Answer:
So length is 7 in while width is 1 in.
Step-by-step explanation:
We are given W is 6 inches less than L which mean as an equation we have W=L-6.
We are given the area of this rectangle, LW=7.
So we have the system:
W=L-6
LW=7.
Replace the second W with what the first W equals:
LW=7
L(L-6)=7
Distribute:
[tex]L^2-6L=7[/tex]
Subtract 7 on both sides:
[tex]L^2-6L-7=0[/tex]
We are luck since the coefficient of L^2 is 1. This means all we have to do is find two numbers that multiply to be -7 add at the same time add up to -6.
Those numbers are -7 and 1 since (-7)(1)=-7 and (-7)+(1)=-6.
So the factored form of our equation is:
(L-7)(L+1)=0
This gives us two equations to solve:
L-7=0 or L+1=0
L=7 or L=-1
L=-1 doesn't make sense for a length so L=7.
L=7 means the length is 7 inches.
If W=L-6 and L=7, then W=7-6=1.
The width is 1 inch since W=1.
So length is 7 in while width is 1 in.
cos155° = _____ -cos25° cos 55° cos(-25)°
Answer:
- cos 25°
Step-by-step explanation:
Cosine function is one of the trigonometric functions. Cosine function is regarded as an even function, which means that f(-x) = f(x). Also, cosine function is positive in the first quadrant and the last quadrant and negative in the second quadrant and the third quadrant. 155° lies in the second quadrant since 155° is smaller than 180°. Therefore, the basic angle or the reference angle of 155° is 180° - 155° = 25°. We know that cos 155° will be negative because it lies in the second quadrant and cos 25° will be positive because it lies in the first quadrant. Since cos 55° is positive, and cos (-25°) = cos 25° by the even function property, therefore option 2 and option 3 are incorrect since cos 155° is negative. Therefore, option 1 is the correct answer i.e. cos 155° = - cos 25°!!!
Answer:
- [tex]cos25^{o}[/tex]
Step-by-step explanation:
Hope This Helps!!!
Scientists released 10 birds into a new habitat in year 0. Each year, there were
three times as many birds as the year before. How many birds were there
after x years? Write a function to represent this scenario.
To model the bird population that triples each year starting with 10 birds, an exponential growth function is used: f(x) = 10 × 3^x, where x is the number of years.
Explanation:To create a function that represents the scenario of birds increasing threefold each year, we need to use an exponential growth model.
The initial population of birds is 10 and then it triples every year.
Therefore, the function that describes the number of birds after x years would be:
f(x) = 10 × 3^x
Here, f(x) represents the number of birds after x years, 10 is the initial number of birds released into the habitat, and 3^x indicates that the population is growing three times each year for x years.
Final answer:
The number of birds after x years can be calculated using the exponential function B(x) = 10 × 3^x, representing the initial population of 10 birds tripling every year.
Explanation:
The scenario describes a population of birds in a new habitat growing exponentially each year. The initial population of birds is 10 (in year 0), and the population triples every year thereafter. To represent this situation mathematically, we can use an exponential function.
To find the number of birds after x years, we can use the following function:
B(x) = 10 × 3^x
Where:
B(x) is the number of birds after x years
10 is the initial number of birds
3 is the growth factor, as the population is tripling each year
x is the number of years since the birds were first released into the habitat
This equation models exponential growth and gives us the predicted population of the birds for any given year x.
find the midpoint between -7+4i and 3-2i
Answer:
-2 + i
Step-by-step explanation:
The midpoint is the average:
[ (-7 + 4i) + (3 − 2i) ] / 2
Combine like terms:
(-4 + 2i) / 2
Divide:
-2 + i
Which represents a perfect cube?
The lengths of two sides of a right triangle are 12 inches and 15 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth. 10.2 inches 24.0 inches 28.2 inches 30.0 inches
Answer:
10.2 inches
Step-by-step explanation:
we know that
In this problem we have two cases
First case
The given lengths are two legs of the right triangle
so
[tex]a=12\ in, b=15\ in[/tex]
Applying the Pythagoras Theorem
Find the length of the hypotenuse
[tex]c^{2}=a^{2} +b^{2}[/tex]
substitute
[tex]c^{2}=12^{2} +15^{2}[/tex]
[tex]c^{2}=369[/tex]
[tex]c=19.2\ in[/tex]
Second case
The given lengths are one leg and the hypotenuse
so
[tex]a=12\ in, c=15\ in[/tex]
Applying the Pythagoras Theorem
Find the length of the other leg
[tex]b^{2}=c^{2} - a^{2}[/tex]
substitute
[tex]b^{2}=15^{2} - 12^{2}[/tex]
[tex]b^{2}=81[/tex]
[tex]b=9\ in[/tex]
Find the difference between the two possible lengths of the third side of the triangle
so
[tex]19.2-9=10.2\ in[/tex]
Answer:
10.2
Step-by-step explanation:
is a pimp ting
Given that f(x) = x2 – 7x – 1, g(x) = 2x – 3, and h(x) = 4x – 5 find each function.
