Answer:
0
Step-by-step explanation:
For a quadratic of the form
ax² +bx +c = 0
The "discriminant" is the expression ...
b² -4ac
For this equation, we have a=1, b=5, c=7, so the discriminant is ...
5² -4·1·7 = -3
When the discriminant is negative there will be two distinct complex roots to the equation, and no real roots.
_____
When the discriminant is zero, there will be one real root with multiplicity 2; when it is positive, there will be two distinct real roots.
Curtis kept track of the number of miles he ran each day for 10 days. By day 4, he had already run 9 miles. How many days did it take Curtis to run 21 miles? 9 days 25 days 30 days 7 days
Answer:
7 days
Step-by-step explanation:
We assume that "by day 4" means "at the end of day 3." Since Curtis had run 9 miles in 3 days, his average rate is 9/3 = 3 miles per day.
It will take Curtis ...
(21 mi)/(3 mi/day) = 7 days
to run 21 miles at that rate.
_____
Comment on the question
There is nothing in the problem statement to suggest that the number of miles run each day is the same. A different assumption than the one we have made will give a different answer.
Which is the simplified form of (9c^-9)^-3
b 1/729 c^27
ANSWER
[tex](9 {c}^{ - 9} )^{ - 3}=\frac{{c}^{ 27} }{729} [/tex]
EXPLANATION
The given expression is
[tex](9 {c}^{ - 9} )^{ - 3} [/tex]
Recall that:
[tex] ({a}^{m} )^{n} = {a}^{mn} [/tex]
We use the law of exponents to get
[tex](9 {c}^{ - 9} )^{ - 3} = 9^{ - 3} {c}^{ - 9 \times - 3} [/tex]
Let us multiply in the exponents to get:
[tex](9 {c}^{ - 9} )^{ - 3} = 9^{ - 3} {c}^{ 27} [/tex]
Recall again that:
[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]
This implies that:
[tex](9 {c}^{ - 9} )^{ - 3} = \frac{1}{ {9}^{ 3} } \times {c}^{ 27} [/tex]
We expand the power to get:
[tex](9 {c}^{ - 9} )^{ - 3} = \frac{1}{9 \times 9 \times 9} \times {c}^{ 27}[/tex]
[tex](9 {c}^{ - 9} )^{ - 3}=\frac{1}{729} \times {c}^{ 27} [/tex]
We multiply out to get:
[tex](9 {c}^{ - 9} )^{ - 3}=\frac{{c}^{ 27} }{729} [/tex]
Answer:
Step-by-step explanation: the answer is b
PLEASE HELP ME
A system of linear equations is graphed.
Which ordered pair is the best estimate for the solution to the system?
(1/2, 1)
(1, 1)
(0, 1/2)
(1/2, 0)
Answer:
(1/2, 0)
Step-by-step explanation:
The solution to a system of equations graphically is where they intersect on the graph. In a coordinate, the x is first and the y is second. Where our lines cross is ON the x-axis. This means that y = 0 here. Because we are to the right of the origin, we are in positive x values. Because we are between x = 0 and x = 1, the best estimate from our choices is x = 1/2. The coordinate for the solution is best represented by (1/2, 0)
If ABCD is a rectangle, and m∠ADB=55°, what is the value of x?
Answer: OPTION D.
Step-by-step explanation:
Rectangles have four right angles (angles of 90 degrees).
The point of intersection of the diagonals divides each one of them into two equal parts.
Knowing this, we can conclude that:
[tex]m\angle c=m\angle b=55\°[/tex]
(Observe the figure)
Therefore, since the sum of the interior angles of a triangle is 180 degrees, we can find the value of "x":
[tex]x+m\angle c+m\angle b=180\°\\x=180\°-55\°-55\°\\x=70\°[/tex]
Answer:
70 degrees
Step-by-step explanation:
55*2= 110
180-110=70
Please Help!
f(x)=2x^2+5 square root (x-2)
f(6) = _____
Answer:
f(6) = 82
Step-by-step explanation:
f(x) = 2x^2+5 sqrt(x-2)
Let x =6
f(6) = 2(6)^2+5 sqrt(6-2)
= 2 * 36 + 5 sqrt(4)
= 72+5*2
= 72+10
=82
f(6) = 82
Explain your thinking, is the 07385200131-1 UPC code valid?
a,. Using multiplication and addition to check the digits it is invalid because the total is 51 and does not end in a 0
b. Using multiplication and addition to check the digits it is invalid because the total is 31 and does not end in a 0
c. Using multiplication to check the digits it is invalid because the total is 78 and does not end in a 0
d. Using multiplication and addition to check the digits it is invalid because the total is 45 and does not end in a 0
Answer:
a. Using multiplication and addition to check the digits, it is invalid because the total is 51 and does not end in a 0
Step-by-step explanation:
The sum of alternate digits is multiplied by 3. Those digits are ...
0 3 5 0 1 1 . . . . sum of 10
The sum of remaining alternate digits is added to that.
7 8 2 0 3 1 . . . . sum of 21
The result of the arithmetic ...
mod(3×10 + 21, 10) = 1 . . . . . should be zero for valid GTIN-12 UPC code
If all goes according to plan, the function A(t)=200(1.1)^tA(t)=200(1.1) t A, left parenthesis, t, right parenthesis, equals, 200, left parenthesis, 1, point, 1, right parenthesis, start superscript, t, end superscript will model the amount of potatoes, AAA, in bushels, produced by Burian's farm ttt years from now, and the function R(t)=5000(1.111)^tR(t)=5000(1.111) t R, left parenthesis, t, right parenthesis, equals, 5000, left parenthesis, 1, point, 111, right parenthesis, start superscript, t, end superscript will model the revenue, RRR, in dollars, earned from selling these potatoes. Let PPP be the proposed price of a single bushel of potatoes ttt years from now. Write a formula for P(t)P(t)P, left parenthesis, t, right parenthesis in terms of A(t)A(t)A, left parenthesis, t, right parenthesis and R(t)R(t)R, left parenthesis, t, right parenthesis.
Answer:
The formula for P(t) in terms of R(t) and A(t) is:[tex]P(t)=\frac{R(t)}{A(t)} =\frac{5000(1.111)^t}{200(1.1)^t}[/tex]
It can be simplified in terms of t as:[tex]P(t)=25(1.01)^t[/tex]
Explanation:
I will rewrite the question removing the errors, for better understanding:
If all goes according to plan, the function A(t)=200(1.1)^t will model the amount of potatoes, A, in bushels, produced by Burian's farm t years from now, and the function R(t)=5000(1.111)^t will model the revenue, R, in dollars, earned from selling these potatoes. Let P be the proposed price of a single bushel of potatoes t years from now. Write a formula for P(t).You must depart from the equation that relates revenue (R), price (P), and number of items sold.
Revenue = Price × Number of itemsR (t) = P(t) × A(t)There you see that you can solve for P(t), which is the unknown function:
P(t) = R(t) / A(t)Substituting you get:
[tex]P(t)=\frac{R(t)}{A(t)} =\frac{5000(1.111)^t}{200(1.1)^t}[/tex]Divide the coefficients (5,000 / 200) and apply the power properties for the quotients of powers with the same power:
[tex]P(t)=25(1.111/1.1)^t=25(1.01)^t[/tex]A rectangular dartboard has an area of 648 square centimeters. The triangular part of the dartboard has an area of 162 square centimeters. A dart is randomly thrown at the dartboard.
Assuming the dart lands in the rectangle, what is the probability that it lands inside the triangle?
Answer:
The probability that the dart lands inside the triangle is 0.25
Step-by-step explanation:
* Lets explain how to find the probability of an event
- The probability of an Event = Number of favorable outcomes ÷ Total
number of possible outcomes
- P(A) = n(E) ÷ n(S) , where
# P(A) means finding the probability of an event A
# n(E) means the number of favorable outcomes of an event
# n(S) means set of all possible outcomes of an event
- P(A) < 1
* Lets solve the problem
- A rectangular dartboard has an area of 648 cm²
- The triangular part of the dartboard has an area of 162 cm²
- A dart is randomly thrown at the dartboard
- The dart lands in the rectangle
∴ The area of the rectangle is the set of all possible outcomes n(S)
- The probability P(A) that the dart lands inside the triangle
∴ The area of the triangle is set of favorable outcomes of an
event n(E)
∵ P(A) = n(E) ÷ n(S)
∴ P(T) = area of the triangle ÷ area of the rectangle
∵ Area of the rectangle is 648 cm²
∴ n(S) = 648
∵ The area of the triangle is 162 cm²
∴ n(E) = 162
∴ P(T) = 162 ÷ 648 = 1/4 = 0.25
* The probability that the dart lands inside the triangle is 0.25
Point w is located at negative 2 3 on a coordinate plane W is reflected over the x-axis to create Point ww.W is then reflected over the y-axis to create point w what ordered pair describes the location of Point wa explain how you determine your answer
Answer:
W'' = (2, -3)
Step-by-step explanation:
Reflection over the x-axis changes the sign of the y-coordinate.
So, point W' is (-2, -3).
Reflection over the y-axis changes the sign of the x-coordinate.
So, point W'' is (2, -3).
___
The answer can be determined by doing the reflections algebraically, as above, or by doing them on a graph, as below.
Solve the following system of equations by using the elimination method. 2x + 4y = 8 and 3x – 3y = 12
Answer:
(x, y) = (4, 0)
Step-by-step explanation:
It is convenient to first put the equations into standard form by eliminating common factors. The first equation has a factor of 2 that can be removed; the second equation has a factor of 3 that can be removed. Then you have ...
x +2y = 4x -y = 4Subtracting the second equation from the first eliminates the x variable. That gives you ...
(x +2y) -(x -y) = (4) -(4)
3y = 0 . . . . . . simplify
y = 0 . . . . . . . divide by 3
Substituting this value into either equation above, you get ...
x + 0 = 4
x = 4
The solution is (x, y) = (4, 0).
Please answer this multiple choice question correctly for 30 points and brainliest!!
Answer:
B. 88°
Step-by-step explanation:
In a properly drawn circle graph, the central angle is proportional to the size of the number being displayed. Here, 122 of 500 selected football. Since the total angle of a circle is 360°, that fraction is ...
(122/500)×360° = 87.84° ≈ 88°
Working at a constant rate, pump x pumped out half of the water in a flooded basement in 4 hours. then pump y was started and the two pumps, working independently at their respective constant rates, pumped out the rest of the water in 3 hours. how many hours would it have taken pump y, operating alone at its own constant rate, to pump out all of the water that was pumped out of the basement
Answer:
24 hours.
Step-by-step explanation:
This is one of those problems where the easiest way to do is just to reason it out without trying to devise a formula.
Call the water in the basement = w
Therefore w/2 = 4*x where x is the rate of the pump. The statement means that 1/2 the water in the basement is pumped out by x in 4 hours.
Now x and y work together. They (together ) pump out the rest of the water which is also w/2
w/2 = 3x + 3y Now you can equate the two values for w/2
4x = 3x + 3y Subtract 3x from both sides.
4x-3x = 3x-3x + 3y
x = 3y
Now you have to be very careful in interpreting what you found. It takes pump y three times as long to do anything as it does x.
So here's the reasoning part.
x by itself will empty the basement in 8 hours. It takes x four hours to get 1/2 the water out.
It will take pump y 3 times as long to pump out that basement. 3*8 = 24 hours
Which equation is represented by the graph below?
For this case we discard options A and B, since by definition, the graph does not correspond to the function of the Neperian logarithm.
We tested option C:
[tex]y = e ^ x[/tex]
Doing [tex]x = 0[/tex]we have:
[tex]y = e ^ 0[/tex]
Every number raised to zero power is 1.
So, we have:
[tex]y = 1[/tex]
We have the point (0,1)
If we try option D:
[tex]y = e ^ x + 1[/tex]
Doing x = 0 we have:
[tex]y = e ^ 0 + 1\\y = 1 + 1\\y = 2[/tex]
We have the point (0,2)
So, we note that the correct option is option C
ANswer:
Option C
Answer: Third option.
Step-by-step explanation:
Observe that the graph tends to zero when [tex]x<0[/tex] and "y" tends to infinite when [tex]x>0[/tex]
The function [tex]y=lnx[/tex] is not defined for values of "x" less than zero, therefore the equations of the options 1 and 2 do not represent the graph attached.
Observe that the function cuts the y-axis at [tex]y=1[/tex], while the function [tex]y=e^x+1[/tex] cuts the y-axis at [tex]y=2[/tex], therefore the equation of the last option does not represent that graph.
Finally, the equation that represents the graph is:
[tex]y=e^x[/tex]
Solve the system of equations using substitution.
y = −2x + 1
4x + 2y = −1
A.(0, −3)
B.(−3, 0)
C.No solution
D.Infinitely many solutions
Answer:
C. No solution.
Step-by-step explanation:
y = −2x + 1
4x + 2y = −1
Substituting y = -2x + 1 in the second equation:
4x + 2(-2x + 1) = -1
4x - 4x + 2 = -1
2 = -1 which is absurd so there is no solution.
What computation will give you the seventh number
Answer:
42 + 14
Step-by-step explanation:
By counting the rows and columns, you'll notice the following:
1) The first pattern has 2 columns and increase by 1 column each time you move to the right.
2) The first pattern has 1 row and increase by 1 row each time move to the right.
3) To get to the 7th number, you will have to move to the right 6 times.
Hence,
1) if you start with 2 columns, and move 6 times to the right, each time adding one column you will end up with 2 + 6 = 8 columns
2) if you start with 1 row and move 6 times to the right, each time adding one row, you will end up with 1 + 6 = 7 rows
3) You will end up with a pattern with 8 columns and 7 rows and the number of dots will be 8 x 7 = 56.
If you work out all the answers, yo uwill see that only 42 + 14 gives you 56.
Blake and Ned work for a home remodeling business. They are putting the final touches on a home they renovated. Working alone, Blake can paint one room in 9 hours. Ned can paint the same room in 6 hours. How long will it take them to paint the room if they work together?
Answer: The time taken by both of them if they work together is given by
[tex]3\dfrac{3}{5}\ hours[/tex]
Step-by-step explanation:
Since we have given that
Time taken by Blake to paint one room = 9 hours
Time taken by Ned to paint one room = 6 hours
Work done by Blake = [tex]\dfrac{1}{9}[/tex]
Work done by Ned = [tex]\dfrac{1}{6}[/tex]
Total work done by both of them together is given by
[tex]\dfrac{1}{6}+\dfrac{1}{6}\\\\=\dfrac{3+2}{18}\\\\=\dfrac{5}{18}[/tex]
So, the time taken by both of them if they work together is given by
[tex]\dfrac{18}{5}=3\dfrac{3}{5}\ hours[/tex]
Blake can do the work in 9 and part of work in 1 hour = 1/9
Ned can paint the same room in six hours, as well as do part of work in 1 hour = 1/6
If they do it together = 1/9+1/6=5/118, and they can do 5/18 part of work in hour = 1
So, they can do whole work in hours = 1/5/18=3.6
So if they do it together it will only take 3.6 hours.
Given trapezoids QRST and WXYZ, which statement explains a way to determine if the two figures are similar?
A. Verify corresponding pairs of sides are congruent by translation.
B. Verify corresponding pairs of angles are proportional by translation.
C. Verify corresponding pairs of sides are proportional by dilation.
D.Verify corresponding pairs of angles are congruent by dilation.
for two figures to be proportional, their corresponding pair of sides must retain a proportion, regardless of rotation or translation of the figure.
so if we simply verify that all corresponding pairs of sides are proportional under transformation, if they are, then the figures are similar.
Answer:
The correct option is C. Verify corresponding pairs of sides are proportional by dilation
Step-by-step explanation:
The scale factor is the ratio between the dimensions in two similar figures. The term "similar figures" refers to figures that have the same shape but different sizes.
So, a dilation is a transformation created by a scale factor.
That is, a dilation that is smaller or larger than the original figure can be created.
To obtain a measure of the large figure and have the value of the small figure, this value is multiplied by the scale factor.
To obtain a measure of the small figure and the value of the large figure, this value is divided by the scale factor.
In other words, the scale factor is the radius that determines the proportional relationship between the sides of similar figures. In order for the pairs of sides to be proportional to each other, they must have the same scale factor. That is, similar figures have congruent angles (Dilation keeps the measure of the corresponding angles are equal) and sides with the same scale factor.
For example, a scale factor of two means that each side of the larger figure is exactly twice as large as the corresponding side in the smaller figure.
Given the above, the correct option is C. Verify corresponding pairs of sides are proportional by dilation
The Food Mart grocery store has a candy machine. Each time a customer inserts a quarter, 7 candies come out of the machine. The machine holds 15 pounds of candy. Each pound of candy contains about 180 individual candies. Assume the number of candies is never less than zero.
1. About how many candies are in the machine when it’s full?
2.Write a recursive formula to represent the number of candies remaining in the machine.
3.Write an explicit formula to represent the number of candies remaining in the machine for any number of customers
Answer:
2700 candiesc(0) = 2700; c(n) = c(n-1) -7c(n) = 2700 -7n2693, 2686, 2679Step-by-step explanation:
1. The number of candies in the machine is the product of the number of pounds of candy and the number of candies in a pound:
(15 lbs)(180 candies/lb) = 2700 candies
__
2. c(0) = 2700; c(n) = c(n-1) -7 . . . . the new number of candies is 7 fewer than after the previous customer. After no customers, the number is the original 2700 candies.
__
3. As the recursive formula tells us, the initial number of candies is 2700, and the number decreases at the rate of 7 per customer. The number remaining after n customers is ...
c(n) = 2700 -7n
__
4. Evaluating the above formula for n=1, 2, 3, we get ...
c(1) = 2700 -7 = 2693 . . . . candies remaining after 1 customer
c(2) = 2700 -7·2 = 2686 . . . 2 customers
c(3) = 2700 -7·3 = 2679 . . . 3 customers
Sarah wants to hang a mirror in her room. The mirror and frame must have an area of 15 square feet. The mirror is 3 feet wide and 4 feet long. Which quadratic equation can be used to determine the thickness of the frame, x
Answer:
x^2 + 7x - 3 = 0
Step-by-step explanation:
I think you meant "width of the frame" from outside of frame to outside of mirror.
Let x represent the width of the frame.
Area of mirror is (3 ft)(4 ft) = 12 ft^2. Total area of mirror and frame is 15 ft^2. The 3 ft^2 difference is the area of the frame.
But you were asked to find a quadratic equation that would give you the "width" of the frame.
The "new" width would be 3 + x and the "new" height would be 4 + x.
Then the area of the mirror and frame together would be
A = (3 + x)(4 + x) = 15 ft^2, or
12 + 7x + x^2 = 15 ft^2, or
x^2 + 7x - 3 = 0. This is the desired quadratic equation.
When answer choices are given, please share them when you post a question. Thank you.
please help asap
A rectangular playground is 8 meters wide. It is 3 times as long as it is wide.
What is the area of the playground?
Answer:
192 m²
Step-by-step explanation:
If it were as long as it is wide, the area would be that of an 8-meter square:
(8 m)² = 64 m²
It is 3 times as long, so the area is 3 times that value:
3 × 64 m² = 192 m²
Answer:
192 m²
Step-by-step explanation:
The width of the playground is 8m.
Now it's length is three times more than its width.
thus its length is 8*3 = 24.
The area thus is 24*8 = 192 m²
WILL GIVE BRAINLIEST!! A spinner is divided into eight equal sections. Each section is labeled with one number, from 1-8. Maggie spins the pointer on the spinner five times, each at a different speed. Four of the times the pointer lands on the section labeled 7. Which statement BEST explains these results?
A. The section labeled 7 is slightly bigger than the other sections.
B. The section labeled 7 appears more than once on the spinner.
C. The pointer of the spinner is not balanced.
D. The bottom of the spinner is not flat.
Answer:
d
Step-by-step explanation:
explanation- I think there a dent or something like the surface of the number seven being slightly high blocking the pointer and causing it to stop.
The statement that BESTexplains the results obatined is, the bottom of the spinner is not flat.
Effect of the section labled 7 on the spinner
There is ony one explanation to the reason why the pointer will land on te section labled 7 four out of the five times.
The bottom of the spinner may not be flat and the section labled 7 could also be dented causing the spinner to land at this section each time it is spinned.
Thus, we can conclude that, the statement that BESTexplains the results obatined is, the bottom of the spinner is not flat.
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Un rombo tienen un angulo de 22 grados. Cuanto vale la suma de sus angulos que no midan 22 grados???!!!???!!!????
The answer is:
The sum the other angles that do not measure 22° is equal to 316°.
[tex]158\°+158\°=316\°[/tex]
Why?To find the sum of the rest of the angles, we need to remember that a rhombus has two adjacent and equal angles, and also it has two opposite and equal angles.
So, we are given that the rhombus has an angle of 22°, and to calculate the other angles, let be the given angle an adjacent angle, so:
[tex]360\°=2*AdjacentAngles+2*OppositeAngles\\\\360\°=2*22\°+2*OppositeAngles\\\\2OppositeAngles=360\°-2*22\°=316\°\\\\OppositeAngles=\frac{316\° }{2}=158\°[/tex]
Hence, we have that the sum of its other angles that do not measure 22° is equal to 316°.
Have a nice day!
Need help with math question
ANSWER
[tex]x = 22 \: units[/tex]
EXPLANATION
The length of the two chords in the diagram are the same because equal chords are equal distance from the center.
We can see that the two chords are all 12 units from the center.
The line from the center meeting the chords at right angles bisects these chords.
Therefore
[tex]x = 2 \times 11[/tex]
[tex]x = 22 \: units[/tex]
Multiply [4 0 -1 2 -3 -1] multiplied by [0 1 -3 1] A. [0 4 -6 3 -3 4] B. [0 -4 -6 1 3 -4] C. [-4 4 -3 -1 6 -4] D. [0 4 -6 1 3 -4]
Answer:
[tex]\text{D. }\left[\begin{array}{cc}0&4\\-6&1\\3&-4\end{array}\right][/tex]
Step-by-step explanation:
It would be helpful to know the numbers of rows and columns, so we don't have to guess.
Any number of on-line calculators and/or graphing calculators can multiply these matrices for you. Excel and other spreadsheets can do this, too. Forming the 6 sums of 2 products is tedious to do by hand.
For example, the term in the product matrix at row 1 column 2 is the sum of products of the numbers in row 1 of the first matrix and column 2 of the second matrix:
4·1 + 0·1 = 4
_____
The attachment shows the matrix multiplication on a TI-84 calculator.
Vectors can be multiplied by scalars, where each component of the vector is multiplied by the scalar. In the student's question, direct multiplication isn't possible due to different number of components in both vectors. However, we can partially apply the concept to illustrate vector and scalar multiplication.
Explanation:The question being asked here is about multiplying vectors within the subject of Mathematics. It's important to note that vectors can be multiplied by scalars, and each component of the vector is multiplied by the scalar. In this question, it seems there might be a typo because the two vectors have a different number of components and cannot be multiplied directly.
However, multiplication of vectors by scalars does not involve reversing signs or changing magnitude based on whether the scalar is negative or positive. If Vector A is multiplied by a scalar c, all components of Vector A are simply multiplied by c.
So, applying this concept to part of the vectors in the question, we would get [0, 4, -3] when [4, 0, -1] is multiplied by the scalar 0 and 1 respectively.
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Outline the steps for taking cross sections of a rectangular prism.
Answer:
find a suitable cutting toolcut the prism on the plane of interestStep-by-step explanation:
A cross section is the intersection of a cut plane with the object of interest. In a classroom setting, we often try to do the cross sectioning mentally or with diagrams, rather than physically cutting anything. Sometimes, there is no substitute for actually performing the cut to see what the cross section looks like.
For certain samples that don't take kindly to cutting, we sometimes encase them in a block of material that helps them hold their shape during the process. Sometimes the "cutting" is performed by grinding away the portion of the material on one side of the cut plane.
Answer: Place 3 points on 2 or 3 edges or faces.
Connect the points to form a triangle.
Extend the triangle to form a plane.
Determine where the plane intersects the edges of the solid.
Step-by-step explanation:
if RSTU is a rhombus?
Answer:
It's B.
Step-by-step explanation:
It might be a square because a rhombus is defined as a parallelogram with 4 equal sides. A square is a rhombus with each angle = 90 degrees and has 4 equal sides.
Please answer this multiple choice question correctly for 30 points and brainliest!!
Answer:
C. 1.8 m × 1.1 m
Step-by-step explanation:
Actual dimensions will be 18 times those shown:
18×6.0 cm = 108 cm ≈ 1.1 m18×9.8 cm = 176.4 cm ≈ 1.8 mThe approximate window dimensions are 1.8 m × 1.1 m.
Identify the diameter of the disc. HELP ASAP!!
Answer:
9 1/16 in
Step-by-step explanation:
When chords cross, the distances from their point of intersection to the circle have the same product for each chord. For the 9-in chord, those two distances are 4.5 inches. For the diameter, the distances are 4 in and (d-4) in, where d is the diameter of the circle. Then ...
4.5^2 = 4(d -4)
d = 4.5^2/4+4 = 9 1/16 . . . . inches
The diameter is 9 1/16 inches.
_____
Comment on the diagram
The fact that the 9-inch chord looks very much like a diameter tells you the actual diameter won't be much different than that. These figures are not always drawn to scale, and are sometimes misleading. However, if the actual diameter were in the neighborhood of 16 inches, the perpendicular bisector shown would need to be about 1.4 inches instead of 4 inches.
Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 29% each week. The following function represents the weekly weed growth: f(x) = 86(1.29)x. Rewrite the function to show how quickly the weeds grow each day.
A.f(x) = 86(1.04)x; grows approximately at a rate of 0.4% daily
B.f(x) = 86(1.04)7x; grows approximately at a rate of 4% daily
C.f(x) = 86(1.29)7x; grows approximately at a rate of 20% daily
D.f(x) = 86(1.297)x; grows approximately at a rate of 2% daily
The function f(x) = 86(1.29)x represents a weekly weed growth rate of 29%. To convert this to a daily growth rate, we use the formula (1+0.29)^(1/7) - 1, which equates to an approximate daily growth rate of 4%. Therefore, the function can be rewritten as: f(x) = 86(1.04)x.
Explanation:Your question involves the function that represents the weed growth in a garden: f(x) = 86(1.29)x. Here, 1.29 refers to the growth rate of 29% per week. However, you want to rewrite the function to show how quickly the weeds grow each day.
To get a daily growth rate from a weekly one, we use the formula: daily growth rate = (1 + weekly growth rate)^(1/7) - 1. For the given function, this translates to a daily growth rate of (1 + 0.29)^(1/7) - 1, which is approximately 0.04, or 4%. Therefore, the function rewrite will be:
f(x) = 86(1.04)xThis function shows that the weeds grow at approximately 4% each day. So, the correct answer is Option B: f(x) = 86(1.04)x; grows approximately at a rate of 4% daily.
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To find the daily growth rate of the weeds, we divide the weekly growth rate by 7. The correct function is f(x) = 86(1.04)x, which represents a daily growth rate of approximately 0.4%.
Explanation:To find how quickly the weeds grow each day, we need to convert the rate of growth from weekly to daily.
Since there are 7 days in a week, we can divide the weekly growth rate by 7 to get the daily growth rate.
In this case, the function f(x) = 86(1.29)x represents the weekly weed growth, so to find the daily growth rate, we use the function f(x) = 86(1.29/7)x.
Simplifying this expression, we get f(x) = 86(1.04)x.
Therefore, the correct answer is A. f(x) = 86(1.04)x; it grows approximately at a rate of 0.4% daily.
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NEED HELP WITH A MATH QUESTION
Answer:
x=6.6 cm
Step-by-step explanation:
The angle force at the point where the tangent touches the circle is 90° hence the triangle is a right angle triangle . We can apply the Pythagorean relationship in this case
Given the hypotenuse as x+ 8.45 and the base as x and height as 13.5 then;
a²+b²=c² .................where a=x , b= 13.5 and c x+8.45
x² +13.5²= (x+8.45)²
x²+182.25=x²+8.45x+8.45x+71.4025
x²+182.25=x²+16.90x+71.4025-----------------collect like terms
x²-x²+ 182.25-71.4025=16.90x
110.8475=16.90x-------------------divide by 16.90 to remain with x
110.8475/16.90 = x
x=6.5590
x= 6.6 cm