Anna needs to find the area of a figure that can be separated into a square and a triangle. The base of the triangle is 18 cm, and its height is 10 cm. The length of the side of the square is equal to the base of the triangle. Which expression can Anna use to find the area of the figure?

The dimensions are either 4 units by 2 units or 2 units by 4 units.

To draw a rectangle with a perimeter of 12 units and an area of 8 square units, we need to find the dimensions of the rectangle first.

Let  l be the length of the rectangle and w be the width of the rectangle.

We know that the perimeter of a rectangle is given by: P = 2(l + w) =12

12 = 2(l + w) ,6 = l + w

Also, the area of a rectangle is given by: A = l * w = 8

Now, we need to find a pair of numbers  l  and  w  that satisfy both equations:  6 = l + w and  8 = l * w

One such pair is l = 4  and  w = 2 , because ( 4 + 2 = 6 ) and ( 4 * 2 = 8 ).

This rectangle has a length of 4 units and a width of 2 units, with a perimeter of 12 units and an area of 8 square units.

Step-by-step explanation:

[tex]-4x-7+10x=-7+6x\\\\(-4x+10x)-7=-7+6x\\\\6x-7=-7+6x\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\-7=-7\qquad\bold{TRUE}\\\\Answer:\ \text{Infinitely many solutions}[/tex]

Final answer:

By simplifying the given linear equation and combining like terms, we find that the single solution is x = 0. Verification confirms that this solution is valid as it satisfies the original equation.

Explanation:

The equation presented by the student is a linear equation with the variables on both sides. To solve this equation, we will combine like terms and isolate the variable x on one side of the equation.

First, let's simplify the equation by combining like terms:

-4x - 7 + 10x = -7 + 6x

Combine x terms on the left side and numerical terms on the right:

6x = 0

Finally, divide by the coefficient of x to solve for x:

x = 0

This value of x is the single solution to the equation. It's important to note that there are no other solutions in this case, as it's a simple linear equation and not a quadratic or higher-order polynomial equation.

Verification

To verify that x = 0 is indeed a solution, we can substitute it back into the original equation:

-4(0) - 7 + 10(0) = -7 + 6(0)

All terms involving x drop out, confirming that -7 = -7 is an identity, making x = 0 a valid solution.

To find the combined width of the three tables, add up their individual widths.

To find the combined width of the three tables, we need to add up their individual widths.

The first table is 3 feet 11 inches wide, which is equivalent to 3 feet 11 inches + 0 feet 11 inches = 3 feet 22 inches.

The second table is 6 feet 10 inches wide, which is equivalent to 6 feet 10 inches + 0 feet 10 inches = 6 feet 20 inches.

The third table is 3 feet 7 inches wide, which is equivalent to 3 feet 7 inches + 0 feet 7 inches = 3 feet 14 inches.

Adding up the widths: 3 feet 22 inches + 6 feet 20 inches + 3 feet 14 inches = 12 feet 56 inches.

Therefore, the combined width of the three tables is 12 feet 56 inches.

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Brand had 2 5/12 cups of chili left over from the second batch (option A). This was determined by solving the equation 1 1/3 + x = 3 3/4 using improper fractions and subtraction.

To find out how many cups of chili were left over from the second batch, we need to solve for x in the equation 1 1/3 + x = 3 3/4. Firstly, convert the mixed numbers to improper fractions: 1 1/3 becomes 4/3 and 3 3/4 becomes 15/4.

Now the equation looks like this: 4/3 + x = 15/4. To find x, subtract 4/3 from both sides of the equation.

15/4 - 4/3 = (15*3 - 4*4)/(4*3) = 45/12 - 16/12 = 29/12.

Now convert the improper fraction back to a mixed number. 29/12 is 2 and 5/12. So Brand had 2 5/12 cups of chili left over from the second batch (option A).

Final answer:

To find 300% of the difference between 23 and 27, you first calculate the difference, which is 4, and then multiply by 3, giving the result of 12.

Explanation:

The question asks us to calculate 300% of the difference between 23 and 27. First, let's find the difference between these two numbers: 27 - 23 = 4. Now, to find 300% of 4, we multiply 4 by 3 (since 300% is the same as multiplying by 3): 4 imes 3 = 12. Therefore, 300% of the difference between 23 and 27 is 12.This is the final answer.

Step-by-step explanation: We are given three rectangular figures A, B and C.

We need to determine which polygons are similar and which are not.

Note: The sides of similar figures are in proportion.

Let us check first A and B figures.

150/108 = 50/36

100/72 = 50/ 36.

We can see 150/108 = 100/72 = 50/ 36.

Sides are in proportion of Polygons A and B.

Let us check first A and C figures.

150/132 = 25/22

100/80 = 5/4.

We can see 150/132 ≠ 100/80.

Sides are not in proportion of Polygons A and C.

Let us check first B and C figures.

