Given:
The function is
[tex]f(x)=2x^2+kx-9[/tex]
The remainder when f(x) is divided by x+6 is 57.
To find:
The value of k.
Solution:
According to the remainder theorem, if a polynomial function f(x) is divided by (x-a), then f(a) is the remainder.
The remainder when f(x) is divided by x+6 is 57.
Using remainder theorem, we get f(-6)=57.
Putting x=-6 in the given function.
[tex]f(-6)=2(-6)^2+k(-6)-9[/tex]
[tex]57=2(36)-6k-9[/tex]
[tex]57=72-6k-9[/tex]
[tex]57=63-6k[/tex]
On further simplification, we get
[tex]6k=63-57[/tex]
[tex]6k=6[/tex]
[tex]k=\dfrac{6}{6}[/tex]
[tex]k=1[/tex]
Therefore, the value of k is 1.
Answer:
person above lol
Step-by-step explanation:
Solve: 2x + 3y = 1
y = -23 +11
Answer:
x = 18.5
y = -12
Step-by-step explanation:
First, solve y:
y = -23 + 11
y = -12
Then, solve the main problem:
2x + 3y = 1
(Substitute y)
2x + -36 = 1
2x - 36 = 1
2x = 1 + 36 = 37
x = 37 / 2
x = 18.5
Forty students went on a trip on Wednesday. On Thursday, 15% less students went on a similar trip. How many students went on the trip on Thursday?
Answer:
34
Step-by-step explanation:
40 * .15= 6
40-6 = 34
okkk so you do 40 * .15 because you just put a decimal point before all percentages to convert it into number
40*.15= 6
then subtract 6 to the original amount
40-6=34
34 students went on the trip on thursday cause 6 students got killed by bears in the last trip.
I NEED HELP ASAP!!!!!!!
Answer:
9/25 = 36%
Step-by-step explanation:
First add up all of the students (150)
Then divide 54 by 150, 0.36
0.36 = 36% = 9/25
What is the exact area of a circle having diameter 3 in.?
Answer:
2.25π square inches
Step-by-step explanation:
Area = π[tex]r^{2}[/tex]
Diameter = 2r
So in this case, radius = 1.5 inches
Plugging that into the area formula produces the answer
Answer these three question for a brainlist, 5 stars and a thanks for extra
12 (3 + 4) =
36 + 48
0.84
123 + 124
15 + 16
The equation that passes through (3,6) and is perpendicular to 3x - 4y = - 2
a
y = - 4/3x + 3 1/3
b
y = - 3/4x + 10
c
y = - 4/3x + 10
d
y = 3/4x + 10
Answer:
C
Step-by-step explanation:
We want the equation of the line that passes through (3, 6) and is perpendicular to:
[tex]3x-4y=-2[/tex]
First, convert the second equation into slope-intercept form:
[tex]-4y=-3x-2\Rightarrow \displaystyle y=\frac{3}{4}x+\frac{1}{2}[/tex]
So, we can see that the slope of the line is 3/4.
The slopes of perpendicular lines are negative reciprocals of each other.
Therefore, the slope of the new line is -4/3.
It passes through the point (3, 6).
We can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute:
[tex]\displaystyle y-(6)=-\frac{4}{3}(x-3)[/tex]
Distribute:
[tex]\displaystyle y-6=-\frac{4}{3}x+4[/tex]
Therefore:
[tex]\displaystyle y=-\frac{4}{3}x+10[/tex]
The answer is C.
In a class, the ratio of girls : boys is 5:3.
What fraction of the class are boys?
please answer urgent , high points up for grabs , please give good explanation
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
uh
Step-by-step explanation:
Answer:
wtffffffffffffffffffff
if f(x)=x²-18x+91, solve for x when f(x)=10
Answer:
x = 9
Step-by-step explanation:
x²-18x+91 = 10
x²-18x+81 = 0
(x-9)(x-9)= 0
x = 9
check:
9² - 18 (9) + 91
81-162+91 = 10
Why thank you for helping me and I will mark brainliest if you’re right :)
Answer:
Choice #1) 4.7 cm
Step-by-step explanation:
circumference of full circle = 2(r)(3.14)
a full circle would be = 2(3)(3.14) = 18.84 cm
It is 1/4 circle so 18.84/4=4.7 cm
Answer:
10.7
Step-by-step explanation:
1. I first grabbed a ruler to measure the other straight side of the figure.
2. Both of the straight sides were 3 cm so I knew that the answer had to be greater than 6 cm.
3. I then estimated that the other side was longer than the 3 cm.
4. I then had to my logic to figure out the answer and I very quickly realized that 4.7 cm would not make since because that is less than 6 cm. I know 7.7 cm would not make since because I knew the curved side was longer than 3 cm not shorter. 18.8 cm did not make since because that answer has WAY to much cm. Using the process of elimination, 10.7 cm was the only answer that made since.
Which set of ordered pairs would define a line with a negative slope?
A.
(5, 5) and (0, 1)
B.
(3, 6) and (5, 1)
C.
(2, 3) and (7, 6)
D.
(2, 3) and (-4, -1)
Answer:
I believe it is B
Step-by-step explanation:
Im not good at explaing, but if you move forward three units and up 6, then draw a point, then go forward to 5 units and down to one unit and connect those dots, the line would be going down to the right
The function y=f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -1?
Answer:
The average rate of change of the function is: 0
Step-by-step explanation:
The function y = f(x) is graphed below.
From the graph it is clear that:
at x = -8, the value of f(-8) = -10
at x = -1, the value of f(-1) = -10
We have to determine the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -1.
so
at x₁ = -8, f(x₁) = f(-8) = -10
at x₂ = -1, f(x₂) = f(-1) = -10
Using the formula to determine the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -1.
Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]
= [f(-1) - f(-8) ] / [-1-(-8)]
= [-10 - (-10)] / [-1+8]
= [-10 + 10] / 7
= 0 / 7
= 0
Therefore, the average rate of change of the function is: 0
A CD is circular and has a diameter of 6 centimeters. Which is closest to the area of the CD? Use 3.14 for π
Answer:
28.26 cm²
Step-by-step explanation:
Area of a circle = πr²
r = diameter/2
r = 6/2 = 3
A = (3.14)(3)²
A = 28.26 cm²
Which is equivalent to (125)*?
125
125 3x
1253
125/5
Answer:
A
Step-by-step explanation:
it only makes sense, hope this helped
PLEASE HELP the rise of the ramp is 8 ft tall and the run of the ramp is 16 ft long what is the slope of the ramp
Answer:
1/2 because it is...........
Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.
Answer:
AB = 4.62 m∠A = 22° m∠B = 68°
Step-by-step explanation:
Tan A = 1.7/4.3 = .39534...
m∠A = arctan .39534... ≅ 22°
m∠B = 90 - 22 = 68°
AB = [tex]\sqrt{1.7^{2} + 4.3^{2} } = \sqrt{2.89 + 18.49} = \sqrt{21.38} = 4.62[/tex]
how can I solve this problem
Answer:
50
Step-by-step explanation:
the angle that they want you to find is complementary to the angle that equals 40. Complementary means they will add up to equal 90. 90-40=50 so ADB = 50
PLEASE ANSWER QUICKLY! THIS IS FOR A STUFY GUIDE DUE IN 5 MINUTES!!!!!
6CO2 + 6H2O ———» C6H12O6 + 6O2
Is the equation above balanced or unbalanced? ___________
a- need to add coefficients
b- I don't know
c- Unbalanced
d- Balanced
Answer:
It's Balanced
Step-by-step explanation:
A simple word equation that can be used to describe the process of photosynthesis is carbon dioxide + water —> glucose + oxygen + water. So it's a balanced chemical equation for the process can be written as 6CO2 + 6H2O —> C6H12O6 + 6O2
Hope this helps!
