The polynomial for the given operation A, B, and C will be (-x²-x-1),(-x²-x-1), and (-x²-x-1).
What exactly is a polynomial?A polynomial is an algebraic statement made up of variables and coefficients.
Variables are sometimes known as unknowns. We can use arithmetic operations like addition, subtraction, and so on. However, the variable is not divisible.
a)Given polynomials;
⇒(3x − 2x² + 4) + (x² - 4x - 5)
⇒− 2x²+x²+3x-4x+4-5
⇒-x²-x-1
b)The opposite of the given polynomial is found by changing the sign in the polynomial as;
⇒3x² - x + 1
⇒(-3x²) -(- x) + (-1)
⇒-3x²+x-1
c)The subtraction operation in the polynomial is found as;
(x² + 3x-4) - (4x-2x²-3)
(x²-2x²)+(+3x-4x)+(-4+3)
-x²-x-1
Hence,the polynomial for the given operation A, B, and C will be (-x²-x-1),(-x²-x-1), and (-x²-x-1).
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please help question attached below!
Answer:
4.97
Step-by-step explanation:
h(x) = -3x² + 5
h(0.1)
x = 0.1
h(0.1) = -3(0.1)² + 5
0.1² = 0.01
-3(0.01) + 5
-3(0.01) = -0.03
-0.03 + 5 = 4.97
Here are two fractions.
7/6
6/7
Work out which of the fractions is closer to 1
You must show your working.
Here are two fractions.
The correct answer is 6 / 7 as it is closer to 1.
What is a fraction?The fraction is defined as the division of the whole part into an equal number of parts.
The number near 1 will be calculated as:-
7/ 6 = 1.1666
6 / 7 = 0.8571
Difference of the first ratio from one.
1.1666 - 1 = 0.1666
Difference of the second ratio:-
1 - 0.8571 = 0.1429
So the difference of 6 / 7 is lower than the difference of the fraction 7 / 6 from one.
Therefore the correct answer is 6 / 7 as it is closer to 1.
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Need help with my question
Answer:
See below ~
Step-by-step explanation:
What is the rat population in 1993?⇒ Number of years since = 0 ⇒ t = 0
⇒ Apply in the formula
⇒ n(0) = 73e^(0.02 × 0)
⇒ n(0) = 73e⁰
⇒ n(0) = 73,000,000 rats
=============================================================
What does the model predict the rat population was in the year 2009?⇒ Number of years since 1993 : 2009 - 1993 = 16 ⇒ t = 16
⇒ Applying in the formula
⇒ n(16) = 73e^(0.02 × 16)
⇒ n(16) = 73e^(0.32)
⇒ n(16) = 73 × 1.37712776 × 10⁶
⇒ n(16) = 100.530326 x 10⁶
⇒ n(16) = 100,530,326 rats
Answer:
Given function:
[tex]\large \text{$ n(t)=73e^{0.02t} $}[/tex]
where:
t is the number of years since 1993n(t) is the rat population measured in millionsTo calculate the rat population in 1993, substitute [tex]t = 0[/tex] into the function:
[tex]\large \begin{aligned}\implies n(0) & =73e^{0.02(0)}\\& = 73 \cdot 1\\& = 73 \sf \: million\end{aligned}[/tex]
To calculate a prediction of the rat population in 2009, first determine the value of t by subtracting the initial year of 1993 from the given year of 2009:
[tex]\large \text{$ \implies t=2009-1993=16 $}[/tex]
Substituting the found value of t into the function to find the predicted number of rats in 2009:
[tex]\large \begin{aligned}\implies n(16) & =73e^{0.02(16)}\\& = 73e^{0.32}\\& = 100.5303268...\\ & = 100.5 \sf \: million\:(1\:dp)\end{aligned}[/tex]
[tex]-3/z+7/4z=5/z-25[/tex]
Answer:
z = 1/4
Step-by-step explanation:
See attached image
Answer:
z = 5
Step-by-step explanation:
simplify
5/(z-25) first
turning it into
((0 - 3/z) + 7/4z) - 5/(z - 25) = 0
then simplify 7/4z
((0 - 3/z) + 7/4z) - 5/(z-25) = 0
when the fractions denominator is 0 then the numerator must be 0
turning the equation into
-25 * (z - 5) = 0
solve
-25 = 0
something that is not zero cannot equal zero.
z - 5 = 0
5 - 5 = 0
z = 5
hope this helps:)
The height of an arrow is shot upward at an initial velocity of 40 meters per second can be modeled by h=40t-5t^2 where h is the height in meters and t is the time in seconds. Find the time is take for the arrow to reach the ground. Can someone please explain this to me thanks
We are given the equation for the height of the arrow. If you graph it, you see that it's a parabola and that the arrow kinda peaks and then falls back down. Another way of thinking about this problem is that you're looking for the time when the height is 0. You can see on the graph that there are two times that h=0. The first is obviously at t=0, when the arrow hasn't left the ground yet. The second is what we're looking for, when the arrow reaches the ground.
To solve this, let's set h=0. So 0=40t-5t^2. If you factor this, you get 5t(8-t) = 0. Continuing that leads to 5t=0 where t=0 which we already knew, and 8-t=0 where t=8. So that second time is when the arrow is back on the ground. Therefore your answer is 8 sec.
what is the sum of the exterior angles of 28-gon
Answer:
360 degrees
..............
Find the area of the following parallelgram
Answer:
6 cm²
Step-by-step explanation:
The formula to find the area of the parallelogram is :
Area = Base × Height
Given that,
Base ⇒ 3cm
Height ⇒ 2 cm
Let us find now.
Area = Base × Height
Area = 3cm × 2cm
Area = 6 cm²
A boat heading out to sea starts out at Point A, at a horizontal distance of 1315 feet
from a lighthouse/the shore. From that point, the boat's crew measures the angle of
elevation to the lighthouse's beacon-light from that point to be 12°. At some later
time, the crew measures the angle of elevation from point B to be 8°. Find the
distance from point A to point B. Round your answer to the nearest foot if
necessary.
Answer: 674 ft
Step-by-step explanation:
[tex]\tan 12^{\circ}=\frac{y}{1315} \\ \\ 1315\tan 12^{\circ}=y[/tex]
[tex]\tan 8^{\circ}=\frac{y}{x+1315} \\ \\ (x+1315)\tan 8^{\circ}=y \\ \\ (x+1315)\tan 8^{\circ}=1315 \tan12^{\circ} \\ \\ x \tan 8^{\circ}+1315 \tan 8^{\circ}=1315 \tan 12^{\circ} \\ \\ x \tan 8^{\circ}=1315 \tan 12^{\circ}-1315 \tan 8^{\circ} \\ \\ x=\frac{1315 \tan 12^{\circ}-1315 \tan 8^{\circ}}{\tan 8^{\circ}} \approx \boxed{674 \text{ ft}}[/tex]
correlation and regression analysis
for 12 days, Keisha keeps track of how much water she drinks per day. her results are shown below
1 1/2quarts 2 1/4quarts 2quarts 1 1/2quarts 1 3/4 quarts 1 1/2 quarts
1 1/4quarts 2quarts 2 1/4quarts 1 1/2quarts 2 quarts 1 /2quarts
what is the amount of water that Keisha drinks during 12 days ?
what is the average amount of water that Keisha drinks per day ?
at how many days did Keshia drink at least the average amount of water?
STRETCH YOUR THINKING on day 13 Keisha drinks 1 quart of water how does that affect the average amount of water she drinks ? EXPLAIN
The total amount of water that Kiesha drinks in 12 days is 20 quarts
The average amount of water she drinks per day is 1 2/3 quarts
The number of days that Keshia drinks at least the average amount of water is 6 days
If she drinks 1 quart of day 13, the average reduces.
What is the average ?The total amount of water drank in the 12 days can be determined by adding the quarts for each day together. When they are added together, the number is 20 quarts.
Average = total amount drank / number of days 1 2/3 quarts
New average = 20 + 1 / 13 = 21 / 13 = 1 7/13 quarts
The average reduces because the quart drank on the 13th day is less than the amount of water drank on the other days.
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The diagram shows a right angled triangle. 11cm 8cm and x degrees. Find the size of angle x. Give your answer correct to 1 decimal place.
The size of the unknown angle "x"
Solution:We'll have to check which one is appropriate from SOHCAHTOA.
In this question hypotenuse and adjacent is given so, we'll have to use cos.
[tex]\large\boxed{Formula: cos \: (A)= \frac{adj}{hyp}}[/tex]
Let's solve!
Let's substitute the values according to the formula.
[tex]cos \: x= \frac{8}{11}[/tex]
We'll have to use cos inverse.
[tex]x= {cos}^{-1}( \frac{8}{11} )[/tex]
[tex]x= 43.34175823[/tex]
Now we'll have to round off to 1 decimal place.
The value in hundredths place is less than 5 so we won't have to round up.
So, the final answer is:
[tex]\large\boxed{x= 43.3°}[/tex]
Therefore, the size of the unknown angle "x" is 43.3°
in euclidean geometry any three points not on the same line can lie on how many planes?
Answer:
1 plane
Step-by-step explanation:
In Euclidean geometry, three non-collinear points will define exactly one plane.
__
Two points will define a line. That line can exist in an infinity of different planes.
A third point not on the line can only lie in exactly one plane with that line.
Three non-collinear points in Euclidean geometry can lie on one unique plane.
In Euclidean geometry, any three non-collinear points (points not lying on the same line) uniquely determine a plane.
This means that there is only one plane that contains all three of those points.
So, given three non-collinear points, you can find exactly one plane that passes through all of them.
Hence, if the three points not on the same line can lie on one plane.
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Construct a triangle with the given conditions. Questions are on the picture.
Answer + Step-by-step explanation:
Question 4 :
Construct the angle 0MN :
1) Draw a segment MO
2) Put the protractor so that it is in line with the segment MO
At the same time ,line up the points M with the little circle of the protractor.
3) Spot 40° on the protractor ,then draw a point.
4) Use the ruler to connect point M through that point
Construct the angle MON :
1) Put the protractor so that it is in line with the segment MO
At the same time ,line up the points O with the little circle of the protractor
2) Spot 70° on the protractor ,then draw a point.
3) Use the ruler to connect point O through that point.
Construct the point N :
N is the point of intersection of the lines that go (respectively) through M and O.
Question 6 :
1) Draw a segment XZ such that XZ = 2.
2) construct the angle ZXY = 25°. (follow the steps described in the Previous question).
NOTE : ∠Z = 180 - (∠X + ∠Y) = 180 - (25 + 45) = 110°
3) construct the angle XZY = 110° . (follow the steps described in the Previous question)
4) Y is the point of intersection of the lines that go (respectively) through X and Z.
which of the sequences is an arithmetic sequence A. -20,-27,-34,-41,-48, ... B. 1,5,10,15,20, ... C.154,71,8,5,2, ... D. 12,-24,36,-48.60, ...
Answer:
A and B are arithmetic sequences. they have a set and consistent increase/decrease in each term.
Step-by-step explanation:
Solve the system of equations
−5x−3y=−28 and x+2y=0 by combining the equations
Answer: (8, -4)
Step-by-step explanation:
-5x - 3y = -28
x + 2y = 0
1. Multiply both sides of the bottom system by 5 to cancel the x out
5(x+2y=0)
5x + 10y = 0
2. rewrite
-5x - 3y = -28
5x + 10y = 0
3. add
0x + 7y = -28
4. divide by 7
7y = -28
5. y = -4
6. plug in -4 for y in one of the original equations
x + 2(-4) = 0
7. simplify
x = 8
9. solution is
(8, -4)
Based on the measures
provided in the diagram,
determine the measure of
BC.
(You may assume that point A is the
center of the circle.)
O 130⁰
O 25⁰
O 50⁰
O 100⁰
The measures of BC will be 100°. Option D is correct.
What exactly is a circle?It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.
The angle at the center is twice as large as the angle at the perimeter.
BC = 2 ×∠CDB
BC=2×50°
BC= 100°
Hence option D is correct.
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please please help. i need to submit this in 15 minutes!!!
∆ADB is ~ ∆BEC because <D and <E are right angles which are equal to 90°.
What is a right angle?A right angle is defined as an angle that is formed when two straight line are perpendicular at an intersection creating a 90° angle when measured.
From the diagram, ∆ADB is ~ ∆BEC because <D and <E are right angles which are equal to 90°.
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a rectangular mural measures 3.5ft by 5.5ft. Rosalie creates a new mural that is 1.5 ft longer. What is the perimeter of Rosalie's new mural?
The perimeter of Rosalie's new rectangular mural is given by P = 21 feet
What is the Perimeter of a Rectangle?The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P of rectangle = 2 ( Length + Width )
Given data ,
Let the perimeter of the rectangular mural be represented as P
Now , the equation will be
Let the initial length of the rectangular mural be L = 3.5 feet
Let the initial width of the rectangular mural be W = 5.5 feet
Now , the new mural is having an extra length of 1.5 feet
So , the new length of the rectangular mural is L₁ = 3.5 + 1.5 = 5 feet
Now , Perimeter P of rectangle = 2 ( Length + Width )
Substituting the values in the equation , we get
Perimeter of rectangular mural = 2 ( 5 + 5.5 )
On simplifying the equation , we get
Perimeter of rectangular mural P = 2 x 10.5
Perimeter of rectangular mural P = 21 feet
Hence , the perimeter of rectangular mural is 21 feet
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Answer:
1400
Step-by-step explanation:
8 marks] In how many ways can the letters of the word "UNDERDOG" be arranged such that the first and last letters are same and no two vowels are together?
The letters of the word "UNDERDOG" can be arranged in 144 ways.
Number of ways "UNDERDOG" can be arrangedThere are only two letters that are the same which are D, then the remaining letters are 6 letters.
V, E, O are vowels
N R G
The vowels are not joined together
For N, R, G A³3
There are 4 openings A³4
Hence:
A³4· A³3=4×3×2×3×2×1
A³4· A³3=144
Therefore the letters of the word "UNDERDOG" can be arranged in 144 ways.
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Will give 50 points for the answer to this
Answer:
( 3, -2 )
Step-by-step explanation:
3, -2 is on the line so it is a solution
the rest of the points aren't in the shaded area or on the line therefore they are not a solution
Have a great day! :)
A water barrel has a total volume of 1.25 cubic meters (m3). Use the fact that 1 foot is approximately equal to 0.3048 m to convert this volume to cubic feet (ft3). Round your answer to the nearest tenth. Do not type the units in the space below.
Answer:
see the attachment photo!
It’s geometry… need help solving
Answer:
Angle 1 = 90 degree
Angle 2 = 55 degree
Angle 3 = 35 degree
Step-by-step explanation:
A rhombus has four equal sides. Since the intersection angle of a rhombus is always 90 degree, angle 1 is 90 degree
Angle 3 = 180 degree - 90 degree - 55 degree = 35 degree
Angle 2 = 180 degree - 90 degree - 35 degree = 55 degree
Jax drew an angle that turns through
80 one-degree angles. Which is the
measure of the angle Jax drew?
When Jax drew an angle that turns through 80 one-degree angles, the measure of the angle will be 80°.
How to depict the angle?It should be noted that when an angle turns through a particular degree, it'll be said to have an identical degree.
In this case, when Jax drew an angle that turns through 80 one-degree angles, the measure of the angle will be 80°.
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Put these numbers in order, starting with the largest.
Largest
293,000
545,417
779,500
459,300
273,481
Smallest
To calculate the density of an object,you wpuld?
Paula and Pedro were selling water bottles to raise money for their school. The ratio of water bottles Paula sold to water bottles Pedro sold is 3:5. If together Paula & Pedro sold a total of 72 water bottles, how many did each sell?
Step-by-step explanation:
x = number of bottles Paula sold
y = number of bottles Pedro sold
x + y = 72
x = 72 - y
x/y = 3/5
(72 - y)/y = 3/5
5(72 - y) = 3y
360 - 5y = 3y
360 = 8y
y = 45
x + y = 72
x + 45 = 72
x = 27
so,
Paula sold 27 water bottles, and Pedro sold 45.
A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours. After the leak is fixed, the height of the water is 4.75 feet. The equation 4.75 = x + (negative 0.25) can be used to find x, the original height of the water in a pool.
What was the original height of the water in the pool in feet?
4.5
5.0
6.5
7.0
An equation is formed of two equal expressions. The original height of the water in the pool in feet is 5.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the equation, 4.75 = x + (-0.25) can be used to find x, the original height of the water in a pool. Therefore, the height of the fool in the beginning is,
4.75 = x + (-0.25)
4.75 + 0.25 = x
x = 5
Hence, the original height of the water in the pool in feet is 5.
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Which item is the U.S. Treasury most known for issuing?
-CDs
-savings notes
-bonds
-investment notes
Answer:
Bonds
Step-by-step explanation:
A bond is a fixed-income instrument that represents a loan made by an investor to a borrower (typically corporate or governmental).
A woman sprints at a rate of 19 ft/s. How many minutes will it
take her to sprint 600 feet ?
[tex]\begin{array}{ccll} feet&seconds\\ \cline{1-2} 19 & 1\\ 600& x \end{array} \implies \cfrac{19}{600}~~=~~\cfrac{1}{x} \\\\\\ 19x=600\implies x=\cfrac{600}{19}\implies \stackrel{\textit{about half a minute}}{x\approx 31.58~seconds}[/tex]
Answer:
10/19 min ≈ 0.5263 min
Step-by-step explanation:
The woman's sprinting speed is given in feet per second, and we are asked for it in minutes per 600 feet. To find the time, we can use the relation ...
time = distance / speed
Using the given numbers will give a time in seconds, so we need to do a units conversion to find the answer in minutes.
__
setuptime = distance/speed
time = (600 ft) / (19 ft/s) = (600/19) s
Converting the units gives ...
time = (600/19) s × (1 min)/(60 s) = (600·1)/(19·60) min
evaluationThe time it takes the woman to sprint 600 feet will be ...
time = 600/(19·60) min = 10/19 min ≈ 0.5263 min
Which expression represents “2 times the difference of x and 5”?
Answer:
2(x-5)
Step-by-step explanation:
Hope this helps
Answer:
2 · (x - 5)
Step-by-step explanation:
2 · (x - 5)
2 ·
"2 times"
when multiplication- or "times" is said, it can be shown in multiple ways. Multiplication can be shown as a×b , a·b , (a)(b)
(x - 5)
"difference of x and 5"
when difference is noted, the first number listed is the one written first. The difference between 2 and x is ( 2 - x ); the difference between x and 2 is ( x - 2).