What is the slope of the line in the graph?

The solution to the inequality is all values of x less than 5. We can write the solution set using interval notation as (-∞, 5).

To solve the inequality -5x - 3 + 2x > -18, we need to isolate the variable x on one side of the inequality sign.

Starting with the given inequality:

-5x - 3 + 2x > -18

Simplifying the left-hand side by combining the like terms:

-3x - 3 > -18

Adding 3 to both sides:

-3x > -15

Dividing both sides by -3, and reversing the inequality sign since we are dividing by a negative number:

x < 5

Therefore, the solution to the inequality is all values of x less than 5. We can write the solution set using interval notation as (-∞, 5).

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For the given equation 6+(x/2)=1/4(x-4)-1 the solution is x= -32. So, option D is correct.

A solution is a process of giving the unknown variables values that make the equation's equality true. A value or group of values (one for each unknown) that, when substituted for the unknowns, cause the equation to produce an equality is known as a solution.

In order to build an equation, the equal sign is placed between two numerical or variable expressions, as in 3x+5=11. The solution to an equation is a number that may be used as the variable to generate a true number statement. 6+5=11 is true, as stated by the formula 3(2)+5=11. The solution is consequently 2,

6+(x/2)=1/4(x-4)-1

(12+x)/2=(x-4-4)/4

24+2x=x-8

x= -32

Therefore, option D is correct.

For the given equation 6+(x/2)=1/4(x-4)-1 the solution is x= -32. So, option D is correct.

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Answer:

270 girls

Step-by-step explanation:

Total number of students = 380

Play musical instrument = 70%

Boys who play musical instrument = 60%

Number of girls who play musical instrument = 200

How many girls are in the class?

Number of play musical instrument = 70% of 380

(0.7 * 380) = 266

Since number of girls who play musical instrument = 200

Then number of boys who play = (266 - 200) = 66

Hence, 66 boys is equivalent 60% of the boy's population

Let population of boys = b

0.6b = 66

b = 110

Number of girls in class :

Number of boys + number of girls

110 + number of girls = 380

Number of girls = 380 - 110

Number of girls = 270

Answer:

X>-4

Y>-18

X>-7

I hope this helps

Answer:

The factored form is,

\((4a^2+2a+1)(4a^2-2a-1)\)

Step-by-step explanation:

We have,

\(16a^4-4a^2-4a-1\\factoring,\\We\ can \ write \ 16a^4 \ as \ (4a^2)^2\\Also,\\then we have,\\(4a^2)^2-(4a^2+4a+1)\\Now, 4a^2 + 4a + 1 \ is \ a \ perfect \ square,\\4a^2 + 4a + 1 = (2a)^2 + 2(2a) + 1\\= (2a + 1)^2\\so, we \ have,\\(4a^2)^2 - (2a + 1)^2\\\)

Using the difference of square formula,

\(x^2 - y^2 = (x+y)(x-y)\\with,\\x = 4a^2,\\y = 2a+1,\\we \ get,\\(4a^2+2a+1)(4a^2-2a-1)\)

Which is the factored form,

Answer:

\(\mbox{\large y = -\dfrac{3}{5}x - 4}\)

Step-by-step explanation:

The given equation is
\(\mbox{\large 6x + 10y = - 40}\)

The slope-intercept form of the equation of a line is
\(y = mx +b\)

where
m = slope

b = y-intercept

Subtract 4x from both sides of \(\mbox{\large 6x + 10y = - 40}\)

\(6x - 6x + 10y = - 6x-40\\\\\rightarrow \quad 10y = -6x - 40\\\\\text{Divide both sides by 10}\\\rightarrow \quad \dfrac{10y}{y} = -\dfrac{6}{10}x - \dfrac{40}{10}\\\\y = -\dfrac{6}{10}x - 4\\\\\dfrac{6}{10} = \dfrac{3}{5}\\\\\text{Equation of the line in slope-intercept form is: }\\\\y = -\dfrac{3}{5}x - 4\)

The main answer is: D. 4

To determine the value of x when (f o g)(x) is -8, we need to find the input value that produces an output of -8 when the composite function (f o g) is evaluated.

Given the choices, we can substitute each option into the composite function and check the resulting output.

Let's assume that (f o g)(x) = -8.

A. (f o g)(-4) = -8

B. (f o g)(0) = -8

C. (f o g)(3) = -8

D. (f o g)(4) = -8

By substituting these values into the composite function, we find that only option C, (f o g)(3), yields an output of -8. Therefore, the value of x when (f o g)(x) is -8 is 3. So, the correct answer is option C: 3.

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Answer:

The ratio of milk cartons drunk to total milk cartons put out= 3 : 5

Step-by-step explanation:

Total milk cartons put out for breakfast=100

Milk cartons left after breakfast=40

Total milk cartons drunk during breakfast = Total milk cartons put out for breakfast - Milk cartons left after breakfast

=100 - 40

=60

Total milk cartons drunk during breakfast = 60

What is the ratio of milk cartons drunk to total milk cartons put out?

Total milk cartons drunk during breakfast : Total milk cartons put out for breakfast

= 60 : 100

=3 : 5

The ratio of milk cartons drunk to total milk cartons put out= 3 : 5

Because lines a and b are parallel and lines e and f are parallel, the value of "x" is 82 degrees.

Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance. Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that connect at a straight angle (90 degrees). Parallel lines are lines in a plane that never intersect, no matter how far they are extended. The distance between the parallel lines is continuous since they never intersect.

Here,

Remember that vertical angles are generated by crossing lines that form two non-adjacent angles. These angles are congruent because they have the same vertex.

Take a look at the attached figure. Because lines "a" and "b" are parallel, the angles 82° and x° are vertical angles. As a result, they are congruent.

The value of "x" is 82 degree as lines a and b are parallel and lines e and f are parallel.

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Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Step-by-step explanation:

Theoretical probability describes how likely an event is to occur. We know that a coin is equally likely to land heads or tails, so the theoretical probability of getting heads is 1/2. Experimental probability describes how frequently an event actually occurred in an experiment.

EXAMPLE-

Theoretical probability:

For instance, since a flipped coin has two sides and each side is equally likely to land up, the theoretical probability of landing heads (or tails) is exactly 1 out of 2.

Experimental probability:-

For example, the probability of getting a head if you flip a coin is ½, since only 2 things could happen (a head or a tail) and each one has an equal chance of occurring.

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An organized group of integers with a shared variance among each succeeding word is known as an arithmetic sequence. Hence, the right response is (b). 1/3, 1/9, 1/15, 1/21, 1/27.

Which collection of numbers doesn't fit the definition of an arithmetic sequence?

The following instances don't constitute arithmetic sequences: 1.) 2,4,8,16 is not true since the first with second terms differ by 2, while the third and fourth terms differ by 4, and the fifth and sixth terms differ by 8. There are no shared differences, hence the sequence is not arithmetic.

Is the number sequence 2 2 2 2 2 arithmetic?

The series cannot be an arithmetic sequence, however it may be defined. It does, nevertheless, have a common ratio across succeeding words, namely 1, which results in its geometric growth.

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Answer:

6 or 4

Step-by-step explanation:

put 4 on each table which means you need 6 tables

or

put 6 on each table which means you need 4 tables

Step-by-step explanation:

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Answer:

456 drinks

Step-by-step explanation:

just multiply 11.40×40 and you get 456. that's how many drinks you can afford. hope i helped.

As we can conclude from the graphical method that this system has no common intersection point they have no solution.

Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given system of equations are x + 2y = 4, 3x + 6y = 6, 3x - y = 5 and

6x - 2y = 10.

The graphical representation of these equations are attached in the image below.

As we can observe , 3x - y = 5(green line)  and 6x - 2y = 10(purple line) are coinciding with each other so they have infinite no. of solutions.

x + 2y = 4(red) and 3x + 6y = 6(blue) are parallel to each other and hence have no solution.

And in together all these 4 lines have no common intersection point so they have no solution.

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To compare fractions using equivalent fractions, we need to find a common denominator, convert each fraction to an equivalent fraction with that denominator, and then compare the numerators directly.

To compare fractions 3/4 and 7/12 using equivalent fractions, we need to find a common denominator for both fractions. A common denominator is a number that is divisible by all the denominators of the fractions being compared. In this case, the least common denominator (LCD) for 4 and 12 is 12.

To convert 3/4 to an equivalent fraction with a denominator of 12, we need to multiply both the numerator and denominator by 3. This gives us the equivalent fraction of 9/12.

To convert 7/12 to an equivalent fraction with a denominator of 12, we need to multiply both the numerator and denominator by 1. This gives us the equivalent fraction of 7/12.

Now that both fractions have the same denominator, we can compare them directly. We can see that 9/12 is greater than 7/12 since 9 is greater than 7. Therefore, 3/4 is greater than 7/12.

This method allows us to compare fractions with different denominators and make accurate comparisons based on the relative size of the numerators.

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GIVEN

A compound interest account with a principal of $9500 accumulating to $11346 in 7 years, compounded annually.

TO FIND

The interest rate.

SOLUTION

The compound interest formula is given to be:

where

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed.

From the question, the following parameters are seen:

Therefore:

Solve for r:

Multiply by 100:

ANSWER

The interest rate required to get a total amount of $11,346.00 from compound interest on a principal of $9,500.00 compounded once per year over 7 years is 2.57% per year.

Given a table of polygons

For the first row,

Given that the 1 exterior angle of the polygon is given, to find the number of sides, n, the formula is

The number of sides, n, of the polygon is three, thus it is a triangle.

A regular triangle has

For the second row

Given that sum of the interior angles of the polygon is 720°, to find the number of sides of the polygon,

Using the formula to find the sum of the interior angles of a polygon which is

Since the number of sides is 6, thus, it is a hexagon.

For a regular hexagon, is tas

The table is shown below

Using sampling concepts, the correct option regarding the validity of the inference is given as follows:

B) Yes, this is a valid inference because she took a random sample of the neighborhood.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents. If I had taken 1000 residents just from Buffalo, it would not be a representative sample.

In this problem, all addresses in the neighborhood are considered, hence a random sample was taken and the correct option is given as follows:

B) Yes, this is a valid inference because she took a random sample of the neighborhood.

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Answer:

6a3-18a

Step-by-step explanation:

i got u fam ...........

The parametric curves that trace out the unit circle are (a) (cost, sin t) and (c) (sin t, cos t).

(a) In the parametric curve (cost, sin t), the x-coordinate is given by cost and the y-coordinate is given by sin t. By using the trigonometric identity cos^2 t + sin^2 t = 1, we can see that the x-coordinate squared plus the y-coordinate squared equals 1, which represents the equation of the unit circle. Therefore, this curve traces out the unit circle.

(c) Similarly, in the parametric curve (sin t, cos t), the x-coordinate is given by sin t and the y-coordinate is given by cos t. Again, by applying the trigonometric identity sin^2 t + cos^2 t = 1, we find that the equation of the unit circle is satisfied. Hence, this curve also traces out the unit circle.

(b) The parametric curve (sin 2t, cos t) does not trace out the unit circle. The x-coordinate is given by sin 2t, which has a period of π. As a result, the curve does not cover the entire unit circle.

(d) Similarly, the parametric curve (sin 2t, cos 2t) also does not trace out the unit circle. The x-coordinate is given by sin 2t, which has a period of π. Hence, the curve only covers half of the unit circle.

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Answer:

Step-by-step explanation:

If Gary's age is 14 then

Ash is 4 years younger = 14 - 4 = 10

And Oak is 5 times Gary's age = 14 x 5 = 70

So total ages = 70 + 14 + 10 = 94

The length of the hypotenuse is: 8.64 meters

The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that;

In any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The Pythagorean theorem can be defined as; fundamental theorem in mathematics that relates to right triangles.

In this case, the two shorter sides have lengths 8.49 meters and 1.61 meters, so the length of the hypotenuse can be found by calculating the square root of the sum of the squares of these lengths:

i.e.  √(8.49^2 + 1.61^2) = √(72.0201 + 2.5881) = √74.6082 = 8.64 m

So, the length of the hypotenuse is approximately 8.64 meters.

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Option (e) 16t^2 = 81 is the equation that can be solved for t to find the time (in seconds) when the diver hits the water.

The equation that can be solved for t to find the time (in seconds) when the diver hits the water is:

d(t) = 16t^2 = 81

We want to find the value of t that satisfies this equation, which represents the time it takes for the distance fallen to reach the height of the water surface.

To solve for t, we can start by dividing both sides of the equation by 16:

t^2 = 81/16

Next, we can take the square root of both sides to isolate t:

t = ±√(81/16)

t = ±(9/4)

Since time cannot be negative, we discard the negative solution, and we get:

t = 9/4

Therefore, the time it takes for the cliff diver to hit the water surface is 9/4 seconds, or approximately 2.25 seconds.

Option (e) 16t^2 = 81 is the equation that can be solved for t to find the time (in seconds) when the diver hits the water.

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Answer:

5 hours and 35 minutes

Step-by-step explanation:

If you add the 45 and 50 minutes, you get 95 minutes, but an hour is only 60 minutes. So you subtract 60 and you're left with 35 minutes. You add the new hour onto the other 4 hours and you get 5 hours total.

Answer: 5 hours and 35 minutes

Step-by-step explanation: 2 + 2 = 4      45 + 50 = 95      95- 60 = 35

Step-by-step explanation:

\(3 \sqrt{3 \:} + \sqrt{3} \)

Simplify,then combine each:

\( = 4 \sqrt{3} \)

or

\(3 \sqrt{3 \:} + \sqrt{3} \)

=5.196+1.732

=6.928

\( \approx6.930\)

Answer:

\(\dfrac{c}{2}\)

Step-by-step explanation:

We can simplify the given expression by canceling like terms.

Remember that anything divided by itself is 1.

ex:

\(\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2\)

Applying this logic to the given expression:

\(\dfrac{a}{2b} \cdot \dfrac{bc}{a}\)

↓ simplify multiplication of fractions

\(\dfrac{a \cdot bc}{2b \cdot a}\)

↓ rewrite to align like variables

\(\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}\)

↓ separate out variables that are divided by each other

\(\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}\)

↓ represent them as 1

\(1 \cdot 1 \cdot \dfrac{c}{2}\)

↓ rewrite without unnecessary 1's

\(\dfrac{c}{2}\)