Answer:
A. To determine the value of a, set up and solve a system of equations in two variables. The value of a is 2
Step-by-step explanation:
Given the coordinates F(b+1, a+2, M(3,5) and G(2a, 3b+3), if M is the midpoint of F and G then, to get the value of a and b we will use the formula for calculating the midpoint a shown;
M(X, Y) = (x₁+x₂/2, y₁+y₂/2)
X = x₁+x₂/2 and Y = y₁+y₂/2
From the given coordinates x₁ = b+1, y₁ = a+2, x₂ = 2a, y₂ = 3b+3, X = 3 and Y = 5
Substituting the given parameters into the formula, we can form up a simultaneous equation and get the value of a.
To determine the value of a, set up and solve a system of equations in two variables
For the X coordinates;
X = x₁+x₂/2
3 = b+1+2a/2
6 = 2a+b+1
2a+b = 5 ............... 1 * 1
For the Y coordinates;
5 = a+2+3b+3/2
cross multiply
10 = a+2+3b+3
collect like terms
a+3b = 10-2-3
a+3b = 5 ........ 2 * 2
Solving the resulting simultaneous equation to get the value of a
multiply equation 1 by 1 and 2 by 2 to have the resulting equations;
2a+b = 5 ...........3
2a +6b = 10.......... 4
subtract 3 from 4
(2a-2a)+(b - 6b) = 5-10
0-5b = -5
b = -5/-5
b = 1
substitute b =1 into equation 1 to get a;
2a + b = 5
2a + 1 = 5
2a = 5-1
2a = 4
a = 2
From the calculation above it is seen that the value of variable a can be determined and it is equivalent to 2
Answer the following questions about this figure.
PLS HELP ME
Answer:
143
Step-by-step explanation:
First, figure out the measurement of angle 2. Take 180 degrees (the total of the triangle) and subtract 90 (the right angle) and 53 (the given measurement of angle 1). 180-90-53=37
Angle 2 measures 37 degrees. The measurements of angles 2 and 3 need to equal 180 when added together as they form a straight line, so take the total (180) and subtract the value of angle 2 (37). 180-37=143
Angle 3 measures 143 degrees
how many centimeters are in 32 metered
Answer:
3,200
Step-by-step explanation:
A meter is equivalent to 100 centimetres, so if you did 32 x 100, you'd get your answer :)
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $82,910, and the variable costs will be $10.75 per book. With the other method, the one-time fixed costs will total $22,110 , and the variable costs will be $23.25 per book. For how many books produced will the costs from the two methods be the same?
Answer:
When 4864 books are sold
Step-by-step explanation:
Create an equation where x is the number of books produced:
The first method will be represented by 10.75x + 82,910
The second method will be represented by 23.25x + 22,110
Set these equal to each other and solve for x:
10.75x + 82,910 = 23.25x + 22,110
82,910 = 12.5x + 22,110
60,800 = 12.5x
4864 = x
So, the costs will be the same for both methods when 4864 books are sold
if
a+1/a=4-root15 find a^2 +1/a^2
62 is the correct answer of this question
The perimeter of a playing field for a certain sport is 334ft. The field is a rectangle, and the length is 47 ft longer than the width. Find the dimensions.
Answer:
The dimensions of the rectangle = 60ft by 107ft
Where 60 ft = Width of the playing field
107ft = Length of the playing field
Step-by-step explanation:
A playing field is Rectangular is shape, hence,
The formula for Perimeter of a rectangle = 2(L + W)
P = 334 ft
L = 47 + W
W = W
Hence we input these values in the formula and we have:
334 = 2(47 + W + W)
334 = 2(47 + 2W)
334 = 94 + 4W
334 - 94 = 4W
240 = 4W
W = 240/4
W = 60
There fore, the width of this playing field = 60 ft
The length of this rectangle is calculated as:
47 + W
47 + 60
= 107 ft
The length of this playing field = 107ft
Therefore the dimensions of the rectangle = 60ft by 107ft
21-m=9 anyone know this ?
Answer:
m=12
Step-by-step explanation:
21-m=9
-m=9-21
-m=-12
m=12
Answer:
12
Step-by-step explanation:
21-m=9
21-9=12
m=12
Can anyone solve this word problem?
Answer:
Mrs. Davis package is 30 ounces
Step-by-step explanation:
x for ounces
mailbox plus=0.25x+5
united package=0.35x+2
since Mrs.Davis noticed that she is going to pay same price then:
0.25x+5=0.35x+2
5-2=0.35x-0.25x
3=0.10x
x=3/0.10
x=30 ounces
Mrs. Davis package is 30 ounces
check:
0.25x+5=0.25(30)+5= 12.5 dollars
o.35(30)+2=12.5 dollars
A line passes through the point (4,–2) and is perpendicular to the line with the equation y = 2∕3x + 4. What's the equation of the line? Question 1 options: A) y = –3∕2x – 4 B) y = 2∕3x + 3 C) y = 3∕2x – 8 D) y = –3∕2x + 4
Answer:
Step-by-step explanation:
perp. -3/2
y + 2 = -3/2(x - 4)
y + 2 = -3/2x + 6
y = -3/2x + 4
answer is D
Given: {(−2, 3), (−1, 2), (0, 2), (−2, 9)}. Is this relation a function? Explain.
Answer:
No
Step-by-step explanation:
(-1,2) and (0,2) have the same y value. Functions cannot share the same y value
The relationships represents by {(−2, 3), (−1, 2), (0, 2), (−2, 9)} is not function.
Given that, {(−2, 3), (−1, 2), (0, 2), (−2, 9)}. Is this relation a function is to be specified.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
In the relation {(−2, 3), (−1, 2), (0, 2), (−2, 9)}
(−2, 3), (−2, 9) are two pairs that show two images of one pre-image that why it is not a function.
Thus, the relationships represents by {(−2, 3), (−1, 2), (0, 2), (−2, 9)} is not function.
Learn more about function here:
brainly.com/question/21145944
#SPJ2
What is the simplified expression for the expression below? –1(2x + 3) – 2(x – 1)
Answer:
-4x - 1.
Step-by-step explanation:
-1(2x + 3) - 2(x - 1)
= -2x - 3 - 2x + 2
= -4x - 1.
Answer:
-4x -1
Step-by-step explanation:
-2x -3 -2x + 2
In the diagram AB Is the perpendicular bisector of PH. Help
Answer:
1,2 and 5 are your right answers! Please vote Brainliest!
Step-by-step explanation:
(3x+4) and (2x−3). What is the perimeter of the park?
Answer: 10x-2
Step-by-step explanation:
I assume this is a rectangular park
Formula for perimeter: 2(l + w)
l= 3x+4
w= 2x-3
--------------------------------------------------------
Use PEMDAS to simplify (basic operation from left to right)
ParenthesesExponentsMultiplication and DivisionAddition and subtraction2(l+w)
=2[(3x+4)+(2x-3)]
=2[3x+4+2x-3]
=2[5x-1]
=10x-2
At what value(s) of x does f(x) = -x4 + 2x2 have a critical point where the graph changes from decreasing to increasing?
Hope the graph helps!
Help me ill give u a thanks!
Answer:
11. 68.6 mph
12. 5/6 page (0.83)
Step-by-step explanation:
You simply divide them (remember the word "per" means divide).
[tex]\dfrac{120}{1 \frac34} \approx 68.6[/tex]
[tex]\dfrac{8 \frac13}{10} = \frac56[/tex]
1-8 Homework Exercises Course 2 Mathematics Common Core
POSSIBLE POIN The value of the expression is (Do without a calculator. Leave your answer as a reduced improper fraction and use "" as your fraction bar.)
What is the image of (–9,-5) after a dilation by a scale factor of 5 centered
at the origin?
Answer: (-45,-25)
Step-by-step explanation:
Multiply each coordinates value by the scale factor to find the new point.
-9 * 5 = -45
-5 * 5 = -25
(-45,-25)
3 is multipled by the cube of a number.
Answer:
Cube of a number is three times of the same number. Cube of any mathematical expression is represented by the superscript 3. For example a 3 of the number is a x a x a. It can also be told as the number multiplied by its square. a 3 = a x a 2 can you please help me
Step-by-step explanation:
Last year, Kenia got a 350 on her 6th Grade Math EOG. This year Kenia earned a 399, which was a high enough score to make a Level 4. What was the percent of increase in Kenia's score?
Answer:
14%
Step-by-step explanation:
Last year's score = 350
This year's score = 399
What was the percent of increase in Kenia's score
Percentage increase= (new score - old score) / old score × 100
= (399-350) / 350 × 100
= 49 / 350 × 100
= 0.14 × 100
= 14%
The percent of increase in Kenia's score is 14%
Tina learns 2 new appetizer recipes during each week of culinary school. After 19 weeks of culinary school, how many total appetizer recipes will Tina know?
Answer:
38 recipes
Step-by-step explanation:
1 week=2 recipes
19 week=19×2 recipes
=38 recipes
Plz,marks me as a brainest ok.
HELPPP!!
SIMPLIFY!!!
5x²-7y+3x²-8y
Answer:
8
x
2
−
15
y
Step-by-step explanation:
Hope that helps
Triangle MNO is a right triangle with one leg = 15ft and the other leg = 18ft. Calculate the
length of the hypotenuse to the nearest hundredth of a foot (2 decimal places)
Answer:
Length of the hypotenuse = 23.43ft
Step-by-step explanation:
First leg = 15ft
Second leg = 18ft
Length of the hypotenuse = ?
In a right angle triangle,
Hypotenuse^2 = opposite^2 + Adjacent^2
Let first leg and second leg of the triangle be opposite and adjacent respectively
Hypotenuse^2 = opposite^2 + Adjacent^2
= 15^2 + 18^2
= 225 + 324
= 549
Hypotenuse^2 = 549
Find the square root of both sides
√Hypotenuse^2 = 549
Hypotenuse = 23.43ft to the nearest of a hundredth
Length of the hypotenuse = 23.43ft
describe a real-world situation using opposites
Answer:
The real world using opposite would be like calling it perfect or or saying that it is normal now days. Hope this helps!
Let f(x) = 3x² - x, find f(-3) *
Answer:
30
Step-by-step explanation:
if f(x)=3x^2 - x then,
f(-3)=3*-3^2 -(-3)
=3*9 +3
=27+3
=30
So, The value of f(-3) is 30
Hope Thiswill be helpful for you.
Pat and Julie share some money in the ratio 2 : 5 Julie gets $45 more than
Pat. How much money did Pat get? (SHOW WORKING)
plsssss helppp
Answer:
Pat receives $18.
Step-by-step explanation:
Pats get 18 dollars because he only gets 40 percent of what Julie gets and 40% of 45 is 18.
What is the value of x in the equation −x = 3 − 4x + 15?
Answer:
x = 6
Step-by-step explanation:
First of all you should collect like terms
-x = 18 - 4x
Then you should move the variable to the left
-x + 4x = 18
After that you should collect like terms
3x = 18
Finally divide both sides by 3
x = 6
Hope this helps!
Answer:
6
Step-by-step explanation:
It is known that 2.2< (square root of 5) <2.3. Find all possible values of the expression: 3− (square root of 5) Answer in the format of the picture.
Answer:
.7<3-square-root 5<.8
Step-by-step explanation:
I dont understand hot to find g(3)
The answer to this equation is 4. This is because since the function is g(3), you plug in x with 3. 3*3 = 9. 9+7 = 16. The square root of 16 is equal to 4, so that is your answer.
What is the range of these wages £140 £525
Which of the following is a rational number? 79, 80, 81, 82