Find the unit rate. 7/8 square foot in 1/4 hour.Enter the correct answer in the box.

Answer:

x² - 6x + 2, and the remainder is -54

Step-by-step explanation:

I have attached an image of me dividing it.

Answer:

24u^2

Step-by-step explanation:

Divide the figure into two quad-l's.

5x4

2x2

------

20

4

-----

24

-----

The answer is 24 units squared.

Hope this helped!

Answer:

q = 4p - 32

Step-by-step explanation:

P = 1/4q + 8

Making q the subject

P - 8 = 1/4q

Divide both sides by 1/4

q = (p - 8) ÷ 1/4

= (P - 8) × 4/1

= 4p - 32

q = 4p - 32

Answer:

$42

Step-by-step explanation:

D

Answer:

BC = 4

Step-by-step explanation:

The the ratio for the corresponding sides of the two triangles would be equal. Therefore:

6/x = 3/2

Cross multiply

x*3 = 2*6

3x = 12

3x/3 = 12/3

x = 4

✅BC = x = 4

The remaining amount of salt that Tom needed to pour was 67.59 grams.

To subtract in mathematics is to take something away from a group or a number of objects.

In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.

The group's total number of items decreases or becomes lower when we subtract from it.

As per the given,

The total amount that Tom needs to pour = 84.99 grams

Amount poured = 17.4 grams

Remaining = 84.99 grams - 17.4 grams = 7.59 grams

Hence "The remaining amount of salt that Tom needed to pour was 67.59 grams".

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Answer:

x+2 domain: (-infiniy, +infinity) or -infinity<x<infinity

1/x +2 domain: (-infinity, 0) and (0, infinity) or 0<x<0

The total pay that Nelly will get for last week is £220.

From the information given, the following can be deduced:

£8 per hour for the first 15 hours

£10 let hour for any extra hour.

The above are applicable for Monday to Friday.

£16 is the rate for Saturdays.

The number of hours that Nelly worked from Monday to Friday will be:

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

= 17 hours

On Saturday, he worked 5 hours.

The total earnings will be:

= (£8 × 15) + (£10 × 2) + (£16 × 5)

= £120 + £20 + £80

= £220

The total amount is £220.

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The number of gallons must be a whole number will be 114 gallons.

Let d be the diameter of the circle. Then the area of the circle will be

A = (π/4) d² square units

At the recreation area, there is a pool molded like a circle with a measurement of 24 yds. A ring-molded way circumvents the pool. Its width is 6 yds.

The area of the path will be given as,

A = (π/4) (24 + 6 + 6)² - (π/4) (24)²

A = (π/4) [36² - 24²]

A = (π/4) [720]

A = 565.5 square yards

We will give another layer of covering to the way. On the off chance that one gallon of covering can cover 5 yd². Then the number of gallons of coating is given as,

⇒ (565.5) / 5

⇒ 113.097

⇒ 114 gallons

The number of gallons must be a whole number will be 114 gallons.

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Answer

1/9

Step-by-step explanation:

Hope this helps

Answer:

0.11111111111

Step-by-step explanation:

1/9 = 0.11111111111

Answer:

10^8 choices

Step-by-step explanation:

You have 10 numbers to choose from for each digit of the code.

There are 8 digits of the code.

You have 10*10*10*10*10*10*10*10 = 10^8 choices in total.

Number of possible codes are  \(10^{8}\)

In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements

Given,

Number of digits in passcode = 8

The numbers 0-9 may be used for any digit. Therefore total of 10 numbers

Here repetition is allowed.

Therefore, each of the 8 vacant place can be filled in the succession of 10 different ways

Number of possible codes are = 10×10×10×10×10×10×10×10 = \(10^{8}\)

Hence, the number of possible codes are  \(10^{8}\)

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Answer:

x = 1 or x =  3  / 2  or x = −5 or x =  1  / 3

Refer the attachment for steps

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The average rate of change of the function over the interval is 4

From the question, we have the following parameters that can be used in our computation:

y = 4x + 1

The interval is given as

[-1, 1)

The function is a linear function

This means that it has a constant average rate of change

From y = 4x + 1, we have

Rate = 4

Hence, the rate is 4

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Given equation is,

Thus, x= -2.

Answer: Should be 150mm

Step-by-step explanation:

Find the surface area of each figure. Round answers to the nearest tenth, if necessary

2 mm-

2/5 mm

10 mm

3 mm

O

75 mm2

150 mm2

92 mm2

86 mm2

The required differentiation of the function f(x) = sin(6 In(x)) is f'(x) = 6 cos(6 ln(x))/x.

Given the function f(x) = sin(6 In(x)).

To differentiate the function f(x), we need to use the Chain Rule in terms of the functions h(x) and g(x), which states that

if g is differentiable at x and h is differentiable at g(x), then the composite function F= h og defined by F(x) = (g(x)) is

differentiable at x and F' is given by the following.

'(x) = h'(g(x)).g'(x)We can let g(x) = 6 In(x) and h(x) = sin(x).

Now, we can rewrite f(x) as f(x) = h(g(x)) = sin(6 In(x)).

To differentiate this function, we will differentiate h(g(x)) using the Chain Rule.

f'(x) = h'(g(x)) × g'(x)

Substituting the values of h(x) and g(x), we havef'(x) = cos(6 ln(x)) × (6/x) = 6 cos(6 ln(x))/x

Thus, the required differentiation of the function f(x) = sin(6 In(x)) is f'(x) = 6 cos(6 ln(x))/x.

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The correct answer is C. It is the graph of f(x) translated 11 units to the left.

The correct answer is:

C. It is the graph of f(x) translated 11 units to the left.

When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.

In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.

The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.

Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.

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Answer:

1/2

Step-by-step explanation:

Answer:  0 is the answer

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Rewrite the fractions as improper fractions:

2 1/4 = 9/4

1 4/5 = 9/5

Rewrite the fractions to have a common denominator:

9/4 = 45/20

9/5 = 36/20

The sum is adding the two together:

45/20 + 36/20 = 81/20

Rewrite as a mixed number:

81/20 = 4 1/20

Product is multiplication:

For multiplying you can use different denominators so you can use the first improper fractions:

9/4 x 9/5 = (9x9)/(4x5) 81/20

Rewrite as a mixed number: 4 1/20

Now subtract to find the difference: 4 1/20 - 4 1/20 = 0

The difference = 0

There are 165 pink flowers in the garden.

Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b, then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers. The ratio and proportion are the two important concepts, and it is the foundation to understand the various concepts in mathematics as well as in science.

Let the number of blue flowers be x, so that number of pink flowers be x + 75

The total flowers will be = 2x + 75

Total share , 6 + 11 = 17

blue's share = 6/17 x (2x + 75)

so that,

6/17 x (2x+75) = x

by cross multiplying

6(2x+75) = 17x

Multiply out

12x + 450 = 17x

collect like terms

17x - 12x = 450

5x = 450

x = 450/5

x = 90

Total pink flowers , x + 75 = 90 + 75

which is 165

In conclusion, the total number of pink flowers would be 165

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Answer:

378 individuals

601 individuals

Explanation:

We know that the population after t years is described by:

So, to know the population after 6 years, we need to replace t by 6 and calculate P(t). Then:

In the same way, we can calculate the population after 10 years replacing t by 10. So:

Therefore, the answers are:

378 individuals

601 individuals

The length of the rectangle is 48 yards.

Let's denote the width of the rectangle as "w" yards.

According to the information given, the length of the rectangle is 32 yards less than 10 times its width. So, the length can be represented as: 10w - 32 yards.

The formula for the area of a rectangle is length times width: Area = length × width.

Given that the area of the rectangle is 384 square yards, we can set up an equation:

Area = length × width

384 = (10w - 32) × w

Now, let's solve for the width (w):

384 = 10w² - 32w

0 = 10w² - 32w - 384

Dividing the equation by 2 to simplify:

0 = 5w² - 16w - 192

Now we have a quadratic equation. We can either factor it or use the quadratic formula to solve for "w." Let's use the quadratic formula:

w = (-b ± √(b² - 4ac)) / 2a

For our equation, a = 5, b = -16, and c = -192. Plugging these values into the formula:

w = (16 ± √((-16)² - 4 × 5 × (-192))) / (2 × 5)

w = (16 ± √(256 + 3840)) / 10

w = (16 ± √4096) / 10

w = (16 ± 64) / 10

This gives us two possible solutions for the width:

w = (16 + 64) / 10 = 8 yards

w = (16 - 64) / 10 = -4.8 yards

Since width can't be negative, we'll ignore the second solution.

So, the width of the rectangle is 8 yards. Now, let's find the length using the earlier expression:

Length = 10w - 32

Length = 10 × 8 - 32

Length = 80 - 32

Length = 48 yards

Therefore, the length of the rectangle is 48 yards.

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The required intermediate step is (x-5)² = 25 for the equation -5x² - 50x = -250.

Completing the square is a method used to rewrite the equation in the form (x+a)²=b. The intermediate step involves adding and subtracting the square of half of the coefficient of x in the equation.

To complete the square for the equation -5x² - 50x = -250:

First, we'll add and subtract (1/2 * 50)² = 625/4 on both sides of the equation:

-5x² - 50x + 625/4 = -250 + 625/4

Next, we'll factor out the x term on the left side of the equation:

-5x² - 50x + 625/4 = -250 + 625/4

-5(x² - 10x) + 625/4 = -250 + 625/4

-5(x² - 10x + 25) + 625/4 = -250 + 625/4

-5(x - 5)² + 625/4 = -250 + 625/4

The intermediate step is in the form of (x-5)² = (625/20 + 250)/5

So, the intermediate step is (x-5)² = 25

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Answer:

y = 4√x

Step-by-step explanation:

Finding the constant of proportionality, k

Equation

Answer:

Y will equal

4√x as the answer

Answer: one senior ticket is $8 and one student ticket is $14

Hope this helps a little

Answer:

the answer is yes i took the test

Step-by-step explanation:

1. The Fill ups are as follow:

AB² +  BC² = AC. AD + AC. CD

2. Segment addition postulate

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

BC/ AC = CD/ BC and AB/ AC = AD/ AB

Now, BC² = AC. CD  and AB² = AC. AD

Using, Addition Property of Equality

AB² +  BC² = AC. AD + AC. CD

and, AB² +  BC² = AC (AD + CD)  [factor]

AD + CD = AD (segment addition postulate)

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PLATO

i got it correct :)

Answer:

The function that passes through (0, 0) is \(f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} - \frac{1}{6}\).

Step-by-step explanation:

Firstly, we integrate the function by algebraic substitution:

\(\int {x^{2}\cdot e^{2\cdot x^{3}}} \, dx\) (1)

If \(u = 2\cdot x^{3}\) and \(du = 6\cdot x^{2} dx\), then:

\(\int {e^{2\cdot x^{3}}\cdot x^{2}} \, dx\)

\(\frac{1}{6}\int {e^{u}} \, du\)

\(f(u) = \frac{1}{6}\cdot e^{u} + C\)

\(f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} + C\)

Where \(C\) is the integration constant.

If \(x = 0\) and \(f(0) = 0\), then the integration constant is:

\(\frac{1}{6}\cdot e^{2\cdot 0^{3}} + C= 0\)

\(C = -\frac{1}{6}\)

Hence, the function that passes through (0, 0) is \(f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} - \frac{1}{6}\).