What are the ordered pairs of the
solutions for this system of equations?
f(x) = x2 – 5x + 3; f(x) = -3

Answers

Answer 1

Start by writing the system down, I will use [tex]y[/tex] to represent [tex]f(x)[/tex]

[tex]y=x^2-5x+3\wedge y=-3[/tex]

Substitute the fact that [tex]y=-3[/tex] into the first equation to get,

[tex]-3=x^2-5x+3[/tex]

Simplify into a quadratic form ([tex]ax^2+bx+c=0[/tex]),

[tex]x^2-5x+6=0[/tex]

Now you can use Vieta's rule which states that any quadratic equation can be written in the following form,

[tex]x^2+x(m+n)+mn=0[/tex]

which then must factor into

[tex](x+m)(x+n)=0[/tex]

And the solutions will be [tex]m,n[/tex].

Clearly for small coefficients like ours [tex]5,6[/tex], this is very easy to figure out. To get 5 and 6 we simply say that [tex]m=3, n=2[/tex].

This fits the definition as [tex]5=3+2[/tex] and [tex]6=2\cdot3[/tex].

So as mentioned, solutions will equal to [tex]m=3, n=2[/tex] but these are just x-values in the solution pairs of a form [tex](x,y)[/tex].

To get y-values we must substitute 3 for x in the original equation and then also 2 for x in the original equation. Luckily we already know that substituting either of the two numbers yields a zero.

So the solution pairs are [tex](2,0)[/tex] and [tex](3,0)[/tex].

Hope this helps :)


Related Questions

There are nine squares in a 3 x 3 square grid. Four of them will be painted white, how many will be painted black?
I need good explanation, not just the answer, will we use division? Mult?

Answers

Answer:

5 squares will be painted black.

Step-by-step explanation:

There are 9 squares, and 4 of them will be painted white, so that means that the remaining squares will be painted black. 9-4=5, so 5 squares will be painted black.

Hope this helped! :)

Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 25 mph in a direction 340°. The second sails at 29 mph in a direction 210°. Assuming that both boats maintain speed and heading, after 5 hours, how far apart are the boats?

A. 157.4 mi
B. 212 mi
C. 175 mi
D. 244.8 mi

Answers

9514 1404 393

Answer:

  D. 244.8 mi

Step-by-step explanation:

The law of cosines can be used to find the distance between the boats.

The first boat will have traveled (5 h)×(25 mi/h) = 125 mi. The second boat will have traveled (5 h)×(29 mi/h) = 145 mi. The angle between their travel directions is 340° -210° = 130°.

  c² = a² +b² -2ab·cos(C) . . . . . for a=125, b=145, C=130°

  c² ≈ 59951.05

  c ≈ √59951.05 ≈ 244.8 . . . miles

The boats are about 244.8 miles apart after 5 hours.

One of the angles of a pair of complementary angles is 50°. Find the ratio of the pair of complementary angles​

Answers

Answer:

4:5

Step-by-step explanation:

A pair of complementary add up to 90, given that one of them is 50, we can do this: x + 50 = 90

solve it and we get x = 40

40 + 50 = 90, so 40 and 50 are the pair of complementary angles.

As for it's Ratio, we can just get the pair and have it as 40:50 but we can reduce it to 4:5

7
Timon makes $12 an
hour working at the
refinery, but he makes
$20 an hour overtime
(when he works more
than 40 hours a week).
Last week, he worked
57 hours. How much
did Timon make?
(before taxes

Answers

Answer:

$820

Step-by-step explanation:

he worked 57 hours.

so, 40 regular hours and 17 overtime hours.

therefore, he earned

40×12 + 17×20 = 480 + 340 = $820

What is the y-intercept of the line?
a) (3,0)
b) (0,3)
c) (2,0)
d) (0,2)

Answers

I don’t know because I don’t have the x

Find the area of a circle that has a radius of 60.4 m. Put your answer as yards squared rounded to 1 decimal.

