Answer: The fundamental theorem of algebra states that the equation 2x^2+8x+14=0 has at least one complex root, which means that there are numbers that can be plugged into x that make the equation equal to zero. ✅
PLEASEEEE GIVE BRANLIEST
Step-by-step explanation:
The fundamental theorem of algebra states that for any non-constant polynomial equation with real or complex coefficients, there is at least one complex root (or solution).
In the case of the equation 2x^2+8x+14=0, the theorem guarantees that this equation has at least one complex root, which means that there are numbers that can be plugged into x that will make the equation equal to zero.
So, the fundamental theorem of algebra guarantees that for the equation 2x^2+8x+14=0, there exists at least one complex solution that makes the equation true. In this case, the solutions are x = -1+i and x = -1-i ✅
Anya was rowing up the river and noticed it takes longer to row upstream than downstream. She knows that in still water she can row 9 mph. She timed herself rowing approximately 4 miles upstream and then back in 1.5 hours. She then calculated the current of the river.
If the speed of boat in still water iss 9 mph and takes 1.5 miles to go and come 4 miles uptream and downward then the current of the river is 9.24 mph.
Given that the speed in still water be 9 mph, time to travel 4 miles upstream and downward is 1.5 hours.
We are required to find the speed of current of the river.
let the speed of current be c mph.
Effective speed in downstream=9+c
Effective speed in upstream=9-c
Total time=1.5 hours.
Total distance=4 miles.
Time for upstream stream+ time for downward stream=1.5 hours
2/(9+c)+2/(9-c)=1.5
18-2c+18+2c=1.5(9+c)(9-c)
36=1.5(81-[tex]c^{2}[/tex])
36=121.5-1.5[tex]c^{2}[/tex]
1.5[tex]c^{2}[/tex]=121.5-36
[tex]c^{2}[/tex]=85.5
c=9.24 mph.
Hence the speed of the current of the river is 9.24 mph.
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PLEASE GUYS THIS IS THE HARDEST MATH PORBLEMS PLEASE ASAP PLEASE I NEED HELP PLEASE T_T
The simplified form of R(x) is [tex]R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}[/tex]
Simplifying an expressionFrom the question, we are to simplify the expression
From the given information,
[tex]f(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30}[/tex]
and
[tex]g(x) =\frac{x^{2}-9x+20 }{x^{2}-12x+36}[/tex]
Also,
[tex]R(x) = f(x) \div g(x)[/tex]
∴ [tex]R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \div \frac{x^{2}-9x+20 }{x^{2}-12x+36}[/tex]
[tex]R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \times \frac{x^{2}-12x+36 }{x^{2}-9x+20}[/tex]
Factoring each of the quadratics
[tex]R(x) =\frac{x^{2}-7x-4x+28 }{x^{2}-6x-5x+30} \times \frac{x^{2}-6x-6x+36 }{x^{2}-4x-5x+20}[/tex]
[tex]R(x) =\frac{x(x-7)-4(x-7) }{x(x-6)-5(x-6)} \times \frac{x(x-6)-6(x-6) }{x(x-4)-5(x-4)}[/tex]
[tex]R(x) =\frac{(x-4)(x-7)}{(x-5)(x-6)} \times \frac{(x-6)(x-6)}{(x-5)(x-4)}[/tex]
Simplifying
[tex]R(x) =\frac{(x-7)}{(x-5)} \times \frac{(x-6)}{(x-5)}[/tex]
[tex]R(x) =\frac{(x-7)(x-6)}{(x-5)(x-5)}[/tex]
[tex]R(x) =\frac{x^{2} -6x-7x+42}{x^{2} -5x-5x+25}[/tex]
[tex]R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}[/tex]
Hence, the simplified form of R(x) is [tex]R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}[/tex]
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10 points please help me
Answer:
(a)
A = 3
B = 17
C = 8
D = 15
(b)
surface area = 240
(using the formula)
The cost of a fan is Rs 1,600. If Mrs. Khadka purchased it with 13% VAT, how muc did she pay for it?
Answer:
Rs 1808
Step-by-step explanation:
Sp=Selling price
Mp=main price
Sp=Mp+Mp*VATSp=Rs 1600+Rs 1600*13%Sp=Rs 1600+Rs 208Sp=Rs 1808Matt's four cousins are coming to visit. There are four identical rooms that they can stay in. If any number of the cousins can stay in one room, how many different ways are there to put the cousins in the rooms
The total number of different ways there are to put the cousins in the rooms is; 15
How to use probability combinations?When we count the number of cousins staying in each room, it means that the possibilities are as follows; (4,0,0,0), (3,1,0,0), (2,2,0,0), (2,1,1,0), (1,1,1,1).
1) (4,0,0,0): This means that there is only 1 way to put all the cousins in the same room due to the fact that the rooms are identical.
2) (3,1,0,0): This means that there are 4 ways to choose which cousin will be in a different room than the others.
3) (2,2,0,0): This means that there are 3 ways to choose which of the other cousins will also stay in that room, and then the other two are automatically in the other room.
4) (2,1,1,0): This means that the number of ways to choose which cousins stay in the same room is; 4C2 = 6
5) (1,1,1,1): This means that there is only one way for all the cousins to the total number of possible arrangements is;
1 + 4 + 3 + 6 + 1 = 15each stay in a different room.
Therefore, the total number of possible arrangements is;
1 + 4 + 3 + 6 + 1 = 15
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match the following vocabulary
1. the distance around a circle
2. a portion of the circumference of a circle
3. the distance from the center to any point on a circle
4. the distance through the center between points on a circle
5.
the degree measurement of an arc (in reference to its central
angle)
6. an arc which measures less than 180°
7. an arc which measures exactly 180°
arc length
circumference
diameter
minor arc
arc measure
radius
semicircle
The properties of a Circle with their definitions are; As highlighted below
How to identify Properties of a Circle?1) The distance around a circle is called; Circumference
2) A portion of the circumference of a circle is called; Arc Length
3) The distance from the center to any point on a circle is called; Radius.
4) The distance through the center between points on a circle is called; Diameter
5) The degree measurement of an arc (in reference to its central
angle) is called; Arc Measure
6) An arc which measures less than 180° is called; Minor arc
7) An arc which measures exactly 180° is called; Semi Circle
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Please help Urgent
1. Explain the steps to use coordinates in calculating the perimeter and area of polygons? Explain your procedure when working with diagonal sides and irregular shapes on the coordinate plane.
2. Explain how the distance formula and slope formula are used to classify various quadrilaterals and triangles.
The way to use the distance formula to classify quadrilateral include:
Use the distance formula to measure the lengths of the sides.Use the slope to check whether the sides are perpendicular and form right angles.Use the slope to check whether the diagonals are perpendicular to eachHow to illustrate the information?The steps to calculate the perimeter and area of a polygon:
Step 1: Plot the given points on the graph.
Step 2: Connect the points and identify the figure.
Step 3: Determine lengths by counting the grid lines.
Step 4: Use a formula to calculate the perimeter and area if one exists.
Step 5: If there are no formulas for a figure, the perimeter can be calculated by summing the lengths of the sides. We might estimate the area without an area formula by counting the number of small squares enclosed.
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A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer. Find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet above the ground.
The rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet above the ground is 1/20 degree/sec.
What is angle of elevation?It is described as a relationship between an oblique line from the observer's eye to an item above his eye and the horizontal plane. This angle eventually develops above the surface. The angle of elevation is made in such a way that it is above the observer's eye, as the name suggests.
Calculation for the rate of change of angle of elevation-
According to the question,
A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer.
The balloon is 100 feet above the ground.
Let the height of the balloon be 'h' ft.
Then tanØ = h/100
h = 100tanØ
Differentiate the above equation with respect to time.
dh/dt = 100 sec² Ø (dØ/dt)
We know dh/dt = 10 ft/sec.
when h = 100
tanØ = 100/100 = 1/1
tanØ = Perpendicular/Base
On comparing above two equations,
Perpendicular = 1; Base = 1.
By Pythagoras the hypotenuse is,
H² = P² + B²
= 1² + 1²
= 2
H = √2
Now, calculate the value of cosØ.
cosØ = B/H = 1/√2
Squaring both side
cos² Ø = 1/2
sec² Ø = 1/cos² Ø
sec² Ø = 2
The main equation was,
dh/dt = 100 sec² Ø (dØ/dt)
Substitute the values,
dØ/dt = (dh/dt )/100 sec² Ø
= (10)/(100×2)
dØ/dt = 1/20 degree/sec.
Therefore, the rate of change of the angle of elevation of the balloon from the observer is 1/20 degree/sec.
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. If sin(x + y)=sin x.cos y+cos x.sin y, then find the value of sin 75 degrees
Answer:
[tex]\sf \dfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]
Step-by-step explanation:
Trigonometry:75 = 45 + 30
Sin (x + y) = Sin x *Cos y + Cos x * Sin y
Sin (45 + 30) = Sin 45 * Cos 30 + Cos 45 * Sin 30
[tex]\sf =\dfrac{1}{\sqrt{2}}*\dfrac{\sqrt{3}}{2}+\dfrac{1}{\sqrt{2}}* \dfrac{1}{2}\\\\\\=\dfrac{\sqrt{3}}{2\sqrt{2}}+\dfrac{1}{2\sqrt{2}}\\\\\\=\dfrac{\sqrt{3}*\sqrt{2}}{2*\sqrt{2}*\sqrt{2}}+\dfrac{1*\sqrt{2}}{2\sqrt{2}*\sqrt{2}}\\\\\\=\dfrac{\sqrt{6}}{2*2}+\dfrac{\sqrt{2}}{2*2}\\\\\\=\dfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]
If a single 2 hp motor draws 13.8 amps on 115 volt ac current, how much current would 9 identical motors pull?
what is the answer and how do you solve it?
The current drawn by 9 identical motors will be 124.2 amps current
Current is the flow of electrical charge carriers like electrons. Current flows from negative to positive points. The SI unit for measuring electric current is the ampere (A). One ampere of current is defined as one coulomb of electrical charge moving past a unique point in a second.
since , one motor of 2hp draws = 13.8 amps current
hence , 9 identical motor will pull = 13.8 * 9 (each will pull same amount of current )
= 124.2 amps current
The current drawn by 9 identical motors will be 124.2 amps current
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If d(4)= 68. thus, joe travels 68 mi in 4 hours. then how much mi does joe travel in 45 minutes
Given that, Joe travels 68 mi in 4 hours, the number of miles Joe will travel in 45 minutes is 12.75.
How many miles did joe travel in 45 minutes?Given that;
Joe travels 68 miles in 4 hoursjoe travel x miles in 45 minutesFirst, we convert 4 hours to minutes: 4 × 60 = 240 minutes
Now,
Joe travels 68 miles in 240 minutes
Joe will travel x miles in 45 minutes
We have;
x × 240 = 68 × 45
x × 240 = 3060
x = 3060 / 240
x = 12.75 miles.
Given that, Joe travels 68 mi in 4 hours, the number of miles Joe will travel in 45 minutes is 12.75.
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Chandra invests $75 every month at 4.8%/a compounded monthly for 8 years. What is the total amount of Chandra's investments after 8 years? Show your work.
The total amount of Chandra's investments after 8 years is $110.03
Compound interestThe formula for calculating the compound interest is expressed as;
A = P(1+r/n)^nt
where
P is the amount invested = $75
r is the rate. = 0.048
t is the time =8years
n = 12 (monthly)
Substitute
A = 75(1+0.048/12)^96
A = 75(1.467)
A = 110.03
Hence the total amount of Chandra's investments after 8 years is $110.03
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It cost jose $8.70 to send 87 text messages how much will it cost to send 10 text messages
Answer:
$1.00 = 10 cent each
Step-by-step explanation:
When solving the following system of equations, which variable would be the easiest to solve for? 2x + y = 9 3x - 2y = 17
Answer:
In my opinion, it would be 'y', since it is already on its own (in the first equation) without any coefficients.
Answer:
x.
Step-by-step explanation:
x because if you multiply the first equation by 2 and add the result to equation 2 , the y's will cancel out.
2x + y = 9 Times 2:-
4x + 2y = 18
3x - 2y = 17 Adding:-
7x = 35
x = 5.
A doctor estimates that a particular patient is losing bone density at a rate of 3% annually. the patient currently has a bone density of 1, 500 kg / m * g ^ 3 the doctor writes an exponential function to represent the situation. which should the doctor use for a and b in a function written in the form f(x) = a * b ^ x where f(x) represents the bone density after x years ?
Answer:
a = 1500 b = .97
Step-by-step explanation:
1500 ( .97)^x = bone density after n years
3% loss leave 97% each year (.97 in decimal)
The triangles are similar. Find the value of the variable.
You’ve gone to visit your friend in Germany. As you’re getting dressed for a day out, your friend tells you it’s 16 degrees (Celsius) outside. The formula for degrees Celsius in relation to degrees Fahrenheit is
C=(5f-160)/(9)
a. Invert this equation to solve for Fahrenheit.
b. Tell what the temperature is in degrees Fahrenheit.
c. What kind of clothing should you wear for the day to be comfortable at that temperature?
d. Is there a temperature at which Celsius and Fahrenheit are described by the same number? Explain how you would find that number.
If 15 actuators have failed today, what is the probability that a) at least 10 are repairable? b) from 3 to 8 are repairable? c) exactly 5 are repairable?
The probabilities of at least 10 are repairable is 1/3. and probabilities of from 3 to 8 are repairable is 1/5*8/15 and probabilities of exactly 5 are repairable is 1/3.
According to the statement
we have given that If 15 actuators have failed and we have to find the probabilities on some conditions.
we know that the formula of probabilities is
probability = possible outcomes / total outcomes
So,
at least 10 are repairable = 1 - (10 are not repairable)at least 10 are repairable = 1 - 10/15
at least 10 are repairable = (15 - 10)/15
at least 10 are repairable = (5)/15
at least 10 are repairable = 1/3
from 3 to 8 are repairable = 3/15 *8/15from 3 to 8 are repairable = 1/5 *8/15
exactly 5 are repairable = 5/15exactly 5 are repairable = 1/3
These are the probabilities of the given conditions.
So, The probabilities of at least 10 are repairable is 1/3. and probabilities of from 3 to 8 are repairable is 1/5*8/15 and probabilities of exactly 5 are repairable is 1/3.
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What is the domain of the exponential function shown below?
F(x) = 5.3*
O A. All real numbers except 5
OB. All real numbers
C. x<0
OD. x>0
The function will exist on all real numbers. Hence the domain of the exponential function given is all real numbers
Domain of a functionThe domain are independent values of an expression for which it exist. The standard exponential equation is expressed as y = ab^x
Given the exponential function as shown:
y = 5(3)^x
The function will exist on all real numbers. Hence the domain of the exponential function given is all real numbers
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Which of the following formulas, when evaluated using rational values for the variables, will result in an irrational number?
please help me with this!!!!!!!!!
Answer: 18
Step-by-step explanation:
By the exterior angle theorem,
[tex]x+18+x+12=x+48\\\\2x+30=x+48\\\\x+30=48\\\\x=18[/tex]
Answer:
x = 18
Step-by-step explanation:
The sum of two interior angles im a triangle is equal to one exterior angle that is supplementary to the third interior angle:
x + 18 + x + 12 = x + 48 add like terms
2x + 30 = x + 48 transfer like terms to the same side of the equation
2x - x = 48 - 30
x = 18
Which could be the missing data item for the given set of data if the median of the complete data set is 15?
11, 23, 12, 18, 11, 10, 19, 15, 19, 21, 13, 17, 24, 14
A. 16
B. 18
C. 20
D. 11
The missing data item for the given set of data if the median of the complete data set is 15 is 11; option F
MedianMedian = 15Mission data = nData set: 11, 23, 12, 18, 11, 10, 19, 15, 19, 21, 13, 17, 24, 14
Median = Sum of data + n / number of data
15 = (11+23+12+18+11+10+19+15+19+21+13+17+24+14) + n / 15
15 = 214 + n / 15
15 × 15 = 214 + n
225 = 214 + n
n = 225 - 214
n = 11
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Describe fully the single transformation which takes shape A to shape B.
The single transformation which takes shape A to shape B as in the task content is a 90° clockwise rotation and a 6 units shift rightward.
What transformation is responsible for taking A to B?By observation, it follows that the orientation of the shape A differs from that of B as it lags by 90° in the clockwise direction.
Additionally, the resulting image from a 90° clockwise rotation about the left vertice of A still reguires that A be shifted 6 units rightwards to yield shape B.
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How can a right triangular cross-section be created from a right triangle ?
Answer:
in a triangle prism each cross section parallel to the triangular base is a triangle congruent to the base
The table gives the average age of airplanes per airline at Camila’s local airport. By what percent is the number of airlines with an average airplane age of 14 less than the number of airlines with an average airplane age of 11 ?
The percentage that the number of airlines with an average airplane age of 14 is less than the number of airlines with an average airplane age of 11 is:
B. 20%.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
The percentage of airlines with an average age of 14 years is:
[tex]P = \frac{2}{15} \times 100\% = 13.33\%[/tex]
The percentage of airlines with an average age of 11 years is:
[tex]P = \frac{5}{15} \times 100\% = 33.33\%[/tex]
The difference is:
33.33% - 13.33% = 20%.
Hence option B is correct.
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Mrs. Laura is between 50 and 80. If you divide her age by 9, the remainder is 1. If you divide by 4, the remainder is 1. How old is Mrs. Laura?
Answer: 73
Step-by-step explanation:
I think she's 73? You have to take multiples of nine and see if they work! I did 72 since I knew that 72 goes into 9 equally and if she is 73 there would be a remainder of 1. After that, I stuck with 73 and since I knew that 18 times 4 is also 72, I knew that 73 divided by 4 would give me 18 with a remainder of 1.
The solution is 37 years, that is, Mrs. Laura's age is 37 years old.
Given information in the problem:
1. Mrs. Laura's, L age is between 50 and 80.
2. When you divide age by 9, the remainder is 1.
3. When you divide age by 4, the remainder is also 1.
To find L exact age, start by checking multiples of 9 that leave a remainder of 1 when divided by 4:
9 × 1 + 1 = 10 (remainder of 1 when divided by 4)
9 × 2 + 1 = 19 (remainder of 1 when divided by 4)
9 × 3 + 1 = 28 (remainder of 1 when divided by 4)
9 × 4 + 1 = 37 (remainder of 1 when divided by 4)
9 × 5 + 1 = 46 (remainder of 2 when divided by 4)
9 × 6 + 1 = 55 (remainder of 3 when divided by 4)
9 × 7 + 1 = 64 (remainder of 0 when divided by 4)
Check multiples of 4 that leave a remainder of 1 when divided by 9:
4 × 1 + 1 = 5 (remainder of 1 when divided by 9)
4 × 2 + 1 = 9 (remainder of 1 when divided by 9)
4 × 3 + 1 = 13 (remainder of 4 when divided by 9)
4 × 4 + 1 = 17 (remainder of 8 when divided by 9)
From the above calculations, see that the only common number between the two sets of multiples is 37.
So, L's age is 37 years old.
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Find the volume of the regular pyramid.
Geometry question don’t understand 1 and 3
A person has a 0.125 probability of getting the number 3 on a roll of an eight-sided die. if a person rolls the die 24 times, and gets a 3 on one-half of the rolls, what is the difference between the theoretical probability and the experimental probability of the person getting the number 3 on a roll?
The difference between the theoretical probability and the experimental probability of the person getting the number 3 on a roll is 0.375.
In the question, we are given that a person has a 0.125 probability of getting the number 3 on a roll of an eight-sided die.
This means that the theoretical probability of rolling a 3 on an eight-sided die is 0.125.
Also, we are informed that a person rolls the die 24 times, and gets a 3 on one-half of the rolls, that is, 1/2 * 24 = 12 rolls.
Thus, the experimental probability of rolling a 3 on an eight-sided die = 12/24 = 1/2 = 0.5.
In the question, we are asked to find the difference between the theoretical probability and the experimental probability of the person getting the number 3 on a roll.
The difference = The experimental probability - The theoretical probability,
or, the difference = 0.5 - 0.125 = 0.375.
Thus, the difference between the theoretical probability and the experimental probability of the person getting the number 3 on a roll is 0.375.
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4. Given: 21 22
Prove: all b
What is the missing reason in the proof?
1.41 42
2.21 24
3. 2224
1
4. all b
4
2
Statements | Reasons
1. Given
2. Vertical angles are congruent.
3.?
4. If two lines and a transversal form
congruent corresponding angles,
then the lines are parallel.
b
Vertical angles are always equal and congruent.
What we vertical angles?The information is incomplete. An overview will be given. It should be noted that vertical angles simply means the angles that are opposite each other when two lines cross.
Vertical angles are always equal and congruent. When two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel.
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