In which step did Rena make the first error?
Answer: Step 4
Step-by-step explanation:
Rena made the first mistake in step 4 because she left the terms [tex]2^{3} and (-1)^{21}[/tex] in the denominator, when in the previous step they were also in the denominator but raised to -1, which means that they should be in the numerator.
The right step 4 would be:
[tex]\frac{2^{3} (-1)^{21} }{2^{6} } =\frac{-1}{2^{3} } =\frac{-1}{8}[/tex]
Answer: step 4
!!
Step-by-step explanation:
Using these integers 12345789 you put them in 2 groups of 4 coming up with the same summ
What is the reflection image of (5,-3) across the line y = -x?
Set m contains the values {-12, -7, 4, 11} and set n contains the values {-3,2,8}. What is the greatest possible difference of m^2 - n^2 ?
A. 76
B. 117
C. 140
D. 153
Answer:
C. 140
Step-by-step explanation:
We want m^2 to be the largest value it can be, so ignoring the sign of m the largest value of |m| is 12
(-12)^2 = 144 which is the largest value of m^2
We want n^2 to be the smallest it can be, so ignoring the sign of n the smallest value of |n| is 2
(2)^2 =4
m^2 -n^2
144-4 = 140
What is the distance between the points (-4, 1) and (6, 8)?
Round your answer to the nearest hundredth.
Answer:
12.21
Step-by-step explanation:
Step 1: You got to find the distance between your x's
Step 2: You got to find the distance between your y's
Step 3: Apply Pythagorean Theorem: That is do:
[tex]\sqrt{ (\text{ distance of x})^2+( \text{ distance of y})^2}\\[/tex]
So x distance is 10 (I just did 6-(-4))
So y distance is 7 (I just did 8-1 )
As per the formula, I'm going to square both... Then add those squared results together like so 100+49=149
Last step is the square root...
[tex]\sqrt{149} \approx 12.21 [/tex]
Answer:
12.21
Step-by-step explanation:
hope it helps
Evaluate a + b for a = 2 and b = 3.
For this case we have the following expression:
[tex]a + b[/tex]
We must evaluate the expression to:
[tex]a = 2\\b = 3[/tex]
Substituting the values in the expression we have:
[tex]2 + 3[/tex]
Equal signs are added and the same sign is placed.
So:
[tex]2 + 3 = 5[/tex]
Finally, the value of the expression is 5.
Answer:
[tex]a + b = 5[/tex]for[tex]a = 2[/tex] and[tex]b = 3[/tex]
while you calculate the distance do you start from the bottom or the top?
Answer:
You start at the bottom
Distance, often assigned the variable d, is a measure of the space contained by a straight line between two points. Distance can refer to the space between two stationary points (for instance, a person's height is the distance from the bottom of his or her feet to the top of his or her head) or can refer to the space between the current position of a moving object and its starting location.
Suppose that the height of the slide is 2 feet,
when x = 20. What is the average rate of change
over the entire slide?
The average rate of change over the entire slide is [tex]\( \frac{1}{10} \)[/tex] feet per foot.
To find the average rate of change over the entire slide, we need to calculate the change in height divided by the change in distance over the entire slide.
Let's denote:
- [tex]\( h_1 \)[/tex] as the initial height (when x = 0),
- [tex]\( h_2 \)[/tex] as the final height (when x = 20).
Given that the height of the slide is 2 feet when ( x = 20 ), we have:
[tex]\[ h_2 = 2 \, \text{feet} \][/tex]
We also know that the height of the slide is 0 feet when ( x = 0 ), so:
[tex]\[ h_1 = 0 \, \text{feet} \][/tex]
Now, the change in height ([tex]\( \Delta h \)[/tex]) over the entire slide is:
[tex]\[ \Delta h = h_2 - h_1 = 2 \, \text{feet} - 0 \, \text{feet} = 2 \, \text{feet} \][/tex]
The change in distance ([tex]\( \Delta x \)[/tex]) over the entire slide is simply the distance traveled, which is:
[tex]\[ \Delta x = 20 \, \text{feet} \][/tex]
The average rate of change over the entire slide ([tex]\( \text{Avg ROC} \)[/tex]) is then:
[tex]\[ \text{Avg ROC} = \frac{\Delta h}{\Delta x} \][/tex]
[tex]\[ \text{Avg ROC} = \frac{2 \, \text{feet}}{20 \, \text{feet}} \][/tex]
[tex]\[ \text{Avg ROC} = \frac{1}{10} \][/tex]
The average rate of change of the slide height is calculated as 0.1 feet per foot, indicating that the height increases by 0.1 feet for every foot along the slide.
Step by step calculation:
The average rate of change of a function over an interval is calculated using the formula:
Average Rate of Change = (Change in Height) / (Change in Distance)In this problem, we know the height ( extit{y}) of the slide at x = 20 feet is 2 feet. Let's assume the starting height at x = 0 is 0 feet.Using the points (0, 0) and (20, 2), we apply the formula:Average Rate of Change = (2 - 0) / (20 - 0) = 2 / 20 = 0.1 feet per foot
This means the height increases by 0.1 feet for every foot traveled along the length of the slide.
There are three kids. The sum of individual squares of their body weights (2 + 2 + 2) is 100. The sum of the product of their weights taking two friends at a time i.e. + + is 150. What will the weighing machine read if all the three kids stand on it at the same time?
Answer:
20
Step-by-step explanation:
Givens
Let child one = x
Let child two = y
Let child three = z
Equations
x^2 + y^2 + z^2 = 100
xy + xz + yz = 150
Solution
There's a trick here. The square of their weights added together is equal (with some modification) to the given conditions. Start by squaring (x+y+z).
(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2xz + 2yz
Take out 2 as a common factor from the last three terms.
(x + y + z)^2 = (x^2 + y^2 + z^2+ 2(xy + xz + yz) )
Substitute the given conditions into the equation. (x^2 + y^2 + z^2) = 100 and 2*(xy + xz + yz) = 2 * 150
(x + y + z)^2 = 100 + 2*150
(x + y + z)^2 = 100 + 300
(x + y + z)^2 = 400
Take the square root of both sides.
sqrt(x+y+z)^2 = sqrt(400)
x + y + z = 20
Note
This answer tells you nothing about the values of x y and z. On the other hand it does not ask for the values of x y and z.
what is the quotient? 5/4c^2÷15/7c assume c is not equal to 0
Answer:
The quotient is [tex]\frac{7}{12c}[/tex]
Step-by-step explanation:
Given expression is: [tex]\frac{5}{4c^2}\div \frac{15}{7c}[/tex]
While dividing two fractions, first we need to change the division sign into multiplication and then flip the second fraction.
So, we will get.....
[tex]\frac{5}{4c^2}\div \frac{15}{7c}\\ \\ =\frac{5}{4c^2}\times \frac{7c}{15}\\ \\ =\frac{35c}{60c^2}\\ \\ = \frac{7}{12c} \ \ [Dividing\ both\ numerator\ and\ denominator\ by\ 5c][/tex]
So, the quotient is [tex]\frac{7}{12c}[/tex]
Answer:
the answer is B
Step-by-step explanation:
just did the assignment on edge
Nick found the quotient of 8.64 and 1.25....
Answer:
No, the power multiplied to 8.64 should havean exponent of zero.
HOPE THIS WILL HELP YOU
Answer:its the second one or b
Step-by-step explanation:
The table shows a pattern of exponents.
What is the pattern as the exponents decrease?
Answer:
Option C is correct.
Step-by-step explanation:
We need to find the pattern as the exponent decreases.
the first value in the table is 125.
if we divide 125 by 5 i.e 125/5 we get 25
the next value in the table is 25
if we divide 25 by 5 i.e 25/5 we get 5
the next value in the table is 5
if we divide 5 by 5 i.e 5/5 we get 1
the next value in the table is 1
if we divide 1 by 5 i.e 1/5 we get 1/5
the next value in the table is 1/5
if we divide 1/5 by 5 i.e 1/5*5 we get 1/25
the next value in the table is 1/25
So, the pattern is if we divide the previous value by 5 we get the next value in the table.
So, Option C is correct.
Answer:
The answer is C
Step-by-step explanation:
I just took the test
Tickets to see a movie cost $5 for children and $8 for adults. The equation 5x + 8y =
80 represents the number of children (x) and adults (y) who can see the movie with
$80. If no adults see the movie, how many children can see the movie with $80?
a) 13
b) 16
c) 6
d) 10
Answer:
16 chlildren
Step-by-step explanation:
5x+8y=80
y=0
5x=80
x=8-0/5=16
Answer:
Step-by-step explanation:
The answer is B.16
Since the equation is 5x+8y=80
There are no parents so it equation will turn into 5x+8(0)=80, AKA, 5x=80
Using algebra, 5x=80 will x=80/5
which is 16
Simplify (5√2-1)^2
10 √2+51
-10 √2+51
41 √2
The function f(x)=603(1.3)^x represents the number of students enrolled at a university x years after it was founded. Each year, the number is students is______ the number the year before.
Answer: 0.3 times
Step-by-step explanation:
Answer:
1.3 times
Step-by-step explanation:
The function [tex]f(x)=603(1.3)^{x}[/tex] represents the number of students enrolled at a university, x years after it was founded.
So the sequence will be formed to represent the number of students will be
f(1) = 603(1.3)
f(2) = 603(1.3)²
f(3) = 603(1.3)³
and so on.
Now the common ratio between second and first term will be
= [tex]\frac{(603)(1.3)^{2}}{603(1.3)}=1.3[/tex]
Therefore, second term of the sequence will be 1.3 times of the first term.
Answer will be - "Each year, the number of students will be 1.3 times the number the year before".
i need help asap please
Answer:
C
Step-by-step explanation:
Given the inequality
(x - 3)(x + 5) ≤ 0
Find the zeros by equating to zero
(x - 3)(x + 5) = 0
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x + 5 = 0 ⇒ x = - 5
Thus the domain is split into 3 intervals
--------------------------------------------------------------
- ∞ < x ≤ - 5 → (1)
- 5 ≤ x ≤ 3 → (2)
3 ≤ x < + ∞ → (3)
Select a test point in each interval and check validity
x = - 10 → (- 13)(- 5) = 65 > 0 ← not valid
x = 0 → (- 3)(5) = - 15 < 0 ← valid
x = 10 → (7)(15) = 105 > 0 ← not valid
Solution is { x | - 5 ≤ x ≤ 3 }
Given the function f(x)=0.5|x-4| -3, for what values of x is f(x)=7
Answer:
x = -16 or x = 24Step-by-step explanation:
[tex]f(x)=0.5|x-4|-3\\\\f(x)=7\Rightarrow0.5|x-4|-3=7\qquad\text{add 3 to both sides}\\\\0.5|x-4|=10\qquad\text{multiply both sides by 2}\\\\|x-4|=20\iff x-4=\pm20\\\\x-4=-20\qquad\text{add 4 to both sides}\\x=-16\\\\x-4=20\qquad\text{add 4 to both sides}\\x=24[/tex]
For 2 cups of flour for every 3 cups of milk. If u use 6 cups of flour, how many cups of milk do you need?
Answer:
9 cups of milk
Step-by-step explanation:
2 cups of flour - 3 cups of milk
4- cups of flower - 6 cups of milk
6 cups of flower - 9 cups of milk
Please mark brainliest and have a great day!
Answer:
9 cups of milk
Step-by-step explanation:
2 cups of flour need 3 cups of milk
1 cup of milk needs 3/2 cups of milk
:. 6 cups of milk will need
(6 x 3/2) = 18/2
= 9 cups of milk
Select the solution(s) of the original equation. x=sqrt 2 x=1 x=i x = - sqrt 2 x=-i
Answer:
A. x = √2
B. x = 1
D. x = -1
E. x = -√2
Step-by-step explanation:
Correct 100%
Without the complete equation, we cannot provide a definitive solution. However, it seems like you are dealing with a quadratic equation where possible solutions can be found using the quadratic formula, '-b ± √ (b² - 4ac) / 2a'. Please provide the full equation for a more precise answer.
Explanation:The original equation mentioned in your question is missing, but I'll assume you are referring to solutions of the equation x² = √ ( 2x² - 1 ). This equation can be solved by first simplifying the condition as 2(x² - 1)² ≤ 1. Following the standard method for solving quadratic equations, we can use the quadratic formula -b ± √ (b² - 4ac) / 2a. Unfortunately, without a full equation, we cannot provide a comprehensive answer. Please, provide the complete equation for a more accurate solution.
Learn more about Solving equations here:https://brainly.com/question/17595716
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The latitude value of Liverpool is 53.41 degrees, and the longitude value is -2.99 degrees. The latitude value of Melbourne is -37.81 degrees, and the longitude value is 144.96 degrees. The two cities are degrees apart in latitude. The two cities are degrees apart in longitude. Reset Next
Answer:
degrees apart in latitude: 91.22
degrees apart in longitude: 147.95
Step-by-step explanation:
Liverpool and Melbourne are two cities that are located very far away from each other. Liverpool is located in the northwestern part of England, while Melbourne is located in the southeastern part of Australia, so understandably their latitudes and longitudes are very different. In order to get to the distance in degrees between these two cities in latitude and longitude, we just simply need to sum the degrees of both of them and we will get to the result. The reason why simple summing will do the job is because they are on separate hemispheres, with Liverpool being on the Northern and Western Hemisphere, while Melbourne being on the Southern and Western Hemisphere.
Latitude distance:
53.41 + 37.81 = 91.22
Longitude distance:
2.99 + 144.96 = 147.95
Answer:
degrees apart in latitude: 91.22
degrees apart in longitude: 147.95
A baker makes a cake shaped like a hexagonal prism of it takes 32 ounces of batter to make a cake with height of 5 inches which Of These is the area of hexagonal base use 1 ounce ~3.125
A) 25 square
B)20 Square
C) 15.625 square
D) 100 square
Answer:
c
Step-by-step explanation:
Follow below steps:
The area of the hexagonal base of the cake:
Calculate the volume of the cake: 32 ounces * 3.125 = 100 cubic inches.
The volume of a hexagonal prism: Volume = area of base * height. Since height is 5 inches, the area of the base is 100 / 5 = 20 square inches.
Combine like terms to create an equivalent expression
-2.5(4x-3)
Hello!
Answer:
[tex]\boxed{-10x+7.5}[/tex]
Step-by-step explanation:
Distributive property: a(b+c)=ab+ac
[tex]-2.5*4x-(-2.5)*3[/tex]
[tex]-4*2.5x+3*2.5[/tex]
Simplify.
[tex]4*2.5=10[/tex]
[tex]3*2.5=7.5[/tex]
[tex]=-10x+7.5[/tex]
[tex]\boxed{-10x+7.5}[/tex], which is our final answer.
I hope this helps you!
Have a nice day! :)
Thanks!
Answer:
The answer is -10x+7.5
Step-by-step explanation:
(HELP PLEASE!) Which expression is equivalent to? Assume.
Answer:
Option 1
Step-by-step explanation:
Given expression is:
[tex]\frac{(2mn)^{4}}{6m^{-3}n^{-2}} \\=\frac{2^{4}m^{4}n^{4}}{6m^{-3}n^{-2}}\\=\frac{16m^{4}n^{4}}{6m^{-3}n^{-2}}\\=\frac{8*2*m^{4}*n^{4}}{2*3*m^{-3}*n^{-2}} \\=\frac{8*m^{4+3}n^{4+2}}{3}\\=\frac{8m^{7}n^{6}}{3}[/tex]
So option 1 is the correct answer ..
A quality control manager at a factory selects 7 lightbulbs at random for inspection out of every 400 lightbulbs produced. At this rate how many lightbulbs will be inspected if the factory produces 20000 lightbulbs?
Answer:
350 lightbulbs
Step-by-step explanation:
First, we need to find the rate of lightbulbs that are inspected. This can be calculated as the division between the number of lightbulbs selected for inspection and the number of light bulbs produced. This is:
Rate = 7/400 =0.0175
That means that for every lightbulb produced, 0.0175 are inspected. Then if the factory produces 20000 light bulbs, the number of light bulbs inspected is:
20000*0.0175 = 350 lightbulbs
By solving for the unknown, the number of lightbulbs inspected can be determined as 350.
The quality control manager selects 7 lightbulbs out of 400 for inspection.
To find the number of lightbulbs inspected, we set up a proportion:
7 lightbulbs / 400 lightbulbs = x lightbulbs / 20000 lightbulbs
Solving for x gives:
x = (7/400) * 20000 = 350 lightbulbs inspected.
How many 5-digit numbers can be formed using the digits 0,1,2,3,4,5,6, if repetition of digits is not allowed?
A. 119
B. 16,807
C. 2,520
D. 120
To find the number of 5-digit numbers that can be formed using the digits 0-6 without repetition, we use permutations. The answer is 5,040.
Explanation:To find the number of 5-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, 6 (without repetition), we need to use the concept of permutations.
Since repetition is not allowed, for the first digit, we have 7 choices (0 cannot be the first digit). For the second digit, we have 6 choices (since one digit has been used). For the third digit, we have 5 choices (since two digits have been used), and so on.
Therefore, the number of 5-digit numbers that can be formed is 7 x 6 x 5 x 4 x 3 = 5,040.
The diameter of circle A is EF.
True
False
That is true.
The diameter is a line that passes through the center of a circle.
Answer: True is the answer
Which of the following theorems verified that angle xyz is congruent too angle uwv?
Answer:
Option B. AA
Step-by-step explanation:
we know that
Angle-Angle (AA) Similarity Postulate, states that If two angles of one triangle are congruent to two angles of another, then the triangles must be similar
In this problem
In the triangle XYZ
∠X=70°
∠Y=90°
∠Z=90°-70°=20° (remember that angle X and angle Z are complementary)
In the triangle UWV
∠V=20°
∠W=90°
∠U=90°-20°=70° (remember that angle V and angle U are complementary)
therefore
Traingles XYZ and UWV are similar by AA Similarity Postulate
Solve for x
6(x-1) =9(x+2)
Answer:
ive got you fam <3 your answer is x= -8
Step-by-step explanation:
isolate the variable by dividing each side by factors that dont contsin the variable
Which equation represents the line that passes through the points (-6,7) and (-3,6)?
Answer:
y= -1/3x+5
Step-by-step explanation:
If you apply the changes below to the absolute value parent function, f(x) =|x|
what is the equation of the new function?
• Shift 5 units right.
• Shift 7 units down,
Answer:
The new function is g(x) = Ix - 5I - 7 ⇒ answer C
Step-by-step explanation:
* Lets revise the translation of a function
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* Now lets solve the problem
∵ f(x) = IxI
∵ f(x) is shifted 5 units to the right
∵ If the function f(x) shifted to the right by h units
∴ g(x) = f(x - h)
- Change IxI to Ix - 5I ⇒ (1)
∵ f(x) is shifted 7 uints down
∵ If the function f(x) shifted down by k units
∴ g(x) = f(x) - k
- Change f(x) to f(x) - 7 ⇒ (2)
- From (1) and (2) the new function is:
g(x) = Ix - 5I - 7
* The new function is g(x) = Ix - 5I - 7