Jim and Gail invested a total of $3,600 in a stock, in a ratio of 5:7. The stock made $6,450 on top of the initial capital. If the payoff is done in the same ratio, how much does Gail get?

Answer:

The  length of the hypotenuse of the isosceles right triangle with leg of length  unit is:

√2 units.

Step-by-step explanation:

Let a and b denote the leg of a right triangle and c denote the hypotenuse of the right triangle.

Now we apply the Pythagorean Theorem as:

[tex]c^2=a^2+b^2[/tex]

Now as triangle is isosceles.

Hence, a=b=1 unit

[tex]c^2=1^2+1^2\\\\c^2=2\\\\c=\sqrt{2}[/tex]

         Hence, the length of the hypotenuse is:

              √2 units.

Final answer:

The expanded form of 38,072 is 30,000 + 8,000 + 70 + 2, where each term represents the digit's value as a product of its place value.

Explanation:

The expanded form of the number 38,072 is written by separating each digit according to its place value and expressing it as the digit multiplied by the power of ten that represents its position. Therefore, the correct expanded form is:

30,000 + 8,000 + 70 + 2

To understand this, we can consider the place value of each digit in the number 38,072. The '3' is in the ten-thousands place, so it is 3 times 10,000, which is 30,000. The '8' is in the thousands place, so it is 8 times 1,000, which is 8,000. The '0' stands for no hundreds, so we skip it. The '7' is in the tens place, so it is 7 times 10, which is 70. Finally, the '2' is in the ones place, which is just 2.

The costs per ride for Thrill and Splash amusement parks can be represented by the equations y = 40 + 5x and y = 60 + 3x respectively. Equating these will give us the number of rides where the costs at both parks will be the same.

The cost of visiting each park can be represented as a linear equation. For Thrill amusement park it can be written as y = 40 + 5x, where y is the total cost, 40 is the entry fee and 5x represents the cumulative cost of the rides, with x being the number of rides. For Splash Water Park, the equation is y = 60 + 3x, where 60 is the entry fee and 3x is the cost of the individual rides. To find out when the costs per ride at the two parks will be the same, we solve the system of equations by setting the two equations equal to each other: 40 + 5x = 60 + 3x.

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The probability that both pieces of bubble gum picked are grape flavored is 3/38, calculated by multiplying the probability of picking a grape piece first (6/20) and then another after the first is given away (5/19).

The question asks us to calculate the probability that both pieces of bubble gum picked from the bag are grape flavored. The bag contains six grape, nine sour apple, and five regular flavored pieces. To find the probability that both pieces are grape, we calculate the probability of picking one grape piece and then another grape piece after the first has been given away.

The total number of pieces initially is 6 (grape) + 9 (sour apple) + 5 (regular) = 20 pieces. The probability of picking a grape piece first is 6/20. After giving it away, there are 5 grape pieces left and the total number of pieces in the bag is now 19. The probability of then picking another grape piece is 5/19. To find the overall probability of both events occurring, we multiply the individual probabilities: (6/20) * (5/19) = 30/380 = 3/38.

Therefore, the probability that both pieces are grape is 3/38.

Final answer:

Gabriela's current age is found by setting up algebraic equations based on the information that Kevin is twice as old as Gabriela now, and was six times as old 12 years ago. Solving the equations, we find that Gabriela is 15 years old.

Explanation:

Finding Gabriela's Current Age:

The problem statement tells us that Kevin is currently 2 times as old as Gabriela and that 12 years ago, Kevin was 6 times as old as Gabriela. To solve for Gabriela's current age, let us use algebra. Let's denote Gabriela's current age as G and Kevin's current age as K. The given information can be translated into the following two equations:

Substituting the first equation into the second, we get:

2G - 12 = 6(G - 12)

Expanding both sides:

2G - 12 = 6G - 72

Moving all terms involving G to one side and constant terms to the other side, we get:

2G - 6G = -72 + 12

-4G = -60

Dividing both sides by -4 to solve for G:

G = 15

So, Gabriela is currently 15 years old.

Answer:  The required ordered pair is (1, 0).

Step-by-step explanation:  We are given to find an ordered pair (x, y) that is a solution to the following equation:

[tex]3x-y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find an ordered pair, we should either take a value of x and find the corresponding value of y,

or,

we should take a value of y and find the corresponding value of x.

Let us consider that

x = 1.

Then, from equation (i), we get

[tex]3\times 1-y=3\\\\\Rightarrow 3-y=3\\\\\Rightarrow y=3-3\\\\\Rightarrow y=0.[/tex]

Thus, the required ordered pair is (1, 0).

Answer:

Cone

Step-by-step explanation:

We are given that a triangle ABC .

We have to find that what shape is formed when a triangle ABC is rotated about side AB.

A given triangle ABC is  a right triangle.

When we rotate the figure about side AB then the figure will be cone .The side AB will be height of cone and side AC will be radius of cone.

Hence, when a triangle ABC is rotated about side  AB, the cone is formed.

Answer: Cone

1) An Isosceles triangle has three sides, in which two sides are of the same length and the third has a different length. It has two angles of the same value and a third angle with a different value, as well.

In the figure is shown that angles Y and Z are the same, then the sides of this angles must be of the same length. This means that:

XY=XZ

(9n+12)ft=(15n-6)ft      

From this equation we have to find n:

9n-15n=-6-12

-6n=-18

[tex]n=\frac{-18}{-6}[/tex]    

n=3

2) The measure of the leg XY in ft

XY=(9n+12)ft

Substitute the value of n calculated in the first question:

XY=(9(3)+12)ft

XY=39 ft

3) The measure of the leg XZ in ft

XZ=(15n-6)ft

Substitute the value of n calculated in the first question:

XZ=(15(3)-6)ft

XZ=39ft

A triangle is isosceles triangle when the two sides and two angle of the triangle in equal in measure.

A triangle is isosceles triangle when the two sides and two angle of the triangle in equal in measure.

Given information-

The length of the side [tex]XY[/tex] is ([tex]9n+12[/tex]).

The length of the side [tex]XZ[/tex] is ([tex]15n-6[/tex]).

The measure of angle,

[tex]m\angle Y=m\angle Z[/tex]

For the isosceles triangle, the two sides and two angle of the equal in measure.

As the measure of angle,

[tex]m\angle Y=m\angle Z[/tex]

Thus the opposite side of this angles must be equal. Thus,

[tex]XY=XZ[/tex]

Put the values as,

[tex]9n+12=15n-6\\15n-9n=12+6\\6n=18\\n=3[/tex]

Hence the value of n is 3 units.

The length of the side [tex]XY[/tex] is ([tex]9n+12[/tex]).

Put the value of n,

[tex]XY=9n+12\\XY=9\times3+12\\XY=27+12\\XY=39 \rm ft[/tex]

Hence the measure of  leg XY is 39 feet.

The length of the side [tex]XZ[/tex] is ([tex]15n-6[/tex]).

Put the value of n,

[tex]XZ=15n-6\\XZ=15\times3-6\\XZ=39\rm ft[/tex]

Hence the measure of  leg XZ is 39 feet.

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Answer:

I believe the answer is "A circle is a set of all points in a plane that are the same distance from a fixed point called the center." I am 95% sure but please correct me if I am wrong. Hope this possibly helps someone!

Step-by-step explanation:

Answer:

  y = 1716 -143x

Step-by-step explanation:

You want an equation for the amount owed after x months on a purchase of $1716 paid at the rate of $143 per month.

After x months, the amount paid will be 143·x. The amount owed is the difference between the original purchase price and the amount paid:

  owed = $1716 - paid

  y = 1716 -143x . . . . . . . . . the amount Jonathan still owes after x months

The solution is 2 glasses

The number of 1/4 quart-sized glasses to fill the lemonade is given by the equation A = 2 glasses

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of 1/4 quart-sized glasses to fill the lemonade be A

Now , the equation will be

The amount of lemonades = 1/2 quart of lemonade

The size of the glasses = 1/4 quart-sized glasses

So , the equation will be

A x 1/4 quart-sized glasses =  1/2 quart of lemonade  

On simplifying the equation , we get

A / 4 = 1/2

Multiply by 4 on both sides of the equation , we get

A = ( 1/2 ) x 4

A = 2 glasses

Therefore , the value of A is 2 glasses

Hence , the number of glasses is 2

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Answer:

Hello! The correct answer is 298.7 [tex]cm^{2}[/tex]

Step-by-step explanation:

I am just confirming!

If sin x = 0.5, cos x is approximately 0.87.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

To find cos x, we can use the identity: cos² x + sin² x = 1

We are given that sin x = 0.5.

We can substitute this into the identity to solve for cos x:

cos² x + sin² x = 1

cos² x + (0.5)² = 1

cos² x + 0.25 = 1

cos² x = 0.75

cos x = ±√0.75

We take the positive square root since cosine is positive in the first and fourth quadrants.

Evaluating the square root gives:

cos x ≈ 0.87 (rounded to two decimal places)

Therefore,

cos x is approximately 0.87.

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Answer:

A. Similar

Step-by-step explanation:

We are given the measurements of ΔQRS and ΔTUV as,

QR = RS = 4, QS = 2 with ∠Q = ∠S = 76°, ∠R = 28°

TU = UV = 12, TV = 6 with ∠T = ∠V = 76°, ∠U = 28°

Now, we see that,

These triangles have different side lengths. So, option C i.e. same sides is not correct.

Also, they are different in size. So, option D i.e. same size is not correct.

Since, they do not have same size, they cannot overlap each other. Thus, are not congruent. So, option B is also not correct.

Thus, we see that from SAS Similarity and the measurements,

QR = RS = 4 and ∠R = 28°

TU = UV = 12 and ∠U = 28°

Both the triangles are similar to each other.

Hence, option A is correct.