Tom is going to the fair in town and wants to eat lunch.a hot dog costs $2 and a cheeseburger costs $3.Write an equation that represents the possible combinations of how many of each he can buy for $10.​

The required balance of Hall's account after 11 years is \($A = 2145.1$\).

The formula to calculate compound interest is:

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

Where:

A = Final amount

P = Principal amount

r = Annual interest rate (as a decimal)

n = Number of times the interest is compounded per year

t = Time (in years)

Here, P = 920, r = 0.08, n = 1 (compounded annually), and t = 11 years.

Plugging in the values:

\($A = 920(1 + \frac{0.08}{1})^{1\times 11}$\)

\($A = 920(1.08)^{11}$\)

\($A = 2145.1$\)

Therefore, the balance of Hall's account after 11 years is \($A = 2145.1$\).

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Answer:

ture

Step-by-step explanation:

The formula for calculating the balance of an account with continuous compounding is given by A = Pe^(rt), where A is the final amount, P is the initial principal balance, r is the annual interest rate (expressed as a decimal), t is the time in years, and e is the mathematical constant approximately equal to 2.71828.

In this case, the initial principal balance P is $3600, the annual interest rate r is 8% or 0.08 as a decimal, and the time t is 3 years. Plugging these values into the formula gives us:

A = 3600 * e^(0.08 * 3)

Evaluating this expression gives us a final amount of approximately $4293.25 in the account after three years.

A. Ram spent $18 on six pens and six books. The grand total is $72.

B. The cost of each pen is $9.

C. The variable is called x.

What is an equation?

A set of variables, constants, and mathematical operations such as addition, subtraction, multiplication, or division balanced by the equal sign is known as an equation. The equation's left-hand side (LHS) is on the left side, and its right-hand side (RHS) is on the right side (RHS).

Here, we have

Given: the equation 6x + 18 = 72:

A. The issue is that Ram spent $18 on six pens and six books. The total amount he paid is $72.

B. The following equation will be used to demonstrate this:

6x + 18 = 72

Compile similar terms.

6x = 72 - 18

6x = 54

On dividing,

x = 54 / 6.

x = $9

Hence, each pen will set you back $9.

C. The variable's value is x = 9.

Hence, the pen's price is 9.

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2 1/4 miles => 1 week

1 mile => 1 ÷ 9/4

( 9/4 is an improper fraction of 2 1/4 )

12 1/2 miles => ( 1 ÷ 9/4 ) × 25/2

= 50/9

= 5 5/9 weeks

( 25/2 is an improper fraction of 12 1/2 )

Therefore, it will take 5 5/9 weeks for the company to replace the stretch of road.

( you can round it off to 6 weeks if the qn specify to give to the nearest whole number )

Answer:

Step-by-step explanation:

if quadratic

(-3)²+5=9+5=14

so f(x)=x²+5

or

if linear

(-3)+17=14

f(x)=x+17

if  cubic

(-3)³-2(-3)²-3(-3)+14=14

f(x)=x³-2x²-3x+14

so on.

The percent of error can be found by dividing the difference in weights by the predicted weight.

290 - 258 = 32 pounds

32/258 = 0.124

0.124 = 12.4% approximately was the percent of error

Bottom left is the one you need

This is the same as writing y = sqrt(4(x+5)) - 1

===============================================

Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

----------

Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

----------

Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

----------

The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

The height of the monument is 30 meters.

We have,

Let's assume the height of the monument is "h" meters.

From the top of the building, the angle of elevation to the top of the monument is equal to the angle of depression to the foot of the monument. This forms a right triangle with the building, the monument, and the ground.

In this triangle, the opposite side of the angle of elevation is the height of the building, which is given as 30 meters.

The opposite side of the angle of depression is the height of the monument, which is "h" meters.

Since the angles of elevation and depression are equal, the triangle is an isosceles triangle.

Therefore, the opposite sides are equal in length.

By setting up the equation:

h = 30

Thus,

The height of the monument is 30 meters.

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Answer:

x=13

Step-by-step explanation:

If you're doing Delta Math.

The required value of x is 13 units which is determined by the property of the triangle's interior angles.

The triangle ΔFGH has :

m∠F = (3x-15)

m∠G = (8x+8)

m∠H = (2x+18)

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry

We know that the sum of interior angles is always 180 degrees in the triangles.

