Answer:
[tex]\frac{\sqrt{3} }{3} or \frac{1}{\sqrt{3} }[/tex]
Step-by-step explanation:
We can break the problem into three parts,
tan45 = sin(45)/cos(45)=[tex]\frac{\frac{\sqrt{2}}{2} }{\frac{\sqrt{2}}{2} } =1[/tex]
[tex]tan^{2}30 =(tan30))^{2}=(sin30/cos30)^2=((1/2)/(\sqrt{3}/2))^2 =(1/\sqrt{3})^2[/tex]
[tex]tan60=sin60/cos60=\frac{\sqrt{3}/2 }{1/2} =\sqrt{3}[/tex]
Then, [tex]tan45*tan^230*tan60=1*(1/sqrt(3))^2*sqrt(3)=1/sqrt(3)=sqrt(3)/3[/tex]
Therefore, the solution is sqrt(3)/3
3/4(2/3 + 4/3) - 9 / 1/2 x 1/3
a. -52 1/2
b. - 5 1/4
c. - 4 1/2
d. -4 7/9
Answer: a. -52 1/2
Step-by-step explanation:
Given:
3/4(2/3 + 4/3) - 9 / 1/2 x 1/3
[tex]\displaystyle \frac{3}{4}(\frac{2}{3} +\frac{4}{3} )-\frac{9}{\frac{1}{2} *\frac{1}{3} }[/tex]
Add and multiply:
[tex]\displaystyle \frac{3}{4}(\frac{6}{3} )-\frac{9}{\frac{1}{6} }[/tex]
Simplify and divide:
[tex]\displaystyle \frac{3}{4}(2 )-54[/tex]
Multiply:
[tex]\displaystyle 1.5-54[/tex]
Subtract:
a. -52 1/2
HELP HELP HELP HELP
HELP HELP HELP
Answer: The base should be 4.
Step-by-step explanation:
1. We draw a triangle shape like the image.
(The steps was showed in the image).
write the equations after translating the graph of y = | 1/2 x -2 | + 3 one unit to the right
Using translation concepts, the equation of the graph is:
y = |0.5x - 2.5| + 3.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The function is:
y = |0.5x - 2| + 3.
When it is shifted one unit to the right, we have that x -> x - 1, hence:
y = |0.5(x - 1) - 2| + 3
y = |0.5x - 2.5| + 3.
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The expression x-y equals 0.7 if x and y have certain values. Evaluate the following expression with the same values of x and y
y-x
Answer:
-0.7
Step-by-step explanation:
Given x - y = 0.7
We will assign x and y random values that has a difference of 0.7
x = 1.3
y = 0.6
Using these 2 values,
y-x = 0.6-1.3
= -0.7
As you can see here , you will get a reversed value when you reverse the expression.
What value of k makes the statement true?
x² (2x³ + 7x²yª) = 2xªyª + 7x³y8?
By apply the distributive property of multiplication, the value of k which makes the statement true is 1.
What is the distribution property?Mathematically, the distributive property of multiplication is given by tis expression:
x(y + z) = xy + xz.
Next, we would apply the distributive property of multiplication to the given equation by distributing to the left-hand side using xy⁴:
k(2x⁴y⁴ + 7x³y⁸) = 2x⁴y⁴ + 7x³y⁸
Dividing both sides by the common factor, we have:
k = (2x⁴y⁴ + 7x³y⁸)/(2x⁴y⁴ + 7x³y⁸)
k = 1.
In conclusion, the value of k which makes the statement true is 1.
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Complete Question:
What value of k makes the statement true?
[tex]x^k[/tex]y⁴(2x³ + 7x²y⁴) = 2x⁴y⁴ + 7x³y⁸
Hello, i am having a hard time solving this. If anyone can please explain how to solve it in order for me to solve future questions of the same type?
f(x) = 5x3 – 2x and g(x) = 3x3
perform the following :
f(g(x))
g(f(x))
----- Thank you for your help
Answer:
Step-by-step explanation:
[tex] \underline{\large\bf \color{pink}{ Question :- }}[/tex]
The ages of Roony and Herald are 5x and 7x. If four years later, the sum of their ages will be 56 years, then form an equation and solve for x.
[tex] \\ \\ \\ [/tex]
Thank uh !
Answer:
x = 4
Step-by-step explanation:
The ages now are 5x and 7x.
The ages in 4 years are 5x + 4 and 7x + 4.
5x + 4 + 7x + 4 = 56
12x + 8 = 56
12x = 48
x = 4
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
4Step-by-step explanation:
• Given —
Age of Roony = 5x
Age of Herald = 7x
• After four years —
Age of Roony = (5x + 4)
Age of Herald = (7x + 4)
• Now, According to the question —
→ (5x + 4) + (7x + 4) = 56
→ 12x + 8 = 56
→ 12x = 56 - 8
→ 12x = 48
→ x = 4
Hope it helps you (`▿▿▿▿´ƪ)A welder's electrical arc has a temperature ranging from 500°C to 20 000°C. What is this in degrees Fahrenheit?
932°F to 36032°F
Step-by-step explanation:Celsius and Fahrenheit are both measures of temperature. However, Celsius is a metric measurement, and Fahrenheit is used in the USA primarily.
Conversion Formula
To convert the Celsius measurements to Fahrenheit we can use the formula:
(°C × 9/5) + 32 = °FSo, in this formula, you can plug in whatever Celsius value you have in and solve for Fahrenheit. To convert from F to C you can use the second formula:
(°F − 32) × 5/9 = °CSolving for Fahrenheit
Now that we have the formula, we can plug in the 2 Celsius values to find the new range.
First, plug 500°C in
(500°C × 9/5) +32 = °FNext, multiply the terms within the parentheses
(900) + 32 = °FFinally, add the last terms
932 = °FThen, plug in 20000°C
(20000°C × 9/5) + 32 = °FNext, multiply the terms within the parentheses
(36000) + 32 = °FLastly, add the terms together
36032 = °FThis means that, in Fahrenheit, the temperature range of the welder's electrical arc is 932°F to 36032°F. This is a total range of 35100°F.
600 feet of fence surround a rectangular playground that is 100 feet wide. how long is the playground
Answer:
Half of the perimeter is 300 feet.
If 100 feet are in the width, then 200 feet are in the length
Step-by-step explanation:
Perimeter is the sum of the lengths and the widths of the rectangle.
So P= l + l + w + w
perimeter is 600 and the width is 100.
so substituting in
600= 100 + 100 + l + l
600 = 200 + 2 l
solve for l
l = 200
hope this helps
Answer:
150 feet
Step-by-step explanation:
Length of playground = L + L + B + B
600 = 100 + 100 + 2L
600 = 200 + 2L
600 - 200 = 2L
300 = 2L
L = 300/2
L = 150
Therefore, the length of the playground is 150 feet.
Which of the following is not a true bi-conditional statement?
A. A quadrilateral is a square if and only if it has 4 congruent sides and 4 right angles.
B. Jane goes to the beach if and only if it is a sunny day.
C It is the weekend if and only if today is Saturday or Sunday.
D A number is even if and only if it is divisible by two.
Jane goes to the beach if and only if it is a sunny day.
========================================================
Reason:
A regular conditional statement is in the form "If P, then Q" where P and Q are placeholders for other statements.
For example, we can replace "P" with "it rains" and replace "Q" with "the grass gets wet". This means "If P, then Q" becomes "If it rains, then the grass gets wet".
It's hopefully clear that the example above is a one way street. It points in only one direction. The act of raining leads directly to the grass being wet. However, we cannot go in reverse. If we see the grass is wet, it doesn't mean it rained. Perhaps someone turned on a hose or sprinkler system. P leads to Q, but Q does not lead to P.
In short, all of what is mentioned so far is considered a regular conditional statement. So far we haven't addressed bi-conditional statements.
----------------
Bi-conditional statements are conditionals that work in reverse.
An example would be "If a figure is a square, then it has 4 congruent sides and 4 right angles". That conditional statement works in reverse. Therefore "If a figure has 4 congruent sides and 4 right angles, then the figure is a square" is also true simply by what it means to be a square.
So the format "If P, then Q" can be reversed to "If Q, then P" to have an equivalently true statement. The common practice is to use "if and only if" to help shorten things.
We would have the template "P if and only if Q" which is the same as "Q if and only if P". The order doesn't matter since we can reverse things just fine.
Often you'll find bi-conditional statements when it comes to definitions. The term "weekend" literally means the day is either Saturday or Sunday, which is why choice C is another bi-conditional. A very similar situation applies to choice D as well.
--------------------
We've found that choices A, C and D are bi-conditional statements. They can be ruled out. We're left with choice B.
This is not a bi-conditional. Why not? It's assumed that Jane would go to the beach on a sunny day, but perhaps she enjoys the beach just fine on cloudy days. There's also the fact she could be doing other things on sunny days. The presence of the sun doesn't automatically mean the beach. If you said "It gets warm if and only if it's a sunny day", then I think this is more in line with a bi-conditional.
This is why choice B is the final answer.
A tourist buys a nepali flag at a discount of 15% but pays
10% VAT,if she pays rs170 for VAT.calculate the discount amount
so he paid Rs 170 for VAT
total amount paid = 170 x 10 = 1700
discount is 15%
so therefore
amount before discount = 1700/(1–0,15) = 2000
discount = 2000 x 15% = Rs 300
The 15% discount amount for the Nepali flag is 255 rupees.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
VAT = 10%
Discount = 15%
10% = 170 rupees
Multiply 15/10 on both sides.
15/10 x 10% = 15/10 x 170
15% = 255 rupees.
Thus,
The discount amount is 255 rupees.
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Select the correct answer.
Which function is the inverse of function f if the domain of f is ?
The inverse function of f(x) is [tex]f^{-1}(x) = \sqrt{x - 6}[/tex] and the domain is x > 6
How to determine the inverse function?The function is given as:
f(x) = x^2 + 6
Rewrite as:
y = x^2 + 6
Swap x and y
x = y^2 + 6
Subtract 6 from both sides
y^2 = x - 6
Take the square root
[tex]y = \sqrt{x - 6}[/tex]
Rewrite as:
[tex]f^{-1}(x) = \sqrt{x - 6}[/tex]
Hence, the inverse function of f(x) is [tex]f^{-1}(x) = \sqrt{x - 6}[/tex] and the domain is x > 6
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What's the value? (yelping for help)
cos(20°) is the correct answer.
Congratulations! This is the unit circle. Literally everyone hates this. Everyone takes this in Trigonometry though, and it's required. I literally failed Trigonometry because of this and had to retake it when getting my degree in Mathematics.
So, what is the x-coordinate of this? Well, for any angle or (angle in triangle) [tex]\alpha[/tex], the coordinates are always ([tex]cos(\alpha), sin(\alpha)[/tex]).
In this case, angle [tex]\alpha[/tex] is 20°, and so the x-coordinate will be cos(20°) while the y-coordinate will be sin(20°).
Hope this helped!
Answer: cos 20
Step-by-step explanation:
Question is in the picture, please help.
Answer:
1)The equation is 3^N, where N starts at 4 and goes down 1 each time
2) 1 would be the 5th term
Step-by-step explanation:
3^4=81
3^3=27
3^2=9
3^1=3
3^0=1
From the diagram below, if the sides AD = 3 and DC = 27, and BD = X + 3, find x.
Select one:
a.
36
b.
9
c.
16
d.
6
Answer: 6
Step-by-step explanation:
By the geometric mean theorem,
[tex]\frac{BD}{3}=\frac{27}{BD}\\\\(BD)^{2}=81\\\\BD=9\\\\\implies x=9-3=6[/tex]
Answer:
x = 6
Step-by-step explanation:
BD is the height of the triangle.
We can find the height of this triangle using one of the Euclidian Theorem:
h^2 = AD*DC rewrite the equation using the given information
(x + 3)^2 = 3*27 multiply
(x + 3)^2 = 81 find the root of both sides
x + 3 = 9 subtract 3 from both sides
x = 6
In a lab experiment, the decay of a radioactive isotope is being observed. On the first day of the experiment the mass of the substance was 1400 grams and mass was decreasing by 10% per day. Write a recursive formula to represent the mass of the radioactive sample on the day of the experiment.
The recursive formula is mathematically given as
a_n=1266.77e^n
What is the recursive formula?Generally, the equation for the decay is mathematically given as
[tex]at=a_oe^{-\lambda t}[/tex]
Hence
a1=1400e^{-0.1 (1)}
In conclusion,
[tex]a_n=1400e^{-0.1 (n)}\\\\a_n=1266.77e^n[/tex]
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A line is perpendicular to the line 3x - 4y= 2 and passes through the point (1, - 2). Which of the following
is an equation of the line?
Answer:
Last option, y = -4/3x - 2/3
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
number that describes both the direction and the steepness of the line
slope = rise/run
b represents the y-intercept
point where crosses the y-axis
Given:
line 3x - 4y = 2passes through the point (1, - 2)Let change 3x - 4y = 2 into y = mx + b form,
3x - 4y = 2
subtract 3x from both sides,
3x - 3x - 4y = 2 - 3x
- 4y = 2 - 3x
divided both sides by -4 to get y alone,
- 4y / -4 = 2 - 3x / - 4
y = (3x / 4) - (2 / 4)
→ y = (3/4)x - (1/2)
Slope of perpendicular lines to another is the negative reciprocal
(ex. slope of 2 becomes -1/2)
So for y = (3/4)x - (1/2) the slope will be,
slope = -4/3
We need to find b (y-intercept),
we know it passes through point (1, - 2)
a point is (x, y) format
y = -(4/3)x + b
plug in the point (1, - 2),
-2 = -4/3(1) + b
-2 = -4/3 + b
add 4/3 to both sides to get b alone,
-2 + 4/3 = -4/3 + 4/3 + b
-2/3 = b
the perpendicular line equation is,
y = -4/3x - 2/3
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Find NM=
Help me please thanks
A triangle is a three-edged polygon with three vertices. The length of the side MN is 3 cms.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The triangle formed by MN, MO, NO is an equilateral triangle, with the length of each side of the triangle equal to the radius of the triangle. Therefore, the length of MN will be,
MN = r
Now, the length of arc MN can be written as,
2 × π × r × (60° /360°) = π
r = 360 / (60 × 2)
r = 3
Hence, the length of the side MN is 3 cms.
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PLEASE HELP
Which is the simplified form of the expression
The simplified form of the expression ( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )² is [tex]\frac{1}{3^8}[/tex].
Hence, option B is the correct answer.
What is the simplified form of the expression?Given the expression;
( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )²
First, we use the properties of exponents.
( 2⁻²ˣ⁻³ × 3⁴ˣ⁻³ ) × ( 2⁻³ˣ² × 3²ˣ² )
( 2⁶ × 3⁻¹² ) × ( 2⁻⁶ × 3⁴ )
We take out the parentheses, such that;
2⁶ × 2⁻⁶ × 3⁻¹² × 3⁴
Note that: 2⁶ × 2⁻⁶ = 1, as [tex]2^6*2^{-6}=2^{6+(-6)}=2^0=1[/tex]
Hence, we have
1 × 3⁻¹² × 3⁴
3⁻¹²⁺4
3⁻⁸
Next, we express with positive exponent
[tex]\frac{1}{3^8}[/tex]
The simplified form of the expression ( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )² is [tex]\frac{1}{3^8}[/tex].
Hence, option B is the correct answer.
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two cyclists leave towns 74 miles apart at the same time and travel towards each other. one cyclist travels 3 mi/h faster than the other. If they meet in 2 hours, what is the rate of each cyclist?
The rates of each cyclist are 17mi/h and 20mi/h
What is rate?
Rate is a ratio that compares two different quantities which have different units.
In this comparison, one unit is taken to be a standard unit in which the other is compared with.
Analysis:
Let the speeds of both cyclists be x, x+3
distance travelled by x cyclist = 2x
distance travelled by (x+3) cyclist = 2(x+3)
Total distance = 2x + 2(x+3) = 74 miles
2x +2x +6 = 74
4x + 6 = 74
4x = 74 - 6
4x = 68
x = 68/4 = 17mi/h
The other cyclist speed is x +3 = 17 +3 = 20mi/h
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What is the sum of the polynomials?
(6x+7+x²)+(2x²-3)
O-x²+6x+4
O3x²+6x+4
O9x + 4
O gx² +4
Answer:
3x² + 6x + 4
Step-by-step explanation:
6x + 7 + x² + 2x² - 3
→ Collect like terms
x² + 2x² + 6x + 7 - 3
→ Simplify
3x² + 6x + 4
Answer:
3x^2+6x+4
Step-by-step explanation:
We can find the sum of the polynomials by combining like terms.
(6x+7+x²)+(2x²-3)
x^2+2x^2+6x+7-3
3x^2+6x+4
A group of marketing students at a large university wants to determine the proportion of first year students who use certain types of social media. The students want their estimate to be within 0.03 of the true proportion with a 95% level of confidence. Two years ago, a similar study determined the proportion to be 0.796. How large of a sample is required
The required sample size is 694.
Given a student wants to make a guess within 0.03 of the true ratio with a 95% confidence level.
Margin of Error, E = 0.03
significance level α=0.05 {95% confidence}
A given estimate of the percentage of population p is p = 0.79.
The critical value for the significance level α = 0.05 is Zc = 1.96. This can be determined using either Excel or a normal probability table.
Use the following formula to calculate the minimum sample size required to estimate the percentage of population p within the required margin of error.
n≥p(1-p)(Zc÷E)²
n=0.796×(1-0.796)(1.96÷0.03)²
n=693.1016
Therefore, the resample sizequired to meet the condition is n ≥ 693.1016 and must be an integer. From this, we conclude that the minimum sample size required is n = 694.
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One evening 1500 concert tickets were sold for the fair mount jazz festival. tickets cost 20 for covered pavilion seats and $10 for lawn seats total receipts were 23,000 how many tickets of each were sold
A total of 800 tickets for the covered pavilion and 700 tickets for lawn seats were sold, solved using a system of equations.
We assume the number of covered pavilion tickets sold to be x and the number of lawn seat tickets sold to be y.
As a total of 1500 tickets were sold, we can form an equation:
x + y = 1500 ... (i),
as we had only those two types of tickets.
The cost of each covered pavilion ticket = $20.
Hence, the total revenue from covered pavilion tickets = $20x.
The cost of each lawn seat ticket = $10.
Hence, the total revenue from lawn seat tickets = $10y.
The total receipts were said to be $23,000.
Thus, we can represent this as an equation:
20x + 10y = 23000 ...(ii).
Combining (i) and (ii), we get a system of equations:
x + y = 1500 ... (i).
20x + 10y = 23000 ... (ii).
Dividing equation (ii) by 10, we get:
2x + y = 2300 ... (iii).
Subtracting (i) from (iii), we get:
2x + y = 2300.
x + y = 1500.
(-) (-) (-)
____________
x = 800.
Substituting x = 800 in (i), we get:
x + y = 1500,
or, 800 + y = 1500,
or, y = 1500 - 800,
or, y = 700.
Thus, a total of 800 tickets for the covered pavilion and 700 tickets for lawn seats were sold, solved using a system of equations.
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What is the LCM of 24 ,40,30
Answer:
LCM(24,30,40)=120.The Least common multiple for three numbers 24,30 and 40 is 120
Step-by-step explanation:
Tablets are on sale for 15% off the original price (t), which can be expressed with the function p(t) = 0.85t. Local taxes are an additional 8% of the discounted price (p), which can be expressed with the function c(p) = 1.08p. Using this information, which of the following represents the final price of a tablet, with the discount and taxes applied, based on its original price?
Using proportions, it is found that the expression that represents the final price is given as follows:
C(t) = 0.918t.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, we have that:
With the discount, the price is of 0.85t.With the taxes, the price is increased by 8%, hence multiplied by 1.08.Thus the expression for the final cost is:
C(t) = t x 0.85 x 1.08 = 0.918t.
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If a soccer team made 28 penalty shots out of 100, what fraction and what
percentage of penalty shots did the team miss? Choose two answers.
24. A pizzeria sells a medium pizza for $5.99 plus $0.75 for each topping.
They also sell a large pizza for $6.99 plus an additional $0.50 per topping.
After how many toppings will the medium and large pizzas cost the same
amount?
The pizzas will cost the same at 4 toppings.
The pizzas will cost the same at 5 toppings.
The pizzas will cost the same at 6 toppings.
The pizzas will never cost the same amount.
Answer:
a.) The pizzas will cost the same at 4 toppings
Step-by-step explanation:
Medium Pizza:
$5.99 + $0.75x
Large Pizza:
$6.99 + $0.50x
Find x
$5.99 + $0.75x = $6.99 + $0.50x
0.25x = 1
x = 4
Complete the following chart below.
FIll in the missing blanks.
[tex]y=2(x+1)^2+6[/tex]
The vertex (−1,6)
Equation of axis of symmetry is x = -1
minimum at (-1,6)
[tex]y=\frac{-(x-1)}{2} ^2-4[/tex]
The vertex (1,-4)
Equation of axis of symmetry is x = 1
maximum at (1,-4)
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
[tex]y=2(x+1)^2+6[/tex]
The vertex (−1,6)
Equation of axis of symmetry is x = -1
minimum at (-1,6)
[tex]y=\frac{-(x-1)}{2} ^2-4[/tex]
The vertex (1,-4)
Equation of axis of symmetry is x = 1
maximum at (1,-4)
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Which statement about the function represented by this graph is true? A curve rises from (0, 2), (2, 3 point 9), (4, 4), (5, 4 point 1), (6, 4 point 9), (8, 5), (9, 5), and (10, 5) on the x y coordinate plane. A. The function has an inverse because it passes the vertical line test. B. The function does not have an inverse because it does not pass the horizontal line test. C. The function does not have an inverse because it never crosses the x-axis. D. The function has an inverse because it passes the horizontal line test.
The true statement about the function which is represented by this graph is: D. the function has an inverse because it passes the horizontal line test.
What is the horizontal line test?The horizontal line test states that if the graph of function (f) is intersected by any horizontal line more than once, then, the function (f) doesn't have an inverse.
Conversely, if the graph of function (f) isn't intersected by any horizontal line more than once, then, the function (f) has an inverse.
By critically observing the graph of the given function (f) shown in the image attached below, we can logically deduce that it has an inverse because it passed the horizontal line test.
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Answer: D. The function has an inverse because it passes the horizontal line test.
Step-by-step explanation:
Got it right on test.
Write 10x10x10x10x10x10 with an exponent explain how you decided what exponent to write
Answer:
10^6
Step-by-step explanation:
exponents show how many times a number multiplies by itself
in this case, 10 multiplies by itself 6 times, so the answer should be 10^6