Let f(x) = 4 – x^2, g(x) = 2 – x. Find (f + g)(x) and its domain.

For line A,

if we increase x by 1 unit then y increases by 4 units i.e. (1,3) and similarly another point becomes

(2,7).

For line B,

if we increase x by 1 uni then y also increases by 1 unit i.e ( 1,1) and similarly another points becomes (2,2),(3,3),(4,4), etc.

For line C,

if we increase x by 3 units then y increases by 1 units i.e.(3,1) and similarly another points becomes

(7,2) and so on.

In above lines, the value of x is exactly equal to that of y in line B.

therefore, line B has constant proportionality between x and y.

To find the line with a constant of proportionality of 111 between y and x, we calculate the slope for each line. Line A has a slope of 111, making it the correct answer.

To determine which line has a constant of proportionality of 111, we need to examine the slope of each line. The slope represents the ratio of the change in the y-values to the change in the x-values for any two points on the line. If the slope is the same for all points on the line, then it has a constant of proportionality. Let's calculate the slopes for lines A, B, and C:

Line A: Let's choose two points: (0, 0) and (1, 111). The slope is (111 - 0) / (1 - 0) = 111 / 1 = 111.

Line B: Let's choose two points: (0, 0) and (1, 1110). The slope is (1110 - 0) / (1 - 0) = 1110 / 1 = 1110.

Line C: Let's choose two points: (0, 0) and (1, 11100). The slope is (11100 - 0) / (1 - 0) = 11100 / 1 = 11100.

Therefore, the line with a constant of proportionality of 111 is Line A.

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Answer:

B. 28 minutes

Step-by-step explanation:

According to the given statement,

William weeds the whole garden in 45 minutes, then in one minute he will weed 1/45 of the garden

and

similarly, 1/75 of the garden in one minute.

When they both will work together, they will weed (1/45+1/75) of the garden in one minute

Solving the equation:

= [tex]\frac{1}{45}+ \frac{1}{75}\\= \frac{75+45}{3375}\\ =\frac{120}{3375}\\ = 0.036[/tex]

Garden weeded in one minute by both = 0.036

So, number of minutes to weed whole garden = 1/0.036

= 27.77 minutes

Rounding off will give us: 28 minutes

So,

Option B is the correct answer ..

The simplified form of ratio of  [tex]3\sqrt7[/tex] and [tex]5\sqrt7[/tex] is equal to 3/5 by factorizing the numerator and denominator and by  dividing it.

Given that simplify 3 square root of 7 over 5 square root of 7 that is [tex]3\sqrt7 / 5\sqrt7.[/tex]

To find the ratio of  [tex]3\sqrt7[/tex] and [tex]5\sqrt7[/tex] is equal to 3/5 by factorizing the numerator and denominator and by  dividing it by following steps:

Step 1: Factorize the numerator and denominator.

Numerator [tex]= 3\sqrt7 = 3(\sqrt7)[/tex]

Denominator [tex]= 5\sqrt7 = 5(\sqrt7)[/tex]

Step 2: Divide both numerator and numerator by common factor gives:

Ratio = numerator/denominator

[tex]= \sqrt7(3)/\sqrt7(5)[/tex]

Divide both numerator and numerator by [tex]\sqrt7[/tex] gives:

= 3/5.

Therefore, the simplified form of ratio of [tex]3\sqrt7[/tex] and [tex]5\sqrt7[/tex] is equal to 3/5 by factorizing the numerator and denominator and by  dividing it.

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Answer:

The answer is 2.

Step-by-step explanation:

The equation for finding the axis of symmetry is:

x=-\frac{b}{2a}

Plug the numbers from the equation in:

a=1

b=-2

x=-\frac{-2}{2(1)}

Solve:

x=\frac{2}{1}

x=2

hope this helps :)

Answer:

Mass of pilot whale is 1.2 X 10 ^4 times massive than Mass of clownfish.

Step-by-step explanation:

Mass of clown fish = 2.5 X 10 ^-1 kg

Mass of pilot whale = 3 X 10 ^ 3 kg

Find the ratio of Mass of pilot whale to the ratio of Mass of clown fish

Mass of pilot whale : Mass of clown fish

3 X 10 ^ 3 : 2.5 X 10 ^-1

It can be written as

3 X 10 ^ 3 / 2.5 X 10 ^-1

1.2 x 10^4

So, Mass of pilot whale is 1.2 X 10 ^4 times massive than Mass of clownfish.

x in (-oo:+oo)

2/7 = x/14 // - x/14

2/7-(x/14) = 0

2/7-1/14*x = 0 // - 2/7

-1/14*x = -2/7 // : -1/14

x = -2/7/(-1/14)

x = 4

x = 4

i hope this helps

Answer:

x*14 = 7*4

Step-by-step explanation:

So, 1 cube equals 1/4 unit.

4 cubes will equal 1 whole unit.

If the volume of the rectangular prism is 3 cubic units, all you have to do is multiply.

4*3=12

So it would take a total of 12 cubes to fill the prism.

Hope this helps.

Answer:

Let g be the golden ticket; t be the regular ticket; p be the platinum ticket.

119g + 100t + 6p = 6592

t = 3/4g

p = 2g

119g + 100(3/4)g + 6(2g) = 6592

g = 32

t = 3/4(32) = 24

p = 32(2) = 64

A golden ticket costs $32. A regular ticket costs $24. A platinum ticket costs $64. Hope this helps!

Answer:

Let g be the golden ticket; t be the regular ticket; p be the platinum ticket.

119g + 100t + 6p = 6592

t = 3/4g

p = 2g

119g + 100(3/4)g + 6(2g) = 6592

g = 32

t = 3/4(32) = 24

p = 32(2) = 64

Step-by-step explanation:

Answer:

1/6 * 1/6 = 1/36 or 0.027%

Step-by-step explanation:

This is because there is a 1/6 chance the cubes will land on 3. Sincer there is 2 of them, multiply them by each other. Do not add.

Hope this helps!

Answer:

Option "A" might be the correct option

Step-by-step explanation:

By the Angles of Intersecting Chords Theorem, When two chords intersect inside a circle, then the measure of the angle formed is one half the sum of chord's intercepted arcs.

In the diagram : -

⇒ ∠ 1 = 38°

Now, again by the diagram,

∠1 and ∠2 are linear pairs,

⇒ ∠1 + ∠2 = 180°

⇒ 38° + ∠2 = 180°

⇒ ∠2 = 142°

Answer:

38,142.

Step-by-step explanation:

The measure of angle 1 = the sum of the measure of the 2 arcs / 2

= (36 + 40) / 2

= 38 degrees.

11 • 55 = 55

The starfish had 55 arms all together.

Hope this helps!

I think the answer is 32,2000cm^3

Answer: C

Step-by-step explanation: i got 100% on test

Answer:

The equation is:

[tex]S=\frac{a_n*r-a_1}{r-1}[/tex]

[tex]S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}[/tex]

The sum is:

[tex]S=\frac{211}{243}[/tex]

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

If the sequence is infinite, the formula is:

[tex]S = \frac{a_1}{1-r}[/tex]

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

Step-by-step explanation:

We must calculate the radius of the geometric series

[tex]r =\frac{a_{n+1}}{a_n}\\\\r=\frac{\frac{2}{9}}{\frac{1}{3}}\\\\r=\frac{2}{3}[/tex]

The first term of the series is: [tex]a_1=\frac{1}{3}[/tex]

The last term of the series is: [tex]a_n=\frac{16}{243}[/tex]

If the sequence is finite then the formula is:

[tex]S=\frac{a_n*r-a_1}{r-1}[/tex]

[tex]S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}[/tex]

[tex]S=\frac{211}{243}[/tex]

