Answer:
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Precalculus Examples
Popular Problems Precalculus Find the Properties 16x^2+16y^2-16x+24y-3=0
16
x
2
+
16
y
2
−
16
x
+
24
y
−
3
=
0
Add
3
to both sides of the equation.
16
x
2
+
16
y
2
−
16
x
+
24
y
=
3
Divide both sides of the equation by
16
.
x
2
+
y
2
−
x
+
3
y
2
=
3
16
Complete the square for
x
2
−
x
.
Tap for more steps...
(
x
−
1
2
)
2
−
1
4
Substitute
(
x
−
1
2
)
2
−
1
4
for
x
2
−
x
in the equation
x
2
+
y
2
−
x
+
3
y
2
=
3
16
.
(
x
−
1
2
)
2
−
1
4
+
y
2
+
3
y
2
=
3
16
Move
−
1
4
to the right side of the equation by adding
1
4
to both sides.
(
x
−
1
2
)
2
+
y
2
+
3
y
2
=
3
16
+
1
4
Complete the square for
y
2
+
3
y
2
.
Tap for more steps...
(
y
+
3
4
)
2
−
9
16
Substitute
(
y
+
3
4
)
2
−
9
16
for
y
2
+
3
y
2
in the equation
x
2
+
y
2
−
x
+
3
y
2
=
3
16
.
(
x
−
1
2
)
2
+
(
y
+
3
4
)
2
−
9
16
=
3
16
+
1
4
Move
−
9
16
to the right side of the equation by adding
9
16
to both sides.
(
x
−
1
2
)
2
+
(
y
+
3
4
)
2
=
3
16
+
1
4
+
9
16
Simplify
3
16
+
1
4
+
9
16
.
Tap for more steps...
(
x
−
1
2
)
2
+
(
y
+
3
4
)
2
=
1
This is the form of a circle. Use this form to determine the center and radius of the circle.
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
Match the values in this circle to those of the standard form. The variable
r
represents the radius of the circle,
h
represents the x-offset from the origin, and
k
represents the y-offset from origin.
r
=
1
h
=
1
2
k
=
−
3
4
The center of the circle is found at
(
h
,
k
)
.
Center:
(
1
2
,
−
3
4
)
These values represent the important values for graphing and analyzing a circle.
Center:
(
1
2
,
−
3
4
)
Radius:
1
image of graph
Are these lines perpendicular?
X
yes
no
Answer:
[tex]\huge\boxed{\sf No.}[/tex]
Step-by-step explanation:
Perpendicular lines:
When two lines intersect each other at 90 degrees, they are said to be perpendicular lines.
Answer:
The given lines are not perpendicular lines since they do not intersect each other at 90 degrees.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807what is the product of 9,028 x 100,000
Answer:
902,800,000
Step-by-step explanation:add the 5 zeros from 100,000 to 9,028
solve the equation on the interval [0, 2π).
3(sec x)^2 -4=0
[tex] \: \: \: \: \: [/tex]
[tex]x = \frac{\pi}{6} , \frac{(k)\pi}{6} , \frac{(5)\pi}{6} , \frac{(k)\pi}{6} [/tex]
refer to the attachmenthope it helpsThe price of a skateboard was reduced from $150 to $90. By what percentage was the price of the skateboard reduced?
Answer:
jjjjStep-by-step explanation:
For f(x)=−2x+4, find f(x) when x=−3.
Dado P(x) = x2– kx + 2, hallar el valor de k para que P( – 2)=8
Shape 1 and shape 2 are plotted on a coordinate plané. Which statement about the shapes is true?
Answer:
We need to see all of the choices, but they are congruent and reflected and rotated.
Step-by-step explanation:
How much will the taxi driver earn if he takes one passenger 4.8 miles in another passenger 7.3 miles explain your process
Answer:
12.1x+t
Step-by-step explanation:
since we do not get a specific amount we must add 4.8 and 7.3 and substitute the amount the driver earns per mile with x and use t as a variable if they charge something like $5 just to get in before driving
12 red cars is what part of 48 total cars
Answer: 1/4
Step-by-step explanation: i think it is 1/4 bc 48 is the total and 12 can go in 48 4 times
i hope this helped have a good day
This means that 12 cars are green,12 cars are blue,and 12 cars are yellow/white. which means there are 4 groups of cars which all together equals 48 which is 48 divided by 12 equals 4 or just do 12 +12+12+12+48 or
4+4+4+4+4+4+4+4+4+4+4+4=48
Meaning there are 4 groups and 12 is 1 part of them which makes 1/4
jill spent $215.70 on books. math books cost $28.50 and english books cost 21.70. if she bought a total of 9 then how many of each kind did she buy
Which equation, when graphed, has x-intercepts at (2, 0) and (4, 0) and a y-intercept of (0, â€"16)? f(x) = â€"(x â€" 2)(x â€" 4) f(x) = â€"(x 2)(x 4) f(x) = â€"2(x â€" 2)(x â€" 4) f(x) = â€"2(x 2)(x 4).
To find the equation, for the x-intercepts at (2, 0) and (4, 0) and a y-intercept of (0, –16) we have to find the nature of the curve.
The correct option is f(x) = –2(x – 2)(x – 4).
Given:
The x-intercepts at (2, 0) and (4, 0).
The y-intercept of (0, –16).
The nature of the graph is quadratic curve. Write the general equation for x-intercept.
[tex]y=a(x-2)(x-4)[/tex]
Where is [tex]a[/tex] number
Substitute 0 for [tex]x[/tex].
[tex]y=a(0-2)(-4)\\y=8a[/tex]
We have y-intercept of (0, –16).
[tex]-16=8a\\a=-2[/tex]
The equation would be,
[tex]f(x) = -2(x - 2)(x - 4).[/tex]
Thus, the correct option is f(x) = –2(x – 2)(x – 4).
Learn more about equitation here:
https://brainly.com/question/3337307
what does c equal : c - 12 =-4
Answer:
c = 8
Step-by-step explanation:
c - 12 = -4
Add 12 on both sides
c = 12 + (-4)
c = 8
1. Simplify 3(2x - y) + 6y.
5x + 7y
6x + 3y
2x + 3y
6x - 7y
Answer:
6x + 3y
Step-by-step explanation:
3(2x - y) + 6y ← distribute parenthesis by 3
= 6x - 3y + 6y ← collect like terms
= 6x + 3y
[tex]\huge\boxed{Hi\: there!}[/tex]
Here, we use the Distributive Property:
[tex]a(b+c)=ab+ac[/tex]
3(2x-y)+6y=6x-3y+6y
Combine like terms:
6x+3y
[tex]\huge\boxed{Therefore,\: our \:equation\: is:6x+3y}[/tex]
[tex]\huge\bf{Good \:luck \:with \:your \: studies! :)\\~Unknown Dreamer}[/tex]
What can you multiply by to find:
50% of a number?
10% of a number?
75% of a number?
Answer:
number · 0.50 = 50% of a number
number · 0.10 = 10% of a number
number · 0.75 = 75% of a number
Step-by-step explanation:
50% = 0.50
10% = 0.10
75% = 0.75
what are 43.6÷8 use compatible numbers using the quotient
Answer:
7.3
Step-by-step explanation:
if you multiply the number by to end at 4 the results you gave will be the same of three times the number decreased by 7
Answer:
11
Step-by-step explanation:
Let the number be x,
2x+4 = 3x-7
Collect like terms
2x-3x= -4-7
-x =. -11
Multiply both sides by -1
x. =. 11
Oh and I think you made a typo and missed the 2, " if you multiply the number by 2 to end at 4..........."
Hope This Helps :)
in a school there are 542 girls and boys. how many pupils are there in that school?
Answer:
There are 1084 pupils in that school.
Step-by-step explanation:
If there are 542 girls and boys then you would have to double 542 to get the total number of people. So, there are 1084 people in that school.
Hope this helps!
Answer:
1084
Step-by-step explanation:
542+542
Solve. 2/3x+5/6=3 1/3 Enter your answer as a mixed number in simplest form in the box.
Answer:
10/3
Step-by-step explanation:
[tex] \bf \huge \: Question:[/tex]
Find the value of x
[tex]\bf \huge \: Equation \: provided:[/tex]
[tex]\sf \dfrac{2}{3} +5/6= 3\dfrac{1}{3} [/tex]
[tex]\bf \huge \: Solution:[/tex]
[tex] \bf \: Convert\: The\: mixed \: fraction \: to \: improper \: f raction:[/tex]
[tex]\sf \longmapsto \: \dfrac{2}{3} x + \dfrac{5}{6} = \dfrac{10}{3} [/tex]
[tex]\underline{\bf Subtract \: 5/6 \: from \: both \: sides : }[/tex]
[tex]\sf \longmapsto \dfrac{2}{3 }x + \dfrac{5}{6} - \red{ \dfrac{5}{6} } = \dfrac{10}{3} - \red{ \dfrac{5}{6} }[/tex]
[tex] \bf \: On \: Simplification:[/tex]
[tex]\sf \longmapsto \dfrac{2}{3} x + 0 = \dfrac{20 -5 }{ 6 } [/tex]
[tex]\sf \longmapsto \dfrac{2}{3} x = \dfrac{5}{2} [/tex]
[tex]\underline{ \bf \: Multiply \: both \: sides \: by \: 3/2:}[/tex]
[tex]\sf \longmapsto\red{ \dfrac{3}{2}} \times \dfrac{2}{3} x = \red{\dfrac{3}{2} } \times \dfrac{5}{2}[/tex]
[tex]\bf On \: Simplification:[/tex]
[tex]\sf \longmapsto1 \times \dfrac{15}{4} [/tex]
[tex]\sf \longmapsto \: \dfrac{15}{4} [/tex]
[tex]\underline{\bf Answer\: In \: mixed\: fraction:}[/tex]
[tex]\sf \longmapsto \: 3\dfrac{3}{4} [/tex]
______________________________________
[tex]\underline{ \bf \: Henceforth,The\: value\: of\: x \: is:}[/tex]
[tex] \boxed{\huge\boxed{ \tt x = 3\dfrac{3}{4} }}[/tex]
PLEASEEEE HELP FOR BRAINLIST!!!!!!!!!
Same thing as before!
First, we can get rid of d(x) simply by looking at it because we can tell it's linear (it's a straight line). If we look at the table, we can see a(x) is also linear because it has a steady rate of growth. b(x) and c(x) both represent exponential growth. The curved shape of b(x) shows us this is exponential growth, and the exponent in c(x) tells us it's also exponential.
a farmer has sheep and hen. the sheep and hens together have 100 heads and 356 legs how many sheep and hen are there
Answer:
22 hens and 78 sheep
Step-by-step explanation:
Let the number of hens = x
Number of sheep = y
Total heads = 100
x + y = 100 --------------------(I)
x = 100 - y
Number of legs of 'x' hen = 2*x = 2x
Number of legs of 'y' sheep = 4*y = 4y
total legs = 356
2x + 4y = 356 -----------------------(II)
Substitute x = 100 -y in equation (II)
2(100 - y) + 4y = 356
2*100 - 2*y + 4y = 356
200 - 2y + 4y = 356 {Combine like terms}
200 + 2y = 356 {Subtract 200 from both sides}
2y = 356 - 200
2y = 156 {Divide both sides by 2}
y = 156/2
y = 78
Plugin y = 78 in equation (I)
x + 78 = 100
x = 100 - 78
x = 22
22 hens and 78 sheep
HELP ASAP PLEASE?!
The graph at the right shows Jeremy's distance from home each hour he is on a car trip. How many miles will he be from home after 10 hours?
A) 350 miles
B) 400 miles
C) 500 miles
D) 550 miles
Answer:
The answer is (C) because every time the hour goes up, the mile goes up by 5 so if you continue to count up by 5's you would get 500 at 10.
The sum of two integers is 2. Their difference is 10. What are the two integers?
Answer:
6 and -4
Step-by-step explanation:
a + b = 2
a - b = 10
Solve:
from the first eq.
a = 2 - b
replacing this value in the second eq.
(2-b) - b = 10
2 - 2b = 10
-2b = 10 - 2
-2b = 8
b = 8/-2
b = -4
from the second eq.
a - b = 10
a - (-4) = 10
a + 4 = 10
a = 10 - 4
a = 6
Check:
from the first eq.
6 + (-4) = 2
6 - 4 = 2
lines y = -x+2 and y=x+1
point of intersection of the linear equations is
(0,2)
(0.5, 1.5)
(-1,0)
(2,0)
[tex]\\ \sf\Rrightarrow y=-x+2[/tex](1)
[tex]\\ \sf\Rrightarrow y=x+1[/tex](2)
Now
[tex]\\ \sf\Rrightarrow -x+2=x+1[/tex]
[tex]\\ \sf\Rrightarrow -2x=-1[/tex]
[tex]\\ \sf\Rrightarrow x=0.5[/tex]
Put in eq(2)
[tex]\\ \sf\Rrightarrow y=0.5+1[/tex]
[tex]\\ \sf\Rrightarrow y=1.5[/tex]
Convert the following from factored form to standard form.
f\left(x\right)=\left(x+5\right)\left(x-1\right)f(x)=(x+5)(x−1)
Answer:
the mmic is back still swords rund eep
Step-by-step explanation:
Are these geometric shapes ASA, SSS, SAS or None?
I WILL GIVE BRAINLIEST TO BEST ANSWER!
refer to image.
Answer:
4)ASA
6) ASA
2) SSS
8) SAS
Step-by-step explanation:
numbers 4 and 6 are ASA because we have 2 congruent angles and one congruent side. Also, they r in the pattern angle, side, angle. Which makes it ASA
number 2 is SSS because all 3 sides are congruent
number 8 is SAS because because there are 2 congruent sides and one congruent angle. They are seen in the pattern side, angle, side. Which makes it SAS
hope that helps and I apologize about earlier
have a wonderful day!
Answer:
2) None, 4) ASA, 6) ASA, 8) ASAStep-by-step explanation:
#2We have two parallel sides.
This gives us two pairs of alternate interior angles and one pair of vertical angles.
In total 3 congruent angles. This is not enough to state congruence.
None
#4We have two pairs of congruent angles and an included common side.
This is good to state the triangles are congruent by ASA
#6Similarly to above question, we have two pairs of congruent angles and an included common side.
This is good to state the triangles are congruent by ASA
#8We have one pair of congruent sides and the parallel sides gives us two pairs of alternate interior angles and a pair of vertical angles.
We can state the triangles are congruent by ASA as the congruent side is included.
Thomas invested $1498.00 at 6% simple interest per annum calculate How long it will be before his investment earns $449.40
Answer:
t = 6 years
Step-by-step explanation:
Use the simple interest formula: i = prt, where p is the principal, r is the interest rate as a decimal fraction, and is the elapsed time, in years.
Here we want to know how long it will take for the interest alone to reach $449.40. We first solve i = prt for t, obtaining t = i/(pr).
Here, the length of time is t = ($449.40) / (0.06*$1498.00). This works out to
t = 5.9947, or approximately 6 years.
t = 6 years
Sarah is 2 inches taller than the quotient of billy’s height and 5. Let b represent Billy’s height. write an expression that represents Sarah’s height
Answer:
1
Step-by-step explanation:
5(x+1) = 12
5(x+1) = 5x + 12
5(x+1) = 5x + 5
5(x=1) = 0
what one is an infinite solution
Answer:
[tex]2 + \frac{b}{5} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Write the equation of the line parallel to y - 3x=4 and containing (3,10)
15 points in 4 quarters
Is this u asking a question or just saying 15 points in 4 quarters?
is the change of rate always constant
In mathematics, a constant rate of change is a rate of change that stays the same and does not change.