what is the solution to this system of equations? 5X + 2y =29 X + 4y=13
Answers
The solution of the system of equation [tex]5x+2y = 29[/tex] ; [tex]x+4y =13[/tex] will be (3,2) and this can be determined by using the arithmetic operations.
Given :
[tex]5x+2y = 29[/tex] ----- (1)
[tex]x+4y =13[/tex] ----- (2)
Now, solve for x in equation (2).
[tex]x = 13-4y[/tex] --- (3)
Now, put the value of x obtained above in equation (1).
[tex]5(13-4y)+2y=29[/tex]
[tex]65-20y+2y=29[/tex]
[tex]36=18y[/tex]
[tex]y=2[/tex]
Now, put the value of y in equation (3).
[tex]x=13-(4\times 2)[/tex]
[tex]x=5[/tex]
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Related Questions
What is the median distance jumped 7.48, 7.60, 7.15, 7.44, 7.73, 7.72
Answers
8.find the result when 40 is INCREASED by 85%
10.find the result when 350 is DECREASED by 10%
28.find the result when 24 is INCREASED by 75%
30.find the result when 30 is DECREASED by 85%
Answers
Let 40 be 100%.
Step 1. Calculate 85% of 40.
If 40 is 100%, how much will be 85%:
40 : 100% = x : 85%
x * 100% = 40 * 85%
x = 40 * 85% / 100% = 34
Step 2: Add given value to 40 (since it is increased):
40 + 34 = 74
Q10. The answer is 315.
Let 350 be 100%.
Step 1. Calculate 10% of 350.
If 350 is 100%, how much will be 10%:
350 : 100% = x : 10%
x * 100% = 350 * 10%
x = 350 * 10% / 100% = 35
Step 2: Distract given value from 350 (since it is decreased):
350 - 35 = 315
Q28. The answer is 42.
Let 24 be 100%.
Step 1. Calculate 75% of 24.
If 24 is 100%, how much will be 75%:
24 : 100% = x : 75%
x * 100% = 24 * 75%
x = 24 * 75% / 100% = 18
Step 2: Add given value to 24 (since it is increased):
24 + 18 = 42
Q10. The answer is 4.5.
Let 30 be 100%.
Step 1. Calculate 85% of 30.
If 30 is 100%, how much will be 85%:
30 : 100% = x : 85%
x * 100% = 30 * 85%
x = 30 * 85% / 100% = 25.5
Step 2: Distract given value from 30 (since it is decreased):
30 - 25.5 = 4.5
round 624 to the nearest hundred
Answers
For any positive number b not equal to 1 and any number or variable n, evaluate the following expression.
logb(b^n) =
with logb being the base
Answers
If: [tex]log_x(y^{z}) = z*log_x(y) [/tex]
Then: [tex]log_b( b^{n}) = n*log_b(b) [/tex]
If: [tex]log_x(y) = \frac{log_z(y)}{log_z(x)} [/tex]
Then: [tex]log_b(b) = \frac{log_z(b)}{log_z(b)} =1[/tex]
Therefore:
[tex]log_b( b^{n}) = n*log_b(b) =n*1=n[/tex]
Answer:
[tex]log_{b} b^{n}[/tex] = n.
Step-by-step explanation:
Given : [tex]log_{b} b^{n}[/tex] , b is any positive number not equal to 1 and n is any number.
To find : Evaluate the expression [tex]log_{b} b^{n}[/tex].
Formula used : [tex]log_{b} x^{y}[/tex]. = y ∙ [tex]log_{b}[/tex](x) and
[tex]log_{b}(b) = 1.
Solution : We have [tex]log_{b} b^{n}[/tex].
By logarithm rule : [tex]log_{b} x^{y}[/tex]. = y ∙ [tex]log_{b}[/tex](x).
Then [tex]log_{b} b^{n}[/tex] = n∙ [tex]log_{b}[/tex](b).
By logarithm rule : [tex]log_{b}(b) = 1.
Now, n∙ [tex]log_{b}[/tex](b) = n.
Therefore, [tex]log_{b} b^{n}[/tex] = n.
Three largest earthquakes ever recorded took place in chile, russia, and alaska. they measured 9 1/10, 9.5, & 9 1/5 on the richter scale. the largest earthquake was in chile. the earthquake in russia was smaller than the one alaska. what did the three earthquakes measure on the richter scale
Answers
The earthquake in chile measured the largest number on the richter scale: 9.5
The earthquake in russia is the smallest and measured on the richter scale : 9.1
The earthquake in alaska measured greater than the one in russia on the richter scale : 9.2
HOPE THIS HELPED
Final answer:
The largest earthquakes recorded in Chile, Russia, and Alaska measured 9.5, 9.1, and 9.2 on the Richter scale respectively, with Chile's earthquake being the largest and Russia's the smallest.
