Answer:
x² - x - 2 = 0
Step-by-step explanation:
plotting the graph of x and y,we have that the root of the equation is -1 or 2
x = -1 or 2
the eqn therefore is;
x² - (sum of the root)x + (product of the root) =. 0
x² - (-1+2)x + (-1*2) = 0
x² - x - 2 = 0
Applying the Factor Theorem, it is found that the quadratic function is:
[tex]p(x) = x^2 - x - 2[/tex]
------------------------
The Factor Theorem states that if a polynomial [tex]p(x)[/tex] has roots [tex]x_1, x_2, ..., x_n[/tex], it is described by the following equation:
[tex]p(x) = a(x - x_1)(x - x_2)...(x - x_n)[/tex]
In which a is the leading coefficient.
For this quadratic function, the roots are [tex]x_1 = -1, x_2 = 2[/tex], as [tex]y(-1) = y(2) = 0[/tex], thus:[tex]p(x) = a(x - (-1))(x - 2)[/tex]
[tex]p(x) = a(x + 1)(x - 2)[/tex]
[tex]p(x) = a(x^2 - x - 2)[/tex]
When x = 0, p(x) = -2, and we use this to find a.
[tex]p(x) = a(x^2 - x - 2)[/tex]
[tex]-2 = a(0^2 - 0 - 2)[/tex]
[tex]2a = 2[/tex]
[tex]a = \frac{2}{2}[/tex]
[tex]a = 1[/tex]
Thus, the quadratic function is:
[tex]p(x) = x^2 - x - 2[/tex]
A similar problem is given at https://brainly.com/question/24380382
daria bought a lemonade cup for $9 . each refill cost $2 . last month daria spent $31 on mug and refills . How many refills did she buy?
Answer:
Daria bought 11 refills of lemonade last month
Step-by-step explanation:
The equation is:
y = 2x + 9
The cup costs 9 dollars and is 2 dollars per refill
She spent 31 dollars so:
31 = 2x +9
Now we can solve!
2x + 9 = 31
Subtract 9 from both sides!
2x = 22
Divide both sides by 2!
x = 11
We know x is the amount of refills so,
Daria bought 11 refills of lemonade last month!
Holly missed 7 of 181 school days this year. Approximately what percent of school days was Holly in attendance?
Answer:
96.13%
Step-by-step explanation:
181-7=174. 174/181
What whole number is closest to the square root of 80
Answer:
8.94427191
Step-by-step explanation:
8.95 or the closet answer from this
wyatt opend a savings account 4 years ago. the account earns 4%interest compounded quarterly if the current balance is $1,000.00 how much did he deposit initially round your answer to the nearest cent
Answer:
He deposited initially $852.82
Step-by-step explanation:
The rule of the compound interest is [tex]A=P(1+\frac{r}{n})^{nt}[/tex], where
A is the new amountP is the initial amountr is the rate in decimaln is the period of the timet is the time∵ Wyatt opened a savings account 4 years ago
∴ t = 4
∵ The account earns 4% interest compounded quarterly
∴ r = 4% = 4 ÷ 100 = 0.04
∴ n = 4 ⇒ compounded quarterly
∵ The current balance is $1,000.00
∴ A = 1,000
→ Substitute these values in the rule above to find P
∵ 1,000 = [tex]P(1+\frac{0.04}{4})^{4(4)}[/tex]
∴ 1,000 = [tex]P(1+0.01)^{16}[/tex]
∴ 1,000 = [tex]P(1.01)^{16}[/tex]
→ Divide both sides by [tex](1.01)^{16}[/tex]
∴ 852.8212622 = P
→ Round it to the nearest cent (2d.p)
∴ P = 852.82
∴ He deposited initially $852.82
Math Trainer
Lesson 5.1 - Evaluate
Evd
<<
2131415 516
718
9
Find the new amount given the original amount and the percent of change.
$7; 40% increase
The new amount is $
Answer:
Its chicken
Step-by-step explanation:
Answer:
$11
Step-by-step explanation:
Calculate the slope of a line that passes through the points (3, -20) and (5, 8).
6
14
26
4
Answer:
14
Step-by-step explanation:
Use rise over run, (y2 - y1) / (x2 - x1)
Plug in the points:
(y2 - y1) / (x2 - x1)
(8 + 20) / (5 - 3)
28 / 2
= 14
So, the slope is 14.
A tree casts a shadow 24 feet long at the same time a man 6 feet tall casts a shadow 4 feet long. Find
the number of feet in the height of the tree.
Answer:
22ft
Step-by-step explanation:
Well the man is 6ft and you take away 2 to get to 4ft so you will do the same with the tree.
Answer:
so this is what I did 24X4=96
Step-by-step explanation:
have a nice day
The ratio of boys to girls in a class is 5:6. How many boys are there if there are 33 students in the class?
Answer:
15.
explaination:
let x be the number which we have to times to the ratio.
(5+x) + (6+x) =33
5x + 6x =33
11x = 33
x=3
so we need to times 3 the ratio to get the actual number.
boys: 5 × 3 =15
girls:6 × 3 = 18
checking the answer: 15+ 18 = 33
Dustin's Lawn Care Service Customer Amount Paid Mrs. Schmitt $15.75 Mr. Jones $9.25 Mrs. Adams $22.50 Mr. Meyer $50.00 How much more does Dustin get paid to mow Mr. Meyer's lawn than to mow the other three lawns combined? Enter your answer in the box. I need helppppp!
Answer: $2.50
Step-by-step explanation:
The following payments are made by Dustin's Lawn Care Service Customer
Mrs. Schmitt = $15.75
Mr. Jones = $9.25
Mrs. Adams = $22.50
Mr. Meyer = $50.00
To get our answer, we need to add all the payments of the other three. This will be:
= $15.75 + $9.25 + $22.50
= $47.50
The answer will now be:
= $50.0 - $47.5
= $2.50
The dockland building in hamburg, germany is built in the shape of a parallelogram. What is the length of the flight of stairs that runs from the ground to the rooftop? Round your answer to the nearest meter. Show your work.
Answer:
The length of the flight of stairs is 52 m
Step-by-step explanation:
In parallelograms, opposite sides are equal in length
In the given figure
∵ The building is built in the shape of a parallelogram
∵ The length of the flight of stairs is one side of it
→ We can find it by finding the hypotenuse of the right triangle
whose legs are 47 m and 22 m
∴ The length of it = the length of the hypotenuse of the right Δ
→ By using the Pythagoras Theorem
∵ h = [tex]\sqrt{(leg1)^{2}+(leg2)^{2}}[/tex]
∵ leg1 = 47 and leg2 = 22
∴ h = [tex]\sqrt{(47)^{2}+(22)^{2}}[/tex]
∴ h = [tex]\sqrt{2209+484}[/tex]
∴ h = [tex]\sqrt{2693}[/tex]
∴ h = 51.89412298
∵ h represents the length of the flight of stairs
∴ The length of the flight of stairs = 51.89412298 m
→ Round it to the nearest meter
∴ The length of the flight of stairs = 52 m
Which graph best represents the download speed of a large file?
P.S. I will give brainliest to the best answer!
Answer:
graph d because it starst out slower and then ends off faster
The graph that correctly represents the given case is B.
What is the slope of straight line?The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference.
The negative slope indicates the rate of decrease while the positive shows the rate of increase.
All the graphs are examined one by one as follows,
(A) In the graph A, The slope is negative.
Which implies the the speed will slow down.
(B) In the graph B, The slope is positive.
Which implies the the speed will rise up.
(C) ) In the graph C, The slope is zero.
Which implies the the speed will be constant.
(D) In the graph D, The slope is positive and it has a y intercept.
Which implies the the speed will rise from a non zero value.
Thus, in order to download a large file the suitable graph is (B).
Hence, the given case can be represented by graph B.
To know more about slope click on,
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Pls help this is due at 8am it’s currently 6:36am
Answer:
207
Step-by-step explanation:
1. False. 0 does not equal to 6. No answers.
2. False. x=0 means the answer is 0.
3. True.
4. False. 2 does not equal -2. No answers.
5. True.
Code: (6*6*6)-(3*3)=207
Answer:
no entiendo. adonde estas la pregunta?
Step-by-step explanation:
I need help ASAAAPPP
Answer:
y = 1
Step-by-step explanation:
Since the line never crosses the x-axis, the equation just looks like this: y = 1, because 1 is where the line crosses the y-axis.
what is the second equation for this??
Step-by-step explanation:
She spent nine dollars in the second equation, so it would be one adult ticket and two children's tickets, or 1x + 2y= 38
Solve the system using substitution. 5x-y=73 and 2y=x
Answer:
Point form:( [tex]\frac{146}{9} \\\\[/tex], [tex]\frac{73}{9}[/tex])
Equation form: x= [tex]\frac{146}{9}[/tex], y= [tex]\frac{73}{9}[/tex]
Step-by-step explanation:
Plz mark brainliest.
Which expression is equivalent to three times the sum of six and five?
A. 3 × 6 + 5
B. 3 × 5 + 6
C. 3(6 + 5)
D. 3 + (5 × 6)
Answer: C 3(6+5)
3 multiplied by the sum or (6+5)
Mariza é costureira e, para determinar o comprimento de elástico, em cm, que utiliza na confecção de determinado modelo de calça, ela recorre à expressão x2+2y . Nessa expressão, x e y são medidas que variam de acordo com o tamanho da calça a ser produzida. Para o tamanho P dessa calça, ela utiliza x=40 cm e y=15 cm
Solve for x. 5(x - 3) + 4(x + 3) = 3(x - 1)
Answer:
x = 0
Step-by-step explanation:
5(x - 3) + 4(x + 3) = 3(x - 1)
5x - 15 + 4x + 12 = 3x - 3
5x + 4x + 12 - 15 = 3x - 3
9x - 3 = 3x - 3
9x = 3x - 3 + 3
9x = 3x
9x - 3x = 3x - 3x
6x = 0
6x ÷ 6 = 0 ÷ 6
x = 0
Answer:
5( x− 3 ) + 4 ( x +3)
9x − 3 = 3(x− 1 ) Simplify 3 ( x − 1 ) .
9 x − 3 = 3 x − 3
Move all terms containing x to the left side of the equation.
6 x − 3 = −3
Move all terms not containing x
to the right side of the equation.
6 x = 0
Divide each term by 6 and simplify.
x = 0
imagine going on question cove
Answer:
Is this a real question...or....
Answer:
They kinda suck
Step-by-step explanation:
Ngl they suspend/ban ppl for no real reason :l and wonder why ppl don't visit they site
HELP ILL MARK BRAINLIEST!
After u write the expression explain the reasoning you used please!
Answer:
194 yards
Step-by-step explanation:
Perimeter of the proposed parking lot
= 52 + 40 + 20 + (40 - x) + 24 + 10 + (52 - 20 - 24) + x
= 112 + (40 - x + x) + 34 + (52 - 44)
= 146 + 40 + 8
= 194 yards
Brainliest 5 stars Thanks!
Use the Remainder Theorem.
Answer:
If f(1)=0 then 1 is a root and (x-1) is a factor of f(x). divide f(x) by (x-1). you now have a quadratic. Find its roots by methods you know.
actually this factors by grouping:
f(x)=x³+3x²-x-3
= x²(x+3)-1(x+3)
=(x+3)(x²-1)
=(x+3)(x-1)(x+1) // difference of squares
By zero product property roots are
-3, -1, 1
Your keys drop from the top of the tower and fall straight to the ground. You want to know how far from the base of the tower the keys landed. Draw a right triangle that will help you solve the problem. Label each triangle with the information you know
Answer:
46.35m
Step-by-step explanation:
150sin(72)=46.35
What is the solution for -3x ≥ 36? x ≤ -12 x ≥ -12 x ≤ -108 x ≥ -108
Answer:
its a
Step-by-step explanation:
Answer
im postive its A:)
Step-by-step explanation:
15) A car salesman earns $700 per week plus 2.5% commission on his sales. If he
sold two cars for a total of $75,000 last week, how much did he make?
Please help!
Answer:
$2575
Step-by-step explanation:
For this problem, we need to form an equation that represents the car salesman's weekly income. We are given that he makes at least $700 per week and that he makes 2.5% commission for his sales. Let n represent the total amount of sales the car salesman made. So we can build the equation as follows:
f(n) = 0.025n + 700
Note that if we let n = 0 (He made no sales) then he will make his minimum weekly income of $700.
So let's use our formula to calculate how much he made for the week given he made $75000 in sales.
f(75000) = 0.025(75000) + 700
f(75000) = 1875 + 700
f(75000) = 2575
Hence, the car salesman made $2575 for the week.
Cheers.
What is a scale factor?
The ratio of weight of similar 2-D figures
The ratio of corresponding angles of similar figures
The ratio of corresponding sides of similar figures
The ratio of volume of similar 2-D figures
Answer:
Here is some helpful information from my mini lessons.
Step-by-step explanation:
If two objects have the same shape, they are called "similar." When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles shown are similar, compare their corresponding sides. Here you'll learn that the ratio of the perimeters of similar figures is equal to their scale factor and that the ratio of their areas is equal to the square of their scale factor. If two polygons are similar, then the ratio of the lengths of any two corresponding sides is called the scale factor. This means that the ratio of all parts of a polygon is the same as the ratio of the sides.
Principal: $100 Interest Rate: 5% Time: 6 months What is the interest?
if (6^2)^x = 1, what is the value of x? explain your answer.
Answer:
X = 0
Step-by-step explanation:
What are the x-intercept and the y-intercept of the graph of 9x − 7y = −63?
Answer:
x-intercept: 7; y-intercept: −9.
Step-by-step explanation:
Answer:
x=-7
y=-9
Hope I helped you
[tex] \frac{3}{4} + \frac{1}{2} [/tex]
please help I forgot how to do this
Answer:
5/4
Step-by-step explanation:
You just need to multiply 1/2 by 2 to give you a common denominator:
3/4+2/4
From there you can add the numerators:
5/4
HTH :)
89 x 89, whats the answer?
Answer:
7921 is the correct answer
Answer:
7,291
Step-by-step explanation:
Just multiply. 89 x 89