Mathematics High School

The length of a rectangle is 3 meters less than twice the width. if the area of the rectangle is 527 square​ meters, find the dimensions.

Answers

Answer 1
The rectangle is 17 meters wide and 31 meters long. To solve this problem, first work out the equation for the length of the rectangle. Using the information given, we find that length (L) is given by L=2W-3. Next we setup the formula for the area of a rectangle, A=(W)(L). We are told that the area is 527 sq. meters, so our equation is 527=(W)(L). We also know that L=2W-3, so we can plug that into the equation for area as well which gives us 527=W(2W-3), which can be written 0=2(W^2)-3W-527. We now need to solve this equation for W. Factoring the left side we get, 0=(W-17)(2W+31). Thus, either (W-17)=0 or (2W+31)=0 must equal zero. Solving these two equations, we get W=17 or W=-15.5. Since we are looking for the width (which is a length), we know it cannot be negative and therefore the width must be 17 meters. Now that we know the width, we can plug W=17 back into the equation for length (L=2W-3). Doing this give us L=2(17)-3 which is equal to 31. Thus the length is 31 meters.
Answer 2

Answer:

w=17

l=31

Step-by-step explanation:

correct

Related Questions

What is the value of x? I don't know if I'm right so did i get this answer right? please help i need help ASAP

Answers

3/5 =0.6

40 *0.6 = 24

2x+10 =24

2x=14

x = 14/2 = 7

The set of all x values that make up the function is called the

Answers

Domain. I'm pretty sure. please comment if wrong

what did the candle say to the match

Answers

YOU LIGHT UP MY LIFE

What does it mean when the average is less than the median?

Answers

This is common for a distribution that is skewed to the right (that is, bunched up toward the left and with a "tail" stretching toward the right). Similarly, a distribution that is skewed to the left (bunched up toward the right with a "tail" stretching toward the left) typically has a mean smaller than its median.

please help me with this, thanks !!

Answers

Y=4 and the slope of the problem would be -5

Kim's softball team is playing in the championship game. They are losing by a score of 171717 to 666. There are 444 innings to go. Kim wants to know how many runs her team needs per inning to win the game if the other team does not score. (Each run is worth 111 point.) Let rrr represent the number of runs per inning. Assume that the team scores the same number of runs per inning, and write an inequality to determine the number of runs per inning needed to win the game.

Answers

171717-666 = 171051 runs are needed.

171051 / 444 = 385.25 points per inning are needed

385.25 / 111 = 3.47 runs are needed per inning, round up to 4


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Answers

Greetings!

Substitute:
[tex]x+y=1000 \\ x=1000-y[/tex]
Now we can input this into the other equation so, we only have one variable.

Solve for y.
[tex]0.05(1000-y)+0.06y=57[/tex]
Distribute the parenthesis.
[tex]50-0.05y+0.06y=57[/tex]
Combine Like Terms.
[tex]50-0.01y=57[/tex]
Add -50 to both sides.
[tex](50-0.01y)+(-50)=(57)+(-50)[/tex]
Simplify.
[tex]0.01y=7[/tex]
Divide both sides by 0.01.
[tex](0.01y)/0.01=(7)/0.01[/tex]
Simplify.
[tex]y=700[/tex]

Input this value into the other equation.
[tex]x+700=1000[/tex]
Add -700 to both sides.
[tex](x+700)+(-700)=(1000)+(-700)[/tex]
Simplify.
[tex]x=300[/tex]

The answer would be 300,700

Hope this helps.
-Benjamin

I really need help with these problems please come it will mean a lot if u help.

Answers

1. 59 degrees

2. 59 degrees

3. would be 4

I'm not for sure about the other ones...


I need help with #17

Answers

The van's consumption is 200/10  = 20 miles per gallon

so for 480 miles we need  480 / 20  = 24 gallons

Justin is constructing a line through point Q that is perpendicular to line n. He has already constructed the arcs shown. He places his compass on point B to construct an arc. What must be true about the width of the compass opening when Justin draws the arc?
A .It must be wider than when he constructed the arc centered at point A.

B It must be the same as when he constructed the arc centered at point A.

C. It must be equal to BQ .

D.It must be equal to AB .


Answers

B. It must be the same as when he constructed the arc centered at point A. This problem would be a lot easier if you had actually supplied the diagram with the "arcs shown". But thankfully, with a few assumptions, the solution can be determined. Usually when constructing a perpendicular to a line through a specified point, you first use a compass centered on the point to strike a couple of arcs on the line on both sides of the point, so that you define two points that are equal distance from the desired intersection point for the perpendicular. Then you increase the radius of the compass and using that setting, construct an arc above the line passing through the area that the perpendicular will go. And you repeat that using the same compass settings on the second arc constructed. This will define a point such that you'll create two right triangles that are reflections of each other. With that in mind, let's look closely at your problem to deduce the information that's missing. "... places his compass on point B ..." Since he's not placing the compass on point Q, that would imply that the two points on the line have already been constructed and that point B is one of those 2 points. So let's look at the available choices and see what makes sense. A .It must be wider than when he constructed the arc centered at point A. Not good. Since this implies that the arc centered on point A has been constructed, then it's a safe assumption that points A and B are the two points defined by the initial pair of arcs constructed that intersect the line and are centered around point Q. If that's the case, then the arc centered around point B must match exactly the setting used for the arc centered on point A. So this is the wrong answer. B It must be the same as when he constructed the arc centered at point A. Perfect! Look at the description of creating a perpendicular at the top of this answer. This is the correct answer. C. It must be equal to BQ. Nope. If this were the case, the newly created arc would simply pass through point Q and never intersect the arc centered on point A. So it's wrong. D.It must be equal to AB. Sorta. The setting here would work IF that's also the setting used for the arc centered on A. But that's not guaranteed in the description above and as such, this is wrong.

Answer:

just to confuse yall less it is indeed b!

Step-by-step explanation:

took the test on k12

y1=4(5x-1), y2-=5x+1 and y1 is 344 more than 2 times y2

Answers

 [tex]y_1=4(5^x-1)[/tex] and [tex]y_2=5^x+1[/tex]

[tex]y_1=344+2y_2[/tex]
[tex]y_1=344+2(5^x+1)[/tex]
[tex]4(5^x-1) = 344 + 2(5^x+1)[/tex]
[tex](4)(5^x)-4=344+2(5^x)+2[/tex]
[tex]4(5^x)-2(5^x)=344+2+4[/tex]
[tex]2(5^x)=350[/tex]
[tex]5^x= \frac{350}{2} [/tex]
[tex]5^x=175[/tex]
[tex]log(5^x)=log(175)[/tex]
[tex]x(log(5))=log(175)[/tex]
[tex]x= \frac{log175}{log5} [/tex]
[tex]x=3.21[/tex] (rounded to two decimal places)

If a certain number is added to both the numerator and denominator of the fraction 7 6 76, the result is 3 2 32 . find the number.

Answers

Assuming that the right statement is that if a certain number is added to both the numerator and the numerator of the fraction 7/6, the result is 3/2, find the number, the solution if found in this way:

Call x the number (certain number)

=> (7+x) / (6 +x ) = 3/2

=> (7 + x)*2 = 3*(6 + x)

=> 14 + 2x = 18 + 3x

=> 14 - 18 = 3x - 2x

=> - 4 = x

verification> ( 7 - 4) / ( 6 - 4) = 3 / 2

Answer: the number is  - 4.


The number 0 belongs to which classification?

A. irrational numbers

B. natural numbers

C. integers

D. all of the above

Answers

Your answer will be C. Integers
The answer is C. Integers

The sum of two numbers is 67 . the larger number is 5 more than the smaller number. what are the numbers?

Answers

Call the numbers x and y. According to the first sentence, x + y = 67. According to the second sentence, x = y + 5. You can combine these two equations to find the values of these variables:

x + y = 67
(y + 5) + y= 67
2y = 62
y = 31

You can use this to find x by plugging in y to either original equation:

x = y + 5
x = 31 + 5
x = 36

write a word phrase for each algebraic expression

1. 25 - 6

2. 2/3y + 4

factor each expression

3. 45c + 10d

4. 27 - 9x + 15y

Simplify the expression.

5. 3(t - 4) - 8 (2 - 3t )

6. 12x + 24

Answers

1.) Twenty five minus six

Answer:


Step-by-step explanation:

1)Twenty five minus sixty percent times a number.



What is the area of a triangle with vertices at (−2, 1) , (2, 1) , and ​ (3, 4) ​ ? Enter your answer in the box.

Answers

if you locate the three vertices on a grid, you will see that the length of the base is the distance between -2 and 2, which is 4, and the height is the distance between 4 and 1, which is 3
the area of a triangle is half of base times height
1/2 of 3*4=6

“all integers are rational numbers” true or false? why?

Answers

true
Every rational number can be written as a fraction a/b , where a and b are integers. ... If a number is a whole number, for instance, it must also be an integer and a rational.
true
Every rational number can be written as a fraction a/b , where a and b are integers. ... If a number is a whole number, for instance, it must also be an integer and a rational

How to solve for a side of a right triangle when you only know one side?

Answers

Well if you know the area of the triangle you can use that to find the other lengths or else just use the Pythagorean Theroem.

Hope I helped :)
If you only know one side, then that's not enough information to solve for any other part of a triangle. You also need to know the measures of the angles at each end of it. In a right triangle, that means you need to know one of the acute angles (since you already know the right angle).

Two cars leave town going in opposite directions. one car is traveling 55 miles per hour (mph), and the other car is traveling 40 mph. how long will it take before the cars are 285 miles apart?

Answers

The distance, d, traveled by a car going at speed, s, in time, t, is
d = st

Car 1 travels distance 1, d1, at s1 = 55 mph, for t1 time.
Car 2 travels distance 2, d2, at s2 = 40 mph, for t2 time.

The two distances add to 285 miles, so
d1 + d2 = 285
The two times are equal, so t1 = t2 = t

d1 = 55t1
d2 = 40t2

d1 = 55t
d2 = 40t

d1 + d2 = 55t + 40t

d = 95t

285 = 95t

95t = 285

t = 3

Answer: It will take 3 hours.

Note:
This problem shows you that if two cars are traveling along the same line in opposite directions, the speed at which they are distancing themselves is the sum of the two speeds. We can solve the problem in a simpler way:

55 mph + 40 mph = 95 mph

d = st

285 = 95t

t = 3

Answer: 3 hours.

Write an equation for the line parallel to the given line that contains
C(4,8);y=-3x+4

Answers

parallel line means they have the same slope 
y = mx + b 
where m = slope 
y = -3 + 4
here the slope is negative 3
y = -3x + b
plug in (4, 8)
8 = -3(4) + b 
b = 8 + 12
b = 20

The answer is y = -3x + 20

Angle a has the property that twenty eight times times its complement is equal to thirteen times its supplement. find the measure of angle
a.

Answers

< a....its complement is (90 - a) and its supplement is (180 - a)

28(90 - a) = 13(180 - a)
2520 - 28a = 2340 - 13a
-28a + 13a = 2340 - 2520
- 15a = - 180
a = -180/-15
a = 12 <=== so < a = 12

1. Create a circle. Show and explain the difference between the following:
a. secant line and tangent line
b. inscribed angle and central angle

2. Describe the steps necessary to construct an inscribed circle in a triangle and contrast this with the steps you take to construct a circumscribed circle.

3. Demonstrate on the whiteboard how to find the center and radius of a circle using an equation. Be sure to provide a unique example of your own that shows how to find both of these.

4. A classmate is having difficulty finding the measures of
5. The world’s largest round pizza, which also happened to be gluten-free, was set in December 2012 by five Italian chefs. The diameter of this pizza was 131 feet. If this pizza was cut into 50 slices, what would be the area of each slice and the length of the crust for the slice? Explain what concepts of a circle these calculations related to.

Answers

1. 
a.
A secant line is a line which intersects the circle at 2 different points. 

A tangent line is a line which has only one point in common with the circle.

Check picture 1: The orange line s is a secant line, the blue line t is a tangent line.


b.
An inscribed angle is an angle formed by using 3 points of a circle. 

The main property of an inscribed angle is that its measure is half of the measure of the arc it intercepts.

Check picture 2: If  [tex]m(\angle KML)=\beta[/tex], then the measure of arc KL is [tex]2 \beta [/tex].

A central angle is an angle whose vertex is the center of the circle, and the 2 endpoints of the rays are points of the circle.

The main property is: the measure of the central angle is equal to the measure of the arc it intercepts. 

Check picture 2

2.
To construct the inscribed circle of a triangle, we first draw the 3 interior angle bisectors of the triangle.
They meet at a common point called the incenter, which is the center of the inscribed circle.
We open the compass, from the incenter, so that it touches one of the sides at only one point. We then draw the circle. (picture 3)

To draw the circumscribed circle, we first find the midpoints of each side. We then draw perpendicular segments through these (the midpoints.) They meet  at one common point, which is the circumcenter: the center of the circumscribed circle.
We open the compass from the circumcenter to one of the vertices of the triangle. We draw the circle, and see that it circumscribes the triangle.

(picture 4)

3.

Given an equation of a circle: [tex]x^2-2x+y^2+6y+6=0[/tex].

To determine the center and the radius of the equation we must write the above equation in the form :

                              [tex](x-a)^2+(y-b)^2=r^2[/tex].

Then, (a, b) is the center, and r is the radius of this circle. We do this process by completing the square.

Note that [tex]x^2-2x[/tex] becomes a perfect square by adding 1, and 
[tex]y^2+6y[/tex] becomes a perfect square by adding 9. 

Thus we have:

[tex]x^2-2x+y^2+6y+6=0\\\\(x^2-2x+1)+(y^2+6y+9)-4=0\\\\(x-1)^2+(y+3)^2=2^2[/tex]

Thus, the center is (1, -3), and the radius is 2.

4. Not complete


5.

The radius of the pizza is [tex]\displaystyle{ \frac{131}{2}ft=65.5ft [/tex].

The surface of a circle with radius r is given by the formula [tex]\displaystyle{  A=\pi r^2[/tex],
and the circumference is given by the formula C=2πr.

Thus, the area of the whole pizza is given by [tex]\displaystyle{ A=\pi r^2= \pi\cdot65.5^2=4290.25 \pi [/tex] (square ft).

Each of the 50 slices, has an area of [tex]\displaystyle{ \frac{4290.25 \pi}{50} =85.805 \pi [/tex] (square ft)

Notice that the perimeter (the crust) of a slice is made of 2 radii, and the arc-like part.
The arc is 1/50 of the circumference, so it is [tex] \displaystyle{\frac{2 \pi r}{50} = \frac{2\cdot65.5\cdot \pi }{50}= 2.62 \pi [/tex].

So the perimeter of one slice is 65.5+65.5+2.62π=131+2.62π

Final answer:

The differences between secant and tangent lines, and between inscribed and central angles, involve the number of intersection points with the circle and the position of the vertex, respectively. Constructing an inscribed circle involves finding the incenter, while a circumscribed circle requires finding the circumcenter. To find the center and radius of a circle using its equation, we use the standard form (x - h)² + (y - k)² = r².

Explanation:

Differences Between Secant Lines, Tangent Lines, Inscribed Angles, and Central Angles

A secant line is a line that intersects a circle at two points, while a tangent line touches the circle at exactly one point. An inscribed angle is an angle formed by two chords in a circle that meet at one point in the circle, whereas a central angle is an angle whose apex (vertex) is the center of the circle.

Constructing Inscribed and Circumscribed Circles in a Triangle

To construct an inscribed circle (incircle) of a triangle, draw the angle bisectors of the triangle's angles to find the incenter, and then use this point to draw the circle that touches all three sides of the triangle. For a circumscribed circle (circumcircle), draw the perpendicular bisectors of the triangle's sides and the point where they intersect will be the circumcenter; use this as the center to draw the circle that passes through all three vertices of the triangle.

Finding the Center and Radius of a Circle Using an Equation

Given a circle's equation in the standard form (x - h)² + (y - k)² = r², the center is at point (h, k), and the radius is the square root of r². For example, if we have the equation (x - 3)² + (y + 2)² = 16, the center is (3, -2) and the radius is 4 units.

Area and Length of the Crust of a Circular Pizza Slice

For the world's largest round pizza with a diameter of 131 feet, the radius would be 65.5 feet. The area of each slice is a fraction of the whole pizza's area, which can be found using the formula A = πR², and the length of the crust for the slice corresponds to the arc length of that slice.

Area of whole pizza = 3.14 * 65.5² ≈ 13478.2 ft²

Area of each slice = total area /50 = 13478.2/50 ≈ 269.5 ft²

Length of crust =  2πR * (slice area/total area)

= 2 * 3.14 * (1/50)

≈ 0.125 ft

Simplify (s)(-3st)(-1/3).
A.) -3 1/3 t
B.) s^2t
C.) 3s^2t 
(If this format is too weird I have added a screenshot)

Thanks in advance!

Answers

the answer is b!!!!!!
The 3 will cut off each other and the s will be squared so the answer is B..s^2.t

1. round the result to 2 decimal places. -0.9x+2.8=4.1
a) -2.56
b) -2.56
c) -1.44
d) 2.20

2. jordan has 650 pennies. he plans to give 85 to his brother and split with his twin sister. he wants to know how many pennies to keep for himself. which equation models the situation?
a) 2(85+2x=650
b) 85(x-2)=650
c) 85x=650
d) 85+2x=650

Answers

1. -0.9x+2.8=4.1
First subtract 2.8 from both sides.
-0.9x = 1.3
Now divide both sides by -0.9.
x = -1.4444..
This can be rounded to -1.44
c) -1.44

2. Jordan has 650 pennies. He'll give 85 to his brother and split the rest with his sister.
d) 85+2x=650

A share of stock in the Lofty Cheese Company is quoted at 251/4. Suppose you hold 30 shares of that stock, which you bought at 201/4. If you sell your stock at 251/4, how much profit do you get or lose?

Answers

You'll make a profit of $150.

To calculate the profit from buying and selling stocks, subtract the buying price per share from the selling price per share and then multiply by the number of shares. For 30 shares of the Lofty Cheese Company stock, the profit would total $150.

The question involves calculating the profit from buying and selling stocks. When selling the Lofty Cheese Company stock quoted at 251/4 per share, we need to calculate the profit based on the purchase price (201/4) and the selling price (251/4) for 30 shares.

To find the profit per share, subtract the buying price from the selling price:

Selling Price per Share = 251/4

Buying Price per Share = 201/4

Profit per Share = Selling Price - Buying Price = 251/4 - 201/4 = 5

Then, multiply the profit per share by the total number of shares:

Number of Shares = 30

Total Profit = Profit per Share times Number of Shares = 5 times 30 = 150

Therefore, you would realize a total profit of $150 by selling your 30 shares of the Lofty Cheese Company stock.


The functions graphed show the snowfall, in inches, in two cities after x hours.

Select each correct answer.



Middletown had a faster rate of snowfall.

Smithville had a faster rate of snowfall.

Snow fell in Smithville at a rate of 4 inches per hour.

Middletown already had snow on the ground at the beginning of the storm.

Answers

The answer Fam is............. Smithville had a faster rate of snowfall., And..Snow fell in Smithville at a rate of 4 inches per hour.

we know that

the formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

in this problem

the rate of snowfall is equal to the slope of the linear equation

so

Let

x-------> the time in hours

y---------> the snowfall in inches

Step 1

Find the slope of the line of the Smithville city

Let

[tex]A(0,0)\\B(5,20)[/tex]

substitute the values in the formula above

[tex]m=\frac{20-0}{5-0}[/tex]

[tex]m=4\frac{inches}{hour}[/tex]

Step 2

Find the slope of the line of the Middletown city

Let

[tex]A(0,0)\\B(5,15)[/tex]

substitute the values in the formula above

[tex]m=\frac{15-0}{5-0}[/tex]

[tex]m=3\frac{inches}{hour}[/tex]

Step 3

Verify the statements

case A) Middletown had a faster rate of snowfall

The statement is False

Because Smithville had a faster rate of snowfall with [tex]4\frac{inches}{hour}[/tex]

case B) Smithville had a faster rate of snowfall

The statement is True

case C) Snow fell in Smithville at a rate of 4 inches per hour

The statement is True

case D) Middletown already had snow on the ground at the beginning of the storm

The statement is False

Because at the beginning of the storm the value of the snow is equal to zero

therefore

the answer is

Smithville had a faster rate of snowfall

Snow fell in Smithville at a rate of 4 inches per hour

I NEED QUICK HELP QUICK!!! PLEASE HELP ME SOMEONE!! THANK YOU!!

Which graph does NOT represent a function?

Answers

B or A, either A is not passing the vertical line test or B is just not a real function most likely A, DO. NOT. flame me if I got it wrong

Answer:

ITS B!!!

Step-by-step explanation:

find the length of the arc on a circle of radius 12 feet intercepted by a central angle of 150°.

Answers

Let A = arc length of circle

A = 2πr•(degree/360°)

A = 2π(12)(150°/360°)

A = 24π(150°/360°)

Calculate the right side to find A and you're done. Take it from here.

Your Turn: Find the equation of a line that is parallel to y=2x+7, and passes through the point (-4, 7). SHOW YOUR WORK

Answers

Parallel lines have the same slope. Let's fill that into the slope-intercept equation.
y=2x+b

Now, we can use the point we are given to find the y-intercept.
7=2(-4)+b
7=-8+b
b=7+8
b=15

Finally, we can substitute all the information we have discovered to complete the slope-intercept equation.
y=2x+15

the ratio of girls to boys in a tennis club is 4:5 if there are 144 children in the club how many girls are there

Answers

4:5 means 4 girls to every 5 boys

4+5=9

144/9 = 16

4 *16 = 64 girls

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