The value of unknown number y for the equation 8 superscript y baseline = 16 superscript (y+2) is -8.
How to simplify power raised by another number?When the power of a number is raised by another number, then multiply both the powers and the result of this product keep as the power of the number.
Let suppose there is a number a. For this number the above rule can be given as,
[tex](a^m)^n=a^{m\times n}\\(a^m)^n=a^{mn}[/tex]
The expression which consist unknown variable y is given as,
[tex]8^y=16^{y+2}[/tex]
The above equation can be written as,
[tex](2\times2\times2)^y=(2\times2\times2\times2)^{y+2}\\(2^3)^y=(2^4)^{y+2}\\(2)^{3y}=(2^)^{4y+8}[/tex]
As the base of both side of the equation is same. Thus, the value of their exponent can be compared.
[tex]3y=4y+8\\4y-3y=-8\\y=-8[/tex]
Thus, the value of unknown number y for the equation 8 superscript y baseline = 16 superscript (y+2) is -8.
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Answer:
f(x)=3/2 x
Step-by-step explanation:
it starts at 0 and rise 3 and goes over 2
The answer is [tex]f(x)=\frac{3}{2}x[/tex]
First, you must find 2 points.
(0,0) (2,3)
Then, you must use the slope equation
[tex]\frac{3-0}{2-0}=\frac{3}{2}[/tex]
The line crosses the y axis at 0, so there is no y intercept
[tex]f(x)=\frac{3}{2}x[/tex]
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Step-by-step explanation:
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1. Which is the smallest set of real numbers that contains the value below? -18 /6
A. Irrational Numbers
B. Rational Numbers
C. Natural Numbers
D. Integers
Answer:
Integers
Step-by-step explanation:
The correct option to choose is the integers option. Integers are simply whole numbers.
Thus-18/6 = -3
The term -3 is a whole number
So the term to choose is the integers option
The smallest set of real numbers that contains the value -18 /6 is an integer.
The smallest set of the real number that contains the value -18/6 can be determined after we have simplified the expression -18/6.
To simply the given expression, we will divide both the numerator and the denominator by 6, by doing so, we have:
= -3
Now, the smallest set of the real number is = -3 which is an integer
This is because an integer is a whole number that is not a fraction and can be negative or positive.
The reason why it is not a natural number is because of the negative sign, since we know that natural numbers are numbers with positive signs only.
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The perimeter of a rectangle is 64 feet. The length of the rectangle is 3 times the width of the rectangle. If w represents the width of the rectangle, the equation that represents the perimeter is 2 (3 w) + 2 w = 64. Which shows the first step that should be taken to verify that the width of the rectangle is 8? A regular hexagon and a rectangle have the same perimeter, P. A side of the hexagon is 4 less than the length, l, of the rectangle. The width of the rectangle, w, is 2 less than the length of the rectangle. What is the perimeter of the hexagon?
Step-by-step explanation:
given the perimeter is
64ft
the length l= 3w
we know that the perimeter of a rectangle is given as
P=2l+2W
but L=3w
64=2(3w)+2w
64=6w+2w
64=8w
divide both sides by 8 we have
w=64/8
w=8ft
also
let the lenght of the rectangle be l
side of hexagon=l-4
perimeter of hexagon
P=5(l-4)
P=5l-20
width of rectangle w=l-2
perimeter of rectangle= 2l+2w
but w=l-2
5l-20= 2l+2(l-2)
5l-20=2l+2l-4
5l-20=4l-4
5l-4l=-4+20
l=16ft
perimeter of hexagon
P=5(l-4)
put l=16
perimeter of hexagon
P=5(16-4)
p=5(12)
P=60ft
Answer: 2(3(8))+(2+8)=64 or c
Step-by-step explanation:
You have to replace w with 8 meaning 8 is now the width, therefore, c is the correct answer.
. A bakery sells 1,230 cakes during a holiday season. One-third of them are caramel cakes, one-half are chocolate cakes, and the remaining are banana cakes. What is the total amount earned by the bakery by selling the cakes during the holiday season?
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]Cakes = 1230[/tex]
[tex]Caramel = \frac{1}{3}[/tex]
[tex]Chocolate = \frac{1}{2}[/tex]
[tex]Banana = ??[/tex]
Required
Determine the total amount earned
The given parameters can't be used to determine the total amount earned.
However, we'll make some assumptions
First, we need to solve for the amount of each cake sold
[tex]Caramel = \frac{1}{3}[/tex]
[tex]Caramel = \frac{1}{3} * 1230[/tex]
[tex]Caramel = 410[/tex]
[tex]Chocolate = \frac{1}{2}[/tex]
[tex]Chocolate = \frac{1}{2} * 1230[/tex]
[tex]Chocolate = 615[/tex]
[tex]Banana = 1230 - 410 - 615[/tex]
[tex]Banana = 205[/tex]
Assume that:
Each caramel were sold at x
Each chocolate were sold at y
Each banana were sold at z
[tex]Total\ Amount = 410 * x + 615 * y + 205 * z[/tex]
[tex]Total\ Amount = 410x + 615y + 205z[/tex]
F and g are functions such that
F(x)=3/x2 and g(x)=2x3
A) find f(-4)
B) find fg(1)
a. The value of f(-4) is [tex]3 \div -8[/tex]
b. The value of fg(1) is [tex]3\div 4[/tex]
Calculation of the value of f(-4) and fg(1):Since [tex]F(x)=3\div x\times 2\ and\ g(x)=2\times x\times 3[/tex]
So,
a. The value of f(-4) is
[tex]= 3\div (-4)(2)\\\\= 3\div -8[/tex]
And,
b. The value of fg(1) is
[tex]= 3\div (2(1)^3)(2)\\\\= 3\div (2)(2)\\\\= 3\div 4[/tex]
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Matt is going to sign up for the "Fruit of the Month Club." He must pay a $25 enrollment fee, as well as $17 each month to continue his membership. He is going to stop receiving fruit once he has spent $280. Write the equation of this problem in Slope-Intercept form (hint: y=mx+b): How much as he spent on fruit after 5 months? In how many months until he has spent $280?
Answer:
He spent on fruit after 5 months is $110.
In 15 months he spent $280.
Step-by-step explanation:
Fixed pay for membership is $25
And enrollment fee is $17 for each month.
The equation represents this situation is
y= 17 x + 25
He is going to stop receiving fruits once he spent $280.
Now, to find how much he spent on fruit after 5 months is plugin x as 5 into
y=17x+25 for x
y=17(5)+25
y=85+25
y=110 dollars
Now, to find how many months until $280 is to plug in y as 280 then solve the equation for x.
280 = 17 x+25
Subtract both sides 25
255 =17 x
Divide both sides by 17
x= 15 months
eight increased by a number *
O 8n
n - 8
8/n
O
n + 8
Answer:
n+8
Step-by-step explanation:
"A number" signifies the need for a variable, in this case, n. The keyword increased shows that the operation is addition. So put it together and you get n+8.
Answer:
the answer to it is n + 8. :3
above it says find the missing angle measurement.
Answer:
1) 53
2) 35
3) 28
4) 42
Step-by-step explanation:
Sum of angles in all triangles is 180 so add the two known angle measurements and subtract from 180.
In the adjoining figure , AB = 6 , BC = 8 , [tex] \angle[/tex] ABC = 90° , BD ⊥ AC and [tex] \angle[/tex] ABD = [tex] \theta[/tex] , find the value of sin [tex] \theta[/tex].
Here we are given with a triangle with smaller triangles formed due to the altitude on AC. Given:
AB = 6BC = 8<ABC = 90°BD ⊥ AC<ABD = [tex] \theta[/tex]We have to find the value for sin [tex] \theta[/tex]
So, Let's start solving....
In ∆ADB and ∆ABC,
<A = <A (common)<ABC = <ADB (90°)So, ∆ADB ~ ∆ABC (By AA similarity)
The corresponding sides will be:
[tex] \sf{ \dfrac{AD}{AB} = \dfrac{AB}{AC} }[/tex]
We know the value of AB and to find AC, we can use Pythagoras theoram that is:
AC = √6² + 8²
AC = 10
Coming back to the relation,
[tex] \sf{ \dfrac{AD}{6} = \dfrac{6}{10} }[/tex]
[tex] \sf{AD = \dfrac{6 \times 6}{10} = 3.6}[/tex]
In ∆ADB, we have to find sin [tex] \theta[/tex] which is given by perpendicular/base:
[tex] \sf{\sin( \theta) = \dfrac{AD}{AB} }[/tex]
Plugging the values of AD and AB,
[tex] \sf{\sin( \theta) = \dfrac{3.6}{6} }[/tex]
Simplifying,
[tex] \sf{ \sin( \theta) = \dfrac{3}{5} = \boxed{ \red{0.6}}}[/tex]
And this is our final answer.....
Carry On Learning !
Simplify a - {b - [C- (d - e) -f]-g}.
Answer:
C+a−b−d−f+g+e
Step-by-step explanation:
what is x+x+y×y simplified
Answer:
x+x+yxy
= x^2 + y^2
x^2 + y^2 is the answer.
What is a simplification in math?In mathematics, genuinely or simplification is reducing the expression/fraction/hassle in a less complicated form. It makes the problem smooth with calculations and fixing.
Does simplifying suggest fixing?Associated with "simplification" troubles are some "solving" troubles. just as a few expressions include parentheticals or even nested grouping symbols, so additionally do some equations. The simplification manner is identical, whether we're running with expressions (and consequently handiest simplifying) or equations (so we are also solving).
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Choose an equivalent expression for 106 ÷ 104.
Answer:
10^2
Step-by-step explanation:
When we divide exponents we subtract the exponenets in the top (in this case 6-4). This will give us 10^2. You can also check this.
The equivalent expression for 10⁶ ÷ 10⁴ will be 10². Then the correct option is A.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The numbers are given below.
10⁶ and 10⁴
The division of the numbers 10⁶ and 10⁴ will be given below.
⇒ 10⁶ ÷ 10⁴
⇒ 10⁶ / 10⁴
⇒ 10⁶⁻⁴
⇒ 10²
The equivalent expression for 10⁶ ÷ 10⁴ will be 10². Then the correct option is A.
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- A quadratic model for a certain stock on Wall Street is P=-3d2 + 50d, where d
represents the days of trading and P is the price per share.
a. What is the maximum price per share of the stock?
Help please I’m stuck
Answer:
208.333
Step-by-step explanation:
A quadratic model for a certain stock on Wall Street is given by :
[tex]P=-3d^2+50d[/tex] ...(1)
(a) We need to find the maximum price per share of the stock. For maximum value, put :
[tex]\dfrac{dP}{dd}=0[/tex]
[tex]\dfrac{d(-3d^2+50d)}{dd}=0\\\\-6d+50=0\\\\d=\dfrac{50}{6}\\\\d=8.34[/tex]
price per share of the stock is maximum when the value of d = 8.34. Put the value of d in equation (1).
[tex]P=-3(8.34)^2+50(8.34)\\\\P=208.333[/tex]
So, the maximum price per share of the stock is 208.333.
d/4=9 what is d? pls help‼️
Lisa bought 5 CDS from a store. The price of each CD was the same. After she bought the CDs, her account balance showed a change of -$64.95. What would have been the change to Lisa’s account balance had she only bought 1 CD from the store?
Answer:
47
Step-by-step explanation:
They are dumpy because they can’t try
I need help on this
Answer: Second company (in the table), aka #1 toys, produces at a slower rate
============================================================
Explanation:
The equation y = 123x is in the form y = mx+b with m = 123 as the slope. The slope is the rate of change telling us how many toys per minute are produced. In this case, 123 toys per minute is the rate for the first company.
----------
We'll need the slope of the other function. So we need to pick two rows from the table and use the slope formula. I'll pick the first two rows.
m = (y2-y1)/(x2-x1)
m = (1320-600)/(11-5)
m = 720/6
m = 120
The second company produces at a rate of 120 toys per minute. This is the smaller rate, so this company produces at a slower speed.
Sketch a graph to represent the situation. Label each section.
You buy two shirts. The third one is free.
all and
Answer:
for every 2 shirts, the 3rd is free
Step-by-step explanation:
Prove that in any triangle the length of a side is less than the half of the perimeter in statement reason format.
Answer:
Proved
Step-by-step explanation:
I am going to pose c as the largest side in a random triangle
If so then remember that, by the triangle inequality, a + b > c. Let's start from there...
Statement: | Reasoning:
1. a + b > c 1. Triangle Inequality
2. a + b + c > c + c (adding c on both sides), 2. Algebra + Def. Of Perimeter
a + b + c > 2c (simplified)
Perimeter > 2c (definition of perimeter)
c < 1/2 * Perimeter
The prove of statement ''in any triangle the length of a side is less than the half of the perimeter'' is shown.
What is Perimeter?
The sum of all sides of a quadrilateral is called a perimeter.
Given that;
The statement is,
''In any triangle the length of a side is less than the half of the perimeter''.
Now,
Let sides of triangles are a, b and c.
The triangle inequality is;
a + b > c
Add both side by c;
a + b + c > c + c
a + b + c > 2c .... (i)
Since, Perimeter of a triangle with sides a, b and c is;
Perimeter (P) = a + b + c
Substitute value of perimeter in equation (i), we get;
a + b + c > 2c
P > 2c
c < P/2
Thus, In any triangle the length of a side is less than the half of the perimeter.
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SOMEONE PLEASE HELP ME IM STRUGGLING ON THIS PROBLEM 7 I NEED HELPPP
Answer:
B——A for top two
C——D for bottom two
The number of pages Caitlin reads over time is shown in the table below.
Caitlin's Reading Log
Hours
2 4 5
Number of Pagos 90 180 225
Part A. What is Caitlin's rate of reading?
Part B. Victoria reads at the rate of 60 pages per hour. What is the difference in the number of pages Victoria and Caitlin will read in 6 hours?
Enter the correct numbers in the boxes.
A.
pages per hour
B.
pages
Endpoint: (2,5) midpoint (3,4)
Missing endpoint:
Answer:
(4,3)
Step-by-step explanation:
Help please!!! Anything would be appreciated :3
Which of the following shows a translation of f(x) two units down?
Answer:
f(x) - 2
Step-by-step explanation:
I just took the quiz
Seven subtracted from twice a number gives 41, find this number.
Answer:
2x -7 = 41
2x = 41 +7
2x = 48
x = 24
The sum of two consecutive odd integers the first of which 2n+1
Answer:
4n+4
Step-by-step explanation:
If the first odd integer is 2n+1, the second must be 2n+3.
Add them and get 2n+1+2n+3 = 4n+4.
Example: if n=5 the numbers are 11 and 13 and their sum is 24
4*5 + 4 = 24.
what is the slope of a line perpendicular to the line whose equation is x+y=-1
Answer:
perpendicular is opposite and reciprocal
Step-by-step explanation:
The slope is -1 and the reciprocal/ perpendicular is 1x
Answer:
the answer is 1
Step-by-step explanation:
#6 please help me gang
In golf, a golfer must have a score of 0 in order to be at par. A golfer scores 4 above par on the first hole, 3 below par on the second hole, and 1 below par on the third hole. Write an expression to solve for their score. What is the golfer's score?
Answer:
The expression to solve the golfer's score is X = A + B + C
The golfer's score is 0 (The golfer is at par)
Step-by-step explanation:
The given information are;
The score the golfer must have = 0
The score, A, the golfer has on the first hole = +4
The score. B, the golfer has on the second hole = -3
The score. C, the golfer has on the third hole = -1
Therefore, the expression to calculate the golfer's score, X, is given as follows;
The golfer's score = The score the golfer has on the first hole + The score the golfer has on the second hole + The score the golfer has on the third hole
The expression to solve the golfer's score is given as follows;
X = A + B + C
The golfer's score = 4 - 3 - 1 = 0
The golfer's score = 0.
Answer:
3
Step-by-step explanation:
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Answer:
h=[tex]\frac{b\sqrt{3} }{2}[/tex]
Step-by-step explanation: