If f(x)=2x2-5and g(h)=3x+3 find f-g (x)

[tex]\left\{\begin{array}{ccc}y=6x+2&(*)\\y=x+17&(**)\end{array}\right\\\\\text{Substitute}\ (*)\ \text{to}\ (**):\\\\6x+2=x+17\qquad\text{subtract 2 from both sides}\\6x=x+15\qquad\text{subtract x from both sides}\\5x=15\qquad\text{divide both sides by 5}\\\boxed{x=3}\\\\\text{Put the value of x to the second equation}:\\\\y=3+17\\\boxed{y=20}\\\\Answer:\ \boxed{D.\ (3,\ 20)}[/tex]

Answer:

D ( 3, 20 )   For A pex

Step-by-step explanation:

Answer:

1) 7/6 or 1 1/6     2)7/55 of a foot longer      3) 13/4 or 3 1/4 cups of milk

4) 56/5 or 11 1/5 feet

Step-by-step explanation:

Let's go over this.

1) If the question asks how much cereal George eats in all, then you must add.

To do this, we must find 2/3 + 1/2. Also, we need to find the common denominator, so that is 6. 2/3 x 2= 4/6. 1/2 x 3= 3/6. Now, it is easier to add. 4/6 + 3/6= 7/6, or 1 1/6.

2) We must find the common denominator again. This is 55, since this is the LCM of 11 and 5. 3/11 x 5= 15/55. 2/5 x 11= 22/55. Now, since the orange fish is longer, 22/55 - 15/55 = 7/55 of a foot longer.

3) This is simple. 13/8 "doubled" is the same as 13/8 x 2, or 13/8 x 2/1. 13 x 2 = 26, and 8 x 1 =8. Our fraction will be 26/8, and we can simplify this to 13/4, or 3 1/4 cups of milk.

4) We can convert these two fractions to improper fractions. 2 1/3 = 7/3, and 4 4/5= 24/5. 7/3 x 24/5= 7 x 24/3 x 5 which is 168/15. The fully simplified fraction is 56/5, or 11 1/5 feet.

5) We must divide 2 1/2 and 4. 2 1/2 = 5/2, and 5/2 divided by 4 is the same thing as 5/2 x 1/4, which is 5/8 of a candy bar.

6) For this problem, we need to find the number of friends. We are supposed to divide 4 and 1/2. 4 divided by 1/2 is equal to 4/1 x 2/1, which is 8. Jack can split his candy bar pieces to 8 friends.

I hope this helped!

Answer: choice A. 40 liters

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

Explanation:

x = number of liters of the 50% alcohol solution

If we have x liters of 50% alcohol, then we have 0.50*x liters of pure alcohol. This is added to 0.90*40 = 36 liters of pure alcohol (from the 90% solution).

So far we have 0.50*x + 36. This expression represents the total amount of pure alcohol. We want a 70% solution, so we want 70% of the total 40+x meaning 0.50*x + 36 is to be set equal to 0.70*(40+x) and we solve for x as shown below

0.50*x + 36 = 0.70*(40+x)

0.50*x + 36 = 0.70*(40)+0.70*(x)

0.50*x + 36 = 28+0.70*x

36 - 28 = 0.70*x - 0.50x

8 = 0.20x

0.20x = 8

x = 8/0.20

x = 40

So that is why the answer is choice A. 40 liters

Answer:

Answer in simplified form is:

(sinФ - cosФ)² + (sinФ + cosФ)² = 2

Step-by-step explanation:

Given,

(sinФ - cosФ)² + (sinФ + cosФ)²

This can be simplified as:

(sin²Ф + cos²Ф - 2sinФcosФ) + (sin²Ф + cos²Ф +2sinФcosФ)

We know that : sin²Ф + cos²Ф = 1

So,

( 1 - 2sinФcosФ) + (1 + 2sinФcosФ)

or 1 + 1 -2sinФcosФ + 2sinФcosФ

or 2

Hence we got  (sinФ - cosФ)² + (sinФ + cosФ)² = 2

Answer:

I do believe the radius of P is PN

Question

What is radius of circle P?

Answer:

Step-by-step explanation:

MN is the diameter, so half diameter is the radius, PN is your answer (remember that PM is also a radius)

Answer:

51869 ft

Step-by-step explanation:

If he climbed both mountains, then we add the heights together

22834 + 29035

51869 ft

Answer:

51,869 ft

Step-by-step explanation:

Add the two heights.

22,834 ft + 29,035 ft = 51,869 ft

Answer:

The equation of the line would be y = -15/24x + 6

Step-by-step explanation:

In order to find the equation of the line, you need to start by using the slope formula with the points given. This will give you the slope.

m(slope) = (y2 - y1)/(x2 - x1)

m = (11 - 7/2)/(-8 - 4)

m = (15/2)/-12

m = 15/-24

m = -15/24

Now that we have the slope, we can use that and either point to find the equation in point-slope form.

y - y1 = m(x - x1)

y - 11 = -15/24(x + 8)

y - 11 = -15/24x - 5

y = -15/24x + 6

Answer:The answer on ed is y= -5/8x + 6

Step-by-step explanation:

Answer: 320

Step-by-step explanation:

[tex]a_n=a_1(r)^{n-1}\quad \text{where}\ a_1\ \text{is the first term, r is the ratio, n is the term}[/tex]

[tex]a_7=5(2)^{7-1}[/tex]

   [tex]=5(2)^{6}[/tex]

   [tex]=5(64)}[/tex]

   [tex]=320[/tex]

Answer:

The 7th term in Geometric Sequence is 320

Step-by-step explanation:

Given : the geometric sequence whose first term is 5 and whose common ratio is 2.

To Find : 7th term

Solution :

Using the formula of Geometric Sequence :

[tex]a_{n} =a_{1} *r^{n-1}[/tex]    --(A)

Since,

[tex]a_{1}=5[/tex]

r =2

n = 7 (term no. need to calculate)

Putting these values in ---(A)

⇒[tex]a_{7} = 5*2^{7-1}[/tex]

⇒[tex]a_{7} = 5*2^{6}[/tex]

⇒[tex]a_{7} = 5*64[/tex]

⇒[tex]a_{7} =320[/tex]

Hence the 7th term in Geometric Sequence is 320

Answer: 6

The remainder theorem says that if we divide p(x) over x-k, then the remainder is r = p(k)

In this case, we have p(x) = x^2+5 and x-k = x+1 = x-(-1). So k = -1 is plugged into p(x) to get

p(x) = x^2+5

p(-1) = (-1)^2+5

p(-1) = 1+5

p(-1) = 6

That is why the remainder is 6. You can use polynomial long division or synthetic division to confirm this answer.

Answer:

The remainder would be 6.

Step-by-step explanation:

Final answer:

The unit rate of 2134 meters in 212 hours is approximately 10.063 meters per hour. This calculation involves dividing the total distance by the total amount of time.

Explanation:

To find the unit rate of 2134 meters in 212 hours, we need to calculate how many meters are covered in one hour. The unit rate is computed by dividing the total distance by the total time.

The calculation is as follows:

Unit rate = Total distance / Total time

Unit rate = 2134 meters / 212 hours

Calculating this gives us a unit rate of approximately 10.063 meters per hour. It's important to make sure that the result is reasonable. If you travel a certain distance in a given number of hours, dividing the distance by the time should give you how many meters you travel in one hour, which in this case, it does.

Answer:

4

Step-by-step explanation:

UPC (Universal Product Code) is a numeric symbol used in retail products. UPC has two variants, an 11 digit UPC Type A bar code and and 6 digit UPC Type E bar code.

The given UPC code 78007305233 is an 11 digit UPC Type A bar code.

1) From the right to the left, starting with odd position, we need to assign the odd/even position to each digit.

0 E 0 E 0 E 0 E 0 E 0                [0 stands for Odd, E stands for Even]

7 8 0 0 7 3 0 5 2 3 3

2) Summing up all digits in the odd positions and multiplying the result by 3

(7+0+7+0+2+3)*3 = 19 * 3 = 57

3) Summing up all digits in the even positions

8+0+3+5+3 = 19

4) Summing up the results of step three and four

57 + 19 = 76

5) Now, divide the result of the fourth step by 10. The check digit would be the number which adds the remainder to 10. In our case, upon dividing, 76 by 10 we get the remainder 6. The check digit is the result of 10-6 = 4.

Answer:

25

Step-by-step explanation:

Formula

2xy + 1

Givens

x = 3

y = 4

Solve

2*(3)*(4) + 1

24 + 1

25

9.915 mi and that's all and that helped friend me please thanks stay pretty

Answer:

9.91 miles

Step-by-step explanation:

Refer the attached figure

Forest Ranger at point A observes the fire at angle of 41° north of east i.e.∠CAB = 41°

The distance between the two rangers is 15 miles i.e. AB = 15 miles

Forest Ranger at point B observes the fire at at 56° north of west. i.e.∠CBA= 56°

Now we are supposed to find who is closest to the fire

So, we are supposed to find the length of AC and BC

So, first calculate ∠ACB

We will use angle sum property of triangle

Angle  sum property of triangle  : Sum of all angles of triangle is 180°

So, ∠CBA+∠ACB+∠CAB =180°

56°+∠ACB+41° =180°

97°+∠ACB =180°

∠ACB =180°-97°

∠ACB =83°

Now to find  AC and BC we will use law of sines

[tex]\frac{a}{sin A}=\frac{b}{Sin B}=\frac{c}{SinC}[/tex]

Refer the attached figure

[tex]\frac{AC}{sin 56}=\frac{BC}{Sin 41}=\frac{15}{Sin83}[/tex]

So, [tex]\frac{BC}{Sin 41}=\frac{15}{Sin83}[/tex]

[tex]BC=\frac{15}{Sin83} \times Sin 41[/tex]

[tex]BC=9.91478[/tex]

[tex]\frac{AC}{sin 56}=\frac{15}{Sin83}[/tex]

[tex]AC=\frac{15}{Sin83} \times sin 56[/tex]

[tex]AC=12.5289[/tex]

So, BC< AC

So, the ranger who is closest to fire is at a distance of 9.91 miles .

So, Option 1 is true

Answer:78.5

Step-by-step explanation

3.14×r^2

Area of a circle whose radius is 5 meters is 78.55square meter

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry

The formula for area of circle is Area equal to pi r square

A=πr²

The radius is given which is 5 meters

r=5

Substitute the r value in Area of circle formula

A=3.142×5²

We know that five square is twenty five.

=3.142×25

=78.55

Hence  area of a circle whose radius is 5 meters is 78.55square meter.

To learn more on Circles click:

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Answer:

Associative Property of Addition.

Step-by-step explanation:

It states that no matter how the numbers are ordered, the result will be the same. Feel free to look it up on google for more information :)

Answer:

The answer is Associative Property of Addition. Hope I helped!

Answer:

£120

Step-by-step explanation:

First calculate 25% of £160 then subtract this from the £160.

25% of 160 = 25/100  * 160

= 1/4 * 160 = £40.

£160 - £40  = £120  (answer).

Answer:

The answer is $120

Step-by-step explanation:

First you must find 25% of $160

First, I found out what is 25% of 16

Next, made 25% = 1/4

Then, 1/4 of 16 is also 16 divided 4 and you will get 4

Then, you add the zero on the back and make it $40

Finally, subtract 40 from 160 and that will be your answer

160 - 40 = $120

Answer:

-1.5, -1.6, -1.7, -1.8, -1.9

Step-by-step explanation:

A rational number is a number that can be written as the ratio of two integers.

-1.5 is a rational number between -2 and -1

-1.5  can be written as -15/10

-1.6  is a rational number between -2 and -1

-1.6 can be written as -16/10

1.7  is a rational number between -2 and -1

-1.7 can be written as -17/10

1.8  is a rational number between -2 and -1

-1.8 can be written as -18/10

1.9  is a rational number between -2 and -1

-1.9 can be written as -19/10

Answer:

the answer is:

b

d

e

Functions are used to show relationships between variables. The true statements are:

I've added as an attachment, the table of values of f(x)

Next, we test the given options

(a) f(x) > 0 over the interval ([tex]-\infty[/tex], 3).

Using the table of f(x), the values in ([tex]-\infty[/tex], 3) are values less than 3; i.e. -3 to 2.

If f(2) = 0, then f(x) > 0 is not true

(b) f(x) ≤ 0 over the interval [0, 2].

The values in [0, 2] are values from 0 to 2; i.e. 0, 1 and 2.

If f(0) = 0, f(1) = -3 and f(2) = 0

Then, f(x) ≤ 0

(c) f(x) < 0 over the interval (−1, 1).

Using the table of f(x), the values in (-1, 1) are values between -1 and 1; i.e. 0

If f(0) = 0, then f(x) < 0 is not true

(d) f(x) > 0 over the interval (–2, 0).

Using the table of f(x), the values in (-2, 0) are values between -2 and 0; i.e. -1

If f(-1) = 3, then f(x) > 0 is true

(e) f(x) ≥ 0 over the interval [2, [tex]\infty[/tex])

Using the table of f(x), the values in [2, [tex]\infty[/tex]) are values from 2; i.e. 2 and 3

If f(2) = 0 and f(3) = 15, then f(x) ≥ 0  is true

Hence, the true statements are:

Read more about functions over interval at:

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the answer is 9x(to the power of 2)−42x+49

Answer: slope is 5 and y-intercept is 15

Step-by-step explanation:

you pay 5 dollars each hour or whatever the time is and have to pay $15 to get in the cab. So the $15 is a must pay.

Answer:

You pay $5\time and must pay $15 to ride in it.

Answer:

the golf ball travels 4,295.52 inches in 20 seconds

Step-by-step explanation:

the ball spins around 340 revolutions per minute

340 revolutions per 60 seconds

60 seconds = 340 revolutions

1 seconds = [tex]\frac{340}{60} = 5.667[/tex]

so its around 5.7 revolutions in 1 second

1 second = 5.7 revolutions

 20 seconds = 5.7 * 20 = 114 revolutions

In 20 second ball spins 114 revolutions

To find distance traveled in 1 revolution we find the circumference of circle

circumference of circle = 2* 3.14 * r

r is the radius = 6 in

circumference of circle = 2* 3.14 * 6= 37.68 inches

In 1 revolution ball travels 37.68 inches

In 114 revolution ball travels 37.68 * 114 = 4295.52 inches

the golf ball travels 4,295.52 inches in 20 seconds

Answer:

the x-coordinate

Step-by-step explanation:

The slope intercept form is: y = mx + c

where m⇒ slope

          c ⇒ y-intercept

          (x,y) is a point on the graph the  satisfy the equation representing that graph.

∴ x is the x-coordinate of a point on the line.  

Answer:

B & D

Step-by-step explanation:

The quadratic formula can be used to solve for x for any quadratic. Recall a quadratic is any function whose highest exponent known as degree is 2. Looking at the answer selections, A has one term with exponent 3. This isn't possible in the formula. Looking at answer C, the term with exponent 2 has the same coefficient on each side of the equal sign. When it is rearranged these will cancel out no exponent of 2 will be in the equation anymore. Only B & D work after being rearranged and simplified

The two equations after simplifying will give quadratic equations are:-

x ²-6x-7=2x² and 5x²-3x+10=2x².

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

Solving for the quadratic equation:-

Option B:-

x ² -   6x   -   7  =   2x²

- 2x²   +   x ² -   6x   -   7  =  0

x ²  +  6x  +  7  =  0

Option D:-

5x²   -   3x   +   10  =    2x².

5x²  -  2x². -   3x   +   10  =   0

3x²  -   3x  +  10  =  0

Therefore two equations after simplifying will give quadratic equations are- x ²-6x-7=2x² and 5x²-3x+10=2x².

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[tex](f\cdot g)(x)=f(x)\cdot g(x)\\\\\text{We have}\ f(x)=x+7\ \text{and}\ g(x)=\dfrac{1}{x-13}.\\\\\text{Substitute}\\\\(f\cdot g)(x)=(x+7)\cdot\dfrac{1}{x-13}=\dfrac{x+7}{x-13}\\\\\text{The domain:}\\\\x-13\neq0\qquad\text{add 13 to both sides}\\\\x\neq13\\\\Answer:\ \boxed{x\in\mathbb{R}-\{13\}}\to\boxed{\text{All real numbers except 13}}[/tex]

Answer: Alternate Interior Angles Theorem (choice B)

If you have two parallel lines, and cut them with a third line, then you'll form two pairs of alternate interior angles. Alternate interior angles are angles that that are on the inside of the parallel "train tracks", but they are on opposite sides of the transversal line.

Answer:

32

Step-by-step explanation:

XY means x times y

and x = 8 or x is 8

and y = 4 or y is 4

so 4 times 8 is 32

so

XY = 32

Answer:

First of all, I expect you fulfill your word and give what you promise... ha ha just kidding, I already solved a question like this one, please see below explanation.

1. Tessellation is the covering of a surface with pattern(s) of flat shapes so that there are no overlaps or gaps. It is also called Tiling.

2. Triangles, Squares, and Hexagons are regular polygons.

3. Previous three shapes create a regular tessellation pattern because all their sides and all their angles are the same. the intersection point of the interior angles is called "Vertex". For a regular tessellation, the pattern is identical at each Vertex.

Unlike the triangle and quadrilateral case, the Pentagon's angle sum of 540° is not helpful when trying to fit a bunch of Pentagons around a vertex. Therefore, even though the Pentagon is a regular polygon, it cannot tessellate.

4. See attached screenshot of 3 tessellations created with Tessellation Artist Software online.

Answer:

12/24

Step-by-step explanation:

A ratio is a comparison of two quantities and can be written in several forms including fractions. It is most commonly written in fraction form or a:b.

To write a ratio, we count the number of each quantity we are comparing. The number of shaded squares is 12. While the total number of squares is 24. We write the ratio as shaded : total.

12:24 or

[tex]\frac{12}{24}[/tex] or

0.5 as a decimal.

Answer: 56

Step-by-step explanation: The pattern is 8 x 3.5 = 28, 10 x 3.5 = 35, 12 x 3.5 = 42... so 16 x 3.5 = 56

Answer:

56

Step-by-step explanation: