Answer:
[tex]a = \{1,4,9,16,25,36,49,64,81,100\}[/tex]
Step-by-step explanation:
Given
[tex]ax^2 - 64[/tex]
Required
Determine possible values of a
For the expression to be a difference of two squares, then a must be a perfect square between 1 and 100 (inclusive).
Let [tex]a = k^2[/tex] where [tex]k \ge 1[/tex]
When k = 1
[tex]a = 1^2 = 1[/tex]
k = 2
[tex]a = 2^2 = 4[/tex]
k=3
[tex]a = 3^2 = 9[/tex]
It goes on until k = 10
[tex]a = 10^2 = 100[/tex]
So, the possible values of a are:
[tex]a = \{1,4,9,16,25,36,49,64,81,100\}[/tex]
25/35 Marks
Find the midpoint of A and B where A has coordinates (8, 2)
and B has coordinates (3,8).
Answer:
[tex]\displaystyle (\frac{11}{2},5)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Midpoint Formula: [tex]\displaystyle (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Step-by-step explanation:
Step 1: Define
Point A(8, 2) → x₁ = 8, y₁ = 2
Point B(3, 8) → x₂ = 3, y₂ = 8
Step 2: Find Midpoint
Simply plug in your coordinates into the midpoint formula to find midpoint
Substitute in points [Midpoint Formula]: [tex]\displaystyle (\frac{8+3}{2},\frac{2+8}{2})[/tex][Midpoint] [Fraction] Add: [tex]\displaystyle (\frac{11}{2},\frac{10}{2})[/tex][Midpoint] Divide: [tex]\displaystyle (\frac{11}{2},5)[/tex]Benjamin uses a $20 bill to pay for his lunch. He received more than $5 in change. Which number line shows the possible cost of Benjamin's lunch?
Answer:
i dont see a number line, attach a pic pls
Step-by-step explanation:
Write the polynomial in standard form: x^2+4-3x
Answer:
x^2-3x+4
Step-by-step explanation:
explain what the Diameter is and how is the radius related to it.
What can the radius and Diameter help us find?
Answer:
The diameter is any straight line that passes through the center of the circle, which endpoints can lie on. The radius is half the diameter. They help us find the circumference of a circle
Answer:
The diameter is the length of the line through the center that touches two points on the edge of the circle. It is related to the radius because whatever the diameter is is double what the radius is. In differential geometry, the diameter is an important global Riemannian invariant.
Step-by-step explanation:
Explain how to do this please!
Answer:
4 children per counselor
Step-by-step explanation:
Since the question is asking children per counselor, divide the children/counselor. Check all of the rows by dividing the children by counselor to make sure the constant of proportionality is correct. If you divide correctly, the constant of proportionality you get is 4.
Hope it helps!
Answer:
there is 4 students per conceler.
Step-by-step explanation:
please mark as brainllist.
: Susan bought a 6-month $1,400 certificate of deposit. At the end of 6 months, she
received $126 simple interest. What annual rate of interest did the certificate pay?
-6p-3=9 what does p equal
Answer:
-2
Explanation:
-6 x -2 = 12
12 - 3 = 9
Answer:
p=-2
Step-by-step explanation:
Move the -3 to the other side by adding 3 on both sides:
-6p-3+3=9+3
The equation now looks like this:
-6p=12
Divide -6 on both sides:
-6p/-6=12/-6
The equation now looks like this:
p=-2 which is the answer
Hope this helps!
-(x-3)=-7 I need help with this equation
Answer:
x = 10
Step-by-step explanation:
Given
- (x - 3) = - 7 ( divide both sides by - 1 )
x - 3 = 7 ( add 3 to both sides )
x = 10
me need help whit math
Answer:
0.39%
hope this helps
A circle has a diameter of 6ft. What is the area of the circle?
Very easy!! (i think-_-) A≈28.27 ft2 :))
Adding up inches in a perimeter
Answer:
To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width).
Step-by-step explanation:
Mariah ordered 50 beads. 8 of the beads were blue. What percent of the beads were blue?
Answer:
16%
Step-by-step explanation:
Hope this helps :D
What is the perimeter of this figure
40 in.
10 in.
50 in.
18 in.
Answer:
236
Step-by-step explanation:
100+100+36=236
Answer:
C. 180
Step-by-step explanation:
)Suppose is a real number with 0 < < 4 . Set = sin( − ), = cos( + ), = sin( − ), and = cos(2 − ). Arrange the values , , , and in increasing order, and explain how you determined their order.
