point G is on line segment FH. GIVEN FH = 5× +2, GH =5× - 9, AND FG = × + 5, determine the numerical length of FG?

Answers

Answer 1
[tex]FH=FG+GH[/tex]

repalce the values

[tex](5x+2)=(x+5)+(5x-9)[/tex]

and solve for x

[tex]\begin{gathered} 5x-x-5x=5-9-2 \\ -x=-6 \\ x=6 \end{gathered}[/tex]

the value of x is 6

now replacing on FG

[tex]\begin{gathered} FG=x+5 \\ FG=6+5 \\ FG=11 \end{gathered}[/tex]

Point G Is On Line Segment FH. GIVEN FH = 5 +2, GH =5 - 9, AND FG = + 5, Determine The Numerical Length

Related Questions

write an equation of the lines that passes through each point with the given slope

Answers

4. the equation of the line is of the form y = mx + b, where:

m = - 2

and b:

[tex]\begin{gathered} 0=-2(3)+b \\ 0=-6+b \\ 6+0=-6+b+6 \\ b=6 \end{gathered}[/tex]

therefore the equation is:

[tex]y=-2x+6[/tex]

5. m = -5

for b:

[tex]\begin{gathered} 4=-5(5)+b \\ 4=-25+b \\ 4+25=-25+b+25 \\ b=29 \end{gathered}[/tex]

equation is:

[tex]y=-5x+29[/tex]

find the derivative f(x) = 4x^5 /e^x

Answers

Answer:

f'(x) = 20x^4 /e^x - 4x^5/e^{2x}

Explanation:

The derivative of a quotient is the denominator times the derivative of the numerator minus

the numerator times the derivative of the denominator all over the square of

the denominator. In this case that would be e^x * 5*4*3*2 + 4*5*6*7/(e^{2x})

Two functions g and f are defined in the figure below. Find the Domain and Range of the composition f°g. write your answers in set notation.

Answers

Answer:

Domain: {0, 3, 6}

Range: {5 }

Explanation:

The domain of the composite function is the intersection of the domain of f(x) and G(x).

[tex]D=Df(x)\cap Dg(x)[/tex][tex]D=\mleft\lbrace0,3,6\mright\rbrace[/tex]

The range of the function is now restricted by the domain of the composite function. Therefore, the range is found by evaluating the function at the points in the domain of f(x). Doing this gives

[tex]R=\mleft\lbrace5\mright\rbrace[/tex]

Note: we did not include 7 in the domain since the input value 5 is not in the domain of f(g(x)).

Solving systems of equations using substitution. y=7+x. y=3x +9

Answers

ok

y = 7 + x

y = 3x + 9

By substitution, I'll substitute "y"

7 + x = 3x + 9

7 - 9 = 3x - x

-2 = 2x

2x = -2

x = -2/2

x = -1

Find y

y = 7 - 1

y = 6

Result

x = -1, y = 6

what is true about the purple and blue triangles? why ?

Answers

Looking at the image, we can see that the purple and blue triangles are both right triangles.

Also, we can see that both triangles have the hypotenuse equal 1 unit, since the hypotenuses are the radius of the circle.

Date: Name: Slope: EXIT TICKET ſmiles 240 220 200 Unit Rate: 180 160 140 120 100 How might you be traveling on this graph? 80 60 40 20 hour 25 30 0 0 5 10 15 20

Answers

Recall that in order to find the slope of a line we just need two points on the line of the form (x, y)

And the slope will be determined by the formula:

slope = (y2 - y1) / (x2 - x1)

in our case, we can find two very clearly determined points in the intersection the line makes with the grid at the points: (5, 120) and (15, 180)

Therefore the slope becomes:

slope = (280 - 120) / (15 - 5) = 160 / 10 = 16 miles/hour

Notice that the units of the slope are miles per hour since the y values represent miles, and the x values represent time in hours.

We notice also that at time ZERO (0 hours) the person is not at the origin, but at 90 miles from the origin.

Therefore the equation that represents this graph in point slope form can be written as:

y = 16 x + 90

where y is the distance from the origin in miles, and x is the elapsed time in hours.

This representation tells us that the person is travelling at a constant speed of 16 miles per hour.

The unit rate is 16 miles per one hour

If one wants to plot this line using the point-slope form, one needs to use the value of the slope (16 mi/h) and one point where the line goes. We can pick for example the point (0,90) which is where the line intersects the y axis, and the location the person is at time zero.

Once you mark that point on the plane , then you move to the right ONE unit (for ONE hour), and 16 units up (for the 16 miles covered during that hour, and then you have a second point created that fashion. Then, you join these points.

I will be marking what I just told you in the graph you provided. Give me a few minutes to draw the process.

Notice the point where we start (in orange), then we move to the right 1 hour and up the equivalent to 16 miles, and we get a new point (in red) that tells us the location "y value" at that time. This new point is the starting value for the next point, which again is obtained by moving to the right one hour and up anither 16 units (these steps are marked with green segments). The nex point we get with this procedure is the one depicted in light blue.

At the end you join the points you created this way with a straight line to complete the graph.

Expand the partial sum and find its value type your answer as an improper fraction:sigma (sum) starting value (k) at 0 ending value 3, function is 4/k!The sum is Answer

Answers

Solution:

Given:

[tex]\sum_{k\mathop{=}0}^3\frac{4}{k!}[/tex]

This implies that the value of k starts from 0 and ends at 3.

Thus, the partial sum is expanded to be

[tex]\frac{4}{0!}+\frac{4}{1!}+\frac{4}{2!}+\frac{4}{3!}[/tex]

Where

[tex]\begin{gathered} \frac{4}{0!}=\frac{4}{1}=4 \\ \frac{4}{1!}=\frac{4}{1}=4 \\ \frac{4}{2!}=\frac{4}{2}=2 \\ \frac{4}{3!}=\frac{4}{6}=\frac{2}{3} \end{gathered}[/tex]

Thus, we have

[tex]\begin{gathered} 4+4+2+\frac{2}{3} \\ =\frac{32}{3} \end{gathered}[/tex]

Hence, the sum is

[tex]\frac{32}{3}[/tex]

Brand A milks costs 5.28 for 2 gallons. brand B milk costs 10.40 for 4 gallons. which is the better deal per gallon and by how much?

Answers

To determine the price per gallon we need to divide the cost by the number of gallons.

For Brans A we have:

[tex]C_A=\frac{5.28\text{ dollar}}{2\text{ gallon}}=2.64\text{ dollar/gallon}[/tex]

For Brand B:

[tex]C_B=\frac{10.4\text{ dollar}}{4\text{ gallon}}=2.6\text{ dollar/gallon}[/tex]

The better price is for Brand B since:

[tex]2.6<2.64[/tex]

The difference is:

[tex]2.64-2.6=0.04[/tex]

Solve.3x+y=42x+y=5Use the linear combination method. (−3, 13)(−3, 12)(0, 4)(−1, 7)

Answers

We have the following system of equations:

[tex]\begin{gathered} 3x+y=4 \\ 2x+y=5 \end{gathered}[/tex]

The linear combintation method is a process of adding two algebraic equations so that one od the variables is eliminated.

In this regard, by multiplying the second equation by -1, we obtain an equivalent system of equations:

[tex]\begin{gathered} 3x+y=4 \\ -2x-y=-5 \end{gathered}[/tex]

Then, by adding both equations, we can eliminate the variable y, that is,

[tex]\begin{gathered} 3x-2x+y-y=4-5 \\ \text{which gives} \\ x=-1 \end{gathered}[/tex]

Once we know the result for x, we can substitute its values into one of the orginal equations. Then, if we substitute x=-1 into the first equation, we have

[tex]3(-1)+y=4[/tex]

which gives

[tex]\begin{gathered} -3+y=4 \\ \text{then} \\ y=7 \end{gathered}[/tex]

Therefore, the solution is ( -1, 7), which corresponds to the last option.

Hari finds that 20 thumbtacks have a mass of about 3.6 grams. There are about 0.035 ounces in 1 gram. About how many ounces do 20 thumbtacks weigh? A 0.13 oz B 0.0063 Oz C 0.7 oz D 0.18 oz

Answers

A)0.13

Explanation

so

[tex]\begin{gathered} \text{if} \\ 20\text{ thumbtacks}\rightarrow3.6\text{ grams} \\ \end{gathered}[/tex]

to find the weigth of the 20 thumbtacks we need to convert the 3.6 grams( the acutal weigth of 20 thumbtacks) into ounces by using a rule of three

[tex]\begin{gathered} \text{if } \\ 1\text{ gram}\rightarrow0.035\text{ ounces} \\ 3.6\text{ gram}\rightarrow x\text{ ounces} \\ \frac{1}{0.035}=\frac{3.6}{x} \\ x=3.6\cdot0.035 \\ x=0.126 \\ \text{rounded} \\ x=0.13 \end{gathered}[/tex]

[tex]A)0.13[/tex]

I hope this help you

Is this correct? Please help I have a test on this 11.    Work backwards to write a quadratic equation that will have solutions of x = 12 and x = 2.

Answers

EXPLANATION

Given the variables:

x=12 and x=2

Supposing that both values are roots of a quadratic equation:

x-12 = 0 x -2 = 0

Multiplying both roots:

(x-12)(x-2) = 0

Applying the distributive property:

[tex]x^2-2x-12x+12\cdot2=0[/tex]

Adding and multiplying like terms:

[tex]x^2-14x+24=0\text{ \lbrack{}SOLUTION\rbrack}[/tex]

3. Two partners are starting a landscape business. The total investment is $45,000. John is one of thepartners. He invested 4/9 of the amount. How much money did John invest in the business?

Answers

Two partners invested a total of 45,000 dollars and one of the partners, John invested 4/9 of the amount which 45000. That means John's own contribution is four-ninths of the total amount and that can be derived as follows;

John = 4/9 * 45000

John = (4 * 45000)/9

John = 180000/9

John = 20000

John's investment therefore is $20,000

What is the volume of a cube with a length of 0.178 cm

Answers

Explanation: To solve this question we will work with the conversion from cm to mm as follows

[tex]\begin{gathered} 1cm=10mm \\ 1mm=0.1cm \end{gathered}[/tex]

Step 1: First let's convert our length from cm to mm to be able to visualize our problem better as follows

[tex]\begin{gathered} once\text{ 1cm=10cm} \\ then\text{ 0.178cm=1.78mm} \end{gathered}[/tex]

Step 2: Now once the cube has all the sides equal we can use the cube's volume formula to calculate as follows

[tex]V_{cube}=side^3=1.78^3=5.639752mm^3\cong5.64mm^3[/tex]

Step 3: Now all we have to do is to transform back to cm if we want to get the volume in centimetres

[tex]\begin{gathered} once\text{ 1mm=0.1cm} \\ then\text{ 5.64mm=0.564cm}^3 \end{gathered}[/tex]

Final answer: So the final answer is

[tex]\cong0.564cm^3[/tex]

.

the sum of twice a number and five is 11 . find the number?

Answers

Solution

Let the number be represented by x

[tex]2x+5=11[/tex]

Now, solve x

[tex]\begin{gathered} 2x=11-5 \\ 2x=6 \\ divide\text{ both sides by 2} \\ \frac{2x}{2}=\frac{6}{2} \\ \\ x=3 \end{gathered}[/tex]

The final answer

The number is 3

[tex]x=3[/tex]

If a, b, and c are digits for which the following holds, then a +b+c= 9 a 1-7 2 b= c 8 2a+b+c=

Answers

Answer:

11

Explanation:

Given the difference:

[tex]\begin{gathered} \; \; 9\text{ a 1} \\ -7\text{ 2 b} \\ ---- \\ \; \; c\text{ 8 2} \end{gathered}[/tex][tex]\begin{gathered} 11-9=2 \\ \text{Therefore, b=9} \end{gathered}[/tex][tex]\begin{gathered} 10-2=8 \\ 10+1=11 \\ \text{Therefore, a=1} \end{gathered}[/tex]

Lastly:

[tex]\begin{gathered} (9-1)-7=1 \\ \text{Therefore: c=1} \end{gathered}[/tex]

We then have:

[tex]\begin{gathered} \; \; 9\text{ 1 1} \\ -7\text{ 2 }9 \\ ---- \\ \; \; 1\text{ 8 2} \end{gathered}[/tex]

Therefore:

a+b+c=9+1+1=11

Lauryn has earned the following score on her Ap physics exams : 24/30, 17/20, 34/40, 50/50 and 72/80 what score must lauryn earn on her sixth exam in order to maintain at least an 85% average?Lauryn must earn at least a ----- percent.If lauryn score a 75% on her sixth exam will she keep her average of at least an 85 type YES or NO .what would lauryn's average score be if she scores a 85% on the sixth exam?

Answers

First, we have to transform the fractions into percentage as follows:

24/30*100 = 80%

17/20*100 = 85%

34/40*100 = 85%

50/50*100 = 100%

72/80*100 = 90%

Let's call x to the score on her sixth exam. The average of the six exams is:

(80 + 85 + 85 + 100 + 90 + x)/6

This average must be equal to or greater than 85, then

(80 + 85 + 85 + 100 + 90 + x)/6 ≥ 85

80 + 85 + 85 + 100 + 90 + x ≥ 85*6

80 + 85 + 85 + 100 + 90 + x ≥ 510

x ≥ 510 - (80 + 85 + 85 + 100 + 90)

x ≥ 70

Lauryn must earn at least a 70 percent.

If Lauryn score a 75% on her sixth exam will she keep her average of at least an 85. YES, because its greater than 70%

If she scores a 85% on the sixth exam, Lauryn's average score would be

Average = (80 + 85 + 85 + 100 + 90 + 85)/6 = 87.5%

Differentiate.F(x) = (6x + 1)²F'(x) =1600

Answers

we have the function

[tex]f(x)=(6x+1)^2[/tex]

Find out the derivative

[tex]\begin{gathered} f^{\prime}(x)=2(6x+1)^{2-1}(6x+1)^{\prime} \\ f^{\prime}(x)=2(6x+1)(6) \\ f^{\prime}(x)=12(6x+1) \\ f^{\prime}(x)=72x+12 \end{gathered}[/tex]

The answer is

f'(x)=72x+12

6. Place a check next to the fractions that are equivalent * 12/18 6/12 20/25 16/18 2/4 2/3 4/5 8/9

Answers

[tex]\begin{gathered} \frac{12}{18} \\ \frac{12}{18}=\frac{2}{3} \end{gathered}[/tex][tex]\begin{gathered} \frac{20}{25} \\ \frac{20}{25}=\frac{4}{5} \end{gathered}[/tex][tex]\begin{gathered} \frac{16}{18} \\ \frac{16}{18}=\frac{8}{9} \end{gathered}[/tex][tex]\begin{gathered} \frac{6}{12} \\ \frac{6}{12}=\frac{2}{4} \end{gathered}[/tex]

which equivalent ratio proportional relationship with the constant proportionality equals -2 select all that apply

Answers

The expression that represent proportional relationship has the form:

[tex]y=kx[/tex]

where k is the constant of proportionality.

In this case we are looking for a relationship of the form:

[tex]y=-2x[/tex]

or something equivalent. If we multiply both sides by two we get:

[tex]2y=-4x[/tex]

Those two are the relations that fulfill the conditions given.

give the rectangular form of the complex number represented in the graph.A. -5 -2iB. 5-2iC. 5+2iD. -5+2i

Answers

Solution

[tex]z=a+bj[/tex]

The rectangular form of a complex form is given in terms of 2 real numbers a and b in the form: z=a+jb

The polar form of the same number is given in terms of a magnitude r (or length) and argument q (or angle) in the form: z=r|_q

You can "see" a complex number on a drawing in this way:

[tex]\begin{gathered} a=-5 \\ b=2 \\ a+bj \\ -5+2i \end{gathered}[/tex]

In this case the numbers a and b become the coordinates of a point representing the complex number in the special plane (Argand-Gauss) where on the x axis you plot the real part (the number a) and on the y axis the imaginary (the b number, associated with j).

Therefore the correct answer is -5 + 2i

Hence the answer is Option D

a field mouse has been doing some parkour training after implementing a new workout program he can now jump along a parabolic path given byf(x)=-.2x^2+1.6x a) how far can the mouse jump horizontally (round to the nearest ft)?b) with his new workout program can the mouse jump over 3 ft fence

Answers

a.

Given the equation of the jumps as;

[tex]f(x)=-0.2x^2+1.6x[/tex]

We want to find the range of the jump.To do this let us substitute f(x) = 0 and solve for x;

[tex]\begin{gathered} f(x)=-0.2x^2+1.6x=0 \\ -0.2x^2+1.6x=0 \\ -0.2x^2=-1.6x \\ \text{divide both sides by -0.2x} \\ \frac{-0.2x}{-0.2x}^2=\frac{-1.6x}{-0.2x} \\ x=8\text{ ft} \end{gathered}[/tex]

Therefore, the mouse can jump 8 ft horizontally.

b.

We want to know if the mouse can jump over a 3ft fence;

Let's substitute x=8/2 =4 into the equation to get the maximum height the mouse can reach;

[tex]\begin{gathered} f(x)=-0.2x^2+1.6x \\ f(4)=-0.2(4)^2+1.6(4) \\ f(4)=3.2ft \end{gathered}[/tex]

since the maximum height is more than 3ft, it means the mouse can jump higher than 3 ft.

since the maximum height the mouse can jump is 3.2ft, and the fence is 3 ft, the difference between the maximum height and the height of the fence is;

[tex]\begin{gathered} 3.2ft-3.0ft \\ =0.2ft \end{gathered}[/tex]

So, the mouse can jump 0.2ft higher than the 3ft fence.

Therefore, the mouse can clear it with 0.2 ft.

[tex]\text{Yes, the mouse can clear it by 0.2ft}[/tex]

9. The table shows the heights of four rock climbers climbed. List the climbers in decreasing order. * Name Height (ft) 25 Cindy Todd 10.9 13.75 Meghan Kurt 17 O Todd, Meghan, Cindy, Kurt O Cindy, Todd, Meghan, Kurt O Kurt, Todd, Cindy, Meghan O Cindy, Kurt, Meghan, Todd

Answers

To order the climbers in decreassing order we start with the one that clibs the most

[tex]Cindy,\text{ Kurt, Meghan, Todd}[/tex]

Find the exact length of the midsegment of the trapezoid with the verticesA(2, 0), B(8,-4), C(12, 2), D(0, 10).The length of the midsegment is

Answers

First, let's graph the trapezoid.

The midsegment refers to a segment that goes from the midpoint of BC and the midpoint of AD.

Let's find the midpoints using the following formula

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex][tex]\begin{gathered} M_{BC}=(\frac{8+12}{2},\frac{-4+2}{2})=(\frac{20}{2},-\frac{2}{2})=(10,-1) \\ M_{AD}=(\frac{2+0}{2},\frac{0+10}{2})=(\frac{2}{2},\frac{10}{2})=(1,5) \end{gathered}[/tex]

Now, we use the distance formula to find the length of the midsegment

[tex]\begin{gathered} d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ d=\sqrt[]{(-1-5)^2+(10-1)^2}=\sqrt[]{(-6)^2+(9)^2} \\ d=\sqrt[]{36+81}=\sqrt[]{117} \\ d\approx10.8 \end{gathered}[/tex]Hence, the length of the midsegment is 10.8, approximately.

I really need help solving this practice from my ACT prep guide

Answers

Solution:

The question is given below as

[tex]\tan \mleft(\frac{\pi}{3}\mright)+\sin \mleft(\frac{5\pi}{6}\mright)\cos \mleft(-\frac{3\pi}{4}\mright)[/tex]

Step 1:

Using the following identity below

[tex]\sin \mleft(x\mright)=\cos \mleft(\frac{\pi}{2}-x\mright)[/tex]

By applying the identity above, we will have

[tex]\begin{gathered} \sin \mleft(\frac{5\pi}{6}\mright)=\cos \mleft(\frac{\pi}{2}-\frac{5\pi}{6}\mright) \\ \sin (\frac{5\pi}{6})=\cos (\frac{3\pi-5\pi}{6}) \\ \sin (\frac{5\pi}{6})=\cos (-\frac{2\pi}{6}) \\ \sin (\frac{5\pi}{6})=\cos (-\frac{\pi}{3}) \end{gathered}[/tex]

Step 2:

Use the property below

[tex]\cos \mleft(-x\mright)=\cos \mleft(x\mright)[/tex]

By applying the property above, we will have

[tex]\begin{gathered} \cos \mleft(-\frac{\pi}{3}\mright)=\cos \mleft(\frac{\pi}{3}\mright) \\ \cos \mleft(-\frac{3\pi}{4}\mright)=\cos \mleft(\frac{3\pi}{4}\mright) \end{gathered}[/tex]

The question above then becomes

[tex]\begin{gathered} \tan (\frac{\pi}{3})+\sin (\frac{5\pi}{6})\cos (-\frac{3\pi}{4}) \\ \tan (\frac{\pi}{3})+\cos (\frac{\pi}{3})\text{.}\cos (\frac{3\pi}{4}) \end{gathered}[/tex]

Using the following trivial identities, we will have

[tex]\begin{gathered} \tan \mleft(\frac{\pi}{3}\mright)=\sqrt{3} \\ \cos \mleft(\frac{\pi}{3}\mright)=\frac{1}{2} \\ \cos (\frac{3\pi}{4})=\frac{-\sqrt[]{2}}{2} \end{gathered}[/tex]

By substituting the above trivial identities, we will have

[tex]\begin{gathered} \tan (\frac{\pi}{3})+\cos (\frac{\pi}{3})\text{.}\cos (\frac{3\pi}{4}) \\ \sqrt[]{3}+\frac{1}{2}\times\frac{-\sqrt[]{2}}{2} \\ =\sqrt[]{3}-\frac{\sqrt[]{2}}{4} \\ =\frac{4\sqrt[]{3}-\sqrt[]{2}}{4} \end{gathered}[/tex]

Hence,

The SECOND OPTION is the right answer

[tex]\frac{4\sqrt[]{3}-\sqrt[]{2}}{4}[/tex]

For each system, choose the best description of its solution.If applicable, give the solution.The system has no solution.The system has a unique solution:(x, y) = 0.0System Ax+3y+9 = 0-x-3y=-9The system has infinitely many solutions.They must satisfy the following equation:p= 0The system has no solution.System BThe system has a unique solution:(x, y) = 0.0x-4y=-8-x-4y= -8The system has infinitely many solutions,They must satisfy the following equation:

Answers

Answer:

(A)System A has no solution

(B)System B has a unique solution (x,y) = (0,2).

Explanation:

System A

Given the system of equations:

[tex]\begin{gathered} x+3y+9=0 \\ -x-3y=-9 \end{gathered}[/tex]

Rewrite both equations in the slope-intercept form:

[tex]\begin{gathered} Equation\; 1\colon3y=-x-9$$\textcolor{red}{\implies y=-\frac{x}{3}-\frac{9}{3}}$$ \\ Equation\; 2\colon3y=-x+9\textcolor{red}{\implies y=-\frac{x}{3}+\frac{9}{3}} \end{gathered}[/tex]

On observation, the slopes of the two equations = -1/3.

This means that the two lines are parallel and thus, the system has no solution.

System B

Given the system of equations:

[tex]\begin{gathered} x-4y=-8 \\ -x-4y=-8 \end{gathered}[/tex]

Add both equations:

[tex]-8y=-16[/tex]

Divide both sides by -8.

[tex]\begin{gathered} \frac{-8y}{-8}=\frac{-16}{-8} \\ y=2 \end{gathered}[/tex]

Substitute y=2 into the first equation to solve for x.

[tex]\begin{gathered} x-4y=-8 \\ x-4(2)=-8 \\ x-8=-8 \\ x=-8+8 \\ x=0 \end{gathered}[/tex]

The system has a unique solution (x,y) = (0,2).

What is the equation that best represents the trend line on the scatter plot?A. y= 2/3x + 22B. y= -2/3x + 22C. y= -4/3x + 22D. y= 4/3x + 22

Answers

We have to identify the equation of the trend line.

We can see that the trend is decreasing, so the slope has to be negative. Knowing that, we can discard options A and D because they have positive slopes.

The y-intercept is y = 22, but both options B and C have the same y-intercept.

We can then look at the value of the slope: we can see that y decreases 2 units per 3 units of increase of x. This means that we can express the slope as:

[tex]m=\frac{\Delta y}{\Delta x}=\frac{-2}{3}=-\frac{2}{3}[/tex]

Then, the equation of the trend line is:

[tex]y=-\frac{2}{3}x+22[/tex]

Answer: B. y= -2/3x + 22

What would be the length of the outdoor room if thevolume was 30 cubic yards? Round your answer to thenearest tenth of a yard.Show your work.

Answers

Given that,

The volume of room = v = 30 cubic yards

length of room = l = ?

width of room = w

height of room = h

The volume of room (v) is calculated as:

v = l * w * h

Now, put the values in the formula, we get

30 = l*w*h

30/ (w*h) = l

or

l = 30/ (w*h)

Therefore, the length of room would be 30/ (w*h).

Case 2:

If it is a cubic room with same height, length and width. Then, we can write the volume equation as:

v = l * l * l (as l = w = h)

30 = l^3

or

l^3 = 30

l = 30^1/3

l = 3.107 yard

or

l = 3.1 yard (rounded to tenth of a yard)

The height h in feet of a projectile launched vertically upward from the top of a 96-foot tall tower has an initialvelocity of 80 ft/sec.-Write the equation that represents this scenario. -What is the maximum height of the projectile? -How long did it take the projectile to reach its maximum height? -How long will it take the projectile to hit the ground?

Answers

The equation must be

[tex]h(t)=96+80\cdot t-\frac{1}{2}\cdot32.17\cdot t^2[/tex]

What is 36,219 to the nearest thousand

Answers

Answer:

36,000

Step-by-step explanation:

42,612,133,285 in standard form

Answers

The standard form is ascending order if we apply that here we get.

42, 133, 285, 612

That is all.

Other Questions
147) Find x^4 + 1 / x^4 if x - 1/x = 5Pls refer to pic for details What are the terms in the expression 10p + 3q + 2? Responses10, 3, and 2 p and q 10p, 3q, and 2 10 and 3 8(4+v)+38v=11v Solve the equation. The solution set is For the graph to the right, describe the composition of transformations that maps KXH to NGP? Thanks. how much energy is required to take 15g of ice from -25 degrees Celsius to 55 degrees Celsius. draw a phase change graph for this question. if 25 grams of liquid water releases 75j of heat when water cools from 88 degrees Celsius what is the final temperature? (optional) In the __________ design, a composer furnishes music for one stanza of poetry, and this music is repeated over and over for further stanzas. 18b^3 + 12b^2 + 6b = _____ 6b compared with unconscious information processing, conscious information processing is relatively select one: a. fast and especially effective for solving routine problems. b. slow and especially effective for solving routine problems. c. fast and especially effective for solving new problems. d. slow and especially effective for solving new problems. Please help me Ill mark you brainly who came up with 6.022x10^23? How would you justify that triangle PQR is similar to triangle STU. Select all true statements based on the diagram segment DC is congruent to segment AB segment DA is congruent to segment CB Line DC is parallel to line AB line DA is parallel to line CB angle CBE is congruent to angle DEA angle CEB is congruent to angle DEA Bagged lettuce takes an interesting journey from field to store. Assoon as it is picked, it is stored in a refrigerated truck to preventwilting. The lettuce is separated, washed, and bagged in a factory thatis also refrigerated. Then it is trucked to distribution centers and eventually to stores.Which detail from the text best supports the inference that cold temperaturesare necessary to keep lettuce fresh?A. separated, washed, and baggedB. it is pickedC. stored in a refrigerated truck to prevent wiltingD. journey from field to store. in the diagram below of triangle GHJ,K is a midpoint of GH and L is a midpoint of HJ. If m A park ranger driving on a back country road suddenly sees a deer in hisheadlights 20 m ahead. The ranger, who is driving at 11.4 m/s, immediatelyapplies the brakes and slows down with an acceleration of 3.80 m/s2. Howmuch distance is required for the ranger's vehicle to come to rest? Onlyenter the number, not the units. Please help I dont get how to do it 1/6d+2/3=1/4(d-2) A total of 400 students were surveyed. How many more students were surveyed than favor visiting Florida? which awnser does [tex]( { \sqrt{s} })^{2} [/tex]simplify to, for any nonnegative real number s? 9 10^5 is(A) ______times as larger as 3 10^3 5 10^-3 is( B)______time as smaller as 5 10^-2 I'm stuck on this problem for like an hour I also need to show my work to get it right.