Narek and his family are driving home from vacation and
plan on taking their time. They drive the same amount of
miles every day. After 4 days of driving, they are 400
miles from home. After 8 days of driving, they are 250
miles from home. Let x represent the number of days
Narek and his family are driving home from vacation and
y represent how far away from home (in miles) they are.

Answer:

x = 1/3

Step-by-step explanation:

•3x - 1 = 1 - 3x *group like terms*

•3x + 3x = 1 + 1 *remember whenever you transpors the sign changes*

•6x/6 = 2/6

• x = 1/3

Answer:

[tex] \sf \: 19c + 30 [/tex]

Step-by-step explanation:

Given expression,

→ 1(19c + 30)

Let's simplify the expression,

→ 1(19c + 30)

→ 1(19c) + 1(30)

→ (1 × 19)c + (1 × 30)

→ (19)c + (30)

→ 19c + 30

Hence, answer is 19c + 30.

Answer:

x=44

Step-by-step explanation:

x32=10+x/2

Multiply the 2 from x over 2 to reverse the division equation.

2*x32=10+x/2*2

That results in 2 multiplying 32x and 2 multiplying the 2 in x over 2.

Because multiplication is the reverse of division, the 2's will cancel out and reduce x over to 2 to simply x.

2*32 is 64, include the x before the 64 just like the given equation exemplifies with the x before the 32.

The equation looks like the following once put together: x64=10+x

Subtract the x from the 10+x side of the equation underneath the x64.

x64=10+x

-x          -x

Which equals x63=10.

To receive the answer to this question, you have to divide the 63 on both sides.

63 divided by 63x leaves you with just the x.

63 divided by 10 leaves you with 6.3 in decimal form.

Thus, x equals 6.3.

To check if it's right, insert 6.3 for both x's.

(6.3)*32=10+(6.3)/2

Solve.

201.6=10+3.15

201.6=13.15

Clearly, this doesn't work.

So, I'm assuming you actually meant: 32=10+x/2.

Hence, you would multiply 2 on both sides.

2*32=10+x/2*2

We've established that 32*2 is 64 and the 2's would cancel out.

64=10+x

Subtract the 10 on both sides.

54=x

To see if this one is correct, plug in 54 to the x.

32=10+(54)/2

Divide 54 by 2 which equals 27.

32=10+27

32=37

Nope, that doesn't work either.

Thus, instead of multiplying by 2, we would first need to subtract the 10.

32=10+x/2

-10 -10

32-10 is 22 and it would leave the other side with just x over 2.

22=x/2

Now, we would have to multiply the 2 on both sides.

22*2=44 and x/2*2 gives us x.

So, 44=x.

Let's check.

32=10+(44)/2

32=10+22

32=32

Finally, we have our match.

In conclusion, x=44.

Hope this helps.

Answer: 3x=13

Step-by-step explanation:

The person is blind. They did what they were supposed to except the fact that they didn't multiply the 8 by the -1.

Answer: The error is in step 3

Explanation:

In step 2, they multiplied both sides by 8 to clear out the fractions. In step 3, they forgot to distribute the 8 to each term inside the parenthesis.

This is what the steps should look like

[tex]\frac{3\text{x}}{8}-1=\frac{5}{8}\\\\\\8\left(\frac{3\text{x}}{8}-1\right)=8\left(\frac{5}{8}\right)\\\\\\3\text{x}-8 = 5\\\\\\3\text{x} = 13\\\\\\\text{x} = \frac{13}{3}\\\\\\[/tex]

In step 4, we added 8 to both sides. Afterward, divide both sides by 3 to fully isolate x.

The improper fraction 13/3 is the same as the mixed number 4 & 1/3.

Answer: 45 yrs old

Step-by-step explanation:

Car A  = 9 yrs old

Car B = X yrs old

The ratio for the cars are

Car A : Car B

or

2 : 5

You want to make it easier to read so you make both the ratio number and the given age number (9) the same number.

Multiply Car A age by 2 to make it 18 and the Ratio 2 by 9 to make it 18. This makes them the same number. Since you did this to one side, you have to do it on the other side by multiplying the 5 by 9 which is 45.

Your new ratio is now

18 : 45

This means Car B is 45 yrs old

The equation x + 7 = 2 will have the value of x as 5.

We are given the equation:

x + 2 = 7

We need to solve the equation to find the value of x.

We will first subtract 2 from both the sides:

x + 2 - 2 = 7 - 2

So, subtracting 2 from both the sides, we get that:

x = 5

the value of x for the equation will be 5.

Therefore, the equation x + 7 = 2 will have the value of x as 5.

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See attachment for the graph and the function is a continuous function.

The function definition is given as:

f(x) =  [ x-4 if x < 2

         [-2x+2 if x ≥2

The above function is a piecewise function.

So, we plot each function by its domain

Having said that, the next step is to plot the graph of the functions in f(x) according to their domain

See attachment for the graph

Also, the function is a continuous function.

This is so because there is no break in the function value i.e. domain and range are the set of all real values

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Each pound of brand B costs 0.33 dollars less than each pound of brand A.

Here we need to find the cost per pound for both brands, to get that, we need to get the quotient between the costs and the number of pounds.

For brand A the cost is $37.80 and you get 35 pounds, then the cost per pound is:

A = $37.80/35 = $1.08

Then each pound for brand A costs 1.08 dollars.

Now let's do the same for brand B, the cost is $33.75, and you get 45 pounds, then the cost per pound is:

B = $33.75/45 = $0.75

Then each pound for brand B costs 0.75 dollars.

So brand B is cheaper, and the difference is:

1.08 dollars -  0.75 dollars = 0.33 dollars.

Each pound of brand B costs 0.33 dollars less than each pound of brand A.

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The fraction of the carpet covered by the rug will be 1/15.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L×W square units

A rectangular carpet estimates 10 m by 6m. Some portion of the rug is covered by a square rug of length 2 m.

The area of the carpet is given as,

A = 10 x 6

A = 60 square meters

The area of the rug is given as,

a = 2 x 2

a = 4 square meters

A fraction of the carpet is covered by the rug is given as,

⇒ 4 / 60

⇒ 1 / 15

A fraction of the carpet covered by the rug will be 1/15.

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The missing diagram is attached below.

Answer:

Step-by-step explanation:

4+2=6

6/2=3

Answer: 12

Step-by-step explanation: we know that a^2 + b^2 = c^2, pythagorean theorem. We're given a and c in this case, which are 16 and 20 respectively. so that means 16^2 + x^2 = 20^2. After evaluating the equation, we get 256+ x^2 =400. now subtract 256 from both sides and then we get x^2 = 144. take the square root of both sides and we end up with x = 12.

Answer:

A

Step-by-step explanation:

[tex]450 - 300 = 150 \\ 150 \div 2 = 75t \\ the \: average \: rate \: of \: growth \: per \: year \: is \: 75 \: student \: per \: year[/tex]

The abbreviated formula is -4xy (5x(x-y) - y(4x + y)).

The answer to the question is that common words outside of the brackets can be used to simplify the supplied equation.

Therefore,

Required expression is -4xy(5x2 - 9xy -y2), which is equivalent to -4xy(5x2 - 5xy - 4xy -y2).

The final formula will be: -4xy(5x(x-y) - y(4x + y)).

Therefore, the abbreviated formula is: -4xy(5x(x-y) - y(4x + y)).

In mathematics, simplification is a technique that makes a complex equation simpler in a less complex way. This approach makes expression calculation possible.

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Here is a diagram of a straightedge and compass construction. c is the center of one circle, and b is the center of the other. Since both segments begin at point B, their lengths are equal.

Both segments begin at point B, their lengths are equal.

Since the radius of the smaller circle is the distance from its center (B) to its edge, length BD equals length AB.

Using the attached diagram

The larger circle's center is at C, while

Point B is the location of the smaller circle's center.

The smaller circle passes through the larger circle, dividing it into two segments, BD and AB, which extend from the smaller circle's center to their intersecting edges.

As a result, since both segments begin at point B, their lengths are equal.

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Using the concept of even and odd functions, it is found that, considering the function has a local max at (-1,3):

For a function increasing on [2,5], we have that:

Hence, considering the function has a local max at (-1,3):

For a function increasing on [2,5], we have that:

For even functions it will decrease because we have that f(4) > f(3), for example, hence f(-4) > f(-3).

For the odd function it will increase because if f(4) > f(3), then f(-3) > f(-4) due to the negative signal.

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Using it's concept, the range of the function f(x) = -x + 5 in the domain [-3,2] is [3,8], and the graph is given at the end of the answer.

The range of a function is the set that contains all possible output values of the function for a given domain(set of input values). In a graph, the range is given by the vertical axis, that is, by the values of y.

From the graph shown at the end of the answer, y assumes values between 3 and 8, hence the range is of [3,8].

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Answer: (1/75)

Step-by-step explanation:

[{6*(10^4)*(3^3)}/{(6^5)*(5^6)}]

= (1/75)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{6\times10^4\times3^3}{6^5\times5^6}}[/tex]

[tex]\mathsf{= \dfrac{6\times10\times10\times10\times10\times3\times3\times3}{6\times6\times6\times6\times6\times5\times5\times5\times5\times5\times5}}[/tex]

[tex]\mathsf{= \dfrac{6\times100\times100\times9\times3}{36\times36\times6 \times25\times25\times25}}[/tex]

[tex]\mathsf{= \dfrac{6\times 10,000\times9\times3}{1,296\times6 \times 625\times5}}[/tex]

[tex]\mathsf{= \dfrac{60,000\times 27}{7,776\times 15,625}}[/tex]

[tex]\mathsf{= \dfrac{1,620,000}{12,150,000}}[/tex]

[tex]\mathsf{= \dfrac{1,620,000\div 1,620,000}{12,150,000\div1,620,0000}}[/tex]

[tex]\mathsf{= \dfrac{1}{75}}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{1}{75}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The Perimeter of polygon ABCD = 21.6 units.

The perimeter of figure ABCD = sum of all its sides = AB + BC + CD + AD.

To find each of the sides, apply the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

A(-5, 5)

B(0, 3)

C(-2, -2)

D(-7, 0)

AB = √[(0−(−5))² + (3−5)²]

AB = √29

AB ≈ 5.4 units

BC = √[(0−(−2))² + (3−(−2))²]

BC = √29

BC ≈ 5.4 units

CD = √[(−7−(−2))² + (0−(−2))²]

CD = √29

CD ≈ 5.4 units

AD = √[(−7−(−5))² + (0−5)²]

AD = √29

AD ≈ 5.4 units

The Perimeter of polygon ABCD = 5.4 + 5.4 + 5.4 + 5.4 = 21.6 units.

Therefore, the Perimeter of polygon ABCD = 21.6 units.

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Answer:

8456/1000 Is the fraction of 8.456

Answer:

1057/125

Just write the number in a calculator and press equal. It'll give you the number in fraction

Two column proof is a way to portray proofs in geometry.A two column proof always has two columns, one for statement and the other for reason.

The rules of a two column proof are, every statement should be numbered, every statement should have a reason. There is no order for the statements but it is better to maintain logocal order.Reasons for the statements are theories, previously proved theorems that justify the statement.

A,B,C,D are on a line and we have to prove that if AB=CD then AC=BD

Statements                                                  Reasons

1.A,B,C,D are collinear                               1.given

2.AB=CD                                                     2.given

3.BC=BC                                                     3.reflexive

4.AB+BC=BC+CD                                       4.adding 2 and 3

5.AB+BC=AC and BC+CD=BD                  5. Segment addition

6.AC=BD                                                     6.Substitution

Thus it is proved by two column proof that if AB=BC then AC=BD

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We can use inequality, 24. |m| greater than or equal to 10 then the possible to value is =  |14|.

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Based on the given conditions, formulate,

24. |m| greater than or equal to 10

So, we can write,

24 + m ≥ 10

m ≥ 10 - 24

We can sum or difference,

m ≥ -14

Then,

|m| ≥ |-14|

Hence,

|m| ≥  |14|

Therefore,

24. |m| greater than or equal to 10 then the possible to value is =  |14|.

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Answer:

-175

Step-by-step explanation:

thats the answer to the question

The number of 8-inch long pieces of ribbon that the other class cut is 9.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

Given that Students in 3 art classes cut 728 inches of ribbon into 8-inch long pieces. Therefore, the number of ribbon that 3 classes together cut is,

Number of ribbon cut by 3 classes together = 728 inches / 8 inches = 91

Further, it is given that two of the classes together cut 656 inches of ribbon. Therefore, the number of ribbon that 2 classes together cut is 656.

Number of ribbon cut by 2 classes together = 656 inches / 8 inches = 82

Now, the number of  8-inch long pieces of ribbon that the other class cut can be written as,

Number of pieces cut by other class

= Number of ribbon cut by 3 classes together - Number of ribbon cut by 2 classes

= 91 - 82

= 9

Hence, the number of 8-inch long pieces of ribbon that the other class cut is 9.

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Answer:

Uhh the answer should be x^3 + y^3 + z^3 for k

Step-by-step explanation:

That's what it says in question, which is the answer.

Pls brainlieset :0?

Answer:

g=−28

Step-by-step explanation:

-74 = g/7 + -70

Let's solve your equation step-by-step.

−74=g/7−70

Step 1: Simplify both sides of the equation.

−74=g/7−70

−74=1/7g+−70

−74=1/7g−70

Step 2: Flip the equation.

1/7g−70=−74

Step 3: Add 70 to both sides.

1/7g−70+70=−74+70

1/7g=−4

Step 4: Multiply both sides by 7.

7*(1/7g)=(7)*(−4)

g=−28

Answer:

17

Step-by-step explanation:

[tex]\sf |-3d-6|+|-5-d^2| \quad for\:\: d = -3[/tex]

Given expression:

[tex]\sf |-3d-6|+|-5-d^2|[/tex]

substitute d = -3

[tex]\sf |-3(-3)-6|+|-5-(-3)^2|[/tex]

simplify following inside parenthesis

[tex]\sf |9-6|+|-5-9|[/tex]

simplify by combining integers

[tex]\sf |3|+|-14|[/tex]

if |-a| or |a| then equals to a

[tex]\sf 3+14[/tex]

evaluate:

[tex]\sf 17[/tex]

Answer:

17

Step-by-step explanation:

Given expression:

[tex]|-3d-6|+|-5-d^2|[/tex]

To evaluate for d = -3, substitute d = -3 into the expression:

[tex]\implies |-3(-3)-6|+|-5-(-3)^2|[/tex]

[tex]\textsf{Apply exponent rule} \quad a\cdot a=a^2:[/tex]

[tex]\implies |(-3)^2-6|+|-5-(-3)^2|[/tex]

[tex]\textsf{Apply exponent rule} \quad (-a)^2=a^2:[/tex]

[tex]\implies |3^2-6|+|-5-3^2|[/tex]

[tex]\implies |9-6|+|-5-9|[/tex]

Subtract the numbers:

[tex]\implies |3|+|-14|[/tex]

[tex]\textsf{Apply absolute rule} \quad |a|=a, \quad a\geq 0[/tex]

[tex]\implies 3+|-14|[/tex]

[tex]\textsf{Apply absolute rule} \quad |-a|=a, \quad a > 0[/tex]

[tex]\implies 3+14[/tex]

Add the numbers:

[tex]\implies 17[/tex]

in fig. 3.1 the value of  x  is 20° , in fig. 3.2 the value of  x  is 40° ,  in fig.  the value of  3.3 x  is 10° ,  in fig. 3.4 the value of  x  is 120°.

In planar geometry, an angle is a shape made up of two rays or lines that share an endpoint. The English word "angle" derives from the Latin word "angulus," which means "corner." The vertex and the two rays are referred to as the sides of an angle, respectively, and are the shared termini of two rays.

3.1

straight lines makes an angle of 180° thus ,

              x + 2x + 120 = 180

                3x = 60

                  x = 20°

3.2

    sum of the angles of triangle is = 180°

     105 + 35 + x = 180

      140 + x = 180

       x = 40°

3.3

       since it is an isoceles triangle so the opposite angles to equal sides are equal

140 + 4x = 180

4x = 40

x = 10°

3.4

parallel  line theorem  state that alternate angles are equal

so ,

    180= x + 60

x = 120 °

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Answer:

The true statements are the 1st, 2nd, and 4th statement.