Answer:
b < c < a < d
Step-by-step explanation:
P.S - The exact question is -
Given - Suppose x is a real number with 0 < x < [tex]\frac{\pi }{4}[/tex] . Set a = sin([tex]\pi[/tex] - x) ,
b = cos([tex]\pi[/tex] + x) , c = sin( x - [tex]\pi[/tex]) , d = cos(2[tex]\pi[/tex] - x)
To find - Arrange the values of a, b, c, d in increasing order , and explain
how you determined their order.
Proof -
Firstly draw a unit circle where you indicate the following
A = ( cos(x), sin(x) )
B = ( cos( [tex]\pi[/tex] - x) , sin ([tex]\pi[/tex] - x) )
C = ( cos([tex]\pi[/tex] + x), sin ([tex]\pi[/tex] + x) )
D = ( cos (2[tex]\pi[/tex] - x) , sin (2[tex]\pi[/tex] - x) )
As we have given that 0 < x < [tex]\frac{\pi }{4}[/tex]
⇒sin (x) and cos(x) are positive and sin(x) < cos(x)
The figure is as follows :
Now
By seeing point B , we can say that
sin ([tex]\pi[/tex] - x) = sin (x) = a
By seeing point C , we can say that
cos([tex]\pi[/tex] + x) = -cos (x) = b
By seeing point C , we can say that
sin( x - [tex]\pi[/tex]) = -sin(x) = c
By seeing point D , we can say that
cos(2[tex]\pi[/tex] - x) = cos(x) = d
As sin(x) < cos(x) ⇒ a < d
-sin(x) > -cos(x) ⇒ c > b ⇒ b< c
and as we know that -sin(x) < sin(x) ⇒ c < a
∴ we get
b < c < a < d
Solve the system of equations.
- 5y + 8x = -18
5y + 2x = 58
х=
y =
Answer:
x = 4 and y = 10
Step-by-step explanation:
-5y + 8x = -18
5y + 2x = 58
First you will want to get rid of y from both equations, so you add both equations together.
You will get 10x = 40, then subtract 10 from both sides and you get x = 4.
Now substitute x as 4 in any of the equations to get y.
-5y + 32 = -18
-5y = -50
y= 10
Answer:
x = 4
y = 10
A pilot is traveling at a height of 30,000 feet above level ground. She looks down at
an angle of depression of 6° and spots the runway. As measured along the ground, how
many miles away is she from the runway? Round to the nearest tenth of a mile.
Answer:
540.6 mi
Step-by-step explanation:
The angle of depression = angle of elevation = 6°
Let x = the distance to the runway.
tan 6 = 30000/x
xtan 6 = 30000
x = 30000/tan 6 =285430.9 ft
285430.9336.../5280 = 540.6 mi
A pilot is flying 30,000 feet above the surface of the earth. She notices the runway when she looks down at a 6° depression then she is 540.6 miles away from the runway.
What is meant by angle of depression?A depression angle is formed when the viewer is higher than the object they are looking at. When a viewer looks at an object at a closer distance than themselves, an angle is formed under the horizontal line drawn at the viewer's eye level and the line connecting the object to the viewer's eye.
Elevation angle is the angle formed when a person stands on the ground and looks at an object above the ground at a height above the person's height. This is the basic difference between the two angles. Both angles are calculated using trigonometry concepts.
The angle of depression is defined as the angle formed by the horizon and the line connecting the object to the viewer's eye. This angle depends on two factors: altitude and distance.
Given: A pilot is flying 30,000 feet above the surface of the earth. She notices the runway when she looks down at a 6° depression.
The angle of depression = angle of elevation = 6°
Let x be the distance to the runway.
tan 6 = 30000/x
simplifying the above equation, we get
x tan 6 = 30000
x = 30000/tan 6 = 285430.9 ft
285430.9336/5280 = 540.6 mi
She is 540.6 mi away from the runway.
To learn more about angle of depression, refer to:
brainly.com/question/27865363
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What is the coefficient of 8 term in the expansion of 2( + 1)10?
Answer:
180
Step-by-step explanation:
2(8+1)10
add the number in parenthesis
2(9)10
18x10
180
What is the length of segment AB?
12!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the least common denominator of the rational expressions below?
2/7 - 7/4x^2+12x
O A. 4x^2(x + 3)
O B. x^2(x + 3)
O c. x^2(x + 3)
O D. 4x^2(x+3)
Answer:
A. 4x^2(c+3)
Step-by-step explanation:
passes through (-1, -5) and (2, 6)
Answer:
[tex]y = \frac{11}{3}x + -\frac{4}{3}[/tex]
Step-by-step explanation:
[tex]y = mx + b\\m = \frac{-5 - 6}{-1 - 2} = \frac{-11}{-3} = \frac{11}{3} \\\\y = \frac{11}{3}x + b\\6 = \frac{11}{3}(2) + b\\6 = \frac{22}{3} + b \\6 - \frac{22}{3} = b \\b = -\frac{4}{3}\\\\y = \frac{11}{3}x + -\frac{4}{3}[/tex]
Diego pours 8 ounces of water from a full bottle of 36 ounces. What is the percent of decrease of water in the bottle?
Answer:
The answer is 22%.
Step-by-step explanation:
All you need to do to figure this out is to divide 36 by 8.
8/36=.222222
Hope this helps!
The angular speed for a Wind turbine with blades turning at a rate of 19 revolutions per minute is
Answer
The answer to the question is 3.157 revolutions per second.
Step-by-step explanation:
The reason is because speed is the distance the object travels in a second.
So, we know that the wind turbine is moving 19 revolutions per minute, so therefore to find the number of rotations the wind turbine is doing per second we have to do 60/19 because there is 60 seconds in a minute.
Therefore, if we do that equation we get the answer, as 3.157 revolutions per second!
I hope this answer helps!
3sin60°+xcos30°.tan45°=xcot30°
Answer:
x = (6[tex]\sqrt{2}[/tex])/(4[tex]\sqrt{2}[/tex] -3)
Step-by-step explanation:
sin60 degree = [tex]\sqrt{3}[/tex] /2
cos30 degree = 1/2
tan 45 degree = sin45 degree / cos45 degree = ([tex]\sqrt{2}[/tex]/2)/([tex]\sqrt{2}[/tex] /2) = 1
cot 30 degree = cos30 / sin30 = ([tex]\sqrt{3}[/tex] /2)/(1/2) = [tex]\sqrt{3}[/tex]
so, let us plug the above values in the given eqution and solve for x
3([tex]\sqrt{3}[/tex] /2 ) + x(1/2) *1 = x([tex]\sqrt{3}[/tex])
3([tex]\sqrt{3}[/tex] /2 ) = x([tex]\sqrt{3}[/tex]) -x(1/2)
3([tex]\sqrt{3}[/tex] /2 ) = x(([tex]\sqrt{3}[/tex])-(1/2)) (by taking x as a common factor)
3([tex]\sqrt{3}[/tex] /2 ) = x(((2[tex]\sqrt{3}[/tex])-(1))/2)) (making the same common denominator
now devide both sides by (((2[tex]\sqrt{3}[/tex])-(1))/2))
x = 3([tex]\sqrt{3}[/tex] /2 ) / (((2[tex]\sqrt{3}[/tex])-(1))/2))
x = 3([tex]\sqrt{3}[/tex] ) / ((2[tex]\sqrt{3}[/tex])-(1))
A farmer fed 9 bags of food to his 5 cows. Each cow ate the same amount of food. How many bags of food did each cow eat?
Answer:
1.8 bags
Step-by-step explanation:
you just divide 9 by 5
The number of bags of food that each cow eats will be 1.80 bags.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A farmer fed 9 bags of food to his 5 cows. Each cow ate the same amount of food.
Then the number of bags of food that each cow eats will be given as,
⇒ 9 / 5
⇒ 1.80 bags
The number of bags of food that each cow eats will be 1.80 bags.
More about the Algebra link is given below.
https://brainly.com/question/953809
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good at math & need points? help!!
Answer:
D
Step-by-step explanation:
Two vertices of a rectangle are (−10, −7) and (−10, 18) .
What is the length of this side of the rectangle?
Answer:
The length of the side of the rectangle is 11 units.
Answer:
11 units
Step-by-step explanation:
did the unit test in K12
Find the value of f(-9).
y = f(x)
please help me will give you brainliest!!
Answer:
yes, no, no, yes
Step-by-step explanation:
Plug in each point into both equations to see which ones fit.
For the first point, (4,1) it works for both equations.
1=-2( 4 ) + 9, 1= -8 + 9, 1=1
4( 4 )+2( 1 )=18, 16 + 2 = 18, 18 = 18
Do it for the rest of the points and plug them in and you get,
no for (5,-3) because -1 does not equal to -3
no for (6,0) because -3 does not equal to 0
(-5,19) is yes because 19=19 and 18=18
Please mark me brainliest
17/8x+3/4x+1/6-7/12x+18/3 simplify
Answer:
55x + 148/24
Explanation:
What is the area or the figure below? THE FIRST TO ANSWER GETS MARKED AS BRAINLIEST
Answer:
168 in.²
Step-by-step explanation:
it is the correct answer