Answers
Let -4x - 15y = 17 be known as equation 1 and -x + y = -13 as equation 2.
To solve the system of equations, we need to determine the value of the "x" and "y" variables. Let us start by determining the value of the y variable.
Note: Since the second equation looks easier to solve for y (in my opinion), I will determine the value of y in the second equation.
This can be done by isolating y on one side of the equation.
Equation 2: [tex]\bold{-x + y = -13}[/tex]
Add "x" on both sides of the equation:
[tex]\implies -x + y = -13[/tex]
[tex]\implies -x + y + x = -13 + x[/tex]
[tex]\implies y = -13 + x[/tex]
Therefore, the value of y is -13 + x. Let us substitute the value of y, obtained from equation 2, into equation 1 to determine the value of x.
Equation 1: [tex]\bold{-4x - 15y = 17}[/tex]
Substitute the value of y in the equation:
[tex]\implies 4x - 15y = 17[/tex]
[tex]\implies -4x - 15(-13 + x) = 17[/tex]
Simplify the distributive property:
[tex]\implies -4x - 15(-13 + x) = 17[/tex]
[tex]\implies -4x + (195 - 15x) = 17[/tex]
[tex]\implies -4x + 195 - 15x = 17[/tex]
Combine like terms on both sides:
[tex]\implies -4x + 195 - 15x = 17[/tex]
[tex]\implies -19x + 195 = 17[/tex]
Subtract 195 on both sides of the equation:
[tex]\implies -19x + 195 = 17[/tex]
[tex]\implies -19x + 195 - 195 = 17 - 195[/tex]
[tex]\implies -19x = -178[/tex]
Divide -19 on both sides of the equation:
[tex]\implies -19x = -178[/tex]
[tex]\implies \dfrac{-19x}{-19} = \dfrac{-178}{-19}[/tex]
[tex]\implies \bold{x = \dfrac{178}{19} }[/tex]
Now, substitute the value of x in -13 + x to determine the value of y. Once determined, we can put the solution in (x, y) form.
[tex]\implies y = -13 + x[/tex]
[tex]\implies y = -13 + \dfrac{178}{19}[/tex]
[tex]\implies y = \dfrac{-247}{19} + \dfrac{178}{19}[/tex]
[tex]\implies \bold{y = \dfrac{-69}{19} }[/tex]
∴ Solution ⇒ (x, y) ⇒ (178/19, -69/19)
Therefore, the solution to the following system of equations is (178/19, -69/19)
Learn more about system of equations: https://brainly.com/question/13024262
Related Questions
are any of these equivalent to 3/8 ?
2/7
8/3
9/24
5/18
Answers
Answer:
9/24 is
Step-by-step explanation:
Yup
-BaconSoup the scientist LOL
Answer:
9/24
Step-by-step explanation:
[tex]\frac{2}{7}= 0.28571428571\\\\\frac{3}{8}= 0.375\\\\\frac{2}{7}\neq \frac{3}{8}\\\\ \frac{8}{3}= 2.666...\\\\\frac{8}{3} \neq \frac{3}{8}\\\\\frac{9}{24}=\frac{9/3}{24/3} =\boxed{\frac{3}{8}}\\\\ \boxed{\frac{9}{24}=\frac{3}{8}}\\\\\frac{5}{18}= 0.27777...\\\\\frac{5}{18} \neq \frac{3}{8}[/tex]
Hope this helps.
This is Amy's box of candies.
She has already eaten 6 of them.
What fraction of the candies has Amy eaten?
Answers
Answer:
[tex] \frac{6}{9} [/tex]
or
[tex] \frac{2}{3} [/tex]
Step-by-step explanation:
There are nine in total and she has eaten 6, so the fraction would be 6/9.
If you need to simplify it it would be 2/3.
A store orders 22 boxes of light bulbs. Each box has 148 bulbs.
Which is the best estimate of the total number of bulbs the store orders?
plzzz answer.
Answers
Answer:
estimate, 3000. exact answer 3256
Step-by-step explanation:
hope this helps
there are 8 dinner rolls in a package. how many packages will be needed to feed 88 people if each person has 2 dinner rolls
Answers
Answer:
22
Step-by-step explanation:
8 times 10= 80 +8=88. now thats 11 packages. 11 times 2=22
HELLLLLPPPPPPPP MY SISTER HAS LATE HOMEWORKKKKK she need help with number 4. the empty space is the part where She need to show how She got her answer so if someone could help that would mean the world to me and her
Answers
Answer:
13
Step-by-step explanation:
13x4=52 that would be in the check section or whatever but she did really good
Answer:
Your sister did the equation perfectly. That's exactly how I would work it, and the answer is 13.
Find the domain of the vector function. (Enter your answer in interval notation.) r(t) = t − 2 t + 2 i + sin(t)j + ln(36 − t2)k
Answers
Answer:
The domain of the vector function is : ( -6, -2) ∪ ( -2, 6)
Step-by-step explanation:
The given vector function can be correctly expressed as:
[tex]r(t) = \dfrac{t-2}{t+2}i + sin \ tj + In(36-t^2) k[/tex]
The domain of the given function can be determined by finding the domain of each respective component.
To start with [tex]\dfrac{t-2}{t+2}[/tex]
Not defined, t = -2
Thus, the domain of the first component of the vector = [tex]( - \infty , -2) \cup ( 2, \infty )[/tex]
The 2nd component = sin t
No restriction on t
The 3rd component of the function is ㏑(36 - t²)
Let recall that natural is defined for +ve numbers,
i.e.
36 - t² > 0
(6 + t) (6 - t) > 0
Thus, it satisfies the inequality -6 < t < 6
The third domain = (-6,6)
Overall;
The domain of the vector function is : ( -6, -2) ∪ ( -2, 6)
Domain of a function is the set all possible inputs for that function.The domain of the given vector function is,
[tex](-6, -2) \cap (-2,6)[/tex]
What is domain?
Domain of a function is the set all possible inputs for that function.
Given information-
The vector function given in the problem is,
[tex]r(t)=\dfrac{t-1}{t+2} \hat i++sin(t)\hat j+ln(49-t^2)\hat k[/tex]
To find the domain of the above vector function, we need to find the domain of each function of vector quantity.
Lets find the domain of [tex]\hat i[/tex] first which is given by,
[tex]\dfrac{t-2}{t+2}[/tex]
This function is defined at all values except, t equals to -2 as the function is not defined at,
[tex]t=-2[/tex]
Hence the domain of component [tex]\hat i[/tex] is,
[tex](-\infty, -2) \cap (\infty,2)\\[/tex]
Lets find the domain of [tex]\hat j[/tex] first which is given by,
[tex]\sin(t)[/tex]
Two trigonometry function sine and cosine defined for all real number.
This function is defined at all real numbers. Hence the domain of component [tex]\hat j[/tex] is
Lets find the domain of [tex]\hat k[/tex] first which is given by,
[tex]\ln(36-t^2)[/tex]
Set the above argument greater than zero to find where the expression is defined.Thus,
[tex](36-t^2)>0\\(6+t)(6-t)>0[/tex]
Therefore,
The domain of it should be [tex](-6,6)[/tex]
Hence the domain of the given vector function is,
[tex](-6, -2) \cap (-2,6)[/tex]
Learn more about the domain here;
https://brainly.com/question/10197594
Determine the coordinate of the point shown. It’s on a (3,-5) (1,-2) (1.5, -2.5) (-2.5, 1.5)
Answers
Answer:
its a function
slope form:y+5=-1.18·(x-3)
(-2.5,1.5)
Step-by-step explanation:
The ratio of employees who own a red car to employees who own a black car is
1:5. If there are 6 employees who own a red car, how many employees own a
black car? *
Answers
Answer:
There would be 30 black cars.
Since the ratio is 1:5
And we know that there are 6 red cars,
we basically just input it in our ratio
so it would look like 6:x
Now, we just have to plug in for x.
To do that, you have to multiply 6 by 5
To match the ratio.
So that would give us 6:30
And if we divide by 5 we should get our original ratio.
I know this seems confusing haha, but I hope you get it, it's not as hard as it looks !!
Pls I need answer quick, pls
Answers
Answer:
its a hope this helps
Step-by-step explanation:
3. Which is equivalent to the expression below?
4.5m + 8 - 2.3m - 3.5
A.6.7m
B. 6.8m + 4.5
C 2.2m + 11.5
D. 2.2m + 4.5
Answers
Answer:
D. 2.2m + 4.5
Step-by-step explanation:
Solve the system, enter ur answer as an ordered triple.
Answers
Answer:
x = 1, y = -1, z = 3
Step-by-step explanation:
x - 2y + 2z = 9
y + 2z = 5
z = 3
According to the last equation, z is equal to 3 so we can plug that in and our new 2 equations will be:
x - 2y + 6 = 9
y + 6 = 5
We can subtract 6 from both sides of the second equation to end up with:
y = -1
Now plugging this into the first equation, we have:
x + 2 + 6 = 9
x + 8 = 9
Subtract 8 from both sides
x = 1
solve each system by graphing.
Answers
at the zoo,the ratio of monkeys to gorillas is 5:1
Answers
Answer:
thats a statement
Step-by-step explanation:
My house is 20 miles from yours, but on the map it is only 4 mm away.
What is the scale of the map?
A. 1 mm = 5 mi
B. 1 mm = 20 mi
C. 1 mi= 20 mm
D. 20 mm = 4 mi
E. 5 mi = 4 mm
Answers
Answer:
A. 1mm = 5mi
Step-by-step explanation:
20 mi divided by 4 mm would simplify down to 5 mi per 1mm. If there is 4 mm then there is 5mi*4mm which equals out to 4 mm = 20 mi.
A scale of the map is the relationship between the distance on the map to the actual distance. The scale of the map is 1 mm: 5 miles (ml). Thus the option A is the correct option.
To find out the scale of the map, we have to know about scaling of map.
What is the scaling of map?
The scaling of map is the ratio or relationship between the distance of the map to the original distance.
Given information-
The distance of the two houses on the ground is 20 miles.
The distance of the two houses on the map is 4 mm.
Suppose the scale of the map is [tex]s[/tex].
As the 20 miles distance on the ground is same as the 4 mm distance on the map.
Thus the scale of the map can be given as,
[tex]s=\dfrac{4\rm mm}{20\rm miles} \\s=\dfrac{1\rm mm}{5\rm miles}[/tex]
Hence the scale of the map is 1 mm: 5 miles (ml). Thus the option A is the correct option.
Learn more about the scale of map here;
https://brainly.com/question/10283478
The vertices of ΔMNO are M (1, 3), N (4, 9), and O (7, 3). The vertices of ΔPQR are P (3, 0), Q (4, 2), and R (5, 0). Which conclusion is true about the triangles?
The ratio of their corresponding sides is 1:2.
The ratio of their corresponding angles is 1:2.
They are similar by the definition of similarity in terms of a dilation.
They are congruent by the definition of congruence in terms of rigid motions.
Answers
C. They are similar by the definition of similarity in terms of a dilation.
The conclusion about the triangles is (c) they are similar by the definition of similarity in terms of a dilation.
The coordinates are given as:
[tex]M = (1,3)[/tex]
[tex]N = (4,9)[/tex]
[tex]O = (7,3)[/tex]
[tex]P =(3,0)[/tex]
[tex]Q = (4,2)[/tex]
[tex]R = (5,0)[/tex]
Start by calculating the lengths of the triangles using the following distance formula
[tex]d = \sqrt{(x_1-x_2)^2 + (y_1 -y_2)^2}[/tex]
So, we have:
[tex]MN = \sqrt{(1 -4)^2 + (3 - 9)^2}[/tex]
[tex]MN = \sqrt{45}[/tex]
[tex]MO = \sqrt{(1 -7)^2 + (3 - 3)^2}[/tex]
[tex]MO = 6[/tex]
[tex]NO = \sqrt{(4 -7)^2 + (9 - 3)^2}[/tex]
[tex]NO = \sqrt{45}[/tex]
[tex]PQ = \sqrt{(3 -4)^2 + (0 - 2)^2}[/tex]
[tex]PQ = \sqrt{5}[/tex]
[tex]PR = \sqrt{(3 -5)^2 + (0 - 0)^2}[/tex]
[tex]PR = 2[/tex]
[tex]QR = \sqrt{(4 -5)^2 + (2 - 0)^2}[/tex]
[tex]QR = \sqrt{5}[/tex]
So, we have:
[tex]MN = \sqrt{45}[/tex] [tex]PQ = \sqrt{5}[/tex]
[tex]MO = 6[/tex] [tex]PR = 2[/tex]
[tex]NO = \sqrt{45}[/tex] [tex]QR = \sqrt{5}[/tex]
The above means that the triangles are not congruent.
