MATHEMATICS COLLEGE

Solve the inequality 5y + 4 < 3y + 17

Answers

Answer 1

Answer:

Answer:

y<13/2

Step-by-step explanation:

5y + 4 < 3y + 17

5y-3y<-4+17

2y<13

y<13/2

Answer 2

Answer:

Answer:

y<6.5

Step-by-step explanation:

5y+4<3y+17

Subtract 3 from both sides

2y+4<17

Subtractc4 from both sides

2y<13

Divide both sides by 2

y<6.5

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The slope of a line is 2. The y-intercept of the line is –6. Which statements accurately describe how to graph the function? A. Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
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Answers

Answer:

Step-by-step explanation:

Slope is positive 2 so we have to move 1 point right and 2 points up.

Secondly y-intercept is -6 so ,point is (0,-6)

Two guy wires from the top of a 200-foot radio antenna are anchored to the ground by two large concrete posts. The antenna is perpendicular to the ground and between the two posts. If the angles of depression from the top of the antenna to each of the posts is 46o and 48o respectively, then the distance between the two posts is:_______

Answers

Answer: 373.22 feet

Step-by-step explanation:

The attached photo contains the diagram illustrating the scenario. 2 right angle triangles ACD and BCD are formed.

The distance between the two posts is AD + BD

To determine AD, we would apply the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side

Tan 46 = 200/AD

AD = 200/Tan 46 = 200/1.0355

AD = 193.14

To determine BD, we would also apply the tangent trigonometric ratio. Therefore

Tan 48 = 200/BD

BD = 200/Tan 48 = 200/1.1106

BD = 180.08

Therefore, the distance between the two posts is

193.14 + 180.08 = 373.22 feet

A gym has yoga classes each class has 14 students if there are c classes write an equation to represent the total number of students s taking yoga

Answers

Answer:

14 times c = s

Step-by-step explanation:

6.3% of the 6,540,000 Indiana residents were listed as Hispanic or Latino in 2012, how many people would this be?

Answers

Answer:

412020

Step-by-step explanation:

It is given that,

6.3% of the 6,540,000 Indiana residents were listed as Hispanic or Latino in 2012. We need to find the no of people for this.

Using the concept of percentage as follows :

$(6.3)/(100)* 6540000 =412020$

Hence, there would be 412020 people.

P (-5, -6), Q (-1, 2), R (4, 4)Scale factor = 2

P' =

Q' =

R' =

Answers

P’(-10,-12) Q’(-2,4) R’(8,8)

Help me out please and thank you

Answers

Answer: 1

========================================================

Explanation:

We're given the height in relation to base BC, so we need to find the length of this base. This is the same as finding the distance from B to C.

Turn to the distance formula

$d = \text{Distance from B to C}\n\nd = √((x_1-x_2)^2+(y_1-y^2)^2)\n\nd = √((-2-(-3))^2+(-1-(-2))^2)\n\nd = √((-2+3)^2+(-1+2)^2)\n\nd = √((1)^2+(1)^2)\n\nd = √(1+1)\n\nd = √(2)\n\n$

Coincidentally, the base and height are the same. This won't always be the case.

Now we can find the area of the triangle

$A = \text{Area of triangle}\n\nA = (1)/(2)*\text{Base}*\text{Height}\n\nA = (1)/(2)*√(2)*√(2)\n\nA = (1)/(2)*√(2*2)\n\nA = (1)/(2)*√(4)\n\nA = (1)/(2)*2\n\nA = 1\n\n$

The area of the triangle is 1 square unit.

See diagram below.

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