. ∠1 and ∠3 are complementary and ∠1 ≅ ∠2. Which one of these statements will always be true?

Final answer:

Using the Pythagorean theorem, it is determined that the ladder reaches 12 feet up the side of the house when the base is placed 5 feet away.

Explanation:

To solve for the height at which the ladder reaches the house, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle.

In this scenario, the ladder represents the hypotenuse (c), the distance from the base of the ladder to the house gives one leg of the triangle (a), and the height the ladder reaches up the side of the house is the other leg (b).

According to the Pythagorean theorem, a² + b² = c². Plugging in our known values allows us to solve for b²:

Therefore, the top of the ladder will be 12 feet above the ground.

Final answer:

The transformation is a translation where you subtract 3.2 from the x-coordinate and add 0.7 to the y-coordinate. Using this rule, Y' is (4.3, 5.7) and Z' is (4.8, 4.7).

Explanation:

The student is asking about a translation transformation in a coordinate plane. Given the original and translated coordinates for point X, we can determine the translation rule by calculating the differences between the coordinates.

The x-coordinate has changed from 6 to 2.8, a decrease of 3.2, and the y-coordinate has changed from -2 to -1.3, an increase of 0.7. Thus, the translation rule is to subtract 3.2 from the x-coordinate and add 0.7 to the y-coordinate.

To find the translated coordinates for points Y and Z, we apply the same rule:

In summary, Y' is (4.3, 5.7) and Z' is (4.8, 4.7).

To find the translation rule, we used the given coordinates of X and X' to determine a translation vector of (-3.2, 1). Using this rule, the coordinates of Y' are (4.3, 6) and Z' are (4.8, 5).

Given the vertices of triangle XYZ: X(6, -2.3), Y(7.5, 5), and Z(8, 4), and knowing that vertex X when translated has coordinates X'(2.8, -1.3), we need to determine the translation rule.

Hence, the coordinates of the translated points are Y'(4.3, 6) and Z'(4.8, 5).

here is the complete question-Triangle XYZ has vertices X(6, -2.3), Y(7.5, 5), and Z(8, 4). When translated, X` has coordinates (2.8, -1.3). Write a rule to describe this transformation. Then find the coordinates of Y' and Z'.

If Joe walked 4/9 of a mile in 4/5 of an hour then the unit rate is  5/9 miles/hour.

A division is a process of splitting a specific amount into equal parts.

The distance walked by Joe is 4/9 of a mile.

The time taken by Joe to walk 4/9 of a mile is 4/5 of an hour.

We need to find the unit rate in miles per hour.

To find this we just need to divide 4/9 by 4/5.

Rate = Distance/Time

Distance = 4/9 miles

Time = 4/5 hour

Rate  = 4/9 ÷ 4/5

Rate = 4/9 × 5/4

Rate = 5/9 miles/hour.

Hence, if Joe walked 4/9 of a mile in 4/5 of an hour then the unit rate is  5/9 miles/hour.

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The mass of the fruit is 74 grams and the mass of the yoghurt is 111 grams.

Given :

Solution :

Now to form a linear equation first let x be the mass in gram. Than total mass of the desert is given by:

[tex]3x+2x=185[/tex]

[tex]5x = 185[/tex]

[tex]x = \dfrac{185}{5}[/tex]

x = 37 grams

Therefore the mass of the fruit = [tex]2 \times 37[/tex] = 74 grams and the mass of the yoghurt = [tex]3\times 37[/tex] = 111 grams.

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Area = (L1 + L2)*h/2

Area = 18

L1 + L1 = 6

h = ???

18 = (L1 + L2)*h/2

18 = (6) * h/2 Multiply both sides by 2

36 = 6h Divide by 6

36/6 = h

h = 6

So the square is 6 by 6

Area square = s^2 where s is the side of the square.

Area = 6^2 = 36 

so your answer will be 6^2 = 36 

Final answer:

Chantelle will cover 1.25 miles each hour of her hike.

Explanation:

To find out how many miles Chantelle will cover each hour of her trip, we need to divide the total distance of 82.5 miles by the total time of 8.25 hours per day for 8 days.

First, we calculate the total time of the trip by multiplying the hours per day (8.25) by the number of days (8): 8.25 hours/day x 8 days = 66 hours.

Next, we divide the total distance by the total time: 82.5 miles / 66 hours = 1.25 miles/hour.

Therefore, Chantelle will cover 1.25 miles each hour of her hike.

To solve the equation, we first distribute the 2 on the left, then collect like terms and finally isolate x. The solution to the equation 2(x + 3) = x + 10 is x = 4.

To solve the equation 2(x + 3) = x + 10, we will first distribute the 2 on the left-hand side of the equation to get 2x + 6. Therefore, the equation becomes: 2x + 6 = x + 10.

The next step is to collect like terms. To do this, we subtract x from both sides, which gives us: x + 6 = 10.

Finally, to solve for x, we subtract 6 from both sides of the equation: x = 4. Hence, the solution to the equation 2(x + 3) = x + 10 is x = 4.

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Final answer:

x = 4

Explanation:

To solve the equation 2(x + 3) = x + 10, we first expand the left side of the equation:

2 × x + 2 × 3 = x + 10

2x + 6 = x + 10

Now subtract x from both sides to move all x terms to one side:

2x - x + 6 = 10

1x + 6 = 10

Subtract 6 from both sides to solve for x:

x = 10 - 6

x = 4

Thus, the solution to the equation is x = 4. Checking the solution, we substitute x back into the original equation:

2(4 + 3) = 4 + 10

2(7) = 14

14 = 14

Answer:

It’s y=-2 on edge

The volume of the prism with the given dimensions is;

V = 12x³ - 30x²

We are given that the formula for the volume of a cube is;

V = Lwh

where;

L is length

w is width

h is height

We are given;

L = (24x² + 6x)/(x -1)

w = 2x - 5

h = (x² - x)/(4x + 1)

This means that;

V = [(24x² + 6x)/(x - 1)] × (2x - 5) × [(x² - x)/(4x + 1)]

Now, let us factorize the terms that can be factorized;

(24x² + 6x)/(x - 1) can be factorized into; [6x(4x + 1)/(x - 1)]

Similarly;[(x² - x)/(4x + 1)] can be factorized into [x(x - 1)/(4x - 1)]

Using the factorized terms to get the volume now;

V = [tex]\frac{6x(4x + 1)}{x -1} * (2x - 5) * \frac{x(x - 1)}{4x + 1}[/tex]

(x - 1) will cancel out and also 4x + 1 will cancel out to give;

V = 6x * x * (2x - 5)

V = 6x²(2x - 5)

V = 12x³ - 30x²

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Answer: C)  The range between the maximum and minimum values for taco truck 2 is greater than the range between the maximum and minimum values for taco truck 1.

Given is the Principal amount, P = 1600 dollars.

Given the Annual interest is 7% i.e. r = 0.07

Given the Compounding period is semi-annually i.e. n = 2.

Given is the Time of investment, t = 33 years.

It says to find the Final Value of invested amount in the account after 33 years.

We know the formula for Future Value of Money is given as follows :-

[tex] Future \;\;Value = P*(1+\frac{r}{n})^{nt} \\\\
Future \;\;Value = 1600*(1+\frac{0.07}{2})^{(2*33)} \\\\
Future \;\;Value = 1600*(1+0.035)^{66} \\\\
Future \;\;Value = 1600*(1.035)^{66} \\\\
Future \;\;Value = 1600*(9.684185201) \\\\
Future \;\;Value = 15494.69632 \\\\
Future \;\;Value = 15,494.70 \;\;dollars [/tex]

Hence, the final balance would be 15,494.70 dollars.

Answer:

After 33 years balance in the account  = A= $15494.696

Explanation:

We will applying the compound interest formula.

[tex] A =  P(1 +\frac{r}{n})^{nt} [/tex]  

Where,

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years

Given that,

P = $1,600

r = 7%  =  [tex] \frac{7}{100}  [/tex] = 0.07

n = 2 (because of twice in a year)

t = 33 years

A= [tex] 1600(1 + \frac{0.035}{2}) ^{2*33}  [/tex] 

A =[tex]  1600 (1.035)^{66}  [/tex] 

A= $15494.696