729x¹⁵ + 1000
This is a case of a sum of cubes.
729 is the cube of 9
1000 is the cube of 10
x¹⁵ is the cube of x⁵
A sum of perfect cubes can be factored into
(a + b) (a² - ab + b²)
(9x⁵+ 10) ((9x⁵)²-(9x⁵)(10) + 10²)
(9x⁵ + 10) (81x¹⁰ - 90x⁵ + 100) THIS IS THE FACTORIZATION
9x⁵ (81x¹⁰ - 90x⁵ + 100) + 10(81x¹⁰ - 90x⁵ + 100)
729x¹⁵ - 810x¹⁰ + 900x⁵ + 810x¹⁰ - 900x⁵ + 1000
729x¹⁵ - 810x¹⁰ + 810x¹⁰ + 900x⁵ - 900x⁵ + 1000
729x¹⁵ + 1000
Which of the following equations is of a parabola with a vertex at (3, 0)?
Oy=x^2+3
o y=x^2-3
Oy= (x+3)^ 2
y=(x-3)^ 2
Answer:
D. y = (x - 3)²
Step-by-step explanation:
The parabola formula in vertex form is:
y = a(x - h)² + k
where the vertex is located at (h, k). Replacing with vertex (3, 0) we get:
y = a(x - 3)² + 0
y = a(x - 3)²
In all possible options the leading coefficient a is equal to one. Therefore:
y = (x - 3)²
1. Solve for w in the equation W/5 = 25
A.W = 5
B.W = 125
C. W = 30
D.W = 20
Answer: w = 125
Explanation: Since w is being divided by 5, to solve for w,
multiply both sides of the equation by 5.
On the left side, the 5's will cancel
and on the right side, 25(5) is 125.
So w = 125.
Please do not do this problem in your head.
Show the work that it takes to get w by itself.
90 POINT QUESTION!!!
A 13 ft ladder is resting on a wall. The angle the ladder makes with the floor is 45 degrees. How high off the ground is the top of the ladder?
Use the function y=13cos(theta) to find the answer
Answer: 9.19 ft
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.
Sin α = opposite side / hypotenuse
Where α is the angle of elevation of the ladder to the ground, the hypotenuse is the longest side of the triangle (in this case is the length of the ladder), and the opposite side (x) is the height of the top of the ladder above the ground.
Replacing with the values given:
Sin 45 = x/ 13
Solving for x
sin45 (13) =x
x= 9.19 ft
Feel free to ask for more if needed or if you did not understand something.
find the area of a shape shown
Answer:
the answer is 78
Step-by-step explanation:
3x6 is 18
4x3 is 12
4x3 is 12
6x6 is 36
added together it is 78
Use the data set to answer the question. {22,26,28,35,45,63,91} What is the mean absolute deviation (MAD) of the data set? Enter your answer as a number rounded to the nearest tenth, like this: 42.5
Answer:
[tex]M.A.D = 18.9[/tex]
Step-by-step explanation:
Given: 22,26,28,35,45,63,91
Required: Mean Absolute Deviation
The first step is to solve for the mean of the given data
[tex]Mean = \frac{\sum x}{n}[/tex]
where x->22,26,28,35,45,63,91 and n = 7
[tex]Mean = \frac{22+26+28+35+45+63+91}{7}\\Mean = \frac{310}{7}\\Mean = 44.29[/tex]
Then; subtract the calculated mean from each data
[tex]22 - 44.29 = -22.29\\26 - 44.29 = -18.29\\28 - 44.29 = -16.29\\35 - 44.29 = -9.29\\45 - 44.29 = 0.71\\63 - 44.29 = 18.71\\91 - 44.29 = 46.71[/tex]
Get Absolute Values of the above results
[tex]|-22.29| = 22.29\\|-18.29| = 18.29 \\|-16.29| = 16.29\\|-9.29| = 9.29\\|0.71| = 0.71\\|18.71| = 18.71\\|46.71|= 46.71[/tex]
Calculate the mean of the above result to get the M.A.D
[tex]Mean = \frac{\sum x}{n}[/tex]
[tex]M.A.D = \frac{22.29+18.29+16.29+9.29+0.71+18.71+46.71}{7}\\M.A.D = \frac{132.29}{7}\\M.A.D = 18.8985714286\\M.A.D = 18.9[/tex]
If g(x) = -4x + 5, find g(x+4).
Answer:
g(x + 4) = -4x - 11
Step-by-step explanation:
Since g(x) = -4x + 5, g(x + 4) = -4(x + 4) + 5
g(x + 4) = -4x - 11
Area of circle =
12 x square units
36 y square units
6 Square units
what is the slant height for given pyramid to the nearest to the whole unit?
A 7 cm
B 5 cm
C 9 cm
D 8 cm
Answer:
B 5 cm
Step-by-step explanation:
The bottom leg of the shaded triangle is 1/2 of the length of the side, so is 3 cm. The vertical leg of the shaded triangle is the height of the pyramid, given as 4 cm.
The slant height is the hypotenuse of the shaded triangle, so can be found from your knowledge of the 3-4-5 triangle, or from the Pythagorean theorem.
If s is the slant height, then ...
s^2 = 3^2 + 4^2 = 9 +16 = 25
s = √25 = 5
The slant height is 5 cm.
Classify the following triangle. Check all that apply.
Answer:
B.
F.
Step-by-step explanation:
Look at the angle. It is obtuse so the triangle is obtuse.
The sides are congruent so it is an isosceles.
Answer:
B,F
Step-by-step explanation:
sides are equal.
One angle=104°>90°
so itis an isosceles obtuse triangle.
Find the perimeter of a square that has a side that is 4.5 meters long.
Answer:
[tex]18m[/tex]
Step-by-step explanation:
[tex]P=4a=4*4.5=18m[/tex]
Answer:
Perimeter = 18m
Step-by-step explanation:
square = has four sides
P = perimeter
P = 4 · 4.5 = 18m
Perimeter = 18m
The recipe calls for 5 cups of strawberries for every 3 cups of whipped
cream. Write this comparison as a ratio.
OA) 5:3
OB) 3:5
OC) 5>3
OD) 3/5
Answer: OA) 5:3
Step-by-step explanation:
5:3
5 to 3. Or 5/3. Are the 3 ways that you.can write a ratio.
Answer:
OA, OB, OD
Step-by-step explanation:
It does depend on which side each number is on. If you are comparing the stawberries to whipped cream it would be 5:3 (OA).
But if you were to compare whipped cream to stawberries it would be 3:5 (OB) or 3/5 (OD)
PLEASE HELP WILL GIVE BRAINLIEST
Tell the slope and y-intercept of the graph of this linear equation
-3x + 2y = 8
(the slope is a fraction)
Answer:
The slope is 3/2 and the y intercept is 4
Step-by-step explanation:
We want to write in the form
y = mx+b where m is the slope and b is the y intercept
-3x+2y = 8
Add 3x to each side
-3x+3x+2y = 3x+8
2y = 3x+8
Divide each side by 2
2y/2 = 3x/2 + 8/2
y = 3/2x +4
The slope is 3/2 and the y intercept is 4
Consider the statement P: x + 9 = 10. Which of the following is an equivalent statement? Question 13 options: A) R: x > 0 B) Q: x – 9 = 10 C) S: x = 1 D) ∼P: x + 9 ≠ 10
Answer:
C) S: x = 1
Step-by-step explanation:
Answer:
C) S: x = 1
explination
Simplify by dividing 3/5 ÷ (-9/4)
Answer:
4/15
Step-by-step explanation:
You would have to multiply the fractions, but first reciprocate the dividend.
3/5 * 4/9
Multiply
3 * 4 = 12
5 * 9 = 45
12/45
Simplify using LCM, or the factor that applies to both sides which in this case is 3
12/3 = 4
45/3 = 15
The answer is 4/15
Answer:
4/-15
Step-by-step explanation:
[tex]\frac{3}{5}[/tex] ÷ [tex]\frac{-9}{4}[/tex]
Invert the second fraction and multiply
[tex]\frac{3}{5}[/tex] ×[tex]\frac{4}{-9}[/tex]
= [tex]\frac{12}{-45}[/tex]
Simplify:
=[tex]\frac{4}{-15}[/tex]
which choice is equivalent to the product below when x≥x
Answer:
B.
Step-by-step explanation:
If you dont understand what I wrote, just ask!
Answer:
B
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Given
[tex]\sqrt{6x^2}[/tex] × [tex]\sqrt{3x}[/tex]
= [tex]\sqrt{18x^3}[/tex]
= [tex]\sqrt{9(2)x^2(x)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex] × [tex]\sqrt{x^2}[/tex] × [tex]\sqrt{x}[/tex]
= 3 × [tex]\sqrt{2}[/tex] × x × [tex]\sqrt{x}[/tex]
= 3x × [tex]\sqrt{2}[/tex] × [tex]\sqrt{x}[/tex]
= 3x[tex]\sqrt{2x}[/tex] → B
Solve the equation using square roots.
[tex](x+2)^{2} = 36[/tex]
Answer:
x = 4, x = - 8
Step-by-step explanation:
(x+ 2)² = 36
√(x+2)² = + √36 √(x+2)² = -√36
x+2 = 6 x+2 = -6
x= 4 x = - 8
You accept a job as an environmental engineer that pays a salary of $45,000 in the first year. After the first year, your salary increases by 3.5% per year.
Write a rule giving your salary for your nth year of employment.
a ( n ) = ______
Answer:
a(n) = 45000 (1.035)n-1Answer:
a(n) is equal to $45,000
(1.035)n-1
Step-by-step explanation:
The length of a rectangle is given by x + 2 and its width is equal to 3. Give a simplified expression of the area of this rectangle.
Given:
Length,l = x + 2Breadth,b = 3To find out:
Find the area of rectangle?
Formula used:
Area of rectangle = length × breadth
Solution:
We know that,
Area of rectangle = length × breadth
= ( x + 2 ) × 3
= 3x + 6
Simplify the following expression 3^2/5 x 3^-7/5. I think it is 1/3. 3^-5/5
Answer:
1/3
Step-by-step explanation:
3^2/5 x 3^-7/5
We know that a^b* a^c = a^(b+c)
3^(2/5 -7/5)
3^ (-5/5) = 3^ -1
We know that a^-b = 1/ a^b
3^-1 = 1 / 3
What is f(5)
-8
-1
1
8
Answer:
f(5) = -8
Step-by-step explanation:
f(5) is the output value when the input value is 5
Reading the chart,
f(5) = -8
peta has 4 friends now. last year she had 12. what is the percent of change?
Answer:
we simply see 4 has multiplied by -3
-12 = 4 x -3
This becomes -300%
We then add the 100 = initial amount onto a negatove percentage = -300 +100 = -200% change.
Step-by-step explanation:
3.00 x 4 = 12
4 + 8 = 12
4 x -2.00 = -8 being the change. The answer is -2.00 = -200%
Shows part of the answer and proves the answer is -200%
The rectangular prisms below have the same size and shape.
What is the combined volume, in cubic inches, of the prisms?
A: 8
B: 16
C: 32
D:64
sarah wants to open up her own coffee shop. It costs her $3 to make each cup of coffee, plus she has to pay a $24 renter's fee for her shop. She sells the coffee for $5 per cup. How many cups of coffee does she has to sell before she can start making a profit? *
Answer:
5
Step-by-step explanation:
So you divide 24 by 5 and you get 4.8 so you round it up to 5
What is the maximum value?
Answer:
the maximum value is 3
Step-by-step explanation:
The maximum value of the function y = -2+5sin(pi/12(x-2)) is determined by taking the first derivative of the function. The first derivative is equal ( 5 pi/ 12 )* sin ((pi/12) (x-2)) = 0. x is equal to 4472 through the calculator. Substituting to the original equation, the maximum value is 3.
why are triangles congruent ?
Explanation:
Basically triangles are congruent when they have the same shape and size.
Two triangles are congruent if they have :
exactly the same three sides and
exactly the same three angles.
Tips Area :
If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent too :)
If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent too ;)
If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent too ^^
Hope that help :)
Please help with this
Answer:
x=35
Step-by-step explanation:
When a is parallel to b, the two angles will add to 180
x+ 3x+40=180
Combine like terms
4x+40 =180
Subtract 40 from each side
4x= 180-40
4x= 140
Divide by 4
4x/4 = 140/4
x=35
What is the x-coordinate of the solution to the following system of equations? x − 2y = 2 3x + y = 6 x = −2 x = 0 x = 2 x = 3
Answer:
Answer C. x = 2
Step-by-step explanation:
Given:
x − 2y = 2
3 * ( x ) + y = 6
You need to group the x-coordinates of the system of equations.
Rewrite x − 2y = 2 , in such a way that it starts with x =...
x = 2y + 2
Substitute x = 2y + 2 in 3 * ( x ) + y = 6, which gives:
3 * ( 2y + 2 ) + y = 6
6y + 6 + y = 6
7y = 0
y = 0
Substitute y = 0 in x = 2(y) + 2 gives x = 2*0 + 2
So x = 2, which is answer C.
x - 6x + 2x - 2x
x - 6x + 0
-5x
The x-coordinate of the solution to the following system of equations x − 2y = 2 and 3x + y = 6 is x = 2. Option c is correct.
system of equations is given as,
x − 2y = 2 - - - - (1)
3x + y = 6 - -- - - -(2)
x coordinate of the solution to the following system of equations to be determined.
the equation is the relationship between variables and is represented as a polynomial equation.
x − 2y = 2 - - - - (1)
3x + y = 6 - -- - - -(2)
From equation 1
x = 2y +2
put x in equation 2
3 (2y + 2) + y = 6
6y + 6 + y = 6
7y = 0
y = 0
Put y = 0 in x = 2y + 2
x = 2(0) + 2
x = 2
Thus, The x-coordinate of the solution to the following system of equations x − 2y = 2 and 3x + y = 6 is x = 2.
Learn more about the equation here:
brainly.com/question/10413253
#SPJ2
A piggy bank contains only nickels, dimes, and quarters. There is a total of 105 coins and the total value of those coins is $10.75. Find a general solution of the number of each coin. List three possible specific solutions.
Which is a characteristic of a studio apartment?
a)typically has multiple bedrooms
b)has multiple floors
c)has multiple units in the same building
d)has one room for the kitchen, living room, and bedroom
Answer:d
its a apartment thats just one big room
How many yellow-collared macaws would
have a combined mass of 1 kilogram?
PLS HELP BEST ANSWER GETS BRAINLESST AND A FOLLOW
