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3 years ago

Solve the inequality: −1<|2 x − 3|<7

Mathematics

1 answer:

andriy [413]3 years ago

5 0

Answer:

Step-by-step explanation:

1. subtract over the x on the right side of the inequality so you get 4x<16 divide 4 over to get x alone the inequality turns into x<4.

2. subtract over the x on the right side so you get 11x<22 divide over 11 to get x<2

3. Add over 10 to get -8x>7x+30 subtract over 7x to get -15x>30 divide by -15 to get x<-2 make sure to flip over the sign since you're dividing by a negative

4. Add over the 4 to get 13x<12x+3 subtract over 12 and get x<3

5. I can't solve five since their is no inequality sign, the answers show it both ways so i need a starting one to go off on but it is either A or B just flip over the original sign and that will be the answer .

6. Distribute the 7 to get 7x-14<-5 add over the 14 and get 7x<9 divide over the 7 and get x<9/7

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A quantity b varies jointly with c and d and inversely with eWhen b is 18, c is 4, d is 9, and e is 6What is the constant of var

777dan777 [17]

Answer:

constant of variation = 3

Step-by-step explanation:

we know that b varies jointly with c and d

so:

b∝c∝d

and b varies inversely with e, so

b∝ $\frac{1}{e}$

and i will call the constant of variation k, this way we can make an equation for b in the following form:

$b=k\frac{cd}{e}$

this satisfy that b varies jointly with c and d (if b increases, c and d also increase) and inversely with e (if b increases, e decreases)

we know that when b is 18, c is 4, d is 9, and e is 6:

$b=18\\c=4\\d=9\\e=6$

substituting this in our equation for b:

$b=k\frac{cd}{e}\\ 18=k\frac{(4)(9)}{6}$

and we solve operations and clear for the constant of variation k:

$18=k\frac{36}{6}\\ 18=6k\\\frac{18}{6}=k\\ 3=k$

the constant of variation is 3.

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3 years ago

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Equation for, One half the sum of 8 and x

Ahat [919]

Answer:

$\frac{8 + x}{2}$

Step-by-step explanation:

First, we have to write 8 + x, but since it's half of that we write it as a fraction with a 2 on the bottom to halve it.

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3 years ago

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What translation rule can be used to describe the result of the composition of T < 4, −10 >(x, y) and T < −1, −9 >(x

Vikki [24]

The first translation picks a point and adds 4 to its x coordinate, and subtracts 10 from the y coordinate. In other words, it moves the point 4 units to the right and 10 units down.

Similarly, the second translation subtracts 1 to the x coordinate, and subtracts 9 from the y coordinate. In other words, it moves the point 1 unit to the left and 9 units down.

So, if you perform one translation after the other, you move the point 4 units to the right and 1 unit to the left along the x axis, and 10 units down and 9 more units down along the y axis.

The net result is a translation of 3 units to the right and 19 units down.

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3 years ago

The water reaches a max height when the horizontal distance from the firefighter to the building is approximately __m. Round to

elena-s [515]

The horizontal distance from the firefighter at which the maximum height of water occurs is 10.83m

<u>Explanation:</u>

Given:

h(x) = -0.026x² + 0.563x + 3

where,

h(x) is the height of the water

Initial speed, u = 14m/s

angle, θ = 30°

(a)

Horizontal distance = ?

h(x) = ax² + bx + c

the vertex is found at x = -b/2a

where,

x = distance to the maximum height

As compared to the equation given:

a = -0.026

b = 0.563

Thus,

$x = \frac{-0.563}{2 X -0.026} \\\\x = \frac{0.563}{0.052}\\ \\x = 10.83m$

Therefore, horizontal distance from the firefighter at which the maximum height of water occurs is 10.83m

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3 years ago

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anygoal [31]

Answer:

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Explanation:

The slope is 5, and the y intercept is 8 so following the format of the equation, the equation for this line is:

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