Solve 6x - 2 = 4x + 13 for x.
15/2
112
3/12

Answer:

[tex]33\dfrac{1}{3}\text{ quarts of grape juice}\\ \\66\dfrac{2}{3}\text{ quarts of sparkling water}[/tex]

Step-by-step explanation:

A recipe for sparkling grape juice calls for 1.5 quarts of sparkling water and 3/4 quart of grape juice.

The ratio of sparkling water to grape juice is

[tex]1.5\div \dfrac{3}{4}=\dfrac{3}{2}\div \dfrac{3}{4}=\dfrac{6}{4}\div \dfrac{3}{4}=6\div 3=2\div 1[/tex]

So, to make 100 quarts of punch you need x quarts of grape juice and 2x quarts of sparkling water.

Hence,

[tex]x+2x=100\\ \\3x=100\\ \\x=\dfrac{100}{3}=33\dfrac{1}{3}\text{ quarts of grape juice}\\ \\2x=66\dfrac{2}{3}\text{ quarts of sparkling water}[/tex]

Answer:

66 1/3

Step-by-step explanation:

pleas mark me as brainliest

Answer:

yes

Step-by-step explanation:

rational numbers are

Fractions

Decimals

repeating decimals

decimals that stop and don't go forever

percent

perfect square and cube roots

whole numbers

Answer:

236

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 4 and d = 8, thus

[tex]a_{30}[/tex] = 4 + (29 × 8) = 4 + 232 = 236

Answer:

700%

Step-by-step explanation:

The price increased from $0.30 to $2.40. What is the rate of increase, in percentage?

We can use the formula shown below:

[tex]\frac{New-Old}{Old}*100[/tex]

Where

New Price is 2.40 and the Old Price is 0.30

We substitute and calculate:

[tex]\frac{New-Old}{Old}*100\\\frac{2.40-0.30}{0.30}*100\\=7*100\\=700[/tex]

Hence,

Price increased 700%

As it is proved that the equation has no solution, Derick is correct

Step-by-step explanation:

Given

[tex]-3(4n + 2) = -4n + -2 (4n - 6)[/tex]

We have to solve the equation in order to check if Derick was solved the equation correctly or not.

So,

Applying distributive property first

[tex]-12n -6 = -4n -8n +12\\-12n-6 = -12n+12\\-12n+12n-6 = 12\\-6 = 12[/tex]

As the variable is already cancelled in the equation there is no unique solution.

In order for an equation to have infinite solutions the constant on both sides of equation should be same which is not the case in the given equation

So,

As it is proved that the equation has no solution, Derick is correct

Keywords: Linear equations, variables

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Final answer:

Upon simplification, the equation results in a contradiction (-6 = 12), proving Derick's conclusion of no solution to be correct.

Explanation:

To determine if Derick's conclusion that the equation -3(4n + 2) = -4n + -2 (4n - 6) has no solution is correct, we first simplify the equation. Distributing the coefficients on both sides gives:

-12n - 6 = -4n - 8n + 12

Combining like terms on the right side leads to:

-12n - 6 = -12n + 12

Adding 12n to both sides and simplifying:

-6 = 12

This statement is a contradiction, implying that there is no value of n that can satisfy the original equation, meaning Derick's conclusion of no solution is correct.

Answer:

m = ± 5

Step-by-step explanation:

Given

4² + 2² - (- 3²) = m² - (- 1²) + ([tex]\sqrt{3}[/tex])² ← evaluate exponents

noting that - 3² = - 9 and - 1² = - 1

16 + 4 - (- 9) = m² - (- 1) + 3, that is

20 + 9 = m² + 1 + 3

29 = m² + 4 ( subtract 4 from both sides )

25 = m² ( take the square root of both sides )

m = ± 5

Answer:

x=2.5, y=-5. (2.5, -5).

Step-by-step explanation:

5y+2(2.5)=-10

5y+5=-10

5y=-10-5

5y=-15

y=-15/5

y=-5

Answer:

(2.5, -3)

Step-by-step explanation:

We are told up front that x = 2.5.  Substituting 2.5 for x in the second equation, we get:

5y + 2(2.5) = -10.

Carrying out the indicated multiplication:

5y + 5 = -10.

Then 5y = -15, and y = -3.

The solution in the form (x, y) is (2.5, -3).

Answer:

what is your question???????

Answer:

see explaination

Step-by-step explanation:

a) $4.50 × ? = $36 $36 ÷ $4.50 = ?

b) 8 (divide)

c) replace question marks with x and solve algebraically still equals 8

Mathematics is algebraic over the field of real numbers: of or pertaining to a component that is the root of a polynomial equation with coefficients from a specific field.

A General Rule for Equation Solving

a) $4.50 × ? = $36 $36 ÷ $4.50 = ?

b) 8 (divide)

c) replace question marks with x and solve algebraically still equals 8.

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Answer:10 people

Step-by-step explanation:

7 times less showed up so, 70 divided by 7 is 10. 10 guests attended.

The James family expected 70 guests for their party, but 7 times fewer showed up. By dividing the expected guest number by 7 (70 ÷ 7), we find that 10 guests attended the party.

The James family expected 70 guests to attend their independent day party. However, 7 times fewer guests showed up than expected. We can calculate this by dividing the expected number of guests by 7.

Step 1: Identify the total number of guests expected which is 70.

Step 2: Divide the expected number of guests by 7. This is because the actual number of attendees was 7 times fewer than the expected.

Step 3: Perform the division: 70 ÷ 7 = 10.

So, 10 guests attended the independent day party hosted by the James family.

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Answer:

It's the first choice:  3x^2y(3x^2 - 2xy + y^2).

Step-by-step explanation:

9x4y − 6x3y2 + 3x2y3

We take the Greatest Common Factor which is  3x^2y:

= 3x^2y(3x^2 - 2xy + y^2).

Answer:

3x^2y(3x^2 - 2xy + y^2)

Step-by-step explanation:

You can give the guy above me a crown now lol 4 years later

Answer:

5x^2+6x-1

Step-by-step explanation:

Remember that (f+g)(x)=f(x)+g(x).

(3x^2+7x)+(2x^2-x-1)

3x^2+2x^2+7x-x-1

5x^2+6x-1

The sum of the functions f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, represented by (f+g)(x), equals to 5x^2 + 6x -1.

In mathematics, particularly in algebra, the operation (f+g)(x) represents the sum of the two functions f(x) and g(x). In order to find the sum, you simply carry out the addition operation on the functions term by term. Given your functions f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, the sum (f+g)(x) is then calculated as follows:

Therefore, (f+g)(x) = 5x^2 + 6x -1.

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Answer:

No it is not

Step-by-step explanation:

well if you see any number that is could be written as a  fraction is rational. square root of 9 is 3,  but in this case the square root of 2 is irrational, so it is a irrational number.

Yes, the fraction √ 2/9  is a rational number​

A rational number is a type of real number, which is in the form of p/q where q is not equal to zero. Any fraction with non-zero denominators is a rational number.

Some of the examples of rational numbers are 1/2, 1/5, 3/4, and so on.

The number “0” is also a rational number, as we can represent it in many forms such as 0/1, 0/2, 0/3, etc. But, 1/0, 2/0, 3/0, etc. are not rational, since they give us infinite values.

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Answer:

h(x+2)= x² +5

Step-by-step explanation:

h(x)= x² +5 -2x

h(x+2)= (x+2)² +5 - 2(x+2)

h(x+2)= x² +4x+4+5-4x-4

h(x+2)= x² +5

Answer:

x=5

Step-by-step explanation:

let, width of rectangle=b=6 units

length of rectangle=l=2x+8

given area of rectangle=108 units squared

area of rectangle=lb

108=(2x+8)6=12x+48

108-48=12x

x=[tex]\frac{60}{12}[/tex]

x=5  answer

Answer: 5u/s

Step-by-step explanation:

the ball rolls a total of 5 units from x=-5 to x=0. It traveled  this total distance in one second. Therefore the ball goes 5 units per second.

Answer:

y=-5x+1

Step-by-step explanation:

The equation is: y=mx+b

m = the slope of the line

b = the y-intercept (0,b)

The y-intercept is (0,1) so b = (0,1)

So the equation would be y =mx+1

Now in order to calculate the slope, the equation is:

y₂-y₁    over

x₂-x₁

So we should use the points (-3,13) and (1,-7).

-7-13 over (over means a fraction symbol)

1+3

Simplify:

-20 over 4   =-5/1    = -5    

M=-5

So the equation is now:

y=-5x+1

Answer:

Step-by-step explanation:

You need to do some solving simultaneously to get these values.  Your quadratic equation is of the form

[tex]ax^2+bx+c=y[/tex]

Use the coordinates you've been given to solve 3 equations.  It will be super simple if we start with the coordinate (0, 1).  Here's why (obvious after some substitution is done):

[tex]a(0)^2+b(0)+c=1[/tex] which gives us that

c = 1.  Now we have a variable to plug in for c to solve for a and b.  Again, we have coordinates that we can use to create 2 more equations:

[tex]a(-3)^2+b(-3)+1=13[/tex] and, simplified:

9a - 3b = 12

and the second equation is:

[tex]a(1)^2+b(1)+1=-7[/tex] and, simplified:

a + b = -8

Now combine the 2 bold equations and solve by elimination or substitution to find either a or b.  I chose elimination and multiplied the second equation by 3 to get a new equation:

3a + 3b = -24

Using the elimination method:

9a - 3b = 12

3a + 3b = -24

You can see that the b's subtract each other away, leaving us with

12a = -12 so

a = -1

Now plug -1 in for a to solve for b:

-1 + b = -8 so

b = -7 and the quadratic is

[tex]-x^2-7x+1=y[/tex]

Answer:

1. m∠B=110°

2. 560 cm3

3. Numerical data

4. 2000 cm3

5. 50%

Step-by-step explanation:

1. The explanation of part 1 is given in the attachment.

2. Given dimensions : 10 cm, 8 cm, and 7 cm.

Let Length of cuboid =10 cm

breadth/width of cuboid  =8 cm

height of cuboid = 7cm

Volume of cuboid = length *width* height

=( 10 *8*7) cm3

=(560) cm3

3. Age, Birth date  and weight are the types/examples of "Numerical Data" because these all are describe in terms of numeric values.

4. 1 liter = 1000 cm3   or   1 cm3 = 0.001 liter

1.5 liters =(1.5*1000) cm3 = (15*100) =1500 cm3

1 dm3 =1000 cm3

0.35 dm3 = (0.35*1000) cm3 = (35*10) cm3 =350 cm3

Given expression: 1.5 litre + 0.35 dm3 + 150 cm3 =               cm3

1500 cm3 + 350 cm3 +150 cm3 = 2000 cm3

5. If A=(1/2)B, then B : A = 50 %

Ratio: B : A

B : (1/2) B

1: (1/2)

50 % (The value of A is half of the value of B)

Answer:

Zeros are [tex]x=-2\pi,-\pi,0,\pi,2\pi[/tex]

Step-by-step explanation:

[tex]f(x)=0\\-4\sin x=0\\\sin x=0\\[/tex]

[tex]\sin(-2\pi)=0\\\sin(-\pi)=0\\\sin(0)=0\\\sin(\pi)=0\\\sin(2\pi)=0[/tex]

It's B) 0, ±pi, ±2pi on edge

Answer:

(-1,4)

-1 is x and 4 is y

You have to plug it in for the equation:

4= 3(-1)+5

4= -3+5

4 = 2

the answer is no solution because 4 does not equal to 2

Answer:The cost increases $3.99 for every additional movie rented.

Step-by-step explanation:

Answer:

Step-by-step explanation:

In this situation, the rate of change means the cost per movie.

Specifically, the cost is $3.99 per movie. In other words, the cost increases $3.99 when the number of movies increases by 1.

We could also say it like the cost increases $3.99 for every additional movie.

Therefore, among the options the second choice is correct, because specifies the right ratio of change that the table shows.

You can get this ratio of change by subtracting $7.98 - $3.99 = $3.99. Then, if you sum this difference to $7.98, you would get $11.97, and then $15.96, and so on. That means the ratio of change is $3.99 per movie.

Answer:

4.583 or 55/12

Step-by-step explanation:

A = 5, B = -22 and C = 4, D = -6. 5 multiplied by -22 is equal to -110, and 4 multiplied by -6 is equal to -24. Because a negative divided by a negative is a positive by the same rules of multiplication of negatives is a positive, just get rid of any negative signs in the equation. Now you have 110 / 24. 110/24 is equal to 4.583 or 55 / 12 in fraction form.

Answer:

No.6*0 isn't 6, and divisor can not be zero.

Step-by-step explanation:

Hope this helps and have a nice day;)

Answer:

the answer is b beacause

Step-by-step explanation:

when you multiply 14.95 times 6 it equals b

Answer: 65

Step-by-step explanation:

Let the number of games be x, this means that the cost of x games will be 0.69x.

There is also a one-time registration fee of $14.95 , this means that for Sammy to register and buy game with $60 , the equation will be

14.95 + 0.69x =60

subtract 14.95 from both sides

0.69x = 60 - 14.95

0.69x = 45.05

divide through by 0.69

x = 45.05/0.69

x = 65.28985507

Therefore , the maximum number of games she can buy is 65

Answer:

√50 lies between 7.07 and 7.08.

Answer:

Step-by-step explanation:

Here we need to use Ohm's Law, because we have electric current, voltage and resistances. This law state: [tex]V=IR[/tex]

So, first we need to calculate the total resistance to then find the voltage. The resistances can be placed in two ways: in parallel, in series.

The pair 4 and 8 ohms are parallel, so we solve:

[tex]R_{T}=\frac{1}{R_{1}}+\frac{1}{R_{2}}[/tex]

[tex]\frac{1}{R_{T}}=\frac{1}{4}+\frac{1}{8}=\frac{8+4}{32}=\frac{12}{32}=\frac{3}{8}[/tex]

Which is, [tex]R_{T}=frac{8}{3}[/tex]

Now, this total resistance of parallels ones is placed in series with the 3 ohm resistance, in this case we just sum, because they are in series:

[tex]R=3+\frac{8}{3}=\frac{9+8}{3}=\frac{17}{3}=5.67 ohm[/tex]

Now that we have the total resistance of the circuit, we use the Ohm's Law:

[tex]V=IR\\V=(0.6A)(5.67ohm)=3.4 Volt[/tex]

Therefore, the right answer is B.

Answer:

They traveling at [tex]0.37\ m/s[/tex] in backward direction.

Step-by-step explanation:

Given mass of Ammy [tex]m_1=55kg[/tex]

and velocity is forward at [tex]v_1=3m/s[/tex]

Also, mass of Jenny [tex]m_2=40kg[/tex]

Who is travelling in opposite direction [tex]v_2=-5m/s[/tex]

Let velocity in forward direction is positive and velocity in backward direction is negative.

Also, velocity after crash is [tex]v[/tex]

As they crashed into each other and they moved as one mass. We can apply principle of conservation of momentum.

Conservation of momentum says momentum before collision should equal to momentum after collision.

[tex]m_1v_1+m_2v_2=(m_1+m_2)v[/tex]

[tex](55\times3)+(40\times(-5))=(55+40)v\\\\165-200=95v\\\\-35=95v\\\\v=\frac{-35}{95}=-0.368m/s[/tex]

So, velocity after collision [tex]v[/tex]≅[tex]-0.37m/s[/tex] is in opposite direction. That is the direction of Jenny.

Answer:

C

Step-by-step explanation:

I just did the test

Answer:

c

Step-by-step explanation: