Given : f(x) = 6x - 2 and g(x) = 2x + 4 .
Need To Find : Functions : (I). (f+g)(x) &, (II). (f-g)(x) .
ㅤ(I) (f+g)(x)
[tex]\sf\quad\dashrightarrow \:\: \big(\:f\:+\:g\: \big)\:x\: \:\\\sf\quad\dashrightarrow \:f \big(x \big)\:+\:g \big(x \big)\:\:\\\sf\quad\dashrightarrow \: \big(6x-2 \big)\:+\: \big(2x+4 \big)\:\:\\\sf\quad\dashrightarrow \:6x-2\:+\:2x+4\:\:\\\pmb{\sf\quad\dashrightarrow \:8x \: +\: 2\:}\:\\[/tex]
ㅤ(I) (f-g)(x)
[tex]\sf\quad\dashrightarrow \:\: \big(\:f\:-\:g\:\big)\:x\: \:\\\sf\quad\dashrightarrow \:f\big(x\big)\:-\:g\big(x\big)\:\:\\\sf\quad\dashrightarrow \:\big(6x-2\big)\:-\:\big(2x+4\big)\:\:\\\sf\quad\dashrightarrow \:6x-2\:-\:2x-4\:\:\\\pmb{\sf\quad\dashrightarrow \:4x \: -\: 6\:}\:\\[/tex]
Find the mean of the following data : 9, 15, 17, 18, 6, 20, 8, 5, 18, 18, 10, 5, 14, 12, 10, 7
A. 18
B. 11
C. 12
D. 15
Answer:
C.
Step-by-step explanation:
9+ 15+ 17+ 18+6+ 20+ 8+ 5+ 18+ 18+ 10+ 5+ 14+ 12+ 10+ 7=192
192/16=12
Hope this helps!
If not, I am sorry.
What is the answer to this question
Answer:
3/2,6
Step-by-step explanation:
Answer:
answer is 6/4 because 18/6=3,12/4=3 so,
Surface area of this shape please(step by step if you can)
Answer: 151.2 ft²
Step-by-step explanation:
The surface area, in this case, is the area of all the shapes given combined.
For the rectangles:
A = L * W
For the triangles:
A = [tex]\frac{L*W}{2}[/tex]
-> See attached
Now, we will add them altogether.
54 + 54 + 27 + 16.2 = 151.2 ft²
B Which of the statements is true about the polygons below E D 120 degrees C 90 90 60 60 120 degrees 90 90 F D Polygon A Polygon B A. It is possible to circumscribe a circle around each polygon because they are both quadrilaterals. B. It is not possible to circumscribe a circle about either polygon because they are both quadrilaterals. C. It is possible to circumscribe a circle about the parallelogram on the left only, because opposite angles must be supplementary D. It is possible to circumscribe a circle about the rectangle because its opposite angles are supplementary
The statement that is true about the polygons is: the opposite angles of the rectangle are supplementary, therefore, a circle can be circumscribed about the rectangle.
What is a Circumscribed Quadrilateral?An circumscribed quadrilateral is a quadrilateral whose four side lie tangent to the circumference of a circle. The opposite angles in an inscribed quadrilateral are supplementary, that is, when added together, their sum equals 180 degrees.
From the two figures given, the opposite angles of the rectangle are supplementary, therefore, a circle can be circumscribed about the rectangle. (Option D).
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Evaluate the functions for the given input values.
f(x) = x² + 1
g(x) = 2f(x)
g(-3) =
g(2) =
g(7) =
Answer:
g(-3) = 20
g(2) = 10
g(7) = 100
Step-by-step explanation:
g(x) = 2f(x) tells us that g(x) is two times f(x). Instead of f(x) we can write (x² + 1).
g(x) = 2f(x)
g(x) = 2(x² + 1)
Multiply.
g(x) = 2x² + 2
Now that we have g(x) we just substitute values in the function.
g(-3) = 2(-3)² + 2
= 2(9) + 2
= 18 + 2
= 20
g(2) = 2(2)² + 2
= 2(4) + 2
= 8 + 2
= 10
g(7) = 2(7)² + 2
= 2(49) + 2
= 98 + 2
= 100
The residents of city voted.
on whether to raise property
taxes. The ratio of yes votes
to no votes was 5 to 4. If
there were 6741 total votes,
how many no
votes were there?
Answer:
2996
Step-by-step explanation:
5x + 4x = 6741
9x = 6741
x = 6741/9
x = 749
to get the no votes,
4x i.e 4*749
=> 4*749 = 2996
hope this helps :)
Answer:
2996
Step-by-step explanation:
You want to estimate the proportion of students at your university in favor of a longer spring break. Changing the confidence level from 95% to 90% will make the necessary sample size ________ if the margin of error stays the same.
Changing the confidence level from 95% to 90% will make the necessary sample size decrease if the margin of error stays the same.
How to complete the blank?From the question, we understand that the confidence level decreases from 95% to 90%
When the confidence level decreases, the sample size increases because the standard error increases
Hence, the statement that completes the blank is decrease
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Select all the possible names for the shape.
The possible names for the shape in the image are Parallelogram and Quadrilateral since it has two equal opposite sides which are parallel.
What are the possible names of the given shape?First we take a look of the properties of the likely names;
Properties of Parallelograms
Opposite sides are parallel.Opposite angles and sides are congruent.Same-Side interior angles (consecutive angles) are supplementary.Diagonals of a parallelogram bisect each other,Properties of Quadrilaterals
Has four sides.Two diagonals.some of interior and exterior angle gives 360 degree.Properties of Rectangles
Opposite sides are parallel and equal to each other.Each interior angle is equal to 90 degrees.The diagonals bisect each otherProperties of Rhombus
Rhombus has four interior angles.The opposite angles of a rhombus are equal to each other.All four sides are equalProperties of Trapezoids
The bases (the top and bottom) are parallel to each otherThe base angles and the diagonals of an isosceles trapezoid are equal.The side lines are not parallelFrom the properties, the shape is not a rectangle because each of the interior angle is not 90 degrees. It is not a Rhombus because all its sides are not equal. It is not a Trapezoid because only the bases are parallel to each each other.
Hence, the possible names for the shape in the image are Parallelogram and Quadrilateral since it has two equal opposite sides which are parallel.
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Select the correct answer. What is the value of the expression when a = -2, b = 3, and c = -6?
Answer:
Where is the expression?
Step-by-step explanation:
Please write the expression.
please help, i need it done by today but dint know how to solve it
Answer:
B
C
B, C
Step-by-step explanation:
Equation for each tree's growth.
A: y = 4x + 5
You are correct.
B: Your slope is correct, 4.5
Equation of height: y = 4.5x + 3
C: It starts at 10 inches, so in y = mx + b, b = 10.
Now we find the slope from points on the graph (0, 10) and (3, 20).
slope = m = (20 - 10)/(3 - 0) = 10/3
Equation: y = 10x/3 + 10
Questions:
Which tree is growing fastest:
The slope is the rate of growth.
Answer: B since it has the greatest slope.
Tallest tree when planted:
The y-intercept is the4 initial height.
Answer: C since it was 10 inches tall at planting.
Challenge:
A: 4x + 5 = 4(6) + 5 = 29
B: 4.5x + 3 = 4.5(6) + 3 = 30
C: 10x/3 + 10 = 10(6)/3 + 10 = 30
Trees B and C were both 30 inches at 6 months. Tree A was 29 inches.
Answer: B and C
Solve for x. Round to nearest tenth
SOMEONE PLEASE HELP ME WITH THIS ILL GIVE YOU BRAINLIST ANSWER
Image above
Answer:
x ≈ 4.4
Step-by-step explanation:
using the tangent ratio in the right triangle
tan43° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{UV}{VW}[/tex] = [tex]\frac{4.1}{x}[/tex] ( multiply both sides by x )
x × tan43° = 4.1 ( divide both sides by tan43° )
x = [tex]\frac{4.1}{tan43}[/tex] ≈ 4.4 ( to the nearest tenth )
The value of x, Round to nearest tenth is,
⇒ x = 4.4 units
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
A triangle is shown in image.
Now, We can formulate;
tan 43° = Opposite / Base
⇒ tan 43° = 4.1 / x
⇒ 0.932 = 4.1 / x
⇒ x = 4.1 / 0.932
⇒ x = 4.39
⇒ x = 4.4 units
Thus, The value of x, Round to nearest tenth is,
⇒ x = 4.4 units
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[tex]\sqrt{25-10\sqrt{3}+3[/tex] Simplify this
[tex] \sqrt{25 \: - \: 10 \sqrt{3} \: + \: 3} [/tex]
Factor the indicated expression:[tex] \sqrt{(5 \: - \: \sqrt{3} ) ^{2} } [/tex]
Simplified the index index the root and also the exponent using the number 2.[tex] \boxed{ \bold{5 \: - \: \sqrt{3} }}[/tex]
MissSpanish
What is the value of x?
(Round your answer to
the nearest tenth.)
Answer:
x ≈ 8.7
Step-by-step explanation:
given 2 secants from an external point to the circle, then
the product of the external part of one secant and the entire secant is equal to the product of the external part of the other secant and the entire secant , that is
6(6 + x) = 4(4 + 18) ← distribute parenthesis on both sides
36 + 6x = 4 × 22 = 88 ( subtract 36 from both sides )
6x = 52 (divide both sides by 6 )
x ≈ 8.7 ( to the nearest tenth )
A drum full of rice weighs 241/6 kg. If the empty drum weighs 55/4 kg, find the weight of rice in the drum.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the diagonal of the rectangular solid with the given measures. (Part of the answer is provided for you.)
l = 18, w = 10, h = 2
Answer:
Step-by-step explanation:
Length=18
Width/Breadth =10
Height=2
The formula for a diagonal face of a cuboid is=√(l²+ b²)
Face diagonal=√(18²+10²)
= 20.59 to 2.d.p
The formula for the body diagonal of a cuboid is=√(l² + b² + h²)
Body diagonal=√(18² + 10² + 2²)
=20.69 to 2.d.p
Halle deposited $4000 into an account that earns 5% interest each year. the growth of her investment can be expressed by the exponential equation a = 4000(1 + 0.05)t , where a is the amount in the account after t years. in how many years will her account exceed $10,000?
After 18.8 years, Halle account exceed $10,000 if Halle deposited $4000 into an account that earns 5% interest, each year.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]
where a is a constant and a>1
We have an exponential equation:
[tex]\rm a = 4000(1+ 0.05)^t[/tex]
Plug a = $10,000
[tex]\rm 10000 = 4000(1+ 0.05)^t[/tex]
After calculating:
[tex]\rm 1.05^t= 2.5[/tex]
t = 18.78 ≈ 18.8 years
Thus, after 18.8 years, Halle account exceed $10,000 if Halle deposited $4000 into an account that earns 5% interest each year.
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Solving a
Try it
Solve for the width in the formula for the area of a rectangle.
W=A-I
Xw = Al
W = 1/A
W = A/l
The expression w = A/l can be used to find the width of the rectangle if the area and length of the rectangle are given.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
Let's suppose the width of the rectangle is w and the length of the rectangle is l
Then, the area of rectangle(A) can be given as:
A = lw
divide by l on both the sides:
A/l = lw/l
A/l = w
or
w = A/l
Thus, the expression w = A/l can be used to find the width of the rectangle if the area and length of the rectangle are given.
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36. in a group of 5 freshman, 10 sophomores, 3 juniors, and 2 seniors, how many ways can a president, vice president, and treasurer be elected?
Using the permutation formula, it is found that the people can be chosen for the roles in 6840 ways.
The order in which the people are chosen is important, as there are different roles, hence the permutation formula is used.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 3 people will be chosen from a set of 20 people, hence the number of ways is given by:
[tex]P_{20,3} = \frac{20!}{17!} = 6840[/tex]
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help me please thank you :D
Answer:
5/7 - 2/6 = 16/42
Choice 4^th
Step-by-step explanation:
Given equation:
5/7 - []/6 = 16/42
To Find:
The missing numerator
Solution:
Let us assume that the missing numerator is x.
Then the equation will be:
[tex] = > \cfrac{5}{7} - \cfrac{x}{6} = \cfrac{16}{42} [/tex]
Solve the equation to get our solution.
[tex] = > \cfrac{5}{7} - \cfrac{1x}{6} = \cfrac{16}{42} [/tex]
You'll need to re-write this equation as:
[tex] = > \cfrac{ - 1x}{6} + \cfrac{5}{7} = \cfrac{8}{21} [/tex]
Subtract 5/7 from both sides:
[tex] = > \cfrac{ - 1x}{6} + \cfrac{5}{7} - \cfrac{5}{7} = \cfrac{8}{21} - \cfrac{5}{7} [/tex]
[tex] = > \cfrac{ - 1}{6} x = \cfrac{ - 1}{3} [/tex]
Multiply both sides by 6/-1:
[tex] = > \cfrac{ \cancel{- 1}}{ \cancel6} x \times \cfrac{ \cancel6}{ \cancel{- 1}} = \cfrac{ \cancel{- 1}}{ \cancel3} \times \cfrac{ \cancel6 {}^{2} }{ \cancel{ - 1} }[/tex]
[tex] = > \boxed{ x = 2}[/tex]
Hence,
5/7 - 2/6 = 16/42
Choice 4^th
[tex] \rule{225pt}{2pt}[/tex]
The circle below has a center D and its diameter is 10 feet. Given that m angle A D B equals 35 degree, find the length of major arc stack A C B with overparenthesis on top.
A circle with center D and points A B C on the circle. Angle A D B is 35 degrees formed by radius B D and A D.
Group of answer choices
35 over 36 straight pi feet
325 over 18 straight pi feet
325 over 36 straight pi feet
35 over 18 straight pi feet
The length of major arc ACD in the circle with center D is given as (325/36)π feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The length of major arc ACD = [(360 - 35) / 360) * 2π(10/2) = (325/36)π feet
The length of major arc ACD in the circle with center D is given as (325/36)π feet
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A 12 m ladder propped against a wall forms an angle of 60° with the ground. Determine
how far the top of the ladder is from the ground. Include a diagram.
Answer:
the top of the ladder is approx 8.485 meters off the ground
written explanation included
Step-by-step explanation:
I should probably write this out in one note but bear with me, please.
Assuming the ground and the wall meet at a 90° angle
therefore the angles of the triangle formed are 90°, 30°, and 60°
756 x 300??????? ?????????
Answer:
226,800
Step-by-step explanation:
Calculator
Answer:226,800
Step-by-step explanation:
A new movie was released over the weekend with 8 show times. 124 people saw the movie during the first 2 show times. If people come to the movie at the same rate, how many saw it over the weekend?
Answer:
496 people
Step-by-step explanation:
If 124 people attend 2 show times, in 8 show times (8 is four times of 2 show times; 8 / 2 = 4) there will be 124 · 4 people.
124 · 4 = 496.
In 8 show times, there will be 496 people who view the movie
(Or, if there are 124 people in 2 shows, it means that there were 62 people in each show [assuming the crowd was split evenly], and if there were 8 shows, there would be 62 · 8 people, 62 · 8 = 496)
What is the range of the function graphed below?
On a coordinate plane, a graph shows a curve with two points. A solid point is at (1, 3) and an open point is at (4, negative 3).
1 less-than-or-equal-to y less-than 4
Negative 3 less-than y less-than-or-equal-to 3
Negative 2 less-than-or-equal-to y less-than-or-equal-to 3
Negative 3 less-than-or-equal-to y less-than 4
Answer:
Negative 3 less-than y less-than-or-equal-to 3
Step-by-step explanation:
By looking at a coordinate plane, we can easily see the range
remember, a closed dot means includes , and an open dot means does not include
[closed dot]
(open dot)
the range is all possible y-values. so, all y values shown are
3 which it includes
to -3 which it excludes / does not include
so, all y values are greater than -3 and less than or equal to 3
The entrance to the louvre museum in paris is a pyramid made of glass and steel. the height of the pyramid is 22 meters and the base is a square with a width of 35 meters. what is the volume of the louvre pyramid to the nearest cubic meter?
Based on the calculations, the volume of this louvre pyramid is equal to 8,983 cubic meter..
Given the following data:
Base width = 35 meters.
Height = 22 meters.
How to calculate the volume of a pyramid?Mathematically, the volume of a pyramid can be calculated by using this formula:
Volume = 1/3 × base area × height
For the base area, we have:
Area = w²
Area = 35² = 1,225 m².
Substituting the parameters into the formula, we have;
Volume = 1/3 × 1,225 × 22
Volume = 1/3 × 26,950
Volume = 8,983 cubic meter.
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can someone do this for me please?! Just the answer pls
Answer:
see the attachment photo!
Can you guys pls help me with this math question
Answer:
Dimensions: 125 m x 250 m
Area: 31,250 m²
Step-by-step explanation:
Given information:
Total amount of fencing = 500mOnly 3 sides of the land need to be fencedFirst, let us assume that the land is rectangular in shape.
Let [tex]y[/tex] = length of the side opposite the river
Let [tex]x[/tex] = length of the other 2 sides of the land
Therefore, we can create two equations from the given information:
Area of land: [tex]A= xy[/tex]
Perimeter of fence: [tex]2x + y = 500[/tex]
Rearrange the equation for the perimeter of the fence to make y the subject:
[tex]\begin{aligned} \implies 2x + y & = 500\\ y & = 500-2x \end{aligned}[/tex]
Substitute this into the equation for Area:
[tex]\begin{aligned}\implies A & = xy\\& = x(500-2x)\\& = 500x-2x^2 \end{aligned}[/tex]
To find the value of x that will make the area a maximum, differentiate A with respect to x:
[tex]\begin{aligned}A & =500x-2x^2\\\implies \dfrac{dA}{dx}& =500-4x\end{aligned}[/tex]
Set it to zero and solve for x:
[tex]\begin{aligned}\dfrac{dA}{dx} & =0\\ \implies 500-4x & =0 \\ x & = 125 \end{aligned}[/tex]
Substitute the found value of x into the original equation for the perimeter and solve for y:
[tex]\begin{aligned}2x + y & = 500\\\implies 2(125)+y & = 500\\250+y & = 500\\y & = 250\end{aligned}[/tex]
Therefore, the dimensions that will give Christine the maximum area are:
125 m x 250 m (where 250 m is the side opposite the river)
The maximum area is:
[tex]\begin{aligned}\implies \sf Area_{max} & = xy\\& = 125 \cdot 250\\& = 31250\: \sf m^2 \end{aligned}[/tex]
help please i need answers fast if you help or try to help tysm *hearts*
Answer:
C. 3rd one Fraction 10/24
Step-by-step explanation:
3/4 - 2/6 = 0.41 or = 10/24 or it could be equal to 5/12 are 10/24, 15/36, 20/48 and 25/60 or as Decimal 0.41
Step-by-step explanation:
Hope This Helped
A grocery store sells a bag of 6 oranges for $2.34. If Mav spent $1.95 on oranges, how many did she buy?
Answer:
5 oranges
Step-by-step explanation:
to solve this problem we need to make a cross-multiplication equation
2.34 is to 6 as 1.95 is to ?
? is the number of oranges that are needed to be found that were bought
2.34/6 = 1.95/?
Now we cross multiply 6 and 1.95 = 11.7
11.7/2.34 = 5
Give brainliest, please!
hope this helps :)
Answer: She bought 5 oranges
Step-by-step explanation:
We need to find out how much one orange costs first, so we do:
$2.34 ÷ 6or = $0.39
Thirty-nine cents is how much one orange cost.
Now you multiply the initial value of 1 orange by 5, so:
$0.39 x 5 = $1.95, $1.95 =5 oranges
You can also do $1.95 divided by $0.39 which is 5.
(you can multiply till you find the number or divide the given number by the other divided number)
Therefore, that means Mav bought 5 oranges.
Select all the correct answers.
What are the solutions to this equation?
5 - √√(x² - 9) = 7
1
-√17
√17
There are no solutions.
-1