Answer:
This polynomial can be simplified to a difference of squares
[tex]16a^2 - 4a + 4a - 1=(4a-1)(4a+1)[/tex]
Step-by-step explanation:
Simplify the expression
[tex]16a^2 - 4a + 4a - 1\\\\16a^2- 1[/tex]
remember that 4 ^ 2 = 16
Therefore
[tex]16a^2- 1= 4^2a^2 -1[/tex]
Remember that
[tex](4a) ^ 2 = 4 ^ 2a ^ 2[/tex]
[tex]4^2a^2 -1=(4a)^2 -1[/tex]
As [tex]1 ^ 2 = 1[/tex] then
[tex](4a)^2 -1= (4a)^2 -1^2[/tex]
Remember that [tex]c ^ 2 -b ^ 2 = (c + b) (c-b)[/tex]
In this case [tex]c = 4a[/tex] and [tex]b = 1[/tex]
Finally
[tex](4a)^2 -1^2 = (4a-1)(4a+1)[/tex]
3/4n-18=1/4n-4 can someone answer this please
Answer:
n = 28
Step-by-step explanation:
3/4n - 18 = 1/4n - 4 (eliminate fractions by multiplying each value by 4)
(3/4n * 4) - (18 * 4) = (1/4n * 4) - (4 * 4)
3n - 72 = 1n - 16 (move values with variable to same side)
3n - 1n - 72 = 1n - 1n -16
2n - 72 = -16 (move numeric values to same side)
2n - 72 + 72 = -16 + 72
2n = 56 (isolate n by dividing out the 2)
2n/2 = 56/2
n = 28
40 points | Sierra and Alek each have five cousins. Their ages are listed below.
Sierra’s cousins: 2, 11, 12, 13, 15
Alek’s cousins: 9, 11, 11, 12, 13
Which of the following statements is true?
A.For both sets of data, the median is equal to the mean.
B.The ages of Sierra's cousins are more spread out than those of Alek's cousins.
C.The mean age of Sierra's cousins is greater than that of Alek's cousins.
D.There are no outliers.
Find the mean for both:
Sierra: 2 + 11 + 12 + 13 + 15 = 53
53/5 =10.6
Median is the middle value = 12
Alek: 9 + 11 + 11 + 12 + 13 = 56
56/5 = 11.2
Median = 11
A: The medians do not equal the mean.
B: Sierra's are more spread out, ( no identical ages and a greater range ).
C: Sierra's mean is less than Alek.
D. Sierra has an outlier (2).
The answer would be B
Which of the following is the solution to 3/x + 2/(x+1) = 3/5x?
-11/6
-6/11
11/6
6/11
Answer:
3/x + 2/(x+1) = 3/5x
[3 · 5(x + 1) + 2 · 5x] / 5x(x + 1) = 3(x + 1) / 5x(x + 1)
3 · 5(x + 1) + 2 · 5x = 3(x + 1)
15x + 15 + 10x = 3x + 3
15x + 10x - 3x = -15 + 3
22x = -12
x = -12/22 = -6/11
The diameter of a circular tablecloth is 72 inches. Find the area and circumference. Use 3.14 as an approximation for pi.
Please show work
Answer:
Part 1) The area is [tex]A=4,069.44\ in^{2}[/tex]
Part 2) The circumference is [tex]C=226.08\ in[/tex]
Step-by-step explanation:
step 1
Find the area
we know that
The area of a circle (circular tablecloth) is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=72/2=36\ in[/tex] ------> the radius is half the diameter
[tex]\pi =3.14[/tex]
substitute
[tex]A=(3.14)(36)^{2}[/tex]
[tex]A=4,069.44\ in^{2}[/tex]
step 2
Find the circumference
we know that
The circumference of a circle (circular tablecloth) is equal to
[tex]C=\pi D[/tex]
we have
[tex]D=72\ in[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]C=(3.14)(72)[/tex]
[tex]C=226.08\ in[/tex]
Find the value of x in the figure below. Round to the nearest tenth.
Answer:
The correct answer option is 20.3.
Step-by-step explanation:
We are given a right angled triangle with one known angle and one known side length and we are to find the value of x.
To find the value of x, we will use the appropriate trigonometric ratio.
[tex] sin 5 2 = \frac { x } { 2 5 . 8 } [/tex]
[tex] x = sin 52 \times 2 5 . 8 [/tex]
x = 20.3
Answer:
20.3Step-by-step explanation:
Use the sine:
[tex]sine=\dfrac{opposite}{hypotenuse}[/tex]
We have
[tex]opposite=x,\ hypotenuse=25.8,\ \sin52^o\approx0.788[/tex]
Substitute:
[tex]\dfrac{x}{25.8}=0.788[/tex] multiply both sides by 25.8
[tex]x\approx20.3[/tex]
f and f^-1 are functions
If f(4)=2, then f^-1(2)=?
Step-by-step Answer:
f and f^(-1) are inverses of each other within a specified domain, with the property that
y=f(x) <=> (is equivalent to) f^(-1)(y)=x
since
2=f(4), by the definition of inverse functions, f^(-1)(2) = 4
-4, -2, -2 hope that will help you
Step-by-step explanation:
Solve the proportion below. X/6=6/4 x=?
Answer:
x=9
Step-by-step explanation:
We have been given the following proportion;
x/6 = 6/4
In order to solve for x, we simply make x the subject on the left hand side;
To do this we multiply both sides by 6,
(x/6)*6 = (6/4)*6
x = 36/4
x = 9
The value of x is thus 9
if you simplify the answer you get its x=9
What percent is equivalent to 3/10? 0.3% 3% 10% 30%
Answer:
30%
Step-by-step explanation:
I really need help to graduate!
Answer:
option 1 is correct:
y = -5cos(2x - π)
............................................................h............................................................help............................................................
Answer:
D (136 -2a) + (3a+39) = 180
Step-by-step explanation:
Since XQR = 180
<XQM + < MQR = XQR
136 -2a + (3a+39) = 180
A ball is thrown from first base to second base and then from second base to home plate. How many feet has the ball been thrown?
A. 90 √2
B. 90 + 90 √2
C. 180 √2
D. 270 √2
Answer:
B. 90 + 90 √2
Step-by-step explanation:
From first base to the second base, it will travel 90 feet.
From the second base to the home plate, it will travel a longer distance. How much? Well, if you look at the layout of the field, you'll see that if you draw a line from second base to the home plate, you'll form two rectangular triangles, one with the 1st base, another one with the 3rd base.
The line from the 2nd base to home plate is the hypotenuse, which we can easily find by:
h²=90² + 90²
h = √(2 * 90²)
h = 90 √2
So, from second base to home plate, the ball has traveled 90 √2
Overall: 90 + 90 √2
determine the missing side lenght of a right triangle when given a=14 and b=7
Answer:
√245 or 15.65247...
Step-by-step explanation:
a² + b² = c²
14² + 7² = c²
196 + 49 = c²
245 = c²
√245 ≈ c
When you have a right triangle, you can use the Pythagorean Theorem to find the missing side length. (but it only works for RIGHT triangles)
Pythagorean Theorem:
a² + b² = c² Since you know a=14 and b=7, plug it into the equation
(14)² + (7)² = c²
196 + 49 = c²
245 = c²
√245 = c or 15.6524758425 = c
a fair die is tossed four times. Find the probability of obtaining each of the following. 5 on all four tosses
Answer:
[tex]\dfrac{1}{1296}[/tex]
Step-by-step explanation:
When a fair die is tossed once, there are 6 possible outcomes: 1, 2, 3, 4, 5, 6.
The probability of rolling 5 is [tex]\dfrac{1}{6}.[/tex]
When a fair die is tossed four times, the probability of rolling 5 all four times is
[tex]\dfrac{1}{6}\cdot \dfrac{1}{6}\cdot \dfrac{1}{6}\cdot \dfrac{1}{6}=\dfrac{1}{6^4}= \dfrac{1}{1296}[/tex]
What are the coordinates of point B?
A. (1.3)
B. ( 3.1)
C.(-3.1)
D.(1.-3
B is the correct answer
y=5x Identify the dependent and independent variables.
Independent is x. Dependent is y
Answer:
Independent : x
Dependent: y
Step-by-step explanation:
y= 5x
The independent variable is the variable we change
Independent : x
The dependent variable depends on the value of the other variable
Dependent: y
What is the measure of
60°
50°
65°
70°
Answer:
∠G = 50°
Step-by-step explanation:
The measure of the angle between the 2 tangents is
[tex]\frac{1}{2}[/tex] ( major arc - minor arc )
minor arc HF = 130° and major arc HF = 360° - 130° = 230°
Hence
∠G = 0.5(230° - 130°) = 0.5 × 100° = 50°
solve the equation for t.
1/2 t +8 = 5/2 t - 10
Simplif 1/2t to t/2
t/2 + 8 = 5/2t - 10
Simplify 5/2t to 5t/2
t/2 + 8 = 5t/2 - 10
Multiply both sides by 2
t + 16 = 5t - 20
Subtract t from both sides
16 = 5t - 20 - t
Simplify 5t - 20 - t to 4t - 20
16 = 4t - 20
Add 20 to both sides
16 + 20 = 4t
Simplify 16 + 20 to 36
36 = 4t
Divide both sides by 4
36/4 = t
Simplify 36/4 to 9
9 = t
Switch sides
t = 9
Answer:
t = 9.
Step-by-step explanation:
1/2 t + 8 = 5/2 t - 10
- 8 -5/2 t
1/2 t - 5/2 t = -10 - 8
-2t = -18
t = 9.
11. Find three consecutive odd integers such that their sum decreased by
the second equals 50.
The numbers you are looking for are 23, 25, and 27. Let's start by defining a variable. Let x be the first of the three odd numbers. Since odd numbers are 2 apart, that means that the other two numbers are x + 2 and x + 4.
Now, their sum is x + (x + 2) + (x + 4) which equals 3x + 6.
Decrease that by the second number, x + 2. That means: 3x + 6 - (x + 2), which is equal to 2x + 4.
So now we know that 2x + 4 = 50, and we can solve that easily:
2x + 4 = 50
2x = 46
x = 23
Therefore, the three odd numbers are 23, 25, and 27. Hope this helps! Please mark Brainliest. Thank you v much! :)
The answer to the problem is the three consecutive odd integers 23, 25, and 27.
Explanation:Let's solve the problem step by step. We are looking for three consecutive odd integers. A useful way to express consecutive odd integers algebraically is as x, x+2, and x+4, where x is any odd integer.
The problem states that the sum of these integers minus the second one equals 50. This provides the equation: x + (x+2) + (x+4) - (x+2) = 50. Simplifying this equation, we get 2x + 4 = 50. We can further simplify to find that x = 23.
So, the three consecutive odd integers are 23, 25, and 27.
Learn more about Consecutive Odd Integers here:https://brainly.com/question/32448319
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Find the maximum/minimum value.
y= -2x2 - 16x - 29
Final answer:
The maximum value of the quadratic function y = -2x^2 - 16x - 29 is 3, occurring at x = -4, found by determining the vertex of the parabola, which opens downwards due to the negative coefficient of the x^2 term.
Explanation:
To find the maximum or minimum value of the quadratic function y = -2x² - 16x - 29, we can utilize the properties of parabolas. Since the coefficient of the x² term is negative, the parabola opens downwards, meaning the vertex will give us the maximum value. The vertex of a parabola given by y = ax² + bx + c is found at the x-coordinate x = -b/(2a). Substituting the values from the given equation:
x = -(-16)/(2*(-2)) = -16/(-4) = -4
Now, we substitute this value back into the original equation to find the y-coordinate of the vertex:
y = -2(-4)² - 16(-4) - 29
y = -2(16) - 64 - 29
y = -32 + 64 - 29
y =3
Therefore, the maximum value of the function is 3, and it occurs at x = -4.
On January 1, 2010, Lucita bought a car for $25,000. If the car depreciates at a rate of 15% per year, which equation can find the value of the car on December 31, 2017?
Answer:
Equation that can find the value of the car on December 31, 2017 is:
A= 25000*(1-0.15)^7 and the value of car after 7 years is $8014.427.
Step-by-step explanation:
Price of car = $ 25,000
Rate of depreciation = 15 %
Formula used:
A= P(1-r)^n
where p= price of car
A= new price of car after depreciation
r = rate of depreciation i.e. 15/100 = 0.15
n= time in years 2017 - 2010 = 7 years
Putting values in formula:
A= 25000*(1-0.15)^7
A= 25000*(0.85)^7
A= $8014.427
So, Equation that can find the value of the car on December 31, 2017 is:
A= 25000*(1-0.15)^7 and the value of car after 7 years is $8014.427.
Answer:
The pattern is pretty clear. After $n$ years, in $200n$ the price will be:
$a_n= a_0(0.85)^{n-1}$
Step-by-step explanation:
In the formula I=P·r·t, what does P stand for? a. Percent: the interest rate expressed as a percentage b. Principal: the amount of money you initially invested c. Period: how often the interest is calculated d. Payout: how much money you end up with
Answer:
B) Principal: the amount of money you initially invested
Step-by-step explanation:
The given formula I=P·r·t is of Interest
In this formula
I is simple interest
r is the interest rate
t is the amount of time
P is the principle amount invested on which interest is calculated
hence of the given options, option b is correct i.e.
Principal: the amount of money you initially invested !
Answer: Option 'b' is correct.
Step-by-step explanation:
Since we have given that
[tex]I=\dfrac{P\times R\times T}{100}[/tex]
Here, I stands for Simple interest
R stands for rate of interest
T stands for time period
P stands for the principal amount i.e. the amount of money you initially invested.
