The following two triangles have the same angles, and are similar. What is the ratio of hypotenuse to base for the triangles?

Marlie's federal unsubsidized student loan will accrue $3,627.34 in interest over a 4.5-year non-payment period, given a 4.29% annual interest rate.

The subject of this problem is calculating interest accrued on an unsubsidized student loan. First, we need to understand that the 4.29% interest is an annual rate. So, for 4.5 years, the rate would become: 4.29% * 4.5 = 19.305%.

To calculate the amount of interest that will accrue during this period, we simply multiply this by the principal loan amount ($18,800). So, $18,800 * 19.305% = $3,627.34. Therefore, Marlie will accrue $3,627.34 in interest over this 4.5-year period.

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Marlie, who took a Federal Unsubsidized student loan that accumulates interest over time, will accrue $3,628.83 in interest during her 4.5 years of non-payment.

The subject of this question is about interest calculation on a Federal Unsubsidized student loan. Interest on an unsubsidized loan like Marlie's accumulates from the time the loan is disbursed until it's paid in full, including during the non-payment period. The interest that will accrue can be calculated using the formula I = PRT, where 'I' is the interest, 'P' is the principal amount (the initial amount of loan), 'R' is the annual interest rate in decimal, and 'T' is the time the money is borrowed for in years.

In Marlie's case, P = $18,800, R = 4.29/100 = 0.0429, and T = 4.5. Therefore, the interest accrued will be I = 18800 * 0.0429 * 4.5. After performing the calculation, the total interest that Marlie will accrue over the non-payment period is $3,628.83.

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[tex](14x+21y)(6ab-3a) = 3a(2b - 1)(14x + 21y)[/tex]

Solution:

Given that,

[tex](14x+21y)(6ab-3a)[/tex]

We have to factor out terms and write as a product of 2 binomials and monomial

A monomial is a mathematical expression with only one term, while a binomial is a mathematical expression with two terms.

From given expression,

[tex](14x+21y)(6ab-3a) = (14x + 21y)(3 \times 2ab -3a)[/tex]

3 and a are common factors in second bracket

[tex](14x+21y)(6ab-3a) = 3a(2b - 1)(14x + 21y)[/tex]

Hence, the product of two binomial is written in two binomial and a monomial

Answer:50%

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

The height of the tree is 60 meters.

Explanation:

Let the height of the tree be x. The tree casts a shadow of [tex]x-49[/tex] meters and the distance from the top of the tree to the end of the shadow is [tex]x+1[/tex] meters.

The sides of the triangle are attached in the image below:

Using pythagoras theorem,

[tex]x^{2}+(x-49)^{2}=(x+1)^{2}[/tex]

Expanding, we get,

[tex]2 x^{2}-98 x+2401=x^{2}+2 x+1[/tex]

[tex]2 x^{2}-98 x+2400=x^{2}+2 x[/tex]

[tex]2 x^{2}-100 x+2400=x^{2}[/tex]

[tex]x^{2}-100 x+2400=0[/tex]

Solving the equation using the quadratic formula [tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex], we get,

[tex]x=\frac{-(-100)\pm\sqrt{(-100)^{2}-4 \cdot 1 \cdot 2400}}{2 \cdot 1}[/tex]

Simplifying, we have,

[tex]x=\frac{100\pm\sqrt{10000-9600}}{2}[/tex]

[tex]x=\frac{100\pm\sqrt{400}}{2}[/tex]

[tex]x=\frac{100\pm{20}}{2}[/tex]

Thus,

[tex]x=\frac{100+20}{2} \\x=\frac{120}{2} \\x=60[/tex]  and  [tex]x=\frac{100-20}{2} \\x=\frac{80}{2} \\x=40[/tex]

where the value [tex]x=40[/tex] is not possible because substituting the value [tex]x=40[/tex] in [tex]x-49[/tex] results in negative solution. Which is not possible.

Hence, the value of x is 60.

Thus, The height of the tree is 60 meters.

The estimated value of 19% of 44 is 8 as per the percentage rule and rounding decimals rule.

The correct option is 8.

To estimate 19% of 44, we can start by finding 10% of 44, which is simply moving the decimal point one place to the left. So, 10% of 44 is 4.4.

Next, we can estimate 5% of 44 by dividing 10% by 2. This gives us 2.2.

Now, to estimate 19% of 44, we can add the estimates for 10% and 5%. So, 4.4 + 2.2 equals 6.6.

Given the options of 8, 9, 9.5, and 10, we can see that the estimate of 19% of 44 is closest to 9.

Therefore, the estimated value of 19% of 44 is 8.

It's important to note that this is an estimation, and the actual value of 19% of 44 is 8.36. The estimation technique used here is a quick approximation that can be useful in situations where an exact calculation is not required or when a rough estimate is sufficient.

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The complete question:

Estimate 19% of 44.
The available options are:

8, 9, 9.5, and 10.

Answer:

          [tex]\large\boxed{\large\boxed{5ft}}[/tex]

Explanation:

A ramp is modeled by a right triangle with hypotenuse equal to the length of the ramp, horizontal leg equal to the ground length(horizontal run), and vertical leg equal to the rise.

Hence, you can use Pythagora's theorem:

            [tex](13ft)^2=(12ft)^2+y^2[/tex]

Solve of the y, which represents the rise:

              [tex]y^2=(13ft)^2-(12ft)^2=169ft^2-144ft^2=25ft^2\\\\y=5ft[/tex]

Final answer:

Using the Pythagorean theorem with the length of the ramp as the hypotenuse (13 feet) and the horizontal distance covered (12 feet), it is determined that the ramp rises 5 feet high.

Explanation:

To determine how high the ramp rises, we can use the Pythagorean theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (adjacent and opposite).

Let's denote:

Using the Pythagorean theorem:

a² + b² = c²

Substituting the known values:

12² + b² = 13²

144 + b² = 169

To find b, we subtract 144 from both sides of the equation:

b² = 169 - 144

b² = 25

Taking the square root of both sides gives us the height:

b = √25 = 5 feet

Therefore, the ramp rises 5 feet high.

Polynomial functions with an even degree have y-axis symmetry is a true statement.

Explanation:

A function symmetrical with respect to the y-axis is called an even function. A function that is symmetrical with respect to the origin is called an odd function. f(x). Since f(−x) = f(x), this function is symmetrical with respect to the y-axis.

So a function that has an even degree in it, be it a polynomial function, has a y-axis symmetry always. The equations with odd degrees may or may not have a y axis symmetry.

Answer:32

Step-by-step explanation:

The pattern seems to double each time there is a new week. By the fourth week he saved $8, and it asks how much he saved by the sixth week. We know $8 x 2 = 16 and 16 x 2 = 32, SO, by the sixth week Mikhail saved $32!

Answer:

isnt it n 24

Step-by-step explanation:

Answer:

the right answer is b

Step-by-step explanation:

since its square root does not result in an integer

Answer:

B

Step-by-step explanation:

Answer: B

Step-by-step explanation:

The monthly rate is $45 for this cellphone plan.

Step-by-step explanation:

Given,

Amount charged for cell phone = $60

Amount paid by Regina for 24 month plan = $1140

Number of months = 24

Let,

m be the monthly rate for cellphone plan

Number of months * Monthly rate + cellphone charges = Amount paid

[tex]24m+60=1140\\24m=1140-60\\24m=1080[/tex]

Dividing both sides by 24

[tex]\frac{24m}{24}=\frac{1080}{24}\\m=45[/tex]

The monthly rate is $45 for this cellphone plan.

Keywords: subtraction, division

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Answer:

$120

Step-by-step explanation:

2/3 of Mary's money + 1/2 of Mary's money is equal to 7/6 of Mary's money

7/6 of Mary's money = $210

Mary's money = m

210 = 7/6*x

180 = x

Mary's money = $180

Suzy's original money = 2/3 of 180

2/3 * 180 = 120

Answer:

B. The probability that the second dart hits the center given that the

first dart hits the center

Step-by-step explanation:

P(BA) is also called the "Conditional Probability" of B given A.

B. The probability that the second dart hits the center given that the first dart hits the center

The following information should be considered;

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Answer:

392 students

Step-by-step explanation:

Given: 3/8 of the seventh grade students were taking advanced math at the beginning of the year.

          Seven dropped out by the end of the year.

          There are 140 students taking advanced math at the end of the year.

Lets assume total number of students of seventh grade be "x".

As given, 3/8 of the seventh grade students were taking advanced math at the beginning of the year.

∴ Number of student took advanced maths at the beginning= [tex]\frac{3}{8} \times x= \frac{3x}{8}[/tex]

We know, 7 student dropped out of advanced math by the end of the year.

Now, forming an equation to determine number of students taking advanced math at the end of the year.

⇒ [tex]\frac{3x}{8} -7= 140[/tex]

Solving the equation  to find number of student in seventh grade.

⇒ [tex]\frac{3x}{8} -7= 140[/tex]

Adding both side by 7

⇒ [tex]\frac{3x}{8} = 140+7[/tex]

Multiplying both side by 8

⇒[tex]3x= 147\times 8[/tex]

Dividing both side by 3

⇒[tex]x= \frac{147\times 8}{3}[/tex]

∴ [tex]x= 392[/tex]

Hence, there are 392 students in seventh grade.

Volume of the cylinder is 3696 m²

Step-by-step explanation:

⇒ V = 22/7 × 14² × 6 = 3696 m²

Answer:

5 (for c only)

Step-by-step explanation:

for c:

1st cleaning company: [tex]y=17x+15[/tex]

2nd cleaning company: [tex]y=20x[/tex]

set up as a system of equations. for them to cancle out make the y of one equation negative. I'll be making the second one negative ( it doesn't matter though)

it will look like:

[tex]y=17x+15[/tex]

[tex]-y=-20x[/tex]

make the two equations on top of eachother and line the terms up. Then combine them. The variable "y" will cancle out and you'll be left with

[tex]0=-3x+15[/tex]

then you will add 3x to both sides to get [tex]3x=15[/tex] then divide both sides by 3 to get [tex]x=5[/tex]

if you plug in 5 for x into both of the original equations you will see that they will both make $100 in five hours. So you answer is 5

Answer:

112.5

Step-by-step explanation:

25/100 x450/1 =

11250/100=112.5

Final answer:

The dilution ratio of a solution when 150 microliters of it contains 90 microliters of saline is 3:5. This means there are 3 parts saline to every 5 parts of the total solution.

Explanation:

If 150 microliters of a solution contains 90 microliters of saline, the dilution ratio of the solution can be described as the volume of saline to the total volume of the solution. To find this ratio, divide the volume of saline by the total solution volume:

Ratio = Volume of Saline / Total Volume of Solution

Ratio = 90 µL / 150 µL

By dividing the two volumes, you get a ratio of 0.6, which can also be expressed as 3:5 after multiplying both numerator and denominator by 10 to eliminate the decimal. This means there are 3 parts of saline to every 5 parts of the total solution.

The dilution ratio is therefore 3:5.

Answer:

$98.00

Step-by-step explanation:

$2000.00 x .049=$98.00

Answer:

Yes each side will always be of the same size unless you are purposely trying to make an uneven shape

Step-by-step explanation:

Answer:

c. 43*

Step-by-step explanation:

1) 180-133= 47

2) 80-90= 90

3) 90+47= 137

4) 180-137= 42*

Answer:

Always write it except if distributing 1. This does NOT apply for -1!

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=−3x+5;5x−4y=−3

Step: Solve: y=−3x+5for y:

Step: Substitute: −3x+5foryin5x−4y=−3:

5x−4y=−3

5x−4(−3x+5)=−3

17x−20=−3 (you have to simplify both sides of the equation)

17x−20+20=−3+20(then add 20 to both sides)

17x=17

17x

17

=

17

17

(Divide both sides by 17)

x=1

Step: Substitute1forxiny=−3x+5:

y=−3x+5

y=(−3)(1)+5

y=2( again Simplify both sides of the equation)

The Answer Is:

x=1 and y=2

Am I incorrect?

Expression: [tex]\((x - 3)(x + 5)\)[/tex]. If original is 10 × 10, new is 105 sq ft. New is 5 sq ft larger.

1. **Expression representing the two binomials for the area of Talia's new bedroom:**

Let [tex]\( x \)[/tex] represent the original length of the square bedroom.

The original bedroom's dimensions: [tex]\( x \times x \)[/tex]

The new bedroom's dimensions: [tex]\( (x - 3) \times (x + 5) \)[/tex]

So, the expression representing the two binomials would be: [tex]\((x - 3)(x + 5)\)[/tex]

2. **Finding the difference in size between old and new bedrooms:**

If the original bedroom measured 10 feet by 10 feet, then [tex]\( x = 10 \)[/tex] (since it's a square).

Substituting into the expression: [tex]\( (10 - 3)(10 + 5) = (7)(15) = 105 \)[/tex] square feet.

So, the new bedroom's area is 105 square feet.

The original bedroom's area is [tex]\( 10 \times 10 = 100 \)[/tex] square feet.

The difference is: [tex]\( 105 - 100 = 5 \)[/tex] square feet.

Therefore, her new bedroom will be 5 square feet larger than her old bedroom.

The complete question is here:

Talia has a square bedroom. Her family is moving and her bedroom in her new apartment will be 3 feet shorter in one direction and 5 feet longer in the other direction. Write an expression that represents the two binomials you would multiply together to find the area of Talia's new bedroom.

2nd Part

If Talia's old bedroom measured 10 feet by 10 feet, how much larger or smaller will her new bedroom be?

Answer:

5.175

Step-by-step explanation:

Answer:

5.175

Step-by-step explanation: