The expression y2 – 10y + 24 has a factor of y – 4. What is another factor of y2 – 10y + 24? y – 20 y – 14 y – 8 y – 6

The sum of b and c is equal to 54.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Given is the following quadratic equation -

x² - 6x + 66

x² - 6x + 9 - 9 + 66

x² - 3x - 3x + 9 - 9 + 66

x(x - 3) - 3(x - 3) - 9 + 66

(x - 3)² + 57

The given form of resultant is -

(x + b)² + c

On comparing, we get -

b = - 3

c = 57

Therefore -

b + c = -3 + 57 = 54

Therefore, the sum of b and c is equal to 54.

To solve more questions on quadratic equation, visit the link below-

https://brainly.com/question/1863222

#SPJ2

Final answer:

An equivalent fraction for 4/21 can be found by multiplying the numerator and denominator by the same non-zero number, such as 2 to get 8/42.

Explanation:

An equivalent fraction for 4/21 is a fraction that has the same value but is expressed with different numerator and denominator. To find an equivalent fraction, you can multiply or divide both the numerator and denominator by the same non-zero number. For example, if we multiply the numerator and denominator by 2, we will get 8/42, which is an equivalent fraction to 4/21. It's important to note that this new fraction can be simplified further, just like 4/21 can be simplified to its lowest terms if there were any common factors.

The given equation is:

x y – 5000 = y

Rewrite this to create an explicit equation:

x y – y = 5000

y ( x – 1) = 5000

y = 5000 / (x – 1)

Derive to get dy / dx:

dy = - 5000 dx / (x – 1)^2

dy / dx = - 5000 / (x – 1)^2

So plugging in x = 6,

dy / dx = - 5000 / (6 – 1)^2

dy / dx = - 200

Answer:

[tex]\frac{dy}{dx}|_{x=6}= -200[/tex]

Step-by-step explanation:

Given : Demand equation [tex]xy − 5,000 = y[/tex]

To Find [tex]\frac{dy}{dx}|_{x=6}[/tex]

Solution :

[tex]xy- y= 5000[/tex]

[tex]y(x-1)= 5000[/tex]

[tex]y= \frac{5000}{x-1}[/tex]

Differentiating with respect to x

[tex]\frac{dy}{dx}= \frac{-5000}{(x-1)^2}[/tex]

Now substitute x = 6

[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{(6-1)^2}[/tex]

[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{5^2}[/tex]

[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{25}[/tex]

[tex]\frac{dy}{dx}|_{x=6}= -200[/tex]

Hence [tex]\frac{dy}{dx}|_{x=6}= -200[/tex]  =T-shirts per dollar

The contrapositive of 'If v≥4, then v≤4' is not true because it would imply 'If v>4, then v<4', which is logically inconsistent.

No, the contrapositive of the given conditional statement 'If v≥4, then v≤4' is not true. This is because the contrapositive of a conditional statement is always logically equivalent to the original statement. The contrapositive inverts and negates both the hypothesis and the conclusion. So the contrapositive of the original statement would be 'If v>4, then v<4', which does not hold true as a statement can't be both greater and less than 4 at the same time.

Contrapositive is the term used when the implication and its converse are both negated. In the context of the given conditional statement, this practice does not validate the original statement.

The data on student heights and weights suggests a strong positive correlation, implying that as a student's height increases, their weight tends to increase as well.

The data provided on student's heights and weights suggests a linear relationship. To complete the sentences based on the data:

The data seems to have a correlation coefficient close to positive one. This indicates that the weight of a student increases as the height of the student increases.

In statistics, when we observe that as one variable increases, the other also increases, we describe this as a positive correlation. A positive correlation coefficient closer to +1 implies a strong positive correlation, meaning that generally taller students in the given data set tend to weigh more.

Final answer:

The correlation coefficient for the given data is approximately 0.86, indicating a positive correlation between height and weight.

Explanation:

The data seems to have a correlation coefficient close to 0.86. This indicates that the weight of a student increases as the height of the student increases.

To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. After completing the square and rearranging the equation, we find that the equation in vertex form is y = 171(x + 7391/4) - 17113/4.

To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is given by y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Let's rearrange the equation to isolate the x terms on one side and the y term on the other side: 162x + 9x + y = -731 - 2

Combine like terms: 171x + y = -733

Now, we can complete the square for the x terms. Divide the coefficient of x by 2 and square the result. Add this value to both sides of the equation: 171x + y + (171/2)^2 = -733 + (171/2)^2

Simplify: 171x + y + 7391/4 = 17113/4

Finally, we can rewrite the left side as a binomial squared and simplify the right side: 171(x + 7391/4) + y = 17113/4

Therefore, the equation in vertex form is: y = 171(x + 7391/4) - 17113/4

If the 4 states have to be in a specific order say ABCD, then the total number of different possible routes is:

 43P4 = 2,961,840

So the probability is:

1 / 2,961,840 = 3.38 x 10^-7

But if the 4 states can be in any order such as DBAC, ACBD etc, then the total number of different possible routes is:

 43C4 = 123,410

So the probability is:

1 / 123,410 = 8.1 x 10^-6

No I don’t think it is practical to list all the different possible routes to select the one that is best. We can simply use mathematical models to solve for that one.

2A on 2A + 3B + 3C = 8 pieces

The probability:

[tex]\dfrac{2}{8}=\dfrac{2:2}{8:2}=\dfrac{1}{4}[/tex]

[tex]\dfrac{1}{4}=\dfrac{1}{4}\cdot100\%=25\%[/tex]

Answer:

  36

Step-by-step explanation:

36 is a factor of both numbers

_____

If the smaller divides the larger with no remainder, then the smaller number is the greatest common factor.

If there is a remainder, replace the larger number with that and repeat the process.

multiply 4/5 by 10

4/5 * 10 = 40/5 = 8 inches total

I believe we are to find for values in this problem.

a. The graph of the function

b. The domain and range

c. The slope

d. The c intercept value

Answers:

a. see the graph photo attached

b. The domain is the set of all x that can be input to the function. Since x is the distance and we know that distance cannot be negative hence the domain is:

x ≥ 0

So the range starts from x = 0:

c (x) = 0.5 * 0 + 70 = 70

Therefore the range is:

c ≥ 70

Domain: x ≥ 0                     Range: c ≥ 70

c. A linear equation has a general form of:

y = mx + b

where m is the slope

From the given equation, the slope is 0.5.

slope = 0.5

d. The c intercept is simply the value of c when x is equal to 0

c intercept = 70

Answer:Given function: c(x) = 0.5x+70.Where c is the cost (in dollars) and x is the number of miles you drive the truck.If we compare given function by slope-intercept form y=mx+b, we get Slope m = 0.5 in fractions could be written as 1/2.And y-intercept b =70.So, in order to graph it, we need to plot y-intercept at 70 first and then plot some more points using rise/run = 1/2.The red line is the graph for the given function.We can see that starting value of cost is $70 for 0 number of miles.x values represents domain and C(x) represents range.We can take x values greater than or equal to 0 and C values greater than equal to 70.Therefore, Domain: x≥0 and Range : C(x) ≥ 70.

Step-by-step explanation:Credit:User named PiaDeveau thanks for providing the answer and hope this helps

:)

The missing mean square (MS) for the treatment is 252.64, and there were 6 blocks used in the experiment. The p-value is less than 0.01, indicating a statistically significant effect of the treatment.

To fill in the blanks of the ANOVA table provided, we will perform some calculations. The mean square (MS) for the treatment can be found by dividing the sum of squares (SS) for the treatment by its degrees of freedom (df). Hence, for the treatment:

MS treatment = SS treatment / df treatment = 1010.56 / 4 = 252.64

Given that the total df equals 29 and the df for treatment and error sum up to 24 (4 + 20), the df for blocks will be:

df total - df treatment - df error = 29 - 4 - 20 = 5

Therefore, the number of blocks used in this experiment equals the df for blocks plus 1, giving us:

Number of blocks = df blocks + 1 = 5 + 1 = 6 blocks

As for the p-value associated with the F-statistic, we cannot calculate the exact value, but it is indeed lower than the conventional alpha levels (0.05, 0.01). So we describe the p-value as being less than 0.01

Conclusions:

With an F-statistic of 29.84 and a p-value much lesser than conventional alpha levels, we can conclude that there is a statistically significant effect of the treatment on the outcome variable.

The specific p-value bounds are not provided, but given that it is very low, the results are statistically significant. Thus, we can reject the null hypothesis that there is no effect of the treatment.