Hence, Option 'b' is correct.
Solve the inequality and graph the solution on a number line
Answer:
[tex]y\leq -1/3[/tex]
The graph in the attached figure
Step-by-step explanation:
we have
[tex]-3(5y-4)\geq 17[/tex]
Applying the distributive property on the left side
[tex]-15y+12\geq 17[/tex]
Subtract 12 both sides
[tex]-15y\geq 17-12[/tex]
[tex]-15y\geq 5[/tex]
Multiply by -1 both sides
[tex]15y\leq -5[/tex]
Divide by 15 both sides
[tex]y\leq -5/15[/tex]
Simplify
[tex]y\leq -1/3[/tex]
The solution is the interval -------> (-∞, -1/3]
All real number less than -1/3
In a number line the solution is the shaded area down of y=-1/3 (close circle)
The graph is the attached figure
Which of the following are exterior angles? Check all that apply.
The correct answers are: C. Angle 4 F. Angle 6 In mathematics, exterior angles are formed outside between any side of a shape and a line extended from the next side.
The correct answer is option C and F.
In a triangle, the sum of the measures of the interior angles is always 180 degrees. Since angles 5, 3, and 1 are interior angles, their sum is 180 degrees.
The sum of the measures of the exterior angles of a triangle is always 360 degrees. Therefore, the sum of exterior angles 4, 6, and 2 is also 360 degrees.
Now, to determine the individual measures of the exterior angles, we know that the sum of the measures of the linear pairs (an exterior angle and its adjacent interior angle) is 180 degrees.
Therefore, angle 4 is an exterior angle since it forms a linear pair with angle 1.
Similarly, angle 6 is an exterior angle since it forms a linear pair with angle 3.
Angle 2 is not an exterior angle since it does not form a linear pair with any other angle in the given triangle.
So, the correct answers are:
C. Angle 4
F. Angle 6
Learn more about Exterior angles here:
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The mean height of plants is 18 inches. The height of seven plants are 12 inches, 13 inches, 15 inches, 15 inches, 17 inches, 23 inches, and 24 inches. Find the height of the eighth plant.
Answer:
25 inches
Step-by-step explanation:
i first started with 18×8=144 then i did 144-119 and got 25.
Lines kand n are perpendicular. If the slope of line k is -6, what is the slope of
line n?
Answer:
B
Step-by-step explanation:
The slope would be 1/6
The playlist consists of 21 songs by The Working Mamas, 12 songs by Chef Mo Cheese, 36 songs by the Snippers, 54 by Lucy and The Jungle Cats, and 27 by Nuestra Paradise. If her playlist randomly shuffles through each song, what is the probability of The Working Mamas being played? Write the answer as a percent.
Answer:
14%
Step-by-step explanation:
Answer:
The answer is 14%
Step-by-step explanation:
What is bigger 2/4 or 1/8
I think that 2/4 would be bigger because 2/4 is the same as 1/2 and 1/2 is bigger than 1/8. Imagine a pizza, if i have 1/2 of a whole pizza i would have more pizza than a friend who had 1/8 of the whole pizza.
I hope this helps :)
If you simplify 2/4, you will get 1/2. 1/2 is bigger than 1/8.
Proof:
Draw 2 mental circles in your head. then draw lines that will make the circles out of 2 and out of 8. Now color in 1/2 of the first circle and 1/8 of the second circle. You can see that the 1/2 is bigger than the 1/8.
Hope I helped, sorry if I'm wrong ouo.
~Potato.
Copyright Potato 2019.
Jim has a bag of marbles. In the bag are 12 red, 10 blue, 15 white, and 13 black marbles. Without looking he pulls a marble out of the bag. What is the probability he pulls a white marble? Enter your answer as a decimal.
Answer:
0.3
Step-by-step explanation:
In the bag are 12 red, 10 blue, 15 white, and 13 black marbles.
So total = 12 + 10 + 15 + 13 = 50 marbles
The probability he pulls a white marble = 15/50 = 0.3
Harold has 4 cups of trail mix. He wants to give 1/3 cup trail mix to each camper in his group.There are 8 campers in his group. Does he have enough trail mix for all the campers?Explain.
What is the probability of you picking an odd number from 75 to 100?
Step-by-step explanation:
Odd numbers are any numbers that end with 1, 3, 5, 7, 9.
Out of the numbers inbetween 75 & 100, the odd numbers are:
75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99,
which makes 13.
Set the amount of numbers you got over the total amount.
13/27
You have a 13/27, or 48.15% chance of picking an odd number.
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