A is the equation representing proportional relationship .
What is proportional relationship ?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.
CalculationIf the y intercept is anything but 0, then the linear function is not proportional. So C is not proportional (2 is the y intercept)
B is a quadratic and it will not give proportional results. y/x is not a constant.
D has no x value and is not going to give a proportional result. y/x is undefined.
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the product of 5 - 2i and i is
Answer:
5i + 2
Step-by-step explanation:
(5-2i)(i)
5i - 2i^2
i^2= -1
5i -2(-1)
= 5i + 2
BD bisects ABC, m/ABD = 2(3x), and m/ABC = 42°.
What is the value of x?
In the given triangle ABC where BD bisects ABC and according to the values of the given angles, the value of x is found out to be 3.5.
It is given to us that -
BD bisects ABC.
m/ABD = 2(3x) ----- (1)
and, m/ABC = 42 ------- (2)
We need to find out the value of x.
Since BD bisects triangle ABC,
The angles created with respect to the bisector are equal.
=> m/ABD = m/CBD ----- (3)
Also, it is also known that -
m/ABD + m/CBD = m/ABC ----- (4)
Substituting equation (3) in equation (4),
m/ABD + m/CBD = m/ABC
=> m/ABD + m/ABD = m/ABC
=> 2 m/ABD = m/ABC ----- (5)
Substituting the values of m/ABD and m/ABC from equation (1) and (2) in equation (5), we get
2 m/ABD = m/ABC
=> 2*2(3x) = 42
=> 12x = 42
=> x = 3.5
Thus, according to the values of the angles of the triangle, the value of x is 3.5.
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6. Find the are of the Rectangle
776
in
13
in
Answer:
about 3.09
Step-by-step explanation:
A = l x w
A = 13/7 x 7/6
A = 1.857 x 1.666
A = 3.09
Hope it helps!
Someone please Help!! 30 Points
There are currently 1,250 pine trees on Judy's plot of land. The number of pine trees on her land is currently decreasing at a rate of 14% per year.
Which of the following graphs shows the number of pine trees, Np, on Judy's land x years from now?
Answer: we would need to see the graphs to address this question fully, but you should look for the graph that starts at x = 0, 1250 and decreases by 14% compared to the previous year
so for example, x = 1, the y value should be 1250 - (0.14)(1250)
Step-by-step explanation:
The expression -7y is a ____. (20 Points!!) (Please help!)
Term
Constant
Variable
Answer:
constant
Step-by-step explanation:
-7y is a contant
Pls do this for me asap
a) The area of the rectangle has the following inequality: 12 ≤ 6 · x ≤ 36.
b) The value of the variable x has the following inequality: 2 ≤ x ≤ 6.
How to build and interpret an inequality associated to the area of an rectangle
The area of a rectangle (A) is described by the following formula:
A = b · h
Where:
b - Base of the rectangleh - Height of the rectanglea) If we know that b = 2 · x and h = 3, then the area of the rectangle is:
A = (2 · x) · 3
A = 6 · x
And the inequality is:
12 ≤ 6 · x ≤ 36
b) And the solutions for the values of x are represented by the following inequality:
2 ≤ x ≤ 6
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Can someone please help me answer this?
Answer:
sol y=5x+15 (see photo for calc)
Lina picks a 4 digit number.
The number is more than 5000.
The number is odd.
The second digit is a prime number.
How many different possible numbers could Lina pick?
Answer:
1000
Step-by-step explanation:
The easiest way to go about this is by turning our number into ABCD.
A will be in the 1000th spot, B 100th, C 10th, and D 1st.
A has to be ≥ 5. So 5, 6, 7, 8, 9.
B has to be a prime number. 2, 3, 5, 7.
C is able to be any number it wants, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Since the number is odd, D has to be 1, 3, 5, 7, 9.
A has 5 different possibilities. B has 4, C has 10, and D has 5.
You'll then multiply all of these numbers for your answer.
5 * 4 * 10 * 5 = 1000
the scatter plot below was constructed using data on length and inches (x) of several alligators and weight in pounds (y)right if you sent this describing the relationship between weight and length for these alligators
Answer
We are told that the relationship describing the weight and length, for alligators.
The length in inches is presented on the x-axis and the weight in pounds is presented on the y-axis.
The observations about this include
- From the scatterplot, we can see that the more the length of the alligator (that is, as x increases), the weight of the alligator also increases (that is, y increases too).
- This points to a direct relationship between the length of alligator and the weight of the alligator.
- Small alligators weigh light weights and longer alligators are heavy.
Hope this Helps!!!
Brian had p pencils. Then he bought 4 more.
How many does he have now? due tm pleaseeeeeeeeeeeeee help
Answer: The number of pencils Brian has is p+4
Step-by-step explanation:
Because p is the original number of the pencil ( we don't know how many are there so we keep it p). Then he bought 4 more which mean +4, so the answer is p+4
How do you divide x by a fraction, or an example of dividing x by a fraction.
SOLUTION
Now this is how I can divide x by a fraction.
Let's divide x by
[tex]\frac{2}{3}[/tex]So
[tex]x\text{ divided by }\frac{2}{3}[/tex]Now to do this, change division to multiplication. When you do this, the fraction reverses. That is the number up will come down and the number down will go up.
So, this becomes
[tex]\begin{gathered} x\text{ divided by }\frac{2}{3} \\ x\times\frac{3}{2} \end{gathered}[/tex]x on its own means x over 1, that is
[tex]\begin{gathered} x\times\frac{3}{2} \\ \frac{x}{1}\times\frac{3}{2} \\ m\text{ultiplying we have } \\ \frac{3x}{2} \end{gathered}[/tex]So this is how to divide x by a fraction.
Mr. March sells popcorn at his theater. He uses 3 3/4 cups of unpopped corn to make 15 bags of popped corn. Write an equation for the number of bags of popcorn b that can be made with c cups of unpopped corn.
The equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn is
b = 4c.
Given, Mr. March sells popcorn at his theater.
He uses 3(3/4) cups of unpopped corn to make 15 bags of popped corn. We have to write an equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn.
Now, according to the question
3(3/4) cups = 15 bags
15/4 cups = 15 bags
1 cup = 4 bags
So, in 'c' cups he will make, 4c bags
therefore, 4c = b
Hence, the equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn is
b = 4c.
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Type the correct answer in each box. Use numerals instead of words. This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form? Graph shows upward parabola plotted on a coordinate plane. The parabola has vertex at (2, minus 8) with the left slope at (0, 0) and the right slope at (4, 0).
The function’s equation written in factored form and in vertex form are respectively;
f(x) = 2x(x - 4)
f(x) = 2(x - 2)² - 8
How to Interpret Quadratic Graphs?The factored form of a quadratic function is;
f(x) = a(x - p)(x - q)
where:
p and q are the x-intercepts
a is a constant
Now, we are given x-intercepts as; (0, 0) and (4, 0)
Thus;
f(x) = a(x - 0)(x - 4)
f(x) = ax(x - 4)
To find a, substitute the given vertex (2, -8) into the equation and solve for a:
2a(2 - 4) = -8
-4a = -8
a = 2
Thus;
f(x) = 2x(x - 4)
The vertex form of a quadratic equation is;
f(x) = a(x - h)² + k
where:
(h, k) is the vertex
a is constant
Since vertex is (2, -8), then we have;
f(x) = a(x - 2)² - 8
Put the coordinate (0, 0) to find a;
0 = a(0 - 2)² - 8
4a = 8
a = 2
Thus;
f(x) = 2(x - 2)² - 8
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survey of 100 shoppers, were asked whether they have access to a computer at home. and if they have a personal email account. A) what % of shoppers have an email account?B) what % of shoppers do NOT have computer access at home?
Answer:
A). 34%
B). 62%
Explanation:
Part A:
How many shoppers have an email account?
The answer is 32 + 2 = 34 shoppers have an email account.
What percent of the total shoppers are 34 shoppers?
We know the there are 100 shoppers in total ( 32 + 2 + 6 + 60 = 100); therefore, 34 shoppers is
[tex]\frac{34}{100}\times100\%=34\%[/tex]Hence, 34% of the shoppers have an email account.
Part B:
How many shoppers do not have computer access at home?
The answer is 2 + 60 = 62 shoppers do not have computer access at home.
Now, what percent of the total number of shoppers is 62 shoppers?
The answer is
[tex]\frac{62}{100}\times100\%=62\%[/tex]Meaning, 62% of the shoppers do not have computer access at home.
Hence, to summerise
A). 34%
B). 62%
There are 27 students in Mrs. Mello's class. fin the total number of pages they read by the end of November.
The total number of pages they read by the end of November is 2916 pages.
As the question, Chapter 1 has 35 pages, Chapter 2 has 38 pages and Chapter 3 has 35 pages. All these pages are read by all 27 students by the end of November.
⇒ Total number of pages in Three chapters [tex]=35+38+35[/tex]
[tex]=108[/tex]
⇒ Total number of pages in all three chapters read by one student = 108
⇒ Total number of pages read by 27 students
[tex]= total number of pages in three chapters * 27[/tex]
[tex]=108*27[/tex]
[tex]=2916[/tex]
Therefore, The total number of pages 27 students read by the end of November = 2916.
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The full question is
There are 27 students in Mrs. Mello's class. fin the total number of pages they read by the end of November.
What are the domain and range of g(x) = −4?
Answer:
look at attached image!
Step-by-step explanation:
3(2y + 3) + 6(3y – 1) = 1 – 7y
Answer:
y = - [tex]\frac{2}{31}[/tex]
Step-by-step explanation:
3(2y + 3) + 6(3y - 1) = 1 - 7y ← distribute parenthesis and simplify left side
6y + 9 +18y - 6 = 1 - 7y
24y + 3 = 1 - 7y ( add 7y to both sides )
31y + 3 = 1 ( subtract 3 from both sides )
31y = - 2 ( divide both sides by 31 )
y = - [tex]\frac{2}{31}[/tex]
Question 3 Part B (2.02, 2.04): The table of values represents a linear function
(x), where x is the number of weeks that have passed and g(x) is the balance
n the bank account.
Write the equation of the line in point slope form (1 point):
Write the equation of the line in slope-intercept form (1 point):
Write the equation of the line in standard form (1 point):
X
0
5
10
g(x)
$1,250
$750
$250
The point slope form is [tex]y-1250=-100x[/tex]. The slope intercept form is [tex]y=-100x+1250[/tex]. The standered form of line is [tex]100x+y=1250[/tex].
What is equation of line?
The algebraic form of representing set of points is known as the equation of line.
The point slope form is as follows:
[tex]y-y_{1}=m(x-x_{1})[/tex] ... (1)
Here, [tex]y_{1}[/tex] is [tex]y[/tex] co-ordinates, [tex]x_{1}[/tex] is [tex]x[/tex] co-ordinates, and [tex]m[/tex] is the slope.
Also, slope is given by the following expression:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Hence, equation (1) can be written as follows:
[tex]y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})[/tex] ... (2)
Consider the following points:
[tex](g(x_{1}),x_{1})=(1250,0)\\(g(x_{2}),x_{2})=(750,5)[/tex]
substitute values in equation (2).
[tex]y-1250=\frac{750-1250}{5-0}(x-0)\\y-1250=-100x[/tex]
On comparing the above equation with equation (1), the value of slope [tex]m=-100[/tex]
Now, calculate the slope intercept form.
The following form is known as the slope intercept form:
[tex]y=mx+c[/tex]
Here, [tex]c[/tex] is the [tex]y[/tex] intercept that the value of [tex]y[/tex] when [tex]x=0[/tex] .
Substitute the value of slope that is -100 and value of g(x) when x =0 that is 1250 for [tex]c[/tex] in the above equation.
[tex]y=-100x+1250[/tex] ... (3)
Standered form of a line is as follows:
[tex]Ax+By=C[/tex]
Here, A,B, and C are integeres.
Rearrange equation (3) as follows:
[tex]y=-100x+1250\\100x+y=1250[/tex]
Hence, the point slope form is [tex]y-1250=-100x[/tex]. The slope intercept form is [tex]y=-100x+1250[/tex]. The standered form of line is [tex]100x+y=1250[/tex].
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Answer:
Step-by-step explanation:
I’m confused because I don’t know how to answer this question
SOLUTION:
We are to find the domain of the given exponential function shown;
The domain of exponential functions is all real numbers.
So the correct option is D
help me please , for 20 points
Answer:
A
Step-by-step explanation:
First off we can see that there are 46 pencils - and 7 students - so we can divide the two
46/7 is not a whole number, so we need to find a number that can be multiplied by 7, and is right below 46.
If you multiply 7 by 6, you get 42, which is the highest you can get with multiply by 7, which is also below 46.
Now that we know that each student gets 6 pencils, we need to find out how many are left.
We can do 46 (total pencils) minus 42 (pencils given) to get a leftover of 4 pencils, so the answer is A.
help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
The length of short side x is 4.5 units, the length of short side x+5 is 9.5 units and the length of longest side is 10.5 units.
By Pythagorean theorem,
[tex]( Hypotenuse)^{2} = (Base)^{2}+ (Perpendicular)^{2}[/tex]
Let base = x+5
perpendicular = x
Hypotenuse = x+6
[tex](x+6)^{2} = x^{2} +(x+5)^{2}[/tex]
[tex]x^{2} +12x+36 = x^{2} +x^{2}+10x+25[/tex][tex]2x^{2} +10x+25-x^{2} -12x-36=0[/tex]
[tex]x^{2} -2x-11=0[/tex]
[tex]x = \frac{-(-2) + \sqrt{4 - 4(1)(-11)} }{2*1}[/tex] or [tex]\frac{-(-2) - \sqrt{4 - 4(1)(-11)} }{2*1}[/tex]
[tex]x=\frac{2 + \sqrt{4 +44} }{2}[/tex] or [tex]\frac{2 - \sqrt{4 +44} }{2}[/tex]
[tex]x = \frac{2 + \sqrt{48} }{2}[/tex] or [tex]\frac{2 - \sqrt{48} }{2}[/tex]
[tex]x = \frac{2+2\sqrt{12} }{2}[/tex] or [tex]\frac{2-2\sqrt{12} }{2}[/tex]
[tex]x = 1+\sqrt{12}[/tex] or [tex]1-\sqrt{12}[/tex]
[tex]x = 1+3.5[/tex] or [tex]1-3.5[/tex]
[tex]x = 4.5[/tex] or [tex]-2.5[/tex]
As, length can't be negative, we will take x = 4.5
Therefore, x = 4.5
x + 5 = 4.5 + 5
= 9.5
x + 6 = 4.5 + 6
= 10.5
Hence, the length of short side x is 4.5 units, the length of short side x+5 is 9.5 units and the length of longest side is 10.5 units.
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A driver accelerates her car from rest to a velocity of 35.9 mi/hr in 8.2 seconds. What is the acceleration of the car?
The acceleration of the car will be 0.002 m / s².
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The velocity of the car = 35.9 m/hr
The time take by car = 8.2 seconds
Now,
Since, We know that;
⇒ Acceleration = (Final velocity - Initial velocity) / Time
Since, The driver accelerates her car from rest to a velocity of 35.9 mi/hr.
So, Initial velocity = 0
And, Final velocity = 35.9 m / hr
= (35.9 / 3600) m/s
= 0.01 m / s
So, We get;
⇒ Acceleration = (Final velocity - Initial velocity) / Time
⇒ Acceleration = (0.01 - 0) / 8.2
⇒ Acceleration = 0.01 / 8.2
⇒ Acceleration = 0.002 m / s²
Thus, The acceleration of the car will be 0.002 m / s².
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Question 3 of 30
sin 0=/941 and cos 0 =-40/41. Find tan 0.
O A. 40/9
OB. 9/40
C. -40/9
D. - 9/40
Answer:
answer Is -9/40
Step-by-step explanation:
the formula Is
tan0= sin0/cos0
tan0= (9/41)/(-40/41)
tan0=(9/41)*(-41/40)
tan0= -9/40
Circle O has a center of (-1,5) and passes through the point (2,9) write the equation in center radius form and standard form
Firstly, calculate the radius r of the circle using distance between two points
[tex]\begin{gathered} r\text{ = }\sqrt[]{(2-(-1))2+(9-5)^2} \\ r=\text{ }\sqrt[]{(2+1)^2+(4)^2} \\ r=\sqrt[]{3^2+4^2} \\ r=\sqrt[]{9+16} \\ r=\sqrt[]{25} \\ r=\text{ 5} \end{gathered}[/tex]Then use the radius r=5 and the center (-1 , 5) to find the equation of the circle
[tex]\begin{gathered} r^2=(x-h)^2+(y-k)^2 \\ 5^2=(x-(-1))^2+(y-5)^2 \\ 5^2=(x+1)^2+(y-5)^2 \end{gathered}[/tex]The center radius form is
[tex]5^2=(x+1)^2+(y-5)^2[/tex]The standard form is
[tex]\text{ 25}^{}=(x+1)^2+(y-5)^2[/tex]Naomi opened a savings account 7 years ago. the account earns 8% interest compounded monthly if the current balance is 1,000.00 how much did she despoit initially
Madeline earns $17,500 annually. What is the gross amount of hersemimonthly paycheck?a. $2,916.67b. $1,458.33c. $729.17d. $673.08
Given:
Annual earnings = $17,500
Asked: What is the gross amount of her semimonthly paycheck?
Solution:
To find the answer, we need to divide first the annual earnings by 12 to get the monthly paycheck. After that, we will divide it by 2 because we are looking for the semimonthly paycheck.
[tex]\begin{gathered} \frac{17,500}{12}=1,458.33 \\ \frac{1,458.33}{2}=729..17 \end{gathered}[/tex]ANSWER: C. $729.17
Solve for z in -3 < z-1 < 3.Give the result in the interval notation and graph on a number line
Answer:
(-2,4)
Explanation:
Given the inequality:
[tex]-3First, we add 1 to all parts of the inequality.[tex]\begin{gathered} -3+1We can represent this in interval notation as:[tex](-2,4)[/tex]The solution set is graphed on the number line below:
Charlotte states that (43)3
can be rewritten as 218
. Which of the following explains how she is correct? Select all that apply.
The statement that explains why Charlotte's submission is correct is that (4³)³ simplifies to (4⁹) and (4⁹) simplifies to 2¹⁸
How to determine why Charlotte's submission is correct?From the question, the expression is given as
(43)3
Rewrite the expression properly
So, we have the following representation
(4³)³
Apply the law of indices to rewrite the exponents in the expression properly
So, we have
(4³)³ = 4³*³
Next, we evaluate the products
So, we have the following notation
(4³)³ = 4⁹
Solving further, we need to express 4 as the square of 2
So, we have
(4³)³ = (2²)⁹
Apply the law of indices to rewrite the exponents in the expression properly
So, we have
(4³)³ = 2²*⁹
Next, we evaluate the products
So, we have the following notation
(4³)³ = 2¹⁸
Hence, Charlotte's expression is correct
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Possible question
Charlotte states that (4³)³ can be rewritten as 2¹⁸. Which of the following explains how she is correct? Select all that apply.
3. Evaluate:
Suppose you want to buy something for $60, and you have
$15 saved up so far. Then your grandmother calls and says she
will chip in for your purchase. She doesn't tell you the amount
of money she will give you yet, so you just consider it x
dollars. Write the expression that represents the equation.
The expression that represents the equation is x + 15 = 60
The total money needed to buy something is $60
And the saved up amount is $15
The amount of money that the Grandmother contributes is x
The saved up amount and the grandmothers contribution is equal to the total amount required to purchase
We need to write the expression that represents the equation.
x + 15 = 60
Therefore, the expression that represents the equation is x + 15 = 60
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Manuel took a total of 20 quizzes over the course of 2 weeks. How many weeks of school will Manuel have to attend this quarter before he will have taken a total of 90 quizzes? Assume the relationship is directly proportional.
Manuel will attend the quarter in 9 weeks.
Given,
In the question:
Total taken quizzes is 90
Manuel took a total of 20 quizzes over the course of 2 weeks.
To find the how many weeks of school will Manuel have to attend this quarter ?
Now, According to the question:
Based on the given conditions :
Formulate:
Let the no. of weeks be x
Total quizzes = 90
Here, The relationship is directly proportional.
20/2 = 90/x
If the fraction is defined, the denominator cannot be equal 0.
Solve the equation:
10 = 90/x
10x = 90
x = 9
Hence, Manuel will attend the quarter in 9 weeks.
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