Find the slope of the following equation. Simplify your answer.
5x + 2y = -10 And do not tell me it’s m= - 5/2 because clearly that’s not an option
Answers
The correct answer is: [D]: " [tex]m = \frac{-5}{2}[/tex] ".
______
Step-by-step explanation:
We are given:
" 5x + 2y = -10 " ; Find the slope of the equation.
______
Rewrite this equation in slope-intercept format ;
that is: " y = mx + b " ;
in which:
y remains as single value, as an 'output' ; or 'dependent
variable', on the 'y-axis' (if graphed);
isolated on the 'left-hand side' of the equation.
m is the coefficient of x in the equation; and represents the slope; for which we shall solve.
{If there is no slope, then "m = 0" ; and "[0 * x = 0]." };
And the "slope-intercept format" is: "y = b" }.
b represents the "y-intercept" ; i.e. when the line crosses the
"y-axis" when graphed; that is, the "y-value" of the "coordinate" of the "y-intercept" ; [i.e. the value of "y" when "x = 0" ; so; " (0, b) ".
{ Note: b can equal "0" ; in those cases: y = mx + 0 ; write as " y = mx "}.
{ If there is no slope, [i.e. "m = 0" ; and no "y-intercept" ; [i.e. "b = 0"];
Then: write the equation accordingly—e.g. " y = [whatever number the graph represents]." }.
Also, note that b can be a "negative number"; as well.
In that case, write an equation in "slope-intercept format" ; that is;
→" y = mx + b " ; as: " y = mx " .
______
Given: " 5x + 2y = -10 " ;
Let's rewrite: ↔ " 2y + 5x = -10 " ; to get the "y-value" a bit closer to the 'left-hand side' of the equation.
Then: Let's subtract 5x from Each Side of the equation;
2y + 5x − 5x = -10 − 5x ;
to get: " 2y = -10 − 5x " ;
______
Method 1):
We have: " 2y = -10 − 5x " ;
Divide Each Side by 2 ; to isolate y on the 'left-hand side' of the equation, and to rewrite as an equation in the slope-intercept format :
2y / 2 = (-10 − 5x)/2 ;
→ [tex]y =\frac{-10-5x}{2}= \frac{-10}{2}-\frac{5x}{2}[/tex] ;
→ [tex]\frac{-10}{2} =[/tex] -10 ÷ 2 = -5 ;
Rewrite the equation by replacing " [tex]\frac{-10}{2}[/tex] " ; with: -5 ;
→ [tex]y = -5 - \frac{5x}{2}[/tex] ;
Then, rewrite to get the equation in "slope-intercept format"
→ [tex]y = -5 - \frac{5x}{2}[/tex] ;
[tex]= -5 + (-\frac{5x}{2})[/tex] ; ↔ Rewrite:
[tex]= \frac{-5x}{2} + (-5)[/tex] ; ↔ Rewrite again:
[tex]=\frac{-5x}{2} -5[/tex] ;
→ [tex]y = \frac{-5x}{2} -5[/tex] .
Note: " [tex]\frac{-5x}{2} = \frac{-5}{2} x[/tex] " ;
→ [tex]y = \frac{-5}{2}x-5[/tex] ;
This is the equation written in "slope-intercept format" ;
that is: " y = mx + b " ;
in which:
y is isolated as a single variable on the 'left-hand side' of the equation;
m = [tex]\frac{-5}{2}[/tex] ; which is the slope; which is also the "coefficient" of x ;
b = -5 ; which is the 'y-coordinate' of the "y-intercept" of the graph;
So, the slope; "m = -5/2" ; is the correct answer; which corresponds to:
Answer choice: [D]: " m = [tex]\frac{-5}{2}[/tex] " .
______
Method 2):
Given: " 5x + 2y = -10" ; Find the slope of the line.
We want to rewrite the equation in the "slope-intercept format" ;
" y = mx + b " ; as explained above;
to get the correct answer for m, the slope of the line.
" 5x + 2y = -10 " ↔ Rewrite as:
2y + 5x = -10 ; since we want to isolate y as a single variable on the 'left-hand side' of the equation; and by rearranging & rewriting this equation, the 2y is closer to the 'left' of the equation.
Now, subtract 5x from Each Side of the equation:
2y + 5x − 5x = -10 − 5x ;
to get: 2y = -10 − 5x ;
Now, Let's multiply the entire equation (i.e. "Each Side") by -1 ;
to make the equation easier to handle;
-1(2y) = -1 (-10 − 5x) ;
For the 'left-hand side' of the equation:
-1*2y = -2y
For the 'right-hand side' of the equation:
Note the 'distributive property of multiplication'; as follows:
a(b + c) = ab + ac ;
Likewise:
-1(-10 − 5x) = (-1 *-10) + (-1 *-5x) ;
= (10) + (5x) = 10 + 5x ;
Now, rewrite the entire equation:
-2y = 10 + 5x ; ↔ Rewrite as;
-2y = 5x + 10 ;
Then, we divide Each Side of the equation by -2 ;
to isolate y as a "single variable" on the 'left-hand side' of the equation;
and to rewrite the equation in "slope-intercept format" ;
-2y / -2 = (5x + 10) /-2 ;
→ [tex]y=\frac{5x+10}{-2} =\frac{5x}{-2} +\frac{10}{-2} =\frac{5x}{-2}+(-5) =\frac{5x}{-2}-5[/tex] ;
→ [tex]y=\frac{5x}{-2} - 5[/tex] ;
which is written in "slope-intercept format" ; that is:
" y = mx + b " ;
in which:
y is isolated as a single variable on the 'left-hand side' of the equation;
m = [tex]\frac{5}{-2}[/tex] ; which does equal " [tex]-\frac{5}{2}[/tex] " ; which does equal " [tex]\frac{-5}{2}[/tex] " ;
which is the slope of the equation, as well as the 'coefficent of x' ;
b = -5 ; which is the 'y-coordinate' of the "y-intercept".
______
As such:
The correct answer choice is: [D]: " m = [tex]\frac{-5}{2}[/tex] " .
{Note: This is consistent with the answer choice from Method 1 above.}
______
Hope this answer and explanation is helpful.
Best of luck to you!
______
Related Questions
PLEASEEE HELP first one to actually gets it right gets the crown thingy
Answers
Answer:
Step-by-step explanation:
Your first two photos are correct.
For your third photo, move your second dot one more to the right as you accidentally put 1.7 instead of 1.8.
For the first dot of -8/5 you should move it 8 more to the left. This is because:
-8/5 = -1 3/5 = -1.6
For your fourth photo
9/2 = 4 1/2 = 4.5
-7/2 = -3 1/2 = -3.5
For your fifth photo
-5 2/3 ≈ -5.66
5 1/3 ≈ 5.33
the area A of a rectangle is represented by the formula A=lw where l is the length and w is the width. write an equation that makes it easy to find the width of the rectangle if we know the area and the length
Answers
Answer:
See below
Step-by-step explanation:
A = l w looking for w...... divide both sides of the equation by ' l '
A/l = w Done.
pls help will give brainliest
Answers
Answer: The answer for X' is -1,8, and the answer for X'' is 3,14
Step-by-step explanation:
When talking about reflections across the x-axis, the formula would be: (x,y)---> (x, -y) so you first start out with -1, -8 then translate it to -1,8, because you swap the y. Then you add 4 to -1 because you move 4 to the right which gives you 3, and then you add 6 to 8 because you move up 6, which gives you 14, so your final answer is 3,14
Angelina’s family owns a mini-golf course. When discussing the business with a customer, she explains there is a relationship between the number of visitors and hole-in-one winners. If x is the number of visitors and y is the number of winners, which conclusion is correct?
The ordered pair (–2, 7) is viable.
The ordered pair (0, 7) is viable.
The ordered pair (17, 3) is viable.
The ordered pair (20, 5) is non-viable.
Answers
The conclusion which is correct among the answer choices as given in the task content is; The ordered pair (17, 3) is viable.
Which conclusion among the answers choices is correct?It follows from the task content that the conclusion which is valid be identified among the answer choices.
Since it is given that; there is a relationship between the number of visit and hole-in-one winners.
The statement above indicates that the number of visitors must be greater than the number of winners. This follows from the fact that there is no winner if there are no visitors.
Hence, since x is the number of visitors and y is the number of winners, the ordered pair which is viable is; (17, 3).
The ordered pair (20, 5) is viable too. However, the last answer choice indicates that it id not and hence, is incorrect.
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Answer:
(17,3)
Step-by-step explanation:
I got it on FLVS
Solve p3 = −512.
answers are
p = ±8
p = −8
p = ±23
p = −23
Answers
Option b) p = -8 is correct, when p³ = 518.
Define cube root.A integer y such that y3 = x is known as the cube root of a number x in mathematics. All nonzero complex numbers have three different complex cube roots, while all nonzero real numbers have exactly one real cube root and two complex conjugate cube roots. We are aware that adding three times to any number yields the cube of that number. Additionally, the inverse action of cubing a number is known as the cube root of a number. For instance, 63 has a cube value of 216. In that case, 216's cube root is equal to 6.
Given,
Equation
p³ = -518
Multiplying cube root each side
p = -∛518
p = -8
Option b) p = -8 is correct, when p³ = 518.
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1. En los siguientes problemas, los puntos A, B, C forman siempre un triángulo rectángulo, encuentra el valor pedido en cada caso. Utiliza si es necesario
Answers
Las medidas de los lados desconocidos de las tres figuras son listadas abajo:
A) AC = 3
B) AC = 13
C) AB = 17
¿Cómo determinar los lados desconocidos de triángulos y rectángulos?
En este problema tenemos que dos casos de triángulos rectángulos y un caso de rectángulo. Por geometría euclídea, un rectángulo se forma uniendo dos triángulos rectángulos de iguales medidas. Las medidas de los lados faltantes se determina con el teorema de Pitágoras:
Caso A - Triángulo rectángulo
AC = √(BC² - AB²)
AC = √(5² - 3²)
AC = √(25 - 16)
AC = √9
AC = 3
Caso B - Rectángulo
AB = DC
AC = √(AD² + DC²)
AC = √(AD² + AB²)
AC = √(5² + 12²)
AC = 13
Caso C - Triángulo rectángulo
AB = √(AC² + BC²)
AB = √(8² + 15²)
AB = 17
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Fill in the missing number.
_groups of 3 equal 27.
Answers
Answer:
9 groups of 3 equal 27
Step-by-step explanation:
Fill in the missing number.
9 groups of 3 equal 27
because 9 × 3 = 27
7(u - 4) = 28 solve for u simplify your answer as much as possible
Answers
Answer:
u = 0
Step-by-step explanation:
7(U + 4) = 28 Distribute the 7
7u + 28 = 28 Subtract 28 from both sides
7u = 0 Divide both sides by 7
u = 0
Answer:
7(u - 4) = 28
7u - 28 = 28
+28 +28
7u = 56
÷7 ÷7
u = 8
8x - 3 > 2(4x + 1 )
Find x. Pleaseeee help me. Best answer gets 35 points
Answers
Answer:
There's no real solutions
Step-by-step explanation:
8x - 3 > 2(4x + 1 ) multiply inside the parenthesis with 2
8x - 3 > 8x + 2 transfer like terms to the same side of the inequation
8x - 8x > 3 + 2
0 > 5 this is not correct so we say there's no real solution to this inequation
HELP IM MARKING BRAINLEIST
Answers
Answer:
x = 104
y = 74
Step-by-step explanation:
According to the figure, the quadrilateral has two pairs of parallel, opposite sides. That makes the quadrilateral a parallelogram.
In a parallelogram, opposite sides are congruent and opposite angles are congruent.
Because of congruent sides:
x - 7 = 97
x = 104
Because of congruent angles:
y = 74
What is the range of the function shown
in the graph below?
Answers
Range of the given graph is (-∞,+∞)
Range of the function y=f(x) is all possible value of y for different value of x. Here value of x for which function is defined, known as domain of the function while the value of y for corresponding value of x is known as range of function.
In the graph of the function the value of x (on X-axis) for which graph is plotted known as domain of graph while the value of y on the Y-axis is known as range of graph.
In simple word we can say X-axis denotes domain and Y-axis denotes range
Thus, from the graph it seems very clear that the range of the given function or graph will lie between -∞ to +∞
we can also write as y∈ (-∞,+∞)
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Pls help due tomorrow!!
Answers
Answer:
Where is the question?
Step-by-step explanation:
use the data in attend for this exercise. (i) in the model of example 6.3, argue that dstndfnl/dprigpa < b2 1 2b4 prigpa 1 b6atndrte. use equation (6.19) to estimate the partial effect when prigpa 5 2.59 and atndrte 5 82. interpret your estimate
Answers
These are the coefficients of x1 and x2 respectively, and helps us to know the the significance of the independent variable in predicting the independent variable.
We are given the following information:
The estimate regression equation for a model involving two independent variables and 10 observations follows:
y= 29.1270+0.5906x1+0.4980x2
where x1 and x2 are the two independent variable and y is the dependent variable.
a) The regression line is of the form:
y=b0+b1 x1+b2 x2
where b0 is the y intercept and b1 , b2 are the coefficients of x1 and x2
Comparing, we get,
b1 = 0.5906
b2= 0.4980
These are the coefficients of x1 and x2 respectively, and helps us to know the the significance of the independent variable in predicting the independent variable.
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chegg tell whether each sequence is arithmetic. if the sequence os arithmetic, identify the common difference and find the indicated term 3,5/2,3/2,-3/2,...
Answers
Take the 2nd term and minus the 1st term.
Now take the 3rd term and minus the 2nd term.
Notice that the differences are the same. Hence there is a common difference (difference of -0.5).
So it is an arithmetic sequence.
Using the following graph, write the equation of a line that is parallel to the given line and passes through the point (0, 0).
(Write your answer is slope intercept form. The y= is already typed for you, so only type the remainder of the equation using NO spaces!)
Answers
Answer:
y=-x
Step-by-step explanation:
Slope of the line = -1
Parallel line slope = -1, y intercept 0
y = -x
:]
find 7% of 41 do not round your answer
Answers
[tex] \frac{7}{100} \times 41 \\ = 2.87[/tex]
ATTACHED IS THE SOLUTION
here are the first 5 terms in a number sequence 7 10 13 16 19
write an expresstion, in terms of n, for the nth term of this number sequence.
Answers
Answer:
[tex]a_{n}[/tex] = 3n + 4
Step-by-step explanation:
there is a common difference between consecutive terms , that is
10 - 7 = 13 - 10 = 16 - 13 = 19 - 16 = 3
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 7 and d = 3 , then
[tex]a_{n}[/tex] = 7 + 3(n - 1) = 7 + 3n - 3 = 3n + 4
17/20= t + ( - 13/20) t = ?
Answers
Answer:
t = 3/2
Step-by-step explanation:
You want to know the value of t that satisfies 17/20= t + ( - 13/20).
SolutionAdd 13/20 to both sides of the equation.
17/20 +13/20 = t -13/20 +13/20
30/20 = t . . . . . simplify
3/2 = t . . . . . . . reduce the fraction
The solution is t = 3/2.
Select the correct answer. The sum of two consecutive numbers is 157. This equation, where n is the first number, represents the situation: 2n + 1 = 157. What is the first number?
Answers
Answer:
78
Step-by-step explanation:
2n + 1 = 157
2n = 157 - 1
2n = 156
n = 156 ÷ 2
n = 78
Hello! I need some assistance with this homework question, pleaseQ7
Answers
You have the following function:
[tex]f(x)=x^2+8[/tex]In order to calculate
[tex]\frac{f(x+h)-f(x)}{h}[/tex]Consider that f(x + h) is given by:
[tex]f(x+h)=(x+h)^2+8=x^2+2xh+h^2[/tex]Then, by replacing f(x) and f(x+h) into the difference quotient and by simplifying, you get:
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{x^2+2xh+h^2+8-x^2-8}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{2xh+h^2}{h}=\frac{h(2x+h)}{h}=2x+h \end{gathered}[/tex]Hence, the result to the quotient difference is 2x + h
in the computer game world of warcraft, some of the strikes are critical strikes, which do more damage. assume that the probability of a critical strike is the same for every attack, and that attacks are independent. during a particular fight, a character has 243 critical strikes out of 534 attacks.
Answers
Answer: whats the question?
Step-by-step explanation:
Driver A and B have two different routes. Driver A's route is 80km, and driver B's route is 100km. Driver B travels 10km/h faster than driver A and finishes 10 minutes earlier. What are the speeds of each driver?
Answers
Speed of Driver A is 30 km/h.
Speed of Driver B is 40 km/h
Define speed.The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
Given Data
Driver A and B have two different routes. Driver A's route is 80km, and driver B's route is 100km. Driver B travels 10km/h faster than driver A and finishes 10 minutes earlier.
Distance = Speed (Time)
Distance for Driver A: 80 kilometers
Consider Driver A's speed to be A km/h.
Driver A's time was [tex]\frac{80}{A}[/tex] hours.
Distance for Driver B is 100 kilometers
Speed of Driver B: A + 10 km/h
Driver B's time was equal to 100/(A + 10) hours.
Arrived 10 minutes early, or [tex]\frac{10}{60}[/tex], or [tex]\frac{1}{6}[/tex]hour.
100/(A + 10) = [tex]\frac{80}{A}[/tex] - [tex]\frac{1}{6}[/tex]
600A = 480(A + 10) - A(A + 10)
600A = 480A + 4800 - A² - 10A
A² +130A - 4800 = 0
A² + 160A - 30A - 4800 = 0
A(A + 160) - 30(A + 160) = 0
(A - 30)(A + 160) = 0
A = 30 since speed cannot be negative.
Speed of Driver A is 30 km/h.
Speed of Driver B: 40 km/h
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when Iris -12 - (-12), she got a difference of -24. Is her answer correct? If not, what mistake did she make?
Answers
Answer: Her answer is incorrect.
Step-by-step explanation: You have to distribute the negative sign to (-12), once you do that the (-12) becomes a positive making the equations -12 + 12 resulting in your answer being 0 not -24.
Please help asap it's going to go overdue if I don't get an answer ):
Answers
2. distributive property (multiplying out)
3. addition property of equality (how it turned to -4x)
4.division property of equality (when you divide the equation by -4)
what is the slope of a line perpendicular to the line whose equation is x+4=28
Answers
The slope of a line perpendicular to the line is -4
The equation is x -4y = 28
The equation for the line is
y = mx + c
where m = slope
c = y-intercept
Here the equation is x - 4y = 28
4y = x - 28
y = x/4 - 7
So the slope of this line is 1/4
Now we have to find the slope of the line perpendicular to that line.
We know that,
m1 × m2 = -1
1/4 × m2 = -1
m2 = -4
Therefore the slope of the line perpendicular to the line is -4.
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The complete question is:
Find the slope of a line perpendicular to x-4y=28
What is the density for an unknown liquid with a mass of 6 grams and a volume of 12 mL?.
Answers
1) Considering that
[tex]undefined[/tex]Find f(-9) if f(x) =1x -8
Answers
Hello!
To solve for f(-9)
==> must simply plug in '-9' into the x's position
==> [tex]f(-9) = 1(-9)-8=-9-8=-17[/tex]
Hope that helps!
Stephen is in first grade, and his class is creating pasta necklaces! There are two types
of pasta to use on the necklaces: long macaroni pieces, and small rotelle pieces which
look like wheels w|th spokes. The directions are to have no more than 35 pieces of
hold 20 macaroni noodles or 55
pasta on a necklace, and each string IS long enough to
pieces of rotelle.
Select the statement below that is not true.
Answers
Stephen's necklace, to start can accommodate 12 macaroni noodles and 23 rotelle pieces.
Necklace of Stephen can have 35 rotelle pieces.
Stephen's pendant can have 10 pieces of rotelle and 5 macaroni noodles.
explanation:
-
Option A is accurate because 35 pieces of pasta—the maximum permitted per necklace—are obtained by adding 12 macaroni noodles to 23 pieces of rotelle.
Option B is incorrect because the sum of the allowed 35 pasta pieces plus the 15 macaroni noodles and 21 rotelle pieces equals 36 pasta pieces.
Option C is accurate because 35 pieces of Rotelle do not exceed the upper limit.
Despite the fact that they still add up to the maximum allowed, Option D is false since a string
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Cole drove from Los Angeles to San Francisco to visit friends.
Cole drove the speed limit which was 70 miles/hour. If Cole's
driving time for the trip was 6 hours, how many miles did Cole
drive?
Answers
Answer:
420 miles
Step-by-step explanation:
GivensWe are given that Cole drove a distance at a speed of 70 miles/hour. We are also shown that the driving time was 6 hours.
We are asked to find how many miles Cole drove.
SolveRealize that since the speed is constant, it can be multiplied by the driving time to find the mileage.
Therefore, multiply the speed limit by the driving time:
[tex]\text{70 miles/hour} \times \text{6 hours} = \text{420 miles}[/tex]
Final AnswerTherefore, Cole drove 420 miles.
Answer:
420 miles
Step-by-step explanation:
Is known:
70 miles / hour
Question:
how many miles will it cover in 6 hours?
70mil/jam × 6 hour
= 420 miles
StudyForEducation.
HELP PLEASEE!!!! my last question and hardest one
Answers
If you plug this into a graphing calculator, the same graph appears. So, y would have to equal 1x + (-3)