In function notation, f(x)is used instead of the letter ___ to represent the __________ variable.

Step-by-step explanation:

First expression ...

[tex] = {ax}^{3} y[/tex]

[tex] = a \times x \times x \times x \times y[/tex]

Second expression.....

[tex] = b {x}^{4} {y}^{3} [/tex]

[tex] = b \times x \times x \times x \times x \times y \times y \times y[/tex]

HCF = common factor...

[tex] = x \times x \times x \times y[/tex]

[tex] = {x}^{3} y[/tex]

[tex]hence \: {x}^{3} y \: is \: the \: answer....[/tex]

Answer: HCF =

x³y

Step-by-step explanation:

HCF of ax³y and bx⁴y³

ax³y = a . x . x . x . y

bx⁴y³ = b . x . x . x . x . y . y . y

Common Factors = x . x . x . y

HCF = x . x . x . y

HCF = x³y Answer

therefore, the HCF of ax³y and bx⁴y³ is x³y.

hope that helps...



note: the dot (.) represents multiplication.

Answer:

f(3) = - 10

Step-by-step explanation:

given

f(n) = f(n - 2) + f(n - 1) , then

f(3) = f(3 - 2) + f(3 - 1) = f(1) + f(2) = - 6 + (- 4) = - 6 - 4 = - 10

[tex]f(3)=f(1)+f(2)=-6+(-4)=-10[/tex]

Answer:

m∠A = 90°

Step-by-step explanation:

In isosceles triangle base angles are congruent. That means we can equate measurments of angle B and angle C and solve for x!

m∠B = m∠C

11x - 10 = 7x + 10

4x - 10 = 10

4x = 20

x = 5

Now let's insert x back in the expressions for angles.

m∠B = (11x − 10)° = (11(5) − 10)° = 45°

m∠C = (7x + 10)° = (7(5) + 10)° = 45°

Sum of all angles in the triangle is 180°. Let's make an equation.

m∠A + m∠B + m∠C = 180°

m∠A + 45°+ 45° = 180°

m∠A  = 90°

Answer:

  260 square feet

Step-by-step explanation:

The area of a rectangle is given by the formula ...

  A = LW

The area of two same-size rectangular rooms will be double the area of one of them.

__

Each room has an area of ...

  A = LW = (13 ft)(10 ft) = 130 ft²

The order for carpet must be for 2 times the area of one room:

  carpet order = 2 × 130 ft² = 260 ft²

Jerry should order 260 square feet of carpet.

Answer:

give that 13.3cm is 15% of a certain length, what is the complete length

Answer: A,B and D ARE THE CORRECT ANSWERS

Step-by-step explanation:

The correct function shown in the graph is,

⇒ log₁₀ (ax) = 1

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

It has been given that the point (3,1) is on the graph. For the point (3,1) to be on the graph, the following must hold true:

⇒ log₁₀ (ax) = 1

or , ax = 10¹ = 10

Thus, x  = 10/a

So, in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option D, that is, when a = 3. That will make x = 3.33 and thus, .

⇒ log (3 × 3.33) = 0.99 ≈ 1

Thus, out of the given options only Option D seems to be the most probable answer.

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The true statement about the quadratic function is that it has two distinct real zeros

The given parameters are:

The first highlight above means that, the function can be represented as:

y = a(x - x1)(x -x2)

Where x1 and x2 are the x-intercepts

This also means that the quadratic function has two distinct real zeros

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Answer:

$ 4.50

Step-by-step explanation:

2% of the price = 9 cents

.02 x   = 9

x = 9 / .02 = 450 cents     or  $4.50

[tex]\\ \rm\Rrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow sin52=\dfrac{AC}{BC}[/tex]

[tex]\\ \rm\Rrightarrow sin52=\dfrac{9.2}{B C}[/tex]

[tex]\\ \rm\Rrightarrow B C=\dfrac{9.2}{sin52}[/tex]

[tex]\\ \rm\Rrightarrow B C=9.3[/tex]

Answer:

11.7  (3 s.f.)

Step-by-step explanation:

Given information:

As one of the given angles is 90°, the triangle is a right triangle.

Draw the triangle using the given information (see attached) to help visualize the problem.

To calculate the length of BC, use the sine trigonometric ratio:

[tex]\sf \sin(\theta)=\dfrac{O}{H}[/tex]

where:

From inspection of the attached triangle:

Substitute the values into the formula and solve for BC:

[tex]\implies \sf \sin(52^{\circ})=\dfrac{9.2}{BC}[/tex]

[tex]\implies \sf BC=\dfrac{9.2}{\sin(52^{\circ})}[/tex]

[tex]\implies \sf BC=11.67496758...[/tex]

[tex]\implies \sf BC=11.7\:\:(3 \:s.f.)[/tex]

Therefore, the length of BC is 11.7 (3 s.f.).

The measure of ∠ABP and ∠ABC are 32° and 64° respectively.

Any line which divides an angle into two equal halves is a bisector of that angle.

Analysis:

Since the arcs at D and E are drawn with the same radius and arc using center D and E are intersected by line PB( which is the bisector of the full arc with center B) then ∠ABP = ∠PBC = 32°.

∠ABC = ∠ABP + ∠PBC

∠ABC = 32 + 32 = 64°

In conclusion, ∠ABP and ∠ABC are 32° and 64°

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Answer:ABP is 32 degrees, and ABC is 64 degrees

Step-by-step explanation: bi hope this helped if not sorry:)

Answer:

the last one 1/6

Step-by-step explanation:

1/2 x 1/3 = 1/6

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the slope of this graph; we are provided with two points:

[tex]\star~\mathrm{(6,0)}[/tex]

[tex]\star~\mathrm{(0,-5)}[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Here's the formula:

[tex]\star~\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}[/tex]

Where

y2 and y1 are y-coordinates

x2 and x1 are x-coordinates

Substitute the values:

[tex]\star~\mathrm{\cfrac{-5-0}{0-6}}}[/tex]

Simplify!

[tex]\star~\mathrm{\cfrac{-5}{-6}}}[/tex]

Simplify more!

[tex]\star~\mathrm{\cfrac{5}{6}}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Answer:

[tex]\textsf{x = 45}[/tex]

Here, the given 2 angles are complementary angles. The sum is 90 degrees as indicated by the right angle symbol.

[tex]\textsf {Solving :}[/tex]

[tex]\implies \textsf{x - 2 + 47 = 90}[/tex]

[tex]\implies \textsf{x + 45 = 90}[/tex]

[tex]\implies \textsf{x = 45}[/tex]

Answer:0.124402866242

Step-by-step explanation:here’s my attempt: dv/dt=d/dt(4pi/3r^3). 100=d/dt((4pi/3)*(8+X*t)^3) at t=0. 100/(4(pi)*8^2)=x where x is the rate of change of the radius. Not 100% sure though

Answer:

False

Step-by-step explanation:

Here's a simple little trick to tell wether a system of inequalities has any solutions or not, just by looking at it:

By following this logic, since the system given has different slopes, it only has one solution. Therefore your answer is false.

Hope this helps you.

The 48 flies of them will live longer than 21 days if there are 300 houseflies in the study.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have mean u = 18 days

SD = 3 days

X = 21 days

From the formula:

Z = (X - u)/SD

Z = (21 - 18)/3 = 1

P(x<21) = 0.84134

P(x>21) = 1 - P(x<21) = 0.15866

Number of flies = 300×0.15866 = 47.59 ≈ 48 flies

Thus, the 48 flies of them will live longer than 21 days if there are 300 houseflies in the study.

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Step-by-step explanation:

Hopefully this is helpful?

The closest to the maximum number of cups the punch bowl can hold is 30

The given parameters are:

1 cup = 15 cubic inches

Diameter of bowl, d = 12 inches

The radius is the half of the diameter.

So, we have:

r = 6

The volume of the bowl is then calculated using:

[tex]V = \frac{2}{3}\pi r^3[/tex]

This gives

[tex]V = \frac{2}{3}\pi * 6^3[/tex]

Evaluate

V = 452.16

The maximum number of cups is then calculated using:

Cups = 452.16/15

Evaluate

Cups = 30.1444

Approximate

Cups = 30

Hence, the closest to the maximum number of cups the punch bowl can hold is 30

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Answer:

The last option y= -2x-3

Step-by-step explanation:

this equation passes through the point (-2,1)

Answer:

D where the funds to start and operate your business.........

The linear function that has a different rate of change from y = -3x+4 is A, a function with a y-intercept of -4 that passes through the point (-3,-13)

An intercept is the point where a straight line or a curve meets with the x or y axes.

Analysis:

The rate of change is the same as slope. The slope of y = -3x + 4 is -3,

All other functions Except A have a slope of -3.

for linear function A,

if y = mx + c, c = -4, x = -3, y = -13

-13= -3m - 4

-3m = -9

m = 3

In conclusion, linear function A with a y-intercept of -4 passing through the point (-3,-13) has a different rate of change from y = -3x + 4

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The probability of getting two red chips is:

P = 1/21.

The probability of getting a red chip is equal to the quotient between the number of red chips and the total number of chips.

There are 4 blue chips and 3 red chips, for a total of 7 chips.

For the first draw, the probability of getting a red one is:

p = 3/7.

For the second draw, now there are 2 red chips and 6 chips in total, so now the probability is:

q = 2/6 = 1/3

Then the joint probability, given by the product between the two individual probabilities, is:

P = q*p = (3/7)*(1/3) = 1/21.

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Answer:

therees nothing here to help you with?

Step-by-step explanation:

srry abt that but add the square number

The cost of the ice needed to make 50 snow cones is $54.50.

The first step is to determine the volume of the snow cone.

Volume of the snow cone =volume of a cone + volume of the hemisphere

Volume of the cone = 1/3πr²h

1/3 x 3.14 x 10.2 x (8.3/2)² = 183.87 cm³

Volume of the hemisphere = 2/3πr³

2/3 x 3.14 x (8.3 / 2)³ = 224.43 cm³

Total volume = 224.43 cm³ + 183.87 cm³ = 408.30 cm³

Volume of 50 snow cones =  408.30 cm³ x 50 = 20,414.82

Total grams of ice needed = density x volume

0.697 x 20,414.82 = 14,229.13 grams

Convert gram to 1kg

1kg = 1000g

= 14,229.13 grams  / 1000 = 14.23kg

Cost of the ice = 14.13 x 3.83 = $54.50

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Answer:

1. 2507.034 g

2. 1243mg

   0.001243kg

   1,243,000 mcg

3. 162.5g

Step-by-step explanation:

1. First of all we need to convert 30mg and 2.5kg to gram.

⇒ 1 gram = 1000 milligrams

         x     =  35mg  

⇒ 1000mg(x) = 35mg

⇒ x = 35mg    =   35   =  0.035g

        1000mg    1000

Next we convert 2.5kg to gm.

⇒ 1 kilogram = 1000g

     2.5kg   =   x  

(We then criss cross)

⇒ x = 2.5kg × 1000g = 2500g  = 2500g

                 1kg                    1

Now that we converted them all to gram, we will add them.

⇒ 30mg + 2.5kg + 7g = 0.035g + 2500g + 7g = 2507.035 ≈ 2507g

2.  We convert 1.234g into

a. mg

⇒ 1 gram = 1000 milligram

    1.243g = x

⇒ x = 1.243g × 1000mg = 1243mg = 1243mg

                1g                      1

b. kg

⇒ 1 kilogram = 1000gram

                  x =   1.243 gram

⇒ x = 1.243g × 1kg  =   1.243kg = 0.001243kg = 1.243 × 10⁻³ kg

                1000g            1000

c. mcg

⇒  1 gram = 1000000mcg

    1.243g =  x

⇒ x = 1.243g × 1,000,000mcg  = 1,243,000mcg = 1,243,000mcg

                        1 g                                   1

3. We need 500 aspirin, the amount of grams needed and we know that one tablet contains 325mg.

So now we can derive the formula such that:

⇒ 1 tablet      = 325mg

   500 tablet =  x

But first we need to convert 325mg to grams.

⇒ 1 gram = 1000mg

      x   =  325mg

⇒ x = 325mg × 1 g = 325g = 0.325g

              1000mg     1000

So now instead of using 325mg we can use 0.325g.

⇒ 1 tablet   =  0.325g

    500 tablets =  x

⇒ x = 500 tablets × 0.325g  =  162.5g = 162.5g

                      1  tablet                   1

The estimate of the percentage expression 66 2/3% of 2,600 is 1733.33

The expression is given as:

66 2/3% of 2,600

Rewrite as:

66 2/3% * 2,600

Express the fraction as an improper fraction

200/3% * 2,600

Remove the percentage sign

200/300 * 2,600

Evaluate the product

1733.33

Hence, the estimate of the percentage expression 66 2/3% of 2,600 is 1733.33

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Answer:

The answer would be Set: "S" = the set of natural numbers greater than 11.

Hope this helps!

The value of the quotient of 0.378 ÷ 0.3 is 1.26

The quotient of 0.378 ÷ 0.3 is

The expression is given as:

0.378 ÷ 0.3

Rewrite as a fraction

0.378/0.3

Multiply the fraction by 1

Express 1 as 1000/1000

0.378/0.3 * 1000/1000

Evaluate the product

378/300

Divide 378 by 300

1.26

Hence, the quotient of 0.378 ÷ 0.3 is 1.26

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Omar ran 950 meters farther than Paula. Option A is correct.

The total number of centimeters they both ran is 745000 centimeters. Option D is correct.

The distance between two objects can be determined by finding their difference.

From the given information:

The way to solve this is by converting all the distances to meters.

The total number of centimeters they both ran is:

= (420000+325000) centimeters

= 745,000 centimeters

Therefore, we can conclude that Omar ran 950 meters farther than Paula. The total number of centimeters they both ran is 745000 centimeters.

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Answer:

Omar ran 950 meters farther than Paula. Option A is correct.

The total number of centimeters they both ran is 745000 centimeters. Option D is correct.

How do we determine the distance between two objects?

The distance between two objects can be determined by finding their difference.

From the given information:

Paula ran 3 1/4 kilometers

Omar ran 4200 meters

The way to solve this is by converting all the distances to meters.

Paula = 3250 meters

Omar = 4200 meters

Difference in their distance = (4200 - 3250) meters

Difference in their distance = 950 meters.

The total number of centimeters they both ran is:

= (420000+325000) centimeters

= 745,000 centimeters

Therefore, we can conclude that Omar ran 950 meters farther than Paula. The total number of centimeters they both ran is 745000 centimeters.

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Step-by-step explanation: