Solve the equation and check the solution.
a minus 2 and one-half = 1 and one-half

A.a = 1
B.a = 3 and one-half
C.a = 4
D.a = 4 and one-half

Answer:

? = 42 degrees

Step-by-step explanation:

The 105 is part of a 180 degree angle so we do 180-105 giving us 75 degrees. and the sum of the internal angles of a triangle should equal 180. so we add 57 + 75 giving us 132. 180-132 will be 48 degrees.

Answer:

See below

Step-by-step explanation:

The larger is  

7-6 = 1 unit bigger than the smaller....and this unit = 24 gallons

   each unit is 24 gallons

larger barrel holds   24 * 7 = 168 gal

smaller barrel holds  24 * 6 = 144 gal

Answer:

Small barrel=144 large barrel=168

Step-by-step explanation:

The ratio is 6 to 7 so lets assign x as a factor.

6x=Small barrel (S)

7x=Large barrel (L)

7x-6x=x

x is the difference so x is 24

x=24

6*24=144=S

7*24=168=L

The coordinates of A'', B'' and C'' are (-1, 4), (-4, 3) and (-1, 2) respectively.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given triangle has coordinates,

A(2, -2), B(5, -3) and C(2, -4).

First the triangle is translated by the rule (x, y) → (x - 1, y + 6)

A(2, -2) becomes A'(2 - 1, -2 + 6) = A'(1, 4).

B(5, -3) becomes B'(5 - 1, -3 + 6) = B'(4, 3)

C(2, -4) becomes C'(2 - 1, -4 + 6) = C'(1, 2)

Then the translated triangle is reflected across the Y axis.

When reflected a point (x, y) across the Y axis, y coordinate remains same and x coordinate flips.

A'(1, 4) becomes A''(-1, 4)

B'(4, 3) becomes B''(-4, 3)

C'(1, 2) becomes C''(-1, 2)

Hence the vertices of the triangle after undergoes translation and reflection becomes A''(-1, 4), B''(-4, 3) and C''(-1, 2).

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Answer:

The ∠B is 60*

Step-by-step explanation:

Answer:

200,000 x 1.09^14 =668345.4054

So, 668,345

Hope this helps!

Answer:

24.5 inches need to be cut

Step-by-step explanation:

To determine the area of this figure, we first need to identify its shape. From the given measurements, it appears to be a rectangle with two right-angled triangles on opposite corners.

Here are the steps to calculate the area:

1. Identify the base and height of the rectangle: The base is 5 km, and the height is 3 km.
2. Calculate the area of the rectangle: Area = base × height = 5 km × 3 km = 15 square kilometers.
3. Identify the base and height of the two right-angled triangles: Both triangles have a base of 1 km and a height of 1 km.
4. Calculate the area of one right-angled triangle: Area = 0.5 × base × height = 0.5 × 1 km × 1 km = 0.5 square kilometers.
5. Calculate the combined area of both right-angled triangles: 2 × 0.5 square kilometers = 1 square kilometer.
6. Add the area of the rectangle and the combined area of the triangles to get the total area: 15 square kilometers + 1 square kilometer = 16 square kilometers.

The area of the figure is 16 square kilometers.

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Answer:

5 + 10\(\sqrt{3}\)

= 22.3205080757

Step-by-step explanation:

Answer:

≈ 13,7 inches

Step-by-step explanation:

Just use trigonometry (sin or cos) from the right triangles ∆ABC and ∆ADC

The procedure the researcher will use is called stratification sampling.

A stratified sample is created by separating a population into similar subpopulations (strata) and taking a representative sample from each. Stratified sampling is used by researchers to ensure that specific subgroups are represented in their samples. Additionally, it helps them estimate the characteristics of each group precisely. This method is used in many surveys in order to better understand the differences between subpopulations. The term stratified sampling is also used to refer to stratified random sampling.

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a. The absolute change in city employees who ride the bus to work is 2%.

b. The relative change in city employees who ride the bus to work is approximately 11%.

c. The relative change in city employees who ride the bus to work is approximately 11%.

d. The relative change of around 11% indicates an increase in the proportion of city employees riding the bus to work compared to last year.

a. The absolute change in city employees who ride the bus to work can be calculated as the difference between this year's percentage (20%) and last year's percentage (18%):

Absolute change = 20% - 18% = 2%

b. The absolute change of 2% indicates that the number of city employees riding the bus to work has increased by 2 percentage points compared to last year.

c. The relative change in city employees who ride the bus to work can be calculated as the absolute change divided by the previous year's percentage, multiplied by 100:

Relative change = (Absolute change / Previous year's percentage) * 100

Relative change = (2% / 18%) * 100 ≈ 11%

d. The relative change of approximately 11% implies that the proportion of city employees riding the bus to work has increased by around 11% compared to last year.

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The consumption bundle that will not be the consumer's choice, given the assumptions of choosing the optimal bundle, is option B) 30 snacks and 12 meals. To determine the optimal consumption bundle, we need to consider the consumer's budget constraint and maximize their utility.

Given that the price of snacks is $4 and the price of meals is $10, and the consumer has $240 remaining on their meal card, we can calculate the maximum number of snacks and meals that can be purchased within the budget constraint.

For option A) 5 snacks and 20 meals, the total cost would be $4 × 5 + $10 × 20 = $200. Since the consumer has $240 remaining, this bundle is feasible.

For option B) 30 snacks and 12 meals, the total cost would be $4 × 30 + $10 × 12 = $240. This bundle is on budget constraint, but it may not be the optimal choice since the consumer could potentially consume more meals for the same cost.

For option C) 20 snacks and 16 meals, the total cost would be $4 × 20 + $10 × 16 = $240. This bundle is also on budget constraint.

Since options A, C, and D are all feasible within the budget constraint, the only bundle that will not be the consumer's choice is option B) 30 snacks and 12 meals. The consumer could achieve a higher level of utility by reallocating some snacks to meals while staying within the budget constraint. Therefore, the correct answer is option B.

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The solution of expression rounded to nearest tenth is -1.1

Rewriting the equation first -

-1.2x = 11.3x + 13.75

Now, shifting 11.3x to other side of the equation and rewriting the equation -

- 1.2x - 11.3x = 13.75

Rewriting the equation according to sign on Left Hand Side

-(1.2x + 11.3x) = 13.75

Performing addition of similar values on Right Hand Side of the equation

-12.5x = 13.75

Solving for the value of x from above mentioned equation -

x = 13.75 ÷ (-12.5)

Performing division to find the value of x

x = - 1.1

The number 1.1 rounded to nearest tenth will be 1.1.

So, the solution of expression rounded to nearest tenth is -1.1

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The U.S. Census Bureau is responsible for collecting and analyzing a vast amount of data related to families in the United States.

This data includes information about the number of households, family size, marital status, and living arrangements. The Bureau also collects data on the number of children who live with their parents or other relatives, as well as the number of children who do not live with their parents.

In 2010, the U.S. Census Bureau reported that there were approximately 7.6 million children who did not live with their parents. Of these children, 54% were living with their grandparents or other relatives, while the remaining 46% were living with non-relatives.

The Bureau collects this data in order to better understand the needs of families and to develop policies that can help support them.

The Census Bureau also collects data on a wide range of other statistics related to families, including income, education, employment, and health. This information is used to identify trends and patterns that can help inform decisions about social programs and policies that affect families.

Overall, the U.S. Census Bureau plays a vital role in providing policymakers and researchers with the data they need to better understand and address the needs of families in the United States.

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Answer:

Expanded Form:

3500

Step-by-step explanation:

Hope this helps!

Answer:

Disagree

Step-by-step explanation:

This is incorrect because say for instance the question asks for the absolute value of 4, it would still be 4, and 4 is not the opposite of 4, it would be -4 if Eric's statement is true

To simplify radical expressions with variables, identify perfect square factors, simplify the radical by taking out the largest possible integer factor that is a perfect square, and then multiply by the remaining factor outside the radical. Repeat the process until no more simplification is possible.

To simplify radical expressions with variables, follow these steps

Factor the expression under the radical sign into its prime factors.

Identify any perfect squares within the factors.

Rewrite the expression with the perfect squares outside the radical sign and the remaining factors inside.

Simplify any remaining radicals if possible.

Combine any like terms if necessary.

For example, to simplify the expression √(12x²y), you would first factor 12x²y into 2 * 2 * 3 * x * x * y. Then, you would identify the perfect square of x² and rewrite the expression as 2x√(3y). Finally, you could simplify further if possible, but in this case, the expression is already in its simplest form.

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Answer:

\(A.\ {28, 30, 58}\)

Step-by-step explanation:

Required

Which of the lengths do not form a triangle

To do this, we make use of triangle inequality theorem which states that.

\(a + b > c\)

\(b + c > a\)

\(a + c > b\)

Where \(a,\ b\ and\ c\) are the sides of the triangle.

So, we have:

\(A.\ {28, 30, 58}\)

\(28 + 30 > 58\) --- False

\(58 + 30 > 28\) --- True

\(28 + 58 > 30\) --- True

\(B.\ {32, 34, 60}\)

\(32 + 34 > 60\) -- True

\(32 + 60 > 34\) -- True

\(34 + 60 > 32\) -- True

\(C.\ {13, 20, 27}\)

\(13 + 20 > 27\) -- True

\(13 + 27 > 20\) -- True

\(20 + 27 > 13\) --- True

\(D.\ {2, 4, 5}\)

\(2 + 4 > 5\) --- True

\(2 + 5 > 4\) -- True

\(5 + 4 > 2\) --- True

From the computations above, only (A) cannot form a triangle

Answer:

1. Yes and for 2. I don't know

Step-by-step explanation:

1. is a monomial because 21/27 is one group

Answer:

(-4)^10

Step-by-step explanation:

According to law of indices

(a^m)^n = a^{mn}

Given

[(-4)²]^5

Using the law above, we I'll multiply the powers

[(-4)²]^5

= (-4)^2×5

= (-4)^10

Hence the required answer is (-4)^10

Answer:

  (c)  two right triangles, each with both legs 40 inches long

Step-by-step explanation:

You want to know which pair of triangles are congruent, given their descriptions.

There are basically 4 theorems that allow you to claim congruence of triangles:

  AAS, ASA, SAS, SSS

A fifth one applies to right triangles only: HL.

These tell you that you need to have three matching parts: 3 sides, 2 sides and the angle between (except right triangle), or 1 side and 2 angles.

An isosceles triangle with only one or two sides defined is not sufficient.

A right triangle with only the hypotenuse defined is not sufficient.

A right triangle with two legs and the (right) angle between them has a sufficient number of matching parts to be able to claim congruence to another triangle similarly defined.

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:  Hello!

I don't remember all of the postulates to these, but I hope this will help you! Vertical angles are congruent, so both angles SRT and PRQ are congruent.  This also means that line segments PQ and ST are congruent.  You also know that angles Q and S are congruent which is given.  By the ASA Theorem, when two angles and a side are congruent, then the triangles are congruent.

Gerard concluded that triangle with given sides cannot be used as  building-frame support because it is not right triangle, he come to this conclusion because the Pythagoras-theorem is not satisfied.

In order to check if a triangle is "right-triangle", Gerard used the Pythagorean theorem. According to this theorem, in right triangle, the square of length of hypotenuse (the side opposite the right angle) is equal to sum of squares of other two sides,

So, the squares of the given sides are :

Square of √95 feet = (√95)² = 95 feet

Square of 8 feet = 8² = 64 feet

Square of √150 feet = (√150)² = 150 feet

We see that, 95 feet + 64 feet = 159 feet ≠ 150 feet,

Since the square of the longest side (√150) is not equal to the sum of the squares of the other two sides (√95 and 8), the Pythagorean-theorem is not satisfied.

Therefore, Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 feet is not a right triangle.

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The given question is incomplete, the complete question is

Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 cannot be used as a building frame support on the house because it is not a right triangle. How did Gerard come to that conclusion? explain.

Answer:

you're right

Step-by-step explanation:

I checked by writing the first 5 terms

a1: 5

a2: 8

a3: 11

a4: 14

a5: 17

and then checked using the function to see if they matched up and they did

Answer:

A = 180 units²

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = \(\frac{1}{2}\) h (b₁ + b₂ )

where h is the perpendicular height and b₁, b₂ the parallel bases

The triangle on the left is right with h = 24 (7- 24- 25 triangle )

Here h = 24, b₁ = 4 and b₂ = 7 + 4 = 11 , then

A = \(\frac{1}{2}\) × 24 × (4 + 11) = 12 × 15 = 180 units²

Answer:

y=58°

x=122°

Step-by-step explanation:

y=58°[°•°being corresponding angles]

Now,

x+y=180[°•°co-interior angles]

or, x=180-58

•°•x=122

Answer:

the answer is 69

Step-by-step explanation:

for your answer you need to understand fast that when you add 34 and 35 what will be the answer you need to think that your answer will be cirrect or not and its very easy question

Prefix expressions, also known as Polish notation, are mathematical expressions in which the operator comes before the operands. For example, "+ 2 3" represents the sum of 2 and 3.

Sure, I can help you modify your code to ask the user for prefix expressions and evaluate each expression until the result is zero. Here's the updated code:

import java.io.*;
import java.util.*;

class Prefix {
 // Check if the character is an operand (integer or not)
 static boolean isOperand(char c) {
   if (c >= 48 && c <= 57) {
     return true;
   } else {
     return false;
   }
 }

 // Evaluate the prefix expression
 static double evaluate(String exp) {
   Stack stack = new Stack<>();
   // Reading each element from backwards
   for (int j = exp.length() - 1; j >= 0; j--) {
     if (isOperand(exp.charAt(j))) {
       // Convert exp[j] to digit and push it onto the stack
       stack.push((double) (exp.charAt(j) - 48));
     } else {
       if (exp.charAt(j) == ' ') {
         continue;
       } else {
         double op1 = stack.pop();
         double op2 = stack.pop();
         switch (exp.charAt(j)) {
           case '+':
             stack.push(op1 + op2);
             break;
           case '-':
             stack.push(op1 - op2);
             break;
           case '*':
             stack.push(op1 * op2);
             break;
           case '/':
             stack.push(op1 / op2);
             break;
           case '%':
             stack.push(op1 % op2);
             break;
         }
       }
     }
   }
   return stack.pop();
 }

 public static void main(String[] args) {
   Scanner sc = new Scanner(System.in);
   String exp;
   double result;
   do {
     System.out.println("Enter a prefix expression (operators come first): ");
     exp = sc.nextLine();
     result = evaluate(exp);
     System.out.println("Result: " + result);
   } while (result != 0);
   System.out.println("Exiting...");
 }
}

Here's how the updated code works:
- We modified the code to remove the flag variable and use a do-while loop instead. The loop will continue to ask the user for input until the result of the expression is zero.
- We also changed the stack declaration to use generics and named it "stack" instead of "Stack".
- We updated the method names to use proper Java naming conventions (e.g. isOperand instead of Operand, evaluate instead of Prefix_evaluation).

Here's an example output:
Enter a prefix expression (operators come first):
+ 3 4
Result: 7.0
Enter a prefix expression (operators come first):
* + 1 2 3
Result: 9.0
Enter a prefix expression (operators come first):
/ * 3 4 2
Result: 6.0
Enter a prefix expression (operators come first):
- 10 5
Result: 5.0
Enter a prefix expression (operators come first):
% 7 3
Result: 1.0
Enter a prefix expression (operators come first):
/ 3 0
Result: Infinity
Enter a prefix expression (operators come first):
- 3 3
Result: 0.0
Exiting...

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Answer:

A) -16y+24

Step-by-step explanation:

Distribute -3 with 4y and -8

-12y+24-4y

Add -12y and -4y

-16y+24

Answer is -16y+24

Hope this helps!

Answer:

J

Step-by-step explanation: