Questlon 14 of 25 What is the slope of the line containing (-3, 1) and (1, -2)? O A. A - 3 O B. 4 O c. - 3 4 O D. SUBMIT

Questlon 14 Of 25 What Is The Slope Of The Line Containing (-3, 1) And (1, -2)? O A. A - 3 O B. 4 O C.

Answers

Answer 1

Answer:

C - 3/4

Step-by-step explanation:


Related Questions

Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west at 18 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later?
mi/h

Answers

The rate at which the distance between the two cars increased four hours later is 30 mi/h.

How to determine the rate?

First of all, we would determine the distances travelled by each of the cars. The distance travelled by the first car after four (4) hours is given by:

Distance, x = speed/time

Distance, x = 24/4

Distance, x = 6 miles.

For the second car, we have:

Distance, y = speed/time

Distance, y = 18/4

Distance, y = 4.5 miles.

After four (4) hours, the total distance travelled by the two (2) cars is given by this mathematical expression (Pythagorean theorem):

z² = x² + y²

Substituting the parameters into the mathematical expression, we have;

z² = 6² + 4.5²

z² = 36 + 20.25

z² = 56.25

z = 7.5 miles.

Next, we would differentiate both sides of the mathematical expression (Pythagorean theorem) with respect to time, we have:

2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt)

Therefore, the rate of change of speed (dz/dt) between the two (2) cars is given by:

dz/dt = [x(dx/dt) + y(dy/dt)]/z

dz/dt = [6(24) + 4.5(18)]/7.5

dz/dt = [144 + 81]/7.5

dz/dt = 225/7.5

dz/dt = 30 mi/h.

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Answer:

30 mi / hr

Step-by-step explanation:

First find out how far the cars are apart after 4 hours

24 * 4 = 96 mi = y

18 * 4 = 72 mi = x

Now use the pythagorean theorem

   s^2 =  ( x^2 + y^2 )                shows s = 120 miles apart at 4 hours

Now s^2 = x^2 + y^2     Differentiate with respect to time ( d  / dt )

       2 s ds/dt    =  2x dx/ dt  + 2y dy / dt

             ds/dt    =   (x dx/dt + y dy/dt)/s

                           =  (72(18)  + 96(24)) / 120

               ds/dt   = 30 mi/hr

What is the area of the triangle 9 2 12

Answers

The given diagram is a traingle with base 12 units, height 4 units, and one side 9 units.

Since base (b) and height (h) are known, we can use the following formula for the area (A) of the triangle,

[tex]A=\frac{1}{2}bh[/tex]

Substitute the values and simplify the expression,

[tex]\begin{gathered} A=\frac{1}{2}\times12\times4 \\ A=6\times4 \\ A=24 \end{gathered}[/tex]

Thus, the area of the given triangle is 24 square units.

A student rolled 2 dice. What is the probability that the first die landed
on a number less than 3 and the second die landed on a number
greater than 3?

Answers

So what’s the probability you ask?
So the first dice can get either 1 or 2 and the second dice can have 4 5 or 6
So we need any one of these outcomes
(1,4) (1,5) (1,6) (2,5) (2,6) (2,4)
Clearly total no of outcomes is 36 (6x6)
Thus probability= 6/36 = 1/6

help pleaseeeeeeeeeeeeeeee

Answers

Answer:

(b) f(2) = 28

(c) f(-2) = -20

Step-by-step explanation:

f(2) = -2^3 + 7 x 2^2 - 2 x 2 + 12           f(-2) = -2^3 + 7 x -2^2 - 2 x -2 + 12


1. Calculate Exponents


-2^3 = -8                                               -2^3 = -8

2^2 = 4                                                  -2^2 = -4

-8 + 7 x 4 - 2 x 2 + 12                           -8 + 7 x -4 - 2 x -2 + 12


2.  Multiply (left to right)


7 x 4 = 28                                               7 x -4 = -28

2 x 2 = 4                                                 2 x -2 = -4

-8 + 28 - 4 + 12                                    -8 - 28 - (-4) + 12


3. Add (left to right)


-8 + 28 = 20                                           -8 + -28 = -36

20 - 4 = 16                                              -36 - (-4)= -32

16 + 12 = 28                                            -32 + 12 = -20

Solve-2x-16=2x-20.
Ox=1
O no solutions
○ * = −1
all real numbers

Answers

x = 1


First, move the terms.
-2x - 2x = -2 + 20

Collect like terms
-4x = -20 + 16 —> -4x = -4


Divide both sides
x = 1

A local video game store sells used games and new games. A new game costs$64, including tax. A used game costs $43, including tax. Luis bought 3 more used games than new games. Luis spent $343. How many used games did Luis purchase?

Answers

Given:

new game cost - $ 64

used game cost - $ 43

Luis spent $ 343

Required:

Number of used games Luis purchased

Solution

Let: x be the number of new games Luis bought

x + 3 be the number of used games Luis bought

Total cost = $ 343

Total Cost = (No. of new games bought)(Cost of new games) + (No. of used games bought)(Cost of used games)

$ 343 = ( x ) ( $ 64 ) + ( x + 3 ) ( $ 43 )

343 = 64x + 43 ( x + 3 )

343 = 64x + 43x + 129

343 - 129 = 107x

214 = 107x

2 = x

x = 2

x be the number of new games Luis bought 2

x + 3 be the number of used games Luis bought 2 + 3 = 5

Answer:

Luis purchased 5 used games

To check:

Substitute x into the equation,

343 = x ( 64 ) + (x + 3 ) (43)

343 = 2 ( 64 ) + (2 + 3)(43)

343 = 2 (64) + (5) (43)

343 = 128 + 215

343 = 343

The computed value of x satisfies the equation, Our answer is correct.

7Lines a and bare parallel cut by transversal line t solve for the value of x25x + 4a3x + 14

Answers

These angles measure the same they are interior alternate angles.

3x + 14 = 5x + 4

Solve for x

3x - 5x = 4 - 14

Simplify like terms

-2x = -10

x = -10/-2

Result

x = 5

What needs to occur for a geometric series to converge?

Answers

Given a Geometric Series:

[tex]\sum_{n\mathop{=}1}^{\infty}a\cdot r^{n-1}[/tex]

Where "r" is the ratio.

By definition:

[tex]undefined[/tex]

Simplify completely.a.4x212 xwhen x +0.b. (2t)(3t)(t)c. (3x² - 4x +8)+(x² +6x-11)d. (3x² + 4x – 8) - (x² + 6x +11)

Answers

The expression in 4a) is given below

[tex]\frac{4x^2}{12x}[/tex]

Collecting similar terms using the division rule of indices, we will have

[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]

The above expression therefore becomes

[tex]\begin{gathered} \frac{4x^2}{12x} \\ =\frac{4x^2}{12x^1} \\ =\frac{1}{3}\times x^{2-1} \\ =\frac{1}{3}\times x \\ =\frac{x}{3} \end{gathered}[/tex]

Hence,

The final answer = x/3

15 Which of the digits from 2 to 9 is 5544
divisible by?

Answers

Answer:

All of em, except 5

Step-by-step explanation:

5544 / 2 = 2772

5544 / 3 = 1848

5544 / 4 = 1386

5544 / 6 = 924

5544 / 7 = 792

5544 / 8 = 693

5544 / 9 = 616

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BRAINLIEST!!!!! AND 100
POINTS!!!!!

If angle a measures 42 degrees, then what other angles would be congruent to angle a and also measure 42 degrees?

Answers

If angle "a" measures 42° the the other angles that will be congruent to angle "a" and also measure 42° will be angle d, angle e and angle h .

In the question ,

a figure is given ,

From the figure we can see that 2 parallel lines are cut by a transversal .

So ,

angle a = angle d   .......because vertically opposite angles .

angle a = angle e   ...because corresponding angles are equal in measure

also

angle e = angle h      .... because vertically opposite angles .

Therefore , If angle "a" measures 42° the the other angles that will be congruent to angle "a" and also measure 42° will be angle d, angle e and angle h , the correct option is (a) .

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Please help! I can also change the vent graph to different kinds as well.

