The water level of a tank every minute since it began filling is indicated by segments A,B,and C on the graph

Given:

To graph each pair of inequalities and indicate the solution set with cross hatching or shading

Solution

Determine the x and y intrcept of each of the given ineqiualities

Plot the graph as shown below

It can be observed that the solution set is unbounded, as shown by the cross hatching

h = 2A/(a+b)

Explanation:

A=1/2(a+b)h

To solve for h, we will make h the subject of formula

The first thing we will do is bring the 1/2 to the other side of the equation:

To make h stand alone, we would divide both sides by the values in the bracket:

Therefore, h = 2A/(a+b)

The relative frequency (RF) can be calculated as follows:

where RF is the relative frequency, F is the value of the frequency, and ∑F represents the sum of all frequencies.

Using a spreadsheet, we can get the following table:

Based on this table, we can see that ∑F = 40. Thus, we have to divide each frequency by 40 to get the relative frequency. As an example, using the first, second, and third row:

Answer:

The equation y = -4 is a horizontal line at the point -4 in the y-axis.

In order to find a perpendicular line to this equation, we can choose any vertical line in the form:

Where 'a' is any real constant.

So an equation for a line perpendicular to y = -4 would be:

Divide the numerator by the denominator:

50 divided by 9 = 5 with a reminder of 5

Write the whole number (5) , and use the remainder as a numerator and 9 as the numerator:

5 5/9

To know the depth of the drawer you need to know that the shelf paper is the area of the interior faces of the drawer, then:

A = 846sq in

the area is equal to:

Where:

Ab is the area of the base of the drawer

Al is the area of the laterals of the drawer

The Area of the base is:

And the area of the laterals is the sum of the area of every lateral:

Then:

The we clear the x:

The question simply means when you divide two numbers, the one that will result to 7

Hence;

36 ÷ 5 = 7.2

H is the correct option

PQ is just the line segment that connects the points P and Q, so if both point are in the interior of and angle, the line segment connecting them has to be also in the interior of this angle, so true.

There are 8 total outcomes. Now, we need to find where P(<7).

This means the outcomes where the number is less than 7.

There are 6 numbers under the 7 = 1,2,3,4,5,6

The probability is given by the next formula:

Where:

Number of favorable outcomes = 6

Total of possible outcomes = 8

Replacing these values:

Simplify the expression, divide both numbers by 2:

The correct answer is the second one.

remember that the area of a trapezoid can be expressed as

Replace in the formula taking into account that B is the greater base, b is the smallest base and h is the height of the trapezoid.

The area of the trapezoid is 3,200 sqft.

Given:

is given.

Required:

Which option is not appropriate.

Explanation:

Now we check all the option for this

which is appropriate

which is not appropriate

which is appropriate

which is appropriate

Final answer:

The true statement regarding the expression is that D. The kennel charges $25 for the first day and $15 per day after the first day.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, Cameron put his dog Buddy in a kennel while he went on a long business trip and the equation y = 15x + 25 shows the total charge y that Cameron will pay to put Buddy in a kennel for x days.

Therefore, option D illustrate this.

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

We are asked to prove that triangles △PQR and △TSR are congruent.

Let us write the statements and reasons to prove that the given triangles are congruent.

We are given that R is the midpoint of QS and PT

This means that QR ≅ SR and also PR ≅ TR by the property of "Definition of midpoint"

So, now we have 3 equal sides in both triangles

Therefore, by the property of "Side-Side-Side" (SSS) the given triangles are congruent.

Recall that the rule of transformation for a point (x,y) reflected over the x-axis is:

and the rule of transformation for a point translataled n units to the left is:

Therefore, point B(4,2) reflected over the x-axis:

and then translated 3 units to the left has as image the following point:

Given expression is

Now, solving it as:

So,

is the required solution.

Given that one-fourth of the class are girls;

And one half of the girls in the class are wearing dresses;

The fraction of the class that are girls with dresses is;

Therefore, the fraction of the

Answer:

Step-by-step explanation:

The distance between the points is found using the given coordinates and the distance formula.

The distance formula is based on right triangle and Pythagorean theorem and is the calculation of the hypotenuse provided the legs are known.

So the right order of operations is attached for you below.

You have found most of it, just small correction is needed.

Answer:

1., 2., 4., 5., 6., 3., 7.

Step-by-step explanation:

1. Draw a right triangle by dropping a vertical side and a horizontal side. (See attachment).

2. Determine the vertical side (2 units) and horizontal side (6 units) lengths by counting on the grid (be careful of the scale), or using the vertical coordinated (3 to 1) and horizontal coordinate (-2 to 4).

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

Therefore:

4. Use the Pythagorean Theorem for right triangles to determine the diagonal length:

[tex]\implies \sf 2^2+6^2=c^2[/tex]

[tex]\sf 5.\quad 4 + 36 = c^2[/tex]

[tex]\sf 6. \quad 40 = c^2[/tex]

[tex]\sf 3.\quad \sqrt{40}=\sqrt{c^2}[/tex]

7.  √40 is between √36 and √49, so between 6 and 7 - closer to 6, so about 6.3 units.

Hello!

We have the equation of the line y = -4.

Let's put this equation in a cartesian plane:

Notice that this equation will be always constant. So, as we just have a straight line with no inclination, the slope is 0.

The value of 10P4 is 5040

Permutations and combinations are defined as the various ways in which objects from a set may be selected, generally without replacement, to form subsets.

Given 10P4

we have to evaluate the value of 10P4

10P4 is in the form of npr

Formula for npr = n!/(n-r)!

Here n =10 and r=4

Now substitute the values in the formula

(10! )/(10-4)!

= (10! )/6!

=(10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(6 x 5 x 4 x 3 x 2 x1)

= 10 x 9 x 8 x 7

= 5040

Therefore the value of 10P4 is 5040

To learn more about permutations and combinations visit

https://brainly.com/question/13387529

#SPJ9

Answer:

The value of 10P4 is 5040

Permutations and combinations are defined as the various ways in which objects from a set may be selected, generally without replacement, to form subsets.

Given 10P4

we have to evaluate the value of 10P4

10P4 is in the form of npr

Formula for npr = n!/(n-r)!

Here n =10 and r=4

Now substitute the values in the formula

(10! )/(10-4)!

= (10! )/6!

=(10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(6 x 5 x 4 x 3 x 2 x1)

= 10 x 9 x 8 x 7= 5040

Step-by-step explanation:

62 u² (square units)

1) A rectangular prism is made up of 6 rectangles. So we can write them out:

2 rectangles (3 x 2)

2 rectangles ( 5 x 2)

2 rectangles ( 5 x 3)

2) Therefore the Total Surface Area of that prism can be found by applying the formula for the area of each rectangle times 2. Like this:

3) Hence the answer is 62 u² (square units)

At the beggining the ratio of cats to dogs is

because ratio indicates a fraction (12 cats divided by 9 dogs)

After the adoption there were 11 cats and 8 dogs, then the ratio is

Since

Answer:

Given that to solve

a) 2(q+4)=16

we get,

Dividing 2 on both sides we get,

Answer is: q=4

b)7j+2=12+5j

we get,

Dividing 2 on both sides, we get

c) 12z=60-3z

we get,

Dividing 15 on both sides we get,

Okay, here we have this:

Let's take the endpoints of UCONN as x and those of SCSU as y. So:

x=y+2

And:

So the UCONN points of the first half are: x/3. And since they were tied SCSU had the same points at the first half.

And those UCONN points of the second half are 2x/3, and the SCSU points at the end were then x/3+48.

So, we obtain that:

y=x/3+48

x=(x/3+48)+2

x=x/3+50

x-x/3=50

2x/3=50

2x=150

x=75

And, replacing in y:

y=75/3+48=25+48=73

Finally we obtain that the final score was: UCONN 75: SCSU 73

The slope of the trend line is 32.4, and it represents the change of s per 1 hour.

Then, as the slope is 32.4 it represents: For an increase of 1 h in study time the test score will increase by approximately 32.4

To determine which pattern could represent points on the graph, we notice that the following points are on the graph:

We can infer that the point

is also on the line.

Therefore, the pattern that could be contained in the graph is:

Answer: Option A.

1) Considering that the 1st property of Logarithms tells us:

2) Let's evaluate that:

• Notice that we've descended that exponent x, to become a factor (3rd line).

• Then divided both log with a common base, in this case, base 10.

3) Hence that equation yields 1/2 as its result.

Given data:

The given function is f(x)=9x^2-180=0

The given expression can be written as,

Thus, option (A) is correct.

as x approaches 8, x approaches 8

it's just 8

The subject of the formula is [tex]\pi r = {r(R^{2}- r^{2})}[/tex]

Given, 

V = πr (R²-r²)

then to find r in terms of the other values divide both the sides by the multiplier of r.

r is multiplied by πr²

Now divide both sides by V

[tex]\frac{V}{\pi r } = \frac{\pi r(R^{2}- r^{2})}{\pi r}[/tex]

[tex]\frac{V}{\pi r } = {(R^{2}- r^{2})}[/tex]

[tex]{\pi r } = \frac{{(R^{2}- r^{2})}}{V} \\\\\pi r^{2} = {r(R^{2}- r^{2})}[/tex]

Hence the answer is the subject of the formula is [tex]\pi r = {r(R^{2}- r^{2})}[/tex]

To learn more about expressions click here https://brainly.com/question/4344214

#SPJ9

​

SOLUTION

Solve for the value of x using supplementary angles

If the sum of two angles is 180 degrees then they are said to be supplementary angles, which form a linear angle together.

To solve using the supplementary angle rule

Add the two angles together

Divide both side by 5

Hence the value of x = 37 degree

The measure of Angle 1 = <1 = 4x-5 = 4(37) - 5 = 143 degree

The measure of Angle 2 = <2 = x = 37 degree