What is this equation in slope-intercept form? -3x-2y=30

To find the number of computers given the ratio of computers to desks and the number of desks, set up a proportion and solve for the unknown value.

In this question, we are given the ratio of computers to desks, which is 2 to 3. We are also given the number of desks, which is 15. To find the number of computers, we can set up a proportion:

2 computers / 3 desks = x computers / 15 desks

By cross-multiplying and solving for x, we find that there are 10 computers.

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case a) [tex]c+7 \leq 3[/tex]

[tex]c+7 \leq 3\\ c\leq3-7\\c\leq -4[/tex]

the solution is the interval-------> (-∞,-4]

the answer case a) in the attached figure

case b) [tex]c-3 > 1[/tex]

[tex]c-3 > 1\\c > 1+3\\c> 4[/tex]

the solution is the interval-------> (4,∞)

the answer case b) in the attached figure

case c) [tex]c-7< 3[/tex]

[tex]c-7< 3\\ c<3+7\\ c< 10[/tex]

the solution is the interval-------> (-∞,10)

the answer case c) in the attached figure

Inequalities are used to represent unequal expressions.

[tex]\mathbf{(a)\ c + 7 \le 3}[/tex]

Subtract 7 from both sides

[tex]\mathbf{c \le -4}[/tex]

The above means that:

Hence, graph (b) represents [tex]\mathbf{c + 7 \le 3}[/tex]

[tex]\mathbf{(b)\ c - 3 > 1}[/tex]

Add 1 to both sides

[tex]\mathbf{c > 4}[/tex]

The above means that:

Hence, graph (c) represents [tex]\mathbf{c - 3 > 1}[/tex]

[tex]\mathbf{(c)\ c - 7 < 3}[/tex]

Add 7 to both sides

[tex]\mathbf{c < 10}[/tex]

The above means that:

Hence, graph (a) represents [tex]\mathbf{c - 7 < 3}[/tex]

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Let

[tex]f(x)=x^{2}-1[/tex]

[tex]g(x)=x+1[/tex]

we know that

The function f(x) is a vertical parabola open upward

the vertex is the point [tex](0,-1)[/tex] ------> is a minimum

The function g(x) is a linear equation

The y-intercept is the point [tex](0,1)[/tex] -----> for [tex]x=0[/tex] find the value of g(x)

therefore

the answer in the attached figure

The graph that can be used to find the solution of the given polynomial is given by option C) and this can be determined by using the given data.

Given :

Equation  --- [tex]x^2 -1 = x+1[/tex]

The following steps can be used in order to determine the graph that can be used to find the solution of the given polynomial:

Step 1 - Separate LHS and RHS of the given polynomial.

[tex]\rm y = x^2-1[/tex]   --- (1)

y = x + 1   --- (2)

Step 2 - Draw the graph of a line (y = x + 1) that passes through the points (-1,0) and (0,1).

Step 3 - Now, draw the graph of the equation (1). The shape of this graph is the upward parabola.

Step 4 - The two graphs intersect each other at (-1,0) and (2,3).

From the above steps, it can be concluded that the correct option is C).

For more information, refer to the link given below:

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38 pizzas times 8 slices each =

38 *8 = 304 slices total

Answer: c: 60

Step-by-step explanation:

i did the test

To solve this question:

Doing this, we get that the system is, with the 3 equations:

[tex]9a^2 + 3b + c = 8[/tex]

[tex]75a + 15b + 3c = 20[/tex]

[tex]36a + 6b + c = 5[/tex]

Equation of a parabola:

A parabola is a second degree polynomial, having an standard equation of:

[tex]y = ax^2 + bx + c, a \neq 0[/tex]

Point (3,8)

This means that when [tex]x = 3, y = 8[/tex]. So

[tex]y = ax^2 + bx + c, a \neq 0[/tex]

[tex]8 = a\times3^2 + 3b + c[/tex]

[tex]9a^2 + 3b + c = 8[/tex]

Thus, [tex]9a^2 + 3b + c = 8[/tex] is the first equation.

(5,20/3)

This means that when [tex]x = 5, y = \frac{20}{3}[/tex]. Thus

[tex]y = ax^2 + bx + c, a \neq 0[/tex]

[tex]\frac{20}{3} = a\times5^2 + 5b + c[/tex]

[tex]25a + 5b + c = \frac{20}{3}[/tex]

[tex]75a + 15b + 3c = 20[/tex]

Thus, [tex]75a + 15b + 3c = 20[/tex] is the second equation.

(6,5)

This means that when [tex]x = 6, y = 5[/tex]. Thus

[tex]y = ax^2 + bx + c, a \neq 0[/tex]

[tex]5 = a\times6^2 + 6b + c[/tex]

[tex]36a + 6b + c = 5[/tex]

Thus, [tex]36a + 6b + c = 5[/tex] is the third equation.

After all, the system of equations is:

[tex]9a^2 + 3b + c = 8[/tex]

[tex]75a + 15b + 3c = 20[/tex]

[tex]36a + 6b + c = 5[/tex]

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The student must make monthly payments of $1,020.63 to repay the $3,000 loan with $61.88 in interest over 3 months.

The student has borrowed $3,000 for 3 months and the interest incurred on this loan is $61.88. To find the monthly payment, we need to add the total interest to the principal borrowed and then divide it by the number of payments (which is 3 in this case).

The total repayment amount is calculated as $3,000 principal + $61.88 interest = $3,061.88.

Now, we divide the total repayment amount by the number of monthly payments:

Monthly Payment = Total Repayment Amount / Number of Payments

Monthly Payment = $3,061.88 / 3

Monthly Payment = $1,020.63

Therefore, the student will need to make monthly payments of $1,020.63 to repay the $3,000 loan over 3 months.

Answer:

103.8

Step-by-step explanation:

calculator

Answer:  

Step-by-step explanation:

the arrows on the end of the line means it continues

 both the domain and the range for this graph is negative infinity to infinity

Answer: 141.75

Step-by-step explanation: Yw future edge users

Final answer:

Using the Triangle Inequality Theorem and given a perimeter of 20 units for a triangle with integer side lengths, the maximum length of one side is found to be 15 units.

Explanation:

To determine the maximum length of one side of a triangle with integer side lengths and a perimeter of 20 units, we must apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Given a perimeter of 20 units, if we denote the longest side as x, and the other two sides as y and z, we must satisfy two conditions:

x + y + z = 20 (perimeter condition)

x < y + z (Triangle Inequality Theorem)

Since the triangle has different integer side lengths, the largest x can be is when y and z are consecutive integers because this allows for the largest possible x. If we try the smallest integers, 1 and 2, for y and z, their sum is 3. To satisfy the triangle inequality, the largest possible integer for x would be 20 - 1 - 2 = 17. However, this does not satisfy the inequality x < y + z, because 17 is not less than 3.

Next, we increase y and z to 2 and 3, respectively, which sums up to 5. Thus, for x, we have 20 - 2 - 3 = 15. Since 15 is less than 2 + 3, it satisfies the condition required by the Triangle Inequality Theorem. Therefore, the maximum length of any one side of the triangle is 15 units.

Emma should have used division to represent the quotient of six and x, and she should have used parentheses to show that -2 is multiplied by (4.5 - x). Hence the correct options are 1 and 5.

Emma made two errors in translating the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." First, instead of representing the quotient of six and x, she incorrectly wrote 6x, which implies multiplication rather than division. The correct representation should be 6/x.

Second, Emma failed to use parentheses to show that -2 is multiplied by the difference of x and 4.5. The correct expression should be -2(x - 4.5) to ensure proper order of operations. These errors impact the accuracy of the translated equation, and correcting them would yield a more faithful representation of the original statement. Hence the correct options are 1 and 5.

Complete question:

Emma read the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." She translated it as shown below 6x=-2x-4.5 What errors did Emma make? Select two options

She should have used division to represent the quotient of six and x.

She should not have included an equal sign.

She should have used parentheses to show that -2 is multiplied by (x-4.5).

She should have subtracted the difference (x-4.5) from -2.

She should have used parentheses to show that -2 is multiplied by (4.5-x).

Emma made the following errors in her translation:

E. She should have used parentheses to show that -2 is multiplied by (x-4.5). Emma’s equation, 6x = -2x - 4.5, lacks parentheses around the expression (x-4.5). To correctly represent the difference of x and 4.5 being multiplied by -2, she should have written -2(x-4.5).

D. She should have subtracted the difference (x-4.5) from -2. Emma’s equation does not correctly account for the subtraction of the difference (x-4.5) from -2. The correct equation should be 6x = -2(x-4.5).

The other options are not relevant to Emma’s specific errors in translating the statement.

Emma made the following errors in her translation:

E. She should have used parentheses to show that -2 is multiplied by (x-4.5). Emma’s equation,

6x = -2x - 4.5, lacks parentheses around the expression

(x-4.5). To correctly represent the difference of x and 4.5 being multiplied by -2

, she should have written

-2(x-4.5)

.D. She should have subtracted the difference(x-4.5) from -2

. Emma’s equation does not correctly account for the subtraction of the difference

(x-4.5)

from

-2

The correct equation should be

6x = -2(x-4.5)

Complete question:

Emma read the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." She translated it as shown below 6x=-2x-4.5 What errors did Emma make? Select two options

A. She should have used division to represent the quotient of six and x.

B. She should not have included an equal sign.

C. She should have used parentheses to show that -2 is multiplied by (x-4.5).

D. She should have subtracted the difference (x-4.5) from -2.

E. She should have used parentheses to show that -2 is multiplied by (4.5-x).