How many cubes are needed to build the base of this structure?

So, the product of (9x - 2)(3x - 8) in standard form is: [tex]27x^2 - 78x + 16[/tex]

To multiply the expressions (9x - 2) and (3x - 8)

Step 1: Use the distributive property

(9x - 2)(3x - 8) = 9x * (3x) + 9x * (-8)

(9x - 2)(3x - 8) = -2 * (3x) - 2 * (-8)

So , perform the multiplications:

Multiply the terms:

[tex]9x * 3x = 27x^2[/tex]

9x * (-8) = -72x

-2 * 3x = -6x

-2 * (-8) = 16

Combine like terms:

[tex]27x^2 - 72x - 6x + 16[/tex]

Simplify further by combining like terms:

27x^2 - 78x + 16

So, the product of (9x - 2)(3x - 8) in standard form is: [tex]27x^2 - 78x + 16[/tex]

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10 -:- 5. This is the answer. Hope this helps:)

(18)

2.5% of 129,500 is

$129500 * 0.025 = $3237.50 is the commission on the sale

(19)

sales $3012

commission 3.5% of sales: 0.035 * 3012 = $105.42

Raquelle's total earnings: $290 + 105.42 = $395.42

Answer:

The answer is A) When you want to change cars frequently.

Step-by-step explanation:

Answer with explanation:

Car lease means you don't want to buy the car , you want to use it for various Purposes or you love riding or driving different cars.

⇒Changing cars completely ,means you are interested in distinct brand of cars that is in leasing.

⇒When you want to keep a car for several years , it means you love that thing and either you don't have enough money to buy or you are in two minds ,so either you lease it or take a loan for that thing.

⇒When you like the idea of owning a car, it means you take loan for it,not to lease it.

¬Option A  is most appropriate.

   When you want to change cars frequently

Answer:

81

Step-by-step explanation:

x^2 − 18x + 9^2 = 17 + 9^2

=> x^2 − 18x + 81 = 17 + 81

1. 4x = 7(x - 3)   GIVEN

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

2. 4x = 7x - 21     DISTRIBUTIVE PROPERTY

4x - 7x = 7x - 7x - 21

3. -3x = -21    SUBTRACTION PROPERTY OF EQUALITY

-3x : (-3) = -21 : (-3)

4. x = 7      DIVISION PROPERTY OF EQUALITY

1. Given

2. Distributive Property

3.Subtraction Property of Equality

4. Division Property of Equality

$6 dollars on candy because 35+25+10=70, 76-70=$6

Answer:

The man got a 8% raise.

Step-by-step explanation:

Percentage change        = [Increase or decrease in value / Original Value]*100

Increase in hourly wage = [tex]13.5-12.5[/tex]

                                         =[tex]1[/tex]

Percentage raise             = [Increase in hourly wage / Initial hourly wage]*100

                                         =[tex]\frac{1}{12.5} *100[/tex]

                                         = [tex]8[/tex]%

The man got a 8% raise.

The man's hourly wage increased from $12.50 to $13.50 which, following the formula for calculating percentage change, indicates that he received an 8 percent raise in his hourly wage.

Given that the man's hourly wage increased from $12.50 to $13.50, we can use the formula for calculating the percentage change to find out what percent raise he got.

The formula for calculating the percentage change is as follows:

[(change in quantity)/(original quantity)] × 100

In this case, the change in quantity (the man's wage increase) is $1.00 (13.50 - 12.50), and the original quantity (the man's original wage) is $12.50.

Plugging these values into the formula, we get:

[1.00/12.50] × 100

This calculates to an 8 percent wage increase. Therefore, the man got an 8 percent raise in his hourly wage.

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Answer: 100

Step-by-step explanation:

[(25 - 11) + (15 - 9)] * 5

=[    14      +      6    ] * 5

=             20             * 5

=                     100

The Equation ( x= 11): 3x + 3 = 2(x + 7) and 6(x + 2) - x = 4(x + 4) + 7

The Equation ( x= 3): 0.8x + 5 = 0.2(40 - x), 2(x - 5) + 7 = x and

                                    ½(x + 8) + 3/2x = 10

The Equation ( x= 1/2): 5(x - 1) - 6x = -11x and ½x + 1/4 = x

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

1.  0.8x + 5 = 0.2(40 - x)

Solving for x, we get

0.8x + 5 = 0.2(40 - x)

0.8x + 5 = 8 - 0.2x

x + 5 = 8

x = 3

2. 2(x - 5) + 7 = x

Solving for x, we get

2(x - 5) + 7 = x

2x - 10 + 7 = x

2x - 3 = x

-3 = -x

3 = x

3. 3x + 3 = 2(x + 7)

Solving for x, we get

3x + 3 = 2(x + 7)

3x + 3 = 2x + 14

3x = 2x + 11

x = 11

4.  5(x - 1) - 6x = -11x

Solving for x, we get

5(x - 1) - 6x = -11x

5x - 5 - 6x = -11x

5x - 6x = -11x + 5

5x - 6x + 11x = 5

10x = 5

x = 1/2

5.  6(x + 2) - x = 4(x + 4) + 7

Solving for x, we get

6(x + 2) - x = 4(x + 4) + 7

6x + 12 - x = 4x + 16 + 7

5x + 12 = 4x + 23

5x = 4x + 11

x = 11

6.  ½(x + 8) + 3/2x = 10

Solving for x, we get

½(x + 8) + 3/2x = 10

½x + 4 + 3/2x = 10

½x + 3/2x = 6

2x = 6

x = 3

7.  ½x + 1/4 = x

Solving for x, we get

½x + 1/4 = x

1/4 = ½x

½ = x

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Its x^2 if x > -1

x = 3  so the answer is 3^2  = 9

14.50 times 0.20 = 2.9

He would give a $2.90 as a tip of 20% from a bill of $14.50

Apply the vertical line test. Think of a vertical line moving from left to right in the graph. If the graph of the relation intersects the vertical line in more than one point in any position of the vertical line, then the relation is not a function.

The only graph that passes the vertical line test is the graph at the bottom right.

The graph at the bottom right is a function. All others are not.

The queen might've asked the king to measure the rug to demonstrate humility, responsibility, highlight practical skills, or grasp the concept of measurement. Without specific context, however, it's hard to pinpoint an exact reason.

Without specific context, it's difficult to provide an exact reason for the queen asking the king to measure a rug. However, in general, English literature often showcases rulers partaking in ordinary tasks as a means of demonstrating humility, responsibility, or attention to detail. For instance, the queen might have wanted the king to measure the rug in order to prove that he can attend to ordinary matters as well as royal duties, or perhaps to prove himself practical and not merely ceremonial. It could also be a ploy to make the king grasp the concept of measurement, size or area, by doing the task himself.

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Answer:

B

Step-by-step explanation:

I got it correct on edg

Answer:

b

Step-by-step explanation:

Answer:

option d

Step-by-step explanation:

Solve each inequality and check which inequality has -12 as a solution

a. [tex]x+6<-8[/tex]

Subtract 6 from both sides

[tex]x<-14[/tex]

b. [tex]x+4>-6[/tex]

Subtract 4 from both sides of the inequality to get x alone

[tex]x>-10[/tex]

c.[tex]x-3>-0[/tex]

Add 3 on both sides

x>3

d. [tex]x+5<-4[/tex]

Subtract 5 from both sides

x<-9

-12 lies below -9. So x<-9 has -12 in its solution

The first thing you would do is "bring" the 10 over by subtracting 10 from both sides

[tex]3x^2+13x-10=0[/tex]

Now, you would want to factor

[tex](3x-2)(x+5)=0[/tex]

Then, set each factor equal to zero, and solve

3x-2 = 0

3x = 2

x = 2/3

AND

x+5 = 0

x=-5

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The determinant is given as:

D = -b ±√(b² - 4ac) / 2a

The values of x are:

x = (-13 + √17) / 6

x = (-13 - √17 ) / 6

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

x + 3 = 4 is an equation.

3x + 4x = 4 is an equation.

We have,

3x² + 13x = 10

This can be written as:

3x² + 13x - 10 = 0

Using the Middle term factorization.

3x² + (10 + 3)x - 10 = 0

3x² + 10x + 3x - 10 = 0

This is not possible so,

Using determinant.

3x² + 13x - 10 = 0

a = 3, b = 13 and c = -10

Now,

Determinant is given as:

D = -b ±√(b² - 4ac) / 2a

D = -b + √(b² - 4ac) / 2a

D = [-13 + √(169 + 120)] / 6

D = (-13 + √17) / 6 _____(1)

D = -b - √(b² - 4ac) / 2a

D = -13 - √(169 + 120) / 6

D = (-13 - √17 ) / 6 ______(2)

Thus,

The values of x are:

x = (-13 + √17) / 6

x = (-13 - √17 ) / 6

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Answer:

Option D

0.6

Step-by-step explanation:

Given that there are 5 colour marbles in a large bag.

The colours are red, orange, yellow, blue and green.

Also given that there are equal amounts of each colour

Let n be the no of marbles of each colour.

Then total no of marbles = 5(n) = 5n

No of red,blue and yellow marbles = n+n+n = 3n

Prob of drawing a red or blue or yellow = P(red)+P(blue)+P(yellow)

= [tex]\frac{n}{5n} +\frac{n}{5n} +\frac{n}{5n}  = \frac{3n}{5n}[/tex]

= 0.60

Afaik you just plug these into y=mx+b (slope intercept form)

I would think the answer to be y = (-3/5)x + 4

Answer:

y=-3/5x+4

Step-by-step explanation:

y=mx+b

place x to the other side of the equation

x=15/2.5

x=6

Answer:

6

Step-by-step explanation:

If you take 15 and divide it. by 2.5 you. get 6

The function for the given situation is f=60h+75.

Given that, a plumber's fees f are $75 for house calls and $60 per hour h for each hour worked.

We need to model a function for the given situation.

Functions are the fundamental part of calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h.

According to the question, we can model function as follows:

f=60h+75

Therefore, the function for the given situation is f=60h+75.

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The regular price of the jeans was $50. We know this because he saved $20 when the pants were 40% off so for every 10% percent it is $5, so 100% is $50 if that makes sense, if you need more thorough explanation let me know. :)

The sum 1 + 3 + 5 + + 7 + 9 + ... + 39 in sigma notation is represented as ∑(from n=1 to n=20)[1 + (n-1)*2]. This notation communicates the series' progression and key characteristics.

The sum 1 + 3 + 5 + + 7 + 9 + ... + 39 can be represented in sigma notation as follows: Let the general term of this arithmetic series be a_n = 1 + (n-1)*2, where n is the term number. This formula is for a sequence where the difference between each number is 2 (an arithmetic sequence). Thus, the series 1 + 3 + 5 + + 7 + 9 + ... + 39 in sigma notation can be written as ∑(from n=1 to n=20)[1 + (n-1)*2]. Here, n = 1 is the starting point, n = 20 is the end point which is calculated by (39-1)/2 + 1 because the sequence is an arithmetic sequence with common difference 2 and first term 1, and 1 + (n-1)*2 is the formula for the nth term.

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The sum 1 + 3 + 5 + ... + 39 can be written in sigma notation as Σ(1 + (i - 1)2) for i from 1 to 20.

To express the sum 1 + 3 + 5 + 7 + 9 + ... + 39 in sigma notation, we first need to realize that this is an arithmetic series where each term increases by 2. The first term a1 is 1, and the common difference d is 2. We can find the number of terms n in the series by using the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d.

Since 39 is the last term, we have 39 = 1 + (n - 1)2, which simplifies to n = 20.Now we know our series goes from the 1st term to the 20th term, and the formula for the ith term is ai = 1 + (i - 1)2. Therefore, the series in sigma notation is written as:  Σ(1 + (i - 1)2) for i from 1 to 20.

-3.

Hope this helped.

Answer:

x = -3

Step-by-step explanation:

Solving for value of x

−x + (−3) = x + 3              

-x -3 = x + 3                     [subtract x from both side]

-x -3 -x = x + 3 -x

-2x -3 = 3                       [add 3 to both side]

-2x -3 + 3 = 3 + 3

-2x = 6                          [divide both side by -2]

[tex]\frac{-2x}{-2}[/tex] = [tex]\frac{6}{-2}[/tex]

x = -3

A

f(x) = 2x + 1

f(3) = 2*3 + 1 = 7

B

g(x) = x^2

g(7) = 7^2

g(7)= 49

C

f(g(x)) = 2(g(x) + 1

f(g(x)) = 2 x^2 + 1

f(g(3) = 2* 3^2 + 1

f(g(3) = 19

D

g(f(x)) = (f(x))^2

g(f(x)) = (2x + 1)^2

g(f(3)) = (2*3 + 1)^2 = (6 + 1)^2 = 49

E

f(g(x)) = 2*g(x) + 1

f(g(x)) = 2*x^2 + 1

f(g(3)) = 2*3^2 + 1

f(g(3)) = 2 * 9 + 1

f(g(3)) = 18 + 1

f(g(3) = 19

F

f(g(x)) = 2(g(x)) + 1

f(g(x)) = 2*x^2 + 1  

Starting with 113+ (2x+5)=180, combine like terms and to get 118+2x=180.  Subtract 180-118, which gives you 62.  Then you have 2x=62.  Divide both sides by 2 to get a final answer of x=31.

Hey there!!

Given :

... 113 + ( 2x + 5 ) = 180

Subtract 113 on both sides

... 2x + 5 = 180 - 113

... 2x + 5 = 67

Subtract 5 on both sides

... 2x = 62

Divide by 2 on both sides

... x = 31

The value of x is 31.

Hope my answer helps!!

Answer:

If you can maintain this speed you will travel 120 km in 1 hour.

Explanation:

The translated question is, A cheetah can travel 20 kilometers in 10 minutes. If I could maintain this speed for one hour, how many kilometers would you travel?.

 Let us find the speed of cheetah

            Distance traveled =  20 km

            Time taken = 10 minutes = 10/60 = 1/6 hours

            So speed = [tex]\frac{20}{\frac{1}{6} } =120[/tex]km/hr.

 So speed of cheetah = 120 km/hr, which means cheetah will travel 120 km in 1 hour.

If you can maintain this speed you will also travel 120 km in 1 hour.

Here are the answers below that I got. Hope this helps mate. Cheers.

Answer:

As mention in the explanation steps.

Step-by-step explanation:

The following expression or phrase to each box are helpful to complete the proof.

(1). We say that ∠ACB and ∠BCD are supplementary, from linear pair of postulate.

(2). ∠ACB + ∠BCD =180°, because ∠ACB and ∠BCD are supplementary (from the difinition of supplementary angles).

(3). ∠ACB +45° = 180° because ∠BCD =45°(substitute).

(4).Subtraction properties of equality ( because we subtract 45 degree from both sides of the previous equation).

(5). ∠ABC is obtuse, because m∠ABC grater than 90°.

(6). From the definition of obtuse triangle (ΔACB is an obtuse triangle because ∠ACB =135 degree which is grater than 90 degree).

Answer:

24 ounces.

Step-by-step explanation:

Given that the ratio of blue paint to yellow paint in a green paint mixture is 2:3.

Actual ounces used for blue paint = 16

By ratio and proportion property we have

2:3 = 16:x where x is the actual ounces of yellow paint used.

Simplify using ratio rules

if a:b = c:d then ad = bc

We get

2x=3(16) = 48

Divide by 2

x = 24

Hence 24 ounces of yellow paint to be used.

Answer:

24 ounces. to be exact

Step-by-step explanation: