1.) 2p -4 > 16

2.) 7c +11 < -3

3.) m/5 +3 < -7

4.) -3z -9 > 12

Solve and graph the following inequalities

can someone help solve these 4 questions.

Hey there!

The length of the hypotenuse is about 11 centimeters.

To solve this, we use the formula \(a^2+b^2=c^2\), where \(c\) is the hypotenuse leg and \(a\) and \(b\) are the other sides. So we can plug the numbers in to the formula:

\(5^2 + 10^2 = c^2\)

Now we get the squares of 5 and 10:

\(25 + 100 = c^2\)

Add 25 and 100:

\(125 = c^2\)

Take the square root from both sides:

\(11.18033... = c\)

The length of the hypotenuse is about 11 centimeters.

Hope it helps and have an amazing day!

The length of Hypotenuse = 11.18 cm

In mathematics, the Pythagoras theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides.

Given,

In right angle ΔABC

AB = 5 cm

BC = 10 cm

AC = ?

By the Pythagoras theorem,

AC² = AB² + BC²

AC² = 5² + 10²

AC² = 25 + 125

AC = √125 = 11.18

Hence, 11.18 cm is the length of Hypotenuse AC .

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Answer:

Surface area of the box is 3345cm^2

Step-by-step explanation:

First you need to find the surface area of the sides. In order to find the sides you would do 70cm times 15cm to find one of the area of the sides. This would give you that one of the area is 1050cm^2. Since there are three you need to multiply by 3. This means that all the rectangles on the side would have a surface area of 3150cm^2. Then you need to find the area of the triangles. So the Area= Height times (1/2)base. Area= 13cm* times 7.5cm. Therefore the area of the triangle is equal to 97.5cm^2. Since there are two this means that the surface area of the two triangles would be equal to 195cm^2. Then in order to find the total surface area you would need to add the triangles with the rectangles which is equal to 3150cm^2 plus 195cm^2 which totals to 3345cm^2.

Therefore the total surface area for the triangle box is 3345cm^2

Answer:

f(x)=4x(x-3)

Vertex=3/2, -9

Step-by-step explanation:

First, factorize it.

That is equal to 4x(x-3)

Therefore, x intercepts are 0 and 3, as  at least one of them need to be 0.

To find the vertex, first find the x of the vertex, which you can do by finding the average of the x intercepts, so it will be 3/2

Then, find the y, by making x in the original equation equal 3/2. This will give us -9 as the y.

The vertex will by 3/2, -9

Answer:

Assuming you're trying to find where the lines intersect (their solution), the point where they intersect is (1/2 , 1).

Step-by-step explanation:

When you are trying to find the point where two lines intersect, you have to find the x and y values of that point. To do that, just set the lines equal to each other.

First, since y must equal y:

y = y

-4x + 3 = 4x - 1

Now solve for x:

-8x + 3 = -4

-8x = -4

8x = 4

x = 1/2

We just found the x value of the shared point. Now we need to find the y value of that point. Again, since the two lines share this point, plugging in the x value will result in the same y value for both lines.

So just plug in x to any of the equations: (I think y=4x-1 is easier)

y(1/2) = 4(1/2) - 1     or      y = 4(1/2) - 1  (it doesn't matter how you write it)

y(1/2) = 2 - 1           or      y = 2 - 1

y(1/2) = 1

So the point is:

(1/2 , 1)

To check you can plug in the y value you find, 1 in this case, and solve for x. If you get the same x value as before, everything is correct.

So:

(1) = -4x + 3

-2 = -4x

1/2 = x    or    x = 1/2

Great! Everything is correct.

This may seem like a very long process, but it is very easy. Just find the x and y values that the lines share by setting the lines equal to each other.

Answer:

B?

Step-by-step explanation:

Answer:

9 + b is an expression

Step-by-step explanation:

Expressions don't have the = sign in them but equations do.

Answer:

4(x-1)(x² + 3x + 3)

Step-by-step explanation:

First get a common factor from the coefficients and factorise as shown below.

4(x³ + 2x² - 3)

Notice how 1 is a solution to the cubic equation:

Substitute 1 into the equation to get 4 + 8 - 12 = 0 (when equation is set to zero)

thus (x-1) is a factor.

4(x-1)(x² + 3x + 3)

Answer:

College students sleep less than typical american

Step-by-step explanation:

H0: u >= 7

H1: u <7

This test is left tailed that is 1 tailed.

Significance alpha = 0.05

Degrees of freedom = 50-1 = 49

Using t distribution table at alpha = 0.05 and df = 49

Critical value = -1.677

We find t test

= 6.8 - 7/(0.9/√50)

= -0.2/0.9/√50

= -1.5713

-1.5713 is greater than -1.6777 so we fail to reject the null hypothesis

Using excel p value = 0.061 which is greater than 0.05

So we conclude that college students sleep less than typical american

Answer:

y=24/35

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

Alternate interior angles so they are congruent. So, 13x+5=12x+12. Subtract 12x and get x+5=12. Subtract 5 and you get x=7

Miranda has $130 of discretionary income per month after all her needs are met with the list above. The answer is option D.

To calculate Miranda's discretionary income, we need to first add up her expenses:

$60 + $85 + $195 + $55 + $575 = $970

Next, we need to calculate her monthly income.

Since Miranda gets paid semi-monthly, we'll need to multiply her paycheck amount by 24 (the number of pay periods in a year) and divide by 12 (the number of months in a year):

$550 x 24 / 12 = $1,100

Now we can calculate her discretionary income by subtracting her expenses from her income:

$1,100 - $970 = $130

Therefore, Miranda has $130 of discretionary income per month after all her needs are met with the list above. The answer is option D.

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Answer:

do you have a picture of the equations? then I can help you when you do

Answer:

Because equations is not counting, and multiply is not addition.  

Step-by-step explanation:

Addition is: a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum. It is one of the essential mathematical functions we use in our everyday activities. There are many situations in which we add numbers.

Like lets say you have 1 apple, and your friend gives 2 more, then you have 3. If you have 4 apples, and your friend gives 5 more, then you have 9 apples.

Its always better to start with the bigger number, it makes it easier, like 2 + 1 = 3, or 5 + 4 = 9.

Now multiplication is harder. Multiplication is: the basic explanation of multiplication is adding a number, with respect to another number, repeatedly. For example, if we are multiplying 2 by 3, that means 3 is added to itself two times, i.e. 3 + 3 = 6. This is a simple technique for kids to multiply numbers.  

(Answer) 2 x 2 would equal 4. (Explanation) Add a 2, with respect to 2, repeatedly, would equal 4.

(Answer) 4 x 4 would equal 16. (Explanation) Add a 4, with respect to 4, repeatedly, would equal 16.

Answer: Step-by-step explanation:

because 1 + 2  does equal 3 but 4 + 5 does not equal to 6 because it equals to 9.

and 2 x 2  does equal to 4 but 4 x 4 does not equal to 8 because it equals to 16.

The equations are y = 30x + 13 and y = 28x + 15. And the charge less for cleaning 4 mattresses is $127 given by company B. Then the amount of money saved to clean 7 mattresses is $22.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let 'x' be the number of mattresses and 'y' be the total cost. Then the equations are given as,

Company A: y = 30x + 13

Company B: y = 28x + 15

The amount for x = 4 is given as,

Company A: y = 30 (4) + 13 = $133

Company B: y = 28 (4) + 15 = $127

The amount for x = 4 is given as,

Company A: y = 30 (7) + 13 = $223

Company B: y = 28 (7) + 15 = $211

Then the amount of money saved is given as,

⇒ $233 - $211

⇒ $22

The amount of money saved to clean 7 mattresses is $22.

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The division property of equality simply tells us that if we divide both sides of an equation by the same number, then the equation remains the same.

It should be noted that when the denominator of a fraction is equal to 1, and the numerator is nonzero, the value of the fraction is equal to the numerator of the fraction.

Fractions simply means, numbers that are not whole.

If the numerator is nonzero, and the denominator is 1; then the fraction has a value of the numerator.

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Answer:

When the denominator of a fraction is equal to 1 and the numerator is nonzero, the value of the fraction is equal to the numerator of the fraction.

Step-by-step explanation:

I took a 2.12 math quiz in K12 and got it 100% Correct! Yes!

Answer:

it is a parabola with max of -4

so domain (-∞,∞)

Step-by-step explanation:

Answer:

78°

Step-by-step explanation:

Angles on a straight line = 180°

AD is the straight line

Angle BFA = 48

Angle CFD = 54

54 + 48 = 102

180 - 102 = 78

Therefore, Angle BFC = 78°

The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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Answer: $1.50

Step-by-step explanation: 1. subtract the 3.25 from 4.50 to get a difference that is the price of the added hotdog 2. now that you know each hot dog cost $1.25 you can do 3.25 - 2(1.25) to get 0.75 which is the price of one soda. 3. You can no multiply $0.75 by two (the amount of sodas) to get the answer $1.50.

Answer:

The binary equivalent of the decimal number 38.37510 is 100110.0112. Therefore, the correct option is: 100110.011

Step-by-step explanation:

To convert the decimal number 38.375 to binary, we can convert the integer part (38) and the fractional part (0.375) separately and combine them.

For the integer part:

38 divided by 2 gives a quotient of 19 with a remainder of 0.

19 divided by 2 gives a quotient of 9 with a remainder of 1.

9 divided by 2 gives a quotient of 4 with a remainder of 1.

4 divided by 2 gives a quotient of 2 with a remainder of 0.

2 divided by 2 gives a quotient of 1 with a remainder of 0.

1 divided by 2 gives a quotient of 0 with a remainder of 1.

Reading the remainders from bottom to top gives the binary equivalent of the integer part: 1001102.

For the fractional part:

0.375 multiplied by 2 gives a product of 0.75, and the whole number part is 0.

0.75 multiplied by 2 gives a product of 1.5, and the whole number part is 1.

0.5 multiplied by 2 gives a product of 1, and the whole number part is 1.

Continuing this process until we get a fraction of 0 or reach the desired precision gives the binary equivalent of the fractional part: 0.0112.

Combining the two parts, we get the binary equivalent of the decimal number 38.37510: 100110.0112.

The reason is that to convert a decimal number to binary, we need to represent both the integer part and fractional part in binary separately, and then concatenate them to get the final binary representation.

So, to convert the decimal number 38.37510 to binary, we first convert the integer part, which is 38, to binary using the division-by-2 method as explained in the previous answer. This gives us 100110 in binary.

Next, we convert the fractional part, which is 0.375, to binary using the multiplication-by-2 method as explained in the previous answer. This gives us 0.011 in binary.

We then concatenate the two binary values to get the final binary representation of 38.37510, which is 100110.0112.

Therefore, the correct option is 100110.011.

The functions and its domain are a representation of their dependance on one another.

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). In the given question, we have two functions and we are required to find the composite of which ever form of the functions as well as the domain of the said function.

\(f(x) = \frac{3}{x}, g(x) = 2x + 8;\\(f.g)(x) = \frac{3}{2x + 8}\)

The domain of the function is given as

\(domain = (-\infty , -4) U (-4, \infty)\\\)

In the second composition of the function,

\((g.f) = \frac{6}{x} + 8\\domain = (-\infty, 0) U (0, \infty)\)

The third composition of function

\((f.f) = x\\domain = (-\infty, \infty)\)

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Answer:

the value of x that makes the equation true is x = 3.5.

Step-by-step explanation:

To find the value of x that makes the equation 18x + 5 - 3 = 65 true, we need to simplify the equation and solve for x.

Starting with the equation:

18x + 5 - 3 = 65

First, combine like terms:

18x + 2 = 65

Next, isolate the term with x by subtracting 2 from both sides:

18x = 65 - 2

18x = 63

Finally, divide both sides of the equation by 18 to solve for x:

x = 63 / 18

x = 3.5

Therefore, the value of x that makes the equation true is x = 3.5.

The answer is:

Steps & work :

First, I focus only on the left side.

Combine like terms:

\(\sf{18x+5-3=65}\)

\(\sf{18x+2=65}\)

Subtract 2 from each side:

\(\sf{18x=63}\)

Now, divide each side by 18:

\(\sf{x=\dfrac{63}{18}\)

Clearly, this fraction is not in its simplest terms, and we can divide the top and bottom by 9:

\(\sf{x=\dfrac{7}{2}}\)

\(\therefore\:\:\:\:\:\:\stackrel{\bf{answer}}{\boxed{\boxed{\tt{x=\frac{7}{2}}}}}}\)

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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Answer:

Step-by-step explanation:

\(d^2=(x2-x1)^2+(y2-y1)^2\\ \\ d^2=(-3-5)^2+(4-4)^2\\ \\ d^2=64\\ \\ d=8\)

Step-by-step explanation:

directly proportional means

y = kx

with k being a constant factor for all values of x.

we get k by using the given data point (10, 15).

15 = k×10

k = 15/10 = 1.5

so, now for the other tree we know k and x and calculate y

y = 1.5×14.4 = 21.6 m

it is 21.6 m tall (its height is 21.6 m).

Answer:

Step-by-step explanation:

5x+9y=-3             Multiply both sides by 8

40x+72y=-24

-53x-8y=-3  Multiply both sides by 9

-477x -72y= -27

sum the equations vertically to eliminate one variable  

40x+72y= -24

-477x-72y= -27       (the y cancels out )

-477x =-51                (-24 + -27=-51)

-477x=-51 / -477       divide both sides by -477

x =51/437

5x 51/437=9y= -3   substitute the value of x

y= -174 /437

(x,y) = (51/437,  -174/437)

The rental cost in dollars per square foot is $11,00

Cost of renting 1.250 square feet = $13, 750 per month

Rental cost per square foot = Total renting cost / total renting area

= $13, 750 per month / 1.250 square feet

= $11,000

Hence, $11,000 is the rental cost in dollars per square foot.

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The question is incomplete:

On a certain map , 3 inches represents 15 miles. Briarwood and Middletown are 15 inches apart on map.What is actual distance between Briarwood and Middletown?

A. 25 miles

B. 30 miles

C. 50 miles

D. 75 miles

Answer:

D. 75 miles

Step-by-step explanation:

With the information provided, you can use the rule of three to find the distance between Briarwood and Middletown:

3 inches  → 15 miles

15 inches →      x

x=(15*15)/3= 75 miles

According to this, the answer is that the actual distance between Briarwood and Middletown is 75 miles.

Bob had 50 pencils in the beginning.

A fractional number is expressed in the form -

x/y    {where y ≠ 0)

Given is that Bob gave four - fifths of his pencils to Barbara, then he gave two - thirds of the remaining pencils to bonnie.

Assume that he had {x} pencils in the beginning. We can write -

4x/5 + 2/3(x - 4x/5) = 10

4x/5 + 2x/3 - 8x/15 = 10

x(4/5 + 2/3 - 8/15) = 10

x = 10/0.93

x = 50

Therefore, Bob had 50 pencils in the beginning.

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{QUESTION IN ENGLISH -

Bob gave four fifths of his pencils to Barbara, then he gave two thirds of the remaining pencils to bonnie, if he ended up with 10 pencils for himself... how many pencils did bob have at the beginning?}