The solution for x in the equation is x = 2
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the solution of the equation?The equation is given as
x + 4 = 6
Subtract 4 from both sides of the equation
So, we have
x + 4 - 4 = 6 - 4
Evaluate the like terms
So, we have
x = 2
Hence, the solution for x in the equation is x = 2
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1. Factor by grouping
a² + ab - 56b²
Answer: (a-7b)(a+8b)
Step-by-step explanation:
a² + ab - 56b²=
a² + 8ab -7ab - 56b²=
a(a+8b) -7b(a+8b)=(a-7b)(a+8b)
a normal window has the shape of a rectangle surmounted by a semicircle. if the perimeter of the window is 34 ft, express the area A of the window as a function of the width x of the window
The 34 feet perimeter and width, x, of the window which is in the shape of a rectangle surmounted by a semicircle is, A = 17•x - x²•(1/2 - π/8)
How can the area of the window be expressed as a function of x?The shape of the window = A rectangle surmounted by a semicircle
Perimeter of the window, P = 34 feet
Width of the window = x
Required; The area, A, of the window as a function of x
Solution:
Diameter of the semicircle = x
Length of the semicircular arc = π•x/2
Let y represent the height of the window, we have;
P = 2•y + x + π•x/2 = 34
Therefore;
y = (34 - (x + π•x/2))/2 = 17 - x•(1 + π/2)/2
Area of the window, A = x × y + π•x²/8
Which gives;
A = x × (17 - x•(1 + π/2)/2) + π•x²/8 = 17•x - x²/2 - x²•π/8
A = 17•x - x²/2 - x²•π/8 = 17•x - x²•(1/2 - π/8)
Therefore;
Window area, A = 17•x - x²•(1/2 - π/8)
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6. Explain why (4, 1) is not a solution to the equation y=3x + 1.
Answer:
x is 4 and y is 1
So we put 3 x 4 + 1
if it's equal 1 (since y is 1)
but in this case it equals 13 so it's wrong
Answer:
see explanation
Step-by-step explanation:
to determine if (4, 1 ) is a solution of the equation, substitute the x and y coordinates into the equation and if both sides are equal then it is a solution.
y = 3(4) + 1 = 12 + 1 = 13 ≠ 1
since y ≠ 13 then (4, 1 ) is not a solution to the equation
shonda went for a drive in her new car. She drove for 147.5 miles at a speed of 59 miles per hour. For how many hours did she drive?
Answer:
2.5
Step-by-step explanation:
By Using s = d/ t
So t = d / s
t = 147.5 / 59= 2.52d+\sqrt[3]{-45d} d=75
Answer:
Given d = 75, respectively,
135
Step-by-step explanation:
[tex]2\left(75\right) = 2 \cdot 75\\= 150\\\\\sqrt[3]{-45\left(75\right)}\\\left(75\right)=75\\\sqrt[3]{-45\cdot \:75}\\45\cdot \:75=3375\\\sqrt[3]{-3375}\\\sqrt[3]{-3375}=-\sqrt[3]{3375}\\-\sqrt[3]{3375}\\-\sqrt[3]{15^3}\\\sqrt[3]{15^3}=15\\=15\\\\=150-15\\=135[/tex]
20 times 40 answer please
Answer: 800
Step-by-step explanation:
Answer:
800
Step-by-step explanation:
1 N b In Fig. R49 b, PT is a tangent at T to circle LMNT such that PT || LN. i Show that ANTL is isosceles. ii Find NTM. T M 498 L 36° P
Answer:
don't know that i'm looking for that to
Mark all of the statements that are true.
A. The domain for this function is the set {-5).
B. All real numbers are in the range of this function.
C. The domain for this function is all real numbers.
D. The range for this function is the set {-5).
E. This graph is not a function because the value of y is the same for every value of x
Option E:
This graph is not a function because the value of y is the same for every value of x
Solution :
Domain:
The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs.
For example, when we use the function notation f:R→R, we mean that f is a function from the real numbers to the real numbers. In other words, the domain of f is the set of real number R (and its set of possible outputs or codomain is also the set of real numbers R).
relation represents y as a function of x
1) is NOT a function of if there are two or more points with the same − , but
− .
2) is a function of if each has a different
There is a technique called the vertical line test that is often used to determine if a graph represents y
as a function of x
In this question only a horizontal line is present.
Option E:
This graph is not a function because the value of y is the same for every value of x
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Please help find the range
Answer:
Any Nber between 0-58 or 1-59
Step-by-step explanation:
Well you are already given the range which is 58. The question is asking for two number that are in the range. The range 58 means it can't be greater than 59. The range is how far apart the great y vaule is from the lowest y vaule.
Hope this helps!
