Solve 2x2 + x − 4 = 0. x2 + x + = 0

Final answer:

The inequality to represent the number of days, d, Kyle can rent equipment with $121 is 25 + 13d ≤ 121. After solving, the result is d ≤ 7, meaning Kyle can rent the equipment for at most 7 days.

Explanation:

To represent the number of days, d, that Kyle can rent equipment given he has $121, we set up an inequality taking into account the flat rate and the daily insurance cost. The equipment rental company charges a flat rate of $25 plus $13 per day for insurance. Therefore, the cost for d days would be $25 + $13d. Since Kyle has $121, we can write the inequality as:

25 + 13d ≤ 121.

This inequality shows that the total cost of renting the equipment for d days, which includes the flat rate and the per-day insurance cost, must be less than or equal to the amount Kyle has.

To solve for d, subtract 25 from both sides:

13d ≤ 121 - 25

13d ≤ 96

Now, divide both sides by 13 to find the maximum number of days Kyle can rent the equipment:

d ≤ 96 / 13

d ≤ 7

Thus, Kyle can rent the equipment for at most 7 days.

Kyle can rent equipment for at most 7 days with $121, considering a flat rate of $25 and a $13 per day insurance charge, as represented by the inequality 25 + 13d ≤ 121.

To find the inequality that represents the number of days, d, for which Kyle can rent equipment given that he has $121, we need to consider both the flat rate and the per day insurance charge.

The flat rate for renting equipment is $25, and the daily insurance charge is $13 per day. So, the cost for d days would be the flat rate plus the daily charge times the number of days, which can be represented by the following equation:

Cost = Flat rate + (Insurance charge per day × Number of days)

Cost = 25 + 13d

Since Kyle only has $121, he can spend up to that amount. Therefore, the inequality would be:

25 + 13d ≤ 121

To solve for d:

13d ≤ 121 - 25

13d ≤ 96

d ≤ 96/13

≤ 7.38

Since Kyle can't rent equipment for a fraction of a day, we take the whole number part of the division result. This means that Kyle can rent the equipment for at most 7 days.

The value of the sample median is 172.

The value of the sample mean is 169.4.

The value of the sample variance is 52.3

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

The heights in centimeters of 5 students are: 165, 175, 176, 159, 172

Now,

Arrange the heights in order.

159, 165, 172, 175, 176

Median = 172

Mean = (159 + 165 + 172 + 175 + 176) / 5 = 847 / 5 = 169.4

Sample variance.

= ∑ (x - Mean)² / (n - 1)

= 209.2 / 4

= 52.3

∑ (x - Mean)²

= (159 - 169.4)² + (165 - 169.4)² + (172 - 169.4)² + (175 - 169.4)² + (176 - 169.4)²

= 108.16 + 19.36 + 6.76 + 31.36 + 43.56

= 209.2

Thus,

The sample mean = 169.4

The sample median = 172

The sample variance = 52.3  

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b.)x³-7x²+3x+36

(x-4)(x²-3x-9)

Distribute x and -4 to x²-3x-9

=x²(x)-3x(x)-9(x)+x²(-4)-3x(-4)-9(-4)

=x³-3x²-9x-4x²+12x+36

Combine all liked terms

=x³-7x²+3x+36

Answer:

d. -8

Step-by-step explanation:

Remember that you cannot possibly divide anything by 0, so if the denominator gives as a result 0, you are dealing with an impossibility, in order for a franction to give as a result 0, the numerator has to be 0, so we just need to equalize the numerator to 0 and solve for x to know how can we make the rational expression 0:

2x+16=0

2x=-16

x=-16/2

x=-8

So in order to make the expression equal to 0 x needs to be equal to -8,

To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100. 43% can be written as the ratio 43 to 100 or 43/100.

Therefore, 43% can be written as the fraction 43/100.

The three consecutive odd integers such that the sum of the smallest and 7 times the largest is 68 are: Integers 5, 7 and 9.

Let;

The question however suggests that;

The sum of the smallest number and 7 times the largest number is 68.

Therefore;

In essence,

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Answer:

its (A)

Step-by-step explanation:

Final answer:

The length of the third side of a triangle with side lengths of 8 and 13 must be greater than 5 units and less than 21 units according to the triangle inequality theorem.

Explanation:

To find the range for the length of the third side of a triangle given two sides with lengths of 8 and 13, we can use the triangle inequality theorem.

This theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides and greater than the absolute value of their difference.

The inequalities for the third side, let's call it c, are:

Therefore, we can say:

So the length of the third side must be greater than 5 units and less than 21 units.

Answer:

Step-by-step explanation:

As in any "solve for ..." problem, you reverse (undo) the operations done to the variable of interest. Generally, you do that in reverse order.

1. y is divided by z then the quotient added to x. To solve for y, we subtract x, then multiply by z.

... w - x = y/z . . . . . . . subtract x from the given equation

... z(w -x) = y . . . . . . . multiply by z

___

2. To solve for z, it is more convenient to start with the equation for y that is the result of the first question. We divide that by the coefficient of z.

... z = y/(w -x)

From w=x+y/z, the value of y = z(w - x)

w=x+y/z

This is changing the subject formula. The first thing to do is to subtract x from both sides. This will be:

w - x = x + y/z - x

w - x = y/z

Then, we cross multiply

z(w - x) = y

Therefore, y = z(w - x)

Since y = z(w - x)

Then, to get the value of z goes thus:

z = y/(w - x)

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The solution is, the graph of f(x) is vertically stretched by a factor of 3 and shifted 7 units down, as f(x) = x changes to h(x) = 3x² - 7.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

here, we have,

Given that,

here is a graph of f(x) = x which is transformed into h(x) = 3x² - 7.

The graph of a the equation -

f(x) = x

is a straight line.

now, we get, When it is squared and multiplied by 3, we get -

h(x) = 3x²

which is a parabola stretched by a factor of 3 in vertical direction along    

+ y axis.

When 7 is subtracted, it will shift the graph down by 7 units.

h(x) = 3x² - 7

Therefore, the graph of f(x) is vertically stretched by a factor of 3 and shifted 7 units down, as f(x) = x changes to h(x) = 3x² - 7.

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Complete question:

What is the effect on the graph of f(x) = x when it is transformed to

h(x) = 3x2 - 7?

A. The graph of f(x) is vertically stretched by a factor of 3 and shifted

7 units down.

B. The graph of f(x) is horizontally compressed by a factor of 3 and

shifted 7 units to the right.

C. The graph of f(x) is horizontally stretched by a factor of 3 and

shifted 7 units down.

D. The graph of f(x) is vertically stretched by a factor of 3 and shifted

7 units to the right

Answer: old selling priceof businesss math text rose = $138.89

Explanation:

In year 2015, Price of business math text rose = $150

Suppose privious price (year 2014)= x dollars

Previous price is 8% less than the price in 2015 because given that $150 is 8% more than previous year price.

Now write the linear equation for the given information:

x + 8% of x = 150

Solve for x

x + [tex] \frac{8}{100} [/tex]x = 150

x + 0.08x = 150

1.08x = 150

divide 1.08 both the side

x = [tex] \frac{150}{1.08} [/tex]

x = $138.89

Old selling price = $138.89

The sequence 1/4, 1/2, 3/4 increases by 1/4 for each subsequent term, defining it as an arithmetic sequence with a common difference of 1/4.

To find a rule for the sequence 1/4, 1/2, 3/4, we can examine the pattern and observe that the sequence consists of fractions that increase by 1/4 each step. Starting with 1/4, when we add 1/4, we get 1/2, and adding another 1/4 to 1/2 gives us 3/4. So the rule of the sequence can be written as 'start at 1/4 and add 1/4 each step'. This pattern is an arithmetic sequence with a common difference of 1/4.

The probability that the money will be in next pocket is 0.25.

We have a pair of cargo pants with six pockets and $10 in one of the pockets.

We have to find out the probability that the money will be in the next pocket you check after checking two pockets without success.

The formula to calculate the probability of an event is -

In the question it is given -

Total  money = $10

Total no. of pockets = 6 = n(S)

After two unsuccessful check in two pockets, new sample space =

n(S') = n(S) - 2 = 4

Hence, the probability that the money will be in the next pocket you check is -

P(A) = [tex]\frac{1}{4} = 0.25[/tex]

Hence, the probability that the money will be in next pocket will be  0.25.

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