To turn 4√5 into an entire radical, the expression is rewritten as a single radical expression, √80, by identifying that 4 is a perfect square (4²), and multiplying it by the number inside the original radical (5) to get the product under one radical sign.
To turn 4√5 into an entire radical, we need to rewrite it as a single radical expression, effectively reversing the process of simplifying radicals. Let's start by recognizing that 4 is a perfect square and can be written as 4². So, we have 4 (the square root of 5), which can be expressed as √(4² × 5).
Here are the steps to convert 4√5 into an entire radical:
Identify the square of the number outside the radical: 4² = 16.
Multiply the square by the number inside the radical: 16 × 5 = 80.
Write the product under a single radical sign: √80.
Now, the expression 4√5 has been turned into an entire radical, √80.
Hakeem's frog made three quick jumps. The first was 1 meter. The second jump was 85 centimeters. The third jump was 400 millimeters. What was the total length in centimeters of the frog's three jumps?
Answer: 225 Centimeters
Step-by-step explanation:
S = p/(q + p(1 − q)) solve for q
integrate 1/((x^5)*sqrt(9*x^2-1)) ...?
in 2000 the average cost for a gallon of gasoline was 1.40 in 2007 the average cost for a gallon of gasoline is 2.60 what is the percent of increase rounded to the nearest whole number
So basically the answer would be 86%
The revenue from selling x shirts is r(x) = 12x.
The cost of buying x shirts is c(x) = 5x + 20.
The profit from selling x shirts is p(x) = r(x) – c(x).
What is p(x)?
A. p(x) = 7x – 20
B. p(x) = 17x + 20
C. p(x) = 17x – 20
D. p(x) = 7x + 20
Answer:
p(X)=7x-20
Step-by-step explanation:
correct answer
slope of j (0,0) , k (-2,8)
The slope of the line passing through points J (0,0) and K (-2,8) is calculated using the slope formula and results in a slope of -4.
The question asks to calculate the slope of the line passing through points J (0,0) and K (-2,8). The slope of a line is found by the formula
slope = (y'' - y') / (x'' - x'), where (x', y') and (x'', y'') are the coordinates of two distinct points on the line. Substituting the given points into this formula gives us
slope = (8 - 0) / (-2 - 0) = 8 / -2 = -4.
what is 1/4% in dollars of 3 million dollars
What is the surface area of a sphere with a radius of 11 units? Leave it in pi
Answer:
[tex]\text{Area of sphere is }484\pi units^2[/tex]
Step-by-step explanation:
Given the radius of sphere 11 units
we have to find the surface area of sphere
Radius=11 units
As area of sphere can be calculated as
[tex]\text{Area}=4\pi r^2[/tex]
[tex]=4\pi (11)^2=484\pi units^2[/tex]
[tex]\text{Area of sphere is }484\pi units^2[/tex]
1. Determine whether each coefficient is positive or negative
2. Choose the coefficient closest to 0
3. Choose the coefficient with the greatest value
Graph A & C are negative
Graph B & D are positive
The coefficient closest to 0 is B
The coefficient with the least value is A
Hope this helped :3
How many solutions are there to this equation?
5(x + 10)- 25= 5x + 25
a. 1
b. 0
c. infinitely many
Choose the right answer.
Two hundred fifty tickets are sold at a fund raiser. If Sarah buys 15 tickets, the probability that she will win the prize quilt is
6%
7.5%
15%
Answer:
Option A. 6%
Step-by-step explanation:
250 tickets are sold at a fund raiser.
Sarah buys 15 tickets.
The probability that she will win the prize quilt = [tex]\frac{15}{250}[/tex]
= 0.06 = 6%
The probability that Sarah will win is 6%.
. Each U.S. coin is mapped to its monetary value. Tell whether this situation represents a function. Explain your reasoning. If the situation represents a function, give the domain and range.
Given the triangle shown here, the first steps in the proof of the law of sines are:
A. Set sinA = b/k and sinB = k/a and solve for k in both equations.
B. Set sinA = k/b and sinB = a/k and solve for k in both equations.
C. Set sinA = -k/b and sinB = -k/a and solve for k in both equations.
D. Set sinA = k/b and sinB = k/a and solve for k in both equation.
How many solutions are there to the equation below?
13x + 195 = 13(x + 15)
A. 0
B. 1
C. infinitely many
You have $270 in your bank account. You plan to save $80 from your paycheck each week. Which graph shows your bank account balance at the end of each week?
Answer: The below graph shows the given situation.
Step-by-step explanation:
Let x represents the number of week, and y represents the total balance in the account after x weeks.
Since, initially the amount in the account = $ 270
According to the question,
Every week $80 is saved.
Thus, the total saving in x weeks = 80 × x = 80x
Since the total amount in x weeks = Initial amount + total saving.
⇒ y = 80x + 270
Which is the equation of line that shows the given situation.
x-intercept of the line is (-27/8,0)
y-intercept = (0,270)
If x=1 y = 350
If x=2 y= 430
If x=3 y =510
Thus, the points of the line are (1,350), (2,430), (3,510)
Hence we can draw the graph with help of above information.
Area of a kite
Solve for d2: A=1/2d1d2
Answer:
The value of the equation for [tex]d_2[/tex] is [tex]d_2=\frac{2A}{d_1}[/tex].
Step-by-step explanation:
Consider the provided equation.
[tex]A=\frac{1}{2}d_1d_2[/tex]
We need to solve the equation for [tex]d_2[/tex].
Multiply both the sides by 2.
[tex]2A=2\times \frac{1}{2}d_1d_2[/tex]
[tex]2A=d_1d_2[/tex]
Divide both sides by [tex]d_1[/tex].
[tex]\frac{2A}{d_1}=\frac{d_1d_2}{d_1}[/tex]
[tex]d_2=\frac{2A}{d_1}[/tex]
Hence, the value of the equation for [tex]d_2[/tex]is [tex]d_2=\frac{2A}{d_1}[/tex].
How many solutions to this equation?
145 = 10x - 8x
A. 2
B. 1
C. infinitely many
6) If sec theta+tan theta = P. PT sin theta=P^2-1/P^2+1 ...?
∠1 is decomposed into two nonoverlapping angles, ∠2 and ∠3. let m∠1 = 130° and m∠3 = 75°. what type of angle is ∠2?
a. acute
b. obtuse
c. right
d. straight
What is the simplified form of each expression?
A. 729x33
B. 3x33
C. 729x29
D. 3x29
The simplified form of each expression is as follows:
[tex]A. \( 729 \times 33 \) simplifies to \( 3^6 \times 33 \) B. \( 3 \times 33 \) simplifies to \( 3 \times 3 \times 11 \) or \( 3^2 \times 11 \). C. \( 729 \times 29 \) simplifies to \( 3^6 \times 29 \). D. \( 3 \times 29 \) simplifies to \( 3 \times 29 \).[/tex]
To simplify these expressions, we recognize that 729 is a power of 3, specifically [tex]\( 3^6 \)[/tex], and that 33 and 29 are prime numbers. Therefore, we can express each product in terms of its prime factors.
A. For the expression [tex]\( 729 \times 33 \)[/tex] , we know that 729 is [tex]\( 3^6 \)[/tex] and 33 is a prime number. Thus, the simplified form is [tex]\( 3^6 \times 33 \)[/tex].
[tex]B. For the expression \( 3 \times 33 \), we can further break down 33 into \( 3 \times 11 \), since 33 is the product of these two prime numbers. Therefore, the simplified form is \( 3^2 \times 11 \) or \( 3 \times 3 \times 11 \).[/tex]
[tex]C. For the expression \( 729 \times 29 \), similar to expression A, 729 is \( 3^6 \) and 29 is a prime number. Hence, the simplified form is \( 3^6 \times 29 \).[/tex]
[tex]D. For the expression \( 3 \times 29 \), both 3 and 29 are prime numbers, so the expression is already in its simplest form and cannot be simplified further. Thus, the simplified form remains \( 3 \times 29 \).[/tex]In summary, the simplified forms are:
[tex]A. \( 3^6 \times 33 \) B. \( 3^2 \times 11 \) or \( 3 \times 3 \times 11 \) C. \( 3^6 \times 29 \) D. \( 3 \times 29 \)[/tex]
Marietta is selling cheeses for the holiday fund raiser. Monday she sole 7/9 of the boxes of cheeses. Tuesday she restocked her supply and sold 0.85 of the boxes of cheeses. Which day did she sell more boxes? Explain and show.
HELP ASAP!!!
The best-selling book Samantha has been waiting for hit the shelves at $21.56. What percent discount was this off the cover price of $26.95?
A. 20%
B. 25%
C. 30%
D. 35%
72/60 in simplest form
Which rule represents the translation of hexagon DEFGHI to hexagon D'E'F'G'H'I'?
(x, y)→(x - 8, y - 7)
(x, y)→(x - 7, x - 8)
(x, y)→(x - 4, x - 5)
(x, y)→(x - 5, y - 4)
Solve. How can I solve this division 12 divided by 144140
According to given question, 12 divided by 144140 is approximately 0.000083158.
To divide 12 by 144140, simply perform the division:
12 ÷ 144140 ≈ 0.000083158
So, 12 divided by 144140 is approximately 0.000083158.
Division is a mathematical operation used to distribute a quantity or a number of items into equal parts. It involves finding out how many times one number (called the divisor) can be subtracted or taken away from another number (called the dividend) until there is nothing left or the subtraction cannot be done anymore.
The result of the division is called the quotient, and it represents the number of equal parts or groups that the dividend can be divided into by the divisor. In the division expression "a ÷ b," where "a" is the dividend and "b" is the divisor, the quotient is represented by "a/b."
For example, in the division 12 ÷ 3:
12 is the dividend (the total quantity to be divided).
3 is the divisor (the number of equal parts to divide the dividend).
The quotient is 4, as 12 can be divided into 4 equal parts of size 3.
Division is the opposite operation of multiplication. If you have two numbers, the product of their multiplication can be divided by one of the numbers to get the other number. For example, 12 × 3 = 36, and 36 ÷ 3 = 12.
To know more about division here
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What is difference between a tilt level and a dumpy level?
A tilt level and a dumpy level are both surveying instruments used for measuring horizontal distances and vertical elevations. The main difference is that the tilt level has a built-in compensator that eliminates the need for manual leveling, while the dumpy level requires manual leveling before each use.
Explanation:A tilt level and a dumpy level are both surveying instruments used for measuring horizontal distances and vertical elevations. However, there are some key differences between the two.
Tilt Level: A tilt level, also known as a tilting level, is a type of level that utilizes a compensator mechanism to maintain a level plane even when the instrument itself is not level. This compensator allows for accurate measurements and eliminates the need for manually leveling the instrument each time.
Dumpy Level: A dumpy level, on the other hand, is a more traditional type of level that requires manual leveling before each use. It consists of a telescope mounted on a tripod, and the instrument is adjusted using leveling screws to ensure that it is perfectly horizontal. The dumpy level does not have a compensator like the tilt level, so the instrument needs to be leveled manually to obtain accurate measurements.
In summary, the main difference between a tilt level and a dumpy level is that the tilt level has a built-in compensator that eliminates the need for manual leveling, while the dumpy level requires manual leveling before each use.
Which of the following describes the non-rigid transformation in the function shown below?
y-1=-(3x+1)^2
A. The graph is shifted 3 units down.
B. The graph is stretched vertically by a factor of 3.
C. The graph is reflected across the x-axis.
D. The graph is stretched horizontally to 1/3 the original width.
Answer:
the graph is stretched horizontally to 1/3 the original width
Step-by-step explanation:
the graph is also reflected and translated but those are rigid transformations and this is asking about the non rig transformations
A commuter must pass through five traffic lights on her way to work, and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits, as shown below.
X= # of red P(x)
0 0.05
1 0.25
2 0.35
3 0.15
4 0.15
5 0.05
a. How many red lights should she expect to hit each day?
b. What's the standard deviation?
c. Find the mean and standard deviation of the number of red lights the commuter should expect to hit on her way during a 5 day work week.
Answer:
a) 2 red lights
b) SD = 1.26
c) mean = 10, SD = 1.26
Step-by-step explanation:
a) The number of red lights she expects to hit by day can be gotten by calculating the mean of the distribution.
[tex]E(X) = \sum xP(x)[/tex]
[tex]E(X) = (0*0.05) + (1*0.25) + (2*0.35) + (3*0.15) + (4*0.15) + (5*0.15)\\E(X) = 2.25[/tex]
Since the number of lights cannot be a decimal, she expects to hit 2 lights each day
b)
Variance, [tex]V(X) = \sum(x- \mu)^{2} P(x)[/tex]
[tex]V(X) = [(0-2.25)^{2}*0.05] + [(1-2.25)^{2}*0.25] + [(2-2.25)^{2}*0.35] + [(3-2.25)^{2}*0.15] + [(4-2.25)^{2}*0.15] + [(5-2.25)^{2}*0.05][/tex]
V(X) = 0.253 + 0.391 + 0.022 + 0.084 + 0.459 + 0.378
V(X) = 1.587
Standard Deviation, [tex]SD = \sqrt{V(X)}[/tex]
[tex]SD = \sqrt{1.587}[/tex]
SD = 1.26
c) In a 5 day work week, the commuter is expected to hit an average of 5* 2 red lights, i.e. mean = number of red lights hit per day * number of days
mean = 2 * 5
mean = 10
The standard deviation will not change, SD = 1.26
How do you prove that ABE is congruent to DBC?
The line y = –2x – 8 is graphed. Which ordered pairs are solutions to the equation? Check all that apply.
A) (–8, 8)
B) (–6, 2)
C) (–2, 4)
D) (0, –4)
E) (2, –12)