F(x)= 5x^2+6, g(x)= 7x find (f o g)(x), find (g o f)(x), find f(g(-4)), fine g(f(5))

Ages of Mark, Brett and Carl are 80 years, 60 years and 70 years respectively.

Solution:

Given that

Brett is 18 years younger than Mark.

Carl is 10 years younger than Mark.

The sum of the ages of Brett, Mark, and Carl is 212

Need to determine age of Brett, Mark, and Carl.

Let assume age of mark in years be represented by variable x

As it is given that Brett is 18 years younger than Mark , so if we subtract 18 from the age of Mark we will get age of Brett ,

=> Age of Brett = x – 18

Also given that Carl is 10 years younger than Mark , so if we subtract 10 from the age of Mark we will get age of Carl ,

=> Age of Carl = x – 10

Given sum of ages of Brett, Mark, and Carl is 212

=> Age of Mark + Age of Brett + Age of Carl = 212

=> x + ( x – 18 ) + ( x – 10) = 212

=> 3x – 28 = 212

=> 3x = 212 + 28

Age of Mark = x = 80 years

Age of Brett = x – 18 = 80 – 18 = 62 years

Age of Carl = x – 10 = 80 – 10 = 70 years

Hence Ages of Mark , Brett and Carl are 80 years, 60 years and 70 years respectively.

I think the answer is 90 degrees because both triangles are 90, but you're only finding KN and KL which is on ONE triangle not both. SO there's a 90 degree angle on the top triangle. So I'd go with 90, but I could be wrong.

Answer:

24

Step-by-step explanation:

If we want to cover the base of the prism having dimensions 2 cm × 1 cm with [tex]\frac{1}{2}[/tex] cm length of cube, then there will be (4 × 2) = 8 cubes that can occupy the base.

Width is 1 cm, so there can fit 2 cubes of length [tex]\frac{1}{2}[/tex] cm and length is 2 cm, where 4 cubes of length [tex]\frac{1}{2}[/tex] cm can fit. So, in total (4 × 2) = 8 cubes of [tex]\frac{1}{2}[/tex] cm length.

Now, height of the prism is [tex]\frac{3}{2}[/tex] cm where 3 cubes of length [tex]\frac{1}{2}[/tex] cm can fit.

Therefore, in total there can be (8 × 3) = 24 cubes of [tex]\frac{1}{2}[/tex] cm length. (Answer)

Answer:

24 cubes

Step-by-step explanation:

Please see the pictures below:  

(I hope this helped! :) )

Answer:

22

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

Answer:

3.0 grams of the element are left after 18 minutes

Step-by-step explanation:

Recall that an exponential decay that can be studied with the following formula for the amount of material (A) as a function of time (t):

[tex]A(t)=A_0(1-r)^t[/tex]

where:

[tex]A_0[/tex] is the starting amount of the substance (in our case 820 grams)

r is the rate of decay (which in our case given as 26.8% can be written in decimal form as 0.268

and t is the time in minutes (in our case t = 18 minutes)

Then we have:

[tex]A(t)=A_0(1-r)^t\\A(18)=820*(1-0.268)^18\\A(18)=820*(0.732)^18\\\\A(18)=2.985\,grams[/tex]

which can be rounded to 3.0 grams

Answer: 3.0

Step-by-step explanation:

a=820

r= rate= 26.8%=0.268

b=1-r=1-0.268=0.732

y=820(0.732)^18

y=2.985474

y=3

The question is missing the figure. So, the figure is attached below.

Answer:

237.375 ft³

Step-by-step explanation:

Given:

Side length of bigger cube is, [tex]S_1=8\ ft[/tex]

Side length of smaller cube is, [tex]S_2=6.5\ ft[/tex]

Now, volume of the bigger storage unit is given as:

[tex]V_1=S_1^3\\V_1=S_1\times S_1\times S_1\\V_1=8\times 8\times 8=512\ ft^3[/tex]

Volume of the smaller storage unit is given as:

[tex]V_2=S_2^3\\V_2=S_2\times S_2\times S_2\\V_2=6.5\times 6.5\times 6.5=274.625\ ft^3[/tex]

Now, difference in the volume of the two storage units is given as:

[tex]V_1-V_2=512-274.625=237.375\ ft^3[/tex]

Therefore, the difference in their volumes is 237.375 ft³.

To find the difference in volume between two cube-shaped storage units, determine the length of one side for each cube, calculate their volumes with the formula 'Volume = side length cubed', and subtract one volume from the other.

To calculate the difference in volume between the two cube-shaped storage units, follow these steps:

For example, let's assume the side length of cube 1 is 2 meters and the side length of cube 2 is 3 meters. The volume of cube 1 will be 2^3 or 8 m³ and the volume of cube 2 will be 3^3 or 27 m³. The difference in volume between the two cubes would be 27 m³ - 8 m³ = 19 m³.

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Answer:

$2

Step-by-step explanation:

x = daylily

y = geranium

1x + 5y = 22

13x + 1y = 30

Multiply second equation by 5 and subtract the two equations.

1x + 5y = 22

- (65x + 5y = 150)

-64x = -128

x = 2

So one daylily costs 2 dollars

Answer:

The rate of interest paid on the principal amount is 8%.

Step-by-step explanation:

Here, Principal Amount = $2,000

Time = 3 months = (3/ 12 ) Years = 0.25 years

Rate = R

Interest Amount  = $40

Now, as we know :

Simple Interest  = [tex]\frac{P \times R \times T}{100}[/tex]

⇒[tex]40  = \frac{2,000 \times R \times 0.25}{100}\\\implies R = \frac{40 \times 100}{2000 \times 0.25}   =8[/tex]

or, R = 8%

Hence, the rate of interest paid is 8%.

Answer:

Any of the set of metallic elements occupying a central block (Groups IVB–VIII, IB, and IIB, or 4–12) in the periodic table, e.g., iron, manganese, chromium, and copper. Chemically they show variable valence and a strong tendency to form coordination compounds, and many of their compounds are colored.

Step-by-step explanation:

The value of square root of 25/64 will be;

⇒ 5/8

A square root of a number is a value that multiplied by itself gives the same number.

Given that;

The number is,

⇒ square root of 25/64

⇒ √(25 / 64)

Now,

Since, The number is,

⇒ √25/64

⇒ √ (5×5 / 8×8)

⇒ 5 / 8

Thus, The value of √ 25/64 = 5/8

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Answer:

9

Step-by-step explanation:

Length: a

Width: b

ab = 54

a = b + 3

=> (b + 3)b = 54

=> b^2 + 3b = 54

=> b^2 + 3b - 54= 0

=> (b - 6)(b + 9)

=> b = 6 AND b = -9

Rectangular's sides > 0 => b = 6

Hope it's helpful :)

Answer:

1. See the attached figure to this answer.

2. Lines A and B are parallel to each other.

3. Line Z is the transversal.

4. The same side interior angles are ∠ 4, ∠ 6 & ∠ 3, ∠ 5.

5. The alternate interior angles are ∠ 3, ∠ 6 & ∠ 4, ∠5

6. Corresponding angles are ∠ 1, ∠ 6 & ∠ 2, ∠ 5 & ∠ 3, ∠ 7 & ∠ 4, ∠ 8.

7. Alternate interior angles are ∠ 4, ∠ 5 & ∠ 3, ∠ 6 (Answer)

Step-by-step explanation:

1. See the attached figure to this answer.

2. Lines A and B are parallel to each other.

3. Line Z is the transversal.

4. The same side interior angles are ∠ 4, ∠ 6 & ∠ 3, ∠ 5.

5. The alternate interior angles are ∠ 3, ∠ 6 & ∠ 4, ∠5

6. Corresponding angles are ∠ 1, ∠ 6 & ∠ 2, ∠ 5 & ∠ 3, ∠ 7 & ∠ 4, ∠ 8.

7. Alternate interior angles are ∠ 4, ∠ 5 & ∠ 3, ∠ 6 (Answer)

Answer:

The answers are below:

Step-by-step explanation:

Answer 1: Attachment.

Answer 2: Line A is parallel to line B.

Answer 3: Line Z is a Traversal.

Answer 4:

[tex]\angle 3 \ and \ \angle 5\ and\\ \angle 4 \ and \ \angle 6\\[/tex] are the same side interior angles.

Answer 5:

[tex]\angle 3 \ and \ \angle 6\ and\\ \angle 4 \ and \ \angle 5\\[/tex] are the alternate interior angles.

