PLEASE HELP!!!!!!! Two lines, E and F, are represented by the equations given below. Line E: 5x + 5y = 40 Line F: x + y = 8 Which statement is true about the solution to the set of equations? (4 points) Question 2 options: 1) It is (40, 8). 2) It is (8, 40). 3) There is no solution. 4) There are infinitely many solutions.

The factored form of 3x² + 14x + 8 is (3x + 4)(x + 2).

Factor is a number that can be divided evenly into another number. Factors are used in mathematics to simplify equations, calculate percentages, and solve problems. Factors can also be used to identify the greatest common factor (GCF) between two or more numbers. Factors can also be used to find the least common multiple (LCM) of two or more numbers.

This is the product of the two binomials (3x + 4) and (x + 2),which are the factors of the equation.

The process of factoring an equation involves breaking it down into its component parts,

which in this case are 3x² + 14x + 8. The factors of this equation are determined by first finding the greatest common factor (GCF) of the terms, which in this case is 3x + 4.

Then, the GCF is divided by each of the terms to determine the other factor. For example, 3x² / 3x + 4 =x + 2.

When the two factors are multiplied together, the result is the original equation.
To know more about factor click-
https://brainly.com/question/25829061
#SPJ4

Step-by-step explanation:

The expression can be simplified to -3 - x² which is a concave downward parabola with a maximum at y=-3. Hence all values are less than or equal to -3 and thus negative.

Answer:

12. 1/4= 0.25 and 20/100÷20/20= 1/5 =0.20

Hence 0.25 =/ 0.20

Answer:

1.4³ has three decimal places.

1.4³=2.744

Step-by-step explanation:

(1.4)3

1.4 as a fraction = 1 and 4/10. We can reduce this to lowest terms by dividing the numerator and denominator or 4/10 by 2 to get the equivalent fraction 1 and 2/5

then we raise it to power 3 then we get 2.744

Step-by-step explanation:

this is the answer...............

The experimental probability that at least one student in a group of 4 students has brown eyes is approximately 0.8704, or 87.04%.

To find the experimental probability that at least one student in a group of 4 students has brown eyes, we can consider the complementary event, which is the probability that none of the students have brown eyes.

Given that 40% of students have brown eyes, the probability that a single student does not have brown eyes is 1 - 0.4 = 0.6.

Therefore, the probability that all 4 students do not have brown eyes is:

\(0.6 * 0.6 * 0.6 * 0.6 = 0.6^4 = 0.1296\)

To find the probability that at least one student has brown eyes, we subtract the probability that none of them have brown eyes from 1:

1 - 0.1296 = 0.8704

So, the experimental probability that at least one student in a group of 4 students has brown eyes is approximately 0.8704, or 87.04%.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

a) If r₁ is rational, then 12 is also rational.

b) If one of the roots is rational, then it can be written as p/q where p, q are integers, q divides a and p divides c.

Given that a, b, c are integers, with a ≠ 0. Let ₁ and 2 be the roots of

ax² + bx+c.

We need to show the following :

a) If r₁ is rational, then so is 12

b) If a root is rational, then it can be written as p/q where p, q are integers, q divides a and p divides c.

a) Let r₁ be rational.

Therefore, r₂= (b/a) - r₁ is also rational. Sum of roots ₁ and 2 is equal to -b/a.

Therefore,r₁ + r₂ = -b/a

=> r₂= -b/a - r₁

Now,

12= r₁ r₂

= r₁ (-b/a - r₁)

= -r₁² - (b/a) r₁

Therefore, if r₁ is rational, then 12 is also rational.

b) Let one of the roots be r.

Therefore,

ax² + bx+c

= a(x-r) (x-q)

= ax² - (a(r+q)) x + aqr

Now comparing the coefficients of x² and x, we get- (a(r+q))=b => r+q=-b/a ...(1) and

aqr=c

=> qr=c/a

=> q divides a and p divides c.

Now, substituting the value of q in equation (1), we get

r-b/a-q

=> r is rational.

Therefore, if one of the roots is rational, then it can be written as p/q where p, q are integers, q divides a and p divides c.