As per the property of triangles,

m∠F + m∠G + m∠H = 180°

(3x-15) +  (8x+8) + (2x+18) = 180°

Rearrange the terms of variable x in the above equation,

3x + 8x + 2x - 15 + 8 +18 = 180°

13x + 11 = 180

13x = 196

x = 169/13

x = 13

Therefore, the required value of x is 13 units

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Answer:

y=2x -1

Step-by-step explanation:

Finding x-intercepts and y-intercepts

1-To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y.

2-To find the x-intercept, set y = 0 \displaystyle y=0 y=0.

3-To find the y-intercept, set x = 0 \displaystyle x=0 x=0.

Using word problems and equations, Sarah worked for 10 hours and Penelope worked for 5 hours

This is a word problem and in order to solve this, we need to translate mathematical statements in form of word problems into mathematical equations.

Let's assume that Sarah worked x hours.

Given that Sarah can iron 30 shirts per hour, the total number of shirts she ironed is 30x.

Since Penelope worked half the hours of Sarah, Penelope worked x/2 hours.

Given that Penelope can iron 35 shirts per hour, the total number of shirts she ironed is 35 * (x/2) = (35/2)x.

The total number of shirts ironed by both Sarah and Penelope is 475 shirts.

So, we can write the equation: 30x + (35/2)x = 475.

To solve this equation, we can simplify it: (60/2)x + (35/2)x = 475, which becomes (95/2)x = 475.

Now, we can solve for x: x = (475 * 2) / 95 = 10.

Therefore, Sarah worked 10 hours and Penelope worked half of that, which is 5 hours.

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The domain of the function or relation is {6, 9, -4 and 2}

The function is represented by the set of relation or ordered pairs

The ordered pairs in the relation are:

(x, y)  = (6, -3), (9, -3), (-4, 1) and (2, 1)

Remove the y values in the above domain

x = 6, 9, -4 and 2

The x values represent the domain of the function

Hence, the domain of the function or relation is {6, 9, -4 and 2}

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Answer:

Simplify the expression.

Exact Form:

48 /5

Decimal Form:

9.6

Mixed Number Form:

9  3 /5  Is what I believe sorry if i got this wrong but i hope this was helpful!

Answer:

Step-by-step explanation: A

Answer: b

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

Answer:

$324

Step-by-step explanation:

let x be the amount of money she had at first , then

\(\frac{1}{3}\) x + \(\frac{1}{9}\) x = 144 ( multiply through by 9 to clear the fractions )

3x + x = 1296

4x = 1296 ( divide both sides by 4 )

x = 324

she had $324 at first

Answer:

D.

Step-by-step explanation:

at + ab = c

subtract ab from both sides

at= c - ab

divide a from both sides

t = c - ab/a

Answer:

Step-by-step explanation:

ax² + bx + c = y

Plug in data points to get a system of equations in three unknowns.

(0.5,18): 0.25a + 0.5b + c = 18

(1,24): a + b + c = 24

(1.5,22): 2.25a + 1.5b + c = 22

Solving the system:  a = -16, b = 36, c = 4

y = -16x² + 36x + 4

When x = 1.7, y = -16·1.7² + 36·1.7 + 4 = 18.96 ft

Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

Answer:

If a swimming pool contains 6.8 × 10³ gallons of water and is leaking at a rate of 12-1 gallons per second, then it will take (6.8 × 10³) / (12-1) = 6800 / 11 ≈ 618.18 seconds for all of the water to leak out of the pool. Since there are 3600 seconds in an hour, it will take approximately 618.18 / 3600 ≈ 0.17 hours or about 10 minutes for all of the water to leak out of the pool.

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can start by using the leak rate to determine how much water is lost in one second:

12-1 gallons/second

Next, we can set up an equation to determine how many seconds it will take for all of the water to leak out of the pool:

6.8 × 10³ gallons / (12-1 gallons/second) = x seconds

Simplifying the expression on the left-hand side, we get:

6.8 × 10³ gallons / (12-1 gallons/second) = 6.8 × 10³ gallons / 11 gallons/second

= 618.18 seconds

Therefore, it will take 618.18 seconds for all of the water to leak out of the pool. To convert this to hours, we can divide by the number of seconds in an hour:

618.18 seconds / 3600 seconds/hour ≈ 0.172 hours

Therefore, it will take approximately 0.172 hours, or about 10.3 minutes, for all of the water to leak out of the pool.

Answer:

x = 18

y = 6

Step-by-step explanation:

In triangle UTR, measures of all angles are equal (60°). (given)

Therefore, it is an equilateral triangle.

So, it's sides will also be equal.

In triangle TRS, m angle T = m angle S

So, RT = RS = 11 (sides opposite to the equal angles are equal)

In triangle URT,

UT = RT (sides of equilateral triangle)

x - 7 = 11

x = 11 + 7

x = 18

In triangle TRS,

m angle T = m angle S = 5y°

m angle R = 180° - 60° = 120° (Linear pair angles)

5y° + 5y° + 120° = 180°

10y° = 180° - 120°

10y° = 60°

y = 60/10

y = 6

Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends. He is incorrect

From the information, Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends.

Let's add (-3) + (-4)

It should be noted that the addition is equal to -7.

It should be noted that this doesn't corelate with what Luciana said.

Therefore, she is incorrect. It's only correct for positive numbers.

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Answer:

In a function that is represented by Y=mx+b b would be the y-intercept

Definition of y-intercept. : the y-coordinate of a point where a line, curve, or surface intersects the y-axis.

The stock price according to the constant growth dividend model is $68.11 (rounded to two decimal places).

The market value of a share of ownership in a publicly traded corporation is referred to as a stock price.

It is the price that investors are prepared to pay to purchase or sell the company's shares at a specific time, depending on the company's financial performance, its future growth prospects, and the state of the market as a whole.

Investors, analysts, and other members of the financial community pay careful attention to the stock price as it is frequently viewed as a significant indicator of the company's overall worth and health.

According to the constant growth dividend model, the stock price (P) is given by the formula:

P = D / (r - g)

where D is the last dividend, r is the required rate of return, and g is the growth rate of dividends.

Substituting the given values, we get:

P = 5.95 / (0.1188 - 0.0314)

P = 5.95 / 0.0874

P = 68.11

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The solution of the inequality is -1 ≤ x ≤ 3.

To solve the inequality |2x(x-1)+12| ≤ 18, we can break it down into two separate inequalities:

2x(x-1) + 12 ≤ 18

-(2x(x-1) + 12) ≤ 18

Solving the first inequality:

2x(x-1) + 12 ≤ 18

2x² - 2x + 12 ≤ 18

2x² - 2x - 6 ≤ 0

Solving the second inequality:

-(2x(x-1) + 12) ≤ 18

-2x(x-1) - 12 ≤ 18

-2x² + 2x - 12 ≤ 18

2x² - 2x + 30 ≤ 0

Now, let's solve each inequality separately.

For the first inequality, 2x² - 2x - 6 ≤ 0:

We can factor this quadratic equation:

(2x + 2)(x - 3) ≤ 0

To determine the sign of the inequality, we need to consider the intervals where the expression is positive or negative. We set each factor equal to zero to find the critical values:

2x + 2 = 0 => x = -1

x - 3 = 0 => x = 3

Plotting these critical values on a number line and testing intervals, we find that the solution is -1 ≤ x ≤ 3.

For the second inequality, 2x² - 2x + 30 ≤ 0:

This quadratic equation does not have real solutions, so there are no solutions to this inequality.

Combining the solutions from both inequalities, we have -1 ≤ x ≤ 3.

To graph the solution, we plot the interval -1 ≤ x ≤ 3 on the number line. The shaded region on the number line represents the solution set.

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Answer:

D. \(\frac{4x^{2} \sqrt{29}}{29}\)

Step-by-step explanation:

Given the expression:

 \(\frac{40x^{2} \sqrt{x^{12} } }{10x^{2} \sqrt{29x^{8} } }\)

divide by the common factor to have;

\(\frac{4\sqrt{x^{12} } }{\sqrt{29x^{8} } }\) = \(\frac{4(x^{12}) ^{\frac{1}{2} } }{(29x^{8}) ^{\frac{1}{2} } }\)

        = \(\frac{4x^{6} }{\sqrt{29}x^{4} }\)

        = \(\frac{4x^{2} }{\sqrt{29} }\)

Rationalize the denominator, we have;

\(\frac{4x^{2} }{\sqrt{29} }\) x \(\frac{\sqrt{29} }{\sqrt{29} }\)

So that,

\(\frac{4x^{2} \sqrt{29} }{29}\)

Thus,

\(\frac{40x^{2} \sqrt{x^{12} } }{10x^{2} \sqrt{29x^{8} } }\) = \(\frac{4x^{2} \sqrt{29} }{29}\)

The correct option is D.