Study the system of equations below.
x + y =-4
x - y = 10 What is the solution to the system of
equations?
A (-4, 10)
B (10, 4)
C(3,-7)
D(7,-3)

Answer:

Part A   ---->    2

Part B   ---->     2 (2x - 1) (x + 5)

Part C   ----->    See explanation below

Step-by-step explanation:

Given expression is
4x² + 18x - 10

Part A

The greatest common factor (GCF) of the terms 4x², 18x and 10 is the largest number that divides into all three numbers without a remainder

To find this
Find the prime factors of each of the terms
4x² = 2 · 2 · x · x
18x = 2 · 3 · 3 · x
10 = 2 · 5

The  prime factor common to all 3 is 2

Therefore the GCF of the expression is 2

Part B

The factored expression can be obtained by factoring out the GCF

4x² + 18x - 10 = 2(2x² + 9x - 5)

We can further factor the term in parentheses:
2x² + 9x - 5

To do this,

Break the expression into groups:

= (2x² - x) + (10x - 5)

Factor x from 2x² - x:     x(2x - 1)

Factor 5 from 10x - 5:    5(2x - 1)

Therefore
(2x² - x) + (10x - 5) = x(2x - 1) + 5(2x - 1)

Factor out the common term 2x -1 to get
(2x - 1)(x + 5)

Therefore
4x² + 18x + 10 = 2 (2x - 1) (x + 5)

Part C
Checking if factorization is correct

Multiply (2x - 1)(x + 5) using the FOIL method
= 2x ·x + 2x · 5 + (-1) · x + (-1) · 5

= 2x² + 10x  -1x -5

= 2x² + 9x - 5

Multiply the whole expression by 2
2 · 2x² + ² · 9x - 2 · 5

= 4x² + 18x + 10

which is the original expression

So the factorization is correct

Answer:

429  i think

Step-by-step explanation:

The claim is: Testing if the time spent completing the obstacle course is improved by the energy drink

The null and the alternate hypotheses are added below

From the question, we have the following parameters that can be used in our computation:

The table

Also, we have the following statistical question

Is there sufficient evidence at α = 0.05 to conclude that the students did better the second time?

This means that the null hypothesis are

H1: There is no significant difference in the time spent to complete the obstacle course before and after drinking the new energy drink.

The alternate hypothesis is the opposite of the null hypothesis

So, we have

H2: There is no significant difference in the time spent to complete the obstacle course before and after drinking the new energy drink.

Lastly, the claim is that

Testing if the time spent completing the obstacle course is improved by the energy drink

Read more about test of hypothesis at

https://brainly.com/question/14701209

#SPJ1

Answer:

see below

Step-by-step explanation:

The Reason for #1 is literally GIVEN to you.

Statement #2: Since the Base Angles of an isosceles triangle are congruent, this statement should be ∠CAB≅∠CBA.

Reason #3: Notice that the statement repeats itself (AB=AB). This demonstrates the REFLEXIVE property.

Reason #4: (Clue) Note which items have been Given or Proven congruent and use it as the triangle congruence property. It helps to actually mark them. Your choices are SSS, SAS, ASA, and AAS.

Reason #5: (Clue) Since the triangles of which AM and BN are of part are now proven congruent, these Corresponding Parts are Congruent as well.

a.  There are 4 sample points in the sample space.

a) There are 4 sample points in the sample space.

b) The tree diagram and sample space are:

HH (two heads)

HT (one head, one tail)

TH (one head, one tail)

TT (two tails)

c) The probability that no tails are tossed (two heads) is 1/4 or 0.25.

d) The probability that exactly one tail is tossed (HT or TH) is 1/2 or 0.5.

e) The probability that two tails are tossed is 1/4 or 0.25.

f) The probability that at least one tail is tossed (HT, TH, or TT) is 3/4 or 0.75.

Learn more about probability at: https://brainly.com/question/13604758

#SPJ1

Stan used 19/40 of a gallon of gasoline.

Given that;

At first, Stan's lawn mower had 1/8 of a gallon of gasoline in the tank. When it got finished, he put 6/10 of a gallon of gasoline in the tank.

Hence, It means that the number of gallons of gasoline that he has already put in the tank is

1/8 + 6/10 = 29/40 of a gallon.

Now, After he mowed, 1/4 of a gallon was left in the tank.

Therefore, the total amount of gasoline Stan used is

29/40 - 1/4 = 19/40 of a gallon

Thus, the total amount of gasoline Stan used is, 19/40 of a gallon

Learn more about the addition visit:

https://brainly.com/question/25421984

#SPJ1

Answer:

28

Step-by-step explanation:

i did 7 times 4

Answer:

-36

Step-by-step explanation:

-1/2x<18

multiply each term by LCM=2

-1/2x×2<18×2

the 2on the left hand side will cancel each other leaving

-x <36

divide both sides by -1

-x/-1>36/-1

(note the equality sign changes because following the laws when you divide by a negative number the sign will change

X>-36

Answer:

Step-by-step explanation:

x>-36 is the anwser brainlist whould be aprecited and verifed

Answer:

O (x + 1)2 + (y + 2)² = 9

Step-by-step explanation:

This is because the distance between points A and B is 3 units, and the distance between points B and C is 4 units, making the triangle a 3-4-5 right triangle. Point B is located at (-1, 1), which is 3 units away from point A (-1, -2) and 4 units away from point C (-5, 1). Therefore, the circle with center (-1, -2) and radius 3 would pass through point B, and its equation would be:

(x + 1)2 + (y + 2)² = 3²

(x + 1)2 + (y + 2)² = 9

The statement that is not true is: C. The translation of a line is a pair of parallel lines.

In geometry, a transformation is a procedure that modifies a figure's position, size, or shape. Translation, rotation, reflection, and dilation are the four main categories of transformations.

Every point in a figure is translated by the same amount and in the same direction. A rotation revolves a figure around the centre of rotation, a fixed point. A figure is reversed over a line known as the line of reflection in a reflection.

In relation to a fixed point known as the centre of dilation, a dilation expands or contracts a figure by a specific scale factor.

The statement that is not true is: C. The translation of a line is a pair of parallel lines as translation is a transformation that moves every point of a figure the same distance in the same direction.

Learn more about transformation here:

https://brainly.com/question/29297263

#SPJ1

______________________________

______________________________

Step-by-step explanation:

m=y1-y2/x1-x2

m=2-8/5-8

m=-6/-3

m=2

y=m(x-x1)+y1

y=m(x-8)+8

y=2x-16+8

y=2x-22

Answer: Y=mx+c

Step-by-step explanation:

The Slope-Intercept Form can be written in the form: y = mx + c Where “m” is the slope of the line “c” is the y-intercept of the equation of the line

Answer:

Step-by-step explanation:

it should be shaded at the 76

Answer:

Your answer is E) 1/2 , -6 , 5

Step-by-step explanation:

Find the slope between (-6,5) then simplify and you will get 1/2

The number of birds in Mrs. Tillman's yard depends on the number of birdhouses in a linear fashion, with each birdhouse containing 8 birds

To find the number of birds (b) in a given number of bird houses (h), we can use the formula: b = 8h

Now, we can complete the table:

Number of bird houses (h) Number of birds (b)

1 8

2 16

3 24

4 32

5 40

So, the number of birds in Mrs. Tillman's yard depends on the number of birdhouses in a linear fashion, with each birdhouse containing 8 birds.

Read more about tables here:

https://brainly.com/question/12151322

#SPJ1

Mrs. Tillman has bird houses in her yard, with eight birds living in each bird house. Complete the table to show how the number of birds (b) depends on the number of bird houses (h):

Number of bird houses (h) Number of birds (b)

1

2

3

4

5

Answer:

{3, 6, 9, 12, 15}

Each of these numbers is divisible by 3

Step-by-step explanation:

Answer:

[tex]f(t) = 8e^{0.223144t}[/tex]

All real numbers greater than 5 can be expressed in interval notation as:

(5, ∞)

Interval notation is a way of representing an interval on a number line. Simply, it is a method of writing subsets of the real number line.

All real numbers greater than 5 can be expressed in interval notation as:

(5, ∞)

Where the round bracket "(" means 5 is not included in the interval, and the infinity symbol "∞" means the interval continues indefinitely to the right.

Learn more about interval notation on:

https://brainly.com/question/29130032

#SPJ1

The outlier does not affect the mode

The outlier will increase the mean.

The outlier will not affect the median.

The outlier will increase the mean because  it will significantly increase the sum of the values.

The presence of an outlier will not affect the median, as it only changes the position of the middle value.

The mode is the value that occurs most frequently in a data set. In this case, the mode will not be affected because the outlier is not the most frequent in the data set and only appears once.

Learn more about outliers on:

brainly.com/question/24123584

#SPJ1

The horizontal asymptotes of the function is y = 0 and the y-intercepts is (0, 1).

An exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid.

In this problem, the graph of the function f(x) = (1/4)ˣ is attached below the question and the characteristics of the graph are;

1. The domain of the function is {x|x ∈ R}

2. The range of the function is {y|y > 0}

3. The horizontal asymptotes is y = 0

4. The x-intercepts does not exists

5. The y-intercepts are (0, 1)

Learn more on graph of exponential function here;

https://brainly.com/question/2456547

#SPJ1

a) The probability of selecting exactly 3 award-winners before selecting a SENIOR is  0.078875

b)The probability of selecting more than 2 award-winners before selecting a JUNIOR is 0.135437

c)The probability of selecting 2 or fewer award-winners before selecting a SOPHOMORE is 0.252744

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.

(a) The probability of selecting a SENIOR is 0.65, and the probability of not selecting a SENIOR is 0.35.

Since we are selecting award-winners until we select a SENIOR, the first two selections must not be SENIORS, and the third selection must be a SENIOR.

the probability of selecting exactly 3 award-winners before selecting a SENIOR is:

P(not SENIOR) x P(not SENIOR) x P(SENIOR) = 0.35 x 0.35 x 0.65 = 0.078875

(b)Therefore, the probability of selecting more than 2 award-winners before selecting a JUNIOR is:

P(not JUNIOR) x P(not JUNIOR) x P(JUNIOR) = 0.77 x 0.77 x 0.23 = 0.135437

To find the probability of selecting more than 2 award-winners, we can subtract this value from 1, since the only other possibility is selecting exactly 2 award-winners before selecting a JUNIOR:

P(more than 2) = 1 - P(exactly 2) = 1 - (P(not JUNIOR) x P(JUNIOR) x P(not JUNIOR)) = 1 - (0.77 x 0.23 x 0.77) = 0.567911

(c) The probability of selecting a SOPHOMORE is 0.12, and the probability of not selecting a SOPHOMORE is 0.88.

Since we are selecting award-winners until we select a SOPHOMORE, we can keep selecting SENIORS and JUNIORS until we select a SOPHOMORE.

Therefore, the probability of selecting 2 or fewer award-winners before selecting a SOPHOMORE is:

P(SOPHOMORE) + P(not SOPHOMORE) x P(JUNIOR) x P(SOPHOMORE) + P(not SOPHOMORE) x P(not JUNIOR) x P(JUNIOR) x P(SOPHOMORE) = 0.12 + (0.88 x 0.23 x 0.12) + (0.88 x 0.77 x 0.23 x 0.12) = 0.252744

To know more about event, visit:

https://brainly.com/question/12961938

#SPJ1

Answer:

137 yd2

Step-by-step explanation:

The exponential function giving the balance of the account after t months is:

[tex]y = 100(1.02)^t[/tex]

The yearly growth factor is given as follows:

26.82%.

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

Hence the function is:

[tex]y = 100(1.02)^t[/tex]

The yearly growth factor can be obtained as follows:

[tex](1.02)^{12} = 1.2682[/tex]

Increase of 26.82% each year, which is composed by 12 months.

More can be learned about exponential functions at brainly.com/question/2456547

#SPJ1

The accounting equation is:

Assets = Rs. 2,19,500

Liabilities = Rs. 1,000

Capital = Rs. 2,10,500

The accounting equation is:

Assets = Liabilities + Capital

(a) Commenced business with cash of Rs. 1,00,000 and Machine of Rs. 50,000.

Assets = Cash + Machine = Rs. 1,00,000 + Rs. 50,000 = Rs. 1,50,000

(b) Purchased goods for cash Rs. 30,000 and credit Rs. 10,000.

Assets = Cash + Inventory = Rs. 1,30,000

Liabilities = Accounts Payable = Rs. 10,000

(c) Sold goods for cash Rs. 25,000 and credit Rs. 15,000.

Assets = Cash + Accounts Receivable + Inventory = Rs. 1,70,000

Liabilities = Accounts Payable = Rs. 10,000

(d) Goods taken by the owner for private use Rs. 2,000.

Assets = Cash + Accounts Receivable + Inventory - Drawings = Rs. 1,68,000

(e) Cash paid to creditors Rs 8,000.

Assets = Cash + Accounts Receivable + Inventory - Drawings = Rs. 1,60,000

Liabilities = Accounts Payable - Rs. 8,000 = Rs. 2,000

(f) Cash received from debtors Rs. 14,500 in full settlement.

Assets = Cash + Inventory - Drawings = Rs. 1,74,500

Liabilities = Accounts Payable - Rs. 8,000 = Rs. 2,000

Capital = Rs. 1,70,500

(g) Received a loan of Rs. 5,000 from Mr. Dipendra.

Assets = Cash + Inventory - Drawings = Rs. 1,79,500

Liabilities = Accounts Payable - Rs. 8,000 + Loan Payable Rs. 5,000 = Rs. 1,000

Capital = Rs. 1,74,500

(h) He introduced additional capital Rs. 40,000.

Assets = Cash + Inventory - Drawings = Rs. 2,19,500

Liabilities = Accounts Payable - Rs. 8,000 + Loan Payable Rs. 5,000 = Rs. 1,000

Capital = Rs. 2,10,500

Therefore, the accounting equation is:

Assets = Rs. 2,19,500

Liabilities = Rs. 1,000

Capital = Rs. 2,10,500

Learn more about Accounting equation at https://brainly.com/question/28246336

#SPJ1

the first mechanic charged $55 per hour and the second mechanic charged $100 per hour. we solve this by forming equation by by given data.

what is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables,

In the given question,

Let's assume that the first mechanic charged x dollars per hour and the second mechanic charged y dollars per hour.

From the problem, we know that:

The first mechanic worked for 20 hours, so he charged 20x dollars.

The second mechanic worked for 15 hours, so he charged 15y dollars.

Together, they charged a total of $2600, so we have:

20x + 15y = 2600

The sum of the two rates was $155 per hour, so we have:

x + y = 155

We can use these two equations to solve for x and y. First, we can rewrite the second equation as:

y = 155 - x

Then, we can substitute this expression for y into the first equation:

20x + 15(155 - x) = 2600

Simplifying and solving for x, we get:

20x + 2325 - 15x = 2600

5x = 275

x = 55

Now that we know x, we can use the second equation to find y:

y = 155 - x = 155 - 55 = 100

Therefore, the first mechanic charged $55 per hour and the second mechanic charged $100 per hour.

To know more about equation , visit:

https://brainly.com/question/29657983

#SPJ1

The conditional value probability is solved and P ( J ) = 0.1105

Given data ,

P(JIK) = 0.35, P(KJ) = 0.95, P(K) = 0.3

We can use Bayes' theorem to find P(J):

P(J | K) = P(K | J) * P(J) / P(K)

0.35 = 0.95 * P(J) / 0.3

0.35 * 0.3 = 0.95 * P(J)

0.105 = 0.95 * P(J)

P(J) = 0.105 / 0.95

P(J) = 0.1105

Hence , the probability is P ( J ) = 0.1105

To learn more about Baye's theorem click :

https://brainly.com/question/29598596

#SPJ1

To determine which size bag has the lower price per ounce, we need to calculate the price per ounce for each bag.

For the 7 oz bag, the price per ounce is:

1.10 / 7 = 0.1571

For the 9 oz bag, the price per ounce is:

1.46 / 9 = 0.1622

Therefore, the 7 oz bag has the lower price per ounce, at approximately $0.16 per ounce, compared to the 9 oz bag at approximately $0.16 per ounce. So, if the goal is to get the most value for your money, it would be better to purchase the 7 oz bag of raisins.

The probability that a randomly selected test score will fall in the interval 360 to 380 is the option (3), 0.24.

To calculate the probability that a test score falls between 360 and 380, we need to standardize these values by subtracting the mean and dividing by the standard deviation.

This gives us:

z(360) = (360-350)/18 = 0.56

z(380) = (380-350)/18 = 1.67

We can then use a standard normal distribution table or a calculator to find the area under the curve between these two z-scores.

The probability is approximately 0.24.

Therefore, the answer is option (3), 0.24.

Read more about probability here:

https://brainly.com/question/24756209

#SPJ1

Answer:

x = 65

Step-by-step explanation:

let the number be 'x'.

If 86 is added to a number, the result is 44 less than three times the number. Therefore the equation will be,

=> 86 + x = 3x - 44

Rearranging,

=> x - 3x = -44 - 86

=> -2x = -130

=> x = 130/2

=> x = 65