Note that the resultant expression after simplifying simplify square root of 3y² if y<0 is: y√3
What is the rationale for the above result?Note that we need to take a factor out of the square root: √(3y²) , where y<0.
The given expression is √(3y²)
Recall that to take out a factor out of the square root that factor must have a degree in multiple of 2 such as x², x⁴, (x-2)⁴, thus,
√(3y²) = √3y²
⇒ √3 √y²
⇒ √3 (y²)[tex]^\frac{1}{2}[/tex]
⇒ √3 (y)[tex]^\frac{2}{2}[/tex]
= y √3
Thus, having simplified the expression √(3y²), the result is: y √3.
Learn more about Math Expressions:
https://brainly.com/question/14961928
#SPJ1
7. In triangle ACE points B, D and F are midpoints of the sides. If AC=48
and FB=23. Find EC. The diagram is not to scale. 2 points
Since points D and F are the intersections of sides AC and AE, In triangle respectively, DF is parallel to EC and so EC is twice as long as DF. Thus, the value of side EC is 32.
What is the triangle?Given that it has 3 components and three vertices, a triangle qualifies as a polygon. It has a fundamental geometric form. Triangle ABC is the name given to a triangular with the corners A, B, and C. When the three aspects are not collinear, Euclidean geometry yields a single plane and triangle. Triangles are regarded as polygons since they have 3 components and three corners. The points where a triangle's three sides meet are referred to as its corners. Three triangle angles are multiplied to get 180 degrees.
Given :
Triangle ACE
The midpoint of EC is side, where AC = 38 B.
D sits in the middle of EC.
The center of AE is F.
DF = 16.
Given that D is the midpoint of EC and that F is the midpoint of AE, it follows that DF is parallel to AC.
If DF and AC are parallel, then DF and AC are equal to twice each other and DF equals 16. Thus, EC equals 32.
=>EC = 2*DF
=>EC = 2*16
=>EC = 32
It follows that if points B, D, and F are the midpoints of the sides of the triangle ACE, then DF is parallel to AC and EC = 2 x DF = 32.
To know more about triangle visit:
brainly.com/question/2773823
#SPJ1
If x = 3 and y = -4, evaluate:2x2 – 5xy + y
Remember to show your work separately to be submitted in dropbox.
Answer:
[tex]74[/tex]
Step-by-step explanation:
[tex]2 {x}^{2} - 5xy + y \\ 2 \times {3}^{2} - 5 \times 3 \times - 4 + ( - 4) \\ 2 \times 9 - 15 \times - 4 - 4 \\ 18 + 60 - 4 \\ 78 - 4 \\ = 74[/tex]
Hope this helps you.
Can I have the brainliest please?
have a nice day!
Answer:
74
Step-by-step explanation:
2x² - 5xy + y
Substitute x and y into the equation.
2(3)² - 5(3)(-4) + (-4)
Square the three.
2(9) - 5(3)(-4) + (-4)
Multiply the 2 and the 9.
18 - 5(3)(-4) + (-4)
Multiply 3 and -4.
18 - 5(-12) + (-4)
Multiply -5 and -12.
18 + 60 + (-4)
Add 18 and 60.
78 + (-4)
or
78 - 4
Subtract
74
Dev has a rectangular garden in his backyard. The length is 2 feet greater than twice the width.
A. Write an equation to determine the perimeter of the garden.
B. What is the perimeter of Dev’s garden if the width is 5 feet?
Answer:
Step-by-step explanation:
L = 2W + 2 (length is 2 ft greater than twice the width)
A. The perimeter of the garden is P = 2L + 2W, which here is:
P = 2(2W + 2) + 2W, or P = 4W + 4 + 2W, or P = 6W + 4
B. If W = 5 ft, then P = 6(5 ft) + 4 ft = 34 ft
The temperature of the water in a hot water tank is recorded at 15 minute intervals after the heater is switched on. \begin{matrix} \text{Time (x minutes)} & \text{15} & \text{30} & \text{45} & \text{60} & \text{75} & \text{90}\\ \text{Temperature} (y ^\circ C) & \text{20} & \text{30} & \text{40} & \text{50} & \text{60} & \text{70}\\ \end{matrix} Time (x minutes) Temperature(y ∘ C) 15 20 30 30 45 40 60 50 75 60 90 70 a. Plot a graph of these data on your GDC. b. Find the linear model, T(x), for the temperature of the liquid with respect to time. c. Find the temperature of the water after 85 minutes.
Answer: a. Plotting a graph of the data on a graph paper, you can represent the time on the x-axis and the temperature on the y-axis. And plot the given points (15,20), (30,30), (45,40), (60,50), (75,60), (90,70) as ordered pairs on the graph. This will give you a line graph, showing the temperature increasing over time.
b. To find the linear model, T(x), for the temperature of the liquid with respect to time, you can use the slope-intercept form, y = mx + b, where y is the temperature, x is the time, m is the slope and b is the y-intercept. Using two of the given points, you can find the slope of the line by calculating the change in y over the change in x,
m = (y2 - y1) / (x2 - x1).
where x1,y1 and x2,y2 are two distinct points on the graph.
Once you have the slope, you can use one of the points to find the y-intercept, by substituting the point's coordinates into the slope-intercept form equation and solving for b.
Once you have the slope and y-intercept, you can write the linear model as T(x) = mx + b
c. To find the temperature of the water after 85 minutes, you can substitute the value of x = 85 into the linear model equation that you found in the previous step to get the corresponding value of y (temperature).
Please keep in mind that the temperature and time value here are random and are not based on any real-life scenario, and they were provided to show you the concept of linear model.
Step-by-step explanation:
ASAP 100 POINTS PLUS BRAINLIEST
A local rent-to-own business has a television set advertised with a purchase price of $1,095. 0. Calculate the APR if the finance terms are $29. 99 per week for 73 weeks. Round the final answer to the nearest tenth. (4 points)
73. 4%
71. 4%
81. 2%
Based on the provided information, the APR is 71.4%.
Annual Percentage Rate (APR) is defined as the interest rate which is charged by a lender on an annual basis, expressed in the form of a percentage. The formula for APR is given by
APR = (((Interest Charge+Fees)/(Loan Principal))/(Number of days in loan term)) * 365 * 100
The finance terms in the given case is $29.99 per week for 73week. Hence,
Total amount paid = 29.99*73 = $2,189.27
Loan principal = $1,095
Interest charged = Total amount paid – Loan principal amount = 2,189.27 – 1,095 = $1,094.27
Fees = 0 (as it not mentioned in the question)
Number of days in loan terms = 73*7 = 511 days
Substituting the values in the formula,
APR = ((1094.27/1095)/511) * 365 * 100
APR = 71.4%
Learn more about Annual Percentage Rate (APR):
https://brainly.com/question/28860134
#SPJ4
What is $2.63 in cents
Answer:
263 cents
Step-by-step explanation:
Answer:
263¢
Step-by-step explanation:
Determine the vertical distance and the horizontal distance of point P and point Q. (a) P=4m Q=6m.
if you dog like something
What is the simplified form of StartRoot 144 x Superscript 36 Baseline EndRoot?
The simplified form of expression is, 12x⁶.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ √144 x³⁶
Now, By the property of square root;
⇒ √ ab = √a × √b
We get;
⇒ √144 x³⁶ = √144 × √x³⁶
And, By using the exponent property, we get;
⇒ xᵃᵇ = xᵃ × xᵇ
So, We get;
⇒ √144 x³⁶ = √144 × √x³⁶
= √144 × √x⁶ × √x⁶
= √12×12 × √x⁶ × √x⁶
= 12 × x⁶
= 12x⁶
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
The longer base of a trapezoid is 8 ft. The longer base of a similar trapezoid is 13 ft. The area of the smaller trapezoid is 240 ft2. What is the area of the larger trapezoid?
Answer:
390 ft²
Step-by-step explanation:
The longer base of a trapezoid is 8 ft. The longer base of a similar trapezoid is 13 ft. The area of the smaller trapezoid is 240 ft² What is the area of the larger trapezoid?
We solve the above question using proportion
(Longer base/Area of trapezoid) smaller trapezoid = (Longer base/Area of trapezoid) bigger trapezoid
Let the the Area of the bigger trapezoid = x
Hence,
= 8ft/240ft = 13ft/x ft
Cross Multiply
8ft × x = 240ft × 13ft
x = 240ft² × 12 ft/8 ft
x = 390 ft²
Select the correct answer from the drop-down menu. A whole number is 6 more than 2 times another number. The sum of the two numbers is less than 50. This can be written in an inequality as x + 2x + 6 < 50, where x represents the smaller number. From the set {13, 14, 15, 16, 17}, the values of x for which the inequality holds true are .
Answer:
[tex]x = \{13,14\}[/tex]
Step-by-step explanation:
Given
[tex]x + 2x + 6 < 50[/tex]
Required
True values of x
We have:
[tex]x + 2x + 6 < 50\\[/tex]
[tex]3x + 6 < 50[/tex]
Collect like terms
[tex]3x < 50-6[/tex]
[tex]3x < 44[/tex]
Divide both sides by 3
[tex]x < 44/3[/tex]
[tex]x < 14.67[/tex]
This means that x has a value lesser than 14.67.
Hence, the valid values are:
[tex]x = \{13,14\}[/tex]
Answer: (13,14)
Step-by-step explanation:
27.78% Has a number
Answer:
.2778
Step-by-step explanation:
Help please
Determine the sum of the measures of the interior angles of a dodecagon (12-sided polygon).
540°
360°
1,800°
2,160°
Answer:
Below
Step-by-step explanation:
Formula for sum of interior angles of a n - gon
(n-2) * 180
for this 12 sided 'gon
(12-2) * 180 = 1800°
( and for a 'regular' dodecagon each would be 1800/12 = 150°
Answer:
Option C) 1,800°
Step-by-step explanation:
To Find : Interior Angles of a Decagon
In order to find interior angles of any polygon we usually use the formula
(n-2)x180
Over Here it is a 12 sided polygon
So,
(12-2)x180
10x180
1800
Hence the interior angles of a decagon is 1800°
I will report files and unhelpful answers!
For his phone service, Frank pays a monthly fee of $28, and he pays an additional $0.05 per minute of use. The least he has been charged in a month is $88.20.
What are the possible numbers of minutes he has used his phone in a month?
Use for the number of minutes, and solve your inequality for.
Answer:
m > = 1204 minutes
Step-by-step explanation:
28 + 0.05m>=88.20
Subtract 28 from both sides. Then divide both sides by 0.05 to get:
m >=1204 minutes
Answer:
The answer is 1204 minutes.
Step-by-step explanation:
First, take away the monthly fee of 28$ of 88.20$. This gets you 60.20$. Then you divide by 0.05$ because this is how much for each minute. 60.20$/0.05$= 1204. Meaning it is 1240 minutes.
88.20-28= 60.20
60.20/0.05= 1240
Hope these formulas help! (:
Four people each roll a fair die once. Quantity A: The probability that at least two people will roll the same number Quantity B: 70%
How likely something is to occur is known as its probability.Probability when die rolled 1st time is 6C1 i.e. (1,2,3,4,5,6).
Find the probability ?How likely something is to occur is known as its probability.We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.
Probability when die rolled 1st time=6C1 i.e. (1,2,3,4,5,6) suppose 1 comes, then 2nd time it should not be .as it is given that no 2 people will roll same number.
so 2nd time probability=5C1 i.e. (2,3,4,5,6). same way 3rd and 4th time probability=4C1 and 3C1 respectively.Probability that no one rolls the same no. = 6*5*4*3and total possibility =6^4
p(same number)= 6*5*4*3/ 6^4
= 5/18
p(no same number will roll)=1-5/18
=13/18
To learn more about probability refer
https://brainly.com/question/25870256
#SPJ4
The expression 8x +12y represents the sum of Harry and Mike's total monthly wages, where x represents the number of hours Harry worked and y represents the number of hours Mike worked. What is another way to write the expression, and what can you conclude from rewriting it in this way? 8(x +1. 5y); Harry's hourly wage is 1. 5 times Mike's. 8(x +1. 5y); Mike's hourly wage is 1. 5 times Harry's. 12(8x+y); Harry's hourly wage is 8 times Mike's. 8(x + 4y); Mike's hourly wage is 4 times Harry's.
this is a question of arithmetic and the solution is as follows,
The expression 8x + 12y represents the sum of harry and mike’s total monthly wages.
