Considering the definition of an equation and the way to solve it, a person will devote 28 years watching TV and 6 years sleeping.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.
The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.
To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseBeing "x" the number of years watching TV, and knowing that:
The number of years sleeping will exceed the number of years watching TV by 22.A person will devote 34 years to sleeping and watching TV.the equation in this case is:
x + (x+22) =34
Solving:
x + x =34 -22
2x= 12
x= 12 ÷ 2
x=6
As the number of years sleeping will exceed the number of years watching TV by 22, then x +22= 6 +22= 28 years.
Finally, a person will devote 28 years watching TV and 6 years sleeping.
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Factorize completely
(m+n) (2x-y)-x(m+n)
Answer:
(m+n) [x-y]
Step-by-step explanation:
(m+n) (2x-y)-x(m+n)
We can factor out (m+n)
(m+n) [(2x-y)-x]
Combine like terms
(m+n) [2x-x-y]
(m+n) [x-y]
What is the difference of the given values to the correct level of precision?
22.108 L
– 5.80 L
wice a number added to a smaller number is 5. The difference of 5 times the smaller number and the larger number is 3. Let x represent the smaller number and y represent the larger number. Which equations represent the situation?
2 y + x = 5. 5 x minus y = 3.
2 x + y = 5. 5 y minus x = 3.
2 y + x = 5. y minus 5 x = 3.
2 x + y = 5. x minus 5 y = 3.
Answer:
2 y + x = 5 , 5 x − y = 3
Step-by-step explanation:
suppose x represents the smaller number and y represent the larger number.
Then
• The statement: “Twice a number added to a smaller number is 5”
means 2 y + x = 5
On the other hand,
•• The statement: “The difference of 5 times the smaller number and the larger number is 3”
means 5 x − y = 3
riangle A″B″C″ is formed using the translation (x + 0, y + 2) and the dilation by a scale factor of 2 from the origin. Which equation explains the relationship between segment AC and segment A double prime C double prime? (1 point) coordinate plane with triangle ABC at A negative 3 comma 3, B 1 comma negative 3, and C negative 3 comma negative 3
The relationship between segment AC and segment A double prime C double prime is AC = A''C'' /2.
What is a Scale Factor ?The ratio by which the new image is bigger or smaller than the original image is the scale factor.
It is given that
Triangle A″B″C″ is formed using the translation (x + 0, y + 2)
and the dilation by a scale factor of 2 from the origin.
coordinate plane with triangle ABC at A (- 3, 3), B (1, - 3), and C (- 3, -3).
segment AC is equal to A''C'' over 2
Scale factor = 2
The coordinates are
A (- 3, 3), B (1, - 3), and c (- 3, -3) is translated using (x + 2, y + 0),
new coordinates
A'(- 1, 3), B'(3, - 3), and C'(- 1, -3).
The dilation by a scale factor of from the origin
A″ (-2, 6), B″ (6, -6) and C″(-2, -6)
By the distance formula
AB = [tex]\rm \sqrt {52}[/tex]
A''B'' = [tex]\rm \sqrt{ 8^2 + 12^2}\\[/tex] = 2 [tex]\rm \sqrt {52}[/tex]
Therefore
AB = A''B'' /2
Similarly AC = A''C'' /2
The relationship between segment AC and segment A double prime C double prime is AC = A''C'' /2.
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What is the value of a in this equation?
Substituting into vertex form, we can write the equation of the parabola as
[tex]y=a(x-0)^{2}+9\\\\y=ax^{2}+9[/tex]
To find the value of a, we can substitute in the coordinates of another point the graph passes through, such as (3,0).
[tex]0=a(3)^{2}+9\\\\0=9a+9\\\\-9=9a\\\\a=\boxed{-1}[/tex]
find x and y
please help i don’t understand this !
Answer:
x = 47°
y = 27°
Explanation:
The angles lie on parallel lines which sum ups to 180 degrees.
Solve for x2x + 1 + 85 = 180
2x = 180 - 86
2x = 94
x = 47
Solve for y2y + 126 = 180
2y = 180 - 126
2y = 54
y = 27
Please help!!! What is the slope of a line that is perpendicular to this line?
[tex]\frak{Hi!}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
If two lines are perpendicular to each other, their slopes
are negative inverses of each other.
