Answer:
Step-by-step explanation:
The difference quotient in general looks like
[tex]\frac{f(x+h)-f(x)}{h}[/tex] Sometimes the symbol "delta x" [tex]\Delta x[/tex] is used instead of h.
For the exponential function, the difference quotient is
[tex]\frac{e^{x+h}-e^x}{h}[/tex]
Answer:
For those who dont want to read, its A.
Step-by-step explanation:
Edge 2021
24
÷
6
+
39
÷
3
+
19
?
Answer:
36
Step-by-step explanation:
=4+13+19
=17+19
=36
Answer:
Pemdas
Step-by-step explanation:
24/6 = 4
39/3 = 13
4 + 13 + 19 = 36
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:
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.
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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.
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
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:
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?
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The three steps which Patel could use to solve the quadratic equation include the following:
A. 8(x² + 2x + (2/2)²) = -3 + 8.
B. x = -1 ±√5/8
E. 8(x² + 2x) = -3.
How to solve the quadratic equation?In order to solve the given quadratic equation, we would use the completing the square method as follows;
Separating the variables in the quadratic equation from constant, we have the following;
8x² + 16x + 3 = 0
8x² + 16x = -3
By factorizing the common variables in the quadratic equation from constant, we have the following;
8(x² + 2x) = -3 (step 1).
By completing the squares in the brackets and then balancing the expression on the right-hand side, we have the following;
8(x² + 2x + (2/2)²) = -3 + 8 (step 2).
8(x² + 2x + 1) = -3 + 8
8(x + 1)² = 5
Dividing both sides of the quadratic equation by 8, we have the following;
(x + 1)² = 5
Taking the square root of both sides of the quadratic equation, we have the following;
(x + 1) = ±√5/8
x = -1 ±√5/8 (step 3).
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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.
If pentagon OPQRS is dilated by a scale factor of from the origin to create O'P'Q'R'S', what is the ordered pair of point S'
Option (D) that is (3.5, 8.75) is the ordered pair of point S.
What is ordered pair?An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order. It aids visual comprehension by locating a point on the Cartesian plane. An ordered pair's numeric values can be integers or fractions. Two variables are frequently represented by ordered pairs. We mean x = 7 and y = -2 when we write (x, y) = (7, -2). The x-coordinate is the number that corresponds to the value of x, and the y-coordinate is the number that corresponds to the value of y.
Here,
The ordered pair of point S is option (D), which is (3.5, 8.75).
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Complete question: Pentagon OPQRS is shown on the coordinate plane below:
Pentagon OPQRS on a coordinate plane with ordered pairs at O negative 1, 2, at P negative 5, 3, at Q negative 3, negative 2, and R 2, 1, at S 2, 5.
If pentagon OPQRS is dilated by a scale factor of seven over four from the origin, to create O’P’Q’R’S’, what is the ordered pair of point S’?
Margo borrows $700, agreeing to pay it back with 8% annual interest after 16 months. How
much interest will she pay?
After 16 months, Margo will pay $74.67 interest
We know that the simple Interest Formula
I = P × r × t
Where: P = Principal Amount
I = Interest Amount
R = Rate of Interest as a percent
r = Rate of Interest in decimal
r = R/100
t = Time Periods involved
Here we have been given P = $700, t = 16 months and R = 8%
First we convert interest rate R percent to r a decimal
r = R/100
= 0.08 per year,
Now we convert time from months to years .
16 months ÷ 12 months/year
= 1.333333 years,
Using above formula of simple interest,
I = P × r × t
I = 700 × 0.08 × 1.333333
I = $ 74.67
Hence, the simple interest accumulated on a principal of $ 700.00 at a rate of 8% per year for 16 months is $ 74.67.
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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!
it takes 32 pounds of seed to completely plant a 5 -acre field. How many acres can be planted per pound of seed?
The number of acres that can be planted per pound of seed is 0.16.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
32 pounds = 5-acre field
Divide 32 into both sides.
1 pound = 5/32 acre field
1 pound = 0.16 acre field
Thus,
0.16-acre field can be planted per pound of seed.
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Find the surface area and volume of the following figure. Round to nearest hundredth. Used 3.14
Answer:
Surface area of cylinder = 250.94 yd², Volume = 305.20yd³
Step-by-step explanation:
Formula for the total surface area of a cylinder is T. S. A. =2πrh+2πr²
T. S. A. =2πrh+2πr²
π=3.14 , h=7.1, r = 3.7
T. S. A. = 2(3.14)(3.7)(7.1) + 2(3.14)(3.7)²
T. S. A. = 250.94 yd²
----------------------------------------------------------------------------------------------------------------
V=πr²h
V = (3.14) (3.7)²(7.1)
V= 305.20 yd³
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:
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 name of longest side of triangle?
Answer: Hypotenuse
Step-by-step explanation:
The Hypotenuse is known as the longest side of a triangle.
Draw the image of quadrilateral ABCD under the translation (x, y) to (x-7, y+1).
help me please!
What does r equal?
Answer: r = ________
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]
Classify each statement about the function f(x)=2x^3+8 as true or false.
The domain of the function is all real numbers.
The domain of the function is all real numbers.
The range of the function is (0, [infinity]).
The y-intercept is (0, 0).
The center of symmetry is (0, 8)
Statement A,B is true rest all statement are false about the given function.
Given the function: [tex]2x^3+8[/tex]
Statement A:
The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value).
For the function 2x^3 + 8, the domain is all real numbers, which is represented as (-infinity, +infinity).
It is because the expression inside the function, 2x^3, is defined for all real numbers.
so above statement is true.
Statement B:
statement A and B are same so it's also true.
Statement C:
The range of a function is the set of all possible output values (y-values) that the function can produce.
For the function 2x^3 + 8, the range is also all real numbers (-infinity, +infinity)
It is because the function is a polynomial of odd degree (3) and it does not have any restriction on the output value. Since the function does not have any restriction, it can take any real number as an output value and thus the range is all real numbers.
so this statement is false.
Statement D:
The y-intercept of the function 2x^3 + 8 is 8. It is the point at which the graph of the function crosses the y-axis, which occurs when x = 0. So when x = 0, y = 2(0)^3 + 8 = 8.
so this statement if false.
Statement E:
A function has a center of symmetry if it is unchanged (i.e. is symmetric) when reflected across a line or point. The line or point across which the function is symmetric is called the axis of symmetry or center of symmetry.
The function 2x^3 + 8 does not have a center of symmetry. It is because the function is a polynomial of odd degree and it does not have any symmetry. The polynomials of odd degree are not symmetric about any point or line.
So this statement is also false.
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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
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?
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help pls! Given m||n, find the value of x.
(4x-6)
(8x-6)
Answer:
To find the value of x that makes the expression (4x-6) equal to (8x-6). To do this, you can set the two expressions equal to each other and solve for x:
4x - 6 = 8x - 6
4x = 8x
4x - 8x = 0
-4x = 0
x = 0
So, the value of x that makes (4x-6) equal to (8x-6) is x=0.
Answer:
-4x = -12 Divide each side by '-4'.
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:
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
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.
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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.
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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
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.