Answer:
(f - g)(x) = [tex]3^{x}[/tex] + 8x + 4
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= [tex]3^{x}[/tex] + 10x - (2x - 4) ← distribute parenthesis by - 1
= [tex]3^{x}[/tex] + 10x - 2x + 4 ← collect like terms
= [tex]3^{x}[/tex] + 8x + 4
HURRY PLEASE
What is measure of
First, find the supplement of the angle that is 105 degrees.
105 + 75 = 180
Now, we can find complete the lower left triangle's angles.
39 + 75 + ? = 180
? = 66 degrees
The 66 degree angle of the lower left triangle and angle x are vertical angles. Vertical angles are congruent.
Therefore, the measure of angle x is 66 degrees.
Hope this helps!
Need help in this pls
Answer:
6
Step-by-step explanation:
The arc length is (2)(pi)(27)(40/360)=6pi.
So, k=6.
The length of a rectangle is 6 more than twice the width. if the area is 40 cm^2, find the length and breadth of the rectangle
Answer: 3.217 & 12.434
Step-by-step explanation:
If we use w to represent the width, the length will be 6 more than 2 times w.
Hence, the length is [tex]2w+6[/tex].
The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.
[tex]A=w(2w+6)[/tex]
We can also substitute 40 in for A as it's given in the question.
[tex]40 = w(2w+6)[/tex]
Distributing w by multiplying it by both terms in the parentheses, we get
[tex]40 = 2w^2+6w[/tex]
We can make the equation simpler by dividing both sides by 2.
[tex]20 = w^2+3w[/tex]
Subtracting both sides by 20 will make the left-hand side 0.
[tex]0=w^2+3w-20[/tex]
Now that we have put this quadratic equation into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.
For reference, the quadratic formula is
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a is 1, b is 3, and c is -20.
Substituting, we get
[tex]w=\frac{-3\pm\sqrt{3^2-4(1)(-20)}}{2(1)}[/tex]
[tex]w= \frac{-3\pm\sqrt{9+80}}{2}[/tex]
[tex]w=\frac{-3+\sqrt{89}}{2}\hspace{0.1cm}or\hspace{0.1cm}\frac{-3-\sqrt{89}}{2}[/tex]
Since the second solution results in a negative number, it cannot be the length of w.
[tex]w=\frac{-3+\sqrt{89}}{2}\approx3.217[/tex]
The width/breadth of the rectangle is 3.217 cm.
To calculate the length, let's substitute the width into the expression for the length:
[tex]l=2(3.217)+6[/tex]
[tex]l=12.434[/tex]
The length of this rectangle is 12.434 cm.
Please help and explain how to solve
Answer:
$ 7.52
Step-by-step explanation:
Find charge per minute
59 - 23 min = 36 minutes cost 16.32 - 10.56 = $ 5.76
or $5.76 / 36 min = 16 cents per min
from 59 to 78 = 19 more minutes x .16/min = $ 3.04
so from 59 to 78 will leave 10.56 - 3.04 = $7.52
20 POINTS
good morning, can you please help me
The area of the paper that remains is 391.04 cm²
Calculating areaFrom the question, we are to calculate the area of the remaining part of the paper
Area of the paper that remains = Area of rectangle - 2×Area of semicircle
Area of the paper that remains = (l×w) - 2(πr²/2)
Area of the paper that remains = (l×w) - (πr²)
Where l is the length of the paper
w is the width if the paper
and r is the radius of the semicircle
From the given information,
l = 37 cm
w = 16 cm
r = w/2 = 16/2 = 8 cm
Putting the parameters into the equation,
Area of the paper that remains = (37×16) - (3.14(8)²)
Area of the paper that remains = 592 - (3.14×64)
Area of the paper that remains = 592 - 200.96
Area of the paper that remains = 391.04 cm²
Hence, the area of the paper that remains is 391.04 cm²
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Which equation is the inverse of Y equals 9X Square -4
[tex]y = 9x {}^{2} - 4 \\ flip \: x \: and \: y \\ x =9 (y ) {}^{2} - 4 \\ solve \: for \: the \: inverse \: of \: y \\ x + 4 = 9(y ) {}^{2} \\ y {} {}^{2} = \frac{x + 4}{9} \\ you \: can \: split \: it \: into \: two[/tex]
[tex]y {}^{(1)} = \sqrt{ \frac{x + 4}{9} } \\ y {}^{(2)} = - \sqrt{ \frac{x + 4}{9} } [/tex]
What is the shape of the graph of the function?
h(t)=0.6\cdot 3.2^th(t)=0.6⋅3.2
t
The graph of a function f exists the set of all points in the plane of the form (x, f(x)).
