AABC is similar to AADE. Enter the congruence statements that must be true.
The congruence statements that must be true are

Based on the information, the Stafford loan will have a lower balance by $527.14 at the time of repayment

Using the formula for compound interest, the total cost of the loan can be calculated as follows:

Total cost of Stafford loan = $11,650 x (1 + 0.0595/12)^(12*0.5) = $12,652.14

Total cost of PLUS loan = $12,436.41 x (1 + 0.0655/12)^12 = $13,179.28

Therefore, the Stafford loan will have a lower balance at the time of repayment by $527.14 ($13,179.28 - $12,652.14).

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Answer:

which language is this

The possible price for the items if the store sells $600 is (c) $40

From the question, we have the following parameters that can be used in our computation:

The supply-demand graph

If the store sells $600, then there is a supply worth of $600

The equation of the supply line is calculated as

y = mx + c

Where

c = y = 0

i.e. c = 100

So, we have

y = mx + 100

Using another point on the graph, we have

30m + 10 = 400

So, we have

m = 13

This means that

y = 13x + 100

For a supply of 600, we have

13x + 100 = 600

So, we have

13x = 500

Divide by 13

x = 38.4

Approximate

x = 40

Hence, the possible price for the items is (c) $40

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Answer:

because it is a square, you just need to make a square with the side lenghts all being a or b

Step-by-step explanation:

Answer:

Samantha got 85 questions right.

Step-by-step explanation:

90% of 50 is 45.

80% of 50 is 40.

40 + 45 = 85

:)

Answer:

95

Step-by-step explanation:

Im pretty sure It's 95 because if you get a 90% on a test with 50 questions, you would've gotten 45 correct. If you get an 80% on a test with 50 questions, you would've gotten 40 correct. Then add them.

The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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Answer:

Bacteria Growth The number N of bacteria in culture is modeled by N= 250e^kt where t is the time in hours. If N = 280 when t= 10, estimate the time required for the population to double in size.

Step-by-step explanation:

(⁠◔⁠‿⁠◔⁠)(⁠◔⁠‿⁠◔⁠)(⁠◔⁠‿⁠◔⁠)

Answer:

6.40

Step-by-step explanation:

For this we will divide,

look below for a explanation

Purchase Price:

$64

Discount:

(64 x 90)/100 = $57.60

Final Price:

64 - 57.60 = $6.40

Answer:

436, 4297, 4301

Step-by-step explanation:

look at the digits carefully and arrange them

There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

(i) Zeroes of the polynomial:

In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:

From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.

We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:

We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.

The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a

Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,

we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0

Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))

Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

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The equation Hats 2030=230.09+23x represents a linear relationship between the number of years since 2010 (x) and the projected number of hats sold in the year 2030.

The slope of the equation, 23, indicates that for each additional year since 2010, the projected number of hats sold in 2030 increases by 23. The y-intercept of the equation, 230.09, represents the projected number of hats sold in 2030 if x is equal to zero (i.e., in the year 2010). This equation can be used to forecast future hat sales based on past trends and can help businesses and organizations plan for inventory and production needs. However, it is important to note that unforeseen events, changes in consumer behavior, and other factors can impact actual hat sales and should be considered when making business decisions.

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Answer:nice do it

Step-by-step explanation:

what is it about

show the problem

Step-by-step explanation:

The average number of enrollments per day at the Sunnyside Daycare is 21.

An average is a result obtained by summing some numerical values and then dividing the total by the number of values or variables.

An average is the mean, which is one of the central tendency values.

Day          Number of Enrollments

Monday                 17

Tuesday                19

Wednesday         23

Thursday              14

Friday                  25

Saturday             28

Total =               126

Average enrollments = 21 (126/6)

Thus, the average number of enrollments per day at the Sunnyside Daycare is 21.

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What was the average number of enrollments per day?

Given,

A glass block window is made of two different-sized glass squares.

The window has side lengths of 40 inches. The large glass squares have side lengths of 10 inches.

40 × 10 = 400

Answer:

smallest: 40 kg, medium: 60 kg, largest quantity: 80 kg

Step-by-step explanation:

divide into 2 : 3 : 4

find the total quantities: 2 + 3 + 4 = 9 quantities.

9 quantities → 180 kg

1 quantities → \(\frac{180}{9}\) kg

1 quantities → 20 kg

Finding what the question asked for:

2 quantities → 20*2 → 40 kg

3 quantities → 20*3 → 60 kg

4 quantities → 20*4 → 80 kg

Answer:

Smallest quantity is 40 kg

Largest quantity is 80 kg

(in case you need it the middle quantity is 60 kg)

Step-by-step explanation:

In the ratio there are 9 total parts (2+3+4). If you divide the 180 kg by 9 you will get 20kg. You can now multiply the 20kg by each ratio (20×2, 20×3, and 20×4) to divide the sugar into the ratio.

20×2= 40 kg

20×3= 60 kg

20×4= 80 kg

Answer:

25/3 ft/s

Step-by-step explanation:

Height of pole , h=15 ft

Height of man, h'=6 ft

Let BD=x

BE=y

DE=BE-BD=y-x

All right triangles are similar

When two triangles are similar then the ratio of their corresponding sides are equal.

Therefore,

\(\frac{AB}{CD}=\frac{BE}{DE}\)

\(\frac{15}{6}=\frac{y}{y-x}\)

\(\frac{5}{2}=\frac{y}{y-x}\)

\(5y-5x=2y\)

\(5y-2y=5x\)

\(3y=5x\)

\(y=\frac{5}{3}x\)

Differentiate w.r.t t

\(\frac{dy}{dt}=\frac{5}{3}\frac{dx}{dt}\)

We have dx/dt=5ft/s

Using the value

\(\frac{dy}{dt}=\frac{5}{3}(5)=\frac{25}{3}ft/s\)

Hence, the tip of  his shadow moving  with a speed 25/3 ft/s when he is 45 feet from the pole.

Answer:

The tip pf the shadow is moving with speed 25/3 ft/s.

Step-by-step explanation:

height of pole = 15 ft

height of man = 6 ft

x = 45 ft

According to the diagram, dx/dt = 5 ft/s.

Now

\(\frac{y-x}{y}=\frac{6}{15}\\\\15 y - 15 x = 6 y \\\\y = \frac{5}{3} x\\\\\frac{dy}{dt} = \frac{5}{3}\frac{dx}{dt}\\\\\frac{dy}{dt}=\frac{5}{3}\times 5 =\frac{25}{3} ft/s\)

Answer:

58.66 is the radius of the circle

Explanation

factoring we get:

For the expression to be zero, we have two options:

and

Answer

v= 2 , 3

Answer:

200

Step-by-step explanation:

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

\(120^{2}\) + \(160^{2}\) = \(c^{2}\)

14400 + 25600 = \(c^{2}\)

40000 = \(c^{2}\)

\(\sqrt{40000}\) = \(\sqrt{c^{2} }\)

200 = c

Jesus love you.

Answer:

see below

Step-by-step explanation:

d= original price

so d−0.25d = full price less 25%

0.75d is the same - paying (1-25%) = 75% of original price

The value of the functions for the condition is,

1. f(x + h) = 3(x + h)² - (x + h) + 5,

2. (fog)(x) =  27x² -33x + 15,

3. f(g(h(-1))) = 16,060.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

Given f(x) = 3x² - x + 5

g(x) = -3x + 2

h(x) = -5x³

1. Find f(x + h),

so  f(x) = 3x² - x + 5

substitute x = x+ h

f(x + h) = 3(x + h)² - (x + h) + 5

2. (fog)(x),

f(g(x))

g(x) = -3x + 2

f(-3x + 2)  = 3(-3x + 2)² - (-3x + 2) + 5

f(g(x)) = 3(9x² + 4 - 12x) - 2 + 3x + 5

f(g(x)) = 27x² + 12 - 36x - 2 + 3x + 5

f(g(x)) = 27x² -33x + 15

3. Find f(g(h(-1)),

h(x) = -5x³

g(x) = -3x + 2

g(h(x)) = -3(-5x³)² + 2

g(h(x)) = -75x⁶ + 2

f(x) = 3x² - x + 5

f(g(h(x))) = 3(-75x⁶ + 2)² - (-75x⁶ + 2) + 5

f(g(h(x))) = 3(5625x¹² + 4 - 300x⁶) + 75x⁶ - 2 + 5

f(g(h(x))) = 16875x¹² + 12 - 900x⁶ + 75x⁶ -2 + 5

f(g(h(x))) = 16875x¹² - 825x⁶ + 10

substitute x = -1,

f(g(h(-1))) = 16875(-1)¹² - 825(-1)⁶ + 10

f(g(h(-1))) = 16,060

Hence  f(x + h) = 3(x + h)² - (x + h) + 5,

2.f(g(x)) = 27x² -33x + 15,

3. f(g(h(-1))) = 16,060.

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The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.

Mutually exclusive events are events that cannot occur at the same time, or that do not have any overlap. In the case of flipping a coin, the possibility of getting a head and the possibility of getting tails are independent of each other, and both can occur simultaneously. Therefore, the chance that you will get heads or tails when you flip a coin once is not mutually exclusive.

On the other hand, the other events listed (B, C, and D) are mutually exclusive. The chance that you will only study for the test alone or with a friend cannot occur simultaneously, as you can either study alone or with a friend, but not both. Similarly, the chance that you will meet your friends for pizza or at a Chinese restaurant for dinner today at 6 cannot occur at the same time, as you can either go to the pizza place or the Chinese restaurant, but not both. And the chance that you will answer the ringing phone or take a walk cannot occur simultaneously, as you can either answer the phone or take a walk, but not both.

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The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.

this question is related to probability.

mutually exclusive

Mutually exclusive events are those events that do not occur at the same time.

For example, when a coin is tossed then the result will be either head or tail, but we cannot get both the results. Such events are also called disjoint events since they do not happen simultaneously.

probability

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

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Answer:

it is an acute scalene triangle

Answer:

Since the lengths of the triangle are 4,5, and 6, which are almost equal, then the triangle cannot be obtuse. It's right triangle

Answer:

0.5 meters a second or 0.5:1

Step-by-step explanation:

10 meters ÷ 20

_______________

20 seconds ÷ 20

=  

0.5 meters

_______________

1 second  

Answer:

#8 might be y= -3x + 5

Step-by-step explanation:

This may help

Answer: B i think

Step-by-step explanation:

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms.

Answer:

C. (3,25) and (7,9)

Step-by-step explanation:

Answer:

26.36

Step-by-step explanation:

Hundredths are the second decimal place from the decimal. You would round up to 26.36 because the number before that is up to 5. If it was below 5 you would round down to 26.35.