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galben [10]
3 years ago
12

Cary is 9 years older than Dan. In 7 years, the sum of their ages will equal 93. Find both of their

Mathematics
1 answer:
a_sh-v [17]3 years ago
3 0
Cary's age is 9 years MORE than Dan's age.
Cary's age is Dan's age, but with 9 more years added to that.
Here is how we can express that,
\rm C=D+9
In 7 years, Cary will be C+7 years old,
and Dan will be D+7 years old.
In 7 years, the sum of their ages,
(C+7) and (D+7) will equal 93.

Here is how we can express that:
\rm (C+7)+(D+7)=93

You have a system of two equations involving two unknowns. You have a couple of nice options here. You can apply substitution or elimination to complete the problem.
You might be interested in
What is the value of x?
STatiana [176]
I thought it was 5 because the 55 degrees given is equal to the angle above it. If you look, there are 4, 90 degree angles so the 8x-5 has to equal 35 to make 90 but idk
3 0
3 years ago
Beverly says f(a)=9.3 has multiple solutions. Stephanie says f(9.3)=a has multiple solutions. Who is correct?
RUDIKE [14]

Beverley is right

explanation

there is 3 answers

0,9,3

hope this helps

cauculator link: https://www.symbolab.com/solver/functions-calculator

:D

from Kenny

all the best!

4 0
2 years ago
A projectile is fired with muzzle speed 220 m/s and an angle of elevation 45° from a position 30 m above ground level. Where doe
Allushta [10]

Answer:

  • 4968.6 m from where it was fired
  • 221.33 m/s

Step-by-step explanation:

For the purpose of this problem, we assume ballistic motion over a stationary flat Earth under the influence of gravity, with no air resistance.

We can divide the motion into two components, one vertical and one horizontal. For muzzle speed s and launch angle θ, the horizontal speed is presumed constant at s·cos(θ). The initial vertical speed is then s·sin(θ) and the (x, y) coordinates as a function of time are ...

  (x, y) = (s·cos(θ)·t, -4.9t² +s·sin(θ)·t + h₀) . . . . . where h₀ is the initial height

To find the range, we can solve the equation y=0 for t, and use this value of t to find x.

Using the quadratic formula, we find t at the time of landing to be ...

  t = (-s·sin(θ) - √((s·sin(θ))²-4(-4.9)(h₀)))/(2(-4.9))

  t = (s/9.8)(sin(θ) +√(sin(θ)² +19.6h₀/s²))

For s = 220, θ = 45°, and h₀ = 30, the time of flight is ...

  t ≈ 31.939 seconds

Then the horizontal travel is

  x = 220·cos(45°)·31.939 ≈ 4968.6 . . . . meters

__

As it happens, the value under the radical in the above expression for time, when multiplied by s, is the vertical speed at landing. The horizontal speed remains s·cos(θ), so the resultant speed is the Pythagorean sum of these:

  landing speed = s·√(cos(θ)² +sin(θ)² +19.6h₀/s²) ≈ s√(1 +0.012149)

  ≈ 221.33 m/s

_____

Note that the landing speed represents the speed the projectile has as a consequence of the potential energy of its initial height being converted to kinetic energy that adds to the kinetic energy due to its initial muzzle velocity.

6 0
3 years ago
Order the following numbers from least to greatest<br> numbers:1 8/25,1.3,5/4
Brut [27]

Answer:

i think it 5/4, 3.1, 1 8/25

Step-by-step explanation:

let me know if its right

8 0
3 years ago
It takes Santa 5 minutes to fly 35 miles with the wind .It takes him 7 minutes to fly 35 miles against the wind determine the sp
Dmitrij [34]

Answer: Santa's speed in still air is 6 miles per minute

Speed of the wind is 1 mile per minute

Step-by-step explanation:

Let x represent the speed of Santa in still air. It is assumed that in still air. She is flying with the wind. If the speed of the wind is y, then him total speed is x + y

It takes Santa 5 minutes to fly 35 miles with the wind.

Speed = distance / time

It means that

x + y = 35/5 = 7

It takes him 7 minutes to fly 35 miles against the wind. This means that his total speed will be x - y

Speed = distance/time. Therefore,

x - y = 35 /5 = 5 - - - - - - 1

Substituting x = 7 - y into equation 1, it becomes

7 - y - y = 5

-2y = 5 - 7 = -2

y = -2/-2 = 1

x = 7 - y = 7 - 1

x = 6

3 0
3 years ago
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