The two triangles shown are
OA. both similar and congruent
OB. only similar
OC. neither similar nor congruent
OD. only congruent

Answer:

a = 6, b = 22.5

Step-by-step explanation:

One triangle is 2.5 times bigger than the other.

9*2.5=22.5 which means b = 22.5

15/2.5=6 which means a = 6

Similar triangles may or may not be congruent.

The values of a and b are 6 and 22.5, respectively.

Because the triangles are similar, then the following equivalent ratios are true.

\(\mathbf{10 : 4 = b : 9 = 15 : a}\)

First, we calculate b using:

\(\mathbf{10 : 4 = b : 9}\)

Express as fraction

\(\mathbf{\frac{10 }{ 4} = \frac{b } 9}\)

\(\mathbf{2.5 = \frac{b } 9}\)

Multiply both sides by 9

\(\mathbf{b = 2.5 \times 9}\)

\(\mathbf{b = 22.5}\)

Next, we calculate a using:

\(\mathbf{10 : 4 = 15 : a}\)

Express as fractions

\(\mathbf{\frac{4}{10} = \frac{a}{15}}\)

Multiply both sides by 15

\(\mathbf{a= 15 \times \frac{4}{10}}\)

\(\mathbf{a= 6}\)

Hence, the values of a and b are 6 and 22.5, respectively.

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The amount of Duane's first payment that goes to interest is approximately $26.47.

To determine the amount of Duane's first payment that goes to interest, we need to use the amortization formula for a loan.

The formula to calculate the interest portion of a loan payment is:

Interest = Remaining Balance * Monthly Interest Rate.

Let's calculate the interest for the first payment using the given information:

Loan Amount = $5,000.00

Monthly Payment = $118.57

First, we need to calculate the monthly interest rate:

Monthly Interest Rate = Annual Interest Rate / 12

= 6.5% / 12

= 0.00542

Next, we need to calculate the remaining balance after the first payment:

Remaining Balance = Loan Amount - Principal Paid

= $5,000.00 - $118.57

= $4,881.43

Finally, we can calculate the interest portion of the first payment:

Interest = Remaining Balance * Monthly Interest Rate

= $4,881.43 * 0.00542

= $26.47

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The fountain will occupy a fraction of 50/173 of the Total area of the courtyard.

Let A be the area of the courtyard and F be the area of the fountain.

We know that the area of the stone-covered part of the courtyard is 246 square feet.

So, the area of the whole courtyard is A = 246 + F square feet.

The fraction of the area of the courtyard occupied by the fountain is given by:

F / A = F / (246 + F)

We can simplify this expression by multiplying the numerator and denominator by the reciprocal of the denominator:

F / A = F / (246 + F) * (1 / (246 + F))

F / A = F / (246 * (246 + F))

F / A = 1 / (246 / F + 1)

We don't know F yet, but we can use the fact that the fountain is rectangular to set up an equation relating the length and width of the fountain:

F = L * W

where L is the length of the fountain and W is the width of the fountain.

We also know that the perimeter of the fountain is 50 feet:

2L + 2W = 50

Simplifying this equation, we get:

L + W = 25

Solving for one variable in terms of the other, we get:

L = 25 - W

Substituting this expression for L into the equation for F, we get:

F = (25 - W) * W

Expanding this expression, we get:

F = 25W - W^2

We also know that the cost of the fountain is $600, which includes installation. So, we can set up another equation relating the cost of the fountain to its dimensions:

1.5LW = 600

Substituting 25 - W for L, we get:

1.5(25 - W)W = 600

Expanding and simplifying this equation, we get:

W^2 - 25W + 400 = 0

Solving this quadratic equation, we get:

W = 20 or W = 5

We reject the solution W = 5 because it implies a negative length for the fountain, which is not physically possible. Therefore, the width of the fountain is W = 20 feet and its length is L = 25 - W = 5 feet.

The area of the fountain is therefore:

F = L * W = 5 * 20 = 100 square feet

The fraction of the area of the courtyard occupied by the fountain is

F / A = 100 / (246 + 100) = 100 / 346 = 50 / 173

So, the fountain will occupy a fraction of 50/173 of the total area of the courtyard.

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For the given expression, the addition of coefficients is \(5x^2 + 2x - 7\).

In algebra, a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression. In other words, it is the number that is being multiplied by the variable.

Addition is a basic mathematical operation that combines two or more numbers or quantities to produce a sum. It is denoted by the plus sign (+). When two or more numbers are added, the result is called the sum or total.

First, we need to combine like terms by adding the coefficients of terms with the same variable(s) raised to the same power.

\((6x^2 + 10x - 7) + (-x^2 - 8x)\)

\(= 6x^2 + (-x^2) + 10x + (-8x) - 7\) (grouping like terms together)

\(= (6x^2 - x^2) + (10x - 8x) - 7\) (rearranging terms)

\(= 5x^2 + 2x - 7\) (combining the coefficients)

Therefore, the final answer for the addition of coefficients is \(5x^2 + 2x - 7.\)

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The calculated length of the segment MN in the triangle is 20

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

The triangle

The third angle in the triangle is calculated as

Third angle = 180 - 50 - 50

Evaluate

Third angle = 80

The length of the segment MN is then calculated as

MN/sin(50) = 20/sin(50)

This gives

MN = sin(50) * 20/sin(50)

Evaluate

MN = 20

Hence, the length of the segment MN in the triangle is 20

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Answer:

cos P = 53 degrees

cos Q = 37 degrees

Step-by-step explanation:

cos P = \(\frac{adjacent}{hypothenuse}\)

cos P = \(\frac{24}{40}\)

cos P = 0.60

Cos-1 of 0.60 is 53.13 (round to the nearest whole number)

cos P = 53 degrees

cos Q = \(\frac{adjacent}{hypothenuse}\)

cos Q = \(\frac{32}{40}\)

cos Q = 0.80

Cos of 0.80 is 36.86 (round to the nearest whole number)

cos Q = 37 degrees

To check anser:

90 + 53 + 37 = 180

180 = 180

a * (b + c) = a * b + a * c

x(y + z) + x(w + y) + w(x - z) = xy + xz + xw + xy + xw - wz = 2xy + xz + 2xw - wz

Answer: 2.

Answer:

\(\boxed{\boxed{\tt 2)\: 2xy + xz + 2xw - wz}}\)

Step-by-step explanation:

\(\tt x(y + z) + x(w + y) + w(x - z)\)

Expand by distributing terms:

\(\tt xy+xz+xw+xy+xw-zw\)

Combine like terms:

\(\tt xy+xy+xz+xw+xw-zw\)

\(\tt (xy+xy)+xz+(wx+wx)-wz\)

Simplify:

\(\tt 2xy+xz+2wx-wz\)

Answer: $9,000

Step-by-step explanation:

First calculate the total dividends that Company Y plans to pay.

= 12,000,000 * 15%

= $1,800,000

Then calculate the amount that Mutual fund X will get.

They own 0.5% of the total stock of Company Y so they will get;

= 0.5% * 1,800,000

= $9,000

Answer:

\(\frac{1}{7}\) probability that the next president of the United States was born on Monday

Step-by-step explanation:

A theoretical probability is given by the number of desired outcomes divided by the number of total outcomes.

The next president of the United States was born on Monday

Any person, including the next president of the United States, can be born on 7 possible days: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday or Saturday, one of which is Monday.

So

\(\frac{1}{7}\) probability that the next president of the United States was born on Monday

The median will be greater than the mean in a left-skewed distribution

We have,

In statistics, skewness is a measure of the asymmetry of a probability distribution around its mean.

A distribution is said to be skewed left if it has a long tail on the left side and the bulk of the data is on the right side.

When the data is skewed left, it means that the distribution is being pulled towards the left side.

This is because there are a few extreme values on the left side that are pulling the mean in that direction.

In contrast, the median is the middle value of the dataset, and it is not influenced by outliers.

For a left-skewed distribution,

The median will be greater than the mean because the mean is being pulled towards the left by the few extreme values.

In a data distribution that is skewed left, the mean will be less than the median.

This is because the mean is sensitive to outliers and is pulled towards the direction of the skewness, while the median is not affected by extreme values and is a more robust measure of central tendency.

Therefore,

The median will be greater than the mean in a left-skewed distribution

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The exact value of sinθ = 15.5/23

And, The exact value of cosθ = 17/23

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

The terminal side of angle θ intersects the unit circle in the first quadrant at x=17/23.

We know that;

The given parameters are represented as;

⇒ (x, y) = ( cos θ , sin θ )

Here, x = 17/23

Hence, We get;

⇒ cos θ = 17/23

Now, Using the following trigonometry identity;

⇒ cos²θ + sin²θ = 1

⇒ (17/23)² + sin²θ = 1

⇒ 289/529 + sin²θ = 1

⇒ sin²θ = 1 - 289/529

⇒ sin²θ = 529 - 289 / 529

⇒ sin²θ = 240/529

⇒ sin θ = √240/529

⇒ sinθ = 15.5 / 23

Thus, The exact value of sinθ = 15.5/23

And, The exact value of cosθ = 17/23

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Answer:

f•g(x) = f(x)•g(x)

f•g(x) = (2x-1) (x²-2x+1)

= 2x³-4x²+2x-x²+2x-1

= 2x³-5x²+4x-1

The value of x in the lines is 126 degree

We are given that;

Three parallel line and one intersecting line

Angles= (x-6) and 60

Now,

By supplementary angles property

Angle 1 + Angle 2 = 180 degree

Substituting the values of angles

x-6 + 60 = 180

x + 54 = 180

x = 180-54

x = 126

Therefore by supplementary angles answer will be 126 degree.

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Answer:

Both X and Y are equal to 15 multiply by the square root of 2.....(i just do not know how to type the symbol on my keyboard)

Step-by-step explanation:

So for X:

X=30 sin 45

=15 multiply by the square root of 2

For Y:

Y=30 cos 45

=15 multiply by the square root of 2

But you could also use theorem of Pythagoras

Answer:

2/3 pounds of lima beans

Step-by-step explanation:

2 divided by 3 = 2/3 = 2/3

Hope this helps!

Answer:

2/3 pounds (Option B)

Step-by-step explanation:

Using unitary method ,

3 families will receive = 2 pounds of lima beans.

(Dividing both the sides by 3)

⇒ \(\frac{3}{3}\)  family will receive = \(\frac{2}{3}\) pounds of lima beans

⇒ 1 family will receive = \(\frac{2}{3}\) pounds of lima beans.

∴ Each family will receive 2/3 pounds of lima beans.

Answer:

58

Step-by-step explanation:

you have 2 2 by 2 squares and 1 5 by 10 rectangle

The product of 5 × 5ab × 5, a, b is 125ab5 when written in its most Simple form

The expression 5 × 5ab × 5, a, b is equal to 125ab5. The reasoning is that when we multiply 5 by 5ab, we get 25ab, which we then multiply by 5 to get 125ab. Since a, b are variables, the product 125ab5 is the product of 5 × 5ab × 5, a, b, when written in its most simple form.

The expression 5 × 5ab × 5, a, b is an algebraic expression, which consists of numbers, variables, and operators. Variables are usually represented by letters or other symbols, while operators such as +, -, ×, ÷, ^ are used to indicate mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. In algebra, expressions can be simplified by combining like terms, expanding brackets, and applying other rules of arithmetic.

The most simple form of an expression is the one that cannot be further simplified.In the given expression, 5 × 5ab × 5, a, b, we can see that the number 5 appears three times, so we can simplify the expression by multiplying the numbers together.

Similarly, we can multiply the variables a and b together to get the term ab. Finally, we write the result as 125ab5, which is the product of 5 × 5ab × 5, a, b, in its most simple form.

Therefore, the product of 5 × 5ab × 5, a, b is 125ab5 when written in its most simple form.

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Answer:

Step-by-step explanation:

1

The amount insurance company will pay is $700000.

We are given that

Age of Mr. lewis= 63

Policy value= $700,000

Now,

If Mr. Lewis dies after paying for the policy for 24 months, he would have paid a total of 24 * $72 = $1728 in premiums. Since he has a five-year level-term life insurance policy with a face value of $700,000, his beneficiaries would receive the full face value of the policy if he dies within the five-year term.

Therefore, by algebra the answer will be $700000.

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Answer:

28.57% chance

Step-by-step explanation:

add them all up which is 14, and if there are 4 white marbles that means its 4/14, which is 28.57 as a percent (2:7 as ratio)

Answer:

can we date plz don't my number 21976198649

The mapping of the function f(x) given as 3x⁴ - 4x³ + 3x² - 5x - 3 is define at; -3, f(-3) = 390 and at 4, f(4) = 537

A function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers

For x = -3;

f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3

f(-3) = 3(81) + 4(27) + 3(9) + 15 - 3

f(-3) = 243 + 108 + 27 + 15 - 3

f(-3) = 390

For x = 4;

f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3

f(4) = 3(256) - 4(64) + 3(16) - 20 - 3

f(4) = 768 - 256 + 48 - 20 - 3

f(4) = 537

Therefore, for the mapping of the function f(x) = 3x⁴ - 4x³ + 3x² - 5x - 3 for the values of x: -3 and 4 we have the results 390 and 537.

Gy, this is the solution:

(7 + 9i) + ( - 5i)

Solving the parenthesis:

7 + 9i - 5i

7 + 4i

Answer:

Pole^2 = 221^2 - 21^2

Pole^2 = 48,841 -441

Pole^2 = 48,400

Pole = 220 cm

Answer is B

Step-by-step explanation:

Answer:

Area = 25m²

Step-by-step explanation:  A=a²=5²=25m²

Answer:

25m²

Step-by-step explanation:

Simply multiply the number of total sides of the shape(4) and  the measurement of each side (5m)

4 sides x 5 meters = 25m²

always put m² after your final answer

(A). the current sale price of the computer system is $543.20.

Therefore, members of the store's loyalty club pay $488.88 for the computer system with their discount.

Find the current sale price. Round to the nearest cent if necessary.

• Members of the store's loyalty club get an additional 10% off their computer purchases. How much do club members pay for the computer with their discount?

To find the current sale price, we first need to calculate the markdown amount. We know that the markdown is 30% of the original selling price, which is $776, so the markdown amount is:

30% of $776 = 0.30 x $776 = $232.80

The sale price is then the original selling price minus the markdown amount:

Sale price = $776 - $232.80 = $543.20

Therefore, the current sale price of the computer system is $543.20.

Next, we need to calculate the price that club members pay after their discount. We know that club members get an additional 10% off the sale price, which is $543.20, so their discount amount is:

10% of $543.20 = 0.10 x $543.20 = $54.32

The price that club members pay is then the sale price minus their discount amount:

Price for club members = $543.20 - $54.32 = $488.88

Therefore, members of the store's loyalty club pay $488.88 for the computer system with their discount.

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