What are all the possible dimensions of the area is 180 square feet?

Let

s-------> is the distance in Kilometer

V-----> the speed of the bicyclist in Km/h

t------> is the time in hours

we know that

[tex]V=s/t[/tex]

in this problem we have

[tex]V=12\frac{Km}{h}[/tex]

Part a) Find s for [tex]t=3.5\ h[/tex]

we know that

[tex]V=s/t[/tex]

solve for s

[tex]s=Vt[/tex]

substitute the values

[tex]s=12*3.5=42\ Km[/tex]

therefore

the answer Part a) is

[tex]42\ Km[/tex]

Part b) Find t for [tex]s=30\ Km[/tex]

we know that

[tex]V=s/t[/tex]

solve for t

[tex]t=s/V[/tex]

substitute the values

[tex]t=30/12=2.5\ h[/tex]

therefore

the answer Part b) is

[tex]2.5\ h[/tex]

Answer:

Part A) 18 km           Part B) 2.5 hours

Step-by-step explanation:

Part A:

Formula: s = 60 - 12t

Substitute numbers:

s = 60 - 12(3.5) = 60 - 42 = 18 km

Part B:

Formula: s = 60 - 12t

Substitute numbers:

30 = 60 - 12t

30 - 60 = -12t

-30 = -12t

t = 2.5 hours

The congruence statement that does not prove that two triangles are congruent is SSA (Side-Side-Angle).

The SSA congruence is not a valid congruence criterion for triangles because it may not necessarily guarantee congruence.

Having two sides and a non-included angle equal in two triangles does not ensure that all corresponding angles and sides are equal.

In some cases, two triangles with SSA congruence may not be congruent.

The other three congruence criteria (ASA, SAS, SSS) are valid and sufficient to prove congruence between two triangles.

ASA (Angle-Side-Angle):

This criterion states that if two triangles have two corresponding angles and the included side between those angles equal, then the triangles are congruent.

ASA is a valid criterion because it guarantees that all corresponding angles and sides are equal, leading to congruence.

SAS (Side-Angle-Side):

This criterion states that if two triangles have two pairs of corresponding sides and the included angle equal,

then the triangles are congruent. SAS is also a valid criterion because it ensures that the corresponding sides and angles are equal, thus establishing congruence.

SSA (Side-Side-Angle): This criterion states that if two triangles have two pairs of corresponding sides equal and a non-included angle equal,

then the triangles are congruent. SSA is NOT a valid criterion for proving triangle congruence. It is also known as the "ambiguous case" or "the one and only case."

This is because, in some situations, two triangles with SSA congruence may not actually be congruent.

There can be more than one possible triangle that satisfies the given conditions, leading to ambiguity.

SSS (Side-Side-Side): This criterion states that if two triangles have all three pairs of corresponding sides equal,

then the triangles are congruent. SSS is a valid criterion for proving congruence as it guarantees that all corresponding sides are equal, resulting in congruent triangles.

Therefore, ASA, SAS, and SSS are valid congruence criteria that ensure congruence between triangles. However, SSA is not a reliable criterion for proving triangle congruence, as it may lead to multiple possible triangles.

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Final answer:

The compound interest inequality for the investment account is 3500(1 + 0.08)^t < 6000. Solving this, we find that the account will have less than $6,000 for approximately 6 years.

Explanation:

To solve this problem, we will use the formula for compound interest which is [tex]A = P(1 + r)^t,[/tex] where:

We are trying to find the number of years, t, when the account will have less than $6,000, at an annual interest rate of 8%, i.e., r = 0.08.

The inequality will be:

[tex]3500(1 + 0.08)^t < 6000[/tex]

To solve for t, we first divide both sides by 3,500:

[tex](1 + 0.08)^t[/tex]< ≈ 1.7143

Now, take the natural logarithm of both sides:

[tex]ln((1 + 0.08)^t) < ln( 1.7143)[/tex]

t · ln(1.08) < ln(≈ 1.7143)

Divide both sides by ln(1.08) to isolate t and calculate:

t < ≈ ln(≈ 1.7143) / ln(1.08) < ≈ 6.6

Therefore, the investment account will have less than $6,000 for approximately 6 years.

The required three decimals between 0.55 and 0.56 are 0.552, 0.553, and 0.554 which are shown in the number line.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

The numbers on the number line increase as one moves from left to right and decrease on moving from right to left.

We have to determine the three decimals between 0.55 and 0.56

As per the attached number line,

Three decimals between 0.55 and 0.56 are :

⇒ 0.552, 0.553, and 0.554

Hence, the required three decimals between 0.55 and 0.56 are 0.552, 0.553, and 0.554 which are shown in the number line.

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Answer:

The approximate value of milos car 11 years after he purchased it is 3929.

Step-by-step explanation:

The given equation is

[tex]y=20646(0.86)^x[/tex]

Here, y is the estimates the value of a brand of car x years after it was purchased new.

We have to find the approximate value of milos car 11 years after he purchased it.

Substitute x=11 in the given equation.

[tex]y=20646(0.86)^{11}[/tex]

[tex]y=3929.33346204[/tex]

[tex]y\approx 3929[/tex]

Therefore the approximate value of milos car 11 years after he purchased it is 3929.

Answer:

9

Step-by-step explanation:

2w+2L=42

2(12)+2L=42

24+2L=42

-24 on both sides

2L=18

divide by two

L=9

The age of sister will be 97 years.

Using operands and a math operator to calculate a value is referred to as an "operation" in mathematics. The rules that apply to the given operands or numbers are predetermined by the math operator's symbol.

A collection of numbers and operations is an expression in mathematics. The following are the parts of a math expression that do a math operation.

Given David age = 6 years

his sister age = half of David age = 6/2 = 3

David is 3 years older than his sister

equation for ages of both David and his sister is

David age = Sister age + 3

when David is 100 years

sister age = David age - 3 = 100 - 3 = 97

Hence when David is 100 years old his sister will be 97 years.

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Answer:

32.64%

Step-by-step explanation:

Let's define the random variable X in the following way:

X: the volume of a soda in a quart soda bottle. We know that X is normally distributed with a mean of 32 ounces and a standard deviation of 1.2 ounces, i.e.,

[tex]\mu[/tex] = 32 ounces

[tex]\sigma[/tex] = 1.2 ounces

The normal density function for a random variable with a mean of 32 and a standard deviation of 1.2 is given by

[tex]f(x)=\frac{1}{\sqrt{2\pi }1.2} \exp[-\frac{(x-32)^{2} }{2(1.2)^2} ][/tex]

and we need to calculate the following probability

[tex]P(X\leq 31.46)[/tex], this probability is given by

[tex]P(X\leq 31.46) =\int\limits^{31.46}_{-\infty} {\frac{1}{\sqrt{2\pi }1.2} \exp[-\frac{(x-32)^{2} }{2(1.2)^2} ]} \, dx[/tex] = 0.3263552

you can use a computer to calculate this probability or a table from a book. You can use the following instruction in the R statistical programming language for example

pnorm(31.46, mean = 32, sd = 1.2)  with give us 0.3263552, then,

the percentage we are looking for is (0.3263552)(100)=32.64.

Answer:- The total number of roots in the given polynomial function is 2.

Explanation:-

We know that corollary of Fundamental Theorem of Algebra tells that polynomial will have exactly as many roots(m) as its degree(m>0).

The given polynomial function [tex]g(x)=5x-12x^2+3[/tex] is a quadratic polynomial with degree 2.

Thus by corollary of Fundamental theorem of algebra

The total number of roots in the given polynomial function must be 2.

The sum of the measures of the complementary, supplementary, and vertical angles for angle a of 33° is 237°.

The question asks for the sum of the measures of the complementary angle, supplementary angle, and vertical angle for angle a, given that angle a is 33°.

The complementary angle to angle a would be one that adds up to 90° with angle a. Since angle a is 33°, the complementary angle would be 90° - 33° = 57°.

The supplementary angle to angle a is one that adds up to 180° with angle a. The supplementary angle would thus be 180° - 33° = 147°.

The vertical angle to angle a shares the same measure as angle a, because vertical angles are equal. So, the vertical angle measure is 33°.

To find the total sum of these angles, you would add 57° + 147° + 33° = 237°.

If one inlet pipe can fill the pool in 12 hours and the drain can empty it in 20 hours, the combined rate of the two is 1/30 pools per hour. Therefore, it will take 30 hours to fill the pool with the drain open.

The question addresses a common concept in mathematics, which is rates and work problems. To determine the time it takes for the inlet pipe to fill the pool with the drain open, we first have to figure out the rates at which the pipe fills and the drain empties the pool.

If an inlet pipe can fill the pool in 12 hours, its rate of work is 1/12 pool per hour. Similarly, if the drain can empty the pool in 20 hours, then its rate is 1/20 pool per hour.

When both the inlet and drain are open, their combined rate will be the fill rate minus the drain rate, which is (1/12) - (1/20) = 1/30 pool per hour.

Therefore, at the combined rate, it will take 1 divided by 1/30 = 30 hours to fill the pool with the drain open.

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When both the inlet pipe and drain are open, it will take 30 hours to fill the pool, computed by dividing the total work done (1 pool) by the net rate (1/30 pool/hour).

In mathematics, problems such as these are usually solved by working with the concept of rates. In this scenario, we have two rates: the inlet pipe, and the drain. The rate of the inlet pipe is 1 pool per 12 hours, or 1/12 pool/hour. The rate of the drain is 1 pool per 20 hours, or 1/20 pool/hour. The net rate when both are open is thus (1/12 - 1/20) pool/hour, which simplifies to 1/30 pool/hour. To find out how long (t) it will take to fill the pool with both the inlet and drain open, we would use the fact that Rate x Time = Work Done. The Work Done in this case is 1 (equivalent to one pool), and the rate we’ve calculated as 1/30 pool/hour.

So, solving for time, we get:

t = Work Done / Rate = 1 pool / (1/30 pool/hour) = 30 hours.

So, it would take 30 hours to fill the pool with the inlet pipe and the drain open.

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There will be two values for the absolute value of |b-12|=15, that are -3 and 27

Absolute value describes the distance from zero that a number is on the number line, without considering direction. Absolute value describes the distance from zero that a number is on the number line, without considering direction.

The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign,  its magnitude of the number irrespective of the sign of the number.

For example :- the absolute value of 5 is 5, and the absolute value of −5 is also 5.

Given that, find the absolute value of |b-12| = 15,

Solving for b,

|b-12| = 15

Removing the mod, it will give two values in negative and positive,

b-12 = 15 or b-12 = -15

b = 15+12 or b = -15+12

b = 27 or b = -3

Hence, there will be two values for the absolute value of |b-12|=15, -3 and 27

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Answer:

Number of neutrons=5

Step-by-step explanation:

We are given that

Number of protons in lithium=Z=3

Mass number of lithium=A=8

We have to find the neutrons in the isotope lithium-8.

We know that

Number of neutrons=A-Z

Where A= Mass number

Z= Number of protons=Atomic number

Substitute the values then we get

Number of neutrons=8-3=5

Answer : 5

The number of the neutrons that we have in the  isotope lithium-8 is 5 neutrons.

The quantity of protons in an element's nucleus is indicated by the element's atomic number. Lithium has three protons on average because it has an atomic number of three.

You deduct the atomic number from the mass number (the sum of the protons and neutrons in the nucleus) to get the number of neutrons in an isotope. In this instance, the isotope lithium-8, which has a mass number of 8, is present.

Mass number - Atomic number = Number of neutrons

8 - 3 = 5

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