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3 years ago

7

you are given the measure of angle 4. You also know the following angles are supplementary: Angles 1 and 2, angles 2 and 3, angl

es 1 and 4. Explain how you can determine the measures of angles 1, 2, and 3.

1 answer:

Harrizon [31]3 years ago

4 0

If you are given the measure of angle 4, then we know angle 2 is equal since it is a vertical angle. The angle of a line is 180 degrees, so subtract the measure of angle 4 (and/or 2) which will give you the angle measure for both angle 1 and 3, since those are also equal due to vertical angles. Hope that helped! :)

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-x^2+4x-8 <br>axis of symmerty

V125BC [204]

Answer:

$\boxed {\boxed {\sf x=2}}$

Step-by-step explanation:

The axis of symmetry can be calculated using the formula:

$x=\frac{-b}{2a}$

First we must determine a and b from the quadratic: $-x^2+4x-8$ . This is in standard form, with the highest power first in descending order.

Standard form is also: $ax^2+bx+c$

If we compare this to the quadratic given, we can conclude that:

$a= -1 \\b= 4 \\c= -8$

Substitute the values for a and b into the formula.

$x= \frac{-(4)}{2(-1)}$

Multiply in the denominator.

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

Divide.

$x=2$

This can also be determined from the graph. It is the x-coordinate of the vertex or the maximum/minimum. It divides the quadratic into 2 symmetrical halves.

8 0

3 years ago

a company owns two dealerships, both of which sell cars and trucks. the first dealership sells a total of 164 cars and trucks. t

OLEGan [10]

Answer:

294 cars.

Step-by-step explanation:

Let x be the number of cars and y be the number of trucks.

We have been given that the first dealership sells a total of 164 cars and trucks. We can represent this information as:

$x+y=164...(1)$

The second dealership sells twice as many cars and half as many trucks as the first dealership. So the number of cars sold by 2nd dealership will be 2x and number of trucks sold by 2nd dealership will be y/2.

Further, the 2nd dealership sold a total of 229 cars and trucks. We can represent this information as:

$2x+\frac{y}{2}=229...(2)$

We can see that total number of cars sold on two dealerships will be $x+2x=3x$ .

We will use substitution method to solve for x. From equation (1) we will get,

$y=164-x$

Substituting this value in equation (2) we will get,

$2x+\frac{164-x}{2}=229$

Now let us have a common denominator.

$\frac{4x}{2}+\frac{164-x}{2}=229$

$\frac{4x+164-x}{2}=229$

Upon multiplying both sides of our equation by 2 we will get,

$2\times \frac{4x+164-x}{2}=2\times 229$

$4x+164-x=458$

$4x+164-164-x=458-164$

$4x-x=458-164$

$3x=294$

Therefore, the total number of cars sold by two dealerships is 294.

7 0

3 years ago

At a local ice cream parlor, there are 6 different flavors of ice cream from which to select (strawberry, chocolate, vanilla, ro

Neko [114]

Answer:

1/30

Step-by-step explanation:

let, vanilla be the first ice cream.

hence, the probability of choosing vanila= 1/6

let, chocolate be the second ice cream.

hence, the probability of choosing chocolate=1/5

hence, the probability that the next customer's sundae will have vanilla and chocolate (in either order)= (1/6)×(1/5)

=1/30

7 0

3 years ago

ou originally draw a design for an art contest on a 2 in. x 5 in. card. The second phase of the contest requires the drawing to

valentina_108 [34]

Since the largest size of one of the dimensions is 10.5, it has to correspond with the long side of the card, the 5 in. side. To find the proportion of the sides, divide 10.5 by 5. Then, multiply the other side of the card by the quotient.

10.5/5 = 2.1

2.1 * 2 = 4.2

4.2in is the shorter side. Your question asks to round to the nearest tenths, the smallest place value of the answer is already the tenths place.

8 0

3 years ago

A math club is researching a golf tournament fund-raiser. It will cost $1,000 to host the tournament. If it rains, the club will

Luda [366]

Cost of hosting the tournament : $1,000
If it rains, the club will lose the investment: $ -1,000
If it is sunny, the club will collect $4,500 ; profit: 4,500 - 1000 = 3,500

chance of rain is 20%

-1,000 * 20% = -200
3,500 * 80% = 2,800

2,800 - 200 = 2,600 Choice C.

3 0

3 years ago

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