72 square inches. Write an eq

Nitella [24]

Answer: $2x^2-7x=72$ , where x= width of the rectangle ( in inches).

Step-by-step explanation:

Let x= width of the rectangle ( in inches).

Then its length = 2x-7 ( in inches).

Area of rectangle = Length × width

= (2x-7) × (x)

= 2x × x -7 ×x

= 2x²-7x

The area of the rectangle is 72 square inches.

$\Rightarrow\ 2x^2-7x=72$

Hence, the equation that represents the given situation :

$2x^2-7x=72$

7 0

3 years ago

Limit as x approaches 9 of x^2 -81/sqrt of x - 3

Ipatiy [6.2K]

Answer:

108

Step-by-step explanation:

Limit as x approaches 9 of x^2 -81/sqrt of x - 3

First substitute x into the expression

= 9²-81/√9 - 3

= 81-81/3-3

= 0/0 (indeterminate)

Apply l'hospital rule

= lim x -> 9 d/dx(x²-81)/√x - 3

= lim x -> 9 2x/1/2√x

Substitute x = 9

= 2(9)/1/2√9

=18/1/(2(3)

=18 × 6/1

= 108

Hence the limit of the function is 108

7 0

3 years ago

The Insure.com website reports that the mean annual premium for automobile insurance in the United States was $1,503 in March 20

stira [4]

Answer:

a) Option A)

$H_{0}: \mu \geq 1503\\H_A: \mu < 1503$

b) Point estimate of difference = -78

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $1,503

Sample mean, $\bar{x}$ = $1,425

Sample size, n = 25

Sample standard deviation, s = $160

We have to carry a hypothesis test that the mean annual premium in Pennsylvania is lower than the national mean annual premium.

a) First, we design the null and the alternate hypothesis

$H_{0}: \mu \geq 1503\text{ dollars}\\H_A: \mu < 1503\text{ dollars}$

b) Point estimate of the difference between the mean annual premium in Pennsylvania and the national mean

Point estimate of difference =

Mean annual premium in Pennsylvania - National mean

$\text{Point estimate} = \bar{x} - \mu = 1425 - 1503 = -78$

Thus,

Point estimate of difference = -78

5 0

3 years ago

A study of the relationship between age and various visual functions (such as acuity and depth perception) reported the followin

Mila [183]

Answer:

Σxi =56.61

Σxi²=196.23

Step-by-step explanation:

X be the random variable represents area of scleral lamina (mm2) from human optic nerve heads

Σxi can be obtain by adding all x values

Σxi=2.79+2.53+2.78+3.79+2.33+2.72+3.88+4.15+3.79+4.43+3.47+4.47+2.5+3.61+2.77+3.53+3.07=56.61

Σxi =56.61

Σxi² can be obtained by squaring x values and then adding them.

Σxi²=2.79²+2.53²+2.78²+3.79²+2.33²+2.72²+3.88²+4.15²+3.79²+4.43²+3.47²+4.47²+2.5²+3.61²+2.77²+3.53²+3.07²=196.233

Σxi²=196.23

8 0

2 years ago