Rational numbers do NOT include:
infinite decimals
repeating decimals
terminating decimals

Answer:

x = 12

x = 4

Step-by-step explanation:

Answer:

X=12

X=4

Step-by-step explanation:

Step-1 : Multiply the coefficient of the first term by the constant 1 • 48 = 48

Step-2 : Find two factors of 48 whose sum equals the coefficient of the middle term, which is -16 .

-48 + -1 = -49

-24 + -2 = -26

-16 + -3 = -19

-12 + -4 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -4

x2 - 12x - 4x - 48

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-12)

Add up the last 2 terms, pulling out common factors :

4 • (x-12)

Step-5 : Add up the four terms of step 4 :

(x-4) • (x-12)

Which is the desired factorization

Answer:

V=90m³

Step-by-step explanation:

If a rectangular prism has a length of 5 meters, a width of 6 meters, and a height of 3 meters, the volume of the prism is 90m³.

Formula: V=whl

V=whl=6·3·5=90m³

Answer : The length of the rectangle (a) is, 8 cm

Step-by-step explanation :

As we are given that,

Area of rectangle = [tex]24cm^2[/tex]

Length of rectangle = a

Breadth of rectangle = a - 5

As we know that,

Area of rectangle = Length × Breadth

Now put all the given values in this formula, we get the value of 'a'.

[tex]24cm^2=(a)\times (a-5)[/tex]

[tex]24cm^2=a^2-5a[/tex]

[tex]a^2-5a-24=0[/tex]

By the solving the term 'a', we get the value of 'a'.

a = 8

Thus,

Length of rectangle = a = 8 cm

Breadth of rectangle = a - 5 = 8 - 5 = 3 cm

Therefore, the length of the rectangle (a) is, 8 cm

The length a of the rectangle is 8 cm

To solve the above questions, we need to recall some of the formulas as follows:

Area of Square = (Length of Side)²

Perimeter of Square = 4 × (Length of Side)

Area of Rectangle = Length × Width

Perimeter of Rectangle = 2 × ( Length + Width )

Area of Rhombus = ½ × ( Diagonal₁ + Diagonal₂ )

Perimeter of Rhombus = 4 × ( Length of Side )

Area of Kite = ½ × ( Diagonal₁ + Diagonal₂ )

Perimeter of Kite = 2 × ( Length of Side₁ + Length of Side₂ )

Let us now tackle the problem !

Given:

Area of Rectangle = A = 24 cm²

Length of Rectangle = L = a cm

Width of Rectangle = W = (a - 5) cm

Unknown:

Length of Rectangle = a = ?

Solution:

This problem is about Area of Rectangle.

[tex]\text{Area of Rectangle} = \text{Length} \times \text{Width}[/tex]

[tex]A = L \times W[/tex]

[tex]24 = a \times (a - 5)[/tex]

[tex]24 = a^2 - 5a[/tex]

[tex]a^2 - 5a - 24 = 0[/tex]

[tex](a - 8)(a +3) = 0[/tex]

[tex](a - 8) = 0[/tex]

[tex]a = \boxed {8 ~ \text{cm}}[/tex]

Grade: College

Subject: Mathematics

Chapter: Two Dimensional Figures

Keywords: Perimeter, Area , Square , Rectangle , Side , Length , Width

For this case we have that by definition, the point-slope equation of a line is given by:

[tex]y-y_ {0} = m (x-x_ {0})[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}) :( 2,6)\\(x_ {2}, y_ {2}) :( 4,0)\\m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0-6} {4-2} = \frac {-6} {2} = -3[/tex]

We chose a point:

[tex](x_ {0}, y_ {0}) :( 4,0)[/tex]

Substituting in the equation we have:

[tex]y-0 = -3 (x-4)\\y = -3 (x-4)[/tex]

Finally, the equation is: [tex]y = -3 (x-4)[/tex]

Answer:

OPTION C

Answer:

Third option:  [tex]y=-3(x-4)[/tex]

Step-by-step explanation:

The equation of the line in Point-Slope form is:

[tex]y-y_1=m(x-x_1)[/tex]

Where "m" is the slope and [tex](x_1,y_1)[/tex] is a point on the line.

Given the points  (4, 0) and (2, 6), we can find the slope with this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting values, we get:

 [tex]m=\frac{0-6}{4-2}=-3[/tex]

Finally, substituting the slope and the point (4,0) into  [tex]y-y_1=m(x-x_1)[/tex], we get:

 [tex]y-0=-3(x-4)[/tex]

 [tex]y=-3(x-4)[/tex]

Answer:

A. 5(9x-z)

Step-by-step explanation:

45x-5z

We can factor out a 5 from each term

5(9x -z)

Answer:

A.

Step-by-step explanation:

Given the expression, 45x - 5z, you have to think what can be factored out of BOTH terms.

we know 5 is a factor of both terms, so it can be taken out

=

5(9x - z), nothing else can be factored

Answer:

First part:

Set h(t) = 17and solve for t.

-16t²+ 58t + 7= 17

-16t² + 58t - 10 = 0

Solve this quadratic equation for t. You should get 2 positive solutions. The lower value is the time to reach 17 on the way up, and the higher value is the time to reach 17 again, on the way down.

Second part:

Set h(t) = 0 and solve the resulting quadratic equation for t. You should get a negative solution (which you can discard), and a positive solution. The latter is your answer.

The time required to reach 17 feet and the ground by the ball is required.

The time taken to reach 17 feet is 0.181 s.

To reach the ground the time taken is 3.74 s.

The equation is

[tex]h=-16t^2+58t+7[/tex]

[tex]h=17[/tex]

[tex]17=-16t^2+58t+7\\\Rightarrow -16t^2+58t-10=0\\\Rightarrow t=\frac{-58\pm \sqrt{58^2-4\left(-16\right)\left(-10\right)}}{2\left(-16\right)}\\\Rightarrow t=0.181,3.44[/tex]

The time taken reach a height of 17 feet while going up is 0.181 s.

On the ground [tex]h=0[/tex]

[tex]0=-16t^2+58t+7\\\Rightarrow t=\frac{-58\pm \sqrt{58^2-4\left(-16\right)\times 7}}{2\left(-16\right)}\\\Rightarrow t=-0.12,3.74[/tex]

The time taken to reach the ground is 3.74 s.

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Answer:

716 yards

Step-by-step explanation:

Circumference = π × Diameter

2 × Radius = Diameter

2 × 114 = 228

Circumference = π × Diameter

Circumference = π × 228 = 228π = 716.283125018

Answer:

716 yd

Step-by-step explanation:

The circumference of a circle is 2*pi*radius.

The radius is 114 yd so the circumference is 2*pi*114 yd.

Put into the calculator and you obtain 716.283 yd.

The answer to the nearest yard is 716.

Answer:

13. A

14. C.

Step-by-step explanation:

A relation is a function if there is only one y assigned to each x.

That is if you have a set of points, there should be no repeated x value.

So looking at {(0,0),(-2,4),(-2,-4),(-3,7)} this is not a function because you have two x's that are the same. A.

The slope-intercept form of a linear equation is y=mx+b where m is the slope and b is the y-intercept.

The y-intercept is where the graph goes through the y-axis at.  It goes through at -1 so b=-1.

The slope is rise/run.  So starting from the y-intercept (0,-1) we need to find another point to count the rise & run to... How about (3,1)? That works.  You can do the counting if you want. You could also use the slope formula.

To use the slope formula, I just like to line the points up vertically and subtract vertically then put 2nd difference over the 1st difference.

(0,-1)

-(3,1)

--------

-3  -2

So the slope is -2/-3 or just 2/3.

So the equation is y=2/3 x-1

C.

Y = 6

13 + [tex]\frac{6}{y}[/tex] means that we are adding 13 and 1 together because 6 divided by 6 is 1.

13 + 1 = 14

Answer:

35 and 36

Step-by-step explanation:

If the smaller dimension is x, then the larger dimension is x + 1.  Therefore:

2x + 2(x + 1) = 142

2x + 2x + 2 = 142

4x = 140

x = 35

One dimension is 35, and the other dimension is 36.

Answer:

The dimensions of the rectangle are 35 inches by 36 inches.

Step-by-step explanation:

If the length and width are consecutive integers and L=n, then W=n+1 assuming the width is larger.

We are given the perimeter is 142 inches so: 2L+2W=142.

Substituting L=n and W=n+1 we have:   2(n)+2(n+1)=142.

Let's solve it:

2(n)+2(n+1)=142

Distribute:

2n+2n+2=142

Combine like terms:

4n+2=142

Subtract 2 on both sides:

4n=140

Divide both sides by 4:

n=140/4

n=35

Since L=n, then the length is 35 inches.

Since W=n+1, then the width is 36 inches.

The dimensions of the rectangle are 35 inches by 36 inches.

Final answer:

There are three pairs of parallel faces in a cube, as each face has one parallel counterpart. An icosahedron has no parallel faces. When standing between two parallel mirrors, an infinite series of images is theoretically created, but only a finite number can be seen due to practical limits.

Explanation:

To determine the number of pairs of parallel faces in a geometric shape, we have to consider the characteristics of the shape provided. In the case of a cube, which seems to be the most closely related shape mentioned in the details provided, there are three pairs of parallel faces. Each face of a cube is parallel to one other face that is opposite to it. For instance, the top face of the cube is parallel to the bottom face, one of the side faces is parallel to the face directly opposite to it, and the same applies to the front and back faces.

If the student's question instead pertains to an icosahedron, which is mentioned among the details, an icosahedron does not have any parallel faces as it is made up of equilateral triangles, and each face is inclined to the others.

For the discussion question regarding images formed between two parallel mirrors, an infinite number of images would be formed. This is because the mirrors reflect not only the object but also the images in the other mirror, thus creating a series of reflections that seem to go on indefinitely. However, due to practical limitations such as the quality of the mirror and ambient light, only a finite number of these images can actually be observed.

Answer:

After  x/450 minutes

Step-by-step explanation:

The speed uphill is 200 ft/min

The speed down hill is 250 ft/min

Lets take the hiking distance top to down hill is x ft

Remember speed=distance/time

Relative speed =200+250=450ft/min

Time to meet=distance/relative speed

Time to meet=x/450 min

Final answer:

To find out how long it will take until you meet, we need to determine the distances each hiker covers and then divide it by their respective rates.

Explanation:

To find out how long it will take until you meet, we need to determine the distances each hiker covers and then divide it by their respective rates.

The first hiker covers a certain distance while hiking uphill, while the second hiker covers a certain distance while hiking downhill. When they meet, their combined distances will add up to the total distance of the trail.

Let's say it takes x minutes for you to meet. The first hiker covers a distance of 200x feet in x minutes, while the second hiker covers a distance of 250x feet in the same x minutes. When they meet, their combined distances will equal the length of the trail, so we can set up the equation: 200x + 250x = total distance. Solving for x will give us the time it takes for you to meet.

Answer:

B: 1/5

Step-by-step explanation:

If the lines are perpendicular, they have negative reciprocal slopes

s has a slope of -5

t must have a slope of - (1/ -5)

                                    = 1/5

X is left to right. Since the translation is X + 1 , you are adding 1 to the X direction, which moves the shape 1 place to the right.

Y is up and down, the translation is y - 2, which means the shape moves 2 places down.

Looking at one point on the original image, lets use Point C. It is located at X = 2 and Y = 1. Now add 1 to the X and subtract 2 from the y:

The new location for C needs to be X = 2+1 = 3 and Y = 1-2 = -1

The image that has C at (3,-1) is C.

Answer:

910$

Step-by-step explanation:

It's easiest if we just add the width and length together to start which would be 2 sides of the fence so we multiply by 2 to complete the whole perimeter.

80+60 = 140 x 2 = 280

Now you need to multiply 280 by 3.25 because that is what it will cost in the end since the 280 is all of the feet together and the 3.25 is each foot's price.

3.25 x 280 = 910

910$

Answer:

It will take 143 minutes to take the pictures

Answer:

70%

Step-by-step explanation:

The probability it rains on at least one of the days is:

P = P(Sat & not Sun) + P(Sun & not Sat) + P(Sat & Sun)

P = (0.40)(1−0.50) + (0.50)(1−0.40) + (0.40)(0.50)

P = 0.20 + 0.30 + 0.20

P = 0.70

Another way to look at it is 1 − the probability that it doesn't rain on either day.

P = 1 − P(not Sat & not Sun)

P = 1 − (1−0.40)(1−0.50)

P = 1 − 0.30

P = 0.70

There is a 70% probability that it will rain on at least one day.

The probability that it will rain on at least one day over the weekend is 70%, based on independent probabilities given for Saturday and Sunday.

The subject of your question is probability, a branch of mathematics that studies randomness and the likelihood of events occurring. To calculate the probability that it will rain over the weekend, i.e., on at least one of the days (Saturday or Sunday), we first need to find the probability that it won't rain on either day.

The probability it doesn't rain on Saturday is 60% (100% - 40%), and the probability it doesn't rain on Sunday is 50% (100% - 50%). Since these events are independent, we multiply these probabilities to find the joint probability. Therefore, the probability it doesn't rain on either day is 30% (0.6 × 0.5 = 0.3).

Now, this is the case which we don’t want (no rain), so the case we want (that it rains at least one day) is the complementary event of this. Thus, we subtract this from the total probability, which is 1, yielding a 70% (1 - 0.3) probability that it will rain on at least one of the days over the weekend.

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10

If you treat the number as x, then [tex]\frac{1}{2}x=x+5\to-5=\frac{1}{2}x\to-10=x[/tex].

Answer:

A) 6^2 + 11^2 is not equal to 15^2

Step-by-step explanation:

To find out if a right triangle is a right triangle you have to use the Pythagorean Theorem, like it is used in A.

6^2 + 11^2 = 15^2

36 + 121 = 225

157 does not equal 225

So this is not a right triangle

Answer:

Option A

Step-by-step explanation:

Given in the picture is a triangle ABC with three sides given as 6,11 and 15

By the picture itself we can say that the largest angle is obtuse and hence the triangle is not right angled.

Using the converse of Pythagorean theorem that in a right triangle sides square add upto square of hypotenuse let us check whether this applies to this triangle.

Small sides are 6 and 11

Squaring and adding gives

[tex]6^2+11^2 = 187[/tex]

Large side = 11 and square is

[tex]15^2 =225 > 121[/tex]

Hence this is not a right triangle but obtuse

So option A is right

Answer:

The measure of the arc x is 130°

Step-by-step explanation:

we know that

The semi-inscribed angle is half that of the arc it comprises

so

65°=(1/2)[arc x]

solve for x

arc x=(2)(65°)=130°

Answer:

D) 20 in

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h  where r is the radius and h is the height

Substituting what we know

980 pi = pi (7)^2 h

Divide each side by pi

980 pi /pi= pi 49 h/pi

980 = 49h

Divide each side by 49

980/49 = 49h/49

20 =h

Answer:

h ≈ 20 inches

Step-by-step explanation:

Given volume 980 pi inches cubed and radius 7 inches.

Using the height formula for right cylinder

h = V/π r^2

h = 3078.78/π7^2

h ≈ 20 inches

Answer:

[tex]\frac{7\sqrt{5} }{8}[/tex]

Step-by-step explanation:

Using the rules of radicals

[tex]\sqrt{\frac{a}{b} }[/tex] = [tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex]

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Given

[tex]\sqrt{\frac{245}{64} }[/tex] = [tex]\frac{\sqrt{245} }{\sqrt{64} }[/tex]

Simplifying the radicals

[tex]\sqrt{245}[/tex]

= [tex]\sqrt{5(7)(7)}[/tex]

= [tex]\sqrt{49(5)}[/tex]

= [tex]\sqrt{49}[/tex] × [tex]\sqrt{5}[/tex] = 7[tex]\sqrt{5}[/tex]

and

[tex]\sqrt{64}[/tex] = 8

The simplified radical is

[tex]\frac{7\sqrt{5} }{8}[/tex]

Answer:

Step-by-step explanation:

x + 2 = 5       subtract 2 from both sides

x + 2 - 2 = 5 - 2

x = 3

Check:

3 + 2 = 5     CORRECT :)

Add the totals of each item together:

189.99 + 249.95 + 493.68 + 98.75 + 98.75 = 1,131.12

Now multiply that by the tax rate as a decimal:

1131.12 x 0.0725 = 82.01

Now add that to the total of the items:

1,131.12 + 82.01 = $1,213.13 total

For this case we have that the total of the purchase is given by:

Coffee table: $ 189.99

Loveseat: $ 249.95

Sofa: $ 493.68

2 chairs: 2 * $ 98.75 = $ 197.5

Adding up we have: $ 1131.12

Now, we must find the tax amount:

$ 1131.12 ----------> 100%

x ------------------------> 7.25%

Where "x" represents the value of the tax:

[tex]x = \frac {7.25 * 1131.12} {100}\\x = 82.0062[/tex]

Finally, the amount to be paid is:

$ 1131.12 + $ 82.0062 = $ 1213.13

Answer:

Option B

Answer:

Yes, it's undefined.

The slope is undefined.

Step-by-step explanation:

Slope formula:

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\displaystyle \frac{5-(-3)}{6-6}=\frac{8}{0}=0[/tex]

Therefore, the slope is undefined.

Hope this helps!

Answer:

undefined

Step-by-step explanation:

To find the slope of a line, we use the equation

m = (y2-y1)/(x2-x1)

    = (5--3)/(6-6)

   = (5+3)/(6-6)

  =8/0

 Anything divided by 0 is undefined, so the slope is undefined

Answer:

n=4p

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

[tex]3x - y = - 2[/tex]

Step-by-step explanation:

The given line PQ passes through the points P(-5,-13) and Q(5,17) .

Find the slope using the formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

Plug in the points to get:

[tex]m = \frac{17 - - 13}{5 - - 5} [/tex]

[tex]m = \frac{30}{10} [/tex]

[tex]m = 3[/tex]

Use the point-slope formula :

[tex]y-y_1 = m(x - x_1)[/tex]

Substitute the point (5,17)

[tex]y - 17 = 3(x - 5)[/tex]

Expand:

[tex]y - 17 = 3x - 15[/tex]

The standard form is when the equation is put in the form

[tex]ax + by = c[/tex]

Regroup the terms to get:

[tex]3x - y = - 17 + 15[/tex]

The standard form is

[tex]3x - y = - 2[/tex]

Answer:

A. Louisa made an error when determining the original solution of x = 56.

Step-by-step explanation:

1/4x - 3 = 3/8x + 4

To verify x=56 is a solution, substitute x=56 into the equation

1/4(56) - 3 = 3/8(56) + 4

Multiply

14 -3 = 21 +4

Combine like terms

11 = 25

The steps are correct.

x=56 must not be a solution to the equation

Answer:

option A

Step-by-step explanation:

Given that Louisa states that the solution to the equation 1/4x - 3 = 3/8x + 4 is x = 56.

She did the following steps

Step 1 is right because she substituted x=14 to check whether right side = left side

Step 2: Multiplication is done correctly

Step 3: Is incorrect because 11 can never be equal to 25 in Mathematics.

Hence the mistake she did is not in substitution, multiplication or addition/subtraction. But in determining the original solution

Hence A)  Louisa made an error when determining the original solution of x = 56.

Answer:

5/9, 2/7, 3/10 are all rational numbers

Step-by-step explanation:

Remember that all rational numbers are able to be written as a fraction or ratio of two integers.

Answer:

[tex]\frac{2}{7}+\sqrt{121}[/tex]

Step-by-step explanation:

Since, a real number is called rational number if it can be expressed in the form of [tex]\frac{p}{q}[/tex],

Where, p and q are integers,

S.t. q ≠ 0,

If the number is not a rational number then it is irrational,

Now, the sum or difference of two rational numbers is a rational number,

While, the sum or difference of a rational number and an irrational number is an irrational number.

∵ √18, √11 and [tex]\pi[/tex] are irrational numbers,

Also, [tex]\frac{5}{9}[/tex], [tex]\sqrt{16}[/tex] and [tex]\frac{3}{10}[/tex] are rational number,

[tex]\implies \frac{5}{9}+\sqrt{18},\pi+\sqrt{16}, \frac{3}{10}+\sqrt{11}\text{ are irrational numbers}[/tex]

Now,

[tex]\frac{2}{7}\text{ and }\sqrt{121}\text{ are rational numbers}[/tex]

Hence,

[tex]\frac{2}{7}+\sqrt{121}\text{ is rational number}[/tex]