We are given the following system of equations:
[tex]\begin{gathered} x+2y+z=8,(1) \\ 2x+y-z=1,(2) \\ x+y-2z=-3,(3) \end{gathered}[/tex]To solve the system we will add equations (1) and (2):
[tex]x+2y+z+2x+y-z=8+1[/tex]Adding like terms:
[tex]\begin{gathered} 3x+3y=9 \\ x+y=3,(4) \end{gathered}[/tex]Now we multiply equation (2) by -2:
[tex]-4x-2y+2z=-2[/tex]Now we add this equation to equation (3):
[tex]x+y-2z-4x-2y+2z=-3-2[/tex]Adding like terms:
[tex]-3x-y=-5,(5)[/tex]Now we add equations (4) and (5):
[tex]x+y-3x-y=3-5[/tex]Adding like terms:
[tex]-2x=-2[/tex]Dividing both sides by -2:
[tex]x=-\frac{2}{-2}=1[/tex]Now we replace this value of "x" in equation (4):
[tex]\begin{gathered} x+y=3 \\ 1+y=3 \end{gathered}[/tex]Subtracting 1 to both sides:
[tex]\begin{gathered} 1-1+y=3-1 \\ y=2 \end{gathered}[/tex]Now we replace the values of "x" and "y" in equation (1):
[tex]\begin{gathered} x+2y+z=8 \\ 1+2(2)+z=8 \end{gathered}[/tex]Adding like terms:
[tex]\begin{gathered} 1+4+z=8 \\ 5+z=8 \end{gathered}[/tex]Subtracting 5 to both sides:
[tex]\begin{gathered} 5-5+z=8-5 \\ z=3 \end{gathered}[/tex]Therefore, the solution of the system is:
[tex]x=1,\text{ y=2, z=3}[/tex]Select the GCF for each pair of numbers. 9,15 12,18 15,27 30,54
The Greatest common factors for each pair of numbers are;
1, ( 9 , 15 ) = 3
2. ( 12 , 18 ) = 6
3. ( 15 , 27 ) = 3
4. (30, 54) = 6
What is Greatest common factors?
The highest number that divides exactly into two more numbers, is called Greatest common factors.
Given that;
The pairs of numbers are;
1, ( 9 , 15 )
2. ( 12 , 18 )
3. ( 15 , 27 )
4. (30, 54)
Now,
Find the Greatest common factors of the pairs of the numbers as;
1, ( 9 , 15 )
LCM of 9 = 3 x 3
LCM of 15 = 3 x 5
So, GCF of 9 and 15 = 3
2. ( 12 , 18 )
LCM of 12 = 2 x 3 x 2
LCM of 18 = 3 x 3 x 2
So, GCF of 12 and 18 = 3 x 2 = 6
3. ( 15 , 27 )
LCM of 15 = 3 x 5
LCM of 27 = 3 x 3 x 3
So, GCF of 15 and 27 = 3
4. (30, 54)
LCM of 30 = 2 x 3 x 5
LCM of 18 = 3 x 3 x 2
So, GCF of 30 and 54 = 3 x 2 = 6
Thus, The Greatest common factors for each pair of numbers are;
1, ( 9 , 15 ) = 3
2. ( 12 , 18 ) = 6
3. ( 15 , 27 ) = 3
4. (30, 54) = 6
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A cone has a radious of 5inches and a height of 10.125inches.What is the volume of the cone in inch rounded to the nearest tenth?
Answer:
264.9 in³
Explanation:
The volume of a cone can be calculated using the following equation:
[tex]V=\frac{\pi\cdot r^2\cdot h}{3}[/tex]Where π is approximately 3.14, r is the radius of the cone and h is the height.
So, replacing r by 5 in and h by 10.125 in, we get:
[tex]\begin{gathered} V=\frac{3.14\cdot(5)^2\cdot(10.125)}{3} \\ V=\frac{3.14\cdot25\cdot10.125}{3} \\ V=\frac{794.8}{3} \\ V=264.9 \end{gathered}[/tex]Therefore, the volume of the cone is 264.9 in³
find the X and the Y intercepts of the graph of the equation below 8x + 2y equals negative 16
The expresion is:
[tex]8x+2y=-16[/tex]to find the intercepts with the x axis we have to rplace in the equation y = 0, so:
[tex]\begin{gathered} 8x+2(0)=-16 \\ 8x=-16 \end{gathered}[/tex]and we solve for x
[tex]x=-\frac{16}{8}=-2[/tex]the intersection with the x axis is -2
And for the itercepts with the y axis we replace x = 0
[tex]\begin{gathered} 8(0)+2y=-16 \\ 2y=-16 \end{gathered}[/tex]and we solve for y
[tex]y=-\frac{16}{2}=-8[/tex]This means that the intersepts with the y axis is -8
Questlon 14 of 25 What is the slope of the line containing (-3, 1) and (1, -2)? O A. A - 3 O B. 4 O c. - 3 4 O D. SUBMIT
Answer:
C - 3/4
Step-by-step explanation:
12–23. Tony Ring wants to attend Northeast College. He will need $60,000 4 years from today. Assume Tony’s bank pays 12% interest compounded semiannually. What must Tony deposit today so he will have $60,000 in4 years?
Answer:
See below
Step-by-step explanation:
Period = 1/2 year total 4years = 8 periods
i = interest per period in decimal form = .12/2 = .06
initial deposit = ?
Final value = 60 000
60 000 = ? ( 1 + .06)^8
? = 37644.74
Simplify the expression.Can you help me with this one. I'm stuck at 12^x4 - 15x^2
Simplify the given expression as shown below
[tex]\begin{gathered} 3x(4x^4-5x)=3x*4x^4+3x(-5x)=12x^5+(-15x^2) \\ =12x^5-15x^2 \end{gathered}[/tex]Therefore, the answer is 12x^5-15x^2Is 5 ft, 6 ft, 11 ft a right triangle
Answer:
No, not right or a triangle lol
Step-by-step explanation:
This is not a triangle.
5+6=11, it has to be greater :)
your triangle is a straight line.
:]
Write the correct expression for the following statement.
x six times
Use / for division
do not put any spaces
If the area of a parallelogram is 36 cm^2 and has a height of 4 cm, what is the basea cm
Given, the area of the parallelogram, A=36 cm^2.
The height of the parallelogram, h=4 cm.
The area of a parallelogram is,
[tex]A=bh[/tex]Here, b is the base length and h is the height of the parallelogram.
Put values of A and h in the above equation to find base b.
[tex]\begin{gathered} 36=b\times4 \\ \frac{36}{4}=b \\ 9cm=b \end{gathered}[/tex]Therefore, the base of the parallelogram is 9 cm.
4x - 2y = 8Solve for yy = 4x + 8y = -2x + 4y = 2x - 4y = -x
This question has to do with the change in the subject of the formula.
So we will proceed thus:
[tex]\begin{gathered} 4x-2y=8 \\ \text{Making y the subject of formula will give:} \\ \end{gathered}[/tex][tex]\begin{gathered} 4x-8=2y \\ \text{Divide both sides by 2} \\ \frac{4x-8}{2}=\frac{2y}{2} \\ 2x-4=y \end{gathered}[/tex]The correct answer, therefore, is the third option:
[tex]y=2x-4[/tex]For each expression, select all equivalent from the list.
(a) 9x-5x+8x
(b) 9(1+7y)
Answer:
a)12x
b)9+63y
goodluck
Hi, I need help differentiating using the product rule, thanks
Differentiate using the product rule:
g. We take out the constant:
[tex]4\frac{dy}{dx}\left(x\left(3x-2\right)^5\right)[/tex]So:
[tex]=4\left(\frac{d}{dx}\left(x\right)\left(3x-2\right)^5+\frac{d}{dx}\left(\left(3x-2\right)^5\right)x\right)[/tex]Now
[tex]\begin{gathered} \frac{d}{dx}\left(x\right)=1 \\ \frac{d}{dx}\left(\left(3x-2\right)^5\right)=5(3x-2)^4\cdot\frac{d}{dx}\left(\left(3x-2\right)^5\right)=5\left(3x-2\right)^4\cdot\:3=15\left(3x-2\right)^4 \end{gathered}[/tex]Substituting the derivatives found:
[tex]=4\left(1\cdot\left(3x-2\right)^5+15\left(3x-2\right)^4x\right)[/tex]Simplify:
[tex]=4\left(\left(3x-2\right)^5+15x\left(3x-2\right)^4\right)[/tex]Answer:
[tex]=4\left(\left(3x-2\right)^5+15x\left(3x-2\right)^4\right)[/tex]PLEASE HURRY IM SO CONFUSED
What is the product of (−4)(23)(−7)?
Answer:
644
Step-by-step explanation:
-4x23=-92
-92x-7=644
i hope this helped :)
Find the area of a square with a diagonal that measures 4 square root of 2
Let's draw the figure to better understand the scenario:
Let,
s = the measure of the sides of the square
For us to be able to determine the area, let's first find out the measure of its side.
We will be using the Pythagorean Theorem:
[tex]\text{ a}^2+b^2=c^2[/tex][tex]\text{ s}^2+\text{ s}^2=(4\sqrt[]{2})^2[/tex][tex]\text{ 2s}^2=32[/tex][tex]\text{ }\frac{\text{2s}^2}{2}=\frac{32}{2}[/tex][tex]\text{ }\sqrt{\text{s}^2}=\sqrt{16}[/tex][tex]\text{ s = 16}[/tex]Let's now determine the area of the square:
[tex]\text{ Area = s}^2[/tex][tex]\text{ = 4}^2[/tex][tex]\text{Area = 16}[/tex]Therefore, the area of the square is 16.
Please help!!!!!!!!!!!
Which answer choice identifies the relevant information in the problem?
Sarah left the house at 12:15 p.m. to go to the store. She spent $42.20 on 2 books for her children and she spent $5.67 on a toys for her dog, Rover. Sarah arrived home at 1:00 p.m. How much did Sarah spend on each book?
Answer:
$18.26
Step-by-step explanation:
The total price is $42.20
We want to know how much 1 of those books cost
We know that $5.67 were for her dog
So we are gonna subtract that from $42.20
$42.20-$5.67=36.53
Now your gonna divide that by 2 because she got 2 books
So 36.53/2=$18.26
1 book=$18.26
how many ways can nine trophies be arranged on a shelf
we know that
There are: 9 ways to put the first trophy.
8 ways to put the second trophy after putting the first one.
7 ways to put the third trophy after putting the second one.
6 ways .............the third one
5 ways --------> the fourth
4 ways------> 5
3 ways -----> 6
2 ways ----> 7
1 ways-----> 8
therefore
n!
where n=9
9!=9*8*7*6*5*4*4*2*1
9!=362,880
the answer is
362,880 waysSimplify (z9z−3)−2.
1 over z raised to the twelfth power
1 over z raised to the sixth power
−z^12
−z^6
Answer:
A. 1 over z raised to the twelfth power
Step-by-step explanation:
Hope this helps! :))
Please tell me if this is incorrect
Answer:
1 over z raised to the twelfth power
Step-by-step explanation:
In the expression 7^4 = 2,401, the value of the____ is 7.A. BaseB. PowerC. exponent
The value of the base is 7 (option A)
Explanation:Given:
[tex]7^4\text{ = 2401}[/tex]To find:
To complefe the sentence by ill ingthe blanks
In powers and exponents:
[tex]For\text{ }a^b:\text{ a = base, b = exponent}[/tex][tex]\begin{gathered} Applying\text{ same principle:} \\ 7^4:\text{ Base = 7, exponent = 4} \end{gathered}[/tex]The value of the base is 7 (option A)
An item on sale costs 40% of the original price if the original price was $25 what is the sale price
Answer: $10
Step-by-step explanation:
original price = 25
40% = 0.4
25 * 0.4= 10
Which of the following expressions is equivalent to 3x(2+5y)
Answer:
[tex]15xy+6x[/tex]
What are the values of X where f(x)=g(x)Round to the nearest hundredth’s place if necessary.select all that apply
Given:
The functions
[tex]\begin{gathered} f(x)=2Cos(x) \\ g(x)=(x+0.5)^2+1 \end{gathered}[/tex]Required:
What are the values of x where f(x)=g(x).
Explanation:
From graph we can see that function equals at x value (-0.934) and (0.412)
Answer:
The x values are (-0.93) and (0.41)
The vertical height in feet of a projectile on a planet in our solar system at a given time t in seconds is represented by the function h(t)=−6t2+24t . Re-write h(t) in the form h(t)=a(t-h)^2+k and determine the maximum height of the projectile. Show all work.
We are given the following function:
[tex]h(t)=-6t^2+24t[/tex]We will take "-6" as a common factor:
[tex]h(t)=-6(t^2-4t)[/tex]Now, we will complete the square in the expression inside the parenthesis by adding and subtracting the following term:
[tex]undefined[/tex]A group of 175 college students who took math last term were interviewed. They were asked whether they passed their math course and whether they live on campus. Their responses are summarized in the following table. Passed math Failed math Live on campus 49 21 Live off campus 28 77 Х x $ ? (a) What percentage of the students passed math? [% (b) What percentage of the students live on campus? % (C) What percentage of the students who live on campus passed math? []% (d) Is there evidence that students who live on campus tend to pass math more often than average? O No, because the percentage found in part (c) is about the same as the percentage found in part (a). O No, because the percentage found in part (c) is about the same as the percentage found in part (b). ○Yes, because the percentage found in part (C) is much greater than the percentage found in part (a).○yes because the percentage found in part C is much greater than the percent is found in Part B
Given the group of 175 college students who took math last term:
(a) You can identify in the table that the total number of students that passed math is:
[tex]49+28=77[/tex]Therefore, knowing the total number of students that were interviewed, you can determine that the percentage of the students who passed math is:
[tex]\frac{77}{175}\cdot100=44\text{ \%}[/tex](b) Based on the data shown in the table, the total number of students who live on campus is:
[tex]49+21=70[/tex]Therefore, you can determine that the percentage of the students who live on campus is:
[tex]\frac{70}{175}\cdot100=40\text{ \%}[/tex](c) You can identify that 49 students live on campus and passed math. Therefore, the percentage of the students who live on campus and passed math is:
[tex]\frac{49}{49+28}\cdot100\approx63.6\text{ \%}[/tex](d) Knowing that 63.6% of the students who live on campus passed math, 40% of the student who live on campus, and 44% of the students interviewed passed math, you can identify that students who live on campus tend to pass math more often than average, because:
[tex]63.6\text{ \%}>40\text{ \%}[/tex]Hence, the answers are:
(a)
[tex]44\text{ \%}[/tex](b)
[tex]40\text{ \%}[/tex](c)
[tex]63.6\text{ \%}[/tex](d) Last option.
Precalc please help Answers:A. 5 sin 60°/sin 70°B. 5/sin 50° sin 70°C. 5/sin 50°D. 5 sin 50°/sin 70°
step 1
Find out the measure of angle P
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
P+Q+R=180 degrees
substitute given values
P+70+60=180
P=180-130
P=50 degrees
step 2
Applying the law of sines
QR/sin P=PR/sin 70
substitute given values
QR/ sin 50=5/sin 70
QR=(5/sin 70)*sin 50
the answer is option DHELP!
For triangle XYZ, m∠X = 38°, m∠Y = (5x − 11)°, and m∠Z = (4x − 45)°. Find m∠Y.
m∠Y = 22°
m∠Y = 43°
m∠Y = 99°
m∠Y = 158°
The value of m∠Y in triangle XYZ is 99°
How to solve an equationAn equation is used to show the relationship between two or more numbers and variables.
In triangle XYZ, the angles are angle x, y and z. Hence:
∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)
Substituting:
38 + (5x -11) + (4x -45) = 180
Collecting like terms:
9x - 18 = 180
9x = 198
x = 22
m∠Y = 5(22) - 11 = 99°
m∠Y is 99°
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Which equation represents a line which is parallel to the line y=8x-4?A x+8y=-16B x-8y=-40C y-8x=-1D 8x+y=3
Two parallel lines has the same slope.
The given line:
[tex]y=8x-4[/tex]Is written in the form y=mx+b where m is the slope.
The slope is 8
To find the parallel line you need to write the given options in the form y=mx+b by solving y, as follow:
[tex]\begin{gathered} A \\ x+8y=-16 \\ 8y=-x-16 \\ y=-\frac{1}{8}x-\frac{16}{8} \\ \\ y=-\frac{1}{8}x-2 \end{gathered}[/tex]Slope is -1/8 (it is not parallel to given line)
_______________
[tex]\begin{gathered} B \\ x-8y=-40 \\ -8y=-x-40 \\ y=\frac{-x}{-8}-\frac{40}{-8} \\ \\ y=\frac{1}{8}x+5 \end{gathered}[/tex]Slope is 1/8 (it is not parallel to given line)
________________
[tex]\begin{gathered} C \\ y-8x=-1 \\ y=8x-1 \end{gathered}[/tex]Slope is 8 (It is parallel to given line)___________[tex]\begin{gathered} D \\ 8x+y=3 \\ y=-8x+3 \end{gathered}[/tex]Slope is -8 (it is not parallel to given line)
Then, as given line and line in option C have the same slope (8) they are parallel linesMary's dog weighs 25 pounds. How many ounces does the dog weigh? Remember, there are 16 ounces in a pound.
Answer:
400
Step-by-step explanation:
4 x 10^, 20^2
Answer:
25 pounds 16 ounces = 6400
Step-by-step explanation:
Clarissa's division test was a 60% the first six weeks and a 72% the second six weeks. find the percent change. also, label it as increase or decrease.
The percentage change of the division test is 12%.
There is a percentage increase.
How to find percentage change?Percentage change is the difference in values and the percent change from the original value to the new value.
In other words, percentage change can be defined as a percentage change in value due to changes in the old number and new number, and the values can either increase or decrease.
Percentage change is all about comparing old to new values.
The division test was 60% in the first six week.
The division test was 72% in the second six week.
Therefore,
percentage change = 72% - 60%
percentage change = 12%
Therefore, there is a percentage increase by 12%.
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The graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the range of the function.
The range of the graph is 0 <= M <= 5.5
How to find the range of the function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the domain and the range?The domain
On the graph of the function, we can see that:
The x values start from 0 and it ends at 7.5
This means that the domain is 0 <= x <= 7.5
The range
On the graph of the function, we can see that:
The x values start from 0 and it ends at 5.5
This means that the range is 0 <= M <= 5.5
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Answer:
0 <= M <= 5.5
Step-by-step explanation: