Determine if (-2,6) and (4,12) are solutions to the system of equations:

y = x + 8
2y = x2 + 8

A) Both are solutions.
B) Neither is a solution.
C) It cannot be determined
D) Only (-2,6) is a solution.

Answer:

C

Step-by-step explanation:

Since we are dealing with recursive equations, we can use a simple format.

[tex]a_{1}=x \\ \\ a_{n}=a_{n-1}+y[/tex]

x is the starting value and y is the change.

We can see that the change is -5.6 since 5.6 is being subtracted from each term each time.

So the equation would be

[tex]a_n=a_{n-1}-5.6[/tex]

We can check this by plugging in the numbers.

Let's see if -8.3 works, which is the 2nd term in the equation.

[tex]a_2=a_{2-1}-5.6 \\ \\ -8.3=a_{1}-5.6 \\ \\ -8.3=-2.7-5.6 \\ \\ -8.3=-8.3[/tex]

Therefore, the recursive rule is the third one.

Answer:

(1 , 1)

Step-by-step explanation:

Given in the question two equations

Equation 1

y = x² – x + 1

Equation 2

y = x

Equate both equations

x² – x + 1 = x

0 = x² – x + 1 - x

x² – 2x + 1 = 0

x² - x - x + 1 = 0

x(x - 1) -1(x - 1) = 0

(x - 1)(x - 1) = 0

(x-1)² = 0

x - 1 = 0

x = 1

Plug x = 1 in first equation

y = 1² – 1 + 1

y = 1

Answer:

The answer is option A, or (1,1)

Step-by-step explanation:

I just took the test

Answer:

(n - 43)³

Step-by-step explanation:

Let the number be n.

Then the desired expression is (n - 43)³

Answer:

Algebraic expression = (x-43)^3

Step-by-step explanation:

Given , the verbal expression is the cube of the difference of a number and 43.

Let x be the number

Now, according to question

Difference means subtraction  in which a number is subtracted from the other number

Difference of a number and 43

It means 43 is subtracted from x

Now , the algebraic  expression =x-43

Cube of the difference of a number x and 43 =(x-43)(x-43)(x-43)

Cube of a number means multiply a number three times with self .

Therefore, Cube of the difference of a number x and 43=[tex](x-43)\times (x-43)\times(x-43)[/tex]

 Cube of the difference  of a number x and 43=(x-43)^3

Because in multiply  when base same then power of the number added.

I

Answer:

The final temperature of the solution was 5°C

Step-by-step explanation:

we know that

1) At the start of an experiment, the temperature of a solution was -12°C

In this moment the temperature is -12°C

2) During the experiment, the temperature of the solution rose 5°C each hour during 4 hours

so

5°C*4=20°C

In this moment the temperature is -12°C+20°C=8°C

3) The temperature changed by -3°C

In this moment the temperature is 8°C-3°C=5°C

Answer:

The final temperature of the solution was 5°C

Step-by-step explanation:

Answer:

34.

Step-by-step explanation:

A and c —————- Bc 20 +8 is 28

Answer:

The answer is (8,20) on APEX. just did the test. good luck!

Answer:

D) (4,5)

Step-by-step explanation:

Vertex E was dilated by 1/2 because 8/2 = 4. Thus, you will divide all the other coordinates by the same scale factor.

Answer:

Part A) Option C. obtuse

Part B) Option B. acute

Step-by-step explanation:

we know that

Applying the Pythagoras Theorem

if [tex]c^{2}=a^{2}+b^{2}[/tex] ----> is a right triangle

if [tex]c^{2}>a^{2}+b^{2}[/tex] ----> is an obtuse triangle

if [tex]c^{2}<a^{2}+b^{2}[/tex] ----> is an acute triangle  

where

c is the greater side

Part A) A triangle has side lengths 32, 45 and 18. What type of triangle is it?

we have

[tex]c^{2}=45^{2}=2,025[/tex]

[tex]a^{2}+b^{2}=32^{2}+18^{2}=1,348[/tex]

therefore

[tex]c^{2}>a^{2}+b^{2}[/tex]

Is an obtuse triangle

Part B) A triangle has side lengths 44, 36 and 30. What type of triangle is it?

we have

[tex]c^{2}=44^{2}=1,936[/tex]

[tex]a^{2}+b^{2}=36^{2}+30^{2}=2,196[/tex]

therefore

[tex]c^{2}< a^{2}+b^{2}[/tex]

Is an acute triangle

Answer:

110 1/3 or 100.33 degrees (to the nearest hundredth).

Step-by-step explanation:

There are 60 ' (minutes) in a degree.

So 20' = 20/60 = 1/3 of a degree.

