Suppose that the functions g and h are defined for all real numbers x as follows.
g(x) = 4x– 4
h(x) = x-5
Write the expressions for (g+h)(x) and (g-h)(x) and evaluate (g.h)(1).

Answer:

21/2x^2+4x

Step-by-step explanation:

Answer:

- 3.396

Step-by-step explanation:

Given equation is,

[tex]log_{\frac{3}{4}} 25 = 3x-1[/tex]

By using logarithm property,

[tex]log_ax=\frac{log_bx}{log_ba}[/tex]

We get,

[tex]\frac{log25}{log\frac{3}{4}}=3x-1[/tex]

[tex]\frac{1.39794000867}{-0.124938736608}=3x-1[/tex]

[tex]-11.18900388=3x-1[/tex]

Adding 1 on both sides,

[tex]-10.18900388=3x[/tex]

[tex]\implies x = -\frac{10.18900388}{3}=-3.39633462667\approx -3.396[/tex]

Hence, the approximate value of x is -3.396.

First option is correct.

Answer: They might switch options around but if not...

Option A) -3.396

Check the picture below.

bearing in mind that adjacent angles in a parallelogram are supplementary angles.

Answer:

angle B

Step-by-step explanation:

Answer:

[tex]\large\boxed{2<x<3\to x\in(2,\ 3)}[/tex]

Step-by-step explanation:

[tex](1)\\4x-4<8\qquad\text{add 4 to both sides}\\4x<12\qquad\text{divide both sides by 4}\\x<3\\\\(2)\\9x+5>23\qquad\text{subtract 5 from both sides}\\9x>18\qquad\text{divide both sides by 9}\\x>2\\\\\text{From (1) and (2) we have}\ 2<x<3[/tex]

Answer:

[tex]2<x<3[/tex]

Step-by-step explanation:

Given : Inequality [tex]4x-4<8[/tex] and [tex]9x+5>23[/tex]

To find : Solve for x?

Solution :

Inequality 1 - [tex]4x-4<8[/tex]

Add 4 both side,

[tex]4x<12[/tex]

Divide by 4 both side,

[tex]x<3[/tex]

Inequality 2 - [tex]9x+5>23[/tex]

Subtract 5 both side,

[tex]9x>18[/tex]

Divide by 9 both side,

[tex]x>2[/tex]

From Inequality 1 and 2,

[tex]x<3[/tex] and [tex]x>2[/tex]

or [tex]2<x<3[/tex]

Answer:

2

Step-by-step explanation:

So I'm going to use vieta's formula.

Let u and v the zeros of the given quadratic in ax^2+bx+c form.

By vieta's formula:

1) u+v=-b/a

2) uv=c/a

We are also given not by the formula but by this problem:

3) u+v=uv

If we plug 1) and 2) into 3) we get:

-b/a=c/a

Multiply both sides by a:

-b=c

Here we have:

a=3

b=-(3k-2)

c=-(k-6)

So we are solving

-b=c for k:

3k-2=-(k-6)

Distribute:

3k-2=-k+6

Add k on both sides:

4k-2=6

Add 2 on both side:

4k=8

Divide both sides by 4:

k=2

Let's check:

[tex]3x^2-(3k-2)x-(k-6) \text{ with }k=2[/tex]:

[tex]3x^2-(3\cdot 2-2)x-(2-6)[/tex]

[tex]3x^2-4x+4[/tex]

I'm going to solve [tex]3x^2-4x+4=0[/tex] for x using the quadratic formula:

[tex]\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\frac{4\pm \sqrt{(-4)^2-4(3)(4)}}{2(3)}[/tex]

[tex]\frac{4\pm \sqrt{16-16(3)}}{6}[/tex]

[tex]\frac{4\pm \sqrt{16}\sqrt{1-(3)}}{6}[/tex]

[tex]\frac{4\pm 4\sqrt{-2}}{6}[/tex]

[tex]\frac{2\pm 2\sqrt{-2}}{3}[/tex]

[tex]\frac{2\pm 2i\sqrt{2}}{3}[/tex]

Let's see if uv=u+v holds.

[tex]uv=\frac{2+2i\sqrt{2}}{3} \cdot \frac{2-2i\sqrt{2}}{3}[/tex]

Keep in mind you are multiplying conjugates:

[tex]uv=\frac{1}{9}(4-4i^2(2))[/tex]

[tex]uv=\frac{1}{9}(4+4(2))[/tex]

[tex]uv=\frac{12}{9}=\frac{4}{3}[/tex]

Let's see what u+v is now:

[tex]u+v=\frac{2+2i\sqrt{2}}{3}+\frac{2-2i\sqrt{2}}{3}[/tex]

[tex]u+v=\frac{2}{3}+\frac{2}{3}=\frac{4}{3}[/tex]

We have confirmed uv=u+v for k=2.

Answer:

46 units^2

Step-by-step explanation:

The formula for surface area of a rectangular prism is

SA = 2(lw +lh+wh)  where l is length, w is width and h is height

SA = 2 (2.5* 4+ 2.5*2 + 4*2)

      = 2 (10+5+8)

       = 2( 23)

       = 46 units^2

Answer:

46 units^2

Step-by-step explanation:

The formula for surface area of a rectangular prism is

= 2(lw +lh+wh) is the formula

= 2 (2.5* 4+ 2.5*2 + 4*2)

= 2 (10+5+8)

   = 2( 23)

= 46

Step-by-step explanation:

Answer:

a(8)=12582912

Step-by-step explanation:

The 8th term can be determined by the formula:

an = a1 * r^(n-1)

where

n = the term to be found = 8

a1 = 1st number

r = common ratio

Common ratio can be found by dividing the second term by the first term

= 48/6 = 8

Substitute the values in the formula

a(8) = 6 * 8^(8-1)

a(8) = 6 * 8^7

a(8)= 6*8*8*8*8*8*8*8

a(8) = 6 * 2097152

a(8)=12582912 ....

Therefore the 8th term is 12582912 ....

Answer:

12582912

Step-by-step explanation:

You simply need to start by finding the pattern. Divide the second number by the first (the answer is 8), then divide the third number by the second, so on and so on. You will see the answer is always 8 which means each number is getting multiplied by eight to reach the next term. Finally, multiply the last number in the sequence by your answer (8) until you reach the 8th term.

Answer:

f. sqrt 7 meters

Step-by-step explanation:

we use Pythagoras' theorem here,

let the unknown side be x,

therefore,

=> 3² + x² = 4²

=> x² = 16 - 9

=> x = √7 m

Answer:

f. sqrt 7 meters

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem to solve.  We know the hypotenuse is 4 and one leg is 3.  We want to solve for the other leg.

a^2 +b^2 = c^2  where a and b are the legs and c is the hypotenuse.

Substituting into the equation

3^2 + b^2 = 4^2

9+b^2 = 16

Subtracting 9 from each side

9-9+b^2 = 16-9

b^2 =7

Taking the square root of each side

sqrt(b^2) = sqrt(7)

b = sqrt(7) meters

Answer:

The number is 10

Step-by-step explanation:

Let the number be x.

four thirds times = 4/3

According to the statement:

four thrids times the sum of a number and 8 is 24

4/3 *(x+8)= 24

Move  3 to the R.H.S and Multiply 4 with the parenthesis.

4x+32=24*3

4x+32=72

Move constant to the R.H.S

4x=72-32

4x=40

Divide both the terms by 4

4x/4=40/4

x=10

Therefore the number is 10....

Final answer:

To solve the equation, which is four thirds times the sum of a number and 8 equals 24, we isolate the variable by dividing by four thirds and subtracting 8 from both sides, resulting in the number being 10.

Explanation:

The student's question is asking to solve an algebraic equation. Specifically, the equation is: four thirds times the sum of a number and 8 equals 24. To find the number, represented by a variable, we'll denote it as x and translate the statement into the following equation: (4/3) × (x + 8) = 24.

First, we need to divide both sides of the equation by 4/3 to isolate the sum on one side:

(x + 8) = 24 × (3/4)

(x + 8) = 18

Now, subtract 8 from both sides to solve for x:

x = 18 - 8

x = 10

The final answer is that the number is 10. This is obtained through a step-by-step explanation solving the initial equation.

Answer:

-30

Step-by-step explanation:

-3ab        original equation

-3(-2)(-5) .          plug in numerical values

6(-5) .             -3 times -2 is 6

-30 .         6 times -5 is -30.

Answer:

-30

Step-by-step explanation:

Plug in -2 for a & -5 for b in the expression given:

-3ab = (-3)(-2)(-5)

Multiply across. Note that:

Negative number x negative number = positive number.

Positive number x negative number = negative number.

(-3)(-2)(-5) = (6)(-5) = -30

-30 is your answer.

~

Answer:

100,000 dollars.

Step-by-step explanation:

One grand = 1,000$

Multiply.

100 × 1,000

=100,000$

Answer:

no

Step-by-step explanation:

541982/3 = 180,660.667

Step-by-step explanation:

Technically it is divisible by 3, but you would just end up with a decimal or fraction as the answer.

541892 divided by 3 = 180660.666667 or 180,660 666667/1000000

Firstly, find the slope.

Let m = slope

m = (8 - 4)/(1 - 0)

m = 4/1

m = 4

Now use the point-slope formula.

y - y_1 = m(x - x_1)

Pick one of the given points. I will use the point (0, 4) but you can certainly use (1, 8) if you'd like.

We now plug and chug.

y - 4 = 4(x - 0)

y - 4 = 4x

y = 4x + 4

Replace y with f(x).

f(x) = 4x + 4

Did you follow?

Answer:

f(x) = 4 x (2)^x  

Step-by-step explanation:

Answer:

600g chopped tomatoes

450ml of stock

225ml of red wine

Step-by-step explanation:

Times them all by 0.75

Answer:

2x-y = -4

Step-by-step explanation:

We can use the point slope form of a line to write the equation and then convert it to standard form

y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point

y-2 =2(x--1)

y-2 =2(x+1)

y-2 =2x+2

The standard form is Ax +By =C

Subtract 2x from each side

-2x +y -2 =2x-2x+2

-2x+y-2 =2

Add 2 to each side

-2x+y -2+2 =2+2

-2x+y=4

The x term should be positive

Multiply by -1

2x-y = -4

Answer:

I prefer to express solutions to inequalities using interval notation. Both formats are are important but I think interval notation is easier to understand and represents better the solutions.

For example, if you have the following inequation:

x-2> 1

x>3

Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U  (3, inf) instead of 'x>3 or x<-3' which can be confusing.

Answer:

[tex]y = - 3.0625[/tex]

Step-by-step explanation:

The given parabola has equation:

[tex] \frac{1}{4} (y + 3) = {(x - 2)}^{2} [/tex]

Or

[tex]{(x - 2)}^{2} = \frac{1}{4} (y + 3)[/tex]

We compare this to

[tex] {(x - h)}^{2} = 4p(y - k)[/tex]

[tex] \implies \: 4p = \frac{1}{4} [/tex]

[tex]p = \frac{1}{4} \div 4[/tex]

[tex]p = \frac{1}{4} \times \frac{1}{4} [/tex]

[tex]p = \frac{1}{16} [/tex]

The vertex of this parabola is (2,-3)

The directrix is p units below the y-value of the vertex

[tex]y = - 3 - \frac{1}{16} = - 3.0625[/tex]

Answer:

6

Step-by-step explanation:

To find the slope 'm' we use 2 points from the line, those are given in the statement:

[tex]x_{1} =2\\y_{1} =5\\\\x_{2} =3/2\\y_{2} =2[/tex]

[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1}}[/tex]

[tex]m=\frac{2 -5 }{3/2-2}}[/tex]

Finally  m=6

Answer:

About 121.25

Step-by-step explanation:

Step 1: Interpret x and y

y is the number of accidents that occur = ?

x is the speed = 60 km/h

Step 2: Substitute value of x in the equation

y=0.0875x² - 10.5x + 436.25

y=0.0875(60)² - `10.5(60) + 436.25

Step 3: Find the value of y

y=0.0875(60)² - `10.5(60) + 436.25

y = 121.25

Therefore, the right answer is the last option which is 'about 121.25.'

!!

Answer:

○ D. 116°

Step-by-step explanation:

Think of the Unit Circle. You know that half of 360° is 180°, and that angle has a measure of 58°, so you do this:

-58° + 180° = 122°

Now, that chord of the circle drags it a bit by a few units, so that will be approximately 116°.

*This may not be the best explanation I can give, but I gave one.

I am joyous to assist you anytime.

Answer: The inverse is x/5

===============================================

How I got this answer:

The original function has 5x or 5*x, which reads out "five times x"

We have some unknown number x and we are multiplying it by 5. The inverse function undoes everything the original f(x) function does. Since the opposite of multiplicaiton is division, this means our answer involves dividing by 5.

--------

Here is a more algebraic explanation

f(x) = 5x

y = 5x  .... replace f(x) with y

x = 5y

5y = x

y = x/5 .... divide both sides by 5 (to undo the multiplication)

g(x) = x/5 .... replace y with g(x)

here g(x) represents the inverse of f(x)

One useful property of inverses is that f( g(x) ) = g( f(x) ) = x

The area of a full circle would be Area = PI x r^2

The diameter would be the width of the dorr, so the radius would be half that. 34/2 = 17  inches.

Area for a full circle would be 3.14 x 17^2 = 907.46 square inches.

A semi circle is a half circle.

The area would be 907.46 / 2 = 453.73 square inches.

Multiply the area by the cost:

453.73 x 0.95 = 431.04

The answer is C.

Final answer:

To find the cost of the stained glass window, calculate the area of a 34-inch diameter semi-circular window, and then multiply that by the cost per square inch ($0.95). The total cost is approximately $431.17.

Explanation:

To calculate the cost of the stained glass window, we must first find the area of the semi-circular window above the door. Since the width of the door is 34 inches, the diameter of the semi-circle is also 34 inches, which means the radius (r) is half of that, or 17 inches.

Step 1: Calculate the area of the semi-circle
The formula for the area of a circle is A = πr². For a semi-circle, it would be half of that area, so the formula changes to A = (πr²) / 2.
Plugging in the radius, we get A = (3.14 * (17²)) / 2 = (3.14 * 289) / 2 = 453.86 square inches.

Step 2: Calculate the cost of the stained glass
The cost per square inch is $0.95. Multiplying the area by the cost per square inch, we get Total Cost = 453.86 * $0.95 = $431.167, which rounds to $431.17.
The closest cost option given is C. $431.04.

Answer:

[tex]4\sqrt{37} units[/tex] is the perimeter of square ABCD.

Step-by-step explanation:

Coordinates of square ABCD:

A = (3,4), B = (2,-2), C = (-4-1) , D = (-3,5)

Distance formula: [tex](x_1,y_1),(x_2,y_2)[/tex]

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance of AB: A = (3,4), B = (2,-2)

[tex]AB=\sqrt{(2-3)^2+(-2-4)^2}[/tex]

[tex]AB=\sqrt{(-1)^2+(-6)^2}=\sqrt{37} units[/tex]

Given that the ABCD is square, then:

AB = BC = CD = DA

Perimeter of the square ABC = AB +BC + CD + DA

[tex] AB+ AB+ AB+ AB= 4AB=4\sqrt{37} units[/tex]

[tex]4\sqrt{37} units[/tex] is the perimeter of square ABCD.

Your answer would be:

Minimum < Q1 < Median < Q3 < Maximum

Your welcome!

Jesse should use kilograms to weigh the package for postage.

Jesse should use kilograms to weigh the package for postage. The books and documents in the box would likely weigh more than grams, so a larger unit of measurement is needed. Kilograms are a commonly used metric unit for measuring weight, and they are suitable for weighing the package accurately and determining the postage required.

Answer:

100 is the number which can be multiplied to eliminate the decimals....

Step-by-step explanation:

Given:

Which number can each term of the equation be multiplied by to eliminate the decimals before solving

5.6j – 0.12 = 4 + 1.1j

Solution:

Notice that the constants and the coefficients in this equation contains decimal. All the numbers are in decimal up to tenth place except 0.12 which has decimal up to hundredth place.

Therefore, if we want to eliminate the decimal from 0.12 we have to multiply it by 100.

Thus the given equation will be multiplied by 100 to eliminate decimal from the terms.

100(5.6j – 0.12 = 4 + 1.1j)

By multiplying the equation by 100 we get:

560j - 12 = 400 + 110j

Thus 100 is the number which can be multiplied to eliminate the decimals....

Answer:

100

Step-by-step explanation:

Well, to answer this question, you have to find the number/coefficient that has the most numbers after a decimal point (not including trailing zeros), and then use the rule 10^(numbers after the decimal point) to see how to eliminate the decimals. So, 2 digits, 10^2=100

Answer:

The unit vector in the opposite direction of u is:

[tex]\vec{u} =-\frac{1}{\sqrt{23}}<-3i-4,\sqrt{2}>[/tex]

Step-by-step explanation:

To find the unit vector suppose u  that points in the opposite direction as v

[tex]\vec{v}=<-3i,-4\sqrt{2}>[/tex]

we use the formula:

[tex]\vec{u} =-\frac{1}{||\vec{v}||}\vec{v}[/tex]

Finding [tex]||\vec{v}||[/tex]

[tex]||\vec{v}|| = \sqrt{x^2+y^2}\\||\vec{v}|| = \sqrt{(3i)^2+(4\sqrt{2}^2} \\||\vec{v}|| = \sqrt{9i^2+(16*2)}\\ i^2 = -1\\||\vec{v}|| = \sqrt{9(-1)+32}\\||\vec{v}|| = \sqrt{-9+32}\\||\vec{v}|| = \sqrt{23}[/tex]

[tex]\vec{u} =-\frac{1}{\sqrt{23}}<-3i,-4\sqrt{2}>[/tex]

The unit vector in the opposite direction of u is:

[tex]\vec{u} =-\frac{1}{\sqrt{23}}<-3i,-4\sqrt{2}>[/tex]

Answer:

0.5 or 1/2

Step-by-step explanation:

Let A be the event that the number cube is 3 or odd as 3 is also an odd number. So the event space will be:

{1,3,5}

The total number of outcomes are 6 as in:

{1,2,3,4,5,6}

So the probability of tossing 3 or odd number will be:

P(A) = n(A) / n(S)

= 3/6

=1/2

Hence the probability in fraction form is 1/2 and in decimal form is 0.5 ..

Answer:

Answer choice A.

Step-by-step explanation:

The y-intercept is the -8 for the g(x) equation. The chart shows that when x=0, y=-4. This is the y-intercept for f(x). -8 is less than -4.

Answer:

Step-by-step explanation:

[tex]\text{x-intercept is for y = 0}\to(x,\ 0)\\\\\text{y-intercept is for x = 0}\to(0,\ y)\\\\f(x):\\\\\text{From the table:}\\\\(0,\ -4)\to\text{y-intercept is -4}\\(16,\ 0)\to\text{x-intercept is 16}[/tex]

[tex]g(x)=4\sqrt{x}-8\to y=4\sqrt{x}-8\\\\\text{x-intercept:}\\\text{put y = 0 to the equation of the function}\\\\4\sqrt{x}-8=0\qquad\text{add 8 to both sides}\\4\sqrt{x}=8\qquad\text{divide both sides by 4}\\\sqrt{x}=2\to x=2^2\\x=4\leftarrow \text{x-intercept}\\\\\text{y-intercept:}\\\text{put x = 0 to the equation of the function}\\\\y=4\sqrt0-8\\y=0-8\\y=-8\leftarrow\text{y-intercept}[/tex]