In car racing, a car must meet specific dimensions to enter a race. Officials use a template to ensure these
specifications are met. Suppose the least allowable height of a race car is 52 in., the desirable height is 52.5 in., and the
greatest allowable height is 53 in. What absolute value inequality describes heights of the model of race car within the
indicated tolerance?

Answer:

Option (2)

Step-by-step explanation:

To find the solution set of the given inequality we will follow the following steps.

1). Convert the inequality into an equation.

2). Find the solutions from the equation.

3). Check these solutions and intervals on a number line.

Given inequality is 5(x - 2)(x + 4) > 0

Step 1. Equation for given inequality is,

          5(x - 2)(x + 4) = 0

Step 2. Solutions for the given equation will be,

           (x - 2) = 0 ⇒ x = 2

           (x + 4) = 0 ⇒ x = -4

Step 3. Therefore, there will be two critical points on the number line,

           x = 2, x = -4

Now we will check the solutions of the given inequality in the given intervals,

x < -4, -4 < x < 2 and x > 2

For x < -4,

Let the solution is x = -5

5(x + 4)(x - 2) = 5(-5 + 4)(-4 - 2)

                     = 30 > 0

Therefore, x < -4 will be the solution area of the inequality.

For -4 < x < 2,

Let the solution is x = 0

5(x + 4)(x - 2) = 5(0 + 4)(0 - 2)

                     = -40 < 0

Therefore, -4 < x < 2 will not be the solution set for the given inequality.

For x > 2,

Let the solution is x = 3

5(x + 4)(x - 2) = 5(3 + 4)(3 - 2)

                     = 35 > 0

Therefore, x > 2 will be the solution area of the inequality.

Summarizing all steps we find that the solution set of the inequality is,

{x | x < -4 Or x > 2}

Option (2) will be the answer.

Answer:

4 I guess

Step-by-step explanation:

Because

3-1=2

2^2=2*2=4

A midpoint is a point that divides a given line into two equal halves.The answers to the questions are:

1. BC = 89

b. AB = 45

c. AC = 44

2. The coordinate of I is 2.5

3. J = 19

4. MQ = 32

5. NO = 13

6. NO = 23

b. MN = 25

A line segment can be divided into different fractions. Where the point that divides the line segment into equal parts is the midpoint. however, number line is a system that shows the location or positions of all directed numbers.

The given questions can be solved as follows:

1. Given that point A is between BC and AB = 4x -3, BC = 7x + 5, AC = 5x - 16

But,

BC = AB + AC

7x + 5 = (4x -3) + (5x - 16)

          = 9x - 19

7x + 5 = 9x - 19

19 + 5 = 9x - 7x

24 = 2x

x = [tex]\frac{24}{2}[/tex]

x = 12

So that;

a. BC = 7x + 5

         = 7(12) + 5

BC = 89

The value of BC is 89.

b. AB = 4x -3

         = 4(12) - 3

AB = 45

Thus AB has a value of 45.

c.  AC = 5x - 16

          = 5(12) -16

 AC = 44

The value of AC is 44.

2. Given that H is the mid point of GI, and G = 8, I = -3.

Then;

I = 2.5

The coordinate of I is 2.5

3. A midpoint is a point that divides a line segment in to two equal halves. Given that J is the midpoint of KL. KL = 38

J = [tex]\frac{KL}{2}[/tex]

  = [tex]\frac{38}{2}[/tex]

J = 19

The value of the midpoint J is 19.

4. It can be deduced from the conditions given in the question that:

  MQ = MN + NO + OP + PQ

          = 8 + 8 + 16      (NB: OP + PQ = 16)

MQ = 32

Thus, value of MQ is 32.

5. Since P is the mid point of NQ, and OP = 11, OQ = 35

 Then;

PQ  = OQ - OP

      = 35 - 11

PQ = 24

Since, PQ = NP =24

Then;

NO = NP - OP

      = 24 - 11

NO = 13

NO has a length of 13.

6. NO = 2y + 11, OP = 3y - 2, NP = 6y + 3 and MP = 64.

But,

NO + OP = NP

(2y + 11) + (3y - 2) = 6y + 3

5y + 9 = 6y + 3

9 - 3 = 6y - 5y

y = 6

So that;

a. NO = 2y + 11

          = 2(6) + 11

NO = 23

Here, the value of NO is 23.

b. MN = MP - NP

But,

NP = 6y + 3

     = 6(6) + 3

NP = 39

Then;

MN = 64 - 39

MN = 25

So that MN has a value of 25.

Visit: https://brainly.com/question/20751513

Answer:

((7*2)*(8p))

Step-by-step explanation:

The product of 7 and 2 basically means you multiply them. The product of 7 and 2 is 14 and the product of 8p cannot be known because p is undefined so keep it as 8p. the product of 14 and 8p is 112p but the answer I stated above is the unsimplified version.

Answer:

72?

Step-by-step explanation:

V=whl=4 x 2 x9=72

Let the age will be x

4x+2x-28 years

6x-28

x-28 by 6 -4.66

SO THE ANSWER IS 4.66

Answer:

Noi = x

Noy = y

x+y = 26 ... (1)

4x-2y= 28 ... (2)

Solve:

x+y= 26

x= 26-y (keep it)

4x-2y= 28

4(26-y)-2y=28

104-4y-2y= 28

-6y= 28-104

-6y=-76

y= 12,6 (12 years 6 mouths)

x+y= 26

x + 12.6 = 26

x= 26-12.6

x= 13, 4 ( 13 years 4 mouths)

2+3i, x=2−3

Explanation:

Answer

step by step explanation

volume=base area ×height

16 cm2 ×6=96cm2

Because all the angles are congruent (the same), this is an equilateral triangle. All equilateral triangles have congruent angles and congruent sides, so all sides has to be 14.

Answer:

  See below

Step-by-step explanation:

Each point on the triangle moves to half its previous distance from P.

Answer:

30

Step-by-step explanation:

6x

Replace 'x' with 5.

6(5) =

6 * 5 =

30

Hope this helps.

Answer:

30

Step-by-step explanation:

6 x 5 = 30

Answer:

98.1km²

Step-by-step explanation:

The name of the Triangle in this question is: WXV

In the question, we have:

Angle W = ? Unknown

Angle X = 119°

Angle V = 34°

Side w =?

Side x = 26km

Side v = ?

Step 1

We have to find the missing third angle = Angle W

Sum of angles in a triangle = 180°

= Angle W = 180° - (119 + 34)°

= 180° - 153°

Angle W = 27°

Step 2

Find the sides w and v using the sine rule

Sine rule =

a/ sin A = b/ Sin B

Hence for triangle WXV

w/ sin W = x/ sin X = v/ sin V

We have the following values

Angle W = 27°

Angle X = 119°

Angle V = 34°

We are given side x = 26km

a) Finding side w

w/ sin W= x/ sin X

w/sin 27 = 26/sin 119

Cross Multiply

sin 27 × 26 = w × sin 119

w = sin 27 × 26/sin 119

w = 13.49587km

w = 13.5km

b) Finding side v

x / sin X= v/ sin V

26/ sin 119 = v/sin 34

Cross Multiply

sin 119 × v = 26 × sin 34

v = sin 34 × 26/sin 119

v = 16.62324km

v = 16.62km

Step 3

Detemine the area of triangle WXV

We make use heron formula

= √s(s - w) (s - x) (s - v)

Where s = w + x + v/ 2

s = (13.5 + 26 + 16.62)/2

s = 56.12/2

s = 28.06

Area of the triangle = √28.06× (28.06 - 13.5) × (28.06 - 26 ) × (28.06 - 16.62)

Area of the triangle = √9628.137559

Area of the triangle = 98.123073530337km²

Approximately to the nearest tenth =98.1km²

Answer:

It is reduced to the equation of the Theorem of Pythagoras.

Step-by-step explanation:

Any triangle can be modelled by this formula under the Law of Cosine:

[tex]b = \sqrt{a^{2}+c^{2}-2\cdot a\cdot c\cdot \cos B}[/tex]

Where:

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Side lengths, dimensionless.

[tex]B[/tex] - Angle opposed to the side [tex]b[/tex], measured in sexagesimal degrees.

Now, let suppose that angle B is a right angle (90º), so that b is a hypotenuse and a and c are legs. Hence:

[tex]\cos B = 0[/tex]

And the equation is reduced to the form of the Theorem of Pythagoras, that is to say:

[tex]b = \sqrt{a^{2}+c^{2}}[/tex]

Answer:

(x , y )  ---> (x + 6 , y - 3)

Step-by-step explanation:

(x , y )  ---> (x + 6 , y - 3)

P(-1 , 4) -----> P'(-1+6 , 4-3) = P'(5,1)

Comapre P and P' x-coordinate

         -1 + a = 5

                a = 5 +1 = 6

Q(-1, 2) ----->Q'(-1+6 , 2 -3)= Q'(5, -1)

R(3 , 1) ------> R'(3+6 , 1-3)  = R'(9,-2)

[tex]x = 11\frac{42}{99} [/tex]

Step-by-step explanation:

[tex]11.42424242.... = 11. \overline{42} \\ let \: x = 11. \overline{42} .....(1)\\ 100x = 1142.\overline{42}....(2) \\ subtracting \: (1) \: from \: (2) \: \\ 100x - x = 1142.\overline{42} - 11. \overline{42} \\ 99x = 1131 \\ x = \frac{1131}{99} \\x = 11\frac{42}{99} \\ [/tex]

Answer: C

Step-by-step explanation: I did the test

Answer:

15 lawns

Step-by-step explanation:

The Xbox costs $400 and his parents gave him $100. He needs to earn $300 more. $20 each lawn so $100 for 5 lawns. 5 lawns times three.

