a bus traveled 60 km of north of its terminal. From this point, it traveled km east. How far is the bus from the terminal?

A recipe calls 2 1/3 cups of flour,but Paul only has 2 1/6.How much more flour does he need?

Finger [1]

Just estimate both fractions

4 0

3 years ago

2. Ariana has created a paper airplane for her physics class at school where all the students will be testing their planes by se

sergiy2304 [10]

Answer:

2. The airplane will crash into the ground after 5 seconds.

3. The domain of the function is [0,30] and range of the function is $[-\infty,900]$ .

Step-by-step explanation:

2.

Ariana initial attempt is modeled by the function,

$h(x)=x^2-12x+35$

where, h is the height in feet and x is the time in seconds of the paper airplanes path.

If airplane crash into the ground, then $h(x)=0$ ,

$0=x^2-12x+35$

$0=x^2-7x-5x+35$

$0=x(x-7)-5(x-7)$

$0=(x-7)(x-5)$

Equate each factor equal to 0.

$x=5,7$

Therefore the airplane will crash into the ground after 5 seconds.

3.

The height of the rocket in meters is modeled by the function shown below, where t is time in seconds.

$h(t)=-4t^2+120t$

The value of t must be positive because time can not be negative.

Find the zeros of the function.

$0=-4t(t-30)$

$t=0,30$

The leading coefficient is negative, so the it is a downward parabola. Since the zeros of the function are 0 and 30, therefore the function is negative before 0 and after 30.

The height can not be negative, so the domain of the function is

$0\leq t\leq 30$

The vertex of a downward parabola is the maximum point.

Vertex of a parabola,

$(\frac{-b}{2a},h(\frac{-b}{2a}))$

$(\frac{-120}{2(-4)},h(\frac{-120}{2(-4)}))$

$(15,h(15))$

Put t=15 it in the equation.

$h(15)=-4(15)^2+120(15)=900$

$(15,900)$

The range of the function is

$[-\infty,900]$

Therefore the domain of the function is [0,30] and range of the function is $[-\infty,900]$ .

8 0

2 years ago

What is the fewest pairs of corresponding parts that have to be congruent to establish that two triangles are congruent? Once yo

sveticcg [70]

It seems there are always three pairs: SSS, side side side; SAS, side angle side; ASA, angle side angle.

For a right triangle (HL, LL) it seems there are only two items needed, but that's because we already know one angle (it's right).

Once we have congruent triangles, all the corresponding parts are congruent. That's three sides and and three vertices, so I'd answer six. Of course almost everything about the triangles is the same, the area, the perimeter, etc.

3 0

3 years ago

A necklace is being made with beads that are each 1.25 centimeters in diameter. How many beads does it take to make a necklace t

Oliga [24]

Answer: $3.60 will be spent on the necklace.

Step-by-step explanation:

to solve this problem we have to divide the length of the necklace (30cm ) by the diameter of each bead (1.25) to obtain the number of beads needed for the necklace.

So, mathematically speaking:

30 cm / 1.25 cm =24 beads

Now, we have to multiply the number of beads by the cost of each one ($0.15).

24 x 0.15= $3.60

S000, $3.60 will be spent on the necklace.

- Katsuki Bakugou

3 0

3 years ago

It takes Adi 2 hours to drive from home to her office and 3 hours if she drives 15 mph slower. What is the distance between Adi'

Solnce55 [7]

Answer:

90 miles

Step-by-step explanation:

Let ori. speed = z

distance = speed × time

= z × 2

= 2z miles

distance = (z - 15) × 3

= (3z - 45)miles

2z = 3z - 45

z = 45mph

distance = 45 × 2

= 90 miles

distance = (45-15) × 3

= 90 miles

(Correct me if i am wrong)

8 0

3 years ago