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IrinaK [193]
3 years ago
7

Kyle is asked to solve a system of equations by substitution: 2x + 3y = 12 x - 2y = 4 which step should kyle take first? why?

Mathematics
2 answers:
murzikaleks [220]3 years ago
8 0
The correct answer is C
zhuklara [117]3 years ago
7 0

The given system of equations is

2x + 3y = 12 and

x - 2y = 4

From the given set of options, it would be best for Kyle if he takes <u>option C</u> as the first step. That is, "Kyle should solve the second equation for x because x has a coefficient of 1".

This is because it will make further solution easy. Let us know how.

The coefficient of x is 1. Thus, x will be represented as: x=4+2y after adding 2y to both sides. Now, this can be substituted in the first equation and we can solve for y. Once that is done we can easily solve for x using any of the two equations (whichever is the easiest).

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Andrew is buying pencils, and he wants to buy fewer than 25. He plans to give 75% of the pencils to his students and save three
sweet-ann [11.9K]

Answer:

50%

Step-by-step explanation:

the will have 75minis 25

4 0
3 years ago
Read 2 more answers
A retailer spends $25 on a new video game. They have to pay 7.5% sales tax on
shepuryov [24]

Answer:

The tax is $1.88

Step-by-step explanation:

7.5% = 0.075 (divide by 100)

0.075 * $25 = 1.875 or $1.88

7 0
3 years ago
How do I solve an equation like this, one with a negative in front of parentheses?
azamat

The factor outside the parentheses is -1. Distribute using that factor.

2 - (4 - <em>x</em>) = 7<em>x</em> - 5<em>x</em>

<em />

-1 * 4 = -4 and -1 * -<em>x</em> = <em>x</em>

<em />

2 - 4 + <em>x</em> = 7<em>x</em> - 5<em>x</em>

Simplify.

-2 + <em>x</em> = 2<em>x</em>

<em>x</em> = 2<em>x</em> + 2

-<em>x</em> = 2

<em>x</em> = -2

<h3>Answer:</h3>

<em>x</em> = -2

3 0
3 years ago
How to solve these question?
mart [117]
3.) An extreme value refers to a point on the graph that is possibly a maximum or minimum. At these points, the instantaneous rate of change (slope) of the  graph is 0 because the line tangent to the point is horizontal. We can find the rate of change  by taking the derivative of the function.

y' = 2ax + b

Now that we where the derivative, we can set it equal to 0.

2ax + b = 0

We also know that at the extreme value, x = -1/2. We can plug that in as well.

2a (-\frac{1}{2} ) + b = 0

The 2 and one-half cancel each other out.

-a + b = 0

a = b

Now we know that a and b are the same number, and that ax^2 + bx + 10 = 0 at x = -1/2. So let's plug -1/2 in for x in the original function, and solve for a/b.

a(-0.5)^2 + a(-0.5) + 10 = 0

0.25a - 0.5a + 10 = 0

-0.25a = -10

a = 40

b = 40

To determine if the extrema is a minima or maxima, we need to go back to the derivative and plug in a/b.

80x + 40

Our critical number is x = -1/2. We need to plug a number that is less than -1/2  and a number that is greater than -1/2 into the derivative.

LESS THAN:
80(-1) + 40 =  -40

GREATER THAN:
80(0) + 40 = 40

The rate of change of the graph changes from negative  to positive at x = -1/2, therefore the extreme value is a minimum.

4.) If the quadratic function is symmetrical about x = 3, that means that the minimum or maximum must be at x = 3.

y' = 2ax + 1

2a(3) + 1 = 0

6a = -1

a = -1/6

So now plug the a value and x=3 into the original function to find the extreme value.

(-1/6)(3)^2 + 3 + 3 = 4.5

The extreme value is 4.5


7 0
3 years ago
In a circle with a radius of 7 feet, the radian measure of the central angle subtended by an arc with a length of 4 feet is . Th
ivann1987 [24]
We know that
length of a sector=[∅]*r--------> when ∅ is in radians
so
∅=length of a sector/r
for r=7 ft
length of a sector=4 ft
∅=4/7-----> 0.57 radians

the answer part 1) is 0.57 radians

part 2) 
area of a sector=(∅/2)*r²--------> when ∅<span> is in radians
</span>area of a sector=(4/7/2)*7²-----> (4/14)*49----> 14 ft²

the answer Part 2) is 14 ft²
3 0
3 years ago
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