The equation of the line perpendicular to the line −7x+2y=3 having the same y-intercept as 9x+3y=−2 is y = - 2 / 7x - 2 / 3
How to find equation of a line?The equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line is perpendicular to −7x+2y=3.
−7x+2y=3
2y = 7x + 3
y = 7 / 2 x + 3 / 2
Perpendicular lines follows the rule below:
m₁ m₂ = -1
7 / 2 m₂ = -1
7m₂ = -2
m₂ = - 2 / 7
Therefore, the equation of the line also haver the same y-intercept as
9x + 3y = −2.
3y = - 9x - 2
y = -3x - 2 /3
The y-intercept of the equation is - 2 / 3.
Hence
the equation of the line is y = - 2 / 7x - 2 / 3
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A man spends 1/4 of his monthly income on children's school fees and 3/5 and- on home affairs. What fraction of his income is left?
The fraction of the man's income left is 3/20.
What are fractions?In mathematics, a fraction is represented by a numerical value that represents a portion of an entire. A fraction is a piece or section of a whole, where the whole can be any number, a particular value, or an object.Let's assume the monthly income of the man is x.
Income spend on children's school fees = [tex]\frac{1}{4} x[/tex]
Income spend on home affairs = [tex]\frac{3}{5} x[/tex]
The fraction of his income left with the man is,
Total income - Total expenditure
= [tex]x-(\frac{1}{4} x + \frac{3}{5} x)[/tex]
= [tex]x-(\frac{5x+12x}{20})[/tex]
= [tex]x - \frac{17x}{20}[/tex]
= [tex]\frac{3}{20}x[/tex]
So the man has 3/20 of his income left with him.
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K
Some rulers for technical occupations show each inch divided into tenths.
Use the scale drawing below. Change the measurements on the drawing to
decimals and round them to the nearest tenth of an inch.
(a)
(f)
View an example
16
(e)
1.8
3
P
5
16
3
(d)
2
רעון
(c)
1
1
1- in
8
Get more help -
(b)
a) 1.4 to the nearest tenth of the place
b) 1.1 to the nearest tenth of the place
c)0.3 to the nearest tenth of the place
d) 0.5 to the nearest tenth of the place
e) 0.4 to the nearest tenth of the place
f) 0.6 to the nearest tenth of the place
What is decimal ?The full number and the fraction are expressed simultaneously using decimals. By adding a "." (known as a decimal point) in this instance, we will divide the whole number from the fraction. Think about taking an ice cream cone as an illustration. Your purchase of ice cream will cost $2 and 50 cents, the dealer informs you. Currently, you would state that the ice cream cone costs $2.50 if you were to describe this amount in a single number. You may be utilizing decimals unknowingly in a variety of these real-world situations.
a) [tex]1\frac{5}{16} =\frac{22}{16}[/tex]
= 1.375
=1.4 to the nearest tenth of the place
b) [tex]1\frac{1}{8} = \frac{9}{8}[/tex]
=1.125
=1.1 to the nearest tenth of the place
c)[tex]\frac{1}{4}[/tex]
= 0.25
= 0.3 to the nearest tenth of the place
d) [tex]\frac{1}{2}[/tex]
=o.5
=0.5 to the nearest tenth of the place
e) [tex]\frac{3}{8}[/tex]
=0.375
=0.4 to the nearest tenth of the place
f) [tex]\frac{9}{16}[/tex]
=0.5625
= 0.6 to the nearest tenth of the place
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The rate at which a population of bacteria grows is proportional to the size of the population. At 1:00 PM, the population of a certain strain of bacteria was 5,400. At 1:20 PM, the population was 9,000. At what time will the population of bacteria be 25,000?
The time at which the population of bacteria will be 25,000 is 2:49 pm.
Given that:-
Population of bacteria at 1:00 PM = 5,400
Population of bacteria at 1:20 PM = 9,000
The rate at which a population of bacteria grows is proportional to the size of the population.
We have to find the time at which the population of bacteria will be 25,000.
The rate at which population of bacteria grows = 3600 bacteria/ 20 min = 180 bacteria/min
Let the population of bacteria takes t minutes to become 25,000.
Hence, we can write,
5400 + 180t = 25000
180t = 25000 - 5400
180t = 19600
t = 19600/180
t = 108.889
t = 109 minutes = 1 hour 49 minutes
Hence, the time will be 2:49 pm.
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how do i do this problem.
ANSWER
[tex]g(5x)=75x^2\text{ + 5}[/tex]STEP-BY-STEP EXPLANATION:
Given information
[tex]g(x)=3x^2\text{ + 5}[/tex]Find g(5x)?
Step 1: make x = 5x
[tex]\begin{gathered} g(x)=3x^2\text{ + 5} \\ g(5x)=3(5x)^2\text{ + 5} \\ g(5x)=3(25x^2)+5^{} \\ g(5x)=75x^2\text{ + 5} \end{gathered}[/tex]I need help with this question on my assignment please and thank you
Given:
The expression is,
[tex]45x^2y^2+18x^3[/tex]Simplify the expression,
[tex]\begin{gathered} 45x^2y^2+18x^3=9\times5x^2y^2+9\times2x^3 \\ =(9\times5\times x^2\times y^2)+(9\times2\times x^2\times x) \\ \text{Take 9x}^2\text{ common from both the brackets,} \\ =9\times x^2\lbrack5\times y^2\rbrack+9\times x^2\lbrack2x\rbrack \\ =9x^2(5y^2+2x) \end{gathered}[/tex]Answer:
[tex]9x^2(5y^2+2x)[/tex]PLEASE HELP ILL GIVE POINTS AND I ATTACHED THE PHOTO
Use measurements to explain why these two figures
are not congruent.
The circle and the elipse in this problem are not congruent because they are of different classes of conics, hence their measures are different.
What are congruent figures?Congruent figures are figures that are exactly the same, having corresponding sides with the same measure.
In this problem, we have two figures that belong to different groups of conics, which are a circle and an elipse.
The circle has one measure, which is it's radius, while the elipse has two measures, the minor axis and the major axis.
It can be seen visually that the elipse has a horizontal major axis and a vertical minor axis, and the major axis is greater than the minor axis. Since these two measures are not equal, the elipse cannot be congruent with any circle, and it is not congruent with circle B given in this problem.
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Elena buys 8 tokens for $4.40.
At this rate, how many tokens could she buy with $6.05?
Answer: 11
Step-by-step explanation: 8/4.40 = x/6.05
8 times 6.05
Divide by 4.40 is 11
Due to climate change, a certain place experienced an extreme change in weather. The following are the recorded temperatures: 15˚C, 1˚C, -4˚C, 3˚C, -10˚C, -7˚C, and 21˚C. What is the average temperature of all the given days?
The average temperature of all the given days is 19/7˚C or 2.7˚C
The average temperature of all the given days is -19/7˚C or -2.7˚C
The average temperature of all the given days is 61/7˚C or 8.7˚C
The average temperature of all the given days is -61/7˚C or -8.7˚C
Answer: Choice A) The average temp is 19/7 or 2.7 degrees Celsius
=======================================================
Explanation:
Ignore the ˚C and focus on the numbers only
We have this set of values
15, 1, -4, 3, -10, -7, 21
Add them up to get
15+1+(-4)+3+(-10)+(-7)+21 = 19
Then divide that sum over the total number of items in the set, which in this case is 7.
That's how we get to 19/7 which approximates to 2.7 when rounding to one decimal place.
Use implicit differentiation to find ∂z/∂x and ∂z/∂y.
x^4 + y^2 + z^9 = 8xyz
Using implicit differentiation, the derivatives of the function are given as follows:
[tex]\frac{\partial z}{\partial x} = -\frac{4x^3 - 8yz}{9z^8 - 8xy}[/tex][tex]\frac{\partial z}{\partial y} = -\frac{2y - 8xz}{9z^8 - 8xy}[/tex]How does implicit differentiation works?For implicit differentiation, we treat the variables as a function of each other, hence we keep applying the chain rule to find the derivatives.
Supposing a three variable function F(x,y,z) = 0, then the implicit derivatives are given as follows:
[tex]\frac{\partial z}{\partial x} = -\frac{F_x}{F_z}[/tex][tex]\frac{\partial z}{\partial y} = -\frac{F_y}{F_z}[/tex]In standard format, the function is given as follows:
F(x,y,z) = x^4 + y^2 + z^9 - 8xyz.
Hence the partial derivatives are given by:
[tex]F_x = 4x^3 - 8yz[/tex].[tex]F_z = 9z^8 - 8xy[/tex]Then the implicit derivative relative to x is:
[tex]\frac{\partial z}{\partial x} = -\frac{4x^3 - 8yz}{9z^8 - 8xy}[/tex]
The partial derivative relative to y is:
[tex]F_y = 2y - 8xz[/tex]
Then the implicit derivative relative to y is:
[tex]\frac{\partial z}{\partial y} = -\frac{2y - 8xz}{9z^8 - 8xy}[/tex]
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Please answer question 6, I will really appreciate it!!
Answer:
z=16
Step-by-step explanation:
1/4 *16=4
and 4 +8=12
Answer:
is that a z or 2?
Need this today help help help Brainiest
Solve the inequality and graph the solution.
−0.4b + 2.4 < 5.6
number line with an open circle plotted at negative eight and arrow pointing right
number line with a closed circle plotted at negative eight and arrow pointing right
number line with an open circle plotted at negative eight and arrow pointing left
number line with a closed circle plotted at negative eight and arrow pointing left
The graph of the solution to this inequality is: C. number line with an open circle plotted at negative eight and arrow pointing left.
What is a number line?A number line simply refers to a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
Next, we would solve the given inequality as follows:
−0.4b + 2.4 < 5.6
Subtracting 2.4 from both sides, we have:
−0.4b + 2.4 - 2.4 < 5.6 - 2.4
−0.4b < 5.6 - 2.4
−0.4b < 3.2
Dividing both sides by -0.4, we have:
b < -3.2/0.4
b < -8
In conclusion, the circle on a number line should be open and would point to the left when the inequality symbol is <.
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Somebody, please help me ASAP! I have 2 questions
1. Write, then simplify, an expression for the perimeter of the rectangle below.
3x | 6x +5
2. Write, then simplify, an expression for the perimeter of the figure below.
3x + 2 | x | 2x + 5 | 6x - 17
Please help!!!
Answer: for the first one, there is no picture i need a picture to solve it that's also for the second one.
Step-by-step explanation:
hope that helps
Find the first four terms of the binomial series for the function (1+2x)^1/2
The first four terms of the binomial series are 1, x, - x²/2 and - 1/32x³ respectively.
The binomial provided to us is [tex](1+2x)^{1/2}[/tex]
To find out the first four terms of the binomial, we shall first extend the standard binomial (1+x)^n.
(1+x)^n = 1 + nx + [n(n - 1)/2!] x² + [n(n - 1)(n - 2)/3!] x³ +...
As we can see here,
The value of x = 2x,
The value of n = 1/2.
We get,
(1+2x)^1/2 = 1 + 1/2(2x) + [1/2(1/2-1)/2!]x² + [1/2(1/2-1)(1/2-2)/3!]x³ +
(1+2x)^1/2 = 1 + x - x²/2 - 9/4x³ + .....
From the expansion, we can see,
First term = 1
Second term = x
Third term = -x²/2
Fourth term = -1/32x³.
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Question 6
Solve. Write it on paper to solve it.
5y + 4 = 4y + 5
Answer: y=1
Step-by-step explanation:
1. Subtract 4y from both sides to get y + 4 = 5.
2. Then subtract 4 from both sides to get y = 1.
Therefore, you get your answer, y = 1. Hope this helps!
Find the length of side x in simplest radical form with a rational denominator
Length of the side, x = 11/2
radical form, x = √5.5
Define Hypotenuse.The longest side of a right-angled triangle which is the side opposite to the right angle is called hypotenuse. The hypotenuse can be easily found using the Pythagorean theorem. It states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
As given in question, ∅ = 60°,
Using, Cos ∅ = adjacent/hypotenuse :
Cos 60°= x/11
As we know cos 60° = 1/2
1/2 = x/11
x, length of the side = 11/2= 5.5
radical form = 5.5
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Write an expression that is equivalent to 8 using each of the following numbers and symbols once in the expression.
optionsWe want to obtain an expression equivalent to 8 using these symbols and numbers.
The option that exactly matches this is,
[tex](7\text{ }\frac{.}{.}7)^2+7[/tex]That is because,
7 divided by 7 is 1.
1 squared is still one, and;
1 added to 7 is 8.
So one answer is option D.
We also have another answer.
Which is;
[tex](7+7^2)\frac{.}{.}7[/tex]That's because 7 squared is 49, and 7 + 49 is 56.
56 divided by 7 is 8.
So our answers are option C and option D
What is the equation of the line? Please
Answer:
The answer is C.
Step-by-step explanation:
You take 2 values from the graph each for x and y. Use it in finding the gradient:
[tex] gradient = \frac{y2 - y1}{x2 - x1} [/tex]
Your gradient is m. So you replace your answer in the formula:
[tex]y = mx + c[/tex]
where c is the constant
Then you solve solve for x by substituting other values. After finding c, substitute m and c in the equation above but leave x and y like that and you have your equation.
What is the value of x9+(12−y), when x = 2 and y = –5?
Answer: 35
Step-by-step explanation:
1) Substitute the x's and y's
(2)9+(12−(-5))
2) Simplify the numbers inside the equation
18+(12-(-5)
= 18+(17)
= 35
3) Solved.
35
a gear reduction drive has three separate stages with ratio of 3:1,2.38:1 and 4.2:1. the total ratio of the drive is?
The total ratio of the drive is 9.58:1.
What are ratios?A relationship between two quantities that are typically stated as the product of their respective quotients is known as a ratio.The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.Given ratios of the three separate stages of a gear reduction drive are 3:1,2.38:1 and 4.2:1.
To find the total ratio of the drive we have to add the respective ratios.
When the denominator of the ratios are same, as in this case we just have to add the numerators to obtain the result.
Total ratio of the drive = 3:1 + 2.38:1 + 4.2:1 = 9.58:1
So, the total ratio of the drive is 9.58:1.
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Please help I’ll mark you as brainliest if correct !!
Answer:
arithemetic because of the continuos multiplication
Answer:
A. I'm pretty sure would be geometric. and the next numbers would be 729, 2187, 6561
B. is arithmetic and the next numbers would be 46, 55, 64
C.is also arithmetic, and the next numbers would be 32, 36, 40
Nine times the cube of an number
Answer:
9*x³ or 9x³
Step-by-step explanation:
a number = x
cubed = to the power of 3
not really much to explain here
What is the measure of x?
61⁰ 90° 22° 29⁰
X + 7 3x - 5
Need to find 2 successes and 4. Successes probablity first 2
• Given:
[tex]\begin{gathered} n=15 \\ p=0.4 \end{gathered}[/tex]You need to find this probability:
[tex]P(x=4)[/tex]The Binomial Distribution Formula is:
[tex]P(x)=\frac{n!}{(n-x)!x!}p^x(1-p)^{n-x}[/tex]Where "n" is the number of trials, "x" is the number of successes desired, and "p" is the probability of getting a success in one trial.
In this case you know that:
[tex]x=4[/tex]Therefore, by substituting values into the formula and evaluating, you get:
[tex]P(x=4)=(\frac{15!}{(15-4)!4!})(0.4)^4(1-0.4)^{15-4}[/tex][tex]P(x=4)=(\frac{15!}{(11)!4!})(0.4)^4(0.6)^{11}[/tex][tex]P(x=4)\approx0.1268[/tex]• Given that:
[tex]\begin{gathered} n=12 \\ p=0.2 \end{gathered}[/tex]You need to find:
[tex]P(x=2)[/tex]In this case:
[tex]x=2[/tex]Therefore, using the same formula, you get:
[tex]P(x=2)=(\frac{12!}{(12-2)!2!})(0.2)^2(1-0.2)^{12-2}[/tex][tex]P(x=2)=(\frac{12!}{(10)!2!})(0.2)^2(0.8)^{10}[/tex][tex]P(x=2)\approx0.2835[/tex]• Given:
[tex]\begin{gathered} n=20 \\ p=0.05 \end{gathered}[/tex]You need to find:
[tex]P(x\leq3)[/tex]This is:
[tex]P(x\leq3)=P(x=0)+P(x=1)+P(x=2)+P(x=3)[/tex]Therefore, using the formula, set up:
[tex]P(x\leq3)=(\frac{20!}{(20-0)!0!})(0.05)^0(1-0.05)^{20}(\frac{20!}{(20-1)!1!})(0.05)^1(1-0.05)^{20-1}+(\frac{20!}{(20-2)!2!})(0.05)^2(1-0.05)^{20-2}+(\frac{20!}{(20-3)!3!})(0.05)^3(1-0.05)^{20-3}[/tex]Then, you get:
[tex]P(x\leq3)\approx0.9841[/tex]Hence, the answers are:
[tex]P(x=4)\approx0.1268[/tex][tex]P(x=2)\approx0.2835[/tex][tex]P(x\leq3)\approx0.9841[/tex]
Student A and Student B are disagreeing about how to do the following math problem.
Answer: student A
Step-by-step explanation: in multiplication for powers we use to multiply the digits which are 9 and 2 and add the power which is going to be [tex]18y^{5}[/tex]List all the three elements sunsets of the set {1,2,3,4,5}
A list of all the three-element subsets of the given set include the following:
{1, 2, 3} {1, 2, 4} {1, 2, 5} {1, 3, 4} {1, 3, 5} {1, 4, 5}{2, 3, 4} {2, 3, 5} {2, 4, 5}{3, 4, 5}How to determine the three element subsets?In order to determine the three-element subsets from the given set {1, 2, 3, 4, 5}, we would have to calculate the number of ways to choose the three (3) elements by applying a mathematical model referred to as combination.
Mathematically, combination is given by this mathematical equation:
[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]
Where:
n is the number of elements.r is the number of times of choosing elements.Substituting the given parameters into the formula, we have;
Number of ways = ⁵C₃
Number of ways = 5!/(3! × (5 - 3)!)
Number of ways = 5!/(3! × 2!)
Number of ways = [5 × 4 × 3 × 2 × 1]/[3 × 2 × 2 × 1]
Number of ways = 120/12
Number of ways = 10 ways.
Therefore, there are 10 three-element subsets of this set.
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Complete Question:
List all the three-element subsets of the set {1, 2, 3, 4, 5}
what is the range? is this relation a function? explain please
Answer:
Range is called a set of possible outputs..in an realtion or function.
Every relation is not function but all function is relation
Actually some specified relations are called function.
Thanks
Here Range= {5}
For each of the professions in the left column, calculate the annual pay based on full-time, year-round employment consisting of 2,000 hours a year (40 hours per week for 50 weeks per year). Record your calculations under "Annual income" in the table. Then, find the difference between each annual wage figure and a) the poverty threshold and b) the median household income. If the difference is a negative number, record it as such.
The difference between each annual wage figure and the poverty threshold is as shown in the attached completed table.
How to calculate Annual Income?
Annual Income is a term in economics that is calculated by multiplying the Hourly wage by 4,000 hours.
Now, the Difference between annual wage and the federal poverty line is calculated by subtracting the 2019 Poverty threshold of $13,011 from the Annual Income.
The Difference between annual wage and median household income is calculated by deducting the 2019 Median household income of $68,703 from the Annual income. Negative balances are highlighted.
The attached table shows us the completed annual income table
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(-a^4b³)^-4x(a^-3b^4)^5
Answer:
5
Step-by-step explanation:
use math-way
A restaurant serves an "all you can eat" buffet. At the beginning of serve, the value of the inventory is determined to be $1,200, and at the end of the meal period, it is
$800. That meal period the restaurant served 275 customers. The average food cost per customer for that meal period would be
O $3.64.
O $1.45
O $7.27.
O $5.82.
Answer:
1.45
Step-by-step explanation:
1200-800=400
400/275=1.4545454545...
the answer $1.45
A trapezoid has coordinates F (−9, 6), G (−6, 9), H (−3, 9), and I (0, 6).
a. Dilate the trapezoid by a scale factor of 1/3 with a center of dilation at the origin.
b. Is the dilation a reduction or an enlargement? Explain your reasoning.
a) the coordinates of the dilated trapezoid is F'(-3, 2), G'(-2, 3), H'(-1, 3), I'(0, 2)
b) Dilation is reduction.
In this question, we have been given a trapezoid has coordinates F (−9, 6), G (−6, 9), H (−3, 9), and I (0, 6).
a. We need to dilate the trapezoid by a scale factor of 1/3 with a center of dilation at the origin.
The scale factor is 1/3
so, the coordinates of the image would be,
F' = 1/3 (-9, 6)
= (-3, 2),
G' = 1/3(-6, 9)
= (-2, 3),
H' = 1/3 (−3, 9)
= (-1, 3),
and I' = 1/3 (0, 6)
= (0, 2)
b. We know that a dilation is a geometric transformation that either enlarges or reduces a figure in size.
As we know, if the scale factor is between 0 to 1 then the image is reduction and if the scale factor is greater than 1 then the image is enlargement.
Here, scale factor is 1/3 which is 0 < 1/3 < 1
So, in this case the dilation is reduction.
Therefore, a) the coordinates of the dilated trapezoid is F'(-3, 2), G'(-2, 3), H'(-1, 3), I'(0, 2)
b) Dilation is reduction.
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