Subtract (-4x - 2) - (13x + 1)

Answer:

B

Step-by-step explanation:

that's obvious

Answer:

Step-by-step explanation:

In 30, 60, and 90 triangles, it includes sides with ratios 1, 2x, and xsqrt3 with 2x reflective of 90, xsqrt3 of 60, and 1 of 30.
So if 2x = 6, then x = 3 so 3sqrt3 = 5.19. Using the Pythagorean theorem we find that the last length is 3.
If xsqrt3 = 3, then x = sqrt3, angle reflective of 90 is 2sqrt3.

The greater angle has a 67.5° degree measurement. When two angles' measurements add up to 90°degrees, they are said to be complimentary.

Call that angle we're looking for "x" for convenience.

The degree that, if added to x, makes x equal 90° degrees is known as the compliment of x.

We now know that 3x, or 3 times x, is the compliment of x.

With this knowledge, we can construct the following equation:

x + 3x = 90°

combining comparable equations;

4x = 90°

x = 22.5°, when both sides are divided by 4.

As a result,

3x = 3(22.5°) = 67.5° degrees is the measurement of the greater angle, which is the complement of x.

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The value of {h} is equivalent to 6/5.

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes.

Given is the function as follows -

(1/5) + h = (7/5)

We can write the function as -

(1/5) + h = (7/5)

h = 7/5 - 1/5

h = (7 - 1)/5

h = 6/5

Therefore, the value of {h} is equivalent to 6/5.

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The runner on first has distance from second of  90 -25t, where t is the time in seconds since he left 1st base.

The runner on second has a distance from second of  15t, where t is the time in seconds since he left 2nd base

Then the Pythagorean theorem tells us the distance between the runners is :

d = √((90 -25t)² +(15t)²)

The rate of change of distance between the runners is the derivative of this with respect to time.

dd/dt = 2(90-25t)(-25)+2(15t)(15) / (2sqrt(90-25t)^2 + 15t^2)

Replace t with 2 and solve to get: -31

The distance between runners is decreasing at 31 ft/s two second after they leave the bases.

Answer:

A.

Step-by-step explanation:

Let's think of this as a clock.  We can see that the 2 lines start in the same place, around 3 o'clock.  Next, one of the line segments shifts down to around 6 o'clock.  Next, it shifts to about 9 o'clock.  Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.

We can also just use a regular circle, with one of the line segments moving 90 degrees each time.

Hope this helps! :)

Answer:

Ans =C(4,1),(-4,1),(4,6),(-4,6)

The slope which shows  the cost per guest is $35 per guest

The given cost for 50 guests is $2150.

The cost for 75 guests is $3025.

It can also be represented as:

(Guest, Cost) =(50, $2150) & (75, $3025)

The slope can now be calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (50, $2150) & (75, $3025)

Substituting the given values in the equation as follows:

Slope = (3025 - 2150)/(75 - 50)

Slope = 35

Hence, the slope is $35 per guest.

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Answer:

the product of the decimal equivalents of all discount in the series

Answer:

The second choice.

Step-by-step explanation:

A rational number means that you are able to write the number as a fraction with integers in the numerator and the denominator.  An integers are the whole numbers and their opposites ...-3,-2,-1,0,1,2,3...

The square root of 4 is 2.  2 can be written 2/1 (an integer over and integer)

-square root of 2 cannot be written as an integer over an integer.  When this number is written as a decimal number it never repeats and it never terminates so it cannot be written as an integer over and integer.

-2/3 is written in the form of an integer over and integer.

1 can be written 1/1

9/8 is written as an integer over an integer.

The square root of  9/4 would be 3/2. (3/2)(3/2) = 9/4.

2.4 repeating can be written as an integer over an integer.  Any decimal that repeats or terminates can be written as an integer over and integer.  It actual happens to be 22/9.

The square root of 10 written as a decimal does not repeat or terminate so it is not rational.  Only perfect squares are rational.

Answer:

The greatest four consecutive numbers whose sum is less than 1,000 are 248, 249, 250, and 251.

Step-by-step explanation:

Let x be the smallest integer. Then:

x + x + 1 + x + 2 + x + 3 < 1,000

4x + 6 < 1,000

2x + 3 < 500

2x < 497

x < 248.5, so x = 248

So we have the integers 248, 249, 250, and 251.

The number of whole cup of milk that Charlene would use for all 8 packages would be = 8 cups of whole milk.

A square is a type of quadrilateral that has four sides with four angle 90° at each edge.

The number of chocolate square mixture Charlene would use for the party = 8 packages.

The number of packages that require a cup of milk = 1

Therefore the number of whole cups of milk that would be used for the whole 8 packages would be = 8×1 = 8 cups of whole milk.

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Given the decimal (approximate) representation of the number 0.54, it's required to find the equivalent fraction of the number.

If we use the exact number 0.54 and find its equivalent fraction, we notice none of the choices matches our result, so we assume 0.54 is an approximate representation of the real decimal number.

The best way to proceed now is to try each option:

A) 6/12 = 0.5

B) 6/11 = 0.5454...

C) 6/10 = 0.6

D) 6/9 = 0.66...

The best possible choice is B)

Answer:

  94.3

Step-by-step explanation:

You want to know how to fill in the proportion associated with the question, "What is 115% of 82?"

The diagram is intended to help you match parts of the question to parts of the proportion. The attachment shows the intended relation.

The solution is found by multiplying both sides by 82:

  (x/82)·82 = (115/100)·82

  x = 94.3

The question can also be written as a statement:

  "what" is 115% of 82

When written as an equation, "is" means "equals", and "of" means "times":

  what = 115% × 82

Of course, you can use any variable name of your choosing in place of "what". In your diagram, that is "x". And, you know how to write a percentage as a fraction or decimal, so this becomes ...

  x = 115/100 × 82 = 1.15 × 82

All that remains is to evaluate this expression.

  x = 1.15 × 82 = 94.3

So, the answer to the question is ...

  94.3 is 115% of 82.

Answer:

50

Step-by-step explanation:

8 + 10a - 3 + 5a   when a=3

8+10(3)-3+5(3)=

8+30-3+15=

38+15-3=50

Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.

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The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

The three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.

The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.

The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.

The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

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The Question in English

A Basic Education teacher tells his students to choose three digits

different from the set {1, 2, 3, 4, 5} and form mixed numbers by placing the digits

in the locker It also reminds them that the fractional part has to be

less than 1, for example

2

3

5

. What is the difference between the greatest and the least of the

mixed numbers that can be formed?

Answer:

2(2+1)-[2-(-3)]

(2×3)-5

6-5=1

Answer:

4*9

Step-by-step explanation:

It's obvious.

The midpoint of the line segment with the endpoints is (4, 1)

The endpoints are given as:

E= (-2,8) and F = (10, -6)

The midpoint of the line segment with the endpoints is calculated as

Midpoint = 0.5 * (x1 + x2, y1 + y2)

So, we have:

Midpoint = 0.5 * (-2 + 10, 8- 6)

Evaluate the sum

So, we have:

Midpoint = 0.5 * (8, 2)

Evaluate the products

So, we have:

Midpoint = (4, 1)

Hence, the midpoint of the line segment with the endpoints is (4, 1)

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Answer:

38 us liquid quarts

Step-by-step explanation:

The length of the hypotenuse is 10.61 yd.

We have,

The sum of the angles in a triangle = 180

Now,

Two angles are 45.

This means,

The side opposite to angle 45 are equal.

So,

a = c

And,

a = 7.5 yd

Now,

Applying the Pythagorean theorem.

b² = a² + c²

b² = 7.5² + 7.5²

b² = 112.5

b = √112.5

b = 10.61

Thus,

The length of the hypotenuse is 10.61 yd.

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If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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Answer:

Option 1

Step-by-step explanation:

Let's look at the slope; 1/2

it's positive, so the line will go from Quadrant III to Quadrant I. That means that Option 3 is out since it goes from Quadrant IV to Quadrant II.

Next; let's look at the steepness of the lines. Slopes that are fractions less than 1 are flatter than slopes that are greater than 1. Since the slope on Option 1 is flatter than Option 2, that means that Option 1 is a number less than 1, while Option 2 is a number greater than 1.

You can stop here, but we can also triple check using the rise/run.

Start from a point, for example (0,0) on Option 1. To get to the next point that's two whole numbers (1,2) we need to go 2 to the right and one up. Since we rose 1, and ran 2, the slope would be 1/2.

If we do the same with Option 2, we'll find that it rises 3 and runs 2. The slope for this line is 3/2.

Hope this helps!

Answer:

The opponent won 2 sets in 4 matches, 1 set in 4 matches, and 0 sets in 2 matches.

Step-by-step explanation:

Given that in the last week, Daniela has played 10 tennis matches, and she remembers that her opponent had won 1 set in 4 of the matches and her opponent was expected to win a total of 6 sets over the course of 5 matches, but she Can't remember how many times her opponent won 0 or 2 sets, knowing that in total he played 10 games, to determine the number of times his opponent obtained these results, the following calculation must be performed:

5 matches = 6 sets

10 matches = 12 sets

10 - 4 = 6

12 - 4 = 8

8/2 = 4

Therefore, the opponent won 2 sets in 4 matches, 1 set in 4 matches, and 0 sets in 2 matches.

The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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We can draw the following picture:

That is, the coordinates are (80,0)