Answer:
The expression x^3 + ax^2 - 15x + b has a factor of x – 2 and leaves a remainder 75 when divided
by x + 3. Find the value of a and of b.
Let p(x) = x3 + ax2 + bx +6
(x-2) is a factor of the polynomial x3 + ax2 + b x +6
p(2) = 0
p(2) = 23 + a.22 + b.2 +6 =8+4a+2b+6 =14+ 4a+ 2b = 0
7 +2 a +b = 0
b = - 7 -2a -(i)
x3 + ax2 + bx +6 when divided by (x-3) leaves remainder 3.
p(3) = 3
p(3) = 33 + a.32 + b.3 +6= 27+9a +3b +6 =33+9a+3b = 3
11+3a +b =1 => 3a+b =-10 => b= -10-3a -(ii)
Equating the value of b from (ii) and (i) , we have
(- 7 -2a) = (-10 - 3a)
a = -3
Substituting a = -3 in (i), we get
b = - 7 -2(-3) = -7 + 6 = -1
Thus the values of a and b are -3 and -1 respectively.
which one is greater 2.2,0.1,4.5,or 4
Answer:
4.5
Step-by-step explanation:
will mark brainliest!!
Answer:
the angle is 176
Step-by-step explanation:
Why can you use the constant of proportionality with any representation?
Answer:
The number k is called the constant of proportionality. One important way of thinking about this constant k is that it tells us how much y increases by if we increase x by exactly 1. to express that y is directly proportional to x.Proportionality constant can be used with any representation to determine how a variable is changing with respect to others.
Variation is a method comparing the nature of a variable with another variable using a constant called the proportionality constant
For instance, if a variable y is directly proportional to x, it is expressed as;
y ∝ x
y = kx
k is the proportionality constant relating y to x and shows that as the value of y is increasing, the value of x is also increasing and vice versa.
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Help me. Two numbers have a sum of 30. Half of their difference is 7. Find the numbers.
Answer:
the answer is x equals 22 and y equals 8
Step-by-step explanation:
first equation is x+y=30
Second equation is x-y/2=7 that simplify's to x-y=14
then you add then so they will cancel out and you are left with 2x=44 so divide two by both sides which gives x=22
then you subsitute the 22 in the first equation. It will be 22+y=30 then you subtract 22 from the 30 that gives you y=8
so the two numbers are 22 and 8
Hope this helps!!!!
The numbers satisfying the given conditions are 22 and 8.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
We have the following problem -
Two numbers have a sum of 30. Half of their difference is 7.
We can write the equations as -
x + y = 30
1/2(x - y) = 7
Rearranging, we get -
y = - x + 30
y = x - 14
Plot the graph, the point of intersection is the solution. The number will be 22 and 8.
Alternativelyy = - x + 30
y = x - 14
Equating both, we get -
- x + 30 = x - 14
30 + 14 = 2x
2x = 44
x = 22
and
y = 22 - 14
y = 8
Therefore, the numbers satisfying the given conditions are 22 and 8.
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By 2 2 1 S ut at , where S is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time. Which equation represents a in terms of the other variables?
Answer:
Step-by-step explanation:
Given the equation of motion;
S = ut + 1/2 at² where;
u is the initial velocity,
a is the acceleration, and;
t is the time.
We are to express a in terms of u, t and S
Making a the subject of the formula;
S = ut + 1/2 at²
S-ut = 1/2at²
2(S-ut) = at²
a = 2(S-ut)/t²
Hence the acceleration a in terms of other variables is expressed as a = 2(S-ut)/t²
Which method best helps to prevent wind erosion?
rotating crops
decreasing riverbank slopes
more animal grazing
avoiding soil compaction
Answer:
a
Step-by-step explanation:
What is the equation of the line shown in the graph?
Answer:
y=-3
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Round the number to the place of the underlined digit. 4.327
Answer:
Tenths -- 4.3
Hundredths -- 4.33
Thousandths -- 4.327
Ones -- 4
Step-by-step explanation:
Which of the following rules represents the function shown in the table?
A.) f( n) = 3 n
B.) f( n) = n + 3
C.) f( n) = 1/3n
Answer:
the answer is c !!! :)
Step-by-step explanation:
yeah, so period.
Writing a Linear Function to Model a Scenario Pedro works as a newspaper deliverer. He receives a base pay plus an additional amount per newspaper delivered. Last week, Pedro delivered 5 newspapers and earned $37.50. This week, he delivered 20 newspapers and earned $75. Let x equal the number of newspapers Pedro delivers and y be the earnings he receives in dollars. Which linear function models the scenario?
Answer: y= 25+2.5x
Step-by-step explanation:
Let a = base pay , b = additional amount per newspaper.
Given: Last week, Pedro delivered 5 newspapers and earned $37.50.
i.e. 37.50=a+5b (i)
This week, he delivered 20 newspapers and earned $75.
i.e. 75=a+20b (ii)
Eliminate (i) from (ii)
37.50=15b
[tex]\Rightarrow\ b=\dfrac{37.50}{15}\\\\\Rightarrow\ b=2.5[/tex], i.e. additional amount per newspaper= $2.5
Put b= 2.5 in (i)
[tex]37.50=a+5(2.5)\\\\\Rightarrow\ 37.50=a+12.5\\\\\Rightarrow\ a=37.50-12.5\\\\\Rightarrow\ a=25[/tex], i.e. base pay = $20
Let x= Number of newspapers Pedro delivers.
y= Earnings he receives in dollars.
y= 25+2.5x will be the required function.
Ramon plays a game which his older sister he first gains 5 points then loses 8 points and finally gains 10 points what is his final score
Please help I will give you Brainlyest
Answer:
7 points
Step-by-step explanation:
started out w/ 5 points, then loses 8
5 - 8 = -3
gains 10 points
-3 + 10 = 7
In his science class, Ethan is using a microscope that enlarges objects to 100 times their actual size. If the length of a mosquito is 3.5 millimeters, what is the size as seen under the microscope
Answer:
350 millimeters
Step-by-step explanation:
3.5 millimeters x 100 = 350 millimeters
Guys plssssssss! I want to spend time today and tomorrow with my fam before they go back to Washington
If a tree casts a 10 foot shadow at the same time that a yard stick casts a 2 foot shadow, find the height of the tree.
Answer:
is 12 feet
Step-by-step explanation:
I need points dude!
75% of the whole is 180. What's the whole?
.
Write an equation of a line that passes through the
point (-4, 5) and have a slope of 1/2
Answer:
y-5=1/2(x-(-4))
Step-by-step explanation:
equation of a st. line having slope m= ½ and passing through the point (x1,y1)
Any tricks on trigonometry
Answer:
Step-by-step explanation: Tip 1) Always Start from the More Complex Side.
Example Q1) Prove the identity tan⁴x = sec²x (tan²x-1)+1.
Tip 2) Express everything into Sine and Cosine.
Tip 3) Combine Terms into a Single Fraction.
Tip 4) Use Pythagorean Identities to transform between sin²x and cos²x.
Tip 5) Know when to Apply Double Angle Formula (DAF)
Guys pleeease help! I need help asap!
Answer:
10
Step-by-step explanation:
first time they spent 11
2nd time was 1 dollar less
since 1 burrito is 2 dollars 3 is 6
and the 4 tacost were 4 dollars
I might be wrong
Helppp please it’s quick
Answer:
ysh what do you need?
Step-by-step explanation:
estimate the product
HELP! answer for brainlist
Answer: my estimate is 170.1
Step-by-step explanation: tell me if i'm right
Math please help whoever is good at it ! Points 15
Answer:
3
Step-by-step explanation:
2x + 4 = 10
2x = 6
x = 6 ÷ 2
x = 3
What is the exact value of sin(345°)? 30 PTS, WILL DO BRAINLIEST
A) (sqrt3 + sqrt2)/2
B) (sqrt6 + sqrt2)/4
C) (-sqrt3 + sqrt2)/2
D) (-sqrt6 + sqrt2)/4
-Edge 2020
The value of sin (345)= (-sqrt6 + sqrt2)/4= -0.2588
What is Trigonometry?Trigonometry, the area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
sin (345)
Now, using Trigonometric identity
sin(a+ b)=sin a x cos b+ sin b x cos a
Now, expand 345= 300+ 45
sin(300 + 45)=sin 300 x cos 45+ sin 45 x cos 300
sin(300 + 45)= -√3/2 x √2/2 + √2/2 x 1/2
= -√6/4 + √2/4
= -0.2588
Hence, sin (345)= -0.2588
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Plot-1.4 on the number line below
Marla owes her sister $15. She pays her $6 today. Which integer represents the amount of debt she has remaining?
What is the slope of the line?
y - 3 = 5(x-2)
Answer:
5
Step-by-step explanation:
To better see what the slope is (the coefficient of x), write it in slope-intercept form, y=mx+b. The slope-intercept form of [tex]y -3 = 5(x-2)[/tex] is [tex]y=5x-7[/tex]. The slope is the coefficient of x, which is 5.
Hope this helps! :)
solve for x.
7x/2+5=8
Answer:
x=6/7
Step-by-step explanation:
7x÷2+5=8
divide by 2 on both sides:
7x/2+5=8(it's a fraction)
subtract 5 on both sides
7x÷2=3
multiply 2 on both sides
7x=6
divide by seven on both sides
x=6/7
hope this was helpful and the instructions were clear enough!
What is the answer to the problem 4y + 3 - y - 2
Answer:
3y+1
Step-by-step explanation:
4y+3-y-2
3y+3-2
3y+1
Answer:
3+1
Step-by-step explanation:
Subtract the numbers
4+3−−2
4+1−
Evaluate: LWH if L = 0.5, W = 0.2, and H= 0.1
Answer:
0.01
Step-by-step explanation:
Replace the numbers with the variables
0.5*0.2*0.1
0.01
The evaluation of the given LWH is 0.01.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given the Parameters as;
L = 0.5, W = 0.2, and H= 0.1
Now to find the volume we are asked to calculate the LWH
Now Replace the numbers with the variables
LWH = 0.5 x 0.2 x 0.1
LWH = 0.01
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An Ice cream shoppe makes $15 for every 4 milkshakes they sell. If they made $71.25 in one hour on milkshakes, how many did they sell?
Answer:
19
Step-by-step explanation:
For every 3 girls in Mr Hegarty's class there are 2 boys. What is the ratio of girls to boys in the class?
Give your answer in its simplest form.
Answer:
3:2
Step-by-step explanation:
For every 3 girls : there is 2 boys, so it's 3:2
3:6 in simplest form=1:2