Multiply The Fractions. Select The Answer That Is In Simplest Form9x2 1/3 (2024)

(a) The answer of (g.f)(2) is [tex]\sqrt{23}[/tex] .

(b)The answer of (g + f) (2) is [tex]\sqrt{3}[/tex] - 3 .

(c)The answer of (g - f) (-1) is [tex]\sqrt{15}[/tex] .

(d)The answer of [tex]\frac{f}{g}(-1)[/tex] is 0 .

The composition of functions f(x) and g(x) on which g(x) acts first is denoted by f(g(x)) or (f ∘ g)(x). It combines two or more functions to provide another function. In function composition, the output of the function inside the parentheses becomes the input of the outer function.

We have given two functions f(x) = [tex]1-x^2[/tex] and g(x) = [tex]\sqrt{11-4x}[/tex]

(a) Put x = 2 in f(x) we get f(2) = 1 - 4 = -3

(g.f)(2) = g(f(2))

= g(-3)

[tex]=\sqrt{11-4(-3)}\\=\sqrt{11+12} \\=\sqrt{23}[/tex]

which is option (c) .

(b) Put x = 2 in f(x) we get f(2) = 1 - 4 = -3 and g(2) = [tex]\sqrt{11-8} =\sqrt{3}[/tex]

(g + f) (2) = g(2) + f(2)

= [tex]\sqrt{3}[/tex] + (-3)

= [tex]\sqrt{3}[/tex] - 3

which is option (a)

(c) Put x = -1 in f(x) we get f(-1) = 1 - 1 = 0 and g(-1) = [tex]\sqrt{11+4} =\sqrt{15}[/tex]

(g - f) (-1) = g(-1) - f(-1)

= [tex]\sqrt{15}[/tex] + 0

= [tex]\sqrt{15}[/tex]

which is option (b)

(d) Put x = -1 in f(x) we get f(-1) = 1 - 1 = 0 and g(-1) = [tex]\sqrt{11+4} =\sqrt{15}[/tex]

[tex]\frac{f}{g}(-1)[/tex] = f(-1) / g(-1)

= 0 / [tex]\sqrt{15}[/tex]

= 0

which is option (d)

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Answer:

172.63

Step-by-step explanation:

Answer: Ordinarily, no, it wouldn't matter.

Step-by-step explanation: No matter in what order you add it up it will be the same answer in the end.

Answer:

y = 4x + 7

or y - 4x = 7

Step-by-step explanation:

x + 4y = 2

4y = -x + 2

y = -1/4x + 2

The slopes of two perpendicular lines arenegative reciprocals of each other. So the slope of the perpendicular line should be negative reciprocal of -1/4, then it is 4

Given m = 4, y = 3, x = -1

y = mx + b

3 = 4(-1) + b

3 = -4 + b

b = 7

y = 4x + 7

The kinetic energy of hammer is 25 m/s.

How to find the kinetic energy?

The energy an object has as a result of motion is known as kinetic energy in physics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity.

given that

the mass of the hammer is 0.50 kg.

The velocity of the hammer is 10 m/s.

now find the kinetic energy of the hammer.

[tex]kinetic \: energy = \frac{1}{2}m {v}^{2} [/tex]

[tex]kinetic \: energy = \frac{1}{2} \times 0.50 \times {10}^{2} [/tex]

kinetic energy = 0.25 X 100

kinetic energy = 25 m/s.

Hence, the kinetic energy of hammer is 25 m/s.

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According to the given statement the interest that we earn is

= $74,059 . 64

What Is an Annuity's Present Value?

The present value of an annuity seems to be the current worth of future annuity payments based on a predetermined rate of return, as well as discount rate. The higher the discount rate, the smaller the annuity's present value.

According to the given data:

monthly payment is 150

at the age = 30

interest rate = 4

till age of = 65

At age 65, the annuity would be worth $137,059.64.

We only need to determine the amount of interest. = ?

for monthly payments, we need to take n, which equals 12 points now total interest.determined by future value. Substitute minus p m t multiplied by n multiplied by t for all values now.

the amount of interest = deposited amount x year x no of year invested

= 150 x 12x(65-30)

present value = 63000

At age 65, the annuity would be worth $137,059.64.

We know that the interest is = balance - capital

= 137,059.64 - 63000

= $74,059 . 64

According to the given statement the interest that we earn is

= $74,059 . 64

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We have the profit fomula:

P = R - C

= $10.x - ($3.x + 1000)

= $7.x - 1000

1. If the company sells 1000 pens:

P = $7 . 1000 - $1000

= $6000

2. If they want to break even:

P at least = 0

Assume P = 0

=> $7.x - $1000 = 0

=> x = 1000/7 ≈ 142,86

So if they want to break even, they have to sell at least 143 pens

The distance in feet between the ground and the top of the ladder is 16.7 feet.

Let the distance in feet between the ground and the top of the ladder be x.

According to the given question.

Length of the ladder = 17 foot

The distance of the ladder from the base of the wall is 3 feet.

From the given data we can say that we have a right angle triangle in which the hypotenuse is the length of the ladder, base is the distance between the ladder and wall. And the distance between ground and ladder is our perpendicular.

Now according to the Pythagoras theorem,the sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).

Therefore,

17^2 = 3^2 + x^2

⇒ 289 = 9 + x^2

⇒ 280 = x^2

⇒ x = 16.7 feet

Hence, the distance in feet between the ground and the top of the ladder is 16.7 feet.

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The number of miles she should run on Friday is 2 3/4 miles.

Given that, Leah is training to run a half marathon her goal training is to run 20 miles a week. she ran 3 1/2 miles on Monday 4 3/4 miles on Tuesday 5 miles on Wednesday and 4 miles on Thursday.

We need to find how many miles will she need to run on Friday in order to meet her goal.

How to add mixed fractions?

Follow these steps to add mixed fractions:

Add the whole numbers together. Find the lowest common denominator (LCD) of both fractions. The LCD is the lowest number that is evenly divisible by both numbers.Convert the fractions to have the LCD as their denominator.Once you have a common denominator, the fractions can be added by simply adding the numerators.

Now, the number of miles she ran together from Monday to Thursday

=3 1/2 + 4 3/4 + 5 + 4 =(3+4+5+4)(1/2 + 3/4)

=16 (2/4 + 3/4)

=16 5/4

=17 1/4

Remaining miles = 20-17 1/4

=20-69/4

=(80-69)/4

=11/4

=2 3/4

Therefore, the number of miles she should run on Friday is 2 3/4 miles.

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Answer:

6.8%

Step-by-step explanation:

[tex]\frac{21447.20}{315400}[/tex] When you divide this, you get 0.068. This is in decimal form. To change to a percent move the decimal to places to the right 6.8%

Answer:

d

Step-by-step explanation:

Let the number be 'x'.

First find x and then find 130% of x.

30% of x = 25

[tex]\sf \dfrac{30}{100}*x = 25[/tex]

[tex]\sf x = 25*\dfrac{100}{30}\\\\ x = \dfrac{250}{3}\\\\[/tex]

Now, find 130% of x

130% of x = [tex]\sf \dfrac{130}{100}*\dfrac{250}{3}\\\\[/tex]

[tex]\sf = \dfrac{325}{3}\\\\ = 108.3[/tex]

Answer:

75%

Step-by-step explanation:

% = (6/8)(100) = 600/8 = 75

Hope this helps

15.25 multiplied by 7 is 106.75 however you can’t sell .75 of a bushel so she sold 106 bushels, and 220-106 is 114.

She has 114 left after the 7 days and has sold 106.

Answer:

D. [tex]2^9[/tex]

Step-by-step explanation:

[tex]2^6*2^3 = 2^9[/tex]

We can just add the exponents together.

If it were continued another 120 minutes past this, it would be

[tex]2^9*2^3 = 2^1^2[/tex]

Answer:

I am pretty sure it is a i think.

Step-by-step explanation:

just subtract the fractions and you will get 6\10 and the you will simplify and get 3\5. so 3\4 is closest to 3\5.

Step-by-step explanation:

٨-٥٢.....................

answer:

[tex] \frac{6}{5} [/tex]

Answer:

Here us the answer in the attachment

Answer:

the person above is correct

Step- by-step explanation:

Answer:

[tex]13\frac{1}{8}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(-5 \frac{5}{8}\right) \cdot \left(-2 \frac{1}{3} \right)[/tex]

Convert the mixed numbers into improper fractions by multiplying the whole number by the denominator, adding it to the numerator of the fraction, and placing this as the numerator:

[tex]\implies -\dfrac{5 \cdot 8+5}{8} \cdot -\dfrac{2 \cdot 3+1}{3}[/tex]

[tex]\implies -\dfrac{40+5}{8} \cdot -\dfrac{6+1}{3}[/tex]

[tex]\implies -\dfrac{45}{8} \cdot -\dfrac{7}{3}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{a \cdot c}{b \cdot d}:[/tex]

[tex]\implies \dfrac{-45 \cdot -7}{8 \cdot 3}[/tex]

[tex]\implies \dfrac{315}{24}[/tex]

Convert the improper fraction into a mixed number:

[tex]\implies 315 \div 24 = 13\: \text{r}\:3[/tex]

[tex]\implies 13\frac{3}{24}[/tex]

[tex]\implies 13\frac{1}{8}[/tex]

Answer:

Product = 13 1/8

Step-by-step explanation:

The equation is,

→ (-5 5/8) × (-2 1/3)

Now the product of equation will be,

→ (-5 5/8) × (-2 1/3)

→ (-45/8) × (-7/3)

→ (-15 × -7)/8

→ 105/8

→ 13 1/8 {mixed fraction}

Therefore, the product is 13 1/8.

Answer:

1. 1, 9/4

2. 4^4

3. -0.0000000008723

4. -5100023*10^2, -6.6*10^(12)

Step-by-step explanation:

[tex]21^0 = 1;\ n^0\ always\ is\ 1.\\(\frac{2}{3})^{-2} = (\frac{3}{2})^2 = \frac{3^2}{2^2} = \frac{9}{4}; n^m\ is\ performed\ by\ doing\ n*n,\ m\ times.\\i.e.,\\ n^2=n*n;\\n^3=n*n*n;\\ n^4=n*n*n*n\\\\\frac{4^6}{4^2};\ original\\\\\frac{(4^2)^3}{4^2};\ (n^{mc}\ can\ be\ rewritten\ as\ (n^m)^c\\\\\frac{4^2}{4^2}*\frac{(4^2)^2}{1};\ split\ the\ fraction\ into\ two\ parts\ because\ of\ multiplication\ rules.\\\\1*4^4;\ \frac{n}{n}\ can\ be\ written\ as\ 1.\ \frac{n}{1}\ can\ be\ written\ as\ n.\\\\4^4[/tex]

Technically, [tex]4^4[/tex] is 256, but the answer is requested as a number with an exponent.

-8.723 * 10^-10 would be -0.0000000008723.

10^-10 = [tex]\frac{1}{10^{10}}[/tex], which would mean you must move your decimal left by the number of places indicated by the exponent.

[tex]-5.1*10^8-2.3*10^3 = x\\-51*10^7-23*10^2 = x\\10^7=10^{5+2}=10^5*10^2\\-5100000*10^2-23*10^2=x\\-5100023*10^2=x;\ combine\ like\ terms.\\-6*10^5 * 1.1*10^7 = x\\-6*1.1*10^5*10^7;\ rewrite\ for\ simplification.\\-6.6*10^{12}=x[/tex]

Answer:

-12 - 51i

Step-by-step explanation:

[tex]original:(-6-3i)*(5+6i)\\FOIL:(-6)(5)+(-6)(6i)+(-3)(5)+(-3i)(6i)\\Multiply:(-30)+(-36i)+(-15i)+(18i^2)\\Combine\ Like\ Terms:(-30) + (-51i)+(-18i^2)\\i^2\ =\ -1:(-30)+(-51i)+(-18)(-1)\\Multiply:(-30)+(-51i)+(18)\\Combine\ Like\ Terms:(-12) + (-51i)\\Simplify:-12-51i[/tex]

Thing to remember:

[tex]i = \sqrt{-1} \\i^2 = \sqrt{-1}*\sqrt{-1} = \sqrt{-1}^2 = -1\\i^3 = \sqrt{-1}*\sqrt{-1}*\sqrt{-1} = i^2 * i = (-1)*i = -i\\i^4 = \sqrt{-1}*\sqrt{-1}*\sqrt{-1}*\sqrt{-1} = \sqrt{-1}^2*\sqrt{-1}^2 = (-1)*(-1) = 1\\[/tex]

And all powers over 4 repeat such that [tex]i^x\ such\ that\ x\mod4 = y[/tex] is the same as [tex]i^y\\[/tex]:

i.e.:

[tex]i^6 = i^{4+2}= i^4*i^2 = 1*-1 = -1\\\\i^9 = i^{4+4+1}=i^4*i^4*i^1=(1)(1)(i) = i[/tex]

NOTE: x mod 4 simply means the remainder when x is divided by 4.

i.e.:

[tex]7\mod4 = 3\\8\mod4 = 0\\13\mod4 = 1[/tex]

Considering the definition of scale, the length of the Mississippi River on the map is 96.667 cm.

Definition of scale

The scale of a cartographic representation, or map scale, is the relationship of similarity between the real dimensions of the geographical space represented and those of its image on the map.

Scale is the relationship between a real object (for example, the surface of the Earth or a portion of it) and the representation that is made of it.

The scale is represented as a fraction as follows: measured on the map/measured in reality

Length of the Mississippi River on the map

In this case, you know that:

The scale was 5 centimeters represents 120 miles. The actual length of the Mississippi River is 2,320 miles.

Considering the definition of scale, you can calculate the length of the Mississippi River on the map as follow:

5 cm/ 120 miles= measured on the map/2320 miles

(5 cm/ 120 miles)× 2320 miles= measured on the map

96.667 cm= measured on the map

Finally, the length of the Mississippi River on the map is 96.667 cm.

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C

You’d need three of the smaller tubes to equal the larger tube

But three of the smaller tubes cost 5.37, so it is 1.26 cheaper to buy the bigger tube

Answer:

C

Step-by-step explanation:

4 ounce costs $1.79

12 ounce costs $4.11

$1.79 ÷ 4 = 0.4475 per ounce

$4.11 ÷ 12 = 0.3425 per ounce

0.3425 < 0.4475

So the 12 ounce tube is the better buy becaus it is cheaper per ounce.

hope this helps :)

Answer:

14

Step-by-step explanation:

Given the points (-2,1), (3,1), (3,-1), and (-2,-1) that are the vertices of a quadrilateral, you want to find the perimeter.

Perimeter

The perimeter of a plane figure is the sum of the lengths of its sides. When you plot these points, you see they define a rectangle with horizontal sides of length (3-(-2)) = 5, and vertical sides of length (1 -(-1)) = 2. There are two sides of each of these lengths, so the perimeter is ...

P = 2(L+W) = 2(5 +2) = 2(7)

P = 14

The perimeter of the figure is 14 units.

__

Additional comment

When trying to work out measures associated with a set of points, it is often useful to graph those points.

3.75/100.5 = 0.03731343 gallons per mile

0.03731343 x 20 = 0.74626866 = 0.75 gallons after 20 miles.