Know more about the rational

https://brainly.com/question/20400557

#SPJ11

Answer:

32-

Step-by-step explanation:

4 X 8 = 32

Hope this helps-

we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)

Answer:

Step-by-step explanation:

Formulas to Calculate Area of Rhombus

Using Base and Height A = b × h

Using Trigonometry A = b2 × Sin(a)

A = ½ × d1 × d2

1/2 × 25 × 20 =

250 cm²

Answer:

D) 7

Step-by-step explanation:

P=58000(1+0.05)^t

P=58000 x 1.05^t

58000 x 1.05^7= 81611.8245

D) 7

The number of 7 years will take for the profit to exceed $80,000

Mathematical functions with exponents include exponential functions. f(x) = bˣ, where b > 0 and b 1, is a fundamental exponential function.

Given:

A company's profit, currently $58,000, grows at the rate of 5% per year. The amount P after t years can be expressed by the exponential equation

P = 58000(1 + 0.05\()^{t}\)

We have P = 80,000.

So,

80000/58000 = (1 + 0.05\()^{t}\)

1.38 = (1.05\()^{t}\)

Taking log both sides, we get,

t = ln(1.38)/ln(1.05)

t = 0.136/0.02

t = 6.8

t ≈ 7 years.

Therefore, the time required is 7 years.

To learn more about the exponential;

https://brainly.com/question/14344314

#SPJ2

Answer: Mean=16 Median= 15.5

Step-by-step explanation:   for the mean put them all in numerical order then add all the numbers then divide by the number of numbers there are. for the median keep them in numerical order and cross out one on each end then when you get two the last two numbers, find what's in between. for example, if you had 15 and 16 15.5 would be the median.  

Answer:

mean = 16 ; median= 11,12,13,14,15,16,19,19,20,21

Step-by-step explanation:

mean= 15+12+11+19+21+13+14+16+20+19=160

160/10=16

median=11,12,13,14,15,16,19,19,20,21

The probability that exactly two customers in the sample will default on their payments is 0.9997.

This is a binomial probability problem with n = 5 trials and p = 3% = 0.03 probability of success (default) on each trial.

The probability of exactly two defaults can be calculated using the binomial probability formula:

P(x = r) = nCr * p^r  * q^n-r

where q = 1 - p = 1 - 0.03 = 0.97

P(x = 2) = (5C0 × 0.03⁰ × 0.97⁵⁻⁰) + (5C1 × 0.03¹ × 0.97⁵⁻¹) + (5C2 × 0.03² × 0.97⁵⁻²)

P(x = 2) = 0.9997

Learn more about binomial distribution on:

brainly.com/question/29220138

#SPJ1

The probability of observing a value greater than or equal to 12 is 0.1587, which corresponds to option c. 0.1587. The area under the normal curve represents the probability of observing a value within a certain range.

In this case, P(X≤12) is given as 0.8413, which means that the probability of observing a value less than or equal to 12 is 0.8413. To find P(X>=12), we can use the fact that the total area under the normal curve is 1. Since the normal distribution is symmetric, we can subtract the probability of the event from 1 to find the probability of the complementary event.

P(X>=12) = 1 - P(X≤12)

P(X>=12) = 1 - 0.8413

P(X>=12) = 0.1587

Therefore, the probability of observing a value greater than or equal to 12 is 0.1587, which corresponds to option c. 0.1587.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

Answer:

Step-by-step explanation:

Because 7(7)=(-7)(-7)=49 the square roots of 49 are 7 and -7

The set that we must describe is composed of those which are at least 6.5. At least means that these values are either 6.5 or greater. Then if n is any element of this set it meets the following condition:

Then the answer is the first option.

The correct option regarding whether the graph shows a function is given by:

C. Yes; the graph passes the vertical line test.

In a function, one value of the input can be related to only one value of the output. Hence, in a graph, it means that for each value of x(horizontal axis), there can only be one respective value of y(vertical axis), which will mean that the graph will pass the vertical line test.

In this problem, the condition is respected, hence option C is correct.

More can be learned about functions at https://brainly.com/question/12463448

#SPJ1

Answer:

The degrees of freedom, Df = The number of bags produced on Monday - 1

Step-by-step explanation:

The number of degrees of freedom is the limiting number of values that are logically not influenced by other values such that they are capable of having variation

The degrees of freedom = The sample size - 1 = N - 1

Therefore, the degrees of freedom, Df = The number of bags produced on Monday - 1

0.86  is the probability that a randomly selected patient is admitted for something other than coronary care.

What is probability ?

Let H denotes the patients are admitted for heart disease.

Let C denotes the patients are admitted for cancer treatment.

