10. Three math teachers went to Office Depot to buy school supplies. Mr. Smith bought nine boxes of
pencils, three boxes of markers, and twelve packages of notebook paper for $45.75. Ms. Santana
purchased five boxes of pencils, six boxes of markers, and eight packages of notebook paper for
$41.50. While Mrs. Baker spent $128 on twenty boxes of pencils, four boxes of markers, and fifty
packages of notebook paper.
Which of the following systems of equations can determine the price of these items individually?

When the fire is steadily burning at a temperature of 600 degrees, the number of hours needed to run out is 30 hours.

From the information, the fire is steadily burning at a temperature of 600 degrees F and t was stated that the fire is no longer maintained, the temperature drops 20 F every half hour.

Therefore, the appropriate expression to solve the information will be:

Let the number if hours be h

600 - (20 × h) = 0

600 - 20h = 0

20h = 600

Divide

h = 600 / 20

h = 30

Therefore, when the fire is steadily burning at a temperature of 600 degrees, the number of hours needed to run out is 30 hours.

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The equation of the parabola in vertex form is y = - (1 / 4) · x².

In this problem we find a parabola whose axis of symmetry is on the y-axis and the directrix is above the parabola, which means that the least distance between the vertex and the directrix is negative. The equation of the parabola in vertex form is described below:

4 · p · (y - k) = (x - h)²

Where:

If we know that p = - 1 and (h, k) = (0, 0), then the equation of this parabola is:

4 · (- 1) · y = x²

- 4 · y = x²

y = - (1 / 4) · x²

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Answer:

Step-by-step explanation:

First of all AD is 9 units long. Anything less than or equal to 9 is not an answer because the scale factor is greater than 1. That means that anything over 9 will work.

So the answer must be 12 or 15 from those answers given.

Answer:

0 with 0 2 pi cot0=-10 am not sure what It is

The algebraic expression which correctly represents the verbal description; The total cost of the order, t, is 11 dollars multiplied by the number of pizzas ordered, p is; t = 11p.

It follows from the task content that the expression which correctly represents the verbal description be determined.

On this note, since total cost is; t and the number of pizzas ordered is; p.

The required expression is therefore;

t = 11 × p

t = 11p.

Ultimately, the verbal representation of the algebraic expression where total cost of the order, t, is 11 dollars and number of pizzas ordered, is p is given by t = 11p.

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Answer:

[tex] \sf{x=−12}[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

90+x+67+35=180

Step 1: Simplify both sides of the equation.

90+x+67+35=180

(x)+(90+67+35)=180(Combine Like Terms)

x+192=180

x+192=180

Step 2: Subtract 192 from both sides.

x+192−192=180−192

x=−12

The properties used to simplify the problem are associative property of addition, additive inverse, and additive identity.

Consider the given problem;

( 38 + 677 ) + ( - 38 )

The associative properties can be represented as:

( A + B ) + C = A + ( B + C )

Now, we need to check all the options to determine the properties used:

( 38 + 677 ) + ( - 38 ) = 38 + ( 677 - 38 )

( A + B ) + C = A + ( B + C )

Therefore, this is the associative property.

Now,

677 + 0 = 677

A + 0 = A

Thus, this is the additive identity.

Similarly,

677 + [ 38 + ( -38 ) ]

Here, 38 + ( -3 8 ) represents,

A + ( - A ) = 0.

Therefore, this is the additive inverse.

Thus, the properties used to simplify the problem are the associative property of addition, additive identity, and additive inverse properties.

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Answer:

The correct answer is A.

Answer: 40 hours

Step-by-step explanation:

As stated in the question the total amount spent in the month of august is $35.

First of all you have to subtract 15 out of the entire amount spent so that you can start calculating how many hours did Julie use the pool.

(35-15) = 20 (divide the answer with 0.50)

(20/0.50) = 40 (We have to divide to get the amount of hours she spent in pool)

Firstly we will convert the percent R into a decimal value r. For that, we will divide with a hundred,

r = R/100

r = 6/100

r = 0.06 rate per year,

Then solve the equation for A

A = P(1 + r/n) ^ nt

A = 500.00(1 + 0.06/12) ^ (12 x 10)

A = 500.00(1 + 0.005)^ 120

A = $909.70

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $500.00 at a rate of 6% per year compounded 12 times per year over ten years, is $909.70.

I = A - P = $2,000.00

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 4%/100 = 0.04 per year.

Solving our equation:

A = 5000(1 + (0.04 × 10)) = 7000

A = $7,000.00

The total amount accrued, principal plus interest, from simple interest on a principal of $5,000.00 at a rate of 4% per year for ten years is $7,000.00.

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Answer:

[tex]\sf \bf h^{21}[/tex]

Step-by-step explanation:

  We have to multiply the powers.

[tex]\sf \boxed{\bf (a^m)^n=a^{m*n}}[/tex]

       [tex]\sf (h^3)^7=h^{3*7}[/tex]

                [tex]\sf = h^{21}[/tex]

After solving, the factors of equation x²+x-6 are:

So,

Given the equation: x²+x-6

Then,

Factors are: (x+3) and (x-2)

Therefore, after solving, the factors of equation x²+x-6 are:

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The value of x using the change of base formula of logarithm is 25.

What are the various properties of the logarithm?

Out of several properties of logarithms, some of the main properties are given below:

Product Rule

log (ab) = log a + log b

Change of base

log ₇ x = log x / log 7

Power Rule

log a² = 2 log a

Quotient Rule

log (a / b) = log a - log b

Solving the given equation by using the change of base formula

We are given a logarithmic expression: log ₉ x = log ₃ 5

Using properties of the logarithm, we have

log x / log 9 = log 5 / log 3

log x = (log 5 × log 9) / log 3

= (log 5 × 2 log 3) / log 3

= 2 × log 5

= log 5²

log x = log 5²

Applying exponent both sides, we get,

x = 25

Hence, the value of x is 25.

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Answer:

It got colder by 9 degrees

Step-by-step explanation:

For all the values of 'd' the expression 4-d will be less than 4+d.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

Given that 4−d < 4+d. The inequality expression will be solved as:-

4−d < 4+d

4 - 1 < 4 + 1

3 < 5

4 - 2 < 4 + 2
2 < 6

It is concluded that for all the values of d in the given expression the portion 4 - d will be less than 4 + d.

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According to the given cubic equation  8x³-10x² - 21x + 18 = 0 the other value of x will be 4.

Traditionally, a cubic problem can be solved by converting it to a quadratic equation and then solving it using factoring or the quadratic formula. A cubic equation, like a quadratic equation, has three roots.

The typical strategy for solving a cubic problem is to convert it to a quadratic equation and then solve the quadratic using the standard methods, either factoring or using the formula. All of them are cubic equations. A cubic equation, like a quadratic equation, may have two or three real roots.

8x³-10x² - 21x + 18 = 0

x= 2

substituting the value in the equation we get:

8x³-10x² - 21x + 18 = 0

8(2)³-10(2)² - 21(2) + 18 = 0

68 - 40 - 42 + 18 = 0

4 = 0

According to the given equation  8x³-10x² - 21x + 18 = 0 the other value of x will be 4.

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Answer: 3c^2  +4 -5c

Step-by-step explanation:

-2c^2 -c +1 -(-5c^2 -3 +4c)

3c^2  +4 -5c

Answer:

A) [tex]y = \frac74x[/tex]

Step-by-step explanation:

Since the equation's graph passes through the origin, its [tex]c[/tex] value is equal to 0, and, therefore, you will only need to find the slope as the equation is of the template [tex]y = mx[/tex] where [tex]m[/tex] is the slope.

To find the slope, you can substitute the coordinates of the given points into the formula for a line's slope: [tex]y = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]y = \frac{7 - 0}{4 - 0} \to \frac74[/tex]

Therefore, the line's equation is [tex]y = \frac74x[/tex]

After solving the given equation ln(x+2)-ln4=3, the value of [tex]x=e^{4 \ln +3}-2[/tex].

So,

Then,

Therefore, after solving the given equation ln(x+2)-ln4=3, the value of [tex]x=e^{4 \ln +3}-2[/tex].

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The equation that represent amount of oil in the tank at x minutes is

6- 0.2t

A mathematical statement that shows that two mathematical expressions are equal.

Given:

rate of filling the tank = 0.2 feet/ minute

After 15 minutes,

height = 6 feet

let the time take be x minutes

So, the equation that represent amount of oil in the tank at x minutes.

=6- 0.2t

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The sole of AB = 1/7, BC = -5/2, CD= -1/6, DA= -5/3

Here we have to find the slope of the side of the quadrilateral

The formula of the slope between A(x1, y1), B (x2, y2)

  slope = (y2 - y1)/( x2- x1)

Slope of AB , where A = (-5, 3), B = (2,2)

AB = (2-3)/ ( 3- (-5))

     = 1/ 8

Slope of BC, where B= (2,2 ), C = (4, -3)

BC = (-3 -2)/ (4-2)

     = -5/2

Slope of CD, where C= (4,-3), D=(-2,-2)

CD = (-2-(-3))/ (-2-4)

     = 1/ (-6)

     =-1/6

Slope of DA , where D=(-2,-2), A=(-5,3)

DA= (3-(-2))/(-5-(-2))

    = (3+2)/(-5+2)

    = 5/-3

     =-5/3

Therefore the slope of AB, BC, CD, DA = 1/7, -5/2, -1/6, -5/3 respectively.

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The absolute value will always be a positive number while solving an equation that does not involve an absolute value could be any number.

The absolute value of a number n, written |n|, can be described

geometrically as the distance of n from 0 on the number line.

For instance, |42| = 42 and |–42| = 42. Both 42 and –42 are 42 units

from zero.

Algebraically, the absolute value of a number can be defined

piecewise as follows.

|x| = {

 x, for x ≥ 0

–x, for x < 0

Examine the definition carefully. Because –x is the opposite of x,

–x is positive when x is negative. For instance, |–7.4| = –(–7.4) = 7.4.

Thus |x| are |–x| are never negative, and, in fact, |x| = |–x|.

On many graphing utilities, spreadsheets, and CAS, the absolute–

the value function is denoted abs. For example, abs(x–3) = |x–3|.

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Answer:

[tex]\frac{4080n+1585d-188}{240}[/tex]

Step-by-step explanation:

I simplified it to the best possible state

Answer:

x=6.28 0r 0.72

Step-by-step explanation:

The explanation is in the image

The difference in elevations between Mount Ojos del salado and the atacama trench is 15000 meters

From the question, we are to calculate the difference in elevations between Mount Ojos del salado and the atacama trench

From the given information,

"Ojos del salado is the highest mountain in Chile, with a peak at about 6900 meters above sea level"

and

"The atacama trench, just off the coast of Peru and Chile, is about 8100 meters below sea level"

Thus,

With respect to the sea level,

The elevation of Mount Ojos del salado is 6900 meters

and

The elevation of the atacama trench is -8100 meters

Then,

The difference in elevation between Mount Ojos del salado and the atacama trench is 6900 - (-8100) meters

6900 - (-8100)

= 6900 + 8100

= 15000 meters

Hence, the difference in elevations between Mount Ojos del salado and the atacama trench is 15000 meters

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The graph at:

x=-6,-4→intersects directly

x=0→passes through

x=1→tangent

At different x-intercepts, graphs exhibit varying behaviours. On occasions, the graph will intercept the x-axis and cross it. On occasions, the graph will contact the x-axis and then deviate from it. The graphs contact or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities. Higher even powers, such as 4, 6, and 8, will still cause the graph to contact and deviate from the x-axis, but as even power increases, the graph will appear flatter as it does so.The graph will still cross through the x-axis for higher odd powers like 5, 7, and 9, but for each rising odd power, the graph as it approaches and departs the x-axis, it seems flatter.

∴x=-6,-4→intersects directly

x=0→passes through

x=1→tangent

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The time it took to fly through ah fro is 21 hours

x=21 hrs

This is further explained below.

Generally, A cargo aircraft traveled to the repair facility and returned again, and the flight there took an hour less of its total time than the flight back did.

The voyage there had an average speed of 220 miles per hour, whereas the return back had an average speed of 200 miles per hour. I was wondering how many hours the journey took.

Generally, the equation for the distance is  mathematically given as

Dist = speed * time

Therefore

Dist to = dist back

220t = 200(t+1)

220t = 200t + 200

220t - 200 = 200

20t = 200

t = 200/20

t = 10 hrs to

Considering for hours back

10 + 1 = 11 hrs back

Total hrs: 10 + 11 = 21 hrs for the round trip

In conclusion, The trip took

21 hrs

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CQ

a cargo plane flew to the maintenance facility and back it took one hour less time to get there than it did to get back. the average speed on the trip there was 220mph the average speed on the way back was 200mph how many hours did the trip take

Answer:
A. 5 || how? uh counting; -7x      -1/6y      +2z      -xy         +28

B. 3 (2;x | 2;y | 1;z)

C. 28

Hope this helps!

--Blu

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Remember that we're using absolute values. A negative number plus a positive number is the same as a positive number subtracted by another positive number.