What is the graph of a function?
The graph of a function f exists the set of all points in the plane of the form (x, f(x)). We could even describe the graph of f to be the graph of the equation y = f(x). So, the graph of a function exists as a special case of the graph of an equation.
Given: [tex]h(t)=0.6\cdot 3.2^t[/tex]
Substitute the values in the function, we get
t = -2, h(t) = 0.05859375
t = -1, h(t) = 0.1875
t = 0, h(t) = 0.6
t = 1, h(t) = 1.92
t = 2, h(t) = 6.144
t = 3, h(t) = 19.6608
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I need help please?
A. {penguin, seagull, crow}
B.{penguin, seagull, crow, bat, mosquito}
C.{seagull, crow}
D.{seagull, crow, bat, mosquito}
The Outcome of event A and B is simply the intersection of both sets written as A ∩ B is; C: {seagull, crow}
How to write sets notation?From the image, we are given the animals namely; Pig, Penguin, Seagull, Tiger, Crow, Bat, Mosquito.
Now, these animals are classified as either a bird or can fly.
Animals that are birds are; Penguin, Seagull, Crow
Animals that can fly are; Seagull, Crow, Bat, Mosquito.
Now, we are told that;
Event A is the animal is a bird. Thus, the set notation that represents this event A is written as;
A = {Penguin, Seagull, Crow}
Event B is that the animal can fly and again the set notation that represents event B is written as;
B = {Seagull, Crow, Bat, Mosquito}
Now, Outcome of event A and B is simply the intersection of both sets. Thus; A ∩ B = {seagull, crow}
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If u are 13, and ur birthday is 21 of october, how old will you be in 2050?
Answer:
41 years old
Step-by-step explanation:
2050-2022=28 years
13years old +28years = 41 years old (sorry if wrong)
Answer: Based on today's date of 7/19/2022, you will be 41 until October 21, 2050. On October 21, 2050 you will turn 42. You were born in 2008
Step-by-step explanation:
Find the surface area of the composite figure. Round to the nearest tenth if necessary.
The surface area of the composite figure shown in the figure attached is 233.6 cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The surface area of the composite = (6 * 8) + 2(8 * 3.6) + 2(0.5)(6 + 2 + 6 + 2)(3) + (8)(2 + 6 + 2) = 233.6 cm²
The surface area of the composite figure shown in the figure attached is 233.6 cm²
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PLEASE HELP FAST!
A figure has rotational symmetry if a rotation of 180°
or less produces an image that fits exactly on the original figure. Select each degree of rotation that shows the figure below has rotational symmetry.
30 °
45 °
60 °
90 °
120 °
135 °
150 °
180 °
Answer:180 °
Step-by-step explanation:
Answer:
90 degrees
Step-by-step explanation:
The only numbers that are possible to be divided into 180 are these: 30, 45, 60, 90, & 180.
Now to figure out if this figure is symmetrical. It is. Why? Because you can put at least one line through each triangle. 8 in total but 180 cannot be divided by 8. So you could maybe split it in half. 180/4= 45
45x2= 90
Easy: Since there are now, two halves, since it is split up, it could be possible that the answer could be 90. Because 180/2 halves= 90.
The answer is 90
what scale factor can be applied to Cone 1 to make Cone 2?
The scale factor that can be applied to Cone 1 to make Cone 2 is 0.8
What are scale factors?This are constants that is used to enlarge of diminish a given figure of sides of a figure
We can determine the scale factor by finding the ratio of the similar sides of two figures, From the given cones, the ratio of their radius can determine the scale factor that is applied to Cone 1 to make Cone 2
From the given figure;
scale factor = radius of cone 2/radius of cone 1
Given the following parameters
radius of cone 2 = 2 ft
radius of cone 1 = 2.5ft
Substitute
scale factor = 2/2.5
scale factor = 0.8
Hence the scale factor that can be applied to Cone 1 to make Cone 2 is 0.8
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If the ratio of areas of two similar solids is 25:36, what is the linear ratio.
Answer: Hi here go your answer is
25 divides by 36 is 0.69444 or 0.69
Step-by-step explanation:
can someone please help me
answer choices:
A - sin(0°)
B - cos(0°)
C - sin(180°)
D - cos(180°)
E - sin(270°)
F - cos(270°)
Answer:
B
Step-by-step explanation:
Cos(0)=1
since the diagram shows x as (1,0)
Find the zeros of: [tex]f(x)=-\frac{1}{1500} (x^3+10x^2-275x-1500)[/tex], and the use them to find all of the linear factors of the polynomial function
The function f(x) = -(1/1500)(x³ + 10x² - 275x - 1500) the zeros are at (-20, 0), (-15, 0) and (15, 0). Hence the factors of the function are x + 20, x + 15 and x - 15.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the graph of the function f(x) = -(1/1500)(x³ + 10x² - 275x - 1500) the zeros are at (-20, 0), (-15, 0) and (15, 0). Hence the factors of the function are x + 20, x + 15 and x - 15.
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what is the solution of |2x+3|< 19
Answer:
- 11 < x < 8
Step-by-step explanation:
inequalities of the type | x | < a have solutions of the form
- a < x < a
then
| 2x + 3 | < 19
- 19 < 2x + 3 < 19 ( subtract 3 from each interval )
- 22 < 2x < 16 ( divide each interval by 2 )
- 11 < x < 8
Complete the following table:
The students at a High School earned money for an international animal rescue foundation. 82 seniors earned an average $26.75 per student, 74 juniors earned an average $12.25 per student, 96 sophomores earned an average $15.50 per student, and 99 freshmen earned an average $10.85 per student. What was the average collection for a student in this school?
Using the mean concept, the average collection for a student in this school was of $16.13.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
The number of students is given as follows:
82 + 74 + 96 + 99 = 351.
The sum is:
82 x 26.75 + 74 x 12.25 + 96 x 15.50 + 99 x 10.85 = $5662.15
Hence the mean is:
M = $5662.15/351 = $16.13.
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What is the value of -3/2÷-7/2?
The value of the given division operation is 3/7
Division operationFrom the question, we are to determine the quotient of the given division operation
The given division operation is
-3/2÷-7/2
[tex]\frac{-3}{2} \div \frac{-7}{2}[/tex]
[tex]=\frac{-3}{2} \times \frac{2}{-7}[/tex]
[tex]=\frac{-3}{-7}[/tex]
[tex]=\frac{3}{7}[/tex]
Hence, the value of the given division operation is 3/7
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WILL MAKE BRAINLIEST!! Solve for b
Answer: 32
Step-by-step explanation:
The line is straight meaning 180 angle. When finding B you subtract 148 by 180 which would be 32.
What is the maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot
abc =32 ft³ is the maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot.
Calculate a square's area?A rectangle with all equal sides, commonly known as a square. Multiplying the length by the length is the. Using L as the length of each side, solve for L X L = L2,
The maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot This Lagrange multiplier optimization is standard. If the box has a base of a, a height of c, and an area constraint of ab+2ac+2bc−48=0 we wish to optimize V= abc.
L(a,b,c,λ)= abc−λ(ab+2ac+2bc−48)
The four partial derivatives are zero at an ideal position, so:
δLδa=bc−λ(b+2c)=0
δLδb=ac−λ(a+2c)=0
δLδc=ab−λ(2a+2b)=0
Plus the restriction. The first two enlighten:
λ=bcb+2c=aca+2c
Consequently, b(a+2c)=a(b+2c) implies to b=a. The third partial, where b=a, now informs us that a2=4aλ and so λ=a/4 nd by using this information in the second partial, we obtain 4c=a+2c which informs us that c=a/2 .
Now that we've inserted these b and c expressions into the constraint, we get [tex]3a^2=1[/tex] which means that a=4 feet, b=4 feet, and c=2 feet.
The maximum volume is therefore, abc=32 ft³
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AABC is an isosceles triangle. AB is the longest side with
length 9x+3, BC = 4x+6 and CA = 3x+9. Find AB.
Answer:
30
Step-by-step explanation:
Since ABC is isosceles, BC = CA.
4x + 6 = 3x + 9x = 3So, AB = 9(3)+3 = 30.
15. If 3x + 10 = 3y - 2(y + 4), what is the value of y in terms of x? (A) x + 18 (B) 3x+6 (C) 3x + 14 (D) 3x + 18
Answer:
3x + 18
Step-by-step explanation:
3x + 10 = 3y - 2(y + 4)
3x + 10 = 3y - 2y - 8
3x + 18 = y
Answer:
D, 3x + 18.
Step-by-step explanation:
3x + 10 = 3y - 2(y + 4)
3x + 10 = 3y - 2y - 8
3x + 10 = y - 8
y = 3x + 10 + 8
y = 3x + 18.
2x⁴ - 4-7x - 38x²/x - 4
Answer:
2x⁴-45x-8
Step-by-step explanation:
The ratio of boys to girls who play soccer in Mr. Fraser’s class is 14:6. If there were 400students in the school, how many boys would likely play soccer?
Answer:
280
Step-by-step explanation:
Set up a ratio to solve.
Mr. Fraser's class has 20 soccer playing students, and 14 are boys.
14/20 = x/400
Cross multiply. 20x= 5600
Divide by 20 to solve
x= 280
In a bag of 10 marbles, there are 4 blue, 3 red, 2 green,
and 1 yellow. What is the probability that you draw one
marble that is green, DO NOT replace it, and draw another
marble that is yellow?
1
30
O b. 139
OC. 15
45
a.
O d. 7/19
2
Answer: 1/45
Step-by-step explanation: 10 total marbles. 4 are blue 3 are red 2 are green and 1 is yellow. The chance of drawing a green is 2/10 or 1/5. Then there are only 9 marbles left in the bag. So the chance of a yellow marble is 1/9. 1/5 x 1/9 = 1/45.
A city architect is designing a parking garage at city hall. the garage layout is in the shape of a rectangle. the width of the
garage is x + 15, where x is measured in feet. the length of the garage is 49 feet less than 2 times the width. the square
footage (area) that the parking garage covers should be 162 more than 27 times the garage's perimeter. find the length an
width of the parking garage that fits these requirements.
part a
The measure of the length and width of the rectangle is given as 135 feet and 92 feet respectively.
How to determine the dimensionsFrom the information given, we have the following proofs;
Width, w = x+15 Length, l = 2(x+15) - 49Length, l = 2x + 30 - 49
Length = 2x - 19
The formula for perimeter of a rectangle is given as;
Perimeter = 2( length + width)
Substitute the expressions into the formula
Perimeter = 2 ( x+ 15 + 2x - 19 )
Perimeter = 2 (3x - 4)
Perimeter = 6x - 8
We have that the area is 162 more than 27 times the perimeter, which is Area = 27 (perimeter )+ 163
Area = 27(6x-8) + 162
Expand the bracket
Area= 162x - 216 + 162
Area = 162x - 54
But we know that
Area = length × width
Substitute the expressions
Area = (x+15)(2x-19)
Area = 2x² - 19x +30x - 285
Area = 2x² + 11x - 285
Equate the two formulas for area
162x - 54 = 2x² +11x - 285
Collect like terms
2x² + 11x - 285 - 162x + 54 = 0
2x² - 151x - 231 = 0
Solve the quadratic equation
(2x + 3)(x-77) = 0
Let's solve for x
x - 77 = 0
x = 77
The expression for the width;
Width = x+15
Width = 77 + 15
Width = 92 feet
The expression for the length
Length = 2(x+15) - 49
Length = 2 ( 77 + 15) - 49
Length = 154 + 30 - 49
Length = 184 - 49
Length = 135 feet
Thus, the measure of the length and width of the rectangle is given as 135 feet and 92 feet respectively.
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Please help me fast
What is the equation of this graph
Answer-4,5
Step-by-step explanation:
Write an equation of the line point(2,-1) and parallel passing through y=3x-5 write in slope-intercept form
Answer:
y = 3x - 7
Step-by-step explanation:
Since the lines are parallel, the slopes will be the same. In this case 3. Now we have to find the y-intercept. We will use the slope (3), the x (2) and y (-1) to help us do this. We get the x and the y from the ordered pair given(2,-1).
y = mx + b
-1 = 3(2) + b Plug in what you know
-1 = 6 + b Subtract 6 from both sides
-7 = b
Now we can write the equation
y = 3x -7
Determine whether the function f(x) = 3x is even or odd.
The function is even because f(-x) = f(x).
The function is odd because f(-x) = f(x).
The function is even because f(-x) = -f(x).
The function is odd because f(-x) = -f(x).
Answer: The function is even because [tex]f(x)=f(-x)[/tex].
Step-by-step explanation:
[tex]f(x)=3x^4 \\\\f(-x)=3(-x)^4 = 3x^4\\\\\therefore f(x)=f(-x)[/tex]
So, the function is even.