Answer:
x² - 3x - 10 = 0
Step-by-step explanation:
Given there are 2 solutions then the equation is a quadratic.
Since the solutions are x = - 2 and x = 5 then
the factors are (x + 2) and (x - 5) and
f(x) = (x + 2)(x - 5) ← expand factors
= x² - 3x - 10, hence the equation is
x² - 3x - 10 = 0
The equation that yields the solutions x = -2 and x = 5 is: x^2 + 0.00088x - 0.000484 = 0. We can solve this equation using the quadratic formula.
Explanation:The equation that yields the solutions x = -2 and x = 5 is:
x^2 + 0.00088x - 0.000484 = 0
To solve this equation, we can use the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac))/(2a)
Plugging in the values from the equation, we get:
x = (-0.00088 +/- sqrt((0.00088)^2 - 4(1)(-0.000484)))/(2(1))
Simplifying further, we have:
x = (-0.00088 +/- sqrt(0.0000007744 + 0.001936))/0.002
Continuing to simplify, we get:
x = (-0.00088 +/- sqrt(0.0027104))/0.002
Finally, we have the two possible solutions:
x = (-0.00088 + sqrt(0.0027104))/0.002 and x = (-0.00088 - sqrt(0.0027104))/0.002
The perimeter of a triangle is 76 cm. Side a of the triangle is twice as long as side b. Side c is 1 cm longer than side a. Find the length of each side.
Let side B = X
Then side A = 2x
Side C = 2x +1
Mow you have x + 2x + 2x+1 = 76
Simplify:
5x +1 = 76
Subtract 1 from both sides:
5x = 75
divide both sides by 5:
x = 75 /5
x = 15
Side A = 2x = 2*15 = 30 cm
Side B = x = 15 cm
Side C = 2x +1 = 2*15 +1 = 30+1 = 31 cm
HELP ASAP What is the simplified value of the exponential expression 216^1/3
Answer:
Final simplified expression is 6.
Step-by-step explanation:
We have been given an expression [tex]216^{\frac{1}{3}}[/tex].
Now we need to simplify [tex]216^{\frac{1}{3}}[/tex] So let's do that by factoring 216 first so that we can have same repeating factor thrice
[tex]216^{\frac{1}{3}}[/tex]
[tex]=(6*6*6)^{\frac{1}{3}}[/tex]
[tex]=(6^3)^{\frac{1}{3}}[/tex]
Apply formula [tex](x^m)^n= x^{m*n}[/tex]
[tex]=6^{3*\frac{1}{3}}[/tex]
[tex]=6^{1}[/tex]
[tex]=6[/tex]
Hence final simplified form is 6.
Describe the pattern below. Write another pattern that has the same fourth value. Describe your pattern 0.41,0.82,1.64,3.28
Answer:
times 2
Step-by-step explanation:
0.41*2=0.82
0.82*2=1.64
divide by 2...pattern is 3.28,1.64,0.82,0.41
Another pattern with the same fourth term is one where to get the next term in the sequence we multiply the previous one by -2, and the first term is -0.41,
Analyzing the given pattern.
We have the pattern:
0.41, 0.82, 1.64, 3.28
Is ratter easy to see that it is a geometric sequence, such that each term is twice the previous term:
0.82 = 2*0.411.64 = 2*0.813.28 = 2*1.64Now we just want to make another pattern that has the same fourth term, so we can play with the given pattern.
Suppose we start with -0.41, and instead of by 2, we multiply each time by -2, then we get:
a₁ = -0.41a₂ = (-2)*(-0.41) =0.82a₃ = (-2)*(0.82) = -1.64a₄ = (-2)*(-1.64) = 3.28And so on, so we just found another pattern that has the same fourth term, but behaves differently.
If you want to learn more about sequences, you can read:
https://brainly.com/question/9300199
Becky graphs a system of two linear equations and determines that (1,5) and (3,7) are solutions. What does the graph of the system look like? How many solutions are possible? A) curve; two solutions B) two lines; one solution C) two lines; two solutions D) one line; infinitely many
Answer:
D
Step-by-step explanation:
I got it right
There infinitely many solutions are possible. Option D is correct.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
For two intersecting lines, it is not possible that the lines have only two solutions, either the lines have one solution or the lines have infinitely many solutions,
In our case line have infinitely many solutions,
Because the equations of the lines are the same.
Now,
The equation of the line is given as,
y - y₁ = m (x - x₁)
y - 5 = [7-5 / 3-1] (x - 1)
y = x - 1 + 5
y = x + 4
Thus, there infinitely many solutions are possible. Option D is correct.
Learn more about simultaneous equations here:
https://brainly.com/question/16763389
#SPJ5
The tangent and secant functions are undefined for the same values true or false
Answer:
TRUE
Step-by-step explanation:
tanθ = 1/cotθ
cotθ = 0 when θ = ±(1/2)π, ±(3/2)π, … ±[(2n+1)/2]π.
∴ tanθ is undefined when θ = ±[(2n+1)/2]π.
secθ = 1/cosθ
cosθ = 0 when θ = ±(1/2)π, ±(3/2)π, , …, ±[(2n+1)/2]π.
∴ secθ is undefined when θ = ±[(2n+1)/2]π.
The tangent and secant functions are undefined for the same values of θ.
Answer:
True
Step-by-step explanation:
The tangent and secant functions are undefined for the same values.
Secant and tangent are trigonometry function. Each function has fix value for fix angle.
For angle 90° degree or [tex]\dfrac{\pi}{2}[/tex]
As we know,
[tex]\tan90^\circ=\infty[/tex]
[tex]\tan\dfrac{\pi}{2}=\infty[/tex]
[tex]\sec90^\circ=\infty[/tex]
[tex]\sec\dfrac{\pi}{2}=\infty[/tex]
True
∞ is undefined.
Hence, Both tangent and secant are undefined at 90°
PLZ ANSWER RIGHT, POINTS 99!!
Select the correct answer from each drop-down menu.
Consider the following equation.
[tex]0 = x^{2} - 10x - 27[/tex]
Complete each statement about the solutions to the equation.
The negative solution is between (Q1)__ and (Q2)__.
Q1.) A. -13
B. -3
C. -2
D. -12
Q2) A. -1
B. -11
C. -12
D. -2
________________________________________________
The positive solution is between (Q3)__ and (Q4)__.
Q3.) A. 11
B. 1
C. 2
D. 12
Q4.) A. 13
B. 3
C. 12
D. 2
Using the quadratic formula -b +/-√b^2-4(ac) / 2a solve for x:
10 +/-√(-10)^2 -4(1*27) / 2*1
x = 5 +/-2√13
x = -2.21
or x = 12.21
The negative solution is between -2 and -3.
The positive solution is between 12 and 13.
A factory can produce 100 bracelets every 15 minutes. How many bracelets can the factory produce in three and a half hours?
Answer:
1,400 bracelets in 3 and a half hours
Step-by-step explanation:
First you have to find how many minutes are in 3 and a half hours. 1 hour is 60 minutes, so 60 + 60 + 60 is 3 hours or 180 minutes and 30 minutes is a half an hour. Therefore 3 and a half hours equals 210 minutes. Set up an equal proportion: 100 bracelets / 15 min = x bracelets / 210 min. Use algebra to solve: 100 * 210 = 15x → 21000 = 15x → 1400 = x.
1400 bracelets can the factory produce in three and a half hours.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
A factory can produce 100 bracelets every 15 minutes.
So, In one minutes the factory produced
= 100 /15
= 20/3
Now, In three and a half hours ( 210 minutes) the factory can make
= 20/3 x 210
= 20 x 70
= 1400
Hence, In three and a half hours 1400 bracelets can be made.
Learn more about Unitary Method here:
https://brainly.com/question/22056199
#SPJ2
Alecia walked 3/10 of a mile from school,stopped at the grocery store on the way, then walked another 4/10 of a mile home.Georgia walked 67/100 of a mile from school to her home.Which of the girls live farther from school? Explain.
Answer:
Alecia lives farther from school
Step-by-step explanation:
Georgia
we know that
The distance from the school to her home is 67/100 of a mile
[tex]\frac{67}{100}=0.67\ miles[/tex]
Alecia
we know that
The distance from the school to her home is
3/10 of a mile plus 4/10 of a mile
so
[tex]\frac{3}{10}+\frac{4}{10}=\frac{7}{10}=0.7\ miles[/tex]
Compare the distances
[tex]0.7\ miles>0.67\ miles[/tex]
therefore
Alecia lives farther from school
Final answer:
The answer explains that Georgia lives farther from school than Alecia based on the distances they walked.
Explanation:
Alecia: Walked 3/10 mile from school + 4/10 mile back home = 7/10 mile total distance.
Georgia: Walked 67/100 mile total distance.
Alecia vs. Georgia: Alecia walked 0.7 mile, Georgia walked 0.67 mile. Georgia lives farther from the school as 0.7 > 0.67 mile.
Edwina measured the length of this swimming pool by drawing similar triangles as shown. What is the best estimate of p, the length of the swimming pool?
Answer:
Option C. [tex]p=33\ ft[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
In this problem
Using proportion
[tex]\frac{p}{12}=\frac{22}{8}\\ \\p=12*22/8\\ \\p=33\ ft[/tex]
Answer:
c
Step-by-step explanation:
bc i took quiz
When are the x-intercept and the y-intercept of a graph identical?
at the origin
they are same
Answer:
The only time that both intercepts are identical is when they form the line of [tex]x = y[/tex], which is the origin, and MUST be a POSITIVE RATE OF CHANGE [SLOPE].
I am joyous to assist you anytime.
It’s right angle trig
WILL MARK BRAINLIEST!!!
c = 17.78
b = 12.12
............
Answer:
b = 12.1
c = 17.8
Step-by-step explanation:
First, we can solve for c by using sine: sin(47) = 13/c -> c = 13/sin(47) = 17.8 rounded to the nearest 10th.
Then, we can solve for b by using tangent: tan(47) = 13/b -> b = 13/tan(47) = 12.1 rounded to the nearest 10th.
I hope this helped you.
The perimeter of a triangle is given by the formula P = a + b + c. Solved for b, this formula becomes b =
Answer: B) P-a-c.
Step-by-step explanation:
The value of b is P - a - c.
Given,
The perimeter of a triangle is given by the formula P = a + b + c.
We need to solve for b.
What is the perimeter of a triangle?The total length of all three sides of a triangle is called the perimeter of the triangle.
It is given by:
P = a + b + c
Where a,b, and c are the sides of the triangle.
We have,
P = a + b + c
Subtracting a on both sides
P - a = a + b + c - a
P - a = b + c
Subtracting c on both sides
P - a - c = b + c - c
P - a - c = b
We get,
b = P - a - c
Thus the value of b is P - a - c.
Learn more about the Perimeter of a triangle here:
https://brainly.com/question/12901661
#SPJ2
The gravitational force on the earth is six times greater than on the moon. This means objects weigh six times as much on earth as they do on the moon. Write an algebraic expression for the weight of an object on earth if its weight on the moon is m.
Answer:
y=6x
Step-by-step explanation:
let y be the weight of an object on the earth
let x be the weight of the same object on the moon
Since the weight of an object on earth is 6 times greater than the same thing on the moon, You must multiply the weight of something on the moon by six.
Hope this helped!
Final answer:
The algebraic expression for the weight of an object on Earth given its weight on the Moon, denoted as 'm', is 'W = 6m', where 'W' represents its weight on Earth.
Explanation:
The question is asking us to find an algebraic expression for the weight of an object on Earth given its weight on the Moon.
We know that the gravitational force on Earth is six times greater than on the Moon, which means objects weigh six times more on Earth than on the Moon.
If the weight of an object on the Moon is given as m, then the weight of the same object on Earth, W, would be W = 6m.
Identify the graph of 4x^2+5y^2=20 for T(5,-6) and write an equation of the translated or rotated graph in general form. (picture provided)
Answer:
b. ellipse; [tex]4x^2+5y^2-40x+60y+260=0[/tex]
Step-by-step explanation:
The graph of [tex]4x^2+5y^2=20[/tex] an ellipse because the coefficients of the quadratic terms are not the same.
This ellipse is centered at the origin. If this ellipse is translated so that its center is now at [tex](5,-6)[/tex].
Then the translated ellipse will now have equation.
[tex]4(x-5)^2+5(y+6)^2=20[/tex]
We expand to get;
[tex]4(x^2-10x+25)+5(y^2+12y+36)=20[/tex]
[tex]4x^2-40x+100+5y^2+60y+180=20[/tex]
[tex]4x^2+5y^2-40x+60y+100+180-20=0[/tex]
[tex]4x^2+5y^2-40x+60y+260=0[/tex]
Answer:
B
Step-by-step explanation:
just took it on edge and it was right :)
math 23 points help please asap
The answer is A because the rest of them for any given x you get 2 or more values of y
Karleigh walks 5/8 mile to school every day . How far does she walk to school in 5 days
Hello, thanks for using Brainly!
First, our equation is: [tex]5/8[/tex] x [tex]5 = 25/8.[/tex]
Our first step is to simplify.
When you simplify you get 3 1/8.
This is another way you can get it: (Multiply across. )
[tex]Number[/tex] [tex]of[/tex] [tex]the[/tex] [tex]miles = \frac{5}{8}[/tex] [tex]5 = \frac{25}{8} = 3\frac{1}{8}[/tex]
Enjoy your day.
Jacob's daily tips this work week were $99, $78, $58, $91, $90, and $68. Is Jacob correct in thinking that the median best represents how much money he makes in daily tips?
Answer:
no
Step-by-step explanation:
median only shows the amount in the very middle. to represent how much money he makes in daily tips, he needs to find the mean (the average).
Answer:
Little close
Step-by-step explanation:
In statistics, when we have a list of entries to be analyzed we have few figures for observation. These are
Mean , median and mode.
Mean gives the average of all the entries. By average means.
Median gives you the middle most entry.
And mode gives the entry repeated the most.
As by definition we see that , median will give us approximation regarding daily data, hence jacob must consider the median to best represent the money he makes on daily basis.
Bryson makes an annual salary of $42,000 a year. Apply the rule of housing to determine his monthly housing budget.
A. $420
B. $600
C. $875
D. $1,025
Answer:
C. $875
Step-by-step explanation:
The rule of housing is the rule of thumb of not using more than 25% of your gross income. This means that the households supposed limited expenses on housing would be a maximum of 25% only.
So to find the monthly housing budget of Bryson, we simply take his annual salary and multiply it by 25% or 0.25 and then divide the product by 12.
Monthly Housing Budget = ($42,000 * 0.25)/12
Monthly Housing Budget = 10500/12
Monthly Housing Budget = $875
Answer: C. $875
Step-by-step explanation:
CUZ IT IS.... hope all of you guys become successful.
i went to sleep randomly on my bed and i woke up with ducks quacking around me. how do i call the bug exterminator? how many steps do i take toward the phone and the distance?
You don't it's not a bug
Answer:Since You slept randomly, there can’t be a duck in your bedroom, no further explanations is needed.
Step-by-step explanation:
Matt measures 3 peices of string. The first peice is 544 cm , the second peice is 144 cm,and the third peice is 112 cm. How many meters of string does he have altogether
Answer:
[tex]8\ m[/tex]
Step-by-step explanation:
we know that
[tex]1\ m=100\ cm[/tex]
step 1
Sum the 3 pieces of string
[tex]544+144+112=800\ cm[/tex]
step 2
Convert centimeters to meters
[tex]800\ cm=800/100=8\ m[/tex]
Angela is buying a dress that is on sale for 20% off. If the original price of the dress is $60.00, how much money is Angela saving on the dress?
Answer:
$48
Step-by-step explanation:
1. multiply the original price (60) by the percent off (20% or 0.20)
60 * .20 = 12 (the discount)
2. subtract the discount (12) from the origianl price (60)
60-12 = 48
Answer:
12
Step-by-step explanation:
bc i got it right on study island lol
Which explains, on a given day, which island is more likely to have a wind speed close to its median?
Answer:
Country B because the median is closer to the center of the box in the box plot.
Step-by-step explanation:
In the figure attached the box plots show the average wind speeds, in miles per hour, for two different islands (Country A on the top, Country B on the bottom).
The median of Country A is 4 and the center of the box is 5
The median of Country B is 6 and the center of the box is 6.5
Answer:
B
Step-by-step explanation:
Did it on edg
A computer rounded the number 129.257 to the nearest hundredth what is this number rounded to the nearest hundredth
Answer:
it is 129.3 you just round
What is the area of the triangle if the base is 5 centimeters and the height is 6 centimeters?
A. 15 cm2
B. 12 feet
C. 4 m3
D. 16 inches
Answer:
15cm2
Step-by-step explanation:
Area of a triangle is b*h/2
B is 5
H is 6
5 * 6 = 30
30/2 = 15
Answer:
A
Step-by-step explanation:
The area of a triangle is base * height, divided by 2
bh/2 (same thing as multiplying by .5 or 1/2)
given:
base: 5 cm
height: 6 cm
(5 * 6)/2 = 15 cm^2
therefore the answer is A
Use the graph of the function f to determine f(x)
Answer: option a.
Step-by-step explanation:
The [tex]\lim_{x \to a} f(x)[/tex] give us information about the behavior of the function when the variable x gets closer to the value a. In other words, it tells us to what value y gets closer when x gets closer to the value a.
In this case we are evaluating the limits when:
[tex]{x \to -3}[/tex]
[tex]{x \to 0}[/tex]
[tex]{x \to 2}[/tex]
of the function shown in the graph.
As you can observe in the graph, when:
[tex]{x \to -3}[/tex] , [tex]y=3[/tex]
[tex]{x \to 0}[/tex] , [tex]y=0[/tex]
[tex]{x \to 2}[/tex] , [tex]y=-2[/tex]
Which equation is represented by the intersection of the graph below?
Answer:
tan(x) = 1
Step-by-step explanation:
The red curve(s) are y=tan(x). The horizontal line is y=1, so the point(s) of intersection are where tan(x) = 1.
_____
Sine and cosine do not have infinite range.
The range of secant excludes (-1, 1), so the only remaining possibility for the red curve is tan(x).
if you borrow $308 for one year at an interest rate of 6% compounded annually, how much interest will you pay?
Answer: $18.48
Step-by-step explanation: The formula for interest is I = PRT, where I equals interests, P equals the principle, R equals the rate and T is Time.
I = 308 x .06 x 1
I = $18.48
You will pay $18.48 interest for one year.
The function y = x 2 – 4x + 8 approximates the height, y, of a bird, and its horizontal distance, x, as it flies from one fence post to another. All distances are in feet. Complete the square to find and interpret the extreme value (vertex). Select two answers: one extreme value and one interpretation
Answer:
Exterme Value: [tex](2,4)[/tex].
The bird reaches its minimum height which is 4ft affter covering a horizontal distance of 2 ft.
Step-by-step explanation:
The given function is [tex]y=x^2-4x+8[/tex].
We add and subtract the square of half the coefficient of x.
[tex]y=x^2-4x+(-2)^2-(-2)^2+8[/tex].
The first three terms form a perfect quadratic trinomial.
[tex]y=(x-2)^2+4[/tex].
This function is now written in the form [tex]y=a(x-h)^2+k[/tex], where (h,k) is the extreme value(vertex).
The extreme value or the vertex is [tex](2,4)[/tex].
Interpretation:
The bird reaches its minimum height which is 4ft affter covering a horizontal distance of 2 ft.
Answer: minimum at( 2,4)
Step-by-step explanation:
A p e x
Six times a number is greater than 20 more than that number. What are the possible outcomes of that number ?
NEED HELP ASAP BRAINLIEST ANSWER
Four sizes of scaled text are shown
What is the unknown scale size?
Enter your answer as a decimal in the box. Round only your final answer to the nearest thousandth
Answer:
1.172
Step-by-step explanation:
1.954
-1.563
=0.391
So you must minus 0.391 from 1.563
1.563-0.391= 1.172
Answer:
Unknown scale is 1.25
Step-by-step explanation:
Here size of fonts have been enlarged with a scale factor. Scale factor means a common factor by which a sequence is formed.
The given sequence will be a geometric sequence.
So common ratio between 3rd and 4th fonts = [tex]\frac{1.954}{1.563}=1.25[/tex]
This ratio will be same in 1st and second fonts = [tex]\frac{1.25}{1}=1.25[/tex]
So unknown scale size is 1.25