We are given:

 P(H) = 0.16

 P(C) = 0.26

P( H ∩ C ) = 0.8

P(Hc ) = 1 - P(H) = 1 - 0.16  =  0.86

Learn more about probability

brainly.com/question/11234923

#SPJ4

Answer:

35 and 37

Step-by-step explanation:

consecutive ODD numbers, 35 then 37.. 35+37 = 72

In statistics, the "z-score" is used to determine how far away from the mean a data point is. It indicates how many standard deviations the data point is from the mean.

The formula for calculating the z-score is given below:

z = (x - μ) / σ

where: x = data point

           μ = population mean

           σ = population standard deviation

Given a normal population with a mean of 21 and a standard deviation of 6, we can compute the z-score associated with 24 as follows:

z = (x - μ) / σz = (24 - 21) / 6z = 0.50

To compute the z-value associated with 24, we use Appendix B.3 which gives the area under the normal distribution curve for different z-scores.

Looking at Appendix B.3, we find that the area to the left of z = 0.50 is 0.6915 (rounded to 4 decimal places). Therefore, the z value associated with 24 is 0.50.

Note: The answer has been provided in less than 100 words, but the computation involved has been thoroughly explained.

To know more about standard deviation visit :

https://brainly.com/question/29115611

#SPJ11

Answer:

\(\boxed{x = -31}\)

\(\boxed{y = -62}\)

\(\boxed{z = -6}}\)

Step-by-step explanation:

There are a couple of properties of parallelograms that can help solve for the unknowns

Using property 1 that opposite angles are equal we have:
-4x - 5 = 119

⇒  -4x = 119 + 5

⇒ -4x = 124

⇒ x = 124/-4

⇒ x = -31

Using property 2 that consecutive angles are supplementary on angles
(-y - 1)° and 119°:

(- y - 1) + 119 = 180

⇒ - y - 1 + 119 = 180

⇒ - y + 118 = 180

⇒ - y = 180 - 118

⇒ - y = 62

⇒ y = -62

Using property 2 for angles (-10z - 1)° and 119°
(-10z + 1) + 119 = 180

- 10z + 1 + 119 = 180

⇒ - 10z + 120 = 180

⇒ -10z = 180 - 120

⇒ -10z = 60

⇒ z = 60/-10

⇒ z = -6

Answer:

400 meters

0 meters if the puppy can jump really really far ha ha ....

P = 10000x - 100

T = 8000x

10000x - 100 = 8000x  

2000x =  100

x = 1/20 hr

60/20 = 3 minutes

Step-by-step explanation:

A semicircle rotated around its axis gives sphere, rectangle  rotated around its axis gives sphere . and a right triangle  rotated around its axis gives sphere

what is rectangle?

A rectangle is a four-sided flat shape with straight sides and four right angles. It is a type of parallelogram, with opposite sides equal in length and parallel to each other. The area of a rectangle can be calculated by multiplying its length and width, while its perimeter can be found by adding the lengths of all four sides.

In the given question,

A semicircle rotated around its axis gives sphere,

A  rectangle  rotated around its axis gives sphere .

A right triangle  rotated around its axis gives sphere

To know more about rectangle rotation , visit:

https://brainly.com/question/15905456

#SPJ1

The given transformation of a function f(x) - 15 and 15 f(x) represents "f(x) is translated 15 units down and f(x) is vertically stretched by a factor of 15" respectively.

The translation transformation rule for a function is

1) f'(x) = f(x) + a; Vertical translation by 'a' units up.

f'(x) = f(x) - a; Vertical translation by 'a' units down.

2) f'(x) = f(x + a); horizontal translation by 'a' units left

f'(x) = f(x - a); horizontal translation by 'a' units right.

The dilation transformation rule for a function is

1) f'(x) = a f(x);

If a > 1, vertical stretch by a factor of 'a' units

If 0 < a < 1, vertical compression by a factor of 'a' units

2) f'(x) = f(ax);

If a > 1, horizontal compression by a factor of 'a' units

If 0 < a < 1, horizontal compression by a factor of 'a' units.

It is given that f(x) represents the linear parent function.

The transformed functions are given as

f(x) - 15 and 15 f(x)

The transformation f(x) - 15 is a vertical translation of the function f(x) by 15 units down.

The transformation 15 f(x) is a vertical stretch by a factor of 15 units.

Learn more about translation and dilation transformations of a function here:

https://brainly.com/question/28595882

#SPJ1