If y varies directly with x and y=36 when x=6, the value of y is 24 when x=4.
What is direct variation?
The mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other. It is a linear function defined by an equation of the form
y = kx when x is not equal to zero.
Given:
If y varies directly with x and y=36 when x=6
According to given question we have
we can write direct variation equation as
y= k*x
where k is constant
y = 36 when x=6,
36 =k(6)
k=6
So, by putting the value of x=4 we get,
y =kx
y=6*4
y=24
Therefore, If y varies directly with x and y=36 when x=6, the value of y is 24 when x=4.
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NO LINKS!!
Plot the points and find the perimeter and area of each polygon
Answer:
11. 17.7 units
12. 24.7 units
Step-by-step explanation:
The perimeter of a two-dimensional shape is the distance all the way around the outside.
To find the perimeter of a polygon, sum the lengths of its sides.
Use the distance formula to find the length of each side.
[tex]\boxed{\begin{minipage}{4.7 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two endpoints.\end{minipage}}[/tex]
Question 11Given points:
A = (-2, 1)B = (2, 5)C = (5, 1)Use the distance formula to find the length of each side of ABC:
[tex]\begin{aligned}AB & = \sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& = \sqrt{(2-(-2))^2+(5-1)^2}\\& = \sqrt{4^2+4^2}\\& = \sqrt{16+16}\\& = \sqrt{32}\end{aligned}[/tex]
[tex]\begin{aligned}BC & = \sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\& = \sqrt{(5-2)^2+(1-5)^2}\\& = \sqrt{3^2+(-4)^2}\\& = \sqrt{9+16}\\& = \sqrt{25}\\& = 5\end{aligned}[/tex]
[tex]\begin{aligned}AC & = \sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\& = \sqrt{(5-(-2))^2+(1-1)^2}\\ & = \sqrt{7^2+0^2}\\ & = \sqrt{49}\\ & = 7\end{aligned}[/tex]
To find the perimeter, sum the sides:
[tex]\begin{aligned}\sf Perimeter & = AB+BC+AC\\& = \sqrt{32}+5+7\\& = 4\sqrt{2}+12\\& = 17.7\;\sf units\;(nearest\:tenth)\end{aligned}[/tex]
Question 12Given points:
A = (-3, 5)B = (1, 6)C = (3, -2)D = (-1, -3)After plotting the given points, it is clear that the polygon is a parallelogram. As the opposite sides of a parallelogram are equal in length:
AB = DCBC = ADTherefore, we only need to find the length of two sides to calculate the perimeter.
Use the distance formula to find AB and BC:
[tex]\begin{aligned}AB & = \sqrt{(1-(-3))^2+(6-5)^2}\\& = \sqrt{4^2+1^2}\\& = \sqrt{16+1}\\& = \sqrt{17}\end{aligned}[/tex]
[tex]\begin{aligned}BC & = \sqrt{(3-1)^2+(-2-6)^2}\\& = \sqrt{2^2+(-8)^2}\\& = \sqrt{4+64}\\& = \sqrt{68}\end{aligned}[/tex]
Therefore, the perimeter of ABCD is:
[tex]\begin{aligned}\sf Perimeter & = 2(AB+BC)\\& = 2(\sqrt{17}+\sqrt{68})\\& = 6\sqrt{17}\\& =24.7\;\sf units\;(nearest\:tenth)\end{aligned}[/tex]
NEED HELP PLEASE ASAP 9. Evaluate the limit for f (x) = x2 – 4x + 1.
lim
AX-10
f(x + 4x) - f(x)
Δε
2. a and b are both positive integers, therefore -a and- b are negative
integers. Using this, simplify the expression (-a)(- b) and explain.
Answer:
Here both a & b are positive integers that are obtained from the expression (-a)(-b).
Step-by-step explanation:
It is given that a and b are both positive integers, therefore -a and- b are negative integers.
Now, using this we need to simplify the expression (-a)(-b);
Firstly, let us understand what are integers and types of integers;
The collection of whole numbers and negative numbers is known as an integer in mathematics.
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers.
The inverse additives of the equivalent positive numbers are the negative numbers.
Now, let us understand what are positive and negative integers;
In fact, positive integers are a subset of the wider class of numbers known as integers.
Integers with a negative value are those that are less than zero. They exclude decimals and fractions.
Furthermore, the expression given is (-a)(-b) which is the product of two negative integers.
=> (-a)(-b)
=> ab
Therefore, here both a & b are positive integers that are obtained from the expression (-a)(-b).
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A zoo is thinking of adding a dome exhibit a showcase desert animals. The zoo sent out a survey to their current members to see their current members to see if they would be interested in adding this kind of the the zoo. Of 2,000 responses 7/10 indicated that yes they would like dome add it to the zoo how many members want a dome add it to the zoo
Based on the fact that out of 2,000 responses, 7/10 indicated that they would like the zoo to add a dome, the number of members who want a dome to be added to the zoo are 1,400 members.
How many members want the dome added?To find the number of members of the zoo who want the dome to be added to the zoo, the following formula would help:
= Number of members that were surveyed by the zoo x Fraction of members who indicated yes to the dome being added
Solving for the number of members who want the dome added gives;
= 2,000 x 7/10
= 14,000 / 10
= 1,400 members
In conclusion, 1,400 members indicated yes to the dome.
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A grahp is a straight line the point (0.5) can the graph represent a proporttional relationship?
Answer:
No, for a graph to be proportional it needs to go through the point (0.0)
Step-by-step explanation:
Whats 36/12 as a improper fraction
The elementary playground is a 1:6 scale representation of the high school activity field.
If the activity field is 21,600 square feet, what is the area of the playground?
Based on the scale factor of 1:6, if the area of the activity field is 21,600 square feet, the area of the playground is equal to 3,600 square feet.
Given the following data:
Scale factor = 1:6
Area of the activity field = 21,600 square feet.
What is scale factor?A scale factor can be defined as the ratio of two (2) corresponding length of sides, area, or diameter in two similar geometric figures such as equilateral triangles, river, planets in our solar system, etc.
Let E represent the area of the elementary playground.
Let H represent the area of the high school activity field.
Therefore, a mathematical expression which relates the area of the elementary playground to the area of the high school activity field is given by:
E : H 1:6 = x : 21,600
Evaluating, we have:
1/6 = x/21,600
Cross-multiplying, we have:
6x = 21,600
x = 21,600/6
x = 3,600 square feet.
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A blimp can be seen flying at an altitude of 7200 feet above a motor speedway during a race. The slanted distance directly to the pagoda at the start-finish line is d feet. Express the horizontal distance h as a function of d.
The horizontal distance as a function of d can be given as h = √(d + 7200) (d - 7200).
It is given in the question that:
Height at which blimp is flying (AB)= 7200 feet
The slanted distance to the pagoda (BC) = d feet
The horizontal distance (AC) = h
Let the angle made between slanted distance and horizontal distance be θ.
So, cosθ = AC/BC
cosθ = h/d
and also, sinθ = AB/BC
sinθ = 7200/d
Now, we know from the first trigonometric identity that cos²θ = 1 - sin²θ.
=> (h/d)² = 1 - (7200/d)²
=> (h/d)² = (d² - 7200)/d²
=> h² = d² - 7200
=> h = √(d² - 7200)
=> h = √(d + 7200) (d - 7200)
Thus, the horizontal distance as a function of d can be given as h = √(d + 7200) (d - 7200).
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10. During the hockey season, Elena
averaged 5.625 assists per game. What is
5.625 written in expanded form? How is
it written with number names?
Answer:
5 + 6*10^-1 +
Step-by-step explanation:
I got you started... If you still need extra help, let me know.
Stefan has 4 1/2 cups of oats. He uses 3 1/4 cups to make granola bars for a camping trip. He saves the rest of the oats to feed his parrot, Coco. If Coco needs 1/4 of a cup of oats each day, how many days can Stefan feed Coco with the oats he has left
Answer: Stefan can feed Coco for 5 days.
Explanation: After making the granola bars for the camping trip, he has [tex]1\frac{1}{4}[/tex] cups of oats left over.
Coco, the parrot, needs [tex]\frac{1}{4}th[/tex] of a cup of oats for eating each day.
After figuring out the math, Stefan can feed Coco for 5 days.
To double check that 5 days is correct, take 5 times [tex]\frac{1}{4}[/tex] and you will get [tex]1\frac{1}{4}[/tex].
[tex]1\frac{1}{4}[/tex] is what Stefan had left after making the bars, meaning the answer is correct.
----------------------------------------------------------
Hope this helps!
Have a great day and God bless! :)
An object is removed from a hot oven left to cool. After t minutes, the difference between
Answer:
finish quesiton please <3
Step-by-step explanation:
What is the decimal fraction of I) ¹½m is 60cm turn to decimal
Answer:
11.02
Step-by-step explanation:
Which two charges have a sum of 0? (1 point) a +7 charge and +7 charge b −7 charge and −7 charge c +7 charge and −7 charge d +7 charge and 0 charge
The charges which sum up to 0 are +7 charge and −7 charge.
What are integers?An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.
Given:
two charges have a sum of 0
So, taking one by one the pairs of option are
+7 charge and +7 charge
=+ 14 charge
−7 charge and −7 charge
=-14 charge
−7 charge d +7 charge
=0 charge
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Write an equation with a constant and a coefficient and variable where the variable will be equal to four after solving it
Answer:
hi I jgkjglhlih
Step-by-step explanation:
I've ok h l
a farmer buys 1000 pounds of hay which he thinks will last 31 days if his cow eats about 25 pounds of hay per day for how many days more than 31 will the farmers hay
feed the cow
The farmer can 9 days more than 31 days.
given,
farmer buy 1000 pounds of hay
if cow eats 25 pounds of hay per day .
here, 25 x 31 =775
which is less than 1000 ,so that the farmer can feed the cow more than 31 days
1000-775=225
225/25=9
therefore the farmer can 9 days more than 31 days.
There are four basic properties of numbers: commutative, associative, distributive, and identity. You should be familiar with each of these.
distributive property ;
According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
The commutative property states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product.
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3. A question on a course evaluation survey for an introductory statistics course asked, "How
do you rate the class textbook on a scale from 1 to 10, where 1 = Not Helpful and 10 =
Very Helpful?" The distribution below summarizes the students' responses to this
question. (3 pts)
Frequency
8
"
H▬▬▬▬▬▬▬▬▬▬▬o
2 0
9
1
2
3 4
6 7 8 9 10
5
Rating
If you estimate the median and the mean, which statement is the appropriate statement for
the mean and the median?
a. Median=2 and mean = 5
b. Median=3 and mean = 3.5
c. Median = 3.5 and mean = 3
IMAGE ABOVE
The correct statements regarding the mean and the median of the distribution are given as follows:
b. Median = 3 and Mean = 3.5.
What are the mean and the median of a distribution?The mean of a data-set is given by the sum of all values in the data-set, divided by the cardinality of the data-set, which is the number of values in the data-set.The median of a data-set is given by the middle value of the data-set, which is the value for which 50% of the data-set is less than and 50% of the data-set is greater than.From the frequency table, we have that:
5 observations have a value of 1.7 observations have a value of 2.8 observations have a value of 3.6 observations have a value of 4.5 observations have a value of 5.3 observations have a value of 6.1 observations have a value of 7.1 observations have a value of 10.The number of values in the data-set is:
5 + 7 + 8 + 6 + 5 + 3 + 1 + 1 = 36.
Hence the mean is given by:
M = (5 x 1 + 7 x 2 + 8 x 3 + 6 x 4 + 5 x 5 + 3 x 6 + 1 x 7 + 1 x 10)/36 = 3.5.
The median will be the 36/2 = 18th value, which is of 3.
Hence the correct statement is:
b. Median = 3 and Mean = 3.5.
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write a word problem that equals a negative number
Answer:
A submarine submerged at a depth of 40.21 feet dives 57.35 more feet down. What is the new depth of the submarine?
Step-by-step explanation:
Solving:
Rewrite the equation:
It first dived 40.21 feet so our equation is -40.21 + ? so far.
Next it dives another 57.35 feet so the final equation becomes -40.21 + (57.35)
To answer:
-40.21 + (57.35)= -97.56
Hence, the answer would be -97.56
Please help meee I don’t know the answer and I need it done
Answer:
1) 1/8
Step-by-step explanation:
2[tex]2^{-2}[/tex]= 1/2^2 = 1/4
2^-1 = 1/2^1 = 1/2
1/4x1/2=1/8
hope this helps
How do you do
2х² + 3у²
Step-by-step explanation:
so 2 • 2 = 4x then 3•3=9y since they aren't like terms so u have to leave it like that hope this helps
What is 4.5E-11 written in standard form
Answer: 4 * 10^(-11) + 5 * 10^(-12)
Step-by-step explanation:
4.5E-11=
4.5 * 10^(-11)=
(4+.5) * 10^(-11)=
4 * 10^(-11) + 0.5 * 10^(-11) =
4 * 10^(-11) + 5/10 * 10^(-11) =
4 * 10^(-11) + 5 * 10^(-1) * 10^(-11) =
4 * 10^(-11) + 5 * 10^(-1+(-11)) =
4 * 10^(-11) + 5 * 10^(-1-11) = 4 * 10^(-11) + 5 * 10^(-12)
An apple orchard has honey crisp trees and mnintosh trees. The orchard has 1603 honey crisp trees. It has 327 more McIntosh trees than honeycrisp trees. About how many apple trees does the orchard have?
The number of apple trees the orchard have is 3533.
How to find the the number of apple trees in the orchard?The apple orchard has honey crisp trees and McIntosh trees.
The orchard has 1603 honey crisp trees.
It has 327 more McIntosh trees than honey crisp trees.
Therefore,
number of honey crisp trees = 1603
number of McIntosh trees = 327 + 1603
number of McIntosh trees = 1930
Therefore, the number of apples trees the orchard have can be calculated as follows:
number of apples trees = number of McIntosh trees + number of honey crisp trees
number of honey crisp trees = 1603
number of McIntosh trees = 1930
number of apples trees = 1930 + 1603
number of apples trees = 3533
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Without solving state the property or properties that justify why the two equations must have the same solution set.
5(v - 4) = 100 and (v - 4)5 =100
Answer:
Commutative Property of Multiplication
Step-by-step explanation:
What is the Commutative Property of Multiplication?The Commutative Property of Multiplication essentially states that constants and variables can be multiplied in any order and the product will not change.
For example, the multiplication of 5 x 4 = 20 and 4 x 5 = 20 are equivalent. No matter what, you will get the same product.
How This AppliesBoth equations utilize the distributive property, which states that an expression a(b ± c) can be multiplied to create ab ± ac. As such, we can rearrange the a to either the front or end of the expression and retrieve the same results.
Your answer is the Commutative Property of Multiplication.
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can you help me to solve this
Answer:
RDASFD
Step-by-step explanation:
(-2,6) and (1,1) point slope equation
Answer:
[tex]y=-\frac{5}{3}x +\frac{8}{3}.[/tex]
Step-by-step explanation:
[tex]1. \ formula:\\ \frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1};[/tex]
2. according to the formula above:
[tex]\frac{x+2}{1+2} =\frac{y-6}{1-6}; \ = > \ \frac{x+2}{3} =\frac{y-6}{-5};[/tex]
3. finally, 5x+3y=8 ⇔
[tex]y=-\frac{5}{3}x +\frac{8}{3}.[/tex]
1. Simon sold candles to raise money for the school dance. He raised a total of
$25 for selling 10 candles. Find the unit rate (amount earned per candle).
−76 times the difference between a number and 61 is equal to the number plus −89.
Two or more expressions with an equal sign is Equation.-76(x-61)=x-89 is the equation for −76 times the difference between a number and 61 is equal to the number plus −89.
What is Equation?Two or more expressions with an equal sign is called as Equation.
The sentence −76 times the difference between a number and 61 is equal to the number plus −89. We have to express in the form of equation.
−76 times the difference between a number
Let the number be 'x', times means multiplication and difference is subtraction.
-76(x-61)
the number plus −89
x+(-89)
−76 times the difference between a number and 61 is equal to the number plus −89.
-76(x-61)=x+(-89)
-76(x-61)=x-89
Therefore -76(x-61)=x-89 is the required equation.
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How would you classify √11?
Whole Number
Rational Number
Irrational Number
Integer
please help !!
I will really appreciate it!
thank youuu
Step-by-step explanation:
f(g(x)) simply means that g(x) is embedded in f(x) as the input value for f(x).
f(g(x)) = 3(7x + 6) - 1 = 21x + 18 - 1 = 21x + 17
c. is the right answer
g(f(x)) is the other way around. f(x) is now the input value for g(x).
g(f(x)) = 7(3x - 1) + 6 = 21x - 7 + 6 = 21x - 1
a. is the right answer
A line passes through the point (2,−4) and has a slope of 1/2. What is the y-coordinate of the point on the line when x = 8?
A. −1
B. 7
C. −2
D. 8
E. 5
The y-coordinate of the point on the line when x = 8 is -1
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
What is the y-coordinate of the point on the line when x = 8?The given parameters are
Slope, m = 1/2
Point, (x1, y1) = (2, -4)
The linear equation is calculated as
y = m(x - x1) + y1
So, we have
y = 1/2(x - 2) - 4
When x = 8, we have
y = 1/2(8 - 2) - 4
Evaluate
y = -1
Hence, the y-coordinate of the point on the line when x = 8 is -1
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a price was discounted by 20%.and the discounted price is 200€.how many euros are the discount?
Answer:
40€
Step-by-step explanation:
the amount discounted is200€
the 200€ is the amount
hence 100%=200€
what about. 20%
20×200€ ÷100%
= 40€
The discount is applied on 1000 euros.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100. The percent value of one quantity to the other can be calculated by multiplying their ratio by 100.
The discount percent and the discounted price is 20% and €200 respectively.
Suppose the original price be x.
Then, the following equation can be written as,
20% × x = 200
⇒ 20x/100 = 200
⇒ x = 1000
Hence, the original price is obtained as €1000.
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