Given:
[tex](3x+7)^2[/tex] is subtracted from 3.
To find:
The result of the given statement in the standard form of the polynomial.
Solution:
We need to find the result when [tex](3x+7)^2[/tex] is subtracted from 3.
So, the resulted polynomial can be written as:
[tex]P(x)=3-(3x+7)^2[/tex]
On simplification, we get
[tex]P(x)=3-((3x)^2+2(3x)(7)+(7)^2)[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
[tex]P(x)=3-(9x^2+42x+49)[/tex]
[tex]P(x)=3-9x^2-42x-49[/tex]
[tex]P(x)=-9x^2-42x-46[/tex]
Therefore, the resulted polynomial in standard form is [tex]-9x^2-42x-46[/tex].
What is the area of a circle with a diameter of 5.4
P.S Show work
Which is the equation of a hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0)?
The required equation of the hyperbola is expressed as
[tex]\frac{x^2}{10}- \frac{y^2}{15}=1 \\[/tex]
The standard form for calculating the equation of a parabola along the x-axis is expressed as:
[tex]\frac{(x-k)^2}{a^2}-\frac{(y-h)^2}{b^2} = 1 \ ............. 1[/tex] where:
(h, k) is the center
(k±c, h) are the foci
[tex]x=h\pm\frac{a^2}{c}[/tex] is the directrix
From the question given, we can see that foci = (±5, 0)
k±c, h = ±5, 0
k = 0
h = 0
c = 5
From the directrix,
[tex]x=h\pm\frac{a^2}{c}\\x =0\pm\frac{a^2}{5}\\\pm2 = \pm\frac{a^2}{5}\\a^2 = 10\\[/tex]
Also, we need to know that;
a²+b² = c²
10 + b² = 5²
b² = 25 - 10
b² = 15
Substituting the gotten values into the equation of a hyperbola;
[tex]\frac{(x-0)^2}{10}- \frac{(y-0)^2}{15} =1\\\frac{x^2}{10}- \frac{y^2}{15} =1\\[/tex]
This gives the required equation of the hyperbola
Learn more on the equation of hyperbola here: https://brainly.com/question/20409089
Answer:
The answers are between C and D
Step-by-step explanation:
It can't be A or B because they create a horizontal hyperbola, when the directrices are vertical.
please help omg- AAAAAAAAAAAAAAAAAAAAA
Answer: 11. A and B
12. 520 cubic feet.
Step-by-step explanation: 11. The volume for a prism is base x height. Thus, it would be 2 x 3 x 3 or 6 x 3 to get a total of 18 cubic units.
12. The first compartment's volume is 5 x 7 x 8 or 280. The second compartment is 5 x 6 x 8 or 240. The total would be 280 + 240 or 520 cubic feet.
Answer:
11.B
12.520
Step-by-step explanation:
5.7.8=280
5.6.8=240
TOTAL=520
Please help I’m strugglinggg Oml and this is due right now
Answer:
i dont understand thisssssssss im sorrrryy what is c(5)?????? huhhhhhhhhh
Step-by-step explanation:
A piece of string is 120 centimeters long.
How long would the piece of string measure in meters?.
Answer:
1.2m
Step-by-step explanation:
1 meter = 100 cm
120cm * (1m/100cm) = 1.2m
Please help I'm struggling
Answer:
the first is 1/5 what are the other options
Step-by-step explanation:
10)
A) x + 2 y = 1
C) x - 2y = 10
B) x-1= 2
D) x – 2y=
Answer:
B)
Step-by-step explanation:
y-intercept = -2
slope = 1
in slope-intercept form the line would be: y = x - 2
if we subtract 'x' from each side we get:
-x + y = -2
we don't want to leave 'x' as negative so we can multiply each term by -1 to get:
x - y = 2
Help ASAP, mathematics trig
Answer:
D
Step-by-step explanation:
Using the tangent ratio in the right triangle
tanθ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{7}{4}[/tex] , then
θ = [tex]tan^{-1}[/tex] ([tex]\frac{7}{4}[/tex] ) ≈ 60° ( to the nearest degree )
HELPPPPP
What is the area of the actual living room?
Answer:
The answer is 51,200 in².
