Answer:
[tex]\normalsize \textsf{$x = -\dfrac{8}{3}$}[/tex]
Step-by-step explanation:
Given: [tex]\normalsize \textsf{$3(2x - 9) - 4(3x + 4) = 2(x - 12) + \dfrac{7}{3}$}[/tex]
1. Distribute
For 3:
[tex]\normalsize \textsf{$3(2x - 9)$}\\\normalsize \textsf{$3(2x) + 3(- 9)$}\\\normalsize \boxed{\textsf{$6x -27$}}\\[/tex]
For -4:
[tex]\normalsize \textsf{$-4(3x + 4)$}\\\normalsize \textsf{$-4(3x) + -4(4)$}\\\normalsize \boxed{\textsf{$-12x -16$}}\\[/tex]
For 2:
[tex]\normalsize \textsf{$2(x - 12)$}\\\normalsize \textsf{$2(x) + 2(-12)$}\\\normalsize \boxed{\textsf{$2x -24$}}\\[/tex]
Now we have: [tex]\normalsize \textsf{$6x - 27 - 12x -16 = 2x-24 + \dfrac{7}{3}$}[/tex]
2. Combine like terms:
[tex]\normalsize \textsf{$-6x -43 = 2x -\dfrac{72}{3} + \dfrac{7}{3}$}\\\\\normalsize \textsf{$-6x -43 = 2x -\dfrac{65}{3}$}\\\\[/tex]
3. Subtract 2x from both sides:
[tex]\normalsize \textsf{$-6x-2x -43 = 2x -2x -\dfrac{65}{3}$}\\\\\normalsize \textsf{$-8x -43 = -\dfrac{65}{3}$}\\\\[/tex]
4. Add 43 to both sides:
[tex]\normalsize \textsf{$-8x -43 +43 = -\dfrac{65}{3} + 43$}\\\\\normalsize \textsf{$-8x = -\dfrac{65}{3} + \dfrac{129}{3}$}\\\\\normalsize \textsf{$-8x = \dfrac{64}{3}$}[/tex]
5. Divide both sides by -8
[tex]\normalsize \textsf{$-8x = \dfrac{64}{3}$}\\\\\normalsize \textsf{$-8x \div 8 = \dfrac{64}{3} \div -\dfrac{8}{1}$}\\\\\normalsize \boxed{\textsf{$x = -\dfrac{8}{3}$}}[/tex]
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Half of the road the boy walked at a speed of 6 m / min, the other half - at a speed of 4 m / min. Calculate the average walking speed of a boy.
Answer:
5 m/min
Step-by-step explanation:
Initial speed = 6 m/ min
Final speedd = 4 m/ min
[tex]Average\:speed\:=\:\dfrac{total\:speed}{2}[/tex]
Average speed = [tex]\dfrac{ 6 + 4}{2}[/tex]
Avg. Speed = 5 m / min.
Find the measures of a right triangle where one of the acute angles is 3.5 times the other
Answer:
the other two angles are 70° and 20°
Step-by-step explanation:
The measures of a right triangle where one of the acute angles is 3.5 times the other angle, the angles are respectively, 20°, 70°, 90°
What are the sum of interior angles of triangle ?The sum of all the interior angles of a triangle is 180°
Given that,
A right angle triangle,
In which one of the acute angle is 3.5 times the other triangle
Suppose, one of the acute angle = x
then the other triangle = 3.5x
The sum of the triangle = 180°
x + 3.5x + 90° =180°
4.5x = 180 - 90
= 90
x = 90/4.5
= 20
The one acute angle = 20
The another triangle = 3.5 x 20
= 70
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Sam opened a stationery store in his neighborhood. His annual profit grew by $5,000 per year in the first 2 years. Then for 2 years, his annual profit was constant at $10,000 each year. Then his annual profit grew by $10,000 per year for the next 3 years.
Which graph models the piecewise function for the given situation?
Please find attached the image of the graph that models the function.
What is a graph?A graph is a pictorial representation of data. A graph is made up of the x-axis and the y-axis. On this graph, the number of years is on the y-axis and the profit is on the x-axis.
Profit in year 1 = $500 Profit in year 2 = $5000 + $5000 = $10,000Profit in year 3 and 4 = 10,000Profit in year 5 = 10,000 + 10,000 = $20,000Profit in year 6 = 20,000 + 10,000 = $30,000Profit in year 7 = 30,000 + 10,000 = $40,000To learn more about graphs, please check: https://brainly.com/question/21527145
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Answer: other dude is correct
Step-by-step explanation:
All of the following are equivalent, except.
Answer: B.
Step-by-step explanation: This is because you can't possibly have an exponent, there are no two of the same value being multiplied together.
David’s mom recorded the amount of time David spent on homework.
Which measure of central tendency should David’s mom use if she wanted to argue that David did not spend enough time on homework?
The measure of central tendency that David's mum can use to argue is the mean.
What is the Mean of a Data?The mean of a data is the average of the data points in the data distribution. The mean is a measure of central tendency.
If David really spent enough time on homework, the average of the time he uses will give David's mum the mean time spent by David, which she can use for her argument.
Thus, David's mum can use the mean as a measure of central tendency.
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Answer:
mode
Step-by-step explanation:
The full question.the full question you were asking for
Answer:
I'm getting stuck by
[tex] = lim \: \: \: \: \: \: \frac{ {h}^{ \frac{1}{5} } }{h} \\ h > 0[/tex]
Sorry I can't help you out, if you find the answer through FP lmk
80 Points, please help!
If using the method of completing the square to solve the quadratic equation x^2-11x-14=0, which number would have to be added to "complete the square"?
Answer:
±√177/2+11/2
Step-by-step explanation:
Use the formula (b/2)^2 in order to create a new term. Solve for x by using this term to complete the square. Exact Form:x=±√177/2+11/2
x=12.15206734…,−1.15206734…
Answer:
30.25
Explanation:
Quadratic Equation: x² - 11x - 14 = 0
Number added = (b/2)² = (-11/2)² = 30.25
Solving Steps:
x² - 11x = 14[add both sides by 30.25]
x² - 11x + 30.25 = 14 + 30.25[complete square]
(x - 5.5)² = 44.25[exchange sides]
(x - 5.5)² - 44.25 = 0Describe the trend in the scatterplot
Answer:
negative correlation
Step-by-step explanation:
If you were to draw a line of best fit (a line that best expresses the relationship between a group of points), it would have a negative slope.
What is the volume of the right rectangular prism?
15 mm
Î
Area of base = 49 sq. mm
O 64 mm³
3
O 128 mm³
O 735 mm³
O 1,470 mm³
Answer:
735mm³
Step-by-step explanation:
V=A of base×h
=49×15
=735mm³
Amelie solves the following system of equations.
Which values of x and y satisfy this system of equations?
The values of x and y that satisfy this system of equations are 10 and 5 respectively
Simultaneous equationGiven the system of equations
x + y = 20
3x - 3y = 30
_____________________
x + y = 20
x - y = 10
Add the equations
2x = 20 + 10
2x = 30
x = 30/2
x = 15
Substitute
x -y = 10
15 - y = 10
y = 5
Hence the values of x and y that satisfy this system of equations are 10 and 5 respectively
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1.Mary has ( 20xy - 10x²) sweets. She wants to divide the sweets each friend will get in term s of x and y
a) if X=6 and Y=4, how many sweets:
i) Will she give to each friend?
Answer:
X will get 20 sweets and Y will get 30 sweets.
Step-by-step explanation:
Substitute for x and y in in the equation.
20(6)(4) - 10(6)(6)
480-360
=120
Mary has 120 sweets.
