Calculate identity exponents using the exponent of the quotient, degree of exponent, and the law of zero exponent equations and evaluate numerical equations with integer exponents.
The following is an equivalent numeric expression with an integer exponent that uses the quotient, the quotient, zero-degree rule, and the identity exponent, and evaluates the numeric expression.
[tex]2^{5} \\[/tex] × [tex]2^{6}[/tex] = [tex]2^{11}[/tex], using the product of powers.
2² × 2³ = (2×3)² = 6², using the power of a product.
[tex](2^{2})^{6}[/tex] = [tex]2^{12}[/tex], using the power of a power.
The seven laws of exponents are the power rule, the power ratio rule, the power rule, the power rule, the power quotient rule, the power zero rule, and the negative exponent rule. Arithmetic questions, as well as how to multiply, divide and add powers.
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(2-√3)²=7-4√3
How we solve this question ?
Hurry answer please
You make an investment of $2250.00 with an absolute change of ―$350.00. What is your investment now
worth and what was the percent change?
1. The investment of $2,250 with an absolute change of -$350 is now worth $1,900.
2. The percentage change in the worth of the investment is -15.56%.
What is a percentage change?A percentage change refers to the percentage difference between the initial value and the current value.
To compute the percentage change, use the absolute change and divide by the initial value, then multiply by 100.
For this investment of $2,250 which is now worth $1,900, there was a percentage change of -15.56%, implying that it has drastically reduced in value.
Initial Investment Cost = $2,250.00
Absolute change in investment value = $350
Current value of investment = $1,900 ($2,250 + $350)
The percentage change = -15.56% (-$350/$2,250 x 100)
Thus, the investment is currently valued at $1,900, having lost $350 in value, which in percentage terms, is -15.56%.
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The table shows the information about the heights, in cm, of a group of yr11 girls
A linear relationship is shown in the graph.
Which equation best represents the relationship between x and y?
(A) The equation y = ( 1/4 )x + 2 best represents the relationship between x and y.
From the graph, we can see that the line is passing through points ( - 8, 0 ) and ( 0, 2 ).
So, to obtain the equation that represents the best relationship we will substitute the points in the equation to check whether they satisfy or not.
Consider option (a),
y = ( 1/4 )x + 2
For ( - 8, 0) :
0 = ( 1/4 ) × - 8 + 2
0 = - 2 + 2
0 = 0
For ( 0, 2 ):
y = ( 1/4 )x + 2
2 = (1/4) × 0 + 2
2 = 2
Hence, the equation y = ( 1/4 )x + 2 passes through both points.
Consider option (b),
y = 4x - 8
For point ( - 8, 0 )
y = 4(-8) - 8
y = - 32 - 8 = - 40 ≠ 0
For point ( 0, 2)
y = 4(0) - 8 = - 8 ≠ 2
Hence, the equation y = 4x - 8 does not pass through the points.
Consider option (c),
y = ( 1/4 )x - 8
For ( - 8, 0 )
y = ( 1/4 ) × - 8 - 8
y = - 2 - 8 = - 10 ≠ 0
For ( 0, 2)
y = ( 1/4 ) × 0 - 8 = - 8 ≠ 2
Hence, the equation y = ( 1/4 )x - 8 does not pass through points.
Consider option (d),
y = 4x + 2
For point ( - 8, 0 )
y = 4( - 8) + 2
y = - 32 + 2 = - 30 ≠ 0
For point ( 0, 2)
y = 4( 0 ) + 2 = 2
2 = 2
Hence, the equation passes through ( 0, 2) but does not pass through the point ( - 8, 0 ).
Therefore, the equation that represents the relationship between x and y is y = ( 1/4 )x + 2
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Deluxe coffee is to be mixed with regular coffee to make at
least 43 pounds of a blended coffee. The mixture must
contain at least 12 pounds of deluxe coffee. Deluxe coffee
costs $6 per pound and regular coffee $5 per pound. How
many pounds of each kind of coffee should be used to
minimize costs?
Answer:
12 pounds of deluxe and 31 pounds of regular.
Step-by-step explanation:
$227 is the minimum cost.
Answer:
We have to minimize the cost of 51 pounds of blended coffee.
The mixture must contain 13 pounds of deluxe coffee.
Deluxe coffee costs $4 per pound while regular coffee costs $3 for the same amount.
So, we need to maximize the concentration of regular coffee in the blended coffee to minimize our costs, but we must mix 13 pounds of deluxe coffee in order to make the blended coffee as it is the condition given to us in the problem.
Hence, apart from this 13 pounds, all the rest weight in blended coffee should come from the regular one.
Hence, the amount of regular coffee we have to use = (51 - 13) = 38 pounds.
Now, the cost of the 51 pounds of blended coffee
38×3+13×4 = ₹166.
Let f (x) = 3x+4 and g(x) = 4x^2+4x.
After simplifying,
(f∘g)(x) = _____ <---- answer
PLEASE HELP!
It should be noted that the value of (f.g)(x) will be
12x³ + 28x² + 16x.
How to illustrate the information?It should be noted that a function is simply used.to illustrate the relationship between the expressions that's given in the data.
From the information, the following can be illustrated:
f(x) = 3x + 4
g(x) = 4x² + 4x
Therefore, (f.g)(x) will be the multiplication of the variables. This will be illustrated as:
= (3x + 4) × (4x² + 4x)
= 12x³ + 12x² + 16x² + 16x
= 12x³ + 28x² + 16x
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if RS equals 59 and ST equals 10x - 31 find x
The chord RS and chord ST subtends equal angles the center. So length of chord ST is equal to length of chord RS.
Determine the value of x.
[tex]\begin{gathered} RS=ST \\ 59=10x-31 \\ 10x=59+31 \\ x=\frac{90}{10} \\ =9 \end{gathered}[/tex]So value of x is 9.
I need help because i can’t seem to understand it
sinA = 0.37
cosA = 0.93
tanA = 0.40
secA = 1.08
cscA = 2.69
cot A = 2.50
Explanation:Given that a = 4, b = 10. To obtain c, we use the Pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ =4^2+10^2 \\ =116 \\ c=\sqrt{116}=10.77 \end{gathered}[/tex]Now
[tex]\begin{gathered} \sin A=\frac{Opposite}{hypotenuse}=\frac{a}{c} \\ \\ =\frac{4}{10.77}=0.37 \end{gathered}[/tex][tex]\begin{gathered} \cos A=\frac{adj}{hyp}=\frac{b}{c} \\ \\ =\frac{10}{10.77}=0.93 \end{gathered}[/tex][tex]\begin{gathered} \tan A=\frac{opp}{adj}=\frac{a}{b} \\ \\ =\frac{4}{10}=0.40 \end{gathered}[/tex][tex]secA=\frac{1}{cosA}=\frac{10.77}{10}=1.08[/tex][tex]cscA=\frac{1}{sinA}=\frac{10.77}{4}=2.69[/tex][tex]cotA=\frac{1}{tanA}=\frac{10}{4}=2.50[/tex]the time it takes to cover the distance between two cities by car varies inversely with the speed of the car the trip takes 12 hours for a car moving at 32 mph how long does the trip take for a car moving at 24 mph
7. STEM The male Cuban tree frog is about the size of the
female Cuban tree frog. The average size of the female Cuban
tree frog is shown at the right. What is the size of the male
Cuban tree frog? (Example 4)
Answer:
Step-by-step explanation:
The male Cuban tree frog is about 2/5 the size of the female Cuban tree frog. The average size of the female Cuban tree frog is 6 inches. What is the size
What is the value of x?
Answer: Value of x is 16
Step-by-step explanation:
Triangle ABC and ADE are Similar Triangles using Angle-Angle-Angle similarity,
therefore,
[tex]\frac{AB}{BC}=\frac{AD}{DE}[/tex]
AB=x
BC=8
AD=x+6
DE=11
on substituting value,
[tex]\frac{x}{8}=\frac{x+6}{11}[/tex]
on cross multiplying,
11x = 8x+48,
subtracting 8x on both sides,
3x = 48,
dividing both sides by 3,
x=16
Therefore, value of x is 16
Which statement is true regarding the graphed functions?
On a coordinate plane, a straight red line with a positive slope, labeled g of x, crosses the x-axis at (negative 6, 0) and the y-axis at (0, 6). A straight blue line with a negative slope, labeled f of x, crosses the x-axis at (negative 0.75, 0) and the y-axis at (0, negative 2).
The following statement is true about the functions f(x) and g(x):
f(–2) = g(–2)
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the true statement about the functions?A system of linear equations is a collection of at least two linear equations.
In this case, the system of functions is given as
Functions f(x) and g(x)
From the attached graph, we can see that:
The values of the function f(x) at f(2), or f(4) do not have a match to the function g(x) at g(2) or g(4).
However, the functions intersect at x = -2
This means that f(-2) = g(-2)
Hence, the true statement about the functions is f(–2) = g(–2)
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Complete question
Which statement is true regarding the graphed functions?
See attachment
f(4) = g(4) f(4) = g(–2) f(2) = g(–2) f(–2) = g(–2)
Slope intercept form for points through (0,-5) and (4,0)
Answer:
y = (5/4)x - 5
Step-by-step explanation:
(0, -5) and (4, 0)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 0 -(-5) 5
m = ------------- = ------------ = ---------
x₂ - x₁ 4 - 0 4
y - y₁ = m(x - x₁)
y -(-5) = (5/4)(x - 0)
y + 5 = (5/4)x - 0
-5 -5
----------------------------
y = (5/4)x - 5
I hope this helps!
The softball team is selling hats. John bought 3 for $24.00. Stacey bought 5 for $40.00. Jim bought 2 for $16.00.
Why does this verbal description represent a proportional relationship?
The value of the hats bought by John, Stacey, and Jim are $8 per hat. This shows a proportional relationship.
What is a proportional relationship?It should be noted that a proportional relationship is one where it van be expressed as y = kx.
In this case, John bought 3 for $24.00. This will be:
= $24 / 3
= $8 per hat
Stacey bought 5 for $40.00. This will be:
= $40 / 5
= $8 per hat
Jim bought 2 for $16.00. This will be:
= $16/2
= $8 per hat
Therefore, it's a proportional relationship.
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I need help finding an answer, please.
From the given actual height of tower 1083 feet and width 410 feet, the
scale model is equal to 1.98 feet tall.
As given,
Eiffel Tower's actual height = 1083 feet
Eiffel Tower's actual width at base = 410 feet
Scale model's width at base = 0.75 feet
To find: how much tall is the scale model of the Eiffel Tower
Let us assume the height of the scale model of the Eiffel Tower to be x feet
Then by the property of similarity of scale models, ratio of the height of actual Eiffel Tower to its scale model will be equal to the ratio of the width of their base.
=> [tex]\frac{x}{1083} = \frac{0.75}{410}[/tex]
=> x = 1.98 feet
Therefore, the width of the base of the scale model of the Eiffel Tower is 1.98 feet with given actual height and width 1083feet and 410 feet respectively.
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Question
Two sides of a right triangle have lengths of 5 inches and 12 inches. Which of the following could be the
length, in inches, of the third side of the triangle?
A 3
B 8
C 13
D 17
Find the output, d, when the input, t, is 4 for d (t)- 13-4t. d(-2) -
The output of the given equation d (t)- 13-4t. d(-2) when the input is t=4 will be - will be -323
Give an illustration of what is a differential equation?Equations with General Differential. Consider the differential equation y′=3x2, which has a derivative and is an illustration of a differential equation. The variables x and y are related because y is an unidentified function of x. The derivative of y is also on the equation's left-hand side.
What are differential equations used for?The sciences, from which the equations originated and where the solutions found application, were the first to influence the mathematical theory of differential equations.
As the equation says: d(t)=13-4t.d(-2)
First we will calculate d(-2)
d(-2)=13-(4*-2)
d(-2)=21
d(4)=13-4*4*21
d(4)=-323
By this, the Final answer that is output for d would be -323.
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Please help me im begging
Let's say x is the number of ounces. Since the cost for each ounce is $0.85 then we can find the cost for the total amount of ounces by multiplying it by the cost of each one:
$0.85 · x
This is not the total cost, since the total cost has an additional of $5.50. Then the total cost is given by
c = $5.50 + $0.85x
Answer: C: c = 0.85x + 5.50Which expression represents the distance between 14.6 and −5.2 on the number line?
A. |-5.2 + 14.6|
B. |5.2 - 14.6|
C. |14.6 - {-5.2}
Answer:
The correct expression is
C. |14.6 - (-5.2)|
11 of 25 students in class own a dog.What is the ratio of students who own a dog to students in the class?What is the ratio of students who own a dog to students who DON'T own a dog?
Answer:
(a)11:25
(b)11:14
Explanation:
he total number of students in the class = 25
The number of students that own a dog = 11
do not 25-11=14
(a)The ratio of students who own a dog to students in the class will be:
[tex]=11\colon25[/tex](b)The ratio of students who own a dog to students who DON'T own a dog will be:
[tex]=11\colon14[/tex]Find the length and width of a rectangle sandbox, where the length is 3 feet longer than it’s width if you are building it with 22 feet of lumber
Let the length be represented by l and the width, w.
The question says that the length is 3 feet longer than the width. This means that
[tex]l=w+3[/tex]The perimeter of a rectangle is given as
[tex]2(w+l)=P[/tex]The perimeter of the sandbox is given as 22 feet.
Substituting the values for the perimeter and the length (w + 3) into the perimeter formula, we have
[tex]2(w+w+3)=22[/tex]Solving, we have
[tex]\begin{gathered} 2(2w+3)=22 \\ 2w+3=\frac{22}{2} \\ 2w=11-3 \\ 2w=8 \\ w=\frac{8}{2} \\ w=4 \end{gathered}[/tex]Now that we have the value for the width, we can calculate the length as
[tex]\begin{gathered} l=w+3 \\ l=4+3 \\ l=7 \end{gathered}[/tex]The length is 7 feet and the width is 4 feet.
the waiters at a restaurant have agreed to give one third of their tips to the kitchen staff if a waiter collects 72$ how much does he end up keeping
Answer:
48
Since they are giving one third of it to the staff, they are keeping 2 thirds of it for themselves. Two thirds of 72 is 48.
Answer:
He keeps $48.
Step-by-step explanation:
If he gives away 1/3, he keeps 2/3 so that's what we need to calculate.
First find 1/3 of 72 by dividing by 3: 72/3=24
Now to find 2/3, multiply by 2: 24*2=48
(72/3)*2= $48
What is the solution for 2(4x-11)+9 =19
Answer:
x=4
Step-by-step explanation:
Answer:
(2×4x-2×11)+9=19Step-by-step explanation:
Prove that,if one root of the equation ax^2+bx+c=0 is twice the other,then 2b^2=9ac
The proof of the quadratic equation is represented by the equation 18(m₂)² = 18(m₂)²
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax² + bx + c or y = a(x - h)² + k
How to prove the roots of the quadratic equation?The quadratic equation is given as
ax² + bx + c = 0
From the question, we understand that
One of the roots is twice the other
This means that
m₁ = 2m₂
Where m₁ and m₂ are the roots of the quadratic equation
The quadratic equation is then represented as
(x - m₁) * (x - m₂) = 0
Substitute m₁ = 2m₂ in the equation (x - x₁) * (x - x₂) = 0
So, we have
(x - 2m₂) * (x - m₂) = 0
Expand the brackets
So, we have
x² - 2xm₂ - xm₂ + 2(m₂)² = 0
Evaluate the sum and the difference.
So, we have
x² - 3xm₂ + 2(m2)² = 0
In the above equation, we have
a = 1
b = -3m2
c = 2(m₂)²
Recall that
2b² = 9ac
So, we have
2 * (-3m₂)² = 9 * 1 * 2(m₂)²
Evaluate
18(m₂)² = 18(m₂)²
The above equation is true
Hence, it is true that if one root of the equation ax² + bx + c = 0 is twice the other, then 2b² = 9ac
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Cuánto es un entero 1/4 en cm?
Answer:
2.54
Step-by-step explanation:
values around 1/4 inch
# 13 i
MODELING REAL LIFE The post office and the grocery store are both on the same straight road between the
school and your house. The distance from the school to the post office is 376 yards, the distance from the post office
to your house is 929 yards, and the distance from the grocery store to your house is 513 yards.
a. What is the distance from the post office to the grocery store?
yards
b. What is the distance from the school to your house?
yards
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Answer:
What is the role of ethnocentrism in defining the concept of “progress”
Step-by-step explanation:
Need help on another one of these problems I'm working on.
we have that
the solution of the given inequality is the interval
(-infinite,2/3) U (1, infinite)
so
Answer part c is
(-infinite,2/3) U (1, infinite)
Part b
In a number line, the solution is the shaded area at the left of x=2/3 (open circle) and the shaded area at the right of x=1 (open circle)
see the figure below to better understand the problem
please give me a minute to draw the solution
What is the reason for each step in the solution of the equation?
4x−1=−2(x+1)
Solve F(x) for the given domain. Include all of your work in your final answer. Submit your solution.
F(x) = x2 + 2
F(x - h) =
Based on the domain, the equation of the function f(x) is F(x - h) = x^2 - 2xh + h^2 + 2
What is the domain of a function?The domain of the function is the set of input values of the graph
How to determine the solution of the function f(x)?The equation of the function is given as
F(x) = x^2 + 2
The required function is given as
F(x - h)
The above means that the value of x in the function F(x) = x^2 + 2 is x - h
i.e.
x = x - h
So, we substitute x - h for x in the equation F(x) = x^2 + 2
This gives
F(x - h) = (x - h)^2 + 2
Evaluate the exponent
So, we have
F(x - h) = x^2 - 2xh + h^2 + 2
The above equation cannot be further simplified
Hence, the solution of the function f(x) at the given domain is F(x - h) = x^2 - 2xh + h^2 + 2
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PLEASE HELP QUICK!!!!
A candy store sells caramels and milk chocolate by the pound. The table below shows the total cost, in dollars, for a pound of each type of candy the store sells.
Answer:
Conversion of Dollars to Pounds is $1=0.90£
Step-by-step explanation:
b) when you calculate the amount you paid in total for 5 caramels and 4 milk chocolates, the total comes to $97,6 which is close to $100
Hope this helps !!