Answers
The solution of the system of equations are;
⇒ x = - 6 , y = 44 and z = 2
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The system of the equations are,
3x + y - 2z = 22 .... (i)
x + 5y + z = 4 .... (ii)
x = - 3z .... (iii)
Now,
Solve the equations as;
Substitute x = - 3z in both equations, we get;
⇒ 3x + y - 2z = 22
⇒ 3 × -3z + y - 2z = 22
⇒ - 9z + y - 2z = 22
⇒ - 11z + y = 22 .... (iii)
And, x + 5y + z = 4
- 3z + 5y + z = 4
5y - 2z = 4 ... (iv)
Solve equation (iii) and (iv) we get;
⇒ y = 44 and z = 2
So, x = - 3z
⇒ x = - 3 × 2
⇒ x = - 6
Thus, The solution of the system of equations are;
⇒ x = - 6 , y = 44 and z = 2
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Related Questions
Need help please. ASAP
Answers
(2y - 1)/ -3 = -5 , prove y = 8: Hence proved
5n - 42 = 12n, prove n = -6: Hence proved
2x + 30 = -4(5x -2), prove x = -1 : Hence proved
18x - 2(3x + 1) = 5x -16, prove x = -2 : Hence proved
What is Algebra?
One of the many different mathematical disciplines is algebra. Algebra, a common thread that runs through nearly all of mathematics, is the study of mathematical symbols and the rules for using them in formulas.
1) (2y - 1)/ -3 = -5
Solving for y
(2y - 1)/ -3 = -5
multiply both side with -3
(2y - 1) x (-3)/(-3) = (-5)(-3)
2y - 1 = 15
adding 1 both side
2y - 1 + 1 = 15 + 1
2y = 16
dividing 2 both side
2y / 2 = 16 / 2
y = 8
Hence Proved
2) 5n - 42 = 12n
Solving for n
5n - 42 = 12n
adding 42 both side
5n - 42 + 42 = 12n + 42
5n = 12n + 42
adding -12n both side
5n - 12n = 12n - 12n + 42
-7n = 42
dividing -7 both side
-7n/-7 = 42/ -7
n = -6
Hence proved
3) 2x + 30 = -4(5x -2)
solving for x
first simplify -4(5x -2)
2x + 30 = -20x + 8
adding 20x both side
2x + 20x + 30 = -20x + 20x + 8
22x + 30 = 8
adding -30 both side
22x + 30 - 30 = 8 - 30
22x = -22
dividing 22 both side
22x / 22 = -22/22
x = -1
Hence proved
4) 18x - 2(3x + 1) = 5x -16
solving for x
first simplify - 2(3x + 1)
18x - 6x - 2 = 5x - 16
adding -5x both side
18x - 5x - 6x - 2 = 5x - 5x - 16
13x - 6x - 2 = -16
7x - 2 = -16
adding 2 both side
7x - 2 + 2 = -16 + 2
7x = -14
dividing 7 both side
7x/ 7 = -14 / 7
x = -2
Hence proved
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Angle 1,7,3 and 5 all those angles has the same equivalent to the angle 5 angle 2 is supplementary to angle 1 so angle 2 is 30 degrees because 150+ 30 is 180 degrees and we use the same thing that I did in the first step that if angle number to is 30 angle 8,4 and 6 is going to be 30
Answers
Given:-
To find all angle values.
So from the given image. we get,
[tex]\begin{gathered} \angle5+\angle4=180 \\ \angle7+\angle4=180 \\ \angle7+\angle6=180 \\ \angle6+\angle5=180 \end{gathered}[/tex]Also,
[tex]\begin{gathered} \angle1=\angle7 \\ \angle2=\angle4 \\ \angle8=\angle6 \\ \angle3=\angle5 \end{gathered}[/tex]So now we know angle 5 is 150 degrees. so we get,
[tex]\begin{gathered} \angle5+\angle4=180 \\ 150+\angle4=180 \\ \angle4=180-150 \\ \angle4=30 \end{gathered}[/tex]So angle 4 is 30 degree.
Also,
[tex]\begin{gathered} \angle7+\angle4=180 \\ \angle7+30=180 \\ \angle7=150 \end{gathered}[/tex]So angle 7 is 150 degree.
Also,
[tex]\begin{gathered} \angle6+\angle5=180 \\ \angle6+150=180 \\ \angle6=30 \end{gathered}[/tex]So angle 6 is 30 degree.
So now we equate the values. so we get,
[tex]undefined[/tex]which describes the domain of the figure represented below? ANSWER CHOICES :[8,0)(0,8)[0,8)
Answers
We have the following:
The domain is the input values or also the x-axis values.
According to the graph we can see that we go from 0 to 8.
Because the point at 0 is filled, it means that it includes the number and that means that it is a closed interval [].
On the contrary, at point 8, the point is hollow, it means that it reaches 8, but it does not include the number 8, which means that it is an open interval ().
Which means that the correct answer is:
[0, 8)
HELP
QUICKOU#FR{PIEWuf'oieud'f'doifu
Answers
Apply the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, a^2 + b^2 = c^2 where c is the hypotenuse.
a^2 + b^2 = c^2
8^2 + 5^2 = c^2
64 + 25 = c^2
89 = c^2
√89 = √c^2
c = √89
180/9 as a whole number
Answers
Answer:
20
Step-by-step explanation:
180 ÷ 9 = 20
Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]A. 28.53 units²B. 26.47 units²C. 27.28 units²D. 33.08 units²
Answers
Answer
A. 28.53 units²
Explanation
Finding the area of irregular quadrilateral ABCD, we divide the given figure into shapes (two triangles) as shown below:
Then, we find the area of the two triangles.
Triangle ABD:
[tex]\begin{gathered} Area=\sqrt{s(s-a)(s-b)(s-c)} \\ \\ s=\frac{a+b+c}{2}=\frac{2.89+8.59+8.6}{2}=\frac{20.08}{2}=10.04 \\ \\ Area\text{ }of\text{ }triangle\text{ }ABD=\sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)} \\ \\ Area\text{ }of\text{ }triangle\text{ }ABD=\sqrt{10.04(7.15)(1.45)(1.44)} \\ \\ Area\text{ }of\text{ }triangle\text{ }ABD=\sqrt{149.889} \\ \\ Area\text{ }of\text{ }triangle\text{ }ABD=12.24\text{ }unit^2 \end{gathered}[/tex]Triangle ADC:
[tex]\begin{gathered} Area=\sqrt{s(s-a)(s-b)(s-c)} \\ \\ s=\frac{a+b+c}{2}=\frac{4.3+7.58+8.6}{2}=\frac{20.48}{2}=10.24 \\ \\ Area\text{ }of\text{ }triangle\text{ }ADC=\sqrt{10.24(10.24-4.3)(10.24-7.58)(10.24-8.6)} \\ \\ Area\text{ }of\text{ }triangle\text{ }ADC=\sqrt{10.24(5.94)(2.66)(1.64)} \\ \\ Area\text{ }of\text{ }triangle\text{ }ADC=\sqrt{265.346} \\ \\ Area\text{ }of\text{ }triangle\text{ }ADC=16.29\text{ }unit^2 \end{gathered}[/tex]Therefore, the area of the quadrilateral ABCD = the Sum of the two triangles
The area of the quadrilateral ABCD = 12.24 units² + 16.29 units² = 28.53 units²
The value of a in y = ax²+bx+c and the vertex of the parabola are given. How many x-intercepts does the parabola have? Explain how you arrived at this number.a=1; vertex at (2,0)The parabola has x-intercept(s), because the parabola opensand the vertex isthe x-axis.
Answers
Given: The value of 'a' in y = ax²+bx+c is a=2 and vertex is at (2,0).
Required: To find the x-intercepts.
Explanation: The x-coordinate of the vertex is 2. Also, we know that x-coordinate is given by
[tex]x=-\frac{b}{2a}[/tex]Hence, putting the value of x=2 and a=1 we get
[tex]\begin{gathered} 2=-\frac{b}{2(1)} \\ b=-4 \end{gathered}[/tex]Now putting y=0, x=2, a=1, and b=-4 in eq of parabola we get
[tex]\begin{gathered} 0=2^2-4(2)+c \\ c=4 \end{gathered}[/tex]Now the equation of the parabola is,
[tex]y=x^2-4x+4[/tex]Now to find x-intercepts put y=0 i.e.,
[tex]\begin{gathered} x^2-4x+4=0 \\ (x-2)^2=0 \\ x=2,2 \end{gathered}[/tex]Hence there is only one x-intercept at (2,0). The opening of the parabola can be seen in the graph below-
Final Answer: The parabola has one x-intercept because the parabola opens upward and the vertex is on the x-axis.
Suppose you pay only the interest on a loan. Will the loan ever be paid off? Why or why not? I have no idea if this is correct
Answers
No. if only the interest is paid, the principal never decreases
help me with the last question pleaseeeeeeeeeeeeeee
Answers
Answer:
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
Please find it if needed.-The Area of a Rectangle-The Area of a Triangle-The Area of a Square-Or The Area of a Circleand find the area of the composite figure (andplease put the areas separate)FIND THE AREA OF THE SHADED REGION
Answers
First find the area of the rectangle
A = l*w = 9*16 = 144
The unshaded area is a trapezoid
A = 1/2 ( b1+b2) *h = 1/2 ( 5+11) * 4 = 1/2 (16) * 4 =32
The area of the shaded region is
rectangle - trapezoid
144-32
112cm^2
Answer:
112cm²
Step-by-step explanation:
First, let us find the area of the rectangle.
Area = length × width
Area = 16 cm × 9 cm
Area = 144 cm²
Now, let us find the area of the trapezium.
Area = 1/2 ( Sum of the parallel sides ) × height
Area = 1/2 × ( 11 + 5 ) × 4
Area = 1/2 × 16 × 4
Area = 32 cm²
Area of the shaded region.
To find the area of the shaded region, subtract the area of the rectangle from the area of the trapezium.
Area = 144cm² - 32cm²
Area = 112cm²
Find the value of x and the length of ST
Answers
x = 13
The length of ST is 78
Explanation:ST and SR are tangents
From the diagram
ST = 9x - 39
SR = 6x
Note that:
Two tangents drawn from the same point external to a circle are equal
That is, ST = SR
9x - 39 = 6x
9x - 6x = 39
3x = 39
x = 39/3
x = 13
ST = 9x - 39
Suubstitute x = 13
ST = 9(13) - 39
ST = 117 - 39
ST = 78
can somebody please help me with this question
Answers
Carina has a piece of wire that is 301cm long . She bends the wire to make 6 shapes of the same perimeter . She has 97cm of wire left . What is the perimeter of each shape ?
Answers
Answer:
34
Step-by-step explanation:
301 - 97 = 204
204 / 6 = 34
Enter the corredeach column.4. Madam Malkin owns Madam Malkin's Robes for AllOcassions which is a clothing store. She has abudget of $6000 to restock 200 clothing items.She can buy Hogwarts shirts for $12 each, Robes for$24 each, and Quidditch shirts for $36 each. If shewants to have twice as many Quidditch shirts asRobes, how many of each type of shirt should shebuy?11)223HOW MANY QUIDDITCH SHIRTS DID MADAMMALKIN BUY?445
Answers
Let's define some notation first:
H= number of Hogwarts, R= number of robes, Q= number of Quidditch
We can set up the following equation for the total of clothing items:
[tex]H+R+Q=200[/tex]We also know that Q= 2R so we have:
[tex]H+3R=200[/tex]Now we can create an equation for the amount of money and we have:
[tex]12H+24R+36Q=6000[/tex][tex]12H+96R=6000[/tex]Now we can replace H=200-3R and we got:
[tex]12(200-3R)+96R=6000[/tex]And solving for R we got:
[tex]60R=3600[/tex][tex]R=\frac{3600}{60}=60[/tex]And then Q would be:
[tex]Q=2R=120[/tex]Write an equation in point-slope form for the line that passes through the given points.
(-4,7). (6.3)
Answers
Answer:
[tex]y=-\frac{2}{5}x+5.4[/tex]
Step-by-step explanation:
Step 1: plot points
Step 2: find the RISE/RUN (-4/10 or -2/5)
Step 3: find where it intersects the y axis (5.4)
y=mx+b where x and y are varables, m is the slope, and b is the y-int
[tex]y=-\frac{2}{5}x+5.4[/tex]
Hope that helps
what is the product of 24.154 and 0.18
Answers
Answer:
4.34772
4.3 with the correct amount of sig figs but you don't really have to worry about that unless you've talked about it in class
Step-by-step explanation:
the product of two numbers is the result of those two numbers being multiplied. So, 24.154 * 0.18 = 4.34772
If one mini Hershey bar weighs 0.3 ounces how many mini candy bars would you have to eat to eat the same amount as a regular size Hershey bar that weighs 1.55 ounces?
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0.3x=1.55 from here you solve for x. Do this by diving 1.55 by 0.3 to get c alone
x=5.16666 repeating
54 is the product of 3 and Janelle's age
Answers
What is the value of (-3)-4?
Answers
Answer:
-7
Step-by-step explanation:
-3-4=-7
:]
Answer:
-7
Step-by-step explanation:
For each table, determine whether it shows a direct variation.If it does, write its direct variation equation.Not direct variationNot direct varlationXхyу41N1Direct variationEquation:51.2542Direct variationEquation:I78.75105The
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For the right table , y/x = constant = k = 0.5
Part 1: Factorial!2. Explain the steps that you took to calculate it on your calculator.
Answers
Given:
a factorial 14! is given
Find:
we have to evaluate the given factorial
Explanation:
we know, the factorial 14! is calculated as following
14! = 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
14! = 87178291200
or
14! = 8.71783E10
Find an angle e in the interval [0°, 90°) that satisfies each statement. Give answer to the nearest TENTH of a degree. a) sin= 0.3697 degrees b) cos= 0.7265 degrees degrees c) sec= 2.3232 degrees d) csc= 1.1234
Answers
first at all, we are gonna solve this using inverse trigonometric functions
like this:
[tex]\begin{gathered} \sin \alpha\text{ = x} \\ \alpha\text{ = }\sin ^{-1}x \end{gathered}[/tex]for the first case:
a)
[tex]\begin{gathered} \sin \alpha\text{ = }0.3697 \\ \alpha=\sin ^{-1}(0.3697) \\ \alpha=21.697\ldots \\ \alpha\cong20 \end{gathered}[/tex]b)
[tex]\begin{gathered} \cos \alpha\text{ = }0.7265 \\ \alpha=\cos ^{-1}(0.7265) \\ \alpha=43.406\ldots \\ \alpha\cong40 \end{gathered}[/tex]c)
In this case, we are going to use the following trigonometric identity:
[tex]\begin{gathered} \sec \alpha=\frac{1}{\cos \alpha} \\ \end{gathered}[/tex]later,
[tex]\begin{gathered} \sec \alpha=2.3232 \\ \frac{1}{\cos \alpha}=2.3232 \\ \cos \alpha=\frac{1}{2.3232} \\ \alpha=\cos ^{-1}(\frac{1}{2.3232}) \\ \alpha=64.504\ldots \\ \alpha\cong60 \end{gathered}[/tex]d)
In this case, we are going to use the following trigonometric identity:
[tex]\begin{gathered} csc\alpha=\frac{1}{sin\alpha} \\ \end{gathered}[/tex]later,
[tex]\begin{gathered} \csc \alpha=1.1234 \\ \frac{1}{sin\alpha}=1.1234 \\ \sin \alpha=\frac{1}{1.1234} \\ \alpha=\sin ^{-1}(\frac{1}{1.1234}) \\ \alpha=62.892\ldots \\ \alpha\cong60 \end{gathered}[/tex]finally, those are your answers.
rewrite using a single positive exponent (4^-3)^7
Answers
The given expression is
(4^-3)^7
We would apply the law of exponents which is expressed as
(a^- b) = 1/a^b
We can see that
a = 4
b = - 3
Writing it using a single positive exponent, it becomes
4^ - 3 = 1/4^3 = 1/64
The final expression would be
(1/64)^7
X-2y=5 and 2x+3y=10
Answers
Hello!
Let's set up some things:
[tex]x-2y=5[/tex] <-- equation 1
[tex]2x+3y = 10[/tex] <-- equation 2
________________
(equation 1) multiplied by 2
[tex]2x - 4y=10[/tex] <-- equation 3
________________
(equation 2) - (equation 3)
7y = 0
y = 0 <-- equation 4
________________
(equation 4)'s value of y into (equation 1)
[tex]x-2(0) = 5\\x = 5[/tex]
Thus x = 5 and y = 0
Hope that helps!
Which property is shown -2x1/-2=1
Answers
Answer: The answer is Multiplicative Inverse.
Step-by-step explanation: I hope this helps.
Is w = 12 a solution to the inequality below?
Answers
Answer:
No
Step-by-step explanation:
No, it is not a solution. You can find this answer by plugging in 12 for 2 for w.
0>12-132/12
132/12=11
12-11=1
0>1
0 is not greater than 1, so the answer is no.
An irrigation canal is 10 kilometers long and 2 meters deep. It is 4 meters wide at the 2 meters wide at the bottom. How many cubic meters of earth were excavated to make the canal?
Answers
The cross section of the canal will form a trapezoid. First, find the area of the cross section. The area of a trapezoid is defined as
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{a+b}{2}h \\ \\ \text{Given} \\ h=2\text{ meters (2 meters deep)} \\ a=4\text{ meters (4 meters wide)} \\ b=2\text{ meters (2 meters wide at the bottom)} \end{gathered}[/tex]Substitute the following values and we get the area
[tex]\begin{gathered} A=\frac{a+b}{2}h \\ A=\frac{4+2}{2}(2) \\ A=\frac{6}{2}(2) \\ A=6\text{ m}^2 \end{gathered}[/tex]Now that we have the area of the cross section, multiply it to the length of the irrigation canal.
[tex]\begin{gathered} \text{Before multiplying, all units must be the same, convert km to meters} \\ 10\operatorname{km}\rightarrow10,000\text{ meters} \\ 6\text{ m}^2\times10000\text{ meters} \\ \Longrightarrow60000\text{ m}^3 \end{gathered}[/tex]Therefore, they have to excavate 60,000 cubic meters of earth to make the canal.
At many bakeries, there are deals that if you buy twelve donuts, you get a thirteenth one at a discount. Sometimes "13" items is called a baker's dozen. I One store is advertising: Donuts! $1.05 individually, or $13 per baker's dozen. They want to program their cash register to be able to show the exact price for any number of donuts. You will help them by producing a data table, a graph and an algorithm. You will: 1. Fill in and expand the data table 2. Make a scatter plot to show the pattern visually. This means to plot an (x,y) point for every row in the data table. For example the first point can be (1, 1.05) 3. Develop an algorithm to find the cost for any number of donuts. Note: An algorithm is like a set of instructions to solve a problem. They are useful for telling computers or people exactly how to do something. For example, here is an algorithm that finds 15% of a number: Step 1: take any number, callit N.
Answers
Table
Number of donuts Price
1 $1.05
2 $ 2.1
3 $3.15
4 $4.2
5 $5.25
6 $6.3
10 $10.5
slope = (10.5 - 1.05) / 10 - 1
= 9.45 / 9
= 1.05
Equation
y - 10.5 = 1.05 (x - 10)
y = 1.05x - 10.5 + 10.5
y = 1.05x
For 40 donuts
y = 1.05(40)
y = $42
In anatomy, a student learned that the average resting heart rate is between 60 and 100 beats per minute. The student decided to record the heart rate of people over five minutes while waiting in line at the pharmacy. The dot plot shows the results.
Dot plot with 1 dot at 62, 3 dots at 68, 1 dot at 69, 2 dots at 70, 3 dots at 72, 2 dots at 75, 1 dot at 76, 2 dots at 78, 3 dots at 80, and 2 dots at 89
Which statement below best describes the shape of the distribution?
The data is roughly symmetrical distributed, with most values clustered from 68 to 80 beats per minute. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
The data is not symmetrically distributed, with most values clustered from 68 to 80 beats per minute. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
The data is skewed left, with fewer values on the left end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
Answers
The correct option regarding the data-set represented by the dot plot is represented as follows:
The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
Dot plotA dot plot shows the number of times that each observation appears in the data-set.
Hence, the complete data-set in this problem is given as follows:
62, 68, 68, 68, 69, 70, 70, 72, 72, 72, 75, 75, 76, 78, 78, 80, 80, 80, 89, 89.
The mean of a data-set is the sum of the observations divided by the number of observations, hence it is given by:
Mean = (62 + 3 x 68 + 69 + 2 x 70 + 3 x 72 + 2 x 75 + 76 + 2 x 78 + 3 x 80 + 2 x 89)/20 = 74.55.
The median is the middle value of the data-set. The data-set has 20 elements, hence the median is the mean of the 10th and the 11th element, given as follows:
Median = (72 + 75)/2 = 73.55.
The mean is greater than the median, hence the data is right skewed and the correct option is given as follows:
The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
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Answer: A/The data is roughly symmetrical distributed, with most values clustered from 68 to 80 beats per minute.
Step-by-step explanation: Just got it right on the test
Can a table with same input and output be a function like in the picture:
Answers
Yes, because each value of x still corresponds to only one value of y.