|x - 2| + 10 = 12
|x - 2| = 12 -10
|x - 2| = 2
There are 2 solutions:
x-2 = 2 and x-2 = -2
Solve each:
x = 2+2
x = 4
x-2=-2
x =-2+2
x=0
solution: x=0 and x = 4
Solve the following system of linear equations by graphing:4.Ex+3y54 9- 5858615+cilo=Answer 2 PointsKeypadKeyboard ShortcutsGraph the linear equations by writing the equations in slope-intercept form:y =Ixty =IxtIdentify the appropriate number of solutions. If there is a solution, give thepoint:O One SolutionO No SolutionO Infinite Number of Solutions
We have a system of equations:
[tex]\begin{gathered} -\frac{4}{5}x+3y=-\frac{58}{5} \\ \frac{4}{3}x+\frac{9}{5}y=\frac{86}{15} \end{gathered}[/tex]We have to write the equations in slope-intercept form.
We start with the first equation:
[tex]\begin{gathered} -\frac{4}{5}x+3y=-\frac{58}{5} \\ 3y=-\frac{58}{5}+\frac{4}{5}x \\ 5\cdot3y=4x-58 \\ 15y=4x-58 \\ y=\frac{4}{15}x-\frac{58}{15} \end{gathered}[/tex]For the second equation we get:
[tex]\begin{gathered} \frac{4}{3}x+\frac{9}{5}y=\frac{86}{15} \\ \frac{9}{5}y=\frac{86}{15}-\frac{4}{3}x \\ y=\frac{5}{9}\cdot\frac{86}{15}-\frac{5}{9}\cdot\frac{4}{3}x \\ y=\frac{86}{9\cdot3}-\frac{20}{27}x \\ y=-\frac{20}{27}x+\frac{86}{27} \end{gathered}[/tex]To graph the equations we need two points. We can easily identify the y-intercept from the equations, but we have to identify one more point for each equation.
We can give a value to x and find the corresponding value of y.
Then, for example we can calculate y for x = 1 in the first equation:
[tex]\begin{gathered} y=\frac{4}{15}(1)-\frac{58}{15} \\ y=\frac{4}{15}-\frac{58}{15} \\ y=-\frac{54}{15} \end{gathered}[/tex]Then, for the first equation we know the points (0, -58/15) and (1, -54/15).
For the second equation we can do the same, by giving a value of 1 to x (NOTE: we can give any arbitrary value to x, it does not have to be the same for both equations) and calculate y:
[tex]\begin{gathered} y=-\frac{20}{27}(1)+\frac{86}{27} \\ y=-\frac{20}{27}+\frac{86}{27} \\ y=\frac{66}{27} \end{gathered}[/tex]Now we know the points of the second equation: (0, 86/27) and (1, 66/27).
With such fractions we can not make an accurate graph in paper, as they don't match the divisions of the grid.
We can use approximate decimals values for the fractions and graph the points.
The approximations for the first equation are:
[tex]\begin{gathered} (0,-\frac{58}{15})\approx(0,-3.9) \\ (1,-\frac{54}{15})=(1,-3.6) \end{gathered}[/tex]and for the second equation:
[tex]\begin{gathered} (0,\frac{86}{27})\approx(0,3.2) \\ (1,\frac{66}{27})\approx(1,2.4) \end{gathered}[/tex]We can then graph the equations as:
If we graph the equations with the exact points, we get an intersection point at (7,-2).
This intersection is the unique solution to both equations at the same time, so it is the only solution to the system of equations.
Answer:
The equations in slope-intercept form are:
y = 4/15 x + (-58/15)
y = -20/27 * x + 86/27
The system has only one solution: (7, -2).
The coordinates of the midpoint of GH are M(-2,5) and the coordinates of one endpoint are H(-3, 7).
The coordinates of the other endpoint are(
).
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What are the coordinates of the other endpoint
EXPLANATION :
From the problem, we have segment GH and the midpoint is M(-2, 5).
One of the endpoints has coordinates of H(-3, 7)
and we need to find the coordinates of G(x, y)
The midpoint formula is :
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]where (x1, y1) are the coordinates of G
(x2, y2) = (-3, 7) are the coordinates of H
and (-2, 5) are the coordinates of the midpoint.
Then :
[tex](-2,5)=(\frac{x+(-3)}{2},\frac{y+7}{2})[/tex]We can equate the x coordinate :
[tex]\begin{gathered} -2=\frac{x+(-3)}{2} \\ \\ \text{ cross multiply :} \\ -2(2)=x-3 \\ -4=x-3 \\ -4+3=x \\ -1=x \\ x=-1 \end{gathered}[/tex]then the y coordinate :
[tex]\begin{gathered} 5=\frac{y+7}{2} \\ \\ \text{ cross multiply :} \\ 5(2)=y+7 \\ 10=y+7 \\ 10-7=y \\ 3=y \\ y=3 \end{gathered}[/tex]Now we have the point (-1, 3)
ANSWER :
The coordinates of the other endpoint are G(-1, 3)
x-2Question 8 of 15Use the remainder theorem to find P (2) for P (x)=xª − 3x³ +x−9.-(2,01 mismoSpecifically, give the quotient and the remainder for the associated division and the value of P (2)_Quotient =RemainderP (2)=
8)
The remainder theorem states that when a polynomial P(x) is divided by a linear polynomial x-b, the remainder is given by r=P(b).
Thus, in our case,
[tex]P(2)=2^4-3(2)^3+2-9=16-24+2-9=-15[/tex]Then, the Remainder theorem states that if we divide P(x) by x-2, the remainder will be -15.Calculating the quotient of P(x)/(x-2),
Hence, the answers are[tex]\begin{gathered} Q(x)=x^3-x^2-2x-3 \\ Remainder=-15 \\ P(2)=-15 \end{gathered}[/tex]From the diagram below, we can tell that Δ ABC is similar to ____.
From the diagram, we get that
[tex]\measuredangle ABD\cong\measuredangle ADB.[/tex]By the reflexive property of congruence, we know that:
[tex]\measuredangle A\cong\measuredangle A.[/tex]Therefore, by the Angle-Angle criterion:
[tex]\Delta ABC\sim\Delta ADB.[/tex]Answer: [tex]\Delta ADB.[/tex]A(0,3) B(1,6) C(4,6) D(5,3) rotate it around the origin 270 degrees clockwise
Please answer with the coordinates.
♥
The rule for a rotation by 270° about the origin is (x,y)→(y,−x)
so i guess A?
♥
What is the value of x?
The value of x =20 when the angles given are 3x° and (x+40)°.
Given that,
There a picture with 2 lines.
The angles given are 3x° and (x+40)°.
We have to find the x value.
We the alternative angles are equal in an intersecting angles.
Angles that are in opposition to a transversal connecting two lines are known as alternate angles.
x +40=3x
Taking 40 to right side.
x= 3x-40
Taking 3x to left side.
x-3x=-40
Subtracting x ad 3x
-2x=-40
Divide by -2.
x=20
Therefore, the value of x =20 when the angles given are 3x° and (x+40)°.
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Translate into proportion 16.4 is 45% of what number ?
Given:
16.4 is 45%
[tex]\begin{gathered} 16.4\times\frac{45}{100}=\frac{b}{1} \\ \frac{16.4}{b}=\frac{100}{45} \end{gathered}[/tex]Hence, the required option is D.
Does the point (2, 6) satisfy the inequality 2x + 2y ≥ 16?
yes
no
A new cell phone costs $108.99 in the store. What would your total cost be if the sale tax is 7.5% ? Round your answer to the nearest cent, if necessary.
to calculate the tax we need to multiply the % by the price of the cellphone
7.5%=0.075
108.99*0.075=8.17
and the total cost is:
$108.99 + $8.17= 117.16
So the answer is: $
4. Find the midpoint of DK, given the coordinates D (-10, -4) and K is located at the origin.m:|| m:1 m:Midpoint:Equation of the line:
The midpoint between two coordinates can be calculated using the equation
[tex]m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Point D has the coordinates (-10, -4). The problem stated that point K is located at the origin, hence, we can say that its coordinates are (0, 0).
Using the formula stated above to solve the coordinates of the midpoint, we get
[tex]\begin{gathered} m=(\frac{-10+0}{2},\frac{-4+0}{2}) \\ m=(\frac{-10}{2},-\frac{4}{2}) \\ m=(-5,-2) \end{gathered}[/tex]Answer: The midpoint of the line segment DK is located at (-5,-2).
If Martha is x years old and her mother is 5 times older and the sum of their age is 88, how old is Martha?
Let Martha age = x years old
Since her mother's age is 5 times her age, then
Her mother = 5(x) = 5x years old
Since the sum of their ages is 84, then
Add x and 5x, then equate the sum by 84
[tex]\begin{gathered} x+5x=84 \\ 6x=84 \end{gathered}[/tex]Divide both sides by 6 to find x
[tex]\begin{gathered} \frac{6x}{6}=\frac{84}{6} \\ x=14 \end{gathered}[/tex]Martha is 14 years old
I will give brainliest if you help me with this problem not joking
Answer: 9+6+-6+-7
Step-by-step explanation:
im not sure thats my guess tho
Which transformations can be used to carry ABCD ontoitself? The point of rotation is (3, 2). Check all that apply.yB1 23 4 5 6A. Translation four units to the rightB. Dilation by a factor of 2C. Rotation of 180°D. Reflection across the line x = 3
C. Rotation of 180°
D. Reflection across the line x = 3
Explanation:The point of rotation = (3, 2)
From the diagram:
The center of the rectangle = (3, 2)
Note that:
The point of rotation = The center of the rectangle
Therefore, the rectangle ABCD will be reflected across its center, x =3 and y = 2
Also note that ABCD has two lines of symmetry. Therefore, a rotation by 180 degrees will carry ABCD back to itself
the ratio of isabella's money to Shane's money is 5:10.if Isabelle has $55 how much money do Shane have?what about they have together?
Is this correct? If not can u show me how to do it
Given
[tex]k(x+y)=2x-4[/tex]Notice that it is the equation of a line.
Then, since it crosses (10,-2), set x=10 and y=-2 in the given equation, as shown below
[tex]\begin{gathered} x=10,y=-2 \\ \Rightarrow k(10-2)=2*10-4 \\ \Rightarrow k(8)=20-4 \\ \Rightarrow k=\frac{16}{8}=2 \\ \Rightarrow k=2 \end{gathered}[/tex]Thus, the answer is k=2.
help me please asap!!!
The slope of the function is 1/2 and the y - intercept is 2
The standard form of slope-intercept form of line is y = mx + b
where , m is slope of line
and b is y-intercept.
Observing the graph ,
we can say Linear function also passes through two points
At (4,0) on x-axis and at (0,2) on y-axis and
also , the graph is making right angles triangle at (0,0)
Slope of the function = m = Tan∅
Tan∅ = Perpendicular of right triangle / base of triangle
Perpendicular of triangle = 2 unit
and base = 4 unit
Tan∅ = 2/4 = 1/2
Therefore , slope of line = 1/2
equation of line : y = 1/2 x + b
This line is passing through (0,2)
2 = 1/2(0) + b
b = 2
Therefore , the y-intercept = 2
Hence , the equation of line = y = 1/2 x + 2
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using the rule of s-14 - (-2) = -12
We will have:
[tex]-14-(-2)=-12\Rightarrow-14+2=-12\Rightarrow-12=-12[/tex]Solve for y and show steps 75-3.5y-4y=4y+6
Solve for y;
[tex]\begin{gathered} 75-3.5y-4y=4y+6 \\ \text{Collect like terms, which means the values with y would be moved to one side} \\ \text{And the values without y would be moved to the other side} \\ 75-6=4y+4y+3.5y \\ \text{Note that when a positive value moves to the other side of the equation} \\ It\text{ becomes a negative value, and vice versa} \\ 69=11.5y \\ \text{Divide both sides by 11.5} \\ \frac{69}{11.5}=\frac{11.5y}{11.5} \\ 6=y \end{gathered}[/tex]The answer is y equals 6
If the two expressions are equivalent, find value of x
1. Subtract 1/x in both sides of the equation:
[tex]\begin{gathered} \frac{5}{x}-\frac{1}{x}-\frac{1}{3}=\frac{1}{x}-\frac{1}{x} \\ \\ \frac{4}{x}-\frac{1}{3}=0 \end{gathered}[/tex]2. Add 1/3 in both sides of the equation:
[tex]\begin{gathered} \frac{4}{x}-\frac{1}{3}+\frac{1}{3}=0+\frac{1}{3} \\ \\ \frac{4}{x}=\frac{1}{3} \end{gathered}[/tex]3. Multiply both sides of the equation by x:
[tex]\begin{gathered} x\cdot\frac{4}{x}=x\cdot\frac{1}{3} \\ \\ 4=\frac{x}{3} \end{gathered}[/tex]4. Multiply both sides of the equation by 3:
[tex]\begin{gathered} 4\cdot3=\frac{x}{3}\cdot3 \\ \\ 12=x \\ \\ \text{ Rewrite} \\ x=12 \end{gathered}[/tex]Then, the value of x is 12Multiple the binomials (simplify) (y-4)(y-8)
Given
[tex](y-4)(y-8)[/tex]Simplify as shown below
[tex]\begin{gathered} (y-4)(y-8)=y(y-8)-4(y-8)=y^2-8y-4y+(-4)(-8)=y^2-12y+32 \\ \Rightarrow(y-4)(y-8)=y^2-12y+32 \end{gathered}[/tex]The answer is y^2-12y+32
Evaluate the expression when x = 32 and y = 2.
x/14 A. 1/16
B.16/21
D.2
C.4
Answer:
I think its 16/21
Step-by-step explanation:
Answer:
2Step-by-step explanation:
Given x = 14, y = 2x/14
Void "y" because it is not in this equation.= x/14
32/14
= 2.2
≈ 2
Section 5.2-12. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).3x-3y = -6-x+2y = 8
the Given the simultaneous equations
[tex]\begin{gathered} 3x-3y=-6\text{ ------(1)} \\ -x+2y=8\text{ -------(2)} \end{gathered}[/tex]Solving the above equations by substitution method:
Step 1:
From equation 2, make x the subject of the formula
[tex]\begin{gathered} -x+2y=8 \\ \text{making x the subject of formula, we have} \\ x=2y-8\text{ -------(3)} \end{gathered}[/tex]Step 2:
Substitute equation 3 into equation 1
[tex]\begin{gathered} \text{From equation,} \\ 3x-3y=-6 \\ \text{Thus, we have} \\ 3(2y-8)-3y=-6 \\ \text{opening the brackets, we have} \\ 6y-24-3y=-6 \\ \text{collecting like terms, we have} \\ 6y-3y=-6+24 \\ 3y=18 \\ \text{divide both sides by the coefficient of y.} \\ \text{The coefficient of y is 3. Thus,} \\ y=\frac{18}{3}=6 \end{gathered}[/tex]Step 3:
Substitute the value of y in either equation 1 or 2.
[tex]\begin{gathered} \text{From equation 2,} \\ -x+2y=8 \\ \text{Thus,} \\ -x+2(6)=8 \\ -x+12=8 \\ \text{collecting like terms, we have} \\ -x=8-12 \\ -x=-4 \\ x=4 \end{gathered}[/tex]Thus, the values of (x, y) are (4, 6)
Given f(x)=2x-1 and g(x) =x^2 -2A) f(5)B) f(g(3))C) f(a+1) - f(a)D) g(2f(-1))E) g(x+h) -g(x)/h
2x + h
Explanation:
Given the following functions
f(x) = 2x - 1
g(x) = x^2 - 2
We are to simplify the expressionn:
[tex]\frac{g(x+h)-g(x)}{h}[/tex]Substitute the given functions into the expression and simplify
[tex]\begin{gathered} \frac{\lbrack(x+h)^2-2\rbrack-(x^2-2)}{h} \\ \frac{\lbrack\cancel{x^2}^{}+2xh+h^2-\cancel{2}-\cancel{x^2}^{}+\cancel{2}}{h} \\ \frac{2xh+h^2}{h} \end{gathered}[/tex]Factor out "h" from the numerator to have:
[tex]\begin{gathered} \frac{\cancel{h}(2x+h)}{\cancel{h}} \\ 2x+h \end{gathered}[/tex]Hence the simplified form of the expression is 2x + h
identify the rate, base and portion.17% of what number is 60?
For the given question which is;
17% of what number is 60?
We shall begin by determining the value of the number. Let us call the number a.
We can now set up the following equation;
[tex]\begin{gathered} 17\text{ \% of a}=60 \\ 0.17\times a=60 \end{gathered}[/tex]We now divide both sides by 0.17;
[tex]\begin{gathered} \frac{0.17a}{0.17}=\frac{60}{0.17} \\ a=352.9411 \\ \text{Rounded to the nearest whole number,} \\ a=353 \end{gathered}[/tex]So we now have;
"17% of 353 is 60."
The rate is the variable that represents part of the whole and that is 17
The base is the whole number itself which is a 100% value and that is 353
The portion is that part of the whole (base) made up of 17% and that is 60."
ANSWER:
Rate is 17%
Base is 353
Portion is 60
How to find the diagonal side one triangle like the measure with the Pythagorean Theorem
How to find the diagonal side one triangle like the measure with the Pythagorean Theorem
see the attached figure to better understand the p
turn the expression from radical form to exponential expression in fractional form. No need to evaluate just be out in simplest form
To answer this question, we need to remember the next property of radicals:
[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]In this case, we have that:
[tex]\sqrt[3x]{5}[/tex]And we can see that the exponent for 5 is m = 1. Therefore, we can rewrite the expression as follows:
[tex]\begin{gathered} \sqrt[3x]{5}=5^{\frac{1}{3x}} \\ \end{gathered}[/tex]In summary, therefore, we can say that the radical form to an exponential in fractional form is:
[tex]undefined[/tex]Write the percent as decimal 49%
Solution;
Given: The given number in percentage is 49 %
Required: Decimal value of given percentage.
Explanation:
Convert percentage into decimal as follows:
[tex]49\text{ \%=}\frac{49}{100}[/tex][tex]49\text{ \%=0.49}[/tex]Therefore, the required answer is 0.49
Final answer: The de
If ∠2 = 50° and lines a and b are parallel, which of the following angles cannot be determined? *-∠1-∠3-∠4-∠8-None of the above
If you have the angle 2, you can deduce its the supplement,which is the angle 4. In this case the supplement is equal to 130°.
Angle 2 and angle 6 are corresponding angles, so they have the same measure.
Angle 4 and angle 8 are corresponding, so they have the same measure.
Angle 2 and angle 1 are vertically opposite angles, so they have the same measure.
Angle 5 and angle 6 are vertically opposite angles, so they have the same measure.
Angle 7 and angle 8 are vertically opposite angles, so they have the same measure.
Angle 4 and angle 3 are vertically opposite angles, so they have the same measure.
Therefore the answer is None of the above.
A circular arc has measure of 4 cm and is intercepted by a central angle of 73°. Find the radius r of the circle. Do not round any intermediate computations, and round your answer to the nearest tenth.r= __ cm
The arc lenghr is given by:
[tex]s=r\theta[/tex]where s is the arc lenght, r is tha raidus and theta is the angle measure in radians. Since in our problem the angle is given in degrees we have to convert it to radians, to do this we have to multiply the angle by the factor:
[tex]\frac{\pi}{180}[/tex]Then:
[tex]\theta=(73)(\frac{\pi}{180})[/tex]Plugging the value of the arc lenght and the angle in the first formula, and solving for r we have:
[tex]\begin{gathered} 4=r(73)(\frac{\pi}{180}) \\ r=\frac{4\cdot180}{73\cdot\pi} \\ r=3.1 \end{gathered}[/tex]Therefore, the radius of the circle is 3.1 cm.
In △GHI, m∠G = (9x - 2), m∠H = (3x - 19), and m∠I = (3x + 6)". Find m∠G.
Answer:
m∠G = 115 degrees
Explanation:
The sum of the angles in a triangle is 180 degrees.
In triangle GHI:
[tex]\begin{gathered} m\angle G+m\angle H+m\angle I=180\degree \\ \implies9x-2+3x-19+3x+6=180\degree \end{gathered}[/tex]First, solve for x:
[tex]\begin{gathered} 9x+3x+3x-2-19+6=180\degree \\ 15x-15=180\degree \\ 15x=180+15 \\ 15x=195 \\ x=\frac{195}{15} \\ x=13 \end{gathered}[/tex]Therefore, the measure of angle G is:
[tex]\begin{gathered} m\angle G=9x-2 \\ =9(13)-2 \\ =117-2 \\ m\angle G=115\degree \end{gathered}[/tex]The measure of angle G is 115 degrees.