Generally the equation for the The Distributive property is mathematically given as,
a x (b +c) = a x b+ b x c.
Where
8x+12y
Therefore,
= 4 x 2x + 4 x 3x
= 4 x( 2x + 3x)
= 4( 2x + 3x)
Arithmetic
Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division.
Learn more about arithmetic here :-
https://brainly.com/question/11559160
#SPJ4
whats 9- 3x=1+x
i need help
Answer:
9-2x=1
-2x=-8
x=4
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation:
-3x-x=1-9
-4x=-8
x=-8/-4
x=2
plz mark as brainliest
I need help with this question, its confusing.
Which transformation produces another triangle that has the same area as the one shown
A reflection in the line y = -2 and then translation of 2 units right will create the same area so option (C) will be correct.
How to plot a graph?f we shift the triangle anywhere then there will be no change in the area but if we apply the scale factor then since the dimension changes so its area will also change.
In all options, there is a scale factor so it will change area but in option C
A reflection in the line y = -2 reflection gives a mirror image about y = -2 but no changes in area then translation of 2 units right will shift triangle 2 units right but no effect in the area.
Hence "A reflection in the line y = -2 and then translation of 2 units right will create the same area".
To know more about graph of function, check out:
https://brainly.com/question/24335034
#SPJ1
Pat has 6 meters of rope. How many centimeters of rope does pat have?
Answer:
600 centimeters
Step-by-step explanation:
*I WILL GIVE BRAINLIEST
A circle has a circumference of 5 meters. What is the circle's radius?
Use 3.14 for pi and round your answer to the nearest tenth.
Answer:
31.4
Step-by-step explanation:
5 x 2 x 3.14 (pi) = 31.4 rounded.
please help with this!! (No links will be reported)
Answer:
9
Step-by-step explanation:
9 is the only number that is far away from the rest of the number of cakes sold
How do you find Y1 and y2 on a graph?
The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁).
Now, According to the question:
Finding Slope From Two Points Formula
The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁). Here,
m = slope of the line
x₁ = the x-coordinate of the first point
y₁ = the y-coordinate of the first point
x₂ = the x-coordinate of the second point
y₂ = the x-coordinate of the second point
Then rise from A to B = y₂ - y₁
Run from A to B = x₂ - x₁
Then the slope, m = rise/run = (y₂ - y₁) / (x₂ - x₁)
Hence, we derived the slope formula.
Here are the steps to find the slope of a line given two points on it.
In the first point, denote the x coordinate with x₁ and denote the y-coordinate with y₁.In the second point, denote the x coordinate with x₂ and denote the y-coordinate with y₂.Find the differences y₂ - y₁ and x₂ - x₁.Divide the difference of y-coordinates by the difference of x-coordinates to find the slope (m). i.e., m = (y₂ - y₁) / (x₂ - x₁).Learn more about Slope at:
https://brainly.com/question/3605446
#SPJ4
PLEASE HELP ME! WILL MARK BRAINLIEST TO THE FIRST ONE TO ANSWER PROMISE
Answer:
x = 5in
y = 16in
Step-by-step explanation:
Hypotenuse: 32/8 = 4
So, x = 20/4
x = 5
y = 4*4
y = 16
What is the coefficient of y2 in 9xy2z?
The coefficient of y2 in 9xy2z is 9xy.
In mathematics, a coefficient is any integer or symbol that multiplies the variable of a single term or the terms of a polynomial to represent a constant value. It is typically a number, however, in other expressions, a letter might be used instead. In the formula: ax2 + bx + c, for instance, x is the variable and a and b are the coefficients.
A coefficient is what?
A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it. It is assumed that the variables with no associated number have a coefficient of 1.
coefficient of y 2 in 9x(y 2 )z is 9xy.
To know more about Coefficient at:
brainly.com/question/27481600
#SPJ4
find the error & explain why it is wrong: laural had to find the sin 0. what did she do wrong.
Answer:
Step A is incorrect because Lauren identified the wrong formula for sine(θ). Instead, sin(θ) would be equal to opposite / hypotenuse. Then you can substitute getting: 12/15, and once you simplify you get 4/5.
Imagine you have a wood block that is 4 cm wide, 4 cm long, and 8 cm high. It
weights 200 grams.
What is the volume of the block? Be sure to include the units.
Then, imagine that you are cutting the block into 2 exactly equal halves. What is the
volume of one of the pieces (including the units)? How does its volume compare to
that of the original block?
The way that the new volume compares to the original volume of the block is that the new volume is half of the original volume.
How to find the volume of the block?The volume of a rectangular block is gotten from the formula;
Volume = length * width * height
Now, we are given;
Width = 4 cm
Length = 4 cm
Height = 8 cm
Thus;
Volume of block = 4 * 4 * 8
= 128 cm³
Now, if you are cutting the block into 2 exactly equal halves, then you can say that;
New length = 4/2 = 2cm
Thus;
Volume of cut block = 2 * 4 * 8
= 64 cm²
This is concluded to be half of the original block.
Read more about Volume of block at; https://brainly.com/question/1271885
#SPJ1
PLEASE HELP ME 3 friends are camping in the woods, Bert, Ernie and Elmo. They each have their own
tent and the tents are set up in a Triangle. Bert and Ernie are 1 Om apart. The angle
formed at Bert is 30°. The angle formed at Elmo is 105º. How far apart are Ernie and
Elmo?
A.)4 m
B.)5 m
C.)8 m
D.)7 m
The distance between Ernie and Elmo is 20.38 feet.
Consider the distance between Ernie and Elmo be x
What is a law of sine?Law of sines is a formula relating the length of the sides of a triangle to the angles of the triangle.
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
The Sine rule is used to solve angles and sides of triangle.
If a triangle ABC has angles A, B and C at the vertices of the triangles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is;
Given parameters;
A = 30°
a = x = ?
B = 105°
b = 12 m
Therefore, [tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b}[/tex]
0.5/ x = 0.9659 / 12
Cross multiplication;
0.9659x = (12) (0.5)
0.9659x = 6
Divide both sides by 0.9659;
(0.9659x/0.9659) = (6/0.9659)
x = 6.21 m
Since 1 m = 3.281 ft
Then;
6.21 m = (6.21) (3.281) = 20.38 ft
Hence, the distance between Ernie and Elmo is 20.38 feet.
Learn more about law of sines here:
https://brainly.com/question/17289163
#SPJ2
If there is a 50-50 chance of the Sneakers winning today's game, what are the chances that they win their next gam~
Solving the question asked, we can say: If you win tonight, your odds of winning the next game are [tex]$58.33\%$[/tex]. After that, if you lose, you have a [tex]$38.88 \%$[/tex] chance of winning the game.
What is probability?Probability theory is a branch of mathematics that measures the probability that an event or statement is true. The probability of an event is a number between 0 and 1, with approximately 0 indicating that the event is unlikely and 1 indicating that it is certain. Probability is a numerical representation of the disease that a particular event will occur. Another way to express probability is as a percentage from 0% to 100% or 0 to 1. Proportion of occurrences in the complete set of equally likely possibilities leading to a particular occurrence compared to the total number of outcomes.
[tex]$$\begin{aligned}& (2 / 3+1 / 2) / 2=X \\& 1,666 / 2=X \\& 0.58333=X \\& ((2 / 3+1 / 2 / 2) x 2 / 3=X \\& 0.58333 x 0.666=X .3888=X\end{aligned}$$[/tex]
To know more about probability visit:
brainly.com/question/11234923
#SPJ4
PLEASE HELP ANSWER PLEASE
Answer:
c. 7i
Step-by-step explanation:
it has to be an imaginary number
Please help!! I have 10 minutes left!!
1. 110
2. 20
3. 15? IM NOT SURE