Explanation:
The three largest earthquakes ever recorded took place in Chile, Russia, and Alaska. Based on the information provided, the earthquake in Chile was the largest, measuring 9.5 on the Richter scale. The earthquake in Alaska, being larger than the one in Russia but not as large as the one in Chile, would measure 9 1/5, or 9.2, on the Richter scale. Lastly, the earthquake in Russia was the smallest of the three, measuring 9 1/10, or 9.1, on the Richter scale.
These seismic events, marked by their enormity on the Richter scale, underscore the geological dynamics in different regions of the world. The specific magnitudes assigned to each earthquake provide a quantitative measure of their intensity, offering valuable insights for understanding and preparing for such natural phenomena.
Estimate the volume of material in a cylindrical shell with height 30 in., radius 2 in., and shell thickness 0.5 in.
Answers
100 plus the product of a number and -2 equals 50 What is the number?
Answers
100 + (-2 * x ) = 50
100-2x = 50
2x = 100-50
x = 50/2
x= 25
So, your final answer is 25
Hope this helps!
in a carnival drawing,a green ticket wins $1,a yellow ticket wins $5,and a blue ticket wins $10. There are 100 green tickets, 25 yellow tickets and 5 blue tickets. in simplest form, what are the odds in favor of winning $5 or more?
Answers
What is the median of this set of data? 66, 51, 77, 68, 60, 75, 54, 80
Answers
67````````````````````````
If xy^2 = 20, and x is decreasing at the rate of 3 units per second, the rate at which y is changing when y = 2 is nearest to?
Answers
[y^2]' = [20/x]'
2y [dy/dt] = [-20/x^2] [dx/dt]
dy/dt = [-10/yx^2] [dx/dt]
[dx/dt] = - 3 u/s ....(the negative sign was included to account for decreasing)
y = 2 => x(2)^2 = 20 => x = 20/4 = 5
dy/dt = [-10/(2*5^2)] [- 3]
dy/dt = [-1/5][- 3] = 3/5
Answer: dy/dt = 3/5 units/s
Ray is 2 inch taller than Lin, and Ray is 3 inch taller than Sam. What is the average height of ray, Lin and Sam? The median height of Ray, Lin and Sam?
Answers
r - Ray's height
l - Lin's height
s - Sam's height
Ray is 2 inch taller than Lin: r = l + 2 ⇒ l = r - 2
Ray is 3 inch taller than Sam: r = s + 3 ⇒ s = r - 3
The average is the sum of all values divided by the number of values:
[tex]A= \frac{r + l + s}{3} [/tex]
Since l = r - 2 and s = r - 3, then:
[tex]A= \frac{r + (r-2) + (r-3)}{3} = \frac{r+r-2+r-3}{3} = \frac{3r-5}{3} = \frac{3r}{3} - \frac{5}{3} =r-\frac{5}{3}[/tex]
The median means the middle value. Let's first rearrange values so we can find the middle one:
Ray is taller than Lin and Sam, so Ray is the tallest.
Sam is much shorter than Ray comparing to Lin, so Sam is the shortest.
Therefore, values are from the lowest to the highest:
(s, l, r)
⇒ (r-3, r-2, r)
Median of these values is in the middle, so the median height is r-2.
The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam?
A. 13
B. 1
C. 2
D. 12
Answers
Answer:
2 students failed in the final exam.
Step-by-step explanation:
The scores on a final exam were approximately normally distributed.
We know that,
[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]
X = raw score = 60
μ = mean = 82
σ = standard deviation = 11
Putting the values,
[tex]Z=\dfrac{60-82}{11}=-2[/tex]
From Normal distribution table, we get
[tex]P(-2)=0.0227=2.27\%[/tex]
Hence, 2.27% of 85 students failed the final exam.
So the number of students who failed the exam is,
[tex]=85\times 0.0227=1.9295\approx 2[/tex]
Which expression is equaivalent to mn+z
nm+n
z+mz
mz+n
z+nm
Answers
Answer:
D. z+nm
Step-by-step explanation:
Equaivalent to mn+z: Just switch the letters around and you get z+nm
What is 7.58E8 expressed in standard notation?
Answers
1. A circle has a center at (3,5). The point (3,8) is on the circle. What is the circumference of the to the nearest tenth of a unit?
A. 9.4 units
B. 18.8 units
C. 28.3 units
D. 56.5 units
2. A triangle has a perimeter of exactly 24 units. Which of the following could be the vertices of the triangle?
A. (-1 ,3 ), (2,-1), (-1,-1)
B. (6,0), (6,7), (0,7)
C. (-1,-1), (-6,-13), (-9,-9)
D.(-3,-4) (-3,4), (3,4)
3. A circle has an area of approximately 78.5 square units. If the center of the circle is at (2,4). Which of the following points is on the circle?
A. (-6,4)
B. (2,-1)
C.(-4,-4)
D. (2,-9)
4. The end point of a diameter of a circle are A (2,1) and B (5,5). Find the area of the circle in terms of pi.
A. 25/4 pi square units
B. 10 pi square units
C 25 pi square units
D. 5 pi units
Answers
Radius of circle = 3 units
C = 2πr
C = 18.8 units
2. D
The distances between the points add to 24.
3. B
A = πr²
r = √(78.5/π)
r = 5 units
Point from options that is 5 units from (2,4) is (2,-1)
4. A
length of diameter = √[(5 - 1)² + (5 - 2)]
d = 5
r = 5/2
A = πr²
A = 25/4 pi units²
Answer:
1. B
2. D
3. B
4. A
Step-by-step explanation:
how many solutions are there to this equation?
9x - 16 = 9x - 23
a. infinitely many
b. 0
c. 1
Answers
Answer: the correct option is
(b) 0.
Step-by-step explanation: We are given to find the number of solutions for the following linear equation :
[tex]9x-16=9x-23~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the number of solutions of the given equation, we must try to solve the equation and find the value of x.
From equation (i), we have
[tex]9x-16=9x-23\\\\\Rightarrow 9x-9x=-23+16\\\\\Rightarrow 0=-7,[/tex]
which can never be possible.
Thus, the given equation has NO solution.
Option (b) is CORRECT.
Which is a true statement about any two chords that are the same distance from the center of a circle?
A. They are parallel.
B. They are perpendicular.
C. They are congruent.
D. They are similar.
Answers
Answer C. If two chords are the exact same distance from the center of the circle then those two chords must be congruent.
Expression as a decimal number 6x0.1 6x0.01 1x0.001
Answers
Final answer:
To express the given multiplications as decimal numbers: 6 times 0.1 equals 0.6, 6 times 0.01 equals 0.06, and 1 times 0.001 equals 0.001. Moving the decimal point due to multiplication by powers of 10 is the underlying concept.
Explanation:
The student's question involves expressing multiplications involving decimals in decimal form. To convert each term:
6 x 0.1 is moving the decimal point one place to the left in the number 6, which results in 0.6.6 x 0.01 is moving the decimal point two places to the left in the number 6, giving 0.06.1 x 0.001 is moving the decimal point three places to the left in the number 1, resulting in 0.001.When numbers are multiplied by powers of 10, the decimal point is shifted to the right for positive exponents and to the left for negative exponents. Scientific notation is often used for this purpose.
Here are examples demonstrating the use of scientific notation:
0.006 can be expressed as 6 x 10-3 (moving the decimal point three places to the left).0.0000045 becomes 4.5 x 10-6 (the decimal point moves six places to the left).Negative exponents indicate the decimal point moves to the left, whereas positive exponents indicate it moves to the right. For instance, 2.4 x 10-2 is equivalent to 0.024 as the decimal has moved two places to the left.
Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution. The equation 0.10x + 0.15(50 – x) = 0.12(50) can be used to find the amount of 10% alcohol solution Bruce should use. How much of the 10% alcohol solution should Bruce use? mL How much of the 15% alcohol solution should Bruce use?
Answers
We need 50 ml of a 12% alcohol solution.
We have 10% and 15% alcohol solutions and we want 50 ml at 12%
We set up 2 equations (x is volume of 10% y is volume of 15%)
a) x + y = 50
b) .1x + .15y = 6.0 (which is 50 ml at 12% or .12 * 50)
multiplying equation "a" by -.1 then add it to "b"
a) -.1x -.1y = -5
b) .1x +.15y = 6.0
.05y = 1
y = 20 ml of 15% and therefore x would equal 30 ml of 10%
Answer:
0.10x + 0.15(50 – x) = 0.12(50)
Step-by-step explanation:
out of a swarm of bees one fifth part settled on a kadamba blossom; one third on a silihindra flower; three times the difference of those numbers flew to the bloom of a kutaja. one bee, which remained, hovered about in the air. tell me, charming woman, the number of bees
Answers
let x be the # of bees in the swarm, then
[tex]\frac{x}{5}+\frac{x}{3}+3(\frac{x}{3}-\frac{x}{5})+1=x[/tex]
multiply across by 15
[tex]3x+5x+3(5x-3x)+15=15x[/tex]
[tex]8x+3(2x)+15=15x[/tex]
[tex]8x+6x+15=15x[/tex]
[tex]14x+15=15x[/tex]
[tex]15=x\leftrightarrow x=15[/tex]
Water is pumped out of a holding tank at a rate of 6-6e^-0.13t liters/minute, where t is in minutes since the pump is started. If the holding tank contains 1000 liters of water when the pump is started, how much water does it hold one hour later?
Answers
1) Integrate the function, from t =0 to t = 60 minutues to obtain the number of liters pumped out in the entire interval, and
2) Substract the result from the initial content of the tank (1000 liters).
Hands on:
Integral of (6 - 6e^-0.13t) dt ]from t =0 to t = 60 min =
= 6t + 6 e^-0.13t / 0.13 = 6t + 46.1538 e^-0.13t ] from t =0 to t = 60 min =
6*60 + 46.1538 e^(-0.13*60) - 0 - 46.1538 = 360 + 0.01891 - 46.1538 = 313.865 liters
2) 1000 liters - 313.865 liters = 613.135 liters
Answer: 613.135 liters
Your iron works has been contracted to design and build a 500-ft3 square-based, open-top, rectangular steel holding tank for a paper company. The tank is to be made by welding half-inch-thick stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weight as little as possible. What dimensions do you tell the shop to use?
Answers
To minimize the weight of the tank, the base length should be (4/3) times the height. The height should be (3/4)^(1/4) times the fourth root of (2V/π).
Explanation:To find the dimensions that will make the tank weight as little as possible, we need to consider the volume and weight of the tank. Since the tank is square-based, the volume can be calculated by V = bh^2, where b is the length of one side of the base and h is the height.
The weight of the tank can be calculated by multiplying the volume by the density of the stainless steel. W = V * density. Since we want to minimize the weight, we want to minimize the volume.
To do this, we can differentiate the volume equation with respect to b and set it equal to zero. Solving for b, we find that b = (4/3) * h. Substituting this value into the volume equation gives: V = (4/3) * h^3.
To further minimize the volume, we can take the derivative of the volume equation with respect to h and set it equal to zero. Solving for h, we find that h = (3/4)^(1/4) * (2V/π)^(1/4).
How do i convert 16/5 to a mixed number?
Answers
The closest number is 15 (3×5=15) so the whole number would be 3.
Now there will be an extra 1 left over so your answer is going to be 3 1/5
Answer: 3 and 1/5
Step-by-step explanation: To write an improper fraction as a mixed number, divide the denominator into the numerator.
[tex]\sqrt[5]{16}[/tex] = 3 with a remainder of 1
Therefore, 14/5 can be written as the mixed number 3 and 1/5.
Write unit rate for 1.98 for 6
Answers
1.98 miles ÷ 6 hours
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 6
1.98 miles ÷ 6
6 hours ÷ 6
=
0.33 miles
1 hour
=
0.33 miles
hour
= 0.33 miles per hour. I did it in Miles and Hours
4/9 multiplied by 1/8
Answers
Multiply the bottom parts together (denominators): 9 * 8 = 72
Put the top part (4) over the bottom part (72): 4/72
Then, since four goes into 72 eighteen times, and four goes into itself once, you can reduce the fraction down to:
1/18
What is 3.99999..... converted into a fraction?
Answers
Harita must memorize 90 measures of music for her cello solo at a concert. She plans on memorizing 18 new measures for every 3 days of practice. Which equation can be used to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece?
Answers
Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece m = 90 - 6d
Answer:
m=90-6 days or b
Step-by-step explanation:
i got a hundred on the quiz...
If two angles of a triangle measure 43 degrees and 48 degrees the triangle is
Answers
The third angle for the triangle is equal to 89°.
What is geometry?Geometry is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a geometer.
A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C.
Given that the two angles of a triangle measure 43 degrees and 48 degrees. the value of the third angle will be calculated as,
Third angle = 180 - 43 - 48
Third angle = 89°
The complete question is given below.
If two angles of a triangle measure 43 degrees and 48 degrees what is the third angle of the triangle?
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Is 6.5 greater than 6.417
Answers
The product of two rational numbers is _________rational.
sometimes
always
never
Answers
Choose 1st
So, option B is your answer.
Hope this helps!