if 4 times a number is increased by 6, the result is less than 15 than the square of the number. find the number
Answer:
n = 7
n = -3
Step-by-step explanation:
4n+6 = n²-15
4n = n² - 21
n² - 4n - 21 = 0
(n-7)(n+3) = 0
n = 7
n = -3
What does r equal?
Answer: r = ________
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Given:
The quadratic equation is:
[tex]10m^2-7m+3=0[/tex]
To find:
The solutions for the given equation by using the quadratic formula.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the quadratic formula is:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have,
[tex]10m^2-7m+3=0[/tex]
Here, [tex]a=10,b=-7,c=3[/tex]. Using the quadratic formula, we get
[tex]m=\dfrac{-(-7)\pm \sqrt{(-7)^2-4(10)(3)}}{2(10)}[/tex]
[tex]m=\dfrac{7\pm \sqrt{49-120}}{20}[/tex]
[tex]m=\dfrac{7\pm \sqrt{-71}}{20}[/tex]
[tex]m=\dfrac{7\pm i\sqrt{71}}{20}[/tex] [tex][\because \sqrt{-a}=i\sqrt{a},a>0][/tex]
Therefore, the solution set of the given equation is [tex]\left\{\dfrac{7- i\sqrt{71}}{20},\dfrac{7+ i\sqrt{71}}{20}\right\}[/tex]. Hence, the correct option is D.
find the geometric means of the following sequence -7, ?, ?, ?, ?, -1, 127, 357
The sports store sells 5 t-shirts and 10 pairs of shorts for 132.50. The next day they sell 3 t-shirts and 5 pairs of shorts for 69.50. What is the cost of a t-shirt?
Answer:
A) 5t + 10s = 132.50
B) 3t + 5s = 69.50
We multiply B) by -2
B) -6t -10s = -139.00 then we add A)
A) 5t + 10s = 132.50
-t = -6.50
t-shirt price = 6.50
Source: http://www.1728.org/unknwn2.htm
Step-by-step explanation:
George invests $2000 in an account with an interest rate of 5%. Which best represents this?
Y=2000(1.05)^x
Y=2000(.05)^x
Y=2000+ 0.5^x
Y=2000(.95)^x
Answer:
Y=2000(1.05)^x
Step-by-step explanation:
This is because 2000 is the fixed beginning value and should stay by itself.
While the interest rate of 5% is 1.05 because the amount of money George will have will be going up based on the fixed beginning value.
The ratio of adult cats to kittens at a pet care center on Monday was 4:3. There were 15 kittens there that day. Thursday, 22 adult cats were at the pet care center. What is the difference between the number of adult cats at the pet care center on Thursday and Monday?
Answer:
The difference is 2:1.5
Step-by-step explanation:
What is the name of longest side of triangle?
Answer: Hypotenuse
Step-by-step explanation:
The Hypotenuse is known as the longest side of a triangle.
How much money should be put into a savings account now that earns 6.0% a year compounded weekly if you want to have 70000 in 15 years?
If you want to have $70,000 in 15 years, you need start saving money now in a savings account that earns 6.0% annually compounded weekly.
How does compound interest work?When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest.Compounding is effective for both promised and unguaranteed products. All or part of your money could be lost.
Use the compound interest formula and enter the figures you are familiar with. Then find a solution for the unknown number.
A = P(1 +r/n)^(nt)
where A represents the balance of the account, P represents the amount invested, r represents the yearly rate, n represents the number of times per year interest is compounded, and t is the number of years.
Filling in the given values, we have ...
70000 = P( 1 + 0.06/52)^(52*15) = P(2.4583)
P = 70000/2.4583 = 28474.96
You would need to deposit 28474.96 in order to have 70000 in 15 years.
To know more about compound interest visit :-
https://brainly.com/question/14295570
#SPJ1
LESSON 12-1 Properties of Translations Practice and Problem Solving : A / B
We found that translations have the following three properties: line segments are taken to line segments of the same length;
angles are taken to angles of the same measure; and. lines are taken to lines and parallel lines are taken to parallel lines.
Properties of Translations
- Distance Where the lengths of the segments stay the same.
-Angle Measures These remain the same.
-Parallelism Where the parallel lines will stay parallel.
-Collinearity The points will stay on the same line.
-Orientation The order of the letters will stay the same.
learn more about of translation here
https://brainly.com/question/6462661
#SPJ4
please help i will give brainlist!!
Answer:
1157.09
Step-by-step explanation:
2+2/3x=3/7 rewritten no fractions
Answer:
x = 3.1 as a decimal or x = 28/9 as a fraction
Step-by-step explanation:
11. A mom gives her small child either dimes or quarters for helping with odd jobs around the house. At the
end of the day, the child has 9 coins with a total value of $1.20. How many were dimes and how many were
quarters?
Step-by-step explanation:
2 q and 7 dimes kkkkkkkkk
Answer:
q = 2
d = 7
Step-by-step explanation:
System of Equations:
d + q = 9
10d + 25q = 120
Use Substitution:
let d = 9 - q
10(9 - q) + 25q = 120
90 - 10q + 25q = 120
15q = 30
q = 2
d = 7
A sector with a central angle measure of \purpleD{175\degree}175°start color #7854ab, 175, degree, end color #7854ab has a radius of \maroonD{12\,\text{cm}}12cmstart color #ca337c, 12, start text, c, m, end text, end color #ca337c.
Answer: [tex]219.94\ cm^2[/tex]
Step-by-step explanation:
Given
The central angle of a sector measures [tex]175^{\circ}[/tex]
The radius of the circle is [tex]r=12\ cm[/tex]
The area of the sector is given by
[tex]\Rightarrow A=\dfrac{\theta }{360^{\circ}}\pi r^2[/tex]
Insert the values
[tex]\Rightarrow A=\dfrac{175^{\circ}}{360^{\circ}}\cdot \pi \times 12^2\\\\\Rightarrow A=219.94\ cm^2[/tex]
The answer i’m on a timer in a exam
Answer:
67
Step-by-step explanation:
The interior angles of triangles always equal 180 degrees. That means that angle R is equal to 67.
Therefore, angle U is equal to 67, as corresponding angles are the same.
Hope that this helps!
Draw the image of quadrilateral ABCD under the translation (x, y) to (x-7, y+1).
help me please!
It costs $3 to bowl a game and $2 for shoe rental Write an expression for the total cost (in dollars) of g games.
Answer: , P = 2 +3g
Step-by-step explanation:
Simplify by combining like terms:
4a + 3(5a - 2)
Answer:
19a - 6
Step-by-step explanation:
Answer:
4a + 3 ( 5a - 2 )
= 4a + [ 3 ( 5a - 2 ) ]
= 4a + [ 15a - 6 ]
= 4a + 15a - 6
= 19a -6
NEED HELP ASAP
NO LINKS AND NO JUST SAYING HI, PLEASE ANSWER LEGITIMATELY!
THANK YOU!!!! <3
Answer:
x=55
Step-by-step explanation:
The angles are corresponding angles and corresponding angles are equal
3x-60 = x+50
Subtract x from each side
3x-60-x = x+50-x
2x-60 =50
Add 60 to each side
2x-60+60=50+60
2x=110
Divide by 2
2x/2 =100/2
x =55
For any of the vehicles listed in the table,
how many days can you rent the vehicle
before it would be less expensive to rent
for the week?
A person can rent any of the vehicles shown in the table for a minimum of two to three days before it becomes more expensive for a week.
Algebra state that it is the study of the laws and symbols of mathematics as well as the manipulation of these symbols.
The rent of the small car for a week is $250 and for a day is $100. Then,
The maximum number of days that a car could be rented is,
= 250÷100
= 2.5 days
≅ 3 days
Then, for the medium car is,
= 290÷110
= 2.7 days
≅ 3 days
For the luxury car is,
= 325÷120
= 2.7 days
≅ 3 days
For Small van is,
= 350÷150
= 2.3 days
≅ 2 days
For Large van is,
= 390÷170
= 2.2 days
≅ 2 days
We can conclude from the above calculations that a person can rent a car for 2-3 days before it becomes more expensive for a week.
The complete question is -
For any of the vehicles listed in the table, how many days can you rent the vehicle before it would be less expensive to rent for the week?
To know more about algebra:
https://brainly.com/question/29131718
#SPJ4
A 11-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 9 feet from the base of the building. How high up the wall does the ladder reach?
I will mark you brainlist!
Answer:
1. 2 runners
2. 25 runners
3. 24%
4. 15 runners
5. 60%
6. uh I think it's asking the same thing as 3, so 24%?
3. Target is selling two popular toys this year for kids. Toy x is a Power Treads and toy y is an
America Girl Doll. Target pays $8 each for the Power Treads and $14 each for the America Girl
Doll. One unit of Power Treads yields a profit of $2 while an America Girl Doll yields a profit of
$3. Target estimates that no more than 2,000 toys will be sold-every month and does not plan
to invest more than $20,000 in inventory for these toys. How many units of each type of toys
should be stocked in order to maximize the monthly total profit?
What are the vertices? What are the constraints? What is the profit equation?
Answer:
10
Step-by-step explanation:
When it was raining, Elliott drove for 120 miles. When the rain stopped, he drove
20 mph faster than he did while it was raining. He drove for 300 miles after the
rain stopped. If Elliott drove for a total of 10 hours, how fast did he drive while it
was raining?
Answer:
[tex]\boxed{22}.[/tex]
Step-by-step explanation:
Since Elliott drove for a total of 10 hours, and he drove for 120 miles while it was raining and 300 miles after the rain stopped, we know that he drove for a total of 120 + 300 = <<120+300=420>>420 miles.
If he drove for a total of 10 hours and covered a distance of 420 miles, then his average speed was 420 miles / 10 hours = <<420/10=42>>42 mph.
Since Elliott drove 20 mph faster after the rain stopped than he did while it was raining, then we know that his speed while it was raining was 20 mph slower than his average speed of 42 mph. That means his speed while it was raining was 42 mph - 20 mph = <<42-20=22>>22 mph.
Find m/R.
P
(3x + 5)°
2
(8.x-12)
S
8x-12+3x+5=180(sum of straight angles)
8x+3x-12+5=180
11x-19=180
11x=180-19
11x=161
x=161÷11
Step-by-step explanation:
sum of straight angles are 180
What is the area when the diameter is 16?
201.06 square units (rounded to 2 decimal places) is the area of the given circle.
The formula for the area A of a circle is A = πr², where r is the radius of the circle and π is the famous, well-known irrational number pi equal to 3.14159 (rounded to 5 decimal places).
Given that the circle's diameter is 16, and that a circle's radius is equal to half its diameter, the following conclusions can be drawn:
r = d/2
= 16/2
= 8
A=πr2
AND HALF THE DIAMETER IS THE RADIUS (r)
r=8
A= πr2 = π (8) squared = 64 * π = 200.96
or,
Now, substituting the values of r and π into the formula for the area of a circle, we get
A = πr²
= (3.14159)(8²)
= (3.14159)(64)
= 201.06 square units (rounded to 2 decimal places) is the area of the given circle.
Learn more about the area of a circle at:
https://brainly.com/question/14068861
#SPJ4
heyy! i’ll give brainliest please help.
Answer:
The answer is B.
Step-by-step explanation:
Its B because the lower the altitude the higher the pressure, and in this case the air towards the ground is being moved up, which is letting cold air sink back down.
Does anyone know how to do this
The experimental probability of spinning a number less than 3.
7/25.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
The total number of spuns.
= 8 + 6 + 9 + 11 + 9 + 7
= 50
Total number of spuns of the spinner less than 3.
= 8 + 6
= 14
The probability of spinning a number less than 3.
= 14/50
= 7/25
Thus,
The probability is 7/25.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ1
Given: quadrilateral MATH; M(-5,-2), A(-3,2),
T(3,2) and H(1,-2)
Prove: MATH is a parallelogram
State the formula you will be using.
Show all work.
Answer:
MATH is not a parallelogram
Step-by-step explanation:
(sqrt means squareroot)
To prove that quadrilateral MATH is a parallelogram, we can use the following formula:
A quadrilateral is a parallelogram if and only if both pairs of opposite sides are congruent.
In other words, if the lengths of the sides opposite each other in a quadrilateral are the same, then the quadrilateral is a parallelogram.
To prove that MATH is a parallelogram, we need to show that both pairs of opposite sides are congruent.
The first pair of opposite sides consists of segment MA and segment TH. To show that these sides are congruent, we can use the Distance Formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points that define the line segment.
Substituting the coordinates of points M and A, we get:
d = sqrt((-3 - (-5))^2 + (2 - (-2))^2)
= sqrt((-3 + 5)^2 + (2 + 2)^2)
= sqrt(8^2 + 4^2)
= sqrt(64 + 16)
= sqrt(80)
= 8.944
Substituting the coordinates of points T and H, we get:
d = sqrt((1 - 3)^2 + (-2 - 2)^2)
= sqrt((-2)^2 + (-4)^2)
= sqrt(4 + 16)
= sqrt(20)
= 4.472
Since 8.944 is not equal to 4.472, we cannot conclude that MA and TH are congruent. Therefore, MATH is not a parallelogram.
What is the area of a rectangle with a length of 14.4 inches and a width that is one-third of the length?
A. 43.2 in.
B. 51.84 in.
C. 69.12 in.
D. 103.68 in.
If you give the answer, please make sure it is correct and one of the answers on the group of answer choices! Thank you! :)
The area of the rectangle is 69.12 square inches.
What is the area of the rectangle?
We know that for a rectangle of length L and width W, the area is given by the formula:
A = L*W
Here we know that the length is 14.4 inches, then:
L = 14.4 in
And the width is one-third of that length, then we can write:
W = (1/3)*L
Replacing the value of L, we will get:
W = (1/3)*14.4 inches
W = 4.8 inches.
Then the area of the rectangle is:
A= (4.8 in)*(14.4 in) = 69.12 in²
That is the area of the rectangle.
Learn more about areas by reading:
https://brainly.com/question/24487155
#SPJ1