Which of these is a simplified form of the equation 8y + 4 = 6 + 2y + 1y?
5y = 2
5y = 10
11y = 2
11y = 10

[tex] \text{Consider the quadratic function}\\ \\ f(x)=-5x^2-2\\ \\ \text{For a quadratic equation, }f(x)=ax^2+bx+c, \text{ we know that the x-coordinate}\\ \text{of the vertex (h,k) is given by}\\ \\ h=\frac{-b}{2a}\\ \\ \text{on comparing the given equation with standard equation, we have} [/tex]

[tex] a=-5, b=0, c=-2\\ \\ \text{so the x-coordinate of the vertex is }\\ \\ h=-\frac{b}{2a}=-\frac{0}{2(-5)}=0\\ \\ \text{so plug this vlaue of the h in the given function to get the y-coordinate}\\ \text{of the vertex. so}\\ \\ f(x)=-5(0)^2-2=0-2=-2\\ \\ \text{hence the vertex of the parabola is: }(h,k)=(0,\ -2)\\ \\ \text{A second point on the graph can be found by putting x=1, so }\\ \\ f(1)=-5(1)^2-2=-5-2=-7\\ \\ \text{so one other point on the parabola is }(1,-7) [/tex]

The grpah of the quadratic function is shown below:

Answer:(0,-2) (1,-7)

Step-by-step explanation:

Answer:

b.) The graph's x-intercepts are similar to ½(x - 5)(x + 2).

a.) [-2, 0], [5, 0]

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b.) The graph has a maximum value because the graph opens down [-2 = A].

a.) [-3, -4]

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d) [0, -5]

c) -2 = x

b) [-2, -9] → [h, k]

a) -1, 5 = x

Explanation:

b) Both graphs have the binomial of [x - 5][x + 2], so the x-intercepts never altered.

a) Set the binomial equal to zero, and you will get your x-intercepts of [-2, 0] and [5, 0].

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b) When A is negative, your graph will have a maximum value [opens down], whereas when A is positive, your graph will have a minimum value [opens up].

a) According to the Vertex Formula, y = A[X - H]² + K, [H, K] represents the vertex, plus, -H gives you the OPPOSITE TERMS OF WHAT THEY REALLY ARE, so be EXTREMELY CAREFUL labeling your vertex. Additionally, K gives you the NORMAL TERMS.

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d) The y-intercept is your C-term, so in this case, it is [0, -5].

c) To find the axis of symmetry, use this formula:

[tex] \frac{-b}{2a} = x[/tex]

Whatever the opposite of your B-term is, you take that and divide it by twice your A-term.

b) To find the vertex, in this case, you have to go from Standard Form to Vertex Form by completing the square, using this formula to get part of your new C-term:

[tex][\frac{b}{2}]^{2} [/tex]

When done, you get this:

[tex]y = {x}^{2} + 4x + 4 \\ \\ y = [x + 2]^{2} [/tex]

Then, you have to deduct some number from 4 that gave you -5 in the first place, and that integer is -9. So, here is the result:

[tex]y = [x + 2]^{2} - 9[/tex]

From here, we can see that our vertex is [-2, -9].

a) When the binomial is set to equal to zero, you get this:

[tex]{x}^{2} + 4x - 5 \\ \\ [x - 1][x + 5] = 0 \\ \\ 1, \: -5 = x[/tex]

e) See above photograph

I am joyous to assist you anytime.

Answer:

30 is your answer

Step-by-step explanation:

Answer:

Oliver and Peter both uses same length string.

Explanation:

Suppose length of rope or string = x meters

Oliver divide his rope into four equal parts

[tex] \frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4} [/tex]

Each part length is [tex] \frac{1}{4} [/tex]

NOw Oliver used 3 part of the string out of four parts

that means total used string is 3/4

Now peter also have same length of string = x meter

He divides the string eight equal parts and use the 6 parts out of 8

each part length is :[tex] \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} , \frac{x}{8} [/tex]

Use 6x/8

simplify the fraction 6x/8

divide by 2 both numerator and denominator

6x/8 = 3x / 4

So both uses same part of string.

Answer:

1130.973355 is the answer

Step-by-step explanation:

pi10(10+sqrrt((24^2)+(10^2)))

31.416(10+sqrrt(576+100))

31.416(10+sqrrt(676))

31.416(10+26)

31.416(36)

1130.976

Answer:

Write a proportion using the ratios. Find the cross products. If the cross products are equal, then the ratios form a proportion.

Step-by-step explanation:

Answer:

Second graph

Step-by-step explanation:

Given inequality,

x - y - 2 ≥ 0

⇒ x - y ≥ 2

The related equation of the inequality,

x - y = 2

Having x-intercept = (2, 0)

y-intercept = (0,-2),

Also, 0 - 0 ≥ 2 ( False )

Thus, the inequality will not contain the origin,

Again,

'≥' shows the solid line.

Hence, by the above explanation it is clear that the SECOND graph would be the graph of given inequality.

Answer:

The Algebraic expression that correctly represents the phrase 'the difference between 7 and a number squared' is

= 7 - x²

Step-by-step explanation:

Let's represent the unknown number be represented as x

The unknown number is also squared = x²

Therefore, the Algebraic Equation correctly representing the phrase 'difference of 7 and a number squared' is

= 7 - x²

Answer:

13.0

Step-by-step explanation:

Answer:

3000

Step-by-step explanation:

75% of 4000 students

The required, there were 25 chickens and 12 pigs on Old MacDonald's farm.

To solve this problem, we can use a system of equations to represent the number of chickens and pigs on Old MacDonald's farm. Let x be the number of chickens and y be the number of pigs. Then we have:

x + y = 37 (equation 1)

2x + 4y = 98 (equation 2)

Equation 1 represents the total number of animals, and Equation 2 represents the total number of legs. We can simplify equation 2 by dividing both sides by 2:

x + 2y = 49 (equation 3)

Now we have two equations with two variables. We can solve for x and y by using substitution or elimination. Let's use elimination by multiplying equation 1 by 2 and subtracting it from equation 3:

x + 2y = 49

-2x - 2y = -74

x = -25

Solving for x, we get:

x = 25

Substituting x = 25 into equation 1, we get:

25 + y = 37

Solving for y, we get:

y = 12

Therefore, there were 25 chickens and 12 pigs on Old MacDonald's farm.

Learn more about solutions of equations here:

https://brainly.com/question/24553498

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The equations are c + p = 37 and 2c + 4p = 98. Solving the system of equations the numbers are 26 and 11, respectively.

To solve this problem, we can use a system of equations.

Let's assume that the number of chickens is represented by 'c' and the number of pigs is represented by 'p'. Based on the given information, we can create two equations:

1. c + p = 37 (equation 1)

2. 2c + 4p = 98 (equation 2)

We have two equations with two variables, so we can solve this system of equations to find the values of 'c' and 'p'.

Using equation 1, we can express 'c' in terms of 'p': c = 37 - p.

Substituting this into equation 2, we get: 2(37 - p) + 4p = 98. Solving this equation, we find: p = 11.

Substituting the value of 'p' back into equation 1, we find: c = 26.

Therefore, Old MacDonald had 26 chickens and 11 pigs on his farm.

Answer:

Step-by-step explanation:

The problem is about a circular sector, where the angle is 270° and the lenght of the subtended arc is the arc is the unknown variable.

The radius of the drive wheel is

[tex]r=\frac{d}{2}=\frac{14}{2}=7ft[/tex]

The central angle is 270°.

The length of the arc is

[tex]L=\frac{2\pi r \theta}{360\°}[/tex]

Replacing all values, we have

[tex]L=\frac{2(3.14)(7)(270\°)}{360\°}=\frac{11869.2}{360} \approx 32.97[/tex]

Thereofre, the length of the cable is around 32.97 feet.

The average sale per customer for Carla is $4.50.

To find Carla's average sale per customer, we need to determine the total revenue and the total number of customers.

The average sale per customer is calculated by dividing the total revenue by the total number of customers.

Given:

- Total revenue for the month: $4,500

- Total number of customers for the month: 1,000

The average sale per customer is calculated as:

[tex]\[ \text{Average sale per customer} = \frac{{\text{Total revenue}}}{{\text{Total number of customers}}}. \][/tex]

Plugging in the given values:

[tex]\[ \text{Average sale per customer} = \frac{{4,500}}{{1,000}} = 4.5. \][/tex]

Thus, the average sale per customer for Carla is $4.50.  

Question :

Carla sells hot coffee, cider and tea from a sidewalk cart near wall street in new york city. last month she sold $4,500 worth of product to 1,000 customers. she spent $800 on buying her beverages in bulk. her monthly costs are: utilities = $100, salary = $2,000, advertising = $0, insurance = $0, interest = $0, rent (cart) = $600, depreciation = $0. calculate carla's average sale per customer.

Answer:

c is the answer

Step-by-step explanation:

The inequality [tex]\(-6x \geq 30\)[/tex] is equivalent to [tex]\(x \leq -5\)[/tex]. Therefore, the correct answer is option d: [tex]\(x \leq -5\)[/tex].

To solve the inequality [tex]\(-6x \geq 30\)[/tex] and find its equivalent form, follow these steps:

1. Write down the original inequality:

  [tex]\[ -6x \geq 30 \][/tex]

2. Isolate [tex]\(x\)[/tex] by dividing both sides of the inequality by [tex]\(-6\)[/tex]:

  - Note that when dividing both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.

  [tex]\[ \frac{-6x}{-6} \leq \frac{30}{-6} \][/tex]

3. Simplify both sides:

  [tex]\[ x \leq -5 \][/tex]

So, the equivalent inequality to [tex]\(-6x \geq 30\)[/tex] is [tex]\(x \leq -5\)[/tex].

Therefore, the correct answer is:

[tex]\[\boxed{\text{d: } x \leq -5}\][/tex]

Answer:

The correct answer would be:

Step-by-step explanation:

150-shirts

75-jeans