is x greater than less than or equal to 60

1. The equation to slope-intercept form is y = -2/3(x) + 490. The slope is -2/3 and the y-intercept is 490.

2. You should start at the y-intercept (0, 490) and move right by 3 units and downward by 2 units, and then connect the points.

3. The equation in function notation is f(x) = -2/3(x) + 490. The graph of the function is the rate of change with respect to the number of sandwich lunch sold.

4. A graph of the function with intercepts is shown below.

5. The graphs of the functions for the two months both have the same slope but different y-intercept and x-intercept.

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, a linear equation that models Sal's Sandwich Shop's profit is given by;

2x + 3y = 1,470

By subtracting 2x from both sides of the equation and dividing by 3, we have:

2x + 3y - 2x = 1,470 - 2x

y = -2/3(x) + 490

Therefore, the slope is -2/3 and the y-intercept is 490.

Part 2.

In order to graph the equation by using the slope-intercept method, you would start at the y-intercept (0, 490) and move right by 3 units and down by 2 units, and then connect the points.

Part 3.

Next, we would write the equation in function notation as follows;

f(x) = -2/3(x) + 490

where:

The graph represents the rate of change of the function with respect to the number of sandwich lunch sold.

Part 4.

In this context, we would use an online graphing calculator to plot the linear function as shown in the image attached below.

Part 5.

Assuming Sal's total profit on lunch specials for the next month is $1,593 and the profit amounts remain the same, a system of equations to model this situation is given by:

2x + 3y = 1593; y = -2/3(x) + 531.

2x + 3y = 1,470; y = -2/3(x) + 490.

In conclusion, we can logically deduce that the graphs of the functions for the two months both have the same slope but different y-intercept and x-intercept.

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Complete Question:

Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.

The logarithmic equation for 1/4 = 8⁻²/₃ is :

\(log_8(\frac{1}{4}) = \frac{-2}{3}\)

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   \(log_ax=N\)

where, a is the base of function or equation

           x define expression

Mathematically, if  is an exponential function is  \(a^N=x\) then, this can be converted to logarithmic function as  \(log_ax=N\)

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

According to statement,

1/4 = 8⁻²/₃

as , exponential function is  \(a^N=x\)  can be converted to logarithmic function as  \(log_ax=N\)

here, a = 8, N= -²/₃ , x = 1/4

therefore, logarithmic equation is :

\(log_8(\frac{1}{4}) = \frac{-2}{3}\)

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She should expect to have to invest in 1 company.

The probability of success for a single investment is p, and the probability of failure is 1-p. Assuming that each investment is independent of the others, the probability of success for n investments is p^n. Therefore, the expected number of investments before success is 1/p^n. For example, if the probability of success for each investment is 0.1 (10%), then the expected number of investments before success is 1/0.1^n=10^n. So if she expects to have one successful investment, she should expect to have to invest in 10^0=1 investment.

She should expect to have to invest in 1 company.

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If im right, A,E,C is 105 degrees and B,E,D is 90 degrees.

hope this helps

The given expression is

There are three terms in this expression

B. {(0, 3), (-6, 8), (-3, 5), (0, -3), (7, 11)} are the sets of ordered pairs which are the relation that is a function.

To determine whether a set of ordered pairs is a function, we need to determine whether each x-value corresponds to only one y-value. In other words, the x-values in the set should be unique and not repeated.   For the set A. {(2, 4), (2, 6), (2, 8), (2, 10), (2, 12)}, we can see that the x-value 2 is repeated multiple times, and thus, it is not a function.  For the set B. {(0, 3), (-6, 8), (-3, 5), (0, -3), (7, 11)}, each x-value is unique and thus, it is a function.   For the set C. {(8, 1), (-4, 1), (3, 5), (0, 4), (-1, 2)}, we can see that the y-value 1 is repeated twice, and thus, it is not a function.  For the set D. {(-5, -4), (-4, -3), (-3, -2), (-4, -5), (-2, -1)}, each x-value is unique and thus, it is a function.  Therefore, the answer is B. {(0, 3), (-6, 8), (-3, 5), (0, -3), (7, 11)}.

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Answer:5.50 a hour

Step-by-step explanation:

Therefore, the expression equivalent to the given expression \(\sqrt x+11=15\) is \(x=16\).

The given expression is,

\(\sqrt x+11=15\)

It is required to solve the given expression.

Firstly, solve for the constant terms and then take square of both sides of the equation.

The given equation can be solved as,

\(\sqrt x+11=15\\ \sqrt x=4\\ x=4^2\\ x=16\)

Therefore, the expression equivalent to the given expression \(\sqrt x+11=15\) is \(x=16\).

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The equation is equivalent to the given equation is \(\sqrt{x} =15-11\).

Equation; \(\rm \sqrt{x} +11 =15\)

Which equation is equivalent to the given equation?

To determine the equation is equivalent to the given equation following all the steps given below.

Equation; \(\rm \sqrt{x} +11 =15\)

Then,

Subtracting 11 from both sides.

\(\rm \sqrt{x} +11 =15\\\\\rm \sqrt{x} +11-11 =15-11\\\\\rm \sqrt{x} =15-11\)

Hence, the equation is equivalent to the given equation is \(\sqrt{x} =15-11\).

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The answer of the given question based on the circle the answer is given as AC ≈ 39.6.

Radius is  straight line segment that joins the center of circle to any point on its circumference. It is also equal to half  diameter of  circle.

Since AB is tangent to circle E at point A, we know that ∠EAB = 90 degrees, and thus triangle AEB is a right triangle.

Let x be the length of AC. Then, AE = x/2 (since AE is the radius of circle E), and EB = AB - AE = x/2 - x = -x/2.

By the Pythagorean theorem applied to triangle AEB, we have:

AB² = AE² + EB²

28² = (x/2)² + (-x/2)²

784 = x²/4 + x²/4

784 = x²/2

x² = 1568

x ≈ 39.6

Therefore, AC ≈ 39.6.

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Thus, the solution of the expression after adding the like term is found as: \(= \frac{-7}{8}y^{2} + 3\\\).

Once kids have a firm grasp on right fractions, they are exposed to mixed numbers including improper fractions.

Given expression:

\(= \frac{5}{8}y^{2} - 1\frac{1}{2}y^{2} + 3\)

Solving the mixed fraction 1 1/2 = (2*1 + 1)/2 = 3/2

\(= \frac{5}{8}y^{2} - \frac{3}{2}y^{2} + 3\)

Since the degree of the variable 'y' is same in 1st two terms.

Thus, adding the coefficients with sign

\(= \frac{5 - (3*4)}{8}y^{2} + 3\\\)

\(= \frac{-7}{8}y^{2} + 3\\\)

Thus, the solution of the expression after adding the like term is found as: \(= \frac{-7}{8}y^{2} + 3\\\).

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Answer:4

Step-by-step explanation:22-4=18-4=14-4=10-4=6=2

Answer:

Step-by-step explanation:

Answer for seconds in second row:

Answer for glasses in third row:

I hope this helps!

The expanded form of the given logarithms ( log 4 s⁴ t) is =  2log(2) + 4log(s)  + log(t).

The features of the log are used to increase a single logarithm into numerous logarithms (or) compression multiple logarithms together into a single logarithm. A logarithm is simply another way of writing exponents. Thus, logarithm properties are obtained from exponent properties.

log (4 s⁴ t)

can be written as log (4 s⁴ t):

Property used in the solving (log b*c = log b  + log c) and (log ₐᵇ = b log a)

log (4 s⁴) + log( t)

log (4 ) + log(s⁴) + log( t)

Expand log (s⁴) by moving 4 outside the log.

log (4 ) + log(s) + log( t)

The expression also can be written as :

2log(2) + 4log(s)  + log(t)

The expanded form of the given logarithms ( log 4 s⁴ t) is =  2log(2) + 4log(s)  + log(t).

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1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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Answer:

4/9 miles

Step-by-step explanation:

                 \(\sf Area = \dfrac{2}{3} \ square \ miles\\\)

               \(\sf length = 1\dfrac{1}{2}=\dfrac{3}{2} \ miles\)

\(\sf Width \ of \ rectangle = \dfrac{Area}{length}\)

                             \(\sf = \dfrac{2}{3} \div \ \dfrac{3}{2}\\\\ =\dfrac{2}{3}*\dfrac{2}{3}\\\\ =\dfrac{4}{9} \ miles\\\)

Use KCF method for faction division.

K- Keep the first fraction.

C - Change the division to multiplication.

F - Flip the second fraction.

Answer:

a. 7(x+2)

b. 9(x-3)

c. 5(2y-5)

d. 4(2n+7)

e. -3(x+9)

f. -6(x-5)

Step-by-step explanation:

hope this helped <3

Answer:

a. 7(x + 2)

b. 9(x - 3)

c. 5(2y - 5)

d. 2(4n + 7)

e. -3(x + 9)

f. 6(-x + 5)

Step-by-step explanation:

Use distribution for all questions

a. Factor by 7, the greatest common factor.

7x + 14 = 7(x + 2)

b. Factor by 9

9x - 27 = 9(x - 3)

c. Factor by 5

10y - 25 = 5(2y - 5)

d. Factor by 4

8n + 28 = 2(4n + 7)

e. Factor by -3

-3x - 27 = -3(x + 9)

f. Factor by 6

-6x + 30 = 6(-x + 5)

Hope this helps!!

Please mark me brainliest if it is correct :)

clark is faster

Step-by-step explanation:

Answer:

Clark is faster

Step-by-step explanation:

Answer:

Scenario 1 represents a greater speed

Step-by-step explanation:

scenario 1 - find equation of line on graph to compare

- use the points given to find the slope

rate = slope = (y2-y1)/(x2-x1) = (240-60)/(4-1) = 60

y intercept = 0

line equation -> y = 60x

for every mile, 60 miles are traveled

scenario 2 - interpret the equation

for every mile, 50 miles are traveled

Scenario 1 represents a greater speed

Answer:

Hermana

Step-by-step explanation:

Answer:

3:30

Step-by-step explanation:

The equation of the tangent line to the graph of f(x) at the point (1,6) is y = 3x + 3.

To find the equation of the tangent line, we need to determine the slope of the tangent line and the point of tangency.

First, we find the derivative of f(x) using the power rule. The derivative of √(12x+24) with respect to x is (1/2)(12x+24)^(-1/2) * 12, which simplifies to 6/(√(12x+24)).

Next, we evaluate the derivative at x=1 to find the slope of the tangent line at the point (1,6). Plugging in x=1 into the derivative, we get 6/(√(12+24)) = 6/6 = 1.

So, the slope of the tangent line is 1.

Using the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the point of tangency, we substitute (1,6) and the slope of 1 to obtain the equation of the tangent line as y = 1(x-1) + 6, which simplifies to y = x + 5.

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Answer:

0.03%

Step-by-step explanation:

Answer:

it would be -3x-6

Step-by-step explanation:

if you distribute right you will change the two and the positive change into a negative and the last one x is not by itself plus it only change to one

To solve the given inequality, first we have to simplify the given inequality.38 < x + 10 After simplification we get, 38 - 10 < x or 28 < x.

The correct option is B.

The given inequality is 38 < 4x + 3 + 7 - 3x. Simplify the inequality38 < x + 10  - 4x + 3 + 7 - 3x38 < -x + 20 Combine the like terms on the right side and simplify 38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18. The given inequality is 38 < 4x + 3 + 7 - 3x. To solve the given inequality, we will simplify the given inequality.

Simplify the inequality38 < x + 10  - 4x + 3 + 7 - 3x38 < -x + 20 Combine the like terms on the right side and simplify 38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18. Combine the like terms on the right side and simplify38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18.So, the answer is  x > 28. In other words, 28 is less than x and x is greater than 28. Hence, the answer is x > 28.

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Answer: .416666667

Step-by-step explanation: Take 80 and divide it by 192.0= .416666667

The volume of the shaded region is 553.15m³.

A cylinder is a three-dimensional object. It is made up of a prism with a circular base.

Volume of a cylinder = πr²h

Where:

The volume of the shaded region is the volume of the cylinder less the volume of the unshaded region.

Volume of the whole cylinder = 22/7 x 5² x 11 =  864.29 m³

Radius = diameter / 2 = 10 / 2 = 5

Volume of the unshaded region = 22/7 x 3² x 11 = 311.14m³

Radius = diameter / 2 = 6/2 = 3

The volume of the shaded region =  864.29 in³ -  311.14in³ = 553.15m³

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Answer:

8

Step-by-step explanation:

sin35=opp/hyp

opp=sin35(14)=8.03 close to 8

The length h for the given triangle is h units.

The trigonometric ratios are defined for a right angled triangle.

The example of these ratios are sin, cos, tan, cosec, sec and cot.

The trigonometric ratios are useful in determining the heights and distances of the large objects.

The given triangle is a right triangle.

Apply trigonometric ratio to find the length h of the triangle as follows,

Sin 35° = h/14

⇒ 0.573 = h/14

⇒ h = 8.02

It can be approximated as 8.

Hence, the required length is obtained as 8 units.

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Answer:

6

Step-by-step explanation: