Answer:
x=-10
Step-by-step explanation:
2(x+3)=x-4
2x+6=x-4
-2x -2x
6=-x-4
+4 +4
10=-x
-1 -1
-10=x
[tex] \Large{\boxed{\sf x = 10}} [/tex]
[tex] \\ [/tex]
Explanation:Given equation:
[tex] \sf 2(x + 3) = x - 4 [/tex]
[tex] \\ [/tex]
Expand the left side using the following distributive property:
A(B + C) = AB + AC
[tex] \\ [/tex]
Here, A = 2, B = x, and C = 3.
We get:
[tex] \sf 2(x) + 2(3) = x - 4 \\ \\ \sf 2x + 6 = x - 4 [/tex]
[tex] \\ [/tex]
Now, subtract 6 from both sides:
[tex] \sf 2x + 6 - 6 = x - 4 - 6 \\ \\ \sf 2x = x - 10 [/tex]
[tex] \\ [/tex]
Subtract x from both sides :
[tex] \sf 2x - x = x - 10 - x \\ \\ \\ \boxed{\boxed{\sf x = -10}} [/tex]
[tex] \\ \\ [/tex]
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Sphere B is the image of sphere A after dilation by a scale factor of 44. If the volume of sphere A is 50 m^3
3
, find the volume of sphere B, the image.
Step-by-step explanation:
there is no image here. and we don't know, if B is smaller or lager than A.
anyway, the volume of a sphere is
4/3 × pi × r³ = 4/3 × pi × r×r×r
that means the scale factor applying to r (radius) has to be multiplied in 3 times (with every r). so, to compare the volumes, the volume scale factor is cubed the linear scale factor.
44³ = 85184
if B is smaller, then its volume is 50/85184 m³
if B is larger, then its volume is 50×85184 m³
since this a such a big number, you made possibly a typo with the scale factor.
The volume of sphere B, the image of sphere A after dilation by a scale
factor of 44, is approximately 1,223,762.42 cubic meters.
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Since, The volume of a sphere is given by the formula:
V = (4/3) pi r
where V is the volume, pi is the constant 3.14.., and r is the radius of the sphere.
Since, sphere A has a volume of 50 cubic meters, we can use this formula to solve for its radius:
50 = (4/3) pi r
r = (3/4) (50 / pi)
r = (3/(4pi) 50)^(1/3)
r = 2.67 meters
Note that we know,
The radius of sphere A, we can use the scale factor of 44 to find the radius of sphere B:
rₐ = 44 rₓ
rₐ = 44 × 2.67
rₐ = 117.48 meters
Finally, we can use the volume formula again to find the volume of sphere B:
V(B) = (4/3) pi rₓ
V (B) = (4/3) pi (117.48)
V (B) = 1,223,762.42 cubic meters
Therefore, the volume of sphere B, the image of sphere A after dilation by a scale factor of 44, is approximately 1,223,762.42 cubic meters.
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Select all the numbers that are rational
Answer:
-13/3
and the last 2
Step-by-step explanation:
The rational numbers include all the integers, plus all fractions, or terminating decimals and repeating decimals. Every rational number can be written as a fraction a/b, where a and b are integers. For example, 3 can be written as 3/1, -0.175 can be written as -7/40, and 1 1/6 can be written as 7/6.
The principal sent a message to 25 students to ask them to
help pick up litter after school. Only 8 of them showed up.
What percentage of the students came to pick up litter?
Answer: 32%
Step-by-step explanation:
100 / 25= 4
4 x 8 = 32%
I just need an explanation for this. I know the answer is 34 cm, but I don't understand how you get there
Step-by-step explanation:
180 ° - 146°=34°
Where by isosceles triangle is 180
What number is 90% of
140?
Answer:
126
Step-by-step explanation:
Which set of real numbers contains 23 and .45?
rational numbers
integers
natural numbers
whole numbers
Answer:
Option A, rational numbers
Step-by-step explanation:
Step 1: Determine which option is correct
Option B and D are automatically ruled out because only one of them is a whole number and the other one is a decimal. Option C doesn't work also because natural numbers are all the whole numbers that are greater than 1. The only option that makes sense is option A which includes whole numbers and decimals.
Answer: Option A, rational numbers
A chocolate bar measures 30 mm wide, 70 mm long, and four and one over two mm high. Will’s Wrapping Company is making a wrapper to cover the chocolate bar. Use the correct net and determine how much paper will be needed to make the wrapper.
Answer:
minimum of 5100 mm^2
Step-by-step explanation:
Surface area 2 * ( 70 * 30 + 70 * 4.5 + 30* 4.5) = 5100 mm^2
What is the volume of the following rectangular prism and the top of the shape 9 units squared and the hight is 3 2/3
Answer:
2x^3 + 5x^2 - 18x - 45 m
V = lwh
V = (x + 3)(x - 3)(2x + 5)
V = ((x)(x) + (x)(-3) + (3)(x) + (3)(-3))(2x + 5)
V = (x^2 - 3x + 3x - 9)(2x + 5)
V = (x^2 - 9)(2x + 5)
V = (x^2)(2x) + (x^2)(5) + (-9)(2x) + (-9)(5)
V = 2x^3 + 5x^2 - 18x - 45
6. Andy scored 90 on the last history exam. He scored 81 this time. By what percent did his score decrease?
Answer:
His score decreased by 9 percent this time.
Step-by-step explanation:
From his first history exam he had a score of 90 percent. The difference between his first score and present score is given by
90 - 81 = 9
Mamadou surveyed 500 of the students in the school about their favorite color students could choose between blue and red 390 students said their favorite color was red what percentage of the surveys students said their favorite color was blue
Answer:
22%
Step-by-step explanation:
so 500-390 = 110
110 students said their favorite color was blue.
110/500 = ?/100
110 times 100 = 11000
11000/500 = 22
give brainliest, please!
hope this helps :)
40 POINTS!!!
Find the volume of this irregular figure.
Hint: Find the volume of the whole rectangular prism, then subtract the volume of the missing piece, which is also a rectangular prism.
Answer:
470 cm³
Step-by-step explanation:
Volume of rectangular prism = width × length × height
⇒ Volume of whole rectangular prism = 9 cm × 10 cm × 8 cm
= 720 cm³
Side lengths of the missing piece:
width = 5 cmlength = 10 cmheight = 8 cm - 3 cm = 5 cm⇒ Volume of the missing piece = 5 cm × 10 cm × 5 cm
= 250 cm³
⇒ Volume of irregular figure = 720 cm³ - 250 cm³
= 470 cm³
Find the area of a rectangle with a length of 3 feet and a width of 2 7/8 feet
Answer:
8.625 or 8 5/8
Step-by-step explanation:
to find area you multiply length times width.
first, change 2 7/8 to an improper fraction to make multiplying easier. 2 7/8= 23/8.
then, multiply 3/1 (or 3) by 23/8. multiply across to get 69/8. Simplify the fraction to get 8 5/8 or 8.625.
Jodie started washing her car at 10:15 am she finished at 10:50 am how long did it take jody to wash her car.
Answer:
35 minutes
Step-by-step explanation:
this requires us to find out how long it took and because both times given to figure this out are within the same hour it is easy to figure out in this case, 50 - 15 = 35. This is not as simple with all problems like this but because of the times given in this problem its much easier.
Please help fast-
In △LMN , point E is between points L and M, point F is between points M and N, and EF¯¯¯¯¯∥LN¯¯¯¯¯ .
LE=19 cm , LM=31 cm , and MN=124 cm .
What is MF ?
Enter your answer in the box.
Using the triangle proportionality theorem, the length of segment MF in triangle LMN is: 48 cm.
What is the Triangle Proportionality Theorem?The triangle proportionality theorem states that when a segment intercepts two sides of a triangle and it is parallel to a third side, then it divides the side proportionally.
The diagram of triangle LMN is shown below. Using the triangle proportionality theorem, we have:
MF/MN = ME/ML
Plug in the values
MF/124 = (31 - 19)/31
MF/124 = 12/31
MF = (12 × 124)/31
MF = 48 cm
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Which is an example of stratified random sampling created from each given population? A. Deciding who should be the president of the senior class by tossing a coin to choose between two candidates. B. C. Surveying members of a political party by calling people listed in the telephone directory whose last names begin with the letter A. D. Surveying subscribers to a magazine by separating the list of subscribers into four age groups and choosing a sample from each group proportional to its size in the population.
Answer:
the answer is D
Step-by-step explanation:
i just did the test
Answer:
D
Step-by-step explanation:
(see image) please help I need help with this math problem * i give brainlist
QUICK ANSWER PLEASE!!
If M(1; -1) is the midpoint of the line segment AB, where A(-4;y)
and B(x; -5), calculate the value of x and y.
There are 34 students and five teachers going on a trip if each ticket costs $9.50 how much money do they need to raise
hhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
A.
Step-by-step explanation:
Because if she plays for a certain amount of time it would go up. And it she took a break it would be a straight line then go up the same line as the one at the bottom. Thus making your answer A.
There are 6 swimmers in a race. In how many ways can they finish in first and second place?
-12
-30
-120
-360
Answer:
step 1. 6x2=12 first place way
step 2. 12×2=24
step 3. 24+6=30 second place way
Determine which function has the greatest rate of change over the interval [0, 2].
A. c
B. a
C. d
D. b
Answer:
B :a
Step-by-step explanation:
Solve this:
Raj is 12m years old. His son was born when he was 9m years old.
(i) Find Raj's age 5 years later.
(ii) Find the sum of their ages in 5 years' time.
Answer:
i = 17 Years old
ii = 25 years
Step-by-step explanation:
i = 12 + 5 =17
ii = his son was born when he was 9, hes 12 now, so his sons 3. In 5 years time his sons 8 and hes 17, 8+17= 25
Solve for d.
3(d + 2) = 12
d =
Answer:
d = 2
Step-by-step explanation:
3(d + 2) = 12 ( divide both sides by 3 )
d + 2 = 4 ( subtract 2 from both sides )
d = 2
Answer:
d=2
Step-by-step explanation:
3(d+2)=12
divide both side by 3
d+2 =4
substract 2 from both side
d=2
23 +42
0-24
О-3/16
O3/16
Step-by-step explanation:
23+42=65
0-24=-24
0-3/16=-3/16= -1875
03/16=0.1875
groups, A and B, of size 10. In the simulations, group A always plays the role of the treatment group and group B the role of the control group.
After each simulation, she subtracts the average for group A from the average for group B. The distribution of the differences for all 100 simulations is shown in the histogram.
In the original experiment, the average for the treatment group was 1.6 lower than the average for the control group.
In what percentage of simulations is the average for group A at least 1.6 lower than the average for group B?
The percentage of simulations where the average for group A is at least 1.6 lower than the average for group B is 48%.
Data points where the average for group A is at least 1.6 less than BThe following are the data points from the histogram where the average of group A is at least 1.6 less than average of group B.
At least -1.6 lower implies -1.6, -1.5, -1.4, -1.3, -1.2, -1.1, 0, 1, etc.
the first point = (-1.6 - 1.2) (number of simulation = 1)second point = (-1.2, -0.8) (number of simulation = 8)third point = (-0.8, -0.4) (number of simulation = 16)fourth point = (-0.4, 0) (number of simulation = 23)Outcome of simulations = 1 + 8 + 16 + 23 = 48
Percentage of simulation = outcome/total x 100%
Percentage of simulation = (48 x 100%)/100
Percentage of simulation = 48%
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solutia ecuatiei 4x+12= 0 este x =
2x^3-x^2-3x=210
the answer is 5 but I want to know why.
Answer:
[tex]x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]
Step-by-step explanation:
1) Move all terms to one side.
[tex]2x^{3} -x^{2} -3x-210=0[/tex]
2) Factor [tex]2{x}^{3}-{x}^{2}-3x-210[/tex] using Polynomial Division.
1 - Factor the following.
[tex]2x^{3} -x^{2} -3x-210[/tex]
2 - First, find all factors of the constant term 210.
[tex]1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210[/tex]
3) Try each factor above using the Remainder Theorem.
Substitute 1 into x. Since the result is not 0, x-1 is not a factor..
[tex]2*1^{3} -1^{2} -3*1-210=-212[/tex]
Substitute -1 into x. Since the result is not 0, x+1 is not a factor..
[tex]2(-1)^{3} -(-1)^{2} -3*-1-210=-210[/tex]
Substitute 2 into x. Since the result is not 0, x-2 is not a factor..
[tex]2*2^{3} -2^{2} -3*2-210=-204[/tex]
Substitute -2 into x. Since the result is not 0, x+2 is not a factor..
[tex]2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224[/tex]
Substitute 3 into x. Since the result is not 0, x-3 is not a factor..
[tex]2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174[/tex]
Substitute -3 into x. Since the result is not 0, x+3 is not a factor..
[tex]2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264[/tex]
Substitute 5 into x. Since the result is 0, x-5 is a factor..
[tex]2\times {5}^{3}-{5}^{2}-3\times 5-210 =0[/tex]
------------------------------------------------------------------------------------------
⇒ [tex]x-5[/tex]
4) Polynomial Division: Divide [tex]2{x}^{3}-{x}^{2}-3x-210[/tex] by [tex]x-5[/tex].
[tex]2x^{2}[/tex] [tex]9x[/tex] [tex]42[/tex]
-------------------------------------------------------------------------
[tex]x-5[/tex] | [tex]2x^{3}[/tex] [tex]-x^{2}[/tex] [tex]-3x[/tex] [tex]-210[/tex]
[tex]2x^{3}[/tex] [tex]-10x^{2}[/tex]
-----------------------------------------------------------------------
[tex]9x^{2}[/tex] [tex]-3x[/tex] [tex]-210[/tex]
--------------------------------------------------------------------------
[tex]42x[/tex] [tex]-210[/tex]
[tex]42x[/tex] [tex]-210[/tex]
-------------------------------------------------------------------------
5) Rewrite the expression using the above.
[tex]2x^2+9x+42[/tex]
[tex](2x^2+9x+42)(x-5)=0[/tex]
3) Solve for [tex]x.[/tex]
[tex]x=5[/tex]
4) Use the Quadratic Formula.
1 - In general, given [tex]a{x}^{2}+bx+c=0[/tex] , there exists two solutions where:
[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
2 - In this case, [tex]a=2,b=9[/tex] and [tex]c = 42.[/tex]
[tex]x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}[/tex]
3 - Simplify.
[tex]x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]
5) Collect all solutions from the previous steps.
[tex]x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]
What is the area of the figure shown?
Check the picture below.
[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2-r^2) ~~ \begin{cases} R=\stackrel{larger}{radius}\\ r=\stackrel{smaller}{radius}\\[-0.5em] \hrulefill\\ R=10.5\\ r=7 \end{cases}\implies \begin{array}{llll} A=\pi (10.5^2 - 7^2)\implies A=61.25\pi \\\\\\ A\approx 192.42~m^2 \end{array}[/tex]
I need help. Find the ratio of the trig function.
Answer:
tanΘ = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
tanΘ = [tex]\frac{opposite}{adjacent}[/tex]
the opposite side requires to be found.
let the opposite side be x then using Pythagoras' identity in the right triangle
x² + 12² = 20²
x² + 144 = 400 ( subtract 144 from both sides )
x² = 256 ( take square root of both sides )
x = [tex]\sqrt{256}[/tex] = 16
then
tanΘ = [tex]\frac{16}{12}[/tex] = [tex]\frac{4}{3}[/tex]
Select the correct answer. which expression is equivalent to the given expression? assume the denominator does not equal zero. a. b. c. d.
The expression that is equivalent to the expression, [tex](\frac{4m^5n^2}{m^2n} )^3[/tex] is the expression, [tex]64m^9n^3[/tex].
What are Equivalent Expressions?If two expressions are equivalent to each other, it means the value of each of them are the same when simplified or evaluated in their simplest form.
Given the expression,
[tex](\frac{4m^5n^2}{m^2n} )^3[/tex]
Evaluate the expression in its simplest form
[tex](\frac{4m^5n^2}{m^2n} )^3 = (4m^3n^1)^3[/tex]
Multiply the exponents in the bracket by the one outside, then find the cube of 4.
[tex]64m^9n^3[/tex]
Therefore, [tex](\frac{4m^5n^2}{m^2n} )^3[/tex] is equivalent to [tex]64m^9n^3[/tex].
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