Have any questions? Feel free to ask
-12[tex]-12\ \textless \ \frac{1}{2}\left(4x+16\right)\ \textless \ 18[/tex]
The solution to the given inequality is -10 < x < 5.
How to solve a compound inequality involving the and operation?
To solve a compound inequality involving the and operation, we solve each inequality, then find the intersection of these solutions.
For this problem, the inequality is given by:
-12 < 0.5(4x + 16) < 18.
Multiplying all the terms by 2:
-24 < 4x + 16 < 36
Hence:
4x + 16 > -24
4x > -40
x > -10.
4x + 16 < 36
4x < 20
x < 5
The intersection of these two solutions is:
-10 < x < 5.
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A local daycare has a daily operating cost of $900 plus a cost of $250 per child that attend. If a parent pays $420 per child, which inequality could be used to determine the number of children, c, they must accept to make money and become profitable?
a. 450c < 900+ 250c
b. 250c > 900+450c
c. 450c > 900 + 250c
d. 250c < 900 + 450c
450c > 900 + 250c;
For business to be profitable;
Selling price of daycare services > Cost price;
Payment for daycare of 1 child = $450
Payment for daycare of 'c' children = $450 × c;
= $450c;
Operating cost for 1 child = $250;
Operating cost for 'c' children = $250c;
Total daily operating cost = $900 + $250c;
Therefore;
450c > 900 + 250c;
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Anna solves the expression 6(5+3) and gets the result 48. Jojo solves the same expression and gets the result 33. Who is correct?
Answer:
Anna is correct.
Step-by-step explanation:
Using PEMDAS, you need to add the terms in the parentheses first.
After adding, you get 8×6 = 48
Jojo made the mistake of multiplying 6 and 5 first, and then adding 3.
A rectangle has a perimeter of 50 feet. The length is 5 feet more than the width. Find the width and length of the rectangle.
The width of the rectangle = 10 ft
The length of the rectangle = 15 ft.
What is the Perimeter of a Rectangle?The formula for the perimeter of a rectangle is given as:
Perimeter = 2(length + width).
Let x represent the width of the rectangle
Width of the rectangle = x
Length of the rectangle = x + 5
Perimeter of the rectangle = 50 ft
Thus, we would have the following equation:
2(x + 5 + x) = 50
2(2x + 5) = 50
4x + 10 = 50
4x = 50 - 10
4x = 40
4x/4 = 40/4
x = 10
Width of the rectangle = x = 10 ft
Length of the rectangle = x + 5 = 10 + 5 = 15 ft.
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Evaluate the following expression if a = -3 and b = 4. Square root 361 - 2a2 - [b - 17]
Given that a = -3 and b = 4, the numerical value of the expression (√361 - 2a² - [b - 17]) is 14.
What is the numerical value of the expression?Given that;
√361 - 2a² - [b - 17]a = -3b = 4To determine the numerical value of the expression, replace all the occurrence of a and b with -3 and 4 in the respectively and simplify.
√361 - 2a² - [b - 17]
√361 - 2(-3)² - [(4) - 17]
√361 - 2(9) - [4 - 17]
√361 - 18 - [-13]
√361 - 18 + 13
19 - 18 + 13
1 + 13
14
Given that a = -3 and b = 4, the numerical value of the expression (√361 - 2a² - [b - 17]) is 14.
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A school needs 3,198 notebooks for next year. If the notebooks come in packages of 82, how many packages should the school buy?
Answer:
The school should buy 39 packages.
Step-by-step explanation:
3198 notebooks
82 notebooks = 1 package
3198÷82 = 39
(Eg: you have 4 notebooks and there are 2 in each package. How many packages are there? 4÷2 = 2 So 2 packages)
Anna and Julia are at point P. Point Q is due North of point P. They disagree about the shortest route from P to Q. Anna walks on a bearing of 330°, and then changes to a bearing of 040°, which takes her straight to Q. Julia walks 3 km on a bearing of 0200, after which she walks on a bearing of 300°, which then takes her straight to Q. Who took the shorter route?
The Shorter route as per the bearing calculations is taken up by Julia.
What is a bearing?
The angle from the north line, expressed in degrees, is the correct bearing to a given point. The real bearing will simply be referred to as the bearing.A point's bearing is the number of degrees inside the angle measured counterclockwise from the north line towards the line connecting the point and the compass's center.When describing the direction from one point in relation to another, a bearing is utilized.Bearing calculations are illustrated below:
Route Taken up by Anna
360-330= 30°
First angle =90-30= 60°
Second angle= 60+(90-40) =110°
Third angle= 180-(110+30)= 40°
Route taken up by Julia:
First angle =20°
Second angle= 300-(180+20)=100°
Third angle=180-(20+100)=60°
Hence, the Shorter route as per the bearing calculations is taken up by Julia and bearing diagram is attached with the solution as an image.
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5
Polygon ABCD and polygon WXYZ can be mapped onto each other using similarity transformations.
DCD fell
20
18
16
14
12
VA
10
8
6
4
2
D
AS
B
X
dilatio
Y
Which sequence of transformations maps polygon ABCD onto polygon WXYZ?
➜x
0 2 4 6 8 10 12 14 16 18 20
W
mago with
actor of OF
The correct answer is option D.
The polygon ABCD can be mapped on to WXYZ but first it must be enlarged and then it must be mirrored along BC.
The mirror image of ABCD along BC must be enlarged with a scale factor of 2 to map ABCD to WXYZ.
The scale factor is the ratio of the the object to be transformed to the object with which it is to be compared.
Here, the scale factor is 2 and we must enlarge the image of ABCD along BC to get the desired mapping.
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What is (−114)(52)(−4)?
−23,712
−2,792
2,792
23,712
Answer:
Step-by-step explanation:
multiplication no need to care about order
(-114)(52*4)
=(-114)(208)
=(-100-10-4)(200+8)
=-20000-800-2000-80-800-32
=-23712
The product of the given numbers is 23,712.
The given expression is (−114)(52)(−4).
We need to evaluate the given expression.
What are integers multiplication rules?The rules for integer multiplication are as follows:
The product of two positive integers is always positive.The product of two negative integers is always positive.The product of one positive integer and one negative integer is always negative.Now, (−114)(52)(−4) can be evaluated as follows:
(−114)×(52)=-5,928
So, (-5,928)×(-4)=23,712
Therefore, the product of the given numbers is 23,712.
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The perimeter of the triangle shown is 89 meters. Find the length of each side.
Greetings from Brasil...
The perimeter is the sum of all sides of the triangle. In this case
P = (2X) + (X) + (4X - 9)
as P = 89
89 = (2X) + (X) + (4X - 9)
89 = 7X - 9
7X = 98
X = 98/7
X = 14X:
X meters = X = 14
---------------------------------------------
2X:
2X meters = 2 · X = 2 · 14 = 28
---------------------------------------------
(4X - 9):
(4X - 9) meters = (4 · X - 9) = (4 · 14 - 9) = (56 - 9) = 47
1/2(x + 6) = 1/2x - 9
Answer:
i think the question might be wrong.
In a bag there are 72 candy bars. 40 of them are snickers, 24 of them are milky ways, the rest are Kit Kats.
Answer: 8 kitkats
Step-by-step explanation:
40+24= 64
72-64=8
Answer:
Total candy bars to snickers = 72:40 or simplified 9:5
Ratio of kit kats to milky ways = 8:24 or simplified 1:3
Ratio for kit kats to total candy bars = 8:72 or simplified 1:9
Step-by-step explanation:
72 = 40 + 24 + x
x = 8
8. A figure has two pairs of parallel sides and four right angles. The figure is
translated 4 units down. How many parallel sides does the image have?
The image would also have two pairs of parallel sides
How many parallel sides does the image have?The given parameters are:
Two pairs of parallel sides Four right angles. Translation down by 4 unitsThe translation transformation is a rigid transformation
This means that, it keeps the orientation that is being transformed
The initial figure has two pairs of parallel sides
Hence, the image would also have two pairs of parallel sides
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A square window has an area of x2 + 12x + 36 square feet. Find the length of one side of the square. Question 25 options: (x – 6) feet (x + 6) feet (x + 4) feet (x – 9) feet
The length of one side of the square is x+6
Area of a squareThe formula for calculating the area of a square is expressed as:
A = L^2
where
L is the side length of the square
Given the following parameters
A = x^2 + 12x + 36 square feet
A = (x+6)^2
(x+6)^2 = L^2
L = x + 6
Hence the length of one side of the square is x+6
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wHAT IS 1.42 - (-2.9)
[tex] \: \: \: \: \large\bf\implies \: 4.32[/tex]
Step-by-step explanation:[tex] \longrightarrow \bf \: 1.42 - ( - 2.9) \\ \longrightarrow \bf \: 1.42 + 2.9 \\ \longrightarrow \bf \: 4.32[/tex]
Additional information:First of all we know that to do this type of question that is ↓
(-)(-) = +(+)(+) = +(-)(+) = -(+)(-) = -
The length of a rectangular garden is 5 m greater than the width. The area of the garden is 66 m² Find the dimensions of the garden.
L = 10 and w= 5 are the dimensions of the rectangular garden.
What is a rectangle, exactly?
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.Let the width of the garden be a
Length of the garden = a + 5
Area = l * w
66 = ( a+ 5 ) * a
66 = a² + 5a
a² + 5a -66 = 0
a² + 11a - 5a - 66 = 0
a( a + 11 ) -5 ( a + 11) = 0
( a + 11 ) ( a - 5) = 0
so a + 11 = 0 ⇒ a = -11
a - 5 = 0 ⇒ a = 5
Width cannot be negative.
l = a + 5 = 10
w = 5
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ome Tax A certain state uses the following progressive tax rate for calculating individual income tax: Income Range ($) 0 - 2000 2001 - 9000 Progressive Tax Rate 2% 5% 9001 and up 5.4% A Calculate the state income tax owed on a $30,000 per year salary. tax = $[?] Round your answer to the nearest whole dollar amount. Enter
The state income tax owed on a $30,000 per year salary is $1,524
What are the applicable tax rates?
The applicable tax rates are that the first $2,000 of taxable income is taxed at 2%, such that $9000 minus the earlier $2000, is taxed at 5% and any taxable income beyond $9,000 is taxed at 5.4%, in essence, the income tax owed by a taxpayer whose taxable income is $30,000 is computed thus:
income tax on first threshold=$2000*2%=$40
income tax on second threshold=($9000-$2000)*5%=$350
income tax on the last threshold=($30,000-$9,000)*5.4%=$1,134
total state income tax owed=$40+$350+$1,134
total state income tax owed=$1,524
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Watch help video
Find the distance between the two points in simplest radical form.
Answer:
(4, 3) and (-2, 0)
3√5
The distance between two points on an XY plane is calculated using the distance formula, which is employed in coordinate geometry or Euclidean geometry. The x-coordinate, often known as the abscissa, is a point's separation from the y-axis. The y-coordinate, often known as the ordinate, refers to a point's separation from the x-axis. A point on the x-axis has coordinates of the form (x, 0), and a point on the y-axis has coordinates of the form (0, y). We utilize the Pythagoras theorem in this case to determine the separation between any two points in a plane.
Distance formula = √ ( x₁ - x₂)² + ( y₁ - y₂)²
= √ 6² + 3²
=3√5
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How many GRAMS of aluminum are present in 1.40 grams of aluminum sulfate,
Al2(SO4)3?
54 grams of aluminium is present in aluminium sulphate Al₂(SO₄)₃.
What is meant by the term molecular mass/weight?A substance's molecular mass is the sum of the atomic masses of all of the atoms in the molecule of a substance.
It is applied to substances with molecules as constituent particles.The molecular mass expresses the mass of a molecule in relation to the mass of the 12C atom, that is assumed to be 12. Although molecular mass is indeed a dimensionless quantity, it is provided the unit Dalton or atomic mass unit to indicate that the mass is relative to 1/12th this same mass of a single carbon-12 atom.For the given question, the expression is;
aluminium sulphate Al₂(SO₄)₃
As three of aluminium is present in the aluminium sulphate.
And, molecular mass of one aluminium atom is 27 grams;
Thus, for 2 aluminium atoms = 2×27 = 54 grams.
Therefore, the compound aluminium sulphate contains 54 gram of aluminium in it.
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Megan's text messaging plan costs $15 for the first 500 messages and 5¢ for each additional text message. If she owes $21.55 for text messaging in the month of May, how many text messages did she send that month?
Answer:
631
Step-by-step explanation:
This problem can be expressed as:
0.05x + 15 = 21.55
0.05x + 15 - 15 = 21.55 - 15
0.05x = 6.55
0.05x/0.05 = 6.55/0.05
x = 131
We also know that:
0.05x + 15 = x + 500
If x = 131:
x + 500
131 + 500
631
Please help me redo this vin diagram. I will give a Brainly and extra pouts.
Answer:
see attached
Step-by-step explanation:
You want a Venn diagram that represents the flavor preferences of 135 students.
Venn DiagramThe diagram you show is a good start. It usually works best to start by filling in the center spot, where all three circles overlap. You have correctly identified the number liking all three flavors as 15.
Working outward, the next step is to fill in the numbers for those who like two flavors. These numbers already include the number who like all three. This means ...
caramel + vanilla (only) = (caramel + vanilla) (28) - (caramel +vanilla +chocolate (15)
caramel + vanilla (only) = 28 -15 = 13
Similar computations are done for the other "likes 2 only" spots on the diagram:
chocolate + caramel (only) = 31 -15 = 16
chocolate + vanilla (only) = 22 -15 = 7
In like fashion, the numbers for one flavor only need to subtract out the numbers already inside the circle for that flavor.
chocolate (only) = 63 -16 -15 -7 = 25
Finally, the number of students having no preference is found by subtracting the numbers inside the parts of the circles from the total number of students:
no preference = 135 -111 = 24
The attachment shows the completed diagram.
