Calculate the effective rate of interest (to the nearest hundredth percent) of the following Treasury bill. Given: $10,000 Treasury bill, 3.85% for 13 weeks.

We can prove that ΔDEF = ΔHGF as follows; A: Yes, the triangles are congruent by SAS.

How to prove the congruence

Side DE is congruent to GH as seen in the fact that both have two line marks. These are opposite angles (EFD and HFG) and these angles are congruent.

Note that the opposite sides of a triangle are congruent and corresponding angles are also congruent. This is true of angles DEF and HGF. So, we can conclude that the triangles are congruent by SAS.

Complete Question:

Can you prove that ADEF = AHGF? Justify your answer:

A: Yes, the triangles are congruent by SAS. B: Yes, the triangles are congruent by SSS. C: Yes, the triangles are congruent by SSA. D: No, not enough information is given

Final answer:

After purchasing an album for $12.99 from the $50 gift card, the remaining balance is $37.01, which allows the purchase of 37 more single tracks, assuming each track costs $1.

Explanation:

To determine how many songs can be bought with a $50 gift card after purchasing an album for $12.99, we need to subtract the cost of the album from the total amount on the gift card. So, we have:

Subtracting the cost of the album from the gift card amount gives us:

$50 - $12.99 = $37.01

Assuming that each single track costs $1 as per the scenario provided, we can divide the remaining balance by the cost per single track:

$37.01 ÷ $1 per track = 37 tracks

This means that you can purchase 37 more single tracks with the remaining balance on the gift card.

Answer:

B

Step-by-step explanation:

picture:)

A cyclic quadrilateral is a quadrilateral whose vertices all touch the circumference of a circle.

Opposite angles in a cyclic quadrilateral add to 180 degrees. Quadrilateral ABCD is a cyclic quadrilateral.

< A+<C=180

Substituting <A and <B values given in figure:

x+2+x-2=180

Adding like terms:

2x=180

Dividing both sides by 2

x=90°

<A=x+2=90+2=92°

<C=x-2=90-2=88°

<D=x-10=90-10=80°

<B+<D=180

<B=180-80=100°

The angles of the quadrilateral ABCD are

<A=92°

<B=100°

<C=88°

<D=80°

To solve for b in the equation 7b divided by 12 equals 4.2, multiply both sides by 12 and then divide by 7, resulting in b being equal to 7.2.

To solve the equation 7b ÷ 12 = 4.2 for b, we must isolate b on one side of the equation. We can begin by multiplying both sides of the equation by 12 to cancel out the division by 12 on the left side. This results in the equation 7b = 4.2 × 12. To find the value of b, we then divide both sides of the equation by 7:

Therefore, the value of b is 7.2.

To find the value of b in the equation 7b/12 = 4.2, multiply both sides by 12 and then divide by 7 to get b = 7.2. The value of b is 7.2.

The student is asking how to find the value of b in the equation 7b divided by 12 equals 4.2. To solve for b, you can follow these steps:

Therefore, the value of b is 7.2.

Final answer:

The solution set to the given inequality '-3x < 5.92 - 15.4' is {5, 10}.

Explanation:

The student's question seems to be about solving an inequality to find which values from a given set satisfy it. While the inequality itself appears to be incorrectly written or has a typo, I'll assume it's meant to be '-3x < 5.92 - 15.4'.

We can begin by simplifying the right side of the inequality:

5.92 - 15.4 = -9.48

So the inequality becomes:

-3x < -9.48

To solve for x, we divide both sides by -3, remembering to reverse the inequality sign because we are dividing by a negative number:

x > 9.48 / 3

x > 3.16

Now we can compare this result to the set of numbers given: (-10, -5, 0, 5, 10).

The only numbers greater than 3.16 are 5 and 10.

Therefore, the solution set to the inequality is {5, 10}.

Holly used a total of 53/72 cup of chicken for her stir fry, by adding 5/8 cup and 1/9 cup together after converting them to have a common denominator.

Holly is making a stir fry and needs to calculate the total amount of chicken she has used.

Initially, she measures 5/8 cup of chicken and then adds 1/9 cup of chicken.

To find the total amount of chicken used, we need to add these two fractions together.

This is a simple arithmetic operation called fraction addition.

First, we find a common denominator for the two fractions, which in this case is 72 (the least common multiple of 8 and 9).

Next, we convert each fraction to an equivalent fraction with the common denominator.

The fraction 5/8 converts to (5×72)/(8×72) = 45/72, and 1/9 converts to (1×72)/(9×72) = 8/72.

Now that the fractions share a common denominator, we can add them:

45/72 + 8/72 = 53/72

The sum of the two fractions gives us the total amount of chicken used by Holly, which is 53/72 cup.

To find out how much chicken Holly used altogether, we need to add the two fractions together. First, we find a common denominator, then convert the fractions to have that denominator. Finally, we add the numerators and keep the denominator the same. Holly used a total of 53/72 cup of chicken for her stir fry.

To find out how much chicken Holly used altogether, we need to add the two fractions together.

First, we need to find a common denominator for these fractions. The smallest number that both 8 and 9 can divide into is 72.

Next, we need to convert both fractions to have a denominator of 72. To do this, we multiply the numerator and denominator of each fraction by the same number.

For the first fraction, we multiply both the numerator and denominator by 9, obtaining 45/72. For the second fraction, we multiply both the numerator and denominator by 8, obtaining 8/72.

Now that we have both fractions with a denominator of 72, we can add them together. 45/72 + 8/72 = 53/72.

Therefore, Holly used a total of 53/72 cup of chicken for her stir fry.

To find h(x) = f(x) - g(x), we substitute and simplify the given functions. The result is h(x) = 2 × 3ˣ - 3²ˣ. This solution involves basic algebraic manipulation and exponent rules.

Let's start by defining the given functions:

We need to find h(x) = f(x) - g(x). Substitute the expressions for f(x) and g(x):

Now simplify the expression inside the parentheses:

Combine like terms:

Thus, the function h(x) = 2 × 3ˣ - 3²ˣ is found by subtracting g(x) from f(x).

The product 4^3×4^(-3) is equal to 1.

Take care of the exponents.

4^3= 4*4*4

4^3= 64

=4^-3

The product meaning in maths is a number that you get to by multiplying two or more other numbers together.

Make it a fraction to make the power positive.

[tex]=\frac{1}{4^3}[/tex]

Now, simplify.

[tex]=\frac{1}{64}[/tex]

=64* 1/64= 1

Therefore, The product 4^3×4^(-3) is equal to 1.

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The polynomial in standard form after subtraction will be 12a² - 9a + 5.

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.

The polynomial is given below.

-7a² + 3a - 9 and 5a² - 6a - 4

Subtract -7a² + 3a - 9 from 5a² - 6a - 4, then we have

(5a² - 6a - 4) - (-7a² + 3a - 9)

Simplify the equation, then we have

(5a² - 6a - 4) - (-7a² + 3a - 9)

5a² - 6a - 4 +  7a² - 3a + 9

12a² - 9a + 5

The polynomial in standard form after subtraction will be 12a² - 9a + 5.

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9.5000032 i think i'm not sure