In order to solve a system of linear equations using the elimination method coefficient of the eliminated variable should be equal with opposite sign.
As given,
Consider two linear equations
a₁ x +b₁ y +c₁=0 _(1)
a₂ x +b₂ y +c₂=0 _(2)
Now to eliminate x variable equate coefficient of x with opposite sign
Multiply (1) by a₂ and (2) by a₁ and subtract to use elimination method
a₁ a₂ x + b₁ a₂ y + c₁ a₂=0
a₁ a₂ x +a₁ b₂ y + a₁ c₂=0
- - -
0x + (b₁ a₂ -a₁ b₂)y +(c₁ a₂-a₁ c₂)=0
Therefore, in order to solve a system of linear equations using the elimination method coefficient of the eliminated variable should be equal with opposite sign.
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A ball is equipped with a speedometer and launched straight upward. The speedometer reading three seconds after launch is shown at the right; the ball is moving upward. At what approximate times would the ball be moving downward and display the following speedometer readings?
The time shown by the speedometer with speed of 10 m/s is 1 s.
The time shown by the speedometer with speed of 20 m/s is 1 s.
The time shown by the speedometer with speed of 30 m/s is 1 s.
What is the time on the Speedometer?The time read by the speedometer is given as;
t = 3 s.
The speedometer has low precision and as such we can do value approximation.
For the speedometer showing the speed 10 m/s. The time is calculated as, t = (v - u)/g
where g = 10 m/s²
t = (10 - 0)/10
t₁ = 1 seconds
For the speedometer showing the speed 20 m/s. The time is calculated as, t = (v - u)/g
where g = 10 m/s²
t = (20 - 0)/10
t₂ = 2 seconds
For the speedometer showing the speed 30 m/s. The time is calculated as, t = (v - u)/g
where g = 10 m/s²
t = (30 - 0)/10
t₂ = 3 seconds
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A triangle has angles that measure x, (x + 10), and (2x - 6). Solve for x to find the value of each angle, and determine what type of triangle it is.
Group of answer choices
60, 60, 60. Equilateral
40, 40, 100. Obtuse
44, 46, 90. Right
44, 54, 82. Acute
Answer:
44, 54, 82. Acute
Step-by-step explanation:
x + x + 10 + 2x - 6 = 180 (Triangle Sum Theorem)
4x + 4 = 180 (Combine Like Terms)
4x = 176 (Subtraction Property of Equality)
x = 44 (Division Property of Equality)
Now that we have found the value of x, we need to substitute it with the provided angles.
∡1 = x = 44°
∡2 = x + 10 = 54°
∡3 = 2x - 6 = 2(44) - 6 = 82°
So, the answer is an Acute triangle (Option 4).
A ball's position, in meters, as it travels every
second is represented by the position function
s(t) = 2.3t² + 225. What is the velocity of the
ball after 5 seconds?
A ball's position, in meters, as it travels every second is 282.5 sec.
What is addition?Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation. The sum is the entire value, and the addends are the integers that are being added. The mathematical operation of addition is the process of adding two or more numbers together to determine the total, or sum.
Given that,
The position function s(t) = 2.3t² + 225.
The velocity of the ball after 5 seconds is
s(t) = 2.3t² + 225.
t= 5
s(5) = 2.3(5)² + 225.
s(5) = 2.3(25) + 225.
s(5)= 57.5+ 225
s(5)= 282.5
Therefore, it travels every second is 282.5 sec.
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Solve the equation by extracting the square roots. List both the exact solution and its approximation rounded to two decimal places.
(2x − 1)^2 = 18
The exact solution and its approximation rounded to two decimal places are 2. 6213 and 2. 62 respectively.
What is an algebraic expression?An algebraic expression can be described as a mathematical or arithmetic expressions that is composed of arithmetic terms, factors, constants, variables, and coefficients.
These expressions are also made up of arithmetic operations which includes;
DivisionAdditionParenthesesBracketMultiplicationSubtractionFrom the information given, we have that;
(2x − 1)^2 = 18
Find the square root of both sides, we have;
√(2x − 1)^2 = √18
Note that square root rules out the square, we have;
2x - 1 = 4. 24264
collect like terms
2x = 4. 24264 + 1
2x = 5. 24264
Make 'x' the subject
x = 5. 24264/2
x = 2. 6213
Hence, the value is 2. 6213
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please only help me with number 7.
which value is less than 1?
a (1/6)^-8
b (5^-4)^-9
c 2^-3
d 6^-4/6^-5
Answer:
c
Step-by-step explanation:
[tex]a) (1/6)^{-8}=6^8>1 \\ \\ b) (5^{-4})^{-9}=5^{36}>0 \\ \\ c) 2^{-3}=1/8<1 \\ \\ (d) \frac{6^{-4}}{6^{-5}}=6>1[/tex]
20 points please help me asap !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1) 180°-105°-29°
=46° (angles in ∆)
2) 180-78-55
180-78-55 =47° (angle ²)
then angle ¹ is
180-78-47
=55° (angles on a straight line)
3) I just realised I solved angle 2 so I'll make the answer bold for you :)
I hope this is correct lol
What is the equation of the line that passes through the point (3,1)(3,1) and has a slope of -4/3
?
i'm going to assume (3,1)(3,1) was a typo.
here is an equation for a line with a slope of (-4/3) that crosses through (3,1)
y = -4/3x + 5;
steps;
1 = -4/3(3)+ b
1 = -4 +b
5 = b
Answer:i'm going to assume (3,1)(3,1) was a typo.
here is an equation for a line with a slope of (-4/3) that crosses through (3,1)
y = -4/3x + 5;
steps;
1 = -4/3(3)+ b
1 = -4 +b
5 = b
Step-by-step explanation:
write the absolute deviation inequality for the following. Six students measure the acceleration of an object in free fall. The measured values are shown below. The students want to state that the absolute deviation for each measured value x from the mean is at most d. Find the value of d. 0.56, 9.52, 9.73, 9.80, 9.78, 10.91
Six students measure the acceleration of an object in free fall. The students want to state that the absolute deviation for each measured value x from the mean is at most d is 0.86.
What is an absolute deviation?The average of absolute deviations from a central point makes up the average absolute deviation (AAD) of a data collection. It is a statistical summary of the statistical variability or dispersion. A mean, median, mode, or the result of any other central tendency measure or any reference value associated with the specified data set can all serve as the central point in the general form. The mean absolute deviation and the median absolute deviation are part of AAD (both abbreviated as MAD).
Find the mean of the data set first, then use that value to calculate the mean absolute deviation of the data. Divide the total number of data values by the sum of the individual data values. Assess the magnitude of the absolute difference between each data point and and the mean.
The measured data is
x = [10.56, 9.52, 9.73, 9.80, 9.78, 10.91]
There are 6 measurements.
Calculate the mean.
m = (10.56+9.52+9.73+9.80+9.78+10.91)/6 = 10.05
Calculate deviations from the mean.
y = |x - m|
= [0.51, 0.53, 0.32, 0.25, 0.27, 0.86]
The greatest deviation from mean is d = 0.86.
Calculate the average absolute deviation.
(0.51+0.53+0.32+0.25+0.27+0.86)/6 = 0.4567
The answer is: d = 0.86
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h(x)=3x+4 complete the function table help please
The function table should be completed as follows:
x h(x)__
-4 -8
-3 -5
2 10
4 16
5 19
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.
Next, we would evaluate the given function by substituting the value of x as follows:
When x = -4, we have:
Function, h(x) = 3x + 4
Function, h(-4) = 3(-4) + 4
Function, h(-4) = -12 + 4
Function, h(-4) = -8
When x = -3, we have:
Function, h(x) = 3x + 4
Function, h(-3) = 3(-3) + 4
Function, h(-3) = -9 + 4
Function, h(-3) = -5
When x = 2, we have:
Function, h(x) = 3x + 4
Function, h(2) = 3(2) + 4
Function, h(2) = 6 + 4
Function, h(2) = 10
When x = 4, we have:
Function, h(x) = 3x + 4
Function, h(4) = 3(4) + 4
Function, h(4) = 12 + 4
Function, h(4) = 16
When x = 5, we have:
Function, h(x) = 3x + 4
Function, h(5) = 3(5) + 4
Function, h(5) = 15 + 4
Function, h(4) = 19
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mike is a good athlete.Mike's father is a good athlete.Mike's sister is a good athlete.Therefore,Mike's son will be a good athlete. (Inductive or Deductive?)
is 0.1213141516... a rational number
Answer:
No, because any number than produces and decimal that continuse forever is not rational.
Step-by-step explanation:
Hope it helps! =D
Two different lines are shown below with two points given from each line. Use the slope-intercept form or point-slope form to find the equation of each line.
Line A
Points: (–5, –2), (–5, 7)
Line B
Points: (7, –5), (–2, –5)
Line A has
.
The equation of line A is
.
Line B has
.
The equation of line B is
.
We have a vertical and a horizontal lines, the equations are:
Line A: x = -5 (vertical one)
Line B: y = -5 (horizontal one)
How to find the equations of the two lines?Remember that the general linear equation in the slope-intercept form is:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Now, line A passes through (–5, –2), (–5, 7), then the slope is:
a = (7 + 2)/(-5 + 5) = 9/0
Notice that if we divide by zero, the slope tends to infinity, so we have a vertical line.
In this case, the line A will be x = -5.
Now line B passes through points: (7, –5), (–2, –5)
Then the slope is:
a = (-5 + 5)/(-2 - 7) = 0/-9 = 0
Then the line is:
y = 0*x + b
And passes through (7, –5), then:
-5 = 0*7 + b
-5 = b
So this line is y = -5.
Concluding, we have:
Line A: x = -5
Line B: y = -5
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Answer:
Line A: no slope
The equation of line A is x = -5
Line B has a slope of 0
The equation of line B is y = -5
Step-by-step explanation:
I did it already :)
See below for question
Value of x is 2 and value of k is 0.999.
What is volume?Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.
Given Data
At t=0, Water Volume is 3,000 Litres
The volume of water in the tank equals t hours later.
As it is also stated, there is x% less water in the tank at the conclusion of every hour than there was at the beginning.
After an hour, the amount of water is equal to 3,000 - = 3,000 - 30 x
Water consumption after two hours = (3,000 - 30 x) - (3,000 - 30 x)
×= (3,000 - 30 x) (3,000 - 30 x)
Also,
= 288120
⇒300000 - 3000 x - 3000 x + 30 x²
= 288120
⇒ 30 x ² - 6,000 x + 11880= 0
When we multiply both sides by 30, we get
⇒ x² - 200 x + 396=0
reducing the quadratic equation to factors
(x -198)(x-2) = 0
x = 198,
x = 2
Which suggests that x = 2 might be the answer to this equation.
Also,
V₁ = 3000- 30(2)
V₁ = 3000 - 60
V₁ = 2940
k = [tex]\frac{2940}{3000}[/tex]
k = 0.999(approximately)
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What is the slope equation for (1,-1) and (5,-17)
Answer:
slope(m) is -4
Step-by-step explanation:
[tex]m=\frac{-17-(-1)}{5-1} \\\\m=\frac{-16}{4} \\\\m=\frac{-4}{1} \\\\m=-4[/tex]
now substitute with one of the points
y=mx+b
-1=-4+b
+4 +4
3=b
now you have both m and b
y=-4x+3
WILL GIVE BRAINLEST I HAVE 5 MINUTE 30 points, Solve for x, look at picture for more info.
The numerical value of x in the two congruent alternate exterior angles is 20.
What is the numerical value of x?Alternate exterior angle theorem states that "if a transversal intersects two parallel lines, the alternate angle s formed are congruent.
From the diagram, the two angles forms an alternate exterior angle , the two angles are congruent.
( 5x - 8 ) = ( 3x + 32 )
Solve for x
5x - 8 = 3x + 32
Collect like terms by moving all terms containing variable x to left and the constant terms to the right side of the equation.
5x - 8 = 3x + 32
5x - 3x = 32 + 8
2x = 40
Divide both sides by 2
2x/2 = 40/2
x = 40/2
x = 20
Therefore, the numerical value of x is 20.
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pls pls help whoever gets it right gets marked brainliest
Answer:
A
Step-by-step explanation:
mark me brainliest
A car traveling at a speed of 30.0 m/s encounters an emergency and comes to a complete stopHow much time will it take for the car to stop if its acceleration is -4.0 m/s
Answer:
Step-by-step explanation:
I need all of them answered they all have the same question. Use function notation to write the equation of the line.
The equation of each line using function notation is:
1. C. f(x) = 3x - 1.
2. D. f(x) = x.
3. D. f(x) = 4x + 4.
4. B. f(x) = -3/2x - 2
How to Write the Equation of a Line Using Function Notation?To use function notation, substitute the value of the slope (m) and the value of the y-intercept (b) into f(x) = mx + b.
Slope (m) = rise/run.
Y-intercept (b) is the point on the y-axis when the line intercepts the y-axis.
1. Slope (m) = rise/run = 3/1
Slope (m) = 3
Y-intercept (b) of the line = -1.
Substitute m = 3, and b = -1 into f(x) = mx + b:
f(x) = 3x - 1
The equation is: C. f(x) = 3x - 1.
2. Slope (m) = rise/run = 2/2
Slope (m) = 1
Y-intercept (b) of the line = 0.
Substitute m = 1, and b = 0 into f(x) = mx + b:
f(x) = (1)x + 0
f(x) = x
The equation is: D. f(x) = x.
3. Slope (m) = rise/run = 4/1
Slope (m) = 4
Y-intercept (b) of the line = 4.
Substitute m = 4 and b = 4 into f(x) = mx + b:
f(x) = 4x + 4
The equation is: D. f(x) = 4x + 4.
4. Slope (m) = rise/run = -3/2
Slope (m) = -3/2
Y-intercept (b) of the line = -2.
Substitute m = -3/2 and b = -2 into f(x) = mx + b:
f(x) = -3/2x - 2
The equation is: B. f(x) = -3/2x - 2
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last week, 3/4 of the students in Mr. Zanker's class went on a field trip. 5/8 of the students in Mr. Haynes's went. What is the average fraction of students in the two classes who went on the field trip?
The average fraction of students in Mr. Zanker's class and Mr. Haynes who went on the field trip is 11/8.
How can the fraction be calculated?From the question, the fraction of the students in Mr. Zanker's class that attended the field trip is 3/4.
The fraction of the students in Mr. Haynes class that attended the field trip is 5/8 .
Then the we can calculate the average fraction of student in the class of the two teacher is
= (3/4 + 5/8) = 11/8.
Therefore, the average fraction of the number of the student can be calculated as 11/8.
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Which angle is an acute angle?
Answer: angle CPB is an acute angle.
Answer: C. ∠CPB is the correct answer.
Step-by-step explanation:
George has a health insurance premium that costs $4,300.00. His employer pays 3/4 of the premium and George pays 1/4. What is the amount that George must pay?
Answer:
1075
Step-by-step explanation:
4300x0.25
Solve 3x2 4x = 2. quantity of 2 plus or minus square root of 10 all over 6 quantity of negative 2 plus or minus 2 square root of 10 all over 3 quantity of negative 2 plus or minus square root of 10 all over 3 quantity of negative 4 plus or minus square root of 10 all over 3
Main Answer:
[tex]x=\frac{-2\±\sqrt{10}}{3}[/tex]
Explanation:
The given equation is,
[tex]3x^{2} +4x=2[/tex]
The
The quadratic formula to find the value of x for the equation [tex]ax^{2} +bx+c=0[/tex] is,
[tex]x=\frac{-b\±\sqrt{b^{2}-4ac}}{2a}[/tex]
The values are,
a = 3, b = 4, c = -2
Now, substitute the values of a, b and c
[tex]x=\frac{-4\±\sqrt{(4)^{2}-4(3)(-2)}}{2(3)}[/tex]
[tex]x=\frac{-4\±\sqrt{16-12(-2)}}{6}[/tex]
[tex]x=\frac{-4\±\sqrt{40}}{6}[/tex]
[tex]x=\frac{-4\±2\sqrt{10}}{6}[/tex]
[tex]x=\frac{2(-2\±\sqrt{10})}{6}[/tex]
[tex]x=\frac{-2\±\sqrt{10}}{3}[/tex]
Find the perimeter of this semi-circle with diameter, d = 23cm. Give your answer rounded to 1 DP.
The perimeter of the semi-circle is 59.1 cm
In this question, we have been given the diameter if the semi-circle
d = 23 cm
We need to find the perimeter of the semi-circle.
We know that, the perimeter of the semi-circle of radius 'r' is P = πr + 2r
For diameter d = 23 cm, the radius would be,
r = 11.5 cm
So, the perimeter would be,
P = πr + 2r
P = π × 11.5 + 2 × 11.5
P = (π + 2) × 11.5
P = 59.13 cm
Therefore, the perimeter of the semi-circle is 59.1 cm
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solve this please. i have no idea what to do
-3/2<h<0 is the answer.
How to simplify it?Given,
1+5h <h+1 <7+5h
Solution:
1+5h <h+1 <7+5h
If a < u <b, then a<u , u<b
Therefore,
1+5h <h+1 and h+1 <7+5h
1+5h <h+1
1+5h= h+1
4h = 0
h = 0
Therefore,
h<0
h+1 <7+5h
h+1 = 7+5h
4h = -6
h = -3/2
h > -3/2
Combine the intervals
h<0 and h> -3/2
By combining the above two, we get
-3/2<h<0
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If 18 inches is equal to 1 and 1/2 feet, how many feet long is a 36 inch board, a 72 inch board, and a 144 inch board? (Show work)
Pls help!!
18 inches= 1 1/2 feet= 1.5 feet
18 inches = 1.5 feet
what is distance ?
Distance is a numerical or occasionally qualitative measurement of how far apart objects or point are . it is a total movement of an object without any regard to direction.
(1) Now we make a proportion to find feet for given inches
feet/inches = feet / inches
1.5/18 = x/36
1.5 * 36 = 18*x
54 = 18 x (Divide by 18 on both sides)
x = 3
3 feet long is a 36 inch board
(2) 72 inch board
1.5 * 72 = 18*x
108 = 18 x (Divide by 18 on both sides)
x = 6
6 feet long is a 72 inch board
(3) 144 inch board
1.5 * 144 = 18*x
216 = 18 x (Divide by 18 on both sides)
x = 12
12 feet long is a 144 inch board
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suppose you have a binary randomized controlled experiment designed to measure the causal effect of x on y. let the control group be identified by x
The differences-of-means estimator, denoted by E(Y|X=1) -E(Y|X=0), is an estimator of the causal effect of X on Y because the differences-of-means estimator estimates that (A) the change in the expectation of Y as a result of an observation being in the treatment group as opposed to the control group.
What is binary?A binary number is a number that has been expressed using the base-2 or binary numeral system, which uses only two symbols, typically "0" and "1." With a radix of 2, the base-2 numeral system is a positional notation. A bit, or binary digit, is the term used to describe each digit. Two is used as the base representation for binary numbers. As an illustration, (101)₂ (101)₂. A bit is a term used to describe each digit in a binary number. As an illustration, the three-bit binary system (111)₂ (111)₂ is used.So, in the given situation: The differences-of-means estimator estimates the change in the expectation of Y as a result of an observation being in the treatment group as opposed to the control group, and is denoted by E(Y|X=1) -E(Y|X=0).
This estimator is used to determine the causal effect of X on Y.Therefore, the differences-of-means estimator, denoted by E(Y|X=1) -E(Y|X=0), is an estimator of the causal effect of X on Y because the differences-of-means estimator estimates that (A) the change in the expectation of Y as a result of an observation being in the treatment group as opposed to the control group.
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The complete question is given below;
Suppose you have a binary randomized controlled experiment designed to measure the causal effect of X on Y. Let the control group be identified by X = 0 and the treatment group by X = 1.
The differences-of-means estimator, denoted by E(Y|X=1) -E(Y|X=0), is an estimator of the causal effect of X on Y because the differences-of-means estimator estimates:
A. the change in the expectation of Y as a result of an observation being in the treatment group as opposed to the control group.
B. the expectation of Y for observations within the control group.
C. the expectation of Y for observations within the treatment group.
D. All of the above.
Write an algebraic expression to represent each statement
three times a number, d, less 5
what is the GCF of 18a^4b^9c^2 and 34a^6b^5 and 22a^8bc^7
The greatest common factor, GCF, of the given terms is 2a⁴b
Determining Greatest Common Factor (GCF)From the question, we are to determine the GCF of the given expressions. GCF means Greatest common factor
The given expressions are 18a^4b^9c^2 and 34a^6b^5 and 22a^8bc^7
First, we will write the expressions properly
The given expressions are 18a⁴b⁹c² and 34a⁶b⁵ and 22a⁸bc⁷
To determine the GCF of the expressions, we will express each one of them as a product of their factors
That is,
18a⁴b⁹c² = 2 × 3 × 3 × a × a × a × a × b × b × b × b × b × b × b × b × b × c × c
34a⁶b⁵ = 2 × 17 × a × a × a × a × a × a × b × b × b × b × b
22a⁸bc⁷ = 2 × 11 × a × a × a × a × a × a × a × a × b × c × c × c × c × c × c × c
Hence, the GCF is 2 × a × a × a × a × b = 2a⁴b
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Ella is testing out a new studying method and wants to know if it works. She decides to compare her spelling test scores from last week and this week. On last week's test, Ella spelled 16 out of the 20 words correctly. On this week's test, she spelled 13 out of the 15 words correctly. On which test did Ella get a higher ratio of correctly spelled words to total words?
Answer:
The test where Ella got 13/15 has the higher ratio of correctly spelled words to total words.
Step-by-step explanation:
On the last week's test, Ella got a 16/20, which equates to 80% correctly spelled words compared to total words. On this week's test, she got a 13/15, which equates to 86.6% correctly spelled words compared to total words. Since 86.6 > 80, the test where Ella got a 13/15 has the higher ratio.
3 x [64÷(13-5) - 4] × 42 ÷ 6