Answer: x=-16/11
6+11x+10=0
We add all the numbers together, and all the variables
11x+16=0
We move all terms containing x to the left, all other terms to the right
11x=-16
x=-16/11
Answer:
Vertex:
Roots: [tex]x=\frac{5}{3}[/tex] or [tex]x=2[/tex]
Step-by-step explanation:
The given quadratic equation is:
Let [tex]f(x)=3x^2-11x+10[/tex]
We obtain the vertex form by completing the square;
[tex]f(x)=3(x^2-\frac{11}{3}x)+10[/tex]
Add and subtract the square of half the coefficient of x.
[tex]f(x)=3(x^2-\frac{11}{3}x+(-\frac{11}{6})^2+10-3(-\frac{11}{6})^2)[/tex]
This simplifies to
[tex]f(x)=3(x-\frac{11}{6})^2-\frac{1}{12}[/tex]
Hence the vertex is [tex](\frac{11}{6},-\frac{1}{12})[/tex]
We now solve to obtain:
[tex]3(x-\frac{11}{6})^2-\frac{1}{12}=0[/tex]
[tex]3(x-\frac{11}{6})^2=\frac{1}{12})[/tex]
[tex](x-\frac{11}{6})^2=\frac{1}{36})[/tex]
[tex](x-\frac{11}{6})=\pm \sqrt{\frac{1}{36}}[/tex]
[tex]x=\frac{11}{6}\pm \frac{1}{6}[/tex]
[tex]x=\frac{5}{3}[/tex] or [tex]x=2[/tex]
The sector of a circle with a 12-inch radius has a central angle measure of 60
What is the exact area of the sector in terms of pi
Answer:
24 π square inches
Step-by-step explanation:
The area of a circule is give by the formula A = π r²
Since we have a angle of 60 degrees, that represent 1/6th of the whole area (60 / 360 degrees).
A circle = π * 12² = 144 π square inches
Area of the portion representing 60 degrees of the circle, can easily be calculated with a cross-multiplication:
[tex]\frac{x}{144\pi } = \frac{60}{360}[/tex]
x = 144 π / 6 = 24 π square inches
Use the quadratic formula to solve for the roots in the following equation. 4x 2 + 5x + 2 = 2x 2 + 7x – 1
Answer:
So, The roots are [tex]x= \frac{1+\sqrt{5}i}{2} \,\, and \,\,x= \frac{1-\sqrt{5}i}{2}[/tex]
Step-by-step explanation:
[tex]4x^2 + 5x + 2 = 2x^2 + 7x - 1[/tex]
We need to solve the equation to find the roots using quadratic formula.
The quadratic formula is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Rearranging the above equation:
[tex]4x^2 -2x^2+ 5x-7x + 2+1 =0[/tex]
[tex]2x^2 -2x + 3 =0[/tex]
Where a =2 , b=-2 and c =3 Putting values in quadratic equation and solving:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(2)(3)}}{2(2)}\\x=\frac{2\pm\sqrt{4-24}}{4}\\x=\frac{2\pm\sqrt{-20}}{4}\\\sqrt{-20} \,\,can\,\,be\,\, written\,\, as\,\, 2\sqrt{-5}\\ x=\frac{2\pm2\sqrt{-5}}{4}\\x=\frac{2+2\sqrt{-5}}{4} \,\, and \,\, x=\frac{2-2\sqrt{-5}}{4}\\x=\frac{2(1+\sqrt{-5})}{4} \,\, and \,\, x=\frac{2(1-\sqrt{-5})}{4}\\ x=\frac{1+\sqrt{-5}}{2} \,\, and \,\, x=\frac{1-\sqrt{-5}}{2}\\As \,\,we\,\, know\,\, \sqrt{-1} = i \\[/tex]
[tex]x= \frac{1+\sqrt{5}i}{2} \,\, and \,\,x= \frac{1-\sqrt{5}i}{2}[/tex]
So, The roots are [tex]x= \frac{1+\sqrt{5}i}{2} \,\, and \,\,x= \frac{1-\sqrt{5}i}{2}[/tex]
Answer:
these numbers go in the spaces. short and simple.
1 5
2 2
mark brainliest please!
Step-by-step explanation:
Consider the graph of function f below select the true statement
Answer:
The answer is C, the graph has the y intercept of 2
Step-by-step explanation:
You can see from the graph that the line intercepts the y axis at 2
It wouldn't be the slope of 1/2 because that choice isn't negative and this is a decreasing/negative graph
10 points please help very easy
Answer:
165 KBS and 750 jump rope
Step-by-step explanation:
Find the equation of the line that is perpendicular to y=-2/3x and contain the point (4,-8)
Answer:
y = 3/2x - 14.
Step-by-step explanation:
The slope of the perpendicular line is - 1 / -2/3
= 3/2.
Using the point slope form y-y1 = m(x-x1):
y - (-8) = 3/2(x - 4)
y + 8 = 3/2x - 6
y = 3/2x - 14.
Answer:
y = [tex]\frac{3}{2}[/tex] x - 14
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{2}{3}[/tex] x ← is in this form
with slope m = - [tex]\frac{2}{3}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex], hence
y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation of the perpendicular line
To find c substitute (4, - 8) into the partial equation
- 8 = 6 + c ⇒ c = - 8 - 6 = - 14, so
y = [tex]\frac{3}{2}[/tex] x - 14 ← equation of perpendicular line
Please need help badly. If the area of BAC=8, what is the area of EDF
Answer:im not sure but if im correct the answer should be 6
Step-by-step explanation:im assuming this cause if 8/4 is 2 then take the 2 and times it with the 3
Answer:
Area of ΔEDF = 4.5 in²
Work shown image:
Using a "15% off" coupon, Dianne saved $12.75 on a new chair for her home office. What was the chair's regular price? How much did she pay?
Answer:
The original price was $85
She spent $72.25
Step-by-step explanation:
When x equals the price of the chair:
12.75/15 = x/100
15 x = 1275
x = $85
To find the price she paid:
85 - 12.75 = $72.25
The Wall Street Journal reporter the biggest music comeback in 2014 was vinyl records. Nearly 8 million vinyl were sold in 2014, mostly to younger markets. If there were 15 vinyl record factories pressing records in the United States in 2014, and only 2/3 remain operational in 2015, how many factories closed down?
Answer:
5 factories closed
Step-by-step explanation:
In 2014 there were 15 operating factories.
We know that of those 15 factories only 2/3 remain operative.
If only 2/3 remain operational this means that 1/3 of them closed.
To calculate the number of factories that closed we must multiply the initial number of operative factories by 1/3.
This is:
[tex]15 * \frac{1}{3} = \frac{15}{3} = 5[/tex].
5 factories closed
there are 7 circles in a row. there are 3 rows complete story
Wym is this multiplication
2. What is the external probability of rolling a 4
3 what is the external probability of getting at least one tail
Answer:
2. 1- Experimental probability of rolling a 4 = 40%
3. 2- Theoretical probability is 3% greater than experimental probability.
Step-by-step explanation:
Experimental probability of rolling a 4 = 100 × [tex]\frac{8}{20}[/tex]
= 100 × 0.4
= 40%
Experimental probability of getting at least one tail = [tex]\frac{72}{100}[/tex]
= 0.72
Theoretical probability of getting at least one tail = [tex]\frac{3}{4}[/tex]
= 0.75
Theoretical probability is 3% greater than experimental probability.
is an isosceles trapezoid below x=
Answer:13
Step-by-step explanation:
5x+15=7x-11
7x. 7x
2x+15=11
+15 +15
2x =26
———
2
x = 13
A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal. The value of x is 13.
What is a Trapezoid?A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.
In an isosceles trapezoid, the angles formed at the ends of any one of the parallel lines are congruent. Therefore, we can write,
5x+15 =7x-11
15+11=7x-5x
26=2x
x = 13
Hence, the value of x is 13.
Learn more about Trapezoid:
https://brainly.com/question/8643562
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Match the term with the definition
Answer:
Plane: C) A flat surface that extends infinitively and has no depth; it has length and width
Perpendicular Lines: B) Two lines that intersect at 90° angles
Parallel Lines: E) Two lines that lie within the same plane and never intersect
Circle: D) A set of all points in a plane that are given distance from a plane
Angle: A) A figure consisting of two rays with a common endpoint
I hope this helps
this is 100% correct
plz mark me brainliest
If (-3) exponent -5 = 1/x, what is the value of x?
-243
- 1/243
1/243
243
Answer:
[tex]\boxed {-243}\\[/tex]
Step-by-step explanation:
[tex]\begin{array}{rclr}(-3)^{-5} & = & \dfrac{1}{x}& &\\(-3)^{5} & = & x &\text{Inverted each side of the equation}\\x & = & \boxed {\textbf{{-243}}}\\\end{array}[/tex]
How to write 3.499 an Expanded Form and Word Form? PLEASE HELP ME
(3 x 1 ) + (4 x 0.1) + (9 x 0.01) + ( 9 x 0.001)
OR
3 + 0.4 + 0.09 + 0.009
Three and four hundred ninety-nine thousandths
Hope this helped!
What is the volume of the come with radius 5 m and height 6 m ? Express the answer in terms of pi.
A. 35pi m^3
B. 47pi m^3
C. 50pi m^3
D. 63pi m^3
Answer:
C
Step-by-step explanation:
The volume (V) of a cone is calculated using the formula
V = [tex]\frac{1}{3}[/tex] πr² h
where r is the radius and h the perpendicular height
here r = 5 and h = 6, hence
V = [tex]\frac{1}{3}[/tex] × π × 5² × 6
= 2π × 25 = 50π m³ → C
The volume of the cone is [tex]\( 50\pi \, \text{m}^3 \).[/tex]
How to get the volume of the cone
The formula for the volume v of a cone is given by:
[tex]\[ V = \frac{1}{3} \times \pi \times r^2 \times h \][/tex]
The variables in the formula are:
r is the radius of the base of the cone.
his the height of the cone.
Given a cone with radius r = 5 meters and height h = 6 meters, substitute these values into the formula:
[tex]\[ V = \frac{1}{3} \times \pi \times (5^2) \times 6 \]\[ V = \frac{1}{3} \times \pi \times 25 \times 6 \]\[ V = \frac{1}{3} \times \pi \times 150 \]\[ V = 50 \pi \][/tex]
Therefore, the volume of the cone is [tex]\( 50\pi \, \text{m}^3 \).[/tex]
what makes n true 1/2 (n+4)=6
Answer: N=8
Step-by-step explanation: So 1/2*4=2 then you know that you need 4 to get to six because you already have two. Then 8/2=4 so N=8.
1/2(8+4)=6
4+2=6
6=6
Hope this helped!!!!!
Final answer:
To find the value of n that satisfies the equation 1/2 (n+4)=6, multiply both sides by 2 and subtract 4 from both sides to get n=8.
Explanation:
The student's question asks for the solution to the algebraic equation: 1/2 (n+4)=6. To solve for n, follow these steps:
Multiply both sides of the equation by 2 to get rid of the fraction: n + 4 = 12.Subtract 4 from both sides to isolate n: n = 12 - 4.Simplify the equation to find the value of n: n = 8.Therefore, the value of n that makes the equation true is 8.
Two architectural models are pyramids with bases of equal area. The smaller model has a height of 10 centimeters, and the larger model has a height of 30 centimeters. How many times greater than the smaller model is the larger model’s volume?
Answer:
The larger model’s volume is 3 times greater than the volume of the smaller model
Step-by-step explanation:
we know that
The volume of a pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base of pyramid
h is the height of the pyramid
Find the volume of the smaller model
we have
[tex]h=10\ cm[/tex]
substitute
[tex]V=\frac{1}{3}B(10)[/tex]
[tex]V=\frac{10}{3}B\ cm^{3}[/tex]
Find the volume of the larger model
we have
[tex]h=30\ cm[/tex]
substitute
[tex]V=\frac{1}{3}B(30)[/tex]
[tex]V=\frac{30}{3}B=10B\ cm^{3}[/tex]
To find how many times greater than the smaller model is the larger model’s volume, divide the volume of the larger model by the volume of the smaller model
so
[tex]10B/(\frac{10}{3}B)=3[/tex]
The larger model’s volume is 3 times greater than the volume of the smaller model
NEED ASAP
A person walks for 100 yards then turns through an angle of 60° and walks another hundred yards. How far is she from her starting point?
Please help!! I’m not sure what formula to use!!
Answer:
[tex]100\ yd[/tex]
Step-by-step explanation:
we know that
Applying the law of cosines
[tex]c^{2} =a^{2}+b^{2}-2(a)(b)cos(C)[/tex]
In this problem we have
c-----> is the distance from her starting point
[tex]a=100\ yd[/tex]
[tex]b=100\ yd[/tex]
[tex]C=60\°[/tex]
substitute
[tex]c^{2} =100^{2}+100^{2}-2(100)(100)cos(60\°)[/tex]
[tex]c^{2} =10,000+10,000-10,000[/tex]
[tex]c^{2} =10,000[/tex]
[tex]c=100\ yd[/tex]
What is the midpoint of the x intercepts of f(x)=(x-2)(x-4
Answer:
A. (0,0)
Step-by-step explanation:
both lines run through (4,-4)
they meet at 0 on the Y axis
so the answer is (0,0)
Type the correct answer in the box. If necessary, use / for the fraction bar. A basket contains 14 white eggs, 15 brown eggs, and 11 lemons. Taylor is in a hurry to make breakfast and picks something from the basket at random. The exact probability that Taylor picks an egg from the basket is .
Answer:
29/40
Step-by-step explanation:
A basket contains 14 white eggs, 15 brown eggs, and 11 lemons. The exact probability that Taylor picks an egg from the basket is;
(14+15)/(14+15+11) = 29/40
Answer:
The exact probability that Taylor picks an egg from the basket is 0.725
Step-by-step explanation:
A basket contains 14 white eggs, 15 brown eggs and 11 lemons.
Total number of items in the basket [tex]=14+15+11= 40[/tex]
Total number of eggs in the basket [tex]=14+15= 29[/tex]
Taylor picks one item at random from the basket.
So, the probability that Taylor picks an egg [tex]=\frac{total\ number\ of\ eggs}{total\ number\ of\ items}=\frac{29}{40}=0.725[/tex]
11 cm
63°
9 cm
What is the area of this triangle?
Enter your answer as a decimal in the box
Round only your final answer to the nearest
tenth.
The correct answer is 44.1 [tex]cm^{2}[/tex]. I took the test.
Use the perfect square method
(3x + 3)^2 = 36
Factor out the common term; 3
(3(x + 1))^2 = 36
Use the Multiplication Distributive Property; (xy)^a = x^ay^a
3^2(x + 1)^2 = 36
Simplify 3^2 to 9
9(x + 1)^2 = 36
Divide both sides by 9
(x + 1)^2 = 36/9
Simplify 36/9 to 4
(x + 1)^2 = 4
Take the square root of both sides
x + 1 = √4
Since 2 * 2 = 4, the square root of 2 is 2
x + 1 = 2
Break down the problem into these 2 equations
x + 1 = 2
x + 1 = -2
Solve the first equation; x + 1 = 2
x = 1
Solve the second equation; x + 1 = -2
x = -3
Collect all solutions;
x = 1, -3
After 7 years, what is the total amount of a compound interest investment of an initial
principal of $1685 at a rate of 4.3% compounded quarterly?
A. 1942.18
B.373,709.25
C.2461.55
D.2273.13
Answer:
Option D. $2273.13
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=7\ years\\ P=\$1,685\\ r=0.043\\n=4[/tex]
substitute in the formula above
[tex]A=\$1,685 (1+\frac{0.043}{4})^{4*7}=\$2,273.13[/tex]
A roll of fabric was 120 inches long. A customer bought 3 feet of the fabric.
How many feet of fabric were remaining?
The 7 feet of fabric were remaining.
To solve this problem step by step:
1. Convert the length of the roll of fabric from inches to feet.
- 120 inches ÷ 12 inches/foot = 10 feet
2. Subtract the length purchased by the customer from the total length of the roll.
- 10 feet - 3 feet = 7 feet
So, the customer bought 3 feet of fabric, leaving 7 feet remaining.
1. To convert inches to feet, we know that there are 12 inches in a foot. So, we divide the length of the fabric in inches by 12 to get the length in feet.
- 120 inches ÷ 12 inches/foot = 10 feet
2. Next, we subtract the length purchased by the customer (3 feet) from the total length of the roll (10 feet) to find out how much fabric remains.
- 10 feet - 3 feet = 7 feet
Therefore, the customer bought 3 feet of fabric, leaving 7 feet remaining.
Complete question:
A roll of fabric was 120 inches long. A customer bought 3 feet of the fabric.
How many feet of fabric were remaining?
There is a 90% chance of rain tomorrow and a 30% chance that the baseball game is postpone. What is the probability it will rain tomorrow and the baseball game is postponed.
Hello! :)
The answer is probably from changing first to decimals by dividing by 100: 90 and 30 become .9 and .3.
Then, multiply the two: .9 x .3 = .27
Finally, you multiply .27 by 100 = 27
Add the percentage sign: 27%
So there is a 27% chance that it will rain and the baseball game is postponed.
Very unlikely, I know. ;D
Hope this helped and I hope I answered in time!
Good luck!
~ Destiny ^_^
The probability it will rain tomorrow and the baseball game is postponed is 0.93 .
What is probability ?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
According to classical definition of probability, a random experiment consists of a set of possible outcomes and each set of possible outcomes is equally likely to occur in the course of the event.
How to calculate the given probability ?It is given that there is a 90% chance of rain tomorrow and a 30% chance that the baseball game is postpone.
Let A be the probability that there is a chance of rain tomorrow and B be the probability that the baseball game is postpone.
P(A) = 90% = 0.9 and P(B) = 30% = 0.3 and P(A∩B) = (0.9*0.3) = 0.27 .
The probability it will rain tomorrow and the baseball game is postponed is given by P(A∪B) .
By formula,
⇒ P(A∪B) = P(A) + P(B) - P(A∩B)
⇒ P(A∪B) = 0.9 + 0.3 - 0.27
∴ P(A∪B) = 0.93 .
Therefore, the probability it will rain tomorrow and the baseball game is postponed is 0.93 .
To learn more about concepts of probability, refer -
brainly.com/question/13604758
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Let me know the answer plz
Answer:
J
Step-by-step explanation:
Find the common ratio r of the geometric sequence then multiply a term by r to obtain the next term
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{6}{-36}[/tex] = - [tex]\frac{1}{6}[/tex]
The next 3 terms are
[tex]\frac{1}{6}[/tex] × - [tex]\frac{1}{6}[/tex] = - [tex]\frac{1}{36}[/tex]
- [tex]\frac{1}{36}[/tex] × - [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{216}[/tex]
[tex]\frac{1}{216}[/tex] × - [tex]\frac{1}{6}[/tex] = - [tex]\frac{1}{1296}[/tex]
Answer:
J. [tex]-\frac{1}{36}[/tex], [tex]\frac{1}{216}[/tex], [tex]-\frac{1}{1296}[/tex]
Step-by-step explanation:
We are given the following geometric sequence and we are to find its 8th term:
[tex]-36, 6, -1, \frac{1}{6},...[/tex]
Here [tex]a_1=-36[/tex] and common ratio [tex](r) = \frac{-1}{6}=\frac{-1}{6}[/tex].
The formula we will use to find the next three terms is:
nth term = [tex]a_1 \times r^{(n-1)}[/tex]
5th term = [tex]-36 \times \frac{-1}{6}^{(5-1)}[/tex] = [tex]-\frac{1}{36}[/tex]
6th term = [tex]-36 \times \frac{-1}{6}^{(6-1)}[/tex] = [tex]\frac{1}{216}[/tex]
7th term = [tex]-36 \times \frac{-1}{6}^{(7-1)}[/tex] = [tex]-\frac{1}{1296}[/tex]
i need help please and thank you
My answers are in the picture above.
The acceleration, a, of an object produced when a force is applied is given by the following formula, where F represents the force acting on the object and m represents the mass of the object.
If a has units of meters per second squared and m has units of grams, what must be the units of F?
A.
meters per second
B.
grams·meters per second squared
C.
grams
D.
grams·meters per second
I think it’s b I hop
Bill and Lisa are surveying their classmates about their summer reading. Their questions are given below:
Bill: How many books did you read this summer?
Lisa: Which book was first recommended to be read by the book club during the summer break?
Who wrote a statistical question and why?
Bill, because there will be variability in the responses collected
Lisa, because there can be only one answer to the question
Bill, because every student will give the same answer
Lisa, because there can be many answers to the question
Bill is the one who wrote this statistical question so there will be there will be variability in the responses collected.
Bill, because there will be variability in the responses collected
The sum of four consecutive odd numbers is 40 what is the greatest of the four numbers
Answer:
13
Step-by-step explanation:
First find the average the numbers (40 / 4 = 10)
2 are more and 2 are less
7, 9, 11, 13
An odd number can be written as 2n+1, where n is an integer. Four consecutive odd numbers can be written as 2n-3, 2n - 1, 2n + 1 and 2n + 3. Adding these together gives you 8n, which we are told is 40. So n is 5 and the four consecutive odd numbers are 7, 9, 11 and 13.