Answer:
A
Step-by-step explanation:
Given
x² - 14x = 0
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 7)x + 49 = 0 + 49
(x - 7)² = 49 ( take the square root of both sides )
x - 7 = ± [tex]\sqrt{49}[/tex] = ± 7 ( add 7 to both sides )
x = 7 ± 7 , thus
x = 7 + 7 = 14 or x = 7 - 7 = 0
If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5), (4, 220), and (-2, -20) what would the coefficients a, b, c, and d equal? So confused, I'd greatly appreciate help! Thank you!
Step-by-step explanation:
Step 1: Solve using the first point
(2, 28)
[tex]28 = a(2)^3 + b(2)^2 + c(2) + d[/tex]
[tex]28 = 8a + 4b + 2c + d[/tex]
Step 2: Solve using the second point
(-1, -5)
[tex]-5 = a(-1)^3 + b(-1)^2 + c(-1) + d[/tex]
[tex]-5 = -a + b - c + d[/tex]
Step 3: Solve using the third point
(4, 220)
[tex]220 = a(4)^3 + b(4)^2 + c(4) + d[/tex]
[tex]220 = 64a + 16b + 4c + d[/tex]
Step 4: Solve using the fourth point
(-2, -20)
[tex]-20 = a(-2)^3 + b(-2)^2 + c(-2) + d[/tex]
[tex]-20 = -8a + 4b - 2c + d[/tex]
Step 5: Combine the first and fourth equations
[tex]28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d[/tex]
[tex]8 = 8b + 2d[/tex]
[tex]8 - 8b = 8b - 8b + 2d[/tex]
[tex](8 -8b)/2 = 2d/2[/tex]
[tex]4 - 4b = d[/tex]
Step 6: Solve for c in the second equation
[tex]-5 + 5 = -a + b - c + d + 5[/tex]
[tex]0 + c = -a + b - c + c + d + 5[/tex]
[tex]c = -a + b + d + 5[/tex]
Step 7: Substitute d with the stuff we got in step 5
[tex]c = -a + b + (4 - 4b) + 5[/tex]
[tex]c = -a + b + 4 - 4b + 5[/tex]
[tex]c = -a - 3b + 9[/tex]
Step 8: Substitute d and c into the first equation
[tex]28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)[/tex]
[tex]28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b[/tex]
[tex]28 - 22 = 6a - 6b + 22 - 22[/tex]
[tex]6 / 6 = (6a - 6b) / 6[/tex]
[tex]1 + b = a - b + b[/tex]
[tex]1 + b = a[/tex]
Step 9: Substitute a, b, and c into the third equation
[tex]220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)[/tex]
[tex]220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b[/tex]
[tex]220 - 100 = 60b + 100 - 100[/tex]
[tex]120 / 60 = 60b / 60[/tex]
[tex]2 = b[/tex]
Step 10: Find a using b = 2
[tex]a = b + 1[/tex]
[tex]a = (2) + 1[/tex]
[tex]a = 3[/tex]
Step 11: Find c using a = 3 and b = 2
[tex]c = -a - 3b + 9[/tex]
[tex]c = -(3) - 3(2) + 9[/tex]
[tex]c = -3 - 6 + 9[/tex]
[tex]c = 0[/tex]
Step 12: Find d using b = 2
[tex]d = 4 - 4b[/tex]
[tex]d = 4 - 4(2)[/tex]
[tex]d = 4 - 8[/tex]
[tex]d = -4[/tex]
Answer: [tex]a = 3, b = 2, c = 0,d = -4[/tex]
Answer:
a = 3
b = 2
c = 0
d = -4
Step-by-step explanation:
Form 4 equations and solve simultaneously
28 = a(2)³ + b(2)² + c(2) + d
28 = 8a + 4b + 2c + d (1)
-5 = -a + b - c + d (2)
220 = 64a + 16b + 4c + d (3)
-20 = -8a + 4b - 2c + d (4)
(1) + (4)
28 = 8a + 4b + 2c + d
-20 = -8a + 4b - 2c + d
8 = 8b + 2d
d = 4 - 4b
Equation (2)
c = -a + b + d + 5
c = -a + b + 4 - 4b+ 5
c = -a - 3b + 9
28 = 8a + 4b + 2c + d (1)
28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b
28 = 6a - 6b + 22
6a - 6b = 6
a - b = 1
a = b + 1
220 = 64a + 16b + 4c + d (3)
220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b
220 = 60b + 100
60b = 120
b = 2
a = 2 + 1
a = 3
c = -3 - 3(2) + 9
c = 0
d = 4 - 4(2)
d = -4
In a group of 30 people, 10 drink milk but not tea 5 drink tea
but not milk and 13 drink neither tea nor milk. find how many people drink both tea and milk.
Answer:
2
Step-by-step explanation:
10 + 13 + 5 = 28 who drink either, or, or neither
30 - 28 = 2
Answer:
2 drink both tea and milk
Step-by-step explanation:
30 people - 13 drink neither = 17 - 10 drink milk but not tea = 7 - 5 drink tea but not milk = 2 drink both tea and milk.
A clothing store donated a percent of every sale to hospitals. The total sales were $6,500 so the store
donated $260. What percent of $6,500 was donated to hospitals?
I’m literally confused
Find a numerical value of one trigonometric function of x for cscx = sinx tanx + cosx
Answer:
Step-by-step explanation:
we have
[tex]cscx = sinx tanx + cosx\\\\\frac{1}{sinx}=sinx.\frac{sinx}{cosx} +cosx\\\\\frac{1}{sinx}.sinx.cosx= sinx.\frac{sinx}{cosx}.sinx.cosx+cosx.sinx.cosx\\ cosx= (sinx)^{3} +sinx.(cosx)^{2} \\cosx= sinx[(sinx)^{2}+(cosx)^{2})\\ cosx=sinx.1\\cosx=sinx\\tanx=1\\x=\frac{\pi}{4} +k\pi,k-integer.[/tex]
Answer:
cot x=1
Step-by-step explanation:
got it right
What did the use of atomic bombs during World War II lead to?
A ban on all nuclear weapons for all developed countries for years in the future
The need for a global regulatory body to monitor the use of nuclear weapons
A sharing of all nuclear weapons technology to make all countries equal
An arms race between the United States and Soviet Union
Question 2(Multiple Choice Worth 5 points)
Which of the following is a common argument against the U.S. decision to drop the atomic bomb?
The study of the effect of atomic weapons allowed nuclear power to be used as energy.
The use of the atomic bomb avoided additional loss of life for the Allies.
The Japanese were more willing to surrender than the U.S. military thought.
The dropping of the atomic bomb would act as a deterrent to future wars.
Question 3(Multiple Choice Worth 5 points)
What is the best explanation for why the United States decided to target Hiroshima?
It was a center of communications, military command, and supply point for the Japanese army.
It would have few casualties because it was nearly destroyed by previous bombings.
It was a religiously and culturally significant city for the Japanese monarchy.
It was a city with many family connections to Emperor Hirohito and military leaders.
Question 4(Multiple Choice Worth 5 points)
Many Americans approved of the use of atomic weapons on Japan despite their destructive power because
they believed it would shorten the war and ultimately save American lives
they were eager to see if this new technology was effective in preventing wars
they believed that the atom bomb would cause no more damage than regular bombs
they were told that it was the only certain way to defeat the militant Japanese empire
1. An arms race between the United States and Soviet Union
2. The use of the atomic bomb avoided additional loss of life for the Allies.
3. It was a center of communications, military command, and supply point for the Japanese army.
4. they believed it would shorten the war and ultimately save American lives
5. if i could get brainliest that would be great
Which is equivalent to after it has been simplified completely? Assume m ≠ 0.
Answer:
It's letter A.
The required simplified solution of the given expression is 5m/14√3m. Option C is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
= √[75m⁹/196m⁴]
= √[25m⁴/196[3m]]
= 5m/14√3m [since 25 = 5² and 196 = 14²]
Thus, the required simplified solution of the given expression is 5m/14√3m. Option C is correct.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ6
Consider the cartesian equation of a circle, y=-2+- sqrt 36-(x-1)^2 , verses the parametric equations of the same circle: x=1+6 cos t y=-2+6sin t
What are the advantages of the parametric equations
Answer:
Step-by-step explanation:
Parametric equations shows the relation between a group of quantities by expressing the coordinates of points of a curve and function as one or more independent variables.
From the question given; the advantages of parametric equations given
x = 1 + 6 cos t
y= -2 + 6 sin t
are :
1) For a given value of the independent variable the parametric equation is used exactly one point on the graph
2) the parametric equations have a finite domain
3) the parametric equation is easier to enter into a calculator for graphic
Answer:
That dude was wrong on one of them!
A, C, E
Can Somebody Help Me On This Plzzzz ???????????
Answer:
its D
Step-by-step explanation:
What is the slope of the line?
________
Answer:
3 over 1
no problemnndjdjd
need asap! please help!
Answer:
x = 2
Step-by-step explanation:
7x + 5 = 19
Subtract 5 on both sides
7x = 14
Divide by 7 to isolate x
x = 2
Hope this helps!
Which are these two, please help
Answer:
4. this would be a positive correlation
5. this has no correlation
Step-by-step explanation:
I hope that was the answer you are looking for
Answer:
The first one has a positive association. You can see that if you were to make a like marking the average rate of change, it would be positive.
For the second one, it would actually be both positive and negative. But Since it does both, it has no correlation.
Step-by-step explanation:
Which graph represents the function f(x) =1/3 |x|?
Step-by-step explanation:
f(x) = 1/3|x|
then
f(x) = 1/3x , if x ≥ 0
and
f(x) = -1/3x , if x ≤ 0
the slope of f(x) = 1/3x is 1/3
the slope of f(x) = -1/3x is -1/3
this two above conditions apply on to the fourth graph to the right.
Look at the picture:)
If you need to show multiplication, do not use the letter w. Use the asterisk
(*) symbol instead, or simplify your answer.
Mr. Jones's algebra class has too many students in it. If the class were split
exactly in equal parts to form 3 new classes, each class would have no more
than 14 students in it
Answer:
42 students total, 14*3=42
Step-by-step explanation:
I'm not exactly sure what the question is, but I am assuming that it is , How many students were in the original class?
If you have 14 students in 3 classes, then you need to multiply each class by 14.
14 students × 3 classes = 42 students in the original class
What is the measure of ∠4?
Help plz!!!!! I need help
Answer: J and K
Step-by-step explanation:
[tex]\sqrt{20}[/tex] is about [tex]4.472135[/tex]
Answer:
J and K
Step-by-step explanation:
√20=4.47
4.47 is almost in between J and K in the number line.
Hence, it's J and K.
What is the volume of a sphere with a diameter of 3.2 m, rounded to the nearest tenth
of a cubic meter?
Answer:
Volume of a sphere = 17.164 m³ (Approx)
Step-by-step explanation:
Given:
Diameter of a sphere = 3.2 m
Radius of a sphere = Diameter / 2 = 3.2 / 2 = 1.6 m
Find:
Volume of a sphere = ?
Computation:
[tex]Volume\ of\ a\ sphere =\frac{4}{3}\pi \times r^3 \\\\Volume\ of\ a\ sphere =\frac{4}{3}\times \frac{22}{7} \times (1.6)^3 \\\\Volume\ of\ a\ sphere =\frac{4}{3}\times \frac{22}{7} \times 4.096\\\\Volume\ of\ a\ sphere =17.164[/tex]
Volume of a sphere = 17.164 m³ (Approx)
Answer:
17.2
Step-by-step explanation:
Does choosing a blue marble represent the complement event of choosing a red marble? Explain.
Answer:
No, the probability of choosing a red marble is not the complement of choosing a blue marble.
P(red) + P(blue) = 3/5, not 1.
The number of blue and red marbles does not add to the total number of outcomes.
There are other marbles besides red ones and blue ones.
Step-by-step explanation:
i got it right.
Answer:
The complementary event for choosing a red marble is choosing a blue or purple. The total number of marbles is 5. The probability of choosing a red marble is 1/5, and the complement would be 4/5. That is not the same as choosing a blue marble.
two consecutive integers whose product is 17
Answer:
8 and 9
Step-by-step explanation:
8 comes after 9 and 8 + 9 = 17
Fine the slope of a line parallel to y=-2/5x+4/5
5/2
2/5
-5/2
-2/5
Answer:
-2/5
Step-by-step explanation:
Parallel lines have the same slope to each other. So if one line has a slope of -2/5, the line parallel to it will also have a slope of -2/5.
Hope this helps!
Answer:
-2/5
Step-by-step explanation:
The slope of the parallel line is going to be the same as the original line.
35 POINTS HELP ASAP!!!
Answer: 3
Step-by-step explanation:
[tex]3:1[/tex]
[tex]\frac{3}{1}=3[/tex]
Will Mark Brainliest
Parabola: You must include the focus, vertex, lactus rectum, directrix, and the domain from the equation: y=-(x-0)^2 +15
Hyperbola: You must include the equations of the asymptotes and the domain from the equation: (2y^(2))/(b^(2))-(x^(2))/(a^(2))=7
Ellipse: You must include the foci, vertices, and eccentricity from the equation: 4x^(2)-1x+10y^(2)-50y-1=0
Answer:
Hi, i'm not trying to be rude but, you can search it up. there are many videos that explain it.
Step-by-step explanation:
Draw the shape described below and find its total surface area.
A cylinder 25 ft tall with a diameter of 12 f
Answer:
hope this helps :)
Step-by-step explanation:
8:07
Cylinder volume & surface area (video)
Compute the amount of interest earned in the following simple interest problem.
A deposit of $295 at 7% for 270 days
Answer:
$253.33
Step-by-step explanation:
i did the test
If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the Circle that is not covered by the hexagon? ( with explanation )
Answer:
[tex]\left(100\pi - 150\sqrt{3}\right)[/tex] square inches.
Step-by-step explanation:
Area of the Inscribed HexagonRefer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be [tex]10[/tex] inches (same as the length of each side of the regular hexagon.)
Refer to the second attachment for one of these equilateral triangles.
Let segment [tex]\sf CH[/tex] be a height on side [tex]\sf AB[/tex]. Since this triangle is equilateral, the size of each internal angle will be [tex]\sf 60^\circ[/tex]. The length of segment
[tex]\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}[/tex].
The area (in square inches) of this equilateral triangle will be:
[tex]\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}[/tex].
Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:
[tex]\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}[/tex].
Area of of the circle that is not coveredRefer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is [tex]10[/tex] inches, the radius of this circle will also be [tex]10[/tex] inches.
The area (in square inches) of a circle of radius [tex]10[/tex] inches is:
[tex]\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi[/tex].
The area (in square inches) of the circle that the hexagon did not cover would be:
[tex]\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}[/tex].
Which is an equation for the parabola that has a vertex (6,-3) and passes through the point (2,-2)
Answer:
c
Step-by-step explanation:
Answer:
The Correct Answer is in fact C : x= -4y^2 -24y -30
Step-by-step explanation:
If you look at the image I attached you can see that C is the only one touching those point
Don't forget to like :)
NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
C. l only
Step-by-step explanation:
i need help with thisss hurry!
Answer:
December
Step-by-step explanation:
87-38 = 49
Can someone help me please is this correct?
Answer:
Subtraction.
Step-by-step explanation:
You Subtract 6 on both sides first and then you multiply the denominator which is 11 to the other side of the equal sign.
The graph of quadratic function k is shown on the grid.
у
Which statements are best supported by the graph of k?
11
10
I. The x-intercept is located at(-3,0).
II. The coordinates of the y-intercept are(0,9).
III. The axis of symmetry 15 X=-3.
F I and II only
G I and III only
HII and III only
J
I, II, and III
Answer:
The answer is I, II, and III.
Step-by-step explanation:
Answer: I , II , III
Step-by-step explanation:
