Answer:
Perimeter = 32.44 unit
Area of triangle = 30 unit²
Step-by-step explanation:
By distance formula distance between (a,b) and (c,d) is [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]
So, we have
[tex]AB=\sqrt{(16-2)^2+(2-8)^2}=15.23\\\\BC=\sqrt{(16-6)^2+(2-2)^2}=10\\\\AC=\sqrt{(2-6)^2+(8-2)^2}=7.21[/tex]
Perimeter = 15.23 + 10 + 7.21 = 32.44 unit
We have [tex]s=\frac{15.23+10+7.21}{2}=16.22[/tex]
Area of triangle[tex]=\sqrt{s(s-AB)(s-BC)(s-AC)}=\sqrt{16.22(16.22-15.23)(16.22-10)(16.22-7.21)}=30[/tex]
Area of triangle = 30 unit²
Which expression is equivalent to (25−−√3)14 ?
A.2 2/20
B.2 5/12
C.2 12/5
D.2 3/4
[tex]Use\\\\\sqrt[n]{a}=a^{\frac{1}{n}}\\\\\left(a^m\right)^n=a^{m\cdot n}\\---------------------\\\\\left(\sqrt[3]{2^5}\right)^{\frac{1}{4}}=\left[\left(2^5\right)^\frac{1}{3}\right]^\frac{1}{4}=2^{5\cdot\frac{1}{3}\cdot\frac{1}{4}}=\boxed{2^\frac{5}{12}}\\\\Answer:\ \boxed{\boxed{\big2^{\frac{5}{12}}}}[/tex]
Answer:
I got it wrong, but here's the answer
Step-by-step explanation:
Geometry: The rectangle shown has a perimeter of 34cm and the given area. Its length is 5 more than twice it's width. Write and solve a system of equations to find the dimension of the rectangle
w - width
2w + 5 - length
w + w + (2w + 5) + (2w + 5) = 6w + 10 - perimeter
34 cm - perimeter
The equation:
6w + 10 = 34 subtract 10 from both sides
6w = 24 divide both sides by 6
w = 4 cm
2w + 5 = 2(4) + 5 = 8 + 5 = 13 cm
Answer: Width = 4cm, Length = 13cmWhat is the solution to the system of equations represented by the two lines?
Answer:
(3,1)
Step-by-step explanation:
The answer is (3,1) because that's where both lines intersect.
Answer: the answer is (3,1) :)
Step-by-step explanation:
Please help.
Compare and contrast the processes of solving rational and radical equations
I only need like 2-3 sentences.
Step-by-step explanation:
A rational number can be written as a ratio a/b, where a & b are integers & b \neq 0. Rational numbers are terminating or repeating. The radical sign means "the positive square root of."
Example:
√144 = "the square root of 144" but indicates the positive square root of 144, which is 12
Hope this helps!!! :)
Answer:
Rational equations or expressions (think rational numbers) are any expression which is in fraction form and where the denominator is not equal to zero. Like: [tex]\frac{2}{x} ,\frac{3}{5}[/tex] etc.
Radical expressions are those expressions that contain radicals (square, cube, fourth roots). Like 4 and -4 are the square roots of 16. A square root is written with a radical symbol √ and the number inside the radical symbol is called the radicand.
what is the perimeter of a rectangle with a length of 3x + 3 and a width of x - 1
Answer:
P = 8x+4
Step-by-step explanation:
The perimeter of a rectangle is found by using the formula
P = 2(l+w)
We know l = 3x+3 and
w = x-1
Substitute these values in
P =2(3x+3 + x-1)
Combine like terms
P = 2(4x+2)
Distribute the 2
P = 8x+4
Beanbag chairs that normally sell for 36.50 are on sale for 32.12 find the precent of discount round your answer to the nearest tenth of a precent
Answer: 12.0 %
Step-by-step explanation:
Since according to the question,
The initial price of the chair ( Marked price) = 36.50
And, After the discount the price of the chair = 32.12
Thus, the discount on the price = 36.50 - 32.12 = 4.38
Therefore the discount percentage = [tex]\frac{discount}{marked price} \times 100[/tex]
= [tex]\frac{4.38}{36.50} \times 100[/tex]
= [tex]\frac{438}{36.50}[/tex]
= 12 %
Thus, the percentage of discount = 12.0 %
The length of a rectangular storage room is 3 feet longer than its width. if the area of the room is 40 square feet, find the width.
Answer:
Width of rectangular storage room= 5 feet.
Step-by-step explanation:
Let x be the width of storage room.
We have been given that the length of a rectangular storage room is 3 feet longer than its width. So the length of storage room will be x+3.
We are also given that the area of the room is 40 square feet.
Since the area of a rectangle is length times width.
[tex]\text{Area of rectangle}=\text{Length* Width}[/tex]
Let us substitute our given values in area formula.
[tex]40=x*(x+3)[/tex]
Upon distributing x we will get,
[tex]40=x^2+3x[/tex]
[tex]x^2+3x-40=0[/tex]
Now let us factor out our quadratic equation using splitting the middle term.
[tex]x^2+8x-5x-40=0[/tex]
[tex]x(x+8)-5(x+8)=0[/tex]
[tex](x+8)(x-5)=0[/tex]
[tex]x+8=0[/tex] or [tex]x-5=0[/tex]
[tex]x=-8[/tex] or [tex]x=5[/tex]
Since width can not be negative, therefore, the width of rectangle will be 5 feet.
Let us verify our answer.
Length of rectangular storage room is 3 feet longer than its width. So length will be 5+3=8.
Given: Area=40 square feet.
5*8=40.
Hence, width of rectangular storage room is 5 feet.
The width of the rectangular storage room, considering it is 3 feet shorter than the length and the area is 40 square feet, is 5 feet.
Explanation:The subject of this question is Mathematics and it is typically taught in Middle School. The problem describes a rectangle where the length is 3 feet longer than the width and the area is 40 square feet. The width is x and the length is x + 3 (since it is 3 feet longer). The area of a rectangle is defined as length times width, which can be expressed as 40 = x(x + 3), or x² + 3x - 40 = 0. This can be solved as a quadratic equation. The solutions of this equation are x = 5 and x = -8. But, since dimensions cannot be negative, the width of the room is 5 feet.
Learn more about Rectangular Area here:https://brainly.com/question/36027675
#SPJ3
Victoria's spends 5/9 of her money on a flan and two chicken pies each chicken pie cost 1/6 as much as the fly Victoria has $24 left how much does Victoria spend and how much does a flan cost
Answer:
She spend $30
A flan cost $22.5
Step-by-step explanation:
Let's call x her initial money
After she bought the flan and two chicken pies she has $24.
She spend (5/9)*x in the flan and two chicken, then
x - (5/9)*x = 24
(4/9)*x = 24
x = 24*(9/4)
x = $54
She spend (5/9)*54 = $30
Let's call f the flan cost
Each chicken pie cost 1/6 as much as the flan, then:
30 = f + (1/6)*f + (1/6)*f
30 = (4/3)*f
f = 30*(3/4)
f = $22.5
Victoria had $54 in total. She spent $30 on the flan and two chicken pies altogether. The cost of the flan is $22.50.
The problem presents a situation where Victoria spends a fraction of her money on a flan and two chicken pies. Victoria has $24 left after these purchases. To solve this, we must first calculate the total amount of money Victoria had before making her purchases. Given that 5/9 of her money was spent on the flan and two chicken pies, and she has $24 remaining, we can set up the following equation where x represents the total amount of money:
x - (5/9)x = $24
This simplifies to:
(4/9)x = $24
By multiplying both sides of the equation by (9/4), we find the total amount of money Victoria had:
x = $24 \times (9/4)
x = $54
Victoria spent 5/9 of $54 on the flan and two chicken pies, which is:
(5/9) \times $54 = $30
If each chicken pie costs 1/6 the cost of the flan, we can let f represent the cost of the flan and (1/6)f the cost of each chicken pie. We have 2 chicken pies, so the equation would be:
f + 2 \times (1/6)f = $30
This simplifies to:
f + (1/3)f = $30
Combining like terms, we get (4/3)f = $30 which leads to:
f = $30 \times (3/4)
f = $22.50
So the cost of the flan is $22.50.
If an ambulance is able to respond to car accident located 5 minutes away in 7 minutes, what is the speed of the ambulance in miles per hour?
Answer:
Speed = 42. 86 miles per hour
Step-by-step explanation:
car accident located 5 miles away in 7 minutes
Given distance d= 5 miles
time = 7 minutes. convert minutes into hours
60 minutes = 1 hour
so 7 minutes = 7 / 60 hours
To find the speed we use formula [tex]s= \frac{d}{t}[/tex]
d= 5 and t = 7/60
Plug in the values in the formula
[tex]s= \frac{d}{t}[/tex]
[tex]s= \frac{5}{\frac{7}{60}}[/tex]
[tex]s= 5* \frac{60}{7}[/tex]
s = 42.85714286
Speed = 42. 86 miles per hour
A salesperson had $240,000 in sales last year, which is 60% of the sales she had this year. Which equation could be used to determine x, the salesperson's total amount in sales, in dollars, for this year?
Answer:
$400,000
Step-by-step explanation:
We can write a proportion to find the total amount using the information given. A proportion is two equivalent ratios set equal to each other.
[tex]\frac{60}{100}=\frac{240000}{x}[/tex]
We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.
60x=100(240,000)
60x=24,000,000
y=400,000
Answer:
$400,000
Step-by-step explanation:
Paul's MP3 player has a total of 852 songs. He has 4 different groups of songs. If he puts and equal number of songs in each group, how many songs will be in each group?
Answer:
213
Step-by-step explanation:
You have to divide the 852 songs into the 4 categories.
852/4=
213
Evaluate the summation
Answer:
114
Step-by-step explanation:
The first term (a1) = 1 + 3 = 4 (substituting 1 for i)
The last term (L) = 12 + 3 = 15
So the sum of the 12 terms = (n/2)(a1 + L)
= (12/2) (4 + 15)
= 6 * 19
= 114 (answer)
The value of the summation of arithmetic progression is 114
What is Arithmetic Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the number of terms n = 12
Let the first term a = i + 3
when i = 1
a = 4
So , the first term of the arithmetic progression is a = 4
The second term a₁ = i + 3
when i = 2
a = 5
Now , the common difference d = second term - first term
Common difference d of the arithmetic progression = 5 - 4 =1
So , d = 1
Now , the sum of n terms of an AP is given by
Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Substituting the values in the formula , we get
Sₙ = ( 12/2 ) [ ( 2 x 4 ) + ( 12 - 1 ) x 1 )
Sₙ = 6 [ 8 + 11 ]
Sₙ = 6 x 19
Sₙ = 114
Therefore , the value of Sₙ is 114
Hence , The value of the summation of arithmetic progression is 114
To learn more about arithmetic progression click :
https://brainly.com/question/1522572
#SPJ2
Which term applies when using the method shown to determine if two ratios are proportions
Answer:
I think that there is a part of your question that is missing maybe? What is the method shown?
Step-by-step explanation:
Lola rode her bike for 7/10 of an hour on Saturday and 3/5 of an hour on Sunday.How much longer did she ride her bike on Saturday than Sunday?
Answer:
1/10 of an hour
Step-by-step explanation:
3/5 in a decimal is 6/10 and 7/10 - 6/10 is 1/10 of an hour
Will someone please help me solve this? A girl scout troop sold cookies. If the girls sold 5 more boxes the second week than they did the first, and if they doubled the sales of the second week for the third week to sell a total of 431 boxes of cookies, how many did they sell each week?
Answer:
104 boxes109 boxes218 boxesStep-by-step explanation:
Let b represent the number of boxes of cookies sold the first week. Then b+5 boxes were sold the second week, and 2(b+5) boxes were sold the third week. The total sold was ...
b +(b+5) +2(b+5) = 431
4b +15 = 431 . . . . . . simplify
b = (431 -15)/4 = 104 . . . . . subtract 15, divide by the coefficient of b
First week: b = 104
Second week: b+5 = 109
Third week: 2(b+5) = 218
A watering can dispenses water at the rate of 0.25 gallon per minute. The original volume of water in the can was 6 gallons. Which set of ordered pairs shows the volume of water in the can in gallons (y), as a function of time in minutes (x), from the first minute after the can starts dispensing water?
{(1, 6.0), (2, 5.75), (3, 5.50)}
{(6.0, 1), (5.75, 2), (5.50, 3)}
{(1, 5.75), (2, 5.50), (3, 5.25)}
{(5.75, 1), (5.50, 2), (5.25, 3)}
Answer:
{(1, 6.0), (2, 5.75), (3, 5.50)}
Step-by-step explanation:
That is most likely the answer. Hope this helps
-Kent
Answer:
a is the answer soooo brainlyist
Step-by-step explanation:
A set of cards includes 24 yellow cards, 18green cards, and 18 blue cards. What is the probability that a card chosen at random is not green ?
Answer: 70%
Step-by-step explanation:
Quadrilateral MATH is a square. If MA = 2x – 5 and AT = x + 10, find the perimeter of the square.
Answer:
Perimeter of the square MATH = 100.
Step-by-step explanation:
Given that MATH is a square, it means all sides would be equal to each other.
Given MA = 2x - 5 and AT = x + 10.
we know all sides are equal, so MA = AT.
2x - 5 = x + 10
2x = x + 10 + 5
2x = x + 15
2x - x = 15
x = 15
So, AT = x + 10 = 15 + 10 = 25.
Now the perimeter would be (MA + AT + TH + HM) = 4*AT = 4*25 = 100.
Hence, option D is the correct answer i.e. 100.
Answer:
100
Step-by-step explanation:
Sides of a square are congruent.
2x – 5 = x + 10
x = 15
Sides = 2(15) – 5 = 25
Perimeter = 25 + 25 + 25 + 25 = 100
Two trains begin in Milford and end in Pinkerton, which is 300 miles away. Train A leaves Milford at 10:00 a.M. And travels at a rate of 90 miles per hour. Train B leaves Milford at 8:00 a.M. And travels at 70 miles per hour. Which train(s) will arrive in Pinkerton before 1:00 p.M.?
Answer:
Step-by-step explanation:
Alright, lets get started.
For train A:
Distance from Milford and Pinkerton is 300miles.
Speed of train A is 90 miles per hour.
So, time taken to complete this distance = [tex]\frac{distance}{speed}[/tex]
So, time taken to complete this distance =[tex]\frac{300}{90}=3.333[/tex]
Means train A will take 3.33 hours or say 3 hrs and 19.8 minutes to reach Pinkerton.
So,if it starts at 10:00 AM, then it will reach at 01 hrs 19.8 minutes PM (01:19.8 PM).
For train B:
Speed of train B is 70 miles per hour.
Train B will take time =[tex]\frac{300}{70}=4.29[/tex]
Means 4 hrs and 17.4 minutes.
So, if it starts at 8:00 Am, then it will reach at 12 hrs 17.4 minutes PM(12:17.4 PM).
So, train B will be reaching Pinkerton before 1:00 PM : Answer
Hope it will help :)
Answer:
train B will be reaching Pinkerton before 1:00 PM
Step-by-step explanation:
A recipe for a loaf of bread calls for of a cup of flour. If Milo used 12 cups of flour, how many loafs of bread did he prepare?
A.
18
B.
16
C.
15
D.
12
E.
8
Answer: The answer is D 12 i am pretty sure.
A bag contains 56 marbles 7 red , 8 green , 11 yellow , 17 brown and 13 blues if a marble is chosen at random what is the probability that the marble is green
Answer:
The probability is 1/7 or 14.29%
Step-by-step explanation:
In order to find this, divide the number of marbles that are green by the total number.
8/56 = 1/7 = 14.29%
Decide whether the rates are equivalent. 126 points every 3 games 210 points every 5 games. What is the answer?
Step-by-step explanation:
To find whether the rates are equivalent or not, we will use proportions.
[tex]\frac{126\text{ points}}{3\text{ games}}=\frac{210\text{ points}}{5\text{ games}}[/tex]
Let us simplify our fractions.
[tex]42\frac{\text{ points}}{\text{game}}=42\frac{\text{ points}}{\text{game}}[/tex]
We can see that both unit rates are same, therefore, the rates are equivalent and equal to 42 points per game.
The drawing plan for an art studio shows a rectangle that is 15.2 inches by 8 inches. The scale in the plan is 4 in.: 5 ft. Find the length and width of the actual studio. Then find the area of the actual studio. The length is feet, the width is feet, and the area is square feet.
Answer:
Length: 19 feet
Width: 10 feet
Area: 190 feet[tex]x^{2}[/tex]
Step-by-step explanation:
This is a question about ratio.
Length: let [tex]x[/tex] be the actual length.
[tex]15.2 : x = 4 : 60[/tex]
[tex]x = 19 [/tex]
Width: let [tex]y[/tex] be the actual width.
[tex]8 : y = 4 : 60[/tex]
[tex]y = 10[/tex]
Area: A = xy
[tex] 19 * 10 = 190[/tex]
Final answer:
The actual art studio, based on the scale given, measures 19 feet in length and 10 feet in width, resulting in an area of 190 square feet.
Explanation:
To find the length and width of the actual art studio from the drawing plan, we need to apply the scale given which is 4 inches on the plan representing 5 feet in reality. For calculation, we first write the scale as a ratio: 4 inches ÷ 5 feet. Now, let's calculate the real-life dimensions of the studio.
Length: 15.2 inches on the drawing corresponds to (15.2 ÷ 4) × 5 = 19 feet in reality.
Width: 8 inches on the drawing corresponds to (8 ÷ 4) × 5 = 10 feet in reality.
Next, we calculate the area of the actual studio using the formula for the area of a rectangle, which is length multiplied by width.
Area = Length × Width = 19 feet × 10 feet = 190 square feet.
Which of the following statements represents one of the differences between an experiment and an observational study?
Inclusion of random sample.
Introducing a change to the subgroup.
Ability to calculate the mean.
Ability to draw conclusions.
Answer:
Introducing a change to the subgroup
Step-by-step explanation:
Given there are four statements. We have to find the one which represents one of the differences between an experiment and an observational study.
The answer is option 2. Introducing a change to the subgroup
Experimental and observational studies are both types of studies between which a number of differences can be identified. When conducting research studies, various types of research in order to arrive are adopted according to the need.
An experimental study is a study where the researcher has control over most of the variables.
On the other hand, an observation study is a study where the researcher cannot control any variable but merely observes the subject without controlling any variables.
Answer:
B
Step-by-step explanation:
?Write the equation in standard form. Then factor the left side of the equation.? 2x2 = 28 – x A.) (2x + 7)(x – 4) = 0 B.) (2x – 7)(x + 4) = 0 C.) (2x + 4)(x + 7) = 0 D.) (2x – 4)(x + 7) = 0
2x² = 28 - x
2x²+x-28=0
2x²+8x-7x-28=0
2x(x+4)-7(x+4)=0
(x+4)(2x-7)=0
(2x-7)(x+4)=0
B.) (2x - 7)(x + 4) = 0
What store has the best deal? Tae Store:4 cans for $2.48, Be Cool Store:5 cans for $3.00 or Not Today Store:59 cents per can?
Rectangle R was dilated to form rectangle R' Which is the scale factor of the dilation? 5/4 , 2/1 5/2 5/1
Answer:
I'm not sure if those are the answer choices but your answer should be 5/2
Hope this helps
Step-by-step explanation:
Answer:
5/2
Step-by-step explanation:
Linnea's company's revenue in 20172017 is \dfrac{36}{25} 25 36 ? of its revenue in 20162016. What is Linnea's company's revenue in 20172017 as a percent of its revenue in 20162016 ?
Answer:
144%
Step-by-step explanation:
We are told that Linnea's company's revenue in 2017 is 36/25 of its revenue in 2016..
To find the Linnea's company's revenue in 2017 as a percent of its revenue in 2016, we will have to figure out 36 is what percent of 25.
[tex]\text{Percent}=\frac{36}{25}\times 100[/tex]
[tex]\text{Percent}=36\times 4[/tex]
[tex]\text{Percent}=144[/tex]
Therefore, Linnea's company's revenue in 2017 is 144% of its revenue in 2017.
What’s the area of PQSU? ______sq mi
Answer:
35 mi^2
Step-by-step explanation:
Area of parallelogram = base x height
7 x 5 = 35
Answer:
Area = 35 mi^2
Step-by-step explanation:
Area = b*h
The base is 7 mi
The height is 5 mi
Area = 7*5
Area = 35 mi^2
PLEASE I NEED HELP WITH THIS ONE...I THINK IT IS EITHER A. OR D.
Which of the following is a step in constructing a circle inscribed in a triangle?
A. Construct the perpendicular bisectors of each side.
B. Use a compass to locate the midpoint of each side.
C. Construct the angle bisectors of each side.
D. Use a compass to locate the altitude of each side.
Answer:
Step-by-step explanation:
i'm saying A is the correct answer