Answers

Answer:

13707.2 yards squared

Step-by-step explanation:

meter is almost a yard

60.4 meters = 66.054 yards

area of a circle = Pi * r^2

Pi * (66.054 yards * 66.054 yards)

= 13707.1800324

A camel can drink 15 gallons of water in 10 minutes. At this​ rate, how much water can the camel drink in 6 ​minutes?

Answers

Answer:  9 gallons

Work Shown:

(15 gallons)/(10 minutes) = (x gallons)/(6 minutes)

15/10 = x/6

15*6 = 10*x ... cross multiplication

90 = 10x

10x = 90

x = 90/10

x = 9

The camel can drink 9 gallons in 6 minutes. This is assuming that the unit rate is kept the same.

Expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of logs.



ln(1/49^k)

Answers

9514 1404 393

Answer:

  -2k·ln(7)

Step-by-step explanation:

49 is a perfect square, so the argument of the log function can be written as ...

  1/46^k = 1/(7^2)^k = 1/7^(2k) = 7^(-2k)

Then the log of it is ...

  ln(7^(-2k)) = -2k·ln(7)

(-1/2^5)×2^3×(3/4^2) [EVALUATE]​

Answers

Step-by-step explanation:

here's the answer to your question

first to answer gets brainiest
Which line plot displays a data set with an outlier?

Answers

Answer:

Bottom left graph

Step-by-step explanation:

The outlier will always be the number apart or greater than all of the other numbers in the graph

hence, the answer is the bottom left graph

PLS PLS PLS ANSWER!!!!!

Answers

Answer:

1. 0.02                      

2. 100%

3. 3.66

4. 125

                                                        Hope this helps c;

what value makes the equation

Answers

Answer:

n = .25

Step-by-step explanation:

For the equation to be true, both sides must be equal.

20 * 4 * 3 * n = 5 * 12

240 * n = 60

n = 60/240

n = .25

Answer:

1/4

Step-by-step explanation:

20×n×4×3=5×12

or, 240n=60

or, n=60/240

or, n=1/4

Answered by GAUTHMATH

PLEASE HELP!! MIGHT GIVE BRAINLIEST!!!!!

Graph a line with x - intercept of -2 and has a slope of 3

Answers

Answer:

The answer must be between 20 and 5000 characters

a neon light flashes 5 times every 10 seconds. show that the light flashes 43200 times in a day ​

Answers

There are 86400 seconds in one day. Divide that by 10 to get the intervals of the flashes. You get 8640. Multiply that by 5 because the flashlight flashes 5 times, 8640 times in one day. The result is 43,200.

Answer: 432000

Step-by-step explanation: (Amount of seconds in a day ->) 86400÷2 (<- 5 times every 10 seconds is 1 flash every 2 seconds so yes, 2) = 43200 (<-Yay Answer-! )

add the missing sequence ​

Answers

Answer:

a) 2, 6, 10, 14, 18, 22

b)60, 59, 57, 54, 50, 45

c)240, 120, 60, 30, 15, 7 1/2

Step-by-step explanation:

The answer was already there.

PLEASE HELP ASAP! I have been working on this same subject for three days & still keep getting it wrong.

Find the area of the figure. (Sides meet at right angles.)
3m
2m
5m
2m
3m
3m
3m

Answers

Answer:

[tex]2 \times 5 = 10 \\ 3 \times 11 = 33 \\ 10 + 33 = 43 \\ 43 {m}^{2} [/tex]

hey please give brainly

Parallelograms geometry acellus pls help

Answers

Answer:

x = 60

Step-by-step explanation:

Recall: one of the properties of a parallelogram is that consecutive angles are supplementary. This means they add up to given 180°

2x and x are consecutive angles. Therefore:

2x + x = 180

3x = 180

Divide both sides by 3

3x/3 = 180/3

x = 60

Which similarity statement is true?

Answers

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Answer:

  (a)  ΔWZY ~ ΔWXZ ~ ΔZXY

Step-by-step explanation:

In order for the similarity statement to be correct, the corresponding sides need to be listed in the same order.

A: ΔWZY lists sides in order short leg (WZ), long leg (ZY).

  ΔWXZ lists sides in order short leg (WX), long leg (XZ).

  ΔZXY lists sides in order short leg (ZX), long leg (XY).

The first similarity statement is correct.

__

You can compare this to an incorrect one, the last one, for example.

ΔYZW lists sides in order long leg (YZ), short leg (ZW).

ΔXZW lists sides in order long leg (XZ), hypotenuse (ZW). Hypotenuse and short leg are not corresponding sides, so the similarity statement is incorrect.

For the given piecewise function, evaluate for the specified value of x.

Answers

Answer:

g(-3) = 1

Step-by-step explanation:

The x-value -3 lies within the given interval x ≤ -3, and so the correct piecewise function is x + 4, not -4 or -1.  Evaluating x + 4 at x = -3 yields 1.

Thus, g(-3) = 1

The required value of the function g(x) at x = -3 , g(-3) is +1.

Given that,
A function is given with their domain,
g(x) = x + 4 when x≤
g(x) = 4 when -3 < x < 3
g(x) = - 1 when x ≥ 3

What are functions?

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here, Function has been given with their respective limit in which the function is defined,
For the value of g(-3) the value of x = -3 lies in the limit x ≤ -3
So for this limit, we have a function,
g(x) = x + 4
g(-3) = - 3 + 4
g(-3) = +1

The required value of the function g(x) at x = -3 , g(-3) is +1.

learn more about function here:

brainly.com/question/21145944

#SPJ5

write your answer in simplest radical form​

Answers

Answer:

a = sqrt(2)

Step-by-step explanation:

This is a right triangle so we can use trig functions

sin theta = opp / hyp

sin 30 = a / 2 sqrt(2)

2 sqrt(2)  sin 30= a

2 sqrt(2) * 1/2 =a

sqrt(2) =a

Which of the following functions is graphed below?

Answers

Answer:

C

Step-by-step explanation:

the reason is , to find which function is graphed , you need

to know the intercepts of the possible answers you are given.

so when you take 'C ' for instance, and when you find the X and Y intercept you get the point (6,-6)

The question says Simplify 7log7(49)

Answers

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Answer:

 14

Step-by-step explanation:

  [tex]7\log_7(49)=7\log_7(7^2)=7\cdot2=\boxed{14}[/tex]

An organic farm has been growing an heirloom variety of summer squash. A sample of the weights of 40 summer squash revealed that the mean weight is 402.7 grams and the standard deviation 8.8 grams. What is the probability that the mean weight for a sample of 40 summer squash exceeds 405.5 grams?
a. 0.3783.
b. 0.0228.
c. 1.0000.
d. 0.5000.

Answers

Answer:

b. 0.0228

Step-by-step explanation:

We are given that

n=40

Mean,[tex]\mu=402.7 g[/tex]

Standard deviation, [tex]\sigma=8.8[/tex]g

We have to find the probability hat the mean weight for a sample of 40 summer squash exceeds 405.5 grams.

[tex]P(x>405.5)=P(\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}>\frac{405.5-402.7}{\frac{8.8}{\sqrt{40}}})[/tex]

[tex]P(x>405.5)=P(Z>\frac{2.8}{\frac{8.8}{\sqrt{40}}})[/tex]

[tex]P(x>405.5)=P(Z>2.01)[/tex]

[tex]P(x>405.5)=1-P(Z\leq 2.01)[/tex]

[tex]P(x>405.5)=1-0.977784[/tex]

[tex]P(x>405.5)=0.022216[/tex]

Hence, option b is correct.

Select the correct answer.
Solve for x.




B.

C.

D.