Xbox cost =400

Daniel's money =100

Xbox cost - Daniel money=300

yard cost =20

therefore 400 -100 /20

Daniel's need 15 yards to get the xbox

Answer:  D) right 9 units

Step-by-step explanation:

The Vertex form of a quadratic equation is: y = a(x - h)² + k     where

        → h is the horizontal shift (+ is right, - is left)

        → k is the vertical shift (+ is up, - is down)

y = f(x - 9)

            ↓

           h=9

Since h is positive, the graph moves 9 units to the RIGHT

Answer:

The graph of y = f(x) will shift right 9 units.

Step-by-step explanation:

If the -9 is inside the parenthesis, the graph g(x) shifts 9 points to the right.

Answer:

C-D/A=B

C minus D all of that over A = B

Answer:

5

Step-by-step explanation:

-4-(3+6²)÷13-1²•(-12)=

PEMDAS

parrenthesis:

-4-81÷13-1² x (-12)

exponent:

-4-81÷12 x (-12)

multiplication:

-4-81÷ (-144)

divison:

- 4 - (- 9)

subtraction (Actaully addition +):

= 5

-(- makes plus so -4 + 9 makes 5

Hope this helps, have a good day!! :)

Answer:

3

Step-by-step explanation:

First right out all the data in numerical order from left to right.

2, 2, 2, 3, 4, 5, 7

The median is the middle number in the set.  If there is an even amount of data points, find the average of the two middle numbers.  If there is an odd number of data points, like in this data set, just take the middle number as you median.

There are 7 data points in this set so the fourth number in the set written in numerical order would be your median.

When writing this set out in numerical order, repeated numbers must be repeated, we find that the fourth, or middle, number is 3.  Therefore, 3 is the median of this data set.

Answer:

y = (1/4)x+1.5

Step-by-step explanation:

Answer:

D or 16

Step-by-step explanation:

For perimeter, the formula is 2(L + W) where L is length, and W is width.

So 2 ( 2 + 6 )

= (4 + 12)

= 16

Answer:

the dog was running 3mph faster than david

Answer:

b is ur answer mate ....

Answer:

Let the cost of hiring diving equipment be X

Given,

cost of hiring diving equipment=X

cost of hiring wet suit =1/3 of X

Total cost of both =$144

Now,

X+1/3X=$144

or, (3X+X)/3=$144 ( taking l.c.m.)

or, 4X/3=$144

or, 4X=$144*3

or, X=$432/4

or, X=$108

Therefore, he paid $36 which is 1/3 of x to hire wetsuit.

Answer:

A

because x is the horizontal axis and it is moved forward by two because of the addition of 2

Answer:

9

Step-by-step explanation:

This is a right triangle.  We can use the Pythagorean theorem to determine the missing side.

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

a^2 + 12 ^2 = 15^2

a^2 +144 =225

a^2 = 225-144

a^2 = 81

Taking the square root of each side

a = 9

Answer:

9

Step-by-step explanation:

Because the triangle is a right triangle we can use the Pythagorean Theorem to solve for the missing side.

Pythagorean Theorem: a² + b² = c²

where

a = short leg

b = long leg

c = hypotenuse ( longest side )

we are given the hypotenuse and long leg and need to find the short leg

given hypotenuse (c) = 15

given long leg (b) = 12

short leg (a) = ?

to find the short leg plug in the known values into the Pythagorean Theorem and solve for a

a² + b² = c²

b = 12 and c = 15

a² + 12² = 15²

solve for a

a² + 12² = 15²

apply exponents

a² + 144 = 225

subtract 144 from both sides

a² = 81

take the square root of both sides

√a² = √81

a = 9

opposite angles of a llgrm are equal.

ABCD is a llgrm.

let angle A = 63 degree

so opposite angle of A is C is also 63.

let angle B=x degree =angle D

sum of all angles of a llgrm is 360 degree

angle A + angle B + angle C + angle D=360

63+x+63+x=360

126+2x=360

2x=360-126

x= 134/2

x=67

so the other angles are

A=63 B =67 C = 63 D = 67

All credit goes to

bijaymourya8114