Then divide 120 by 6 and 4
120/6= 20 sweets and 120/4 =30 sweets
What is the probability you spin something larger than 10
The probability you spin something larger than 10 will be 1 / 2.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The given data is:-
There are 8 numbers in the spinner.We need to find the probability of a number greater than 10.The probability will be calculated as:-
Total numbers = 8
Numbers greater then 10 are = 13 , 16 , 22 , 42 = 4
Probability = 4 / 8 = 1 / 2
Therefore the probability you spin something larger than 10 will be 1 / 2.
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Which angle is vertical to ∠EID?
Answer:
C
Step-by-step explanation: It's vertical to the angle, together it makes 368 degrees
Answer:
C) Angle HIA
Step-by-step explanation:
Vertical Angles are the angles directly across from each other in a transversal. In this case, angled EID and HIA are vertical to each other (which also makes them congruent).
Hope it helps!
5x + 3 - 2x = 5. What is the value of x?
Answer:
x = 2/3
Step-by-step explanation:
5x + 3 - 2x = 5
3x = 5-3
3x = 2
x = 2/3
give brainliest please!
hope this helps :)
find the value of x in 4^2x / 4^x = 64
Answer:
sorry I don't know
Step-by-step explanation:
sorry
Greg has a piece of rope 18 ft long. He wants to cut it into two pieces so that the longer piece is 2 ft less than 3 times the length of the shorter piece.
How long will each piece of rope be?
Enter your answers in the boxes.
Shorter piece:
ft
Longer piece:
ft
Answer:
Shorter = 4ft.
Longer = 10ft.
Step-by-step explanation:
Shorter = x
Longer = 3x - 2
Piece of rope = 18
(3x - 2) + x = 18
4x - 2 = 18
4x = 16
x = 4 (shorter piece)
Longer piece
3x - 2
3(4) - 2
12 - 2 = 10
y² + 2y - 48 ( factor the polynomial )
Answer:
(y - 6)(y + 8)
Step-by-step explanation:
Find two numbers that add to 2 and multiply to -48. Then put them in the form above. Afterwards, use FOIL (First, Outside, Inside, Last) to check the factoring and you get: y² + 2y - 48
Have a great day! :)
Answer:
−8, 6
Step-by-step explanation:
Write the factored form using these integers. (y−8) (y+6)
37, 42, 48, 51, 52, 53, 54, 54, 55
PLEASE HELP ASAP ILL MAKE YOU THE BRAINIEST
Write the ratio for sin A
Answer:
Step-by-step explanation:
Formula
The sin(A) = opposite / hypotenuse
Givens
Opposite = CB = 11
Hypotenuse = AB = 61
Solution
Sin(A) = 11/61
Sin(A) = 0.1803
Answer
Sin(A) = 11/61
Sin(A) = 0.1803
Can someone please answer this math?
The volume of the cylinder will be 621.72m³.
How to calculate the volume?Thw volume of a cylinder will be:
= πr²h
= 3.14 × 3² × 22
= 621.72 m³
The volume of the cone will be:
= 1/3πr²h
= 1/3 × 3.14 × 2² × 12
= 25.12m³
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Write the two equations that represent this information
Answer:
where is the information?
Step-by-step explanation:
Tom and Kathy want to borrow $35,000 in order to build an addition to their home. Their bank will lend them the money for 12 years at an interest rate of 5 3/8%. How much will they pay in interest to the bank over the life of the loan?
What figure is a dilation of Figure A by a factor of 12?
A quadrilateral labeled figure A. The sides are labeled 2 inches, 4 inches, 1 inch, and 5 inches, clockwise about the figure.
Note that the images are not necessarily drawn to scale.
A.A quadrilateral. The sides are labeled 1 inch, 3 inches, 0.5 inch, and 4 inches, clockwise about the figure.
B.A quadrilateral. The sides are labeled 4 inches, 8 inches, 2 inches, and 10 inches, clockwise about the figure.
C.A quadrilateral. The sides are labeled 3 inches, 5 inches, 2 inches, and 6 inches, clockwise about the figure.
D.A quadrilateral. The sides are labeled 1 inch, 2 inches, 0.5 inch, and 2.5 inches, clockwise about the figure.
The dilation factor for the question should be 1/2 as per options
So
dilated lengths are
2(1/2)=1in4/2=2in1/2=0.5in5/2=2.5inOption D
Answer:
D
Step-by-step explanation:
Figure A is dilated by a scale factor of 1/2.
Hence, new dimensions will be :
⇒ 1/2 × 2 = 1 inch
⇒ 1/2 × 4 = 2 inches
⇒ 1/2 × 1 = 0.5 inch
⇒ 1/2 × 5 = 2.5 inches
Option D has the right dimensions
A school sold all but 5 of ta school sold all but 5 of their old computers for r1200 each the school received r18000 from the sale. how many comps did the school originally old computers for r1200 each the school received r18000 from the sale. how many comps did the school originally have
Answer:
20
Step-by-step explanation:
The proceeds from the sale can be described by an equation involving the original number of computers.
__
setupLet n represent the number of computers the school originally had. Then n-5 is "all but 5" and is the number sold. Each is sold for ₹1200, and the value of the sale is ₹18000. This can be expressed by the equation ...
(n -5)×1200 = 18000
__
solutionThis 2-step linear equation can be solved by dividing by the coefficient, and adding the opposite of the constant.
n -5 = 18000/1200 = 15 . . . . . divide by 1200
n = 15 +5 = 20 . . . . . . . . . . add the opposite of -5
The school originally had 20 computers.
4 divided by 5/7 in its mixed form and simplest form
[tex]4\div\cfrac{5}{7}\implies \cfrac{4}{1}\div\cfrac{5}{7}\implies \cfrac{4}{1}\cdot \cfrac{7}{5}\implies \cfrac{28}{5}\implies 5\frac{3}{5}[/tex]
Q
7/0
The mean weight of 8 girls in a group is 35 kg. The individual weights of seven of then
are 35kg, 28kg, 43kg, 25kg, 33kg, 51kg, and 22kg. Find the weight of the 8th girl.
The weight of the 8th girl in the class is 43 kg
How to determine the weight of the 8th girl?The given parameters are:
Mean weight = 35 kg
Weight of 7 girls = 35kg, 28kg, 43kg, 25kg, 33kg, 51kg, and 22kg
Let the weight of the 8th girl be x.
Mean is calculated using:
Mean = Sum/Count
So, we have:
(35+ 28+43+25+33+51+22 + x)/8 = 35
Evaluate the sum
(237 + x)/8 = 35
Multiply both sides by 8
237 + x = 280
Subtract 237 from both sides
x = 43
Hence, the weight of the 8th girl is 43 kg
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ΔXYZ has angles with the following measurements:
m∠X=(10x-33)°
m∠Y=(4x-19)°
m∠Z=(100-2x)°
What are the measures of the three angles?
Answer:
Below in bold.
Step-by-step explanation:
The 3 angles add up to 180 degrees as they are in a triangle.
So 10x - 33 + 4x - 19 + 100 - 2x = 180
12x = 180 + 33 + 19 - 100
12x = 132
x = 11.
So the 3 angles are
10(11) - 33 = 110 - 33 = 77 degrees
4(11) - 19 = 25 degrees
100 - 2(11) = 78 degrees
The dimensions of a right rectangular prism are 1.5 cm,0.5 cm and 2. 25 cm.
What is the volume of the prism?
[100 POINTS] What is the measure of the arc from A to B that does not pass through C?
(Fill in the blanks)
Answer:
the answer to the questions is 140
Central angle
2(40)=80°So measure of arc BC is 80°
Use inscribed angle theorem
The measure of arc from A to B that doesn't pass through C is
180-mBC180-80100°awnser this pls im in a bad mood
Answer:
I think its 1/6 and if I'm wrong I'm very sorry but I think its 1/6
Step-by-step explanation:
Answer:
it's [tex]7* \frac{1}{6} =\frac{7}{6}[/tex]
Step-by-step explanation:
Yeah same, have a great day I guess i don't know I'm not in the mood