108/132 = 9/11.

72/80 = 9/10.

We can see 108/132 ≠ 72/80.

Sides are not in proportion of Polygons B and C.

The range of the numbers 3, -97, -15, -42 is 100.

The range of a set of numbers is the difference between the largest and smallest numbers in the set. To find the range of the numbers 3, -97, -15, -42, we first need to find the largest and smallest numbers. The largest number is 3 and the smallest number is -97. Subtracting the smallest number from the largest number gives us a range of 100.

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The value of the equation y = 3x^2 - 18x + 15 can be found by substituting different values of x and calculating the corresponding value of y.

The value of the equation y = 3x^2 - 18x + 15 can be found by substituting different values of x and calculating the corresponding value of y. For example, if we substitute x = 1, we get y = 3(1)^2 - 18(1) + 15 = 0. So, when x = 1, y is 0.

To find more values, we can create a table of values by substituting different x values into the equation. The resulting values of y can be plotted on a graph to see the pattern and shape of the equation.

Table of Values:

This equation represents a quadratic function in the form of y = ax^2 + bx + c, where a = 3, b = -18, and c = 15.

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The height of the wall if A repairman leans the top of an 8 ft ladder against the top of a stone wall, the base of the ladder is 5.5 ft from the wall, is 5.81 feet.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine, cosine, and tangents are their names and acronyms (tan).

Given:

A repairman leans the top of an 8 ft ladder against the top of a stone wall, the base of the ladder is 5.5 ft from the wall,

Calculate the height of the wall as shown below,

Assume the height of the wall is x then,

x² + base² = ladder height²

x² + 5.5² = 8²

x² = 64 - 30.25

x² = 33.75

x = √33.75

x = 5.81 ft

Thus, the height of the wall is 5.81 feet.

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Option D, which is x + 2y^2 - 7, is a trinomial as it contains exactly three terms.

A trinomial is an algebraic expression with three terms.

These terms are usually separated by '+' or '-' signs. Let's examine the options given to identify a trinomial:

Therefore, Option D is the correct answer as it is the expression that contains exactly three terms, making it a trinomial.

Answer:

The area of the circle is equal 28.3 cm² to the nearest tenth.

Step-by-step explanation:

To find the area of the circle that has a radius of 3, we will simply use the formula;

Area of a cirle = π r²

where π is a constand and r is the radius.

From the question given π = 3.14   and r=3

We can now proceed to insert the value into the formula;

Area of a cirle = π r²

                        =3.14×3²

                         =3.14×9

                           =28.26

                            ≈28.3 cm²

Therefore, the area of the circle is equal 28.3 cm² to the nearest tenth.

It will take 4 yrs for Rajeev to reach 200$

To find out after how many years Rajeev will have at least $200 in his account, we can use the formula for compound interest. P = $175, A = $200, r = 0.04, n = 1, and t = ? Substituting these values into the formula and solving for t, we find that it will take approximately 7.38 years for Rajeev to have at least $200 in his account.

To find out after how many years Rajeev will have at least $200 in his account, we can use the formula for compound interest, which is given by:

A = P(1 + r/n)^(nt)

Where:

In this case, we have:

Substituting these values into the formula, we get:

$200 = $175(1 + 0.04/1)^(1t)

Simplifying the equation, we have:

1.1429 = (1.04)^t

To solve for t, we can take the logarithm of both sides:

log(1.1429) = log((1.04)^t)

Using logarithmic properties, we have:

t log(1.04) = log(1.1429)

Dividing both sides by log(1.04), we get:

t = log(1.1429)/log(1.04)

Using a calculator, we find that t ≈ 7.38

Therefore, it will take approximately 7.38 years for Rajeev to have at least $200 in his account.

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Answer: The answer is B) 11.25

Step-by-step explanation: I got it right

The exponential function will be written as:

y = 12 (0.56) ^ (t/4)  

y=12 (0.56^ (1/4)) ^t

but

0.56^ (1/4) = 0.8651

thus plugging the value in y we get:

y=12 (0.8651) ^t

in two decimal places we get:

y=12 (0.87) ^t

The equation q^2=36 has two solutions because both a positive and a negative number squared can result in a positive number. The solutions are q=6 and q=-6, illustrating the concept of integer powers and square roots.

To solve the equation q squared equals 36 (q2 = 36), we look for the number that, when multiplied by itself, gives the product of 36. In mathematics, finding a value that satisfies this condition involves taking the square root of both sides of the equation. Thus, we have two potential solutions since both positive and negative values can be squared to yield a positive result.

The square root of 36 is 6, so our equation gives us two possible solutions: q = 6 or q = -6. This demonstrates the concept of integer powers, where for instance, raising 4 to the power of 3 (43) means multiplying 4 by itself three times. When dealing with the square root, we are essentially doing the opposite: we are asking what number multiplied by itself gives us the original number under the square power.