"The sum of two numbers is 20" can be translated mathematically into the equation:
x + y = 20.
"... and their difference is 10" can be translated mathematically as:
x - y = 10
We can now find the two unknown numbers, x and y, because we now have a system of two equations in two unknowns, x and y. We'll use the Addition-Subtraction Method, also know as the Elimination Method, to solve this system of equations for x and y by first eliminating one of the variables, y, by adding the second equation to the first equation to get a third equation in just one unknown, x, as follows:
Adding the two equations will eliminate the variable y:
x + y = 20
x - y = 10
-----------
2x + 0 = 30
2x = 30
(2x)/2 = 30/2
(2/2)x = 15
(1)x = 15
x = 15
Now, substitute x = 15 back into one of the two original equations. Let's use the equation showing the sum of x and y as follows (Note: We could have used the other equation instead):
x + y = 20
15 + y = 20
15 - 15 + y = 20 - 15
0 + y = 5
y = 5
CHECK:
In order for x = 15 and y = 5 to be the solution to our original system of two linear equations in two unknowns, x and y, this pair of numbers must satisfy BOTH equations as follows:
x + y = 20 x - y = 10
15 + 5 = 20 15 - 5 = 10
20 = 20 10 = 10
Therefore, x = 15 and y = 5 is indeed the solution to our original system of two linear equations in two unknowns, x and y, and the product of the two numbers x = 15 and y = 5 is:
xy = 15(5)
xy = 75
Solve x2 – 6x + 9 = 0 by completing the square.
Answer:
11/6
Step-by-step explanation:
See the steps below:)
2
Find the area of the shape.
Either enter an exact answer in terms of or use 3.14 for it and enter your answer as a decimal.
units?
Answer:
3pi or 9.42
Step-by-step explanation:
3/4x3.14x2x2=3pi or 9.42
A bag of marbles has 10 red marbles, 4 green marbles, and 6 blue marbles. A marble is randomly drawn from the bag before another marble is drawn, without replacement. What is the probability that a green marble and then a red marble are selected? Enter your answer as a fraction in simplest form in the box.
Answer:
2/19
Step-by-step explanation:
i just took the test and no one helped me i got is wrong but when you go back to review it it tells you the answer hope im not too late
Find the measurement of angle FRQ
Answer:
90 degrees
Step-by-step explanation:
I need help with this question I don’t understand it much?
Answer:
-5
Step-by-step explanation:
I think the m is for measure of line AB
what is 5 times 1/10 in simplest form.
Answer:
1/2
Step-by-step explanation:
5 x 1/10 = 0.5
0.5 = 1/2
Answer:
1 / 2
Step-by-step explanation:
4.4s + 6.2 = 8.8s - 1.8
please help
Answer:
s = 1.81
Step-by-step explanation:
4.4(1.81)+6.2=8.8(1.81)-1.8
plug in and multiply if you'd like to clarify :)
Answer:
=Steps
4.4s+6.2=8.8s−1.8
Multiply both sides by 10
4.4s· 10+6.2· 10=8.8s· 10−1.8· 10
Refine
44s+62=88s−18
Subtract 62 from both sides
44s+62−62=88s−18−62
Simplify
44s=88s−80
Subtract 88s from both sides
44s−88s=88s−80−88s
Simplify
−44s=−80
Divide both sides by −44
−44s
−44 =
−80
−44
Show Steps
Simplify
s=
20/11
Step-by-step explanation:
Someone help me pls!!!!????
Answer:
Greatest would be Chlorine Krypton Argon Fluorine and least Hydrogen
Answer:
J, I, G, K, H.
Step-by-step explanation:
The elements go from least to greatest, and since they are negatives, we sort them from the highest negative to the lowest negative.
find the slope of the line passing through
-2, 7 ) and ( 0, 1 )
Answer:
-3
Step-by-step explanation:
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized.
y = 0 + 1x + 2x2 +
where
y = traffic flow in vehicles per hour
x = vehicle speed in miles per hour
The following data were collected during rush hour for six highways leading out of the city.
Traffic Flow () Vehicle Speed ()
1256 35
1330 45
1226 30
1335 50
1349 50
1124 25
a. Use the data to compute the coefficients of this estimated regression equation (to decimals).
b. Using , test for a significant relationship. (to decimals) -value (to decimals) The relationship - Select your answer - significant.
c. Estimate the traffic flow in vehicles per hour at a speed of miles per hour (to decimals). vehicles per hour.
Answer:
I don't know this stuff yet but I'll keep looking
A stadium has 8,436 seats that are divided into 12 different sections. Each section has the same number of seats.
How many seats are in each of the 12 sections? please show the work
Answer:
703
Step-by-step explanation:
You divide the 8436 by 12.
1. You can't divide the 8 by 12 so skip that
2. You can divide 84 by 12 so you get 7
3. Bring down the 3 (you have 0 as a remainder). You can't divide that so put a 0
4. Bring down the 6 and divide that (36) and you get 3
5. Your final answer would be 703.
HELP JIMTHOMPSON5910
Explain what the diameter of a circle is. If you had the diameter of a circle, how could you solve for the circumference?
The diameter can be thought of as the width of the circle, more or less. More accurately, it's the distance from one point on a circle, through the center, to a point on the opposite side.
If we had a circle at point A, and some point on the edge of the circle point B, then line AB will form a third point C. Point C is on line AB and on the circle. Segment BC is a diameter.
We can measure the diameter with a straight line ruler, but we cannot do the same with the perimeter of the circle. The circumference is just a fancy name for "perimeter". Specifically, it only applies to circles. The way I remember it is that "circle" has "circ" in it, and so does "circumference". Furthermore, we can erase some letters of "circumference" to end up with "fence", which would go along an outer perimeter in a lot of cases. Overall, "circumference" makes me think of "circle fence".
How can we find the perimeter of a circle? Well we could use a cloth ruler to wrap around the edge of the circle. We'd have to make sure that none of the bendable ruler is out of place. So things could get tricky.
To find the circumference with a formula, we'll use this one here
C = pi*d
where pi = 3.14 approximately and d is the diameter
----------------------
For example, let's say the diameter is d = 10 feet. That would lead to a circle perimeter of....
C = pi*d
C = 3.14*10
C = 31.4
The circumference is approximate because pi = 3.14 is approximate. The units for the circumference in this case are in feet, so the distance around this particular circle is about 31.4 feet.
What is the area of a circle with a radius of 4 ft?
(Use 3.14 for Pi.)
Step-by-step explanation:
A = Pi x r^2
r=4_____________
Answer:
50.26548
50.27 Rounded to the hundredths place .
Help plzz will mark brainleast
Answer: I would say that it is 7
Step-by-step explanation:
30 : 24
b : 4 (divide both sides by 6)
5 : 4
Equivalent to 5 would be 7
Sorry if its wrong
What is the relationship between how Jews were portrayed to the public and their persecution during the holocaust?
Hint: Find how they were portrayed to the public by Hitler and then follow that up with How were they persecuted during the Holocaust?
Answer:
Step-by-step explanation:
This is actually in the wrong place. It should probably be in English or History, but I'll answer it anyway.
You need to start by seeing the way they were portrayed in cartoons, in writing (mainly newspapers), on the radio, in speeches and on the streets. Start with the Bible. The Old Testament was about the law mostly and behavior as much as anything. The people who lived and were governed by the OT generally were very pious unless they were rebellious sinners.
The New Testament is a slightly different matter. In most of Europe the peasantry thought the Jews were Christ Killers. That thought was dominent throughout the Middle Ages. It isn't true. Jesus was a Jew, so were the disciples, so were the huge crowds that followed Him to at least hear what he had to say.
It was only the ruling classes (The Pharisees, the Sadducees, and the scribes and teachers), that were not fond of Jesus. But that fact was not emphasized. Out of that picture and the displacement of the Jews after the Temple was destroyed, grew the caricatures of what the Jews were.
Anti Semitism was quite common in Europe. Most people fell for the propaganda that said the Jews were the spawn of the Devil. It became easy to kill those that were felt to be evil.
I urge you to start your own study of what happened. Start with the Inquisition.
51
13
14
a) How many words (with or without any meaning) can be formed by arranging the
letters in the word MEDITERRANEAN?
How many words ?
Answer:
may be 13 I hope this is the right answer
help i dont reamember how to do this plz
Consider the following vectors: y = (2,4), v = (-1, -1), and w = (7.-2).
What is the vector for 3u + v- 2w in component form?
(20,15)
(10,7)
(-6,1)
(-9.15)
Answer:
(-9.15)
Step-by-step explanation:
We are given these following vectors:
u = (2,4), v = (-1,-1), w = (7,-2)
What is the vector for 3u + v- 2w in component form?
3u + v - 2w = 3(2,4) + (-1,-1) - 2(7,-2) = (6,12) + (-1,-1) + (-14,4) = (6 - 1 - 14, 12 - 1 + 4) = (-9, 15)
The answer is (-9,15).
which value form the set {0, 1,17, 72 make the equation n+8=9 true
Answer:
n + 8 = 9
therefore 9-8 = 1
pls help this is due in 10 minutes I don’t wanna fail
Answer:
5.12
6.14
7.36
8.17
9.8
10.24
Write the equation of a parabola in conic form with a focus at (-2,-7) and a directrix at y=-1
Need help with this
Answer:
(-2-h)^2+(-7-k)^2=r^2
Step-by-step explanation:
(x-h)^2+(y-k)^2=r^2 this is the normal equation now u just need to substitue those in it
At which root does the graph of f(x) = (x + 4)(x + 735 cross the x-axis?
9514 1404 393
Answer:
both of them: x = -4, x = -735
Step-by-step explanation:
The meaning of "real root" is that the graph intersects the x-axis at that value of x. If the degree of the root is odd, the graph crosses there. (If the degree of the root is even, the graph only touches the x-axis.)
f(x) = (x +4)(x +735)
has real roots at x = -4 and x = -735, so crosses the x-axis in those places.
What is the volume of a sphere with a radius of 10 inches? Round to the nearest hundredth.
What is the volume of a sphere with a radius of 7 feet? Round to the nearest hundredth.
6
What is the volume of the sphere with a diameter of 18 centimeters? Round to the nearest
hundredth
Answer:
5. 4186.67 in³
6. 1436.03 ft³
7. 3052.08 cm³
Step-by-step explanation:
5. Determination of the volume of the sphere.
Radius (r) = 10 in
Pi (π) = 3.14
Volume (V) =?
V = 4/3πr³
V = 4/3 × 3.14 × 10³
V = 4/3 × 3.14 × 1000
V = 4186.67 in³
6. Determination of the volume of the sphere.
Radius (r) = 7 ft
Pi (π) = 3.14
Volume (V) =?
V = 4/3πr³
V = 4/3 × 3.14 × 7³
V = 4/3 × 3.14 × 343
V = 1436.03 ft³
7. Determination of the volume of the sphere.
We'll begin by calculating the radius. This can be obtained as follow:
Diameter (d) = 18 cm
Radius (r) =?
r = d/2
r = 18/2
r = 9 cm
Finally, we shall determine the volume of the sphere. This can be obtained as follow:
Radius (r) = 9 cm
Pi (π) = 3.14
Volume (V) =?
V = 4/3πr³
V = 4/3 × 3.14 × 9³
V = 4/3 × 3.14 × 729
V = 3052.08 cm³
I need help so I can helpl my grandson to pass this quz please and thank you
its in the download pdf.
Answer:
Sorry about the last time this time I could find the images!
First problem: 120
Second problem: I believe its 140 but I dont know for sure so answer that at your own risk please
Third problem: same for this one I think it's 40
Fourth problem: 2160
I need help please this isath i need my grade thx alot
Answer:
A, -475ft
Step-by-step explanation:
Answer: -475 ft
Step-by-step explanation: -95 x 5= -475
Plz help me well mark brainliest if correct.............
Answer:
Yup, 11 is the answer. because 4 -15 is 11.
Angle Relationships
Determine the height of each triangle. Round to the nearest foot.
a. 7 ft
b. 5 ft
c. 8 ft
d. 4 ft
Please select the best answer from the choices provided
Answer:
A. 7 ft
Step-by-step explanation:
I calculated it logically
10. If ABCD is a kite, DB=48 in. and CE=7 in. find DC. *
49 in.
23 in.
25 in.
47 in.
Answer:
25 in.
Step-by-step explanation:
DEC is a right triangle. <DEC is a right angle.
(DE)² + (EC)² = (DC)²
DE = ½DB = ½(48 in.) = 24 in.
(24 in.)² + (7 in.)² = (DC)²
576 in.² + 49 in.² = (DC)²
(DC)² = 625 in.²
DC = 25 in.
Help please this is also for the test
Jonathan is building a circular pond attached to a corner of his house. He wants to put bricks around the entire pond, including the sides that are against the house. The radius of the pond is 6ft.
Approximately how many feet of bricks does Jonathan need for the border of his pond? (Use 3.14 as an estimate for...I can’t put the sign....)
A. 28.26 ft
B. 30.84 ft
C. 37.68 ft
D. 40.26 ft
E. 46.68 ft
Answer:
E
Step-by-step explanation:
3. What is the breadth of a rectangle
whose length and area are 8cm
and 40cm- respectively?
Answer:
area of rectangle = l×b
or,40=8×b
or,40=8b
or,40/8=b
or,b=5cm is ans