A business has $11,080 to spend on new laptops and tablet computers for its salespeople. The laptops cost $515 each. The tablets cost $285 each. The business wants each salesperson to have either a laptop or a tablet. There are 30 salespeople. Create a system of equations that models how many of each type of computer the business should buy.


515x + 285y = 11,080
x + y = 30



515x + 285y = 30
x + y = 11,080

515x + y = 30
x + 285y = 11,080


x + 285y = 30
515x + y = 11,080

9514 1404 393

Answer:

  (x, y) = {(-32/17, 49/17), (-2, 1)}

Step-by-step explanation:

I find a graphing calculator to be quite helpful in finding the solutions.

  (x, y) = {(-1.882, 2.882), (-2, 1)}

__

For this sort of system of equations, substitution works nicely as a solution method.

The first equation tells us ...

  y = 1 - x

Using that in the second equation, we get ...

  16x² +(1 -x)² = 65

  16x² +1 -2x +x² = 65 . . . . . eliminate parentheses

  17x² -2x -64 = 0 . . . . . . . . collect terms, subtract 65

  (x -2)(17x +32) = 0 . . . . . . . factor

Solutions are the values of x that make the factors zero: x = 2, x = -32/17.

The corresponding y-values are ...

  for x=2, y = 1-2 = -1

  for x=-32/17, y = 1-(-32/17) = 49/17

The solutions are ...

  (x, y) = (2, -1)  or  (-32/17, 49/17)

Answer:

\(\huge\boxed{\sf 3(n + 5) \leq 100}\)

Step-by-step explanation:

So, the inequality will be:

3(n + 5) ≤ 100

\(\rule[225]{225}{2}\)

Hope this helped!

The correct number line that can be used to find the distance between the given points (4, -1) and (8, -1) is a number line going from negative 2 to positive 8 in increments of 1, with the points at 4 and 8.Option (A)

The reason for this is that the two points have the same y-coordinate, which means they lie on a horizontal line. To find the distance between them, we simply need to measure the difference between their x-coordinates, which is 8 - 4 = 4. On the given number line, the distance between points 4 and 8 is also 4 units, so we can directly read off the distance as 4 units.

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Answer:

1st one, 4th one, and 5th one

Step-by-step explanation:

Answer:

red, blue and purple

hey There!

for the first one

2*2=4

4*2=8

8*2= 16 so blue is correct

8*8=64 so cyan is not correct

2^8=256 so yellow is not correct

4*4=16 so red is correct

2^4 is the same as 2*2*2*2 which equals 16 so purple is also correct

Answer:

Trapezoid graph

Step-by-step explanation:

Domain: Same as the plot

Domain shape: trapezoid

Range in (x, y) = (2, 7), (3, 13)

I hope this helps you :)

Answe

Step-by-step explanation:

The sum of the first 20 terms of the progression is 120

The given parameters are:

The sum of the first n terms of an arithmetic progression is

Sn = n/2[2a + (n - 1) * d]

So, we have:

S3n = 3n/2[2a + (3n - 1) * d]

Substitute Sn = 18 and S3n = 135 and d = 3

So, we have:

n/2[2a + (n - 1) * 3] = 18

3n/2[2a + (3n - 1) * 3] = 135

Simplify each equation

n[2a + (n - 1) * 3] = 36

n[2a + (3n - 1) * 3] = 90

Expand

[2an + 3n(n - 1)] = 36

[2an + 3n(3n - 1)] = 90

Using a graphing calculator, we have:

a = 3 and n = 3

The sum of the first 20 terms is:

Sn = n/2[2a + (n - 1) * d]

This gives

S20 = 20/2 * [2 * 3 + (3 - 1) * 3]

Evaluate

S20 = 120

Hence, the sum of the first 20 terms of the progression is 120

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Answer:

1,356 hours

Step-by-step explanation:

There are 24 hours in ONE day on earth.

56 days = 1,344 hours

1,344 hours + 12 hours = 1,356 hours

There are 365 days on EARTH.

One day = 24 hours

365 x 24 = 8,760 hours

Answer:

Correct option: first one

Step-by-step explanation:

The equation f(x) = 5x + 1 is a function, because each value of x gives only one  value of y.

Now let's find the inverse by switching f(x) by x and x by f'(x), then isolating f'(x):

\(x = 5f'(x) + 1\)

\(5f'(x) = x - 1\)

\(f'(x) = \frac{x - 1}{5}\)

The inverse f'(x) is also a function, because each value of x gives only one value of x.

So we have that both the equation and its inverse are function, therefore the correct answer is the first option.

Answer:

  A = $6,700(1 +0.0865^t)

  APY = 8.65%

Step-by-step explanation:

Daily compounding of interest results in an annual growth factor of ...

  gf = (1 +r/365)^365 . . . . for APR = r

Your growth factor is ...

  gf = (1 +0.083/365)^365 ≈ 1.086532

Then the growth rate (APY) is ...

  APY = gf -1 ≈ 8.65%

The account value is multiplied by the growth factor each year, so after t years will be ...

  A = P(1 +APY)^t

  A = $6,700(1 +0.0865)^t . . . . . . . 0.0865 is the annual growth rate

Step-by-step explanation: trust me

Answer:

1/8

Answer:

It's - 1/8

Step-by-step explanation:

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer:

x = 22.5

Step-by-step explanation:

Step 1: Write equation

2.4(x - 10) = 8 + 1.2x - 5

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

2.4(22.5 - 10) = 8 + 1.2(22.5) - 5

2.4(12.5) = 8 + 27 - 5

30 = 8 + 22

30 = 30

Answer:

x=22.5

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2.4(x−10)=8+1.2x−5

(2.4)(x)+(2.4)(−10)=8+1.2x+−5(Distribute)

2.4x+−24=8+1.2x+−5

2.4x−24=(1.2x)+(8+−5)(Combine Like Terms)

2.4x−24=1.2x+3

2.4x−24=1.2x+3

Step 2: Subtract 1.2x from both sides.

2.4x−24−1.2x=1.2x+3−1.2x

1.2x−24=3

Step 3: Add 24 to both sides.

1.2x−24+24=3+24

1.2x=27

Step 4: Divide both sides by 1.2.

1.2x

1.2

=

27

1.2

x=22.5

Answer:

x=22.5

Answer:

2,359,000,000

Step-by-step explanation:

Answer:

2,359,000,000 would be the standard form

Step-by-step explanation:

Exponential functions are functions defined by y = ab^x, where a represents the initial value, and b represents the rate

The initial population of the city is 10000, and the growth rate of the population is 4%.

So, the exponential equation is:

\(y = 10000 * 1.04^x\)

The initial population of the city is 12000, and the decay rate of the population is 3%.

So, the exponential equation is:

\(y = 12000* 0.97^x\)

The similarity in both equations is that, they both represent exponential function.

In (a) and (b), we have:

\(y = 10000 * 1.04^x\) ---- city A

\(y = 12000* 0.97^x\) --- city B

When city A exceeds city B, we have the following inequality

\(10000 * 1.04^x > 12000 * 0.97^x\)

Divide both sides by 10000

\(1.04^x > 1.2 * 0.97^x\)

Divide both sides by 0.97^x

\((\frac{1.04}{0.97})^x > 1.2\)

\(1.07^x > 1.2\)

Take the natural logarithm of both sides

\(\ln(1.07)^x > \ln(1.2)\)

This gives

\(x\ln(1.07) > \ln(1.2)\)

Solve for x

\(x > \frac{\ln(1.2)}{\ln(1.07)}\)

\(x > 2.69\)

This means that, the population of city A will exceed city B after 3 years

In (a) and (b), we have:

\(y = 10000 * 1.04^x\) ---- city A

\(y = 12000* 0.97^x\) --- city B

When city A is at least twice city B, we have the following inequality

\(10000 * 1.04^x \ge 2 * 12000 * 0.97^x\)

\(10000 * 1.04^x \ge 24000 * 0.97^x\)

Divide both sides by 10000

\(1.04^x \ge 2.4 * 0.97^x\)

Divide both sides by 0.97^x

\((\frac{1.04}{ 0.97})^x \ge 2.4\)

\(1.07^x \ge 2.4\)

Take the natural logarithm of both sides

\(\ln(1.07)^x \ge \ln(2.4)\)

This gives

\(x\ln(1.07) \ge \ln(2.4)\)

Solve for x

\(x\ge \frac{\ln(2.4)}{\ln(1.07) }\)

\(x\ge 12.9\)

This means that, the population of city A will be at least twice city B after 13 years

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Answer:

profit of 240

Step-by-step explanation:

credit to the person above me

Answer:

The second option (8 132/999)

Step-by-step explanation:

just divide the fractions until you get the correct decimal

If 3100 individuals in a population of 46,785 complain of chronic headaches to one decimal place: 6.6 percent complain of this.

If 3100 individuals in a population,

of 46,785 complain of chronic headaches

then, = 3100/ 46,785

          = 0.066

now change the decimal to a percentage so that we will multiply the decimal by 100

= 0.066 * 100 = 6.6%

To change the percentage to a decimal, divide by 100. So 25% is 25/100, or 0.25. To convert a decimal to a percentage, increase by 100 (simply move the decimal direct 2 spots toward the right).

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An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per second. The rate at which the water level is rising when the water level is 9 cm is 5 cm/s.

To find the rate at which the water level is rising when the water level is 9 cm, we can use similar triangles and the formula for the volume of a pyramid.

Let's denote the rate at which the water level is rising as dh/dt (the change in height with respect to time). We know that the pyramid is being filled at a constant rate of 55 cubic centimeters per second, so the rate of change of volume is dV/dt = 55 cm³/s.

The volume of a pyramid is given by V = (1/3) * base area * height. In this case, the base area is a square with sides of length 6 cm and the height is 14 cm. We can differentiate the volume equation with respect to time, dV/dt, to find an expression for dh/dt.

After differentiating and substituting the given values, we can solve for dh/dt when the water level is 9 cm.

By substituting the values into the equation, we get dh/dt = 5 cm/s.

Therefore, the rate at which the water level is rising when the water level is 9 cm is 5 cm/s.

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Answer:

70 degrees = a

Step-by-step explanation:

Triangle= 180 degrees.

Therefore, since a and the unmarked angle are congruent since it is an isosceles triangle, we subtract 40 from 180, with a result of 140. With 140, we divide by 2 to find the degrees for both the unmarked angle and angle a, since they are congruent. 140/2 = 70, Angle A will equal to 70 degrees

Answer:

1680.25

Step-by-step explanation:

Answer:

x=13

Step-by-step explanation:

15x-15

15*13=195

195-15=180

Answer:

Step-by-step explanation:

X=13 pls mark brainly

Therefore, three sections of the spinner are most likely labeled math.

The students are playing a trivia game, and the game has three different topics that the players can choose from. These three topics are history, science, and math. Every player has to spin a spinner that has eight equal sections to determine which topic they will play.

To solve this question, we need to understand that the spinner has eight equal sections.

There are three different topics in the game, and therefore, it is most likely that there are three sections labeled math.

We can calculate the probability of getting the math topic by dividing the number of math sections by the total number of sections.

Hence, \(\frac{3}{8} = 0.375\)

So, the probability of getting the math topic is 0.375.

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a. We can make a conjecture for a closed-form formula that expresses n in terms of n-2 and n-3. One possible conjecture is:

n = n-2 + n-3

b. The simplest version of the closed-formula is: n = -4.

(a) Let's find expressions for n-2 and n-3 based on the given equations.

From the first equation, n = 2(n-1) + (-2n). Expanding this equation, we get:

n = 2n - 2 + (-2n)

n = 0 - 2

n = -2

Now, substituting n = -2 in the equation n = 2(n-1) + (-2n), we have:

-2 = 2((-2)-1) + (-2)(-2)

-2 = 2(-3) + 4

-2 = -6 + 4

-2 = -2

Therefore, n-2 = -2 and n-3 = -2.

Based on these observations, we can make a conjecture for a closed-form formula that expresses n in terms of n-2 and n-3. One possible conjecture is:

n = n-2 + n-3

(b) To find the simplest version of the closed-formula without a summation term, we substitute the values of n-2 and n-3 into the conjectured formula:

n = (-2) + (-2)

n = -4

Therefore, the simplest version of the closed-formula is:

n = -4.

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Answer:

22

Step-by-step explanation:

replace -2 for every in the equation:

-(-2)x2-9x-2=22

Answer:

f(-2)=14

Step-by-step explanation:

\(f(x) = -x^2 - 9x\\\\f(-2) = -(-2)^2-9(-2)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:exponents}\:\left(-2\right)^2\::\quad 4\\=-4-9\left(-2\right)\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:9\left(-2\right)\::\quad -18\\\\=-4-\left(-18\right)\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:-4-\left(-18\right)\:\\f(-2):\quad 14\)

The correct statements regarding the transformations to the volumes are given as follows:

1. A cone's radius increases x 3: -> The cone's volume will increase x 9.

2. A cone's height increases x 3: -> The cone's volume will increase x 3

3. A sphere's radius increases x 3 -> The sphere's volume will increase x 27.

4. A cylinder's radius increases x 6 -> The cylinders volume will increase x 36.

The equations that give the volumes of each solid are given as follows:

Then the increases are given as follows:

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Answer:

-7x

Step-by-step explanation:

==> -12x + 5x.

==> -12+5xx

==> -7x

Answer:

-7x

Step-by-step explanation:

−12x+5x

Combine Like Terms:

=−12x+5x

=(−12x+5x)

=−7x

Combining like terms - Combining like terms will simplify a math problem and is also the proper form for writing a polynomial. To combine like terms, just add the coefficients of each like term.

The mean of the given set of group numbers is 6.6

Given,

In the question:

The Group of numbers are as follows:

6.1, 5.9, 4.2, 5.9 and 10.7

To find the mean of the given set of group of numbers.

Now, According to the question:

Given is the following data:

6.1, 5.9, 4.2, 5.9 and 10.7

We can find the mean of the given set of data using the formula-

Mean (M) = Σ a[i]/n = (Sum of all the elements)/(total number of elements)

Now, n = 5

and Σ a[i] = 6.1 + 5.9 + 4.2+ 5.9 + 10.7 = 32.8

Putting the values in the formula, we get:

M = 32.8/5 = 6.56 = 6.6

Hence, The mean of the given set of group numbers is 6.6

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