Answer:
x=0.76 or -5.26
Step-by-step explanation:
You can apply the completing square method to solve this ;
[tex]2x^2+9x=8\\\\[/tex]
Rewrite the equation with a zero like below
[tex]2x^2+9x-8=0[/tex]
This is by taking 8 to the left side of the equation
Divide the terms by 2 in x²
[tex]\frac{2x^2}{2} +\frac{9x}{2} -\frac{8}{2} =\frac{0}{2}[/tex]
[tex]=x^2+4.5x-4=0[/tex]
Move the number term to the right side of the equation
[tex]x^2+4.5x=4[/tex]
complete square on the lefts side of the equation, how?
[tex]=(\frac{b^}{2})^2 =(\frac{4.5}{2} )^2=5.0625[/tex]
balance the equation by adding this value to the right side , in this form
[tex]x^2+4.5x+5.0625=4+5.0625\\\\[/tex]
Factorize the left side
[tex](x+2.25)(x+2.25)=9.0625\\\\\\(x+2.25)^2=9.0625\\[/tex]
Eliminate the square on the left side
[tex]x+2.25=\sqrt{9.0625}[/tex]
x+2.25= ± 3.010
Solve for x
x=+3.010-2.25=0.76
or
x=-3.010-2.25=-5.26
Answer:
x = 0.76 or x= -5.26
Step-by-step explanation:
Points to remember
Solution of a quadratic equation ax² + bx + c = 0
x = [-b ± √(b² - 4ac)]/2a
It is given a quadratic equation,
2x² + 9x = 8
⇒ 2x² + 9x - 8 = 0
To find the solution
Here a = 2, b = 9 and c = -8
x = [-b ± √(b² - 4ac)]/2a
= [-9 ± √(9² - 4*2*(-8))]/2*2
= [-9 ± √(81 +64)]/4
= [-9 ± √(145]/4
= [-9 ± 12.04]/4
x = [-9 + 12.04]/4 or x = [-9 - 12.04]/4
x = 0.76 or x= -5.26
Consider the two triangles shown.
A. The given sides and angles cannot be used to show similarity by either the SSS or SAS similarity theorems.
B. The given sides and angles can be used to show similarity by the SSS similarity theorem only.
C. The given sides and angles can be used to show similarity by the SAS similarity theorem only.
D. The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.
Answer:
Option D. The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.
Step-by-step explanation:
step 1
we know that
The SSS Similarity Theorem , states that If the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar
In this problem
[tex]\frac{HG}{JK}=\frac{GF}{JL}=\frac{HF}{KL}[/tex]
Verify
substitute the values
[tex]\frac{48}{12}=\frac{32}{8}=\frac{36}{9}[/tex]
[tex]4=4=4[/tex] ---> is true
therefore
The triangles are similar by SSS similarity theorem
step 2
we know that
The SAS Similarity Theorem , states that two triangles are similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal
In this problem
Two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal
therefore
The triangles are similar by SAS similarity theorem
Answer:
D. The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.
Step-by-step explanation:
Edge 2020 (2021)
What is the slope of the line through (-2,5) and (4,9)
Answer:
2/3
Step-by-step explanation:
slope = run/rise
rise = vertical distance = difference in y-coordinates
run = horizontal distance = difference in x-coordinates
Find the rise = difference in the y-coordinates: 5 - 9 = -4
Find the run = difference in the x-coordinates in the same order: -2 - 4 = -6
Divide the rise by the run: slope = -4/-6
Reduce the fraction: slope = 2/3
(-2, 5) (4, 9)
Y2 - Y1
-----------
X2 - X1
9-5
------- = 4/6
4+2
4/6 simplifies to 2/3
Slope: 2/3
An ellipse has vertices along the major axis at (0, 8) and (0, -2). The foci of the ellipse are located at (0, 7) and
(0, -1). What are the values of a, b, h, and k, given the equation below?
Answer:
The values are a = 5 , b = 3 , h = 0 , k = 3
The equation is x²/9 + (y - 3)²/25 = 1
Step-by-step explanation:
* Lets revise the standard equation of the ellipse
- The standard form of the equation of an ellipse with center (h , k)
and major axis parallel to y-axis is (x - h)²/b² + (y - k)²/a² = 1 , where
-The length of the major axis is 2a
- The coordinates of the vertices are (h , k ± a)
- The length of the minor axis is 2b
- The coordinates of the co-vertices are (h ± b , k)
- The coordinates of the foci are (h , k ± c), where c² = a² - b²
* Now lets solve the problem
∵ The vertices of the ellipse along the major axis are (0 , 8) , (0 , -2)
∴ The major axis is the y-axis
∴ The vertices are (h , k + a) and (h , k - a)
∴ h = 0
∴ k + a = 8 ⇒ (1)
∴ k - a = -2 ⇒ (2)
∵ The foci of it located at (0 , 7) , (0 , -1)
∵ The coordinates of the foci are (h , k + c) and (h , k - c)
∴ h = 0
∴ k + c = 7 ⇒ (3)
∴ k - c = -1 ⇒ (4)
- To find k and a add equations (1) and (2)
∴ (k + k) + (a + - a) = (8 + -2)
∴ 2k = 6 ⇒ divide both sides by 2
∴ k = 3
- Substitute the value of k in equation (1) or (2) to find a
∴ 3 + a = 8 ⇒ subtract 3 from both sides
∴ a = 5
- To find the value of c substitute the value of k in equation (3) or (4)
∴ 3 + c = 7 ⇒ subtract 3 from both sides
∴ c = 4
- To find b use the equation c² = a² - b²
∵ a = 5 and c = 4
∴ (4)² = (5)² - a²
∴ 16 = 25 - b² ⇒ subtract 25 from both sides
∴ -9 = -b² ⇒ multiply both sides by -1
∴ b² = 9 ⇒ take √ for both sides
∴ b = 3
* The values are a = 5 , b = 3 , h = 0 , k = 3
* The equation is x²/9 + (y - 3)²/25 = 1
Answer:
a=5, b=3, h=0, k=3
Step-by-step explanation:
The center of the circle is (0,3) therefore h is 0 and k is 3. If you use a graphing calculator and plot the points given you should find that a=5. Then try to c and use the equation c^2=a^2-b^2 to find b.
if ln2=0.693, what is the value of ln32
Answer:
3.4657359...
Step-by-step explanation:
just put into your phone calculator 32 then hit In.
The value of ln 32 is 3.468 .
What is Logarithm ?Logarithm is an inverse of Exponentiation , The power to which a number must be raised in order to obtain another number is known as a logarithm.
It is given that
ln 2 = 0.693
ln 32 = ?
32 = 2⁵
ln 32 = ln 2⁵
ln aⁿ = n ln a
ln 32 = 5 ln 2
ln 32 = 5 * 0.6936
ln 32 = 3.468
Therefore the value of ln 32 is 3.468 .
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write an expression without exponent that is equivalent to (2^3)(4^3)
Answer:
512
Step-by-step explanation:
Solve the parenthesis first. Note that:
2^3 = 2 * 2 * 2 = (4) * 2 = 8
4^3 = 4 * 4 * 4 = (16) * 4 = 64
Multiply:
8 * 64 = 512
512 is your equivalent expression.
~
Answer:
(2³)(4³) = 2³ x [tex]2^{6}[/tex] = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512
How many more website hits were there on Friday than on Thursday? Horizontal bar graph with number of website hits per day of week contains the following data: Sunday 1900, Saturday 2000, Friday 1000, Thursday 800, Wednesday 1200, Tuesday 1900, and Monday 1300. 100 50 200 150
Answer:
200 more on Friday than thursday
What is the value of y?
y + 30
you can't solve this nor find the value of y because its not a full equation
Answer:
You cant solve for y without knowing the end number.
Step-by-step explanation:
maybe your equation y + 30 = 32 then we would know y is = to 2
Find the area of the kite
Answer:
30 sq. units
Step-by-step explanation:
Multiply the length of the two diagonals together and divide by two
[tex]\frac{d1 * d2}{2}[/tex]
10 * 6 = 60
60/2 = 30
The area of the kite is 30 sq. units
Answer: B
Step-by-step explanation:
How to get the area of a rhombus
( diagonal x the other diagonal )1/2
(6*10)1/2
60*1/2
30
Select the correct answer.
What is the general form of the equation for the given circle?
A.
x2 + y2 − 8x − 8y + 23 = 0
B.
x2 + y2 − 8x − 8y + 32 = 0
C.
x2 + y2 − 4x − 4y + 23 = 0
D.
x2 + y2 + 4x + 4y + 9 = 0
Answer:
B hope I helped.
Step-by-step explanation:
write various of the equation of a line that passes through (-6, 3) and has a slope of - 1/3
part 1:write the equation in point slope form
part 2: rewrite the equation in slope intercept form
part 3: rewrite the equation in a standard form
Answer:
[tex]\large\boxed{y-3=-\dfrac{1}{3}(x+6)-\text{point-slope form}}\\\boxed{y=-\dfrac{1}{3}x+1-\text{slope-intercept form}}\\\boxed{x+3y=3-\text{standard form}}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have
[tex]m=-\dfrac{1}{3},\ (-6,\ 3)\to x_1=-6,\ y_1=3[/tex]
Substitute:
[tex]y-3=-\dfrac{1}{3}(x-(-6))\\\\y-3=-\dfrac{1}{3}(x+6)[/tex]
Convert to the slope-intercept form
[tex]y=mx+b[/tex]
[tex]y-3=-\dfrac{1}{3}(x+6)[/tex] use the distributive property
[tex]y-3=-\dfrac{1}{3}x-2[/tex] add 3 to both sides
[tex]y=-\dfrac{1}{3}x+1[/tex]
Convert to the standard form
[tex]Ax+By=C[/tex]
[tex]y=-\dfrac{1}{3}x+1[/tex] multiply both sides by 3
[tex]3y=-x+3[/tex] add x to both sides
[tex]x+3y=3[/tex]
9⁄11 = ?⁄22
A. 4
B. 18
C. 12
D. 9
Answer:
B; 18
Step-by-step explanation:
9/11 = 18/22
Answer:
the correct answer will be D) 9
Step-by-step explanation:
Rationalize the denominator- 12x/√x-10
ANSWER
[tex]\frac{ - 12x \sqrt{x} - 120x}{ x - 100} [/tex]
EXPLANATION
The given function is
[tex] \frac{ - 12x}{ \sqrt{x} - 10 } [/tex]
In the denominator we have
[tex] \sqrt{x} - 10[/tex]
The conjugate of this surd is
[tex] \sqrt{x} + 10[/tex]
To rationalize this function, we multiply both the numerator and the denominator by the conjugate surd.
[tex]\frac{ - 12x (\sqrt{x} + 10)}{ (\sqrt{x} - 10)(\sqrt{x} + 1)} [/tex]
We apply the identity
[tex] (a + b)(a - b) = {a}^{2} - {b}^{2}[/tex]
in the denominator.
This implies that,
[tex]\frac{ - 12x (\sqrt{x} + 10)}{ (\sqrt{x})^{2} - {10}^{2} } [/tex]
[tex]\frac{ - 12x \sqrt{x} - 120x}{ x - 100} [/tex]
An automobile's radiator has a capacity of fifteen quarts, and it currently contains twelve quarts of a thirty percent antifreeze solution. How many quarts of pure antifreeze must be added to strengthen the solution to forty percent?
2 quarts
3 quarts
4 quarts
Answer:
2 quarts
Step-by-step explanation:
We know that an automobile's radiator has a capacity of fifteen quarts and currently carries twelve quarts of a thirty percent antifreeze solution.
We are to find the number of quarts of pure antifreeze that must be added to strengthen the solution to forty percent.
We can write the following equation for this and solve it:
[tex] 12 + x = y \\ 12 (.30) + 1 x = y ( . 4 0 ) [/tex]
[tex]3.6 + x = 0.4y[/tex]
[tex]0.4(12 + x) = 3.6 + x&\\4.8 + 0.4x = 3.6 + x[/tex]
[tex]x-0.4x=4.8-3.6[/tex]
[tex]0.6x=1.2[/tex]
[tex]x=2[/tex]
Therefore, 2 quarts are needed.
Which linear function has the same slope as the one that is represented by the table?
Answer:
-1/5x +1/2
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Answer:
b.[tex]y=-\frac{1}{5}x+\frac{1}{2}[/tex]
Step-by-step explanation:
We have to find the linear which has same slope as the slope represented by the table.
Slope formula :m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
By using the formula and substitute [tex]y_1=\frac{1}{5},y_2=\frac{7}{50},x_1=-\frac{1}{2},x_2=-\frac{1}{5}[/tex]
Slope=[tex]\frac{\frac{7}{50}-\frac{1}{5}}{-\frac{1}{5}+\frac{1}{2}}[/tex]
Slope=[tex]\frac{-\frac{3}{50}}{\frac{3}{10}}[/tex]
Slope=[tex]-\frac{3}{50}\times \frac{10}{3}[/tex]
Slope=[tex]-\frac{1}{5}[/tex]
a.[tex]y=-\frac{1}{2}x+\frac{1}{10}[/tex]
Compare with
[tex]y=mx+b[/tex]
we get m=[tex]-\frac{1}{2}[/tex]
Slope=[tex]-\frac{1}{2}[/tex]
Hence, option A is false.
b.[tex]y=-\frac{1}{5}x+\frac{1}{2}[/tex]
Slope of given function=[tex]-\frac{1}{5}[/tex]
It is true.
c.[tex]y=\frac{1}{5}x-\frac{1}{2}[/tex]
Slope of given function=[tex]\frac{1}{5}[/tex]
Hence, option is false.
d.[tex]y=\frac{1}{2}x-\frac{1}{10}[/tex]
Slope of given function=[tex]\frac{1}{2}[/tex]
Hence, option is false.
A triangular flag has an area of 493 square meters and a height of 17 meters. What is the length of the base
Answer:
58 meters
Step-by-step explanation:
We are looking for the length of the base of a triangle, given the height and area. The formula for the area of a triangle
A=1/2 bh
relates A= the area, b= length of the base, and h= the height of a triangle, so this is the formula we should use.
We are given that the area of the triangle is A=493 and the height h=17. Substitute this information into the formula and solve for b to find
A=493
493=1/2⋅b⋅17
493=17/2b
58=b
The length of the base is 58 meters.
The length of the base of the triangle is 58 meters.
Given,
A triangular flag has an area of 493 square meters and a height of 17 meters.
We need to find what is the length of the base.
What is the area of a triangle?The area is given by:
= 1/2 x base x height
Find the area of the triangle.
Area = 493 square meters
Height = 17 meters
Area = 1/2 x base x height
493 square meters = 1/2 x base x 17 meters
Multiply 2 on both sides.
2 x 493 = 2 x 1/2 x base x 17
986 = base x 17
Dividing both sides by 17.
986 / 17 = base
Base = 58 meters.
Thus the length of the base of the triangle is 58 meters.
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simplify -|-5+2|
thanks please!
Answer:
-3
Step-by-step explanation:
First, solve what's inside the absolute value lines. -5+2=-3
Because it's in absolute value lines, the negative becomes a positive so |-3|=3
The result is -3 (because we still have that negative sign outside the absolute value lines.
f(x) = 3x - 12, what is (2)?
Answer:
f(2) = -6
Step-by-step explanation:
f(x) = 3x - 12
Plug in 2 for x & solve:
f(2) = 3(2) - 12
Remember to follow PEMDAS. First multiply, then subtract:
f(2) = 3(2) - 12
f(2) = 6 - 12
f(2) = -6
f(2) = -6 is your answer.
~
How many solutions does the following system of equations have?
y=5/2x+2
2y= 5x +4
Answer:
infinite solutions
Step-by-step explanation:
y=5/2x+2
2y= 5x +4
Multiply the first equation by 2
y = 5/2 x +2
2y = 5/2 *2 x +2 *2
2y = 5x +4
Since this is identical to the second equation (they are the same), the system of equations has infinite solutions
All steps for: x/x-2 + x-1/x+1= -1
Answer:
[tex]\large\boxed{x=0\ \vee\ x=1}[/tex]
Step-by-step explanation:
[tex]Domain:\\\\x-2\neq0\ \wedge\ x+1\neq0\\\\x\neq2\ \wedge\ x\neq-1\\\\\boxed{D:\ x\in\mathbb{R}-\{-1,\ 2\}}\\\\=============================[/tex]
[tex]\dfrac{x}{x-2}+\dfrac{x-1}{x+1}=-1\qquad\text{subtract}\ \dfrac{x-1}{x+1}\ \text{from both sides}\\\\\dfrac{x}{x-2}=-1-\dfrac{x-1}{x+1}\\\\\dfrac{x}{x-2}=\dfrac{-(x+1)}{x+1}+\dfrac{-(x-1)}{x+1}\\\\\dfrac{x}{x-2}=\dfrac{-(x+1)-(x-1)}{x+1}\\\\\dfrac{x}{x-2}=\dfrac{-x-1-x+1}{x+1}\\\\\dfrac{x}{x-2}=\dfrac{-2x}{x+1}\qquad\text{cross multiply}[/tex]
[tex]x(x+1)=-2x(x-2)\qquad\text{use the distributive property}\\\\(x)(x)+(x)(1)=(-2x)(x)+(-2x)(-2)\\\\x^2+x=-2x^2+4x\qquad\text{add}\ 2x^2\ \text{to both sides}\\\\3x^2+x=4x\qquad\text{subtract 4x from both sides}\\\\3x^2-3x=0\qquad\text{distributive}\\\\3x(x-1)=0\iff 3x=0\ \vee\ x-1=0\\\\x=0\in D\ \vee\ x=1\in D[/tex]
Answer:
Step-by-step explanation:
I'm taking this to mean
x/(x-2) + (x-1)/(x+1) = -1
Multiply through by (x - 2)*(x + 1) to get rid of the denominator on the left.
x(x + 1) + (x - 1)(x - 2) = -1 * (x - 2)(x + 1)
Remove the brackets on the left and right.
Be careful about the right side. Do it in two steps (or three)
x^2 + x + x^2 - 3x + 2 = - (x^2 - 2x + x - 2)
2x^2 - 2x + 2 = - (x^2 - x - 2)
2x^2 - 2x + 2 = - x^2 + x + 2
Bring the right side to the left
2x^2 - 2x + 2 + x^2 - x - 2 = 0
3x^2 - 3x = 0
Factor this
x*(3x - 3) =0
x = 0
3x - 3 = 0
Add 3 to both sides.
3x = 3
Divide by 3
x = 3/3
So either x = 0
or
x = 1
Just to confirm that that is correct, a graph is included which shows the x roots are 0 and 1
Which linear inequality is represented by the graph?
Answer:
Step-by-step explanation:
In this question we will find the equation of the dotted line first.
Since this line passes through two pints (0, 2) and (-3, -7)
So slope of the line will be m = [tex]\frac{y-y'}{x-x'}[/tex]
= [tex]\frac{-7-2}{-3-0}[/tex]
= [tex]\frac{-9}{-3}[/tex]
= 3
y-intercept of the line is c = 2
Now we will put these values in the standard form of the equation
y = mx + c
y = 3x + 2
Now we will check the inequality shown by shaded region
we take a point from shaded region and plug in the value of x and y.
For point ( -2, 0) y = (-2)(2)+2
= -4 + 2 = -2 and 0>-2
So there should be the sign of greater than.
Therefore, inequality will be y > 3x + 2
Linear inequality represented by the graph is y > 3x +2 and this can be determine by using the slope intercept form.
Given :
Two points - (0 , 2) and (-3 , -7)
Slope of the line can be calculated as follows:
[tex]m = \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-7-2}{-3-0}=3[/tex]
y intercept is 2.
Now we know that the slope intercept form is given by:
y = mx + c
y = 3x + 2 --- (1)
To check the inequality we take a point from the shaded region and plug in the value of x and y.
At Point (-3,0), equation (1) can be given by:
y = -9 + 2 = -7 < 0
Than inequality must be y > 3x + 2.
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15 points with easy explanation please
Answer:
that would be 38 degrees
Step-by-step explanation:
Answer:
m∠2 = 38°
Explanation:
m∠2 and 38° are corresponding angles; therefore, they are equivalent.
What is the factored form of 2x^3 + 4x^2 - 4
Answer:
2 ( x ^3 + 2 x^ 2 − 2 )
Step-by-step explanation:
Factor 2 out of
2 x^ 3 + 4 x^ 2 − 4 .
Rachel received a $90 gift card for a coffee store. She used it in buying some coffee that cost $7.74 per pound. After buying the coffee, she had $66.78 left on her card. How many pounds of coffee did she buy?
Answer:
3 pounds
Step-by-step explanation:
type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the given function.
pic below
Change f(x) to y , switch x and y , and solve for y.
The resulting function may be written as:[tex]f^{-1}x=\dfrac{\ln (x+4)}{2}[/tex]
Step-by-step explanation:We know that while finding the inverse of a function the following steps are to be followed:
We first put f(x)=yThen we interchange x and y in the expression.and then we finally solve for y.We are given a function f(x) by:
[tex]f(x)=e^{2x}-4[/tex]
Now, we put
[tex]f(x)=y[/tex]
i.e.
[tex]e^{2x}-4=y[/tex]
Now, we interchange x and y as follows:
[tex]e^{2y}-4=x[/tex]
and finally we solve for y
i.e.
[tex]e^{2y}=x+4[/tex]
Taking logarithmic function both the side of the equation we get:
[tex]2y=\ln (x+4)\\\\i.e.\\\\y=\dfrac{\ln (x+4)}{2}[/tex]
i.e.
[tex]f^{-1}x=\dfrac{\ln (x+4)}{2}[/tex]
The mean monthly rent of students at Oxnard University is $890 with a standard deviation of $206. John's rent is $1,395. What is his standardized z-score?
Answer:
$299
Step-by-step explanation:
Rent+standard deviation 890+206= $1,096
John's rent: $1,395
Z-score: 1395 - 1096=$299
Answer: 2.4515
Step-by-step explanation:
Given : The mean monthly rent of students at Oxnard University is [tex]\mu=\$890[/tex] with a standard deviation of [tex]\sigma=\$206[/tex]
Using the formula , [tex]z=\dfrac{x-\mu}{\sigma}[/tex], we have the standardized z-value for x= 1395 as
[tex]z=\dfrac{1395-890}{206}=2.45145631068\approx2.4515\ \text{ [To the nearest four decimal places.]}[/tex]
Hence, the standardized z-score = 2.4515
Which equation can be used to determine the reference angle, r, if 0=7 pi/12?
Answer:
[tex]r=180-\frac{7\pi }{12}[/tex]
Step-by-step explanation:
To find the reference angle of a given angle, first of all, the quadrant of the given angle is determined.
So for 7pi/12
The quadrant is 2nd.
For the angle belonging to 2nd quadrant the equation for reference angle will be:
r=180 - theeta
[tex]r=180-\frac{7\pi }{12}[/tex]
Which linear function represents the line given by the point slope equation y+1=-3(x-5)
To find the linear form of a point-slope equation, simply solve for y:
y+1=-3(x-5)
*Distribute the -3*
y+1=-3x+15
*Subtract 1 from both sides*
y=-3x+14
Hope this helps!!
Answer:
f(x) = –3x + 14
Step-by-step explanation:
Felix wrote several equations and determined that only one of the equations has no solution. Which of these equations has no solution?
Answer:
3(x-2)+x=4x+6
Step-by-step explanation:
case 1) we have
3(x-2)+x=4x-6
Solve for x
3x-6+x=4x-6
4x-6=4x-6
0=0 ----> is true for any value of x
therefore
The equation has infinite solutions
case 2) we have
3(x-2)+x=2x-6
3x-6+x=2x-6
4x-2x=-6+6
2x=0
x=0
case 3) we have
3(x-2)+x=3x-3
3x-6+x=3x-3
4x-3x=-3+6
x=3
case 4) we have
3(x-2)+x=4x+6
3x-6+x=4x+6
4x-4x=6+6
0=12 ------> is not true
therefore
The equation has no solution
Answer:
3(x-2)+x=4x+6Step-by-step explanation:
The first equation is the one that doesn't have solution. Let's demonstrate this:
[tex]3(x-2)+x=4x+6\\3x-6+x=4x+6\\4x-6=4x+6\\4x-4x=6+6\\0=12[/tex]
As you can observe, the equation doesn't have any solutions, because it result in a false statement.
If we solve the other equations, we would have:
[tex]3(x-2)+x=2x-6\\3x-6+x=2x-6\\4x-6=2x-6\\4x-2x=-6+6\\2x=0\\x=0[/tex]
[tex]3(x-2)+x=3x-3\\3x-6+x=3x-3\\4x-3x=-3+6\\x=3[/tex]
[tex]3(x-2)+x=4x-6\\3x-6+x=4x-6\\4x-6=4x+6\\6=6[/tex]
The last equation has infinite solutions.
Therefore, the only one that doesn't have any solutions is
3(x-2)+x=4x+6
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form.
Answer:
5/12
Step-by-step explanation:
First find the probability on the first roll
The possible results are 1,2,3,4,5,6
evens: 2,4,6
not 2 = 1,3,4,5,6
P(even)= number of evens/total = 3/6 = 1/2
P (not 2) = number of results not 2/ total = 5/6
Since the rolls are independent (do not depend on each other), we can multiply the probabilities
P(even, then not 2) = 1/2 * 5/6 = 5/12
Add.
(2x-7)+(3x - 1)
Answer:
5x - 8
Step-by-step explanation:
(2x - 7) + (3x - 1)
We would first solve for whatever is in the parenthesis, but there is a variable with both expressions, so we need to remove it to simplify:
2x - 7 + 3x - 1
Now combine like terms and simplify:
2x + 3x - 7 - 1
So the answer is 5x - 8
Final answer:
To add the expressions (2x-7) and (3x - 1), simply combine the like terms, resulting in 5x - 8.
Explanation:
When you are tasked with adding the expressions (2x-7) and (3x - 1), you combine like terms. This means you add the coefficients of the same powers of x together and combine the constants. To demonstrate:
(2x-7) + (3x - 1) = (2x + 3x) + (-7 - 1)
You combine the x terms:
2x + 3x = 5x
And then combine the constants:
-7 - 1 = -8
Thus, the sum of the expressions is:
5x - 8