(f + g)(x)
options:
A) x2 – 5x – 4
B) x2 – 11x + 4
C) x2 – 3x – 6
D) x2 – 5x – 6
Answer:
A)
Step-by-step explanation:
(f+g)(x) = f(x) + g(x)
now plug in the expressions of f(x) and g(x) :
(f+g)(x) = [tex]x^{2} -7x-1 + 2x-3[/tex]
we combine like terms we get :
(f+g)(x) = [tex]x^{2} -7x+2x -1-3[/tex]
we simplify we get :
(f+g)(x)=[tex]x^{2} -5x-4[/tex]
so the answer is A)
Answer:a
Step-by-step explanation:
Given: The coordinates of triangle PQR are P(0, 0), Q(2a, 0), and R(2b, 2c).
Prove: The line containing the midpoints of two sides of a triangle is parallel to the third side.
As part of the proof, find the midpoint of PR
Answer:
The line containing the midpoints of two sides of a triangle is parallel to the third side ⇒ proved down
Step-by-step explanation:
* Lets revise the rules of the midpoint and the slope to prove the
problem
- The slope of a line whose endpoints are (x1 , y1) and (x2 , y2) is
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- The mid-point of a line whose endpoints are (x1 , y1) and (x2 , y2) is
[tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]
* Lets solve the problem
- PQR is a triangle of vertices P (0 , 0) , Q (2a , 0) , R (2b , 2c)
- Lets find the mid-poits of PQ called A
∵ Point P is (x1 , y1) and point Q is (x2 , y2)
∴ x1 = 0 , x2 = 2a and y1 = 0 , y2 = 0
∵ A is the mid-point of PQ
∴ [tex]A=(\frac{0+2a}{2},\frac{0+0}{2})=(\frac{2a}{2},\frac{0}{2})=(a,0)[/tex]
- Lets find the mid-poits of PR which called B
∵ Point P is (x1 , y1) and point R is (x2 , y2)
∴ x1 = 0 , x2 = 2b and y1 = 0 , y2 = 2c
∵ B is the mid-point of PR
∴ [tex]B=(\frac{0+2b}{2},\frac{0+2c}{2})=(\frac{2b}{2},\frac{2c}{2})=(b,c)[/tex]
- The parallel line have equal slopes, so lets find the slopes of AB and
QR to prove that they have same slopes then they are parallel
# Slope of AB
∵ Point A is (x1 , y1) and point B is (x2 , y2)
∵ Point A = (a , 0) and point B = (b , c)
∴ x1 = a , x2 = b and y1 = 0 and y2 = c
∴ The slope of AB is [tex]m=\frac{c-0}{b-a}=\frac{c}{b-a}[/tex]
# Slope of QR
∵ Point Q is (x1 , y1) and point R is (x2 , y2)
∵ Point Q = (2a , 0) and point R = (2b , 2c)
∴ x1 = 2a , x2 = 2b and y1 = 0 and y2 = 2c
∴ The slope of AB is [tex]m=\frac{2c-0}{2b-2a}=\frac{2c}{2(b-c)}=\frac{c}{b-a}[/tex]
∵ The slopes of AB and QR are equal
∴ AB // QR
∵ AB is the line containing the midpoints of PQ and PR of Δ PQR
∵ QR is the third side of the triangle
∴ The line containing the midpoints of two sides of a triangle is parallel
to the third side
Answer:
b,c
Step-by-step explanation:
That guy above took so long
x² + 2x – 1 = 0 in English words.
Answer:
x squared plus two times x minus one = zero.
Step-by-step explanation:
(This is a Quadratic equation in the variable x).
Answer:
One less than the sum of square of a number and twice the number is 0
Step-by-step explanation:
[tex]x^2+ 2x - 1 = 0[/tex]
x represents any number. x^2 represents square of a number
2x represents twice the number
[tex]x^2+2x[/tex] can be written as sum of square of a number and twice the number
[tex]x^2+2x-1[/tex]
One less than the sum of square of a number and twice the number
[tex]x^2+2x-1=0[/tex]
One less than the sum of square of a number and twice the number is 0
Urgent help needed
Solve for x. Show your work.
Answer:
First exercise: [tex]x=7[/tex]
Second exercise: [tex]x=2[/tex]
Step-by-step explanation:
According to the Intersecting Secants Theorem the products of the segments of two secants that intersect each other outside a circle, are equal.
Knowing this, in order to solve the first exercise and the second exercise, we can write the following expressions and solve for "x":
For the first exercise, we get:
[tex](5)(5+x)=6(6+4)\\\\25+5x=60\\\\5x=60-25\\\\x=\frac{35}{5}\\\\x=7[/tex]
For the second exercise, we get:
[tex](4)(4+x)=3(3+5)\\\\16+4x=24\\\\4x=24-16\\\\x=\frac{8}{4}\\\\x=2[/tex]
The rule as a mapping for the translation of a rectangle is (x, y) → (x – 2, y + 7). Which describes this translation?
Answer:
The translation is 2 units at left and 7 units up
Step-by-step explanation:
we have that
The rule of the translation is
(x, y) → (x – 2, y + 7)
That means----> The translation is 2 units at left and 7 units up
Answer:
2 units at left and 7 units up
Step-by-step explanation:
If the rule as a mapping for the translation of a rectangle is (x, y) → (x – 2, y + 7), 2 units at left and 7 units up describes this translation.
Suppose you multiplied the cereal box dimensions in a different order:
V = (x)(4x+3)(4x)
First, (X)(4x+3) =
DONE
[tex]\bf V=(x)(4x+3)(4x)\implies \cfrac{V}{4x}=(x)(4x+3)[/tex]
Answer:
[tex]V=(x)(4x+3)(4x)=16x^2+12x[/tex]
Step-by-step explanation:
Given : Expression [tex]V = (x)(4x+3)(4x)[/tex]
To find : Suppose you multiplied the cereal box dimensions in a different order ?
Solution :
The given expression is the product of three numbers,
[tex]V = (x)(4x+3)(4x)[/tex]
First we multiply first two terms,
[tex](x)(4x+3)=4x^2+3x[/tex]
Substitute back,
[tex]V = (4x^2+3x)(4x)[/tex]
Then multiply the left terms,
[tex]V =16x^2+12x[/tex]
Therefore, [tex]V=(x)(4x+3)(4x)=16x^2+12x[/tex]
A.obtuse
B.straight
C.acute
D.right
A. obtuse. The angle R is obtuse.
An obtuse angle is an angle greater than 90° and less than 180°. So, in the image attached we can see that the angle R is greater than 90° and less than 180°.
Which values of a,b and c represent the answer in simplest form
[tex]1 \frac{3}{4}[/tex]
Fractional division is fractional multiplication with the second fraction the reciprocal of itself. This means the problem can be written as [tex]\frac{7}{9}*\frac{9}{4}[/tex]. Fractional multiplication results in the multiplication of the numerators and denominators---in this case, [tex]\frac{7}{4}=1\frac{3}{4}[/tex]
Answer:
Option B) a = 1, b = 3, c = 4
Step-by-step explanation:
We are given the following information in the question:
We are given an expression:
[tex]\displaystyle\frac{7}{9} \div \frac{4}{9} = a\frac{b}{c}[/tex]
The solving of the above expression can be done in the following manner:
[tex]\displaystyle\frac{7}{9} \div \frac{4}{9}\\\\\frac{7}{9}\times \frac{9}{4}\\\\\frac{7}{4} =\frac{(4\times 1) + 3}{4}= 1\frac{3}{4}[/tex]
Comparing the right side of the expression, we have,
[tex]a\displaystyle\frac{b}{c} = 1\frac{3}{4}[/tex]
Comparing, we get,
a = 1, b = 3, c = 4
Option B) s the correct option.
When it is 6:00 a.m. in Honolulu, it is 3:00 p.m. in London. Just before Paul’s flight from Honolulu to London, he called his friend Nigel, who lives in London, asking what kind of clothing to bring. Nigel explained that London was in the middle of some truly peculiar weather. The temperature was currently 30°C, and was dropping steadily at a rate of 1°C per hour. Paul’s flight left Honolulu at 2:00 p.m. Thursday, Honolulu time, and got into London at 12:00 p.m. Friday, London time. What kind of clothing would have been appropriate for Paul to be wearing when he got off the plane? a. shorts and sandals, appropriate for around 90-105°F b. winter wear, appropriate for around 20-45°F c. street clothes, appropriate for around 70-85°F d. a light jacket, appropriate for around 50-65°F
Answer:
b. winter wear, appropriate for around 20-45°F c.
Step-by-step explanation:
Answer:
b. winter wear, appropriate for around 20-45°F
Step-by-step explanation:
When it is 6:00 hours in Honolulu, it is 15:00 hours in London, this means that there are 15 - 6 = 9 hours of difference.
Paul got into London at 12:00 p.m, that is, at 12 - 9 = 3:00 p.m. Friday Honolulu time. Paul’s flight left Honolulu at 2:00 p.m. Thursday, so he spent 25 hours flighting.
When the flight started, the temperature in London was 30 °C, after 25 hours the temperature dropped 25 °C, so it was 30 - 25 = 5 °C.
To convert from °C to °F, we use the following formula:
(x °C × 9/5) + 32 = y °F
Replacing with x = 5
(5 °C × 9/5) + 32 = 41 °F
Find the length of the segment indicated.
Answer: The length of the indicated segment is 14.45 units.
Step-by-step explanation: We are given to find the length of the indicated segment.
From the figure, we note that
A chord is bisected by the radius of the circle that makes a right-angled triangle with hypotenuse measuring 16.1 units and the other two sides measures x units and 7.1 units.
Using Pythagoras theorem, we get
[tex]x^2+7.1^2=16.1^2\\\\\Rightarrow x^2+50.41=259.21\\\\\Rightarrow x^2=259.21-50.41\\\\\Rightarrow x^2=208.8\\\\\Rightarrow x=\pm\sqrt{208.8}\\\\\Rightarrow x=\pm14.45.[/tex]
Since x is the length of side of a triangle, so we get
x = 14.45.
Thus, the length of the indicated segment is 14.45 units.
What is the x-coordinate of the vertex of the parabola whose equation is y = 3x^2 + 12x + 5?
Answer:
(-2,-7)
Step-by-step explanation:
Answer:
x= -2
Step-by-step explanation:
-b/2a = x
-(12)/2(2) = x
-12/6 = x
-2 = x
What is the value of x in the equation 1/2x-3/4=3/8-5/8
Answer:
x=1
Step-by-step explanation:
1/2x-3/4=3/8-5/8
Combine like terms on the right hand side
1/2x-3/4=-2/8
Simplify the fraction
1/2x-3/4=-1/4
Add 3/4 to each side
1/2x-3/4+3/4 = -1/4+3/4
1/2x = 2/4
Multiply each side by 2
1/2x *2 = 2/4*2
x = 4/4
x=1
Answer:
the answer its 1
Step-by-step explanation:
If p —> q and q —> r are true conditional statements,
then p —> r is a true conditional statement.
This is the Law of Detachment.
True or False
Answer:
False; this is the law of syllogism.
Step-by-step explanation:
Law of Detachment is:
1) p->q
2) p
------------------------
Conclusion: q
Law of syllogism is:
1) p->q
2) q->r
---------------------
Conclusion: p->r
Find the equation, in standard form, of the line passing through the points (2,-3) and (4,2).
Answer:
5x - 2y = -4Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
Te formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
===========================================
We have two points: (2, -3) and (4, 2). Substitute:
[tex]m=\dfrac{2-(-3)}{4-2}=\dfrac{5}{2}[/tex]
[tex]y-(-3)=\dfrac{5}{2}(x-2)\\\\y+3=\dfrac{5}{2}(x-2)[/tex]
Convert it to the standard form [tex]Ax+By=C[/tex]:
[tex]y+3=\dfrac{5}{2}(x-2)[/tex] multiply both sides by 2
[tex]2y+6=5(x+2)[/tex] use the coordinates of the point
[tex]2y+6=5x+10[/tex] subtract 6 from both sides
[tex]2y=5x+4[/tex] subtract 5x from both sides
[tex]-5x+2y=4[/tex] change the signs
[tex]5x-2y=-4[/tex]
Len needs $135.75 for a television. How many weeks will it take her to save enough money to buy a television? Equation: t = 25 + 8.25w
Answer:
14 weeks
Step-by-step explanation:
t = 25 + 8.25w
Len needs 135.75
135.75 = 25 + 8.25w
Subtract 25 from each side
135.75-25 = 25-25 + 8.25w
110.75 = 8.25w
Divide each side by 8.25
110.75/8.25 = 8.25w/8.25
13.42424 = w
Since we need at least 135.75, it will take Len a little more than 13 weeks, so it will take Len 14 weeks to have enough money
Answer:
14 weeks
Step-by-step explanation:
It will take 14 weeks for Len to save enough money to buy a television.
t = 25 + 8.25w
135.75 = 25 + 8.25w
Hope this helps!