Answers

Answer:

C. [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]20x - 40 = 100x[/tex][tex]20x - 100x = 40[/tex][tex]- 80x = 40[/tex][tex]x = -\frac{40}{80}[/tex][tex]x = -\frac{1}{2}[/tex]

To measure achievement of third grade students, a school system randomly selects four third grade classes and tests all children in those classes. This is an example of what type of sampling?
a. systematic
b. stratified
c. cluster
d. convenience

Answers

Answer:

Cluster

Step-by-step explanation:

When observations from a large population are divided into groups, such that subjects in each of these groups are similar to one another than those in the other groups. These individual groups of observation are called clusters. In the scenario above, the random group of 4 third grade classes selected represent of cluster or group since all the subjects belong to the class grade which is to be measured and all subjects belonging to the selected cluster or group are to be measured.

What's a radian?

A) The ratio between a circle's diameter and its radius
B) The distance halfway around a circle
C) The ratio between a circle's circumference and its radius
D) An angle made at the center of a circle by an arc whose length is equal to the radius of the circle

Answers

Answer:

The correct answer is d.

What is the value of the expression below?
e^In 4
O A. 12
B. 3
C. 4.
D. 8
SUBMI

Answers

Answer:

C. 4

Step-by-step explanation:

ln(4) = the power of e to get 4.

and then we put e to the power of that answer, so the result must be 4.

There were 230 shoppers at an electronics store on opening day. The specials that day allowed 21​% of shoppers to receive a free set of earbuds and ​25% of shoppers to receive ​$5 off their first purchase. Answer parts a and b.

a. About how many shoppers received a free set of​ earbuds? Use an equivalent fraction to estimate.




b. About how many shoppers received ​$5 off their first​ purchase? Round the number of shoppers to the nearest​ whole number.

Answers

Answer:

a) About 48 of the shoppers, that is [tex]230\frac{21}{100}[/tex] of the shoppers, received a free set of​ earbuds.

b) About 58 shoppers, that is [tex]\frac{230}{4}[/tex] received ​$5 off their first​ purchase.

Step-by-step explanation:

a. About how many shoppers received a free set of​ earbuds?

21% out of 230. So

[tex]230\frac{21}{100} = 2.3(21) = 48.3[/tex]

About 48 of the shoppers, that is [tex]230\frac{21}{100}[/tex] of the shoppers, received a free set of​ earbuds.

b. About how many shoppers received ​$5 off their first​ purchase?

25% out of 230, so:

[tex]230\frac{25}{100} = 230\frac{1}{4} = \frac{230}{4} = 57.5[/tex]

About 58 shoppers, that is [tex]\frac{230}{4}[/tex] received ​$5 off their first​ purchase.

If there are sixty-four knives, forks, and
spoons on the table and each place
setting has two forks, how many places
are set?

Answers

Answer: 32 places

Step-by-step explanation:

So there are 64 forks, and 2 forks per place.

so divide 64 by 2

[tex]64 \div 2 = 32[/tex]

Answer:

16 places are set

Step-by-step explanation:

64/4= 16

PLEASE DONT AWNSER ANYTHING RANDOM I REALLY NEED THIS AND DO YOUR OWN AWNSER
Which statements about the box plot are correct? Check all that apply.

A box and whisker plot. The number line goes from 30 to 80. The whiskers range from 34 to 76, and the box ranges from 42 to 70. A line divides the box at 46.
Fifty percent of the data values lies between 34 and 46.
Seventy-five percent of the data values lies between 42 and 70.
It is unlikely that there are any outliers.
The interquartile range is 24.
The range is 36.

Answers

Answer:

Fifty percent of the data values lies between 34 and 46.

It is unlikely that there are any outliers.

Step-by-step explanation:

drawing out this box plot and looking online for a picture of the same plot:

From the box plot:

median=46

Q1=42

Q3=70

Q3-Q1= IQR=70-42=28

max=76

min=34

Range=max-min=76-34=42

no outliers seen from boxplot

Answer:

that person is right

Step-by-step explanation:

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