The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
The area of a circle with radius "r" is given as,
A = πr²
Since,π = constant.
Removing constant by proportionality.
A ∝ r²
Hence "The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle".
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if h(x)= 1-7x find the value of 23-h(9)=
85
Step-by-step explanation:
Given,
[tex]{ \pink{ \sf{h(x) = 1 - 7x}}} \: { \to} \: { \tt{eq}^{n} (1)}[/tex]
Put x = 9 in Eqⁿ (1)
[tex]{ \pink{ \sf{h(9) = 1 - 7(9)}}}[/tex]
[tex]{ \pink{ \sf{h(9) = 1 - 63}}}[/tex]
[tex]{ \red{ \boxed{ \pink{ \sf{h(9) = - 62}}}}}[/tex]
Let
[tex]{ \green{ \sf{23 - h(9)}}} \: { \to} \: { \tt{ {eq}^{n} (2)}}[/tex]
Substitute the value of h(9) in Eqⁿ (2)
[tex]{ \green{ \sf{23 - ( - 62)}}}[/tex]
[tex]{ \green{ \sf{23 + 62}}}[/tex]
[tex] = { \pink{ \boxed{ \red{ \sf{85}}}}}[/tex]
Find the average rate of change of the given function on the interval [1,6]. g(x)=2x2−x
Answer:13
Step-by-step explanation:
g(1)=2(1)^2-1= 1
g(6)=2(6)^2-6=66
66-1/6-1=13
Paul inherited a stamp collection. Since receiving the
collection, Paul has gone to the store and bought the
same number of new stamps each week to add to his
collection. The equation shown below can be used to
determine the number of stamps (y) in Paul's stamp
collection x weeks after he inherited the stamps.
y = 3x + 40
Based on the equation, which statement is true?
A) The stamp collection had 3 stamps in it when Paul inherited it.
B) So far, Paul has purchased 40 additional stamps for the collection.
C) Since inheriting the collection, Paul has bought 3 new stamps each week.
D) Six weeks after he inherited the collection, Paul's stamp collection contains 18 stamps
Based on the equation y = 3x+40 where y is the number of stamps and x is number of weeks after Paul inherited the stamps, the correct statement is since inheriting the collection, Paul has bought 3 new stamps each week.
According to the question,
We have the following information:
y = 3x+40 where y is the number of stamps and x is number of weeks after Paul inherited the stamps
Now, when we observe this equation carefully, we notice that 3x is added to 40. So, it means that 40 is constant. Then, the number of stamps increasing per week is in the multiplication of 3. Or, in other words, 3 new stamps are bought each week.
For 1st week:
y = 3*1+40
y = 43
For 2nd week:
y = 3*2+40
y = 6+40
y =46
Hence, the correct option is C.
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(42x³ + 16x² + 46x +42) ÷ (7x + 5)
응
Which expression uses the commutative property of addition and the associative property of
multiplication to rewrite the expression 3 (28) +7?
O 7+(3-2).8
O 3 (8-2)+7
O 7+3 (16)
O (3-2) 8+7
The expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 (28) +7 is 7+(3-2).8
The commutative property of addition states that a change in the order of the numbers being added does not affect the sum. We can define commutative property of addition as adding the numbers in any order will give the same answer.
a + b = b + a
3(2x8) + 7 = 7 + 3(2x8)
The associative property of multiplication says that while multiplying three numbers, regardless of the way the numbers are grouped, the end result will always be the same.
a(b x c) = (a x b) c
7 + 3(2x8) = 7 + (3.2)8
Therefore, the expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 (28) +7 is 7+(3-2).8
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i need help answering this question
Answer:
Step-by-step explanation:
there is no question?
Which equation is the inverse of y = 100-x²?
Oy=± √100-x
O y=10± √√x
Oy=100+√x
Oy=+√x-100
Answer:
y = ±√100-x
Step-by-step explanation:
To work out the inverse of this function :
We solve for x then swap x and y :
Solving for x :
y = 100 - x²
Add x² to both sides :
x² + y = 100
Subtract y from both sides :
x² = 100-y
Square root both sides :
x = ±√100-y
Now we have solved for x. Now swap x and y :
y = ±√100-x
This is our final answer and is the first option.
Hope this helped and have a good day
one positive number is 8 more than twice another. if their product is 1242, find the numbers?
Answer:
Step-by-step explanation:
Rationalize the denominator 1/ square root of 2
Answer:
Multiply and divide by √2 . You'll get √22
Step-by-step explanation:
Different liquids freeze at different temperatures, called their freezing points. Liquid acetone, used in nail polish remover, has a freezing point of – 137°F. Water has a freezing point of 32°F. How much warmer is the freezing point of water than the freezing point of acetone? °F
The freezing point of water in relation to the freezing point of acetone, is 169 °F
How to find the difference in freezing points?The difference between the freezing point of water (how much warmer the freezing point of water is) and the freezing point of acetone can be found by the formula:
= Freezing point of water - Freezing point of acetone
Freezing point of water = 32°F
Freezing point of Acetone = – 137°F
In relation to the freezing point of acetone, the degrees warmer that the freezing point of water is:
= 32 - (- 137)
= 32 + 137
= 169 °F
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Use the z-distribution table on pages A-1 and A-2 or technology to solve. Suppose a set of data is normally distributed. Below which z-score do approximately 34 of the data lie?
The z-score under which 3/4 of the data lies is of:
Z = 0.675.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The z-score under which 75% of the distribution lies is the 75th percentile, hence it is the value of Z with a p-value of 0.75.
Looking at the z-table, this value is of 0.675, as 0.675 is the mean of the p-values of Z = 0.67 and Z = 0.68.
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a football team travels to an away game in cars that seat five players and vans that can hold nine players. If there are 47 players on the team find the equation for this situation
The equation to illustrate the information when the football team travels to an away game is 5c + 9v = 47.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
Let cars = c
Let van = v
The equation will be 5c + 9v = 47.
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Car A is travelling east at a steady speed .......
Answer:
for 20 miles per hour
Step-by-step explanation:
.
Write the quadratic equation whose roots are -5 and 4, and whose leading coefficient is 5.
(Use the letter x to represent the variable.)
3
x
2
−
3
x
−
60
=
0
Explanation:
A quadratic equation whose roots are
α
and
β
and leading coefficient is
a
is
a
(
x
−
α
)
(
x
−
β
)
=
0
Hence, the quadratic equation whose roots are
5
and
−
4
and leading coefficient is
3
is
3
(
x
−
5
)
(
x
−
(
−
4
)
)
=
0
or
3
(
x
−
5
)
(
x
+
4
)
=
0
or
3
(
x
2
−
5
x
+
4
x
−
20
)
=
0
or
3
(
x
2
−
x
−
20
)
=
0
or
3
x
2
−
3
x
−
60
=
0
Answer:
5x^2+5x-100=0
Step-by-step explanation:
5(x+5)(x-4)=0
(x+5)(x-4)= 0
x= -5
x= 4
Point M (5,-7) is the midpoint of the line segment CD. If C is (2, "-3)," which of these are the coordinates of D?
Answer:
D(8, -11)
Step-by-step explanation:
You want the coordinates of end point D if C is (2, -3) and the midpoint of CD is M(5, -7).
MidpointThe midpoint is the average of the endpoint coordinates:
M = (C +D)/2
Solving for D, we find ...
D = 2M -C
End pointThen point D is ...
D = 2(5, -7) -(2, -3) = (2·5-2, 2(-7)+3)
D = (8, -11)
Describe the transformers of the parent function, f(x)=x, performed to create g(x).
g(x)= -3 • f(x) + 1
The function g(x) is a reflection over the x-axis and stretch by 3 units and shifted upward by 1 unit of the parent function f(x).
What is a function?A capability is a declaration, idea, or rule that lays out a relationship between two factors. Capabilities might be found all through science and are fundamental for the advancement of huge connections.
The functions are given below.
f(x) = x
g(x) = -3f(x) + 1
g(x) = -3x + 1
The parent function is a reflection over the x-axis and stretch by 3 units and shifted upward by 1 unit.
The functions g(x) and f(x) are shown below.
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Can someone help me with this
Answer:
x=20
Step-by-step explanation:
It looks like the opposite end of the 70 is angle between I and D. So assuming that angle is also 70 I would subtract 90 and 70 which equals 20. X=20
Please solve :) and hurry!
The price for 7 bags of trail mix and 4 bananas is 15.45 dollars.
The expression for x trail bag and y bananas is 1.35x + 1.50y.
How to represent expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
Therefore, the cost of a bag of trail mix at the corner store is 1.35 dollars and the cost of a banana is 1.5 dollars.
The cost for 7 bags of trail mix and 4 bananas can be computed as follows;
let
x = bags of trail mix
y = number of banana
Therefore,
1.35x + 1.50y
1.35(7) + 1.50(4) = 9.45 + 6 = 15.45
Therefore, let's find the expression for x trail bag and y bananas.
Hence,
1.35x + 1.50y
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Gavin deposited money into his savings account that is compounded annually at an interest rate of 9% Gavin thought the equivalent quarterly interest rate would be 2.25% is Gavin correct?
The quarterly interest rate is equal to 2.25%. This implies that Gavin is correct.
How to determine the value of equivalent quarterly interest rate?Mathematically, the compound interest on an investment can be calculated by using this formula:A(t) = P(1 + r/n)^{nt}
Where:A represents the future value.
r represents the interest rate.
n represents the number of times compounded.
P represents the principal.
T represents the time measured in years.
In this scenario, Gavin's savings account is compounded annually at an interest rate of 9%. This ultimately implies that, the equivalent quarterly interest rate would be calculated by dividing the annual interest rate of 9% by 4 as follows:
Quarterly interest rate = 9/4
Quarterly interest rate = 2.25%
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please help I need to find X
Answer:
x = 12
Step-by-step explanation:
if l and m are parallel that means that since the two angles are consecutive interior they add to 180
so add them both and set that to 180
9x - 4 + 5x + 16 = 180
now combine like terms
14x + 12 = 180
subtract 12 from both sides
14x = 168
divide everything by 14
x = 12
that is the answer
Answer:
[tex]\sf x=12^o[/tex]Step-by-step explanation:
Let's find x:-
[tex]\sf 9x-4+5x+16=180^o[/tex]
Combine like terms:-
[tex]\sf 9x+5x-4+16=180[/tex]
[tex]\sf 14x-4+16=180[/tex]
[tex]\sf 14x+12=180[/tex]
Add/Subtract numbers:-
[tex]\sf 14x+12-12=180-12[/tex]
[tex]\sf 14x=168[/tex]
Divide both sides by 14:-
[tex]\sf \cfrac{14x}{14}=\cfrac{168}{14}[/tex]
[tex]\sf x=12^o[/tex]
__________________
Hope this helps!
Have a great day!
16. Doug's family buys 7 postcards while on vacation. Each
postcard costs $0.25 including tax.
Part A
How can Doug use place-value blocks to
find the total cost of the postcards? What is
the total cost?
The total cost is $1.75
What is Place value?The foundation of our entire number system is place value. In this approach, the value of a digit in a number is determined by where it appears in the number. The digits in the numbers 42,316 and 61,432 are distinct from one another.Given that we've done it:
7 postcards were purchased by Doug's family.Each postcard costs $0.25 after tax.The total price is shown by:
7 x 0.25 = $1.75Now, let's display the following in a number line:
Put all the numbers with a difference of 0.25 on the number line, run it seven times, and the result will appear.There are 7 hops between each step of 0.25 duration to get to the needed answer.So, after seven hops, we arrive at 1.75, which is the correct response.
Hence, the total cost is $1.75
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A rectangle has a width (3x-2) and a length of (5x). The rectangle has the same perimeter as a square with a perimeter of 44 units.
Find the value of x.
Check the picture below.
Write an inequality that represents the graph
The line represents that x is anywhere from negative infinity to 1:
x < 1
Answer: x<1
Step-by-step explanation:
X is less than one on the graph because everything on the darker line is the solution.
Ex:
-1<1
please help me i never learned divison im sorry87,628÷931=
Answer:
94.1224489796
this is the answer
Please help! What is the standard form of the following equation?
y= 5x+0.5
-5x+y=-0.5
-5x+y=0.5
-5x-y=0.5
-5x+y= 0.5
The standard form of the equation, 3y = 9x -12, is -5x + y = 0.5. The correct option is the third option -5x+y=0.5
Writing an equation is standard formFrom the question, we are to write the given equation is standard form.
The given equation is
y = 5x + 0.5.
The standard form of a linear equation is
Ax + By = C
Where A, B, and C are constants
x and y are variables
Now, we will write the given equation is the standard form of a linear equation.
y = 5x + 0.5
Subtract 5x from both sides of the equation
y - 5x = 5x - 5x + 0.5
y - 5x = 0.5
Rewrite the equation, so that it would correspond to the standard form of a linear equation
-5x + y = 0.5
Hence, the standard form is -5x + y = 0.5
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How would I solve this? i know how to solve easier variations but not like this the question is:
Write a linear function f with the values f (-1) = 8 and ƒ (5) = 6.
The linear function with values of f(-1)=8 and f(5)=6 is f(x) = [tex]\frac{-x+23}{3}[/tex].
What is linear function?
A straight line on the graph has the equation or formula y = f(x) = px + q is linear function .One independent and one dependent variables are present. X and Y are the independent and dependent variables, respectively. P is the y-intercept or constant term, and it also represents the value of the dependent variable. A straight line on the coordinate plane is represented by a linear function.
Here the given values are f(-1)=8 and f(5)=6.
We know that f(x)=y , Then the points are (-1,8) and (5,6).
Using slope formula ,
=> slope m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = -2/6=-1/3
Now using slope formula,
=> [tex]y-y_1=m(x-x_1)[/tex]
=>y-8=-1/3(x+1)
=>3y-24=-x-1
=> 3y=-x+23
=> y = [tex]\frac{-x+23}{3}[/tex]
Hence the linear function is f(x) = [tex]\frac{-x+23}{3}[/tex].
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write each system of equations as a matrix
Answer:
Step-by-step explanation:
Confused please help.
The image of the corresponding to each slope is attached
What is slope?A line's steepness can be determined by looking at its slope.
Slope is determined mathematically as "rise over run" (change in y divided change in x).
assuming slope is m
m = (y₂ - y₁) / (x₂ - x₁) = change in y / change in x
considering the formula
slope is between 0 and 1 when rise (change in y) is so smaller than run (change in x) hence the line is closer to horizontal
slope is greater than 1 then the rise is more than run, in this case the line is approaching vertical line
numbers less than zero are negative hence slope has a negative value
A horizontal line is a line that has a slope of of zero while vertical lines has its slope as infinity
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Pls help urgent someone hurry please
Proved that the triangle ABW ≅ triangle DCW
In the given question,
The length of WA = The length of WD
The measure of angle 5 = The measure of angle 7
Here we have to prove that one angle and two sides of the triangle ABW is equal to the one angle and two sides of the triangle DCW
Consider the triangle ADW,
In the triangle ADW the length of the WA is equal to the length of WD.
Therefore the measure of angle A is equal to the measure of angle D.
So in triangle ABW and the triangle DCW, one side and two angles are equal.
Therefore the triangle ABW and triangle DCW are congruent
Hence, proved that the triangle ABW ≅ triangle DCW
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Solve the absolute value equation: |6z-3|=5
The required solution of the given absolute value equation is z = 4/3 and z = 1/3.
Given that,
To solve the absolute value equation |6z-3|=5
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
Given the absolute value equation,
|6z-3|=5
Simplify,
6z - 3 = ± 5
Taking (+)
6z - 3 = 5
6z = 8
z = 4/3
Taking (-)
6z -3 = -5
z = -1/3
Thus, the required solution of the given absolute value equation is
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