PLEASE HELP!!! I GIVE HIGH POINTS!!! THANKSSS 15 POINTS!!!
An executive in an engineering firm earns a monthly salary plus a Christmas bonus of
7300 dollars. If she earns a total of 9400 dollars per year, what is her monthly salary in dollars?

Triangle RST is similar to Triangle STV and Triangle RVS because they share the same angles due to the altitude SV being drawn to the hypotenuse in right triangle RST.

In right triangle RST, an altitude SV is drawn to its hypotenuse. This creates two smaller triangles within the larger triangle RST, namely triangle STV and triangle RVS.

When an altitude is drawn to the hypotenuse of a right triangle, it creates three similar triangles. In this case, triangle RST is similar to triangle STV and triangle RVS.

The reason for their similarity is that when an altitude is drawn to the hypotenuse, it divides the right triangle into two smaller triangles, and the resulting triangles have the same angles as the original triangle. In other words, the altitude creates three right triangles with shared angles.

Therefore, the correct answer is:

A. Triangle RVSB

C. Triangle RSVC

E. Triangle TVS

These triangles are similar to triangle RST due to the shared angles created by the altitude SV drawn to the hypotenuse in right triangle RST.

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Answer:

-9

Step-by-step explanation:

16-25=-9

Answer: -9

Step-by-step explanation:

The area of the regular pentagon is about 9 square units.

To find the area of a regular polygon, we need to know the length of the apothem and the perimeter of the polygon. The apothem is the distance from the center of the polygon to the midpoint of one of its sides, and the perimeter is the sum of the lengths of all the sides.

Since the polygon is regular, all of its sides have the same length. Let's call that length "s". We also know that the polygon has 5 sides, so it is a pentagon. To find the perimeter, we can simply multiply the length of one side by the number of sides:

Perimeter = 5s

Now, to find the apothem, we can use the formula:

Apothem = (s/2) x tan(180/n)

Where "n" is the number of sides. For our pentagon, n = 5, so we have:

Apothem = (s/2) x tan(36)

We can simplify this a bit by noting that tan(36) is equal to approximately 0.7265. So we have:

Apothem = (s/2) x 0.7265

Now we have everything we need to find the area. The formula for the area of a regular polygon is:

Area = (1/2) x Perimeter x Apothem

Substituting in the values we found earlier, we have:

Area = (1/2) x 5s x (s/2) x 0.7265

Simplifying this expression, we get:

Area = (s^2 x 1.8176)

Rounding to the nearest whole number of square units, we have:

Area = 9

So the area of the regular pentagon is about 9 square units.

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8.4n - 3.2p

8.4(2) - 3.2(4)

8.8 - 3.8

64 - 24

40

The value is 40//

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Answer:

Step-by-step explanation:

To find the median time between breakdowns, we need to use the fact that the distribution of breakdown times follows an exponential distribution. The exponential distribution has a probability density function of f(x) = λe^(-λx), where λ is the rate parameter and x is the time between breakdowns.

The median time between breakdowns is the time t such that the probability of the time between breakdowns being less than t is 0.5. Mathematically, this can be expressed as P(X < t) = 0.5.

In the case of the Vexing Manufacturing Company, we are given that the average time between breakdowns is 30 minutes. The rate parameter λ of the exponential distribution is the inverse of the average time, which is λ = 1/30.

Using the cumulative distribution function (CDF) of the exponential distribution, we can find the median time t by solving the equation:

P(X < t) = 0.5

1 - e^(-λt) = 0.5

e^(-λt) = 0.5

-λt = ln(0.5)

t = -ln(0.5)/λ

t = 30 ln(2) ≈ 20.8 minutes

Therefore, the median time between breakdowns at the Vexing Manufacturing Company is approximately 20.8 minutes.

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The capacity of the smaller container is 352 ml. Their volumes are related by the cube of their corresponding linear dimensions.

Since the two containers are mathematically similar, their volumes are related by the cube of their corresponding linear dimensions. Let V1 be the volume of the smaller container and V2 be the volume of the larger container. Let h1 and h2 be the heights of the smaller and larger containers, respectively. Then we have:

V1/V2 = (h1/h2)^3

We know that h1 = 30cm and h2 = 75cm, and V2 = 5.5 litres = 5500 ml. Substituting these values, we get:

V1/5500 = (30/75)^3

V1/5500 = 0.064

Multiplying both sides by 5500, we get:

V1 = 352 ml

Therefore, the capacity of the smaller container is 352 ml.

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Answer: b and d

Step-by-step explanation: it’s t only two that make since

The answer is \(a^{2} -(2*4)\)

Definition of square and rectangle

A plane figure having four equal sides and four right (90°) angles in geometry is called a square.

A rectangle is a two-dimensional shape with four sides, four corners, and four right angles. A rectangle's opposite sides are the same length, with one pair being longer than the other.

The area of given square= a²

The area of rectangle= 2*4

Hence the area of shaded region= \(a^{2} -(2*4)\)

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Answer:

r² = (4 - 2)² + (5 - (-2))² = 2² + 7² = 53

So the equation of this circle is

(x - 2)² + (y + 2)² = 53

The limit of the given expression as x approaches 1 from the right is 1.8.

To evaluate the limit of the given expression:

\(lim_{x - > 1} + [ln(x ^ 9 - 1) - ln(x ^ 5 - 1)]\)

We can start by directly substituting x = 1 into the expression:

[ln(1⁹ - 1) - ln(1⁵ - 1)]

= [ln(0) - ln(0)]

However, ln(0) is undefined, so this approach doesn't provide a meaningful answer.

To apply L'Hôpital's Rule, we need to rewrite the expression as a fraction and differentiate the numerator and denominator separately. Let's proceed with this approach:

\(lim_{x - > 1}\)+ [ln(x⁹ - 1) - ln(x⁵ - 1)]

= \(lim_{x - > 1}\)+ [ln((x⁹ - 1)/(x⁵ - 1))]

Now, we can differentiate the numerator and denominator with respect to x:

Numerator:

d/dx[(x⁹ - 1)] = 9x⁸

Denominator:

d/dx[(x⁵ - 1)] = 5x⁴

Taking the limit again:

\(lim_{x - > 1}\)+ [9x⁸ / 5x⁴]

= \(lim_{x - > 1}\)+ (9/5) * (x⁸ / x⁴)

= (9/5) * \(lim_{x - > 1}\)+ (x⁸ / x⁴)

Now, we can substitute x = 1 into the expression:

(9/5) * \(lim_{x - > 1}\)+ (1⁸ / 1⁴)

= (9/5) * \(lim_{x - > 1}\)+ 1

= (9/5) * 1

= 9/5

= 1.8

The complete question is:

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. \(lim_{x - > 1} + [ln(x ^ 9 - 1) - ln(x ^ 5 - 1)]\)

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Answer:

A. 44+4x

B. The error is that Ben forgot to distribute his terms by multiplying 7 by 15 so instead of 30x+7 he should have gotten 30x+105

C. (44+4x)-(12x+20) to solve for difference in perimeter

Step-by-step explanation:

Answer:

isosceles

Step-by-step explanation:

Answer:

X=3  Y=12

Step-by-step explanation:

sorry if i got it wrong xp

Answer: 15

Step-by-step explanation: Pythagorean theorem

8^2+b^2=17^2

64+b^2=289

b^2=225

b=15

Brainliest please

Answer:

15  inches.

Step-by-step explanation:

\(AB=\sqrt{AC^{2}-BC^{2} } =\sqrt{17^{2}-8^{2} } =\sqrt{289-64} =\sqrt{225}= 15 \: ( inches)\)

The relationship between the distance S and time t is:2t^2 = (1/2)a1t^2 + v2t + (1/2)a2t^2.

Let the velocity and acceleration of the first car be v1 and a1 respectively.The velocity of the second car be v2 and acceleration be a2.Let the distance between the two cars at any time after t=0 be given by S.If the initial distance between them is 50 feet, then S=S0+50ft where S0 is the distance between them at time t=0.

From the given conditions, we can set up the following relationships for the two cars.1) For the first car:S=ut+(1/2)at^2 where u is the initial velocity.

2) For the second car:S=vt+(1/2)at^2 where v is the initial velocity.In the first equation, we can substitute u=0 (since it started from rest) and a=a1.

In the second equation, we can substitute v=50ft (since it is 50ft behind) and a=a2.

Substituting the above values in the above two equations, we get:S= (1/2)a1t^2 and

S= 50ft + v2t + (1/2)a2t^2

From the problem statement, we are also given that the lead car is accelerating in such a way that the distance S in feet between the two cars at any time t after t=0 seconds is 50 more than twice the square of t.

Therefore,S = 2t^2 + 50ft

We can now equate the above two expressions for S, and solve for t, to get the relationship between the distance S and time t:

S = 2t^2 + 50ft = (1/2)a1t^2 + 50ft + v2t + (1/2)a2t^2

Simplifying the above expression, we get:2t^2 = (1/2)a1t^2 + v2t + (1/2)a2t^2

Therefore, the relationship between the distance S and time t is:2t^2 = (1/2)a1t^2 + v2t + (1/2)a2t^2.

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What is the likelihood of rolling a 10 on a fair number cube numbered 1-6 is 0

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one

The sample space in the question is 1,2,3,4,5,6

The Probability of rolling a 10 is impossible  since 10 is not a possible outcome on a number cube numbered 1 to 6.

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Answer:

30000

Step-by-step explanation:

200x10x15=30000

The condition that ensures a solution for the mentioned equation is :

1. b₂ = 2b₁ and 6b₁-3b₃ +b₄ = 0.

In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. An equation consists of two expressions joined by an equal sign ("="). Expressions for both sides of the equals sign are called the "left side" and the "right side" of the equation. Usually the right side of the equation is assumed to be zero. If this is accepted, it does not reduce the generality, since it can be done by subtracting the right side from the two sides.

According to the Question:

Given that:

x₁+ 2x₂= b₁       ------------------------- (1)

2x₁ + 4x₂ = b₂  ------------------------- (2)

3x₁ + 7x₂ = b₃   ------------------------ (3)

3x₁ + 9x₂ = b₄   ------------------------ (4)

From equation (1) and (2), we get:

b₂ = 2b₁

After analysis equation (1), we have:

   6b₁-3b₃ +b₄ = 0

Using equation (1), (3) and (4), we get:

3(x₁+2x₂) -6(3x₁+7x₂) + 3x₁ + 9x₂ ≠ 0

Putting the value from equation (1),(3) and (4), we get:

6(x₁+2x₂) -3(3x₁+7x₂) + 3x₁ + 9x₂ = 0

Hence option (1) is correct.

Complete Question:

Consider the following system of linear equations:

x₁+ 2x₂= b₁

2x₁ + 4x₂ = b₂

3x₁ + 7x₂ = b₃

3x₁ + 9x₂ = b₄

which one of the following conditions ensures that a solution exists for the above system.

1. b₂ = 2b₁ and 6b₁-3b₃ +b₄ = 0

2. b₃ = 2b₁ and 6b₁-3b₃ +b₄ = 0

3. b₂ = 2b₁ and 3b₁-6b₃ +b₄ = 0

4. b₃ = 2b₁ and 3b₁-6b₃ +b₄ = 0

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Answer:

Hope that will help you

Step-by-step explanation:

BD = 14.5

The volume of a cube is increased by 27 times its actual volume if the surface area of the new cube is triple that of the original cube.

cube is a 3-dimensional surface having all sides equal.

hence, the volume of a cube=v =\((x)^3\)

where x represent the side of a cube

know if we triple the length of a cube I,e x=3x

        v\(=(3x)^3\\\\=3x*3x*3x\\\\=27x^3\)

hence, if a cube is increased to form a new cube such that the surface area of the new cube is triple that of the original cube.  its volume is increased by a factor of 27.

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The length of the longer base to be 10. Finally, substituting these values into the original formula gives us Total area is = 16 ft².

Using the given formula, we can find the total area to be:

Total area = area of parallelogram + area of trapezoid

= 11 + 1/2(enter your response here + 7)

= enter your response here + 66

= enter your response here ft²

To find the missing values, we need to solve for the unknown side lengths of the parallelogram and trapezoid. From the given information, we know that the area of the parallelogram is 11 and the height of the trapezoid is 1. We can use the area formula for each shape to set up equations in terms of the unknown side lengths.

For the parallelogram, area = base x height = 11. We don't know the base or height, but we know that the opposite sides of a parallelogram are equal in length. Let's call the length of one side x. Then, the length of the other side is also x, and the height is h. Substituting these values into the area formula gives us:

11 = x * h

For the trapezoid, area = (base1 + base2) / 2 * height = 1/2 (enter your response here + 7) * 1. We don't know the lengths of the bases, but we know that they are parallel and that the length of one base is enter your response here greater than the length of the other base. Let's call the length of the shorter base x. Then, the length of the longer base is x + enter your response here, and the height is 1. Substituting these values into the area formula gives us:

1 = (x + enter your response here + x) / 2 * 1

1 = (2x + enter your response here) / 2

2 = 2x + enter your response here

Now we have two equations with two unknowns, which we can solve simultaneously using substitution or elimination. Solving for h in the first equation gives us h = 11 / x, which we can substitute into the second equation:

2 = 2x + enter your response here

2 = 2x + 2h

= 2x + 2(11 / x)

2x^2 = 4x + 22

2x^2 - 4x - 22 = 0

Solving for x using the quadratic formula gives us:

x = (-(-4) ± sqrt((-4)^2 - 4(2)(-22))) / (2(2))

x = (4 ± sqrt(144)) / 4

x = (4 ± 12) / 4

x = -2 or 3

Since the length of a side cannot be negative, the length of the shorter base of the trapezoid is 3. Using this value, we can find the length of the longer base to be 10. Finally, substituting these values into the original formula gives us:

Total area = 11 + 1/2(3 + 7)

= 11 + 5

= 16 ft²

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Answer:

1 1/4

Step-by-step explanation:

3 - 1 = 2

2 - 3/4 = 1 1/4

Reptile stickers come in sheets of 6 and Marine Life stickers come in sheets of 9 .

Number of reptile sticker = 6

Number if marine sticker = 9C

Answer:

not sure if this is what you're looking for but the function would be

f(x) = x-5

Answer:

the  number of miles that you would drive to go the yellowstone is 814 miles

Step-by-step explanation:

The computation of the number of miles that you would drive to go the yellowstone is shown below:

= First leg of the journey from portland + more drives to yellow stone

= 426 miles + 388 miles

= 814 miles

Hence, the  number of miles that you would drive to go the yellowstone is 814 miles

we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)

Answer:

Step-by-step explanation:

318 / 40 = 7.95

each store got 7 boxes of milk

40 x 7 = 280

318 - 280 = 38

38 boxes got stored

so

true

false

false

true