In the following equations, the value of x represents the price per pound of gravel and the value of y represents the price per pound of sand.2y = 3x + 85y – 15x = -30At what price for sand do the two lines intersect? (Find the value of y.)$10.00$14.00$12.33$6.67

hello

the equation given is

step 1

multiply the coeffiecients with the brackets and the proceed to simplfy

step 2

collect like terms

the value of x = -24

Step-by-step explanation:

so, what's the problem ?

it's all there, we only need to take the calculator (or simply our heads) and do the calculation :

2×5 - 5×2 = 10 - 10 = 0

you see ? that was all that was needed.

put the given values for the variables into the places of these variables, and then calculate !

that is what variables are for : placeholders for actual values.

Answer:

C

Step-by-step explanation:

Beacuse

10/5=2 it

5 is also a factor

Answer:

50% or 1/2 Could be 100% but i think it is 50%

Step-by-step explanation:

Because Changing the coin will make no difference.

The probability of getting heads is same as the probability of tails which is \(\frac{1}{2}\).

What is the probability?

The concept of probability is used to assign a numerical description to the likelihood of occurrence of an event.

Probability can be defined as the number of favorable outcomes divided by the total number of possible outcomes of an event.

Here given that,

The \(10\) tosses of a coin were all heads, and you switch to a new coin.

So, the probability of getting all heads is \(2^{-n}\)

And we have \(n=10\),

Then, the probability of getting the heads is

\((^{n}C_k)(\frac{1}{2})^k(\frac{1}{2})^{n-k}=2^{-n}(^nC_k)\)

Hence, the probability of getting heads is same as the probability of tails which is \(\frac{1}{2}\).

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Answer:

1988.8 lbs

Step-by-step explanation:

81.36 divided by 0.45 x 11

A table that best represent the equation include the following: H. table H.

In order to determine the table that best represent the equation, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;

When the value of x = 1 in table F, the linear function is given by;

y = x - 12

y = 1 - 12

y = -11 (False).

When the value of x = 0 in table G, the linear function is given by;

y = x - 12

y = 0 - 12

y = -12 (True).

When the value of x = 2 in table G, the linear function is given by;

y = x - 12

y = 2 - 12

y = -10 (False).

When the value of x = 0 in table H, the linear function is given by;

y = x - 12

y = 2 - 12

y = -10 (True).

When the value of x = 4 in table H, the linear function is given by;

y = x - 12

y = 4 - 12

y = -8 (True).

When the value of x = 6 in table H, the linear function is given by;

y = x - 12

y = 6 - 12

y = -6 (True).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

e will be the answer for sure of miles it happene d for the past hours he traveled in and how long

Answer:

The price for a 60-ounce bag of popcorn would be $16

Step-by-step explanation:

Answer:

The price for a 60-ounce bag of popcorn would be $16

Step-by-step explanation:

Function Modeling

The behavior of some parameters that depend on a set of variables can be modeled in several ways, like linear, quadratic, exponential, logarithmic, among many others.

The selection of the model is often a complex decision that involves statistics and data analysis.

The question provides us with four points where the volume of popcorn bags and the price in dollars. The easiest function that can be used is the line.

The equation of a line of the volume V and the price p can be found with the expression

We'll use the first two values (6,10) (8,20)

Simplifying and rearranging, we get the model

To test the accuracy of the model, we compute the values of p for V=35 and for V=48

Since the computed values are equal to those of the table, the model is accurate. We can now predict the price for V=60

The price for a 60-ounce bag of popcorn would be $16

The following can be determined about the slopes and y-intercepts of the system of equations: A. The slopes are different, and the y-intercepts are different.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, we have the following system of equations in standard form:

4x + 2y = −2

x − 3y = 24

By rewriting system of equations in slope-intercept form, we have:

y = -2x - 1  ⇒ m = -2, b = -1

y = x/3 - 8  ⇒ m = 1/3, b = -8

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Answer:

D

Step-by-step explanation:

A and D are both equidistant from the x- axis, that is

A is 3 units above the x- axis and D is 3 units below the x- axis

then the x- axis is the line of symmetry

Answer:\(10n^{2}\)+180

Step-by-step explanation:

Answer:

Exact Form:

4\3

Decimal Form:

1.3

Mixed Number Form:

1 1/3

\(2\frac{6}{9}\) - \(1\frac{3}{9}\) as a mixed number in its simplest form is  \(1\frac{1}{3}\).

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given:

The mixed numbers are \(2\frac{6}{9}\) and \(1\frac{3}{9}\).

Now, subtracting the numbers,

\(2\frac{6}{9}\) - \(1\frac{3}{9}\),

= 24/9 - 12/9

= 12/9

= 4/3

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

Therefore, the value is  \(1\frac{1}{3}\).

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The quotient of  10⁻⁴/10² is 10⁻⁶

Quotient is the result obtained by dividing one quantity by another. It represents the value that is obtained after division.

For example, if you divide 20 by 2, the quotient is 10 because 20 divided by 2 equals 10.

Division law states that:

10ᵃ / 10ᵇ = 10ᵃ⁻ᵇ

In this case have:

10⁻⁴/10² = 10⁻⁴⁻²   (Division law)

10⁻⁴/10² = 10⁻⁶

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The unit rate of computers per day using the graph is that 12 computers are made per day.

The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

So, it is given by:

\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)

\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)

\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)

\(\bold{Slope = 12}\)

Unit rate = 12 computers per day.

The attachment of the graph is given below.

Therefore, the unit rate of computers per day is 12.

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Answer:

(3x² - 6x + 11) - (10x² - 4x + 6) is equivalent to expression -7x² - 2x + 5

(-3x² - 5x - 3) - (-10x² - 7x + 2) is equivalent expression to 7x² + 2x - 5

(12x² + 6x - 5) - (5x² + 8x - 12) is equivalent expression to 7x² - 2x + 7

Step-by-step explanation:

✔️(3x² - 6x + 11) - (10x² - 4x + 6)

Open the bracket by applying the distributive property

3x² - 6x + 11 - 10x² + 4x - 6

Add like terms

-7x² - 2x + 5

Therefore:

(3x² - 6x + 11) - (10x² - 4x + 6) is equivalent to expression -7x² - 2x + 5

✔️(-3x² - 5x - 3) - (-10x² - 7x + 2)

Apply distributive property

-3x² - 5x - 3 + 10x² + 7x - 2

Add like terms

7x² + 2x - 5

Therefore:

(-3x² - 5x - 3) - (-10x² - 7x + 2) is equivalent expression to 7x² + 2x - 5

✔️(12x² + 6x - 5) - (5x² + 8x - 12)

12x² + 6x - 5 - 5x² - 8x + 12

Add like terms

7x² - 2x + 7

Therefore:

(12x² + 6x - 5) - (5x² + 8x - 12) is equivalent expression to 7x² - 2x + 7

-2b + 3 = b - 9

The value of b.

-2b - b = -9 - 3

or, -3b = -12

or, b = -12/-3

or, b = 4

The value of b is 4.

Answer:

b=4

Explanation:

1. Add 2b to each side:  3=3b-9

2. Add 9 to each side: 12=3b

3. Divide by 3: b=4

Answer:

you can make 12 cans of them

The Definition of the Derivative correctly stated by

In mathematics, a derivative is the rate at which a function changes in relation to a variable. Calculus and differential equations issues must be solved using derivatives.

As, we know by definition of derivative

= \(\lim_{h \to 0}\) f(x+h)- f(x) / h

Also, the Derivative also shows the Slope of the secant line.

and, derivative is widely used to the rate of change then it also shows

Instantaneous rate of change.

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Answer: g(f(x)) is equal to -18x² - 27x - 13.

Step-by-step explanation:

To find g(f(x)), we need to substitute f(x) into the expression for g(x).

First, we need to find f(x), which is given by:

f(x) = 3x + 2

Next, we can substitute f(x) into the expression for g(x), which is given by:

g(x) = -2x² - 3x + 5

So we replace x in g(x) with f(x), which gives:

g(f(x)) = -2f(x)² - 3f(x) + 5

= -2(3x + 2)² - 3(3x + 2) + 5       (Substituting f(x) = 3x + 2)

= -2(9x² + 12x + 4) - 9x - 1

= -18x² - 27x - 13

Therefore, g(f(x)) is equal to -18x² - 27x - 13.

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If 4/10 of Lake Okeechobee is covered in a harmful algal bloom in the first month, then 6/10 of the lake is not covered in the bloom.

In the second month, if 90% of the lake is covered in the bloom, then 10% of the lake is not covered in the bloom.

Since the amount of the lake that is covered by the bloom increased from 4/10 to 9/10, this is an increase of:

(9/10) / (4/10) = (9/10) x (10/4) = 2.25 times

Therefore, the algal bloom increased by 2.25 times.

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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12.985 rounded to 2 decimal places is 12.99

Answer:

Step-by-step explanation:

Step 1:

Identify the digit in the hundredths place, as it is the 2nd decimal place.  The 8 is the digit in the hundredths place.

Step 2:  

Look at the digit in the thousandths place and its value is 5 thousandths, so increase the digit in the hundredth's place to 9.

Step 3:

The new number is 12.99 rounded to the 2nd decimal place.

Answer:

sorry

Step-by-step explanation:

Answer:

A (top left)

Step-by-step explanation:

Assuming that the dot is multiplying the numbers, we get the function:

\(f(x) = 8^{x}\)

First, lets knock off the obviously wrong answers.

Substitute 0 into the x spot, as anything to the power of zero is one.

\(f(0) = 8^{0}=1\)

Automatically, the two answers on the right are incorrect, as y is not equal to 1 when x is 0.

Next, lets substitute 1 into the x spot, as anything to the power of one is itself.

\(f(1) = 8^{1} = 8\)

As a result, the top left graph is correct, as y is equal to 8 when x is 1, unlike the bottom left graph.

Answer:

  5/10

Step-by-step explanation:

An equivalent fraction will have the numerator and denominator multiplied by the same value.

The denominator of 2 must be multiplied by 5 to get a denominator of 10. Then the equivalent fraction is ...

  \(\dfrac{1}{2}=\dfrac{1}{2}\cdot\dfrac{5}{5}=\dfrac{1\cdot5}{2\cdot5}=\boxed{\dfrac{5}{10}}\)

Answer:

Step-by-step explanation:

Let's break down the expression step by step:

Nine raised to the power of 1/3:

9^(1/3) = ∛9 = 2.0801

Twenty-seven raised to the power of 1/2:

√27 = 5.1962

Two raised to the power of 1/6:

∛2 = 1.1225

Combining the previous results:

(2.0801 * 5.1962) / 1.1225

Three raised to the power of 1/3:

∛3 = 1.4422

Combining the final result:

(2.0801 * 5.1962) / 1.1225 * 1.4422

(2.0801 * 5.1962) / 1.1225 * 1.4422 ≈ 9.7085

Therefore, the value of the given expression is approximately 9.7085.

Step-by-step explanation:

to control fever a doctor recommend that a child should be given one mg of certain medicine for every 0. 07 kg body weight if the those is proportional to the body weight of the child then the quantity of medicine for a child of body weight to 24.92 kg

The Length of the rod is 3/5 meters.

The civil engineer wants to find the length of a rod that stretches for 1 meter and can be given by the function x=2y^(3/2).

To find the length of the rod, we need to integrate the function x=2y^(3/2) with respect to y. Integrating both sides of the equation,

we have:'int dx = int 2y^(3/2) evaluating the left-hand side gives x = 2/5 y^(5/2) + C, where C is the constant of integration. To find the value of C,

we use the given information that the rod stretches for 1 meter. At y = 0, x = 0 since the rod has no length when it is not stretched. At y = 1, x = 1 since the rod stretches for 1 meter.

Therefore, we have:1 = 2/5 (1)^(5/2) + C1 = 2/5 + CC = 3/5 Substituting C = 3/5 back into the equation for x,

we have:x = 2/5 y^(5/2) + 3/5

The length of the rod is given by the value of x when y = 1. Substituting y = 1,

we have:x = 2/5 (1)^(5/2) + 3/5 = 3/5

The length of the rod is 3/5 meters.

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Answer:

The backpack costs $42.40.

Step-by-step explanation:

Answer: $42.40 is the backpack cost

Step-by-step explanation:

Answer: I think its A im not sure tho

Step-by-step explanation:

Answer:

300 N right

Step-by-step explanation:

Happy Birthday!

2500-2200=300

the right side is pulling with 300N more force therefore 300N right is the correct answer

The general equation of the circle is :

Where r is the radius of the circle

And ( h , k ) is the center of the circle

Given the equation :

making the given equation like the general form :

So, by comparing the equations :

So, the center of the circle = ( h , k ) = ( -1 , 1 )

And the radius of the circle = r = 2