Helpeoepeoeoeo show work
IMPORTANT THIGNS TO REMEMBER:
Has 20 lb. dog food!Gives dog 1 3/5 everyday!Find how much eaten after 2 days!Find how much is left!ANSWER:
Dog has eaten 3 1/5 after 2 days!
There is 16 4/5 left in bag!
EXPLANATION:
Since she gives 1 3/5 to her dog everyday and their asking for 2 days you would multiply 1 3/5 × 2 OR add 1 3/5 + 1 3/5
Which would give you 3 1/5
So, the dog has eaten 3 1/5 lb. of dog food in 2 days.
However then, you would subtract 20 lb. - 3 1/5 lb. because there is 20 lb. dog food in all and the dog has eaten 3 1/5 of it. This would give you 16 4/5 lb.
Meaning there is 16 4/5 lb. left in the bag of dog food!
. How many dozen must be sold to make a profit of $90? Make a Selection: A. 45 B. 25 C. 30 D. 8
solve for u 5u + 9 - 4u = 17 (also don't have the answer be a fraction)
Answer:
=8
Step-by-step explanation:
Answer:
u=8
hope this helps
Step-by-step explanation:
solve this plz????? thx
Answer:
AOD i think
Step-by-step explanation:
Answer:
angle aob
Step-by-step explanation:
Write the equation of the line in slope-intercept form: y=mx+b
Given: Point (1,3) Slope: 2
Answer:
y=2x+1
Step-by-step explanation:
y-y1=m(x-x1)
y-3=2(x-1)
y-3=2x-2
y=2x-2+3
y=2x+1
Recipe B uses 9 ounces of flour to make 12 servings of dough. How many flour is in per serving?
Answer:
Step-by-step explanation:
9/12 ounce = 3/4 = .75 ounce flour
Select the solution(s) to the following equation: (3x−2)(x+5)=0 SELECT ALL THAT APPLY
x=3/2
x=5
x=-5
x=2/3
x=-2/3
x=-3/2
Answer:
Step-by-step explanation:
Check by direct substitution. If we begin by checking x = 3/2, we substitute 3/2 for x in (3x - 2)(x + 5), obtaining (9/2 - 2)(3/2 + 5), which is NOT zero. Therefore x = 3/2 is not a solution.
(3*5−2)(5+5)=0 False. x = 5 is not a solution.
(3*[-5]−2)([-5+5)=0 True. x = -5 is a solution
x = 2/3: (3*2/3 - 2)( ) = 0. True x = 2/3 is a solution
x = -2/3: ( )( ) = -17 1/3; so x = -2/3 is not a solution
x = -3/2: ( ) ( ) = -22 3/4; so x = -3/2 is not a soution
PLEASE HELP ME ?!?!?!
Answer:
19
Step-by-step explanation:
Which of the following sets of measures
cannot be the lengths of the sides of a right
triangle?
A
5 cm, 12 cm, and 13 cm
B
9 cm, 12 cm, and 17 cm
C
1 cm, 2.4 cm, and 2.6 cm
D
2.5 cm, 6 cm, and 6.5 cm
you can use the formula of pythagoras theorem to know what of them is wrong
in the first case
-5^2 + 12^2 =169
13^2=169 ( it's a right equation so it can be lengths of right angle tri )
in the second case
_9^2 + 12^2 =225
17^2 not equal 225
so these are the lengths that can't be a right angle triangle
A number divided by 3 and then 4 is added to the quotient.the result is 8.find the number
Answer:
12
Step-by-step explanation:
8-4= 4 So, 4 is the quotient.
4x3= 12 So 12 is the original number
12/3 + 4= 8
i need help i will mark u brainlest
Answer:
3rd one
Step-by-step explanation: