Answer:
The solution to the system of equations is [tex]\displaystyle \big(\frac{56}{29}, -\frac{16}{29}\big)[/tex].
Step-by-step explanation:
We are given a system of equations:
[tex]\displaystyle \left \{ {{-3x+4y=-8} \atop {8x-y=16}} \right.[/tex]
We need to solve these by substitution, so we need to solve one equation for a variable and then substitute the value of that variable into the other equation. After doing this and solving for the opposite variable, we need to insert this into the original equation and solve for the initial variable.Therefore, to solve one of the equations, we will solve it to put it in slope-intercept form and solve for y. The easier equation to work with is equation two.[tex]\displaystyle 8x - y = 16\\\\-y = -8x + 16\\\\\frac{-y}{-1}=\frac{-8x+16}{-1}\\\\y = 8x - 16[/tex]
Now, we've solved for y. So, we can substitute this into either equation and solve for x.
[tex]\displaystyle -3x + 4(8x -16)=-8\\\\-3x + 32x - 64 = -8\\\\29x - 64 = -8\\\\29x = 56\\\\\frac{29x}{29}=\frac{56}{29}\\\\x = \frac{56}{29}[/tex]
Now, we substitute our value for x into one of the original equations and solve for y.
[tex]\displaystyle 8\big(\frac{56}{29}\big)-y=16\\\\-y = 16 - 8\big(\frac{56}{29}\big)\\\\-y=\frac{16}{29}\\\\\frac{-y}{-1}=\frac{\frac{16}{29}}{-1}\\\\y = -\frac{16}{29}[/tex]
Therefore, the solution to our system of equations is:
[tex]\displaystyle \big(\frac{56}{29}, -\frac{16}{29}\big)[/tex]Given vectors u = ⟨2, –3⟩ and v = ⟨1, –1⟩, what is the measure of the angle between the vectors?
Answer:
The measure of the angle between the vectors = Ф = 11.30°
Step-by-step explanation:
Given
u = ⟨2, –3⟩v = ⟨1, –1⟩[tex]\mathrm{Computing\:the\:angle\:between\:the\:vectors}:\quad \cos \left(\theta \right)\:=\frac{\vec{a\:}\cdot \vec{b\:}}{\left|\vec{a\:}\right|\cdot \left|\vec{b\:}\right|}[/tex]
Next, find the lengths of the vectors:
[tex]\mathrm{Computing\:the\:Euclidean\:Length\:of\:a\:vector}:\quad \left|\left(x_1\:,\:\:\ldots \:,\:\:x_n\right)\right|=\sqrt{\sum _{i=1}^n\left|x_i\right|^2}[/tex]
u = ⟨2, –3⟩
[tex]\:\:\left|u\right|\:=\sqrt{2^2+\left(-3\right)^2}[/tex]
[tex]=\sqrt{13}[/tex]
u = ⟨2, –3⟩
[tex]|v|=\sqrt{1^2+\left(-1\right)^2}[/tex]
[tex]=\sqrt{2}[/tex]
Finally, the angle is given by:
[tex]\mathrm{Computing\:the\:angle\:between\:the\:vectors}:\quad \cos \left(\theta \right)\:=\frac{\vec{a\:}\cdot \vec{b\:}}{\left|\vec{a\:}\right|\cdot \left|\vec{b\:}\right|}[/tex]
cos (Ф) = 5/√26
Ф = arc cos (cos (Ф)) = arc cos (5 √26) / (26)
Ф = 11.30°
Thus, the measure of the angle between the vectors = Ф = 11.30°
Answer:
The Answer is A. 11.3
Step-by-step explanation:
got it right. Also thats just the letter answer :)
All of the students in the sixth grade either purchased their lunch or brought their lunch from home on Thursday.
65% of students purchased their lunch
63 students brought their lunch from home
How many students are in the sixth grade?
O A 98
B. 106
O C. 180
D. 240
189 is 90% of what number
Answer:
I believe the answer is 210.
Step-by-step explanation:
Answer:
Assume the unknown value is 'Y'
189 = 90% x Y
189 =
90
100
x Y
Multiplying both sides by 100 and dividing both sides of the equation by 90 we will arrive at:
Y = 3 x
100
90
Y = 210%
Answer: 189 is 90 percent of 2
Step-by-step explanation:
theres a another way
189x100÷90 which your answer will give 210
YO I NEED HELP WITH THIS ASAP!!!!! ITS WORTH A LOT OF POINTS!!!!! PLS LOOKS AT THE ATTACHMENT BELOW!
Answer:
1. (0,5)
2. 3 / -1
3. F(x) = -3x + 5
A plane is 20,000 ft. In the air and descending at a rate of 25 ft. Per minute. Write an equation to represent this situation where y is the height of the plane after x minutes.
Answer:
y=20000-25xStep-by-step explanation:
Step one:
given data
initial height of plane= 20000ft
rate of descending= 25ft per minute
let x be the number of minutes it took the plane to descend
and let y be the height after x minutes
Step two:
Required
the mathematical expression for the height
the expression for the situation mathematically is
y=20000-25x
Question 5
On problem #18, which variable will be the easiest to isolate in order to solve the system using
substitution?
A: x, in the top equation
B: y. in the top equation
C: x, in the bottom equation
D: y, in the bottom equation
Can someone please please please help me!
PLEASE HELP ME ASAP IM REALLY CONFUSED!!!
Answer:
AB and DE's length are congruent, meaning they are the same.
Step-by-step explanation:
If we made a line between C and F, and flip it on the other side. We would see it is congruent.
Can someone please tell me what range and domain is. and how to tell what an independent and dependent variable are please
Answer: The dependent variable is the Y axis of a graph, or the side of the graph that is vertical. The independent variable is the X axis of a graph, or the side of the graph that is horizontal. Domain is the input of a mathematical function, and the range is the output!
Hope this helps :)
range is the difference between the largest and smaller; “ To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.”
domain is the set of all possible x-values which will make the function able to work and will output real y-values. You must remember that in a function x can NEVER have more than one output (y)
“A independent variable is a variable (often denoted by x ) whose variation does not depend on that of another”. The independent variable is the variable the experimenter changes or controls and is assumed to have a direct effect on the dependent variable
“A dependent variable is a variable (often denoted by y ) whose value depends on that of another.” The dependent variable is the variable being tested and measured in an experiment, and is 'dependent' on the independent variable.
I hope that was understandable
When solving an absolute value inequality, the fact of whether it is a "greater than/greater than or equal to" as opposed to "less than/less than or equal to" will change the way you solve the problem, depending on which sign it is.
True
False
Answer:
true
Step-by-step explanation:
taking the test
When solving an absolute value inequality, the fact of whether it is a "greater than/greater than or equal to" as opposed to "less than/less than or equal to" will change the way to solve. It is True.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true.
These values are called solution to that equation or inequality.
A Set of such values is called solution set to the considered equation or inequality.
When solving an absolute value inequality, the fact of whether it is a "greater than/greater than or equal to" as opposed to "less than/less than or equal to" will change the way you solve the problem, depending on which sign it is.
The given statement for inequality is True.
Learn more about inequalities here:
https://brainly.com/question/27425770
#SPJ2
Write the slope-intercept form of the following equation. Y +
2 = 3/2(x-4)
Answer:
y=3/2x-8
Step-by-step explanation:
Step 1: Begin by distributing the 3/2 to the parentheses. This would result with 3/2x-6.
Step 2: Subtract both sides by 2 to isolate the variable, y. This would result with y=3/2x-8.
Question 3 (10 points)
(02.06 MC)
In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)
AB and CD are parallel lines, and PQ and PR are transversals which intersect AB at P and CD at Q and R. Angle APQ is labeled as 65 degrees, angle QPR is equal to x, angle PRD is equal to 120 degrees.
Answer:
X = 53
X= 115 - 62
Step-by-step explanation:
Part A: 62 + X = 115
X= 115 - 62
X = 53
Part B:
APQ + QPR = PRD
Dont copy off of me because im not for sure this is the right awnser
The measure of angle x is 55.
And to get 55 you first need to find angle BPR.
So, what you would do is 180 - 120 and that equals 60.
So, this means that angle BPR is 60 degrees.
Ok, so now to find the angle of x.
You first need to do 65 + 60 + x =180.
Since we don't know the value of x, we do 65 + 60 and that gives us 125.
So, 180 - 125 = 55.
So, X = 55.
what are the integers of 58
Answer:
{1,2,29,58}
Step-by-step explanation:
As the only factors of 58 are {1,2,29,58} , there are no two consecutive integers whose product is 58
Answer:
1,2,29.58
Step-by-step explanation:
:)
An object launched straight puwar from the ground level wiht an initional velocity of 32 feet per second.The formula H=32T-16T^2 gives it heigtht,h,in feet after t second. At what time does the object hit the ground?
Answer:
2 secs after
Step-by-step explanation:
Given the height of the object modeled by the eqaution;
H(t) = 32T - 16T² where;
T is the time in seconds
The object hits the ground when h(t)= 0
Substitute H = 0 into the equation and get t as shown;
0 = 32T - 16T²
0-32T = -16T²
-32T = -16T²
32T = 16T²
32 = 16T
T = 32/16
T = 2secs
Hence the object hits the ground after 2 secs
What is percent decrease 2.26 to 0.98
Which graph represents the equation y = 3/4 x - 3
Answer:
Step-by-step explanation: you forgot to attach the file but it should look like this i think
Answer:
slope is 3/4
y-intercept is (0,-3) Thats where you put your first point on the y-inter on -3
x y
0 -3
4 0
Put your second point at 4 (on the x)
then your slope is rise /run 3/4
then you should get your line on your graph
Step-by-step explanation:
determine the type of triangle
function: f(x) = 2x + 1
It x = 0, what is the y output?
Answer:
1
Step-by-step explanation:
i think i helped successfully
Answer:
y= 1
Step-by-step explanation:
In the equation, the 1 means that it's the y-intercept
And whenever x is 0, then the y value is the y-intercept
So since x=0, then y=1
I’ll mark you brainlist
Answer:
3
Step-by-step explanation:
Y OVER X is the answer .
PLS ANSWER I HAVE TO FINISH MY TEST BY THE END OF CLASS WHICH IS IN 5 MIN!!! I WILL GIVE BRAINLIST!!!!!!
Geno invested $2,000 into an account that earns 8.5% interest compounded annually. How much interest will Geno earn after 3 years?
A. $554.58
B. $513
C. $2,513
D. $2,554.58
Answer:
8.5% interest would yield $170 annually for a total interest earnings of $513
Step-by-step explanation:
I need these questions answered ASAP can you help me with 12,13,14 pls
96 =-8(p-5)
help pls
Answer:
p = −7
Step-by-step explanation:
96=−8(p−5)
96=(−8)(p)+(−8)(−5)(Distribute)
96=−8p+40
Step 2: Flip the equation.
−8p+40=96
Step 3: Subtract 40 from both sides.
−8p+40−40=96−40
−8p=56
Step 4: Divide both sides by -8.
−8p /−8 = 56 /−8
4 ten and 17 hundredth in decimals UNSERIOUS ANSWERS REPORTED
Answer:
40.17
Step-by-step explanation:
4 ten: 4 × 10 = 40
17 hundredth: 17 × 0.01 = 0.17
4 ten and 17 hundredth in decimals: 40 + 0.17 = 40.17
To get to the top of the mountain, Charlie drove 6 miles east and 8 miles south. Then he hiked the rest of the way to the top which was about 2 miles high. Assuming Charlie started at (0, 0, 0), what is the total distance he traveled to the top of the mountain?
a.) 8.7 miles
b.) 12 miles
c.) 10.2 miles
d.) 16 miles
Answer:
actually it's 10.2 miles
Step-by-step explanation:
he drove six miles at first and than 8 miles south, afterwards he hiked the rest of the way to the top.
Help me I don't know how to find the percent of discount to the nearest percent
Find the percent of discount to the nearest percent.
skateboard: regular price, $24
sale price, $15.50
help. PLEASE.
Answer:8.5
Step-by-step explanation:
Answer:
step one
find the difference between marked price and the selling price, which is 24-15.50=8.5
step two apply the formula which is, difference divided by marked or original price and then multiple by 100
eg (8.5÷24) × 100= 35.4
so now round off to the nearest percent that's 35%
-28=r/7-26 send help lauvs
Answer:
r is equal to negative 14.
Step-by-step explanation:
i need help passing geometry
One interior angle of a regular octagon is
Answer:
135 degreesTo find the measure of the angles, we know that the sum of all the angles is 1080 degrees (from above)... And there are eight angles... So, the measure of the interior angle of a regular octagon is 135 degrees.The General Rule
Shape Sides Each Angle
Octagon 8 135°
Nonagon 9 140°
... ... ...
Any Polygon n (n−2) × 180° / n
Which of the following does not have the same value as 15 ^6
Answer:
B
Step-by-step explanation:
(15^3)^3 because the exponent outside of the parentheses multiplies both the 15 and the exponent inside the parentheses, so it's not 15^6, its 15^2 ^6
Somebody plz help me I’m failing
What is 80% as a fraction in reduced form? 4 118 * 10 O
Answer:
4/5 make me brainliest
Step-by-step explanation:
Answer:
B. 4/5
Step-by-step explanation:
We know that 80% as a fraction is 8/10, but that is not simplified. Both of the numbers have a common factor. We need to divide both by the GCF (Greatest Common Factor). The GCF of both numbers is 2. 8/2 is 4, and 10/2 is 5. That means the answer is 4/5. I hope this helps!