[tex]\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{ \begin{array}{llll} \textit{\small "z" varies directly with }x^2\\ \textit{\small and inversely with }y^2 \end{array}}{ z=\cfrac{kx^2}{y^2}}\qquad \textit{we know that} \begin{cases} z=76\\ x=5\\ y=2 \end{cases} \implies 76=\cfrac{k(5)^2}{(2)^2} \\\\\\ 76=\cfrac{25k}{4}\implies \cfrac{4}{25}\cdot 76=k\implies \cfrac{304}{25}=k~\hfill \boxed{z=\cfrac{304x^2}{25y^2}} \\\\\\ when \begin{cases} x=9\\ y=9 \end{cases}\implies z=\cfrac{304(9)^2}{25(9)^2}\implies z=\cfrac{304}{25}\implies z= 12.16[/tex]
Model−−−−−: P=2,320(1.2)x
The model is used to estimate the deer population in a region, where x is the number of years after the year 2009. Using the model, estimate the deer population in the year 2018
The population of the deer in year 2018 would be 11971.
Given,
In the question:
The model is used to estimate the deer population in a region, where x is the number of years after the year 2009. Using the model, estimate the deer population in the year 2018
Model is given as:
P = 2,3201 [tex](1.2)^x[/tex]
Now, According to the question:
The number of years from 2009 to 2018 = 9
Here, the equation that shows the deer population after x years since 2009,
P = 2,3201 [tex](1.2)^x[/tex]
Substitute x=9 in the above equation,
P = 2,3201[tex](1.2)^9[/tex]
P = 2320(5.15978)
P ≈ 11971
Hence, the population of the deer in year 2018 would be 11971.
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The graph represents the function f(x) = x2 + 3x + 2. If g(x) is the reflection of f(x) across the x-axis, g(x) = . (Write the function in standard form. Use ^ to indicate an exponent.)
The reflection of the graph in the x-axis gives the function
g(x) = -x² - 3x - 2
The given function is of the form f(x) = x² + 3x + 2 which represents a parabola.
The vertex of the function is at (-3/2 , -1/4)
The focus is at ( 3/2 , 0 )
The axis of symmetry is 2x+3 = 0 and the directrix is at 2x + 1 = 0
Now when the parabola is reflected along the x-axis we get
the focus at ( -3/2 , 0 )
the vertex is at (-3/2 , 1/4)
Axis of symmetry remains the same
The directrix becomes 2y-1 =0
The red graph denotes the function f(x) while the blue graph denotes the function g(x) reflected on the x-axis.
Hence the reflection on the x-axis gives the function g(x) = -x² - 3x - 2
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
The equations that are true for x = –2 and x = 2 include the following:
x² – 4 = 0
4x² = 16
How to determine the true equations?In order to determine which x-values are true solutions based on the given equations, we would have to test each of the x-values by substituting their values into the equations as follows;
When x = -2, we have:
x² – 4 = 0
(-2)² – 4 = 0
4 - 4 = 0 (True).
When x = 2, we have:
x² – 4 = 0
(2)² – 4 = 0
4 - 4 = 0 (True).
When x = -2, we have:
x² = -4
(-2)² = -4
4 = -4 (False).
When x = -2, we have:
3x² + 12 = 0
3(-2)² + 12 = 0
3(4) + 12 = 0
12 + 12 = 0
24 = 0 (False).
When x = -2, we have:
4x² = 16
4(-2)² = 16
4(4) = 16 (True).
When x = 2, we have:
4x² = 16
4(2)² = 16
4(4) = 16 (True).
When x = -2, we have:
2(x – 2)² = 0
2(-2 – 2)² = 0
2(-4)² = 0
2(16) = 0
32 = 0 (False).
When x = 2, we have:
2(x – 2)² = 0
2(2 – 2)² = 0
2(0) = 0 (True).
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Complete Question;
Which equations are true for x = –2 and x = 2? Select two options
x² – 4 = 0
x² = -4
3x² + 12 = 0
4x² = 16
2(x – 2)² = 0
it takes matilda twice as long to complete a research project
A fruit punch has a ratio of 2 cups of powder mix for every 5 gallons of
water.
Represent the ratio relationship using a graph.
How many cups of powder mix are used with 9 gallons of water?
HELLLLPSSS PLEASE LAST SECOND
Answer:
3.6 cups
Step-by-step explanation:
We have to make a proportion to solve this.
[tex]\frac{2cups}{5 gallons}[/tex] = [tex]\frac{x cups }{9 gallons}[/tex]
9 x 2 = 18
18 / 5 = 3.6.
Which statement about odd functions is correct?
Answer:
at least put the possible answers
Yellow and red dye are mixed in a 9 : 2 ratio
to make 44 litres of an orange-coloured dye.
A further 8 litres of red dye are added to the
mixture. What is the new ratio of yellow to red
dye in its simplest form?
Answer:
9 : 4
Step-by-step explanation:
Ratio:
Find the quantity of yellow and red dye in the mixture.
Yellow : Red = 9 : 2
Total share = 9 + 2 = 11
[tex]\sf \text{Quantiy of yellow} = \dfrac{9}{11}*44[/tex]
= 9 * 4
= 36 litres
[tex]\sf \text{Quantity of Red}= \dfrac{2}{11}*44[/tex]
= 2 * 4
= 8 litres.
Now, 8 litres of red dye is added.
New quantity of red dye = 8 + 8 = 16 liters.
New ratio of Yellow to red = 36 : 16
= (36÷4) : (16÷4)
= 9 : 4
A survey of 25 people was conducted to determine their favorite color. 13 people like Red, 8 people like blue and 13 people like yellow. 5 people like both Red & Blue, 4 people like both Blue & yellow, 7 people like both Red & yellow and 2 people like all three colors.
Question: How many did not like any of the three colors?
The number of people who do not like any of the three colour is 5, using the set theory.
What is Set theory?
A subfield of mathematics called set theory studies sets and their characteristics. Set theory's fundamental ideas are straightforward and seem to stand on their own. The set theory appears to be straightforward, but it is actually a very complex topic. Mathematicians have specifically demonstrated how almost all mathematical ideas and conclusions may be formalized within the theory of sets. This is regarded as one of the pinnacles of contemporary mathematics. Given this accomplishment, it is possible to assert that set theory serves as the foundation for mathematics.
In the given question, we have:
Total number of people in the survey = 25;
Number of people like red = 13;
The number of people who like blue = 8;
The number of people who like yellow = 13;
5 people like both Red & Blue,
4 people like both Blue & yellow,
7 people like both Red & Yellow
2 people like all three colors.
Let n be the number of people who do not like any of the three colour.
Using the concept of set theory, we can write it as:
3 + 4 + 1 + 5 + 2 + 3 + 2 + n = 25;
⇒20 + n = 25;
n = 25 - 20
n = 5;
Hence, The number of people who do not like any of the three colour is 5;
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Answer any of these two! If you can answer both I could possibly give you brain^^ THANK YOU
Answer:
12. [tex]\frac{1}{z^{2} }[/tex]
13. x⁶
Step-by-step explanation:
*Note: When multiplying two of the same variables you add the exponents. When dividing two of the same variables you subtract the exponents. When a variable to a power is raised to another power you multiply the exponents.
[tex](z^{6} z^{-5} )^{-2}[/tex]= [tex](z^{6+(-5)} )^{-2}[/tex]= [tex](z^{6-5} )^{-2}[/tex]= [tex](z^{1}) ^{-2}[/tex]= [tex]z^{1*-2}[/tex]= [tex]z^{-2}[/tex]= [tex]\frac{1}{z^{2} }[/tex]*Note: When there is a negative exponent the whole term is flipped (the reciprocal of the term).[tex]\frac{1}{x^{-6} }[/tex]= x⁶in a major need of help
Answer:
B and D are the correct answers.
A population of 50 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain up to 600 deer. Absent constraints, the population would grow by 70% per year.
If It is estimated that the sanctuary can sustain up to 600 deer. Absent constraints, the population would grow by 70% per year. After one year is 85 and after two years is 144.50.
How to find the population growth?Using this formula
A = P(1+r)t
Where:
A = Amount
P = Principal
r =Interest rate
t = time
Let plug in the formula
After one year:
A = 50(1+0.70)^1
A = 50(1.70)^1
A= 85 deer
After two years:
A = 50(1+.70)^2
A = 50(1.70)^2
A = 50(2.89)
A = 144.50 deer
Therefore the population growth is 85 deer and 144.5 deer.
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The complete question is:
A population of 50 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain up to 600 deer. Absent constraints, the population would grow by 70% per year.
how many after one year
how many after two years
write the number 4 as a fraction with a denominator of 15
Answer:
60/15
Step-by-step explanation:
A fraction is simply a portion of a whole number, so 1/15 is the number 1 split into fifteen equal parts, therefore 15/15 = 1.
So 4 as a fraction with fifteen as the denominator would be 15/15 x 4, which equals 60/15.
Please help!!! Will give Brainliest to the first person that answers!
Answer:
Below
Step-by-step explanation:
m = motorcylce speed
c = car speed = 2m-30
difference in speeds = 2m-30 - m = m-30
in two hours this speed accumulates 20 miles (rate * time = distance)
2 (m-30) = 20
2m - 60 = 20
m = 40 then c = 2m-30 = 50 mph
Which of the following shows an example of the identity property of 0?
O 3.5+ 3.5 = 7
○ 4.8+(-4.8) = 0
O 0+ (8.2) = -8.2
O-1.6+ 3.2 = 1.6
draw the graph of the linear inequality 2x – 3y < 12?
Answer:
The following question has been answered in the attached document. If there are any queries kindly let me know they will be resolved shortly.
PRO TIP:
don't forget to mention y=0 on x axis and x=0 on y axis whenever you are drawing a graph as it accounts for 1/2 mark in board exams.
The line cuts the y axis at (0, -4) Also (0,0) satisfies the inequality So the shaded region is towards (0, 0). Since there is a strict inequality, the line is a broken line
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, [tex]\geq[/tex], [tex]\leq[/tex]
A one degree inequation is known as linear inequation.
The given linear inequality is
2x - 3y < 12
For the point on x axis for the line 2x - 3y = 12
we put y = 0
[tex]2x - 3\times 0 = 12\\2x = 12\\x = \frac{12}{2}\\x = 6[/tex]
The line cuts the x axis at (6, 0)
For the point on y axis for the line 2x - 3y = 12
we put x = 0
[tex]2\times 0 - 3y = 12\\-3y = 12\\y = \frac{12}{-3}\\y = -4[/tex]
The line cuts the y axis at (0, -4)
Also (0,0) satisfies the inequality
So the shaded region is towards (0, 0)
Since there is a strict inequality, the line is a broken line
The graph has been shown in the figure attached
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what is y times equals negative 42
Answer:
I am thinking the answere is -6 x 7 but I'm not completely
Jai read 3 books in 2 months. What was his rate of reading in books per month
Jai rate of reading in books per month is 1.5 books per month.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this case, Jai read 3 books in 2 month, his rate of reading in books per month will be:
= Number of books / Number of months
= 3 / 2
= 1.5 books per month
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Solve (x – 3)2 = 49. Select the values of x. –46 -4 10 52
Answer:
10
Step-by-step explanation:
I guess your question is
[tex] {(x - 3)}^{2} = 49[/tex]
[tex]x \: - 3 = \sqrt{49} \\ x - 3 = 7 \\ x = 7 + 3 \\ x = 10[/tex]
we want to factor the following expression: (x - 3)^2 - 64y^4 which pattern can we use to factor the expression? u and v are either constant integers or single variable expression.
The factored expression of (x - 3)^2 - 64y^4 is given as follows:
(x - 3)^2 - 64y^4 = (x - 3 + 8y²)(x - 3 - 8y²).
What is the subtraction of perfect squares?The subtraction of perfect squares is a notable product that gives the simplification of an expression containing the subtraction of perfect squares as follows:
a² - b² = (a - b)(a + b).
In this problem, the expression is presented as follows:
(x - 3)^2 - 64y^4
This expression is a subtraction of perfect squares, as the terms are given as follows:
Term a: square root of (x - 3)² = x - 3.Term b: square root of 64y^4 = 8y².Then the expressions are given as follows:
a - b = x - 3 - 8y².a + b = x - 3 + 8y².Then the factored expression is presented as follows:
a² - b² = (a - b)(a + b).
(x - 3)² - 64y^4 = (x - 3 + 8y²)(x - 3 - 8y²).
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1)if a number is trebled and 10 is subtracted from it and then multiply the result by 5 the answer is 55 what is the number
The number represented in the statement is 7
How to determine the number?The statements in the question can be highlighted as:
A number is trebled10 is subtracted from the resultThe result is then multiplied by 5The final result is 55When represented as an equation, we have
5(3x - 10) = 55
Where x represents the number
Divide both sides by 5
3x - 10 = 11
Add 10 to both sides
3x = 21
Divide by 3
x = 7
Hence, the result is 7
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If you are god in math the I have a question do it
Answer:
I am definitely not one...Lol
Step-by-step explanation:
The length of the rectangular lot is 25 ft longer than twice the width. If the perimeter of the lot cannot exceed 350 ft, what is the greatest width possible?
The greatest width possible in line is 0.8.
What is line?
a line is an infinitely long to the object with no width, depth, or curvature. Thus, the lines are the one of one-dimensional objects, though they may exist on it two, three, or higher of the dimension spaces. The word line may also refer to a line are the segment in everyday life, which has two points to denote its ends.
Sol-As per the given question The line r has slope 8 and coordinate (0.8).
The slope of the line r will not change.
And intercept is the addition of their ordinate will be.
Intercept = 5+3
Intercept = 8
So, the line r has slope 8 and coordinate (0.8).
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Determine whether the series converges or diverges...
The series as represented in the task content is divergent and hence; diverges.
What convergence and divergence in series?It follows from the task content that the series defined by the summation expression as represented above is to be identified as divergent or convergent.
It is noteworthy to know that;
If a sequence converges, it means that the limit of the sequence exists as n → ∞. Also, if the limit of the sequence as n → ∞ does not exist, Then, such series is said to diverges.
Therefore, by evaluation as the limit of the expression k sin²k / 1 + k³ as k → ∞ is; Undefined and hence does not exist.
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UP FOR THE CHALLENGE?! PLEASE HELP!
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 110.5° is added to the data, how does the mean change and by how much?
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 101° is added to the data, how does the mean change?
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 71° is changed to 93°, which of the following measures changes the most and what is the new value?
Answer:50%
Step-by-step explanation:
1234567891011121314151617`81910
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equations that represent the circle having a diameter of 12 units and a center lying on y-axis are; x² + (y – 3)² = 36, and x² + (y + 8)² = 36.
What is the standard form of the equation of a circle?The standard form of the equation of a circle is (x - h)² + (y - k)² + r², where (h, k) is the center of the circle, and r is its radius.
We have given that circle having a diameter of 12 units, will have a radius of 12/2 = 6 units. Thus, r = 6.
Since we know that circle having the center on the y-axis will have a center as (0, k) as all points on the y-axis have x-coordinate 0.
Thus, the equation of the circle, with a diameter of 12 units is;
x² + (y - k)² = 6², or,
x² + (y - k)² = 36.
From the given options, the equations x² + (y – 3)² = 36, and x² + (y + 8)² = 36, are correct.
Thus, the equations that represent the circle having a diameter of 12 units and a center lying on y-axis are; x² + (y – 3)² = 36, and x² + (y + 8)² = 36.
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Find the area of this parallelogram
Answer:
84unit square
Step-by-step explanation:
how many years do I need the 3
The answer is: " 84 cm² " ; or, write as: " 84 square centimeters."
____
Step-by-step explanation:
Note the formula for the area; "A" ; of a parallelogram—as follows:
A = b * h ;
in which:
A = the Area of this parallelogram given in the attached image;
for which we shall solve; in units of: cm² ;
or, write as: " square centimeters "
→ {since all the measurements shown in the image are in units of:
"cm" ["centimeters"].}
____
b = " base length " = 12 cm {as shown in the image};
____
h = " perpendicular height " = 7 cm {as shown in the image} .
____
To find the area; A :
We plug our given values into the equation/formula:
→ A = b * h ;
= (12 cm) * (7 cm) ;
= 12 * 7 * cm * cm ;
A = 84 cm² .
_____________
Note of interest: The following quadrilaterals are also parallelograms:
squares, rectangles, and rhombuses [or, "rhombi"].
_____________
The answer is: " 84 cm² " ; or, write as: " 84 square centimeters."
___
Hope this is helpful to you.
Wishing you well in your academic endeavors!
___
You have to make a balloon payment on your house five years from now of $15,000. If money can earn an average of 6 percent a year for the five-year period, how much will you have to place in the account today to have the $15,000 in five years?
The future value of an investment with such details must have a present value of $11120.58
Present ValuePresent value (PV) formula finds application in finance to calculate the present day value of an amount that is received at a future date. The present value formula (PV formula) is derived from the compound interest formula. The compound interest formula is,
FV = PV(1 + r/n)^nt
We can substitute the values into the formula
15000 = PV(1 + 0.06/12)^12*5
15000 = PV(1.005)^60
PV = 11120.58
The present value of an investment to give a future value of $15000 at 6% rate in 5 years is $11120.58
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Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x = −7 and x = 5 and passes through the point (0, −2)
The equation for the parabola with the given characteristics is:
y = (2/35)*(x + 7)*(x - 5)
How to get the equation of the parabola?We know that for a parabola that has the zeros x₁ and x₂, and a leading coefficient a, can be written as:
y = a*(x - x₁)*(x - x₂)
In this case, the roots (zeros) are at X =-7 and x = 5
Then we can write:
y = a*(x + 7)*(x - 5)
Now we also know that it passes through the point (0, -2), then we can write:
-2 =a*(0 + 7)*(0 - 5)
-2 = a*-35
2/35 = a
Then the equation for the parabola is:
y = (2/35)*(x + 7)*(x - 5)
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Please tell me answer ASAP
Adam has notes of RS.100, RS.50 and RS.10. The ratio of these notes is 2 : 3:5 respectively and the total amount is RS.200,000. Find the number of notes of each kind.
The number of notes of Rs. 100 is 1000, Rs. 50 is 1500, and Rs. 10 is 2500.
The ratio describes the number of times one number contains another. It helps to establish a relationship between two or three quantities.
The ratio between any two quantities is described as a:b. This can also be written as a to b or a/b.
The ratio of RS.100, RS.50, and RS.10 is 2:3:5.
From the given ratio, consider
the number of Rs. 100 is 2xthe number of Rs. 50 is 3xthe number of Rs. 10 is 5x.The total amount is given as RS.200,000. This can be written as,
[tex]\begin{aligned}100\times2x+50\times 3x+10\times5x&=200,000\\200x+150x+50x&=200,000\\400x&=200,000\\x&=\frac{200,000}{400}\\x&=500\end{aligned}[/tex]
Therefore,
the number of Rs. 100 is 2(500) = 1000the number of Rs. 50 is 3(500) = 1500the number of Rs. 10 is 5(500) = 2500To know more about ratios:
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