If the sequence is infinite then by definition as the radius  are [tex]0 <| r | <1[/tex] then the formula for the sum of the geometric sequence is:

[tex]S = \frac{a_1}{1-r}\\\\S = \frac{\frac{1}{3}}{1-\frac{2}{3}}\\\\S =1[/tex]

Answer:

A

Step-by-step explanation:

got it right on edge

Answer:

D

Step-by-step explanation:

Supplementary angles sum to 180°

Subtract the given angle from 180 for the supplement, that is

180° - 89° = 91° ← the supplementary angle

Final answer:

The supplement of an 89° angle is found by subtracting it from 180°, giving us 91°. Therefore, the correct answer is 91°, which is option D.

Explanation:

To find the supplement of an angle, we need to know that supplementary angles add up to 180 degrees. Given an angle that measures 89°, we can find its supplement by subtracting the given angle from 180°.

So, 180° - 89° = 91°.

The supplement of an angle that measures 89° is 91°, which corresponds to option D.

Answer:

second choice

third choice

Step-by-step explanation:

righty whighty edg 2020

From the given diagram of triangle DEF:

Triangle DEF is shown in the image attached below/.

Triangle DEF has the following sides:

The triangle also shows that:

Also,

In summary, from the given diagram of triangle DEF:

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Answer:

Blank 1 ⇒ supplementary

Blank 2 ⇒ complementary

Step-by-step explanation:

* Lets revise some facts to solve the problem

- The tangent to a circle is a line touch the circle at one point

- The tangent and the radius of a circle are perpendicular to each

 other at the point of contact

- If the two angles are supplementary, then the sum of their measure

 is 180°

- If the two angles are complementary, then the sum of their measure

 is 90°

* Now lets solve the question

∵ CB and CA are two tangents to the circle O at B and A

∵ OB and OA are radii

∴ OB ⊥ BC at point B and OA ⊥ AC at point A

∴ m∠OBC = 90° and m∠OAC = 90°

- In figure CBOA is a quadrilateral

∴ The sum of the measures of its interior angles is 360°

∵ m∠CBO + m∠BOA + m∠OAC + m∠BCA = 360°

∵ m∠CBO = 90° , m∠OAC = 90°

∴ 90° + m∠BOA + 90° + m∠BCA = 360°

∴ 180° + m∠BOA + m∠BCA = 360° ⇒ subtract 180 from both sides

∴ m∠BOA + m∠BCA = 180°

∴ ∠BOA and ∠BCA are supplementary

- In Δ CBO

∵ The sum of the measures of the interior angles of any triangle is 180°

∴ m∠BOC + m∠BCO + m∠CBO = 180°

∵ m∠CBO = 90°

∴ m∠BOC + m∠BCO + 90° = 180° ⇒ subtract 90° from both sides

∴ m∠BOC + m∠BCO = 90°

∴ ∠BOC and ∠BCO are complementary

Answer:

Blank 1: Supplementary

Blank 2:Complementary

Step-by-step explanation: I picked these and got it right

Answer:

53:2 Im sure.

Ratio is a comparison of two quantities. Online Simplifying ratios calculator is a ratio simplifier that simplify ratios in to its simplest form. For that ones should know the greatest common factor of both numerator and denominator. And then divide these two by the common factor. By using ratio in simplest form calculator one can simplify ratio from the high value to lower value in an easy way.

Answer:

Change values to whole numbers.

Convert any mixed numbers to fractions.

Convert 3 1/8

3 1/8 = 25/8

We now have:

5 : 3 1/8 = 5 : 25/8

Convert the whole number 5 to a fraction with 1 in the denominator.

We then have:

5 : 3 1/8 = 5/1 : 25/8

Convert fractions to integers by eliminating the denominators.

Our two fractions have unlike denominators so we find the Least Common Denominator and rewrite our fractions as necessary with the common denominator

LCD(5/1, 25/8) = 8

We now have:

5 : 3 1/8 = 40/8 : 25/8

Our two fractions now have like denominators so we can multiply both by 8 to eliminate the denominators.

We then have:

5 : 3 1/8 = 40 : 25

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 40 and 25 is 5

Divide both terms by the GCF, 5:

40 ÷ 5 = 8

25 ÷ 5 = 5

The ratio 40 : 25 can be reduced to lowest terms by dividing both terms by the GCF = 5 :

40 : 25 = 8 : 5

Therefore:

5 : 3 1/8 = 8 : 5

Step-by-step explanation:

Hello There!

To find a cylinder, we use the formula Pi*radius “squared” *height

First, let’s put in our values. Our radius is 5 but in our formula, we have to square 5 so we get a product of 25.

Then we multiply 25 by 9 because you will see in our formula we have to multiply by the height. 25*9 equals 225

Now, we are putting our value in terms of pi so our answer would be 225

Answer “C”

Answer:

175

Step-by-step explanation:

APEXX!!!!

Answer:

C.

Step-by-step explanation:

Answer:

The correct answer is C.

Step-by-step explanation:

We have given some pattern in the series.

We need to find the next step which follows and continue the series.

We know that, we have three given patterns in the question. In the first we have given a pattern which is made by the joining of three dots, and in the second pattern made by the joining of five dots and in the third pattern made by the joining of the five dots.

In the following way, we can say that the next step in the series and fourth pattern follows same pattern as given in the above. That's why next pattern made by the joining of seven dots, but in the following given options next to next pattern is given which is joining by nine dots, therefore we choose option which is the next step in the series.

[tex]\bf \begin{array}{llll} term&value\\ \cline{1-2} a_5&36\\ a_6&36\left( \frac{1}{3} \right)\\ a_7&36\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\\ a_8&36\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\\ a_9&36\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\\ a_{10}&36\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right)\left( \frac{1}{3} \right) \end{array}[/tex]

[tex]\bf a_{10}=36\left( \frac{1}{3} \right)^5\implies a_{10}=36\cdot \cfrac{1^5}{3^5}\implies a_{10}=\cfrac{36}{243}\implies a_{10}=\cfrac{4}{27}[/tex]

Answer:

see explanation

Step-by-step explanation:

Given that y varies inversely as x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition

x = 2 when y = 2

k = yx = 2 × 2 = 4, hence

y = [tex]\frac{4}{x}[/tex] ← equation of variation

Answer:

12a−9

Step-by-step explanation:

Distribute:

=(3a)(3)+(3a)(−a)+(3)(a2)+(3)(−3)+3a

=9a+−3a2+3a2+−9+3a

Combine Like Terms:

=9a+−3a2+3a2+−9+3a

=(−3a2+3a2)+(9a+3a)+(−9)

=12a+−9

Answer:

3 (4 a - 3)

Step-by-step explanation:

Simplify the following:

3 a (3 - a) + 3 (a^2 - 3) + 3 a

3 a (3 - a) = 9 a - 3 a^2:

9 a - 3 a^2 + 3 (a^2 - 3) + 3 a

3 (a^2 - 3) = 3 a^2 - 9:

3 a^2 - 9 - 3 a^2 + 9 a + 3 a

Grouping like terms, 3 a^2 - 3 a^2 + 9 a + 3 a - 9 = (9 a + 3 a) - 9 + (-3 a^2 + 3 a^2):

(9 a + 3 a) - 9 + (-3 a^2 + 3 a^2)

9 a + 3 a = 12 a:

12 a - 9 + (-3 a^2 + 3 a^2)

3 a^2 - 3 a^2 = 0:

12 a - 9

Factor 3 out of 12 a - 9:

Answer:  3 (4 a - 3)

Step 1: Set the two equations equal to each other and solve for x.

3x -5 = 6x - 8

3x + (-5+5) = 6x -8 + 5

(3x - 6x) = (6x - 6x) - 3

-3x/-3  = -3/-3

x = 1

Step 2: To solve for y take one of the given equation of your choice (for the purpose of this explanation I will only do y = 3x - 5) and replace x with 1, then solve for y

y = 3(1) - 5

y = 3 - 5

y = -2

(1,-2)

Check:

-2 = 3(1) - 5 ---> - 2 = -2

-2 = 6(1) - 8 ---> -2 = -2

Hope this helped!

Answer:

x=1

and y= -2

Step-by-step explanation:

y=3x-5 y=6x-8

On equating the two equations:

3x-5= 6x-8

Taking terms of x on one side and constant terms on the other

6x-3x= 8-5

3x= 3

Dividing both sides by 3, we get

x=1

Now, putting value of x in y=3x-5, we get

y=3-5

 = -2

Hence, Solution is:

x=1 and y= -2

Answer:

-2

Step-by-step explanation:

2x + y = 10               Subtract 2x from both sides.

2x-2x + y = 10 - 2x  Combine the left.

y = 10 - 2x

The slope is the number in front of the x -- in this case - 2

The answer is - 2

Answer:

40 cm

Step-by-step explanation:

Multiply the length, the width, and the height. You can multiply them in any order to get the same result. The formula for finding the volume of a rectangular solid is:

Volume = Length * Height * Width,

or V = L * H * W.

Answer: 42.5

Step-by-step explanation:

The answer is 42.5

Answer: 42.5 cm

Step-by-step explanation: Its really simple. You multiply 8.5 cm and 5 cm to get 42.5 cm.

Answer:

x-6

Step-by-step explanation:

Let the number be x

Then the algebraic expression  “six less than a number” can be represented as:

x - 6

So, "six less than a number” can be represented as: x - 6

Answer:

x = 3

x = -5

Step-by-step explanation:

(9)(x+1)(x+1) = 144

(9)(x²+2x+1) = 144

9x²+18x+9 = 144

9x²+18x = 135

x²+2x = 15

x(x+2) = 15

x = 3

x= -5

Answer: [tex]x_1=3\\x_2=-5[/tex]

Step-by-step explanation:

Divide boht sides of the eqeuation by 9:

[tex]\frac{9(x+1)^2}{9}=\frac{144}{9}\\\\(x+1)^2=16[/tex]

Remembert that:

[tex](a+b)^2=a^2+2ab+b^2[/tex]

Then, applying this, you get:

[tex]x^2+2(x)(1)+1^2=16\\x^2+2x+1=16[/tex]

Subtract 16 from both sides:

[tex]x^2+2x+1-16=16-16\\x^2+2x-15=0[/tex]

Factor the quadratic equation. Find two numbers whose sum be 2 and whose product be -15, then:

[tex](x-3)(x+5)=0\\x_1=3\\x_2=-5[/tex]

The answer is:

The domain for the function is all the real numbers,

Domain:(-∞,∞)

Since we are working with fractions, the only restriction that we will have for the function is when the denominator of the function tends to 0.

We are given the function:

[tex]f(x)=\frac{1}{x^{2}-5x+25 }[/tex]

Where, the denominator is given by the expression:

[tex]x^{2}-5x+25[/tex]

For the given expression (quadratic equation), we have that:

[tex]a=1\\b=-5\\c=25[/tex]

Calculating the discriminat of the quadratic function, in order to know if the denominator of the function has roots (zeroes) at the real numbers, we have:

[tex]Discriminant=b^{2} -4ac[/tex]

[tex]Discriminant=-5^{2} -4(1)(25)[/tex]

[tex]Discriminant=25 -100=-75[/tex]

Now, as we know, if the discriminant of a quadratic function is less than 0, the quadratic function has no roots in the real numbers.

Therefore, since the denominator (quadratic function) has no roots in the real numbers, the domain for the function will be equal to all the real numbers.

Domain:(-∞,∞)

Hence, the answer is the third option, the domain for the function is all the real numbers,

Domain:(-∞,∞)

Have a nice day!