To find the angle ∠KL, knowing m∠KJL = 27°, it is essential to apply the properties of tangents and circles.
The angle ∠KJL can be determined using the properties of tangents and circles. Since JK is a tangent to circle C, we know that angle ∠KJL is equal to half of the intercepted arc KL. Therefore, if m∠KJL = 27°, then m∠KL = 2 × 27° = 54°.
Suppose the dial on the spinner is spun 2 times in a row.
X is the number of times the dial lands on region A or B.
Which table represents the probability distribution for the variable X?
Step-by-step explanation:
A, B, and C have the same area. So P(A) = 1/3 and P(B) = 1/3, which means P(A or B) = 2/3.
P(success) = 2/3 and P(failure) = 1/3.
The probability of 2 failures is:
P = (1/3)² = 1/9
The probability of 2 successes is:
P = (2/3)²= 4/9
The probability of 1 success and 1 failure can be found either with binomial probability, or simply by subtracting the probabilities we found earlier from 1.
P = 1 - 1/9 - 4/9
P = 4/9
So the answer is the one in the bottom left corner.
Answer: C
X P
0 1/9
1 4/9
2 4/9
Step-by-step explanation:
Screenshot provided
Joel is looking at cost for using a gym. He could pay $50 per month for unlimited use or he could pay $12 per month plus $4 visit. How many visits would he have to make each month to make each month to make the $50 per month unlimited use option the cheapest one?
He would have to make 10 visits at the ($12 per month + $4 each visit) gym to make the ($50 per month for unlimited visits) gym the cheapest option.
Explanation:
12 + (4 x 10) =
12 + (40) = $52
Answer:
He would have to use it more than 10 times in the month.
Step-by-step explanation:
4x+12>50
4x=38
x> 9.5
4(10)+12>50
52>50
Samantha sends her son, Barry, to a preschool center on certain days. The cost of preschool is $45 per day along with a fixed monthly charge of $70. Last month, Samantha paid a total of $880 to the preschool center. Let d represent the number of days Barry spent at the preschool center last month. Which equation represents this situation, and how many days did Barry attend preschool last month?
A. 880 = 90d + 45; 9 days
B. 880 = 70d - 45; 21 days
C. 810 = 45d; 19 days
D. 880 = 45d + 70; 18 days
Answer: Option D
D. [tex]880 = 45d + 70[/tex]; [tex]18\ days[/tex]
Step-by-step explanation:
We know that the cost of preschool is $ 45 per day plus a monthly fee of $ 70.
We also know that a total of $ 880 was paid last month
To write an equation that represents this situation, let us call "d" the number of days that Barry attends school
So the cost was:
[tex]45d + 70 = 880[/tex]
Now we solve the equation for the variable d
[tex]45d= 880-70[/tex]
[tex]d= \frac{810}{45}[/tex]
[tex]d= 18\ days[/tex]
Therefore answer is the option D
A bacteria culture is doubling in size of every day. If the bacteria culture starts at 5,200, write an equation for its population size,p, as a function of the number of days ,d, since it started
The answer is:
The equation is:
[tex]Total(t)=5200*(2)^{t}[/tex]
Why?It's an exponential growth problem, we can calculate the exponential growth using the following equation:
[tex]Total(t)=StartPopulation*(1+r)^{\frac{t}{2}}[/tex]
Where,
Total, is the total population after "t" time in days.
Start population, for this is equal to 5,200
r,is equal to the percent of growth, for this case it's 100% each day.
t, is the time elapsed.
So, rewriting the equation, we have:
[tex]Total(t)=5200*(1+\frac{100}{100})^{t}[/tex]
[tex]Total(t)=5200*(1+1)^{t}[/tex]
[tex]Total(t)=5200*(2)^{t}[/tex]
Have a nice day!
Use technology or a z-score table to answer the question.
The expression P(z < 2.87) represents the area under the standard normal curve below a given value of z.
What is P(z < 2.87)?
A. 0.0021
B. 0.0027
C. 0.9973
D. 0.9979
Answer:
D
Step-by-step explanation:
I usually use a z-score table, but you can do this with a calculator.
If we go to a z-score table, we first look up the first two digits (in this case, 2.8) in the far left column. Then we find the hundredths digit in the top row (0.07). Where they intersect is P(z < 2.87).
P(z < 2.87) = 0.9979
Answer D.
Using the normal distribution, it is found that the correct option regarding P(z < 2.87) is given by:
D. 0.9979
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Hence, P(z < 2.87) is the p-value of Z = 2.87, which is of 0.9979, hence option D is correct.
More can be learned about the normal distribution at https://brainly.com/question/24663213
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Two cards are drawn in a row without replacement. What is the probability of drawing three pink cards?
a) 1/30
b) 2/15
c) 6/45
d) 2/9
None of the above (0)
Only two cards are drawn, so it is impossible for three of them to be pink.
If you meant to type that two of them were pink cards, then the answer is B. 2/15
First, find the probability of drawing a pink card first. There are 10 cards, and 4 of them are pink, so the probability is 4/10, which can be simplified to 2/5.
Now find the probability for the second card to be pink. There are now 9 cards, and 3 of them are pink, so the probability is 3/9, or 1/3.
Finally, multiply the probabilities together. First, multiply the numerators together. 2 * 1 = 2. Now, multiply the denominators together. 5 * 3 = 15. So, the final probability is 2/15
The graph of y=cos x is transformed to y=a cos(x−c)+d by a vertical expansion by a factor of 3, then translated π/2 units left and 2 units up. The new equation is:
y = 3 cos (x + π/2) + 2
y = 1/3 cos (x - π/2) + 2
y = 3 cos (x - π/2) - 2
y = 3 cos (x - π/2) + 2
Answer:
y = 3 cos (x + π/2) + 2
Step-by-step explanation:
The transformed equation of y = Cos x is y=a cos(x−c)+d
Where
a is the amplitude. (if a > 1 we have vertical stretch/compression of factor a)if function is translated c units left, it will be +c and if c units right, it will be -cd is the vertical shift. If +d, then it is translated d units up and if -d, it is translated d units downKeeping these points in mind, the correct equation should have a = 3, c = + π/2, and d = +2
So we can write:
y = 3 cos (x + π/2) + 2
first answer choice is right.
The function F is defined by F(x)= 12 x + 1 2 . Use this formula to find the following values of the function:
F(3)
F(-12)
F(1/3)
F(3/4)
F(k)
F(a/2)
F(x-1)
F(x+h)
Just solving for one of these would be really helpful!
Answer:
Step-by-step explanation:
I will assume that you meant F(x)= 12x + 12. If you meant a fraction, write 1/2.
Then F(3) = 12(3) + 12 = 48
F(-12) = 12(-12) + 12 = -132.
F(1/3) = 12(1/3) + 12 = 4 + 12 = 16
Please verify what you meant. Then I will answer the remaining questions.
[tex]\(F(3) = 48\), \(F(-12) = -132\), \(F\left(\frac{1}{3}\right) = 16\), \(F\left(\frac{3}{4}\right) = 21\), \(F(x) = 12x + 12\).[/tex]
To find the values of the function [tex]\(F(x) = 12x + 12\)[/tex] for the given inputs:
1. F(3): Substitute x = 3 into the function: F(3) = 12(3) + 12 = 36 + 12 = 48.
2. F(-12): Substitute x = -12 into the function: F(-12) = 12(-12) + 12 = -144 + 12 = -132.
3. [tex]\(F\left(\frac{1}{3}\right)\)[/tex]: Substitute [tex]\(x = \frac{1}{3}\)[/tex] into the function: [tex]\(F\left(\frac{1}{3}\right) = 12\left(\frac{1}{3}\right) + 12 = 4 + 12 = 16\).[/tex]
4. [tex]\(F\left(\frac{3}{4}\right)\)[/tex]: Substitute [tex]\(x = \frac{3}{4}\)[/tex] into the function: [tex]\(F\left(\frac{3}{4}\right) = 12\left(\frac{3}{4}\right) + 12 = 9 + 12 = 21\).[/tex]
5. F(k): Substitute x = k into the function: F(k) = 12k + 12.
6. [tex]\(F\left(\frac{a}{2}\right)\)[/tex]: Substitute [tex]\(x = \frac{a}{2}\)[/tex] into the function: [tex]\(F\left(\frac{a}{2}\right) = 12\left(\frac{a}{2}\right) + 12 = 6a + 12\).[/tex]
7. F(x-1): Substitute x = x-1 into the function: F(x-1) = 12(x-1) + 12 = 12x - 12 + 12 = 12x.
8. F(x+h): Substitute x = x+h into the function: F(x+h) = 12(x+h) + 12 = 12x + 12h + 12.
These are the values of the function for the given inputs.
40 points (i know it says 20 pts but i gave 40) ! SHOW WORK PLEASE, I need answers soon!
Use the quadratic formula to solve 2x^2=5x+6. Im sure the answer is -2x-6, but I need someone to help me double check.
Answer:
[tex]\large\boxed{x=\dfrac{5-\sqrt{73}}{4}\ or\ x=\dfrac{5+\sqrt{73}}{4}}[/tex]
Step-by-step explanation:
[tex]\text{The quadratic formula for}\ ax^2+bx+c=0\\\\\text{If}\ b^2-4ac>0,\ \text{then the equation has two different solutiions:}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\text{If}\ b^2-4ac=0,\ \text{then the equation has one solution:}\ x=\dfrac{-b}{2a}\\\\\text{If}\ b^2-4ac<0,\ \text{then the equation has no solution.}[/tex]
[tex]\text{We have}\ 2x^2=5x+6.\ \text{Convert to the form of}\ ax^2+bx+c=0:\\\\2x^2=5x+6\qquad\text{subtract}\ 5x\ \text{and}\ 6\ \text{from both sides}\\\\2x^2-5x-6=0\\\\a=2,\ b=-5,\ c=-6\\\\b^2-4ac=(-5)^2-4(2)(-6)=25+48=73>0\\\\x=\dfrac{-(-5)\pm\sqrt{73}}{2(2)}=\dfrac{5\pm\sqrt{73}}{4}[/tex]
On Saturday, Carrie went to the store and bought 4 loaves of bread and 1 gallon of milk for a total of $12.50. The next weekend, she went to the same store and spent 11.50 on 2 loaves of bread and 2 gallons of milk. The prices had not changed. What is the price for 1 gallon of milk
Answer:
The price of one gallon of milk is $3.5
Step-by-step explanation:
Let
x----> the price of one loaves of bread
y----> the price of one gallon of milk
we know that
4x+y=12.50 ----> equation A
2x+2y=11.50 ----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (2.25,3.5)
see the attached figure
therefore
The price of one loaves of bread is $2.25
The price of one gallon of milk is $3.5
4. What is the area of the scalene triangle shown (ABC), if AO = 10 cm, CO = 2 cm, BC = 5 cm, and AB = 12.20 cm? (Triangle AOB is a right triangle.)
60.0 is the area of the triangle
A rectangular prism has length 14 cm, width 3.4 cm, and height 11.6 cm. Identify the volume of the prism to the nearest tenth. HELP PLEASE!!
Answer:
552.16 cm^3
Step-by-step explanation:
Just multiply the lenght together.
The volume of the rectangular prism is approximately 552.16 cubic cm.
To find the volume of a rectangular prism, you need to multiply its length, width, and height.
Given that the length is 14 cm, the width is 3.4 cm, and the height is 11.6 cm, we can calculate the volume as follows:
Volume of a rectangular prism = Length × Width × Height
Volume of a rectangular prism = 14 cm × 3.4 cm × 11.6 cm
Volume of a rectangular prism ≈ 552.16 cm³ (rounded to the nearest tenth)
Therefore, the volume of the rectangular prism is approximately 552.16 cubic cm.
Learn more about the volume here:
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Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, negative 2, and 2
Which of the following functions best represents the graph?
f(x) = x3 + x2 − 4x − 4
f(x) = x3 + x2 − x − 1
f(x) = x3 + 3x2 − 4x − 12
f(x) = x3 + 2x2 − 6x − 12
Answer:
f(x) = x3 + 3x2 − 4x − 12
Step-by-step explanation:
A polynomial which falls tot he left and rises to the right is a function with a positive leading coefficient. Its formed by the x-intercepts or zeros x = -3, -2 and 2. The zeros form the factors (x+3)(x+2)(x-2). Multiply the factors using the distributive property to find the function in standard form.
(x+3)(x+2)(x-2)
(x^2 + 3x + 2x + 6)(x-2)
(x^2 + 5x + 6)(x-2)
x^3 + 5x^2 + 6x -2x^2 - 10x - 12
x^3 + 3x^2 - 4x - 12
A triangle has a base of 9 inches and a height of 8 inches. What is the area of the triangle?
72 square inches
36 square inches
18 square inches
17 square inches
Answer: Option B
Step-by-step explanation: If You Found The Area Of The Triangle You Would Get An Answer Of 36 Square Inches. Have A Great Day!
The area of a triangle with a base of 9 inches and a height of 8 inches is found using the formula A = ½ × base × height, resulting in 36 square inches.
Explanation:To find the area of a triangle, the formula A = ½ × base × height is used, where A represents the area, base is the length of the base of the triangle, and height is the measure from the base to the opposite vertex at a right angle. In this instance, the base of the triangle is 9 inches and the height is 8 inches. By plugging these values into the formula, you get the following calculation:
A = ½ × 9 in × 8 in = ½ × 72 in² = 36 in²
Therefore, the area of the triangle is 36 square inches.
If ΔABC is reflected across the y axis what are the coordinates of C?
A. (3, -5)
B. (5, -3)
C. (-3, -5)
D. (-5, 3)
Answer:
D
Step-by-step explanation:
The reflection across the y-axis has the rule:
(x,y)→(-x,y).
So, the vertices of the triangle ABC after reflection across the y-axis will have coordinates:
A(1,3)→A'(-1,3);B(3,6)→B'(-3,6);C(5,3)→C'(-5,3).Hence, correct option is D
Answer:
d (-5,3)
Step-by-step explanation:
just flip it over to the other side.
HALP PLEASE NEED HALP, ASAP??
Answer:
5
Step-by-step explanation:
since -4 *-2 = 8 and -8+8=0
0*-2=0
0+5=5
Mike has a collection of 16 antique tin toys, including 2 airplanes. If Mike randomly selects a toy, what is the probability it will be an airplane? (Write the probability as a fraction in simplest form) A) 1 2 B) 1 4 C) 1 8 D) 1 16
Answer:
C. 1/8
Step-by-step explanation:
This is because the number two goes into sixteen eight times. This is the simplest form of the fraction.
To determine whether the inverse of a function is a function you can perform the horizontal line test.
true or false
Answer:
[tex]\boxed{\text{TRUE}}[/tex]
Step-by-step explanation:
If a horizontal line intersects the graph of a function in all places at exactly one point (the horizontal line test), the inverse of the function is also a function.
For example, the inverse of a hyperbola (like ƒ(x) =1/x) is a function, because every horizontal line intersects with the graph at exactly one point.
However, the inverse of a parabola (like ƒ(x) = x²) is not a function, because a horizontal line intersects with the graph at two points.
Please explain btw you can use symbols to use things like √ ² ³
Answer:
the correct solution is letter A.
Step-by-step explanation:
We have the following expression:
6sqrt(7) - 5x*sqrt(7) - x*sqrt(7)
Grouping the expression, we have:
=sqrt(7)*[6 - 5x - x]
=sqrt(7)*[6 - 6x]
= 6*sqrt(7)- 6x*sqrt(7)
So the correct solution is letter A.
What is the length of BC¯¯¯¯¯ ?
Enter your answer in the box.
units
Answer:
Just finished test answer is 17
Step-by-step explanation:
The length of the side BC of the triangle ABC will be 17 units.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The two triangular legs and their opposing angles are congruent in an isosceles triangle.
The triangle is an isosceles triangle. Then the side AB is equal to the side AC. Then the value of 'x' is given as,
AB = AC
2x - 8 = x + 9
2x - x = 8 + 9
x = 17
The length of the side BC of the triangle ABC will be 17 units.
More about the triangle link is given below.
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64 POINTS AWARDED, PLEASE ANSWER ASAP!!!!!
What is the area of a rectangle with vertices at (7, 3), (12, 3), (12, 11), and (7, 11)?
Answer:
40 units^2
Step-by-step explanation:
This is because your figure has a height of 8 and a width of 5. 8*5=40 so there u go! Please mark brainliest
Answer:
Area of rectangle = 40 square units
Step-by-step explanation:
Points to remember
Distance formula
Length of a line segment with end points (x₁, y₁) and (x₂, y₂) is given by,
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Area of rectangle = Length * Breadth
To find the length and breadth
Here a rectangle with vertices at (7, 3), (12, 3), (12, 11), and (7, 11)
Length1 = √[(x₂ - x₁)² + (y₂ - y₁)²]
√[(12 - 7)² + (3 - 3)²] = √5² = 5
Length2 = √[(x₂ - x₁)² + (y₂ - y₁)²]
√[(12 - 12)² + (11 - 3)²] = √8² = 8 units
Therefore Length of rectangle = 8 and
Breadth of rectangle = 5 units
To find the area of rectangle
Area = Length * Breadth
= 8 * 5 = 40 square units
Cameron 's book log shows he read a total of 1 1/2 hours each week for 4 weeks. How many total minutes did he read?
Answer:
360 minutes
Step-by-step explanation:
(1.5 h/wk)·(4 wk)·(60 min/h) = 1.5·4·60 min = 360 min
Multiply reading time per week by the number of weeks to get reading time. Multiply the number of hours by the number of minutes in an hour to get minutes.
Verify the equation below with each of the values listed for z to find a solution . 3-2z=1/10
For this case we have the following equation:
[tex]3-2z = \frac {1} {10}[/tex]
We must find the value of z that represents the solution of the equation:
We follow the steps below:
We multiply by 10 on both sides of the equation:
[tex]10 (3-2z) = 1[/tex]
We apply distributive property to the terms of parentheses;
[tex]30-20z = 1[/tex]
We subtract 30 from both sides of the equation:
[tex]-20z = 1-30\\-20z = -29[/tex]
We divide between -20 on both sides of the equation:
[tex]z = \frac {-29} {- 20}\\z = \frac {29} {20}\\z = 1.45[/tex]
If we substitute the value of z in the original equation, equality is satisfied.
Answer:
[tex]z = 1.45[/tex]
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
A spinner has five equal sections that are numbered 1 through 5.
In which distributions does the variable X have a binomial distribution?
Select EACH correct answer.
When the spinner is spun three times, X is the sum of the numbers the spinner lands on.
When the spinner is spun multiple times, X is the number of spins until it lands on 5.
When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.
When the spinner is spun five times, X is the number of times the spinner lands on 1.
Answer: C & D
Step-by-step explanation:
A binomial experiment must satisfy ALL four of the following:
A fixed number of trials Each trial is independent of the others There are only two outcomes (Success & Fail) The probability of each outcome remains constant from trial to trial.A) When the spinner is spun three times, X is the sum of the numbers the spinner lands on.
→ #3 is not satisfied (#4 is also not satisfied)
B) When the spinner is spun multiple times ...
→ #1 is not satisfied
C) When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.
→ Satisfies ALL FOUR
A fixed number of trials = 4 Each trial is independent of the others = each spin is separate There are only two outcomes = Not Odd & Odd The probability of each outcome remains constant from trial to trial = P(X = not odd) = 0.50 for each spinD) When the spinner is spun five times, X is the number of times the spinner lands on 1.
→ Satisfies ALL FOUR
A fixed number of trials = 5 Each trial is independent of the others = each spin is separate There are only two outcomes = 1 & Not 1 The probability of each outcome remains constant from trial to trial = P(X = 1) = 0.17 for each spinIn the triangle below, 8/15 represents which ratio?
tanB
tanC
sinB
cosC
Answer:
tan(B)
Step-by-step explanation:
we know that
The tangent of an angle is equal to divide the opposite side to the angle by the adjacent side to the angle
In this problem
tan(B)=AC/AB
substitute
tan(B)=8/15
URGENT MATH HELP!! WILL MARK BRAINLIEST!! GIVING 25 POINTS!!
CORRECT ANSWERS ONLY!!!
Question 1
A cooking show currently has about 223,000 regular viewers. The number of regular viewers has been decreasing at a rate of 4.7% per year.
Which is the best prediction for the number of regular viewers the show will have in 6 years?
Question 1 options:
35,420
37,167
104,810
167,056
Question 2 (3 points)
A population of 30,000 fish is expected to shrink at a rate of 7.5% per year.
Which is the best prediction for the fish population in 8 years?
Question 2 options:
2813
3469
16,079
27,750
Question 3 (3 points)
Bromine-82 has a half-life of about 35 hours.
After 140 hours, how many milliliters of an 80 mL sample will remain?
Question 3 options:
65 mL
20 mL
10 mL
5 mL
Question 4 (3 points)
Polonium-218 has a half-life of about 3 minutes.
After 15 minutes, how many milligrams of a 120 mg sample will remain?
Question 4 options:
1.875 mg
3.75 mg
4.8 mg
7.5 mg
Question 8 (3 points)
Pippa is holding the end of her kite string 1.4 m above the ground. The kite string rises at a 63° angle of elevation. Pippa has let out all 75 m of string.
To the nearest tenth of a meter, how high above the ground is the kite?
Question 8 options:
34.0 m
35.4 m
66.8 m
68.2 m
Question 9 (3 points)
Using his telescope, Tommy watches a bald eagle as it sits on the top of a cliff. The telescope is positioned so that the line of sight to the eagle forms a 38° angle of elevation. The telescope sits 1.3 m above the ground and the base of the telescope is 116 m from the base of the cliff.
To the nearest tenth of a meter, how high above the ground is the eagle?
Question 9 options:
90.6 m
91.9 m
148.5 m
149.8 m
Question 10 (3 points)
A photographer's camera sits on a tripod that is 1.8 m above the ground. The base of the tripod is 44 m from the base of a tree. The photographer spots a woodpecker in the tree at a 39° angle of elevation.
To the nearest tenth of a meter, how high above the ground is the woodpecker?
Question 10 options:
37.4 m
36.0 m
35.6 m
34.2 m
The best prediction for the fish population is 16,079.
Hello i hope you are having a good day :)
Question 1 : A cooking show currently has about 223,000 regular viewers. The number of regular viewers has been decreasing at a rate of 4.7% per year. Which is the best prediction for the number of regular viewers the show will have in 6 years? = y = 223000(1-0.047)⁶ = 223000(0.953)⁶ = 167,056.
Question 2 : A population of 30,000 fish is expected to shrink at a rate of 7.5% per year. Which is the best prediction for the fish population in 8 years? = 30,000(1−7.5/100)8≈ 16078.9
Question 3 : Bromine-82 has a half-life of about 35 hours. After 140 hours, how many millilitres of an 80 ml sample will remain? = Divide 80(1/2)^4 to get 5.
Question 4 : Polonium-218 has a half-life of about 3 minutes. After 15 minutes, how many milligrams of a 120 mg sample will remain? = 3.75 mg
Question 8 : Pippa is holding the end of her kite string 1.4 m above the ground. The kite string rises at a 63° angle of elevation. Pippa has let out all 75 m of string. To the nearest tenth of a meter, how high above the ground is the kite? = 68.2 m
Question 9 : Using his telescope, Tommy watches a bald eagle as it sits on the top of a cliff. The telescope is positioned so that the line of sight to the eagle forms a 38° angle of elevation. The telescope sits 1.3 m above the ground and the base of the telescope is 116 m from the base of the cliff. To the nearest tenth of a meter, how high above the ground is the eagle? = 91.9 m
Question 10 : A photographer's camera sits on a tripod that is 1.8 m above the ground. The base of the tripod is 44 m from the base of a tree. The photographer spots a woodpecker in the tree at a 39° angle of elevation. To the nearest tenth of a meter, how high above the ground is the woodpecker? = 37.4 m
For the function below, state the x-coordinate of the x-intercept that is located to the fight of the origin.
[tex]f(x)=x^3-9x[/tex]
Answer:
x = 3
Step-by-step explanation:
It should NOT be "fight of the origin", rather "right of the origin".
Now let's move on to solve the question...
The x-intercept is found by setting the function equal to 0. Thus:
0 = x^3 - 9x
Let's solve this using algebra:
[tex]0=x^3-9x\\0=x(x^2-9)\\0=x(x-3)(x+3)[/tex]
Hence, x = -3 and x = 3
The coordinate that is to the right of the origin is the positive one, so x = 3 is the x-intercept we are looking for.
Eric is 3 times older than his sister alyssa.Eric is 15 years old write an equation to find out a alyssa's age
Do 15 divided by 3 equals 5
Final answer:
To determine Alyssa's age, we set up the equation 15 = 3A, based on the assumption that Eric being '3 times older' than Alyssa means he is 3 times her age. We divide both sides by 3 to get Alyssa's age, which is 5 years old.
Explanation:
To find Alyssa's age, we need to write an equation based on the information provided: Eric is 3 times older than his sister Alyssa, and we know that Eric is 15 years old. The phrase '3 times older' would technically mean 3 times Alyssa's age plus her age again (Alyssa's age times 4). However, this phrase can sometimes be used colloquially to mean '3 times Alyssa's age,' which is more common. So, we need clarification on the intended meaning. If we assume the latter, more common interpretation, the equation based on the information provided would be:
Let A be Alyssa's age. Since Eric is 15 years old and 3 times Alyssa's age, we have: E = 3A, where E is Eric's age.
Substituting Eric's age into the equation, we get: 15 = 3A
To find Alyssa's age, we then divide both sides by 3: 15 / 3 = A
Alyssa's age A would then be 5 years old. So, the equation to find Alyssa's age is: 15 = 3A
Please help ..........
Answer:
(a)
Step-by-step explanation:
Using Pythagoras' theorem
11² + 12² ? 16²
121 + 144 ? 256
265 > 256 ⇒ acute triangle
If the left side < right side then obtuse
If the left side = right side then right
Suppose the lengths of two strings are 10 cm and 70 centimeters describe how the lengths of these two strings compare
The 10 cm string is 7 times smaller than the 70 cm string