To simplify the expression xz^3*4x^4z^5, the exponents of the like bases are added together resulting in 4x^5z^8. This application of exponent rules shows that the exponents on the same base are summed during multiplication.
Explanation:To simplify the expression xz^3*4x^4z^5, we need to apply the rules of exponents. Specifically, when multiplying two expressions with the same base, we add their exponents.
Beginning with the variable x, we have an implied exponent of 1 on the standalone x, so when combined with x^4, we get x^(1+4), which simplifies to x^5.
Next, we apply the same rule to the variable z.
The expression z^3 multiplied by z^5 becomes z^(3+5), which simplifies to z^8. Finally, we multiply these results by the constant 4 to get our simplified expression:
4x^5z^8.
As an example to clarify this process, imagine a simpler case like (5^3)^4.
This could be written out as multiple fives multiplied by each other, illustrating that the exponents are indeed added together when multiplying like bases, just as we did with x and z in our original expression.
After one hour, the hare had finished 2/3 of a 100-yard race. In that same time, the tortoise had finished 42 3/4 yards. How much farther had the hare run than the tortoise?
Answer:
23 11/12 yards or 23.9166 yards
Step-by-step explanation:
2/3 of 100 yard race is equivalent to 66 2/3 yards. Tge difference between the above and 42 3/4 yards covered by tortoise will be
66 2/3- 42 3/4= 23 11/12 yards or 23.91666 yards
what is 1735/1000 written as a decimal?
Answer:
[tex]\frac{1735}{1000}[/tex] as a decimal is 1.735.
Step-by-step explanation:
To convert a fraction into a decimal, you first have to put the fraction into simplest form.
1. Simplest form
[tex]\frac{1735}{1000} = \frac{347}{200}\\\[/tex]
To do this you must find a number you can equally divide both numbers by.
That number in this situation, 5.
[tex]1000/5= 200\\1735/5= 347\\1735:1000 = 347:200\\\frac{1735}{1000} =\frac{347}{200}[/tex]
Now you must make this simplest formed fraction into a mixed number.
2. Simplest form into Mixed number
[tex]\frac{347}{200}= 1\frac{147}{200}[/tex]
To do this you see how many times the denominator, the bottom number of the fraction, goes into the numerator, the upper part of the fraction.
Since 200 x 2 = 400 and since 400 > 347 this means...
200 goes into 347, once.
Finally, subtract and divide.
Remember put the whole number in front of the mixed number, before the decimal
3. Subtract, divide, decimalize
[tex]147/200= 0.735\\\\1\frac{147}{200}= 1.735[/tex]
Hopes this helps you!
Have a good afternoon!
Quincy has a piece of pipe that is 2/3 yard long - he uses 3/4 to repair a sink. What length of the pipe will he use for the sink?
Answer:
hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Step-by-step explanation:
Answer:
Step-by-step explanation
Length of pipe =2/3yard
3/4 of pipe = 3/4 × 2/3
= 2/4 = 1/2 yard
Eric can wrap 50 gift boxes in one hour. On this basis, Samantha computed the number of gifts he can wrap in 0.05 hour. How many significant digits are there in Samantha’s result?
A) 1
B) 2
C) 3
D) 4
Answer:
The answer is B).2
Step-by-step explanation:
any 0 after the decimal is significant. .05 should be the answer.
Answer:
It is not 2 i got it wrong
Step-by-step explanation:
i think it is one
3 Maddie's little brother spilled ketchup on one of her homework problems.
Assuming that the number under the spill is greater than zero, fill in the bubble
to show what Maddie should be able to tell for sure about the answer, even
though she can't see the other number.
O The answer will be less than 3.
O The answer will be less than the ketchup-covered number.
O The answer will be a fraction.
O The answer will be greater than the ketchup-covered number.
b.Explain your answer. How do you know the statement you chose is true?
Final answer:
Maddie should be able to tell for sure that the answer will be greater than the ketchup-covered number.
Explanation:
Based on the information provided, Maddie should be able to tell for sure that the answer will be greater than the ketchup-covered number. We can make this determination by comparing the known quantity, which is '3', with the fact that the obscured number is greater than zero. As long as the missing number is positive, any amount added to '3' would result in a sum that is larger than '3'.
If the hidden number is greater than zero and we add it to '3', the result must logically be greater than '3'. This concept is grounded in the basic principles of arithmetic, where adding a positive number to another number increases the total. Therefore, regardless of what the ketchup-covered number is, provided it is more than zero, the sum will indeed be larger than the visible number '3'.
Consider m= y2-y1 x2 - x1 which x1 and x2-values would determine that he line is vertical? Justify your answer
Answer:
Step-by-step explanation:
hello :
m= (y2-y1)/( x2 - x1) is the slope
this line is verticalwhen : x2 = x1
Mathematical
5. PRACTICE 2 Draw a Conclusion is the statement below
always, sometimes, or never true? Give at least two examples to
support your reasoning. The LCM of two numbers is the product
of the two numbers.
Vocab
Vocabulary Check
Answer:
Sometimes true
Step-by-step explanation:
Examples:
Denominators are 2 & 3
LCM is 6 (2×3 = 6)
True here
Denominators are 2 & 6
LCM is 6 (2×6 = 12)
Not true here
PLEASE HELP ME!!! 5 POINTS
What does Florida's state constitution include in its first article?
A. Declaration of rights
B. Description of the state flower
C.Image of the state flag
D. Plans for the Capitol building
Hello.
The answer is A. The Declaration of Rights.
Answer:
c. image of the state flag
What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 39
Step-by-step explanation:
The sum of all three angles of a triangle will ALWAYS be 180 degrees.
So, simply subtract 39 and 103 from 180 and you will find your answer.
180 - 39 - 102 = 39
Answer:
39
Step-by-step explanation:
There are 180degrees in a triangle. So 102+39=141than we have to do 180-141 to get out answer of 39
The graph of which function has an axis of symmetry at x = 3?
The graph of y = 2(x - 3)² + 2 has an axis of symmetry at x = 3
The graph of which function has an axis of symmetry at x = 3?
From the question, we have the following parameters that can be used in our computation:
The quadratic functions
A quadratic function is represented as
y = a(x - h)² + k
Where,
The axis of symmetry is at x = h
Using the above as a guide, we have the following:
The graph of y = 2(x - 3)² + 2 has an axis of symmetry at x = 3
Question
The graph of which function has an axis of symmetry at x = 3?
y = 4(x + 3)²
y = 2(x - 3)² + 2
y = x² + 2
y = 2(x + 5)² + 2
Generally, horses are faster than donkeys. A horse can reach speeds of 55 mph (or approximately 88.50 kph). Most donkeys top out at 30 mph over short distances. What is the top speed of most donkeys in kph? Round your answer to two decimal places.
Answer:
48.30 kph
Step-by-step explanation:
55mph - 88.50kph
1mph - 1.61 kph
30 mph - 48.30 kph
Horses can reach speeds of 55 mph (approximately 88.50 kph), while most donkeys top out at 30 mph over short distances.
A conversion factor is a number that is used to multiply or divide one set of units into another. The acceptable factor to an equivalent value must be utilized when a conversion is crucial.
Given that,
Horses can reach speeds of 55 mph (approximately 88.50 kph).
Most donkeys have a top speed of 30 mph over short distances.
Here the top speed of most donkeys is asked.
To convert miles per hour (mph) to kilometers per hour (kph),
Use the conversion factor of 1.60934.
Calculate the top speed of most donkeys in kph:
Given: Top speed of most donkeys = 30 mph
Conversion: 30 x 1.60934
≈ 48.28 kph
Hence, the top speed of most donkeys, rounded to two decimal places, is approximately 48.28 kph.
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A square calendar has sides that are 20 Inches long. What is the calendar's perimeter?
inches
Answer:
80 in.
Step-by-step explanation:
to find the perimeter of a shape you add all of the side lengths together
20+20+20+20
Using digits 0-9 at most one time,fill in the boxes o make the sum of the interior angles of a triangle .
Step-by-step explanation:
The interior angles of a triangle add up to 180.
There are many possible answers. One example is 90 + 12 + 78.
22/25, end fraction of a number is what percentage of that number
Answer:
88%
Step-by-step explanation:
To get the percentage of 22/25. All that is needed to do is to multiply it with 100. Because A percentage is 100.
Thus: 22/25 gives 0.88 as a decimal, multiplied by the percentage figure 100
0.88 times 100 will give 88%.
Which means 22 is 88% of 25.
In other words to turn a fraction or decimal to a percentage, all that is needed to do of just to multiply that fraction or decimal by 100, and then it will give the percentage.
is this true or false
Answer:
False.
Step-by-step explanation:
xy is one term.
Each term in an algebraic expression is separated by a + or - sign.
For example, x^2 - xy + y^2 has 3 terms
hi! i could really use some help....
Answer:
with what
Step-by-step explanation:
At lavernes swimwear there are 6 bikini styles and 2 other types of swimsuit what percent of the swimsuit styles are bikinis?
Answer:
33.33%
Step-by-step explanation:
6 bikini styles and 2 other types
so, total types is 3
so, bikinis is only 1 of the 3, which is 1/3 or 33.33%
Bikini styles: 6
Othe types: 2
Overall: 6+2=8
Bikini percentage: 6/8=3/4=75%
Answer: 3/4 or 75%
What is the remainder when x^{6}-4x^4+4x^2-10 is divided by x+3?
Answer:
431
Step-by-step explanation:
Let
[tex]p(x) = {x}^{6} - 4 {x}^{4} + 4 {x}^{2} - 10[/tex]
We want to find the remainder when this polynomial is divided by x+3.
We use the remainder theorem.
Which says that, when p(x) is divided by x-a, the remainder is p(a)=R.
Therefore the remainder when p(x) is divided by x+3 is p(-3).
[tex]p( - 3) = {( - 3)}^{6} - 4 { (- 3)}^{4} + 4 {( - 3)}^{2} - 10[/tex]
We evaluate:
[tex]p( - 3) = 729 - 4 (81)+ 4 {( 9)} - 10[/tex]
We multiply to get;
[tex]p( - 3) = 729 - 324+ 36- 10[/tex]
We simplify to get:
[tex]p( - 3) =431[/tex]
Therefore the remainder is 431
To ride your favorite roller coaster, you must be at least five feet tall but
less than seven feet tall. Let h represent any height that can ride the roller
coaster.
Answer:
5 ≤ h<7
Step-by-step explanation:
the rider has to be more than at least 5 feet tall, so h is greater than or equal to 5 (5 ≤ h), but they have to be less than 7 feet tall (h<7) so, therefore, we get 5 ≤ h<7
Question 3 (Multiple Choice Worth 1 points)
(02.05 MC)
Write the equation of a function whose parent function, f(x) = x + 8, is shifted 2 units to the right.
Og(x) = x - 6
O g(x) = x -
11111
x
0
|
+ III
x
M
|
x
M
O g(x) = x + 2
|
O g(x) = x + 6
Answer:
[tex]g(x) = x + 6[/tex]
Step-by-step explanation:
The parent function is given as:
[tex]f(x) = x + 8[/tex]
We want to find a new function that results after shifting f(x), 2 units to the right.
Let that function be g(x), then
[tex]g(x) = f(x - 2)[/tex]
We replace x by x-2 in f(x) to get:
[tex]g(x) = x - 2 + 8[/tex]
When we simplify, we obtain:
[tex]g(x) = x + 6[/tex]
What is the answer 4x+10=-26
Answer: x = -9
Step-by-step explanation:
Subtract 10 from both sides:
4x + 10 - 10 = -26 - 10
Simplify:
4x = -36
Divide both sides by 4:
4x/4 = -36/4
simplify:
-36/4 = -9
Answer: x = -9
Answer:
x = -9
Step-by-step explanation:
4x+10 = -26
-10 -10
[tex]\frac{4x=-30}{4}[/tex]
x = -9
The scatter plot shows the number of hours 15 students spent studying for a 20-item quiz and their quiz scores. Which BEST describes the data?
A) The data cluster along a line and there is no outlier.
B) There is no association between the time the students spent studying and their quiz scores.
C) There are clusters around the 1 hour and the 2 hours of studying. The point (3.5, 20) is an outlier.
D) There is a nonlinear association between the time the students spent studying and their quiz scores. The point (3.5, 20) is an outlier.
Answer: The answer is C
Based on the information given, the best description of the data is the data cluster along a line and there is no outlier.
Option A is the correct answer.
What is a scatterplot?A scatterplot is a type of graph used to display the relationship between two variables.
It is a collection of points on a two-dimensional plane, where each point represents a pair of values for the two variables being plotted.
One variable is typically plotted on the x-axis (horizontal axis), and the other variable is plotted on the y-axis (vertical axis).
We have,
The scatter plot shows a linear pattern where the data points are clustered around a line.
As the number of hours spent studying increases, the quiz score tends to increase as well.
There do not appear to be any outliers in the data that would significantly affect the relationship between the hours spent studying and the quiz scores.
Thus,
Based on the information given, the best description of the data is the data cluster along a line and there is no outlier.
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Suppose you invest 1500$ in an account payin 4.75% Annual interest. Find the account balance after 5 years
Answer:4850.51
Step-by-step explanation:
Please help! Question is attached to the image :)
The volume of the smaller room is B. 768 cubic feet.
Step-by-step explanation:
Step 1:
The entire length for both rooms is 20 feet. As the large room has a length of 12 feet, the length of the smaller room is [tex]20-12=[/tex] 18 feet long.
The width of the prism is 12 feet and a height of 8 feet.
The volume of a rectangular prism is determined by multiplying its length, its width, and its height.
The small room's length = 8 feet,
The small room's width = 12 feet, and
The small room's height = 8 feet.
Step 2:
The volume of a rectangular prism [tex]= (l)(w)(h).[/tex]
The volume of the smaller room [tex]= (8)(12)(8)= 768.[/tex]
So the volume of the smaller room is 768 cubic feet which is option B.
Use the Distributive Property to express
24 + 36
Answer:
12(2 + 3)
Step-by-step explanation:
To use the distributive property, we must find a common factor between the two numbers. The greatest common factor or 24 and 36 is 12. Let's just use that. We get:
[tex]12(2+3) = 24+36[/tex]
That's our answer!
Answer:
12 ( 2 + 3 )= + 36
Step-by-step explanation: GCF between 24 and 36 by prime factorization should be:
24 = 2 * 2 * 2 * 3
36 = 2 * 2 * 3 * 3. what they both have in common between the prime factorization of both of the numbers are 2*2*3 which is GCF and equivlent to 12.
Rewrite the equation below so that it does not have fractions four -4/9 times equals two over three do not use decimals in your answer please help me I’ll give you 10 points
The equation is 36 - 4x = 6.
Solution:
To write the equation without fraction.
[tex]$4-\frac{4}{9} x=\frac{2}{3}[/tex]
[tex]$\frac{4}{1} -\frac{4}{9} x=\frac{2}{3}[/tex]
The denominators must be same to add/subtract the fractions.
LCM of 1, 9 and 3 = 9.
Multiply first term by [tex]\frac{9}{9}[/tex] and [tex]\frac{2}{3}[/tex] by [tex]\frac{3}{3}[/tex] to make the denominator same.
[tex]$\frac{4\times9}{1\times9} -\frac{4}{9} x=\frac{2\times3}{3\times3}[/tex]
[tex]$\frac{36}{9} -\frac{4}{9} x=\frac{6}{9}[/tex]
[tex]$\frac{36-4x}{9} =\frac{6}{9}[/tex]
Multiply by 9 on both sides.
[tex]$\frac{36-4x}{9}\times9 =\frac{6}{9}\times9[/tex]
Both 9 in the numerator and denominator get canceled.
36 - 4x = 6
This term does not have fraction.
Hence the equation is 36 - 4x = 6.
the length of a rectangle is four feet longer than the width. the area is 21. find the dimension
The dimensions of the rectangle are: Width = 3 feet, Length = 7 feet.
The formula for Area of rectangle
Area = length x width
Given:
Area of rectangle = 21 square feet.
Let the width of the rectangle is w feet.
According to the given information, the length of the rectangle is four feet longer than the width,
So, length = w + 4 feet.
So, Area of rectangle = length x width
21 = w (w+4)
[tex]\[21 = w^2 + 4w\][/tex]
[tex]\[w^2 + 4w - 21 = 0\][/tex]
Solve this quadratic equation, set it equal to zero:
w² + 7w -3w -21 =0
w(w+7)-3 (w+7)= 0
(w+7)(w-3) =0
Setting each factor equal to zero:
w+ 7 =0
w= -7
or, w - 3 =0
w = 3
So, the length of rectangle is
= 3+ 4
= 7 feet
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Select all that are asymptotes of the
tangent graph.
x = pi/4
x=pi/2
x=pi
x=3pi/2
x=3pi
Answer:
[tex]x = \frac{\pi}{2} [/tex]
[tex]x = \frac{3\pi}{2} [/tex]
Step-by-step explanation:
The tangent function is
[tex]y = \tan(x) [/tex]
We can rewrite it as:
[tex]y = \frac{ \sin(x) }{ \cos(x) } [/tex]
This graph has vertical asymptotes at where the denominator is zero.
[tex] \cos(x) = 0 \\ \implies \: x = \frac{\pi}{2} \: or \: \frac{3\pi}{2} [/tex]
The correct options are : (b) [tex]\( x = \frac{\pi}{2} \)[/tex] and (d) [tex]\( x = \frac{3\pi}{2} \)[/tex]
The asymptotes of the tangent graph are the vertical lines where the tangent function is undefined. The tangent function, [tex]\(\tan(x)\)[/tex], is undefined where the cosine function is zero, which happens at:
[tex]\[ x = \frac{\pi}{2} + k\pi \quad \text{for integer values of } k \][/tex]
So, let's check each given value to see if it fits this form.
1. [tex]\( x = \frac{\pi}{4} \)[/tex]
[tex]\[ \frac{\pi}{4} \neq \frac{\pi}{2} + k\pi \][/tex]
This is not an asymptote.
2. [tex]\( x = \frac{\pi}{2} \)[/tex]
[tex]\[ \frac{\pi}{2} = \frac{\pi}{2} + 0 \times \pi \][/tex]
This is an asymptote.
3.[tex]\( x = \pi \)[/tex]
[tex]\[ \pi \neq \frac{\pi}{2} + k\pi \][/tex]
This is not an asymptote.
4. [tex]\( x = \frac{3\pi}{2} \)[/tex]
[tex]\[ \frac{3\pi}{2} = \frac{\pi}{2} + \pi \][/tex]
This is an asymptote.
5.[tex]\( x = 3\pi \)[/tex]
[tex]\[ 3\pi \neq \frac{\pi}{2} + k\pi \][/tex]
This is not an asymptote.
The asymptotes of the tangent graph from the given options are:
[tex]\( x = \frac{\pi}{2} \)[/tex]
[tex]\( x = \frac{3\pi}{2} \)[/tex]
The complete Question is
Select all that are asymptotes of the
tangent graph.
a. x = pi/4
b. x=pi/2
c. x=pi
d. x=3pi/2
e. x=3pi
There are 12 animals in a farm.
Some are cows
The rest are chickens
There are 28 animal legs in all.
How many cows are there?
How many chickens are there?
Answer:
2 cows 10 chickens
Step-by-step explanation:
2 X 10 = 20
4 X 2 = 8
20 + 8 = 28
What is the value of y?
A. y = -1
B. y = 0
C. y = 1
D. y = 3
Step-by-step explanation:
The centroid divides the length of each median in 2:1 ratio.
The length of the part between the vertex and the centroid is twice the length between the centroid and the mid-point of the opposite side.
In case of median KM,
K is the vertex and M is the midpoint of the side JL
KT = 2× TM
5y+3 = 2(y+3)
5y+3= 2y +6
5y-2y= 6-3
3y = 3
y= 1