f(x)=2x g(x)=3x+1 find f(4)

Answer:

x = 2

Step-by-step explanation:

The triangle has two congruent legs

For the Pythagorean theorem we have:

x^2 + x^2 = 8

2x^2 = 8

x^2 = 4

x = 2

Answer:

x < -3 and x > 5

Step-by-step explanation:

x² - 2x - 8 > 7

~Rewrite in standard form

x² - 2x - 15 > 0

~Factor

(x + 3)(x - 5) = 0

~Solve for both factors

x + 3 = 0

x = -3

x - 5 = 0

x = 5

Best of Luck!

Answer:

1.2

Step-by-step explanation:

- 8. 3 + 3. 7 = -4

-4 - 4 .4 = - 8. 4

-8.4 + 9.2 = 1.2

Step-by-step explanation:

1/5=1/5×1000=200

1/2 of 200

1/2×200=100

Answer:

Step-by-step explanation:

(y2-y1)/(x2-x1)

Answer:

$57 interest

Step-by-step explanation:

For an interest rate of 19% ; the monthly interest will be 19/100 = 0.19

4 months interest will be (0.19 * 4)/12 = 0.0633

so now, the value of the interest will be

0.0633 * 900 = $57

Answer: x=4

Step-by-step explanation:

Concept:

There are three ways to solve the system of equations

Here, we would use substitution because we have two same variables.

--------------------------------------------------------------------------------------------------

Solve:

Given

y = -2x + 8

y = x - 4

Substitute

-2x + 8 = x - 4

Add 4 on both sides

-2x + 8 + 4 = x - 4 + 4

-2x + 12 = x

Add 2x on both sides

-2x + 12 + 2x = x + 2x

12 = 3x

Divide 3 on both sides

12 / 3 = 3x / 3

x = 4

Hope this helps!! :)

Please let me know if you have any questions

Answer:

D. Subtract 9y from both sides of the equation.

Step-by-step explanation:

A. Divide both sides of the equation by 36.

B. Multiply both sides of the equation by 6.

C. Add 9y to both sides of the equation.

D. Subtract 9y from both sides of the equation.

Given:

9y - 6x = 36

To solve for x

Step 1: subtract 9y from both sides

9y - 6x - 9y = 36 - 9y

- 6x = 36 - 9y

Step 2: Divide both sides by -6

- 6x / -6 = (36 - 9y) / - 6

x = (36 - 9y) / - 6

The answer is

x = (36 - 9y) / - 6

Answer:

d

Step-by-step explanation:

a) (0, 1)

The graph will cross the y-axis at the y-intercept. We can easily find this value by putting the given equation into slope-intercept form (y = mx + b).

y - 4x = 1

y = 4x + 1

The y-intercept is (0,1).

b) k = 6.5

We first need to find c, or the y-intercept. This is given to us on the graph, where the line crosses the y-axis at (0,-3).

Therefore, our line is y = 2x - 3.

Then, we can plug in 10 for y from the point (k,10) and solve for k (which is the same as x).

10 = 2x - 3

13 = 2x

x = 6.5

Hope this helps!

Answer:

(-2, -7) or (3, 18)

Step-by-step explanation:

Start with your 2 equations

y = x^2 + 4x - 3

y = 5x + 3

Because both equal y, we substitute:

x^2 +4x -3 = 5x+ 3

x^2 - x - 6 = 0

Factor:

(x + 2) (x - 3) = 0

Solutions for x: -2 or 3 since if either of the numbers in parentheses is 0, the equation is 0 (0* anything = 0).

Then plug -2 in for x in either equation:

y = 5* -2 + 3

y = -7

So ( -2, -7) is a solution.

Plug 3 in for x in either equation:

y = 5*3 + 3

y = 18

So ( 3 , 18) is a solution.

Hope that helps, let me know if I did anything wrong!

Answer:

(- 2, - 7 ) and (3, 18 )

Step-by-step explanation:

Given the 2 equations

y = x² + 4x - 3 → (1)

y = 5x + 3 → (2)

Substitute y = x² + 4x - 3 into (2)

x² + 4x - 3 = 5x + 3 ( subtract 5x + 3 from both sides )

x² - x - 6 = 0 ← in standard form

(x - 3)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 3 = 0 ⇒ x = 3

Substitute these values into (2) for corresponding values of y

x = - 2 : y = 5(- 2) + 3 = - 10 + 3 = - 7 ⇒ (- 2, - 7 )

x = 3 : y = 5(3) + 3 = 15 + 3 = 18 ⇒ (3, 18 )

Answer:

D. 68 degrees

Step-by-step explanation:

Remember, the total degree of a triangle is 180 degrees, not 360 like a rectangle.

To solve, set up an equation.

[tex]y+(y-12)+56=180[/tex]

Solve:

[tex]2y+44=180[/tex]

Subtract 44 from both sides

[tex]2y=136[/tex]

Divide both sides by 2

y=68

I hope this helps!

Answer:

68

Step-by-step explanation:

The sum of the angles of a triangle add to 180

y + y-12 +56 = 180

Combine like terms

2y+ 44 = 180

Subtract 44 from each side

2y+44 = 180-44

2y = 136

Divide by 2

2y/2 = 136/2

y = 68

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the function is not given. A little explanation to assist you is as follows;

From the attached image, one can sense that the function is a piece-wise function.

Now, assume the function is as follows:

[tex]f(x) =\left \{ {{2x + 1\ -1 < x < 3} \atop {4x + 7, x \ge 3}} \right.[/tex]

To calculate f(2), we make use of:

[tex]f(x) =2x + 1[/tex]   [tex]-1 < x < 3[/tex]

Because 2 is within [tex]-1 < x < 3[/tex]

So:

[tex]f(2) = 2 * 2 + 1 =5[/tex]

Similarly, to calculate f(3)

We make use of

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

Because 3 is within [tex]x\ge 3[/tex]

So:

[tex]f(3) = 4 * 3 + 7 =19[/tex]

Answer:

-2x + 3y = -19

Step-by-step explanation:

y + 1 = 2/3(x-8)

multiply by 3 to get rid of the fraction

3(y + 1 = 2/3(x-8)

3y + 3 = 2(x-8)

simplify

3y + 3 = 2x - 16

3y - 2x = -19

-2x + 3y = -19

hope it helps✓✓✓✓✓✓✓✓✓

Answer: A for 10

Step-by-step explanation:

Answer:

Loss= x

profit=y

x=1/4y

4x=y

Let cost = c

c-x= 15000

c+4x=18000

c+4x-(c-x)=18000-15000

5x=3000

x=600

c-x=15000

c-600=15000

c=15600

c+4x=18000

c+2400=18000

c=15600

Cost= Rs15600

Brainliest please

Answer:

Step-by-step explanation:

This is a very interesting problem. We are given the slope and one point, which makes this funner than normal ;)

Filling in the slope formula with what we are given:

[tex]-\frac{3}{5}=\frac{y-2}{x-(-3)}[/tex] which simplifies to

[tex]-\frac{3}{5}=\frac{y-2}{x+3}[/tex]

Since slope is rise over run, the rise number is -3; the run number is 5. That means that the equation to find the y coordinate comes from -3 = y - 2; the equation to find the x coordinate comes from 5 = x + 3 (keep in mind that you could have made the x coordinate the negative one; it doesn't matter. You will get the same answer regardless...promise).

Solving for y:

-3 = y - 2 and

y = -1

Solving for x:

5 = x + 3 and

x = 2

Let's check those coordinates in the slope formula and see if our slope is in fact -3/5:

[tex]m=\frac{-1-2}{2-(-3)}=-\frac{3}{5}[/tex] so we're all good!

The coordinates of B are (2, -1)

Step-by-step explanation:

You have 5 digits.Youdonot say if duplication is allowed. I will assume not

For the first digit you have 5 choices. One of the 5 digits is gone.

You now have 4 digits to choose from. You pick one. Now you have but 3 left.

The total answer if 5*4*3*2*1 = 120

Answer:

10%

Step-by-step explanation:

The percentage decrease in price = [tex]\frac{decrease amount}{original amount}[/tex] x 100%

Original amount = 250,000

New amount = 225,000

Decrease in amount = 250,000 - 225,000

                        = 25,000

So that;

Percentage decrease in price = [tex]\frac{25000}{250000}[/tex] x 100%

                                           = 0.1 x 100%

Percentage decrease in price = 10%

The price of the apartment dropped by 10% of its original price.

Answer:

20.4

Step-by-step explanation:

that is the procedure above

Answer:

Step-by-step explanation:

Answer:

Calculator cost = $34

Step-by-step explanation:

x + (x+140) = 208

2x + 140 = 208

x=34

Answer:

Hello

Answer B: 32.58°

Step-by-step explanation:

[tex]sin (\widehat{A})=\dfrac{35}{65} \\\\\widehat{A}=arcsin(\dfrac{7}{13} )=32.5789...^o[/tex]

yes it is possible, although it doesn't always occur.

Your answer is: True

Answer:

4

Step-by-step explanation:

Mean: the sum of all numbers divided by the amount of numbers

In this case it will be the sum of all frequency divided by the amount of pens

Mean = 5 + 7 + 3 + 5 + 3 + 2 / 6

Mean = 25/6

Mean = 4.16

The mean is approximately 4

Answer:

a. The start-up cost for the teenagers company is $50

b. The number of mugs the teenager must sell to break even are 5 mugs or 25 mugs

c. The number of mugs that will give maximum profit is 15 mugs

d. The profit if she sells 10 mugs is $30

Step-by-step explanation:

The given profit function for selling x number of mugs is presented as follows;

f(x) = -0.4·x² + 12·x - 50

a. The start-up cost in dollars is given by the value of the profit function at the start, where, x = 0, as follows;

Start-up cost = f(0) = -0.4×0² + 12×0 - 50 = -50

The negative sign represents amount put in the business

The start-up cost = (The initial) $50 put into the business.

b. The break even point is the point where, the revenue and costs are equal

At break even point; Revenue = Cost

∴ Profit, at break even point, f(x) = Revenue - Cost = 0

From the profit function, we get;

At the break even point, f(x) = 0 = -0.4·x² + 12·x - 50

Dividing by -0.4 gives;

0/(-0.4) = 0 = (-0.4·x² + 12·x - 50)/(-0.4) = x² - 30 + 125

0 = x² - 30 + 125

∴ (x - 25)·(x - 5) = 0

The number of mugs the teenager must sell before she breaks even, x = 5 mugs or x = 25 mugs.

c. From the general form of a quadratic equation,  which is; y = a··x² + b·x + c, the formula for the x-values at the maximum point is; x = -b/(2·a)

Comparing the profit function to the general form of the quadratic equation we have at the maximum point;

x = -12/(2×(-0.4)) = 15

Therefore, the number of mugs that will give maximum profit, x = 15 mugs.

d. The profit from selling 10 mugs, f(10) is given as follows;

f(10) = -0.4 × 10² + 12 × 10 - 50 = 30

The profit from selling 10 mugs, f(10) = $30

Answer:

is it 6 with the 10

Step-by-step explanation:

Answer:

y = 6/5 x + 2/3

Step-by-step explanation:

A equation is given to us and we need to express it in , mx + b form . The given equation to us is,

[tex]\rm\implies 6 = \dfrac{15y - 10}{3x} [/tex]

Move 3x to LHS , we will get ,

[tex]\rm\implies 6 * 3x = 15y - 10 \\\\\rm\implies 18x = 15y - 10 \\\\\rm\implies 15y = 18x + 10 \\\\\rm\implies y =\dfrac{18x+10}{15} \\\\\rm\implies \boxed{ \bf y = \dfrac{6}{5}x + \dfrac{2}{3}}[/tex]

This is the required answer .

Answer:

Solution given:

The area of a circle =80.86cm²

we have:

The area of a circle =πr²

substituting value of area of circle we get

80.86cm=3.14*r²

dividing both side by 3.14

80.86/3.14=3.14*r²/3.14

25.75=r²

doing square root on both side

[tex]\sqrt{25.75}=\sqrt{r²}[/tex]

r=5.07cm

The length of radius is 5.07cm

The length of the radius is 5.07 cm.

The area of the circle is given by;

[tex]\rm Area \ of \ circle=\pi r^2\\\\Where: \ r = radius[/tex]

The area of a circle is 80.86cm^2.

The length of the radius is;

[tex]\rm Area \ of \ circle=\pi r^2\\\\ 80.86=\pi r^2\\\\r^2=\dfrac{80.86}{3.14}\\\\r^2=25.75\\\\r=5.07[/tex]

Hence, the length of the radius is 5.07 cm.

Learn more about radius here;

https://brainly.com/question/11952845

#SPJ2

Answer:

x = 2

Step-by-step explanation:

Given 2 intersecting chords in a circle, then

The product of the parts of one chord is equal to the product of the parts of the other chord , that is

12x = 6(x + 2) = 6x + 12 ( subtract 6x from both sides )

6x = 12 ( divide both sides by 6 )

x = 2

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

The term 'secant' refers to a line segment that intersects a circle in two places. When two secants intersect inside a circle, one can use the product of lengths theory to form ratios between the parts of intersection between the secants. This ratio can be described as the following, let ([tex]secant_A[/tex]) and ([tex]secant_B[/tex]) represent the two secants in the circle. Part (1) and (2) will refer to the two parts formed after the intersection of the secants.

[tex](secant_A_1)(secant_A_2)=(secant_B_1)(secant_B_2)[/tex]

Use this formula in the given situation, substitute the given values in and solve for the unknown,

[tex](secant_A_1)(secant_A_2)=(secant_B_1)(secant_B_2)[/tex]

[tex](6)(x+2)=(12)(x)[/tex]

Simplify,

[tex](6)(x+2)=(12)(x)[/tex]

[tex]6x+12=12x[/tex]

[tex]12=6x[/tex]

[tex]x=2[/tex]

Answer:

2/9

Step-by-step explanation:

f(x) = 2•3^x

Let x = -2

f(-2) = 2•3^-2

We know that a^-b = 1/a^b

f(-2) = 2• 1/3^2

     = 2/9

f(x) = 2 * 3^x

f(-2) = 2 * 3^-2

f(-2) = 2 * 1/3^2

f(-2) = 2 * 1/9

f(-2) = 2/9

Hope this helps!

Answer:

y=x-5

Step-by-step explanation:

Hi there!

We want to write an equation of the line that passes through the points (8,3) and (0,-5) in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope, and b is the y intercept

So let's first find the slope of the line

The formula for the slope calculated from two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We have everything needed to find the slope, but let's label the values of the points to avoid any confusion

[tex]x_1=8\\y_1=3\\x_2=0\\y_2=-5[/tex]

Now substitute into the formula

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

m=[tex]\frac{-5-3}{0-8}[/tex]

Subtract

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

Simplify

m=1

The slope is 1

Here is the equation of the line so far:

y=1x+b (can also be written as y=x+b)

We need to find b

The equation passes through both (8, 3) and (0, -5), so we can substitute the values of either one of them as x and y to solve for b

Let's take (8, 3) for example

Substitute 8 as x and 3 as y

3=1(8)+b

Multiply

3=8+b

Subtract 8 from both sides

-5=b

Substitute -5 as b into the equation

y=x-5

Hope this helps!

Answer:

7

Step-by-step explanation:

when dividing exponents of the same base, subtract the exponents.

b^4 / b^(-3) = b^(4-(-3)) = b^7

Answer:

7

Step-by-step explanation:

In a division , subtract the exponents.

b^4/b^-2 = b^[4 - (-3)] = b^(4 + 3) = b^7

Answer: 7