Answer:

110 1/3°

Step-by-step explanation:

Recall that 1° = 60'.  Then 20' is 1/3 of 1°, or (1/3)°.

Then 110° 20' = 110° + (1/3)° = 110 1/3°.

Answer: $72000

Answer: TRUE

Step-by-step explanation: This is true, because there is an infinite amount of real numbers in both, and they are both countably infinite (so these infinities are equal). Hope this helps!

Area of circle

= 90/360 x π x (10)^2

= 1/4 π x 100

= 25 π meter^2

Final answer:

The area of a sector with a central angle of 90° and a radius of 10 meters is calculated using the formula A = θ/360 × πr². Substituting the given values, the area is found to be 25π m². The correct answer is D. 25π meters².

Explanation:

Finding the Area of a Sector

To find the area of a sector with a central angle of 90° in a circle with a radius of 10 meters, we use the formula for the area of a sector, which is A = θ/360 × πr², where θ is the central angle in degrees, π is the mathematical constant approximately equal to 3.14159, and r is the radius. Since the central angle θ is 90°, and the radius r is 10 meters, we have:

A = 90°/360° × π × (10 m)²
= 0.25 × π × 100 m²
= 25π m².

Therefore, the correct answer is D. 25π meters².

Answer:

Step-by-step explanation:

1)  x/5 = 10

multiply by 5 : x = 50

2)  x + 2 = 15

add -2 :  x = 13  

3)  5x = 40  

divid by 5  :  x =8

4)  2y = 44

divid by 2 : y = 22

5. r - 15 = 30

add 15 ;  5r =45

divid by 5 :  r = 9

Answer:

See explanation

Step-by-step explanation:

Zeroe of the function is such velue of x at which f(x)=0.

1. Consider the function [tex]f(x)=-x(3x-2)^2 (x+9)^5.[/tex]  

Zeros are:

[tex]-x(3x-2)^2(x+9)^5=0\\ \\x=0\text{ or }x=\dfrac{2}{3}\text{ or }x=-9.[/tex]

Zero [tex]x=0[/tex] has multiplicity of 1, zero [tex]x=\dfrac{2}{3}[/tex] has multiplicity of 2, zero [tex]x=-9[/tex] has multiplicity of 5.

At [tex]x=0[/tex] or [tex]x=-9[/tex] the graph of the function crosses the x-axis, at [tex]x=\dfrac{2}{3}[/tex] the graph of the function touches the x-axis.

2. Consider the function [tex]f(x)=x^3+10x^2+25x=x(x^2+10x+25)=x(x+5)^2.[/tex]  

Zeros are:

[tex]x(x+5)^2=0\\ \\x=0\text{ or }x=-5.[/tex]

Zero [tex]x=0[/tex] has multiplicity of 1, zero [tex]x=-5[/tex] has multiplicity of 2.

At [tex]x=0[/tex] the graph of the function crosses the x-axis, at [tex]x=-5[/tex] the graph of the function touches the x-axis.

Answer:

Step-by-step explanation:

[tex]\sum\limits_{n=1}^{42}2n-3\\\\a_n=2n-3\\\\a_{n+1}=2(n+1)-3=2n+2-3=2n-1\\\\a_{n+1}-a_n=(2n-1)-(2n-3)=2n-1-2n+3=2=constant\\\\\text{Therefore it's an arithmetic sequence with first term}\\\\a_1=2(1)-3=2-3=-1\\\\\text{and common difference}\\\\d=2[/tex]

[tex]\text{The formula of a sum of terms of an aithmetic sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{Substitute:}\\\\n=42,\ a_1=-1,\ d=2:\\\\S_{42}=\dfrac{2(-1)+(42-1)(2)}{2}\cdot42=[-2+(41)(2)](21)=(-2+82)(21)\\\\=(80)(21)=1680[/tex]

Answer:

8.4

Step-by-step explanation:

hope it helped

Answer:

x = 88.2

Step-by-step explanation:

The angle at the top of the triangle = 90° - 10° = 80°

and the left side of the triangle is x ( opposite sides of a rectangle )

Using the tangent ratio in the right triangle

tan80° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{500}{x}[/tex]

Multiply both sides by x

x × tan80° = 500 ( divide both sides by tan80° )

x = [tex]\frac{500}{tan80}[/tex] ≈ 88.2

I’m not quite sure what the function is but if it’s sine the period is pi/8

ANSWER

The period is

[tex] \frac{\pi}{8} [/tex]

EXPLANATION

The given function completes four cycles on the interval

[tex]

[ - \frac{\pi}{4} , \frac{\pi}{4} ][/tex]

Therefore the period is

[tex] = \frac{ \frac{\pi}{4} - \frac{\pi}{4} }{4} [/tex]

Simplify the numerator:

[tex] = \frac{ \frac{\pi}{2}}{4} [/tex]

Simplify further to get:

[tex]= \frac{\pi}{8} [/tex]

Answer:

1

Step-by-step explanation:

The amplitude is the maximum distance away from the middle of the wave. Here we can see that the middle of the wave is the x axis and the farthest point (largest difference between the y coordinate of the x-axis, or the line y = 0, and the wave) is 1 unit away.

Answer:

1

Step-by-step explanation:

Answer:

0.22

Step-by-step explanation:

The point estimate is the average of the upper and lower bounds of the interval.

Answer:

9

Step-by-step explanation:

6 / 2 (1 + 2) = 9

PEMDAS

Parentheses first

1+2 =3

Substitute this in

6 / 2 (3) = 9

Multiplication and Division from left to right

Division first

6/2 =3

Substitute this in for 6/2

3 (3) =9

3*3 =9

Answer:

D:Point A and point B are the same distance from the origin.

Step-by-step explanation:

hope this helps :)

Answer:

D

Step-by-step explanation:

Hit the THANKS button pls >.<

  V

  V

  V

Answer:

Step-by-step explanation:

The volume of a rect. prism is V = (length)(width)(height).

Here the volume is V = (4 in)(6 in)(5 in) = 120 in³ or 120 in^3

Note:  Please use " ^ " to indicate exponentiation:  120 in^3

Answer:

120 in 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

You can't answer c. There is not enough information.  Other than there are 14 boys that went, you know nothing about how many went.

Girls going = (3/5) * 20 = 12

Girls not going = 20 - 12 = 8

Answer:

(-8,5)

Step-by-step explanation:

The output corresponds to the y-value of an ordered pair while the input corresponds to the x-value of an order pair.

An ordered pair is written like this (x,y)

Answer:

The center is at [tex](2,4)[/tex]

3 units

Step-by-step explanation:

You can observe in the graph a circle.

The x-coordinate and the y-coordinate of the center of the circle shown in the figure are:

[tex]x=2[/tex] and [tex]y=4[/tex]

Therefore, the point of the center of the circle is:

[tex](2,4)[/tex]

 You can observe that the diameter goes from -1 to 5, then the diameter is:

[tex]diameter=1units+5units\\\\diameter=6units[/tex]

The radius is half the diameter. Therefore, you can say that the radius of this circle is:

[tex]radius=\frac{diameter}{2}\\\\radius=\frac{6units}{2}\\\\radius=3units[/tex]

ANSWER

The center is (2,4)

The radius is 2√2 units

EXPLANATION

Each of the ticks is 1 unit

Counting two ticks from the origin to the right and 4 units up will land us at the center of the circle.

Hence the center is (2,4)

The circle passes through (0,2).

The radius is

[tex]r = \sqrt{ {(2 - 0)}^{2} + {(4 - 2)}^{2} } [/tex]

[tex]r = \sqrt{8} = 2 \sqrt{2} [/tex]

There were 3 different fish caught, Salmon, Herring and Flounder.

4/9 were Herring, 2/9 were Salmon, 4/9 +2/9 = 6/9

This means 3/9 were Flounders ( 3/9 + 6/9 = 9/9 = 1)

3/9 can be reduced to 1/3.

1/3 of the fish were Flounders.

Divide the amount of flounders by the portion caught:

12 / 1/3 = 12 * 3/1 = 36 total fish.

Now you have total number of fish, multiply the total by each portion for each type of fish.

Total fish = 36

Herring = 4/9 x 36 = 16

Salmon = 2/9 x 36 = 8

Answer:

  124°

Step-by-step explanation:

Supplementary angles add to 180°.

  56° + second angle = 180°

Subtract 56° from both sides of the equation:

  second angle = 180° - 56° = 124°

Answer: 4.59

sin(35)=x/8

8*sin(35)=x

x=4.59

The value of x in the given triangle round to the nearest hundredths is:

                           4.59

From the given triangle we observe that the side x is the opposite side corresponding to angle 35°.

i.e. we will use sine trignometric ratio in the triangle to get the value of x.

We know that:

[tex]\sin 35=\dfrac{x}{8}ddd[/tex]

Since the sine of an angle is the ratio of opposite side to the hypotenuse of the right angled triangle.

i.e.

[tex]x=8\times \sin 35\\\\i.e.\\\\x=8\times 0.5736\\\\i.e.\\\\x=4.588[/tex]

which is approximately equal to 4.59  units.

Answer: The lower quartile is Q1) is your minimum & your maximum is quartile Q3) bc is the larger one

Step-by-step explanation:

c

a

e

b

d

is none of your answer.

Answer:

person above is correct

Step-by-step explanation:

show them some love