Jack is two years older than bob. If bob is x years old, what is the sum of jacks age and bobs age

The equation of the graph is [tex]x = \frac 1{24}y^2[/tex]

Generally, a point is represented as:

(x,y)

The line x = -6 means that:

(-6, y)

So, we calculate the distance between (x,y) and (-6, y) as follows:

[tex]d = \sqrt{(x + 6)^2 + (y - y)^2}[/tex]

This gives

[tex]d = \sqrt{(x + 6)^2 }[/tex]

Next, we calculate the distance between (6,0) and (x, y) as follows:

[tex]d = \sqrt{(x - 6)^2 + (y - 0)^2}[/tex]

This gives

[tex]d = \sqrt{(x - 6)^2 + y^2}[/tex]

Equate both distance expressions

[tex]\sqrt{(x + 6)^2} = \sqrt{(x - 6)^2 + y^2}[/tex]

Square both sides

[tex](x + 6)^2 = (x - 6)^2 + y^2[/tex]

Expand

[tex]x^2 + 12x + 36 = x^2 - 12x + 36 + y^2[/tex]

Evaluate the like terms

[tex]12x = - 12x + y^2[/tex]

Add 12x to both sides

[tex]y^2 = 24x[/tex]

Make x the subject.

[tex]x = \frac 1{24}y^2[/tex]

Hence, the equation of the graph is [tex]x = \frac 1{24}y^2[/tex]

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Answer:

First one

Step-by-step explanation:

Supplementary angles basically means which angles added together equals 180 degrees, 180 degrees is also a straight line.

So the answer would be the first one because both the angles added together is 180.

Answer:

7:43 am.

Step-by-step explanation:

it was  1/2 full one minute ago then another 1/2 = 1/4 full 2 minutes ago.

Knowing how the bus fills, we want to find the time where the bus is one-quarter full.

The bus is one-quarter full at 7:43 am.

We know that at 7:45 am the bus is full. Let's say that the full bus has N people inside.

Each minute the population doubles, so if we go backwards, each minute the population is divided by 2.

One minute before, the bus must have half of the above population, meaning that at 7:44 am, the bus has N/2 people.

Another minuter before the people inside is halved again, then at 7:43 am we will have (N/2)/2 = N/4 people.

And if N is the people in a full bus, then N/4 represents the buss a quarter full.

Then we can answer the question as:

The bus is one-quarter full at 7:43 am.

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Answer:

5x² - 36x - 81

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define expression

5x² - 36x - 81

Step 2: Simplify

We cannot simplify the expression down further.

Answer:

x = infinite amount of solutions

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define systems

4x - 3y = 1

-8x + 6y = -2

Step 2: Rewrite systems

-8x + 6y = -2

Step 3: Redefine systems

4x - 3y = 1

y = 4/3x - 1/3

Step 4: Solve for x

Substitution

Here we see that 1 does indeed equal 1.

∴ x = all real numbers/infinite amount of solutions

Step 5: Graph

Check the systems.

We see that the 2 equations are the same line.

Step-by-step explanation:

The sample space of a random experiment is the collection of all possible outcomes. An event associated with a random experiment is a subset of the sample space. The probability of any outcome is a number between 0 and 1. The probabilities of all the outcomes add up to 1.

Answer:

north

Step-by-step explanation:

Answer:

After solving [tex](45x-7)4x=57[/tex] we get [tex]\mathbf{x=0.645 \ or \ x = -0.490}[/tex]

Step-by-step explanation:

We need to solve the equation: [tex](45x-7)4x=57[/tex]

Solving:

[tex](45x-7)4x=57[/tex]

Multiply 4x with terms inside the bracket

[tex]180x^2-28x=57[/tex]

[tex]180x^2-28x-57=0[/tex]

We need to solve above equation to find value of x

Using quadratic formula for finding value of x: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a=180, b=-28 and c=-57

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-28)\pm\sqrt{(-28)^2-4(180)(-57)}}{2(180)}\\x=\frac{28\pm\sqrt{784+41040}}{360}\\x=\frac{28\pm\sqrt{41824}}{360}\\x=\frac{28\pm204.51}{360}\\x=\frac{28+204.51}{360} \ or \ x=\frac{28-204.51}{360}\\x=0.645 \ or \ x = -0.490[/tex]

Values of x are [tex]\mathbf{x=0.645 \ or \ x = -0.490}[/tex]

So, After solving [tex](45x-7)4x=57[/tex] we get [tex]\mathbf{x=0.645 \ or \ x = -0.490}[/tex]

Answer:

The answer is -6.

Step-by-step explanation:

You have to substitute x = -4 into the expressions :

3x - x + 2

= 3(-4) - (-4) + 2

= -12 + 4 + 2

= -6

Answer:

$36

Step-by-step explanation:

Answer:

$36.

Step-by-step explanation:

(Hot dog) 2 for 5: Unit price is 5/2 = 2.5

(Soda) 3 for 3 so unit price is 1 for 1.

6 sodas = 6 dollars

12 Hot dogs = 12. x 2.5 = 30 dollars.

Price for both = 30 + 6 = 36.

Answer:

67

Step-by-step explanation:

You have to use fractions to show your work and I'm not going to do that but just know that it is the answer.

Answer:

3

Step-by-step explanation:

You solve the inner first, then move to the outer.

Let's look at g(3) first. It is stated in the problem that g(3) = 2.

We then use this value for f(x). It is stated in the problem that f(2) = 3.

The answer is 3.

Answer:

Asriel Dreemurr

Step-by-step explanation:

Answer:

clearly the gay robot

hes my favorite <3

Answer:

The logarithmic function for x = 2y is written as y = log2 x or f(x) = log2 x. The number 2 is still called the base. In general, y = logb x is read, “y equals log to the base b of x,” or more simply, “y equals log base b of x.” As with exponential functions, b > 0 and b ≠ 1

Step-by-step explanation:

ttygytex x so r5f3ygthttg

Answer:

16% of the cockroaches have weights less than 78 grams.

Option A is correct.

Step-by-step explanation:

Mean = 80 g

Standard Deviation = 2

We need to find percent of the cockroaches have weights less than 78 grams so, x=78

First we will find z using formula:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Putting values of x, mean and Standard Deviation to find z

[tex]z=\frac{x-\mu}{\sigma}\\z=\frac{78-80}{2}\\z=-1[/tex]

We need to find P(z<-1)

Looking in the normal distribution table

[tex]P(z<-1)=0.15866\\P(z<-1)\approx 0.16\\Converting \ into \ percentage\\P(z<-1)=16\%[/tex]

So, 16% of the cockroaches have weights less than 78 grams.

Option A is correct.

==================================================

Explanation:

Expand out the expression using the FOIL rule

(x+7)(x-7)

x^2 - 7x + 7x - 49

1x^2 + 0x - 49

We see that a = 1, b = 0, c = -49

-------------

Another way to expand is to do the following

(x+7)(x-7)

y(x-7) .... let y = x+7

xy - 7y .... distribute

x( y ) - 7( y )

x( x+7 ) - 7( x + 7 ) ... replace y with x+7

x^2 + 7x - 7x - 49 .... distribute

1x^2 + 0x - 49

We get the same result.

-------------

Lastly, a shortcut can be used as yet another method to expand.

The shortcut is the difference of squares rule

(a + b)(a - b) = a^2 - b^2

In this case, a = x and b = 7, so,

(a + b)(a - b) = a^2 - b^2

(x + 7)(x - 7) = x^2 - 7^2

(x + 7)(x - 7) = x^2 - 49

(x + 7)(x - 7) = 1x^2 + 0x - 49

Answer:

t≤4

Step-by-step explanation:

58.40≥36+5.60t  

Solve like any equation

58.40≥36+5.60t  subtract 36 from both sides

22.40≥5.60t  divide by 5.60

t≤4

Answer:

(0, 2)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define systems

-2x - 8y = -16

2x - 7y = -14

Step 2: Solve for y

Elimination

Step 3: Solve for x

Step 4: Graph

Check the system.

Answer:

I believe the answer is the triangle has an area of 256 inches. I may be wrong though.

Step-by-step explanation:

Answer:

128  in²   but only type 128 to complete the answer

Step-by-step explanation:

Answer:it would be 15 quarters and 10 dimes

Step-by-step explanation:

15 quarters is 3.75 and 10 dimes is $1, add them up you get $ 4.75

Answer:

15 quarters and 10 dimes

Step-by-step explanation:

25x + 10(25-x) = 475

x = 225/15

x = 15

So that has to mean he has 10 dimes

Hope this helps!!!

Answer:

x < 16

Step-by-step explanation:

4x < 64

To solve for x, we simply divide by 4 on both sides. This results us with:

x < 16

#teamtrees #WAP (Water And Plant)

4x <64

Divide both sides by 4:

x < 16

Answer:

n+n= 2n

[tex](3n) ^{2} = 9n ^{2} [/tex]

5(n+2)=5n+10

2(n+1)=2n+1

[tex]n \div 4 = \frac{n}{4} [/tex]

[tex]n(n - 2 = n{2} - 2n[/tex]

Answer:

A=14.4 dollars

B= x = regular price x discount then subtract the regular price with the discount

C=21.6 dollars

Step-by-step explanation:

Answer:

what are the fractions

Answer:

answer 28ab³ I think maybe

The area of the right-angled triangle is represented as the monomial [tex]12a^3b^4[/tex].

Here,

The formula to calculate the area of a right-angled triangle is:

Area = (1/2) * base * height

In this case, the right-angled triangle has a height of [tex]6ab^3[/tex] and a base of [tex]4a^2b[/tex].

Now, let's substitute these values into the formula:

Area = [tex](1/2) * 4a^2b * 6ab^3[/tex]

Now, simplify the expression:

Area = [tex]2 * a^2b * 6ab^3[/tex]

To find the monomial representation, multiply the coefficients and add the exponents of like terms:

Area = [tex]12a^{(2+1)}b^{(1+3)[/tex]

Finally, simplify the exponents:

Area = [tex]12a^3b^4[/tex]

So, the area of the right-angled triangle is represented as the monomial [tex]12a^3b^4[/tex].

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Answer:

Cousin has a greater range of score.

Step-by-step explanation:

Range = Highest No. - Lowest No.

Range of cousin's score = +6 - (-2)

                                        = +6+2 = 8

Range of friend's score = -2 - (-3)

                                       = -2 + 3  = 1

Cousin has a greater range of score.

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

Answer is D

Step-by-step explanation:

Answer:

The answer would be D.

Step-by-step explanation: