[tex]9.6\times 10^9~~ = ~~(2\times 10^5)(4.8\times 10^n)\implies \cfrac{9.6\times 10^9}{2\times 10^5}~~ = ~~4.8\times 10^n \\\\\\ \cfrac{9.6}{2}\times \cfrac{10^9}{10^5}~~ = ~~4.8\times 10^n\implies 4.8\times 10^{9-5}~~ = ~~4.8\times 10^n \\\\\\ 4.8\times 10^4~~ = ~~4.8\times 10^n\implies \cfrac{4.8\times 10^4}{4.8}=10^n\implies \cfrac{4.8}{4.8}\times 10^4=10^n \\\\\\ 1\times 10^4=10^n\implies 10^4=10^n\implies 4 = n[/tex]
What are the key features of the quadratic function f(x) = 2(x - 3)2 + 4
The vertex, focus and axis of symmetry of the given function are (3, 4), (3, 33/8) and 3 respectively.
The given quadratic function is f(x) = 2(x - 3)² + 4.
We need to find the key features of the given quadratic function.
What is the quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.
Now, the key features of the given quadratic function as follows:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (3, 4)
Focus: (3, 33/8)
Axis of Symmetry: x=3
Directrix: y=31/8
Plot these points (1, 12), (2, 6), (3, 4), (4, 6) and (5, 12) on the graph.
Therefore, the vertex, focus and axis of symmetry of the given function are (3, 4), (3, 33/8) and 3 respectively.
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he second of a triangle is 6 more than the first angle. The third angle is 12 less than the first angle. Find all three angles if the sum of their angles is equal to 180°
Answer:
Let first angle be x
x+x+6+x-12=180°
3x-6=180°
3x=186
x=63°
First angle=63°
Second Angle=69°
Third angle=51°
Hope it helps you
Examine the diagram.
XX
15
3/7
26
4 8
Angle 4 and angle
angles.
are alternate interior
Answer:
angle 5
Step-by-step explanation:
Given transversal x crossing lines y and z and angles numbered 1 to 8, you want the number of the angle that is an alternate interior angle to angle 4.
Alternate interior anglesIn this context, "alternate" mean the angles are on opposite sides of the transversal. "Interior" means the angles are between the lines the transversal crosses.
The term "alternate interior angles" is used to refer to angles that have their vertices at the intersection points where the two lines cross the transversal. (It excludes angles that have the same vertex, or do not share a side.)
The angle that is an alternate interior angle relative to angle 4 is angle 5.
$72 is 4.5% of what amount
$72 is 4.5% of 6.25 amount. 6.25 Percentage of 72 is 4.5.
By considering the given information
[tex]72\times x=4.5\\x=\frac{4.5}{72}\times 100\\ x=6.25[/tex]
A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it. percent, which is a relative value used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
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$72 is 4.5% = $3.24
Solution :
The percentage is a rate or proportion per hundred,
The percentage is also used more generally to mean any proportion, as in Studies have shown that a large percentage of people love cute animals.
A percent is one one-hundredth (1/100) of something. The percentage refers to the rate or proportion of that one hundred. Usually, you will see the word percentage used in math equations or statistics or when someone is measuring the increase and decrease in rates
$72 is 4.5% =?
$72 is 10% = $7.2
$72 is 5% = $7.2 /2 = $3.6
$72 is 1/2%= $72 * .5/100 = $.72*.5 = $ 0.36
$72 is 4.5% = 5% - .5% = $3.6- $.36 = $3.24
$72 is 4.5% = $3.24
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SOMEONE HELP ME BEFORE I PASS OUT
1. |X|≤8
2. |X|≤27
Answer: 1. [-8, 8]
2. [-27, 27]
Step-by-step explanation:
1. |X|≤8
x≤8 or x>=-8
-8<=x<=8 ==> [-8, 8]
2. |X|≤27
x≤27 or x>=-27
-27<=x<=27 ==> [-27, 27]
2(3x-2)-4x+1= 9 solve for x
5f+2h=100
Solve for F
Solving for the variable gives f = 100 - 2h/5
What is subject of formula?Subject of formula can be defined as the variable that is expressed in terms of other variables in a given expression, function of equation.
It is the variable worked out in an equation and left to stand on its own on one side of the equality sign
Given the equation;
5f+2h = 100
To make 'f' the subject of formula, we take the following steps;
Take '2' over the equality sign
5f = 100 - 2h
Now, let's make 'f' the subject by dividing both sides by its coefficient which is 5
We have;
5f/5 = 100 - 2h/5
Divide through
f = 100 - 2h/5
Thus, solving for the variable gives f = 100 - 2h/5
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What is 80% of 63? Do not round your answer.
Answer:
What is 80% of 63?
50.4 is the right answer
Alf earns £9.00 per hour and works 33 hours each week. He spends a total of £24.40 each week travelling to and from work. Next month he is getting a 4% pay rise but his travel costs are increasing by 15%.
How much extra will he have each week?
Answer:
£8.22
Step-by-step explanation:
9x33=£297
297-24.40=£272.60
297×4%=£11.88
297+11.88=£308.88
24.40×15%=£3.66
24.40+3.66=£28.06
308.88-28.06=280.82
280.82-272.60=£8.22
will the sum of 5 + (-2) be positive or negative? what is the sum? show your work.
Answer:
positive the answer is 3
Step-by-step explanation:
Bashir was out at a restaurant for dinner when the bill came. His dinner came to $32.
After adding in a tip, before tax, he paid $39.36. Find the percent tip.
Answer:
23%
Step-by-step explanation:
39.36-32=7.36
7.36/32=.23
23 percent
Kayla started a book club at her school. The number of girls in the book club was one more than twice the number of boys. If there are 21 girls in the book club, how many boys are in the club?
Answer:
10
Step-by-step explanation:
(21-1)/2
i need help with this
which measurements best approximate the lengths of the legs, to the nearest tenth of a centimeter, of a right triangle if the hypotenuse is 70 cm and the shorter leg is one-third the length of the longer leg?
The length of the base will be equal to 65.99 centimeters.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
The formula for the Pythagorean theorem is given below:-
H² = B² + P²
Given that in a right triangle if the hypotenuse is 70 cm and the shorter leg is one-third the length of the longer leg.
P = 70/ 3 cm
H = 70 cm
The value of the leg will be calculated as:-
H² = B² + P²
70² = B² + (70/3)²
B² = 70² - (70/3)²
B = √4355
B = 65.99 cm
Therefore, the length of the base will be equal to 65.99 centimeters.
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The cost c of a shirt is less than $27. 50.
Can someone please help mee (20 points
brainliest!!!)
Answer:
60,000
Step-by-step explanation:
going straight across the line we can see that for $140 the demand in thousands 60
so
you can buy 60,000 units
Answer:
60 because oficial the line goes to 60
lindsay bedford works at the baseball cap shop she is paid $6.50 per hour plus $0.45 for each cap she embroiders how many caps must she embroider to earn at least $85
Lindsay Bedford should embroider 73 caps.
Let us assume the number of number of caps needed to be embroidered for desired earning be x. Now, forming the equation to solve for x, thus, finding the required number of caps.
Equation -
6.50*8 + 0.45*x = 85
Now solving this equation for the value of x.
Performing multiplication of numbers on Left Hand Side
52 + 0.45x = 85
Shifting the product from Left Hand Side to Right Hand Side
0.45x = 85 - 52
Performing subtraction on Right Hand Side to find the value of x
0.45x = 33
Shifting 0.45 to denominator on Right Hand Side
x = 33÷0.45
Performing division to find the value of x
x = 73.3
The number of caps can not be in fraction. So, we will round off the digit to find exact number of caps.
Number of caps = 73
Therefore, Lindsay Bedford needs to embroider 73 caps.
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The complete question is -
Lindsay Bedford works at a baseball cap shop. She is paid $6.50 per hour plus $0.45 for each cap she embroiders. How many caps must she embroider to earn at least $85 in an 8-hour day?
URGENT 1000 POINTS. BRAINLIEST GIVER...
(6.03 x 10^9) + (4.3 x 10^11) = (0.0603 x 10^11) + (4.3 x 10^11) = 4.3603 x 10^11 in scientific notation. explain step by step!
Answer:
see image.
Step-by-step explanation:
Basically, what's happening here is you are adjusting one of the terms so that they both have the same exponent. Then you can factor out that 10^11 term and just add the two remaining terms.
see image.
9. Mr. Crowley bought lunch for himself and eight of his employees.
Each had a sandwich platter that costs $5.85 and a drink that
costs $1.25. Five of the employees had dessert that costs $1.50.
Mr. Crowley gave the delivery person $80 and told her to keep
the change as a tip. How much was the delivery person's tip?
Answer:
$8.60
Step-by-step explanation:
Let x = the tip
80 - x = 9(5.85 + 1.25) + 5(1.50)
80 -x = 63.90 + 7.5
80 - x = 71.40 Subtract 80 from both sides
-x = -8.60 Divide both sides by -1
x = 8.60
M, N and P are points on a circle, centre O.
MON is the diameter of the circle.
MP = 3.5 cm
PN = 9.7 cm
Angle = 90º
Work out the circumference of the circle.
Give your answer correctly to 3 significant figures.
Step-by-step explanation:
just draw what I have done
What proportion of sample size n =10 will have a mean salary greater than $60,000
Answer:
n/10 x 10/60,000
Step-by-step explanation:
I think it's right please don't report
Answer:
N/10 x 10/60,000
Write an algebraic expression for the statement: the income earned at $9.25 per hour for x hours
Answer:
9.25x
Step-by-step explanation:
The shaded diagram represents a block of land.
What is the area of the block?
By using Heron's formula and standard formula for the area of a triangle, the area of the composite figure is 921006.497 square meters.
What is the area of a composite figure?
In this problem we must determine the area of a composite figure, which consists in subtracting the area of an isosceles triangle from the area of the equilateral triangle:
Big triangle
The area of the big triangle is determined by Heron's formula:
s = [3 · (520 m)] / 2
s = 780 m
A = √[(780 m) · (1560 m - 520 m)³]
A ≈936693.077 m²
Small triangle
H = (520 m) · sin 60°
H ≈ 450.333 m
h = 450.333 m - 390 m
h = 60.333 m
A = 0.5 · (520 m) · (60.333 m)
A = 15686.580 m²
Then, the area of the composite figure is 921006.497 square meters.
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can someone please help me or imma get an F! :')
Answer:
17,84,9,34,71,35,18
Step-by-step explanation:
Please help with this. I have to finish it today
Note: can you make it where i can say it Infront of my class?
Answer:
The coordinates of W,X,Y,Z are W= (3,4) X= (1,4) Y= (2,1) Z= (4,2)
Step-by-step explanation:
When you reflect the coordinates to the other side of the graph, you get these^^^^ coordinates.
Quadrilateral ABCD is dilated at center (0, 0) with scale factor to form quadrilateral 1/2; A^ prime B^ prime C^ prime D^ prime . What is the length of overline A^ prime B^ prime ?
The length with scale factor to form quadrilateral 1/2, A'B' is √5 units when AB is √20.
What is distance formula?The formula to find the distance between the two points is usually given by
d=√((x2 – x1)² + (y2 – y1)²).
Given :
Quadrilateral ABCD is dilated at the center (0,0) with a scale factor of 1/2 to form quadrilateral A'B'C'D'.
Points - A(0,4), B(4,2), C(4,-4), and D(-2,-2).
So, the points of the quadrilateral ABCD becomes:
A' (0, 2)B' (2, 1)C'( 2, -2)D'(-1 , -1)So, length of A'B'
AB = √(4-0) ² +(2 -4)²
AB = √16 + 4
AB = √20
AB = 2√5
A'B' = 1/2 AB
A'B' = √5
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Please Help
Thanks In advance
Answer:
4
Step-by-step explanation:
you do cross multiplication
you do 3x12÷9
A company makes a profit of $55 per software program and $45 per video game. The company can produce at most 225 software programs and at most 275 video games per week. Total production cannot exceed 450 items per week. How many items of each kind should be produced per week in order to maximize the profit?
Use linear programming to solve. Show all your work.
Answer:
they should produce 225 software programs and 225 video games per week.
Step-by-step explanation:
limit 450
there are 2 factors the software and video games.
450•2= 225
Which statement is true?
The Mississippi River in Iowa is at an elevation of 279 and Death Valley, in California is at an elevation of -282 feet. Which statement is true?
A |279| > |-282|
B |279| < |-282|
C 279 = 282
D 279 < -282
Answer:
Step-by-step explanation:
if we consider mod then the negative turns to positive and positive remains positive so it will be
279 < 282 which is l279l < l-282l
I need help asap (Fractions)
Answer:
Step-by-step explanation:
3 3/4 = 15/4
15/4 divided by 3/4 = 5