Answer: [tex]g(f(a))=1.07a+50[/tex]
Step-by-step explanation:
The given functions are: [tex]f(a)=1.07a[/tex] and [tex]g(b)= b+50[/tex]
[tex]g(f(a))[/tex] means [tex]f(a)[/tex] is the input of the function [tex]g[/tex].
Thus, [tex]g(f(a))= g(1.07a)[/tex]
Now replacing [tex]b[/tex] as [tex]1.07a[/tex] into the given function of [tex]g(b)[/tex], we will get......
[tex]g(1.07a)= 1.07a+50[/tex]
So, [tex]g(f(a))=1.07a+50[/tex]
Let x = a + bi and y = c + di and z = f + gi Which statements are true? Check all of the boxes that apply. x + y = y + x (x × y) × z = x × (y × z) x – y = y – x (x + y) + z = x + (y + z) (x – y) – z = x – (y – z)
The usual rules of addition and multiplication apply to complex numbers as well as to real numbers. The true statements are ...
x + y = y + x . . . . . . . . . . . . . . . commutative property of addition(x × y) × z = x × (y × z) . . . . . . . . associative property of multiplication(x + y) + z = x + (y + z) . . . . . . . . associative property of additionThe true statements after evaluating the expression based on principle of commutativity and associativity are :
x + y = y + x(x × y) × z = x × (y × z)(x + y) + z = x + (y + z)x = a + bi
y = c + di
z = f + gi
Recall :
Commutative property establishes that, if the ordering of the numbers an addition or multiplication expression, is changed, the result is unchanged : a + b = b + a The Associative property maintains that, the grouping of values in a multiplication operation does not affe t the result of the product. : a × ( b × c) = b × (a × c) = c × (b × a)Evaluating the options :
x + y = y + x ; This is true (Commutative property of addition) (x × y) × z = x × (y × z) (True according to the Associative property) x - y = y - x (False) (x + y) + z = x + (y + z) (True ; Commutative property) (x – y) – z = x – (y – z) (False)Hence, only 3 of the given statements are true, according to the Commutative or Associative rule.
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Which relation is a function?
the diagram on the top left hand side is a function
For each value of x on the domain (x- axis ) there can only be one corresponding value of y in the range (y- axis)
Apart from the diagram on the top left side, the other 3 all fail this definition
While riding her bike to the ocean and back home 7 7 times, Corinne timed herself at 52min 52min , 63min 63min , 66min 66min , 60min 60min , 51min 51min , 69min 69min , and 50min 50min . She had set a goal of averaging 59 59 minutes for her rides. How many minutes will she need to spend on her eighth ride to attain her goal?
this is a late assignment, help a girl out hah..
she would need to ride for 61 minutes
I need some help with this!
(-x³ +3x +4) -(2x³ +7x² -9) = -x³ +3x +4 -2x³ -7x² +9 . . . . eliminate parentheses
= x³(-1-2) +x²(-7) +x(3) +(4+9)
= -3x³ -7x² +3x +13 . . . matches the second choice.
what is the sine value of 7pi/6
A. - sqrt 3 over 2
B. Sqrt 3 over 2
C. - 1/2
D. 1/2
Answer:
C. -1/2
Step-by-step explanation:
7π/6 radians is equivalent to (7π/6)(180°/π) = 210°, a 3rd-quadrant angle whose reference angle is 30°. The sine of angles in the 3rd quadrant is negative.
sin(30°) = 1/2
sin(210°) = -sin(30°) = -1/2
_____
In radians mode, your calculator can tell you this result directly.
C - [tex]\frac{1}{2}[/tex]
sin(7π / 6 )
note 7π\6 is in the third quadrant where sin is negative
the related acute angle to 7π/6 is 7π/6 - π = π/6
sin (7π/6) = - sin(π/6) = - [tex]\frac{1}{2}[/tex]
Which represents a side length of a square that has an area of 450 square inches? 15 sqrt 2 in. 15 sqrt 3in. 112.5 in. 115.5 in.
15√2
area = s² = 450 ← s is length of side
to find s take the square root of both sides
s = [tex]\sqrt{450}[/tex] = [tex]\sqrt{2(9)(25)}[/tex]
= √2 × √9 × √25 = √2 × 3 × 5 = 15√2
15√2 represents a side length of a square that has an area of 450 square inches.
The answer is option A.
How to find the side length of a square?The area of any quadrilateral can be determined by multiplying the length of its base by its height.
area = s² = 450 ← s is length of side
to find s take the square root of both sides
s = √450 = √2(9)(25)
= √2 × √9 × √25 = √2 × 3 × 5 = 15√2
Since we know the shape here is square, we know that all sides are of equal length. From this, we can work backward by taking the square root of the area to find the length of one side.
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the length of the hypotenuse of a right triangle is 13 m. The length of one leg in 5 cm. find the length of the other leg
PLEASE HELP AND FAST!
other leg = 12 cm
using Pythagoras' identity with x as the side to be found, then
x = √(13² - 5² ) = √(169 - 25 ) =√144 = 12
In the troposphere, one layer of the Earth's atmosphere, the temperature decreases with increasing altitude from approximately 17°C at Earth’s surface to –51°C at the boundary with the next layer. By how many degrees Celsius does the temperature change in the troposphere?
WILL GIVE BRAINLIEST AND 99 POINTS!!
What is the measure of ∠ A in this quadrilateral?
Answer:
30°
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360°. You have 3 angles given, so can find the fourth using that fact. (The double arcs on angles B and C mean those angles are congruent. Same symbols are used to mark same-size angles.)
... 360° = A + B + C + D
... 360° = A + 115° + 115° + 100°
... 360° -330° = A = 30°
g(x) = 2x − 1 h(x) = 1 − g(x) The functions g and h are defined above. What is the value of h(0)?
Answer:
h(0) is equal to 2.
Step-by-step explanation:
In order to find this, we first put 0 in for x in the g(x) equation.
g(x) = 2x - 1
g(0) = 2(0) - 1
g(0) = -1
Now that we have this, we can stick the answer for g(x) into the f(x) equation.
f(x) = 1 - g(x)
f(x) = 1 - -1
f(x) = 1 + 1
f(x) = 2
The value of [tex]h(0)[/tex] is 2.
It is given that,
[tex]g(x)=2x-1[/tex][tex]h(x)=1-g(x)[/tex]Explanation:
We have,
[tex]h(x)=1-g(x)[/tex]
[tex]h(x)=1-(2x-1)[/tex]
[tex]h(x)=1-2x+1[/tex]
[tex]h(x)=2-2x[/tex]
Substitute [tex]x=0[/tex] in the above function.
[tex]h(0)=2-2(0)[/tex]
[tex]h(0)=2-0[/tex]
[tex]h(0)=2[/tex]
Thus, the value of [tex]h(0)[/tex] is 2.
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M is the midpoint of segment AB. A has the coordinates (-5,4) and M is at the origin. Find the coordinates of B
Using geometry:
Since M is the origin, point B is the mirror image of point A with respect to the origin. From the origin to point A, you go 5 units left and 4 units up. For the mirror image, start at the origin, and go 5 units right and 4 units down.
Answer: B(5, -4)
Using the midpoint formula:
[tex] x_m = \dfrac{x_1 + x_2}{2}~~~and~~~y_m = \dfrac{y_1 + y_2}{2} [/tex]
[tex] 0 = \dfrac{-5 + x_2}{2}~~~and~~~0 = \dfrac{4 + x_2}{2} [/tex]
[tex] 0 = -5 + x_2~~~and~~~0 = 4 + x_2 [/tex]
[tex] -x_2 = -5~~~and~~~-4 = x_2 [/tex]
[tex] x_2 = 5~~~and~~~x_2 = -4 [/tex]
Answer: B(5, -4)
As you can see, both methods give you the same answer.
baseball field.....................
Umm. What is the question?
The design and layout of a Baseball Field Design to the game experience by affecting play flow and ensuring visibility, vital for both players and fans. Elements like the diamond infield and the extensive outfield reflect American sports culture, which emphasizes strategy and skill, and has historically fostered community engagement and identity.
The design and layout of a baseball field significantly impact the experience of the game by determining the flow of play and the visibility of actions, which is crucial for player performance and fan engagement.
Specific elements, such as the diamond shape of the infield and the expansive outfield, align with the American sports culture, which values a balance between strategy and physical skill, offering a variety of play styles from power hitting to meticulous base running.
The historical evolution of professional baseball teams and their ballparks reflects a facet of American identity through sports, as communal spaces like Fenway Park and Forbes Field facilitated a collective civic pride and a space for social interaction among diverse groups including immigrants.
Moreover, participation in sports, even at the informal level of pickup games, represents an integral part of cultural dynamics in American society, aligning with the practice of community building and local support within the cultural geography framework.
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The probable question may be:
How does the design and layout of a baseball field contribute to the overall experience of the game, and what specific elements align with the principles of American sports culture as taught in the curriculum?
The graph below represents the distance of a dog from a trainer after a command is given.
Which statement could describe the dog’s movement 5 seconds after the command was given?
The dog stopped to lie down and obey the trainer’s command.
The dog was running towards the trainer to receive a treat.
The dog was running away from the trainer to chase a squirrel.
The dog was stopped but began running towards the trainer.
Answer:
The dog was running towards the trainer to receive a treat
Step-by-step explanation:
At the point on the graph where Time is 5 (seconds), the slope of the distance vs time curve is negative, indicating the dog is moving toward the trainer. The motivation of the dog is unknown, so the above answer choice involves speculation that is not supported by the problem statement.
Answer:B.The dog was running towards the trainer to receive a treat.
Step-by-step explanation:cuz im right
The class has 14 boys, 12 girls, and one teacher. What is the ratio boys to girls?
Final answer:
The ratio of boys to girls in the class is 14:12, which simplifies to 7:6.
Explanation:
The ratio of boys to girls in the class is determined by comparing the number of boys to the number of girls.
Given that there are 14 boys and 12 girls, the ratio of boys to girls is:
14 boys : 12 girls
This can be simplified by dividing both numbers by the greatest common divisor, which is 2 in this case.
Hence, the simplified ratio is:
7 boys : 6 girls
A piece of copper weighed 4⁄5 of a kilogram and a piece of nickel weighed 3⁄5 of a kilogram. How much more did the piece of copper weigh?
You find the difference in weight by subtacting the weight of the nickel from the weight of the copper.
... (4/5 kg) - (3/5 kg) = (4 -3)/5 kg = 1/5 kg
The piece of copper weighed 1/5 kg more than the piece of nickel.
expand the expression 4(3/2x+5)
A line is drawn so that is passes through the points (-4,0) and (2,3) what is the slope of the line
-1/2
1/2
-2
2
you would use the form y2-y1/x2-x1 so in this case it would be 3-0/2+4 which would be 3/6 but simplify your answer and you get would be 1/2 so your answer is 1/2
slope = [tex]\frac{1}{2}[/tex]
to calculate the slope m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 4, 0 ) and (x₂, y₂ ) = (2, 3)
m = [tex]\frac{3-0}{2+4}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
a. Is it possible for a shape to have both reflectional and rotational symmetry? If so, provide an example with a line of symmetry for reflectional rotation and the minimum degree of rotation for rotational symmetry. If not, explain why.
Yes. For example, the shape I will use is the circle.
No matter how you rotate the circle, it will always look the same. If you reflect the circle over any drawen line in which it passes through the middle, the two halves created would be congruent.
~Rise Above the Ordinary, Senpai
what is the length of the missing side
Answer:
The answers are:
m = 9 and n = 15
Step-by-step explanation:
m/15 = n/25 = 12/20
m/15 = 12/20
m/15 = 3/5
5m = 45
m = 9
n/25 = 12/20
n/25 = 3/5
5n = 75
n = 15
m = 9 and n = 15
Find the length( l ) of the leg in the large right triangle using Pythagoras' identity
l = √(25² - 20²) = √225 = 15
the outer and inner right triangles are similar hence the ratios of corresponding sides are equal
[tex]\frac{25}{n}[/tex] = [tex]\frac{15}{m}[/tex] = [tex]\frac{20}{12}[/tex]
using [tex]\frac{25}{n}[/tex] = [tex]\frac{20}{12}[/tex] (cross-multiply )
20n = 300 ( divide both sides by 20 )
n = 15
using [tex]\frac{15}{m}[/tex] = [tex]\frac{20}{12}[/tex] ( cross-multiply )
20m = 180 ( divide both sides by 20 )
m = 9
Write an equation of the line passing through each of the following pairs of points. d (5, 0), (−3, 0)
The physics scores of 200 students follow a normal distribution with a mean of 75 and a standard deviation of 7. Which conclusion is best supported by this information?
We can say that nearly all of the students got between a 54 and a 96, that 95% got between a 61 and an 89, and about two-thirds got between a 68 and an 82, but there may be other conclusions one may wish to draw.
Which expression is equivalent to the expression 2/3(3 - 1/3)(-1)?
(i'm doing a giveaway worth 25 points if you get the right.)
2/3 (5/3)(-1) = -10/9
Answer:
-7/9
Step-by-step explanation:
2/3(3 - 1/3)(-1) = (1-2/9)(-1) = -1+2/9 = -7/9
Identify and EXPLAIN the ERROR * Show CORRECT WORK and SOLUTION * What STRATEGY did you use for solving this problem *
a store sells rope by the meter The equation p=0.8L represents the price p (in dollars) of a piece of nylon rope that is L meters long. a. How much does the nylon rope cost per meter. b. How long is a piece of nylon rope that costs $1.00
(a) $0.80
(b) 1.25 m
Step-by-step explanation:(a) Put 1 where L is, and evaluate the equation.
... p = 0.8·1 = 0.8
The cost for 1 meter of rope is $0.80.
(b) Put 1 where p is and solve for L.
... 1 = 0.8L
... 1/0.8 = L = 1.25
The length of rope that costs $1 is 1.25 meters.
Answer:
a. $ 0.8
b. 1.25 meters.
Step-by-step explanation:
Given equation that represents the price p (in dollars) of a piece of nylon rope having length L meters,
[tex]p=0.8L[/tex]
a. If L = 1 meter,
The cost of the rope would be,
[tex]p=0.8(1) = \$ 0.8[/tex]
b. if p = $ 1.00,
[tex]\implies 1 = 0.8L[/tex]
[tex]\implies L=\frac{1}{0.8}=1.25[/tex]
Thus, the length of the rope would be 1.25 meters.
I need help with finding X's value.
Please help it's geometry.
See attachment
The marks on the line segments tell you they are the same length, and that the triangle is an equilateral triangle. That tells you the angles are the same size, and all are 60°. This lets you find x and y.
(7x+4)° = 60°
7x = 56 . . . . . . . . divide by °, subtract 4
x = 8 . . . . . . . . . . divide by 7
_____
(8y+12)° = 60°
8y = 48 . . . . . . . . divide by °, subtract 12
y = 6 . . . . . . . . . . divide by 8
Find the missing number of each unit rate 24/4=?/1 and 40/5=?/1
24/4 = 6/1
40/5 = 8/1
The answer is 6/1 and 8/1.
Best of luck.
The missing number unit rate of 24/4=?/1 is 6 and 40/5=?/1 is 8.
We have to determineThe missing number of each unit rate is 24/4=?/1 and 40/5=?/1.
According to the questionLet the missing number be x.
The missing number is determined by cross multiply and then solving for the value of x.
The missing number is,
[tex]\rm \dfrac{24}{4} = \dfrac{x}{1}\\\\24 \times 1 = x \times 4\\\\24 = 4x\\\\x = \dfrac{24}{4}\\\\x = 6[/tex]
And another missing number is,
[tex]\rm \dfrac{40}{5} = \dfrac{x}{1}\\\\40 \times 1 = 5 \times x\\\\40 = 5x\\\\x = \dfrac{40}{5}\\\\x = 8[/tex]
Hence, the missing number unit rate of 24/4=?/1 is 6, and 40/5=?/1 is 8.
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6 divided by 603 is?
Note that both numbers are multiple of 3: you can simplify the ratio as follows
[tex] \dfrac{6}{603} = \dfrac{3\cdot 2}{3\cdot 201} = \dfrac{2}{201} [/tex]
The ratio can't be further simplified because 2 and 201 are coprime. So, the only thing you could do is write down the decimal expansion of the number.
For the record, its period is 33 digits long, and it is
[tex] 0.009950248756218905472636815920398 [/tex]
Answer:
0.00995025
Step-by-step explanation:
What is the solution of sqrt2x+4=15
Answer:
x = 126
Step-by-step explanation:
Square both sides of the equation. (sqrt2x+4)^2 = 16^2
2x+4 = 256
Then you should solve for x. (First Subtract 4 from both sides; Then simplify; Next divide both sides by 2; Finally, simplify once more)
This should give you your answer. (x = 126)
Hope this helps! ^-^
Answer:
x = 72
Step-by-step explanation:
sqrt {2x} +4 = 16
sqrt {2x} = 12
2x = 12 ^ 2
x = 144/2
x = 72
If you wanted to write:
sqrt {2x + 4} = 16
2x + 4 = 16 ^ 2
2x + 4 = 256
2x = 252
x = 252/2
x = 126
Luna's monthly mortgage payment was $2100 last year, and on average, 9% of each payment was interest. If Luna itemizes deductions on her federal income tax return, how much can she deduct for mortgage interest?
Answer:
$2268
Step-by-step explanation:
Luna's total mortgage payments for the year would be
... (monthly payment)×(number of months in a year)
... = $2100×12 = $25,200
Of that, 9% went to interest, so the interest amount is ...
... $25,200×9% = $2268
_____
About percentages
Your calculator may do percentages directly. If not, it can be helpful to realize that the percent symbol (%) means the same thing as /100 (divided by 100). So, 9% = 9/100 = 0.09
Answer:
$2268
Step-by-step explanation:
did it on apXX
PLZ HELP ASAP! ILL MARK BRAINLEST!
Factor completely 12x4 + 6x3 + 18x2.
Prime
3(4x4 + 2x3 + 6x2)
3x2(4x2 + 2x + 6)
3x(4x3 + 2x2 + 6x)
Factor completely 7x3y +14x2y3 − 7x2y2.
7x2(xy + 2y3 – y2)
7x2y(x + 2y2 – y)
7(x3y +2x2y3 − x2y2)
Prime
What is the Greatest Common Factor of x6 and x3?
x4
x3
x2
x
Question 1.) Factor completely [tex]12x^{4}+ 6x^{3}+18x^{2}[/tex]
Since [tex]6[/tex] divides all the three terms of the equation, so we take [tex]6[/tex] common out from the equation.
i.e., [tex]6(2x^{4}+ 1x^{3}+3x^{2})[/tex]
Now, since [tex]x^{2}[/tex] divides all the three terms of the equation, so we take [tex]x^{2}[/tex] common out from the equation.
i.e., [tex]6x^{2}(2x^{2}+ 1x+3)[/tex]
Now, this cannot be factored further as [tex]2x^{2}+ 1x+3[/tex] is a quadratic equation and taking out discriminant of it is:
[tex]D = (1)^2 - 4(2)(3)\\ \ \ = 1- 24\\ \ \ = -23<0[/tex]
Since, the discriminant is less than zero. Therefore, the factored form of the given equation : [tex]12x^{4}+ 6x^{3}+18x^{2}[/tex] is : [tex]6x^{2}(2x^{2}+ 1x+3)[/tex]
Question 2.) [tex]7x^{3}y+ 14x^{2} y^{3} - 7x^{2}y^{2}[/tex]
Since [tex]7[/tex] divides all the three terms of the equation, so we take [tex]7[/tex] common out from the equation.
i.e., [tex]7(x^{3}y+ 2x^{2} y^{3} - x^{2}y^{2})[/tex]
Now, since [tex]x^{2}y[/tex] divides all the three terms of the equation, so we take [tex]x^{2}y[/tex] common out from the equation.
i.e., [tex]7x^{2}y(x+ 2y^{2} - y)[/tex]
Therefore, the factored form of the given equation : [tex]7x^{3}y+ 14x^{2} y^{3} - 7x^{2}y^{2}[/tex] is : [tex]7x^{2}y(x+ 2y^{2} - y)[/tex]
Question 3.) What is the Greatest Common Factor of [tex]x^{6}[/tex] and [tex]x^{3}[/tex] ?
The Greatest Common Factor of two numbers is the biggest number which divides both the given numbers completely.
Now, for the expressions [tex]x^{6}[/tex] and [tex]x^{3}[/tex]:
Since, [tex]x^{3}[/tex] divides both the expressions completely and it is the biggest expression which divides both the expressions.
Therefore, [tex]x^{3}[/tex] is the Greatest Common Factor of [tex]x^{6}[/tex] and [tex]x^{3}[/tex]
Answer:
#2 is definatly B
Step-by-step explanation: