[tex]\text{Width} ~= w ~ cm \\\\ \text{Length}~,l = (20+ w) ~ cm \\\\\text{Area of rectangle} = 1000 cm^2\\\\\\\text{Now,}\\\\l \cdot w = 1000\\\\\implies (20 + w) w= 1000\\\\\implies w^2 +20w -1000=0\\\\\\\implies w = \dfrac{-20 \pm \sqrt{20^2 - 4 \cdot 1 \cdot (-1000)}}{2 \cdot 1}\\\\\\\implies w = \dfrac{-20 \pm \sqrt{4400}}{2}= \dfrac{-20\pm 20\sqrt{11}}2 = -10 \pm 10\sqrt{11}\\\\\text{Width cannot be negative so,} \\\\w= -10+10\sqrt{11}=10\left(\sqrt{11} - 1 \right) ~ cm\\\\[/tex]
[tex]\text{And length,}[/tex]
[tex]l= 20+ 10\left(\sqrt{11} - 1} \right) = 20 + 10\sqrt{11} - 10 = 10 + 10\sqrt{11} = 10 \left(1+ \sqrt{11} \right)~ cm[/tex]
Write a proportion relating the side lengths of the triangle to any other triangle that has the line as a hypotenuse, a horizontal length of x units, and a vertical length of y units.
Answer:
y/x = 2 or y = 2xStep-by-step explanation:
The given triangle has:
Vertical segment = 2 unitsHorizontal segment = 1 unitThe ratio (slope) is:
2/1 = 2For any triangle using same line the proportion is:
y/x = 2 ory = 2xFatima writes down three square numbers.
The total of the square numbers is 30.
Which square numbers did Fatima write down?
Answer:
10
Step-by-step explanation:
Fatima wrote down 3 square numbers
since we don't know the three square we will represent it by any variable (X)
3x=30
so you divide both sides by 3
so we have 3x/3=30/3=10
therefore the answer is 10
The total of the square numbers is 30.
The squares can be from the following.
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
1 + 4 + 25 = 30
The three square numbers are 1, 4, and 25.
What is an expression?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The total of the square numbers is 30.
The squares can be from the following.
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
We can take three squares.
1 + 4 + 25 = 30
This is a perfect case.
Thus,
The three square numbers are 1, 4, and 25.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
Give coordinates for three possible pairs of points for the other two verticies...
Answer:
A) (-1,3) and (4,3)
B) (-1,-7) and (4,-7)
C) (1.5, .5) and (1.5, -4.5)
Step-by-step explanation:
For 1 and 2, because the y-values of the points are the same, the length of the square can be found by subtracting the x-coordinates.
4-(-1)=4+1=5
The length of the side of the square is 5.
1. For the first set of points, the square is above the two given points so just add 5 to the y-values
-2+5=3
This gives you the points:
(-1,3) and (4,3)
2. For the second set of points, the square is below the two given points so subtract 5 from the y-values.
-2-5=-7
This give you the points:
(-1,-7) and (4,-7)
3. The third answer is when the two given points are on opposite corners
of the square.
Here the diagonal is equal to 5 since they are on opposite corners of the square.
The diagonal of a square can be found with the pythagorean theorem
Since we have the diagonal we can find the side lengths we need.
[tex]2s^2=25[/tex]
s=[tex]\sqrt{\frac{25}{2} }[/tex]
s=3.5355
We want the new vertices to be in the middle of the other vertices x-coordinates
[tex]\frac{4-(-1)}{2} =\frac{5}{2} =2.5[/tex]
The new vertices will be 2.5 units away from the other vertices
-1+2.5=1.5
The new vertices will be at x=1.5
Now we need the pythagorean theorem again to find the y-values
[tex](2.5)^2+h^2=(3.5355)^2[/tex]
[tex]6.25+h^2=\frac{25}{2}[/tex]
[tex]h=\sqrt{\frac{25}{2} -6.25}[/tex]
h=2.5
The new vertices will be:
(1.5, -2+2.5)=(1., .5)
(1.5, -2-2.5)=(1.5, -4.5)
Find the equation of the line perpendicular to the given line and passing through the given point.
y = -4x + 2;(-1,4)
Step-by-step explanation:
hope it helps you.......
Stop and answer this question
The first truck carries 35 tons less rice than the second truck. The number of paddy in the first truck is 2/3 of the amount in the second truck. How many tons of paddy does each cart hold?
First truck = x
Second truck = y
x + 35 = y
x = 2/3y
So
2/3y +35=y
1/3y = 35
y = 35*3
y = 105
And ,
x = 2/3y = 70
please ehlp delta math with explanation please
Answer:
134.3
Step-by-step explanation:
In [tex]\triangle{WXZ},[/tex] a right triangle, look at sides XW and XZ.
[tex]\frac{XW}{XZ}=\frac{\text{adjacent}}{\text{hypotenuse}}=\cos{82^\circ}\\\\XW=(XZ)\cos{82^\circ}[/tex]
You now need to find XW.
In [tex]\triangle{XYZ},[/tex] the measure of angle XZY (the one at the top) is 180 - (82 + 67) = 31 degrees.
Using the Law of Sines in triangle XYZ,
[tex]\frac{XZ}{\sin{67^\circ}}=\frac{540}{\sin{31^\circ}}\\\\XZ=\frac{540 \sin{67^\circ}}{\sin{31^\circ}}[/tex]
Put that into the equation for XW above...
[tex]XW=\frac{540\sin{67^\circ}\cos{82^\circ}}{\sin{31^\circ}}[/tex]
A calculator shows that this is approximately 134.3
Write a conditional statement that represents the Euler Diagram.
If a plant is a _________ , then the plant is a _________.
Answer:
if a plant is a carrot , then the plant is a vegetable
Step-by-step explanation:
it just a grammar you should think
someone plz help me!!!!!!!!!!!!!!
Step-by-step explanation:
In the given set of questions regarding the concept of division, it is important to understand the parts of a division problem.
Definitions:In a division problem such as 15 ÷ 3 = 5:
15 represents the dividend, which is the number being divided into groups. 3 represents the divisor, which is the number of groups that divides the dividend. 5 represents the quotient, which is the result of dividing the dividend and the divisor. Solution:Now that we have defined the parts of a division problem, we can proceed to matching the division problems to its corresponding representation of equal groups.
1.) 15 ÷ 3 = 5 ⇒ "There are 5 equal groups of 3."
If you multiply the quotient, 5, by the divisor, 3, it results in the dividend: 5 × 3 = 15. This occurs because multiplication is the opposite mathematical operation of division.
2.) 45 ÷ 5 = 9 ⇒ "There are 9 equal groups of 5."
9 equal groups of 5 = 9 × 5 = 45.
3.) 8 ÷ 4 = 2 ⇒ "There are 4 equal groups of 2."
4 equal groups of 2 = 4 × 2 = 8.
4.) 18 ÷ 6 = 3 ⇒ "There are 3 equal groups of 6."
3 equal groups of 6 = 3 × 6 = 18.
Solve for x:
-15 = x/-0.5
x =
/ = fraction symbol
Answer:
7.5
Step-by-step explanation:
You first have to switch the sides of the numbers. After you do that you multiply both sides by -0.5. Finally, you simplify and get 7.5
Brainliest pls?
Answer:
7.5
Step-by-step explanation:
You can multiply both sides by -0.5.
-15×-0.5=7.5
x=7.5
Hope that helps! :)
I WILL MARK BRAINEST!!!
#6 D and E please!
Answer:
Q1 = 13.5
Q3 = 17.5
Step-by-step explanation:
6d) ===============
12, 12, 13, 14, 14, 17, 17, 17, 17, 18, 19, 20
I counted 12 numbers in this set. The median is the middle number of a sorted set. It's also the 2nd quartile as it is 2 quarters in, or 50% in.
First, find the median. In an even-numbered set, that's the average of the 2 middle numbers. In this case, it's between 17 and 17:
12, 12, 13, 14, 14, 17 === 17, 17, 17, 18, 19, 20
Now the set is split into 2 sets with 6 numbers each. Now, find the median of each of those sets. Again, the median of an even-numbered set is the average of the 2 middle numbers.
To find the first quartile (Q1), find the median of the lower set.
12, 12, 13 === 14, 14, 17
The median here is the average of 13 and 14, so 13.5.
6e) ==============
Exactly the same process as above.
7, 12, 12, 13, 14, 14, 17, 17, 17, 18, 19, 20
12 numbers again.
7, 12, 12, 13, 14, 14 === 17, 17, 17, 18, 19, 20
Now, to find the third quartile, find the median of the upper set.
17, 17, 17 === 18, 19, 20
The median is the average of 17 and 18, or 17.5.
Please help mee please plese
Answer:
C=66, C=25 1/7
Step-by-step explanation:
i
C=pi(d)
C=22/7*21
C=66
ii
C=pi(d)
C=22/7*16
C=25 1/7
7 Mathexcellup logo
I answered the question and got it right.
what is 22 over 7 - 2 over 3 divided by 2
Find the value for x
15 points for you plus brainliest, 5 star and thanks on answer and profile
Answer:
117 units
Step-by-step explanation:
A bird flying 45 feet above a river dives
down 58 feet to catch a fish. Find the
location of the fish relative to the surface of
the water.
what’s y = x +-2 -76
Answer:
y = x - 78
Step-by-step explanation:
y = x +-2 -76
y = x -78
jonshelle is developing a new bread recipe. the relationship between cups of water,w, and cups of flour,f, is w= 3/5f. what is the scale to water to flour
Answer:
3:5
Step-by-step explanation:
ratio!
PLS help im stuck i dont understand how to do the problem
Helppp!! I cant get this wrong lol
Answer:
x = 2
y = -7
Step-by-step explanation:
First, we see that all the terms in the first equation can be divided by 7:
-x + y = - 9
Then we solve for x by adding adding x and 9 to both sides:
-x + x + y + 9 = -9 + 9 + x
it cancels out to:
y + 9 = x
Now, replace x in the second equation with (y + 9):
28(y + 9) - y = 63
Now simplify:
28(y) + 28(9) - y = 63
27y + 252 = 63
27y = 63 - 252
27y = -189
y = -7
Plug in the value for y in the equation for x:
y + 9 = x
-7 + 9 = x
x = 2
Answer:
-7x +7y = -63(i)
28x -y = 63 (ii)
Divide eq(i) by 7
-x + y = -9 (iii)
28x -y= 63 (ii)
Add (iii) and ii
-x + y = -9
28x - y = 63
------------------------
-x +28x +0 = -9 +63
27x = 54
●x = 2
Put x=2 in any eq..
Lets put in eq[i]
-7 (2) + 7y =-63
-14 + 7y = -63
7y = -63 +14
7y=49
●y=7
BRAINLIST PLS
(2x+5) (3x-15)
solve for x
•x=27
•x=20
•x=38
Answer:4799,2475,4941,
Step-by-step
I'm not sure,
but I solved replace the given numbes
For first, (2×27+5)(3×27-15)=4799, for second (2×20+5)(3×20-15)=2475
For third(2×38+5)(3×38-15)=4941
seven million five hundred and forty-two eight hundred in number form pls
Answer:
7,542,800
Step-by-step explanation:
Use the simple interest formula 1=prt find the amount that needs to be invested at 7%per year for 12 years in order to earn 2500$in interest
20
18. Find the values of x and y in the parallelogram PQRS.
vat
PT = 2x, TR = y +3, QT = 3x, TS = 2y
T
27
2x
Р
S
0
Answer:
Step-by-step explanation:
3. Given: DE is a midsegment of AABC. Show all work.
a. Find the value of x and y.
b. What is the length of AC?
Answer:
x = 10
y = 1
DE = 7
AC = 14
Step-by-step explanation:
x + 2 = 24/2
x = 12 - 2
x = 10
y + 6 = x - 3
y = 10 - 3 - 6
y = 1
Complete the description of the piecewise function graphed below.
Step-by-step explanation:
not everything is visible, and the points' coordinates have to optically estimated (particularly for the leftmost point).
I assume, we have the following points :
(-6, 1.5) (-3, 3)
(-3, 2) (1, 2)
(1, 1) (6, -9)
all 3 segments are lines with the basic function definition
y = ax + b
a is the slope of the line function and is always the factor of x.
it is the ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point on the line to another.
b is the y-intercept (the y value when x = 0).
the first segment goes from (-6, 1.5) to (-3, 3).
x changes by +3 units (from -6 to -3).
y changes by +1.5 or 3/2 units (from 1.5 to 3).
the slope of the line is 3/2 / 3 = 3/(2×3) = 1/2
giving us the first part
y = (1/2)x + b
b we get by using the coordinates of one point (e.g. -3, 3) as x and y values and solve for b :
3 = (1/2)×-3 + b
3 = -3/2 + b
6/2 + 3/2 = b
9/2 = b
the full equation is
y = (1/2)x + 9/2 = (x + 9)/2
the second segment is a flat, horizontal line and is simply
y = 2
the third segment goes from (1, 1) to (6, -9) :
x changes by +5 units (from 1 to 6).
y changes by -10 units (from 1 to -9).
the slope of the line is -10/5 = -2
giving us the first part
y = -2x + b
b we get by using the coordinates of one point (e.g. 1, 1) as x and y values and solve for b :
1 = -2×1 + b
1 = -2 + b
3 = b
the full equation is
y = -2x + 3
The answer is in the pic below!
Last year the French club raised $300 at their fall fundraiser. This year they raised $450. What is the percent increase in the amount raised?
(IN YOUR OWN WORD'S)
Answer:
50%
Step-by-step explanation:
Actual increase = $150
% increase = (actual change ÷ start value) × 100
= (150 ÷ 300) × 100
= 0.5 × 100
= 50%
What list shows these in order from least to greatest?
Square W: A= √325 in.2
Square X: A= 3π/.5 in.2
Square Y: A= 5.5π in.2
Square Z: A= 17.92 in.2
1. Z, Y, W, X
2. X, W, Z, Y
3. Y, Z, W, X
4. W, X, Y, Z
Answer:
4 i am not sure for this answer guess
Help algebra 2 please
Answer:
it should be C I guess.
Im sorry if it is wrong
A scientist tracks wolf populations in two parks. One population consists of 20 wolves and is increasing by an average of 2 per year. The other consists of 15 wolves and is increasing by an average of 3 per year. Write an equation that can be used to determine how many years, y, it will take for the two populations to be equal.
Answer:
it will take 5 years for them to be equal
Step-by-step explanation:
1st year they will be 22-18
2nd year they will be 24-21
3rd year they will be 26-24
4th year they will be 28-27
Finally the 5th year they will be 30-30
What property is illustrated in the following equation?
8 + 5 = 5 + ?
The answer is communitive property.
Answer: 3
Step-by-step explanation: Did it recently.
0.36 in simpliest form with the line over the 6
Answer:
11/30
Step-by-step explanation:
Let x = 0.366666666.....
Then
100x = 36.6666666....
10x = 3.6666666...
subtracting 100x - 10x eliminates the trailing 6s
90x = 33
divide both sides by 90
x = 33/90
reduce
x = 11/30