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Question:
What is the solution to the linear equation?
[tex]x - \frac{2}{3}x - \frac{1}{2} = \frac{1}{3} + \frac{5}{6}x[/tex]
Answer:
[tex]x = \frac{-5}{3}[/tex]
Step-by-step explanation:
Given
[tex]x - \frac{2}{3}x - \frac{1}{2} = \frac{1}{3} + \frac{5}{6}x[/tex]
Required
Simplify
[tex]x - \frac{2}{3}x - \frac{1}{2} = \frac{1}{3} + \frac{5}{6}x[/tex]
Add [tex]\frac{1}{2}[/tex] to both sides
[tex]x - \frac{2}{3}x - \frac{1}{2} + \frac{1}{2} = \frac{1}{3} + \frac{5}{6}x + \frac{1}{2}[/tex]
[tex]x - \frac{2}{3}x = \frac{1}{3} + \frac{5}{6}x + \frac{1}{2}[/tex]
Subtract [tex]\frac{5}{6}x[/tex] from both sides
[tex]x - \frac{2}{3}x - \frac{5}{6}x= \frac{1}{3} + \frac{5}{6}x + \frac{1}{2} - \frac{5}{6}x[/tex]
[tex]x - \frac{2}{3}x - \frac{5}{6}x= \frac{1}{3} + \frac{1}{2} + \frac{5}{6}x- \frac{5}{6}x[/tex]
[tex]x - \frac{2}{3}x - \frac{5}{6}x= \frac{1}{3} + \frac{1}{2}[/tex]
Take LCMs
[tex]\frac{6x - 4x -5x}{6}= \frac{2+3}{6}[/tex]
[tex]\frac{-3x}{6}= \frac{5}{6}[/tex]
Multiply both sides by 6
[tex]6 * \frac{-3x}{6}= \frac{5}{6} * 6[/tex]
[tex]-3x= 5[/tex]
Divide both sides by -3
[tex]\frac{-3x}{-3}= \frac{5}{-3}[/tex]
[tex]x = \frac{5}{-3}[/tex]
[tex]x = \frac{-5}{3}[/tex]
Answer:
x=-5
Step-by-step explanation:
Which is the value of the expression (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed? 1 2 8 10
Answer: B: 2
Step-by-step Explanation
Answer:
C, 8
Step-by-step explanation:
I took the test on edge 2021
The average wage for an electrician in CA is $25.47/hour. That is 11% above the national average. What is the national average?
Answer:
$22.95/hour.
Step-by-step explanation:
It is given that the average wage for an electrician in CA is $25.47/hour. That is 11% above the national average.
Let as consider x be the national average.
11% above the national average is
[tex]x+\dfrac{11}{100}x=x+0.11x=1.11x[/tex]
The average wage for an electrician in CA is 11% above the national average. So,
[tex]1.11x=25.47[/tex]
Divide both sides by 1.11.
[tex]x=\dfrac{25.47}{1.11}[/tex]
[tex]x=22.945945...[/tex]
[tex]x=22.95[/tex]
Therefore, the national average is $22.95/hour.
Answer: 22.95
Step-by-step explanation:
For the parallelogram ABCD the extensions of the angle bisectors AG and BH intersect at point P. Find the area of the parallelogram, if DG = GH, AB = 39 in, GP = 12 in.
Answer:
The area of a parallelogram is 360 in.²
Step-by-step explanation:
Where DG = GH
GP = 12 in.
AB = 39 in.
∠DAB + ∠ABC = 180° (Adjacent angles of a parallelogram)
Whereby ∠DAB is bisected by AG and ∠ABC is bisected by BH
Therefore, ∠GAB + ∠HBA = 90°
Hence, ∠BPA = 90° (Sum of interior angles of a triangle)
[tex]cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{AP}{39} = \dfrac{GP}{GH} =\dfrac{12}{GH}[/tex]
We note that ∠AGD = ∠GAB (Alternate angles of parallel lines)
∴ ∠AGD = ∠AGD since ∠AGD = ∠GAB (Bisected angle)
Hence AD = DG (Side length of isosceles triangle)
The bisector of ∠ADG is parallel to BH and will bisect AG at point Q
Hence ΔDAQ ≅ ΔDGQ ≅ ΔGPH and AQ = QG = GP
Hence, AP = 3 × GP = 3 × 12 = 36
[tex]cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{36}{39}[/tex]
[tex]\angle GAB = cos^{-1} \left (\dfrac{36}{39} \right )[/tex]
∠GAB = 22.62°
[tex]cos(\angle GAB) = \dfrac{36}{39} = \dfrac{12}{GH}[/tex]
[tex]GH = \dfrac{39}{36} \times {12}[/tex]
GH = 13 in.
∴ AD 13 in.
BP = 39 × sin(22.62°) = 15 in.
GH = √(GP² + HP²)
∠DAB = 2 × 22.62° = 45.24°
The height of the parallelogram = AD × sin(∠DAB) = 13 × sin(45.24°)
The height of the parallelogram = 120/13 = 9.23 in.
The area of a parallelogram = Base × Height = (120/13) × 39 = 360 in.²
Answer:
360 in2
Step-by-step explanation:
The figure ABCD is a parallelogram, so the side AB is parallel to the side DC, and that means the angle mBAG is equal the angle mHGP.
The angles mHGP and mAGD are vertically opposite angles, so mHGP = mAGD.
The angle mDAG is equal the angle mBAG, so mDAG = mBAG = mHGP = mAGD
The angles mDAG and mAGD are equal, so the triangle DAG is isosceles, that means the side DG is equal the side DA.
In the same way, we can find that the angle mCBH is equal the angle mBHC, so triangle BCH is isosceles, meaning that side BC (which is equal side AD) is equal side CH, so we have that:
DG + GH + HC = AB = 39
GH + GH + GH = 39
GH = 13
in the parallelogram we have the property:
mDAB + mABC = 180°
We have that mGAB = mDAB/2 and mABH = mABC/2, so using this information for the sum of internal angles of triangle APB, we have:
mGAB + mABH + mBPA = 180
mDAB/2 + mABC/2 + mBPA = 180
(180/2) + mBPA = 180
mBPA = 90°
If the triangle APB is a right triangle, we can find the cosine of the angle mHGP:
cos(mHGP) = GP / GH = 12 / 13
Then, we can find the sine of mHGP using:
sin(mHGP)^2 + cos(mHGP)^2 = 1
sin(mHGP)^2 + 144/169 = 1
sin(mHGP)^2 = 25/169
sin(mHGP) = 5/13
If we draw the height of the triangle GPH relative to the side GH, we have:
sin(mHGP) = height / GP
5 / 13 = height / 12
height = 60/13
The triangles GPH and APB are similar (using the case angle-angle), so we can use this relation to find the height 'h2' of the triangle APB:
height / (h2+height) = GH / AB
(60/13) / (h2 + (60/13)) = 13/39 = 1/3
180 / 13 = h2 + (60/13)
h2 = 120/13
Then the area of the parallelogram is:
Area = AB * h2 = 39 * 120/13 = 360 in2
how to solve 4(7-3x)=7(4-2x)
Answer:
Step-by-step explanation:
First, you distribute the 4 and 7 to the stuff inside the parentheses 28 - 12x = 28 - 14x then add 28 to both sides -12x = -14x then add 14x to both sides 2x = 0 then divide both sides by 2 x = 0
Answer:
x=0
Step-by-step explanation:
4(7-3x)=7(4-2x)
Distribute
28 -12x = 28 -14x
Subtract 28 from each side
-12x = -14x
Add 14x to each side
-12x+14x = -14x+14x
2x=0
x =0
Which comes first? Intermediate algebra, or algebra?
Answer
Algebra
Step-by-step explanation:
Intermediate is the same as algebra 2
Answer:
Step-by-step explanation:
Algebra
Find the other endpoint of the line segment with the given endpoint and midpoint.
Find the distance between the two x values: -10 to -7 is 3 units, so add to the midpoint: -7 + 3 = -4
The x value is -4
Now do the same for y:
7 to -3 is 10 units
Because the midpoint is less than the end point subtract:
Y = -3 -10 = -13
Y = -13
The endpoint would be (-4, -13)
please help, i need to pass. which function represents the inverse of function f below?
Answer:
B
Step-by-step explanation:
If you switch the x and y you can solve for the inverse by solving for y like this:
x=3y+5
3y=x-5
y=(x-5)/3
which can be rewritten as B.
A number, y, is equal to the difference of a larger number and 3. The same number is one-third of the sum of the larger number and 9. Which equations represent the situation? A. x + y = 3 and x minus 3 y = negative 27 B. x + y = 3 and x minus 3 y = negative 9 C. x minus y = 3 and x minus 3 y = negative 27 D. x minus y = 3 and x minus 3 y = negative 9
Answer:
D. x - y = 3 and x - 3 y = - 9
Step-by-step explanation:
The descriptions above describe the equation of choice D, so I pick this answer.
Answer:
D
Step-by-step explanation:
just took the test
Penny sells knitted scarves for 12$ each. The cost of supplies to make each scarf is x dollars. How much profit will Penny make if she sells y scarves?
Answer:
If I'm guessing, you're supposed to write an equation. So the answer would be yx + 12y.
Step-by-step explanation:
Answer:
the answer is y(12-x)
Step-by-step explanation:
i took the text and it said i got it right hope i helped have a great day/night and so soorry if i get it wrong byee
Suppose for every dollar change in household wealth, consumption expenditures change by $0.05. If real household wealth declines by $45 billion, potential GDP is $120 billion, and the multiplier effect for the second year after an expenditure shock is 1.1, what is the total change in output relative to the potential for the second year?
Given y = (2x + 3)2, what is the standard form of the given quadratic equation.
Answer:
[tex]y=4x^2+12x+9[/tex]
Step-by-step explanation:
Perform the square of the binomial, combine like terms, and then write the remaining expression in decreasing order of powers of x:
[tex]y=(2x+3)^2\\y=(2x+3)\,(2x+3)\\y=4x^2+6x+6x+9\\y=4x^2+12x+9[/tex]
How many people are on both the golf team and the swim team?
11
6
5
3
Answer:
3 people
Step-by-step explanation:
3 people as per picture
Answer:
3 people's are on both the golf team and the swim team
When constructing an angle bisector of an angle, the first step is to draw
Question 6 options:
A)
two arcs in the interior of the angle.
B)
a segment bisector of both the sides of the angle.
C)
a line passing through the intersection of the arcs and the vertex.
D)
an arc using the vertex as the center, intersecting both sides of the angle.
Drag the expressions to show the order of their quotients from least to greatest
Answer:
A,D,BC
Step-by-step explanation:
Evaluate f(-4) for the function f(x) = 5 - X.
Answer:
9Solution,
[tex]f(x) = 5 - x \\ f( - 4) = 5 - ( - 4) \\ \: \: \: \: \: \: \: \: \: \: \: = 5 + 4 \\ \: \: \: \: \: \: \: \: \: = 9[/tex]
hope this helps....
Good luck on your assignment...
A student is asked to find the length of the hypotenuse of a right triangle. The length of one leg is 26
centimeters, and the length of the other leg is 24 centimeters. The student incorrectly says that the
length of the hypotenuse is 7.1 centimeters. Answer parts a and b.
a. Find the length of the hypotenuse of the right triangle to the nearest tenth of a centimeter.
Answer:
c ≅ 35.4 cm.
Step-by-step explanation:
To find the length of the Hypotenuse of a triangle, the formula a² + b² = c² will need to be used. Therefore:
26² + 24² = c² (c is the hypotenuse)
1252 = c²
√1252 = c
c ≈35.38
Round to tenths place:
c ≅ 35.4 cm. This is the Hypotenuse of the triangle.
What is the square root of -1?
N
-
1
Answer:
there is no square root for -1
because it is there only for natural numbers
not sure because i just learned but ik that there isn't any square root for -1
the bearing of m from N is 70 degree what is the bearing gor N from M ?
Answer:
250°
Step-by-step explanation:
The bearing of N from M is 70° + 180° = 250°
Which expressions are equivalent to -3(2w+6)-4
Answer:
B
Step-by-step explanation:
Am equivalent expression would be 2(-3w+(-11))= -6w-22
Sorry for my first answer
Mark wishing brainliest
Answer:
B. 2(-3w+(-11))
Step-by-step explanation:
-3(2w+6)-4=
-6w-18-4=
-6w-22=
2(-3w+(-11))
Another line “r” is perpendicular to the line 3y = 6x + 9. Find the gradient of the line "r" show your working
Answer:
Line r has a gradient of -1/2
Step-by-step explanation:
Perpendicular lines have a gradient of negative reciprocal to each other such that multiplying both the slopes give -1
=> Gradient of this line = 2
=> Gradient of line perpendicular to it = [tex]\frac{-1}{2}[/tex]
Multiplying both gradients:
=> 2 * [tex]\frac{-1}{2}[/tex]
=> -1
(SO They are perpendicular!)
Which expression is a perfect cube?
12x12y18
O 12x27,125
O 64x15y18
64x27
27,125
Answer:
D: 64 x^27 y^125
Step-by-step explanation:
You can use either a calc or your knowledge of cube roots. I will be using knowledge.
You can automatically rule out a and b as if you take the cube root of 12, no whole number comes out. You are left with c and d. Option D is correct because the cube root of 64 is a whole number (4), the cube root of 27 is a whole number (3), and the cube root of 125 is also a whole number(5).
ANYONE HELP, WILL GIVE BRAINLIEST ANSWER
Write the following phrase as an algebraic expression and simplify if possible. Let x represent the unknown number.
Double a number, minus the sum of the number and two
Answer:
x - 2
Step-by-step explanation:
Rewrite this symbolically: "Double a number, minus the sum of the number and two"
Let x represent the unknown number.
Then: 2x - (x + 2), or 2x - x - 2, or x - 2
Part A: Factor x2y2 + 6xy2 + 8y2. Show your work. (4 points) Part B: Factor x2 + 8x + 16. Show your work. (3 points) Part C: Factor x2 − 16. Show your work. (3 points) (10 points)
Answer:
Part A : y²(x + 2)(x + 4)
Part B: (x + 4) (x + 4)
Part C: (x + 4) (x - 4)
Step-by-step explanation:
Part A: Factor x²y²+ 6xy²+ 8y²
x²y²+ 6xy²+ 8y²
y² is very common across the quadratic equation , hence
= y² (x² + 6x + 8)
= (y²) (x² + 6x + 8)
= (y²) (x² + 2x +4x + 8)
= (y²) (x² + 2x)+(4x + 8)
= (y²) (x(x + 2)+ 4(x + 2))
= y²(x+2)(x+4)
Part B: Factor x² + 8x + 16
x² + 8x + 16
= x² + 4x + 4x + 16
= (x² + 4x) + (4x + 16)
= x( x + 4) + 4(x + 4)
= (x + 4) (x + 4)
Part C: Factor x² − 16
= x² − 16
= x² + 0x − 16
= x² + 4x - 4x - 16
= (x² + 4x) - (4x - 16)
= x (x + 4) - 4(x + 4)
= (x + 4) (x - 4)
THIS ONE IS URGENT I DON'T UNDERSTAND PLEASE HELP ME I WILL GIVE YOU BRAINLIEST/5 stars/Thanks/20 points please help me I would appreciate it!!! There are 2 questions please can you answer them!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Part A = 2
Part B = I'm unsure, sorry.
Step-by-step explanation:
Answer:
Part A= 2
Step-by-step explanation:
What is the coordinate of point P that lies along the directed line segment from Q(2,5) to R7, 12) and partitions the segment in the ratio of 3 to 2?
Your answer.
0 (3, 42)
O(4.5, 8.5)
O (5,9.2)
O (5,7)
Clear answer
Answer:
Step-by-step explanation:B
Simon gets some money for his birthday.
Simon spends ¹/₂ of his money on a bike.
He then gets £20 more from his gran for his birthday.
He spends ¹/₄ of what he has left on a new game.
He has £57 left.
How much does Simon get for his birthday altogether?
Answer:
£112 initial + £20= £ 132
Step-by-step explanation:
Initial amount= x
(x-x/2+20)*3/4= 57(x/2+20)= 4*57/3x/2+20=76x/2=56x=2*56x=112And he received £20, added to initial amount it total to £132
Lets verify the answer:
112112-56= 5656+20=7676-76/4= 76-19= 5757=57Answer:
27
Step-by-step explanation:
(57 ÷ 4_1 +57 _20) ÷2
(57÷3 +57 _20) ÷2
(19+57 _20)÷2
(76 _ 20)÷2
(56 ) ÷2
= 28
Ms. Costello borrows $5000 from a
bank that charges 9.25% interest per
year. What is her total amount due
after one year?
Answer: $5462.50
Step-by-step explanation:
Interest = 5000 x 9.25 / 100 = 462.50
Amount to be paid
= 5000 + 462.50
= 5462.50
I need help pleassseee
Answer:
The length of the radius is 3cm.
Step-by-step explanation:
Given that a circle is inscribed in a square. The side of the circle touches the side of the square which is the diameter. So the diameter of circle is 6cm, in order to find it's radius, you have to duvide it by 2 :
[tex]radius = diameter \div 2[/tex]
[tex]radius = 6 \div 2[/tex]
[tex]radius = 3cm[/tex]
Answer:
[tex]6^{2} - 3^{2} \pi[/tex] = area of the black 7.725666
[tex]x^{2} - r^{2} \pi[/tex]
area of square - area of circle
the diameter of the circle is 6 and half that is the radius = 3
Which system of inequalities is shown?
Answer:
I'm 90 percent sure the answer is A.
Step-by-step explanation:
Janet wanted to determine her average phone call length over 90 days. She collected the phone bills and randomly picked ten entries to look at. The phone call lengths, in minutes, are shown below.
3, 9, 17, 9, 11, 3, 11, 3, 17, 3
Assuming that the sample was representative of all the entries on the bills, what was the mean number of minutes over 90 days?
A. 7
B. 10
C. 8.6
Mean is the average. Add the minutes together and divide by 10.
86 /10 = 8.6
The answer is c