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oee [108]
3 years ago
15

The product of 2 and a number increased by 7 is -36

Mathematics
1 answer:
Sholpan [36]3 years ago
3 0
"The product" means you're multiplying the two numbers.
"a number" refers to a variable.
"increased" means you're adding.

2x + 7 = -36
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What is the distance from the school to the theater?
defon
The "horizontal" distance is 8-2 = 6.
The "vertical" distance is 7-3 = 4.
The Pythagorean theorem tells you the straight line distance is then
  √(6² + 4²) = √52 = 2√13 ≈ 7.21
8 0
3 years ago
When a plane flies into the wind, it can travel 3000 ml in 6 h . When it flies with the wind, it can travel the same distance in
jeka94

Answer:

  • plane: 550 mph
  • wind: 50 mph

Step-by-step explanation:

If p and w represent the speeds of the plane and wind, respectively, the speed into the wind is ...

  p - w = (3000 mi)/(6 h) = 500 mi/h

And, the speed with the wind is ...

  p + w = (3000 mi)/(5 h) = 600 mi/h

Adding these two equations gives us ...

  2p = 1100 mi/h

  p = 550 mi/h . . . . . . . divide by 2

Then the wind speed is ...

  w = 600 mi/h - p = (600 -550) mi/h

  w = 50 mi/h

The rate of the plane in still air is 550 mi/h; the rate of the wind is 50 mi/h.

4 0
3 years ago
Read 2 more answers
We are given that m∠AEB = 45° and ∠AEC is a right angle. The measure of ∠AEC is 90° by the definition of a right angle. Applying
melomori [17]

Answer:

The proof is given below.

Step-by-step explanation:

Given m∠AEB = 45° and ∠AEC is a right angle. we have to prove that EB divides ∠AEC into two congruent angles, it is the angle bisector.

Given ∠AEC=90°      (Given)

∠AEC=∠AEB+∠BEC  

⇒ 90° = 45° +∠BEC      (Substitution Property)

By subtraction property of equality

⇒ ∠BEC = 90° - 45° = 45°    

Hence, both angles becomes equal gives ∠AEB≅∠BEC

Since EB divides ∠AEC into two congruent angles, ∴ EB is the angle bisector.


5 0
3 years ago
Read 2 more answers
What is the area of a rectangle with vertices (-8, -2), (-3,-2), (-3,-6), and (-8,-6)?
Gemiola [76]

Answer:

The area of the rectangle is 20 square units

Step-by-step explanation:

Through the x values of the ordered pairs, we can see that the length of the rectangle is 5

-3-(-8)=5

Through the y-values of the ordered pairs, we can see that the width of the rectangle is 4

-2-(-6)=4

The area can be found by multiplying the length and width, so this means

(5)(4)=20

8 0
3 years ago
Train A and train B leave a central station at the same time. They travel the same speed, but in opposite directions, with train
ratelena [41]
Recall your d  = rt, distance = rate * time

so, keeping in mind that both trains are going at the same speed, say speed of "r" mph, after 212 hours A arrived at station A and after 4 hours, B arrived at station B.

now, the distance covered by train A is say "d", we know both stations are 585 miles apart, so, if train A covered "d" miles in those 212 hours, then train B covered the slack from 585 and d, that is "585 - d".

\bf \begin{array}{lccclll}
&\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\
&------&------&------\\
\textit{Train A}&d&r&212\\
\textit{Train B}&585 - d&r&4
\end{array}
\\\\\\
\begin{cases}
\boxed{d}=212r\\
585-d=4r\\
----------\\
585-\boxed{212r}=4r
\end{cases}
\\\\\\
585=216r\implies \cfrac{585}{216}=r\implies \cfrac{65}{24}=r\implies \stackrel{mph}{2\frac{17}{24}}=r
8 0
3 years ago
Read 2 more answers
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