Answers

Answer:

See below and attached Venn Diagram3

Step-by-step explanation:

No need to change Venn diagrams It is perfectly clear

We will represent the different sets of people using letters A and B for convenienceThat total number of people who "Had Drowsiness" is represented by the maroon circle to the left. )Note some of those participants also belong to the category had Nausea)We will represent the set of all people who had drowsiness as A and the number of people in that set as n(A) = 95 (given)

Similarly, the total number of people who had nausea is represented by the aquamarine circle to the right. (Note that some of these people also had drowsiness) We will represent the set of all people who had  nausea as B and the number of people in that set as n(B) = 77 (given)

The number of people who had both drowsiness and nausea is the intersection area of the two i.e. the Venn diagram area in the middle which overlaps both the circles. This is represented as A and B and we are given that this number n(A and B) = 58
This is the number that would go into the center box in the Venn Diagram

The number of people who had drowsiness but not nausea is the total number of people who had drowsiness - number of people who had both side effectsThis would be n(A) - n(A and B) = 95 - 58 = 37This would be the number that would go into the box on the leftThis is referred to as set difference denoted by A - B i.e. the set of all elements in a but not in B. So we say n(A-B) = 37

Similarly the number of people experiencing nausea but not drowsiness would be set difference B-A and the number of such people would be 77 - 58 = 19This number would go into the box on the right

If we add up all the boxes we get the total number of people who had drowsiness or nausea or both as                   n(A or ) = 37 + 58 + 19 = 114You can also arrive at this number by the formula
               n(A or B) = n(A) + n(B) - n(A and B)
                = 95 + 77 - 58 = 114We subtract n(A and B)= 58 because when
we add n(A) and n(B) we are adding this chunk twice so we need to adjust by removing the duplicate additionIn addition to all these values you will see a box that is outside of any of the circles but inside the circle. This represents the number of people who had no side effects.This number would be 161 - 114 = 47

The completed Venn Diagram is attached for your convenience

The wholesale price for a chair is 194$ . A certain furniture store marks up the wholesale price by 35%. Find the price of the chair in the furniture store.

Answers

The price of the chair will be 261.9 $ .

One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. For example, 1 percent of 1,000 chickens equals 1/100 of 1,000, or 10 chickens; 20 percent of the quantity is 20/100 1,000, or 200.

If we say, 5%, then it is equal to 5/100 = 0.05.

To solve percent problems, you can use the equation, Percent · Base = Amount, and solve for the unknown numbers. Or, you can set up the proportion, Percent = , where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion.

Based on given conditions formulate

x = 194 ×(35%+1)

x= 194 ×1.35

x = 261.9 $ .

Thus The price of the chair will be 261.9 $ .

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Find all the values of x where the tangent line is horizontal.3f(x) = x³ - 4x² - 7x + 12X=(Use a comma to separate answers as needed. Type an exact answer, using radicals

Answers

Given the function:

[tex]h(x)=x^3-4x^2-7x+12[/tex]

Find the first derivative:

[tex]h^{\prime}(x)=3x^2-8x-7[/tex]

The first derivative gives us the slope of the tangent line to the graph of the function. When the tangent line is horizontal, the slope is 0, thus:

[tex]3x^2-8x-7=0[/tex]

This is a quadratic equation with coefficients a = 3, b = -8, c = -7.

To calculate the solutions to the equation, we use the quadratic solver formula:

[tex]$$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$$ [/tex]

Substituting:

[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(3)(-7)}}{2(3)}[/tex]

Operate:

[tex]\begin{gathered} x=\frac{8\pm\sqrt{64+84}}{6} \\ \\ x=\frac{8\pm\sqrt{148}}{6} \end{gathered}[/tex]

Since:

[tex]148=2^2\cdot37[/tex]

We have:

[tex]\begin{gathered} x=\frac{8\pm2\sqrt{37}}{6} \\ \\ \text{ Simplifying by 2:} \\ \\ x=\frac{4\pm\sqrt{37}}{3} \end{gathered}[/tex]

There are two solutions:

[tex]\begin{gathered} x_1=\frac{4+\sqrt{37}}{3} \\ \\ x_2=\frac{4-\sqrt{37}}{3} \end{gathered}[/tex]

I really need help please!

Answers

Answer:

  n < -15/4

Step-by-step explanation:

You want to use the discriminant to find the values of n for which the quadratic 3z² -9z = (n -3) has only complex solutions.

Discriminant

The discriminant of quadratic equation ax²+bx+c = 0 is ...

  d = b² -4ac

The given quadratic can be put in this form by subtracting (n-3):

  3z² -9z -(n -3) = 0

This gives us ...

a = 3b = -9c = -(n -3)

and the discriminant is ...

  d = (-9)² -4(3)(-(n-3)) = 81 +12(n -3)

  d = 12n +45

Complex solutions

The equation will have only complex solutions when the discriminant is negative:

  d < 0

  12n +45 < 0 . . . . . use the value of the discriminant

  n +45/12 < 0 . . . . . divide by 12

  n < -15/4 . . . . . . . subtract 15/4

There will be two complex solutions when n < -15/4.

A parents' evening was planned to start at
15h45. There were 20 consecutive
appointments of 10 minutes each and a
break of 15 minutes during the evening. At
what time was the parents evening due to
finish?
C O 19h15
O 19h20
O 19h00
O 20h00
O 19h30

Answers

The time on which parents evening was due to finish was 19 hour 20 minutes.

What is time and its unit?

Time is the ongoing pattern of existence and things that happen in what seems to be an irreversible order from the past, through the present, and into the future.

It is a component quantity of various measurements used to order events, compare the length of events or the time gaps between them, and quantify rates of change of quantities in objective reality or in conscious experience. Along with the three spatial dimensions, time is frequently considered a fourth dimension.

The International System of Units is built upon the seven base units of measurement stipulated by the Système International d'Unités (SI), from which all other SI units are derived. The primary unit of time is the second. The second can be shortened using either the letter S or the letter sec.

20 consecutive appointments of 10 mins = 20 × 10 mins

                                                                     = 200 min

                                                                      = 3 hours 20 mins

A break of 15 mins = 3 hours 20 mins + 15 min

                               = 3 hours 35 mins

The time that the parents evening due to finish = 15h 45 min +3h 35 mins

                                                                               = 19h 20min

Thus, the time on which parents evening was due to finish was 19h 20min.

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Use the rules of significant figures to answer the following question:43.5694 * 22.07A. 961.58B. 961C. 961.577D. 961.7

Answers

we have that

43.5694 * 22.07=961.576658

therefore

the answer is

961.577 -----> 6 figures

(remember that 43.5694 has 6 figures)

option C

If the Manufacturing Overhead account is closed proportionally to Work in Process, Finished Goods, and Cost of Goods Sold, the related entry will include a ________.

Answers

If the Manufacturing Overhead account is closed proportionally to Work in Process, Finished Goods, and Cost of Goods Sold, the related entry will include a Credit to cost of goods sold for $12000

How  to solve for the cost

The cost of a good is the total amount that was used in the purchase of a particular good form the market.

we have the manufacturing overhead to be = 30000 dollars

the work in progress = 30000 x 25 %

= 30000 x 0.25

= 7500

The finished goods = 30000 x 35 %

= 30000 x 0.35

= 10500

The cost of good sold = 30000 - 10500 - 7500

= 12000

Hence the cost of good sold is 12000

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complete question

Manufacturing overhead applied $ 150,000  

Actual amount of manufacturing overhead costs  120,000  

Amount of overhead applied during the year that is in:    

Work in Process $ 37,500 25 %

Finished Goods  52,500 35 %

Cost of Goods Sold  60,000 40 %

Total overhead applied $ 150,000 100 %

If the Manufacturing Overhead account is closed proportionally to Work in Process, Finished Goods, and Cost of Goods Sold, the related entry will include a ________.

debit to Cost of Goods Sold for $12,000

credit to Cost of Goods Sold for $12,000

credit to Cost of Goods Sold for $30,000

debit to Work in Process for $7,500

Solve for a.5a== ✓ [?]2aPythagorean Theorem: a2 + b2 = c2=

Answers

ANSWER

a = √21

EXPLANATION

This is a right triangle, so we have to apply the Pythagorean Theorem to find the value of a.

We know the length of the hypotenuse which is 5, and the length of one of the legs, which is 2. The Pythagorean Theorem for this problem is,

[tex]a^2+2^2=5^2[/tex]

Subtract 2² from both sides,

[tex]\begin{gathered} a^2+2^2-2^2=5^2-2^2 \\ a^2=25-4 \end{gathered}[/tex]

And take the square root to both sides,

[tex]\begin{gathered} \sqrt[]{a^2}=\sqrt[]{25-4} \\ a=\sqrt[]{21} \end{gathered}[/tex]

Hence, the value of a is √21.

How many gallons of the water are in the filled tank? You must show work with dimensional analysis using the above fact.

Answers

From the question, we can deduce the following:

Length = 5.6 meters

Width = 7.3 meters

Height = 4.5 meters

Where:

1 ft = 0.3048 m

1 cubic foot = 7.48 gallons

Let's find the amount of gallons of water in the tank if the tank is filled to 1 foot below the top of the tank.

Let's first sketch the tank.

We have:

Now, let's find the volume of the tank(total amount of water it can carry).

Apply the formula:

[tex]V=l\times w\times h[/tex]

Thus, we have:

[tex]\begin{gathered} V=5.6\times7.3\times4.5 \\ \\ V=183.96m^3 \end{gathered}[/tex]

Now, to find the amount of water presently in the tank since it is filled 1 ft below the top of the tank, we have:

[tex]\begin{gathered} V=5.6\times7.3\times(4.5-0.3048) \\ \\ V=5.6\times7.3\times4.1952 \\ \\ V=171.5m^3 \end{gathered}[/tex]

Therefore, the volume of the water in the tank is 171.5 cubic meters.

Now, let'c convert from cubic meters to gallons.

Where:

1 foot = 0.3048 m

[tex]1meter=\frac{1}{0.3048}=3.28\text{ feet}[/tex]

Thus, we have:

[tex]\begin{gathered} 1\text{ cubic meter = 3.28}^3=35.29\text{ cubic f}eet \\ \\ 171.5\text{ cubic meters = 171.5 x 35.29 = }6052.235\text{ cubic fe}et \end{gathered}[/tex]

Now, to convert from cubic feet to gallons, where:

1 cubci foot = 7.48 gallon

We have:

[tex]6052.235\times7.48=45273.86\text{ gallons}[/tex]

Therefore, there are 45273.86 gallons of water filled in the tank.

Write and solve an equation that represents the following math sentence.

Twenty-nine equals the sum of 11.5 and the quotient of a number and 2.5.

29 equals 11.5 plus m over 2.5; m = 43.75
29 equals 11.5 plus m over 2.5; m = 7
29 = 11.5 + 2.5m; m = 43.75
29 = 11.5 + 2.5m; m = 7

Answers

The algebraic expression which correctly represents the word phrase and it's solution are respectively; 29 equals 11.5 plus m over 2.5; m = 43.75.

What is the algebraic expression which correctly represents the given word phrase?

It follows from the task content that the algebraic expression of which represents the word phrase is to be determined.

First, the quotient of a number, m and 2.5 can be represented algebraically as; m/2.5.

Therefore, since; Twenty-nine equals the sum of 11.5 and the quotient of a number and 2.5, we have;

29 = 11.5 + (m/2.5)

The solution is therefore as follows;

29 -11.5 = (m/2.5)

17.5 = (m/2.5)

m = 2.5 × 17.5

m = 43.75.

Therefore, the correct answer choice is; 29 equals 11.5 plus m over 2.5; m = 43.75.

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Would the inverse of this graph be a function? Why or why not?

Answers

We will have the following:

*First: We would determine the piecewise function that describes the graph.

Since we can see that the function increases by a factor of 2 and decreases by the same factor we would have:

[tex]f(x)=\begin{cases}2x\colon x\ge0\land x\le4 \\ \\ -2x+16\colon x>4\land\le8\end{cases}[/tex]

This is:

*Second: We calculate the inverse of the piecewise function:

[tex]f^{-1}(x)=\begin{cases}\frac{x}{2}\colon x\ge0\land x\le4 \\ \\ -\frac{x-16}{2}\colon x>4\land x\le8\end{cases}[/tex]

That is:

From this we can see that the inverse of that graph would in fact represent a function, a non-continuous function. [It will represent a function as long as it follows the parameters stablished in the first point]

For people over 50 years old, the level of glucose in the blood (following a 12 hour fast) is approximately normally distributed with mean 85 mg/dl and standard deviation 25 mg/dl ("Diagnostic Tests with Nursing Applications", S. Loeb). A test result of less than 40 mg/dl is an indication of severe excess insulin, and medication is usually prescribed.

What is the probability that a randomly-selected person will find an indication of severe excess insulin?

Suppose that a doctor uses the average of two tests taken a week apart (assume the readings are independent). What is the probabiltiy that the person will find an indication of severe excess insulin?

Repeat for 3 tests taken a week apart:

Repeat for 5 tests taken a week apart:

Answers

Using the normal distribution and the central limit theorem, it is found that:

There is a 0.0359 = 3.59% probability that a randomly-selected person will find an indication of severe excess insulin.Considering the mean of two tests, there is a 0.0054 = 0.54% probability that the person will find an indication of severe excess insulin.Three tests: 0.0009 = 0.09%.Five tests: 0% probability.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score score is positive or negative.From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X in the distribution of interest.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

The mean and the standard deviation of the glucose levels are given, respectively, by:

[tex]\mu = 85, \sigma = 25[/tex]

The probability of a reading of less than 40 mg/dl(severe excess insulin) is the p-value of Z when X = 40, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (40 - 85)/25

Z = -1.8.

Z = -1.8 has a p-value of 0.0359.

For the mean of two tests, the standard error is:

s = 25/sqrt(2) = 17.68.

Hence, by the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (40 - 85)/17.68

Z = -2.55.

Z = -2.55 has a p-value of 0.0054.

For 3 tests, we have that:

s = 25/sqrt(3) = 14.43.

Z = (40 - 85)/14.43

Z = -3.12.

Z = -3.12 has a p-value of 0.0009.

For 5 tests, we have that:

s = 25/sqrt(5) = 11.18.

Z = (40 - 85)/11.18

Z = -4.03

Z = -4.03 has a p-value of 0.

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The sum of the squares of three consecutive odd numbers is 83. Find the numbers.

Answers

In order to represent three consecutive odd numbers, we can use the expressions "x", "x+2" and "x+4".

If we add the square of each number, the result is 83, so we can write the following inequality:

[tex]\begin{gathered} x^2+(x+2)^2+(x+4)^2=83\\ \\ x^2+x^2+4x+4+x^2+8x+16=83\\ \\ 3x^2+12x+20=83\\ \\ 3x^2+12-63=0\\ \\ x^2+4x-21=0 \end{gathered}[/tex]

Let's solve this quadratic equation using the quadratic formula, with a = 1, b = 4 and c = -21:

[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4a}c}{2a}\\ \\ x=\frac{-4\pm\sqrt{16+84}}{2}\\ \\ x=\frac{-4\pm10}{2}\\ \\ x_1=\frac{-4+10}{2}=\frac{6}{2}=3\\ \\ x_2=\frac{-4-10}{2}=\frac{-14}{2}=-7 \end{gathered}[/tex]

If we assume the numbers are positive, the numbers are 3, 5 and 7.

(The other result, with negative numbers, would be -7, -5 and -3).

Solve the system [tex]\left \{ {{5x1 + 5x2 = 5} \atop {2x1 + 3x2 = 4}} \right.[/tex]

Answers

The solution for the given system of equations is x[1] = -1 and x[2] = 2.

What is system of equations?

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.

Given are the following equations as -

5 x[1] + 5 x[2] = 5

2 x[1] + 3 x[2] = 4

Assume that -

x[1] = a    

x[2] = b

Then, we can write the equations as -

5a + 5b = 5

2a + 3b = 4

Now -

5a + 5b = 5

5(a + b) = 5

a + b = 1

a = 1 - b

So, we can write -

2a + 3b = 4

as

2(1 - b) + 3b =4

2 - 2b + 3b = 4

b = 4 - 2

b = 2 = x[2]

Then

a = 1 - 2

a = -1 = x[1]

Therefore, the solution for the given system of equations is x[1] = -1 and x[2] = 2.

To solve more questions on system of equations , visit the link below-

https://brainly.com/question/27911202

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Write the equation of a Circle with the given information.End points of a diameter : (11, 2) and (-7,-4)

Answers

The form of the equation of the circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where (h, k) are the coordinates of the center

r is the radius

Since the endpoints of the diameter are (11, 2) and (-7, -4), then

The center of the circle is the midpoint of the diameter

[tex]\begin{gathered} M=(\frac{11+(-7)}{2},\frac{2+(-4)}{2}) \\ M=(\frac{4}{2},\frac{-2}{2}) \\ M=(2,-1) \end{gathered}[/tex]

The center of the circle is (2, -1), then

h = 2 and k = -1

Now we need to find the length of the radius, then

We will use the rule of the distance between the center (2, -1) and one of the endpoints of the diameter we will take (11, 2)

[tex]\begin{gathered} r=\sqrt[]{(11-2)^2+(2--1)^2} \\ r=\sqrt[]{9^2+3}^2 \\ r=\sqrt[]{81+9} \\ r=\sqrt[]{90} \\ r^2=90 \end{gathered}[/tex]

Now substitute them in the rule above

[tex]undefined[/tex]

A baseball team has home games on Wednesday and Saturday. The two games together earn $4920.00 for the team. Wednesday's game generates $880.00 less than Saturday's game. How much money did Wednesday's game generate?

Answers

Answer:

Wednesday's game generated $2020

Explanations:

Let the amount generated by Wednesday's game be x

Let the amount generated by Saturday's game be y

The two games together earn $4920 for the team. That is,

x + y = 4920....................(1)

Wednesday's game generates $880 less than Saturday's game

x = y - 880.................(2)

Make y the subject of the formula in equation (2)

y = x + 880..................(3)

Substitute equation (3) into equation (2)

x + x + 880 = 4920

x + x = 4920 - 880

2x = 4040

Divide both sides by 2

2x/2 = 4040/2

x = 2020

Wednesday's game generated $2020

you pick a marble and flip a coin how many outcomes are possible

Answers

Solution

A coin has two possible outcome

We have 5 marbles

[tex]2\times5=10[/tex]

The final answer

[tex]10[/tex]

Andre was trying to write 7^4/7^-3 with a single exponent and write 7^4/7^-3= 7^4-3=7^1 Exploit to Andre what his mistake was and what the answer should be...PLEASE THE ANSWER IS URGENT!!

Answers

[tex]\frac{7^4}{7^{-3}}=7^7[/tex]

Here, we want to get what Andre's mistake was and correct it

To answer this, we are supposed to use the division law of indices

We have this as;

[tex]\frac{a^x}{a^y\text{ }}=a^{x-y}[/tex]

Now, in the case of this question, x is 4 and y is -3

So, we have the expression as;

[tex]7^{4-(-3)}=7^{4+3}=7^7[/tex]

His mistake is thus adding the exponents instead of subtracting

John took 30 minutes to bicycle to his grandmother’s house, a total of 2.5 kilometers. What was his speed in km/hr?

Answers

Answer:

5(km)/1(hr)

Step-by-step explanation:

You multiply the 30 minutes to make one hour, and with that, you also multiply the 2.5 kilometers to get 5. You multiply the 2.5 because we multiply both sides of an equation.

Uniform line movement.

We have that the data is:

Time (t) = 30 m = 0.5 h

Distance (d)= 2.5 km

Speed (v) = ?

Since it asks us for the speed in Km/h, we make a time conversion, from minutes to hours. Knowing that 1 hr = 60 minutes, then

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{30 \not{m}*\left(\frac{1 \ h}{60 \not{m})\right)=0.5 \ h } } \end{gathered}$}}[/tex]

To calculate the speed, divide the distance by the time. We apply the following formula:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{Speed=\frac{Distance}{Time} } \end{gathered}$}}[/tex]

We substitute our data in the formula and solve:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=\frac{d}{t} } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=\frac{2.5 \ km}{0.5 \ h} } \end{gathered}$}}[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=5 \ km/h} \end{gathered}$} }}[/tex]

Juan's speed was: 5 km/h.
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