How can you tell if you have completely factored a polynomial?.

A woman 5-feet tall casts an 8-foot shadow. at the same time of day, the shadow of a tree nearby is 120 feet long. in feet, 75 feet  tall is the tree.

Let the tree height = x

From the question, we have

5/8 = x/120

x = (5*120)/8

x = 75 feet

Tree height = 75 feet

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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The given equation 0.39 = \(\frac{39}{100}\) is true. The solution has been obtained by using the decimal numbers.

What are the decimal numbers?

Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.

We are given a decimal number as 0.39. It is given that this number is equivalent to a fraction which is \(\frac{39}{100}\).

This is true because we know that the numbers after the decimals represent the part of a fraction.

The number of digits after the decimal represents the number of zeroes in the fraction.

Hence, the given equation 0.39 = \(\frac{39}{100}\) is true.

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Answer:

\(( {4}^{ \frac{1}{2} } \times \frac{2}{ \sqrt[4]{16} } ) - (10 \div 2)\)

=

\(( { {2}^{2} }^{ (\frac{1}{2}) } \times \frac{2}{ {16}^{ \frac{1}{4} } } ) - 5\)

\((2 \: \times \: \frac{2}{ ({2}^{4}) ^{ \frac{1}{4} } }) - 5\)

\((2 \: \times \: \frac{2}{2} ) - 5\)

= (2×1) -5

= 2 - 5

= -3

Answer:

5040

Step-by-step explanation:

an illustration of permutations

The given parameter is:

number of days

dinners for 7 days

Substitute known values

The area of the unshaded region is 19.5 cm², the answer would be B. 19.5 cm².To determine the area of the rectangle, we need to subtract the area of the unshaded region from the total area of the shape.

Since the area of the unshaded region is given as 19.5 cm², we can subtract it from the total area to find the area of the rectangle.

Let's assume the total area of the shape is represented by 'A'.

Area of the rectangle = Total area - Area of the unshaded region

Area of the rectangle = A - 19.5

Now, let's look at the answer choices:

A. 39 cm²

B. 19.5 cm²

C. 9.75 cm²

D. 4.8 cm²

Since the area of the unshaded region is 19.5 cm², the correct answer would be B. 19.5 cm².

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Answer:

Option A,  9b + 10s is correct

Step-by-step explanation:

The complete question is

At cycle and sport customers can rent bikes, electric scooters, kayaks, canoes, or paddleboards by the hour. Ari is renting a bi ke, and meg is renting an electric scooter. Which expression represents the total cost for Ari to rent a bike for b hours and Meg to rent a scooter for s hours (Please answer ASAP) A. 9b + 10s B. 9 + 10 C. (9+b) + (10 + s) D. 9 + 10 x b + s  

Solution

The price of renting a bike for one hour is $9

The price of renting a scooter for one hour is $10

Given -

Ari rents a bike for b hours and Meg rents a scooter for s hours

Total cost of renting a bike is 9 * b

Total cost of renting a scooter is 10* s

The total cost of renting both the bike and scooter is

9b + 10s

Hence, option A is correct

Answer:

20

Step-by-step explanation:

Solving  for x using the vertical angles we get , the value of x is: x = 20.

Here, we have,

from the given figure we get,

angle (2 + 3x) and angle62 are opposite angles.

we know that,

When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.

so, we have,

angle (2 + 3x) = angle62

(2 + 3x) = 62

or, 3x = 60

or, x = 20

Hence, Solving  for x using the vertical angles we get , the value of x is: x = 20.

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Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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Answer:

A. System C simplifies to 2x - 3y = 4 and 4x - y = 54 by dividing the second equation by three (3).

B. Systems A and C have the same solutions.

C. Systems A and B have different solutions.

Step-by-step explanation:

Given the following system of equations;

System A

2x - 3y = 4  .....equation 1

4x - y = 18  .......equation 2

We would solve the above equations using the elimination method;

Multiplying eqn 1 by 2;

2*(2x) - 2*(3y) = 4*2

4x - 6y = 8  ...... equation 3

Subtracting eqn 2 from eqn 3;

(4x - 4x) + (-6y - (-y)) = 8 - 18

0 + (-6y + y) = -10

-5y = -10

5y = 10

\( y = \frac {10}{5} \)

y = 2

To find the value of x;

2x - 3y = 4

2x - 3(2) = 4

2x - 6 = 4

2x = 4 + 6

2x = 10

\( x = \frac {10}{2} \)

x = 5

Solutions (x, y) = (5, 2)

System B

3x - 4y = 5  ..... equation 1

y = 5x + 3  ..... equation 2

We would solve the equations using substitution method;

Substituting eqn 2 into eqn 1, we have;

3x - 4(5x + 3) = 5

3x - 20x - 12 = 5

-17x - 12 = 5

-17x = 12 + 5

-17x = 17

\( x = \frac {-17}{17} \)

x = -1

To find the value of y;

y = 5x + 3

y = 5(-1) + 3

y = -5 + 3

y = -2

Solutions (x, y) = (-1, -2)

System C

2x - 3y = 4  ..... equation 1

12x - 3y = 54  ...... equation 2

We would solve the above equations using the elimination method;

Subtracting eqn 2 from eqn 1;

(2x - 12x) + (-3y -(-3y)) = 4 - 54

-10x + (-3y + 3y) = -50

-10x + 0 = -50

-10x = -50

10x = 50

\( x = \frac {50}{10} \)

x = 5

To find the value of y;

2x - 3y = 4

2(5) - 3y = 4

10 - 3y = 4

3y = 10 - 4

3y = 6

\( y = \frac {6}{3} \)

y = 2

Solutions (x, y) = (5, 2)

Answer:

  (a)  see attached

Step-by-step explanation:

A table will represent a function if no input (x) values are repeated.

The offered tables can be evaluated as follows:

  (a) x-values {-4, -1, 1, 4}, no repeats. Is a function.

  (b) x-values {2, 2, 3, 3}, both values repeated

  (c) x-values {-5, -5, 5, 5}, both values repeated

  (d) x-values {2, 2, 7, 7}, both values repeated

Answer:

x=0

Step-by-step explanation:

0=6x-2x

0=4x

4x=0

and the answer is x=0

Step 1:

Write the equation of the line in the form of y = mx + c

m = slope

Step 2

Step 3

From the equation

Step 4:

Final answer

The measure of acute angle = 26.6

Answer:

uuuuuuuuu

Step-by-step explauuuuuuuuuuu

The required number of plants from the function is 509 when there are 27 rows.

Given that,

The function g(x) = 18x+23 represents the total number of plants at the gardening store if there are x rows of plants in the field. What is the value of g(27) is to be determined.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Number of plants,
g(x) = 18x+23
Since the number of rows is 27
Now, the number of plants,
g(27) = 27 * 18 + 23
g(27) = 486 + 23
g(27) = 509

Thus, The required number of plants from the function is 509 when there are 27 rows.

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Answer:

m

Step-by-step explanation:

The correct answer is A. The selling price of a bond is affected by the coupon rate and the market interest rate.

If the coupon rate is less than the market interest rate, investors will not be interested in buying the bond because they can get a higher return elsewhere. This results in the selling price of the bond being less than its face value of $10,000.
The selling price of a $10,000 5-year bond will be less than $10,000 if the:
A. Coupon rate is less than the market interest rate

This is because when the coupon rate (the interest paid by the bond) is lower than the market interest rate, investors would prefer to invest in other options that offer a higher return. Therefore, to attract buyers, the bond's selling price would be discounted to compensate for the lower coupon rate.

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Using linear functions, it is found that it will take 7 hours for Michael to deliver as many newspapers as Franklin.

A linear function is modeled by:

y = mx + b

In which:

The linear functions that give the amounts for Franklin and Michael after h hours are given by:

They will be equal when:

F(h) = M(h)

Hence:

26 + 9h = 5 + 12h

3h = 21

h = 7

It will take 7 hours for Michael to deliver as many newspapers as Franklin.

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Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

The slope would be 0

Step-by-step explanation:

At two theaters Paige would be willing to buy a ticket and popcorn.

Consider the following table that shows ticket and popcorn prices at five movie theater chains.

Here, the inequality d < 4. 75 represents the prices d in dollars that Paige is willing to pay for popcorn.

And the inequality d < 8. 00 represents the prices d in dollars that Paige is willing to pay for a movie ticket.

To find: the number of theaters that would Paige be willing to buy a ticket and popcorn

We can observe that the number of theaters that has the movie ticket price less than 8 dollars are two.

The number of theaters that has the popcorn price less than 4.75 dollars are three.

And the number of theaters that has the popcorn price less than 4.75 dollars as well as the movie ticket price less than 8 dollars are two.

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The equation for the total distance that he runs in one day is:

total dsitance = 4*2414 m = 9656m

So, here we know that Edward uns around the park trail 4 times in one day.

So, if D is the total distance of the trail, then the total distance that Edward runs in one day  is 4 times D, then the equation is:

total distance = 4*D

Here we know that the trail is 2414 meters long, then the equation will be:

total dsitance = 4*2414 m = 9656m

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The absolute maximum value of f on the interval [-1,3] is -3 and the absolute minimum value is approximately -1.732.

To find the absolute maximum and minimum values of f(t) = t - (3/t) on the interval [-1, 3], we need to perform the following steps:

1. Find the critical points by taking the derivative of the function and setting it to zero.
2. Evaluate the function at the critical points and the endpoints of the interval.
3. Compare the values to determine the absolute maximum and minimum.

Step 1: Find the critical points.

f(t) = t - (3/t)
To find the derivative, use the power rule and the quotient rule:
f'(t) = 1 - (-3/t^2) = 1 + 3/t^2

Set the derivative equal to zero and solve for t:
1 + 3/t^2 = 0
3/t^2 = -1
t^2 = 3/-1
Since there are no real solutions for t^2 = -3, there are no critical points.

Step 2: Evaluate the function at the endpoints of the interval.

f(-1) = -1 - (3/-1) = -1 + 3 = 2
f(3) = 3 - (3/3) = 3 - 1 = 2

Step 3: Compare the values.
Evaluating f at the critical point and at the endpoints of the interval, we get:
f(-1) = -4
f(3) = -3
f(√3) = √3 - 3/√3 ≈ -1.732
Since there are no critical points and the values at the endpoints are equal, the absolute maximum and minimum values are both 2. Therefore, the absolute maximum and minimum values of the function on the interval [-1, 3] are both 2.

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Answer:

44

Step-by-step explanation:

5*2=10-50=40+4=44

Saving account is an example of a demand account.

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The probability that tails appears on the next toss is 0.5

Given,

In the question:

If I toss a fair coin five times and the outcomes are TTTTT,

To find the probability that tails appears on the next toss is.

Now, According to the question:

The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation.

A sequence of five fair coin flips has a sample space that contains all potential outcomes. \(2^3\) {H, T}  is the sample of a fair coin toss. {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH,...…TTTTT} .

The probability of a tails result on the next flip is always equal to 0.5 It makes no difference if previous outcomes were {TTTTT} , {HHHHH}  or {THTHT} In each of these and all other circumstances, the probability of the next being tails is still 0.5

Hence,  the probability that tails appears on the next toss is 0.5

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Answer:

3

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, subtract 6 and 8x from both sides:

6 (-6) + 10x (-8x) = 8x (-8x) + 12 (-6)

10x - 8x = 12 - 6

2x = 6

Isolate the variable, x. Divide 2 from both sides:

(2x)/2 = (6)/2

x = 6/2

x = 3

3 is your answer.

~

The 19th percentile of x bar is 71.724.

Since the sample size is greater than 30 and the population standard deviation is known, we can use the normal distribution to find the 19th percentile of x bar.

First, we need to find the standard error of the mean (SEM):

SEM = σ/√n = 8/√50 = 1.1314

Next, we need to find the z-score associated with the 19th percentile. We can use a standard normal distribution table or a calculator to find this value, which is approximately -0.877.

Finally, we can use the formula for a confidence interval to find the value of x bar associated with the 19th percentile:

x bar = μ + z*SEM = 73 + (-0.877)*1.1314 = 71.724

Therefore, the 19th percentile of x bar is approximately 71.724.

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