To find the total amount of water needed to water all the plants in the house, the amount of water for a part of the plants is used to set up a proportion. After cross-multiplying and calculating, it is determined that 10/3 liters or approximately 3.33 liters of water is required.
If 4/3 liters of water is enough for 2/5 of the plants, then the amount of water required for all the plants can be found by setting up a proportion. We use cross-multiplication to solve for the unknown amount of water needed to water all the plants.
First, we express the given information as a fraction:
(4/3) liters
---------- = 1 (all the plants)(2/5) plants
Next, we solve for the total water required (let's call it x):
(4/3) / (2/5) = x / 1
We cross-multiply to solve for x:
4/3 * 1 = x * (2/5)
Multiplying both sides by the reciprocal of (2/5), which is (5/2), to isolate x, we get:
(4/3) * (5/2) = x
Now we calculate:
x = (4 * 5) / (3 * 2) = 20/6 = 10/3 liters
Therefore, 10/3 liters of water, or approximately 3.33 liters, is necessary to water all the plants in the house.
f
(
x
)
=
−
x
2
+
6
x
+
13
f(x)=−x
2
+6x+13, determine the average rate of change of the function over the interval
−
1
≤
x
≤
5
−1≤x≤5.
Answer:
The average rate of change of [tex]f(x) = x^2 +6x+13[/tex] is 12
The average rate of change of [tex]f(x) =- x^2 +6x+13[/tex] is 10
Step-by-step explanation:
The average rate of change of f(x) over an interval between 2 points (a ,f(a)) and (b ,f(b)) is the slope of the secant line connecting the 2 points.
We can calculate the average rate of change between the 2 points by
[tex]\frac{f(b) - f(a)}{b -a}[/tex]-------------------(1)
(1) The average rate of change of the function [tex]f(x) = x^2 +6x+13[/tex] over the interval 1 ≤ x ≤ 5
f(a) = f(1)
[tex]f(1) = (1)^2 +6(1) + 13[/tex]
f(1) =1+6+13
f(a) = 20---------------------(2)
f(b) = f(5)
[tex]f(5) = (5)^2 +6(5)+13[/tex]
f(5) = 25 +30 +13
f(5) = 68-----------------------(3)
The average rate of change between (1 ,20) and (5 ,68 ) is
Substituting eq(2) and(3) in (1)
=[tex]\frac{f(5) - f(1)}{5-1}[/tex]
=[tex]\frac{68 -20}{5-1}[/tex]
= [tex]\frac{48}{4}[/tex]
=12
This means that the average of all the slopes of lines tangent to the graph of f(x) between (1 ,20) and (5 ,68 ) is 12
(2) The average rate of change of the function [tex]f(x) = -x^2 +6x+13[/tex] over the interval -1 ≤ x ≤ 5
f(a) = f(-1)
[tex]f(1) = (-1)^2 +6(-1) + 13[/tex]
f(1) =1-6+13
f(1) = 8---------------------(4)
f(b) = f(5)
[tex]f(5) = (5)^2 +6(5)+13[/tex]
f(5) = 25 +30 +13
f(5) = 68-----------------------(5)
The average rate of change between (-1 ,8) and (5 ,68 ) is
Equation (1) becomes
[tex]\frac{f(5) - f(-1)}{5-(-1)}[/tex]
On substituting the values
=[tex]\frac{68 - 8}{5-(-1)}[/tex]
=[tex]\frac{60}{5+1}[/tex]
=[tex]\frac{60}{6}[/tex]
= 10
This means that the average of all the slopes of lines tangent to the graph of f(x) between (-1 ,8) and (5 ,68 ) is 10
Find the 9th term of the geometric sequence
8 , 32 , 128
Answer:
the pattern seems to be to multiply by 4 so the answer would be 524,288
Step-by-step explanation:
8×4= 32×4= 128×4= 512×4= 2048×4= 8192×4= 32768×4= 131072×4= 524,288
The 9th term of the given geometric sequence is 524288.
What do we mean by geometric progression?Geometric Progression is a series/sequence in which every term is a product of its previous term and a constant. The first term is taken as 'a' and the constant is taken as 'r'. So the series goes on like a, ar, ar², ar³, ......, arⁿ⁻¹, where arⁿ⁻¹ represents the nth term.
How do we solve the given problem?We are said that the given sequence is a geometric progression.
We take the first term as a.
∴ a = 8.
The second term is given as 32. This term is the product of the first term 'a' and the constant 'r', that is, this term is ar. To find the value of r, we divide this term by a.
r = ar/a = 32/8 = 4.
The 9th term in the sequence can be found using the formula of the nth term given by,
nth term = arⁿ⁻¹.
∴ 9th term = 8*4⁹⁻¹ = 8*4⁸ = 8*65536 = 524288.
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f(x) =
[tex] \sqrt[3]{x - 3} - 1[/tex]
Which of the following graphs corresponds to the function above?
Answer:
Step-by-step explanation:
the graph correspond to the function f :
SOME ONE PLEASE HELP
Answer
6,000x
Explanation
To work out how many times greater something is compared to another, we have to divide the larger number by the smaller
To put it more simply, imagine you had 30 apples and I had 6. To work out how many times greater your apple collection was than mine, you would divide your 30 by my 6, and find that you had 5 times as many apples as me (30 ÷ 6 = 5).
The principle is the same here, how many more viruses (3 x 10⁹) are there compared to protozoa (5 x 10⁵)?
We do 3 x 10⁹ ÷ 5 x 10⁵
3 x 10⁹ = 3,000,000,000
5 x 10⁵ = 500,000
3,000,000,000 ÷ 500,000 = 6,000 times more
Help me please and thank you
Answer:
The required answer is 218 degree.Step-by-step explanation:
∠AOB = 90 degree.
∠BOC = 52 degree.
Arc CDE = 180 degree, since CE is the diameter.
Hence, Arc EAC = 180 degree.
Besides, Arc EAC = Arc EA + Arc AB + Arc BC = Arc EA + 90 + 52 = Arc EA + 142.
Thus, Arc EA = 180 - 142 = 38 degree.
Arc ADC = 180 + 38 = 218 degree.
PLZZZ HELP DUE BY MIDNIGHT
Tim answered all the questions on his math test but got 10 answers wrong. He received 4 points for every correct answer, and there was no penalty for wrong answers. His score was 76points.
Write an equation to determine the total number of questions (q) on Tim's math test.
Find the total number of questions on his math test.
Answer: (i) 4x - 40 = 76
(ii) 29 questions
Step-by-step explanation:
Let the total number of questions be x.
Since he received 4 points for every correct answer and he got 10 answers wrong , this means he lost 40 points , the equation thus become
4x - 40 = 76
To find the value of x , add 40 to both sides
4x = 116
divide through by 4
x = 29
Therefore , there are 29 questions on his math test
At what point should an open circle be drawn (-1,0) (0,0) (0,1) (1,0)
I think the answer would be (0,0).
Hope this helps! ;)
Answer: (0,0)
Step-by-step explanation: Just confirming, this is the right answer :)
A line passes through (-3,-5) and (5,-4) write equation in point slope form
Answer:
work is shown and attached
Are these equivalent 3r-18 and 3(r-6)
Which expression has a negative value?
Answer:
-3×3×-3×-3 is positive
Answer:
-3 x 3 x -3 x -3 because the answer is -81.
(Bottom Left)
How do you find the difference never 6/8 - 1/7
Answer:
Step-by-step explanation:
6/8 - 1/7
And 6/8 = 3/4
The LCM of 7 and 4 = 28
3/4 - 1/7 = {7(3) - 1(4)}/28
= (21 - 4)/28
= 17/28
8x^2 - 2x = 1 quadratic simplification
Answer:
x = -1/4 = -0.250
Step-by-step explanation:
Sociologists want to determine the probability of exactly 4 out of the next 7 individuals they survey earning over
$50,000 dollars per year. The probability of an individual earning over $50,000 a year is 30%. What is the probability of
exactly 4 out of the next 7 individuals that they survey earning over $50,000?
A. 0.07859
B. 0.07651
C. 0.08311
D. 0.09724
Answer:
the probability of exactly 4 out of next 7 individuals that the sociologists survey earning over $50000 is given by
= [tex]\binom{7}{4} \cdot (0.3)^4(0.7)^{7-4}[/tex] = 0.09724
Step-by-step explanation:
i) This problem is solved by using the Binomial Probability distribution as the sample size is less than 30.
ii) The sample size is 7
iii) It is given that the probability of an individual earning over $50000 is 30% or 0.3 and therefore the probability of an individual not earning over $50000 is ( 1 - 0.3) = 0.7
iv) Therefore the probability of exactly 4 out of next 7 individuals that the sociologists survey earning over $50000 is given by
= [tex]\binom{7}{4} \cdot (0.3)^4(0.7)^{7-4}[/tex] = 0.09724
write the first four terms of the sequence defined by An=20-30(n-1)
The first four terms of sequence is 20, -10, -40, -70
Solution:
Given that we have to find the first four terms of sequence
Given recursive formula is:
[tex]a_n = 20 - 30(n-1)[/tex]
To find the first term, substitute n = 1
[tex]a_1 = 20-30(1-1)\\\\a_1 = 20-30(0)\\\\a_1 = 20[/tex]
Thus the first term of sequence is 20
To find the second term, substitute n = 2
[tex]a_2 = 20-30(2-1)\\\\a_2 = 20-30(1)\\\\a_2 = 20-30\\\\a_2 = -10[/tex]
Thus the second term of sequence is -10
To find the third term, substitute n = 3
[tex]a_3 = 20-30(3-1)\\\\a_3 = 20-30(2)\\\\a_3 = 20-60\\\\a_3 = -40[/tex]
Thus the third term of sequence is -40
To find the fourth term, substitute n = 4
[tex]a_4 = 20-30(4-1)\\\\a_4 = 20-30(3)\\\\a_4 = 20-90\\\\a_4 = -70[/tex]
Thus the first four terms of sequence is 20, -10, -40, -70
what dose 10/31/19 mean to you emos?
Answer:
The return of My Chemical Romance.
Answer:
It means...EVERYTHING.
Step-by-step explanation:
The discount of an item is directly proportional to the original price. The relationship is graphed in the diagram. Determine the discount on a $94 item.
A)
$23.50
B)
$35
C)
$47
D)
$58
9514 1404 393
Answer:
C) $47
Step-by-step explanation:
The arrowhead on the graph shows the discount of an item with an original price of 8 is 4. That is, the discount is half the original price.
The discount on $94 will be half that price, or ...
$94/2 = $47 . . . discount on $94
Two people bought 46 apples. Chris bought 5 times more than Brian. How many apples did Brian buy?
Answer:
7.6667
Step-by-step explanation:
46÷6=7.6667
brian buys 7.6667 apples i believe.
but please round depending on question
will give brainiest In △ABC, angle bisectors
AK
and
BL
are drawn. It is known that m∠BAC =m∠AKC and m∠ABC=m∠ALB. Find all the angles of △ABC.
Answer:
[tex]m\angle CAB=102\dfrac{6}{7}^{\circ}\\ \\m\angle ABC=51\dfrac{3}{7}^{\circ}\\ \\m\angle ACB=25\dfrac{5}{7}^{\circ}[/tex]
Step-by-step explanation:
AK is angle A bisector, then
[tex]m\angle BAK=m\angle KAC=x^{\circ}[/tex]
BL is angle B bisector, then
[tex]m\angle ABL=m\angle CBL=y^{\circ}[/tex]
Consider triangle ABL. The sum of the measures of all interior angles in this triangle is [tex]180^{\circ},[/tex] then
[tex]m\angle BAL+m\angle ALB+m\angle LBA=180^{\circ}\\ \\2x+2y+y=180\\ \\2x+3y=180[/tex]
Consider triangle ABK. In this triangle,
[tex]m\angle AKB=180^{\circ}-2x^{\circ} \ [\text{Supplementary angles}][/tex]
The sum of the measures of all interior angles in this triangle is [tex]180^{\circ},[/tex] then
[tex]m\angle BAK+m\angle AKB+m\angle KBA=180^{\circ}\\ \\x+(180-2x)+2y=180\\ \\2y-x=0[/tex]
Hence,
[tex]x=2y\\ \\2(2y)+3y=180\\ \\4y+3y=180\\ \\7y=180\\ \\y=\dfrac{180}{7}=25\dfrac{5}{7}\\ \\x=\dfrac{360}{7}=51\dfrac{3}{7}[/tex]
Find the measures of the triangle ABC:
[tex]m\angle CAB=2x^{\circ}=102\dfrac{6}{7}^{\circ}\\ \\m\angle ABC=2y^{\circ}=51\dfrac{3}{7}^{\circ}\\ \\m\angle ACB=180^{\circ}-102\dfrac{6}{7}^{\circ}-51\dfrac{3}{7}^{\circ}=25\dfrac{5}{7}^{\circ}[/tex]
The problem is asking to find all angles of an isosceles triangle ABC with angle bisectors AK and BL. The given conditions imply that the triangle has angles of 45°, 45°, and 90°.
The student is asking about an angle bisector problem in triangle geometry. In triangle ABC, the angle bisectors AK and BL are drawn such that m∠BAC = m∠AKC and m∠ABC = m∠ALB. To solve this problem, we need to use the properties of angle bisectors and triangles.
Since AK is an angle bisector, it bisects ∠BAC into two equal angles. Similarly, BL bisects ∠ABC into two equal angles. We also know that the sum of angles in a triangle is 180 degrees.
Let's denote m∠BAC and m∠AKC as 'x'. Similarly, let's denote m∠ABC and m∠ALB as 'y'. Since AK and BL are bisectors, m∠BAK = m∠CAK = x and m∠ABL = m∠CBL = y. Hence, ∠ACB would be 180 - 2x - 2y (sum of angles in a triangle).
We are given that m∠BAC is equal to m∠AKC and m∠ABC is equal to m∠ALB. This implies that the triangle is isosceles with the following angle measurements: m∠BAC = m∠ABC = x (equal base angles in an isosceles triangle), and m∠ACB = 180 - 2x.
Now, since m∠BAC and m∠ABC are equal, we can say that 2x + (180 - 2x) = 180. Simplifying, we find that x = 45 degrees, and thus, all angles of triangle ABC are 45°, 45°, 90°.
Maria is learning to play golf. She has been working particularly hard on driving. Before lessons, her drive average 240 yards. After her first lesson , her drives increase 25% . After her second lesson, they increase another 25%. How far are average drives after two lessons?
The required difference is 160-yard average drives after two lessons.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
We have been given that before lessons, her drive averaged 240 yards.
Here her drive average = 240 yards
After her first lesson, her drives increase by 25%.
Therefore her drive 2 = 240 + 0.25(240) = 320 yards
After her second lesson, they increase another 25%.
Therefore her drive 3 = 320 + 0.25(320) = 400 yards
So, the required difference in yards of average drives after two lessons
⇒ 400 - 240 = 160 yards
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PLS HELP - What is the product?
(2x-1)(x+4)
A- O 2x² - 4
B- O zx²+4
C- 2x?+7x-4
D- O 2x² - 7x-4
Answer:
C. 2x² + 7x - 4
Step-by-step explanation:
Given:
(2x-1)(x+4)
= 2x * (x+4) + (-1) * (x+4) ⇒ Distributive property.
= 2x² + 8x - x - 4 ⇒ Combine like terms.
= 2x² + 7x - 4
The answer is option C. 2x² + 7x - 4
Help me please..... .......thanks
Answer:
Step-by-step explanation:
3/8
D = a - b - c solve for b
To isolate b, add a and subtract c to the entire equation:
D - a + c = -b
Muliply b by -1 to eliminate the negative:
-D + a - c = b
CAN SOMEBODY PLEASE HELP ME??
Answer: According to the pattern i think its 66
Step-by-step explanation:
will mark brainliest
Complete the equation of the line through (-10,3) and (-8,-8)
Answer: 2y + 11x = -104
Step-by-step explanation:
The formula for calculating equation of line given two points is :
[tex]\frac{y-y_{1}}{x-x_{1}}[/tex] = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = -10
[tex]x_{2}[/tex] = -8
[tex]y_{1}[/tex] = 3
[tex]y_{2}[/tex] = -8
substituting the values into the formula , we have :
[tex]\frac{y-3}{x-(-10)}[/tex] = [tex]\frac{-8-3}{-8-(-10)}[/tex]
[tex]\frac{y - 3}{x + 10}[/tex] = [tex]\frac{-11}{2}[/tex]
2(y - 3 ) = -11 ( x +10 )
2y - 6 = -11x - 110
2y + 11x = -110 + 6
2y + 11x = -104
Therefore : the equation of the line in standard form is 2y + 11x = -104
28.71 is what percent of 6.6?
Answer:
28.71 is 435% of 6.6
Step-by-step explanation:
100%/x%=6.6/28.71
(100/x)*x=(6.6/28.71)*x - we multiply both sides of the equation by x
100=0.229885057471*x - we divide both sides of the equation by (0.229885057471) to get x
100/0.229885057471=x
435=x
x=435
give me an example of scale balance illustrating inequalities
Answer: 3x + 1 < 5 which has the same scale as x < 4/3
Step-by-step explanation:
Scale balance involves operating on each side of an equation or inequality, by adding, subtracting, multiplying, or dividing by a certain quantity, without changing the equilibrium of the equation or inequality.
The rules are easy,
* Everything you add to, subtract from, divide with, or multiply by one side of an equation or inequality must be done to the other side.
On Inequalities <, >, ≥, and ≤
* Anything you add, subtract, divide or multiply by the left hand side, the same must be done to the right hand side.
* Anytime you divide by a negative quantity, the inequality changes, and you must change the inequality sign.
Change < to > and vice versa.
Change) ≤ to ≥ and vice versa.
Example
Consider the following inequality.
3x + 1 < 5
subtract 1 from both sides of the inequality
3x + 1 - 1 < 5 - 1
3x < 4
Divide both sides of the inequality by 3
3x/3 < 4/3
x < 4/3
Here is another example.
Consider the following inequality
2y + 1 ≤ 5y + 9
Subtract 1 from both sides
2y + 1 - 1 ≤ 5y + 9 - 1
2y ≤ 5y + 8
Subtract 5y from both sides
2y - 5y ≤ 5y + 8 - 5y
-3y ≤ 8
Divide both sides by -3, but remember, DIVIDING BY A NEGATIVE QUANTITY CHANGES THE INEQUALITY .
-3y/-3 ≥ 8/(-3)
y ≥ -8/3 or -2⅔
I hope this helps, good luck.
( y + 1 ) + 4 = ?
Use one or more properties to rewrite each expression that dose not use parentheses.
To rewrite the expression (y + 1) + 4 without using parentheses, we can distribute 4 to the terms inside the parentheses and then combine like terms.
Explanation:
To rewrite the expression without using parentheses, we can use the distributive property. The distributive property states that multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding them together. In this case, we have (y + 1) + 4, and we can distribute the 4 to both terms inside the parentheses. So, (y + 1) + 4 can be rewritten as y + 1 + 4.Next, we can combine like terms. The terms y and 1 do not have any common variable factors, so they cannot be combined. However, 1 and 4 are both constants, so they can be added together to give us 5. Therefore, y + 1 + 4 simplifies to y + 5.
So, the expression (y + 1) + 4 can be rewritten as y + 5.
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Which shows the expression below in simplified form?
( 7 × 10⁵ ) × ( 5 × 10⁻⁴ )
A. 3.5 × 100
B. 3.5 × 103
C. 3.5 × 102
D. 12 × 101
Please explain how.
Answer:
A. 3.5 × 100
Step-by-step explanation:
( 7 × 10⁵ ) × ( 5 × 10⁻⁴ )
(7×5) ×10^(5+(-4))
(7×5) × 10^(5-4)
35 × 10
350
350 is equivalent to 3.5 × 100
Standard form , or standard index form, is a system of writing numbers which can be particularly useful for working with very large or very small numbers.
It is based on using powers of 10 to express how big or small a number is.
Standard form uses the fact that the decimal place value system is based on powers of 10:
10^0 = 1
10¹ = 10
10² = 100
10³ = 1000
10⁴ = 10,000
In laws of indices a² × a³ = a^(2+3)
I don't understand what this means.
Rewrite the polynomial function (in standard form), classify by its degree, and then determine the end behavior of its graph.
y=2x+3x^3+10
a)Standard form:____
b)Classification:____
c)End Behavior:____
Answer:
a) -3x^3 - 2x + y - 10 = 0
b) it a trinomial
c) not sure. sorry. :(
hope this helps.:)