Solve the system
{f (x) = 2x-1
{g (x) = x^2-4

Answers

Answer 1

Answer:

2 sets of possible solutions:

x=3, y = 5

and

x=-1, y = -3

Step-by-step explanation:

Using the graphical method, (see attached)

you can graph both equations and find their intersection points.

From the attached plot, you can see that the graphs intersect at (3,5) and (-1,-3)

Alternatively, you can solve this numerically by solving the following system of equations. You will get the same answer.

y = 2x + 1 ------------------- eq. (1)

y = x² - 4 ------------------- eq. (2)

Solve The System {f (x) = 2x-1{g (x) = X^2-4

Related Questions

Each pound of fruit costs $4. Write an expression that shows the total cost of the fruit. Use the variable you identified in question 1. Btw the variable I used was "f".

Answers

Answer:

$[tex]4f[/tex]

Step-by-step explanation:

Let's assume [tex]f[/tex] represents the number of pounds of fruit.

We need to multiply the number of pounds of fruit by the cost per pound.

This is $[tex]f * 4[/tex], or in a simpler form, $[tex]4f[/tex].

Final answer:

In this context, the variable 'f' represents the number of pounds of fruit. In the expression '4f', it means that for every pound of fruit, which costs $4, you multiply the number of pounds by that price to get the total cost.

Explanation:

The problem is asking us to provide an equation for the total cost of fruit based on the cost per pound, which is $4. As you identified the variable 'f' in the previous question, let's use that to stand for the number of pounds of fruit.

The written expression for the total cost would then be 4f. This expression says that the total cost is four times the number of fruit pounds ('f') purchased

Learn more about Algebraic Expressions here:

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Four different sets of objects contain 4, 5, 6, and 8 objects, respectively. How
many unique combinations can be formed by picking one object from each
set?

Answers

Answer:

960

Step-by-step explanation:

We can find the number of unique combinations by

Multiplying 4*5*6*8

960

There are 960 possible choices  by picking 1 from each group

Each day for several days, the change in the price of a share of stock was -$3. The total change in price during those days was -$36. Over how many days is the price decline?

Answers

12

Step-by-step explanation:

-36/3 is -12 which means 12 days of decline thank u come again

Final answer:

To determine the number of days over which the price of a stock declined by $36 at a rate of $3 per day, divide the total change by the daily change, resulting in 12 days.

Explanation:

The problem described is a typical arithmetic problem where we want to find out over how many days a stock has declined in price if it dropped by a certain amount each day. To solve this, let's use linear equation reasoning. The total change in the price of the stock is -$36, and the daily change is -$3. We can express the total change (T) as the product of the daily change (d = -$3) and the number of days (n), so we have T = dn.

To find the number of days, we rewrite this equation as n = T/d, and substitute the given values to get n = -$36/-$3. Thus, n = 12. Therefore, the price of the stock declined over 12 days.

What is the total surface area of the square pyramid?

Answers

Answer:

144 in^2

Step-by-step explanation:

There are four triangular sides to this square pyramid.  According to the area-of-a-triangle formula, A = (1/2)(b)(h), which here is A = (1/2)(8 in)(5 in) = 20 in^2.

Thus, the total lateral (side) area is 4(20 in^2) = 80 in^2.

The area of the bottom is (8 in)^2, or 64 in^2.

Thus, the total surface area is 80 in^2 + 64 in^2, or 144 in^2.

Answer:

144

Step-by-step explanation:

x^2 + mx + n = 0, m and n are integers. The only possible value for x is -3. What is the value of m?

plz the solution is necessary

Thanks​

Answers

Answer:

The value of m is 3

Step-by-step explanation:

we have

[tex]x^{2}+mx+n=0[/tex]

step 1

Find the value of n

For x=0

[tex]0^{2}+m(0)+n=0[/tex]

[tex]n=0[/tex]

step 2

Find the value of m

For x=-3

substitute

[tex]x^{2}+mx=0[/tex]

[tex](-3)^{2}+m(-3)=0[/tex]

[tex]9-3m=0[/tex]

[tex]3m=9[/tex]

[tex]m=3[/tex]

6+18p-5=8p+13-2 slove for p

Answers

Answer:

p = 1

Step-by-step explanation:

6+18p-5=8p+13-2           Collect the like terms on the left and right side

6 - 5 + 18p = 8p + 13 - 2

1 + 18p = 8p + 11                Subtract 1 from both sides.

18p = 8p + 11 - 1                 Combine

18p = 8p +  10                    Subtract 8p from both sides

18p - 8p = 10                      Combine the left

10p = 10                             Divide by 10

10p/10 = 10/10

p = 1

which graph represents the solutions for x^2+x-12>0​

Answers

To find the answer, we can use the method of finding x- intercepts by solving the equation.

To solve the equation:

x^2 + x -12> 0

by using cross method,

we can find that 3 x -4 = -12

(x-3)(x+4) = 0

Therefore, x = 3 or x=-4

Hope it helps!

graph C represents the solutions for x^2+x-12>0​

What are inequalities?

Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

How to find which graph represents the solution ?

The given inequality is :

x^2+x-12>0​

Now factorizing the expression we get,

(x-3)(x+4)>0

⇒ x>3 and x<-4

Clearly graph C represents the solutions.

Find more details about "Inequality" here : https://brainly.com/question/25275758

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Given f(x) = x squared - 1 and g(x) = x+ 2, what is the value of h(-2) where h(x) = f(g(x))?

Answers

Answer: [tex]h(-2)=-1[/tex]

Step-by-step explanation:

We need to find [tex]f(g(x))[/tex]. Substitute the function [tex]g(x)[/tex] into the function [tex]f(x)[/tex]:

[tex]f(g(x)) = (x+ 2)^2- 1[/tex]

Now, we know that the function [tex]h(x)[/tex] is [tex]h(x)=f(g(x))[/tex], then:

[tex]h(x)=(x+ 2)^2- 1[/tex]

In order to find the value of [tex]h(-2)[/tex], we must substitute [tex]x=-2[/tex] into the function  [tex]h(x)=(x+ 2)^2- 1[/tex].

Therefore, the value of  [tex]h(-2)[/tex] is:

[tex]h(x)=(x+ 2)^2- 1\\\\h(-2)=(-2+ 2)^2- 1\\\\h(-2)=(0)^2- 1\\\\h(-2)=0-1\\\\h(-2)=-1[/tex]

A standard American Eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. Assuming the weights of standard Eskimo dogs are normally distributed, what range of weights would 99.7% of the dogs have?

Approximately 26–34 pounds
Approximately 24–36 pounds
Approximately 28–32 pounds
Approximately 29–31 pounds

Answers

Answer:

Option 2 - Approximately 24–36 pounds

Step-by-step explanation:

Given : A standard American Eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. Assuming the weights of standard Eskimo dogs are normally distributed.

To find : What range of weights would 99.7% of the dogs have?

Solution :

The range of 99.7% will lie between the mean ± 3 standard deviations.

We have given,

Mean weight of Eskimo dogs is [tex]\mu=30[/tex]

Standard deviation of Eskimo dogs is [tex]\sigma=2[/tex]

The range of weights would 99.7% of the dogs have,

[tex]R=\mu\pm3\sigma[/tex]

[tex]R=30\pm3(2)[/tex]

[tex]R=30\pm6[/tex]

[tex]R=30+6,30-6[/tex]

[tex]R=36,24[/tex]

Therefore, The range is approximately, 24 - 36 pounds.

So, Option 2 is correct.

Answer:

B: Approximately 24–36 pounds

Step-by-step explanation:

Patterns and lines for (0,0) (4,-12)

Answers

-12-0/4-0 = -12/4 = -3

0= -3(0) + b
B= 0

Y= -3x


Hope this helps!

The following system has a solution of x=-5, y=9, z=11.
4x+y+z=12
-4x-y-z=-10
5y-z=9
Please select the best answer from the choices provided
T
F

Answers

False - plug in the bramble for the first equation and you get 40 = 12 which is not true

Answer:

Step-by-step explanation:

false

I need help with B, C, and D​

Answers

B)

as you recall yesterday, the "far arc near arc" formula, well, notice, the angle at XDY intercepts the circle at XY, with a "near arc" of 100°, and a "far arc" of 360° - 100° = 260°.

so using the far arc near arc formula

[tex]\bf \measuredangle D=\cfrac{260-100}{2}\implies \measuredangle D=\cfrac{160}{2}\implies \measuredangle D = 80[/tex]

the twin angles at A and C will take the slack from all interior angles of 180° - 80° = 100°, so then ∡A = ∡C = 50°.

if f(x)=3x+10x and g(x)=4x-2, find (f-g)(x)

Answers

Answer:

(f-g)(x) = 9x + 2

Step-by-step explanation:

(f-g)(x) = (3x+10x) - (4x-2)

          = 3x + 10x - 4x + 2

          = 9x + 2

Answer: 3x + 6x + 2

Step-by-step explanation: would be the other answer for APEX as of 9/13/19

In order for the data in the table to represent a linear function
with a rate of change of -8, what must be the value of m?
Om = 2
Om = 3
Om = 19
m = 35

Answers

Answer:

m = 19

Step-by-step explanation:

With a rate of change of -8

27 - 8 = 19

16 - 8 = 11

so m = 19

Answer:

Third option: [tex]m=19[/tex]

Step-by-step explanation:

The rate of change is the slope of the line.

The formula for calculate the slope is:

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

You know that:

[tex]slope=-8\\y_2=m\\y_1=27\\x_2=11\\x_1=10[/tex]

Then, you can substitute them into the formula:

[tex]-8=\frac{m-27}{11-10}[/tex]

Finally, you must solve for "m":

[tex]-8=\frac{m-27}{11-10}\\\\-8(1)=m-27\\\\-8+27\\\\m=19[/tex]

what is the meaning of the slope of mr taylor's line? pls help! a lot of points

Answers

Answer:

The slope is the percentage of test score per number of days absent

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

y -----> is the percentage of test score

x ----> is the number of days absent

so

That means -----> The slope is the percentage of test score per number of days absent

In this problem the slope is negative

so

If the percentage test score increases----> the number of days decreases

If the percentage test score decreases----> the number of days increases

The angles below are supplementary. What is the value of x?
6x + 48)​

Answers

Answer:

8 is your answer.

Step-by-step explanation:

If i think that i'm doing this right.

6x + 48

6       6   divide by 6 on both sides.

  x = 8    

Hope my answer has helped you!

F= 8/5 (c) + 40 when c=5

Answers

Answer:

F = 48

Step-by-step explanation:

F= 8/5 (c) + 40

Let c=5

F = 8/5 * 5 +40

  = 8 + 40

  = 48

The answer would be F=48

8/5•5+40

Reduce the numbers

8+40

Add

F=48

What is the domain of the function y=^3squareroot of x
PLEASE HELP

Answers

Answer:

[0,∞)

Step-by-step explanation:

We can easily solve this question by plotting the equation with the use of a plotting tool or any graphing calculator.

The equation is

y=3^(√x)

Please see attached image

Since the x is inside a square root, we know that x must be greater or equal to zero.

By looking at the graph, we can check that the domain of the function is

[0,∞)

The perimeter of a rectangle is 18 feet, and the area of the rectangle is 20 square feet. What is the width of the rectangle?

Answers

4 ft or 5 ft

i think thats right

Answer:

The width can be 5 ft   or the width can be 4 ft

Step-by-step explanation:

Perimeter = 2 (l+w)  for a rectangle

Area = l*w for a rectangle

Using perimeter

18 = 2(l+w)

Divide by 2

18/2 = 2/2 (l+w)

9 = l+w

Solving for l

9-w = l

Using area

20 = l*w

Substituing for l

20 = (9-w) * w

20 = 9w - w^2

Subtract 20 from each side

20-20 =-w^2 +9w -20

0 = -w^2 +9w -20

Multiply by -1

0 = w^2 -9w+20

Factor

0 = (w-5) (w-4)

Using the zero product property

w-5 = 0   w-4 = 0

w= 5   w=4

The width can be 5 ft   or the width can be 4 ft

I need some help in this question ​

Answers

x^2 + 2x - 15
factors into (x+5)(x-3)
set this equal to 0 and get that x=-5 and x=3

The perimeter of rectangular photo is 72cm. The length is twice the width what are and width of the photo?

(Hint: The formula for perimeter is 2w+ 21= P where w is the width I is the length and P is the perimeter.)

Answers

Answer:

w =12 cm

l = 24 cm

Step-by-step explanation:

P = 2w + 2l

We know the perimeter is 72 and the length is twice the width (l = 2w)

Substituting P = 72 and l = 2w

72 = 2w + 2(2w)

72 = 2w+ 4w

Combine like terms

72 = 6w

Divide each side by 6

72/6 =6w/6

12 = w

Now we need to find l

l = 2w

l =2*12

l = 24

If f(x) = 4x - 3 and g(x) = x + 4, find (f - g) (x)

Answers

[tex](f-g)(x)=4x-3-(x+4)=4x-3-x-4=3x-7[/tex]

Which of the following is not equal to sin⁡(-230°)?

sin(130°)
-sin(-50°)
sin(50°)
sin(-50°)

Answers

Answer:

sin(-50°) is not equal to sin(-230°)

Step-by-step explanation:

You will be required to use a scientific calculator for this.

Step 1 : Find out the value of sin(-230°)

sin(-230°) = 0.766

Step 2 : Find out all the other values and see if they are 0.766 or not.

sin(130°) = 0.766 (It is equal to sin(-230°))

-sin(-50°) = 0.766 (It is equal to sin(-230°))

sin(50°) = 0.766 (It is equal to sin(-230°))

sin(-50°) = -0.766 (It is not equal to sin(-230°))

!!

Answer:

sin⁡(-230°) =sin(50°)

Step-by-step explanation:

1) sin(-a) = -sina

note : 2)  sina = sinb :   a=b   or a+b =180°

in this exercice :  

sin⁡(-230°) = - sin⁡(230°)  = - sin(-50°)=- (-sin(50°)) =sin(50°)  because :

sin⁡(230°) = sin(-50°)  because ; 230°+(-50°) =180°

           sin⁡(230°)    = -sin(50°)

The sum of one-third of a number and three-fourths of the number exceeds that number by one.

Which equation could be used to find the number?

1/3n = 3/4n + 1
1/3n + n 3/4= n - 1
1/3n + n 3/4= n + 1

Answers

The answer would be...

1/3n + 3/4n = n + 1

^^^That would be the last option

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The correct answer is last option

1/3n + n 3/4= n + 1

Step-by-step explanation:

It is given that,the sum of one-third of a number and three-fourths of the number exceeds that number by one

To find the correct option

Let 'n' be the number, one- third of the number = 1/3(n)

three - fourths of the number = 3/(4n)

Therefore the equation becomes,

1/(n) + 3/4(n)  = n + 1

Therefore the correct answer is last option

bought a new tent to take on the next Cub Scouts camping trip. The center pole of the to tent is 16 ft. tall and the sides of the tent are 20 ft. on the slant. How wide is the base of the tent?​

Answers

Answer:

24 ft

Step-by-step explanation:

The is a center pole and two side poles and the bottom. This triangle can be broken into 2 smaller triangles. When finding the base this requires the quadratic formula. a^2+b^2= C^2

We are given a and c. A is 16 and c is 20. The equation can be changed to c^2-a^2=b^2.

20^2-16^2=b^2

400-256=b^2

144=b^2

12=b

But remember there are two triangles so the base is 2b which is 24

Step by step 24-3x=-27

Answers

For this case we have the following equation:

[tex]24-3x = -27[/tex]

To solve we follow the steps below:

We subtract 24 from both sides of the equation:

[tex]-3x = -27-24\\-3x = -51[/tex]

We divide between -3 on both sides of the equation:

[tex]x = \frac {-51} {- 3}\\x = 17[/tex]

The value of x is 17

Answer:

[tex]x = 17[/tex]

Answer:

[tex]\boxed{x=17}[/tex]

Step-by-step explanation:

Subtract by 24 from both sides.

[tex]24-3x-24=-27-24[/tex]

Simplify

[tex]-27-24=-51[/tex]

[tex]-3x=-51[/tex]

Divide by -3 from both sides.

[tex]\frac{-3x}{-3}=\frac{-51}{-3}[/tex]

Simplify to find the answer.

[tex]-51\div-3=17[/tex]

[tex]x=17[/tex], is the correct answer.

Use the graph of the function y=4^x to answer the following questions

Answers

The domain of a function is all the x-values which it passes through.  The function is a continuous exponential function, and therefore, it will contain every x value.  The answer is:

The domain of the function is negative infinity to positive infinity.

Hope this helps!!

The domain of a function is the set of input values, the function can take.

The domain of the function is negative infinity to positive infinity,

The function is given as:

[tex]\mathbf{y = 4^x}[/tex]

The function is an exponential function, and there are no restriction as to the input values of an exponential function.

i.e: [tex]\mathbf{(-\infty, \infty)}[/tex]

Hence, the domain of the function is negative infinity to positive infinity,

Read more about domain at:

https://brainly.com/question/17440903

Which expressions are equivalent to the one below? Check all that apply. Log^7 1 * Log^5 25

Answers

Answer:

B if you mean log_7 (1)*log_ 5 (25)

Step-by-step explanation:

I think you mean 7 and 5 as bases... like

log_7(1)*log_5(25)

log_7(1)=0 because 7^0=1

log_5(25)=2 because 5^2=25

So you have to perform the following operation 0*2=0

so 0 is definitely one answer

1  and 5*7 are definitely not equal to 0

let's look at last choice now

log_7(7)=1 because 7^1=7

so D is equivalent to saying 2*1 which is 2 not 0

so only one choice works and it is B

Answer this question thanks :)

Answers

First multiply 2 to both sides to isolate h. Since 2 is being divided by h, multiplication (the opposite of division) will cancel 2 out (in this case it will make 2 one) from the right side and bring it over to the left side.

4 < [tex]\frac{h}{2}[/tex]

4 * 2 < [tex]\frac{h}{2}[/tex] * 2

8 < h

For the graph will you have a empty or colored in circle?

If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.

If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.

Which direction will the ray go?

If the variable is LESS then the number then the arrow will go to the left of the circle.

If the variable is MORE then the number then the arrow will go to the right of the circle.

In this case your inequality is:

8 < h OR h > 8

aka 8 is less then h OR h is greater then 8

This means that the graph will have an empty circle and the arrow will go to the right of 8. Look at image below

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

h>8

Step-by-step explanation:

4<h/2

multiply both sides by 2

8<h

You put the names of all the students in your class in a paper bag. There are 19 boys and 12 girls. If you draw a name at random, what is P(boys name)?

Answers

Hello there!

Your question is asking what the probability of picking up a boys name out of the paper bag.

Answer: [tex]\frac{19}{31}[/tex]

In order to solve this problem, we're going to have to find the total amount of names in the paper bag and the amount of boy names there are.

When you read the question, you would find some key information in it.

Key Information:

19 boys

12 girls

With the information above, we can find the probability of picking out a boy name out of the paper bag.

To find the porbability, we're going to need to get the total amount of names in the paper bag. We would just add 19 + 12.

[tex]19+12=31[/tex]

Now, we know that there are 31 total names in the bag.

But, we are trying to find the chances of pulling out a boys name. There are 19 boy names in the bag.

We would use the number 19 as our numerator and 31 as our denominator.

Your fraction should look like this:

[tex]\frac{19}{31}[/tex]

The fraction above would represent the probability to pick out a boy name.

Since 19 is a prime number, we wouldn't simplify the fraction.

Therefore, the chances of picking out a boy name from the paper bag is [tex]\frac{19}{31}[/tex]

[tex]\frac{19}{31}[/tex] should be your FINAL answer.

I hope this helps!Best regards, MasterInvestor
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