Solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

[tex]\sqrt{x-2}[/tex] + 8 = x

Answer:

33 feet.

Step-by-step explanation:

Perimeter of a rectangle = 2*width + 2*length.

So here we have:

2*3 + 2*L = 72  where L = the length.

2L = 72 - 6 = 66

L = 33 feet.

Craig has 72 feet or 24 yards of material, with a stated width of 3 feet (1 yard). Subtracting the width of two sides from the total perimeter (24 yards), we find that the length of Craig's fence is 22 yards.

Craig has 72 feet of material to build a fence around a rectangular flower bed, with the width required to be 3 feet. To calculate the length of the fence in yards, we first need to find out the total perimeter in yards. Since Craig is using all 72 feet of material, this is the perimeter of the fence. We know that 1 yard is equal to 3 feet, so we convert 72 feet to yards.

To do this division, 72 feet ÷ 3 feet per yard = 24 yards. So, Craig has 24 yards of fencing material in total.

If one side (width) of the flower bed is 3 feet, which is equivalent to 1 yard, we must subtract the width of the two opposite sides from the total perimeter to find the total length of the fence. 24 yards total perimeter - 2 yards total width = 22 yards total length. Therefore, the length of Craig’s fence in yards is 22 yards.

Answer:

It will take them 15 minutes.

Step-by-step explanation:

1. Since you are given the information that the two typists are typing a certain amount of words in the same time frame (ie. one minute), you can add the two values together to obtain the total number of words the typists would type together in one minute:

95 + 98 = 193 words

2. To calculate how many minutes it would take them to type 2,895 words, you would simply take this total number of words and divide it by the number of words they collectively type in one minute (found in 1.). Thus:

2895/193 = 15

Therefor, it will take them 15 minutes to type 2,895 words.

Final answer:

To type 2,895 words, they would need approximately 15 minutes.

Explanation:

To solve this problem, we must first find the combined typing speed of both typists when working together.

Speed typist #1 can type 95 words per minute, and speed typist #2 can type 98 words per minute.

Together, they can type 95 + 98 = 193 words per minute.

Next, we need to calculate how many minutes it will take for them to type 2,895 words at this combined rate.

So, we divide the total number of words by the words per minute:

2,895 / 193 = 15 minutes

Therefore, it will take both typists working together approximately 15 minutes to type 2,895 words.

Common difference of a sequence is difference between any two consecutive terms in the sequence.

So let's pick up any two consecutive terms,

0 and 5,

difference between 0 and 5 is 5-0 = 5

so common difference is 5

Answer:

x = 5

Step-by-step explanation:

Since the triangle is right with hypotenuse of 13

Use Pythagoras' identity to solve for x

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 12² = 13²

x² + 144 = 169 ( subtract 144 from both sides )

x² = 25 ( take the square root of both sides )

x = [tex]\sqrt{25}[/tex] = 5

Answer:

The approximate average weight of 1 pallet is 1131 pounds.

Step-by-step explanation:

Given is -  the 18 tires of the fully loaded semi-truck bears approximately 3,300 pounds.

So, total weight bore by 18 tires = [tex]18\times3300=59400[/tex] pounds

Now given that the fully loaded truck holds 26 pallets.

And the unloaded truck weighs = 30000 pounds

So, weight of the load = [tex]59400-30000=29400[/tex] pounds

This is the weight of 26 pallets.

So, weight of 1 pallet = [tex]29400/26=1130.76[/tex] pounds

Hence, the approximate average weight of 1 pallet is 1131 pounds.

The approximate average weight of one pallet of cargo is 1,130.76 pounds.

To find the approximate average weight of one pallet of cargo, we first need to determine the total weight of the fully loaded truck and trailer. We know that the unloaded truck and trailer weigh 30,000 pounds.

Each of the 18 tires bears approximately 3,300 pounds when the truck is fully loaded.

The weight borne by the tires includes the weight of the truck, trailer, cargo, and the weight that would be supported by the 18th tire if it were present.

 First, we calculate the total weight supported by the 18 tires:

[tex]\[ 18 \text{ tires} \times 3,300 \text{ pounds/tire} = 59,400 \text{ pounds} \][/tex]

 However, this total includes the weight of the truck and trailer without the cargo.

To find the weight of the cargo alone, we need to subtract the weight of the unloaded truck and trailer from the total weight supported by the tires:

[tex]\[ 59,400 \text{ pounds} - 30,000 \text{ pounds} = 29,400 \text{ pounds} \][/tex]

 This 29,400 pounds is the total weight of the cargo carried by the 18 tires.

Since there are 26 pallets of cargo, we divide the total cargo weight by the number of pallets to find the average weight per pallet:

[tex]\[ \frac{29,400 \text{ pounds}}{26 \text{ pallets}} = 1,130.76\\[/tex]

 Therefore, the approximate average weight of one pallet of cargo is  1,130.76 pounds.

Answer:1/4(1-3x)

Step-by-step explanation:

Answer:Quadrilateral TRAP has an area that is one-fourth the area of quadrilateral HELP.

Step-by-step explanation: Because you rearrange the squares and it is 1/4

Answer:

Quadrilateral TRAP has an area that is one-fourth the area of quadrilateral HELP.

Step-by-step explanation:

The coordinates of k' after k is rotated 90 degrees about the origin is (-1, -2)

From the question, we have the following parameters that can be used in our computation:

K = (-2, 1)

Transformation:

rotated 90 degrees about the origin

The rule of rotation by 90 degrees about the origin is represented as

(x,y)→(−y,x) .

Substitute the known values in the above equation, so, we have the following representation

K' = (-1, -2)

Hence, the image of K is (-1, -2)

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Answer:

36°

Step-by-step explanation:

An angle whose vertex lies outside a circle whose sides are 2 secants of the circle is

angle = [tex]\frac{1}{2}[/tex] ( larger arc - smaller arc ), that is

42 = [tex]\frac{1}{2}[/tex] ( 120 - smaller ) ← multiply both sides by 2

84 = 120 - smaller, hence

smaller = 120 - 84 = 36°

Answer:

Step-by-step explanation:

(f · g)(x) = f(x) · g(x)

We have f(x) = 4x² and g(x) = x + 1. Substitute:

(f · g)(x) = (4x²)(x + 1)    use the distributive property

(f · g)(x) = (4x²)(x) + (4x²)(1)

(f · g)(x) = 4x³ + 4x²

Answer:

<R It rotates than flips look at the corners

Step-by-step explanation:

Look at the corners

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

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

m - slope

(x₁, y₁) - point

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

The general fom of an equation of a line:

[tex]Ax+By+C[/tex]

We have the equation 3x - 2y = 4 in standard form.

[tex]

f(x)=x+1 \\

g(x)=\dfrac{1}{x} \\

(f\cdot g)(x)=(x+1)\dfrac{1}{x} \\

(f\cdot g)(x)=\underline{\dfrac{x+1}{x}} \\ \\

0=\dfrac{x+1}{x} \\

0=\dfrac{x}{x}+\dfrac{1}{x} \\

0=1+\dfrac{1}{x} \\

-1=\dfrac{1}{x} \\

-x=1 \\

x=1

[/tex]

ANSWER

[tex]y \ne1[/tex]

EXPLANATION

The given functions are

[tex]f(x) = x + 1[/tex]

and

[tex]g(x) = \frac{1}{x} [/tex]

We want to find

[tex](f \times g)(x)[/tex]

We use function properties to obtain:

[tex](f \times g)(x) = f(x) \times g(x)[/tex]

[tex](f \times g)(x) = (x + 1) \times \frac{1}{x} = \frac{x + 1}{x} [/tex]

There is a horizontal asymptote at:

[tex]y = 1[/tex]

Let

[tex]y = \frac{x + 1}{x} [/tex]

[tex]xy = x + 1[/tex]

[tex]xy - x = 1[/tex]

[tex]x(y - 1) = 1[/tex]

[tex]x = \frac{1}{y - 1} [/tex]

The range is

[tex]y \ne1[/tex]

Or

[tex]( - \infty ,1) \cup(1, \infty )[/tex]

Answer:

A

Step-by-step explanation:

The percentage error is 25%.

We have,

The percent error can be calculated using the following expression:

Percent Error = (|Predicted Value - Actual Value| / Actual Value) * 100%

In this case,

Sam predicted he would sell 15 mugs, but he actually sold 20 mugs.

Plugging these values into the expression, we get:

Percent Error = (|15 - 20| / 20) * 100%

Simplifying further:

Percent Error = (5 / 20) * 100%

Percent Error = (1/4) * 100%

Percent Error = 25%

Therefore,

The percent error is 25%.

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ANSWER

[tex]\frac{ {y}^{2} }{ 25} - \frac{ {x}^{2} }{ 64} = 1 [/tex]

EXPLANATION

The given hyperbola has a vertical transverse axis and its center is at the origin.

The standard equation of such a parabola is:

[tex] \frac{ {y}^{2} }{ {a}^{2} } - \frac{ {x}^{2} }{ {b}^{2} } = 1 [/tex]

Where 2a=10 is the length of the transverse axis and 2b=16 is the length of the conjugate axis.

This implies that

[tex]a = 5 \: \: and \: \: b = 8[/tex]

Hence the required equation of the hyperbola is:

[tex]\frac{ {y}^{2} }{ {5}^{2} } - \frac{ {x}^{2} }{ {8}^{2} } = 1 [/tex]

This simplifies to,

[tex]\frac{ {y}^{2} }{ 25} - \frac{ {x}^{2} }{ 64} = 1 [/tex]

Answer:

[tex]\frac{(y^2}{25}-\frac{x^2}{64}=1[/tex]

Step-by-step explanation:

We have been given an image of a hyperbola. We are asked to write an equation for our given hyperbola.

We can see that our given hyperbola is a vertical hyperbola as it opens upwards and downwards.

We know that equation of a vertical hyperbola is in form [tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex], where, [tex](h,k)[/tex] represents center of hyperbola.

'a' is vertex of hyperbola and 'b' is co-vertex.

We can see that center of parabola is at origin (0,0).

We can see that vertex of parabola is at point [tex](0,5)\text{ and }(0,-5)[/tex], so value of a is 5.

We can see that co-vertex of parabola is at point [tex](8,0)\text{ and }(-8,0)[/tex], so value of b is 8.

[tex]\frac{(y-0)^2}{5^2}-\frac{(x-0)^2}{8^2}=1[/tex]

Therefore, our required equation would be [tex]\frac{(y^2}{25}-\frac{x^2}{64}=1[/tex].

Answer:

The equation is x = 4y + 13

Step-by-step explanation:

* Lets talk about the parametric equations

- Parametric equations are a set of equations that express a set

 of quantities as explicit functions of a number of independent

 variables

- Ex: x = at + b and y = ct + d are parametric equations

- We use them to find relation between the variables x and y

* Lets solve the problem

∵ x = 4t + 1 ⇒ (1)

∵ y = t - 3 ⇒ (2)

- The parameter is t to eliminate it find t in terms of x or y

- We will use equation (2) to find t in terms of y

∵ y = t - 3 ⇒ add 3 to both sides

∴ t = y + 3 ⇒ (3)

- Substitute the value of t in equation (3) in equation (1)

∵ x = 4t + 1

∵ t = y + 3

∴ x = 4(y + 3) + 1 ⇒ open the bracket

∴ x = 4y + 12 + 1 ⇒ add like term

∴ x = 4y + 13

* The equation is x = 4y + 13

To eliminate the parameter t from the parametric equations x=4t+1 and y=t-3, solve for t in one equation and substitute into the other. This results in a linear equation y=(1/4)x-13/4, revealing a linear relationship between x and y.

To rewrite the parametric equation by eliminating the parameter, we start with the given equations x=4t+1 and y=t-3. To eliminate the parameter t, we solve one of the equations for t and substitute into the other. From the first equation, we express t as t=(x-1)/4.

We can now substitute this expression for t into the second equation to get y=((x-1)/4)-3. With further simplification, we find the relationship between x and y to be y=(1/4)x-(1+12)/4, which simplifies to y=(1/4)x-13/4. This is a linear equation in x and y showing that the set of points defined by the parametric equations lies on a line.

Answer:

gets smaller.

Step-by-step explanation:

Quick Answer

To give you a short quick answer, the supplement is going to have to decrease or get smaller.

Example

Suppose the acute angle is 10 (anything under 90 will do).

Then the supplement is going to be 180 - 10 = 170

Now suppose the acute angle increase to 50 degrees.

That means the supplement will go from 180 - 50 = 130

Conclusion

As the acute angle gets bigger, the supplement gets smaller. This is an important idea to get clear. Bigger and Smaller or More or Less can be ugly little words, so anytime you come across them, pay attention. It will make your life in science so much easier.

Answer:

Part 1) The inequality that describes the relationship between the number of cookies each one of them has is [tex]x^{2} -30x+224\geq 0[/tex]

Part 2) Jessica has at least 2 cookies more than Martha

Step-by-step explanation:

Part 1) Find the inequality that describes the relationship between the number of cookies each one of them has

Let

x----> the number of cookies when Jessica started

30-x ----> the number of cookies when Martha started

we know that

Each of them ate 6 cookies from their bag

so

The cookies left in each bag are

(x-6)  ----> Jessica

and (30-x-6)=(24-x) ---> Martha

The product is equal to (x-6)(24-x)

The product of the number of cookies left in each bag is not more than 80.

so

[tex](x-6)(24-x)\leq 80\\ \\24x-x^{2}-144+6x\leq 80\\ \\-x^{2} +30x-144-80\leq 0\\ \\-x^{2} +30x-224\leq 0[/tex]

Multiply by -1 both sides

[tex]x^{2} -30x+224\geq 0[/tex]

Part 2) Solve the quadratic equation

[tex]x^{2} -30x+224\geq 0[/tex]

Solve by graphing

The solution is x=16 cookies

so

(30-x)=30-16=14 cookies

therefore

The number of cookies when Jessica started was 16 cookies

The number of cookies when Martha started was 14 cookies

The number of cookies left in each bag  is equal to

Jessica

16-6=10 cookies

Martha

14-6=8 cookies

Jessica has at least 2 cookies more than Martha

part 1- 30

part 2- 2

To simplify it at least those are the answers

12 dm.

The key to solve this problem is using the Pythagoras theorem given by the formula c² = a² + b², where a, b, and c are the sides of the right triangle.

Solving with the values given in the image:

With a = x , b = 5 dm, and c = 13 dm

(13dm)² = (x)² + (5 dm)²

169 dm² = (x)² + 25 dm²

(x)² = 169 dm² - 25 dm²

(x)² = 144 dm²

x = √144 dm²

x = 12 dm

Answer:

[tex]\large\boxed{(5r+2)(3r-4)=15r^2-14r-8}[/tex]

Step-by-step explanation:

[tex](5r+2)(3r-4)\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(5r)(3r)+(5r)(-4)+(2)(3r)+(2)(-4)\\\\=15r^2-20r+6r-8\qquad\text{combine like terms}\\\\=15r^2+(-20r+6r)-8\\\\=15r^2-14r-8[/tex]

Answer: O^2= 71.36

               O=8.45  

Answer:

The complete question is attached.

To find the variance and deviation, we have to use their definition or formulas:

[tex]\sigma=\sqrt{\frac{\sum (x- \mu)^{2} }{N}}[/tex]

So, first we have to find the difference between each number and the mean:

76-81=-5

87-81=6

65-81=-16

88-81=7

67-81=-14

84-81=3

77-81=-4

82-81=1

91-81=10

85-81=4

90-81=9

Now, we have to elevate each difference to the squared power and then sum all:

[tex]25+36+256+49+196+9+16+1+100+16+81=785[/tex]

Then, we replace in the formula:

[tex]\sigma=\sqrt{\frac{785}{11}} \approx 8.45[/tex]

The variance is just the squared power of the standard deviation. So:

[tex]\sigma^{2}=(8.45)^{2}=71.40[/tex]

Tan(angle) = Opposite leg / Adjacent leg

Tan (Angle) = 50/30

Angle = arctan(50/30)

Angle = 59.0 degrees.

Find the length of the ladder using the Pythagorean theorem:

50^2 + 30^2 = X^2

2500 + 900 = x^2

x^2 = 3400

x = √3400

x = 58.3 inches.

Answer:

59.03 deg

58.31 in

Step-by-step explanation:

The wall and the floor form a right angle. The parts of the wall and the floor from the corner until they intersect the ladder are the legs of a right angle. The ladder is the hypotenuse of the right angle.

You can use trigonometry to find the measure of the angle.

For the angle where the ladder touches the floor, the leg along the wall is the opposite leg, and the leg along the floor is the adjacent leg.

Use the tangent ratio.

[tex] \tan A = \dfrac{opp}{adj} [/tex]

[tex] \tan A = \dfrac{50}{30} = \dfrac{5}{3} [/tex]

[tex] A = \tan^{-1} \dfrac{5}{3} [/tex]

[tex] A = 59.03^\circ [/tex]

To find the length of the ladder, which is the hypotenuse of the triangle, you can use trigonometry again or the Pythagorean Theorem.

I'll use the Pythagorean Theorem.

[tex] a^2 + b^2 = c^2 [/tex]

[tex] (50~in)^2 + (30~in)^2 = c^2 [/tex]

[tex] 2500~in^2 + 900~in^2 = c^2 [/tex]

[tex] c^2 = 3400~in^2 [/tex]

[tex] c = \sqrt{3400~in^2} [/tex]

[tex] c = 10\sqrt{34}~in [/tex]

[tex] c \approx 58.31~in [/tex]

Answer:

The functions ordered from least to greatest y-intercept are

1) h(x) -----> y-intercept -1

2) g(x) ----> y-intercept 1

3) f(x) ----> y-intercept 2

Step-by-step explanation:

we know that

The y-intercept (or initial value) is the value of y when the value of x is equal to zero

Part 1) Find the y-intercept of g(x)

Remember that the initial value of the fuction is equal to the y-intercept

a=1 -----> is the initial value

therefore

The y-intercept of g(x) is 1

Part 2) Find the y-intercept of f(x)

Observing the table

For x=0

f(x)=2

therefore

The y-intercept of f(x) is 2

Part 3) Find the y-intercept of h(x)

Observing the graph

For x=0

h(x)=-1

therefore

The y-intercept of h(x) is -1

Answer:

1 3 2

Step-by-step explanation:

Answer:

18%

Step-by-step explanation:

We are given that the cost of a jacket increased from $95.00 to $112.10 and we are to find the percentage increase in the cost of the jacket.

We know that the formula of percentage increase if given by:

Percentage increase = (new value - initial value)/initial value × 100

So substituting the given values to get:

Percentage increase = [tex] \frac { 1 1 2 . 1 0 - 9 5 . 0 0 } { 9 5 . 0 0 } \times 1 0 0 [/tex] = 18%

Answer:

f

Step-by-step explanation:

4x+3

x>1  x=2

4*2+3= 11

y>or = to 11

Answer:

False.

Step-by-step explanation:

This is the absolute value of x  so if x < 0 then f(x) will be x not -x.

The function f(x) = 1/x can be represented as a piecewise function with different cases for x > 0, x < 0, and x = 0. It is not defined at x = 0, and it approaches positive or negative infinity as x approaches 0 from either side.

To represent the function f(x) = 1/x as a piecewise function, we need to consider the nature of the function around x = 0. The function is undefined at x = 0, and it approaches positive infinity as x approaches zero from the negative side and negative infinity from the positive side.

Piecewise Representation:

This can be written as a piecewise function:

Answer:

3 b^5 c^5

Step-by-step explanation:

3•b•b•b•b•b•c•c•c•c•c

There is 1 number 3  = 3

There are 5 letter b   = b^5

There are 5 letter c  = c^5

3 * b^5 * c^5

3 b^5 c^5

Answer:

In 3•b•b•b•b•b•c•c•c•c•c, there is one three, five b's, and five c's. By simplifying the expression, we get 3[tex]b^{5}c^{5}[/tex].

Answer: 1.587 ounces of sodium chloride

Step-by-step explanation:

We know that 1 ounce is equivalent to 28.35 gr.

So we use this as a conversion factor to find the equivalent amount of sodium chloride in ounces.

If we need 45 grams of sodium chloride then this equals to:

[tex]45\ g* \frac{1\ ounces}{28.35\ gr} = 1.587\ ounces[/tex]

Finally you need 1.587 ounces of sodium chloride

Answer:

1.587 ounces

Step-by-step explanation:

We need to measure out 45 grams of sodium chloride using the bottle mentioning units of measure in units.

We are to find the number of ounces of sodium chloride that we will need.

We know that:

1 ounce = 28.35 grams

So using the ratio method to find the number of ounces of Sodium Chloride needed.

[tex]\frac{1 ounce}{x} =\frac{28.35 g}{45 g}[/tex]

[tex]= \frac{45}{28.35} = [/tex] 1.587 ounces

Answer:

The approximate difference between m∠C and m∠A is 45° to the nearest degree

Step-by-step explanation:

* Lets talk about the right triangle

- It has one right angle and two acute angles

- The side opposite the the right angle is called hypotenuse

- The other sides are called the legs of the right angle

- In ΔABC

∵ AC is the hypotenuse

∴ ∠B is the right angle

∴ AB and BC are the legs of the right angle

∴ Angles A and C are the acute angles

∵ m∠B = 90°

- The sum of the measures of the interior angles of a Δ is 180°

∴ m∠A + m∠C = 180° - 90° = 90°

- We will use trigonometry to find the measures of angles A and C

- sin A is the ratio between the opposite side to angle ∠A and the

  hypotenuse

∵ BC is the opposite side of angle A

∴ sin A = BC/AC

∵ BC = 5 cm

∵ AC = 13 cm

∴ sin A = 5/13

- Lets find m∠∠A by using sin ^-1

∴ m∠A = [tex]sin^{-1}\frac{5}{13}=22.62[/tex]

- Lets use the rule of the sum of angles A and C to find the measure

 of the angle C

∵ m∠A + m∠C = 90°

∴ 22.62° + m∠C = 90 ⇒ subtract 22.62 from both sides

∴ m∠C = 67.38°

- Lets find the difference between m∠C and m∠A

∴ The approximate difference between m∠C and m∠A is:

  67.38° - 22.62° = 44.78° ≅ 45° to the nearest degree