Answer:
The second degree polynomial is f(x) = 4x² - 28x + 40
Step-by-step explanation:
* Lets revise the general form of the second-degree polynomial
- The general form of the second degree polynomial is
f(x) = ax² + bx + c, where a , b , c are constant
- The highest power of the variable that occurs in the polynomial
is called the degree of a polynomial.
- The leading term is the term with the highest power, and its
coefficient is called the leading coefficient.
- The leading coefficient is the coefficient of x²
∴ a = 4
∴ f(x) = 4x² + bx + c
- The roots of a polynomial are also called its zeroes, because
the roots are the x values at which the function equals zero
∴ When f(x) = 0, the values of x are 5 and 2
* To find the value of b and c substitute the values of x in f(x) = 0
- At x = 5
∵ 4(5)² + b(5) + c = 0 ⇒ simplify it
∴ 100 + 5b + c = 0 ⇒ subtract 100 from both sides
∴ 5b + c = -100 ⇒ (1)
- At x = 2
∵ 4(2)² + b(2) + c = 0 ⇒ simplify it
∴ 16 + 2b + c = 0 ⇒ subtract 16 from both sides
∴ 2b + c = -16 ⇒ (2)
- Subtract (2) from (1)
∴ 3b = -84 ⇒ divide both sides by 3
∴ b = -28
- Substitute the value of b in (1) or (2) to find c
∵ 2(-28) + c = -16
∴ -56 + c = -16 ⇒ add 56 to both sides
∴ c = 40
∴ f(x) = 4x² - 28x + 40
* The second degree polynomial is f(x) = 4x² - 28x + 40
Answer:
d
Step-by-step explanation:
A sphere has radius of 42 m. If the radius is divided by 6, what is the effect on the surface area? HELP ASAP!
The surface area is multiplied by 6.
The surface area is multiplied by 36.
The surface area is divided by 36.
The surface area is divided by 6.
A sphere with radius [tex]r[/tex] has surface area [tex]4\pi r^2[/tex]. Divide the radius by 6 and you get a surface area of [tex]4\pi\left(\dfrac r6\right)^2=\dfrac4{36}\pi r^2[/tex], so that the final surface area is divided by 36.
Identify m∠KOL. HELP PLEASE!!
Answer:
30°
Step-by-step explanation:
In m KÔL, the angle is Ô and angle Ô is actually 30 degrees ;)
Answer:
m∠KOL = 30°
Step-by-step explanation:
It is given that mKL = 90and mMN = 30∘.
If two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs. So,
m∠KOL= 1/2(mKL− mMN)
Substitute the given values and simplify.
m∠KOL= 1/2 (90∘−30∘)
= 1/2(60∘)
= 30∘
Therefor, m∠KOL=30∘.
Vector u has a magnitude of 5 units and a direction angle of 30°. Vector v has a magnitude of 7 units and a direction angle of 120°. What is the direction angle of their vector sum?
A. 82.21°
B. 84.46°
C. 85.11°
D. 86.13°
Answer:
B. 84.46°
Step-by-step explanation:
Since the vectors are at right angles to one another, even a crude diagram will quickly show you that the direction of the sum is ...
30° + arctan(7/5) ≈ 84.4623° ≈ 84.46°
Which equation describes this statement? The sum of p and q is equal to 24. Let q = 3. p + 3 = 24 p – 3 = 24 p ÷ 3 = 24 p × 3 = 24
For this case we must write algebraically the following statement:
"The sum of p and q is equal to 24"
The sum of p and q is represented as:
[tex]p + q[/tex]
If the sum is equal to 24 we have:
[tex]p + q = 24[/tex]
If they tell us that [tex]q = 3[/tex], then the expression is:
[tex]p + 3 = 24[/tex]
Answer:
[tex]p + 3 = 24[/tex]
In the triangle below, 8/15 represents which ratio?
tanB
tanC
sinB
cosC
Answer:
tan(B)
Step-by-step explanation:
we know that
The tangent of an angle is equal to divide the opposite side to the angle by the adjacent side to the angle
In this problem
tan(B)=AC/AB
substitute
tan(B)=8/15
Answer:
tan(B)
Step-by-step explanation:
Correct
So far, Greg has driven 5.1 miles. He needs to drive a total of 25 miles. How many more miles must Greg drive?
Answer: 19.9
Step-by-step explanation:
25 - 5.1 = 19.9
Answer:
19.9
Step-by-step explanation:
25-5.1
= 19.9
To make sure:
19.9+5.1
=25
I hope this help you.
What is the constant of proportionality in a question like "The cost of 3 pounds is 6.75. What is the Constant of proportionality that relates the cost of dollars,y, to the number of pounds of grapes,x? (Grade 7)
Answer:
Step-by-step explanation:
The constant of proportionality is simply the ratio expressed as a decimal.
So in the example, the constant of proportionality is 6.75 $ / 3 lb = 2.25 $/lb.
What is the volume of a sphere whose radius is 6 ft
Answer:
Option C. [tex]288\pi\ ft^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a sphere is equal to
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
we have
[tex]r=6\ ft[/tex]
substitute
[tex]V=\frac{4}{3} \pi (6)^{3}[/tex]
[tex]V=288\pi\ ft^{3}[/tex]
The volume of the sphere with a radius of 6 ft is 904.78 ft³.
Explanation:The volume of a sphere can be calculated using the formula: V = (4/3)πR³. Given a radius of 6 ft, we can substitute this value into the formula to find the volume:
V = (4/3)π(6 ft)³
V = (4/3)π(216 ft³)
V = 904.78 ft³
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Trigonometric Functions help. What is the length of side AB? Type the correct answer rounded to one decimal place.
Check the picture below.
make sure your calculator is in Degree mode.
Answer:
37.0
Step-by-step explanation:
You have a total of 3 triangles in one here. Triangle ABC, triangle ABD, and triangle DBC. If we can find out the length of side BD in triangle DBC that will help us later. We have angle D and side DC and we are looking for the hypotenuse of that right triangle DBC. The trig ratio that relates the side adjacent to the reference angle to the hypotenuse is the cosine:
[tex]cos(40)=\frac{20}{BD}[/tex]
Solving for BD:
[tex]BD=\frac{20}{cos(40)}[/tex]
That gives us that BD = 26.1
Now that we know that, we can move into the obtuse triangle that shares the side BD with the right triangle. We have that angle BDC is 40 degrees, and since angle ADB is supplementary to angle BDC, then angle ADB measures 180 - 40 = 140. So angle A is 30, angle ADB is 140, so that means that angle ABD is 10. Because triangle ABD is obtuse and not right you cannot use Pythagorean's Theorem. But you can use the Law of Sines. Set it up like this:
[tex]\frac{sin(140)}{AB}=\frac{sin(10)}{10}[/tex]
Solve for side AB:
[tex]AB=\frac{10sin(140)}{sin(10)}[/tex]
In degree mode on your calculator you'll find that side AB is 37.0
A bag contains 2 red balls and 18 green balls. A ball is chosen at random from the bag. What is the BEST answer for the probability of drawing a green ball? A) impossible B) unlikely C) very likely D) certain
Answer:
C) very likely
Step-by-step explanation:
Out of the 20 balls inside of the bag, 18 of them are green.
That means you have a 18/20 or 90% chance of getting a green ball.
Therefore, the probability of drawing a green ball is [tex]90[/tex] % then the option (C) is correct i.e., very likely.
What is the probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.
Here given that,
A bag contains [tex]2[/tex] red balls and [tex]18[/tex] green balls. A ball is chosen at random from the bag.
So,the total balls are [tex]18+2=20[/tex]
Green balls are [tex]18[/tex].
So the probability is
[tex]\frac{18}{20}[/tex] ×[tex]100=90[/tex] %
Hence, the probability of drawing a green ball is [tex]90[/tex] % then the option (C) is correct i.e., very likely.
To know more about the simplification
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Match the type of graph with its description.
1. bar graph
2. line graph
3. scatter plot
4. histogram
5. box-and-whisker plot
a. Compares data that is in categories.
b. Used to see trends in data.
c. Organizes data into 4 groups of equal size, and is often used to compare two sets of data.
d. Shows change over time.
e. Shows frequency of data, using equal intervals with no space between the bars.
1. bar graph - Compares data that is in categories.
2. line graph - Shows change over time.
3. scatter plot - Used to see trends in data.
4. histogram - Shows frequency of data, using equal intervals with no space between the bars.
5. box-and-whisker plot - Organizes data into 4 groups of equal size, and is often used to compare two sets of data.
School is almost over, good luck!!
Suppose f(x)=x-4.
Find the graph for f(1/4x)
Answer:
#4
Step-by-step explanation:
Graph #4 is the correct one. Multiplying x by 1/4 widens the original graph by a factor of 4. That "-4" shifts the graph 4 units to the right.
Expand logb square root of 41/97
Answer:
A
Step-by-step explanation:
logb √(41/97)
Square root can be written in exponent form:
logb (41/97)^½
Using log exponent rule:
½ logb (41/97)
Using log quotient rule:
½ (logb 41 - logb 97)
E is 3 more than D
F is 5 less than D
A). Write an expression for “e” in terms of “d.
B). Write an expression for “f” in terms of “d.
C). Work out E-F and symplify your answer.
Part A:
We are given that E is 3 more than D. This means that to get the value of E, we will simply add 3 to the value of D
Therefore:
E = D + 3
Part B:
We are given that F is 5 less than D. This means that to get the value of F, we will simply subtract 5 from the value of D
Therefore:
F = D - 5
Part C:
To get the value of E-F, we will simply subtract the equation we obtained from part B from the equation we obtained from part A
Therefore:
E - F = (D+3) - (D-5)
E - F = D + 3 - D + 5
E - F = 8
Hope this helps :)
The expression for 'e' in terms of 'd' is e = d + 3. The expression for 'f' in terms of 'd' is f = d - 5. The difference between 'E' and 'F' is 8.
Explanation:A) e = d + 3
To express 'e' in terms of 'd,' we can simply say that 'e' is equal to 'd' plus 3. This is because the question states that 'E is 3 more than D.'
B) f = d - 5
To express 'f' in terms of 'd,' we can say that 'f' is equal to 'd' minus 5. The question states that 'F is 5 less than D.'
C) E - F = (d + 3) - (d - 5) = d + 3 - d + 5 = 8
To find the difference between 'E' and 'F,' we can substitute the expressions we found for 'e' and 'f' into the equation. Simplifying the expression further, we have 'E - F = (d + 3) - (d - 5) = d + 3 - d + 5 = 8.'
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If (x2 – 4) ÷ (x + 2) = x – 2, which polynomial should fill in the blank below?
(x + 2) ´ ______ = x2 – 4
x2 – 4
x – 2
x + 2
x2 – 2
Answer:
x - 2
Step-by-step explanation:
Given expression,
[tex](x^2-4)\div (x+2)=x-2[/tex]
[tex]\frac{x^2-4}{x+2}=x-2[/tex]
Multplying both sides by x + 2 ( Division property of equality )
[tex]\frac{x^2-4}{x+2}\times (x+2)=(x-2)\times (x+2)[/tex]
[tex]x^2-4=(x-2)(x+2)[/tex]
[tex]\implies x^2-4=(x+2)(x-2)[/tex] ( By commutative property )
Thus, SECOND OPTION is correct.
Answer:
X-2 is the correct answer! Edge 2020
Step-by-step explanation:
sketch the graph of y = sin(x) over the interval [-π /2 , π /2 ]
Is it just the regular graph within those numbers?
Correct. It is only interested in the portion of the graph confined to this interval
Alexandria, a car dealer, earns 40% commission of her luxury vehicles sales. Last year, her sales were $480,000. What was the total dollar amount of her commission last year?
Answer:
192,000
Step-by-step explanation:
480,000x.40 = 192,000 commission.
Answer:
480000 * 0.40 = $192,000
The total dollar amount of her commission last year is $192,000
Step-by-step explanation:
On Friday 17.5 total gallons of water were used. on Saturday, 31.5 total gallons were used. On Saturday 24.75 total gallons were used. What is the difference between the water use per load of the dishwasher that uses the most water and the dishwasher that uses the least water
Answer:
6.25 gal
Step-by-step explanation:
Least amount of water used: 17.5 gal
Greatest amount used: 24.75 gal
Difference: 24.75 gal - 17.5 gal = 6.25 gal
The thirstiest dishwasher used 6.25 gal more than the thriftiest dishwasher.
Answer:
0.75
Step-by-step explanation:
friday, it is 4, saturday is 3.5, sunday is 3.25. 4-3.25 is 0.75.
Water is flowing in a circular pipe varying cross-sectional area, and at all points the water completely fills the pipe.a) At one point in the pipe the radius is 0.210 m. What is the speed of the water at this point if water is flowing into this pipe at a steady rate of 1.10 m3/s?b) At a second point in the pipe the water speed is 2.80 m/s. What is the radius of the pipe at this point?
Final answer:
a) The speed of the water at a point in the pipe with a radius of 0.210 m is 7.97 m/s. b) The radius of the pipe at a second point where the water speed is 2.80 m/s is approximately 0.209 m.
Explanation:
a) To find the speed of the water at a point in the pipe, we can use the equation Q = Av, where Q is the flow rate, A is the cross-sectional area of the pipe, and v is the velocity of the water. Given that the flow rate is 1.10 m³/s and the radius is 0.210 m, we can find the area using the formula A = πr². Substituting the values, we have A = 3.14(0.210)² = 0.138 m². Solving for v, we get v = Q / A = 1.10 / 0.138 = 7.97 m/s.
b) To find the radius of the pipe at a second point where the water speed is 2.80 m/s, we can use the equation v = Q / A. Rearranging the equation to solve for the radius, we have r = √(Q / (πv)). Substituting the values, we have r = √(1.10 / (π(2.80))) ≈ 0.209 m.
Select the equation that contains the point (4, -8), and in which the graph of the line has a positive slope.
y – 8 = –4(x + 4)
y – 8 = 4(x + 4)
y + 8 = +4(x – 4)
y + 8 = –4(x – 4)
Answer:
The third equation down is the one you want
Step-by-step explanation:
What you need for this is the point-slope form of a line:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
where y1 is the y coordinate from our point and x1 is the x coordinate from our point. m is the slope. That m has to be positive, according to the instructions. So the first equation and the last one are out, since those are both negative.
If we fit our point into the point-slope form, it looks like this:
[tex]y-(-8)=4(x-(4))[/tex]
which simplifies to
[tex]y+8=4(x-4)[/tex]
and that matches the third equation down.
Based on a poll of 200 citizens, a community action group claims that 40% of the population is in favor of a curfew for children under 18 on weekday nights. A local parent group claims that the poll is not valid and that only 22% of the citizens favor a curfew. To determine whether this sample supports the population proportion of 0.40, a simulation of 100 trials is run, each with a sample size of 50 and a point estimate of 0.22. The minimum sample proportion from the simulation is 0.15, and the maximum sample proportion from the simulation is 0.27. The margin of error of the population proportion is found using an estimate of the standard deviation. What is the interval estimate of the true population proportion?
Answer: (0.18,0.26)
Step-by-step explanation: I just finished the test
Find the product. 3 y2z (2 y2z + 4 yz - y + z )
A. 4 y6z2 + 13 y3z12 - 3 y2z2 - 3 yz
B. 6 y4z2 + 12 y3z2 - 3 y3z + 3 y2z2
C. 6 y2z4 - 12 y2z3 + 3 yz3 - 3 y2z2
D. 3 y4z2 + 3 y3z2 - 6 y3z - 4
Answer:
I believe B. is the correct answer.
6y4z2 + 12y3z2 - 3y3z + 3y2z2
Step-by-step explanation:
Answer:
the answer is 6y4z2 + 12y3z2 - 3y3z + 3y2z2
Step-by-step explanation:
Two trains leave stations 494 miles apart at the same time and travel toward each other. One train travels at 100 miles per hour while the other travels at 90
miles per hour. How long will it take for the two trains to meet? do not do any rounding.
Answer:
The trains will meet after 2.6 hours.
Step-by-step explanation:
Add up the distances traveled by the two trains:
distance1 = (100 mph)(t hours)
distance2 = (90 mph)(t hours)
Sum of distance1 and distance2 = 494 miles = (190 mph)(t hours)
Solving for t, we get t = 494 miles / 190 mph = 2.6 hours
The trains will meet after 2.6 hours.
It will take 2.60 hours for the two trains to meet.
Explanation:To find out how long it will take for the two trains to meet, we can use the formula: time = distance / speed.
Since the trains are traveling towards each other, we can add their speeds together to get the effective speed: 100 mph + 90 mph = 190 mph.
Now we can plug in the values: time = 494 miles / 190 mph = 2.60 hours.
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PLEASE HELP ASAP 50 Pts + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
[tex]f(x)=(x+2)(x-5)(x-6)[/tex]
Step-by-step explanation:
we know that
If the zeros of the function are
x=-2, x=5 and x=6
then
The factors are
(x+2), (x-5) and (x-6)
therefore
The polynomial function in factored form is equal to
[tex]f(x)=(x+2)(x-5)(x-6)[/tex]
is it virtually impossible to completely avoid criticism
Well yes but this doesn't belong in math by the way.
Find the coordinates of the midpoint of a segment with the endpoints
(-4, -14) & (-22, 9).
a. (-13, -2.5)
b. (-15, -2.5)
c. (-18, -4)
d. (-8, -1
Answer:
A es la respuesta a tu pregunta ue acabas de preguntar para que alguien la respondiera.
prove that 5^31–5^29 is divisible by 100.
5^31-5^29
=5^29(5^2-1)
=5^29(25-1)
=5^29(24) ...a
100=5^2x4 ...b
Divide a by b
5^29(24) / 5^2 x 4
=5^27 x 6
This, 5^31-5^29 is divisible by 100.
Hi, help is very much appreciated!
" Make a box-and-whisker plot of the data 5, 7, 2, 6, 7, 10, 12, 7, 9, 13, 5 "
Maybe a visual explanation please :) ( I already have the numbers in order from Least to Greatest. ) ( 2, 5, 5, 6, 7, 7, 9, 10, 12 )
Here's a visual representation. The numbers are a little blurry though.
Power set: let B=(0), then p(b)=?
If [tex]B=\{0\}[/tex] then [tex]p(B)=\{0\}^{B[0]}=\boxed{1}[/tex].
Hope this helps.
At a snack bar, there is a negative correlation between the number of sports drinks sold and the number of hot chocolates sold.
Which variable is most likely the lurking variable that explains the correlation?
ages of customers
number of customers
outside temperature
price of sports drinks
Hi good morning
So answer A. Ages of customers can be the answer
Answer B.Number of customers can be eliminated.
Answer C. Outside temperature can effect the what people want to drink, if its hot sports drink, If its cold Hot chocolate for everyone ! I depends on the temperature.
Answer D. Price of sports drink can be eliminated.
so, MY conclusion is that it could very well be the age group. ( Answer A)
I hope this helps. I am very sorry if it is wrong. At least I tried
Have a good day ^^