If [tex]P(x) = p_nx^n + p_{n-1}x^{n-1}+\ldots+p_0[/tex] is divided by [tex](x-a)[/tex], then [tex]P(x) = (x-a) \cdot Q(x) + R(x)[/tex] for some polynomials [tex]Q,R[/tex]. Moreover, [tex]\deg R < 1[/tex] (because [tex]\deg (x-a) = 1[/tex]), so there exists [tex]\alpha \in \mathbb{R}[/tex] such that [tex]R(x) = \alpha[/tex] for all [tex]x \in \mathbb{R}[/tex]. But if we calculate [tex]P(a)[/tex], it turns out that [tex]P(a) = (a-a)\cdot Q(a) + \alpha[/tex], so [tex]R(x) = \alpha = P(a)[/tex]. [tex]\blacksquare[/tex]
Which equation can be used to find x, the length of the hypotenuse of the right triangle?
Answer:
[tex] \boxed{\sf {18}^{2} + {24}^{2} = {x}^{2}} [/tex]
To Find:
Length of hypotenuse of the right triangle i.e. x
Step-by-step explanation:
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.
[tex] \therefore [/tex]
[tex] \sf \implies {18}^{2} + {24}^{2} = {x}^{2} [/tex]
Answer:
18²+24²=x²
Step-by-step explanation:
to answer this question you must know Pythagorean theorem
a^ 2+b^2 =c^2
a and b stands for the sides with length 24 and 18 and c stands for the HYPOTENUSE . so the correct answer for the above question is 18²+24²=x²
Use the number line to plot –3, 1, and 3.
Which statements are true? Select all that apply.
–3 > 1
–3 = 3
1 < 3
–3 < 1
Answer:
Options 3 and 4 are correct
Step-by-step explanation:
-3>1 is false bc a positive is always greater than a negative
-3=3 is false because a positive is not equal to a negative
1<3 is correct because 1 is less than 3
-3<1 is correct because a negative is always less than a positive.
Answer:
1 < 3
–3 < 1
Step-by-step explanation:
In Exercise 26, find the height of the right prism.
Answer:
h= 9.473684 in.
Step-by-step explanation:
1/2(8)(15)*2+2(15h)+8h=480
120+38h=480
38h=480-120
38h=360
h= 9.473684 in.
7000 cm² is the same area as
.......... m².
Answer:
1000cm²=0.1m²
so 7000cm²=0.7m²
Step-by-step explanation:
please mark me as brainliest
Answer:
0.7
Step-by-step explanation:
Make ratio:
1 square centimeter = 0.0001 square meter
x square meters = 7000 square centimeters
Multiply:
0.0001 × 7000 = 0.7
Hope this helped.
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match each angle measure in degrees with its equivalent measure in radians.
Answer:
315° = 7π/4 rad80° = 4π/9 rad225° = 5π/4 rad324° = 9π/5 radStep-by-step explanation:
Find the attachment in the diagram below,
In order to get the right match, we will use the conversion
180° = πrad
- For angle 315°;
If 180° = πrad
315° = a
Cross multiplying
180a = 315π rad
a = 315π rad/180
a = 63π/36 rad
a = 7π/4 rad
Hence 315° = 7π/4 rad
- For angle 80°;
If 180° = πrad
80° = b
Cross multiplying
180b = 80π rad
b = 80π rad/180
b = 8π/18 rad
b = 4π/9 rad
Hence, 80° = 4π/9 rad
- For angle 225°;
If 180° = πrad
225° = c
Cross multiplying
180c = 225π rad
c = 225π rad/180
c = 15π/12 rad
c = 5π/4 rad
Hence, 225° = 5π/4 rad
- For angle 324°;
If 180° = πrad
324° = d
Cross multiplying
180d = 8324π rad
d = 324π rad/180
d = 27π/15 rad
d = 9π/5 rad
Hence, 324° = 9π/5 rad
4. Alejandro Juarez is paid $829 every two weeks. a. What is Alejandro's yearly salary?
b. How much would Alejandro earn in one month?
Answer:
1. 21,554 PER YEAR
2. 1658 PER MONTH
Step-by-step explanation:
a.
so there are approximately 52 weeks per year
and alejandro juarez gets 829$ per 2 weeks
1..............LETS FIGURE OUT HOW MUCH HE EARNS PER WEEK
SO 829/2=414.5
so he gets 414.5 $ PER WEEK
2............LETS MULTIPLY THE AMOUNT OF MONEY PER WEEK BY THE WEEKS
SO 414.5*52=21554
SO ALEJANDRO JUAREZ EARNS 21,554$ PER YEAR
B.
SO WE ALREDY KNOWS ALEJANDRO EARNS 414.5$ PER WEEK
AND THERE ARE APPROXIMATELY 4 WEEKS IN A MONTH
SO 414.5*4=1658
SO HE EARNS 1658$ PER MONTH
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
State the transformations on the graph of f(x) = ^ x that result in the graph of the given functions.
Write the transformation rule.
find the surface area of the figure below. Round it to the nearest tenth.
Answer:
173.4
Step-by-step explanation:
Surface area of the cone=pi*r*l+pi*r^2=pi*(4)*(9.8+4)=173.4
Pls pls pls pls help me
Answer:
96 cm²
Step-by-step explanation:
Triangular face:
base = 8 cm
height = 6 cm
Area of triangle = [tex]\dfrac{1}{2}*b*h[/tex]
[tex]= \dfrac{1}{2}*8*6\\\\=4*6\\\\= 24 \ cm^{2}[/tex]
Area of 4 triangular faces = 4 * 24 = 96 cm²
Find the indicated side of the
right triangle.
45°
y
6
45
Х
y = [?] /
Answer:
hello dear...
see first of all there's a thm type thing
'' sides opposite to equal angles are equal ''
so here 45 degrees in both sides are equal which leads us that opposite sides are equal as well
so x = 6
now we got value of 2 sides, both are 6 and now applying pythogarus as it is right angle
6^2 + 6^2 = y^2
36+36 = y^2
72 = y^2
y = √72
y = √36*2
y = 6√2
brainliest plssss <33
The scale on a map of Virginia shows that 1 inch represents 20 miles the actual distance from Richmond Virginia to Washington DC is 110 miles on the map how many inches are between the two cities
Answer:
5.5 inches
Step-by-step explanation:
Proportions:
1 inch ⇔ 20 miles
W inch ⇔ 110 miles
W = 110*1/20
W = 5,5 inch
SAT/ACT What is the solution of 1,200 – 5(3x + 30) = 600? A 30 B 50 C 150 D 200 E 250
The answer you are looking for is letter A, x=30.
Solution/Explanation:
First, write out the equation,
1200-5(3x+30)=600
Next, using the Distributive Property,
1200-15x-150=600
Simplify the left side of the equation just a little bit more,
1050-15x=600
Reverse order of terms on the left side, to make it a little bit easier to solve,
-15x+1050=600
Now, subtract 1050 from both sides,
-15x+1050-1050=600-1050
Now, simplify this part of the equation,
-15x=-450
Finally, divide both sides by -15,
So, therefore, the final answer is x=30.
I hope this helped you. Enjoy your day, and take care!
Which property of equality would be used to isolate the variable b in this equation?
3/4 x b = 12
A. addition property of equality
В. subtraction property of equality
C. multiplication property of equality
D. symmetric property of equality
Answer:
C. multiplication property of equality
Step-by-step explanation:
3/4b = 12
Multiply each side by 4/3 using the multiplication property of equality
4/3* 3/4b = 12*4/3
b = 16
rational or irrational? and why
Answer:
Irrational
Step-by-step explanation:
If we evaluate the square root, we realize that the number will not be a perfect square.
Since it is not a perfect square, it will be an unending, never-repeating, decimal.
Therefore, it will be irrational.
How tall is a stack of cube-shaped blocks whose volumes are 375 in3, 648 in3 and 1,029 in3? Round your answer to the nearest tenth. Hint: Volume = s3
Answer:
Step-by-step explanation:
13. Diberi v = u + at, cari nilai t apabila v = v = 42 u=-8 dana - 5.
A.10
B.8
C.6
D.4
Answer:
Lol mcm soalan kamu salah. Pilih A je
Step-by-step explanation:
v = 42u = -8a = -5Masukkan nilai tersebut dalam persamaan v = u + at,
42 = -8 + (-5)t
50 = -5t
t = -10
Round the number 553 to the tens place.
is it 550? because 3 is less than 5 so I replace it with a 0
Answer:
550
Step-by-step explanation:
To round 553 to the tens place, we would need to identify the value of the digit in the ones place.
If the digit in the ones place is greater than 5, we increase the tens place by 1 & convert the ones place into a 0.
If not, we leave the tens place as is & convert the ones place into a 0.
Since 3 is less than 5, we round 553 to 550 so you are correct.
Answer:
Yes
550 has 2 sig figs
553 has 3
Step-by-step explanation:
Can someone help? It can be 3-5 sentences just compare and contrast them.
A line segment has two endpoints. It contains these endpoints and all the points of the line between them. You can measure the length of a segment, but not of a line. A ray is a part of a line that has one endpoint and goes on infinitely in only one direction.
I hope this helps! Brainliest would be appreciated.
line is cool segment is cool ray is cool btw the other persons answer is right
(x+3)(x-5)=(x+3)(x−5)=
Answer:
All real numbers are solutions. 0=0
Step-by-step explanation:
(x+3)(x−5)=(x+3)(x−5)
Step 1: Simplify both sides of the equation.
x2−2x−15=x2−2x−15
Step 2: Subtract x^2 from both sides.
x2−2x−15−x2=x2−2x−15−x2
−2x−15=−2x−15
Step 3: Add 2x to both sides.
−2x−15+2x=−2x−15+2x
−15=−15
Step 4: Add 15 to both sides.
−15+15=−15+15
0=0
All real numbers are solutions.
Find the rate of change for the situation. A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Bryan is getting trained and licensed to be a truck driver. He only has $350 in his bank account. The training is free but gas costs 13 cents per mile. If he travels 1,254 miles, how much money will he have left in his bank account?
A. $186.98
B. $127.32
C. $64.83
D. $206.17
Answer:
186.98
Step-by-step explanation:
The cost of gas is the cost per miles times the number of miles
1254 * .13
163.02
Subtract this from the amount in the bank account
350-163.02
186.98
A vehicle has a will 15 inches in diameter. If the vehicle travels 2 miles, how many revolutions does the wheel make? This is Applications of unit conversions
Find the circumference of the wheel:
Circumference = PI x Diameter = 3.14 x 15 = 47.1 inches.
Every revolution the tire travels 47.1 inches.
1 mile = 5,280 feet, so 2 miles = 5280 x 2 = 10,560 feet.
1 foot = 12 inches.
2 miles = 10,560 feet x 12 = 126,720 inches.
Revolutions = total distance / distance per revolution:
Revolutions = 126,720 / 47.1 = 2,690.45 revolutions ( round answer as needed.)
6 sqrt (x-2) +4 < 28
How do you solve? Btw.. x-2 is under sqrt sign.
Answer:
Step-by-step explanation:
[tex]6\sqrt{x-2}+4<28\\6\sqrt{x-2}<28-4\\\sqrt{x-2}<\frac{24}{6}\\\sqrt{x-2}<4\\\\x-2 <16\\x<16-2\\x<14x-2 \geq 0\\x\geq 2\\so~2 \leq x < 14[/tex]
Choose all of the expressions that are equal to −9. |−9| −(−9) −|−9| −|9| the distance from zero to nine the opposite of nine
Answer:
|−9|, −|−9| and −|9|Step-by-step explanation:
Before we choose all the expression that is equal to -9, we must understand that the modulus of a value can return both its positive and negative value. For example, Modulus of b can either be +b or -b i.e |b| = +b or -b
Hence the following expression are all equal ro -9
a) |−9| is equivalent to -9 because the absolute value of -9 i.e |−9| can return both -9 and 9
b) −|−9| is also equivalent to -9. The modulus of -9 is also equal to 9, hence negating 9 will give us -9. This shows that −|−9| = −|9| = −9
c) −|9| is also equivalent to -9. This has been established in b above.
Answer: -|-9|, -|9|, and the opposite of nine
Step-by-step explanation: The absolute value symbol is | |. |-9| is 9 but add that - to it and it's -9. The absolute value of 9 is 9, add the - to it to get -9.
the opposite of 9 is -9.
Find the product. Express answer in standard form.
(x – - 4)(3x² + 4x – 4)
Answer:
3x³ + 16x² + 12x - 16
Step-by-step explanation:
(x - -4)(3x² + 4x - 4)
(x + 4) (3x² + 4x - 4)
3x³ + 4x² - 4x + 12x² + 16x - 16
3x³ + 4x² + 12x² - 4x + 16x - 16
3x³ + 16x² + 12x - 16
Help pleasee!!! Tyyyyy
Answer:
G. 7
Explanation:
The longest side must be less than the sum of the two shorter sides.
The difference between the longest and shortest sides must be less than the middle side.
l+a = 11
l < (a + 4) ... l < (11 - l + 4)
... 2 l < 15 ... l < 7.5
--Variables
l = 7 (Longest Side/Answer)
a = 4 (Other Missing Length)
m = 4 (Side Given)
Kapil deposited Rs. 1600 in a bank on 1st January 2005. Find the amount in his bank account on 1st January 2006, if the bank pays interest at 8% per annum and the interest is calculated every year on 30th June and 31st December.
Answer:
SI=PRT/100
=10000*5*42/12*100
=1750
SI=1750
TOTAL AMOUNT=PRINCIPLE+SI
=10000+1750
=101750
Cory remembers that his ATV had 4 gallons of gasoline in the tank on Monday. After driving a total of 40 miles during
the week, he has 2 gallons of gas remaining. Find the slope of the graph representing this situation.
Answer:
-1/20
Step-by-step explanation:
For a graph like this you should make the gallons of gas on y-axis and the miles driven on the x-axis.
To find slope the formula is (y2-y1)/(x2-x1)
So in this case it is 2-4/40-0
-2/40
This reduces to -1/20
what is the sum of 1+2+.....+50?
Answer:
sum is 1275
Step-by-step explanation:
[tex]sum = \frac{n}{2} [2a + (n - 1)d] \\ \\ sum = \frac{50}{2} [(2 \times 1) + (50 - 1) \times 1] \\ \\ sum = 25(51) \\ sum = 1275[/tex]
85,58,72,85,46,93 mean,mode,range,median
Answer:
mean: 73.2
mode : 85
range:47
median: 78.5
Step-by-step explanation:
85,58,72,85,46,93
first put the numbers in order from least to highest
46,58,72,85,85,93
mean: is the sum of the terms divided by the number of terms
(85+85+72+58+46+93)/6=73.2 ( rounded to the nearest tenth)
mode : is the element that occurs the most: in this case it is 85 occurs twice
range : subtract the minimum data from max. data: 93-46=47
median : is the middle number, in this case it is even so take the middle two numbers and divide by 2: 85+72/2= 157/2=78.5
median = 78.5
The mean value is 73.
The mode value is 85.
The range value is 47.
The median value is 78.5.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
85,58,72,85,46,93
Mean = (85 + 58 + 72 + 85 + 46 + 93) / 6
Mean = 73
Mode is the number that occurs the most times in the set.
Mode = 85.
Range = Highest value - Lowest value.
Range = 93 - 46 = 47.
The Median is the middle value after arranging the set in order.
46, 58,72,85, 85, 93
Median = (72 + 85) / 2
Median = 78.5
Thus,
The means is 73.
The mode is 85.
The range is 47.
The median is 78.5.
Learn more about mean here:
https://brainly.com/question/23263573
#SPJ2