[(3x-2)(x+6)]-[(x-1)(2x)]=103 steps
Let's solve your equation step-by-step.
(3x−2)(x+6)−(x−1)(2x)=103
Step 1: Simplify both sides of the equation.
x2+18x−12=103
Step 2: Subtract 103 from both sides.
x2+18x−12−103=103−103
x2+18x−115=0
Step 3: Factor left side of equation.
(x−5)(x+23)=0
Step 4: Set factors equal to 0.
x−5=0 or x+23=0
x=5 or x=−23
Answer:
x=5 or x=−23
Given that rectangle LMNO with coordinates L(0,0), M(3,0), N(3,7), O(0,7), P is the midpoint of LM⎯⎯⎯, and Q is the midpoint of NO⎯⎯⎯, which of the following proves that PQ=LO?
Answers attached
The midpoint of a line divides the line into equal segments.
The option that proves PQ = LO is (a)
The given parameters are:
[tex]\mathbf{L = (0,0)}[/tex]
[tex]\mathbf{M = (3,0)}[/tex]
[tex]\mathbf{N = (3,7)}[/tex]
[tex]\mathbf{O = (0,7)}[/tex]
P is the midpoint of LM.
So, we have:
[tex]\mathbf{P = \frac{LM}{2}}[/tex]
[tex]\mathbf{P = (\frac{(0 +3}{2},\frac{0+0}{2})}[/tex]
[tex]\mathbf{P = (\frac{3}{2},0)}[/tex]
Q is the midpoint of NO.
So, we have:
[tex]\mathbf{Q = \frac{NO}{2}}[/tex]
[tex]\mathbf{Q = (\frac{(3 +0}{2},\frac{7+7}{2})}[/tex]
[tex]\mathbf{Q = (\frac{3}{2},7)}[/tex]
Distance PQ is calculated as follows:
[tex]\mathbf{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]
This gives:
[tex]\mathbf{PQ = \sqrt{(3/2 - 3/2)^2 + (0 - 7)^2}}[/tex]
[tex]\mathbf{PQ = \sqrt{ 7^2}}[/tex]
[tex]\mathbf{PQ = 7}[/tex]
Distance LO is calculated as follows:
[tex]\mathbf{LO = \sqrt{(0 - 0)^2 + (0 - 7)^2}}[/tex]
[tex]\mathbf{LO = \sqrt{ 7^2}}[/tex]
[tex]\mathbf{LO=7}[/tex]
So, we have:
[tex]\mathbf{PQ = 7}[/tex]
[tex]\mathbf{LO=7}[/tex]
Thus:
[tex]\mathbf{PQ = LO}[/tex]
Hence, the correct option is (a)
Read more about distance and midpoints at:
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What value of x is in the solution set of 2(3x - 1) = 4x - 6?
О -10
0-5
-3
ОО
О-1
Answer:
-1
Step-by-step explanation:
Step-by-step explanation:
Given by your question
2(3x-1)≥4x-6
Distributive property to take off the parentheses
2×3x-2×1≥4x-6
6x-2≥4x-6
Subtract 4x on both sides (Subtractive property of equality)
6x-2-4x≥4x-6-4x
2x-2≥-6
Add 2 on both sides (Addition property of equality)
2x-2+2≥-6+2
2x≥-4
Divide 2 on both sides (Division property of equality)
2/2 x≥-4/2
x≥-2
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Looking at the options you've provided.
-10 INCORRECT, it is not greater or equal to -2
-5 INCORRECT, it is not greater or equal to -2
-3 INCORRECT, it is not greater or equal to -2
-1 CORRECT, it is greater than -2
Answer:
2(3x -1) = 4x - 6
6x - 2 = 4x - 6
6x -2+2 = 4x -6 + 2
6x - 4x = 4x - 4x -6 + 2
6x - 4x = -6 + 2
2x = -4
2 2
x = -2
Express the interval shown on the number line in inequality notation.
G
T-
10 12
-12
-6
6
-10
8
-8
-2 0
24
-4
A
U
>>
Al
00
IA
00
or
D.
[]
(,) || ()
I
Inequality Notation:
Answer:
Umm Where's The Answer?
Find the value of x within the triangle
Answer:
68.46
Step-by-step explanation:
In order to find the angle, we can use the cosine rule:
c²=a²+b²-2abCos(c)
And rearrange for Cos(c)
(please note that c in this case is x)
So,
x=Cos^(-1) (a²+b²-c²)/2ab
By substituting the values, we get x=Cos^(-1)(4²+4²-4.5^2)/2(4)(4)
=68.46
Please fill in these boxes :)
Answer:
reciprocal of 4= 1/4
reciprocal of 1/3=3
reciprocal of -1/7 = -7
reciprocal of -4/5=-5/4
Step-by-step explanation:
it's explained
(4-1/4+2/3)+(5+4/3-6/5)-(6+7/4+4/5)
Answer:
The answer is 1…
Step-by-step explanation:
Well you can elimate a lot of fractions right off the bat just multiply everything by 60/1.
the final result will be
(240+15+40)+ (300+90-72)- (360+105+24)
Now solve
240-15+40=265
300+90-72=318
360+105+24=513
265+268-489
265+268= 11
533-513=20
bleh i m not sure naymore
Find the x- and y-intercepts for : 4y-6x = 24
Answer:
y-intercept = (0, 6)
x-intercept = (-4, 0)
Step-by-step explanation:
The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates (0, b). It is also the value of y when x = 0.
To find the y-intercept, set x = 0:
4y - 6x = 24
4y - 6(0) = 24
4y = 24
4y/4 = 24/4
y = 6
Therefore, the y-intercept is (0, 6).
The x-intercept is the point the graph where it crosses the x-axis, and has coordinates (a, 0). It is also the value of x when y = 0.
To find the x-intercept, set y = 0:
4(0) - 6x = 24
0 - 6x = 24
-6x/-6 = 24/-6
x = -4
Therefore, the x-intercept is (-4, 0).
Select the correct answer.
Answer: a
Step-by-step explanation:
F (-6,-5) G (3,-4) H(3,-7) the scale factor is = 1/8
Answer:
1/8" = 1'-0" Invert the fraction and multiply by 12
Step-by-step explanation:
i hope this help
the fraction 11 of 9 lies between
Answer:
1.222.......
Step-by-step explanation:
11/9＝1.2222
so it is between 1＆2
Simplify the following expressions by distributing. 4(-w +8)
Answer:
-4w+32
Step-by-step explanation:
distribute the 4 to everything in the ( )
Help pls, will give branliest to right answer
Answer:
Similar AA
Step-by-step explanation:
By Angle-Angle similarity postulate triangle ABC and triangle DEF are similar.
Answer:
C. similar AA
how to find an expression for the perimeter of the rectangle
Answer:
Step-by-step explanation:
To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width). Multiply both the height and width by two and add the results.
9 + x =19 what does x equal?
Answer:
10 because 19 - 9 = 10 it works the same way for addition just swap the signs
expand and simplify (x-7)^2
Answer:
x² - 14x + 49
Step-by-step explanation:
Simplifying (x-7)²:
(x-7)²
= (x-7)(x-7)
= x(x-7) - 7(x-7)
= x² - 7x - 7x + 49
= x² - 14x + 49
Hope this helps and be sure to have a wonderful time ahead at Brainly! :D
calculate the values of 1999.99 and 6049.44
Answer:
8049.43
Step-by-step explanation:
1999.99 + 6049.44
is 513 a composite number?
Answer:
yes, since 513 has more than two factors
have a spook-tastic day
Step-by-step explanation:
3
A line passes through the point (10, 1) and has a slope of
2
Write an equation in slope-intercept form for this line.
Answer:
y = 2x - 19
Step-by-step explanation:
Slope-intercept form: y = mx + b
y = (x , y) = 1
m = slope = 2
x = (x , y) = 10
b = y-intercept
Plug in the corresponding numbers to the corresponding variables:
1 = 2(10) + b
First, simplify, and then isolate the variable, b. Note the equal sign, what you do to one side, you do to the other.
First, multiply 2 with 10:
1 = (2 * 10) + b
1 = 20 + b
Next, subtract 20 from both sides of the equation:
1 = b + 20
1 (-20) = b + 20 (-20)
1 - 20 = b
b = -19
Plug in 2 for m, and -19 for b.
y = 2x - 19 is your slope-intercept form.
~
the area of the floor of a cubical room is 49m .find the area of 4 walls of a room.
Answer: [tex]196m^2[/tex]
Step-by-step explanation:
since it's a cube the floor is in square shape
area of one wall = [tex]a^2[/tex] area of 4 walls = = [tex]4[/tex]×[tex]49[/tex] = [tex]196[/tex]Answer:
SINCE ITS A CUBE OF FLOOR SHAPE.
area of 1 wall=a²
=4
area of 4 wall=4x49
=169m²Ans.
1) One angle is 28° larger than the other. The sum of the measures of two angles is 90°. Find the measure of each angle.
X=_____
Equation:______
Answer:
62
Step-by-step explanation:
Equation: x +28 =90
x = 59°
Measure of one angle = 59°
Measure of another angle = 31°
Equation to calculate the measurement: x + x - 28 = 90Given,
What is angle?In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle.
Given,
Sum of two angles = 90°
One angle is 28° larger than other
Let the measurement of one angle is x
then other angle = x - 28°
But,
x + x - 28° = 90°
2x - 28° = 90°
2x = 90° + 28°
x = 118°/2
x = 59°
one angle = 59°
other angle = 59° - 28° = 31°
Hence, 59° is measure of one angle
and 31° is measure of other angle.
x + x - 28 = 90 is the Equation to calculate the measurement.
Learn more about angle here:
https://brainly.com/question/28451077
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Which equation is equivalent to 15x - 3 = 25
Answer:
Please click above answer.Which of the following is the measure of side a?
23.3
144
8
16
Step-by-step explanation:
it is a right-angled triangle, so the side lengths need to fulfill the Pythagoras rule :
c² = a² + b²
where c is the Hypotenuse, the baseline opposite of the 90 degree angle. and a and b (often called legs) are the sides "enclosing" the 90 degree angle.
so, we have
20² = a² + 12²
400 = a² + 144
a² = 256
a = 16
FYI - we could have picked the right answer also by eliminating the wrong given answer options.
as this is a right-angled triangle :
a cannot be longer than the baseline (20).
that eliminates already the first 2 options.
and then look at the picture : a cannot be shorter than b (the other side line (12)).
that eliminates the third option.
What is the slope of this line?
Answer:
Slope = 2
Step-by-step explanation:
(x₁ , y₁) = ( 1 , 1) & (x₂,y₂) = (-1,-3)
[tex]Slope=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{-3-1}{-1-1}\\\\=\dfrac{-4}{-2}\\\\=2[/tex]
A _____________ _________________ is used to smother small fries on/in objects or on a person.
PLS HELP ME!!!!
Answer:
Ketchup, bottle
Step-by-step explanation:
I am confused on this but hope it help you.
Have a great day!
Write the equation of the graph below in slope intercept form.
Write the answer in slope intercept form and please step by step.
(2,1) and (1,3)=
Step-by-step explanation:
so (2,1) (1,3)
x1,y1 x2,y2
so then it would be
the slope is -1
so the equation is after using your x1 and y1 would be
y-1=-1(x-2)
and after you solve that by using the comunitive property, then it will look like
y-1=-1x+2
then you subtract 1 from the y side and make it
the answer is y=-1x+3
Given the proportion a/b=5/19, what ratio completes the equivalent proportion a/5=?
Answer:
[tex]\frac{b}{19}[/tex]
Step-by-step explanation:
If you cross-multiply in the first proportion you get 19a = 5b
To keep this, if we have a/5, we need b/19 to cross-multiply and still get 19a = 5b
find the equation of perpendicular bisector of the lines with the given word (1,2) and (5,4)
Answer:
y = -2x + 4
Step-by-step explanation:
Slope: (4-2)/5-1) = 2/4 = 1/2
Slope of the perpendicular line: -2
y-intercept: 2 - (-2)(1) = 4
QUICK HELP!!!
Use the table of the probability distribution to find the variance
Answer:
0.9
Step-by-step explanation:
in the diagram, fine pis parallel to side BC. What is the sum of the measures of 21 and 22? B What is the sum of the measures of_1 and _2? P 570 m_1 + m_2= ID 1 A 2 49 c
Answer:
76 women classified with severe hip pain, the WOMAC mean function score was 70.7 with standard deviation of 14.6, and we wish to know if we may conclude that the mean function score for a population of similar women subjects with severe hip pain is less than 75. let alpha is equal