State if the two triangles are congruent. If they are, state which postulate or theorem proves that they are congruent.

The coins used for buying hot chocolate are 8 dimes and 4 nickels.

What are dimes and nickels?

The size of the nickel and dime coins is different, yet they are both silver in color. The dime is smaller than the nickel coin, but having a higher value. The value of each coin can be used to calculate the sum of several coin combinations.

We are given that hot chocolate is bought for $1.00 and only two kinds of coins to make $1.00 with exactly 12 coins.

We know that the value of a nickel is five cents, while that of a dime is ten cents. A dime is therefore equivalent to two nickels in value. The value of a nickel is therefore equal to half the value of a dime.

So, we get that he used 4 nickels and 8 dimes which make 12 coins and 100 cents which is equal to $1.

Hence, the coins used for buying hot chocolate are 8 dimes and 4 nickels.

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Answer:

360

Step-by-step explanation:

The solution is given by the point of intersection of the two lines which is (-1/4, 3/4).

To find the point of intersection of two lines, we need to determine the equations of the lines and then solve them simultaneously.

Finding the equation of the first line passing through the points (-1, 3) and (0, 0).

The slope of the line (m1) can be calculated using the formula:

m1 = (y2 - y1) / (x2 - x1)

Substituting the values (-1, 3) and (0, 0):

m1 = (0 - 3) / (0 - (-1))

= -3 / 1

= -3

Using the point-slope form of the line equation:

y - y1 = m1(x - x1)

Substituting the values (-1, 3):

y - 3 = -3(x - (-1))

y - 3 = -3(x + 1)

y - 3 = -3x - 3

y = -3x

So, the equation of the first line is y = -3x.

Similarly, second line,

The slope of the line (m2) is:

m2 = (2 - 0) / (1 - (-1))

= 2 / 2

= 1

Using the point-slope form with the values (-1, 0):

y - 0 = 1(x - (-1))

y = x + 1

So, the equation of the second line is y = x + 1.

Equating the equations of the lines to find the point of intersection and hence the solution,

-3x = x + 1

0 = 4x + 1

-1 = 4x

x = -1/4

Put x = -1/4 in 2nd equation,

y = x + 1

y = (-1/4) + 1

y = 3/4

Therefore, the point of intersection of the two lines is (-1/4, 3/4).

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The expression given is

Simplifying the expression will yield

This means the values of x are greater that 8

But 4 is not greater the 8

Hence

Therefore x=4 is not a solution, the right option is No

Answer:

  (x, y) = (-1, 5)

Step-by-step explanation:

You want to solve this system of equations by substitution.

The idea of substitution means we want to replace an expression in one equation for an equivalent expression based on the other equation.

Here, the second equation gives an expression equivalent to "y", so we can use that expression in place of y in the first equation:

  5x +2(-2x +3) = 5 . . . . . . . . (-2x+3) substitutes for y

  x +6 = 5 . . . . . . . . . . simplify

  x = -1 . . . . . . . . . subtract 6

  y = -2(-1) +3 = 5 . . . . . use the second equation to find y

The solution is (x, y) = (-1, 5).

__

Additional comment

Choosing substitution as the solution method often works well if one of the equations gives an expression for one of the variables, or if it can be solved easily for one of the variables. The "y=" equation is a good candidate for providing an expression that can be substituted for y.

Any equation that has one of the variables with a coefficient of +1 or -1 is also a good candidate for providing a substitution expression.

  4x -y = 3   ⇒   y = 4x -3 . . . . . for example

The attached graph confirms the solution above.

Answer:

o

Step-by-step explanation:

Answer:

In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.

Step-by-step explanation:

The dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend. This is because the dividend income is calculated by multiplying the number of shares that an investor owns by the amount of the dividend per share.

For example, if an investor owns W = 100 shares of XYZ stock and XYZ distributes a $Y = 5 per share dividend, then the investor's dividend income will be 100 * 5 = 500 dollars.

In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.

Answer:

y = 4

Step-by-step explanation:

The triangles are congruent.

8y = 6y + 8

2y = 8

y = 4

The positive sign indicates that Gunther pulls to the right.

A force that would result in a balanced force for the game is: 45N

First we define a reference system.

Let's assume the horizontal axis as positive towards the right.

Suppose Kiley and Jermaine pull the rope to the left, while Gunther pulls the rope to the right.

The equilibrium equation is given by:

-20-25+F=0

Where,

F: force with which Gunther pulls the rope.

Clearing F we have:

The positive sign indicates that Gunther pulls to the right.

A force that would result in a balanced force for the game is: 45N

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Answer:

Systems with infinitely many solutions are equations that are the same (on top of one another)

Ex:

4x=4 and 2x=2

4x=0, 5x=0

Answer:

  B)  When you're finished, you have a line that bisects your segment

Step-by-step explanation:

An angle bisector is a ray that divides a given angle into two congruent parts. There is no line segment involved.

__

The statement that is not true about this construction is ...

  B) When you're finished, you have a line that bisects your segment

_____

Additional comment

The construction effectively creates an arc of a circle, then creates the perpendicular bisector of the chord of that arc. The center of the circular arc is the vertex of the angle being bisected. The constructed perpendicular bisector of the chord also bisects the angle. (The chord is never actually drawn, and the "circular arc" may be two short arcs across the rays of the angle being bisected.)

The value of f(4) is 28.

it can be found using the fundamental theorem of calculus.

The fundamental theorem of calculus states that if a function f is continuous on an interval and its derivative f' exists on that interval, then the definite integral of f' over the interval is equal to the difference in the values of the original function at the endpoints of the interval.

In this case, we are given that f '(x) is continuous, and that the definite integral of f '(x) over the interval [3, 4] is equal to 18. Therefore, using the fundamental theorem of calculus, we have that f(4) - f(3) = 18, and since f(3) = 10, we can solve for f(4) to get f(4) = 10 + 18 = 28.

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Complete question:

If f(3) = 10, f ' is continuous, and   \(\int\limits^4_3\) f '(x) dx = 18, what is the value of f(4)?

In the 1984 domestic violence study conducted by Sherman and Berk, the ethical concern was that they potentially withheld a beneficial treatment.

The domestic violence study conducted by Sherman and Berk in 1984 raised an ethical concern in that they financially profited from the research. This raises the question of whether their motives were purely altruistic or whether they were driven by financial gain. Additionally, the study did not adhere to special protections for vulnerable populations such as women and children who may have been victims of domestic violence. This raises concerns about the validity and generalizability of the study's findings. Furthermore, the study potentially withheld a beneficial treatment, which raises questions about the ethical responsibility of researchers to ensure that their subjects receive the best possible care. Finally, there are also concerns that the researchers may have deceived their subjects, which raises questions about the integrity and transparency of the research process. In conclusion, the ethical concerns raised by this study highlight the need for researchers to carefully consider the impact of their research on vulnerable populations and to ensure that they adhere to the highest ethical standards.
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(a) The interval on which f is increasing: (0, ∞)

The interval on which f is decreasing: (0, 1)

(b) Local minimum: At x = 1, f(x) has a local minimum value of -1.

There is no local maximum value.

(c) Inflection point: At x ≈ 0.293, f(x) has an inflection point.

The function f(x) = x^2 - x - ln(x) is a quadratic function combined with a logarithmic function.

To find the interval on which f is increasing, we need to determine where the derivative of f(x) is positive. Taking the derivative of f(x), we get f'(x) = 2x - 1 - 1/x. Setting f'(x) > 0, we solve the inequality 2x - 1 - 1/x > 0. Simplifying it further, we obtain x > 1. Therefore, the interval on which f is increasing is (0, ∞).

To find the interval on which f is decreasing, we need to determine where the derivative of f(x) is negative. Solving the inequality 2x - 1 - 1/x < 0, we get 0 < x < 1. Thus, the interval on which f is decreasing is (0, 1).

The local minimum is found by locating the critical point where f'(x) changes from negative to positive. In this case, it occurs at x = 1. Evaluating f(1), we find that the local minimum value is -1.

There is no local maximum in this function since the derivative does not change from positive to negative.

The inflection point is the point where the concavity of the function changes. To find it, we need to determine where the second derivative of f(x) changes sign. Taking the second derivative, we get f''(x) = 2 + 1/x^2. Setting f''(x) = 0, we find x = 0. Taking the sign of f''(x) for values less than and greater than x = 0, we observe that the concavity changes at x ≈ 0.293. Therefore, this is the inflection point of the function.

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B = X(A-AX⁻¹)  which is product of invertible matrices (A,X,A-AX)  therefore B is  invertible and The solution of matrix equation is  X = A⁻¹(A+B).

Since A and X are invertible, we can multiply both sides of the equation  A-AX⁻¹ = X⁻¹B on the left by A⁻¹ to obtain X⁻¹ = A⁻¹B(A - X).

Substituting this expression for X⁻¹ in the equation B = AX⁻¹, we get

B = X(A-AX⁻¹). Thus, B is a product of invertible matrices and is therefore invertible.

The equation A-AX⁻¹= X⁻¹B implies that X⁻¹ is a left inverse of B, since it satisfies X⁻¹B = A-AX⁻¹. Since A, X, and A - AX are invertible, it follows that X⁻¹ is also invertible. Therefore, B is invertible, as it has a left inverse.

To solve for X, we can multiply both sides of the equation by X:

AX - AXX⁻¹= XX⁻¹B

Simplifying the left side:

AX - A = XX⁻¹B

Solving for X:

X = A⁻¹(A+B)

where I is the identity matrix. Thus, X is a solution to the matrix equation A-AX⁻¹= X⁻¹B if A, X, and A-AX are invertible.

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The length of the radius of the circle is 7.5 inches.

The radius formula is easily obtained by halving the circle's diameter. The line segment created when we join a point on a circle's circumference to its exact center is referred to as the ring's radius. The radius of a circle is the separation between its centre and circumference. Always, the diameter is twice the radius. As a result, the formula is created by multiplying the diameter by two.

Given that the diameter of the circle is 15 inches.

The radius of the circle is half the measure of the diameter.

That is,

R = d/2

R = 15/2

R = 7.5 inches

Hence, the length of the radius of the circle is 7.5 inches.

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Answer:

m∠C = 66°

Step-by-step explanation:

Since AB = BD, it means this triangle is an Isosceles triangle and as such;

∠BAD = ∠BDA = 24°

Thus, since sum of angles in a triangle is 180,then;

∠ABD = 180 - (24 + 24)

∠ABD = 180 - 48

∠ABD = 132°

We are told that BC = BD.

Thus, ∆BDC is an Isosceles triangle whereby ∠BCD = ∠BDC

Now, in triangles, we know that an exterior angle is equal to the sum of two opposite interior angles.

Thus;

132 = ∠BCD + ∠BDC

Since ∠BCD = ∠BDC, then

∠BCD = ∠BDC = 132/2

∠BCD = ∠BDC = 66°

Answer:

A = $ 7,299.92

A = P + I where

P (principal) = $ 6,000.00

I (interest) = $ 1,299.92

Step-by-step explanation:

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

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

Answer:

d

Step-by-step explanation:

-x/3<5

-x< 5x3

-x<15

(there is an assumed 1 in front of the x)

-1x<15

x/-1<15* -1

x>-15

sign switches when we deal with negative values mutiplying and dividing

hope this helped<3

Answer:

p = -8

Step-by-step explanation:

Step 1: Write equation

7(p + 3) + 9 = 5(p - 2) - 3p

Step 2: Solve for p

Step 3: Check

Plug in x to verify it's a solution.

Answer:

Step-by-step explanation:

AD = \(\frac{AC}{2}\)

AD = DC = 12

AC = 2AD = 24

~~~~~~~~~~~~~~~~

\(\frac{4y-36}{2}\) = 12

2y - 18 = 12

y = 15

Answer:

12 miles

Step-by-step explanation:

Total miles = Length of trail ×

Number of times she rode

Total miles = 3 miles × 4 times

Total miles = 12 miles

Mika traveled a total of 12 miles.

Answer:

4/15

Step-by-step explanation:

Each fraction is 1/15 less than the previous.

If we make them all the same denominator,

then it would show as:

8/15

7/15

6/15

5/15

The next fraction would be 5/15 - 1/15

which is

4/15

Answer:

4                                                    1

__    because it goes down by ___

15                                                  15

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

3^2 = 9

2*9 = 18

4*6 = 24

18 + 24 = 42

Both the white longhair female cat (w/w; l/l) and the black shorthair male cat (w/w; l/l) are homozygous for the white coat color (w/w) and the longhair trait (l/l).

When these cats mate, all the kittens will inherit one allele for each trait from each parent. Since both parents are homozygous for the white coat color (w/w), all kittens will also inherit the white coat color gene from both parents, resulting in white kittens (w/w). Similarly, both parents are homozygous for the longhair trait (l/l), so all kittens will inherit the longhair allele from both parents, making them longhair kittens (l/l).

In conclusion, all 12 kittens will have a white coat color and long hair, just like their parents. They will look like white longhair kittens, with the genotype (w/w; l/l) for both traits. It is important to remember that being a responsible pet owner includes spaying or neutering your pets to prevent unwanted litters, and finding loving homes for any kittens or puppies that may be born.

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Answer:d=(16-x)30

Step-by-step explanation:

The car traveled 600 miles if it has 10 gallons of gas left in the tank.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that is equal.

To determine the equation that represents the relationship between the distance traveled by car and the amount of gas left in the tank.

Let the distance traveled by car would be d miles,

and the amount of gas left in the tank would be x gallons

Since the car had a 16-gallon fuel tank

So the amount of gas left in the tank would be 16 - x

When driven on a highway, it has a gas mileage of 30 miles per gallon.

To find the equation of the distance we have to calculate the product of gas left in the car and the mileage of the car.

So the required equation as:

⇒ d = (16-x)30.

If it has 10 gallons of gas left in the tank

Substitute x = 10 in the above equation, we get

⇒ d = (16-10)30.

⇒ d = (20)30.

⇒ d = 600.

Therefore, the car traveled 600 miles if it has 10 gallons of gas left in the tank.

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Taylor polynomials of degree 2 and 3 centered at x = 0 for the function f(x) = 16tan(x) are:

P2(x) = 16x + 8x^2

P3(x) = 16x + 8x^2

To find the Taylor polynomials centered at x = 0 for the function f(x) = 16tan(x), we can use the Taylor series expansion for the tangent function and truncate it to the desired degree.

The Taylor series expansion for tangent function is:

tan(x) = x + (1/3)x^3 + (2/15)x^5 + (17/315)x^7 + ...

Using this expansion, we can find the Taylor polynomials of degree 2 and 3 centered at x = 0:

Degree 2 Taylor polynomial:

P2(x) = f(0) + f'(0)(x - 0) + (1/2!)f''(0)(x - 0)^2

= 16tan(0) + 16sec^2(0)(x - 0) + (1/2!)16sec^2(0)(x - 0)^2

= 0 + 16x + 8x^2

Degree 3 Taylor polynomial:

P3(x) = P2(x) + (1/3!)f'''(0)(x - 0)^3

= 0 + 16x + 8x^2 + (1/3!)(48sec^2(0)tan(0))(x - 0)^3

= 16x + 8x^2

Therefore, the Taylor polynomials of degree 2 and 3 centered at x = 0 for the function f(x) = 16tan(x) are:

P2(x) = 16x + 8x^2

P3(x) = 16x + 8x^2

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the capacity of the largest container that can measure the contents of each drum an exact number of times is 36 liters.

To find the capacity of the largest container that can measure the contents of each drum an exact number of times, we need to determine the greatest common divisor (GCD) of the volumes of the drums.

The GCD is the largest positive integer that divides each of the given numbers without leaving a remainder. In this case, we want to find the GCD of 36, 45, and 72.

First, let's find the prime factorizations of these numbers:

36 = 2^2 * 3^2,

45 = 3^2 * 5,

72 = 2^3 * 3^2.

To find the GCD, we take the product of the common prime factors raised to the lowest powers they appear in the factorizations:

GCD(36, 45, 72) = 2^2 * 3^2 = 4 * 9 = 36.

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You can put 14 boxes of candy weighing 3/4 lb each in the bin.

To determine how many 3/4 lb boxes of candy can fit in a bin, we divide the total weight of the bin by the weight of each box.

First, let's convert the mixed number 10 1/2 lbs to an improper fraction.

10 1/2 lbs = (10 * 2 + 1) / 2 = 21/2 lbs

Next, we divide the total weight of the bin (21/2 lbs) by the weight of each box (3/4 lb):

(21/2 lbs) / (3/4 lb) = (21/2) * (4/3) = (21 * 4) / (2 * 3) = 84/6 = 14

As a result, you can fill the bin with 14 boxes of sweets that each weigh 3/4 lb.

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