charlene is a video game designer and wants to make sure that her game can be played on all types of screens. In order for the games to work on both devices with a standard aspect ratio and those with widescreen aspect ratios, the playable area of the games should an aspect ratio of 3:2. This means that the width is equal to 3/2 times the height. On one type of tablet , the playable area of the game on the screen is 54 square inches. Write and solve a system of equations to determine the dimensions of the playable are.

A) width=6 height=9
B) width=6 height=4
C) width=13.5 height=9
D) width=9 height=6

Answers

Answer 1

The correct answer is D) width=9, height=6.

Let w represent the width and h represent the height. The first equation we write deals with the area of the screen:
A=wh

Our playable area is 54, so we have
54=wh

Now we write the equation relating the width and the height. The width is 3/2 times the height; this means
w=3/2h

We will use substitution to solve this. Substitute the value for w from the second equation into the first equation:
54=wh
54=(3/2h)h
54=3/2h²

Divide both sides by 3/2:
54 ÷ 3/2 = 3/2h² ÷ 3/2
54/1 ÷ 3/2 = h²
54/1 × 2/3 = h²
108/3 = h²
36 = h²

Take the square root of both sides:
√36 = √h²
6 = h

The height is 6. Substituting this into our first equation,
54=wh
54=w(6)

Divide both sides by 6:
54/6 = w(6)/6
9=w

The width is 9.

Related Questions

A construction company needs to remove 2 1/6 tons of dirt from a construction site. They can remove 7/8 tons of dirt each hour. What is the total number of hours it will take to remove the dirt?

Answers

Final answer:

It will take the construction company approximately 2 10/21 hours to remove the dirt.

Explanation:

To find the number of hours it will take to remove the dirt, we need to divide the total amount of dirt by the amount of dirt that can be removed each hour. First, we need to convert the mixed number 2 1/6 tons to an improper fraction. 2 1/6 = 13/6 tons. Next, we divide 13/6 by 7/8 to find the number of hours:

13/6 ÷ 7/8 = 13/6 × 8/7 = 104/42 = 2 20/42 = 2 10/21

So, it will take the construction company approximately 2 10/21 hours to remove the dirt.

if i know the diameter of a circle and the approximation for pi, how can I estimate the circumference of a circle?

Answers

The formula for circumference of a circle is [tex] \pi d[/tex].

You can plug in the diameter for [tex]d[/tex] and multiply this by [tex] \pi [/tex] to get the circumference of the circle.

What is the Value of Y?

Answers

The possible answer for y is 72 hope this helps

All angles in a triangle add to 180°
Since we know that one of the angles is 72° and the other two angles are the same..

We can subtract 72° from 180°
180°-72°=108°
Divide the result by 2
108°/2=54°

So the best answer would be B.54°

I hope this helps :)

SOME ONE PLEASE HELP
Choose the correct simplification of the expression (7m3 n)2.
A.14m5n3
B.14m6n2
C.49m5n3
D. 49m6n2

Answers

we have that
the expression (7*m³*n)²

we know that
(7*m³* n)²---------> (7)²*(m³)²* (n)²-----> (7²)*[(m)^(2*3)]* (n²)----> 49*[m^6]*n²

the answer is the option
D. 49m6n2

PLEASE HELP!!!!! I WILL FAIL MATH IF I DONT GET THIS RIGHT!!! WILL MARK BRAINLIEST!!!!!
What is 60 scaled down by a factor of 1/10?
ERGENT

Answers

Comment
You can do this a number of ways.
The first way is to set up a proportion. That's very formal, and is most respected.

Proportion.
x / 60 = 1 / 10 The proportion is reduced by a factor of 10. Cross Multiply.
10 * x = 60 * 1
10x = 60 Divide by 10
x = 60/10
x = 6

Multiply by the scale factor.
Beginning number * scale factor = Final result.
60 * 1/10 = Final Result
60 * 1 / 10 = Final Result
Final Result = 6

This method words even when the numbers are quite complicated.

The density of glass is 2.6 g/cm3 and the density of lead is 11.3 g/cm3. Does this mean there are more particles of lead in 1 cm3 or that the lead particles are heavier than the glass particles? Give reasons for your answer.

Answers

The answer is that there are more particles in 1 cubic cm. this is because within 1 cubic cm lead has 11.3g in compared to the 2.6 glass has. m/v= density. divide the masses over the volume and that will prove your answer.

Final answer:

A higher density means that lead is heavier than glass for the same volume, signifying that lead particles are both heavier and more numerous in a given volume than the glass particles.

Explanation:

The density of a substance tells us how much mass is in a given volume, and it is expressed in g/cm³. Comparing the densities of glass (2.6 g/cm³) and lead (11.3 g/cm³), we can say that a given volume of lead is much heavier than the same volume of glass. This could mean either there are more lead particles or the lead particles are heavier. But from atomic physics, we know that individual lead atoms are indeed heavier than individual silica atoms (which make up glass). Therefore, the higher density of lead signifies that the lead particles are both more numerous and heavier in a given volume than the glass particles.

Learn more about Density here:

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Find the values of x and y that make these triangles congruent by the HL theorem 2x-1 y-1

Answers

Answer
2x−y−1Use CYmath is give you all math question that you need

Can you solve 5a please greatly appreciated.

Answers

Part I)
The module of vector AB is given by:
lABl = root ((- 3) ^ 2 + (4) ^ 2)
lABl = root (9 + 16)
lABl = root (25)
lABl = 5

Part (ii)
The module of the EF vector is given by:
lEFl = root ((5) ^ 2 + (e) ^ 2)
We have to:
lEFl = 3lABl
Thus:
root ((5) ^ 2 + (e) ^ 2) = 3 * (5)
root ((5) ^ 2 + (e) ^ 2) = 15
Clearing e have:
(5) ^ 2 + (e) ^ 2 = 15 ^ 2
(e) ^ 2 = 15 ^ 2 - 5 ^ 2
e = root (200)
e = root (2 * 100)
e = 10 * root (2)

What is the median of the data set? {17, 40, 23, 44, 44, 30} Enter your answer in the box.

Answers

To find the median of the data set, we must first order them from lowest to highest in increasing order. Let's rearrange them in that way:

{17, 23, 30, 40, 44, 44}

Then we begin by crossing one off from each side, until we get to the middle. However, we see that our middle here is both 30 and 40.

What we do in a case like this is add up the two numbers and divide by 2 (essentially find the mean of the two middlemost numbers). Let's do that now:

[tex]30+40=70[/tex]

[tex] \frac{70}{2}=35 [/tex]

So now we know that the median of the set of data is 35.

Answer:

Step-by-step explanation:

given a mean of 7.6 and a standard deviation of 3.1 what is the z-score of the value 10 rounded to the nearest tenth ?
A)0.8
B)0.9
C)1.7
D)5.7

Answers

Answer: Choice A) 0.8

========================================================

Work Shown:

mean = mu = 7.6
standard deviation = sigma = 3.1
x = 10 is the raw score

Use those values to find the z score
z = (x-mu)/sigma
z = (10-7.6)/3.1
z = 2.4/3.1
z = 0.7741935483871
z = 0.8 (approximate answer to the nearest tenth, ie one decimal place)

What is the value of 2x3squared +x2squared when x = 3

Answers

I suspect this is what you mean, if let me know
2x(3)^2+x(2)^2
2(3)(9)+3(4)
54+12=66

This is an EXPLAIN YOUR THOUGHTS question. Be sure to answer ALL parts of the questions and include all your work!

Task: Find the volume of the figure below. (Hint: divide them into two figures you know how to solve for).

Part a) What is your strategy, ie what shapes can you divide the figure into to find the volume?

Part b) What eqautions will you use to find the VOLUME? First state the general equations. Then include the known values into the equation.

Part c) What is the VOLUME? (don't forget units!)

Answers

a) The figure can be reasonably divided into two geometries:
• a rectangular prism
• a hemisphere.

b) The volume of the rectangular prism is given by
   V = lwh
V = (10 cm)(5 cm)(4 cm) = 200 cm³

The volume of the hemisphere is given by
   V = (2π/3)r³
V = (2π/3)(3 cm)³ = 18π cm³

c) The total volume of the figure is
   total volume = (prism volume) + (hemisphere volume)
V = 200 cm³ + 18π cm³
V ≈ 256.549 cm³

Find the measure of the base angles in an isosceles triangle if the third angle measures 47° .... Show work please

Answers

In any triangle, the angle values must add up to 180 degrees. If the third angle is 47 degrees and the remaining two angles are the same value, it would be really simple to solve.
First, subtract 47 from 180. You are left with 133. That is the sum of the two base angles combined.
In order to find the value for EACH base angle, divide 133 by 2. You are left with 66.5.
That is the answer! Both of the base angles are 66.5 degrees each.

Final answer:

Each base angle of the isosceles triangle measures 66.5°, found by subtracting the given angle from 180° and dividing the remainder by 2.

Explanation:

To find the measure of the base angles in an isosceles triangle when one angle measures 47°, we will use the fact that the sum of all angles in any triangle is always 180°.

Additionally, we know from geometry that in an isosceles triangle, the angles opposite the equal sides are equal. Applying these principles, we first subtract the given angle from the total sum of the angles:

180° (total angles in a triangle) - 47° (given angle) = 133°.

Now, since the remaining two angles are equal, we divide 133° by 2 to find the measure of each base angle:

133° ÷ 2 = 66.5°.

Thus, each base angle of the isosceles triangle measures 66.5°.

PLEASE HELP, ASAP!

The diagram shows the view from the top of a rectangular building and the lawn around the building. The building and lawn form the shape of a trapezoid.

What is the area of the lawn?

Enter your answer in the box.

Answers

the area is about 20 feet on 1 side 20 feet on other side 30 feet for bottom and 18 feet for top

a plane can travel 480 miles per hour with the wind and 440 miles per hour Against the Wind find the speed of the wind and the speed of the plane in still air

Answers

wind speed = x

planes speed with wind: 480-x
planes speed against wind: 440+x
set them to equal and solve for x ( wind speed)

480-x = 440 +x

add x to each side:

480 = 440 +2x ( x+x=2x)

480 = 440 +2x
subtract 440 from each side:

40 = 2x

divide both sides by 2
x = 40/2
x = 20

wind speed = 20 miles per hour

speed of plane in still air = 480-20 = 460 miles per hour

Final answer:

The speed of the plane in still air is 460 miles per hour, and the speed of the wind is 20 miles per hour, found by setting up equations using the given speeds with and against the wind and solving them.

Explanation:

The question requires us to find the speed of the wind and the speed of the plane in still air based on the given speeds of the plane traveling with and against the wind. The speed of the plane with the wind is 480 miles per hour, and against the wind is 440 miles per hour. We can use these values to set up two equations:

The plane's speed in still air plus the wind's speed equals 480 mph.

The plane's speed in still air minus the wind's speed equals 440 mph.

Let's denote P as the plane's speed in still air and W as the wind's speed. We can establish two equations based on the aforementioned points:

1. P + W = 480

2. P - W = 440

To find P and W, we add the two equations together:

(P + W) + (P - W) = 480 + 440

2P = 920

P = 920 / 2

P = 460 mph

Now that we have the plane's speed in still air, we can find the wind's speed using either of the original equations:

460 + W = 480

W = 480 - 460

W = 20 mph

Therefore, the speed of the plane in still air is 460 miles per hour and the speed of the wind is 20 miles per hour.

Write the equation of the line with the following characteristics.A horizontal line through the point (0,3)

Answers

Hello!

Because we have been asked to write the equation of a line, we will need to give the answer in slope-intercept form. Slope-intercept form uses the following formula:

y = mx + b

In the above formula, M represents the slope while B represents the y-intercept. We are asked to write the equation of a horizontal line that passes through the given point. Horizontal lines have a slope of zero (0), so we’ll begin by inserting this value into the slope-intercept formula:

y = (0)x + b

Now simplify the right side of the equation:

y = b

Now we must find the y-intercept of the line in question. We are given that it passes through point (0,3). We know that any point taking the form (0,y) lies on the y-axis and, consequently, can be classified as a y-intercept. Therefore, the y-intercept of the given line must be 3. Insert this value into the simplified equation above:

y = b
y = (3)

We have now proven that the equation of the given line is (y = 3).

I hope this helps!

Aiden mixes 630 mL of blue paint with 2 L of red paint to make purple paint how many milliliters of purple paint does Aidan have

Answers

Aiden will have 2630ML.

Here's why: Every liter has 1000 milliliters. so two L is 2000 liters. so 2000+630= 2630 :)

What is the area of triangle ABC

Answers

The answer for this is B

Answer:

8.4

Step-by-step explanation:

mila wants to spend at least $20 on a classified ad in the newspaper. She has $12, how much does she need?

I need an equation with an inequality please:) thank you!

Answers

x >= (at least symbol) $9 since she needs AT LEAST 20$ and she already has 12$ so 12+9>20

Mila needs at least $8 more to reach her goal of spending $20 on a classified ad. The inequality to represent this problem is x ≥ 8, where x is the amount of additional money she needs.

If Mila wants to spend at least $20 on a classified ad and currently has $12, we need to figure out how much more money she needs. We denote the amount of money she needs with the variable x. An inequality that represents this situation is:

12 + x ≥ 20

Subtracting 12 from both sides of the inequality to isolate x, we get:

x ≥ 20 - 12

x ≥ 8

So, Mila needs at least $8 more to have enough for the classified ad.

Which of the following describes the translation of the graph of y = x2 to obtain the graph of y = -x2 + 3?

Answers

f(x + q) - left q units
f(x - q) - right q units
f(x) + q - up q units
f(x) - q - down q units
-f(x) - symmetry with respect to the x--xaxis
f(-x) - symmetry with respect to the y-axis

y = - x² + 3 = -(x² - 3)

3 units down and next symmetry with respect to the x axis.

Look at the picture.

You are building a rectangular deck. The area of the deck should be 250ft². You want the length of the deck to be 5 ft longer than twice its width. What should the dimensions of the deck be?

Answers

I think the answer to this problem is the width is 10 and the length is 25 because of this of this equation 2w^2+5w-250=0
Then..
(2w+25)*(w-10)=0
and you get the answer of w=10 and l=25

six less than four times a number is 26. What is the number?

Answers

Okay, lets see here. So since we know that 26 is six less than the actual answer, we'll add 6 to 26 which gives us 32. Then we'll do 32 divided by 4, which is 8.

Hello there!

The number would be - 8

lets do the work:

(8 x 4) - 6 = 26

Therefore your answer is 8.

Hope this helps!

~DL

What is the value of x?
sin(x+21)°=cos(2x+21)°

Answers

we know that
if sin A=cos B
then
angle A and angle B are complementary angles
so
A+B=90°

in this problem
(x+21)+(2x+21)=90-------> 3x+42=90-------> 3x=48-----> x=16°

Expand the binomial (2x + y^2)^5.

The fourth term in the expansion of the binomial (2x + y^2)^5 is _____

Answers

(2x + y^2)^5 = (2x)∧5 + 5(2x)∧4×y² + 10(2x)∧3×y∧4 + 10(2x)²×y∧6 + 5(2x)y∧8 +y∧10

= 32x∧5 +80x∧4y² + 80x∧3y∧4 + 40x²y∧6 + 10xy∧8 + y∧10

The fourth term of the binomial expansion (2x + y^2)^5 is 40x²y∧6

find the measure of the angle

Answers

The given angle is 55 degree. Thus the angle asked is 55 + 90 = 145 degree angle.

Measure of the Bigger Angle= Measure of Given Angle+Measure of Smaller Angle

Measure of Bigger Angle =Measure of Angle to be Found

Measure of Angle to be Found= Measure of Given Angle + Measure of Smaller Angle

The smaller Angle signifies one quadrant

So, Measure of Smaller Angle = 90°

Measure of Angle to be found=90°+Measure of given Angle

Measure of Angle to be found=90°+55°

Measure of Angle to be found=145°

Answer:145°

Tara has 2 bags of marbles. The first bag contains 6 red marbles,5 blue marbles and 4 green marbles.The second bag contains 3 red marbles,2 blue marbles, and 4 green marbles.Tara will randomly select 1 marble from each bag.What is the probability that Tara will select a blue marble from each bag?

Answers

Answer: Tara will have a 2/27 probability of choosing a blue marble from each bag

solution: First, we need to find the probability for the first bag using (p= number of outcomes/ total of outcomes), the number of outcomes is 5, and the total is 15, so our probability for bag 1 is 5/15.

Then, for the second bag, the number of outcomes is 2, and the total is 9, so the probability for the second bag is 2/9

To find the probability for both of the bags, we have to multiply them: 5/15 × 2/9= 10/135=2/27

Please answer and explain

Answers

TOP QUESTION:
a= one leg
b= other leg
c= hypotenuse

a^2 + b^2= c^2
plug in known numbers

(3)^2 + (2)^2= c^2

9 + 4= c^2

13= c^2
take the square root of both sides

√13= c
13 is not a perfect square

ANSWER: (C) √13 cm
________________

BOTTOM QUESTION:
a= one leg
b= other leg
c= hypotenuse

a^2 + b^2= c^2
plug in known numbers

(6)^2 + (10)^2= c^2

36 + 100= c^2

136= c^2
take square root of both sides

√136= c
136 is not a perfect square

ANSWER: (D) √136 ft

Hope this helps! :)

A plane can travel 640 miles against the wind in the same time it can travel 800 miles with the wind. If the plane can fly 180 mph in calm air, what is the speed of the wind? If x represents the speed of the wind, which expression represents the time it takes for the plane to travel the 640 miles against the wind?

Answers

Answer:

640/(180 - x)

Step-by-step explanation:

The expression for time it takes for the plane to travel the 640 miles is 640/ (180- x).

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Let the speed of the wind be x

Speed of the plane is 180 mph

When plane flew with wind , Speed = (180+x)

When plane flew against the wind , Speed=(180-x)

Since we are given that A plane can travel 640 miles against the wind .

So, Time= Distance / speed

Time= 640/ (180 - x)

Hence, time it takes for the plane to travel the 640 miles is 640/ (180- x)

Learn more about Algebra here:

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A square pyramid is sliced so that the cross section is perpendicular to its base. The cross section intersects the vertex of the pyramid. What is the shape of the cross section?
Question 1 options:

Trapezoid
Triangle
Square
Pentagon

Answers

Question 2. Triangle

B.Triangle Is your answer

On February 1, the electricity meter reading for the Smith residence was 19,423 kilowatt hours. On March 1, the meter read 20,288 kilowatt hours. On April 1, the meter read 21,163 kilowatt hours. a. How many kilowatt hours of electricity did the Smiths use during February? b. How many kilowatt hours did they use during March?

Answers

a. How many kilowatt hours of electricity did the Smiths use during February?

Kilowatt hours of electricity the Smiths used during February:
Meter read on March 1 - meter read on February 1 =
20,288 kilowatt hours - 19,423 kilowatt hours =
865 kilowatt hours
Answer: The Smiths used 865 kilowatt hours of electricity during February

b. How many kilowatt hours did they use during March?

Kilowatt hours of electricity the Smiths used during March:
Meter read on April 1 - meter read on March 1 =
21,163 kilowatt hours - 20,288 kilowatt hours =
875 kilowatt hours
Answer: The Smiths used 875 kilowatt hours of electricity during March

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