Thus,
[tex]\boldsymbol{\sf{Slope\:of\:this\:line=4}}}[/tex]
[tex]\boldsymbol{\sf{Negative \ Inverse=-\displaystyle\frac{1}{4}}}[/tex]. See how this works?
We took 4, then took its opposite, and flopped that over
[tex]\orange\hspace{300pt}\above3[/tex]
Definition-:
Perpendicular lines are lines that intercept each other at a 90 deg. angle, which is usually called the right angle.
The slope of the line below is -2. Use the coordinates of the labeled point to
find a point-slope equation of the line.
(4,-6)
® A. y + 6 = -2(x-4)
B. y-6= -2(x+4)
6 =2(×+4)
D. y + 6 =2(x - 4)
Answer:
Step-by-step explanation:
its A y+6=-2
Question in attached file
The value of the expression [tex]\frac{x^2 + 3y^2}{xy}[/tex] is [tex]\frac{6y^2 + 2xy}{xy}[/tex]
How to solve the expression?The equation is given as:
[tex]x^2 - 2xy - 3y^2 = 0[/tex]
Add 3y^2 to both sides
[tex]x^2 - 2xy = 3y^2[/tex]
Add 3y^2 to both sides
[tex]x^2 + 3y^2 - 2xy = 6y^2[/tex]
Add 2xy to both sides
[tex]x^2 + 3y^2 = 6y^2 + 2xy[/tex]
Divide through by xy
[tex]\frac{x^2 + 3y^2}{xy} = \frac{6y^2 + 2xy}{xy}[/tex]
Hence, the value of [tex]\frac{x^2 + 3y^2}{xy}[/tex] is [tex]\frac{6y^2 + 2xy}{xy}[/tex]
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In rhombus ABCD below, AC=30 cm and BD=18 cm. Find the area of the rhombus .I will give brainliest for the best and correct answer.
what are the zeros of the function f(x)=x^4-4x^2-5
Answer:
[tex]x =\sqrt{5} ,-\sqrt{5} ,-i,i[/tex]
Step-by-step solution:
[tex]0=x^4-4x^2-5[/tex] [tex]u = x^2[/tex]
[tex]0 = u^2-4u-5[/tex]
[tex]0 = (u -5)(u+1)[/tex]
[tex]u = 5[/tex] [tex]u=-1[/tex]
[tex]x^2 =5[/tex] [tex]x^2 = -1[/tex]
[tex]x= +-\sqrt{5}[/tex] [tex]x = +-i[/tex]
??????????????????????????????
Answer:I can’t see
Step-by-step explanation:show fullscreen
Whats the correct answer answer asap for brainlist
Answer:
Spain
Step-by-step explanation:
Pablo Picasso was born in Malaga, Spain.
Answer:
Málaga, Spain
Step-by-step explanation:
A population of bacteria begins with 1500 bacteria and grows to 4500 in one hour.
- Find a function that represents the growth of this culture of bacteria as a function of time.
- How long does it take this culture of bacteria to double?
Thanks TT
The function that represents the growth of this culture of bacteria as a function of time is; P = 1500e^(1.0986t)
How to calculate Exponential Growth?
The formula for exponential growth is;
P = P₀e^(rt)
where;
P = current population at time t
P₀ = starting population
r = rate of exponential growth/decay
t = time after start
Thus, from our question we have;
4500 = 1500 * e^(r * 1)
4500/1500 = e^r
e^r = 3
In 3 = r
r = 1.0986
Thus, the function that represents the growth of this culture of bacteria as a function of time is;
P = 1500e^(1.0986t)
For the culture to double, then;
P/P₀ = 2. Thus;
e^(1.0986t) = 2
In 2 = 1.0986t
t = 0.6931/1.0986
t = 0.631 hours
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Find card(B) given that B={1,3,5,7,9,….9907}
The value of card(B) is card(B) = 4954
How to determine the card(B)?The set is given as:
B={1,3,5,7,9,….9907}
The above set is the set of odd numbers from 1 to 9907.
The number of elements is the cardinality
And it can be calculated using
L = a + (n - 1)d
Where
L = 9907
a = 1
d = 2
So, we have:
9907 = 1 + (n - 1)2
Subtract 1 from both sides
9906 = (n - 1)2
Divide by 2
n - 1 = 4953
Add 1 to both sides
n = 4954
This means that
card(B) = 4954
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The length of the longer leg of a right triangle is 3 cm more than three times the length of the shorter
leg. The length of the hypotenuse is 4 cm more than three times the length of the shorter leg. Find the
side lengths of the triangle.
Length of the shorter leg:________ cm
Length of the longer leg:
cm
Length of the hypotenuse:
_cm
Answer:
the length of the shorter leg : 7 cm
the length of the longer leg : 24 cm
the length of the Hypotenuse : 25 cm
Step-by-step explanation:
a = 3b + 3
c = 3b + 4
and we know the general Pythagoras :
c² = a² + b²
(3b + 4)² = (3b + 3)² + b²
9b² + 24b + 16 = 9b² + 18b + 9 + b²
24b + 16 = 18b + 9 + b²
6b + 7 = b²
b² - 6b - 7 = 0
the general solution to such a quadratic equating is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x is called b.
a = 1
b = -6
c = -7
b = (6 ± sqrt((-6)² - 4×1×-7))/(2×1) = (6 ± sqrt(36 + 28))/2 =
= (6 ± sqrt(64))/2 = (6 ± 8)/2
b1 = (6+8)/2 = 14/2 = 7 cm
b2 = (6-8)/2 = -2/2 = -1 cm
a negative number did not make sense for a side length, so,
b = 7 cm
is our solution for one leg.
a = 3b + 3 = 3×7 + 3 = 24 cm
c = 3b + 4 = 25 cm
True or false? To begin an indirect proof, you assume the converse of wha
you intend to prove is true.
OA. True
OB. False
Answer: B. False
Step-by-step explanation:
You assume the inverse of what you intend to prove is true, not the converse.
If sin(θ)=−24/25, and θ is in Quadrant III, then what is tan(θ/2)?
Recall the Pythagorean identity,
[tex]\sin^2(\theta) + \cos^2(\theta) = 1[/tex]
Since [tex]\theta[/tex] belongs to Q3, we know both [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex] are negative. Then
[tex]\cos(\theta) = -\sqrt{1 - \sin^2(\theta)} = -\dfrac7{25}[/tex]
Recall the half-angle identities for sine and cosine,
[tex]\sin^2\left(\dfrac\theta2\right) = \dfrac{1 - \cos(\theta)}2[/tex]
[tex]\cos^2\left(\dfrac\theta2\right) = \dfrac{1 + \cos(\theta)}2[/tex]
Then by definition of tangent,
[tex]\tan^2\left(\dfrac\theta2\right) = \dfrac{\sin^2\left(\frac\theta2\right)}{\cos^2\left(\frac\theta2\right)} = \dfrac{1 - \cos(\theta)}{1 + \cos(\theta)}[/tex]
[tex]\theta[/tex] belonging to Q3 means [tex]180^\circ < \theta < 270^\circ[/tex], or [tex]90^\circ < \theta < 135^\circ[/tex], so that the half-angle belongs to Q2. Then [tex]\sin\left(\frac\theta2\right)[/tex] is positive and [tex]\cos\left(\frac\theta2\right)[/tex] is negative, so [tex]\tan\left(\frac\theta2\right)[/tex] is negative.
It follows that
[tex]\tan\left(\dfrac\theta2\right) = -\sqrt{\dfrac{1 - \cos(\theta)}{1 + \cos(\theta)}} = \boxed{-\dfrac43}[/tex]
Write each phrase as a mathematical expression.
The sum of the profit, P, times 8 and 6
Mr. Gatting poured the same amount of pepper into each of the cylindrical pepper shakers shown below. The pepper in the shaker on the left is
filled to a height of 45 millimeters.
60 mm
OA 60 millimeters
OB. 95 millimeters
-32 mm
To what approximate height is the shaker on the right filled with pepper?
24 mm-
Note: Figures are not drawn to scale
100 mm
Answer:
80 mm
Step-by-step explanation:
the same amount (and that means the same volume) of pepper is in each shaker.
the volume of a cylinder is
base area × height = pi×r² × height
with r being the radius (which is always half of the diameter).
the volume of the filled in pepper in the first shaker is then
pi×(32/2)²×45 = pi×16²×45 = pi×256×45 = 11,520pi mm³ =
= 36,191.14737... mm³
now let's see what height in the second shaker we will reach by filling the same 11,520pi mm³ of pepper into it.
so, we have
pi×(24/2)²×height = 11,520pi
12²×height = 11,520
144×height = 11,520
height = 11,520/144 = 80 mm
so, the shaker on the right is filled up to 80 mm with pepper.
Answer:
80 mm
Step-by-step explanation:
I got it right on edmentum
2pr+2prh find the surface area of water tower that is 40 feet tall and has a diameter of 30 feet
The Surface area of the cylindrical tower is 5181 ft cube.
How to find surface area of a cylinder?Surface area of cylinder = 2πr² + 2πrh
where
r = radiush = heightTherefore,
r = 30 / 2 = 15 ft
h = 40 ft
Surface area of cylinder = 2πr(r + h)
Surface area of cylinder = 30π(40 + 15)
Surface area of cylinder = 30π(55)
Surface area of cylinder = 1650π
Surface area of cylinder = 5181 ft³
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PLS HELP 1HOUR LEFT Select the expression that is modeled on the number line. A number line from zero to one partitioned into sixths. There are four hops beginning at one sixth and ending at five sixths one sixth plus five sixths
one sixth plus four sixths
five sixths minus one sixth
five sixths minus four sixths
Answer:
one sixth plus 4 sixths
Step-by-step explanation:
from one sixth you have to add 4/6 to get to 5 sixths(5/6)
If the following integral converges, state its value in the space provided. Otherwise, input divergent.
9
2-3
√3
dz
there is a canned food sale at the supermarket. a case of 24 cans of peas is prices at $19.68. at the same rate what is the price of 10 cans?
Answer:
8.2
Step-by-step explanation:
We can find the unit rate of this problem by dividing 18.68 by 24 to get .82. .82*10 is equal to 8.2.
8x + y = 23 plus -10x -y = -27
Answer:
13.5
Step-by-step explanation:
8x+y-10x-y=-27
-2x=-27
x=13.5
Answer:
64
Step-by-step explanation:
What is the slope of a line perpendicular to
the line whose equation is 9x + 3y = 36.
Fully simplify your answer.
[tex]m = \frac{ - u}{v} = \frac{ - 9}{3} = - 3 [/tex]
[tex]km = - 1 \\ k = - \frac{1}{m} = \frac{ - 1}{-3}=1/3 [/tex]
The slope of the perpendicular line will be 1/3.
What is the equation of a perpendicular line?Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation of the line is given below.
9x + 3y = 36
3y = 36 - 9x
y = 12 - 3x
The slope of the given equation is - 3.
Let m be the slope of the perpendicular line. Then the slope of the perpendicular line will be 1/3.
m (-3) = -1
Simplify the equation, then we have
m (-3) = -1
3m = 1
m = 1/3
The slope of the perpendicular line will be 1/3.
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Anyone know how to do area or volume? Any help will do! thanks
Answer:
Volume: x(x+6)(x+2) Area: [tex]x^{2}[/tex] + 8x +12
Step-by-step explanation:
Volume Explanation:
To find the volume of a 3d figure, we must multiply the length, width, and the height. Therefore we multiply (x)(x+6)(x+2)= [tex]x^{3}[/tex] + 8[tex]x^{2}[/tex] + 12x. Simplify this equation and we will get x(x+6)(x+2) for the formula to find the volume of the 3D figure.
Area:
To find the area of a 2D figure, we must multiply length x height. Therefore, we multiply the equations (x+6)(x+2)= [tex]x^{2} + 2x + 6x +12[/tex] to get a final answer of [tex]x^{2} +8x +12[/tex]. This will be the formula when you find the area of the 2D figure in question.
Question 15 (5 points)
image
Which of the following is a true proportion of the figure based on the triangle proportionality theorem?
Question 15 options:
A)
B)
C)
D)
Answer:
You need to attach the pictures and ask again.
Step-by-step explanation:
I cannot see any attachments.
Let p: A number is greater than 25.
Let q: A number is less than 35.
If p q is true, then what could the number be? Select two options.
24
28
32
36
040
A disk is in the form of square and measures 5.25 inches on each side. Find
the diagonal length of the disk?
Answer:
The diagonal length of the desk is 7.42462120246 inches.
Step-by-step explanation:
Since it is a square then all sides are equal which means we can easily formulate the pythagorean theorem on the diagonal length of the desk.
a^2 + b^2 = c^2
A and B are the same (width and length) since it is a square.
5.25^2 + 5.25^2 = c^2
27.5625 + 27.5625 = c^2
55.125 = c^2
Put c^2 under a square root (apply to both sides)
square root of 55.125 = 7.42462120246 = c