To find the distance between the high school at (17,21) and the town park at (28,13), use the distance formula which yields a result of approximately 13.6 miles apart, rounded to the nearest tenth.
When looking at the coordinates of the high school at (17,21) and the town park at (28,13) on a coordinate grid where each unit represents 1 mile, we need to use the distance formula to calculate the distance between the two points. The distance formula is derived from the Pythagorean theorem and is given by:
[tex]Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
Substituting the values -
[tex]Distance = \sqrt{{(28 - 17)^2 + (13 - 21)^2}[/tex]
Calculate the differences and square them:
Distance = [tex]\sqrt{{(11)^2 + (-8)^2}\\[/tex]
Distance = [tex]\sqrt{{121 + 64}[/tex]
Distance = [tex]\sqrt{{185[/tex]
Take the square root to find the distance:
Distance = 13.6 miles
Therefore, the high school and the town park are approximately 13.6 miles apart, rounded to the nearest tenth.
factor X^3-7x^2-5x+35
The answer is (x+7)(x^2-5)
Roy ia training for a race. He swims 1/4 lap in 3/5 minute. At that rate,how many minutes does it take roy to swin each lap?
What is 6.16×106 in standard form?
6,160,000
61,600,000
601,600,000
616,000,000
I think it's the first question but tell me what you think!
what expression is equivalent to 2.2-2.5?
How many solutions does the system have?
x−3y=7
−2x+6y=6
what is the slope of the line that contains the points (0,4) and (4,-2)
A.- 3/2
B.- 2/-3
C. 3/2
D. 2/3
Plz help I give 5 stars
Rochelle and Denae started with The same amount of money in their bank accounts.Rochelle made three withdrawals Of $25 and then wrote a $100 check. Denae deposited five dollars and then wrote a $200 check.
1•Find the total change in the amount of money and Raquel’s account
2• find the total change it in the amount of money in Denae’s account
3• compare the amount of money the two women have in their accounts now
Answer:
1. - $ 175
2. -$ 195
3. Rochelle has $ 20 more than Denae.
Step-by-step explanation:
1. Given,
Rochelle made three withdrawals of $25,
Again she wrote $ 100,
So, the total amount she withdraw = 3 × 25 + 100= 75 + 100 = $ 175,
Thus, the total change in balance in her account = -$175,
2. Denae deposited 5 dollars,
i.e. change in her balance = $ 5,
Then she wrote a $200 check,
i.e. change in her balance = -$200,
Thus, the total change in her account = 5 - 200 = -$ 195
3. ∵ -175 > -195
⇒ Rochelle withdrew less amount,
If both started with the same balance,
Then the amount in Rochelle's account is more than that of Denae's account.
Also, -175- (-195) = -175 + 195 = $ 20
i.e. Rochelle has $ 20 more than Denae.
An American teen consumes 115 grams of sugar less than 4 time the amount of grams of sugar a healthy teen consumes
How many grams of sugar does a healthy teen consumes?
Evaluate. 2−2⋅(12⋅3)−53
The answer is -116. I took the test
i really really need help with this..
A store increases the price of a sweater from $20 to $22.
What is the percent of increase?
Answer:
The percent increase is [tex]\(10\%\).[/tex]
Explanation:
To find the percent increase, we use the formula:
[tex]\[\text{Percent Increase} = \left( \frac{22 - 20}{20} \right) \times 100\%\][/tex]
Given:
- Original price = $20
- New price = $22
Substitute these values into the formula:
[tex]\[\text{Percent Increase} = \left( \frac{22 - 20}{20} \right) \times 100\%\][/tex]
[tex]\[\text{Percent Increase} = \left( \frac{2}{20} \right) \times 100\%\][/tex]
[tex]\[\text{Percent Increase} = \left( 0.1 \right) \times 100\%\][/tex]
[tex]\[\text{Percent Increase} = 10\%\][/tex]
So, the percent increase is [tex]\(10\%\).[/tex]
How do you write 6.012 as a fraction?
The Students at Sunnyside School built a rectangular pyramid of aluminum cans for a world record. The top layer had 2 rows with 3 cans in each row. The second layer had 4 rows of 6 cans. The third layer had 8 rows of 12 cans. How many cans were in the eighth layer of the pyramid?
The eighth layer of the pyramid will have 280,896 cans.
Explanation:To find the number of cans in the eighth layer of the pyramid, we need to observe the pattern in the number of rows and cans in each layer. The pattern is that each layer doubles the number of rows and the number of cans in each row. The eighth layer will have 2^7 (128) rows and 3^7 (2187) cans in each row. Therefore, there will be a total of 128 * 2187 = 280,896 cans in the eighth layer of the pyramid.
Learn more about number of cans in the eighth layer of the pyramid here:https://brainly.com/question/14747504
#SPJ12
A television program lasts for 120 minutes. Of than time, 36 minutes are taken up by commercials. What is the length of the actual program without the commercials?
Please help me to answer these questions!! Thank you in advance.
1 - A string is cut into three pieces in the ratio 5 : 4 : 2. If the longest piece of string is 87 cm longer than the shortest piece of string, find the length of the string before it is being cut.
=
2- A bookstore sold fiction books, textbooks and workbooks last month in the ratio 6 : 5 : 9 respectively. If the store sold 1350 workbooks, what was the total number of fiction books and textbooks sold that month??
=
Final answer:
The total length of the string before being cut was 319 cm. The bookstore, given the ratio of 6:5:9 for fiction books, textbooks, and workbooks, sold a total of 1650 fiction books and textbooks in a month.
Explanation:
Answer to String Ratio Problem
Let's represent the length of the longest piece of string as 5x, the medium piece as 4x, and the shortest piece as 2x, based on the given ratio 5:4:2. According to the problem, the longest piece is 87 cm longer than the shortest piece. Thus, we have:
5x - 2x = 87 cm
3x = 87 cm
x = 29 cm
Now, to find the total length of the string before cutting, we add up all the pieces:
Total length = 5x + 4x + 2x = 11x = 11(29 cm) = 319 cm
So, the string was 319 cm long before it was cut.
Answer to Bookstore Ratio Problem
In the bookstore problem, we're given the ratio of fiction books, textbooks, and workbooks sold as 6:5:9, respectively, and that 1350 workbooks were sold. If we denote the common ratio multiplier as y, we can represent the amounts of each as follows:
Fiction books = 6y, Textbooks = 5y, Workbooks = 9y = 1350
To find y, we solve 9y = 1350:
y = 150
Now, we can calculate the total number of fiction books and textbooks sold:
Fiction books = 6y = 6(150) = 900
Textbooks = 5y = 5(150) = 750
Total fiction books and textbooks = 900 + 750 = 1650
The bookstore sold a total of 1650 fiction books and textbooks.
What is an equation for the linear function whose graph contains the points (2, 5) and (3, 0) ?
Answer: x + 5y - 15 = 0
Step-by-step explanation:
First, we find the slope
Given : x₁ = 2 y₁= 5 x₂= 3 y₂=0
m = y₂ - y₁ / x₂ - x₁
m = 0-5 / 3-2
m = -5 / 1 = -5
equation of a straight line;
y - y₁ = m (x - x₁)
y - 5 = -5(x - 2)
y - 5 = -5x + 10
y + 5x - 15 = 0
Sydney applied the steps below to find the product of (3.1)(–1.6).
Step 1: (3.1)(–1.6) = (–1.6)(3.1)
Step 2: = _______________
Step 3: = (–4.8) + (–0.16)
Step 4: = –4.96
Which expression correctly fills in the blank in Step 2?
(1.6)(3) – (1.6)(0.1)
(–1)(3) + (–0.6)(0.1)
(1)(3) – (0.6)(0.1)
(–1.6)(3) + (–1.6)(0.1)
to get the numbers in step 3
multiply -1.6 by 3
then multiply -1.6 by 0.1
and add them together
answer is D) (–1.6)(3) + (–1.6)(0.1)
Answer:
In Step 2 the expression is Option 4 is correct.
Step-by-step explanation:
Given : Sydney applied the steps below to find the product of [tex](3.1)(-1.6)[/tex].
To find : Which expression correctly fills in the blank in Step 2?
Solution :
Step 1 : Commutative property applied, [tex]ab=ba[/tex]
[tex](3.1)(-1.6)=(-1.6)(3.1)[/tex]
Step 2 - Apply distributive property [tex]a(b+c)=ab+ac[/tex] by re-write 3.1=3+0.1
[tex](3.1)(-1.6)=(-1.6)(3+0.1)[/tex]
[tex](3.1)(-1.6)=(-1.6)(3)+(-1.6)(0.1)[/tex]
Step 3 - Solve the multiple,
[tex](3.1)(-1.6)=(-4.8)+(-0.16)[/tex]
Step 4 - Add the terms,
[tex](3.1)(-1.6)=-4.96[/tex]
Therefore, In Step 2 the expression is Option 4 is correct.
Two-order systems may be solved by subtraction. True False
This is True
answered false got it wrong
Answer:
true
Step-by-step explanation:
8b-12 for b =2.1
We have to evaluate it and idk how
Help me plz number 14
Given: y = (-3/2)x + 15,
Here the slope is -3/2 and the y-intercept is 15.
The y-intercept tells us how many spoonfuls of chips Tiffany has at the beginning of her baking spree. This count decreases with each muffin that she makes, by 1 1/2 spoonfuls.
you have 5 buttons. which is the greatest number of buttons you can give away?
Alonzo and Miguel scored a total of 54 points in the basketball game. Miguel scored four more points than Alonzo. Write and solve a pair of simultaneous linear equations that represents the situation. Interpret the solution.
We will call A and M the scores obtained by Alonzo and Miguel respectively
A + M = 54 (Alonzo and Miguel scored a total of 54 points) Equation 1
M = A + 4 (Miguel scored four more points than Alonzo) Equation 2
We will substitute the value of M for the second equation in the first equation.
A + A + 4 = 54
2A = 54 - 4
A = 50/2 = 25 points (Alonzo scored this.)
M = A +4 = 25+4 = 29 points (Miguel scored this.)
Answer : Alonzo scored 25 points and Miguel scored 29 points
Checking
A + M = 25 points + 29 points = 54 points Check !
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]
need need need need help help help help help help help help help
Answer:
top left is 3/10
top right is 5/10 or 1/2
bottom left is 5/100
bottom right 25/100 or 1/4
Step-by-step explanation:
So to do it, you need to see what place behind the decimal the number is. The one in the top left is in the tens place, so it is 3 over 10. The one on the top right could also be written as 1/2 because both 5 and 10 can be divided by 5 so you divide top and bottom by 5 and it is simplified. The ones that are in the hundreds place, have a hundred in the denominator. If there was a question with three numbers behind the decimal point it would have 1000 in the denominator because it is in the thousands place. I suggest using m a t h w a y its a helpful website for math
mx−y when m=1, x=5, and y=2
Which option below correctly describes the domain of (see image) and explains why the range of b is not all real numbers?
a. The domain is all real numbers less than or equal to 81.
The range is not all real numbers because the square root of a negative number is not a real number.
b. The domain is all real numbers less than or equal to 81.
The range is not all real numbers because the square root symbol applied to a non-negative number is non-negative.
c. The domain is all real numbers greater than or equal to 81.
The range is not all real numbers because the square root of a negative number is not a real number.
d. The domain is all real numbers greater than or equal to 81.
The range is not all real numbers because the square root symbol applied to a non-negative number is non-negative.
Answer:
b. The domain is all real numbers less than or equal to 81; and The range is not all real numbers because the square root symbol applied to a non-negative number is non-negative.
Step-by-step explanation:
The square root function is not defined in the real number system for the square root of a negative number.
In order for the number under the radical sign to be positive, then the value of x must be all numbers less than or equal to 81.
The range cannot be negative numbers, since the square root of a positive number will give a positive answer.
This makes the correct choice b.
The diameter of a merry-go-round is 63 feet. Each person gets to make 23 rounds per ride. How far does each person ride?
Last month, Lana sold 35 necklaces a week at $15 each. However, throughout the month, 6 customers returned their necklaces for a fu refund due to defective clasps. How much did Luna make selling necklaces last month if there were 4 weeks in the last month?
Use a related multiplication equation to show why the equation 5/n = 0 has no solution
how much larger is 400 than 40? how much smaller is 0.2 than 2?
3/4 cup of sugar is needed to make six muffins. How much sugar is in each muffin?
To find out how much sugar is in each muffin, calculate the total grams of sugar in 3/4 cup and then divide that by the number of muffins (six). This will provide the amount of sugar in each muffin, which can be expressed in grams per muffin.
To determine how much sugar is in each muffin when 3/4 cup of sugar is needed to make six muffins, we simply divide the total amount of sugar by the number of muffins. First, we can find out how many grams of sugar are in 3/4 cup of sugar given that there are 200 grams in a full cup. So, we calculate .75 cups of sugar X 200 grams/cup to get the total grams of sugar in 3/4 cup.
Once we have the total grams of sugar for six muffins, we divide that amount by 6 to find out how much sugar is in each muffin. Mathematically, we can set up the following equivalency ratio for a formal solution: 3/4 cups sugar / 6 muffins = sugar per muffin. This will give us the amount of sugar in each individual muffin.