If the graphs of the linear equations in a system are parallel, what does that mean about the possible solution(s) of the system?

Answer:

I don't know what the following sentence is:

But D is the equation to represent the situation

and A is what turns out to be his current age.

(If you want more help, on this question please post the following sentence).

Step-by-step explanation:

Let x represent the current age.

15 years from now his age is 3 times his age 5 years ago means we have the equation:

x+15=3(x-5)

(I added x to 15 because we said 15 years in the future)

Let's solve this to see if makes any sense just for fun:

Distribute:

x+15=3x-15

Add 15 on both sides:

x+30=3x

Subtract x on both sides:

   30=2x

Divide both sides by 2:

   15=x

So this means his current age is 15.

5 years ago his age would have been 10.

15 years in the future his age will be 30.

Is 30 equal to 3 times 10? Yes, it is! The equation does make sense.

Answer:

D,

Step-by-step explanation:

x is the present age of William, 15 years from now is x+15, and that is equal to  3 times 3() the age he had 5 years ago (x-5)., the equation is  x+15=3(x-5)

Answer:

Step-by-step explanation:

[tex]5^{x-2}=625\\\\5^{x-2}=5^4\qquad(5^4=5\cdot5\cdot5\cdot5=625)\\\\5^{x-2}=5^4\Rightarrow x-2=4\qquad\text{add 2 to both sides}\\\\x-2+2=4+2\\\\x=6\\\\\text{check:}\\\\5^{6-2}=5^4=625\qquad\bold{CORRECT}[/tex]

Answer:

C) m∠5 + m∠6 =180°

D) m∠2 + m∠3 = m∠6

E) m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

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The correct equations are:

m∠2 + m∠3 + m∠5 = 180°

m∠2 + m∠5 =  m∠4

m∠5 + m∠6 = 180°

m∠2 + m∠3 =  m∠6

Equation is an expression used to show the relationship between two or more numbers and variables.

From the diagram:

m∠2 + m∠3 + m∠5 = 180° (sum of angles in a triangle)

But:

m∠3 + m∠4 = 180° (angle in a straight line)  

m∠2 + m∠3 + m∠5 = m∠3 + m∠4

m∠2 + m∠5 =  m∠4

Also:

m∠5 + m∠6 = 180° (angle in a straight line)

But:

m∠2 + m∠3 + m∠5 = 180

m∠2 + m∠3 + m∠5 = m∠5 + m∠6

m∠2 + m∠3 =  m∠6

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Answer:

[tex]\large\boxed{a_n=2(-4)^{n-1}=\dfrac{(-4)^n}{2}}[/tex]

Step-by-step explanation:

The explicit equation of a geometric sequence:

[tex]a_n=a_1r^{n-1}[/tex]

The domain is the set of all Counting Numbers.

We have the first term of [tex]a_1=2[/tex] and the second term of [tex]a_2=-8[/tex].

Calculate the common ratio r:

[tex]r=\dfrac{a_{n-1}}{a_2}\to r=\dfrac{a_2}{a_1}[/tex]

Substitute:

[tex]r=\dfrac{-8}{2}=-4[/tex]

[tex]a_n=(2)(-4)^{n-1}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\a_n=(2\!\!\!\!\diagup^1)\left(\dfrac{(-4)^n}{4\!\!\!\!\diagup_2}\right)\\\\a_n=\dfrac{(-4)^n}{2}[/tex]

Answer:

Step-by-step explanation:

A geometric sequence has a common ratio. in this case the common ratio

r = -8/2 = -4.

The explicit formula is an = 2(-4)^(n-1).

Most likely infinite? Just a guess.

Answer:

Step-by-step explanation:

The question says nothing about repetition, so I'm assuming that 943449 is OK,

This can be solved this way

9 10 10 10 10 9

810,000

Answer:

False because on the left side of the equation you are adding 18 and 35 first and on the right you are multiplying 35 and 4 first. This will give you an unequal equation when solved.

Let's solve each side

(18+35)*4=212

but 18+(35*4)=158

Answer:

First exercise: [tex]x=7[/tex]

Second exercise: [tex]x=2[/tex]

Step-by-step explanation:

Acording to the Intersecting Secants Theorem the products of the segments of two secants that intersect each other outside a circle, are equal.

Based on this, in order to solve the first exercise and the second exercise, we can write  the following expressions and solve for "x":

First exercise:

[tex](5)(5+x)=6(6+4)\\\\25+5x=60\\\\5x=60-25\\\\x=\frac{35}{5}\\\\x=7[/tex]

Second exercise:

[tex](4)(4+x)=3(3+5)\\\\16+4x=24\\\\4x=24-16\\\\x=\frac{8}{4}\\\\x=2[/tex]

Answer:

(1,-1)

That is the ordered pair where they cross.

Step-by-step explanation:

The solution of the system is where the pair of lines there cross at.

The intersection is in the fourth quadrant there so your guess should definitely be of the form (positive, negative).

Only one choice is that and it is B.

It really does look like they cross at (1,-1).

To describe how to get from the origin to the intersection, I would say you would need to travel right 1 unit and down 1 unit.

We can even plug in our pair into both equations and see if it works.

y=x-2

y=4x-5

So if we plug in (1,-1) and assuming it is a solution, then both equations will give us the same thing on both sides. Let's try it:

y=x-2

-1=1-2

-1=-1

That's the same thing on both sides.

y=4x-5

-1=4(1)-5

-1=4-5

-1=-1

Again that is the same thing on both sides.

(1,-1) is indeed our solution.

Both the graph and the verification told us that.

Answer:

1, -1

Step-by-step explanation:

A.P.E.X 2021

Answer:

Step-by-step explanation:

Let CD = x

(x + 40)/2 = 31                  The midline is 1/2 the sum of the 2 bases. multiply by 2 on both sides.

x + 40 = 31 * 2

x + 40 = 62                       Subtract 40 from both sides.

x +40-40 = 62 - 40          Combine

x = 22

Check

(22 + 40)/2

62 / 2

31 = PQ

To find the missing length of a trapezoid with similar triangles inside, we use the ratio of the sides of the triangles, which is approximately 8.667 based on the provided lengths.

When determining the missing length of a trapezoid, we need to consider the properties of similar triangles or the geometric shape of a trapezoid itself. The given information suggests a scenario where similar triangles are within a trapezoid and leads to a proportional relationship between the sides of the triangles. If a trapezoid has triangles within it that share an angle, the lengths of the corresponding sides of those triangles will be proportional.

Based on the data provided, if the long sides of the triangles are in the ratio of 13.0 in to 1.5 in, which simplifies to an approximate factor of 8.667, the bottom sides of the triangles - which are the parallel sides of the trapezoid - will also be in the same ratio. By finding the length of the shorter bottom side, we can divide the length of the longer bottom side by 8.667 to get the missing length on the shorter side.

Answer:

8100

Step-by-step explanation:

Step-by-step explanation:

We want to find the length of the square's diagonal.  Since the square has right angles, we can use Pythagorean theorem.

c² = a² + b²

x² = 90² + 90²

x = 90√2

x ≈ 127.3 feet

Answer:

x = 12

Step 1 helps solve the equation, for it helps isolate the x, which is what you are solving for.

Step-by-step explanation:

Isolate the variable x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS:

Step 1: Add 18 to both sides.

6x - 18 (+18) = 54 (+18)

6x = 54 + 18

6x = 72

Step 2: Divide 6 from both sides:

(6x)/6 = (72)/6

x = 72/6

x = 12

x = 12 is your answer.

~

Answer:

[tex]\huge \boxed{X=12}[/tex]

Step-by-step explanation:

Add by 18 from both sides of equation.

[tex]\displaystyle 6x-18+18=54+18[/tex]

Add numbers from left to right.

[tex]\displaystyle 54+18=72[/tex]

[tex]\displaystyle 6x=72[/tex]

Divide by 6 from both sides of equation.

[tex]\displaystyle \frac{6x}{6}=\frac{72}{6}[/tex]

Simplify, to find the answer.

[tex]\displaystyle 72\div6=12[/tex]

[tex]\huge \boxed{x=12}[/tex], which is our answer.

Answer:

4(x - 5)(x + 3)

Step-by-step explanation:

Given

4x² - 8x - 60 ← factor out 4 from each term

= 4(x² - 2x - 15)

To factor the quadratic

Consider the factors of the constant term ( - 15) which sum to give the coefficient of the x- term ( - 2)

The factors are - 5 and + 3, since

- 5 × 3 = - 15 and - 5 + 3 = - 2, hence

x² - 2x - 15 = (x - 5)(x + 3) and

4x² - 8x - 60 = 4(x - 5)(x + 3)

Answer:

a=11.8,b=12,c=8,A=68.7°, B=72°, C= 39.3°

Step-by-step explanation:

Given data:

b = 12

c= 8

a= ?

∠B= 72°

∠C= ?

∠A=?

To find the missing angle we will use law of sine:

a/sinA=b/sinB=c/sinC

Find m∠C.

b/sinB = c/sinC

Substitute the values:

12/sin72°=8/sinC

Apply cross multiplication.

12*sinC=sin72° * 8

sinC=0.951*8/12

sinC=7.608/12

sinC= 0.634

C= 39.3°

Now we know that the sum of angles = 180°

So,

m∠A+m∠B+m∠C=180°

m∠A+72°+39.3°=180°

m∠A=180°-72°-39.3°

m∠A= 68.7°

Now find the side a:

a/sinA=b/sinB

a/sin68.7°=12/sin72°

Apply cross multiplication:

a*sin72°=12*sin68.7°

a*0.951=12*0.931

a=0.931*12/0.951

a=11.172/0.951

a=11.75

a=11.8 ....

To expand and simplify the expression 4(2x+3)+4(3x+2), distribute the 4 to both sets of parentheses and combine like terms to get 20x + 20.

To expand and simplify the expression 4(2x+3)+4(3x+2), we can use the distributive property of multiplication over addition. The distributive property states that for any numbers a, b, and c, a(b+c) = ab+ac.

First, we distribute the 4 to both terms inside the first set of parentheses: 4 * 2x + 4 * 3. This simplifies to 8x + 12. Then, we distribute the 4 to both terms inside the second set of parentheses: 4 * 3x + 4 * 2. This simplifies to 12x + 8.

Combining the like terms, the final simplified expression is: 8x + 12 + 12x + 8 = 20x + 20.

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Answer:

4  3/8

Step-by-step explanation:

1 7/8 × 2 1/3

Change the numbers to improper fractions

1 7/8 = (8*1 +7) /8 = 15/8

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

15/8 * 7/3

Rearranging

15/3 * 7/8

5/1 * 7/8

35/8

Now we need to change this back to a mixed number

8 goes into 35   4 times with 3 left over

4 3/8

Answer:

35/8 or 4 3/8

Step-by-step explanation:

Change each fraction to improper

15/8 * 7/3

multiply

105/24

reduce

35/8

make it mixed if the answer wants it to be

4 3/8

Answer:

See explanation

Step-by-step explanation:

There 2 black shapes (one circle and one square) and 2 white shapes (1 circle and 1 square).

1. The ratio of the number of white shapes to the number of black shapes is 2:2=1:1.

2. The ratio of the number of white circls to the number of black squares is 1:1.

3. The ratio of the number of black circles to the number of black squaress is 1:1.

4. There are 4 shapes and 2 are circles (1 white and 1 black), so circles are [tex]\dfrac{2}{4}=\dfrac{1}{2}[/tex] of all shapes.

Answer:

* The shorter side is 270 feet

* The longer side is 540 feet

* The greatest possible area is 145800 feet²

Step-by-step explanation:

* Lets explain how to solve the problem

- There are 1080 feet of fencing to fence a rectangular garden

- One side of the garden is bounded by a river so it doesn't need

 any fencing

- Consider that the width of the rectangular garden is x and its length

 is y and one of the two lengths is bounded by the river

- The length of the fence = 2 width + length

∵ The width = x and the length = y

∴ The length of the fence = 2x + y

- The length of the fence = 1080 feet

∴ 2x + y = 1080

- Lets find y in terms of x

∵ 2x + y = 1080 ⇒ subtract 2x from both sides

∴ y = 1080 - 2x ⇒ (1)

- The area of the garden = Length × width

∴ The area of the garden is A = xy

- To find the greatest area we will differentiate the area of the garden

  with respect to x and equate the differentiation by zero to find the

  value of x which makes the area greatest

∵ A = xy

- Use equation (1) to substitute y by x

∵ y = 1080 -2x

∴ A = x(1080 - 2x)

∴ A = 1080x - 2x²

# Remember

- If y = ax^n, then dy/dx = a(n) x^(n-1)

- If y = ax, then dy/dx = a (because x^0 = 1)

∵ A = 1080x - 2x²

∴ dA/dx = 1080 - 2(2)x

∴ dA/dx = 1080 - 4x

- To find x equate dA/dx by 0

∴ 1080 - 4x = 0 ⇒ add 4x to both sides

∴ 1080 = 4x ⇒ divide both sides by 4

∴ x = 270

- Substitute the value of x in equation (1) to find the value of y

∵ y = 1080 - 2x

∴ y = 1080 - 2(270) = 1080 - 540 = 540

∴ y = 540

* The shorter side is 270 feet

* The longer side is 540 feet

∵ The area of the garden is A = xy

∴ The greatest area is A = 270 × 540 = 145800 feet²

* The greatest possible area is 145800 feet²

Answer:

Dividing the number of balloon animal per the time he takes to make them you get an average of how many animals per minute Fred the clown can make.20/15=1,3 animals per minuteSince 0,3 is not a complete animal, the correct answer would be "Fred the clown can make 1 animal in 1 minute

Answer: 15 : 20

               6 : 8

               45 : 60

Step-by-step explanation:

First, you have to divide both numbers by 15:

15//15 = 1

20/15 = 4/3

Now you know that Fred can create 4/3 animal balloons in 1 minute.

If he spent 6 minutes creating animal balloons, then he can create 6 times as many animal balloons:

4/3 x 6 = 8

Now that we figured out the first part, we need to figure out how many he can make in 45 minutes.

We can do this by doing the same thing as we did for the first part, except we multiply 4/3 by 45 minutes:

4/3 x 45 = 60

Now that we figured out both parts, we know that our final answer should be:

15 : 20

6 : 8

45 : 60

Hope this helped! <3

[tex](9x-4)-(3x+2)=9x-4-3x-2=6x-6[/tex]

The probability that a player wins the game by adding the numbers from the slips drawn from the box is 40%. If the rule changes and the player multiplies the numbers instead of adding them, the winning probability increases to 70%.

The game consists of drawing two numbers from the box and verifying whether their sum or product is even or odd. In Mathematics, for the sum to be even, both numbers must be odd or both must be even. If we check, we have 2 odd numbers (7, 9) and 3 even numbers (4, 6, 8). The combinations for even sum could be odd-odd or even-even. The total successful events would be 1 (odd-odd) + 3 (even-even) = 4 out of total 10 possible events (5C2), which gives us the probability of the player winning the game as 4/10 or 40%

Now, whether the probability changes when we multiply instead of adding: Yes, it does! In Mathematics, an even number results when multiplying any number by an even number, regardless of whether the other number is odd or even. Therefore, since 3 out of 5 numbers are even, the probability that the player wins if they multiply the two numbers they select instead of adding them is greater, confirmed by calculating combinations again and we find 7 out of 10 possible events yield an even product, therefore probability is 70%, which is greater than that of adding them.

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Answer:

A.) $56

Step-by-step explanation:

1.  Convert 7% into the numerical version by either

    A. Moving the decimal two spaces to the right, giving us .07

                                               or

    B. Making 7% into a fraction, 7/100

2. Now make an equation with the total amount of money (M) multiplied by the interest (P) inside of parenthesis. This will give us 7% of $800 in your case.

                                        (800 × .07) → 56

3.  Then, multiply by the number of years the interest has been accumulated.

                                              56 × 1

The official equation for this is: a = p(1 + r)^t

a = amount at end (initial amount + interest gained)

p = initial amount

r = rate (percent interest)

t = time in years

The correct option will be option A: Man will receive $56 interest in a year.

Simple Interest amount can be calculated by the product of principal amount, rate of interest, and time.

Simple Interest= S.I. =p*t*r/100

where p is the principal amount,

r is interest rate (in %)

t is the time (in year).

Here, given,

principal amount P = $800

rate of interest= r=7%

time=t=1 year

using the above formula,

Simple Interest S.I.= p*t*r/100= (800*1*7)/100= $56

Therefore man will receive $56 interest in a year.

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Since the example circle is not shown, I can not answer thoroughly, but I will try my best.

The equation of a circle: (x - h)² + (y - k)² = r², where (h,k) is the center and r is the radius of the circle.

This means that for the radius to be two units, the right side of the equation is 2² = 4. So either B or d can be right.

Depending on the center of the given circle, we could narrow down to our final answer. If the center is (4,5), B is right, and if (5,4) is the center, D is right.

Due to the fact the example circle isn't proven, I can't solution thoroughly, but I will attempt my exceptional.

The equation of a circle: (x - h)² + (y - okay)² = r²,

in which (h, ok) is in the middle and r is the radius of the circle.

this means that for the radius to be two devices, the proper facet of the equation is two² = four. So either B or d can be right.

depending on the centre of the given circle, we ought to narrow right down to our very last answer. If the centre is (4, five), B is right, and if (five, four) is in the middle, D is proper.

The equation for a circle is given by:

(x-h)2+(y-k)2 = a2

Where (h,k) is the centre and a is the radius of the circle.

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Answer:

Positive real numbers

Step-by-step explanation:

The domain is all the possible values of x.  Here, x represents the time that the ball falls.

Natural numbers are integers greater than 0 (1, 2, 3, etc.).  However, the time doesn't have to be an integer (for example, x=1.5).

Positive integers are the same as natural numbers.

Positive rational numbers are numbers greater than 0 that can be written as a ratio of integers (1/1, 3/2, 2/1, etc.).  However, the time can also be irrational (for example, x=√2).

Positive real numbers are numbers greater than 0 and not imaginary (don't contain √-1).  This is the correct domain of the function.

The domain for the function ƒ(x) = 1,000 - 16x^2 is Positive Real Numbers.

The domain for the function ƒ(x) = 1,000 - 16x^2 is a set of Positive Real Numbers. This is because in real-world situations, such as the height of an object, negative time values do not make sense, and the function itself involves squaring x, which ensures that the result is positive. Therefore, the appropriate set of numbers as the domain for this function would be Positive Real Numbers.

Answer:

the line will pass through yellow and red

Answer:

its simplest form is 4/5

[tex]\bf \textit{height or altitude of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\ \cline{1-1} s=8\sqrt{3} \end{cases}\implies h=\cfrac{8\sqrt{3}\cdot \sqrt{3}}{2}\implies h=\cfrac{8\sqrt{3^2}}{2} \\\\\\ h=4\cdot 3\implies h=12[/tex]

Answer:

30 times

Step-by-step explanation:

Weight of adult blue whale = [tex]9 \times 10^{4}[/tex] kilogram

Weight of an elephant = [tex]3 \times 10^{3}[/tex] kilogram

In order to find how many times a quantity is as compared to the other quantity, we divide the two. So here we have to divide the weight of adult blue whale by the wight of elephant.

[tex]\frac{9 \times 10^{4}}{3 \times 10^{3}}\\= 30[/tex]

This means, adult blue whale is 30 times heavier than the elephant.