Explaining Factored Form The trinomial x2 + bx – c has factors of (x + m)(x – n), where m, n, and b are positive. What is the relationship between the values of m and n? Explain.

Answers

Answer 1

The value of m must be greater than the value of n. When you multiply the binomials, the middle term is the result of combining the outside and inside products. So, bx = –nx + mx, or bx = (–n + m)x. This means that b = –n + m. When adding numbers with opposite signs, you subtract their absolute values, and keep the sign of the number having the larger absolute value. Since b is positive, mmust have the larger absolute value.

Answer 2

Sample Response: The value of m must be greater than the value of n. When you multiply the binomials, the middle term is the result of combining the outside and inside products. So, bx = –nx + mx, or bx = (–n + m)x. This means that b = –n + m. When adding numbers with opposite signs, you subtract their absolute values, and keep the sign of the number having the larger absolute value. Since b is positive, m must have the larger absolute value.

(on the assignment)

Related Questions

A park in a subdivision has a triangular shape two adjacent side of the park are 433 and 520 the angle between the sides is 37 find the area of the park to the nearest square foot hint use theorem 10-8

Answers

Answer:

[tex]67750.644 ft^2[/tex]

Step-by-step explanation:

Given : A park in a subdivision has a triangular shape two adjacent side of the park are 433 and 520 the angle between the sides is 37

To Find: the area of the park to the nearest square foot

Solution:

Refer the attached figure

Area of triangle = [tex]\frac{1}{2} \times a \times b \times sin c[/tex]

a = 433

b=520

Sin c = Sin 37° = 0.6018

Area of triangle = [tex]\frac{1}{2} \times 433 \times 520 \times 0.6018[/tex]

Area of triangle = [tex]67750.644[/tex]

Hence the area of the park is [tex]67750.644 ft^2[/tex]

On a scatter plot, what is the difference of a positive and negative correlation

Answers

Final answer:

On a scatter plot, a positive correlation indicates an increasing relationship between two variables, represented by an upward slope. Negative correlation shows a decreasing relationship, represented by a downward slope. The strength of these relationships is determined by the correlation coefficient.

Explanation:

In a scatter plot, a positive correlation and a negative correlation represent different types of relationships between two variables. A positive correlation suggests that as one variable increases, the other also increases. For example, height and weight are usually positively correlated, as the taller a person is, the more they tend to weigh.

On the other hand, a negative correlation means that as one variable increases, the other decreases. Graphically, this is represented by a downward slope from left to right. An example of this is the relationship between hours of sleep and tiredness, more hours of sleep typically correspond to less tiredness.

The strength of these correlations are determined by the correlation coefficient. A correlation coefficient closer to 1 or -1 indicates a stronger relationship, and a coefficient closer to 0 indicates a weaker relationship.

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What is the area of a square with side lengths of 7 feet?

A.
28 ft

B.
28 ft2

C.
49 ft2

D.
49 ft

Answers

The side lengths of a square is equal, thus length=width, hence the dimensions of our square will be:
length=width=7 ft
hence;
area=length×width
area=7×7
area=49 ft²

Answer:
C.
49 ft2

Pls Pls Pls Pls Pls Pls pls

Answers

The answer is 57 pounds, this is because we just take E380 and times it by .15

Please Help!

A train passes by an observer in 6 seconds and over a bridge 350m long in 20 seconds. Find the speed and length of the train.

Answers

Let x be the length of the train.

On the basis of the observer;
Speed of the train = x/6

On the basis of the bridge;
Total distance covered by any point of the train= 350+x
Speed = (350+x)/20

Equating the two expressions of speed;
x/6 = (350+x)/20
20(x) = 6(350+x)
20x = 2100+6x
(20-6)x = 2100
14x = 2100
x= 2100/14 = 150 m
Speed = x/6 = (350+x)/20 = 150/6 = 500/20 = 25 m/s.

Therefore,
Length of train = 150 m
Speed of train = 25 m/s

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1. Simplify the radical

2. Simplify the radical

3. Simplify the radical

4. Simplify the radical

Answers

the root of 27 is 3root3.

The simplification of the radical is c/3

What are radicals in math?

Radicals in math refer to expressions containing square roots or higher-order roots.

Represented by the radical symbol (√), they involve finding the root of a number. For example, √9 equals 3, as 3 * 3 equals 9.

Simplifying the surd;

√3c²)/√27

= √3 × √c²)/√9 × √3

= √3c/3√3

= c/3

Therefore the simplification of √3c²)/√27 is c/3.

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A two digit number with two different digits has a special property when th sum of its digits is added to the product of its digits the result is the number itself

Answers

When th sum you forgot the e on the

A set of n = 15 pairs of scores (X and Y values) has SSX = 4, SSY = 25, and SP = 6. What is the Pearson correlation for these data

Answers

The Pearson correlation can be calculated by the formula:
[tex]r = \frac{SP}{ \sqrt{SS_{x}SS_{y} } } [/tex]

Therefore:

r = 6 / √(4·25)
= 6 / √100
= 6 / 10
= 0.60

Hence, the Pearson correlation for this set is 0.60

Write an equation in intercept form of the parabola that Passes through (-1,40) and x=-5, 4

Answers

At first I didn't understand what you meant by "x = -5, 4. What I think you meant was "the horizontal intercepts of the graph of this parabola are (-5,0) and (4,0)."

If this is the case, then the equation of the parabola is found as follows:

y=ax^2 + bx + c for the point (-5, 0) is 0=a(-5)^2 + b(-5) + c
for the point (4,0) is 0 = a(4)^2 +b(4) + c
for the point (-1,40) is 40 = a(-1)^2 + b(-1) + c

Here we have 3 equations in 3 unknowns, which is enough to solve for {a,b,c}. Using matrix algebra, I found that a= -2, b= -2, c= 40.

Then one equation for this parabola would be:

y = -2x^2 - 2x + 40

Check this by substitution. Does the point (-5,0) satisfy y = -2x^2 - 2x + 40?
Yes. So y = -2x^2 - 2x + 40 is the general form of the equation of this parabola. To express it in intercept form, factor y = -2x^2 - 2x + 40.

Which function represents a reflection of f(x) = 5(0.8)x across the x-axis? A. g(x) = 5(0.8)–x B. g(x) = –5(0.8)x C. g(x) = 1/5(0.8)x D. g(x) = 5(–0.8)x

Answers

If g(x) is a reflection of f(x) over the x axis, then g(x) = -1*f(x), which can be shortened to g(x) = -f(x). We stick a negative outside the entire f(x) function to flip the signs of each y coordinate. For example, if the point (1,2) was on f(x), then (1,-2) is on g(x).

So f(x) = 5(0.8)^x turns into g(x) = -5(0.8)^x

Answer: Choice B

Answer:

2nd option

Step-by-step explanation:

Identify the pattern for the following sequence. Find the next three terms in the sequence. 5, 2, -1, -4, ____, ____, ____,... a. Subtract 3; -7, -10, -13 b. Add 3; -7, -10, -13 c. Subtract -3; 7, 10, 13 d. Add 3; 1, 4, 7 Please select the best answer from the choices provided

Answers

The correct answer for the completion exercise shown above is the first option (Option a), which is:

a. Subtract 3; -7, -10, -13

The explanation is shown below:

1. You have the following sequence 5, 2, -1, -4

2. The first second number is the result of a substraction:

5-3=2

3. Then you have:

2-3=-1
-1-3=-4
-4-3=-7
-7-3=-10
-10-3=-13

Therefore, the answer is the optiones mentioned before.

Answer:

A.Subtract 3:-7,-10,-13

Step-by-step explanation:

We are given that a sequence

5,2,-1,-4,...

We have to identify the pattern of the givens sequence and next three terms.

[tex]a_1=5,a_2=2,a_3=-1,a_4=-4[/tex]

[tex]a_2-a_1=2-5=-3[/tex]

[tex]a_3-a_2=-1-2=-3[/tex]

[tex]a_4-a_3=-4-(-1)=-3[/tex]

The difference between two consecutive terms are equal.When the difference between two consecutive terms are equal then the sequence is called arithmetic sequence.Hence, the sequence is arithmetic sequence.

[tex]a_5=a_4-3=-4-3=-7[/tex]

[tex]a_6=a_5-3=-7-3=-10[/tex]

[tex]a_7=a_6-3=-10-3=-13[/tex]

Answer:A.Subtract 3:-7,-10,-13

A. 0
B. 4
C. 2
D. -2

Answers

The way to find the midpoint of a segment is to add the coordinates of the points you're trying to do the midpoint for and then divide by two (so it's the midpoint). Sine we're trying to find the midpoint of WQ, we need to add the coordinate of W and the coordinate of Q and then divide by 2. The coordinate of W is -8, and the coordinate of Q is 4. -8 + 4 = -4, divided by 2 is -2. That means that our answer is D, or -2.

please help. there is a picture below

Answers

Two triangles are similar if and only if all corresponding angles are equal (congruence), even if the corresponding sides are equal or not, therefore the answer is true because ΔJKL and ΔRST are similar and the statement above demands that "it must be", namely, this is a sufficient condition.

evaluate a = log(0.1) and b = ln(e^3)

Answers

[tex]log0.1=log\dfrac{1}{10}=log10^{-1}=-log10=-1\to a=-1\\\\lne^3=3lne=3\to b=3\\\\Used:\\\\a^{-1}=\dfrac{1}{a}\\\ loga^b=b\cdot loga\\\\log_aa=1[/tex]

Colby starts with 50 bacteria in his culture and the number of bacteria doubles every 2 hours, and Jaquan starts with 80 bacteria that double every 3 hours. x= number of DAYS. Would Colby's experiment be modeled by... y=50(2)^x y=50(2)^8x or y=50(2)^12x Would Jaquan's experiment be modeled by... y=80(2)^x y=80(2)^8x or y=80(2)^12x

Answers

Given that x=number of days
To model the expressions we use the exponential growth given by:
y=a(b)^nx
where:
a=initial value
b=growth factor
n=24 hours
thus Colby's experiment will be:
y=50(2)^(1/2*24*x)
y=50(2)^(12x)
N/B we multiply by 24 so as to convert days into hours

b] Jaquan's starts with 80 bacteria that double every 3 hours.
a=80, b=2
thus
y=80(2)^(1/3×24×x)
simplifying the above we get:
y=80(2)^(8x)

A quiz consists of two multiple-choice questions. the first question has a total of 7 possible answers followed by the second question which has a total of 3 possible answers. if both questions are answered with random guesses,

Answers

the probability to answer both correctly is 1/7(1/3)=1/21, if that was the question.

The area of a rectangular garden is given by the trinomial x2 + x – 42. What are the possible dimensions of the rectangle? Use factoring.

Answers

x^2 + x - 42 =

= x^2 + 1x - 42
             ^      ^
             |       |
             |      you need two numbers that multiply to -42
             |
           and add to 1

Find two numbers whose product is -42 and whose sum is 1.
The numbers are -6 and 7.

x^2 + x - 42 = (x - 6)(x + 7)

Final answer:

The dimensions of the rectangle given by the trinomial (x² + x – 42) are 7 and 6, which are derived by factoring the trinomial and applying the quadratic formula.

Explanation:

To find the possible dimensions of the rectangle, we start by factoring the trinomial that represents the area of the rectangle, namely x² + x – 42.

This can be factored as (x + 7)(x - 6), which are the roots of the quadratic equation when set to equal zero.

The roots, or solutions to this equation, can be calculated using the quadratic formula, -b ± √b² - 4ac 2a, which includes squaring the coefficient of the x-term, subtracting four times the product of the remaining coefficients, and dividing the result by twice the leading coefficient.

In this case, the dimensions that correspond to these roots, namely length and width, are 7 and -6. However, since dimensions cannot be negative, we disregard -6. Therefore, the possible dimensions of the rectangle are 7 and 6.

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Can someone answer for me please, if you're great at math.

The equation sin (35o) = 12/c can be used to find the length of AB. What is the length of AB? Round to the nearest tenth.

*A <35o ; CB = 12*

Answers

Assuming that c is the length of AB (as is usually the case in the angle-side notation for triangles):
If sin(35) = 12/c, we can transform by multiplying both sides by c, and dividing both by sin(35) to get
c = 12/sin(35)
Evaluating using a calculator gives 20.92 units.

is it always true that trapezoids height is the distance between the 2 bases?

Answers

No. One side can be higher than the other side, therefore, a trapezoids height isn't always the distance between the 2 bases.

What is the probability of flipping a coin 75 times and getting tails 35 times or fewer? Round your answer to the nearest tenth of a percent.

A. 99.7%
B. 32.2%
C. 5.3%
D. 75.6%

Answers

Let X be the number of tail when a coin is flipped n number of times. Let n is the number of times a coin is flipped. Let p be the probability of getting tail on any flip of coin.

Here as coin is fair coin the chance of getting head or tail at any flip is 1/2.

n=75, p =0.5

From given information X follows Binomial distribution with n=75 and p=0.5

The probability that getting tail 35 or fewer times is

P(X ≤ 35) = P(X=35) + P(X=34) + P(X=33) + ....+ P(X=2) + P(x=1)

The Binomial probability is calculated using probability function

[tex] P(X=k) = (nCk) p^{k} (1-p) ^{n-k} [/tex]

For given parameters n=75 and p=0.5 the probability of getting X=k is

[tex] P(X=k) = (75Ck) 0.5^{k} (1-0.5) ^{75-k} [/tex]

Using excel function to find cumulative binomial probability for x=1 to 35 is

=BINOM.DIST(35,75,0.5,1) = 0.322

The probability there will be 35 or fewer tails is 0.322

The percentage of getting 35 or fewer tails is 32.2%

Jerry played with 3 friends today, all at different times. He played with Tommy for 7/8
7start fraction, 7, divided by, 8, end fraction of an hour, then Nathan for 3/4, then Chris for 3/2
How many hours did Jerry play with his 3 friends today?

Answers

To find the total number of hours that Jerry played with his friends, you will add the amount of times he played with each.

7/8 hour+ 3/4 hour + 3/2 hours; create fractions with common denominators.
7/8 + 6/8 + 12/8
25/8 = 3 1/8 hours.

Jerry played with his friends for 3 1/8 hours.

Adrian has been adding 6 cards to his sports card collection each week. He started with 20 cards. Let x be the number of weeks he saves cards. Which inequality would help him find the number of weeks it will take him to have more than 100 cards?

Answers

Final answer:

In this mathematical context, the inequality 20 + 6x > 100 can help Adrian find out the number of weeks he needs to continue his weekly addition of 6 cards to his sports card collection to exceed 100 cards in total.

Explanation:

The subject of this question is Mathematics and it appears to be at a Middle School level. The problem involves understanding and using linear equations and inequalities.

In this situation, Adrian starts with 20 cards and adds 6 more each week. So his total number of cards is represented by the equation 20 + 6x, where x is the number of weeks. If he wants to have more than 100 cards, we set up an inequality like this:

20 + 6x > 100

Thus, the inequality 20 + 6x > 100 allows Adrian to calculate the number of weeks x he needs to continue adding cards to his collection in order to exceed 100 cards total.

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Final answer:

To figure out when Adrian's sports card collection will surpass 100 cards given he is adding 6 cards each week, we can set up the inequality [tex]20 + 6x > 100[/tex]. Solving this gives us that Adrian should wait at least 14 weeks to have more than 100 cards.

Explanation:

The subject of this question is Mathematics, specifically, linear algebra and inequalities. Adrian has a sports card collection which began with 20 cards. Every week, he is adding 6 new cards. The statement that relates his ongoing collections would be: 20 + 6x, where x is the number of weeks. Adrian wants to know when his collection will exceed 100 cards. To determine this, we must set up an inequality: [tex]20 + 6x > 100[/tex]. Solving this inequality gives us [tex]x > (100-20)/6[/tex], or [tex]x > 13.33[/tex]. Therefore, Adrian will need to wait at least 14 weeks to have more than 100 cards in his collection given he is adding 6 new cards per week.

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Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. x - 2; 4x2 - 3x + 22

Answers

Answer:

[tex]x-2[/tex] is not a factor of [tex]p(x)=4x^2-3x+22[/tex].

Step-by-step explanation:

According to the factor theorem, if [tex]x-a[/tex] is a factor of [tex]p(x)[/tex], then [tex]p(a)=0[/tex].

Let [tex]p(x)=4x^2-3x+22[/tex]. If [tex]x-2[/tex] is a factor of [tex]p(x)=4x^2-3x+22[/tex], then [tex]p(2)=0[/tex].

Let us plug in [tex]x=2[/tex] in to the function to see if it will give us zero.

[tex]p(2)=4(2)^2-3(2)+22[/tex]

We simplify to obtain,

[tex]p(2)=4(4)-3(2)+22[/tex]

[tex]p(2)=16-6+22[/tex]

[tex]p(2)=10+22[/tex]

[tex]p(2)=32[/tex]

Since [tex]p(2)\ne0[/tex], [tex]x-2[/tex] is not a factor of [tex]p(x)=4x^2-3x+22[/tex].

Final answer:

According to the Factor Theorem, 'x - 2' is not a factor of the polynomial '4x^2 - 3x + 22'. This determination was made by plugging '2' into the second polynomial and finding that it does not result in zero.

Explanation:

For a polynomial P(x), the Factor Theorem states that if you plug a value 'a' into the polynomial and get zero (P(a) = 0), then x-a is a factor of that polynomial. In this case, you are asked to determine whether 'x - 2' is a factor of the quadratic function '4x^2 - 3x + 22'.

To do so, according to the Factor Theorem, plug the value '2' into the second polynomial function, so we have 4*(2)^2 - 3*(2) + 22 = 16 - 6 + 22 = 32. Because this does not equal zero, we can conclude that 'x - 2' is not a factor of the second polynomial '4x^2 - 3x + 22' based on the Factor Theorem.

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The graph represents the feasible region for the system:

y<=2x
x + y<=45
x <=30

Minimize the objective function P = 25x + 20y.

The minimum value =?
and occurs when x = ?
and y = ?

Answers

We have been given a system of inequalities and an objective function.

The inequalities are given as:

[tex]y\leq 2x\\ x+y\leq 45\\ x\leq 30\\[/tex]

And the objective function is given as:

[tex]P=25x+20y[/tex]

In order to find the minimum value of the objective function at the given feasible region, we need to first graph the region.

The graph of the region is shown below:

From the graph, we can see that corner points of the feasible region are:

(x,y) = (15,30),(30,15) and (30,60).

Now we will evaluate the value of the objective function at each of these corner points and then we will compare which of those values is minimum.

[tex]\text{At (15,30)}\Leftrightarrow P=25\cdot 15+20\cdot 30=975\\ \text{At (30,15)}\Leftrightarrow P=25\cdot 30+20\cdot 15=1050\\ \text{At (30,60)}\Leftrightarrow P=25\cdot 30+20\cdot 60=1950\\[/tex]

Hence the minimum value of objective function is 975 and it occurs at x = 15 and y = 30

Answer:

The minimum value =

975

and occurs when x =

and y =

Step-by-step explanation:

Edge. 2020

Find the area of this shape

Answers

You do A=1/2xhx(b1+b2)
A=1/2x3.6x(3.6+9)
A=1/2x3.6x12.6
A=1/2x45.36
A=22.68

How do I find the values for a, b, and c, to complete the solution?

Answers

Answer:

The values a, b, and c are: a = - 4, b = 3, c = 6

The solutions to the equation are: x = - 4 + 3√6 and x = - 4 - 3√6

Explanation:

1) First step is complete squares:

x² + 8x = 38 ← given

x² + 8x + (8/2)² = 38 + (8/4)² ← add square of the half of 8

x² + 8x + 16 = 38 + 16 ← solve the parenthesis

x² + 8x + 16 = 54 ← combine like terms

2) Second, solve the equation:

(x + 4)² = 54 ← factor the perfect square trinomial

(x + 4) = +/- √54 ← extract square root of both sides

x = - 4 +/- √54 ← subtract 4 from both sides

x = -4 +/- 3√6 ← simplify the root

x = - 4 + 3√6 and x = - 4 - 3√6 ← separate the two solutions

3) Third, compare with the solutions shown:

x = a + b√c and x = a - b√c

⇒ a = -4, b = 3, c = 6

The perimeter of a circle is also known as what?

Answers

Hello there!

The perimeter of a circle is also known as circumference, or the "outside".

Circumference (to solve): 2 × pi × radius

hope this helps!

~DL

Fifty-eight boys were asked if they play football and/or baseball. Thirty-one of them said they do not play baseball. Sixteen of them said they play football. Twenty of them said they do not play baseball or football. Match the following values to their correct places on the two-way table.

Answers

Answer:

5 play Football & Baseball; 22 don't play Football; 11 don't play baseball; 20 don't play either football or baseball. See captures attached. The missing one in your original answer + the one made in Excel.

Step-by-step explanation:

If you fill out the blanks the way explained in the answer, you can prove that the 3 sentences match perfectly. The sum of all of them totals 58.

1. Thirty-one of them said they do not play baseball.

2. Sixteen of them said they play football.

3. Twenty of them said they do not play baseball or football.

By the way, as I mentioned before, I also attached the missing image in your original question.

Have a great day!

Answer:

Here is the answer.

If (-3)^-5=1/x, what is the value x?

Answers

[tex](-3)^{-5} = \frac{1}{x}, \frac{1}{(-3)^{5}} = \frac{1}{x} , (-3)^{5}=x, x= - 243[/tex]

The solution is, x = -243 is the value of (-3)^-5=1/x.

What is algebraic identities?

The algebraic equations are those which are valid for all values of variables in them are called algebraic identities.

Here we have:

Given that,

(-3)^-5=1/x

now, we have to simplify this expression, to get the value o x .

so, we get,

1/(-3)^5=1/x

or, (-3)^5=x

or, x = -243

Hence the value of the expression (-3)^-5=1/x , is x= -243.

(Note the expression asked is different by minus sign, but generally these questions solved as above. It would be a printing mistake)

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Factor this trinomial completely.

2x^2 + 10x + 8

A. 2(x + 4)(x + 1)
B. 2(x – 4)(x – 1)
C. 2(x + 4)(x – 1)
D. 2(x – 4)(x + 1)

Answers

its A. 2(x + 4)(x +1).

The answer is
A. 2(x + 4) (x + 1)

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