Answer:
11 feet
Step-by-step explanation:
All the sides of a square are equal
the area of a square = length²
121 ft² = length²
to determine the length find the square root of the area, 121
√121 = 11 feet
Let's start form the product `x^{2}+11x+30,` and get back to the binomials we started with. Show your steps.
Answer:
Then, the polynomial [tex]x^{2}+11\cdot x + 30[/tex] is equal to the product of the binomials [tex](x+5)[/tex] and [tex](x+6)[/tex].
Step-by-step explanation:
The polynomial [tex]x^{2}+11\cdot x + 30[/tex] is a polynomial of the form [tex]x^{2} - (r_{1}+r_{2})\cdot x + r_{1}\cdot r_{2} = (x-r_{1})\cdot (x-r_{2})[/tex], where [tex]r_{1}[/tex] and [tex]r_{2}[/tex] are the roots of the polynomial. Then, we find the following system of equations:
[tex]-r_{1}-r_{2} = 11[/tex] (1)
[tex]r_{1}\cdot r_{2} = 30[/tex] (2)
After some algebraic handling, the solution of this system is [tex]r_{1} = -5[/tex] and [tex]r_{2} = -6[/tex].
Then, the polynomial [tex]x^{2}+11\cdot x + 30[/tex] is equal to the product of the binomials [tex](x+5)[/tex] and [tex](x+6)[/tex].
Multiple choice. Use the Law of Sines to find the missing angle of the triangle. Find m angle C to the nearest tenth if c = 111 a = 42, and m angle A=22 .
A. 81.9
B. 98.1
Answer:
Both A and B are possible.
Step-by-step explanation:
It's both!
This is a might tricky. First you have to find the altitude. You have to determine if this is a real triangle.
Sin(22) = opposite / hypotenuse. The hypotenuse = 111. The angle is 22
opposite = hypotenuse * sin(22)
opposite = 111 * sin(22)
opposite = 41.58 and this is the altitude.
What have you learned?
Since 42 is larger than 41.58 you have 2 solutions to the triangle. One of the angles is acute, and the other one is obtuse. They are supplementary angles.
Sin(C) / c = Sin(A) / a
Sin(C) = c * Sin(22) / 42
Sin(C) = 111*sin(22)/ 42
Sin(C) = .99003
Sin(C) = 81.9
So that's your first answer. The second answer comes from Finding the supplement to this angle
supplement + 81.9 = 180
supplement = 180 - 81.9
supplement = 98.1
Solve the simultaneous equation
Log(x-1)+2 log y=2 log 3
Log x + log y = log 6
Answer:
x = 2, y = 3
Step-by-step explanation:
Log x + log y = log 6 Log xy = Log 6 xy = 6
y = 6/x
Log(x-1)+2 Log y=2 Log 3
Log(x-1) = 2 Log 3 - 2 Log y = Log 3² - Log y² = Log 9 - Log y² = Log (9 / y²)
x - 1 = 9/y²
x - 1 = 9 / (6/x)² = 9 /(36/x²) = x²/4
4x - 4 = x²
x² -4x + 4 = 0
(x-2)² = 0
x = 2
y = 6/x = 3
ABCD is a kite. Solve for x.
The vertices of a triangle are (-1,3) (6,3) and (-1,-4)
Find the area of the triangle
Please show all workings
Answer:
24.5 unit²
Step-by-step explanation:
Area of ∆
= ½ | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |
= ½ | (-1)(3 -(-4)) + 6(-4 -3) + (-1)(3 - 3) |
= ½ | -7 - 42 |
= ½ | - 49 |
= ½ (49)
= 24.5 unit²
Method 2:
Let the vertices are A, B and C. Using distance formula:
AB = √(-1-6)² + (3-3)² = 7
BC = √(-6-1)² + (-4-3)² = 7√2
AC = √(-1-(-1))² + (4-(-3))² = 7
Semi-perimeter = (7+7+7√2)/2
= (14+7√2)/2
Using herons formula:
Area = √s(s - a)(s - b)(s - c)
here,
s = semi-perimeter = (14 + 7√2)/2
s - a = S - AB = (14+7√2)/2 - 7 = (7 + √2)/2
s - b = (14+7√2)/2 - 7√2 = (14 - 7√2)/2
s - c = (14+7√2)/2 - 7 = (7 + √2)/2
Hence, on solving for area using herons formula, area = 49/2 = 24.5 unit²
Answer:
24.5
Step-by-step explanation:
To find the area with the coordinates provided:
(-1,3), (6,3), (-1,-4)
First we count the units that are inside the triangle which is area.
[tex]\frac{49}{2}[/tex]
So we know that there are [tex]\frac{49}{2}[/tex] units and then we divide 49 by 2 which gets you 24.5.
49 ÷ 2 = 24.5
The answer is 24.5 units.
If you read 98 pages of a book in one week. What is his unit rate of pages read per day
Answer: 14 pages a day
Step-by-step explanation:
98 / 7 = 14
Answer: 14 pages read per day.
Step-by-step explanation:
98/7= 14
Hope this helps!
Can anyone help me please ?
what is the logarithmic form for
[tex]2 { }^{x - 4} = 32[/tex]
Answer:
[tex]2^x-4=32\quad :\quad x=\frac{2\ln \left(6\right)}{\ln \left(2\right)}\quad \left(\mathrm{Decimal}:\quad x=5.16992\dots \right)\\\\2^x-4=32 \\\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\\2^x-4+4=32+4\\\mathrm{Simplify}\\2^x=36\\\\apply exponential rule\\x\ln \left(2\right)=\ln \left(36\right)\\x\ln \left(2\right)=\ln \left(36\right)\\x=\frac{2\ln \left(6\right)}{\ln \left(2\right)}[/tex]
hope it helps:)
Stephanie and Jill share a reward of $65 in a ratio of 1:4. How much does Stephanie
get?
Answer:
Step-by-step explanation:
Each part is equal to 65/(1+4)=$13
Since Stephanie only got 1 part, she got $13.
How long will it take to accumulate $1200
in an account, if you begin with $1000 and
the account pays 6% compounded
monthly?
Answer:
it will take 4 months
Step-by-step explanation:
Can someone Please help Ill mark brainliest.
Which figure shows a reflection of pre-image ABC over the y-axis?
Two right triangles graphed on a grid. Right triangle A B C, with right angle C, is in Quadrant One. Right triangle A-prime, B-prime, C-prime, with right angle C-prime, is in Quadrant Two. The coordinates of triangle A B C are A (one, one), B (three, four), and C (three, one). The coordinates of triangle A-prime, B-prime, C-prime are A-prime (negative one, one), B-prime (negative three, four), and C-prime (negative three, one).
Two right triangles graphed on a grid. Right triangle A B C, with right angle C, is in Quadrant One. Right triangle A-prime, B-prime, C-prime, with right angle C-prime, is in Quadrant Three. The coordinates of triangle A B C are A (one, one), B (three, four), and C (three, one). The coordinates of triangle A-prime, B-prime, C-prime are A-prime (negative one, negative one), B-prime (negative three, negative four), and C-prime (negative three, negative one).
Two right triangles graphed on a grid. Right triangle A B C, with right angle C, is in Quadrant One. Right triangle A-prime, B-prime, C-prime, with right angle C-prime, is in Quadrant Four. The coordinates of triangle A B C are A (one, one), B (three, four), and C (three, one). The coordinates of triangle A-prime, B-prime, C-prime are A-prime (one, negative one), B-prime (three, negative four), and C-prime (three, negative one).
The figure that shows a reflection of pre-image ABC over the y-axis is the third figure.
How to depict the figure?From the complete information, the triangle ABC is reflected over the y axis.
The vertices of the triangle are A(1, 1), B(3, 4) and C(3, 1). The vertices of the images are A(1, 1) = A'(-1, 1). B(3, 4) = B(-3, 4) ans C(3, 1) = C'(-3, 1).
In conclusion, the figure that shows a reflection of pre-image ABC over the y-axis is the third figure.
Learn more about reflection on:
https://brainly.com/question/3643476
A basketball backboard set that sold for $79 is discounted 15% what is this sale price
Answer: $67.15
Step-by-step explanation:
Solve for x = [?]
2x+ 20
3x + 15
2x + 20
Answer:
x=29
Step-by-step explanation:
3x+15+2x+20=180
3x+2x+15+20=180
5x+35=180
5x=180-35
5x=145
x=145/5
x=29
write the equation of the circle given a center of (1,3) and a point on the circle at (-2,7)
Answer:
Ecuación estándar de un círculo
(x−2)2+(y−2)2=25
Forma general de la ecuación de un círculo
x2−4x+y2−4y−17=0
Ecuaciones paramétricas de un círculo
x=5cosθ+2y=5sinθ+2
Step-by-step explanation:
Ecuación Estándar de un Círculo
La ecuación estándar de un círculo con el centro en (x_0, y_0) y radio r es
(x^2-x_0) + (y^2-y_0)=r^2
Ecuaciones Paramétricas de un Círculo
Las ecuaciones paramétricas de un círculo con el centro en (x_0, y_0) y radio r son
x=r cos \theta + x_0\\y=r sin \theta + y_0
Ecuación General de un Círculo
La ecuación general de un círculo con el centro en (x_0, y_0) y radio r es
x^2+ax+y^2+by+c=0,
donde
a=-2x_0\\b=-2y_0\\c=x^2_0+y^2_0-r^2
help pls i need help
Answer:
The second and third one
Step-by-step explanation:
According to the statement, numbers between 4 and 5 is 4.1 - 4.9
But it is doubled so it is 8.2 - 9.8
These numbers are greater than 8 and less than 9
These numbers are also greater than 9 and less than 10
Can you help me fast and show work plsssss I need it now
What is the volume of the rectangular prism below? Use the formula V = lwh. 4 ft 4 ft 8 ft
Answer:
V=128
Step-by-step explanation:
Answer:
V =128ft^3
Step-by-step explanation:
V=lwh=4*4*8=128
100 POINTS, MAHNIFIA PLEASE ANSWER!
SCAMMERS WILL NOT BE TOLERATED!
Answer:
- 3.4(21) = - 71.4
(- 2.3)(- 7.9) = 18.17
9.24 ÷ - 7 = -1.32
(- 8.5) ÷ (- 3.4) = 2.5
- 6.85 ÷ 0.5 = - 13.7
Jesse bought a car for $25,000. The car depreciates approximately 10% of its value each year. What will the car be worth in 5 years?
Answer:
$12,500
Step-by-step explanation:
I got this answer by first taking the purchase price of the car and multiplying it by .10 to see what ten percent of the price was and I got $2,500. Then I took and multiplied 2,500 by 5 years and go 12,500. Then I subtracted 12,500 from the original purchase price to get $12,500. Meaning that the value of the care has decreased by half of the purchase price.
HOPE THIS HELPS!
pls help asap!! will give brainliest
Answer:
i believe the answer is A 90
Step-by-step explanation:
A city library selects a random sample of 1,250 of its patrons and finds that the 90% confidence interval for the
proportion of those who have read an e-book in the previous 12 months is (0.71, 0.75).
Calculate the point estimate and margin of error for the given confidence interval.
Enter both values to 2 decimal places.
The point estimate =
The margin of error =
Answer:
point estimate: .73
margin of error: .02
Step-by-step explanation:
correct on edg
The circumference of the base of the cone is 8.5pi inches. What is the volume of the cone in terms of ne? Round to the nearest hundredth. Enter
your answer in the box.
15 in.
IT in
3
Answer:
8.93h in³
Step-by-step explanation:
The circumference of the base of the cone is 8.5pi inches. What is the volume of the cone in terms of ne? Round to the nearest hundredth. Enter
Step 1
We find the radius of the cone
Base area = 8.5 π inches
Radius = √Area/π
Radius = √8.5 π /π
Radius = √8.5
Radius of the cone = 2.9154759474 inches
Approximately = 2.92 inches
Step 2
We find the volume of the cone
= πr²h/3
Height is not given, so we find in terms of h
= π × 2.92² × h/3
= 8.9288252005h in³
Approximately = 8.93h in³
The
Consider a system of two linear equations in two variables. If the graphs of the equations are not the same line, is it possible for the system to have infinitely many solutions. Explain.
Answer:
No
Step-by-step explanation:
Solutions to systems of equations are points at which the lines of the equations intersect. Knowing this, only equations representing the same line would have infinitely many solutions because they would intersect at every one of each other's points - they're the exact same line. Therefore, if they are not the same line, they would not intersect at each and every point, and would not have infinitely many solutions.
3. An ELA test is worth 100 points. There are a total of 26 questions. They are spelling word questions that are worth 2 points each and vocabulary word questions worth 5 points each. How many of each type of question are there? *
Answer:
There are 10 two point questions and 16 five point questions.
Step-by-step explanation:
x = the number of 2 points questionsy = the number of 5 points questionsx + y = 262x + 5y = 100x = 10 two points questionsy = 16 five points questionsPLEASE HELP ASAP I WILL GIVE BRAINLILIST
Let () = −3(2)^ and () = − 14.
Complete the table to determine the solutions of () = −3(2)^ = () = − 14.
The solution of () = −3(2)
= () = − 14 is = ______
Step-by-step explanation:
-3. 2
-2. 1
-7. 6
i did my best.
Factor completely x2 - 4x - 12
A. Prime
B. (x - 2)(x - 6)
C. (x + 2)(x - 5)
D. (x - 2)(x + 6)
can you explain how to do it?
Answer:
(x-6)(x+2) D
Step-by-step explanation:
first you need to see which two numbers add up to -4 and multiply to -12 which is -6 and 2
Tell which number is greater. 50%, 13/25 HELP MEEEE
Answer:
13/25
Step-by-step explanation:
if you put it in decimal the fraction is greater
Answer:
13/25 is larger then 50%
Step-by-step explanation:
13/25=52%
50%=12.5/25
HELP!!! Which is a solution to the equation?
(x −2)(x + 5) = 18
x = −10
x = −7
x = −4
x = −2
Mark this and return
Answer:x=-7
Step-by-step explanation:
Step-by-step explanation:
I'm not sure it's probably x=-2
Uriel's hiking stick is 3 2/3 feet long, and Nat's is 3 3/8 feet long. Whose walking stick is longer and by how much?
Answer:
Uriel's stick is LONGER by 7/24 feet
Step-by-step explanation:
Uriel's hiking stick is 3 2/3 feet long, and Nat's is 3 3/8 feet long. Whose walking stick is longer and by how much?
The above question is solved as
Uriel's stick - Nat's stick
= 3 2/3 feet - 3 3/8 feet
= 7/24 feet
Hence, Uriel's stick is LONGER by 7/24 feet