Step-by-step explanation:
(4x40)x(8x40)=51,200
Solve w = x + for y.
Reply really fast and give like the work for it too please
Answer:
see below
Step-by-step explanation:
w = x+y/z
Subtract x from each side
w-x = x+y/z -x
w-x = y/z
Multiply each side by z
(w-x) *z = y/z*z
(w-x) *z = y
You can distribute the z if desired
wz -xz = y
Answer:
y = z(w - x)
Step-by-step explanation:
w = x + y/z
Subtract x from both sides
w - x = y/z
Multiply both sides by z
z(w - x) = y
Flip
y = z(w - x)
please help me with full calculations
9514 1404 393
Answer:
see attached
Step-by-step explanation:
When rotation is 180° or 360°, the direction is immaterial. The result is the same no matter which direction you go.
Gerardo makes $18 per hour at Starbucks. Tomorrow he is going to receive a raise totalling 20% of his hourly wage. What will he be making per hour straying tomorrow.
to get his wage for the next day, you would do 18x1.2, which equals 21.6, so he would now be making $21.6 per hour.
What are the values of c and d in the matrix subtraction below? [ 6 8 -11 15 ]-[c+2 3 -5 d-4 ]=[ 22 5 -6 17] C=-14 d= -6 c=-18 d= -6 c=-14 d=2 c=-18 d=2
Answer:
c=-18 d=2
Step-by-step explanation:
[ 6 8 -11 15 ]-[c+2 3 -5 d-4 ]=[ 22 5 -6 17]
The equation tells that when the two matrices are subtracted we get the resultant matrix.
Each element of the first matrix corresponds to each element of the second matrix
From above
6- (c+2)= 22
6- c-2= 22
4-c= 22
-c= 22-4
-c= 18
c= -18
And
15-( d-4)= 17
15- d+4= 17
19-d= 17
-d= 17-19
-d= -2
d= 2
Answer:
D
Step-by-step explanation:
c= -18
d= 2
what is the image of the point (-2,7) after a rotation of 180 degrees counterclockwise about the origin?
Answer:
(- 7, - 5 )
Step-by-step explanation:
What is the distance between two points(2,-6)(-7,1)
Answer:
11.4
Step-by-step explanation:
Find the distance in the x-direction between the x-components: 2 - (-7) = 9.
Similarly: between the y-components: 1 - (-6) = 7
Apply the Pythagorean Theorem: 9^2 + 7^2 = d^2, where d is the desired distance:
81 + 49 = d^2, or d^2 = 130
The distance d is approximately √130 ≈ 11.4
Answer:
Square root of 130
Step-by-step explanation:
Use the distance formula:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
[tex](x_{1}, y_{1} )[/tex] is your first set of coordinates : (2, -6)
[tex](x_{2}, y_{2} )[/tex]is your second set of coordinates : (-7, 1)
Which is a number that can be written as a fraction in the form /?
Answer:
the third one/second one
Step-by-step explanation:
a line passes through point (-10,3) and has a slope of 1/2. write an equation in Ax+By=C form for this line. Use integers for A, B, and C
Answer:
-10, -4
Step-by-step explanation:
how do you give bainlist
If the perimeter of the polygon is 42, AB = ______?
Answer:
AB = 7
Step-by-step explanation:
The polygon pictured is a hexagon, which means that it has 6 equal side lengths. The perimeter is 42. AB is the length of one side.
Perimeter = 6 x length of one side
If you plug everything you know in the equation, you would get...
42 = 6 x length of one side
42 ÷ 6 = 7
So, 7 is the length of AB, since in a hexagon, all sides are the same length.
The length of side AB is 7.
What are regular polygons?A regular polygon is a closed shape that has straight sides of equal length and interior angles of equal measure.
This means that all of the sides and angles of a regular polygon are congruent (i.e., have the same size).
We have,
The given polygon is a hexagon since it has 6 faces.
Now,
The six faces are equal in length.
So,
6 faces length = 42
Now,
Each face = x
And,
6x = 42
x = 42/6
x = 7
Thus,
The length of AB is 7.
Learn more about regular polygons here:
https://brainly.com/question/24328525
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there are 10 children in line. four are girls the rest are boys. which number sentence can be used to find the number of boys in line?
Answer:
Im sorry i dont understand what you mean by sentence but there are 6 boys
Step-by-step explanation:
find the volume of the figure
Answer:
1920
Step-by-step explanation:
Volume of larger rectangular prism: 10 * 8 * 14 = 1120
Volume of smaller rectangular prism: 10 * 10 * 8 = 800
Volume of whole prism: 1120 + 800 = 1920
Hence, your answer is 1920
rewrite each expression as single exponent. Answer all of them Please!
1} 11 to the second power times 11 to the tenth power
2} 13 to the 6 power times 13 to the forth power
3} 14 to the power 9 times 14 to the tenth power
4} 2 to the power 4 times 2 to the forth power
5} 7 to the 8 power times 7 to the 6 power
6} 3 to the power 3 times 3 to the 9 power
Answer:
[tex]11^2 *11^10 \\13^6 *13^4\\14^9 * 14^10\\2^4*2^4\\7^8*7^6\\3^3*3^9[/tex]
Step-by-step explanation:
Please Mark Brainliest for helping
Write an exponential function in the form y=b^x that goes through the points (0,9) and (3,4608)
Answer:
y = 9 * bˣ
Step-by-step explanation:
y = a * bˣ
9 = a * b⁰ = a * 1
a = 9
4608 = 9 * b³
b³ = 512
b = 8
y = 9 * bˣ
Find the area of the complex figure below.
A. 84 in^2
B. 90 in^2
C. 96 in^2
D. 102 in^2
Help correct get brainly lol
Answer:
there are seven variable terms
Step-by-step explanation:
variables are letters (a, b, c, etc.)
i hope this helps :)
Answer:
The answer is 4 because are all separate variables (also combines into one variable)
Step-by-step explanation:
Terry rents a kayak while he is on vacation. He is required to pay a deposit of $95 plus an additional $11.50 per day. Terry only has $150 to spend on kayaking. Write and solve an inequality you can use to determine the maximum number of days Terry can afford to rent a kayak.
Answer:
A maximum of 4 days
Step-by-step explanation:
Inequality: 95 + 11.50x ≤ 150
Okay so the 95 is his fee. Then for everyday, it's 11.50 and we don't know how many days yet, so 11.50x. The 95 dollars and the 11.50x has to equal to or less than 150 since that is how much he has to spend on vaca.
95 + 11.50x ≤ 150
-95 -95
11.50x ≤ 55
/11.50 /11.50
X=4.78260869565
You would round down since he has a budget.
Someone help me with this pls
answer:
=y^(-4+3)
=y^ (-1)
Can someone plz help me on this plz I have the answer just making sure I’m right. Plz no link s
Answer:
B) 63 ft.
Step-by-step explanation:
To find how long it takes for a rotation, we need to find the circumference.
To do so, we use the formula 2(pi)r
To find the radius, we divide the diameter in half :
d = 20
r = d/2
r = 20 / 2
r = 10
Then, we plug that into the formula :
2(pi)10
Insert that into your calculator :
2(pi)10 = 62.83
Simplify :
62.83 = 63 ft.
1.On field day, the P.E. coach divides the students into two groups, Positives and Negatives. He wants to have the same amount of students of each group on each side of a rope, to play Tug-of-War.
He uses the following expression to figure out how many students of a certain group he still needs to create an even match.
–5 + 20
Evaluate the expression and write the answer below. Write only a number, either positive or negative. No letters
Answer:
-15
Step-by-step explanation:
because -5 + 20 = -15.
The coach needs 15 negative players to join the negative team in order to get 20 players (which would make the teams even)
The world's largest ice cream cone was 10 feet tall and 3 feet in
diameter. Ice cream weighs about 19.8 pounds per cubic foot. If this cone
was filled with ice cream to the top without going over, approximately how
many pounds of ice cream could this cone hold?
A. 467 pounds
B. 600 pounds
C. 1,400 pounds
D. 1,866 pounds
Answer:
23.56
Step-by-step explanation:
all you have to do is find the volume
lets set up the equation: V=πr2h 3=π·1.52·10 3≈23.56194
Then round : 23.56
Your final answer is 23.56 You're Welcome!!!