The perimeter of an equilateral triangle is 156 feet find the length of each side

The length of the photograph is 13 cm and the width is 7 cm.

A rectangle is a quadrilateral having the four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

Given that:-

The length and the width will be calculated as:-

let the width = x

length = 2x  -  1

91  =  x  (  2x  -  1  )  =  2x² - x

2x² -  x  -  91  =   0

=  ( 2x  +  13  )  (  x   -  7 )

x  =  - 13  /   2

x  = 7 cm

Length will be  = 2x  -  1 =  2  x  7  -  1  =  13 cm

Therefore the length of the photograph is 13 cm and the width is 7 cm.

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To determine the extent of how many times greater is the number of bacteria in petri dish A than petri dish B, we simply have to take the ratio of the two.

1.75 x 10^18 / 6.25 x 10^15 = 280

So the bacteria in petri dish A is 280 times larger.

In scientific notation:

2.8 x 10^2

Answer:

280 is the answer, I did the test.

$65 * 6 = $390 total monthly payments made

The downpayment made is $125, so the total balance at the end is:

balance = $513 – ($125 + $390)

balance = - $2

There is an excess of 2 dollars at the end.

Sheila's balance at the beginning of the seventh month will be approximately $393.95 after considering the deferred payment and applying the interest rate.

To determine the balance at the beginning of the seventh month, follow these steps:

So, Sheila’s balance at the beginning of the seventh month is approximately $393.95.

Janet has to pay off $65 to reduce her balance to no more than $60.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Janet has a balance of 125 on a credit card on her next statement she wants to reduce her balance to no more than 60.

The amount to be paid will be calculated as,

Amount = 125 - 60

Amount = $65

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Joanna bought 5 3/4 pounds of fruit in all if Joanna bought 1 1/2 pounds of apples, 3/4 pounds of strawberries.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

Joanna bought 1 1/2 pounds of apples, 3/4 pounds of strawberries, 1/2 pounds of grapes, 1 3/4pounds of oranges, and 1 1/4 pounds of pears.

= 1 1/2 + 3/4 + 1/2 + 1 3 /4 + 1 1/4

= 3/2 + 3/4 + 1/2 + 7/4 + 5/4

= (6 + 3 + 2 + 7 + 5)/4

= 23/4

= 5 3/4

Thus, Joanna bought 5 3/4 pounds of fruit in all if Joanna bought 1 1/2 pounds of apples, 3/4 pounds of strawberries, 1/2 pounds of grapes, 1 3/4pounds of oranges, and 1 1/4 pounds of pears.

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For combined classes of Ms. Zombo's and Mr. Stolarski's, the number of boys and girls are determined based on their respective ratios and total number of students. The combined ratio of boys to girls is 29:18.

The question asks for the combined ratio of boys to girls in both Ms. Zombo's and Mr. Stolarski's classes. Firstly, identify the number of boys and girls in each class based on the given ratio and total students. In Ms.Zombo's class, the ratio of boys to girls is 33:22, and there are total 15 students. So, the number of boys is (33/(33+22))*15= 9 boys and 6 girls. Similarly, in Mr.Stolarski's class the ratio is 55:33, there are 32 students, so there are (55/(55+33))*32 =20 boys and 12 girls.

Next step is to combine the classes. The total number of boys from both classes is 9 (from Ms. Zombo's class) + 20 (from Mr.Stolarski's class) = 29 boys. The total number of girls is 6 (from Ms. Zombo's class) + 12 (from Mr.Stolarski's class) =18 girls.

Therefore, the combined ratio of boys to girls from both classes is 29:18.

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Answer:

Having a savings account can contribute to a person’s overall financial well-being. Which one of the following is NOT a benefit of maintaining a savings account?

a.

A savings account provides security in tough financial times

b.

With a savings account, you can invest when the opportunity presents itself

c.

Having a savings account gives individuals the ability to borrow money from members in the community

d.

A savings account allows an individual to fulfill life long dreams

Step-by-step explanation:

C) Having a savings account gives individuals the ability to borrow money from members in the community

x= 11

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The linear equation that gives the cost in dollars, y, in terms of the number of days the ad appears, x is: y = $1.50x + $2.00

The cost of a 7-day ad is $12.50.

Let, the daily rate is "d" dollars and the flat service fee is "f" dollars.

We are given two pieces of information:

One day costs $3.50.

Four days cost $8.00.

Using this information, we can set up two equations:

For one day: d + f = $3.50

For four days: 4d + f = $8.00

Now, we need to solve this system of linear equations to find the values of "d" and "f."

Subtract Equation 1 from Equation 2 to eliminate "f":

(4d + f) - (d + f) = $8.00 - $3.50

3d = $4.50

Now, divide both sides by 3 to solve for "d":

d = $4.50 / 3

d = $1.50

Now that we have the value of "d," we can find the value of "f" by substituting "d" into Equation 1:

d + f = $3.50

$1.50 + f = $3.50

Now, subtract $1.50 from both sides to solve for "f":

f = $3.50 - $1.50

f = $2.00

So, the daily rate (d) is $1.50, and the flat service fee (f) is $2.00.

We get, a linear equation that gives the cost in dollars, y, in terms of the number of days the ad appears, x is: y = $1.50x + $2.00

Now, to find the cost of a 7-day ad, we can use the daily rate and multiply it by the number of days (7):

Cost of a 7-day ad = 7 * $1.50 + $2.00

Cost of a 7-day ad = $10.50+ $2.00 = $12.50

The cost of a 7-day ad is $12.50.

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Part A: Alligators: [tex]\(A(t) = 20 \times (1 + 0.25)^t\), Crocodiles: \(C(t) = 25 + 10t\).[/tex]

Part B: After 4 years: Alligators: ~38, Crocodiles: 65.

Part C: Alligators and crocodiles equal: Solve [tex]\(20 \times (1 + 0.25)^t = 25 + 10t\).[/tex]

Part A:

Let's define the functions to represent the number of alligators and crocodiles in the swamp over the years.

For alligators:

[tex]\[A(t) = A_0 \times (1 + r)^t\][/tex]

Where:

[tex]- \(A(t)\) is the number of alligators in the swamp after \(t\) years.\\- \(A_0\) is the initial number of alligators (20 in this case).\\- \(r\) is the growth rate per year (25% or 0.25).\\- \(t\) is the number of years.[/tex]

For crocodiles:

[tex]\[C(t) = C_0 + n \times t\][/tex]

Where:

[tex]- \(C(t)\) is the number of crocodiles in the swamp after \(t\) years.\\- \(C_0\) is the initial number of crocodiles (25 in this case).\\- \(n\) is the number of new crocodiles joining each year (10 in this case).\\- \(t\) is the number of years.[/tex]

Part B:

To find the number of alligators after 4 years, we use the formula:

[tex]\[A(4) = 20 \times (1 + 0.25)^4\][/tex]

To find the number of crocodiles after 4 years, we use the formula:

[tex]\[C(4) = 25 + 10 \times 4\][/tex]

Part C:

To find when the number of alligators and crocodiles are the same, we set [tex]\(A(t) = C(t)\) and solve for \(t\).[/tex]

[tex]\[20 \times (1 + 0.25)^t = 25 + 10 \times t\][/tex]

This equation can be solved numerically to find the value of \(t\) when the number of alligators and crocodiles are the same.

Answer:

The value of x that makes m || n is x = 20

Step-by-step explanation:

Given a line that is intersected by another two lines (for example line ''m'' and line ''n'' like in the exercise) one of the conditions that makes m || n is that the alternate interior angles must be congruent. Understanding that congruent means the same.

In the exercise, one pair of alternate interior angles are (2x+20)° and 3x°.

We need this two angles to be congruent ⇒ [tex]3x=2x+20[/tex]

Solving this for ''x'' :

[tex]3x=2x+20\\3x-2x=20\\x=20[/tex]

The value of x that makes 3x° congruent to 2x+20° (that makes the alternate interior angles congruents) is x = 20

Answer:

20

Step-by-step explanation:

Theorem:

If two lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel.

Lines m and n are cut by a transversal.

Angles 3x and 2x + 20 are alternate interior angles.

For lines m and n to be parallel, angles 3x and 2x + 20 must be congruent, so their measures must be equal.

3x = 2x + 20

x = 20

Answer: 20

Answer:

The correct option is C) Both plans will work for achieving the goal.

Step-by-step explanation:

Consider the provided information.

Plan A: Save $450 over the next 8 weeks by working 9 hours per week at $7.20 per hour.

For next 8 weeks by working 9 hours per week at $7.20 per hour, you will earn:

[tex]8 \times 9 \times 7.20 = 518.40[/tex]

We need to save $450 which is less than $518.40. Thus, plan A will work.

Plan B: Save $450 over the next 6 weeks by working 15 hours per week at $6.50 per hour.

For next 6 weeks by working 15 hours per week at $6.50 per hour, you will earn:

[tex]6 \times 15 \times 6.50 = $585.00[/tex]

We need to save $450 which is less than $585.00. Thus, plan B will work.

Hence, the correct option is C) Both plans will work for achieving the goal.

length of AC = 10 * sin(30) = 5 cm

Length of CD = 5 /tan(25) = 10.7cm

 answer is C

Answer

Find out the what is the length of CD , AC .

To prove

By using the trignometric identity

[tex]sin B = \frac{Perpendicular}{Hypotenuse}[/tex]

As in ΔABC

∠ B = 30° , AB= 10 cm

put in the trignometric identity

[tex]sin 30^{\circ} = \frac{AC}{10}[/tex]

As

[tex]sin30^{\circ} =\frac{1}{2}[/tex]

[tex]\frac{1}{2} = \frac{AC}{10}[/tex]

[tex]AC = \frac{10}{2}[/tex]

AC = 5cm

Now in the ΔADC

[tex]tan D^{\circ} = \frac{Perpendicular}{Base}[/tex]

∠ D = 25° , AC = Perpendicular = 5 cm

[tex]tan 25^{\circ} = \frac{5}{CD}[/tex]

tan 25 ° =  0.46630765815 (approx)

[tex]CD = \frac{5}{0.46630765815}[/tex]

CD = 10 .7cm ( approx )

Option (C) is correct .

Final answer:

The incorrect statement is that the nucleus of an atom contains protons and electrons; actually, the nucleus contains protons and neutrons, with electrons orbiting around it.

Explanation:

The statement that does not correctly describe the structure of an atom is 'Inside the nucleus of an atom are protons and electrons'. This statement is incorrect because the nucleus of an atom actually contains protons and neutrons, not electrons. Electrons are negatively charged sub-atomic particles that orbit around the nucleus. The nucleus itself is a small, dense center that is positively charged due to the presence of protons, which are positively charged. Neutrons, which have no electric charge, are also found within the nucleus.

Further expanding on atomic structure, the nucleus is very tiny compared to the rest of the atom, which is mostly empty space. The electrons residing in this space are in perpetual motion, creating a cloud-like region around the nucleus. Despite their small mass compared to protons and neutrons, the number of electrons equals the number of protons in a neutral atom, balancing the charge.

Solution:

we have been asked to find that , how many times one number is to the other given numbers.

To do this we will divide the larger number by the smaller number and the resulting number will be the answer of the question.

Here the larger number is [tex]8.5\times10^8[/tex]

The smaller number is [tex]3.4\times 10^5[/tex]

Now lets divide as follows

[tex]\frac{8.5\times10^8}{3.4\times 10^5} =\frac{8.5}{3.4}\times 10^{8-5}\\ \\\frac{8.5\times10^8}{3.4\times 10^5} =2.5\times10^3=2500[/tex]

Hence the correct option is C.

The graph intersects the y-axis the y-coordinate is known as the y-intercept and this can be determined by using the definition of the y-intercept.

Given :

This is a point at which a graph intersects the y-axis. Example: (0, 5) for the equation y = x + 5.

The following steps can be used in order to determine a point at which a graph intersects the y-axis:

Step 1 - According to the example (0, 5) for the equation y = x + 5.

Step 2 - When the graph intersects the y-axis the value of the x-coordinate is zero.

Step 3 - When the graph intersects the y-axis the y-coordinate is known as the y-intercept.

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