So, we determine if they are similar by dividing the corresponding sides
[tex]k = \frac{MN}{PQ} = \sqrt{\frac{45}{5}} = 3[/tex]
[tex]k = \frac{MO}{PR} = \frac{6}{2} = 3[/tex]
[tex]k = \frac{NO}{QR} = \sqrt{\frac{45}{5}} = 3[/tex]
The scale factor is 3.
Hence, the triangles are similar
Read more about similar triangles at:
https://brainly.com/question/14285697
Need answer quick small information
Answers
Answer:
B
Step-by-step explanation:
Factorise: x*x-4*4
(x+4)(x-4)
so the answer is B.
Hope this helps
Merry Christmas!
I sure about this answer
What are the missing angles?
Answers
2. 34
3. 95
4. 38
5. 47
6. 74
7. 59
I hope this helps!!
Slope, m = 3, y-intercept, b = 5
Answers
Answer:
I can't help if I don't have enough to answer sorry
Step-by-step explanation:
What was the battery’s charging level when the charging began?
Answers
Answer:
40%
Step-by-step explanation:
The line starts on 40%
Answer:
40%
Step-by-step explanation:
th line stars by the 40
Are x and 1/x like terms?
Answers
Answer:
no
Step-by-step explanation:
we'll say x=5
5 does not equal 1/5
I really need help please help me
Answers
Answer:
top right
Step-by-step explanation:
If you imagine yourself building with that model you can see its that one
Which point is a solution to this system of inequalities?
y 6
A) (7,-8)
B) (2,-3)
C) (5,-2)
D) (4,1)
Answers
Answer:
h
Step-by-step explanation:
Answer:
the answer is c
Step-by-step explanation:
A pet store sells dog treats and the prices are represented
in the graph
X = number of treats
y = cost (in dollars)
Select the true statement.
Select one
Each treat costs $0.50
Each treat costs $3
Each treat costs $2
Each treat costs 51
Answers
Answer: 1$
Step-by-step explanation:
What is 4(2 + a) = 24
a=
Answers
Answer:
2/5
Step-by-step explanation:
Rearrange terms:
4(2 + a) = 24a
4(a + 2) = 24a
Distrbute:
4(a + 2) = 24a
4a + 8 = 24a
Subtract 8 from both sides of the equation:
4a + 8 = 24a
4a + 8-8 = 24a-8
Simplify:
4a = 24a - 8
Subtract 24a from both sides of the equation:
4a = 24a - 8
4a - 24a = 24a - 8 - 24a
Combine like terms:
-20a = -8
Divide both sides of the equation by the same term:
-20a = -8
-20a/-20 = -8/-20
Simplify:
Cancel terms that are in both the numerator and denominator
Divide the numbers
a = 2/5
I hope that helps! :D
By 27leejaeyFind the coordinates of the midpoint of a segment with endpoints A(-3,7) and B(8,-2)
Answers
Answer:
the midpoint is (2.5, 2.5)
3, -9, 27, -81.......
Neither
Arithmetic
Geometric
Answers
Answer:
Geometric
Step-by-step explanation:
sorry if I am wrong just let me know please
The pottery store can make 176 coffee mugs in an 8 hour day. How many mugs can they make in one hour
Watch your units!
Answers
Answer:
22 per hour
Step-by-step explanation:
8 divided by 176 lol Hope I did it right tho ;-;
Answer:
they can make 22 in one hour.
Solve the formula for the indicated variable.
B=yv+y, for v
The solution is v=?
Answers
Answer: v = B/y -1
B = yv + y = (v + 1)y
=> B/y = v + 1
⇔ [tex]v=\frac{B}{y}-1[/tex]
Step-by-step explanation:
How to find the radius of a cylinder with only knowing it's height and diagonal thing here
Answers
What is |-8|?
-16
-8
08
16
Answers
Answer:
it's 8
Step-by-step explanation:
lol girl I did this in the first day of school in 6th and I got the same answer , -8 is a negative, your supposed to put it back to a non negative when something is negative change it back to positive it's 8!