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ycow [4]
3 years ago
7

5x−4≥12 AND 12x+5≤−4

Mathematics
2 answers:
Molodets [167]3 years ago
4 0

Answer:

No solutions

Step-by-step explanation:

bekas [8.4K]3 years ago
3 0

Answer:

No solutions

Step-by-step explanation:

5x - 4 ≥ 12

<em>Isolate the Variable</em>

5x ≥ 16

<em>Divide both sides by 5</em>

x ≥ 3.2

AND

12x + 5 ≤ -4

<em>Isolate the Variable</em>

12x ≤ -9

<em>Divide both sides by 12</em>

x ≤ -.75

When you say and, you find the area that is covered by both inequalities, but because the inequalities solution sets don't overlap, there are no solutions.

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A toy rocket is launched vertically from 5 feet above ground level with an initial velocity of 112 feet per second. The height h
Masja [62]

Answer:

Step-by-step explanation:

a)The height h after t seconds is given by the equation h(t)=-16t^2+112t+5.

Where 5 represents 5feet above the ground and this is the height from which the rocket was launched.

The equation is a quadratic equation. The plot of this equation on a graph would give a parabola whose vertex would be equal to the maximum height travelled by the rocket.

The vertex of the parabola is calculated as follows,

Vertex = -b/2a

From the equation,

a = -16

b = 112

Vertex = - - 112/32= 3.5

So the rocket will attain maximum height at 3.5 seconds.

It will also take 3.5 seconds to reach the ground. This means it will take a total of 3.5 seconds + 3.5 seconds

= 7 seconds to hit the ground.

b) to find time it will take to be 100 feet above the ground,

-16t^2+112t-95 = 0

Using general quadratic equation formula,

a = -16

b = 112

c = -95

t = [-b+/-√b^2-4ac]/2a

t = [ -112 +/-√112^2-4×-16×-95]/16 × -2

= [-112 +/-√12544-6080]/-32

= (-112+80.4)/-32 or (-112-80.4)/-32

t = 0.9875 or t = 6.0125

So it will take 0.9875 or approximately 1 second to be 100 feet above the ground

7 0
3 years ago
John held a garage sale. He priced all the items at a dime or a quarter. His sales totaled
Nikitich [7]

John held a garage sale. He priced all the items at a dime or a quarter, his sales totaled less than $5, the solution is shaded region in quadrant I.

<h3>What is a slope?</h3>

In mathematics, line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent the slope; reason for this usage is unclear, but it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of equation for a straight line as "y = mx + b" and "y = mx + c," respectively.

He priced all items at a dime or a quarter. His sales totaled less than $5

Since dime =$ 0.10=$0.10 and the quarter =$0.25=$0.25

Let x=x= the number of the items sold for a dime

Let y=y= the number of the items sold for a quarter

0.10x+0.25y<5

0.10x+0.25y<5

Inequality in the slope-intercept form

0.10x+0.25y Subtract 0.10x from both sides

0.25y<-0.10x+5 Divide both sides by 0.25

Subtract 0.10x from both sides

y= -\frac{2}{5}x+20\\

The slope is, -\frac{2}{5} and the y- intercept is 20

Since inequality sign is << so, draw a dashed line

Test point (0,0)(0,0)

Substituting the values 0 for x and 0 for y,

y < -\frac{2}{5}x+20\\\\0 < -\frac{2}{5}(0)+20\\\\0 < +20

Since inequality is true

So, (0,0)(0,0) is solution of the inequality

Shade region containing (0,0)(0,0).

The graph below shows all possible solutions

Since boundary line is dashed and the number of items is always positive

The solution is shaded region in quadrant I

To know more about quadrant visit: brainly.com/question/7196312

#SPJ9

4 0
1 year ago
A concrete patio is 5 2/3 feet wide. It has an area of 36 5/6 square feet. What is the length of the concrete patio
Aneli [31]
The length of the concrete patio is 6 1/2.
I got this answer by dividing 36 5/6 and 5 2/3. Therefore, answer is 6 1/2
4 0
3 years ago
Divide. −4 1/3 ÷ −2 3/5 A. 1 2/3 B. 1 4/5 C. 2 1/5 D. 2 3/5
Inga [223]

a. 1 \frac{2}{3}

trust me it's the correct answer :)

7 0
3 years ago
Gentry poured 23.5 ounces of milk and 7.75 ounces of cream in a mixing bowl.
denpristay [2]
Notice that because the capacity of the bowl is 35.5 ounces, but there has already been 31.25 ounces total added to it (23.5 ounces + 7.75 ounces), all that needs to be done is subtract 31.25 from 35.5:
35.5 - 31.25 = 4.25 ounces of cream could be added
4 0
3 years ago
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