Answer:
y = 2[tex](x - 3)^{2}[/tex] - 1
Step-by-step explanation:
y = 2[tex]x^{2}[/tex] - 12x + 16
y = 2([tex]x^{2}[/tex] - 6x + 8) ( Factor out 2 )
y + 9= 2([tex]x^{2}[/tex] - 6x + 9) + 8 ( Complete the square [tex](\frac{-b}{2} )^{2}[/tex] ) Add 9 both sides
y + 9 = 2 [tex](x - 3)^{2}[/tex] + 8 (Subtract 9 each side)
y = 2 [tex](x - 3) ^{2}[/tex] - 1 ( simplify )
A company borrows $100,000 for 5 years at a simple interest rate of 10.5%. Find the interest paid on the loan
The interest paid on the loan is ?
The total amount paid is ?
Answer:
$52,500
$152,500
Step-by-step explanation:
$100,000 * .105 = $10500
someone help me please with this algebra homework
Which table represents a linear function?
Answer:
C
Step-by-step explanation:
The slope of C is 3/2 and it stays consistent unlike the other ones.
does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of point from centre is less than the radius.
Hence the point lies within the circle.
1. Slope and the properties of perpendicular and parallel can be used to confirm that a polygon is a specific type of
quadrilateral.
What types of quadrilaterals can you determine by using these properties? List at least two types of quadrilaterals.
2. Choose one type of quadrilateral from your answer to Question 1. Explain in complete sentences how you can use
properties of perpendicular and parallel lines, together with slope, to confirm that a given polygon is the type of
quadrilateral you chose. Be sure to clearly state the properties that you need to use.
Please number your responses to the questions as they are shown (1 and 2).
NOTE from Ms. Kliban:
I found this answer on the Internet. *If it were an original answer, below is how I would grade it and why
1. The two would be rectangle and trapezium
2. You can determine with the properties that are given, that it's a polygon because with the slope already known that gives
a in to see which lines are perpendicular to which lines and which aren't. Also, with the properties you can tell if everything
Is parallel lines with the slope formula. Some slopes might be different but doesn't mean the polygon Isn't perpendicular
because two sides can have the same slope and the other two won't
GRADE: First off, in the United States, we don't use the word "trapezlum."
For part 2, it says, you can determine with the properties that are given." What properties? There are no properties given.
There are shapes. The next thing said in part 2 is that the slope is already known. No, it's not. You have to find the slope.
PLEASE HELP!!!!! 70 points !!!!
The grammar is bumpy. In other words, I stumbled over it when I tried to read it.
In order to do well on this assignment, part one only needs to have two quadrilaterals stated. You don't even have to have it
In a sentence.
For part 2. you do need to use complete sentences. You need to explain how to find slope and why you need to find the
slope. Then also explain how parallel and perpendicular lines help you to make sure you have the shape you stated in part
sat
Answer: Rectangle and Trapezium
Step-by-step explanation:
If you have the slopes, then you can tell when two lines are parallel.
A rectangle has two pairs of parallel sides
A trapezium has exactly one pair of parallel sides
We can determine whether a quadrilateral is a rectangle or a trapezium using the slope and the properties of parallel and perpendicular lines.
2. How are the slopes of perpendicular sides related?Product of the slopes of perpendicular lines = -1.
M₁ * M₂ = -1 .
How are the slopes of parallel sides related?Slopes of parallel lines are equal.
M₁ = M₂.
How do we determine a rectangle?Suppose we have a quadrilateral ABCD.
AB and CD are one pair of opposite sides.
BC and DA are another pair of opposite sides.
AB is adjacent to BC. BC is adjacent to CD. CD is adjacent to DA. DA is adjacent to AB.
Slope AB = M₁
Slope BC = M₂
Slope CD = M₃
Slope DA = M₄
For ABCD to be a rectangle, by properties opposite sides need to be parallel and adjacent sides need to be perpendicular.
∴ If M₁ = M₃, M₂ = M₄ (for opposite sides to be parallel)
and if M₁.M₂ = -1, M₂.M₃ = -1, M₃.M₄ = -1, and M₄.M₁ = -1 (for adjacent sides to be perpendicular) then the given quadrilateral ABCD is a rectangle.
Learn more about quadrilaterals, the slope of parallel lines, and the slope of perpendicular lines at
https://brainly.com/question/23935806
https://brainly.com/question/26172639
https://brainly.com/question/1362601
#SPJ2
I have a lot of algebra problems. Someone help me even with this one please!
X -Y =44 will represent the number of glasses of ice tea .
Determine the area of an obtuse triangle with a height
of 11 cm and a base of 22 cm
Step-by-step explanation:
A
=
h
b
b
2
=
11
·
22
2
=
121
cm²
The area of the obtuse triangle with a height of 11 cm and a base of 22 cm is 121 cm².
To determine the area of an obtuse triangle, we can use the formula for the area of a triangle, which is given by:
Area = (1/2) * base * height
In this case, the height of the triangle is given as 11 cm and the base is given as 22 cm.
Substituting these values into the formula, we have:
Area = (1/2) * 22 cm * 11 cm
Calculating this expression, we get:
Area = (1/2) * 242 cm²
Simplifying further, we have:
Area = 121 cm²
The area of a triangle is calculated by multiplying half of the base by the height. In this case, the given height is 11 cm and the base is 22 cm. Substituting these values into the formula, the area of the obtuse triangle is calculated to be 121 cm².
To learn more about area click on,
https://brainly.com/question/8397982
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[tex]\text{Solve for 'x'.}\\\\3x + 15 = 33\\\\\\text{Thank you.}[/tex]
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]x=6[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'...}}\\\\3x + 15 = 33\\--------------\\\rightarrow 3x + 15 - 15 = 33 - 15\\\\\rightarrow 3x = 18\\\\\rightarrow \frac{3x=18}{3}\\\\\rightarrow \boxed{x = 6}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
x=6
Step-by-step explanation:
3x+15=33
or as, 3x=33-15
or as, 3x=18
x=18/3=6
so we got 6 is the answer
PLEASE ANSWER CORRECTLY FOR BRAINLIEST:
25.
26.
27.
29.
Step-by-step explanation:
25.
[tex] \frac{t}{5} = b[/tex]
where b is the no. if 5 dollar bills.
26.
[tex]x +( x + 2) +( x + 4) = x + (x + 2)[/tex]
[tex]3x + 6 + 9 = 2x + 2[/tex]
[tex]3x + 15 = 2x + 2[/tex]
[tex]x + 15 = 2[/tex]
[tex]x = - 13[/tex]
Since x=-13 the intergers are
[tex] - 13[/tex]
[tex] - 11[/tex]
[tex] - 9[/tex]
27.
Represent the function as
[tex]x + x + 6 = 44[/tex]
[tex]2x + 6 = 44[/tex]
[tex]2x = 38[/tex]
[tex]x = 19[/tex]
The shorter piece should be 19 inches.
28.
Solve for h.
[tex]s = 2\pi \times rh + 2\pi {r}^{2} [/tex]
[tex]s - 2\pi {r}^{2} = 2\pi \times rh[/tex]
[tex] \frac{s - 2\pi {r}^{2} }{2\pi \times r} = h[/tex]
29.
[tex] \frac{16 + x}{2} \times 6 = 108[/tex]
[tex] \frac{16 + x}{2} = 18[/tex]
[tex]16 + x = 36[/tex]
[tex]x = 20[/tex]
Is the number of hits to a website in a day a discrete random variable, a continuous random variable, or not a random variable?
Answer:
The random variable is discrete. :)
Step-by-step explanation:
A circle has a circumference of 8, It has an arc of length start fraction, 32, divided by, 5, end fraction. What is the central angle of the arc, in degrees?
Answer:
The central angle of the arc is 288 degrees.
Step-by-step explanation:
The correct question is
A circle has a circumference of 8. It has an arc of length 32/5 . What is the central angle of the arc,in the degrees?
we know that The circumference of the circle subtend a central angle of 360 degrees
so using a proportion
Find out the central angle for an arc of length 32/5
given the polynomial : (3x+4)^5. find the coefficient of x³ !
Answer:
[tex] \displaystyle 4320 {x }^{3} [/tex]
Step-by-step explanation:
to solve binomials like this there's a way called binomial theorem given by
[tex] \displaystyle {(a + b)}^{n} = \sum _{k = 0} ^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]
but for this question we need the following part
[tex] \displaystyle \boxed{ \binom{n}{k} {a}^{n - k} {b}^{k} }[/tex]
from the question we obtain that a,b and n is 3x,4 and 5 since we want to find the coefficient x³ k should be (5-3) = 2 so we have determined the variables now just substitute
[tex] \displaystyle \binom{5}{2} {(3x)}^{5 - 2} \cdot {4}^{2} [/tex]
simplify which yields:
[tex] \displaystyle \boxed{ \bold{4320 {x }^{3}} }[/tex]
and we are done!
Write 2 x 8 x 64 in index notation with the smallest base.
Answer:
Step-by-step explanation:
Prime factorize 8 and 64
8 = 2* 2 * 2 = 2³
64 = 2*2*2 *2*2*2 = 2⁶
2*8*64 = 2* 2³ *2⁶ = 2¹⁺³⁺⁶ = 2¹⁰
In exponent multiplication, if base are same, then add the exponents.
Circle W has a radius of 20 in and right central angle, ZVWX. Find the length of vx. Leave your answer in terms of pi.
5
10
15
20
Answer:
The length of the arc is 10 pi
Step-by-step explanation:
Mathematically, the length of an arc is calculated as;
theta/360 * 2 * pi * r
theta represents the central angle subtended by the arc which is a right angle according to the question (a right angle is 90 degrees)
r is the circle radius which is 20 inches
so we have the length of the arc as;
90/360 * 2 * pi * 20 = 40 pi/4 = 10 pi
I you borrow 500 for 4 years at an annual interest rate of 6% HOW MUCH WILL YOU PAY altogether
Answer:
620
amount= p+i , to find interest .I=500*4*6/100 =120 amount=500+120=620
During the last ten years oliver has played 1200 games of chess oliver has drawn 6% of the games he has lost 33% of the game calculatehow many games og chess oliver won
Answer:
6+33=39 now we subtract from 100
100-39=61
He won 61 percent of the games
now we multiply 1200*0.61=732
so he won 732 of the 1200 games
Hope This Helps!!
Which of the following graphs is the solution set of -10 < 3x - 4<8?
Answer:
The third one
Step-by-step explanation:
The image above is the explanation, hopefully its help
what is the equation of the parabola?
solve the system of equations using the substitution method pls show work
4x+y=7
3x+2y=9
Answer:
x = 1 ; y = 3Step-by-step explanation:
[tex]4x + y = 7 \\ y = 7 - 4x[/tex]
Now we know the value of y is 7 - 4x we plug this value to the second equation with y, So,
[tex]3x + 2(7 - 4x) = 9 \\ 3x + (14 - 8x) = 9 \\ - 5x = 9 - 14 \\ - 5x = - 5 \\ x = \frac{ - 5}{ - 5} \\ x = 1[/tex]
Now to find the value of y we use the first equation
[tex]y = 7 - 4x \\ y = 7 - 4(1) \\ y = 7 - 4 \\ y = 3[/tex]
Hope this helps you :)
Answer:
x = 6/5 or 1.2 y = 11/5 or 2.2
Step-by-step explanation:
4x + y = 7
y = -4x + 7
y = 7 - 4x
3x + 2y = 9
3x + 2(7 - 4x) = 9
3x + 14 - 8x = 9
-5× + 15 = 9
-5x = 9 - 15
-5x = -6
x = -6/-5
x = 6/5
4x + y = 7
4(6/5) + y = 7
24/5 + y = 7
y = 7 - 24/5
y = 35/5 - 24/5
y = 11/5
A radio tower is located on a coordinate system measured in miles. The range of a signal in a particular direction is modeled by a quadratic function where the boundary of the signal starts at the vertex at (4, 2). It passes through the point (5, 4). A linear road connects points (–3, 7) and (8, 2). Which system of equations can be used to determine whether the road intersects the boundary of the tower’s signal?
im sorry i dont know the answer
need help please thanks
Answer:
C
Step-by-step explanation:
All angles in a triangle add up to 180°.
63 + 52 = 115°.
180 - 115 = 65°, so part of the answer is done, y = 65°.
The angle next to y is a vertical angle.
61 + 65 = 126°.
180 - 126 = 54°.
So, x = 54°, y = 65°.
A) { -3 , -1 , 1, 3 , 6 }
B) { 3, -1 , 2, 0, -2}
C) all real numbers
D) {3,-2,-1,0,1,2,3,4,5,6,7,8}
Are the two triangles similar. If so, State how
Answer:
SAS
Step-by-step explanation: every triangle contains a total of 180 degrees if you substract 180 by 60+70(which is 130) you would get 50 degrees which is the exact degree missing in the first triangle, so after confirming that both triangles have an equal degrees on each side the answer would be SAS (which stands for Side-Angle-Side), SAS is the answer you would give to triangles that are congruent(equal)
A circle has a central angle of 6 rad that intersects an arc of length 14 inches. Which equation find the length of the radius, R, of the circle?
Answer:
Step-by-step explanation:
θ=l/r
where θ is central angle in degrees.
l=length of arc.
r=radius of circle.
6=14/r
6r=14
r=14/6=7/3 =2 1/3 inches.
which values are soloutions to the inequality -3x - 4 < 2 ? check all of the boxes that apply
Given:
The inequality is:
[tex]-3x-4<2[/tex]
To find:
The values that are solutions to the given inequality.
Solution:
We have,
[tex]-3x-4<2[/tex]
Adding 4 on both sides, we get
[tex]-3x-4+4<2+4[/tex]
[tex]-3x<6[/tex]
Divide both sides by -3 and change the inequality sign because -3 is a negative value.
[tex]\dfrac{-3x}{-3}>\dfrac{6}{-3}[/tex]
[tex]x>-2[/tex]
Therefore, all the real values greater than -2 are the solutions to the given inequality.
Find the Value of x a.86 b.79 c.65 .72
Answer: D
Step-by-step explanation:
360° - 90° - 90° - 108° = 72°
(Sum of angles in a quadrilateral = 360°)
If < A and < B form a linear pair, and < A = x - 13 degrees, and < B = x + 7 degrees, then find x.
Select one:
a. 124
b. 101
c. 46
d. 93
Answer:
d
Step-by-step explanation:
A linear pair sum to 180° , then
x - 13 + x + 7 = 180
2x - 6 = 180 ( add 6 to both sides )
2x = 186 ( divide both sides by 2 )
x = 93 → d
Solve for xx. Round to the nearest tenth, if necessary.
Answer:
x ≈ 7.1
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos27° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{KL}{KM}[/tex] = [tex]\frac{6.3}{x}[/tex] ( multiply both sides by x )
x × cos27° = 6.3 ( divide both sides by cos27° )
x = [tex]\frac{6.3}{cos27}[/tex] ≈ 7.1 ( to the nearest tenth )
The area of a rectangle is 35ft^2 , and the length of the rectangle is 3 ft more than twice the width. Find the dimensions of the rectangle.
Answer:
1228 is your answer
Step-by-step explanation:
. Evaluate the function rule for the given value.
y = 4.2xfor x = -6
Answer:
y= 4 x 2(6)
y= 4 x -12
y= -48
Step-by-step explanation:
y= 4 x 2(6)
y= 4 x -12
y= -48
Pa-follow po
Thank you