Answer:
a = - 2, b = - 6
Step-by-step explanation:
Substitute the values of the zeros into the polynomial and equate to zero.
x² +(a + 1)x + b
x = - 2 → (- 2)² - 2(a + 1) + b = 0 , that is
4 - 2a - 2 + b = 0
2 - 2a + b = 0 ( subtract 2 from both sides )
- 2a + b = - 2 → (1)
x = 3 → 3² + 3(a + 1) + b = 0, that is
9 + 3a + 3 + b = 0
12 + 3a + b = 0 ( subtract 12 from both sides )
3a + b = - 12 → (2)
Subtract (1) from (2) term by term to eliminate b
5a = - 10 ( divide both sides by 5 )
a = - 2
Substitute a = - 2 into either of the 2 equations and evaluate for b
Substituting into (2)
3(- 2) + b = - 12
- 6 + b = - 12 ( add 6 to both sides )
b = - 6
Thus a = - 2 and b = - 6
A taxi charges $2.00 for the first mile and $1.60 for every additional mile. Rachel is taking a trip that is 4 miles long. How much will she be charged?
Use the number line to find the coordinate of the midpoint of segment DE
Answer:
x1+x2/2
7+11/2
18/2=9
Step-by-step explanation:
The midpoint of segment DE is 9 units.
It is required to find the midpoint of segment DE.
What is midpoint ?The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
Given:
By mid point formula we get,
The midpoint formula is applied when one is required to find the exact center point between two defined points.
The coordinate of point D is 7 units.
The coordinate of point E is 11 units.
According to given question we have,
The midpoint of segment DE
[tex]=\frac{x_{1} +x_{2} }{2} \\=(7+11)/2\\\\=18/2\\\\=9[/tex]
Therefore , the midpoint of segment DE is 9 units.
Learn more details about midpoint here:
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What’s the answer 40=16-8r ?
Answer:
-3
Step-by-step explanation:
40=16-8r
Subtract 16 from both sides.
24=-8r
Now divide by -8
-3=r
Answer:
-3= r
Step-by-step explanation:
40= 16- 8r
subtract 16 from both sides
40-16= 16 - 16 -8r
24= -8r
divide both sides by -8
24/-8 = -8r/-8
-3= r
6x-3 = 5x-5 any got a homie
Answer:
x= -2
Step-by-step explanation:
6x-3 = 5x-5
6x-5x=-5+3
x= -2
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Please Help!! 8 Points!! Brainliest Answer!!
Answer:
right 5 down 3, I believe
Why didn't the butterfly go to the dance? show your thinking!
Answer:
its math roll dont wory ill show with no math and explantion its just awnsers
Step-by-step explanation:
8 i
4 t
11 w
1 a
6 s
9 a
14 m
7 o
10 t
3 h
13 b
5 a
2 L
I couldnt get the last one but i did in the same order as it has it
To solve the question we used the criteria that the solution depends upon the sign, if negative number is greater than sign will be a minus .
if positive number is greater than sign will be a plus.
The sign while addition and subtraction depends on the larger number .
If negative number is greater than sign will be a minus .
if positive number is greater than sign will be a plus.
1.
A. -5+2=-3
B. 7+-3= 4
C. -4+-6=-10
2.
A. 1+-8=-7
B. -6+-12=-18
C. -2+9=7
3.
A. -7+6=-1
B. 5+-8=-3
C. 12+13=25
4.
A. -10+-10=-20
B. 17+-1=16
C. -11+5=-6
5.
A. 4+-9=-5
B. -7+-15=-22
C. -3+12=9
6.
A. 16+-8 = 8
B. -5+20=15
C. -6+6=0
Similarly we can do the remaining solutions.
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What is 0.941941 repeating in fraction form ( simplest form) I need help!!!!
0.941941 converted to a simplified fraction is 941941/1000000
A pasta factory made 328.16 pounds of pasta in 7 minutes. How much pasta, on average, did the factory make each minute?
Answer:
46.88 lb per minute
Step-by-step explanation:
328.16/7
46.88
(9^3)^2 Hurrrrryyyyyyyyyyyyyy
Answer: 531441
Step-by-step explanation:
Convert 6 7/20
into a decimal
Hey there!
ANSWER: [tex]0.35[/tex]EXPLANATION:[tex]6 \frac{7}{20}[/tex] as a decimal
The percentage for 6 7/20 is 35%. So if that was the percent, then the decimal would be 0.35.
[tex]0.35(ANSWER)[/tex]
Hope this helps!
[tex]\text {-TestedHyperr}[/tex]
Find the perimeter of the polygon with the vertices $Q(-3,\ 2),\ R(1,\ 2),\ \ S(1,-2),$ and $T(-3,-2)$ .
Answer:
The perimeter is 16 units.
Step-by-step explanation:
Once you graph all the sides you can easily count and see the perimeter is 16. :)
Mt. Everest is 29,029 feet above sea level. The dead sea is 1,411 feet below sea level what is the difference between the elevations?
Answer:
30,440 feet
Step-by-step explanation:
You simply just add 29,029 and 1411 because if you picture it on a number line, 29,029 would be to get to zero as well as 1411 going up in elevation.
2(10 − 6) 2 + 3(12 − 10)
Answer:
hope this helped you
please mark as the brainliest (ㆁωㆁ)
is 6.458 a rational number
Answer:
It is a rational number
Answer:
Rational
Step-by-step explanation:
6.458 is rational because it is not repeating or infinite.
pleseeeeeeeeeeeeeee helllllllppppp fassttttty pleaseeeeeeeee
Answer:
0.10
Step-by-step explanation:
[tex]0.15 = \frac{15}{100} \\ 0.40 = \frac{40}{100} \\ 0.35 = \frac{35}{100} \\ [/tex]
Since all of them have the denominator as 100,
the total no. of sweets must be 100. So,
No of strawberries= 100-15-40-35
= 10
p(taking a strawberry sweet)= 10/100
= 0.10
Answer:
0.10
Step-by-step explanation: did work
Dylan buys 3.2 pounds of grapes for $2.56. What is the price per pound of the grape.
Answer:
$1.25
Step-by-step explanation:
3.2/2.56=1.25
Answer:
1.25
Step-by-step explanation:
3.2/2.56=1.25 i know because i am the future
(14d2 - 8) + (6d2 - 2d +1)
Step-by-step explanation:
Please help, image is attached! Thanks.
When something is bisected, it is cut into two equal halves.
We know that SV cut RST into two parts.
Those two parts are RSV and VST
RSV = 64 and VST = 64
RST = RSV + VST = 64 + 64 = 128
The correct answer should be 128
Answer:
I.128
Step-by-step explanation:
Since SV bisected angle RST, the angle is split in two by equal parts, therefore RSV + VST = RST
64 + 64= 128
128°= RST
Complete the table and find the balance A if $5000 is invested an an annual rate of 6% for 15 years and compounded n times a year
Answer:
1: 11982.79
2: 12136.31
4: 12216.09
12: 12270.46
365: 12297.10
Step-by-step explanation:
The compound interest formula is A=P*(1+r/n)^nt
P=principal amount
r=rate
n=number of compounds per period
t=number of periods
In this situation, the principal amount is 5,000=P. The rate is 6%, so r=0.06. n is equal to the top number in the table. And this is 15 years, so t=15.
For 1, it would be A=5,000*(1+.06/1)^1*15, or A=5,000(1.06^15), or 11982.79.
For 2, it would be 5,000*(1+.06/2)^2*15, or 5,000*(1.03^30), or 12136.31.
And so forth. Good luck
Anna has amask collection of 60 masks. She keeps 45% of the masks on her wall. How many masks does she keep on her wall?
Answer:27
Step-by-step explanation:
60x.45=27
Create a quadratic function f(x), other than f(x) = x^2, and write it below. Then below the function, state the domain, range, x-intercepts, y-intercept, and f(3).
Answer:
[tex]f(x)=2x^{2}-3[/tex]
[tex]D=(-\infty,\infty)[/tex]
[tex]R=[-3,\infty)[/tex]
x-intercepts: [tex](\frac{\sqrt{6}}{2},0)[/tex] and [tex](-\frac{\sqrt{6}}{2},0)[/tex]
y-intercept: (0,-3)
f(3)=15
Step-by-step explanation:
A quadratic function is any polynomial function whose greatest power is a 2, so [tex]f(x)=2x^{2}-3[/tex] is a nice example of it.
For the domain, as a rule, polynomial functions that have positive whole degrees will be defined for all real numbers, so:
[tex]D=(-\infty,\infty)[/tex]
When talking about quadratic functions, its range will happen from the lowest point (in this case the vertex) to it's highest point (in this case infinity)
In order to find the vertex, we can use the following formula:
[tex]x=-\frac{b}{2a}[/tex]
which is used for quadratic equations in standard form:
[tex]y=ax^{2}+bx+c[/tex]
In this case a=2, b=0 and c=-3, so we get:
[tex]x=-\frac{0}{2(2)}=0[/tex]
Now we know that the range will happen at x=0, so we substitute:
[tex]f(0)=2(0)^{2}-3=-3[/tex]
so the range will be:
[tex]R=[-3,\infty)[/tex]
For the x-intercepts we need to set the given function equal to zero so we get:
[tex]2x^2-3=0[/tex]
and solve for x:
[tex]2x^{2}=3[/tex]
[tex]x^{2}=\frac{3}{2}[/tex]
[tex]x=\pm \sqrt{\frac{3}{2}}[/tex]
which can be rationalized to:
[tex]x=\frac{\sqrt{6}}{2}[/tex] and [tex]x=-\frac{\sqrt{6}}{2}[/tex]
so the x-intercepts are located at:
[tex](\frac{\sqrt{6}}{2},0)[/tex] and [tex](-\frac{\sqrt{6}}{2},0)[/tex]
For the y-intercept, we need to set x=0 so we get:
[tex]f(0)=2(0)^{2}-3[/tex]
[tex]f(0)=-3[/tex]
So the y-intercept is located at:
(0,-3)
and finally, in order to get f(3) we must substitute x for 3 so we get:
[tex]f(3)=2(3)^{2}-3[/tex]
f(3)=15
Which two fractions are equal to 2?
A .1/2
B.2/4
C.2/1
D.2/2
E.4/4
Answer:
1/2 2/4
Step-by-step explanation:
Answer:
it is C. 2/1
Step-by-step explanation:
because 1 goes into 2 twice
HELP ASAP PLEASE HELPPPPPPP PLEASE
Answer:
5 times 3
Step-by-step explanation:
you do 5 time 3. it is 15
-5+9(r+8)
pls show me the work
if PQ=8 and Q lies at -13 where could P be located?
Answer:
In the given figure the point on segment PQ is twice as from P as from Q is. What is the point? Ans is (2,1).
Step-by-step explanation:
There is really no need to use any quadratics or roots.
( Consider the same problem on the plain number line first. )
How do you find the number between 2 and 5 which is twice as far from 2 as from 5?
You take their difference, which is 3. Now splitting this distance by ratio 2:1 means the first distance is two thirds, the second is one third, so we get
4=2+23(5−2)
It works completely the same with geometric points (using vector operations), just linear interpolation: Call the result R, then
R=P+23(Q−P)
so in your case we get
R=(0,−1)+23(3,3)=(2,1)
Why does this work for 2D-distances as well, even if there seem to be roots involved? Because vector length behaves linearly after all! (meaning |t⋅a⃗ |=t|a⃗ | for any positive scalar t)
Edit: We'll try to divide a distance s into parts a and b such that a is twice as long as b. So it's a=2b and we get
s=a+b=2b+b=3b
⇔b=13s⇒a=23s
3/2a-8=11 URGENT ANSWERRRRRRR
Answer:
38/3
Step-by-step explanation:
3/2a-8=11
3/2a=19 add 8 to each side
i forget the rest of the steps smh
Answer:
38/3
Step-by-step explanation:
3/2A-8=11
3A/2=11+8
3A/2=19 CROSS MULTIPLY
3A=38
A=38/3
If the area of a square room is 100 square meters, what is the length of one side of the room in meters?
Answer:
10 meters
Step-by-step explanation:
Area of a square is represented by the following formula:
A= s²
Plug in your area and solve.
√100 m² =√ s² (square both side)
10 m² = s
Thus, your one side length is 10
The side lengths of a rectangle are described as (8x+1) feet and (3x−2) feet. Which expression represents the area of the rectangle in square feet?
Answer:
24x² - 13x -2
Step-by-step explanation:
To get the area of a rectanglenyou have to multiply the length and the width:
(8x+1) (3x−2)
Using Foil Method:
24x² -16x + 3x -2
24x² -13x -2
find the sum of the equation. 1000x+250x=?
Hey there!
ANSWER: [tex]1250x[/tex]EXPLANATION:To solve, you can just add 1000 + 250 and remove x.
[tex]1000+250=1250[/tex]
Now add x.
[tex]1250x[/tex]
[tex]1000x+250x=1250x(ANSWER)[/tex]
Hope this helps!
[tex]-TestedHyperr[/tex]
What is the prime factorization of 96? 8 · 12 2 · 2 · 2 · 2 · 3 25 · 3 25 · 32