42 : 36 : 54 in simplest form

Step-by-step explanation:

We have,

− 3( x + 1)

= − 3x - 3

A. - 3x + (-3)

= − 3x - 3, is equivalent to − 3( x + 1).

B. x - 3

= x - 3, is not equivalent to − 3( x + 1).

C. - 3x + 1

= - 3x + 1, is not equivalent to − 3( x + 1).

D. - 3x - 3

= - 3x - 3, is equivalent to − 3( x + 1).

Thus, A)  - 3x + (- 3) and D) - 3x - 3 are equivalent.

It is true that the solution set of an equation of a circle is all of the points that lie in the circle

The equation of a circle is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where:

Center = (a,b)

Radius = r

The points are represented by (x,y)

The (x,y) can take any value as long as it makes the equation (x - a)^2 + (y - b)^2 = r^2 to be true

Hence, it is true that the solution set of an equation of a circle is all of the points that lie in the circle

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Answer:

False

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

1 1/2 is greater than 1 4/10. Wich is 1/10 less then 1 1/2

Answer:

Yes

Step-by-step explanation:

1 1/2 > 1 4/10

Step 1:  Covert to Improper Fraction

1 1/2 = 2/2 + 1/2 = 3/2

1 4/10 = 10/10 + 4/10 = 14/10

Step 2:  Find Common Denominator

The least common denominator is 10

3/2 * 5/5 = 15/10

14/10 is already good

Step 3:  Evaluate

Is 15/10 more than 14/10?

Yes!!!!

So, 1 1/2 is more than 1 4/10

Answer:

100 ÷ 50 = 2.

Answer:

predictable

Step-by-step explanation:

the opposite of random is predictable

The opposite of 'random' would be a word like 'ordered' or 'systematic', which suggest a set plan or sequence, contrasting with the concept of randomness.

The opposite of the word 'random' would be a term that denotes a sense of order, structure, or predictability. In this context, one example of a word that is the opposite of 'random' is 'ordered' or 'systematic'. These words suggest that things are arranged or occur according to a set plan or sequence, thereby contrasting with the concept of 'random', which indicates a lack of any discernible order or pattern.

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Answer:

(4,3)

Step-by-step explanation:

The orthocenter of a triangle is the point of intersection of the altitudes of the triangle .

The vertices are:

A(-2,5), B(6,5), and C(4,-1)

Slope of (6,5), and (4,-1) is

[tex]m = \frac{5 - - 1}{6 - 4} = 3[/tex]

Slope of altitude through A is

[tex] - \frac{1}{3} [/tex]

The equation of the altitude through A is

[tex]y - 5 = - \frac{1}{3} (x - - 2)[/tex]

[tex]y = - \frac{1}{3} x + \frac{13}{3} [/tex]

The slope of A(-2,5), B(6,5) is zero because it is a horizontal line.

The equation of altitude through (4,-1) will be the vertical line x=4.

This implies that,

[tex]y = - \frac{4}{3} + \frac{13}{3} = 3[/tex]

Hence the orthocenter is (4,3)

Answer:

P - 4

Step-by-step explanation:

Sergio and the other painting collectors have decided to donate a total of 48 paintings all together.

We know that there are 12 collectors in total and they will each donate the same number of paintings.

48 paintings in total

12 collectors

48 / 12 = 4

We now know Sergio will donate 4 paintings from his collection of P paintings. Sergio will have P - 4 paintings left.

We do not know what "P" is equal to, so we cannot give an exact number for how many paintings he will have left. However, we know he will have 4 fewer paintings after donating.

84 pounds of Type B coffee is used

Solution:

Let "x" be the pounds of type A coffee

Let "y" be the pounds of type B coffee

Cost per pound of type A = $ 5.50

Cost per pound of Type B = $ 4.20

This month, Chau made 143 pounds of the blend

x + y = 143

x = 143 - y -------- eqn 1

For a total cost of $677.30. Thus we frame a equation as:

pounds of type A coffee x Cost per pound of type A + pounds of type B coffee x Cost per pound of Type B = 677.30

[tex]x \times 5.50 + y \times 4.20 = 677.30\\\\5.5x + 4.2y = 677.30 -------- eqn 2[/tex]

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

[tex]5.5(143-y) +4.2y = 677.30\\\\786.5 -5.5y + 4.2y = 677.30\\\\5.5y - 4.2y = 786.5 - 677.30\\\\1.3y = 109.2\\\\Divide\ both\ sides\ by\ 1.3\\\\y = 84[/tex]

Thus 84 pounds of Type B coffee is used

To determine how many pounds of type B coffee were used in Chau's coffee blend, we set up a system of equations based on the total weight and total cost of the blend. By substituting one equation into the other, we can solve for the quantity of type B coffee.

Calculating the Blend of Coffee:

To solve the problem, let's use a system of equations to determine how many pounds of type B coffee Chau used in his coffee blend. We have two unknowns here: the amount of type A coffee (let's call it A) and the amount of type B coffee (let's call it B). The total weight of the coffee blend is given as 143 pounds, and the total cost of the blend is $677.30.

The first equation comes from the total weight of the blend:

A + B = 143

The second equation comes from the total cost:

5.50A + 4.20B = 677.30

We can use either substitution or elimination to solve this system. If we solve the first equation for A (i.e., A = 143 - B) and substitute it into the second equation, we get:

5.50(143 - B) + 4.20B = 677.30

After simplifying, we can solve for B to find out how many pounds of type B coffee were used.

Answer:

Solving by method of factorization ,

(y^4-y^3+2y^2+y-1)/(y+1)(y^2-y+1)

Step-by-step explanation:

A sum of two perfect cubes,  a3 + b3 can be factored into  :

            (a+b) • (a^2-ab+b^2)

here a = y and b = 1

hence , expanding y^3+1 in cubic formula ,

(y^3+1) = (y+1)(y^2-(y)(1)-1^2)

(y^3+1)=(y+1)(y^2-y+1)

putting this value of (y^3+1) in the given expression ,

= (y^4-y^3+2y^2+y-1)/(y+1)(y^2-y+1).

Trinomial cannot be factored , hence the final answer is ,

= (y^4-y^3+2y^2+y-1)/(y+1)(y^2-y+1).

The measure of BD ≈ 5.36

Step-by-step explanation:

Let 'x' be the measure of BD and EC.

BC = x+9.28+x

20 = 9.28 + 2x

2x = 20-9.28

x = 10.72/2

x = 5.36 (approx.)

∴ The measure of BD ≈ 5.36

Answer:

$110

Step-by-step explanation:

35+25(3)

Answer: I think it's True :)

Answer:

I feel like it true. Happy yo help!!!

Step-by-step explanation:

Answer:

z = -8.46 - 3.08i.

Step-by-step explanation:

cos 200 = -0.93969 so 9 * cos 200 = -8.46 to the nearest hundredth.

sin 200 = -0.3420 so 9 * sin 200 = -3.08 to nearest hundredth.

Final answer:

You could partially fill one 10-liter gas can with the 7 liters of gas, as 7 divided by 10 is 0.7, and you cannot have a fraction of a physical can.

Explanation:

To find out how many cans we could fill with 7 liters of gas, when a gas can holds 10 liters, we need to perform a simple division.

The calculation is as follows:
Number of cans = Total liters of gas / Liters each can holds = 7 liters / 10 liters = 0.7.

Since you cannot have a fraction of a physical gas can, you would not be able to completely fill a single can with 7 liters of gas.

Therefore, we could partially fill one 10-liter gas can with the 7 liters of gas we have.

Answer:

2007

Step-by-step explanation:

we have

[tex]p(x)=0.65x^{2} -0.047x+2[/tex]

This is a vertical parabola open upward

The vertex represent a minimum

p(x) is the population in thousands for a species of fish

x is the number of years since 1997

Remember that p(x) is in thousands

so

If the population reach 66,530 fish

then

the value of p(x) is equal to

p(x)=66.53

substitute in the quadratic equation

[tex]66.53=0.65x^{2} -0.047x+2[/tex]

[tex]0.65x^{2} -0.047x+2-66.53=0[/tex]

[tex]0.65x^{2} -0.047x-64.53=0[/tex]

Solve the quadratic equation by graphing

The solution is x=10 years

see the attached figure

therefore

Find the year

Adds 10 years to 1997

1997+10=2007

Step-by-step explanation:

First term : 8 - 0 = 8

second term: 8 - 1 = 7

third term : 8 - 2 = 6

The total number of blue cards in the game = 48

Step-by-step explanation:

Total number of blue and yellow cards = 84

let the blue card denote B and yellow card as Y

B = 4

Y = 3

Total number of cards in one round = 7

number of rounds possible = total number of cards / number of cards in one round

= 84/7

= 12

number of blue cards = 12 x 4

= 48

  The total number of blue cards in the game = 48                                                                                                              

Answer:

48

Step-by-step explanation:

Answer:

18 and 335

Step-by-step explanation:

y = 18x + 11

x * y = 6030

x * (18x + 11) = 6030

18x^2 + 11x = 6030

18x^2 + 11x - 6030 = 0

(18x + 335)(x - 18) = 0

18x + 335 = 0                 x - 18 = 0

18x = -335                      x = 18

x = -335/18

x is gonna have to be a positive number...so x = 18

y = 18x + 11

y = 18(18) + 11

y = 324 + 11

y = 335

so ur numbers are 18 and 335

The two positive integer numbers are 18 and 335

What is an Equation?

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.

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 data ,

Let the two numbers be a and b

Now ,

Positive integer is 11 more than 18 times another

a = 11 + 18b   be equation (1)

And , product of a and b is 6030

a x b = 6030   be equation (2)

Now , substituting the value of equation (1) in equation (2) , we get

( 11 + 18b ) x b = 6030

18b² + 11b = 6030

Subtracting 6030 on both sides , we get

18b² + 11b - 6030 = 0   be equation (3)

On simplifying , we get

18b² - 324b + 335b - 6030 = 0

18b ( b - 18 ) + 335 ( b - 18 ) = 0

So ,

( 18b + 335 ) ( b - 18 ) = 0

Now , we got two values for b ,

( 18b + 335 ) = 0

b = -335 / 18

And ,

( b - 18 ) = 0

b = 18

Since , b is a positive integer , the value of b is 18

Now , substituting the value of b in equation (2) , we get

a x 18 = 6030

Divide by 18 on both sides , we get

a = 335

Hence , the two positive integer numbers are 18 and 335

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Answer:

y = - 5x

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = - 10 when x = 2, thus

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{-10}{2}[/tex] = - 5

y = - 5x ← equation of variation

Answer:

Explanation:

8. Joe can chop vegetables in 5 minutes, and Rich can chop the same amount of vegetables in 4 minutes. Working together, how long will it take them to chop that batch of vegetables?

Name v the amount of vegetables

Working together, the combined speed is the sum of the two speeds: v/5 + v/4

Thus, the speed working together is:

            [tex]\frac{v}{5} +\frac{v}{4}=\frac{4v+5v}{20}=\frac{9v}{20}[/tex]

Hence, they can chop 9 times the given amount of vegetables (v) in 20 minutes.

And the time to chop the given amount of vegetables (v) is 20 divided by 9.

               [tex]time=amount/speed\\\\time=v/(9v/20)\\\\time=20v/(9v)=20/9=2.22[/tex]

That is 2.22 minutes to chop all the vegetables working together.

9. At Ricardo's Tacos, four tacos and two orders of chips cost the same as two tacos and four orders of chips. If Ricardo's charges $2.00 for a single order of chips, how much does Ricardo's charge for 1 taco?

Use T for the cost of tacos and C for the cost of orders of chips

Ricardo's charges the same for those orders:

Ricardo's charges $2.00 for a single order of chips:

Substitute C = 2 in 4T + 2C = 2T + 4C and solve:

   Substitution:

   Do the operations:

   Subtract 4 from both sides

   Subtract 2T from both sides

   Combine like terms

   Divide both sides by 2

Hence, Ricardo's charges $2.00 for one taco.

10. Broccoli is $1.69 per pound. Meg paid $8.45 for broccoli. How many pounds did she purchase?

You must divide the amount paid ($8.45) by the unit price ($1.69/lb)

        [tex]\$ 8.45/(\$ 1.69/lb)=5.00lb[/tex]

In the operation, $ appears both in the numerator and the denominator so they cancel out each other. The unit pounds (lb) appears dividing the denominator, thus it passes to the numerator.

Hence, Meg purchased 5.00 pounds

Final answer:

Solving these problems, Joe and Rich can chop vegetables in about 2.22 minutes together. Tacos at Ricardo's cost $2 each, and Meg purchased 5 pounds of broccoli.

Explanation:

Problem Solving in Mathematics

Joe and Rich Chopping Vegetables: Joe can chop vegetables in 5 minutes, while Rich can do the same in 4 minutes. When working together, the rate at which they can chop vegetables combines. This means Joe chops 1/5 of the vegetables per minute and Rich chops 1/4 per minute. Together, they can chop 1/5 + 1/4 = 9/20 of the vegetables per minute. Therefore, working together, they will take 20/9 minutes, or approximately 2.22 minutes, to chop the batch of vegetables.

Cost of Tacos at Ricardo's Tacos: Let's denote the cost of one taco as T. The equation based on the given information is 4T + 2(2) = 2T + 4(2). Simplifying this, we get 4T + 4 = 2T + 8, which reduces to 2T = 4, so one taco costs $2.00.

Meg's Broccoli Purchase: Meg paid $8.45 for broccoli that costs $1.69 per pound. To find out how many pounds she purchased, divide the total cost by the price per pound: $8.45 / $1.69. This calculation results in Meg purchasing 5 pounds of broccoli.

Answer:

+56

Step-by-step explanation:

Hmmm.... do you mean 0.8888...... or just 0.8888.

If you mean point eight repeating the fraction equivalent is just 8/9.

Answer:

Step-by-step explanation:

7/9x + 2 = 5/6.....multiply by the common denominator of 18

14x + 36 = 15 <=== re-written without fractions

14x = 15 - 36

14x = -21

x = -21/14

x = - 3/2...(or - 1 1/2)...ur solution

To rewrite the equation 7/9x + 2 = 5/6 without fractions, we multiply every term by the least common denominator (18) to get 14x + 36 = 15. Subtracting 36 from both sides and solving for x results in x = -21/14.

In order to rewrite the equation without fractions, we can eliminate the fractions by finding the least common denominator (LCD) and multiplying every term in the equation by it.

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Answer:

Length = 10.5units,Area = 68.25 unit²

Step-by-step explanation:

Perimeter =34 units

Width =6.5 units

Perimeter = l+l+w+w

Where l= length and w= width

34 = l + l + 6.5+ 6.5

34.= 2l + 13

Subtract 13 from both sides

2l = 34 - 13

2l = 21

Divide both sides by 2

L= 21/2

Length = 10.5units

If we are to find the area.

Area = length x width

Area = 10.5 × 6.5

Area = 68.25 unit²

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The expression demonstrates distributive property.

Explanation:

The given expression is [tex]17 \times 102[/tex]

Thus, solving the expression results in [tex]1734[/tex]

One student rewrote this expression as [tex]17(100+2)[/tex]

Then, simplified the expression as

[tex]1700+34[/tex]

Thus, [tex]17(100+2)=1700+34[/tex]

The expression demonstrates distributive property and the property can be generally written as

[tex]$a(b+c)=a b+a c$[/tex]

The given expression [tex]17(100+2)[/tex] is of the form [tex]$a(b+c)$[/tex]

Hence, The expression demonstrates distributive property.

The volume of cylinder is 1205.76 cubic inches

Solution:

We have to find the volume of cylinder

The volume of cylinder is given by formula:

[tex]V = \pi r^2h[/tex]

Where "r" is the radius and "h" is the height of cylinder

Given dimensions are:

Radius = 8 inches

Height = 0.5 feet

Convert feet to inches

1 feet = 12 inches

Therefore,

0.5 feet = 12 x 0.5 = 6 inches

Thus, we have got,

height = 6 inches

Substitute r = 8 inches and h = 6 inches in formula:

[tex]V = 3.14 \times 8^2 \times 6\\\\V = 3.14 \times 64 \times 6\\\\V = 1205.76[/tex]

Thus volume of cylinder is 1205.76 cubic inches

Answer:

Infinitely many solutions

Step-by-step explanation:

If we have a system of equation like:

2x+y=4

6x+3y=12

If we make y the subject in the first equation and substitute into the second equation, we get:

6x+3(4-2x)=12

We expand to get:

6x+12-6x=12

6x-6x+12=12

Now the variable adds out to give:

12=12

This statement is true so the equation has infinitely many solution.

Answer:

Explanation:

When the variable adds out means that after all the simplifications, at the end, it will not appear in the final sentence or expression.

Then, if the final sentence is true, and not variable appears, but only constants, the sentence is always true, no matter what value the variable takes.

That means that you can put any value for the variable in the original equation and the equation will be true; hence there are infinite solutions.

This is an example:

1. Equation:

2. Remove the parenthesis:

3. Add like terms on the right side and transpose the variables to the left side:

4. Combine like terms on the left side:

Thus, the variable added out and the final sentence is true. Hence, this equation has infinite solutions, which you can prove substituting the variable with any value.

Answer:

A. 45 in

Step-by-step explanation:

To find area you multiply length and width so you would multiply 9 and 10 but since it is a triangle you would divide by two

Hope this helps!

Answer:

5xA-5xB

Step-by-step explanation:

Answer: 5a-5b

Step-by-step explanation: Distribute the 5 and carry the negative sign over