If p * q = 3p + 2q – 5, then 3 * 2 =

Answer:

u=8

Step-by-step explanation:

48+3u=9u

-3u both sides

48=6u

divide by 6 on both sides

8=u

Answer:

Step-by-step explanation:

y=2/3x+4

The perimeter of the composite figure would be = 21 (to the nearest tenth).

Perimeter is defined as the quantity that is used to evaluate the total length of the sides of an object.

From the given diagram, the composite figure is made up of 6 sides. The addition of these sides is the figures perimeter.

The sides of the composite figure are:

a = 6; b = 12; c = 9; d = 9; e = -9; f = -6.

The perimeter = a + b + c + d + e + f.

= 6 + 12 + 9 +9+ (-9) + (-6)

= 27 - 6

= 21 ( to the nearest tenth)

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Answer:

.58

Step-by-step explanation:

Step-by-step explanation:

x/y = y/z = z/x

x = y²/z = zy/x and y = z²/x

x = y²/z

putting this into the 3rd part of the original equation :

z/x = z/ y²/z = z²/y²

now using the y identity of the second part there :

y = z²/x

z²/y² = z² / z⁴/x² = x²/z² (= z/x per previous equation)

so,

x²/z² = z/x

x³/z³ = 1

x/z = 1

x = z

then

y/z = y/x = z/x (= 1)

and therefore,

y/x = z/x meaning

y = z (and therefore = x)

so,

x = y = z

Answer:

y = [tex]\frac{1}{4}[/tex] x + [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (- 2, 1 ) and (x₂, y₂ ) = (6, 3 )

m = [tex]\frac{3-1}{6-(-2)}[/tex] = [tex]\frac{2}{6+2}[/tex] = [tex]\frac{2}{8}[/tex] = [tex]\frac{1}{4}[/tex] , then

y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (6, 3 ) , then

3 = [tex]\frac{3}{2}[/tex] + c ⇒ c = 3 - [tex]\frac{3}{2}[/tex] = [tex]\frac{3}{2}[/tex]

y = [tex]\frac{1}{4}[/tex] x + [tex]\frac{3}{2}[/tex] ← equation of line

Answer:

24

Step-by-step explanation:

Start by finding the unit price. Unit price is the term for finding the price of one unit of an item, often used in word problems. We find this by dividing the cost of an item after a certain amount is sold, by that amount.

[tex]96/8 = \$12[/tex]

Now, we know the unit price is 12. Divide the end value of everything you sold by the unit price, 12.

[tex]288/12 = 24[/tex]

Therefore, you sold 24 candles.

Hope this helps!

f(x) can be used to replace y and the range at the domain of 3 is 17

From the question, the equation is given as

y = 3x² - 10

The above means that y is a function of x

This means that we can replace y with f(x) which means "a function of x"

Here, we have

Domain value = 3

This means that

x = 3

So, we have

y = 3(3)² - 10

Evaluate

y = 17

Hence, the range is 17

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13.80

Step-by-step explanation:

22 - 4% is your answer

Answer:

X = −2

Step-by-step explanation:

Combine 12x and x to get 13x. Subtract 13x from both sides. Combine 8x and −13x to get −5x. Add 4 to both sides. Add 6 and 4 to get 10. Divide both sides by −5. Divide 10 by −5 to get −2.

Answer: x= -2

Step-by-step explanation:

8x-4=12x+6+x

8x-12x-x=6+4

-4x-x=10

-5x=10

x= -2

Answer:

Step-by-step explanation:

interior angles of polygons:

180(n-2)

1. =180(11-2)

=180(9)

=1620

2. 180(17-2)

=180(15)

=2700

Answer:

10,500 g

Step-by-step explanation:

Half-life is the length of time it takes for half of the radioactive atoms of a radionuclide to decay. In this scenario, the amount of radioactive atoms is halved after 25 minutes. After 75 minutes, then, the amount of radioactive atoms is halved three times. Therefore:

1st half-life: [tex]84000\text{ g}\div{2}=42000\text{ g}[/tex]

2nd half-life: [tex]42000\text{ g}\div{2}=21000\text{ g}[/tex]

3rd half-life: [tex]21000\text{ g}\div{2}=10500\text{ g}[/tex]

Answer:

Step-by-step explanation:

The correct option is c. that is observation is set of recorded values of variables associated with a single entity.

What is observation?

An observation is a case of the data being collected.

For example, if we were collecting data on students in the class, the observations would be each individual student in the class. It could be the student's height, weight, marks scored, etc.

A variable is an attribute or characteristic of the observation we record in our data.

Also an observation in statistics is a value of something of interest measured or counted during a study or experiment: a person’s height, a bank account value at a certain point in time, or number of animals.

Therefore from the given option c is correct.

Observation is set of recorded values of variables associated with a single entity.

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Answer:

so there are 3825 worker in total

Step-by-step explanation:

675=15%

women=85%

how much workers are 5%=675/3 =225

225=5%

how many workers is 85%= 85/5=17

                                    85%=225x17=3825

The other three measures are:

This, I assume, refers to two lines that cross and create four angles.

The same applies to angles 2 and 4 since angles 1 and 3 are vertical angles.

Since vertical angles are congruent in measure, it is simple to determine their measurements.

Hence, the three measures are:

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Answer:

Domain = { -2 , 0 , 2 , 4 }

Range = { 3 }

Step-by-step explanation:

Domain is the x-values that the Function have and Range is the y-values that the Function have corresponding to these x-values

Since the x-values for the Function attached are -2 , 0 , 2 , 4

and the y-values for the Function is 3

Then the Domain = { -2 , 0 , 2 , 4 }

and the Range = { 3 }

Glad to Help

The inequality that represents the quantity of bags of soil Sabrina needs is 1.75x >  42

The bags of soil needed is 24 bags

Inequality as used in math refers to relations that are not precisely equal

Sabrina needs more than 42 ft.³ of soil to top up her raised garden bed

> 42 ft³

each bag of soil contains 1.75 ft.³

let the number of bags of soil be x, such that

1.75x >  42

x > 42 / 1.75

x >  24

Sabrina needs at least 24 bags of soil

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(98 × 100) ÷ 70

= 140%

or

[(98 - 70) × 100] ÷ 70

2800 ÷ 70

40%

basically, 40% increase

The equation of the line that passes through the point (-4, 3) and slope of 3/4 is y = 3x/4+6.

According to the question,

We have the following information:

We have the point (-4,3) and a slope of 3/4.

We know that the following formula is used to find the equation passing through any point:

(y-y') = m(x-x') where m is the slope and in this case, y' = 3 and x' = -4

y-3 = 3/4{x-(-4)}

y-3 = 3/4 (x+4)

Multiplying 3/4 into the bracket:

y-3 = 3x/4 + 3

Moving -3 from the left hand side to the right hand side:

y = 3x/4+3+3

y = 3x/4+6

Hence, the equation of the line that passes through the point (-4, 3) and slope of 3/4 is y = 3x/4+6.

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Answer:

$53.8.

Step-by-step explanation:

10% of $538 is like saying 538 times .10. After you multiply, you get $53.8 as the fee that Monica had to pay.

Arturo can select the days on which to have pizza in 70 ways using combination rule if he chooses any four of the next eight days.

What is combination?

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

In combinations, one can select the items in any order.

Number of combination of a objects chosen from n objects

                                  ⁿCₐ = [tex]\frac{n!}{a! (n-a)!}[/tex]

According to the given question:

To select 4 days out of the next 8 days, use combination rule

ⁿCₐ = [tex]\frac{n!}{a! (n-a)!}[/tex]

⁸C₄ = [tex]\frac{8!}{4! (8-4)!}[/tex]

⁸C₄ = (8x7x6x5x4x3x2x1)/(4x3x2x1)(4x3x2x1)

⁸C₄ = (8x7x6x5)/(4x3x2x1)

⁸C₄ = 70

Therefore there are 70 ways Arturo can select the 4 days out of 8 to have pizza for dinner.

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Solution

From given equation

Slope = -2

and y-intercept is (0,0)

Therefore,

if we put x= 0

then y = -2*0 = 0

if we put x = 1

then y = -2*1 = -2

for graph plotting, see the attachment.

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Solution

From given equation

Slope = -2

and y-intercept is (0,0)

Therefore,

if we put x= 0

then y = -2*0 = 0

if we put x = 1

then y = -2*1 = -2

for graph plotting, see the attachment.

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The required positive number whose product is 25 and whose sum is minimum is 5, 5

Sum of two numbers means adding two same or different number together

Let two positive numbers xy = 25

Divide both side by x

y  = [tex]\frac{25}{x}[/tex]  ----------Equation (1)

Sum of two positive numbers s = x + y  -------Equation (2)

Substitute equation (1) into equation (2)

S = x + [tex]\frac{25}{x}[/tex]

differentiate with respect to x

[tex]\frac{ds}{dx} = \frac{d}{dx} (x + \frac{25}{x} ) = 1 - \frac{25}{x^{2} }[/tex]

[tex]\frac{ds}{dx} = 1-\frac{25}{x^{2} }[/tex]  ---------- Equation (3)

[tex]\frac{ds}{dx} = 0[/tex]

[tex]1[/tex][tex]- \frac{25}{x^{2} }[/tex] = 0  ⇒ [tex]x^{2}[/tex] = 25

x = 5

Differentiate equation (3) again

[tex]\frac{d^{2}s }{dx^{2} } = 0 + \frac{50}{x^{2} }[/tex]

hence, at point x = 5,   [tex]\frac{d^{2} s}{dx^{2} } = \frac{50}{5^{2} }[/tex]  [tex]= \frac{50}{25} = 2[/tex]

Value of s minimum at point x = 5.

substitute the value of x into equation (1)

[tex]y = \frac{25}{x} = \frac{25}{5} = 5[/tex]

Therefore the required positive numbers are 5, 5.

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Answer:

31

Step-by-step explanation:

The solution of expression 20 divided by cos70° is,

⇒ 20 divided by cos70° = 58.82

We have to given that,

A number 20 divided by cos70°.

We can simplify the expression as,

20 divided by cos70°

⇒ 20 ÷ cos 70°

⇒ 20 / cos 70°

⇒ 20 / 0.34

⇒ 20 x 100 / 0.34x100

⇒ 2000/34

⇒ 58.82

Therefore, The solution of expression 20 divided by cos70° is,

⇒ 20 divided by cos70° = 58.82

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Proportionality denotes a linear relationship between two quantities or variables.

A.  Table is mentioned below.

B. Yes, it is a proportional relation.

C. y = 1/24 x

Therefore,

Part C : We know that,

1 day = 24 hours,

⇒ 1 hour = 1/24 day

As a result, the number of days in x hours (say y) = hours number of days in each hour

⇒ y = 1/24 x

Which is an equation of line.

Part A :

Hours       1              2           3           4          5      

Days       1/24       1/12        1/8         1/6       5/24

Part B :

∵ a line passes through the origin always shows a proportional relation,

Since, for (0, 0),

0 = 1/24 (0) ( True )

i.e. there is a proportional relation between number of days and number of hours.

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The linear function with f values f(0) = -3 and f(7) = 11 is f(x) = 2x - 3

linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to the straight line. In case, if the function contains more variables, then the variables should be constant, or it might be the known variables for the function to remain it in the same linear function condition.

if f(0) = -3, it means at x = 0, f(x) = -3

and if f(7) = 11, it means at x = 7, f(x) = 11

So the Linear equation that will yield these results is f(x) = 2x - 3

In conclusion, the Linear function is f(x) = 2x - 3

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Answer:

Let the age of brother be x and that of a sister be y.

(x+y) =16

(x) ×(y) =63

Using the substitution method, x=16-y

Substitute in equation 2

(16-y)(y)=63

16y-y^2=63

Y^2-16y+63=0

P=63

Sum= -16

Factor=(y-7),(y-9)

(y-7)(y-9)=0

Therefore y=7 or y=9

Therefore age of brother = 16-7 =9 0r 16-9=7

Therefore their ages are 9 years and 7 years

The total cost of his order of DVDs will be $32.23.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Samuel orders four DVDs from an internet-based music store. Every DVD costs $9.97. He has a 25% markdown code, and the deal charge is 7.75%.

The cost of DVDs after discount will be given as,

⇒ 4 x $9.97 x (1 - 0.25)

⇒ $29.91

The cost of DVDs after tax will be given as,

⇒ $29.91 x (1 + 0.0775)

⇒ $32.23

The total cost of his order of DVDs will be $32.23.

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