The farmer wants the ratio of horses to cows to equal 5 to 3. He keeps his 45 horses and buys more cows. Workout the number of cows he must buy

Given:

The two functions are:

[tex]f(x)=\sqrt{32x}[/tex]

[tex]g(x)=\sqrt{2x}[/tex]

To find:

The [tex](f\cdot g)(x)[/tex]. Assume [tex]x\geq 0[/tex].

Solution:

We have,

[tex]f(x)=\sqrt{32x}[/tex]

[tex]g(x)=\sqrt{2x}[/tex]

Now,

[tex](f\cdot g)(x)=f(x)\cdot g(x)[/tex]

[tex](f\cdot g)(x)=\sqrt{32x}\cdot \sqrt{2x}[/tex]

[tex](f\cdot g)(x)=\sqrt{32x\times 2x}[/tex]

[tex](f\cdot g)(x)=\sqrt{64x^2}[/tex]

[tex](f\cdot g)(x)=8x[/tex]

Therefore, the correct option is A.

Answer:

[tex]{ \tt{ = 3 \div \frac{2}{5} }} \\ = { \tt{3 \times \frac{5}{2} }} \\ = \frac{15}{2} [/tex]

Answer:

We know that the hypotenuse-leg theorem states that if the hypotenuse and one leg of a right triangle are congruent to hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. hypotenuse(AB) of △BDA equals to hypotenuse (CD) of △DBC.

Answer:

A. HL

Step-by-step explanation:

Answer:

(x + 6)² + (y - 4)² = 9

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k ) = (- 6, 4 ) and r = 3 , then

(x - (- 6) )² + (y - 4)² = 3² , that is

(x + 6)² + (y - 4)² = 9

Answer:

3,4

Step-by-step explanation:

The question is incomplete. The complete question is :

Small Manufacturing Company has a standard overhead rate of $42 per hour. The labor rate is $15 per hour. Overhead is applied based on direct labor hours. Jobs B-1 and B-2 were completed during the month of March. Small incurred 140 hours of indirect labor during the month. Job B-1 used 82 direct labor hours and $3650 worth of direct material used. Job B-2 used 130 direct labor hours and $2,900 worth of direct material. What is the total cost of job B-2? Round to closest whole dollar (no cents).

Solution :

Particulars                                                        Job B-2

Direct material used                                        $ 2,900

Add : Direct labor cost (130 hours x $15)       $ 1,950

Add : overhead cost (130 hours x $ 42)         $ 5,460  

Total Cost of Job B-2                                      $ 10,310

Therefore, the total cost of the Job B-2 is $ 10,310.

Answer: its 20 I think

Answer:

x = 50

I hope this help the side note also help me a lot as well

Answer:

QP ≈ HG

Common side between those angles are QP and HG

so, they should be congruent to prove AAS

Answered by GAUTHMATH

Answer:

+4 and -4

Step-by-step explanation:

x² + 16=0

x=-√16

x=-4 or +4

Hello,

I am going to calculate all the surface areas of the prism:

1) the bases: 2*(6*9)/2=64 (cm²)

2) perimeter of the base: 7+9+7=23 (cm)

3 lateral area: 23*5=115 (cm²)

All surface areas= 64+115=179 (cm²)

What does it means sq ? (for a foreigner) ?

All surface areas= 64+115=179 (cm²)

A three-sided polyhedron consisting of a triangle base, a translated copy, and three faces connecting equivalent sides is known as a triangular prism in geometry. If the sides of a right triangular prism are not rectangular, the prism is oblique.

Given

the bases: 2*(6*9)/2=64 (cm²)

perimeter of the base: 7+9+7=23 (cm)

3 lateral area: 23*5=115 (cm²)

All surface areas= 64+115=179 (cm²)

To know more about triangular prisms refer to:

https://brainly.com/question/3160908

#SPJ2

hello babyyy hpi how you

Answer:

20 cm²

Step-by-step explanation:

Area of the square = 2cm * 2cm = 4 cm²

Area of All triangles = (4cm * 2cm) ÷ 2cm * 4cm = (4cm * 2cm) * 2cm = 16 cm²

Total Area = 4 cm² + 16 cm² = 20 cm²

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

M= 6, -1

Step-by-step explanation:

Factoring these numbers, it will result in (m-6)(m+1). So, m= 6,-1

Answer:

23.4 km

Step-by-step explanation:

We can use a ratio to solve

13 km         x km

--------   = ---------------

5 hours         9 hours

Using cross products

13*9 = 5x

117 = 5x

Divide each side by 5

117/5 = 5x/5

23.4 =x

Answer:

It travel 23.4 km in 9 hours.

Step-by-step explanation:

Given :-

A sea turtle can swim 13 km in 5 hours at this rate speed .

To find :-

How far can it travel in 9 hours.

Solution :-

Sea turtle swim 13 km in 5 hours Then find the how far it can travel in 9 hours.

Let us assume that In 9 hours turtle swim x km.

Now, We solve by using ratio for x.

In 5 hours it swim = 13 km

And, In 9 hours it swim = x km

Calculate for x

5 hours = 13 km

9 hours = x km

Use cross multiplication method , we get

5 × x = 9 × 13

5x = 117

Divide both side by 5

5x / 5 = 117 / 5

x = 23.4

Hence, It can travel 23.4 km in 9 hours.

Answer:

8.8477344 km

Step-by-step explanation:

[tex] \because \: 1 \: ft = 0.000305 \: kilometre \\ \\ \therefore \: 29028 \: ft = 29028 \times 0.000305 \: km \\ \\ = 8.8477344 \: km[/tex]

Answer:

150 different committees can be formed

Step-by-step explanation:

We have 6 boys and 5 girls and we want to select 5 members

Out of these 5 members, two boys are selected

Since two boys are selected, we are left with three girls

So, out of 6 boys, we select 2 boys and out of 5 girls, we select 3 girls

Mathematically, we know that the number of ways in which we can select r items from a total n follows the combinatorial formula;

nCr = n!/(n-r)!r!

With this, we have;

6C2 * 5C3

= (6!/(6-2)!2!) * (5!/(5-3)!3!) = 150 different committees can be formed

Answer:

The answer is "This direct variant (-4,2) is part of it".

Step-by-step explanation:

The equation expresses its direct variation relation

[tex]y = mx ........ (1)[/tex]

Where x and y vary directly, and k vary continuously.

Now so the point (4,-2) is in the direct relation of variation, so from equation (1) we are given,[tex]-2 = 4m[/tex]

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

The equation (1) is therefore converted into

[tex]\to y=-\frac{1}{2}x \\\\\to x + 2y = 0 ......... (2)[/tex]

Then only the point (-4,2) satisfies the connection with the four possibilities (2). Therefore (-4,2) is a direct variant of this.

Answer: 2) A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.

• 3) There are two choices of burritos at a restaurant, vegetarian or beef. The random variable represents the total number out of 254 customers who ordered beef.

• 4) Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes

Step-by-step explanation:

The binomial distribution simply means the probability of success or failure in an experiment. The instances in which the variable described is binomial are given below:

• 2) A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.

• 3) There are two choices of burritos at a restaurant, vegetarian or beef. The random variable represents the total number out of 254 customers who ordered beef.

• 4) Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes.

Option 1 isn't binomial since the number of trails that are given isn't fixed. Option 5 isn't binomial as well

Therefore, the correct options are 2,3 and 4.

Answer:

The correct answer is y = | x + 6 |

Answer:4 and 8?

Step-by-step explanation:

Step 1: Distribute

5x + 10 - 3x > 7 - 4x + 12

Step 2: Combine like terms

2x + 10 > -4x + 19

Step 3: Move all variable terms to one side, and all constants to the other

6x + 10 > 19

6x > 9

Step 4: Divide

x > 9 / 6

x > 1.5

Hope this helps!

Given:

The minimum and maximum distance that the dog may be from the house can be found by using the equation:

[tex]|x-500|=8[/tex]

To find:

The minimum and maximum distance that the dog may be from the house.

Solution:

We have,

[tex]|x-500|=8[/tex]

It can be written as:

[tex]x-500=\pm 8[/tex]

Adding 500 on both sides, we get

[tex]x=500\pm 8[/tex]

Now,

[tex]x=500+8[/tex] and [tex]x=500-8[/tex]

[tex]x=508[/tex] and [tex]x=492[/tex]

The minimum distance is 492 meters and the maximum distance is 508 meters.

Therefore, the correct option is C.

Given:

A figure of a circle.

To find:

The value of x.

Solution:

Central angle theorem: According to this theorem, the central angle on an arc is twice of the subtended angle on that arc.

Using the central angle theorem, we get

[tex]x=2\times 35^\circ[/tex]

[tex]x=70^\circ[/tex]

Therefore, the value of x is 70 degrees.

Answer:

f(f(x)) = 27[tex]x^{4}[/tex] + 18x² + 4

Step-by-step explanation:

To find f(f(x)) substitute x = f(x) into f(x) , that is

f(3x² + 1)

= 3(3x² + 1)² + 1 ← expand parenthesis using FOIL

= 3(9[tex]x^{4}[/tex] + 6x² + 1) + 1 ← distribute parenthesis by 3

= 27[tex]x^{4}[/tex] + 18x² + 3 + 1 ← collect like terms

= 27[tex]x^{4}[/tex] + 18x² + 4

Hello,

[tex](fof)(x)=f(f(x))\\\\=3(3x^2+1)^2+1\\\\=3(9x^4+6x^2+1)+1\\\\\boxed{=27x^4+18x^2+4}[/tex]

Answer: 6

Step-by-step explanation: 7x+2y=48

7x+2(3)=48

7x+6=48

7x=48+6

7x=42

x=42/7

x=6

Answer:

[tex]h(x)= 9x - 18[/tex]

Step-by-step explanation:

Given

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

Required

The inverse

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

Replace f(x) with y

[tex]y = \frac{1}{9}x + 2[/tex]

Swap x and y

[tex]x = \frac{1}{9}y + 2[/tex]

Subtract 2

[tex]x - 2= \frac{1}{9}y[/tex]

Multiply 9

[tex]9x - 18 = y[/tex]

Rewrite as:

[tex]y = 9x - 18[/tex]

So:

[tex]h(x)= 9x - 18[/tex]

Answer:

The length and width that maximize the area are:

W = 2*√8

L = 2*√8

Step-by-step explanation:

We want to find the largest area of a rectangle inscribed in a semicircle of radius 4.

Remember that the area of a rectangle of length L  and width W, is:

A = L*W

You can see the image below to see how i will define the length and the width:

L = 2*x'

W = 2*y'

Where we have the relation:

4 = √(x'^2 + y'^2)

16 = x'^2 + y'^2

Now we can isolate one of the variables, for example, x'

16 - y'^2 = x^'2

√(16 - y'^2) = x'

Then we can write:

W = 2*y'

L = 2*√(16 - y'^2)

Then the area equation is:

A = 2*y'*2*√(16 - y'^2)

A = 4*y'*√(16 - y'^2)

If A > 1, like in our case, maximizing A is the same as maximizing A^2

Then if que square both sides:

A^2 = (4*y'*√(16 - y'^2))^2

      = 16*(y'^2)*(16 - y'^2)

      = 16*(y'^2)*16 - 16*y'^4

      = 256*(y'^2) - 16*y'^4

Now we can define:

u = y'^2

then the equation that we want to maximize is:

f(u) = 256*u - 16*u^2

to find the maximum, we need to evaluate in the zero of the derivative:

f'(u) = 256 - 2*16*u = 0

      u = -256/(-2*16) = 8

Then we have:

u = y'^2 = 8

solving for y'

y' = √8

And we know that:

x' = √(16 - y'^2) = √(16 - (√8)^2) = √8

And the dimensions was:

W = 2*y' = 2*√8

L = 2*y' = 2*√8

These are the dimensions that maximize the area.