The y-intercept is 1/3
Explanation:I'll assume the function is the following:
[tex]f(x)=-\frac{2}{9}x+\frac{1}{3}[/tex]
As you can see, this is the equation of a line written in Slope-intercept form. The general rule of writing lines in this form is:
[tex]y=mx+b[/tex]
Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept, which is the point at which [tex]x=0[/tex]. By comparing our function with the written rule, we can say that the y-intercept is:
[tex]\boxed{b=\frac{1}{3}}[/tex]
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Answer:
[tex]b=\frac{1}{3}[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=-\frac{2}{9}x +\frac{1}{3}[/tex]
This given function is a linear function, because its variables have one as exponent, we can also say that its variables are linear.
This function, as a linear one, it's represented as a line.
Additionally, the form of this function is called slope-intercept form as
[tex]f(x)=mx+b[/tex]
Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
So, in this case
[tex]m=-\frac{2}{9}[/tex] and [tex]b=\frac{1}{3}[/tex]
Therefore, the y-intercept of the given function is
[tex]b=\frac{1}{3}[/tex]
Suppose a ball is thrown directly upward from a height of 7 feet with an initial velocity of 50 feet per second. Use the quadratic formula or a graphing calculator to find the number of seconds it takes the ball to hit the ground. Round the nearest tenth of a second.
Answer:
t = 3.3 seconds
Step-by-step explanation:
From the formula of vertical motion of an object under gravity we can write the equation
[tex]H = ut + \frac{1}{2} gt^{2}[/tex] ....... (1)
Where u is the initial velocity (in feet per second) of throw of the object and t is time of travel in seconds and the value of g i.e. gravitational acceleration is 32 feet/sec².
Now, while a ball is thrown vertically upward with velocity 50 ft/sec from a height of 7 ft then the time of travel of the ball before reaching the ground, the equation (1) will be written as
[tex]- 7 = 50t - \frac{1}{2} \times 32 \times t^{2}[/tex]
As we have selected the upward direction as positive so, gravitational acceleration,g will be negative and as the displacement is downward by 7 feet, so it will be negative.
⇒ 16t² - 50t - 7 = 0 ........ (2)
Now, applying Sridhar Acharya formula,
[tex]t = \frac{-(-50) + \sqrt{(-50)^{2} - 4(16)(-7)}}{2(16)}[/tex] {Neglecting the negative root as t can not be negative}
⇒ t = 3.3 seconds {Rounded to the nearest tenth}
(Answer)
what is the value of x ?
Answer:
the value of x is 7cm.
Step-by-step explanation:
i looked it up on the Internet next u could try n do tht
Answer:
x=65 degrees
Step-by-step explanation:
in a triangle all angles will have to add up to 180 adding the two given you can find the third one.
What is the area of the triangle ADE in the following figure ?
Answer:
Step-by-step explanation:
Hello
Area triangle DCE :
10 x (8/2) / 2 = 10 x 4 / 2 = 20 cm^2
Area triangle ABE = Area triangle DCE
Area ABCD :
10 x 8 = 80 cm^2
Area triangle AED :
Area ABCD - 2 area DCE
= 80 - 2 x 20
= 80 - 40
= 40 cm^2
Here are two students' answers for each question. Do you agree with either of them? Explain or show your reasoning.
How many feet are traveled by a person riding once around the merry-go-round?
⚫ Clare says, "The radius of the merry-go-round is about 4 feet, so the distance around the edge is about 8π feet."
⚫ Andre says, "The diameter of the merry-go-round is about 4 feet, so the distance around the edge is about 4π feet."
Answer:
they are both correct
Step-by-step explanation:
If the radius is 4 feet like Clare says, the circumference would be 2(radius)(pi) which is 8pi.
If the diameter were 4 feet, circumference would be (diameter)(pi), which is 4pi.
-k - (-8k) combining like terms with negative coefficients
Answer:
7k
Step-by-step explanation:
Note that - (- 8k) = + 8k
Given
- k - (- 8k)
= - k + 8k
= 7k
Arlene has 1/3 as many goldfish as Isabelle. Isabelle has 5 times as many goldfish as Anaele. If Anaele has 18 goldfish, how many goldfish does Arlene have?
Answer:
30
Step-by-step explanation:
to find how many Isabelle has, we multiply Anaele's number by 5. 18(5)=90. Isabelle has 90. Arlene has one third (1/3) of the number of Isabelle. So, we divide 90 by 3. 90/3=30. Arlene has 30 goldfish
Multiply. Use the greatest common factor to write each answer in
simplest form
3/4 • 2/3
Circle O is shown. Secant A C intersects tangent C D at point C outside of the circle. Secant A C intersects circle O at point B and tangent C D intersects circle O at point D. Point E is on arc A D. Angle A C D is 57 degrees. Aaron is standing at point C, watching his friends on a Ferris wheel. He knows that he is looking up at a 57° angle and the measure of arc BD is 80°. What is the measure of arc AED?
Answer:
the answer is 194
Step-by-step explanation:
A rectangle has the width of r+3 and a length of 2r+9. What is the perimeter of the rectangle
Answer:
6r+24
Step-by-step explanation:
2(r+3)=2r+6
2(2r+9)=4r+18
(2r+6)+(4r+18)=6r+24
9 inches of rain in 72 hours as a unit rate
Answer:
Step-by-step explanation:
the unit rate of rainfall is [tex]\( \frac{1}{8} \)[/tex] inches per hour.
To find the unit rate of rainfall, which is the amount of rain per unit of time, we divide the total amount of rain by the total time.
Given:
Total amount of rain: 9 inches
Total time: 72 hours
Step 1: Divide the total amount of rain by the total time:
[tex]\[ \text{Unit rate} = \frac{\text{Total amount of rain}}{\text{Total time}} \][/tex]
[tex]\[ \text{Unit rate} = \frac{9 \text{ inches}}{72 \text{ hours}} \][/tex]
Step 2: Simplify the expression:
To simplify the unit rate, we divide 9 by 72.
[tex]\[ \text{Unit rate} = \frac{9}{72} \text{ inches per hour} \][/tex]
Step 3: Simplify the fraction:
[tex]\[ \text{Unit rate} = \frac{1}{8} \text{ inches per hour} \][/tex]
So, the unit rate of rainfall is [tex]\( \frac{1}{8} \)[/tex] inches per hour.
Evaluate the expression when m=6 and n=7
The value of the expression is : 61
Using the expression given :
n + 9mUsing the values of n and m given ;
n = 7m = 6Substituting our values into the expression ;
7 + 9(6)
7 + 54
= 61
Hence, the value of the expression is. 61
Complete Question :
Evaluate the expression n + 9m when m=6 and n=7
Which expression is equivalent to −13(6x+15)−3
The expression is equivalent to −78x − 198.
To simplify the expression −13(6x + 15) − 3, you can start by distributing the −13 across the terms inside the parentheses:
−13 * 6x = −78x
−13 * 15 = −195
So, the expression becomes:
−78x − 195 − 3
Next, combine the constant terms:
−195 − 3 = −198
The simplified expression is now:
−78x − 198
This expression is equivalent to the original expression −13(6x + 15) − 3. It cannot be further simplified as the terms are not like terms and cannot be combined further. So, the answer is −78x − 198.
The expression represents a linear equation where x is the variable. It can be used to find the value of the expression for specific values of x.
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Bonus: In Triangle STP, the measure of <T is twice the measure of <S and the
measure of <P is three times the measure of <S. What is the measure of all three angles?
ENTER ONLY NUMBERS IN THE BOXES:
m<S = degrees
m<T= degrees
m<P= degrees
Answer:
m∠S=30°
m∠T=60°
m∠P=90°
Step-by-step explanation:
we know that
The sum of the interior angles in a triangle must be equal to 180 degrees
so
In the triangle STP
m∠S+m∠T+m∠P=180° ----> equation A
m∠T=2(m∠S) ----> equation B
m∠P=3(m∠S) ----> equation C
Solve the system of equations by substitution
Substitute equation B and equation C in equation A
m∠S+2(m∠S)+3(m∠S)=180°
Solve for m∠S
6m∠S=180°
m∠S=30°
Find m∠T
m∠T=2(m∠S)
m∠T=2(30°)=60°
Find m∠P
m∠P=3(m∠S)
m∠P=3(30°)=90°
Which statement about 1.23 ÷ 0.15 is true?
The dividend should become 15.
The divisor is a whole number.
The quotient does not have a hundredths place.
Answer:
C
Step-by-step explanation:
Final answer:
This answer clarifies the true statement about the division of 1.23 by 0.15, highlighting key misconceptions about the dividend, divisor, and quotient.
Explanation:
Which statement about 1.23 ÷ 0.15 is true?
The dividend should become 15. This statement is false as the dividend after the division remains 1.23.
The divisor is a whole number. This statement is false as 0.15 is not a whole number.
The quotient does not have a hundredths place. This statement is true as the quotient after dividing 1.23 by 0.15 is 8.2, which does not have a hundredths place.
A line has a slope of 8 and includes the points (1, z) and (2,8). What is the value of z?
The value of z is zero
Step-by-step explanation:
The slope is the steepness of the line.
The formula for slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\Here\\(x_1,y_1)\ are\ the\ coordinates\ of\ first\ point\ on\ line\\(x_2,y_2)\ are\ the\ coordinates\ of\ second\ point\ on\ line[/tex]
Here
(x1,y1) = (1,z)
(x2,y2) = (2,8)
So,
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\8 = \frac{8-z}{2-1}\\8=\frac{8-z}{1}\\8-8 = -z\\z = 0[/tex]
The value of z is zero
Keywords: slope, Line
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Factor The Polynomial X2+X-6
Answer:
C) (x-2)(x+3)
Step-by-step explanation:
x^2+x-6=(x-2)(x+3)
Because (x-2)(x+3)=x^2-2x+3x-6=x^2+x-6.
Final answer:
The polynomial x² + x - 6 factors to (x + 3)(x - 2) by finding two numbers that multiply to -6 and add to 1.
Explanation:
To factor the polynomial x² + x - 6, one needs to find two numbers that multiply to -6 (the constant term) and add up to 1 (the coefficient of the middle term, x). These numbers are 3 and -2, because 3 × (-2) = -6, and 3 + (-2) = 1. Therefore, the factored form of the polynomial is (x + 3)(x - 2).
A company has 200 machines. Each machine has 12% probability of not working.
If you were to pick 40 machines randomly, the probability that 5 would not be working is ____ , the probability that all would be working is____, and the probability that at least one machine would be working is______
Using probability and binomial distribution, we determined that the probability of exactly 5 out of 40 machines not working is approximately 0.18. The probability that all machines are working is around 0.024, and the probability that at least one machine is working is almost certain, approximately 1.
To address this problem, we will use the concepts of probability and the binomial distribution.
Calculating the Probabilities:
Let’s denote the probability of a single machine not working as p = 0.12. The probability of a single machine working is q = 1 - p = 0.88.
1. Probability that exactly 5 out of 40 machines are not working
We can use the binomial distribution formula:
P(X = 5) = C(40, 5) * p^5 * q^(40-5)
Where C(40, 5) is the number of combinations of 40 machines taken 5 at a time.
C(40, 5) = 40! / [5!(40-5)!] = 658,008
Therefore:
P(X = 5) = 658,008 * (0.12)^5 * (0.88)^35 ≈ 0.18 (using a calculator for binomial probability)
2. Probability that all 40 machines are working
This can be found by raising the probability of one machine working to the power of 40:
P(all working) = q^40 = 0.88^40 ≈ 0.024
3. Probability that at least one machine is working
The easiest way to calculate this is to find the complement of the probability that none are working and subtract it from 1:
P(none working) = p^40 = (0.12)^40 ≈ 9.0949 x 10^-38 (which is extremely close to 0)
P(at least one working) = 1 - P(none working) ≈ 1 - 0 = 1
Final answer: A company has 200 machines. Each machine has 12% probability of not working. If you were to pick 40 machines randomly, the probability that 5 would not be working is _0.18_ , the probability that all would be working is_0.024_, and the probability that at least one machine would be working is_1_.
Complete question:
A company has 200 machines. Each machine has 12% probability of not working. If you were to pick 40 machines randomly, the probability that 5 would not be working is ____ , the probability that all would be working is____, and the probability that at least one machine would be working is______
If you were to pick 40 machines randomly, the probability that 5 would not be working is 0.186 , the probability that all would be working is 0.011, and the probability that at least one machine would be working is 0.989.
This problem involves probability calculations for a company that has 200 machines, each with a 12% chance of not working. Let's break down the calculations step-by-step:
1. Probability that 5 out of 40 machines are not working:
This can be modeled using the binomial distribution. The binomial formula is:
[tex]P(X = k) = C(n, k) \times p^k \times (1-p)^{(n-k)[/tex]
where:
n = number of trials (40 machines)k = number of successes (5 machines not working)p = probability of success (0.12)C(n, k) = binomial coefficient (number of ways to choose k successes in n trials)For our problem, it becomes:
P(X = 5) = C(40, 5) × (0.12)⁵ × (0.88)³⁵
= 0.186
2. Probability that all 40 machines are working:
This is calculated using the complement probability as follows:
P(All working) = (0.88)⁴⁰
≈ 0.011
3. Probability that at least one machine is working:
This can be calculated using the complement rule:
P(At least one working) = 1 - P(None working)
= 1 - (0.88)⁴⁰
≈ 0.989
bob bought bill an item that cost 193. bill gave him 200. bob then took 100 out of the 200 to buy bill an item for 93. how much does bill owe Bob totally?
Answer:Bob Owes $186 to the store he purchased an item at
Step-by-step explanation:
Circle A has been dissected into 16 congruent sectors. The base of one sector is 1.56 units, and it's height is 3.92 units. what is the approximate area of circle A?
Answer:
48.92
Step-by-step explanation:
A= (1/2)(b)(h)
A=(1/2)(1.56)(3.92)=3.0576
A=(3.0567)(16)=48.9216
A=48.92
The approximate area of Circle A can be found by understanding that the base of a sector is part of the circumference, and using the radius (height) value of 3.92 units in the area formula A = πr². Accounting for significant figures, the area of Circle A is approximately 48 units².
Explanation:To find the approximate area of Circle A, we need to understand that the base of a sector, which is a part of the circumference of the circle, is close to the length of the arc for a small sector. By dissecting the circle into 16 congruent sectors, each sector represents 1/16 of the circle's full circumference. Since the base of one sector is given as 1.56 units, if we multiply this by 16, we would have the total circumference of the circle. However, the value provided for the 'height' is indeed the radius of the whole circle, which is 3.92 units. The area of a circle is calculated using the formula A = πr².
Using the radius (3.92 units), we can calculate the area:
A = π * (3.92 units)²
A = 3.1415927 * 15.3664 units²
A = 48.2544695988 units²
Considering the significant figures provided in the question, we should limit the calculated area of the circle to two significant figures, matching the least number of significant figures we were originally given, which were in the radius measurement. Therefore, the approximate area of Circle A is:
A = 48 units²
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Can the sides of a triangle have lengths 3, 3, and 10?
Answer:
No
Step-by-step explanation:
According to the property of the triangle ,
sum of any two sides should we greater then third side of the triangle.
Here, Measurement of three sides are given as 3,3,5 .
So, sum of the measurement of first two sides is 6.
And third side equals 10.
Clearly 6 is less than 10. So . it violates the property sum of any two sides should we greater then third side of the triangle.
Thus , Sides of a triangle can't be 3,3,10.
Answer:
Yes
Step-by-step explanation:
As long as there are three sides and it forms a triangle, the answer is yes.
Find the solution for 72 < 7x − 5.
1 x < -11
2 x > 11
3 x > 21
4 x < 11
Answer:
Option 2. [tex]x > 11[/tex]
Step-by-step explanation:
we have
[tex]72 < 7x-5[/tex]
Solve the inequality for x
Adds 5 both sides
[tex]72+5 < 7x-5+5[/tex]
[tex]77 < 7x[/tex]
Divide by 7 both sides
[tex]77/7 < 7x/7[/tex]
[tex]11 < x[/tex]
Rewrite
[tex]x > 11[/tex]
PLEASEEEE HELPPPP
What is the y-coordinate?
The x-coordinate of the intersection point of BD and CE IS
2(a+c)
l.y=[*2]x-( 206 )
2.y=[22] 260701)-(2014
3. y = (a 2Jl 2(4+0) )-(2 626)
4. y = 2b(Q+c) -6bc
3(-20)
5, y = 2ab +2bc-6bc
3(2-2)
Answer: 2b/3 (second answer choice)
======================================
Explanation:
The work shown on the screenshot basically shows plugging x = 2(a+c)/3 into the y(x) function and then simplifying. Step 5 isnt fully simplified, so let's combine like terms, factor, and then divide out a pair of (a-2c) terms to get the following:
y = (2ab+2bc-6bc)/(3(a-2c))
y = (2ab-4bc)/(3(a-2c))
y = (2b*a-2b*2c)/(3(a-2c))
y = 2b(a-2c)/(3(a-2c))
y = 2b/3
ok, i need to determine if it can be written as a fraction. Then state the reason.
Answer:
a) YES. Repeating decimal
b) YES. Repeating decimal
c) NO. Decimal neither terminates nor repeats
d) YES. Terminating decimal
Step-by-step explanation:
Any rational number can be written as a fraction, that is, a division of integers.
a) The number [tex]\overline{0.54}[/tex] has a repetitive period of 54. It can be expressed as a fraction because its decimal are repeating forever
b) The number 0.16666... (expressed as a repeating 6) can also be converted to a fraction because it's a repeating decimal
c) The number 0.5473... cannot be expressed as a fraction because the ellipsis (...) means the decimals continue with no limit and no pattern can be found (no repetitive decimal)
d) The number 0.378 can be easily expressed as a fraction because it has a finite number of decimals (no ellipsis) or a terminating decimal
Which of the following is the greatest number?
A. 1.3 * 105
B. 9.8 * 102
C. 9.6 * 104
D. 4.6 * 10-5
Answer:
The greatest number is A. 1.3 * 10⁵
Step-by-step explanation:
Let's find the greatest number:
Option A : 1.3 * 10⁵ = 1.3 * 100,000 = 130,000
Option B : 9.8 * 10² = 9.8 * 100 = 980
Option C : 9.6 * 10⁴ = 9.6 * 10,000 = 96,000
Option D : 4.6 * 10⁻⁵ = 4.6 * 0.00001 = 0.000046
130,000 > 96,000 > 980 > 0.000046
The greatest number is A. 1.3 * 10⁵
4. Tickets for a matinee are $5 for children and $8 for adults. The theater sold a total of 142 tickets for one matince Ticket
sales were $890. How many of each type of ticket did the theater sell?
System of equations:
The theater sold 82 children tickets and 60 adult tickets.
Step-by-step explanation:
No. of tickets sold = 142
Total sales = $890
Cost of one child ticket = $5
Cost of one adult ticket = $8
Let,
x be the number of children tickets
y be the number of adult tickets
According to given statement;
x+y=142 Eqn 1
5x+8y=890 Eqn 2
Multiplying Eqn 1 by 5
[tex]5(x+y=142)\\5x+5y=710\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](5x+8y)-(5x+5y)=890-710\\5x+8y-5x-5y=180\\3y=180[/tex]
Dividing both sides by 3
[tex]\frac{3y}{3}=\frac{180}{3}\\y=60[/tex]
Putting =60 in Eqn 1
[tex]x+60=142\\x=142-60\\x=82[/tex]
The theater sold 82 children tickets and 60 adult tickets.
Keywords: linear equations, subtraction
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A rectangle has a length of 28 meters less than 7 times its width. If the area of the rectangle is 9555 square meters, find the length of the rectangle.
Answer:
7 meters
Step-by-step explanation:
Assume that the length is l and the width is w. Therefore, l is equal to 7 times its width (7*w) minus 28, or l=7*w-28. As we know that w*l = area = 9555, we can plug our value for l in to limit our equation to 1 variable, resulting in w*(7*w-28) = 9555. Adding 28 to both sides to separate the 7w (because we want to solve for that), we get 9583=7w. Then, to solve for the width, we can divide both sides by 7 to get that 9583/7=1369=w. Plugging that back into the formula that w*l=area, we get that 1369*l=9583 -- dividing 1369 from both sides to separate l, we get that l=7.
To find the length of a rectangle where the area is 9555 square meters and the length is 28 meters less than 7 times its width, express the length in terms of the width, use the area to form a quadratic equation, solve for the width, and substitute it back to find the length.
Explanation:To find the length of the rectangle when the area is 9555 square meters and the length is 28 meters less than 7 times its width, let's denote the width of the rectangle as w and the length as l. According to the problem, the length l can be expressed as l = 7w - 28. The area of a rectangle is the product of its length and width, which gives us the equation w × (7w - 28) = 9555.
To find the value of w, we need to solve the quadratic equation 7w2 - 28w - 9555 = 0. Factoring or using the quadratic formula leads to the width, and substituting this back into l = 7w - 28 gives us the length of the rectangle. In solving, ensure to discard the negative value of w as a width cannot be negative.
Once we calculate the width w, the length is found by multiplying it by 7 and then subtracting 28. This process will provide the final length of the rectangle.
find a positive real number such that its square is equal to 15 times the number increased by 286
Answer:
The positive real number is 26
Step-by-step explanation:
Let
x ----> the number
we know that
The algebraic expression that represent this problem is
[tex]x^{2} =15x+286[/tex]
so
[tex]x^{2}-15x-286=0[/tex]
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2}-15x-286=0[/tex]
so
[tex]a=1\\b=-15\\c=-286[/tex]
substitute in the formula
[tex]x=\frac{-(-15)(+/-)\sqrt{-15^{2}-4(1)(-286)}} {2(1)}[/tex]
[tex]x=\frac{15(+/-)\sqrt{1,369}} {2}[/tex]
[tex]x=\frac{15(+/-)37}{2}[/tex]
[tex]x_1=\frac{15(+)37}{2}=26[/tex]
[tex]x_2=\frac{15(-)37}{2}=-11[/tex] ---> the solution cannot be negative
therefore
The positive real number is 26
Which of the following numbers can be expressed as repeating decimals? (5 points) 5 over 7 , 4 over 5 , 7 over 9 , 5 over 8
Answer:
5 over 7 and 7 over 9
Step-by-step explanation:
Answer:
5 over 7 and 7 over 9 is the answer 0w0
Citizens less than 18 years old are not allowed to vote define a variable and write an inequality for the ages of citizens who are not allowed to vote
Answer:
[tex]x < 18[/tex]
Step-by-step explanation:
We are given the following information in the question:
"Citizens less than 18 years old are not allowed to vote"
We define a variable x such that x represents the age of citizens.
We have to write a relationship with the help of an inequality for the ages of citizens who are not allowed to vote.
Citizens less than 18 are not allowed to vote.
So x should be less than 18.
This can be written as:
[tex]x < 18[/tex]
is the required inequality for the ages of citizens who are not allowed to vote.
Which graph represents the function f(x)=2⋅4x ?
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]f(x)=2(4^x)[/tex]
This is a exponential function of the form
[tex]f(x)=a(b^x)[/tex]
where
a is the initial value
b is the base
r is the rate
b=(1+r)
In this problem we have
[tex]a=2\\b=4\\r=b-1=4-1=3=300\%[/tex]
For x=0
[tex]f(0)=2(4^0)[/tex] -----> [tex]f(0)=2[/tex] ---> y-intercept or initial value
For x=1
[tex]f(1)=2(4^1)[/tex] -----> [tex]f(1)=8[/tex]
Identify the graph
using a graphing tool
The graph in the attached figure