Solve the system of equations. If the system has no solution, say that it is inconsistent.
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Answer:
D. The system is inconsistent
Step-by-step Explanation:
Given the below system of equations;
[tex]\begin{gathered} 2x-2y+5z=11\ldots\ldots\ldots\text{Equation 1} \\ 6x-5y+13z=30\ldots\ldots\ldots\text{.}\mathrm{}\text{Equation 2} \\ -2x+3y-7z=-13\ldots\ldots\ldots\text{Equation 3} \end{gathered}[/tex]We'll follow the below steps to solve the above system of equations;
Step 1: Add Equation 1 and Equation 3;
[tex]\begin{gathered} (2x-2x)+(-2y+3y)+(5z-7z)=(11-13) \\ y-2z=-2 \\ y=2z-2\ldots\ldots\text{.}\mathrm{}\text{Equation 4} \end{gathered}[/tex]Step 2: Multiply Equation 3 by 3, we'll have;
[tex]-6x+9y-21z=-39\ldots\ldots\text{.Equation 5}[/tex]Step 3: Add Equation 2 and Equation 5, we'll have;
[tex]4y-8z=-9\ldots\ldots\ldots\text{Equation 6}[/tex]Step 4: Put Equation 4 into Equation 6 and solve for z;
[tex]\begin{gathered} 4(2z-2)-8z=-9 \\ 8z-8-8z=-9 \\ 8z-8z=-9+8 \\ 0=-1 \end{gathered}[/tex]From the above, we can see that we do not have a solution for z, therefore, we can say that the system of equations has no solution, hence, it is inconsistent.
Related Questions
Completing a race) Ned spent 63 minutes walking 11 while If the ratio of time walking to jogging was 9:1, race? 2 minutes did he spend completing the
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While completing the race, Ned spent 63 min walking if the ratio of time walking to jogging was 9:1, how many minutes did he spend completing the race?
Let
x-----> time spent walking
y -----> tiime spent jogging
we have
x/y=9/1
x=9y -----> equation A
we have
x=63 min
substitute in the equation A
63=9y
solve for y
y=7 minutes
therefore
teh answer is
7 minutesi added the choices for the first box as well.
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Looking at the triangles, we see that they have two congruent sides, and the angles between them are congruent too.
Then, the two triangles are related by side-angle-side (SAS), so the triangles are congruent (SAS theorem).
Linus leaves his house and walks 7 blocks West to avoid Lucy. He then walks 3 blocks North to visit Charlie Brown. What is the shortest distance between the houses? Round to the nearest tenth.
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First, draw a schematic representation of that situation:
The shortest distance between the starting point (Linus's house) and the endpoint (Charlie's house) is a straight line. Since a right triangle is formed with the sides of length 7 blocks and 3 blocks, we can use the Pyhtagorean Theorem to find the length of the hypotenuse:
[tex]\begin{gathered} ?=\sqrt[]{3^2+7^2} \\ =\sqrt[]{9+49} \\ =\sqrt[]{58} \\ \approx7.6 \end{gathered}[/tex]Therefore, the shortest distance between those two points would be 7.6 blocks.
Part 1: Person A has a car with the average fuel consumption of 20 miles per gallon. Person B has an average fuel consumption of 30 miles per gallon. Person C has an average fuel consumption of 40 miles per gallon. they are trying to work out how much fuel they will each save if they change cars. Person A, " I am going to buy Person B's car." Person B says, " I am going to buy Person C's car." Person C says that each week they will both save the same amount of fuel.Is person C correct? Part 2: Person C wants to buy a new car. Each week, he wants to save the same amount of fuel as person A saved. What average fuel consumption should person C look for in a new car?
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Let's assum that each person drives 120 miles per week.
Then for person A we have:
[tex]\begin{gathered} 20mi\rightarrow1\text{gal} \\ 120mi\rightarrow xgal \\ \Rightarrow x=\frac{120}{20}=6gal \\ x=6\text{gal} \end{gathered}[/tex]for person B we have:
[tex]\begin{gathered} 30mi\rightarrow1gal \\ 120mi\rightarrow xgal \\ \Rightarrow x=\frac{120}{30}=4gal \\ x=4\text{gal} \end{gathered}[/tex]finally, for person C:
[tex]\begin{gathered} 40mi\rightarrow1gal \\ 120mi\rightarrow xgal \\ \Rightarrow x=\frac{120}{40}=3gal \\ x=3\text{gal} \end{gathered}[/tex]Then, if person A changes to person B's car, we have that the save is:
[tex]6-4=2[/tex]if person B buys person C's car, then the save is:
[tex]4-3=1[/tex]therefore, the savings on gas will be different for both of them and person C is incorrect.
2)Since person A saved 2 gallons, then the new car for Person C must save 2 gallons for each mile traveled.
Then we have the following equation:
[tex]3-x=2[/tex]where 'x' represents the number of gallons consumed in 120 miles. then, solving for x we have:
[tex]\begin{gathered} 3-x=2 \\ \Rightarrow-x=2-3=-1 \\ \Rightarrow-x=-1 \\ x=1 \end{gathered}[/tex]therefore, person C will need to buy a car that uses 1 gallon for eah 120 miles traveled
write in algebraic expression1) quotient of a number b and 36 2) 45 divided into a number r3) sum of 21 and a number x4) a number z less 19 5) a number f divided by 6
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Solution
For this case we can do the following:
1)
[tex]\frac{b}{36}[/tex]2)
[tex]\frac{45}{r}[/tex]3)
[tex]21+x[/tex]4)
[tex]z-19[/tex]5)
[tex]\frac{f}{6}[/tex]What is the value of the expression below? If entering the value as fraction or mixed number, give the answer in lowest term.-0.2 + (-¾) + 2.15 - (-⅖)
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Explanation:
-0.2 + (-¾) + 2.15 - (-⅖)
let's convert the decimal to fractions:
-0.2 = -2/10 = -1/5
2.15 = 215/100 = 43/20
-0.2 + (-¾) + 2.15 - (-⅖) = -1/5 + (-¾) + 43/20 - (-⅖)
Expanading the bracket:
Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.
= -1/5 -3/4 + 43/20 + 2/5
[tex]\begin{gathered} \text{The LCM = 20} \\ =\frac{-1(4)-3(5)+43+2(4)}{20} \\ \end{gathered}[/tex][tex]\begin{gathered} =\frac{-4-15+43+8}{20}=\frac{32}{20} \\ =\frac{8}{5} \\ =1\frac{3}{5} \end{gathered}[/tex]I just need to know the answer to question 11
Answers
Answer:
A number line a closed circle on 8, shading to the left, and a closed circle on 11, shading to the right.
Explanation:
Given the compound inequalities:
[tex]x-1\le7\text{ or }2x\ge22[/tex]First, solve both inequalities:
[tex]\begin{gathered} x-1\le7\implies x\le7+1\implies x\le8 \\ 2x\ge22\implies x\ge\frac{22}{2}\implies x\ge11 \end{gathered}[/tex]Thus, the number line should be the one that represents the solution:
[tex]x\le8\text{ or }x\ge11[/tex]• For x≤8, there is a ,closed circle on 8, and ,shading to the left.
,• For x≥11, there is a ,closed circle on 11, and ,shading to the right.
Therefore, the correct description will be:
A number line a closed circle on 8, shading to the left, and a closed circle on 11, shading to the right.
The last option is correct.
Ahmad is choosing between two exercise routines.In Routine #1, he burns 20 calories walking. He then runs at a rate that burns 10.5 calories per minute.In Routine #2, he burns 46 calories walking. He then runs at a rate that burns 5.3 calories per minute.For what amounts of time spent running will Routine #1 burn fewer calories than Routine #2?Use t for the number of minutes spent running, and solve your inequality for t.0ロロロメロOSDDADxХ5?ExplanationCheck
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Solution:
Let t for the number of minutes spent running
In Routine #1, he burns 20 calories walking. He then runs at a rate that burns 10.5 calories per minute.
This can be represented as 20 + 10.5t
In Routine #2, he burns 46 calories walking. He then runs at a rate that burns 5.3 calories per minute.
This can be represented as 46 + 5.3t
The required inequality is
[tex]\begin{gathered} 20+10.5t<46+5.3t \\ 10.5t-5.3t+20<46+5.3t-5.3t \\ 5.2t+20<46 \\ 5.2t+20-20<46-20 \\ 5.2t<26 \\ \frac{5.2t}{5.2}<\frac{26}{5.2} \\ t<5 \end{gathered}[/tex]The answer is 5 minutes
Find the circumference of a circle with a Diameter = 12 m. Use 3.14 for π and round to 2 decimal places. ANS. C= B_____________. m
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The circumference of a circle is given by the formula
[tex]s=2\cdot\pi\cdot r[/tex]however we also knos that the diameter can be written as
[tex]D=2\cdot r[/tex]meaning that the formula for the circumference can also be written as
[tex]s=D\cdot\pi[/tex]then the circumference for the given information is:
[tex]\begin{gathered} s=12\cdot3.14 \\ s=37.68 \end{gathered}[/tex]John has 44 quarters.Jan has 100 dimes. Whohas more money?
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Note that 10 dimes = $1
Also 4 quarters = $1
That means, 100 dimes equals $10
Also, 44 quarters =
Item Price (dollars) $1,400 $2,400 $3,000 $4,400 Sales Tax (dollars) $112 $192 $240 $352 Based on the table, what is the rate of change? O The rate of change for the sales tax is $0.07 per dollar. O The rate of change for the sales tax is $0.08 per dollar. O The rate of change for the sales tax is $0.06 per dollar. The rate of change for the sales tax is $0.125 per dollar.
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We know that the rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then
[tex]r\text{ = }\frac{Change\text{ in y}}{\text{Change in x}}\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]where (X1,Y1) and (X2,Y2) are points of our model.
So, in this case we have that:
[tex]r\text{ = }\frac{Y2-Y1}{X2-X1_{}}\text{ = }\frac{112-352}{1400-4400}\text{ = }\frac{240}{3000}\text{ = 0.08}[/tex]So, the correct answer is: the rate of change for the sales tax is $0.08 per dollar.
Given the following expressions, you will identify the followingslope, y- intercept , x intercept, domain range , and is the function increasing or decreasing
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Given the following function:
[tex]\text{ 3x - 2y = 16}[/tex]A.) SLOPE
Let's first transform the given equation into the standard slope-intercept form: y = mx + b
Because the m in the equation represents the value of the slope.
We get,
[tex]\begin{gathered} \text{ 3x - 2y = 16} \\ \text{ (3x - 2y = 16)( -}\frac{\text{ 1}}{\text{ 2}}) \\ \text{ -}\frac{3}{2}x\text{ + y = -}\frac{16}{2} \\ \text{ -}\frac{3}{2}x\text{ + y = -}8 \\ \text{ y = }\frac{3}{2}x\text{ - 8} \end{gathered}[/tex]The slope-intercept form of 3x - 2y = 16 is y = (3/2)x - 8. Where m = 3/2.
Therefore, the slope of the function is 3/2.
B.) Y - INTERCEPT
In the standard slope-intercept form : y = mx + b, b represents the y - intercept.
Therefore, in the converted form of the function y = (3/2)x - 8. b is equals to -8.
The y-intercept is 0, -8.
C.) X - INTERCEPT
The x - intercept is the point at y = 0.
We get,
[tex]\text{ 3x - 2y = 16}[/tex][tex]\text{ 3x - 2(0) = 16}[/tex][tex]\text{ 3x = 16}[/tex][tex]\text{ }\frac{\text{3x}}{3}\text{ = }\frac{\text{16}}{3}[/tex][tex]\text{ x = }\frac{\text{ 16}}{\text{ 3}}[/tex]Therefore, the x - intercept is 16/3, 0
D.) DOMAIN RANGE
The function has no undefined points nor domain constraints. Therefore, the domain is
[tex]-\infty\: We usually encounter undefined points when a given value of x will make the denominator equal to zero (0).Example: 2/(3 - x) at x = 3 is undefined.
E.) INCREASING OR DECREASING
The easiest way to determine if the function is decreasing or increasing is by looking at the slope (m). If the slope is greater than 0 (m > 0) or a positive, the function is increasing. If the slope is less than 0 (m < 0) or a negative, the function is decreasing.
Here, the slope is 3/2 which we first solved. Since the slope is greater than zero or a positive, the function is, therefore, increasing.
The answer is increasing.
Totsakan enlarged the size of a photo to aheight of 18 in. What is the new width if itwas originally 2 in tall and 1 in wide?
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Let's begin by identifying key information given to us:
New size: Height = 18 in, Width = ?
Old size: Height = 2 in, Width = 1 in
We will get the width of the new photo by following the explanation below:
[tex]\begin{gathered} 18\colon2=x\colon1 \\ \Rightarrow\frac{18}{2}=\frac{x}{1} \\ \text{Cross multiply, we have:} \\ 2\cdot x=18\cdot1\Rightarrow2x=18 \\ 2x=18 \\ \text{Divide both sides by ''2'', we have:} \\ x=\frac{18}{2}=9 \\ \therefore x=9in \end{gathered}[/tex]Therefore, the width of the enlarged photo is 9 inches
The 5 participants in a 200-meter dash had the following finishing times in seconds)24, 28, 26, 30, 32Send data to calculatorAssuming that these times constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places,
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Given:
Data x: 24, 28, 26, 30, 32
n = 5
Asked: What is the standard deviation of the population?
Formula:
[tex]\text{standard deviation = }\sqrt[]{\frac{\sum ^{}_{}(x-\bar{x})^2}{n}}[/tex]Solution:
Step 1: We will get the average of the data given.
NOTE: Bar x is also the mean or the average.
[tex]\begin{gathered} \bar{x}\text{ = }\frac{24+28+26+30+32}{5}\text{ } \\ \bar{x}=\text{ 28} \end{gathered}[/tex]Step 2: We will subtract the mean from each number.
Step 3: We will square the differences and get the summation.
Step 4: We will substitute the acquired values to find the standard deviation using the formula above.
[tex]\begin{gathered} \text{standard deviation = }\sqrt[]{\frac{\sum ^{}_{}(x-\bar{x})^2}{n}} \\ \text{standard deviation = }\sqrt[]{\frac{40^{}}{5}}\text{ } \\ \text{standard deviation = 2}\sqrt[]{2}\text{ = }2.828427125 \end{gathered}[/tex]ANSWER: standard deviation = 2.83 (Rounded off to 2 decimal places)
Us a tree diagram to find the sample space and the total number of possible outcomesSo which choice is the answer.
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In order to create the tree diagram, first, create the principal branches which is the type of item,
Then, divide the three colors for each of the items
.the, count the final branches to know the possible outcomes, meaning that the number of possible outcomes is 6.
The function h is defined by h (x)=3x² - 4.Find h (3x).
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When we have a function f(x) we can evaluate it for different arguments (the value of x) by replacing the argument in the definition of the function.
In this case, we know h(x) and we have to express h(3x). To do this, we replace x in the original function with 3x:
[tex]\begin{gathered} h(x)=3x^2-4 \\ h(3x)=3(3x)^2-4=3\cdot(3^2x^2)-4=3\cdot9x^2-4=27x^2-4 \end{gathered}[/tex]Answer: h(3x) = 27x²-4
logitechExample 6:Triangle XYZ is graphed below. Draw and label Triangle X'Y'Z' after a dilation using a scale factor oftwo.I.113XWhat will be the coordinates of point Y" after a reflection of polygon X'Y'Z' over the x-axis?Answer
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First answer:
Second Answer:
The coordinates of the Y'' after reflection of poligon X'Y'Z' over the x axis: (-2, -4)
Simplify the Expression [tex]12g + 3 - g {}^{2} + 2[/tex] g=4
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done
Consider parallelogram QRST below.Use the information given in the figure to find m ZR, x, and m ZROS.R.4x1275040°7S
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The opposite angles of a parallelogram are equal, therefore:
[tex]\begin{gathered} m\angle R=m\angle T \\ so\colon \\ m\angle R=75 \end{gathered}[/tex]Opposite sides of a parallelogram are parallel and equal so:
[tex]\begin{gathered} QT=RS \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]∠TSQ and ∠RQS are alternate interior angles, therefore:
[tex]\begin{gathered} m\angle RQS=m\angle TSQ \\ so_{}\colon \\ m\angle RQS=40 \end{gathered}[/tex]Does the equation x = 1 represent a function?How do I know if it represents a function if it doesn't have y axis to show if it is.
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A function is a relation between variables y and x,
where theres only a y value for every x value
In this case x=1 . For every value of x = 1 ,there are infinite values for y , it can take any value , negative or positive.
So this is NOT a function
The following scatter plot represents the relationship between a person's weight and the number of calories the person burns in one minute of jump roping. What type of relationship is shown?
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The scatter plot shows a positive correlation because the points show a linear-trend describing that when x-values (weight) increases then y-values (calories) also increases.
Hence, the relationship is a Positive correlation.
Given the right triangle find the value of sec(90 degree - theta) when a= 12, b= 5, c= 13
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Use the next trigonometric identities:
[tex]\begin{gathered} \sec (90º-\theta)=\frac{1}{\cos (90º-\theta)} \\ \\ \cos (90º-\theta)=\sin \theta \end{gathered}[/tex]Then, the sec(90º - θ) is:
[tex]\sec (90º-\theta)=\frac{1}{\sin \theta}[/tex]The sin(θ) is:
[tex]\sin \theta=\frac{opposite}{hypotenuse}=\frac{5}{13}[/tex]Then:
[tex]\sec (90º-\theta)=\frac{1}{\frac{5}{13}}=\frac{13}{5}[/tex]Then, the sec(90º - θ) is 13/5which functions are correctly graphed?
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Solution
final answer is.
Choice A, C ,D
Ignore the 58.I just need to find the m
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The angles in the question are vertically opposite angles and Vertically opposite angles are equal.
Therefore,
[tex]\begin{gathered} (12x-37)^0=(9x+5)^0 \\ by\text{ collecting like terms we will have} \\ 12x^0-9x^0=5^0+37^0 \\ 3x^0=42^0 \\ \text{divide both sides by 3} \\ \frac{3x}{3}=\frac{42}{3} \\ x=14^0 \end{gathered}[/tex][tex]\begin{gathered} to\text{ measure }\angle y \\ 12x-37+y=180^0 \\ \text{substitute x=}14^0\text{ in the above equation to get y} \\ 12(14)-37^0+y^0=180^0 \\ 168^0-37^0+y=180^0 \\ 131^0+y=180^0 \\ y=180^0-131^0 \\ y=49^0 \end{gathered}[/tex]Therefore,
[tex]\angle y=49^0[/tex].a. Triangle ABC with coordinates A (3, 4), B (7,7), and C (8, 1) is translated 6 units left and 7 units down.
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Triangle ABC with coordinates A (3, 4), B (7,7), and C (8, 1) is translated 6 units left and 7 units down.
we have that
the rule of the translation is
(x,y) -------> (x-6, y-7)
Applying the rule to the coordinates of triangle ABC
A(3,4) ------> A'(3-6,4-7)
A'(-3,-3)
B(7,7) ------> B'(7-6, 7-7)
B'(1,0)
C(8,1) --------> C'(8-6,1-7)
C'(2,-6)
Is my answer correct? 3/4 + 9/16 = 3/16
Answers
Answer:
is not correct because the lcm will be 16 and u will get 21/16
i need help with math
Answers
∠1 and ∠2 are on same side exterior angles. FALSE
∠3 and ∠12 are alternate interior angles. FALSE
∠2 and ∠10 are corresponding angles. TRUE
∠6 and ∠11 are alternate exterior angles. TRUE
What are the different types of angles?Corresponding angles ; Angles that are present in similar locations are said to be in correspondence with one another. The dimensions of both angles are equal
Alternate Interior Angle: This term refers to the angles that are present on the opposing sides of the transversal. They can be found on the inside of the Z that the figure's Z has produced. The angles are both equal to one another.
Alternative Exterior Angle: The alternative exterior angles are those that are externally located and present on the opposing sides of the transversal. Both angles measure the same and they may be seen on the exterior.
To know more about angles and lines ; you may visit the link which is mentioned below:
https://brainly.com/question/1597341
#SPJ13
i need help with math
Answers
Answer:
x = 33
Step-by-step explanation:
Creating an equation
The angles shown are corresponding angles
Corresponding angles are angles that occupy the same position and are on the same side of the transversal. For a better sense of this, kindly review the attached image.
Corresponding angles are congruent ( equal to each other )
This means that 124 = 4x - 8
Solving for x
124 = 4x - 8
==> add 8 to both sides
132 = 4x
==> divide both sides by 4
33 = x
Question 5 of 10According to this diagram, what is cos 16°?
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Explanation
We are given the following:
We are required to determine the value of cos 16° from the diagram given.
We know that according to the trigonometry ratio rules:
[tex]\cos\theta=\frac{adjacent}{hypotenuse}[/tex]So, we have:
[tex]\cos16\degree=\frac{24}{25}[/tex]Hence, the answer is:
[tex]\cos16\operatorname{\degree}=\frac{24}{25}[/tex]A sample of 26 customers was taken at a computer store. Each customer was asked the price of the computer she bought. Here is a summary Number of computers 7, 10,9 Price paid for each (in dollars) 900, 800, 1200 Find the mean price for this sample. Round your answer to the nearest dollar.
Answers
formula for the mean
[tex]\bar{x}=\frac{\sum ^{\infty}_{n\mathop=0}x_i}{n}[/tex]for this exercise n=26
replace data on the formula
[tex]\begin{gathered} \bar{x}=\frac{(7\cdot900)+(10\cdot800)+(9\cdot1200)}{26} \\ \bar{x}=965.385 \end{gathered}[/tex]