Write the equation of the graph

Answer:

The answer is Both a(x) and b(x) have the same output value at x = 2.

Step-by-step explanation:

The answer is Both a(x) and b(x) have the same output value at x = 2. Because when a(x)=b(x) the lines intersect at that point lines intersect they have a point in common. Also, a(x)=b(x) means that the outcomes are the same

The statement that is true about a(x) = b(x) at x = 2 is

Both a(x) and b(x) have the same output value at x = 2.

Option B is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

a(x) and b(x)

At x = 2,

a(x) is equal to b(x)

a(x) = b(x)

This means that,

a(x) and b(x) have the same output value at x = 2.

Both a(x) and (x) have a maximum or minimum value at x = 2.

This is not true because we have to differentiate the function and put it as zero to get the maximum and minimum value at x=2.

Both a(x) and b(x) crosses the x-axis at 2.

This is not true because the function on the graph is at a point of intersection between x = 2 and the y value.

Both a(x) and (x) crosses the y-axis at 2.​

This is not true because the function on the graph is at a point of intersection between x = 2 and the y value.

Thus,

The statement that is true about a(x) = b(x) at x = 2 is

Both a(x) and b(x) have the same output value at x = 2.

Option B is the correct answer.

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[tex]g(b)=3b+13[/tex]

Hope this helps.

r3t40

To find the formula for g(b), isolate the variable a in the given equation by solving step by step. The formula for g(b) is g(b) = 3b + 13.

To write a formula for g(b) in terms of b, we need to isolate the variable a in the equation given. Let's simplify the given equation step by step:

Therefore, the formula for g(b) is g(b) = 3b + 13

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Answer:

2i + 6

Step-by-step explanation:

4-2 = 2

6-3 = 3

2 * 3 = 6

2i

Answer:

9 - 12i

Step-by-step explanation:

Noting that i² = - 1

Expand the factors on the numerator and denominator

(4 - 2i)(6 - 3i) = 24 - 12i - 12i + 6i² = 24 - 24i - 6 = 18 - 24i

(1 - i)(1 + i) = 1 + i - i - i² = 1 + 1 = 2

The division reduces to

[tex]\frac{18-24i}{2}[/tex]

= [tex]\frac{18}{2}[/tex] - [tex]\frac{24}{2}[/tex] i

= 9 - 121i

Answer: 36" = 3 feet

               18" = 1.5 feet

Explanation: 1 foot = 12 inches

Answer:

D

Step-by-step explanation:

I graphed each equation on a piece of paper and on desmos.com

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx+b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We need two points through which the line passes to find the slope:

[tex](0,1)\\(1, -2)[/tex]

We found the slope:

[tex]m = \frac {y2-y1} {x2-x1}\\m = \frac {-2-1} {1-0} = \frac {-3} {1} = - 3[/tex]

So, the equation is of the form:

[tex]y = -3x + b[/tex]

We substitute a point to find "b":

[tex]1 = -3 (0) + b\\1 = b[/tex]

Finally, the equation is:

[tex]y = -3x+1[/tex]

Answer:

Option C

Answer:

The error is in the Step 3

Step-by-step explanation:

we know that

The area of a rectangle is equal to

A=bh

where

b is the base of rectangle

h is the height of rectangle

so

The Step 1 calculating the  Base is correct

The Step 2 calculating the Height is correct

The Step 3 calculating the area of rectangle is not correct

because

A=(8)(7)=56 units² instead of 49 units²

Answer:

The error occurred in step 3

Step-by-step explanation:

The formula of a parallelogram is

A = bh

b is the base of the parallelogram

h is the height of the parallelogram

Step 1: the calculation of the base is correct

Step 2: the calculation of the height is correct

Step 3: 8 x 7 = 49 is incorrect. 8 x 7 should be equal to 56.

Answer:

3 and -5

Step-by-step explanation:

(x-3)(x+5)greater than and =0​

separate

(1).

x - 3 > 0

add 3 to both sides

x > 3

(2).

x + 5 > 0

subtract 5 from both sides

x > -5

So, The solutions are 3 and -5

Answer: [tex](-\infty,-5]\ U\ [3,\infty)[/tex]

Step-by-step explanation:

Given the inequality [tex](x-3)(x+5)\geq 0[/tex], to find the solutions, we need to follow this procedure:

- First case:

[tex]x-3\geq 0[/tex] and  [tex]x+5\geq 0[/tex]

Solve for the variable "x":

[tex]x\geq 0+3\\x\geq 3[/tex]

 [tex]x\geq 0-5\\x\geq -5[/tex]

Then:

[tex]x\geq 3[/tex]

- Second case:

[tex]x+5\leq 0[/tex] and [tex]x-3\leq 0[/tex]

Solve for the variable "x":

[tex]x\leq 0-5\\x\leq -5[/tex]

[tex]x\leq 0+3\\x\leq 3[/tex]

Then:

[tex]x\leq-5[/tex]

Finally, the solution is:

[tex](-\infty,-5]\ U\ [3,\infty)[/tex]

Answer:

Step-by-step explanation:

To solve this problem we need to solve a system of equations. We have two machines:

The machine "Paint Pro" is used for two hours.

The machine "Goldilocks" is used for an hour and a half.

When they are working at the same time, they can paint 55 square feet per minute. Together they painted 5850 square feet of wall.

Therefore, we have the following system of equations:

P + G = 55 ft^2/m

120P + 90G = 5850 ft^2 → 4P + 3G = 195

Solving the system of equations we have that:

P = 25

G = 30

Therefore, the paint pro paints 30sqft per minute and Goldilocks paints 25 sqft per minute.

Answer:

[tex]\large\boxed{(3+\sqrt{-16})(6\sqrt{-64})=-192+144i}[/tex]

Step-by-step explanation:

[tex]\sqrt{-1}=i\to i^2=-1\\\\(3+\sqrt{-16})(6\sqrt{-64})=(3+\sqrt{(16)(-1)})(6\sqrt{(64)(-1)})\\\\=(3+\sqrt{16}\cdot\sqrt{-1})(6\cdot\sqrt{64}\cdot\sqrt{-1})=(3+4i)\bigg((6)(8i)\bigg)\\\\=(3+4i)(48i)\qquad\text{use the distributive property}\ (b+c)a=ba+ca\\\\=(3)(48i)+(4i)(48i)=144+192i^2\\\\=144i+192(-1)=-192+144i[/tex]

The value of the given expression (3+√-16)(6√-64) is (-192+144i).

As the given two factors are complex numbers, therefore, we must know about the value of i

i = √(-1)

i² = (-1)

The solution of the product,

[tex](3+\sqrt{-16})(6\sqrt{-64})\\\\ = (3\times 6\sqrt{-64}) + (\sqrt{-16}\times 6\sqrt{-64})\\\\= (3+4i)(6\cdot 8i)\\\\= (3+4i)(48i)\\\\= 144i + 192(i)^2\\\\= 144i + 192(\sqrt{-1})^2\\\\= 144i + 192(-1)\\\\= -192+144i[/tex]

Hence, the value of the given expression (3+√-16)(6√-64) is (-192+144i).

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Answer:

S(x)=42000 * 1.04^x

Step-by-step explanation:

now = 42000

in 1 year = 42000 *1,04, because 4% increase is to multiply 1,04

in 2 years = 42000 *1,04*1.04 = 42000*1.04^2

in x years = 42000 * 1.04^x

Answer:

[tex]S(x)=42,000*(1.04)^{x}[/tex]

Step-by-step explanation:

We have as data

a = $42,000 (salary during the first year)

x = number of years

i = 4% = 0.04 (annual increase interest)

S(x) = Salary based on the years elapsed

"a" and "i" are constant for each year, while "x" increases one each year.

The function S(x) can be calculated like this:

[tex]S(x)=a*(1+i)^{x}[/tex]

Substituting constant values, we have

[tex]S(x)=42,000*(1+0.04)^{x}[/tex]

Simplifying, we have

[tex]S(x)=42,000*(1.04)^{x}[/tex]

Hope this helps!

[tex]\bf \cfrac{9}{7}+\cfrac{7}{5}\implies \stackrel{\textit{using the LCD of 35}}{\cfrac{(5)9~~+~~(7)7}{35}}\implies \cfrac{45+49}{35}\implies \cfrac{94}{35}\implies 2\frac{24}{35}[/tex]

Answer:

94/35

Step-by-step explanation:

Least common multiples of 7 and 5.

7*5=35

9/7=9*5/7*5=45/35

7/5=7*7/5*7=49/35

Add the numbers from left to right.

49/35+45/35

49+45=94

=94/35

94/35 is the correct answer.

Answer:

$21

Step-by-step explanation:

20% of 35 is 7, then you add 7 to 35 to get 42, then you split the earnings and get 21 dollars.

Answer:

21

Step-by-step explanation:

First find the tip

35 *20%

35*.2

7

He makes 35+7 = 42

But he splits it with his friend

42/2 = 21

He will make 21 and his friend will make 21

The slope of the perpendicular is the negative reciprocal of the original line, so m = -1/(-2) = 1/2.

The general line of slope m through (a,b) is

[tex]y - b = m(x-a)[/tex]

So the line we seek is

[tex] y - 2 = \frac 1 2 ( x - 8)[/tex]

[tex] y = \frac 1 2 x - 2[/tex]

Answer: y = 1/2  x + -2

Answer:

B

Step-by-step explanation:

B is incorrect.  Some systems have infinitely many solutions.

For this case we must make a conversion. We have that by definition 1 liter equals 0.264172 gallons.

So, making a rule of three we have to:

1L ----------------> 0.264172 gallons

15L --------------> x

Where:

x: Represents gallons equivalent to 15 liters.

[tex]x = \frac {15 * 0.264172} {1}\\x = 3.96258[/tex]

Rounding out we have that 15 liters equals 3.96 gallons.

Answer:

3.96 gallons

15 liters is approximately 3.96 gallons.

Given that we need to calculate 15L is approximately how many gallons rounded two decimal places for final answer.

To convert liters (L) to gallons (gal), you need to know the conversion factor between the two units.

The conversion factor between liters and gallons is 1 L = 0.264172 gal.

Now, let's calculate how many gallons are approximately equal to 15 liters:

15 L x 0.264172 gal/L = 3.96258 gal

Rounding to two decimal places, the approximate value is 3.96 gallons.

Therefore, 15 liters is approximately 3.96 gallons.

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Answer:

x=110592

Step-by-step explanation:

[tex]log_{48}x=3 \text{ means } 48^3=x\\\\[/tex]

So x=110592

Answer:

one

Step-by-step explanation:

y = 1/2x + 4

x + 2y = -8

x + 2(1/2 x + 4) = -8

x + x + 8 = -8

2x = -16

x = -8

y = 1/2 (-8) + 4

y = 0

solution: (-8, 0)

Answer: one

The given linear system has a single solution at the point (-8, 0) after solving the equations by substitution.

To determine how many solutions the given linear system has, we can substitute y from the first equation into the second equation:

y =  rac{1}{2}x + 4

x + 2(rac{1}{2}x + 4) = -8

x + x + 8 = -8

2x = -16

x = -8

Then, substituting x into the first equation:

y =  rac{1}{2}(-8) + 4

y = -4 + 4

y = 0

The linear system has a single solution, which is (x, y) = (-8, 0).

Answer:

D. 0.857

Step-by-step explanation:

The coefficient of determination, R-squared, is simply the square of the  correlation coefficient;

R-squared = r^2

R-squared = 0.926^2

R-squared = 0.857

Therefore, the coefficient of determination is 0.857.

Answer:

The correct answer option is D. 0.857

Step-by-step explanation:

We are given the correlation coefficient, of a data set to be 0.926 and we are to find the coefficient of determination to three decimal places.

To find that, we will use the following formula:

Coefficient of determination = [tex] r ^ 2 [/tex]

[tex] r ^ 2 [/tex] = [tex] ( 0 . 9 2 6 ) ^ 2 [/tex] = 0.857

Answer:

The values of y are -33 , -15 , -5 , -5 ⇒ answer C

Step-by-step explanation:

* We will use the substitution method to solve the problem

- The quadratic equation is y = -x² + x - 3

- The values of x are -5 , -3 , -1 , 2

- We will substitute the values of x in the equation to find the

  values of y

# At x = -5

∵ y = -x² + x - 3

∵ x = -5

∴ y = -(-5)² + (-5) - 3 = - 25 - 5 - 3 = -33

∴ y = -33

# At x = -3

∵ y = -x² + x - 3

∵ x = -3

∴ y = -(-3)² + (-3) - 3 = - 9 - 3 - 3 = -15

∴ y = -15

# At x = -1

∵ y = -x² + x - 3

∵ x = -1

∴ y = -(-1)² + (-1) - 3 = - 1 - 1 - 3 = -5

∴ y = -5

# At x = 2

∵ y = -x² + x - 3

∵ x = 2

∴ y = -(2)² + (2) - 3 = - 4 + 2 - 3 = -5

∴ y = -5

* The values of y are -33 , -15 , -5 , -5 ⇒ from left to right

Answer:

20 bottles

Step-by-step explanation:

10*3+b=50

30+b=50

-30      -30

       b=20

Find the vertex:

[tex]\textrm{Use the formula } \frac{-b}{2a} \textrm{ to find the vertex}\\ \\ \frac{-10}{2} = -5\\ \\ \textrm{In order to find the y value plug in -5 back into the function}\\ \\ y=(-5)^2+10(-5)+16\\ y=-9\\\\ \textrm{The vertex of the function is} (-5,-9)[/tex]

Determine if the parabola will open up or down:

[tex]a > 0 \\ \\ 1>0[/tex]

Since the value of a is positive, the parabola will open upwards

Find the x and y intercepts:

Factor [tex]y = x^2+10x + 16[/tex] to find the x intercepts

(x+8)(x+2)

x + 8 = 0

x = -8

x + 2 = 0

x = -2

x intercepts:

x = -2

x = -8

Find the y intercept

[tex]y = 0^2+10(0) + 16\\\\ y=16[/tex]

Hence, C. Graph A best represents the quadratic function [tex]y = x^2+10x + 16[/tex]

Answer:

• The distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.

Step-by-step explanation:

We have to multiply the term  b2/4a2 by a in order to determine the value to add to the left side of the equation so as to balance both sides of the equation.

If we multiply the terms, we get;

[tex]\frac{b^{2} }{4a^{2} }*a=\frac{b^{2} }{4a}[/tex]

Therefore, we shall be adding the term [tex]\frac{b^{2} }{4a}[/tex] to the left side of the equation.

Answer: The answer is choice B.

Step-by-step explanation:

Answer:

325 mi

Step-by-step explanation:

We can write a proportion to solve, putting distance over inches

50 miles       x miles

------------- = -------------

1 inch            6.5 inches

Using cross products

50 * 6.5 = 1*x

325 = x

The distance is 325 miles

Answer:

[tex]176 \leq x \leq 321[/tex]

Step-by-step explanation:

Let

x -----> the number of steaks the restaurant owner can order

we know that

[tex]x\geq 176[/tex] ----> inequality A

[tex]x\leq 321[/tex] ----> inequality B

so

the compounded inequality is equal to

[tex]176 \leq x \leq 321[/tex]

Answer:

FLVS

a

Step-by-step explanation:

x ≥ 176 and x ≤ 321

Answer:

The the vertex is: (2, 4)

Domain: all real numbers

Range: [tex][4 \infty)[/tex]

Step-by-step explanation:

Quadratic functions can be written vertically as follows

[tex]f(x) = a(x-h)^2 +k[/tex]

Quadratic functions can be written vertically as follows

Where the point (h, k) represents the vertex of the quadratic function.

For this type of functions the domain is always all real numbers and the range is [tex][k, \infty)[/tex] or if [tex]a <0[/tex] then the range is [tex](-\infty, k][/tex]

In this case the function is:

[tex]f(x) = (x - 2)^2 + 4[/tex]

So

[tex]h = 2\\k=4[/tex]

The the vertex is: (2, 4)

Domain: all real numbers

Range: [tex][4, \infty)[/tex]

Answer: 29 and 8

Step-by-step explanation:

See photo attached. (:

Answer:

A + B = 37

A - B = 21    we then add the 2 equations

2A = 58

A = 29

B = 8

Step-by-step explanation: