bearing in mind that standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-2}{2-(-3)}\implies \cfrac{-1}{2+3}\implies -\cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=-\cfrac{1}{5}[x-(-3)]\implies y-2=-\cfrac{1}{5}(x+3)[/tex]
[tex]\bf y-2=-\cfrac{1}{5}x-\cfrac{3}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5\left(y-2 \right)=5\left( -\cfrac{1}{5}x-\cfrac{3}{5} \right)}\implies 5y-10=-x-3 \\\\\\ 5y=-x+7\implies x+5y=7[/tex]
Find the value of logarithm log(4)1
Answer:
0.
Step-by-step explanation:
If log(a) x = b
Then by the definition of a logarithm x = a^b.
So let log(4) 1 = y
then 1 = 4^y
but 4^0 = 1
so y = log(4) 1 = 0.
The GCF of 6 and 8 is__
Answer:
2
Step-by-step explanation:
The reason 2 is the Greatest Common Factor of 6 and 8 is because 2 is the only number (other than 1) that you can divide evenly by both numbers without making a fraction. 6/2= 3 and 8/2= 4.
Answer:
Step-by-step explanation:
In general, factor the numbers given into their primes.
6: 2*3
8: 2 * 2 * 2
Take the most you can from the two numbers primes. In this case it is 2.
A slightly more interesting problem is the GCF of 12 and 18
12: 2 * 2 * 3
18: 2 * 3 * 3
Here the two numbers that are common to both factored numbers is 2 and 3
GCF = 2*3
GCF = 6
Factor completely. If a polynomial is prime, state this.
2t^2-19-6t
ANSWER
Prime
EXPLANATION
The given quadratic expression is
[tex] {2t}^{2} - 19 - 6t[/tex]
We rewrite in standard form to obtain
[tex]{2t}^{2} - 6t - 19[/tex]
Comparing to the standard quadratic function in t,
[tex]a {t}^{2} + bt + c[/tex]
We have
[tex]a = 2[/tex]
[tex]b = - 6[/tex]
[tex]c = - 19[/tex]
We find that the product
[tex]ac = 2 \times - 19 = - 38[/tex]
There are no two factors of -38 that sums up to -6.
This means that, the given polynomial does not have rational factors.
Therefore the polynomial is prime.
Triangle ABC has vertices at A(-2, 3), B(-3,-6), and C(2,-
1). Is triangle ABC a right triangle? If so, which angle is the
right angle?
w Ano
A(-2,3)
O No, the triangle has no right angles.
O Yes, the right angle is angle A.
O Yes, the right angle is angle B.
O Yes, the right angle is angle C.
6
5
4 -3 3-2 -1,5
2
6
x
3 4 5
C (2,-1)
B(-3,-6)
Answer:
Yes, the right angle is angle B
Step-by-step explanation:
we have
[tex]A(-2, 3), B(-3,-6),C(2,-1)[/tex]
Plot the vertices
see the attached figure
we know that
If triangle ABC is a right triangle
then
Applying the Pythagoras Theorem
[tex]AB^{2} =AC^{2}+BC^{2}[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AB
[tex]A(-2, 3), B(-3,-6)[/tex]
substitute in the formula
[tex]d=\sqrt{(-6-3)^{2}+(-3+2)^{2}}[/tex]
[tex]d=\sqrt{(-9)^{2}+(-1)^{2}}[/tex]
[tex]AB=\sqrt{82}\ units[/tex]
Find the distance BC
[tex]B(-3,-6),C(2,-1)[/tex]
substitute in the formula
[tex]d=\sqrt{(-1+6)^{2}+(2+3)^{2}}[/tex]
[tex]d=\sqrt{(5)^{2}+(5)^{2}}[/tex]
[tex]BC=\sqrt{50}\ units[/tex]
Find the distance AC
[tex]A(-2, 3),C(2,-1)[/tex]
substitute in the formula
[tex]d=\sqrt{(-1-3)^{2}+(2+2)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(4)^{2}}[/tex]
[tex]AC=\sqrt{32}\ units[/tex]
Verify the Pythagoras theorem
[tex](\sqrt{82})^{2} =(\sqrt{32})^{2}+(\sqrt{50})^{2}[/tex]
[tex]82=82[/tex] ---> is true
therefore
Is a right triangle and the right angle is B
Which relation is a function?
Answer: c
Step-by-step explanation:
Taylor rides her bicycle for 3 hours and is 32 miles from her house. After riding for 6 hours, she is 62 miles away.
What is Taylor's average rate during her trip?
_____ miles per hour
Step-by-step explanation:
10.44 is correct as we have to add both dis and divide by both hrs
In this case, Taylor's average rate is 10 miles per hour.
To calculate Taylor's average rate during her trip, we can use the formula for average speed:
Calculate the total distance traveled: 62 miles - 32 miles = 30 miles.
Calculate the total time taken: 6 hours - 3 hours = 3 hours.
Divide the total distance by the total time to find the average speed: 30 miles / 3 hours = 10 miles per hour.
What is the equation of the line that passes through (7, 4) and (4, -2)?
Answer:
y=2x-10
Step-by-step explanation:
First step: Let's compute the slope. You can directly use the formula for slope given two points here but I just like to like them up and subtract vertically. Make sure you put 2nd difference on top of 1st difference (yes, like a fraction).
(7 , 4)
-(4 , -2)
=======
3 6
So the slope is 6/3 =2.
So we know our line is in the form y=2x+b.
We have to find the y-intercept now. To find b we will use a point that we know is on the line (you know two-just choose one of them) . I will plug in (4,-2) giving me this equation -2=2(4)+b
Solving: -2=8+b
So b=-10
The answer is y=2x-10
a solution consisting of 52 mg of dopamine in 26 mL of solution at a rate of 10 mL/hr what is the flow rate in mg of dopamine per hour
Answer:
20 mg / hour
Step-by-step explanation:
The first step is to find the mg/mL of dopamine.
If there are 52 mg / 26 mL, then there are 2 mg / 1 mL (just reduce the fraction).
If we are losing 10 mL / 1 hour, and there are 2 mg / mL, then the flow rate of dopamine mg / hour is 20.
You can also do this using dimensional analysis.
[tex]\frac{52 mg}{26 mL} (\frac{10 mL}{1 hour})[/tex]
Just cross out the units that cancel in the numerator and denominator (mL in this case), and you're left with mg / hour. Then multiply the numerators and divide by the denominators. You get the same answer.
The first step is to find the mg/mL of dopamine.
If there are 52 mg / 26 mL, then there are 2 mg / 1 mL (just reduce the fraction).
If we are losing 10 mL / 1 hour, and there are 2 mg / mL, then the flow rate of dopamine mg / hour is 20.
You can also do this using dimensional analysis.
[tex]\frac{52 mg}{26 mL} (\frac{10 mL}{1 hour})[/tex]
Just cross out the units that cancel in the numerator and denominator (mL in this case), and you're left with mg / hour. Then multiply the numerators and divide by the denominators. You get the same answer.
What is the domain of the function shown in the table?
X y
-2 0
-1 1
0 2 1 3
Answer:
{-2,-1,0}
Step-by-step explanation:
The domain of a function is defined as the set of x values for which the function is real and defined. The x values represent independent or predictor variable.
The domain of the function is thus;
{-2,-1,0}
These are basically the x values of the function
If X/7=Y/5 then what does 5X equal
Answer:
7y
Step-by-step explanation:
By cross multiplication
[tex] \frac{x}{7} = \frac{y}{5} \\ 5x = 7y[/tex]
Answer:
[tex]5x=7y[/tex]
Step-by-step explanation:
We have the following relationship
[tex]\frac{x}{7}=\frac{y}{5}[/tex]
Based on the relationship between the variables X and Y that we know, we must find out what the expression "5x" is in terms of the variable y.
Then we solve the equation for x
[tex]x=\frac{7y}{5}[/tex]
Now multiply by 5 both sides of equality
[tex]5x=\frac{5*7y}{5}[/tex]
[tex]5x=7y[/tex]
Finally we have that 5x equals 7y
What is the measure of angle 7?
Answer: 95°
Step-by-step explanation: We are given information for Angles 1 and 4, which happen to be vertical angles, meaning they are congruent. Because of this, we can say 3x+10=4x-15, therefore x=25. Angles 1,2,3 and 4 must add up to 360°, and since we know angles 1 and 4 are 85° (3*25 + 10 = 85), we can find angles 2 and 3. 360° - 85° - 85° = Angle 2 + Angle 3. Angle 2 + Angle 3 = 190, and because Angles 2 and 3 are vertical angles and therefore congruent, we can divide 190 by 2 and get that Angles 2 and 3 equal 95°. Because lines b and c are parallel, any corresponding angles created by a transversal are congruent. This basically means Angles 3 and 7 must be congruent, therefore Angle 7 = 95°
Congruent - same meaning as equal
Vertical Angles - each of the pairs of opposite angles made by two intersecting lines.
White shapes and black shapes are used in a game. Some of the shapes are circles. All the other sahpes are squares.
The ratio of the number of white shapes to the number of black shapes is 5:11
The ratio of the number of white circles to the number of white squares is 3:7
The ratio of the number of black circles to the number of black squares is 3:8
Work out what fraction of all the shapes are circles.
Answer:
9/32
Step-by-step explanation:
BC = black circle
BS = black square
WC = white circle
WS = white square
Given:
(WC + WS) / (BC + BS) = 5 / 11
WC / WS = 3 / 7
BC / BS = 3 / 8
Find: (BC + WC) / (BC + BS + WC + WS)
Solve for WC and BC in the last two equations, then substitute into the first:
WC = 3/7 WS
BC = 3/8 BS
WC + WS = 5/11 (BC + BS)
3/7 WS + WS = 5/11 (3/8 BS + BS)
10/7 WS = 5/8 BS
WS = 7/16 BS
Therefore:
WC = 3/7 WS
WC = 3/16 BS
Substitute:
(BC + WC) / (BC + BS + WC + WS)
(3/8 BS + 3/16 BS) / (3/8 BS + BS + 3/16 BS + 7/16 BS)
(9/16 BS) / (2 BS)
9/32
Credit card companies use negative balances to represent when the credit card company owes the customer money and positive balances to represent when the customer owes the credit card company money.
Mya has a balance of 0 dollars with her credit card company.
What does a balance of 0 dollars represent?
Answer:
she owes nothing and the credit card company owes her nothing.
Answer:
It represents that the bank owes her nothing and she doesn't owe the bank anything. So it is neither postive or negative
Step-by-step explanation:
Use the rule y=-x+7to fill in the blank (1,y) is on the graph,then y=
Answer:
y=6
Step-by-step explanation:
y = -x+7
We have the point (1,y)
That means x=1 and we want to find y
Let x=1
y = -1+7
y = 6
The point is (1,6) where x=1 and y =6
Choose two angles that are each separately alternate exterior angles with 412.
41 and 210
112
41 and 26
11
25 and 26
42 and 45
43 and 2
Answer:
∠2 and ∠5
Step-by-step explanation:
we know that
Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal
In this problem
∠12 and ∠2 are alternate exterior angles
∠12 and ∠5 are alternate exterior angles
therefore
∠2 and ∠5 are each separately alternate exterior angles with ∠12
What is the equation in slope intercept form of the perpendicular bisector of the given line segment?
Answer:
y = -4x - 6
Step-by-step explanation:
The equation of a line in point-slope form.
[tex] y - y_1 = m(x - x_1) [/tex]
is the equation of the line containing point (x1, y1) and having slope, m.
The given point of the perpendicular bisector is (-1, -2), so in this case, x1 = -1, and y1 = -2.
We need the slope of the perpendicular bisector. First we find the slope of the segment. We start at point (-5, -3). We go up 1 unit and 4 units to the right, and we are at another point on the segment. Since slope = rise/run, the slope of the segment is 1/4. The slopes of perpendicular lines are negative reciprocals, so the slope of the perpendicular bisector is the negative reciprocal of 1/4, so for the perpendicular bisector, m = -4.
Now we use the equation above and our values.
[tex] y - y_1 = m(x - x_1) [/tex]
[tex] y - (-2) = -4(x - (-1)) [/tex]
[tex] y + 2 = -4(x + 1) [/tex]
[tex] y + 2 = -4x - 4 [/tex]
[tex] y = -4x - 6 [/tex]
Answer:
Step-by-step explanation:
y = -4x - 6
Given this equation in slope-intercept form…
y = 2x + 5
Identify or solve for the following:
Slope
y-intercept
x-intercept
Independent variable
Dependent variable
Domain
Range
Answer:
Slope = 5
y-intercept = (0, 5)
x-intercept = (-2.5, 0)
Independent variable = x
Dependent variable = y
Domain = Any real #
Range = I believe it's any real #
Step-by-step explanation:
The slope of the equation is 2.
The y-intercept is 5.
The x-intercept is -5/2.
The independent variable is x.
The dependent variable is y.
The domain of the equation is any real number.
The range of the equation is any real number.
What is the slope-intercept form?The graph of the linear equation y = mx + c is a line with m as slope, and m and c as the y-intercept.
The equation in slope-intercept form is;
y = 2x + 5
1. The slope of the equation is;
y = mx + c
y = 2x + 5
On comparing m = 2
The slope of the equation is 2.
2. The y-intercept is;
y = mx + c
y = 2x + 5
On comparing c = 5
The y-intercept is 5.
3. The x-intercept is;
y = 0
y = 2x + 5
0 = 2x +5
2x = -5
x = -5/2
The x-intercept is -5/2.
4. The independent variable is x.
5. The dependent variable is y.
6. The domain of the equation is any real number.
7. The range of the equation is any real number.
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the perimeter of a rectangle is 11 inches. the width is 2 inches shorter than the length. find the length of the rectangle.
The perimeter is 11 inches.
One side is 2 inches shorter, so two sides would be 4 inches shorter total.
Subtract 4 from 11 to get 7 inches.
Divide 7 by 4 ( the number of sides):
7 / 4 = 1.75
The shorter side is 1.75 inches.
Now add 2 inches to that for the longer side:
1.75 + 2 = 3.75 inches.
Check: 3.75 + 3.75 + 1.75 + 1.75 = 11
The longer side is 3.75 inches.
What four numbers can equal 15?? Please help!!
Answer:
1,3,5,15
Step-by-step explanation:
these are the factors of 15
Answer:
Step-by-step explanation:
I must assume that you meant, "the sum of which four numbers equals 15?"
15 = 6 + 9
= 3 + 3 + 9
= 3 + 3 + 3 + 6
All of these sets (on the right side) add up to 15. There are four numbers in the last set.
area of shaded segment
Answer:
N/A
Step-by-step explanation:
Which area of shaded segment?
Answer:
Area Of Shaded Segment =
In Pictures
Help me on this one
Answer:
[tex]\large\boxed{3\div\dfrac{1}{5}}[/tex]
Step-by-step explanation:
Each 1 was divided into five equal parts. Each of these parts is 1/5. We calculate how many times 1/5 is in 3.
Four Representations: Equations, Tables, Words,
WARM-UP and Graphs
Select the words that best describe the given
equation Y = X-1
DONE
w the following questions, look at different ways to
represent the relation given by the
equation y = x2 - 1.
Which graph represents the relationship?
The table below shows some values for the given
equation. Find the values of a and b.
a =
Nyt
Intro
Equations are used to represent the relationships between variables. In [tex]y=x^2 -1[/tex], the variables are x & y and the following observations are true for the given equation:
The words that describe [tex]y=x^2 -1[/tex] are: y is 1 less than the square of xThe values of a and b are 3 and 0, respectively.Given that:
[tex]y=x^2 -1[/tex]
[tex]x^2 \to[/tex] the square of x
So, means that: the y is 1 less than the square of x
From the attached table, we have:
[tex]x = -2; y = a[/tex]
This means that:
[tex]a = (-2)^2 - 1[/tex]
[tex]a = 4 - 1[/tex]
[tex]a =3[/tex]
Also, we have:
[tex]x = b; y = -1[/tex]
This means that:
[tex]-1 = b^2 - 1[/tex]
Collect like terms
[tex]b^2 =1-1[/tex]
[tex]b^2 =0[/tex]
Take square roots
[tex]b = 0[/tex]
Hence, the values of a and b are 3 and 0, respectively.
The graph options are not made available. So, I will plot the graph of [tex]y=x^2 -1[/tex].
See attachment for graph of [tex]y=x^2 -1[/tex]
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Answer: In short for ed2020 :
1. 3rd answer
Graph: A
Table: A=3 B=0
one number is 7 more than twice another number, the sum of the numbers is 22. what is one of the numbers?
Answer:
One of the numbers is 5
The other number is 17
Step-by-step explanation:
You could do this just by guessing numbers. But I think you are intended to do it with algebra.
x + y = 22
y = 2*x + 7 Substitute the y value in this equation into the first equation
x + 2x + 7 = 22 Combine the xs on the left.
3x + 7 = 22 Subtract 7 from both sides.
3x+7-7=22- 7 Combine
3x = 15 Divide by 3
3x/3 = 15/3 Combine
x = 5
x + y = 22 Substitute 5 for x
5 + y = 22 Subtract 5 from both sides.
5-5+y = 22-5
y = 17
Answer:
17 or 5
Step-by-step explanation:
I took the test
What is the perimeter of the square in terms of x? The length of each side is 2x-1in.
Answer:
Perimeter of the square = 8x - 4 in
Step-by-step explanation:
Perimeter of the square = 4 * side
= 4 * (2x - 1)
= 8x - 4 in
Are the equations |x-3|=7 and |x|-3=7
Answer:
1. x=4 or x=10
2. x=-10 or x=10
No equivalent
Step-by-step explanation:
1. |x-3|=7 and x-3=7
Absoulte rules.
x-3=-7 and x-3=7
Add 3 both sides.
x-3+3=-7+3
Simplify.
-7+3=-4
x=-4
x-3=7
Add by 3 both sides.
x-3+3=7+3=10
x=10
X=-4, and X=10 is the correct answer.
________________________________
2. |x|-3=7
Add by 3 both sides.
|x|-3+3=7+3
Simplify.
7+3=10
X=10
X=-10 and X=10 is the correct answer.
______________________________
The two equations |x-3|=7 and |x|-3=7, are solved differently. For |x-3|=7, the possible solutions are x=10 and x=-4. For |x|-3=7, the possible solutions are x=10 and x=-10.
Explanation:The two equations you're looking at are: |x-3|=7 and |x|-3=7. They look very similar but they're solved differently because absolute value symbols affect all values inside them together.
For the first equation, |x-3|=7, we solve this by considering the two situations, x-3 = 7 and x-3 = -7. Solve each of these two equations separately, so you get x = 10 and x = -4.
For the second equation, |x|-3=7, firstly, we need to eliminate '-3' from the right-hand side by adding 3 to both sides, leading to |x| = 10. This is then broken down into the two possible situations as before: x = 10 and x = -10.
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If f(x)=9x-8, which of the following is the inverse of f(x) *Apex*
f(x) and y are two different ways of denoting the same thing. Thus...
f(x) = 9x - 8 is the same as y = 9x - 8
Inverse: the inverse of a function is the resulting equation when x and y switch places and the equation is solved for x
SolveSwitch the places of x and y in the given equation:
y = 9x - 8 ---> x = 9y - 8
Solve the new equation for y (isolate y on the left side of the equation)
x = 9y - 8
x + 8 = 9y - 8 + 8
x + 8 = 9y
(x + 8) / 9 = 9y / 9
(x + 8)/9 = y
y = (x + 8) / 9
y = [tex]\frac{x+8}{9}[/tex]
Now you have the inverse of f(x) = 9x - 8:
A) [tex]f^{-1}[/tex] =[tex]\frac{x + 8}{9}[/tex]
Key Termsinverse
Answer:
A. [tex]f^{-1}(x)=\frac{x+8}{9}[/tex]
Step-by-step explanation:
We have been given a function [tex]f(x)=9x-8[/tex]. We are asked to find the inverse function for our given function.
First of all, we will rewrite [tex]f(x)[/tex] as [tex]y[/tex] as:
[tex]y=9x-8[/tex]
To find the inverse function, we will interchange x and y variables and then solve for y.
[tex]x=9y-8[/tex]
Now, we will add 8 on both sides of our given equation.
[tex]x+8=9y-8+8[/tex]
[tex]x+8=9y[/tex]
Switch sides:
[tex]9y=x+8[/tex]
Now, we will divide both sides of our equation by 9.
[tex]\frac{9y}{9}=\frac{x+8}{9}[/tex]
[tex]y=\frac{x+8}{9}[/tex]
Now, we will replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex] as:
[tex]f^{-1}(x)=\frac{x+8}{9}[/tex]
Therefore, the inverse function for our given function would be [tex]f^{-1}(x)=\frac{x+8}{9}[/tex] and option A is the correct choice.
sinx = 1/2, cosy = sqrt2/2, and angle x and angle y are both in the first quadrant.
tan(x+y)=
A. -3.73
B. 1.53
C. 3.00
D. 3.73
Answer:
Option D. 3.73
Step-by-step explanation:
we know that
[tex]tan(x+y)=\frac{tan(x)+tan(y)}{1-tan(x)tan(y)}[/tex]
and
[tex]sin^{2}(\alpha)+cos^{2}(\alpha)=1[/tex]
step 1
Find cos(X)
we have
[tex]sin(x)=\frac{1}{2}[/tex]
we know that
[tex]sin^{2}(x)+cos^{2}(x)=1[/tex]
substitute
[tex](\frac{1}{2})^{2}+cos^{2}(x)=1[/tex]
[tex]cos^{2}(x)=1-\frac{1}{4}[/tex]
[tex]cos^{2}(x)=\frac{3}{4}[/tex]
[tex]cos(x)=\frac{\sqrt{3}}{2}[/tex]
step 2
Find tan(x)
[tex]tan(x)=sin(x)/cos(x)[/tex]
substitute
[tex]tan(x)=1/\sqrt{3}[/tex]
step 3
Find sin(y)
we have
[tex]cos(y)=\frac{\sqrt{2}}{2}[/tex]
we know that
[tex]sin^{2}(y)+cos^{2}(y)=1[/tex]
substitute
[tex]sin^{2}(y)+(\frac{\sqrt{2}}{2})^{2}=1[/tex]
[tex]sin^{2}(y)=1-\frac{2}{4}[/tex]
[tex]sin^{2}(y)=\frac{2}{4}[/tex]
[tex]sin(y)=\frac{\sqrt{2}}{2}[/tex]
step 4
Find tan(y)
[tex]tan(y)=sin(y)/cos(y)[/tex]
substitute
[tex]tan(y)=1[/tex]
step 5
Find tan(x+y)
[tex]tan(x+y)=\frac{tan(x)+tan(y)}{1-tan(x)tan(y)}[/tex]
substitute
[tex]tan(x+y)=[1/\sqrt{3}+1}]/[{1-1/\sqrt{3}}]=3.73[/tex]
Answer:
D. 3.73
Step-by-step explanation:
1/3x^2+2 what does the graph look like
Answer:
The answer in the procedure
Step-by-step explanation:
we have
[tex]\frac{1}{3}x^{2} +2[/tex]
This is a vertical parabola open upward with the the vertex at (0,2)
The vertex is a minimum
The y-intercept is the point (0,2) (value of y when the value of x is equal to zero)
The graph does not have x-intercepts, therefore the solutions of the quadratic equation are complex number
using a graphing tool
see the attached figure
What is the solution to the system of equations? 3x + 10y = -47 5x- 7y = 40
Please and thank u
Answer:
x=1, y=-5
Step-by-step explanation:
Given equations are:
[tex]3x+10y=-47\ Eqn\ 1\\and\\5x-7y=40\ Eqn\ 2[/tex]
In order to solve the equation
Multiplying Eqn 1 by 5 and eqn 2 by 3 and subtracting them
So,
Eqn 1 becomes
15x+50y=-235
Eqn 2 becomes
15x-21y=120
Subtracting 2 from a
15x+50y - (15x-21y) = -235-120
15x+50y-15x + 21y = -355
71y = -355
y = -355/71
y =-5
Putting y= -5 in eqn 1
3x+10(-5) = -47
3x -50 = -47
3x = -47+50
3x = 3
x = 3/3
x = 1
Hence the solution is:
x=1, y=-5
Answer: x=1; y=-5
Step-by-step explanation: To solve this system we can use differente methods, in this case we are going to use substitution:
first equation: 3x+10y=-47
second equation: 5x-7y=40
we are going to isolate x from the first equation:
3x=-47-10y
[tex]x=\frac{-47-10y}{3}[/tex]
now we replace it in the second equation:
[tex]5*\frac{-47-10y}{3}-7y=40[/tex]
and now we solve for y:
[tex]\frac{-235-50y}{3} -7y=40[/tex]
[tex]\frac{-235-50y-21y}{3}=40[/tex]
[tex]-235-71y=40*3[/tex]
[tex]-235-71y=120[/tex]
[tex]-71y=120+235[/tex]
[tex]y=-355/71[/tex]
y=-5
now we replace the value of y in the first equation and solve for x:
[tex]x=\frac{-47-10y}{3}[/tex]
[tex]x=\frac{-47-10(-5)}{3}[/tex]
[tex]x=\frac{-47+50}{3}[/tex]
[tex]x=\frac{3}{3}[/tex]
x=1
30 points
What is the opposite of cosine called and what is its triangle ratio
Answer: Answer is below
Step-by-step explanation: The answer is that the opposite of a cosine is called a hypotenuse. The ratio of the triangle is called a tangent.
I hope this info helps! :V