Choose the equation that represents a line that passes through points (−1, 2) and (3, 1). A)4x − y = −6 B)x + 4y = 7 C)x − 4y = −9 D)4x + y = 2
Answer:
B.
Step-by-step explanation:
I think I'm going to go with the plug in method here.
If you get the same value on both sides, then the point is contained on the line.
A)
4x-y=-6
Test (-1,2): 4(-1)-2=-6
4(-1)-2=-6
-4-2=-6
-6=-6
True; the equation holds for (-1,2).
Test (3,1): 4(3)-1=-6
4(3)-1=-6
12-1=-6
11=-6
False; the equation doesn't hold for (3,1).
A isn't the right choice.
B)
x+4y=7
Test (-1,2): -1+4(2)=7
-1+4(2)=7
-1+8=7
7=7
True, the equation holds for (-1,2).
Test (3,1): 3+4(1)=7
3+4(1)=7
3+4=7
7=7
True, the equation holds for (3,1).
Since the equation held for both (-1,2) and (3,1) then B is the right answer.
-------------------Let's also go ahead and find the equation another way:
(3,1) and (1,-2) are points on your line.
I'm going to write an equation for these points in slope-intercept form first which is y=mx+b where m is slope and b is y-intercept.
I will then rearrange into standard form like your choices are in.
m=slope=rise/run.
To find this, I like to line up the points and subtract and then put 2nd difference over 1st difference.
Like so:
(-1,2)
-(3,1)
---------
-4 1
The slope is 1/-4 or -1/4.
So the equation so far is y=-1/4 x+b since m=-1/4.
Now to find b, I'm going to use y=-1/4 x +b along with one of the given points on the line like (x,y)=(-1,2).
y=-1/4 x+b
2=-1/4 (-1)+b
2=1/4+b
Subtract 1/4 on both sides:
2-1/4=b
7/4=b
So the equation of the line is y=-1/4 x +7/4.
Now the goal is to write in ax+by=c form where a,b,c are integers.
Multiply both sides of y= -1/4 x +7/4 by 4 giving you:
4y=-1x+7
Add 1x on both sides:
1x+4y=7
or
x+4y=7 since 1x=x
So x+4y=7 is the answer if you prefer this way. Well anyway you prefer, this is the correct standard form for this line.
The equation of line that passes through points (-1, 2) and (3, 1) will be
x + 4y = 7
Option B is true.
What is Equation of line?
The equation of line with slope m and y intercept at point b is given as;
y = mx + b
Given that;
The points on the line are (-1, 2) and (3, 1).
Since, The equation of line will be;
y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁)/ (x₂ - x₁) is slope of the line.
And, (x₁, y₁) is the point on the line.
Thus, Slope = (1 - 2) / (3 - (-1))
= (-1)/4
= -1/4
So, The equation of line with slope -1/4 and point (-1, 2) will be;
y - 2 = -1/4 (x - (-1))
4 (y - 2) = - 1(x + 1)
4y - 8 = -x - 1
x + 4y = 8 - 1
x + 4y = 7
So, The equation of line that passes through points (-1, 2) and (3, 1) will be
x + 4y = 7
Learn more about the equation of line visit:
https://brainly.com/question/25969846
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How many seconds are in 240 minutes?
1 minute = 60 seconds
240 minute = 240 × 60 = 14400 seconds
240 minute = 14400 secondsWrite the point slope form of the equation of the line through the given point with the given slope. Show your work!
12) through (4,-4) , slope =-2
Answer:
y+4=-2(x-4)
Simplified- y=-2x+4
Step-by-step explanation:
y+4= -2(x-4)
y+4= -2x+8
-4. -4
y=-2x+4
help me i need this please
Answer:
B.
Step-by-step explanation:
P(something not happening)+P(something happening)=1 or 100%.
So if we have
P(something not happening)+40%=100%
Then the P(something not happening)=60% since 60%+40%=100%.
Yes I was using the event="something not happening" as the complement of something happening.
In fancy notation, some people might write:
[tex]P(A)+P(A')=1[/tex]
or
[tex]P(A)+P(A^c)=1[/tex]
1.) Harold’s truck has broken down and needs some repairs. The hourly pay for labor is $35 per hour, and the cost of the parts is $90. The mechanic’s estimate is $265. How many hours does the mechanic expect to need to fix the truck?
Answer:
5 hours
Step-by-step explanation:
The total amount of the repair is $265 and includes parts and an hourly rate. We are told the parts are $90. Subtract the price of the parts, $90, from the total of $265.
$265 - $90 = $175
The $175 is only due to the hourly rate.
Now we divide the total due to the hours by the hourly rate to find the number of hours.
175/35 = 5
Answer: 5 hours
A right triangle in which one acute angle is a reference angle for a 115 degree angle in standard position intersects the unit circle at (-0.423, 0.906). What is the approximate value of cos 115 degree?
Answer:
[tex]\cos (115\degree)=-0.423[/tex]
Step-by-step explanation:
The parametric equations of a circle is
[tex]x=r\cos \theta[/tex] and [tex]y=r\sin \theta[/tex]
The radius of the unit circle is 1 unit.
This implies that any point on the unit circle is represented by:
[tex]x=\cos \theta[/tex] and [tex]y=\sin \theta[/tex]
where [tex]\theta[/tex] is the angle in standard position,
From the question, the given angle in standard position is [tex]115\degree[/tex].
This angle intersects the unit circle at [tex]x=-0.423[/tex]
But [tex]x=\cos \theta[/tex]
We substitute [tex]\theta=115\degree[/tex] and [tex]x=-0.423[/tex]
This implies that: [tex]\cos (115\degree)=-0.423[/tex]
Find the coordinates of P so that P partitions the segment AB in the ratio 1:1 if
A(13,1) and B(−5,−3)?
.
Answer:
P(4, - 1 )
Step-by-step explanation:
The ratio 1 : 1 represents the midpoint of segment AB
Using the midpoint formula
[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]
with (x₁, y₁ ) = (13, 1) and (x₂, y₂ ) = (- 5, - 3), so
P = [0.5(13 - 5), 0.5(1 - 3) ] = [0.5(8), 0.5(- 2) ] = (4, - 1 )
the midpoint P has the coordinates (4, −1).
To find the coordinates of point P that partitions segment AB in a 1:1 ratio, also known as the midpoint, we use the midpoint formula. Given the coordinates A(13,1) and B(−5,−3), the midpoint formula is ((x1 + x2)/2, (y1 + y2)/2).
Applying the values from A and B:
For x-coordinate: (13 − 5) / 2 = 8 / 2 = 4For y-coordinate: (1 − 3) / 2 = −2 / 2 = −1Therefore, the midpoint P has the coordinates (4, −1).
When the polynomial in P(x) is divided by (x + a), the remainder equals P(a)
Answer:
This is a false statement:
Step-by-step explanation:
According to Remainder Theorem dividing the polynomial by some linear factor x + a, where a is just some number. As a result of the long polynomial division, you end up with some polynomial answer q(x) (the "q" standing for "the quotient polynomial") and some polynomial remainder r(x).
P(x)= (x+/-a) q(x)+r(x)
P(x)=(x+a) q(x)+r(x). Note that for x=-a
P(-a)=(-a+a) q(-a)+r(-a)= 0* q(-a)+ r(-a)
P(-a)=r(-a)
It means that P(-a) is the remainder not P(a)
Thus the given statement is false....
Do you guys know the answer for number 4
Answer:
90
Step-by-step explanation:
90-20%=72
72-20-52
plus everything else doesnt match up and with taxes involved so the oroginal price was 90
The perimeter of a rectangle is 230 feet. The short sides are each 30 feet long, but the lengths of the long sides are unknown. Which equation represents this situation?
30+2a=230
2(30)+2a=230
2(30)a=230
30a=230
Answer:
b
Step-by-step explanation:
because perimeter of rectangle is 2(l+b)
For this case we have that by definition, the perimeter of a rectangle is given by:
[tex]P = 2a + 2b[/tex]
Where:
a: It is the length of the rectangle
b: It is the width of the rectangle
We have as data that:
[tex]P = 230 \ ft\\b = 30 \ ft[/tex]
Then, replacing we have:
[tex]230 = 2a + 2 (30)[/tex]
Answer:
Option B