It would take Mike approximately 0.989 minutes (or about 59 seconds) to wash the car alone.
We have,
Let's start by assigning variables to unknown quantities.
Let m be the time it takes for Mike to wash the car alone (in minutes).
We know that Stephanie takes 17 minutes to wash the car alone, so her rate of work is 1/17 car per minute.
Working together, their combined rate of work is 1/8.24 car per minute.
Using the formula:
(rate of work) = (amount of work) / (time)
we can set up the following equation to represent the work they do together:
1/8.24 = (1 car) / t
where t is the time it takes them to wash the car together.
We can also set up a similar equation for Stephanie's work alone:
1/17 = (1 car) / (t + x)
where x is the extra time it takes Mike to wash the car alone.
Since they are working on the same car, the amount of work done in both cases is the same, so we can set the two equations equal to each other and solve for x:
1/8.24 = 1/(t + x) + 1/17
Multiplying both sides by the least common multiple of the denominators (8.2417(t+x)).
17*(t+x) + 8.24*(t+x) = 8.24*17
Simplifying.
25.24t + 17x = 139.68
We also know that Mike's rate of work is 1/m car per minute.
Since we know the combined rate of work when they work together, we can set up another equation:
1/m + 1/17 = 1/8.24
Multiplying both sides by the least common multiple of the denominators (8.2417m).
178.24m + 8.2417m = 8.2417m + m8.24m
Simplifying.
141.08m = 139.68
Solving for m.
m = 0.989
Therefore,
It would take Mike approximately 0.989 minutes (or about 59 seconds) to wash the car alone.
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I want to know the claim ___ which corresponds to ____
And the opposite ___ which corresponds to ____
The correct values to fill in the missing information are:
Claim: p ≠ 0.5 which corresponds to H0: p = 0.5 (two-tailed test)Opposite: p = 0.5 which corresponds to H1: p = 0.5 (two-tailed test)The test is: two-tailedThe test statistic is: 0.55 (to 2 decimals)The p-value is: 0.5823 (to 4 decimals)Based on this we: Fail to reject the null hypothesisConclusion: There does not appear to be enough evidence to support the claim that the proportion of American adults who eat salad once per week is different from 50% at a significance level of 0.05.What is the sentences about?Claim: The claim is that the proportion of American adults who eat salad once per week is different from 50%, which corresponds to the null hypothesis H0: p = 0.5.
Opposite: The opposite of the claim is that the proportion of American adults who eat salad once per week is equal to 50%, which corresponds to the alternative hypothesis H1: p = 0.5 (Note that in this case, the alternative hypothesis is the opposite of the claim since we are testing for a difference from 50% in the claim).
Therefore, the claim is H0: p ≠ 0.5 (two-tailed test), and the opposite is H1: p = 0.5 (two-tailed test).
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what is the cosine of angle b
For the given right angled triangle cosine of angle B is 5√89/89.(option A).
What is right angled triangle?
It is a particular type of triangle having one angle is 90° or right angle. The adjacent sides of the right angle are called base and the perpendicular and the opposite side of 90° is called hypotenuse.
The given triangle is the right angled triangle. The three sides of a right angled triangle are called base, perpendicular and hypotenuse.
In the given figure base= 5 inches and perpendicular = 8 inches
By Pythagoras theorem at first we will find out the hypotenuse. Let the hypotenuse= c inches
For any right angled triangle,
(perpendicular)² +(base)²= (hypotenuse)²
⇒ (8)² + (5)² = (c)²
⇒ 64+ 25 = c²
⇒ c² =89
⇒ c= ±√89
As hypotenuse cannot be negative
So hypotenuse = √89 inches.
Now to find cosine of angle B that is cos B we will use the trigonometric function.
cos B= Adjacent side/ hypotenuse
= 5/√89
= 5√89/89 [ Multiplying the numerator and the denominator by √89 ]
Hence, cosine of angle B is 5√89/89.
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For an investment of 26,245, a quarterly statement reports that the account is 26,292. The statement reports that for the same quarter, the rate of return of the investment was - 0.02%. Given the information regarding the investment quarterly activity, does the reported rate of return seem reasonable?
No. The reported return rate appears lower than expected.
Rate of returnsTo determine whether the reported rate of return is reasonable or not, we can calculate the expected rate of return based on the investment amount and the ending value of the account.
First, we need to calculate the total number of quarters that have elapsed between the initial investment and the current quarter. Let's assume that the investment has been held for n quarters.
Then, we can use the following formula to calculate the expected rate of return:
Expected rate of return = (Ending value / Initial investment) ^ (1/n) - 1
Plugging in the given values, we get:
n = 1 (since we are only given information for a single quarter)
Initial investment = 26,245
Ending value = 26,292
Expected rate of return = (26,292 / 26,245) ^ (1/1) - 1 = 0.18%
Comparing the expected rate of return of 0.18% with the reported rate of return of -0.02%, we can see that they are quite different. However, it's important to note that a single quarter's rate of return may not be indicative of the overall performance of the investment.
Therefore, while the reported rate of return seems lower than expected, we would need to consider the performance over a longer period of time to make a more informed assessment of the investment's performance.
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You want to place stone pavers around the edges of your concrete patio. The patio is 12ft wide by 14ft long and each stone paver is 14 inches long. How many stone pavers will you need to go around the patio ( not counting the side against the house which is 14ft long)? Round to the nearest whole number
You will need 38/1.17 ≈ 32.48 stone pavers to go around the patio. Rounding to the nearest whole number, you will need 32 stone pavers.
Explain whole numbers
Whole numbers are a set of numbers that includes all natural numbers (positive integers) and zero. They are represented by the symbol "W" and do not include any fractions or decimals. Whole numbers are used in counting, measuring, and representing quantities of discrete objects or entities, and are a fundamental concept in mathematics.
According to the given information
First, let’s convert the length of the stone paver from inches to feet: 14 inches = 14/12 feet = 1.17 feet.
The perimeter of the patio is (12 + 14 + 12) feet = 38 feet. Since each stone paver is 1.17 feet long, you will need 38/1.17 ≈ 32.48 stone pavers to go around the patio. Rounding to the nearest whole number, you will need 32 stone pavers.
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Select all the correct answers. If the measure of angle is , which statements are true? The measure of the reference angle is . The measure of the reference angle is . The measure of the reference angle is . 0 =9/2
The statement cos(theta) = √3/2 is correct.
Which statement is correct?Angles are the angles formed by 2 bisecting lines or surfaces at or near their intersection.
The following information has been provided:
The angle (theta) = [tex]\frac{2\pi }{3}[/tex] measurement has been given to us.
We must determine which propositions are true by determining the measure of angle (theta) = [tex]\frac{2\pi }{3}[/tex]
cos(theta) = [tex]\frac{\sqrt{3} }{2}[/tex]
= cos30
theta = 30
tan(theta)= [tex]-\sqrt{3} = tan(90 + 30)[/tex]
tan(theta) = tan120
theta = 120
sin(theta) = [tex]-\frac{1}{2}[/tex] = [tex]cos(90 + 30)[/tex]
sin(theta) = sin120
theta = 120
Therefore the correct statement is cos(theta) = √3/2
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Complete question:
The measure of angle(theta) Is 2pi/3, which statements are true?
cos(theta) = √3/2
The measure of the reference angle is 30°.
The measure of the reference angle is 45°.
The measure of the reference angle is 60°.
tan(theta) = -√3
sin(theta)=-1/2
You paid $6.99 for a shirt that was 70% off; what was the original price of the shirt?
Answer:
$23.30
Step-by-step explanation:
We Know
You paid $6.99
The shirt was 70% off
$6.99 = 30%
What was the original price of the shirt?
We Take
(6.99 ÷ 30) x 100 = $23.30
So, the original price is $23.30
A rectangular room is 2 feet
longer than it is wide. Its area is 168 square feet. Set this up as a quadratic equation
Answer:
x = -14 and x = 12
Step-by-step explanation:
Let x be the width of the rectangular room in feet. Then, according to the problem, the length of the room is 2 feet longer than the width, or x + 2 feet.
The area of a rectangle is given by the formula A = length × width, so we have:
A = (x + 2) × x = x^2 + 2x
We are also given that the area of the room is 168 square feet, so we set A = 168 and get:
x^2 + 2x = 168
This is a quadratic equation in standard form, where 1x^2 + 2x - 168 = 0. We can solve this equation by factoring or using the quadratic formula. This will give us the value(s) of x, which represents the width of the room. Once we have the width, we can find the length by adding 2 feet to it.
And x is : -14 and 12
A rectangle has a length of x + 4 cm and a width of 2x − 7 cm.
(a) If the perimeter is 36cm, what is the value of x?
(b) What is the area of this rectangle
Answer:
See below!
Step-by-step explanation:
Given data:Length = x + 4 cm
Width = 2x - 7 cm
Part a)Perimeter:
Sum of all sides of a shape is called perimeter.Perimeter of rectangle = 2(length) + 2(width)Put the given data.
36 = 2(x + 4) + 2(2x - 7)
Distribute36 = 2x + 8 + 4x - 14
Combine like terms36 = 2x + 4x + 8 - 14
36 = 6x - 6
Add 6 to both sides36 + 6 = 6x
42 = 6x
Divide both sides by 642/6 = x
7 = x
OR
x = 7Part b)Area of rectangle = length × widthArea = (x + 4)(2x - 7)
Put x = 7
Area = (7 + 4)(2(7) - 7)
Area = 11(14 - 7)
Area = 11(7)
Area = 77 cm²[tex]\rule[225]{225}{2}[/tex]
Answer: (a) x=7
(b) area of this rectangle = 77[tex]cm^{2}[/tex]
Step-by-step explanation:
(a) the perimeter of a rectangle = 2 * [ l + b ]
36 = 2 * [ (x + 4) + (2x - 7) ]
36 / 2 = x + 4 + 2x - 7
18 = 3x -3
18 + 3 = 3x
21 = 3x
x = 7
(b) the area of a rectangle = l * b
l = x + 4 = 11cm
b = 2x -7 = 7cm
therefore, 11cm * 7cm = 77[tex]cm^{2}[/tex]
guys someone help me asap!!!! tell me all that apply for this!
The sequences that show that the two figures are similar, but not congruent, are:
Triangle MNO is translated 3 units to the right, and then dilated about the origin by a scale factor of 0.5, then translated 5 units down, and then reflected across the y-axis to obtain triangle M'NO'. Pentagon EFGHI is dilated about the origin by a scale factor of 2 to obtain pentagon E'F'G'H'I'. Triangle JKL is dilated about the origin by a scale factor of 3 to obtain triangle J'K'L.How to explain the sequenceThis sequence includes a dilation with a different scale factor for each figure and reflections, which preserve the shape of the figures but not their size or orientation.
In conclusion, the correct options are A and C
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What is the linear equation for your line of best fit? What does the slope of this line mean? What does the y-intercept of this line mean? (It's scattered plot points)
Answer:
need better photos
Step-by-step explanation:
Answer: Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.
Step-by-step explanation:
Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.
I don't know this I've tried but I just don't know.
Answer:the median is Q2 aka 105
Step-by-step explanation:
how does cot^2(x)-tan^2(x)=csc^2(x)-sec^2(x)
The proof of cot²(x) - tan²(x) = csc²(x) - sec²(x) is the help of trigonometry
identity and Pythagorean identity .
what is trigonometry identity ?A trigonometric identity is an equation that is true for all values of the variables in the equation, where the variables are trigonometric functions such as sine, cosine, tangent, cotangent, secant, or cosecant.
The Pythagorean identity is a fundamental trigonometric identity that relates the three basic trigonometric functions: sine, cosine, and tangent, in terms of the unit circle or right triangle.
Proof of cot²(x) - tan²(x) = csc²(x) - sec²(x)The identity you provided, cot²(x) - tan²(x) = csc²(x) - sec²(x), is a trigonometric identity that can be derived from the Pythagorean identity and the reciprocal identities. Here's one way to prove it:
Start with the Pythagorean identity:
sin²(x) + cos²(x) = 1
Divide both sides by sin²(x):
1 + cos²(x)/sin²(x) = 1/sin²(x)
Recall that cot(x) = cos(x)/sin(x) and tan(x) = sin(x)/cos(x):
1 + cot²(x) = csc²(x)
Subtracting sec²(x) from both sides:
cot²(x) - tan²(x) = csc²(x) - sec²(x)
Therefore, cot²(x) - tan²(x) = csc²(x) - sec²(x) is a valid trigonometric identity.
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the area of a circle is 144m2 What is the diameter of the circle
Step-by-step explanation:
AREA = pi r^2
144 = pi r^2 shows r = 6.77 m ( or sqrt ( 144/pi) )
then diameter = 2 * r = 13.54 m (or 2 sqrt (144/pi) )
Answer:
7.64
Step-by-step explanation
This is what I did so I take the root of 144 = 12 and 12/3.14 = roughly 3.82 thats the radius and that times 2 = 7.64 have a great day success to homework yay! Have a great day!!! :D
Casey is going to deposit $500 in an account that earns 6% interest for 10 years. How much more interest will
he earn if the account earns an accual compound interest rather than annual simple interest?
The interest he earns in 10 years = $395.42.
What is compound interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest.
Here the Principal P = $500
Rate of interest= 6% = 6/100 = 0.06
Number of years t= 10 years.
Now using compound interest formula then,
=> Amount = [tex]P(1+r)^t[/tex]
=> Amount = 500[tex](1+0.06)^{10[/tex] = [tex]500\times1.06^{10[/tex]
=> Amount = $895.42.
Now interest = $895.42 - $500 = $395.42
Hence the interest he earns in 10 years = $395.42.
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Company A charges a $125 annual fee plus $7 per hour car share fee.
Company B charges $110 plus $10 per hour. What is the minimum number of
hours that a car share needs to be used per year to make company A a better
deal?
OA. 9
B. 6
O C. 5
D. 11
[4x2+(5+1)] devide 2 =
Answer:
7
Step-by-step explanation:
[4x2+(5+1)] ÷ 2
[8+(6)] ÷ 2
14 ÷ 2
7
A theatre contains 457 seats and the ticket prices for a recent play were $54 for adults and $17 for children. If the total proceeds were $14,984 for a sold-out matinee, how many of each type of ticket were sold?
Answer: 195 adult tickets and 262 children tickets
Step-by-step explanation:
Let a be adult tickets and c be children tickets.
We know there are 457 seats.
a + c = 457
We also know the cost of the tickets and how much money was made.
$54a + $17c = $14,984
Now, we have a system of equations we can use to solve.
a + c = 457
$54a + $17c = $14,984
Lastly, we will graph this system, see attached. The point of intersection, or where the lines intersect, is our answer.
195 adult tickets and 262 children tickets.
Answer:
Chidden tickets were 262 and adult tickets were 195 tickets
Step-by-step explanation:
Let x = the number of children tickets
Let y = the number of adult tickets.
x + y = 457
17x + 54y = 14984
Use substitution
x + y = 457 Solve for y
y = 457 -x Substitute 457 -x for y in the equation 17x + 54y = 14984
17x + 54y = 14984
17x + 54(457 -x) = 14984 Solve for x Distributer the 54
17x + 24678 - 54x = 14984 Combine like terms
-37x = -9694 Divide both sides by -37
x = 262
The number of children tickets.
x + y = 457 Substitute 262 for x and solve for y
262 + y = 457 Subtract 262 from both sides
y = 195
The number of adult tickets.
Helping in the name of Jesus.
Aaron writes an algebraic expression to represent the product of 14 and the difference of 18 and 3x. What are the factors in this expression
The factors in this algebraic expression are:
14 And (18 - 3x)
How to find he factors in the algebraic expression ?An algebraic expression can also be written as a list of its constituent parts. Variables, constants, and operators are the components of an algebraic expression. Terms are separated from one another in an algebraic equation by the addition operation.
Algebraic Expressions can be factorized using many methods. The most common methods used for factorization of algebraic expressions are:
Factorization using common factors
Factorization by regrouping terms
Factorization using identities
The algebraic expression written by Aaron to represent the product of 14 and the difference of 18 and 3x is:
14 * (18 - 3x)
The factors in this expression are:
14
(18 - 3x)
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Look at the key below the map that shows the color-scaled performance range. What is the range for 1 Year performance? How does it compare to the 1 Dat performance range? Why do you think this is the case?
1 year performance: -30%, -20%, -10% 0%, 10%, 20%, 30%
1 Day performance : -3%, -2%, -1%, 0, 10%, 20%, 30%
The range of 1 year performance is more than 1 Day performance.
We have,
1 year performance: -30%, -20%, -10% 0%, 10%, 20%, 30%
1 Day performance : -3%, -2%, -1%, 0, 10%, 20%, 30%
Now, the range of 1 year performance
= Highest - lowest
= 30 - (-30)
= 60
and, the range of 1 Day performance
= Highest - lowest
= 30 - (-3)
= 33
Thus, the range of 1 year performance is more than 1 Day performance.
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Correct answer gets brainliest!!!!
Option B
One dimensional objects
Answer:
B. One-dimensional objects
A line segment can "grow" from one-dimensional objects. A line segment is a one-dimensional figure that has two endpoints and connects them with a straight path. One-dimensional objects include lines and curves, and a line segment can be a part of a longer line or curve.
Three-dimensional objects (A) are made up of length, width, and height and cannot "grow" into a line segment, but a line segment can be a part of a three-dimensional object, such as an edge or a diagonal.
Zero-dimensional objects (C) are points, which do not have any length, width, or height. A line segment cannot "grow" from a point, but a point can be one of the endpoints of a line segment.
You are trying to determine if a router you’re thinking of purchasing will give off a strong enough wifi signal to cover the area in your house. The router you have selected will cover an area of 850 ft^2.
The wi-fi router shall not be strong enough to cover the area of the house.
How to determine whether a wi-fi router can cover a given area
According to the statement, we must determine if a wi-fi router can cover all the area of a house, described by a rectangle. The area formula of rectangle is introduced below:
A = b · h
Where:
A - Area, in square feet.b - Base, in feet.h - Height, in feet.Now we proceed to determine the area of the house:
A = (50 ft) · (50 ft)
A = 2500 ft²
The wi-fi router shall not cover the entire area of the house.
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Uncle Fred gives his nephew, Jack, and niece, Jill, £60 between them every year
at Christmas. He splits it between them in the ratio of their ages.
(a) The first time he does this Jack is 1 and Jill is 3. How much does Jill
receive?
(b) How much does Jack receive the following Christmas?
(c) How old will Jack be when he receives £25 from Uncle Fred at Christmas?
a) Jill receives £45
b) Jack receives £20 the following Christmas
c) Jack will be 5/4 years old, which is equivalent to 1 year and 3 months when he receives £25 from Uncle Fred.
Explain the term years
Years are a unit of time measurement used to quantify the duration of one complete orbit of the Earth around the sun. A year consists of 365 days, except in a leap year when an extra day is added. The concept of a year is used in various fields, including astronomy, geology, and history.
According to the given information
(a) Let's first find the total ratio of their ages:
1 + 3 = 4
So Jack's share will be:
1/4 x £60 = £15
And Jill's share will be:
3/4 x £60 = £45
Therefore, Jill receives £45.
(b) The next Christmas, Jack will be 2 and Jill will be 4. We can use the same ratio to find Jack's share:
2/6 x £60 = £20
So Jack receives £20.
(c) Let x be the age of Jack when he receives £25 from Uncle Fred. We know that:
1/4 x £60 = £25
Multiplying both sides by 4/60, we get:
x = 5/4
So Jack will be 5/4 years old, which is equivalent to 1 year and 3 months, when he receives £25 from Uncle Fred.
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A mirror is placed 45 feet from the base of a waterfall by a hiker. The hiker walks backwards until they are 7.5 feet from the mirror. Determine how tall the waterfall is if the hiker is 6 feet tall.
36 ft
39.5 ft
56.25 ft
72 ft
If the hiker is 6 feet tall, then the height of the waterfall will be: 32.57 feet.
How to determine the height of the waterfallWe can solve this problem using similar triangles. Let us call the height of the waterfall "h". Then, the distance from the base of the waterfall to the mirror is also "h" (since the mirror reflects the top of the waterfall down to the hiker's eye).
Using similar triangles, we can set up the following proportion:
(h + 6 feet) / 45 feet = 6 feet / 7.5 feet
Cross-multiplying and simplifying, we get:
h + 6 feet = 270 feet / 7
h + 6 feet = 38.57 feet
h = 32.57 feet
So, the correct height given the variables is 32.57 feet.
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Answer:
36 ft
Step-by-step explanation:
We can use the concept of similar triangles to solve this problem. The ratio of the heights of the hiker and the waterfall is the same as the ratio of their distances to the mirror.
Given:
Distance from mirror to waterfall = 45 feet
Distance from mirror to hiker = 7.5 feet
Hiker's height = 6 feet
Let's set up a proportion:
(Hiker's height) / (Hiker's distance to mirror) = (Waterfall's height) / (Waterfall's distance to mirror)
Substitute the given values:
6 / 7.5 = (Waterfall's height) / 45
Now solve for the height of the waterfall:
Cross-multiply:
6 * 45 = 7.5 * (Waterfall's height)
270 = 7.5 * (Waterfall's height)
Divide by 7.5:
Waterfall's height = 270 / 7.5
Waterfall's height = 36 feet
So, the height of the waterfall is 36 feet.
Among the provided options, the correct answer is:
a) 36 ft
Which of the following equations will produce the graph shown below? A. x²/20 + y²/20 = 1 B. 20x² - 20y² = 400 C. 6x² + 6y² = 144 D. 5x² + 5y² = 80
An equation that will produce the graph shown above include the following: D. 5x² + 5y² = 80.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Based on the information provided above, we have the following parameters:
Radius, r = √16 = √80/5
Center, (h, k) = (0, 0).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 0)² = (√80/5)²
5x² + 5y² = 80.
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7. Which statement is NOT part of a debt-reduction plan? a. Lower debts with the highest interest rates. b. Slow or eliminate credit card spending c. Only pay the minimum amount when possible. d. Use an online debt management calculator.
Pattern A starts at 1 and uses the rule add 5." Pattern B starts at 28 and uses the rule "subtract 4."
What are the next four terms in each pattern?
Enter your answers in the boxes.
For the pattern A, the terms are 6, 11, 16 and 21
For the pattern B, the terms are 24, 20, 16, 12
How to determine the termsTo determine the consecutive terms of the sequence, we need to take note of the rule of each.
From the information given, we have that;
For the Pattern A
Each term is the previous term plus 5
This is represented as;
Pattern A = a + 5,
The first term = 1
Second term = 1 + 5 = 6
Third term = 6 + 5 = 11
Fourth term = 11 + 5 = 16
Fifth term = 16 + 5 = 21
For Pattern B = a - 4
Second term = 28 - 4 = 24
Third term = 24 - 4 = 20
Fourth term = 20 -4 = 16
Fifth term = 16 - 4 = 12
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Find the minimum or maximum of the function y=x^2-9
I will be finding the minimum of this parabolic function.
The function y = x^2 - 9 is a parabola that opens upwards, since the coefficient of the x^2 term is positive. Therefore, the minimum value of the function occurs at the vertex of the parabola.
To find the x-coordinate of the vertex, we can use the formula -b/2a, where the quadratic function is in the form y = ax^2 + bx + c. In this case, a = 1 and b = 0, so the x-coordinate of the vertex is -b/2a = -0/(2*1) = 0.
To find the corresponding y-coordinate of the vertex, we can substitute x = 0 into the function, which gives y = 0^2 - 9 = -9.
Therefore, the minimum value of the function y = x^2 - 9 is -9, which occurs at x = 0.
~~~Harsha~~~
The minimum point of this function is located at (0, -9).
Step-by-step explanation:1. Determine whether it's a minimum or maximum.So from plain sight we can tell we're looking for a maximum point, because the coefficient of x² is positive, it's 1. If the function was y=-x²-9, we would be looking at a minimum point.
2. About the minimum...The vertex if the exact point where a quadratic or any pair exponent function will start to either decay or increase, therefore, it will be the minimum or maximum point.
Formula for "x" value of vertex: [tex]\sf x_{Vertex} =\dfrac{-b}{2a}[/tex].
In this equation, a and b are coefficients extracted when the formula is expressed on its standard form.
Standard form of a quadratic equation: ax² + bx + c = 0
➔ You need to substitute the "y" by a "0", and the formula should look like this:
[tex]\sf 0=x^2-9[/tex]
➔ Reorganizing...
[tex]\sf x^2-9=0[/tex]
3. Extracting the coefficients.Let's expand the previous expression:
[tex]\sf x^2+0x_{} -9=0[/tex]
The coefficients are:
a= 1, beacuse "x²" is being multiplied by 1, which is implicit.
b= 0, because "x" doesn't really exist on the simplified equation.
c= -9.
4. Calculate the "x" and "y" locations of the vertex.Now let's calculate the "x" position of the vertex using the formula from step 2:
[tex]\sf x_{Vertex} =\dfrac{-b}{2a}=\dfrac{-(0)}{2(1)}=0[/tex]
Now, the "y" value can be obtained just by substituting "x" by 0 on the argument of the function:
[tex]\sf y=(0)^2-9\\ \\y=-9[/tex]
Therefore, the vertex, or minimum point of this function is located at (0, -9).
Check out the attached image to verify this information with the graph.
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A group of scientists is conducting an experiment on the effects of media on children. They randomly select 100 children and randomly assign each child to one of four treatment groups. Each treatment group has a specific amount of screen time during a one-week time frame. The first group has no screen time, the second group has two hours of screen time, the third group has four hours of screen time, and the fourth group has six hours of screen time. After the first week, the scientists conduct the same experiment, with the same subject groups, for three more weeks so that each group experiences each of the four treatments. Which statements about this study are true?
1. This study uses blocking.
2. This study uses blinding.
3. This study uses a control group.
4. This study uses a repeated measures design.
5. This study uses random sampling.
This study uses blocking: True. The study randomly assigns each child to one of the four treatment groups, which helps to control for individual differences that could affect the results.
This study uses blinding: It is not mentioned in the scenario whether the study uses blinding or not in individual.
This study uses a control group: True. The first group, with no screen time, serves as the control group. By comparing the results of the other groups to the control group, the scientists can see the effects of different amounts of screen time.
This study uses a repeated measures design: True. Each subject experiences each of the four treatments, so the study design is repeated measures.
This study uses random sampling: True. The study randomly selects group of 100 children for the experiment.
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suppose that a and b are positive for which log9(a) = log15(b) = log25(a + 2b). What is the value of b over a
Thus, the value of b over a for the given logarithmic function is obtained as: b/a = 1 + √2.
Explain about the logarithmic function:The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent with which b must be raised in order to obtain a number x is the logarithm of x to the base b.
A base must still be raised to a certain exponent or power, or logarithm, in order to produce a specific number. If bˣ = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n.
Given that:
log9(a) = log15(b) = log25(a + 2b)
Let , log9(a) = log15(b) = log25(a + 2b) = x
Then,
log9(a) = x (taking antilog)
log3²(a) = x
a = 3²ˣ
log15(b) = x (taking antilog)
log(3*5)(b) = x
b = 3ˣ.5ˣ
log25(a + 2b) = x (taking antilog)
log5²(a + 2b) = x
a + 2b = 5²ˣ
Now,
b²/a = a + 2b
(b/a)² = 1 + 2*(b/a)
If t = b/a, then t² - 2t -1 = 0
On factorization:
t = 1 ± √2 ( a and b are positive integer)
b/a = 1 + √2
Thus, the value of b over a for the given logarithmic function is obtained as: b/a = 1 + √2.
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elem algebra
I tried doing a question on my own, I didn't get it right :(
ANY HELP WILL BE GREAT, THANKSS
Answer:
the missing y coordinate is 2/5
Step-by-step explanation:
You are basically solving for y since you are missing the y coordinate
Since x=5 plug that in and you will get 5+5y=7
subtract 5 on both sides and you will get 5y=2
divide 5 on both sides and you will get 2/5