Answer 6:

[tex]\angle 3 \ and \ \angle 7\ and\\ \angle 4 \ and \ \angle 8\\[/tex][tex]\angle 6 \ and \ \angle 1\ and\\ \angle 5 \ and \ \angle 2\\[/tex] are corresponding pair angles.

Answer 7:

[tex]\angle 8 \ and \ \angle 2\ and\\ \angle 7 \ and \ \angle 1\\[/tex]are the alternate exterior pair angles.

Answer:

55.19 degrees

Step-by-step explanation:

See the given diagram of the triangle attached to this question.

This is a right triangle and one of its angles other than 90° is x degrees.

Now, if we assume c is the hypotenuse and a is the perpendicular, then we can write that  

[tex]\sin x = \frac{\textrm{Perpendicular}}{\textrm {Hypotenuse}} = \frac{a}{c}[/tex]

Now, it is given that a = 7.8 cm and c = 9.5 cm.

Therefore, [tex]\sin x = \frac{7.8}{9.5} = 0.821[/tex]

⇒ [tex]x = \sin^{-1} (0.821) = 55.19[/tex] degrees. (Answer)

As per the graphical diagram, the largest temperature for each day was recorded in four different cities shows n in lines 1 and m

Hence the option B is correct.

Learn more about the weeks the highest temperature recorded in four different cities lines l,m,n p.

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Answer: 20

Step-by-step explanation:

x = 7

y = 3

2x + 2y = 2(x + y)

2(7+3) = 2 • 10 = 20

Answer:

20

Step-by-step explanation:

2(7) + 2(3)

14 + 6

20

Answer:

x=1

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises

so

In this problem

m∠C=(1/2)arc AB

we have

m∠C=(3x+5)°

arc AB=(16x)°

substitute the values

[tex](3x+5)\°=(1/2)(16x)\°[/tex]

solve for x

[tex]3x+5=8x\\8x-3x=5\\5x=5\\x=1[/tex]

Answer:

1

Step-by-step explanation:

Answer:

7,326.64

Step-by-step explanation:

20 is 1/10 times as great as 200.

A number that satisfies this equation is 26

A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32 etc.

Given here the number 6,257.11 , here the digit 2 is in the 100th place hence it is equivalent to 200 and 1/10 th of 200 is 20 . Thus any number with its tenth place with digit 2 is acceptable and 26 is one such number.

Hence, the number is  26

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Answer:

x = 18

Step-by-step explanation:

The length of the midsection is the sum of the two bases divided by 2. Remember that the bases of a trapezoid are the two parallel sides. So that means:

((5x - 11) + (2x + 7)) /2 = 3x + 7

Simplify ((5x - 11) + (2x + 7)) /2:

(5x - 11) + (2x + 7) /2 = (5x + 2x - 11 + 7) /2 = (7x - 4) /2

Therefore:

(7x - 4) /2 = 3x + 7

Now solve this simultaneous equation:

7x - 4 = 6x + 14

7x = 6x + 18

x = 18

Answer:

5/18??? might be wrong

Step-by-step explanation:

The probability that Dale will choose 5 sodas and 3 water is 0.391 and this can be determined by using the concept of probability.

Given :

The following steps can be used in order to determine the probability that he will choose 5 sodas and 3 water:

Step 1 - The concept of probability is used in order to determine the probability that he will choose 5 sodas and 3 water.

Step 2 - First, determine the total number of bottles.

Total Bottles = 9 + 6

                      = 15

Step 3 - So, the probability that he will choose 5 sodas and 3 water is:

[tex]\rm P = \dfrac{\;^9C_5 \times ^6C_3}{\;^{15}C_8}[/tex]

Step 4 - Simplify the above expression.

[tex]\rm P = \dfrac{126 \times 20}{6435}[/tex]

P = 0.391

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Using the given points, solve for a, h, k in  g(x) = [tex]a(x - h)^2[/tex] + k . The function rule is  g(x) = [tex]a(x - h)^2[/tex] + k .

To find the function rule for g(x), which is a translation of the quadratic function[tex]\( f(x) = x^2 \)[/tex], we need to determine the horizontal and vertical shifts based on the given points on the graph. The general form for a translated quadratic function is [tex]\( g(x) = a(x - h)^2 + k \)[/tex], where (h, k) represents the vertex of the parabola.

Let's use the given points (9,10), (5,10), and (7,6) to find the translation values.

1. Vertex Form of Quadratic Function:

The vertex form of a quadratic function is [tex]\( f(x) = a(x - h)^2 + k \)[/tex], where (h, k) is the vertex. Let's find the vertex using the given points.

For (9,10):

[tex]\[ 10 = a(9 - h)^2 + k \][/tex]

For (5,10):

[tex]\[ 10 = a(5 - h)^2 + k \][/tex]

For (7,6):

[tex]\[ 6 = a(7 - h)^2 + k \][/tex]

2. Solve the System of Equations:

Solve the system of equations to find the values of  a ,  h , and  k .

3. Substitute into Vertex Form:

Once you find the values of  a ,  h , and  k , substitute them into the vertex form g(x) = [tex]a(x - h)^2[/tex] + k.

By following these steps, you'll obtain the function rule for g(x), which is a translation of  [tex]f(x) = x^2[/tex]  based on the given points on the graph.

Answer:

The next answer is 3 hours

Step-by-step explanation:

I just did it on edge 2021 :)

Answer:

the first answer is c

Step-by-step explanation:

X+Y=60kg

X=60-Y

X*0.2+Y*0.7=60*0.5

(60-Y)*0.2+Y*0.7=30

12-0.2*Y+0.7*Y=30

0.5*Y=18

Y=36 kg

X=60-36

X=24 kg

The metal worker should use 24 kilograms of the metal alloy that is 20% copper and 36 kilograms of the metal alloy that is 70% copper.

Answer:

36kg 24kg

Step-by-step explanation:

Distance between the points (-3, -4)  is  5

Step-by-step explanation:

Given

points =(-3,-4) and (0,0)

To Find:

The Distance between the two given points =?

Solution:

[tex]Distance =\sqrt{(x2-x1)^2+(y2-y1)^2 }[/tex]

where

[tex](x_1, y_1)[/tex] = coordinates of the first point

[tex](x_2, y_2)[/tex] = coordinates of the second point

So here, we have  

[tex]x_1[/tex] = -3

[tex]y_1[/tex] = -4

[tex]x_2[/tex]  = 0

[tex]y_2[/tex] = 0

So, after putting the values of [tex]x_1[/tex] , [tex]y_1[/tex] , [tex]x_2[/tex] [tex]y_2[/tex]   in the above equation,  we have  

[tex]Distance=\sqrt{(0+3)^2+(0+4)^2 }[/tex]

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

[tex]Distance=\sqrt{(9)+(16) }[/tex]

[tex]Distance=\sqrt{(25)}[/tex]

Distance = 5

Answer:6

Step-by-step explanation:

In a circle, a radius perpendicular to a chord bisects the chord. So BC = CA BC = 6 (given) x (or AC) = 6 Answer = 6. Tell me if I was right. Thanks.

Answer:

it's 6

Step-by-step explanation:

Answer:

x = -9

Step-by-step explanation:

the equation is 2^4x = 8^x - 3.

therefore 2^4x = 2^3(x-3)

since both have powers of 2

therefore

4x = 3(x-3)

4x = 3x - 9

4x -3x = -9

x = -9

Answer:

D) 2^4x=2^3x-9

Step-by-step explanation:

took quiz

Answer:

x=28

Step-by-step explanation:

-7(3+6x)=9(-5x+7)

-21-42x=-45x+63

-21-42x-(-45x)=63

-21-42x+45x=63

-21+3x=63

3x=63-(-21)

3x=63+21

3x=84

x=84/3

x=28

Answer:

x=28

Step-by-step explanation:

-7(3+6x) = 9(-5x+7)

-21-42x=-45x+63

-42x=-45x+84

3x=84

x=28

Answer:

bojdsvj

Step-by-step explanation:dvsDV

I sorry lol i need points :/

Final answer:

To make the most 'appley' juice, use a mixture with a high percentage of pure apple juice and minimal amounts of other ingredients.

Explanation:

To make the most "appley" juice, you would want to use a mixture that has a high concentration of apple juice. In this case, the best choice would be a mixture with a high percentage of pure apple juice and minimal amounts of other ingredients. This would ensure that the flavor of the juice is predominantly apple.

For example, a mixture with 90% apple juice and 10% other fruit juices would have a strong apple flavor. On the other hand, a mixture with 50% apple juice and 50% other fruit juices would have a less pronounced apple taste.

By experimenting with different ratios of apple juice to other ingredients, you can find the mixture that results in the most "appley" juice.