Simplify each sum or difference. State any restrictions on the variables.
1/2x + 1 / 2x

Answer:

EF = 10

Step-by-step explanation:

DE + EF = DF

So, x + 22 + x + 23 = 21

2x + 47 = 21

2x = -26

x = -13

EF = x + 23

EF = 10

An ordered list of terms is a Mathematical Sequences.

In mathematics, informally speaking, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements, or terms). The number of ordered elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence.

Most precisely, a sequence can be defined as a function whose domain is a countable totally ordered set, such as the natural numbers. For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in this example, or infinite, such as the sequence of all even positive integers (2, 4, 6,...). Finite sequences are sometimes known as strings or words and infinite sequences as streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.

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Yes, the given set of numbers can be the measures of the sides of a triangle. The triangle is right-angled.

By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

4.5 + 20 > 20.5

20 + 20.5 > 4.5

20.5 + 4.5 > 20

Hence, these set of numbers can be the measures of the sides of a triangle.

According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:

acute if [tex]a^{2} + b^{2} < c^{2}[/tex]

obtuse if   [tex]a^{2} + b^{2} > c^{2}[/tex]

right if   [tex]a^{2} + b^{2} = c^{2}[/tex]

∴The longest side is 20.5.

Hence, a = 4.5, b = 20 and c = 20.5.

Consider  [tex]a^{2} + b^{2}[/tex] :

= [tex]4.5^{2} + 20^{2}[/tex]

= 420.25.

Now consider [tex]c^{2}[/tex] :

= [tex]20.5^{2}[/tex]

=420.25.

Thus,  [tex]a^{2} + b^{2} = c^{2}[/tex]

Hence, the triangle is right-angled.

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Step-by-step explanation:

-2(x+4)=-3x+x-8

Movemos todos los términos a la izquierda:

-2(x+4)-(-3x+x-8)=0

Sumamos todos los números, y todos los variables

-2(x+4)-(-2x-8)=0

Multiplicamos paréntesis

-2x-(-2x-8)-8=0 Eliminamos

paréntesis

-2x+2x+8-8=0

Sumamos todos los numeros juntos, y todas las variables

=0

x=0/1

x=0

Multiplicative Identity Property

Using math properties like the multiplicative identity property we can solve different expressions and equations.

Definition of Multiplicative Identity Property

The multiplicative identity property states that any number multiplied by 1 equals itself. This means that 18 x 1 = 18. Of course, since this is a property we can apply this idea to any equation.

All of the statements above are true because of the multiplicative identity property.

Uses of the Multiplicative Identity Property

While being able to do simple operations with this property is helpful, there are other uses as well. One of the most prominent uses is finding a great common factor. When adding or subtraction fractions, you must have a GCF. We can use the multiplicative identity property to do this.

Take the expression

To solve this we must multiply [tex]\frac{2}{3}[/tex] by [tex]\frac{2}{2}[/tex]. The multiplicative identity property tells us that since 2/2 = 1, this will not affect the value of the expression (remember that anything times 1 is still equal to itself).

Then, we can solve the expression.

Answer:

Thus, the length of the arc AB will be 5/18 of the circumference of the circle, which equals 2πr, according to the formula for circumference. length of arc AB = (5/18)(2πr) = (5/18)(2π(18)) = 10π. Thus, the length of arc AB is 10π.

Step-by-step explanation:

The 7 days will he have to work per month to make either choice equal financially.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Adam can rent an apartment in the city and walk to work for $615 per month.

He can rent for $500 per month and take the train to work for $5 per day.

According to given question we have

Total rent =$615 per month.

Rent an apartment in the suburbs = $500 per month

train to work= $5 per day

train to work in a month=$5*30=  $150 per month

So, total Rent an apartment in the suburbs

=$500 per month+$150 per month

=$650 per month

Difference

=$650 per month- $615 per month.

=$ 35 per month

$5day==$ 35  month

1 day= $ 35 /5 = $ 7 per month

To work per month to make either choice equal financially in 7 days.

Therefore, the 7 days will he have to work per month to make either choice equal financially.

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Answer:

A. -148

Step-by-step explanation:

3x³ - 2x² + 7y

3(-3)³ - 2(-3)² + 7(-7)

3(-27) - 2(9) - 49

-81 - 18 - 49

-148

I hope this helps!

The boxes will be 1.2 times taller than old boxes.

We are given that increase in amount of juice is achieved by keeping the base same but increasing the height only. So, we are aware that length and width are part of base but height is not. Now, there will 20% increase in volume, so finding the increase in height when volume of boxes is increased.

V₁ = V₂

L₁×B₁×H₁ = L₂×B₂×H₂

We know,  L₁B₁ = L₂B₂

So, relating the height of boxes -

H₂ = H₁ (1 + 20%)

H₂ = H₁ (1 + 0.2)

H₂ = H₁×1.2

H₂ =1.2 H₁

Hence, the larger boxes will be 1.2 times taller than old boxes.

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The slope of the line is - 2 / 5

The equation in standard form is as follows:

2x + 5y = -15

The slope of the line can be found as follows;

using (0, - 3)(5, - 5)

m = -5 + 3 / 5 - 0

m = -2 / 5

slope = -2 / 5

The slope intercept form representation of an equation is as follows:

y = mx + b

where

Therefore,

y = -2 / 5 x + b

using (0, -3),

-3 = - 2 / 5 (0) + b

b = -3

Hence,

y = - 2 / 5 x - 3

The standard form is as follows:

Ax + By = C

Therefore, the equation in standard form is as follows:

2 / 5 x + y = - 3

2x + 5y = -15

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The area of the rectangle if both the length and the width of the rectangle are doubled is 340 yd²

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the length and y represent the width of the rectangle. The area is 85 yd², hence:

xy = 85

If both the length and the width of the rectangle are doubled:

new length = 2x; new width = 2y

new area = 2x * 2y = 4xy = 4(85) = 340 yd²

The area of the rectangle if both the length and the width of the rectangle are doubled is 340 yd²

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Her consumption of x is mathematically given as

x=8

Generally, the equation for Slope  is  mathematically given as

u=x^2y^2 ....1

Therefore

[tex]$ slope=-\frac{m u x}{m v_y}=\frac{-2 x y^2}{2 x^2 y}$[/tex]

slope=-y/x

y=0.875 x

Substitute in (1)

[tex]u=x^2(0.875 x)^2=3136 \\[/tex]

[tex]0.875^2 x^4=3136 \\[/tex]

[tex]x^4=4096[/tex]

x=8

y=7

In conclusion,

x=8

y=7

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Answer:

la correcta es verdadero

The inverse of a function is a mirror image of a graph around y = x thus graph in (A) will be the inverse of a function y = m(x).

The inverse of a function is basically a reverse function or undo of the function.

It means in the inverse function we need to interchange x and y.

Let's consider a function y = 2x + 3

The inverse of y is ⇒ y = (x - 3)/2

Now,

If we draw both graphs, both are mirror images of each other about x = y (as shown below).

Therefore y = m⁻¹(x) will be the mirror image of y = m(x) about y = x.

In option (A) the graph is the only mirror image of graph y = m(x).

Hence "The graph in option (A) shows the inverse of function y = m(x)".

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The explicit formula for the given geometric sequence is: [tex]a_n=2^n[/tex].

Now, Given sequence: 2, 4, 8, 16, ...

=> 2¹, 2², 2³, 2⁴, ....

Thus, the explicit formula for this geometric sequence will be given by:  [tex]a_n=2^n[/tex].

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Answer:

B. Divide both sides by 26

Explanation:

When doing a one step equation you basically want to get the x alone. To do that you need to divide 26x by 26.

26x = 74

26 26

x = 2.8

The ratio of the area of circle X to the area of circle Y is  0. 11

The formula for area of a circle is expressed as;

Area = πr²

Where; 'r' is the radius

For circle X, radius = 1/ 3 meter

Let's find the area

Area = 3. 142 × (1/3)²

Area = 3. 142 × 1/ 9

Area = 0. 35 square meters

For circle Y, radius = 1

Area = 3. 142 × 1²

Area = 3. 142 × 1

Area = 3. 142 square meters

Ratio of circle X to circle Y

= 0.35/ 3. 142

= 0. 11

Thus, the ratio of the area of circle X to the area of circle Y is  0. 11

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Answer:

(0, 8)

(1, 7)

(2, 6)

(3, 5)

(4, 4)

(5, 2)

(6, 1)

Step-by-step explanation:

y - 8 = -x

  +8    +8

y = -x + 8

Slope: -1

             8(*)

              7 -  *

              6 -     *

              5 -          *

              4 -               *

              3 -                    *

              2 -

              1  -

----|-----|-----|---|----|---|--|----|-

                0   1   2   3 4   5

I hope this helps!

Answer:

The answer is 470(32-n).

Step-by-step explanation:

Given:

There were 32 volunteers to donate blood. Unfortunately, n of the volunteers did not meet the health requirements, so they couldn't donate. The rest of the volunteers donated 470 milliliters each.

Now, to find milliliters of blood the volunteers donate.

Total volunteers = 32.

The number of volunteers couldn't donate = n

The rest of volunteers who donated = 32 - n

Milliliters of blood the rest of each volunteers donated = 470 milliliters.

Now, to get the milliliters of blood the volunteers donate, we multiply the number of rest of volunteers who donated blood by the milliliters of blood they donated: 470(32 - n)

Therefore, the answer is 470(32-n).

As we are told that J is between H and K on line segment HK so HJ and JK becomes two different line segments on the same line segment HK

Using the segment addition postulate and the  given values of line segments HJ, JK & HK, we first need to find out the value x first

As we know HJ + JK= HK

                  4x+9 + 3x+3 = 33

                   7x +12 = 33

                   7x= 33-12

                  7x=21

                   x= 21/7

                   x= 3

Hence the values of

Line segment HJ = 4x + 9 = 4× 3+ 9=21

Line segment HJ = 3x + 3 = 3× 3+ 3=12

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                 2x + 3.50y = 225

Given that:

To find:

So, according the question,

Let's assume Delvin sold x pound of strawberries and y pound of blueberries to make $225.

From question,

  if, 1 pound of strawberries = $2

  So, x pound of  strawberries = $2 × x = $2x.

Similarly,

   if, 1 pound of blueberries = $3.50

  So, y pound of  blueberries = $3.50 × y = $3.50y.

Now, we can say that,

    x pound of  strawberries + y pound of  blueberries = $225.

                       2x + 3.50y = 225 -------------(1)

Equation (1) is the system of equation of the question.

In comparison to strawberries, Dalvin sold twice as many pounds of blueberries.

So,

               y = 2x -----------(2)

Now, putting the value of y from eq(2) in the system of equation of the question.

So, we will we get

                       2x + 3.50y = 225 -------------(1)

                 2x + 3.50 × 2x = 225

                             2x + 7x = 225

                                     9x = 225

                                       x = 225/9

                                       x = 25

Now, putting the value of x in eq(2)

So, we will we get

                                       y = 2x -----------(2)

                                       y = 2 × 25

                                       y = 50

Answer:

                 2x + 3.50y = 225

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Answer:1:4

Step-by-step explanation:there are 3 months with the letter j and 12 months so 1:4

Answer:

Ratio of the number of months that begin with the letter J to the total number of months in a year is:

1:4

Step-by-step explanation:

Total number of months in a year=12

Months starting with J are:

January  June  July

Total months starting with J=3

Ratio= 3:12

    =1:4

Hence, ratio of the number of months that begin with the letter J to the total number of months in a year is:

1:4

Answer:

im guessing c?

Step-by-step explanation:

Katty rode the roller coaster four times after riding the slide eight times.

Let R be the number of times she rode the roller coaster

Let S be the number of slides

The following mathematical equation can be created using the information provided:

R + S = 12. ........(i)

25R + 10S = 180 .......(ii)

From equation i, R = 12 - S.

Therefore, 25(12 - s) + 10s = 180

300 - 25s + 10s = 180

300 - 15s = 180

15s = 300 - 180

15s = 120

S = 120/15

S = 8 ,

Therefore R = 12 - S = 12 - 8 = 4

Katty rode the roller coaster four times after riding the slide eight times.

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The nth term of the given geometric sequence, 3, 12, 48, 192, . . . , is a(n) = 3[4^(n - 1)], where a(n) is the nth term.

A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.

a(n) = a r^(n-1)

Where:

a(n) = nth term

a = first term

r = ratio

Given the geometric sequence 3, 12, 48, 192, . . .

Find the ratio,

r = a(n)/a(n-1)

r = a(2)/a(1)

r = 12/3

r = 4

Notice that the ratio between two succeeding terms is always 4.

Substitute the value or r and the first term to the formula to determine expression for the nth term.

a(n) = a r^(n-1)

a(n) = 3[4^(n - 1)]

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By elimination, the solution of the system of equations, x + 2y = 10 and x + y = 6, is (2 , 4).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

Subtracting the two equations will eliminate the variable x.

x + 2y = 10     (equation 1)

x +   y = 6     (equation 2)

0x + y = 4

y = 4

Substitute the value of y to any of the two equation and solve for x.

x + 2y = 10     (equation 1)

x + 2(4) = 10

x = 10 - 8

x = 2

Hence, the solution of the system of equations is (2 , 4).

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The equation of the line y = 6x has 0 and 0 as its x- and y-intercept, respectively.

The equation of a line is an equation containing variable(s) and constant(s) and can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The x-intercept of a line is the value of x when y = 0 while the y-intercept of a line is the value of y when x = 0.

For an equation written in standard form ax + by = c, the x- and y-intercept is as follows:

x-intercept = c/a

y-intercept = c/b

If the equation of the line is y = 6x, then its x- and y-intercept is as follows:

x-intercept = c/a = 0/6 = 0

y-intercept = c/b = 0/1 = 0

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The linear equation that represents this situation is given by 3.80+2.25m=33.05. the number of miles travelled is approximately 13.89 miles.

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution.

Here it is given that the total fare is $33.05

The base fee for the cab is $3.80

Cost per mile is $2.25

Let the distance from Fwam's house and airport be m miles.

Therefore total cost for m miles=2.25m

Total Cost for the cab ride= 3.80+2.25m

But the total cost is $33.05

Hence:

3.80+2.25m=35.05

or, 2.25m=31.25

or, m=13.88888

or, m≈13.89 miles

Hence the distance from the house to the airport is approximately 13.89 miles , which can be calculated from the linear equation:  3.80+2.25m=35.05.

Disclaimer: the complete question is :

Fwam took a taxi from his house to the airport. The taxi company charged a pick-up fee of $3.80 plus $2.25 per mile. The total fare was $33.05, not including the tip. Write and solve an linear equation which can be used to determine m, the number of miles in the taxi ride.

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Answer:

10,168 sq m

Step-by-step explanation:

The are of the cover is

the area of the circular portion of the pool + area of square portion - area common to both circular and square portions

The common portion is 1/4the the area of the circle

The radius of the circular portion = 80-40 = 40m

Area of circular portion = πr² = π (40)³ = 1600π sq m

1/4 this is 160/4 = 400 sq m

Area of square = 80² = 6400 sq m

Total area = 1600π + 6400 - 400π = 1200π + 6400 = 1200 x 3.14 + 6400

= 10,168 sq m

Answer:

hihihihi

Step-by-step explanation:

Step-by-step explanation:

because you need 2 numbers that

(+)=7

and

(x)=8

no 2 whole numbers work

it will have to be decimals

so you can't factorise

so you have to use the quadratic formula

hope this helps :)

Answer:

Step-by-step explanation:

if a quadratic of this form can be factorised the factors are

(x + a)(x + b).

In this case a*b would be = + 8 and a + b would be + 7.

There are no integer values which will give these 2 results so x^2 + 7x + 8 cannot be factorised.

An example of a quadratic that can be factories is x^2 + 8x + 7,

because ab = 7 *1 and a + b = 7 + 1 = 8 so the factors are:

(x + 1)(x + 7).