An equation of the line that passes through the point (0,-1) and whose slope is 2 is?
1) y=2x-1
2) y= 2x+2
3) y= -x+2
4) y= -2x-1

Please show your work!

Answer:

5,120

Step-by-step explanation:

After 3 years, Ariel will have $3,472.88 in the account if no withdrawals or additional deposits are made.

The formula for compound interest is given:

\(A = P(1 +\dfrac{ r}{n})^{(nt)}\)

Where:

A = the final amount,

P = the principal amount,

r = the annual interest rate (as a decimal),

n = the number of times the interest is compounded per year,

t = the number of years,

In this case, we have:

P = $3,000

r = 0.05

n = 1 (compounded annually)

t = 3

Plugging in these values, we get:

\(A = $3,000(1 + \dfrac{0.05}{1})^{(1\times 3)\)

A = $3,000(1.05)^3

A = $3,000(1.157625)

A = $3,472.88

Therefore, after 3 years, Ariel will have $3,472.88 in the account if no withdrawals or additional deposits are made.

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For the equation:

Identify the slope and the y-intercept by comparing with the general equation of a line with slope m and y-intercept b:

The slope of the given equation is equal to 6, and the y-intercept is equal to 4.

Both Mia and Mark agree that the y-intercept is equal to 4, but the slopes of the lines are different.

Notice that the red line has a negative slope, so, by no means that would be the graph of y=4+6x.

Observe that for a change of 1 step over the X-axis, the dotted line has an increase of 6 units over the Y-axis. You can look at the values for x=-1 and x=0. Therefore, the dotted line has a slope of 6 and a y-intercept equal to 4, which are precisely the values given by the equation.

Therefore, Mia is right.

Answer:

D)

Step-by-step explanation:

5x5+5=30

8x9+7=79

24x3+28=100

In summary, the difference between the total number of customers and the total number of business cards is 109,500.

If we examine the pattern established in the initial days, we observe that the number of customers increases by 5 each day, starting from 0. Simultaneously, the number of business cards left increases by 3 more than the previous day's count. To determine the total number of customers over the course of a year, we can sum the arithmetic series, with the first term as 5, the common difference as 5, and the number of terms as 365. This yields a sum of 66,725 customers.

Next, we need to calculate the total number of business cards left. Using the same approach, we have a first term of 3, a common difference of 3, and 364 terms (since no business cards were left on the first day). The sum of this arithmetic series is 66,220 business cards.

Finally, to find the difference between the total number of customers and business cards, we subtract the sum of business cards from the sum of customers: 66,725 - 66,220 = 505. Therefore, the difference between the total number of customers and business cards is 505.

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Answer:

19(degrees)

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Just took the test!:)

Laplace transform of  L[(t²-t+1)δ(t - 2)] is  \(e^{-2s}\)(2/s³ - 1/s² + 1)

Given function,

L(t²-t+1) δ(t - 2)}

Here,

Laplace transform formula,

L{f(t)s(t - \(t_{0}\))} = \(e^{-st_{0} }\) F(s)

L{\(t^{n}\)} = n!/\(s^{n+1}\)

L{1} = 1

Now,

L(t²-t+1) δ(t - 2)} = L{t²δ(t-2) tδ(t-2) +δ(t-2)}

= (2/s³) \(e^{-2s}\) - (1/s²)\(e^{-2s}\) + \(e^{-2s}\)

= \(e^{-2s}\)(2/s³ - 1/s² + 1)

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The solutions to the equation are x= -9 and x = 6

From the information given, we have that;

|x2 + 9x| = 6x + 54

To solve the quadratic equation, collect the like terms, we have;

x² + 9x - 6x = 54

subtract the terms

x² + 3x = 54

Put in standard form

x² + 3x - 54 = 0

Find the pair factors of -54 that add up to give 3 and substitute the values

x² + 9x - 6x - 54 = 0

group in pairs

(x² + 9x) - (6x - 54) = 0

factorize the expressions

x(x + 9) - 6(x + 9) = 0

Then, we have;

x- 6 = 0

x = 6

x + 9 = 0

x = -9

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Answer:

15pi

Step-by-step explanation:

The equation for circumference is C=2πr

In the question you're given the diameter so we need to take 15 and divide by 2

giving us r=7.5

then 7.5*2=15

giving us 15pi

Rolling a total of 8 when two dice are rolled is more likely than rolling a total of 8 when three dice are rolled.

This is because there are more combinations of two dice that can add up to 8 (four combinations; 1-7, 2-6, 3-5, 4-4) than there are combinations of three dice (three combinations; 1-3-4, 2-2-4, 3-3-2).

Therefore, the probability of rolling a total of 8 with two dice is greater than the probability of rolling a total of 8 with three dice.

Additionally, the odds of rolling a total of 8 with two dice can be calculated using the formula (Number of favourable outcomes/Total number of outcomes) x 100%.

In this case, the formula would be (4/36) x 100%, which equals 11.11%. The odds of rolling a total of 8 with three dice is calculated using the same formula, which would be (3/216) x 100%, which equals 1.39%.

This shows that the odds of rolling a total of 8 with two dice is much greater than the odds of rolling a total of 8 with three dice.

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Mathematics is a fundamental subject in education that is essential in the development of an individual’s critical thinking and problem-solving skills. It is one of the primary subjects that are taught in elementary schools and must be taught appropriately for children to understand and gain the required skills. One true statement about mathematics teaching in elementary schools is that it should be student-centered.

Teachers should focus on the child's understanding, individual learning abilities and styles, and progress.The learning experience should not be centered on the teacher but on the students. Teachers should also make the subject engaging and interactive to enable students to grasp the content easily and maintain their interest in the subject. Besides, teachers should develop a personalized learning approach that allows students to learn and understand the subject at their own pace while creating opportunities for individual and group learning. Through such learning approaches, students can develop the required mathematical concepts and competencies such as critical thinking, problem-solving, and decision-making skills that will be beneficial in their future endeavors.

In elementary schools, mathematics teaching should be student-centered. It should be engaging and interactive to enable students to grasp the content easily and maintain their interest in the subject.

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Because the temperature is greater, the relative humidity of the atmosphere is higher.

Water vapor is also measured by relative humidity (RH), which is stated as a percentage but RELATIVE to the air's temperature. In plenty of other terms, it is a comparison between the quantity of water vapor that is really present in the air and the maximum amount water vapor that is possible for the air at the current temperature.

By deducting the temperature just on wet-bulb thermometer from of the temperature just on dry-bulb thermometers and utilizing a relative humidity chart, one may determine the relative humidity.

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Answer:

Your answer will be 5.66

Answer: I have no idea my friend but it's real hard Iwish you luck!

Answer:

16.

Step-by-step explanation:

The formula for a triangle is \(\frac{1}{2} * b * h\)

So, we take the triangle we see and but in in the formula.

\(\frac{1}{2} * 2 * 3 = 3.\)

Multiply that by 4, because there are four triangles that size.

\(3 * 4 = 12.\)

Now, we multiply 2 times 2 because that's the surface area for the bottom.

\(2 * 2 = 4.\)

Now, we add the two.

\(12 + 4 = 16.\)

Answer:

21

Step-by-step explanation:

when you plug in the numbers, it is (6)(1/2)(7)

You then solve in order: 6 x 1/2 = 3

3 x 7 = 21

hope this helps

To solve the given initial value problem using Laplace transforms, we can apply the Laplace transform to both sides of the differential equation and use initial conditions to determine the transformed equation.

By algebraically manipulating the transformed equation, we can find the Laplace transform of the desired solution. Finally, we can use the inverse Laplace transform to obtain the solution in the time domain. Let's denote the unknown function as x(t). Applying the Laplace transform to both sides of the differential equation yields the transformed equation in terms of the Laplace transform variables s and X(s). By substituting the initial conditions x(0) = 0 and x'(0) = 20 into the transformed equation, we can solve for X(s).

After obtaining the Laplace transform X(s), we can manipulate the equation algebraically to isolate X(s) on one side. This may involve factoring, simplifying, and using partial fraction decomposition if necessary. Once we have the equation in terms of X(s), we can apply the inverse Laplace transform to find the solution x(t) in the time domain.

To find y(t), we follow the same procedure, applying the Laplace transform to both sides of the differential equation involving y(t) and using the given initial condition y(0) = y0. Solving for the Laplace transform Y(s), we can then find y(t) by applying the inverse Laplace transform.

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\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{y}\\ a=\stackrel{adjacent}{1}\\ o=\stackrel{opposite}{1} \end{cases} \\\\\\ y=\sqrt{ 1^2 + 1^2}\implies y=\sqrt{ 1 + 1 } \implies y=\sqrt{ 2 } \\\\[-0.35em] ~\dotfill\)

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{\sqrt{2}}\\ o=\stackrel{opposite}{13} \end{cases} \\\\\\ x=\sqrt{ (\sqrt{2})^2 + 13^2}\implies x=\sqrt{ 2 + 169 } \implies x=\sqrt{ 171 }\implies \boxed{x=3\sqrt{19}}\)

The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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Answer:

Yes, the square root of 25 is a whole numbers.

Step-by-step explanation:

Yes, square root of 25 is a rational number.

Answer:

10

Step-by-step explanation:

5 * 9 = 45

45 is the sum of all the ages added up

45 - (5 + 7 + 8 + 15) = 10

The slope of this line is 0.35, which represents the amount that the cost increases for each additional click.

What is equation of straight line ?

Equation of straight line can be as follows, y = mx +b

where m is a slope of line.

Given,

To find , The cost, C, in dollars for advertising on a social networking website is proportional to the number n] of clicks on the advertisement.

When a business is charged $108.50 for 310 clicks on its advertisements.

The cost, C, and number of clicks, n, are related by the equation

C = k * n, where k is the constant of proportionality.

From the given information, we know that C = $108.50 when n = 310. We can use this information to find the value of k:

$108.50 = k * 310

Solving for k:

k = $108.50 / 310

k = $0.35

So, the equation for the relationship between cost and clicks is:

C = $0.35 * n

Therefore, The slope of this line is 0.35, which represents the amount that the cost increases for each additional click.

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(100, 600)

1/6 or 100/600 is the slope. You can find the Y intercept where X = 0, so the Y intercept would be 0. The equation would be Y = 1/6 + 0

Answer:

x=8

Step-by-step explanation:

4x+10 = 2x+26

4x-2x+10=2x-2x+26  [Subtract 2x from both sides]

2x+10=26

2x + 10 - 10 = 26 - 10  [Subtract 10 from both sides]

2x = 1

2x/2 = 16/2  [Divide both sides by 2]

x = 8

CHECK:

Does 4x+10 = 2x+26 when x is 8?

4(8)+10 = 2*(8)+26  ?

32+10 = 16+26    ?

42 = 42   YES

Answer:

\(\large \boxed{\sf x =8}\)

Explanation:

\(\sf \rightarrow 4x + 10 = 2x + 26\)

collect like terms

\(\sf \rightarrow 4x -2x = 26-10\)

subtract like terms

\(\sf \rightarrow 2x = 16\)

divide both sides by 2

\(\sf \rightarrow x = 8\)

Answer:

3

Step-by-step explanation:

Khan Academy

I just took it i hope it helps give some feedback tnx.

Answer:3

Step-by-step explanation:

Took it on khanacademy!

Answer: im pretty sure it should stay the same so 125

Step-by-step explanation:

Responder:

Por favor, consulte la explicación.

Explicación paso a paso:

De la imagen: Los lados ya están etiquetados en el diagrama y, por lo tanto, solo deben ingresarse en la tabla.

La suma de los ángulos de un triángulo es igual a 180 °; los ángulos en los triángulos son correspondientes, entonces;

Triángulo rojo:

Lado faltante = 3,75 cm

Triángulo verde:

12 cm

8 cm

Triángulo azul:

6 cm

4 cm

2,5 cm

Los ángulos que faltan:

Triángulo rojo:

180 - (135 + 28) °

180 ° - 173 °

= 17 °

Triángulo verde:

135 °; 28 °; 17 °

Triángulo azul:

135 °; 28 °

Answer:

j = 31.7

Step-by-step explanation:

j - 9.2 = 22.5

Add 9.2 to each side

j - 9.2+9.2 = 22.5+9.2

j  = 31.7

Answer:

(c).61

Step-by-step explanation:

61 is a prime number. The number is divisible only by 1 and itself.

Answer:

7k

Step-by-step explanation:

-k - -(8k): the - sign cancels out the - in 8k so it would only leave -k+8k=7k

Answer:

7k

Step-by-step explanation:

-k - (-8k)

if there is "-" in front on an inner form, change the sign of each quarter to the form.

-k + 8k

Simplify similar tribes with add or subtract.

= 7k