Answers
Answer:
1)
The hypotenuse is the longest side of a triangle. It is ALWAYS the one across from the right angle (depicted as the box in the corner at 90 degrees). Therefore the 2 sides that intersect the 90-degree angle are "leg" and "leg" and the longest side is the"hypotenuse"
2)
The Pythagorean theorem states: [tex]a^{2} + b^{2} = c^{2}[/tex] where a and b are sides and c is the hypotenuse.
[tex]a^{2} + b^{2} = c^{2} \\8^{2} + 6^{2} = c^{2} \\64 + 36 = c^{2} \\100 = c^{2} \\\sqrt{100} = c\\10 = c[/tex]
For your purposes, a and b do not matter which number you choose as long as you make sure that they are sides and not the hypotenuse.
3)
The Pythagorean theorem states: [tex]a^{2} + b^{2} = c^{2}[/tex] where a and b are sides and c is the hypotenuse.
[tex]a^{2} + b^{2} = c^{2} \\4^{2} + 7^{2} = c^{2} \\16 + 49= c^{2} \\65 = c^{2} \\\sqrt{65} = c\\8.0622 = c[/tex]
Hope that helps!
Related Questions
parabola
described
Write the equation for the
7) A parabola that passes through the point (2, 2) and has a
vertex of (3, -1)
Answers
The most appropriate choice for parabola will be given by-
Equation of parabola that passes through the point (2, 2) and has a
vertex of (3, -1) is
[tex](x - 3)^2 = \frac{y +1}{3}[/tex]
What is parabola?
Parabola is a curve where every point on the curve is equidistant from a fixed point called the focus and a fixed line called the directrix.
Equation of parabola is [tex]y = a(x - h)^2+k[/tex] where (h,k) is the vertex of the parabola
Here,
Equation of the parabola with vertex (3, -1) is
[tex]y = a(x - 3)^2-1[/tex]
The parabola passes through (2, 2)
[tex]2 = a(2-3)^2-1\\2 = a-1\\a=2+1\\a=3[/tex]
Equation of parabola that passes through the point (2, 2) and has a
vertex of (3, -1) is
[tex]y = 3(x-3)^2 - 1\\[/tex]
[tex](x - 3)^2 = \frac{y +1}{3}[/tex]
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The probability that Gavyn wins in a raffle is given by the expression
p. Write down an expression for the probability that Gavyn does not win.
Answers
Explanation:
Let's replace p with something like 0.72
Pick any number between 0 and 1.
This says he has a 72% chance to win
1-p = 1-0.72 = 0.28
and he has a 28% chance of not winning.
For more information, check out "probability complement".
Exit ticket: Joehamster eats 12 muffin morsels every sixth day, 24 celery sticks every 8th oday, and 18 cookies every 10th day. After how many days will he eat all three food items on the same day?
Answers
In order to calculate after how many days all three food items will be eaten in the same day, we need to calculate the least common multiple (LCM) between the periods of 6 days, 8 days and 10 days.
First, let's factorize each number:
[tex]\begin{gathered} 6\to2\cdot3 \\ 8\to2\cdot2\cdot2 \\ 10\to2\cdot5 \end{gathered}[/tex]Then, let's multiply the factors using the maximum number of time they appear in a number, that is, number 2 three times, number 3 one time and number 5 one time:
[tex]2\cdot2\cdot2\cdot3\cdot5=120[/tex]So after 120 days all three food items will be eaten on the same day.
Simplify the expression. Show your work
Answers
Answer:
simplify(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))
Step-by-step explanation:
derivative(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))
limit(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))
taylor_series_expansion(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))
antiderivative(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))
integral(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))
equation_solver(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4))=0)
simplify(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))
Solve for v.
V =
Blank 1:
Answers
Answer:
v=60
Step-by-step explanation:
3v=180
v=60
:]
Percents
Progress:
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your and
Solve this problem, and identify the percent, amount, and base.
What percent of 60 is 45?
O Percent = 75, Amount = 60, Base = 45
O Percent = 45, Amount =27, Base = 60
O Percent = 75, Amount = 45, Base = 60
Percent 60, Amount = 27, Base = 45
Submit
Hold
Answers
The correct option is- Percent = 75, Amount = 45, Base = 60 for the movement of the progress bar.
What is termed as the progress bar?In math, bar notation is a simple method for expressing a repeating number by drawing a line over the number which repeats. Learn regarding infinity, when figures go on forever, and when to use bar notation by exploring the definition as well as examples of bar notion.For the given question,
The movement of the progress bar could be uneven due to questions can be worth more or less (including zero) due-
Type of problemThe individual capacityThe amount of something is stated in terms of a fraction of a hundred. The ratio can be expressed as a fraction of 100.
Base = 60 and the Amount is the 45.
Let the % will be x;
x% of 60 =45
60x =45
x=45/60
x=0.75
To obtain the percentage value, multiply it by 100 as follows:
% x = 0.75 × 100
% x = 75
Thus, the percentage of 60 is 45 will become 75%.
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a farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. what is the maximum area that the farmer can enclose with 48 ft of fence? what should the dimensions of the garden be to give this area? question content area bottom part 1 the maximum area that the farmer can enclose with 48 ft of fence is
Answers
The maximum area that the farmer can enclose for the rectangular garden is 488 sq ft and the dimensions of the rectangular garden are 24ft and 12 ft respectively.
It is given that a farmer decided to enclose a rectangular garden with one side using the barn of a tree and other 3 sides with 48 ft of fencing.
Let the length of the rectangle be y and the breadth of the rectangle be u.
So perimeter of the fencing needed = y + 2u (as one side is barn)
∴ y + 2u = 48
⇒ y = 48 - 2u (equation 1)
Area = yu (equation 2)
Putting the value of variable y from equation 1 in equation 2 we have,
Area = (48-2u)u
∴ Area = 48u - 2[tex]u^{2}[/tex]
⇒ Area = -2[tex]u^{2}[/tex] + 48u
⇒ Area = -2([tex]u^{2}[/tex] - 24u)
⇒ Area = -2([tex]u^{2}[/tex] - 24u + 144) + 288 (using completing the square method)
⇒ Area = -2[tex](u-12)^{2}[/tex] + 288
So the maximum area is 288 sq units as for any value of u the area value will decrease as seen from the above equation.
So if Area = 288
Then yu = 288
⇒ u = 288/y equation 3
Putting this value in Perimeter equation 1 we have,
y = 48 - 2u
⇒ y = 48 - 2 x [tex]\frac{288}{y}[/tex]
⇒ [tex]y^{2} = 48y - 576[/tex]
⇒ [tex]y^{2} - 48y + 576 = 0[/tex]
⇒ [tex](y-24)^{2}[/tex] = 0
Solving we get y = 24 ft
Hence the value of u is calculated as follows:
⇒ u = 288 / y
⇒ u = 288/ 24 = 12 ft
The maximum area that the farmer can enclose is 488 sq ft and the dimensions of the rectangle are 24ft and 12 ft respectively.
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Use Tools Telegraphs were used to send messages before the
telephone was invented. A telegraph operator could interpret about
40 words sent in Morse code per minute. Approximately how many words
sent in Morse code could the operator interpret in 12.5 seconds? State
what strategy and tool you will use to answer the question, explain your
choice, and then find the answer.
Answers
Answer:
stuff and more stuff
Step-by-step explanation:
what’s the answer to the equation
Answers
Answer:
8x-40=200
Step-by-step explanation:
67 - 88 x 90 x 77 + 125 = ?
Answers
i think so is correct
Please help
Quick thank you :)
Answers
Answer:
Ray
Step-by-step explanation:
A ray has a starting point and then continues in one direction.
Gasoline costs $2.20 per gallon. Maddie's mom put 9.5 gallons of gasoline in her car. What was the total cost of the gasoline? Choose the correct answer from the drop-down menu to complete the statement. The total cost of the gasoline can be found by _____ 2.20 and 9.5. The total cost is ______
Answers
Answer:
the multiplication of 2.2.20 and 9.5
Step-by-step explanation:
the total cost is $20.9
(9x-26) (4x+43) (2x-12)
Answers
The value of the expression given as (9x-26) (4x+43) (2x-12) is 72x³ + 134x² -5642x + 13416
How to evaluate the expression?From the question, the expression is given as
(9x-26) (4x+43) (2x-12)
Next, we evaluate the expression in pairs
So, we have
(9x-26) (4x+43) (2x-12) = (9x-26) (4x+43) (2x-12)
Evaluate the first two factors
So, we have
(9x-26) (4x+43) (2x-12) = (36x² + 387x - 104x - 1118) (2x-12)
Evaluate the like terms in the expression
So, we have
(9x-26) (4x+43) (2x-12) = (36x² + 283x - 1118) (2x-12)
Evaluate the first two factors
So, we have
(9x-26) (4x+43) (2x-12) = (72x³ - 432x² + 566x² - 3396x - 2246x + 13416)
Evaluate the like terms
So, we have
(9x-26) (4x+43) (2x-12) = (72x³ + 134x² -5642x + 13416)
Remove the bracket
(9x-26) (4x+43) (2x-12) = 72x³ + 134x² -5642x + 13416
Hence, the solution is 72x³ + 134x² -5642x + 13416
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7) An amusement Park Charges a $50
admission free and $10 for each ride.
which equation can be used to determine
C, the total cost of a day at the amusement
Park, based on n, the humber of rides.?
Answers
Answer:
50+((10n) =
so 50 is how much it cost to walk in the park and 10 is how much each ride (n) cost soif you know how many rides your ride you times that by 10 the add 10 to 50 and you get how much it will cost you for the day
Write the equation of the line that is perpendicular to y = 1 and goes through (4, −9).
Answers
FOR PERPENDICULAR LINES WHEN THEIR GRADIENTS ARE MULTIPLIED THEY GIVE -1
BUT IF WE ARE TO CHECK IN THE LJNE y=1 the gradient is 0
there is no number when multiplied with 0 that will give us -1 it means that the gradient of the line perpendicular to the given one will also be 0
when we substitute in the general equation y=mx+c together with the points
[tex] - 9 = (0)(4) + c \\ c = - 9[/tex]
IT MEANS THE EQUATION OF THE NEW EQUATION WILL BE
[tex]y = - 9[/tex]
HOPE THIS HELPS
what is a four sided shape that has two parallel sides: can be cut into two triangles with a diagonal line through opposite corners?
Answers
The four sided shape that has two parallel sides: can be cut into two triangles with a diagonal line through opposite corners is a parallelogram.
What is a parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure.
The parallelogram is divided into two congruent triangles by each diagonal. The total of the squares of a parallelogram's sides equals the sum of the squares of its diagonals. It is also known as parallelogram law.
A parallelogram is a two-dimensional geometrical shape with two parallel sides. It is a four-sided polygon (sometimes known as a quadrilateral) with parallel sides that are equal in length. The sum of a parallelogram's neighboring angles equals 180 degrees.
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BIG IDEAS MATH
#2 i
The table represents a quadratic function. Write an equation of the function in standard form.
x 3 45 6
y 10 7 10 19
y=
Basic
PAUL BENEDICTO
Check
Answers
The equation of the function in the standard form is:
3x + y = 25.
Given, From the table we can get the dy/dx which is the slope (m) ,
Therefore,
dy/dx = (7 - 10 ) / ( 4 - 3 )
dy/dx = -3
f(x) = ax² + bx + c, where a, b, and c are all numbers and an is not equal to 0, is the definition of a quadratic function. A parabola is the shape of a quadratic function's graph. Despite the fact that a parabola's "width" or "steepness" and opening direction can change.
Now,
( y - y₁ ) = m ( x - x₁ )
Putting the value from the table,
( y - 10 ) = -3 ( x -5 )
⇒ y - 10 = -3x + 15
⇒ 3x + y = 25
Hence the equation of the line in standard form is 3x + y = 25.
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hopt shipping company charges a
flat fee of $9 Plus an additional
$0.18 per pound to ship a package.
Gespil shipping company
flat fee of $10 plus an additional
$0.10 per pound. How many pounds
would a package weigh
that cost the same at
both companines?
Answers
Answer:
Hopt: 10 Gesplil; 6
Step-by-step explanation:
Find the slope and y-intercept of the following equations :
3x-4y = 12
Answers
Kirsten bought a used car for $3,600. She made a $360 down payment on it. How much more does Kirsten owe on the car?
Answers
Answer:
Kirsten owes $3240 more on the car.
Step-by-step explanation:
$3600 - $360 = $3240
how do i create a visual of this
Answers
Answer: Draw a picture of 2 1/2 cups of flour being added to 1 1/2 cups of sugar in a bowl.
Step-by-step explanation: wink wink
18:54:12 simplified
Answers
On simplifying the proportion 18:54:12, we get answer as 3:9:2.
What are the proportional guidelines?The following are crucial proportional characteristics:
If a: b = c: d, then a + c: b + d. Addendum
A - c: b - d if a: b = c: d. Subtrahendo
Dividendo states that if a: b = c: d, then a- b: b = c- d: d.
If a: b = c: d, then a Plus b: b Equals c+d: d. This is known as combining.
To put it another way, if a: b = c: d, then a: c = b: d.
On simplifying,
18:54:12
Firstly, dividing the all numbers by 3
= 6:18:4
Now dividing by 2
= 3:9:2
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suppose that a current recipe yields 30 servings (2 ounces each) and the desired recipe yields 30 servings (5 ounces each). what is the recipe conversion factor?\
Answers
Conversion factor [tex]= \frac{final serving}{initialserving}[/tex][tex]=\frac{5}{2} =2.5[/tex]
The recipe conversion factor is 2.5
What is 7 7/8 • 2 1/4
Answers
Answer:
Step-by-step explanation:
[tex](7\frac{7}{8} )(2\frac{1}{4} ) = \\\\\frac{567}{32} \\\\OR\\17\frac{23}{32}[/tex]
Which statement describes the graph of the system of equations below?
1.5x + 0.2y = 2.68
1.6x + 0.3y = 2.98
The lines are parallel.
The lines overlap at all points.
The lines intersect at (1.6,1.4).
The lines intersect at (3.1,0.5).
Answers
Answer:
3rd answer option (1.6, 1.4)
Step-by-step explanation:
the slope of the lines is different.
to see we transform the equations to the regular slope-intercept form
y = ax + b
with "a" being the slope and "b" being the y-intercept (the y value when x = 0).
1.5x + 0.2y = 2.68
0.2y = -1.5x + 2.68
y = -1.5x/0.2 + 2.68/0.2 = -7.5x + 13.4
1.6x + 0.3y = 2.98
0.3y = -1.6x + 2.98
y = -1.6x/0.3 + 2.98/0.3 = -5.33333...x + 9.93333...
-7.5 is not -5.3333...
so, the lines are not parallel nor overlap at all points.
therefore, they intersect at a point.
(1.6, 1.4) ?
the equations must remain true when using the coordinates :
1.5×1.6 + 0.2×1.4 = 2.68
1.6×1.6 + 0.3×1.4 = 2.98
2.4 + 0.28 = 2.68
2.68 = 2.68 correct
2.56 + 0.42 = 2.98
2.98 = 2.98 correct
yes, they intersect at (1.6, 1.4).
for (3.1, 0.5) already the x coordinate is way too large.
1.5×3.1 or 1.6×3.1 are already by themselves much larger than 2.68 or 2.98.
Which of the following triangles cannot be solved using the sine law
Answers
1. We can use the sine law since we have two angles and one of the angles had the side opposite it.
2. We can use the sine law because we have two angles, we can find the third angle in the triangle. This means we have all three angles. We now have two angles and one of the angles has the side opposite it.
3. We have a right triangle. We could use the sine law because we have the right angle and the hypotense. We have two sides and one angle.
4. We have two sides and the included angle. We cannot use the sine law. We would have to use the law of cosines to solve this problem.
Solve the equation 3 sinx+3 = 1 for 0°
Answers
The value of x after solving the equation 3sinx+3 = 1 for 0° is -46.455.
First, take the equation 3sinx+3 = 1. This is a first order linear equation with a single variable, x. To solve this equation find the value of x.
First subtract three from both LHS and RHS part. The equation becomes
3sinx+3-3 = 1-3,
which is equal to,
3sinx = -2. now divide both LHS and RHS by 3 and the equation becomes, (3sinx)÷3 = -2÷3 solving this we get the equation as sinx = -2÷3.
now take the sine to the LHS we get the equation as,
x = [tex]sin^{-1}[/tex](-2÷3)
so by solving this, the final answer for x is,
x = -46.455
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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!
______
At a carnival it costs $34.92 for 12 tickets. Write an equation that can be used to express the relationship between the total cost (t) and the number of tickets(n) you buy.
Answers
The equation that can be used to express the relationship between total cost and tickets is t = $2.91n.
What is the total cost?The first step is to determine the cost of one ticket. The cost of one ticket can be determined by dividing the total cost of the ticket by the total number of tickets. Division is the operation that is used to determine the quotient of two or more numbers.
Cost of one ticket = $34.92 / 12 = $2.91
The equation that can be used to determine the total cost would have this form:
Total cost = cost per ticket x number of tickets
t = $2.91 x n
t = $2.91n
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-4w = -12 solve for w simplify your answer as much as possible
Answers
Answer:
w = 3
Step-by-step explanation:
-4w = -12
divide both sides by -4:
-4w/-4 = -12/-4
w = 3
Answer:
w=3
Step-by-step explanation:
1. divide -12 by -4
[tex]w = \frac{ - 12}{ - 4} [/tex]
[tex]w = 3[/tex]