Jorie leaves work 30 minutes late. She decides to make up time by taking the toll road instead of side streets. She can travel four times faster by taking the toll road. Create an equation to represent her total travel time, including wait time, where x is the number of minutes the drive was expected to take.
A. y = \frac{1}{4}x -30
B. y = 4x - 30
C. y = \frac{1}{4}x + 30
D. y = 4x + 30

Answer:

Option 2 - 3.2 inches.                      

Step-by-step explanation:

Given : The lengths of two sides of a right triangle are 5 inches and 8 inches.

To find : What is the difference between the two possible  lengths of the third side of the triangle?

Solution :

According to question, it is a right angle triangle

Applying Pythagoras theorem,

[tex]H^2=P^2+B^2[/tex]

Where, H is the hypotenuse the longer side of the triangle

P is the perpendicular

B is the base

Assume that H=8 inches and B = 5 inches

Substitute the value in the formula,

[tex]8^2=P^2+5^2[/tex]

[tex]64=P^2+25[/tex]

[tex]P^2=64-25[/tex]

[tex]P^2=39[/tex]

[tex]P=\sqrt{39}[/tex]

[tex]P=6.24[/tex]

Assume that P=8 inches and B = 5 inches

Substitute the value in the formula,

[tex]H^2=8^2+5^2[/tex]

[tex]H^2=64+25[/tex]

[tex]H^2=89[/tex]

[tex]H=\sqrt{89}[/tex]

[tex]H=9.43[/tex]

Therefore, The possible length of the third side of the triangle is

[tex]L=H-P[/tex]

[tex]L=9.43-6.24[/tex]

[tex]L=3.19[/tex]

Therefore, The difference between the two possible  lengths of the third side of the triangle is 3.2 inches.

So, Option 2 is correct.

The difference between the two possible lengths of the third side, rounded to the nearest tenth, is:

B. 3.2 inches

To determine the difference between the two possible lengths of the third side of a right triangle with given side lengths of 5 inches and 8 inches, we need to consider both cases where the unknown side could be the hypotenuse or one of the legs. We use the Pythagorean theorem, [tex]\(a^2 + b^2 = c^2\)[/tex].

Case 1: The unknown side is the hypotenuse [tex](\(c\))[/tex]

[tex]\[ c = \sqrt{5^2 + 8^2} = \sqrt{25 + 64} = \sqrt{89} \approx 9.4 \, \text{inches} \][/tex]

Case 2: The unknown side is one of the legs [tex](\(a\) or \(b\))[/tex]

Assume the known hypotenuse is 8 inches. Using the Pythagorean theorem, we solve for the other leg.

[tex]\[ 8^2 = 5^2 + x^2 \][/tex]

[tex]\[ 64 = 25 + x^2 \][/tex]

[tex]\[ x^2 = 64 - 25 \][/tex]

[tex]\[ x^2 = 39 \][/tex]

[tex]\[ x = \sqrt{39} \approx 6.2 \, \text{inches} \][/tex]

Difference between the two possible lengths

The two possible lengths of the third side are approximately 9.4 inches and 6.2 inches. The difference between these lengths is:

[tex]\[ 9.4 - 6.2 = 3.2 \][/tex]

Therefore, the difference between the two possible lengths of the third side, rounded to the nearest tenth, is:

B. 3.2 inches

The correct question is:

The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible

lengths of the third side of the triangle? Round your answer to the nearest tenth.

A. 3.1 inches

B. 3.2 inches

C. 10.0 inches

D. 15.7 inches

Answer: B. DE

Since DE spans the entire circle it is the diameter :)

Answer:

B) DE is the diameter.

Step-by-step explanation:

Given  : A circle with center O.

To find : Which of the following segments is a diameter of O.

Solution : We have given circle with center O.

Diameter : A straight line passing from side to side through the center of a circle .

So, segment CF and DE are diameter of a circle which are passes through the center O.

Therefore, B) DE is the diameter.

[tex]\bf 3y+x=9\implies 3y=-x+9\implies y=\cfrac{-x+9}{3}\implies y=\cfrac{-x}{3}+\cfrac{9}{3} \\\\\\ y=\stackrel{\stackrel{m}{~\hfill \downarrow }}{-\cfrac{1}{3}} x+3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

To find the volume of a container in liters, knowing it holds 5.5 gallons, we use the conversion factor that 1 gallon is approximately 3.85 liters. Multiplying this conversion factor with the gallon, we obtain approximately 21.175 liters. Rounded to the nearest hundredth, the volume is 21.18 liters.

The subject of this question falls under Mathematics, particularly volume conversions. Given that 1 liter is approximately equal to 0.26 gallons, you want to find out the volume of a container, to the nearest hundredth of a liter, that holds 5.5 gallons.

To help you understand the process, here is a step-by-step explanation:

Remember, all conversions rely on the accuracy of the conversion factor. In this case, the conversion factor of 1 liter being approximately equal to 0.26 gallons was provided, and we took the inverse of it to convert gallons to liters.

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Answer:

x=6

Step-by-step explanation:

So we have the difference of the intercept arcs divided by 2 is the angle formed by the two tangents there.  

So we have

[tex]\frac{(37x+5)-(23x-5)}{2}=5x+17[/tex]

Clear the fraction by multiplying both sides by 2:

[tex](37x+5)-(23x-5)=2(5x+17)[/tex]

Distribute:

[tex]37x+5-23x+5=10x+34[/tex]

Combine like terms on the left hand side:

[tex]37x-23x+5+5=10x+34[/tex]

Simplify:

[tex]14x+10=10x+34[/tex]

Subtract 10x on both sides:

[tex]4x+10=34[/tex]

Subtract 10 on both sides:

[tex]4x=24[/tex]

Divide both sides by 4:

[tex]x=6[/tex]

Answer:

23x -5 + 37x + 5= 360

x = 6

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

41

-4 ≤2+4x<0

Subtract 2 from all sides

-4-2 ≤2-2+4x<0-2

-4 ≤2+4x<0

Divide all sides by 4

-6/4 ≤4x/4<-2/4

-3/2 ≤x <-1/2

graph is attached

45

2x-3 ≤-4  or 3x+1 ≥4

Lets solve the left side first

2x-3≤-4

Add 3 to each side

2x-3+3 ≤-4+3

2x ≤-1

Divide by 2

2x/2  ≤-1/2

x  ≤-1/2

Now solve the right inequality

3x+1 ≥4

Subtract 1 from each side

3x+1-1 ≥4-1

 3x ≥3

Divide by 3

3x/3 ≥3/3

x≥1

So we have

x  ≤-1/2 or x≥1

see attached

Notice closed circles where there is a greater than equal to  or less than equal to

Answer:

The statements which accurately describe f(x) are

The domain is all real numbers ⇒ 1st answer

The initial value of 3 ⇒ 3rd answer

The simplified base is 3√2 ⇒ last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- The form of the exponential function is f(x) = a(b)^x, where a is the

  initial value , b is the base and x is the exponent

- The values of a and b are constant

- The domain of the function is the values of x which make the function

  defined

- The range of the function is the set of values of y that correspond

  with the domain

* Lets solve the problem

∵ [tex]f(x)=3(\sqrt{18}) ^{x}[/tex]

- The simplest form of is :

∵ √18 = √(9 × 2) = √9 × √2

∵ √9 = 3

∴ √18 = 3√2

∴ [tex]f(x)=3(3\sqrt{2})^{x}[/tex]

∵ [tex]f(x)=a(b)^{x}[/tex]

∴ a = 3 , b = 3√2

∴ The initial value is 3

∴ The simplified base is 3√2

- The exponent x can be any number

∴ The domain of the function is x = (-∞ , ∞) or {x : x ∈ R}

- There is no value of x makes y = 0 or negative number

∴ The range is y = (0 , ∞) or {y : y > 0}

* Lets find the statements which accurately describe f(x)

# The domain is all real numbers

∵ The domain is {x : x ∈ R}

∴ The domain is all real numbers

# The initial value is 3

∵ a = 3

∵ a is the initial value

∴ The initial value of 3

# The simplified base is 3√2

∵ b = √18

∵ b is the base

∵ The simplified of √18 is 3√2

∴ The simplified base is 3√2

- For more understand look to the attached graph

The missing value in your ratio equation /60 = 85/100 is determined by cross-multiplying and solving the resulting equation. By doing this, we find that the missing value is 51.

This is a Mathematics question about ratios and finding missing values in ratios. Let’s solve the equation /60 = 85/100. The missing value in your ratio equation represents a fraction that is equivalent to 85/100. To find the missing value, start by cross-multiplying:

missing value * 100 = 60 * 85

missing value * 100 = 5100

Finally, divide both sides by 100 to isolate the missing value:

missing value = 5100 / 100 = 51.

Therefore, the missing value in your ratio equation is 51.

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Step-by-step explanation:

5^(3b−1) = 5^(b−3)

Since the bases are equal, the exponents must also be equal.

3b − 1 = b − 3

2b = -2

b = -1

Answer:

Quadrant III

Step-by-step explanation:

(-4,5)  is in the II quadrant    because the x is negative and the y is positive

II                       I

(-,+)                     (+,+)            

-------------------------------------  X axis

III                         IV

(-,-)                         (+.-)

reflecting over the x axis means  it would be in the third quadrant

Answer:

Area is one half base times height. So base times height is 36 then divide out the 3 to get 12.

The height of a triangular-shaped mat with an area of 18 square feet and a base of 3 feet is 12 feet. This is determined using the formula A = 1/2 × base × height, and ensuring the answer has the correct number of significant figures when using different units or measurements.

To find the height of a triangular-shaped mat with an area of 18 square feet and a base of 3 feet, we can use the area formula for a triangle: A = 1/2 × base × height. In this case, we need to solve for the height (h).

Area of a triangle = 1/2 × base × height

18 = 1/2 × 3 × height

18 = 1.5 × height

Height = 18 ÷ 1.5

Height = 12 feet

Therefore, the height of the triangle is 12 feet.

Regarding the given examples, when calculating the area of a triangle with different dimensions, remember to convert all measurements to the same unit, typically meters if you need to express in square meters, and then apply the formula A=1/2 × base × height. Ensure the final answer has the correct number of significant figures based on the precision of the given measurements.

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Answer:

left 29226 Right 134

Step-by-step explanation:

volume=base*height

(22*22+(11)^2 *3.14*3/4)*38=29226

((1.4+0.6)*2*0.7+1.4*2*1.4+0.6*1.4+0.6*1.4))* 16=134

Answer:

29,225.78 m^3 to the nearest hundredth.

134.4 m^3.

Step-by-step explanation:

The building:

The area of the floor = area of the square + 3/4 * area of the circle

= 22^2 + 3/4 π 11^2.

The volume of the building =

38 * (22^2 + 3/4 π 11^2)

= 29,225.78 m^3.

The greenhouse:

The sides consist of 2 pairs of trapezoids.

Area of a side  =  2 * (0.6/2)(0.7 + 2.1)  + 2 * (1.4/2)(2.1 + 2.7)

The length is 16 m so:

Volume =  16 * [  2 * (0.6/2)(0.7 + 2.1)  + 2 * (1.4/2)(2.1 + 2.7) ]

= 134.4 m^3.

Answer:

Option C is correct.

Step-by-step explanation:

-x+3y=2

4x-2y=22

In matrix form is represented as:

[tex]\left[\begin{array}{cc}-1&3\\4&-2\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] =\left[\begin{array}{c}2&22\end{array}\right][/tex]

AX=B

[tex]X = A^{-1}B[/tex]

[tex]A^{-1} = |A|/Adj A[/tex]

|A| = (-1)(-2)-(3)(4)

|A| = 2-12

|A| = -10

Adj A = [tex]\left[\begin{array}{cc}-2&-3\\-4&-1\end{array}\right][/tex]

A^-1 = -1/10[tex]\left[\begin{array}{cc}-2&-3\\-4&-1\end{array}\right][/tex]

A^-1 = 1/10[tex]\left[\begin{array}{cc}2&3\\4&1\end{array}\right][/tex]

X= A^-1 B

X = 1/10[tex]\left[\begin{array}{cc}2&3\\4&1\end{array}\right][/tex][tex]\left[\begin{array}{c}2&22\end{array}\right][/tex]

X=1/10[tex]X=1/10\left[\begin{array}{c}2*2+3*22\\4*2+1*22\end{array}\right]\\X=1/10\left[\begin{array}{c}4+66\\8+22\end{array}\right]\\X=1/10\left[\begin{array}{c}70\\30\end{array}\right]\\X=\left[\begin{array}{c}70/10\\30/10\end{array}\right]\\X=\left[\begin{array}{c}7\\3\end{array}\right][/tex]

So, x = 7 and y =3

Hence Option C is correct.

Answer:

7

Step-by-step explanation:

right on edge

Answer:I said B(please don't come for me)Step-by-step explanation:I selected my answer because Canada is apart North America and Chicago, Miami,Tokyo and Mexico are cities and India is a country

Answer:

(-2.3,0.5)

Step-by-step explanation:

Take the second equation we have y= (-16-9X)/10

Then, we will subtitute the value of y on the first equation

8X - 10(-16-9X/10)=-23

Because 10 is denominator, it will delate with the numeber 10 that is multipling the -16-9X. Then the equation is

8X-(-16-9X)=-23  

then: 8x+16+9X=-23  So, 17x=-23-16   => X=-2.3

Then we put the value of X in the first equation so

9 (-2.3) -10y=-16 =>  10y=-16+20.7

So, y=0.5

Answer:

A (-2.3,0.5)

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

The difference of squares is x^2 - y^2 = (x-y) (x+y)

36a^2 = (6a)^2

9 = (3)^2

(6a -3) (6a+3)

This is the difference of squares

The correct answer is a. Yes, 36a² - 9 is a difference of squares

The given expression is [tex]36a^2 - 9[/tex].

To determine if it is a difference of squares we need to identify if it can be written in the form of a² - b², which factorizes to (a + b)(a - b).

We can see that

36a² is a perfect square because it can be written as (6a)² and 9 is also a perfect square because it can be written as 3². Therefore, we can rewrite the expression as:

[tex]36a^2 - 9 = (6a)^2 - 3^2[/tex]

Thus, we can see that the expression 36a² - 9 is a difference of 6a square and 3 square. So, it is indeed a difference of squares.

Answer: a. Yes, 36a² - 9 is a difference of squares

Answer:

Step-by-step explanation:

_____

Good evening ,

_______________

Look at the photo below for the answer.

___

:)

Answer:

Step-by-step explanation:

To find the reference angle for an angle given in degrees, you can follow these steps:

Determine the absolute value of the given angle.

If the angle is more significant than 360 degrees, subtract the largest possible multiple of 360 degrees to bring it within the range of 0 to 360 degrees.

If the angle is negative, convert it to a positive angle by adding 360 degrees.

The reference angle is the acute angle formed between the terminal side of the angle and the x-axis.

Let's apply these steps to the given angle t = -216 degrees:

Absolute value of -216: | -216 | = 216 degrees

216 degrees is already within the 0 to 360-degree ranges, so there is no need to subtract any multiple of 360 degrees.

Since the angle is negative, convert it to a positive angle: 216 degrees

The reference angle is the acute angle formed with the terminal side of the angle, which is 216 degrees.

Therefore, the reference angle for t = -216 degrees is 216 degrees.

Answer:

Answer is 0.3

Step-by-step explanation:

Let the probability that the train arrives on time. = p

The probability that the train leaves on time = 0.8

The probability that the train leaves on time and arrives on time = 0.24

Then the equation will be:

0.8 * p = 0.24

Move the constant value to the R.H.S

p = 0.24/0.8

p = 0.3

Thus the probability is 0.3....

Answer: Observe the image attached.

Step-by-step explanation:

You have  the  points (4, 14), (22, 6), and (16, 18).

It is important to remember that he first number of each point is the x-coordinate of that point and the second number of each one of them is the y-coordinate of that point.

Therefore, knowing the above, you can mark each point, as you can observe in the image attached, and then you can connect the points to form the triangle shown in the image.

Answer:

4/5 or -4/5

Step-by-step explanation:

We are going to use the Pythagorean Identity:

[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]

We are given the value of [tex]\sin(\theta)[/tex] which is 3/5 so plug that in:

[tex](\frac{3}{5})^2+\cos^2(\theta)=1[/tex]

Simplify:

[tex]\frac{9}{25}+\cos^2(theta)=1[/tex]

Subtract 9/25 on both sides:

[tex]\cos^2(\theta)=1-\frac{9}{25}[/tex]

[tex]\cos^2(\theta)=\frac{16}{25}[/tex]

Take the square root of both sides:

[tex]\cos(\theta)=\pm \sqrt{\frac{16}{25}}[/tex]

[tex]\cos(\theta)=\pm \frac{4}{5}[/tex]

Answer:

see explanation

Step-by-step explanation:

a

The tangent and the radius at the point of contact form a right angle

Using Pythagoras' identity on the right triangle formed.

Let x be the distance from the centre to P, then

x² = 4² + 10² = 16 + 100 = 116 ( take the square root of both sides )

x = [tex]\sqrt{116}[/tex] ≈ 10.77 cm (to 2 dec. places )

b

let the required angle be Θ, then

Using the sine or cosine ratio in the right triangle.

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{10}{\sqrt{116} }[/tex]

Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{10}{\sqrt{116} }[/tex] ) ≈ 21.8°

The distance from point P to the center of the circle is approximately 10.77 cm, and the angle between the tangent at P and the line joining P to the center of the circle is 90 degrees.

Let's address each part of the question about a tangent to a circle and its properties:

We can visualize a right triangle where one leg is the radius (4 cm), the other leg is the tangent (10 cm), and the hypotenuse is the line from point P to the center of the circle. Using the Pythagorean theorem (a² + b² = c²), we compute the hypotenuse: c² = 4² + 10², so c² = 16 + 100, which means c = √116, and c ≈ 10.77 cm. So, the distance from P to the center of the circle is approximately 10.77 cm.

An important property of a tangent to a circle is that it is perpendicular to the radius at the point of contact. Therefore, the angle between the tangent and the radius is 90 degrees. Because we are looking for the angle between the tangent and the line joining P to the center, which is the hypotenuse and also includes the radius, the angle remains 90 degrees.

Answer:

Step-by-step explanation:

Rewrite 7(x+5)/(x-3)(x+5) for greater clarity:

7(x+5)

--------------

(x-3)(x+5)

Now cancel the x + 5 terms.  We get:  

     7

-----------

   x - 3

Please note:  the problem statement mentions "which of the following ..."

This implies that there were answer choices.  Please, next time, share those answer choices.  Thank you.

[tex]7(x+5)/(x-3)(x+5) for greater clarity:7(x+5)--------------(x-3)(x+5)Now cancel the x + 5 terms. We get: 7----------- x - 3[/tex]

No. Yes. A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quotient of polynomials, such as x2 + 4x + 4. An irrational algebraic expression is one that is not rational, such as √x + 4.

The steps to solve a rational equation are:

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Answer:

177.6683°

Step-by-step explanation:

If Cos ∅=3√3 then,

The angle is therefore the inverse of the cosine.

∅= Cos⁻¹ (3√3)

= 2.3317°

If Sin is less than zero then the angle lies in the second quadrant of the unit circle.

Therefore the angle in question is 180°-2.3317°

=177.6683°

Answer:

x=-1 y= -5

Step-by-step explanation:

y = – x – 6

y = x – 4

Substitute into y  = -x-6 into the second equation

y =x-4

-x-6 = x-4

Add x to each side

-x-6+x =x-4+x

-6 =2x-4

Add 4 to each side

-6+4 =2x-4+4

-2 = 2x

Divide by 2

-2/2 =2x/2

-1 = x

Now find y

y =-x-6

y = -(-1) -6

y =1-6

y = -5

Answer:

x = -1

y = -5

Step-by-step explanation:

Given:

We'd take one of the equations above and substitute it with the y variable:

x - 4 = -x - 6

-x is smaller, so we add x in both sides:

2x - 4 = -6

Add 4 in both sides:

2x = -2

Divide 2 in both sides:

x = -1

Solve for y

y -(-1) - 6 = -5

y = -5

Our answer is x = -1, y = -5

Answer:

x = 58

Step-by-step explanation:

The angle 51° outside the circle whose sides are a tangent and a secant is

equal to half the difference of the intercepted arcs, that is

51 = 0.5 (160 - x) ← multiply both sides by 2

160 - x = 102 ( subtract 160 from both sides )

- x = -58 ( multiply both sides by - 1 )

x = 58

John's average monthly investment balance for the year is calculated based on the amount invested and the duration of each investment period, resulting in an average balance of $13,680.

To calculate John's average monthly investment balance for the year, we need to consider the length of time each investment amount was held during the year:

Now, we calculate the total investment balance for each period and then find the average:

Therefore, John's average monthly investment balance for the year was $13,680.

Answer: The first option. (2,2)(3,1)(4,2)

Step-by-step explanation:

Answer:

156

Step-by-step explanation:

The prime factorization of 24336 is 2^4*3^2*13^2. The square root of this is the same as dividing the exponent by 2. so 4/2 is and 2/2 is 1. This gives you 2^2*3*13 which is 4*3*13 or 12*13 which is 156.

Answer: 2 gallons

Step-by-step explanation:

1 gallon = 4 quarts

8 divided by 4= 2