Answer:
2
Step-by-step explanation:
2x + y = -8
3x - 5y = -25
It’s substitution
Answer:
x = -5 , y = 2
Step-by-step explanation:
Solve the following system:
{y + 2 x = -8
-5 y + 3 x = -25
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for y:
{y + 2 x = -8
-5 y + 3 x = -25
Hint: | Solve for y.
Subtract 2 x from both sides:
{y = -2 x - 8
-5 y + 3 x = -25
Hint: | Perform a substitution.
Substitute y = -2 x - 8 into the second equation:
{y = -2 x - 8
3 x - 5 (-2 x - 8) = -25
Hint: | Expand the left hand side of the equation 3 x - 5 (-2 x - 8) = -25.
3 x - 5 (-2 x - 8) = (10 x + 40) + 3 x = 13 x + 40:
{y = -2 x - 8
13 x + 40 = -25
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for x:
{y = -2 x - 8
13 x + 40 = -25
Hint: | Isolate terms with x to the left hand side.
Subtract 40 from both sides:
{y = -2 x - 8
13 x = -65
Hint: | Solve for x.
Divide both sides by 13:
{y = -2 x - 8
x = -5
Hint: | Perform a back substitution.
Substitute x = -5 into the first equation:
{y = 2
x = -5
Hint: | Sort results.
Collect results in alphabetical order:
Answer: {x = -5 , y = 2
A, B, and C are points on the circumference of a circle, centre 0. AOB is a diameter of the circle. Prove that angle ACB is 90° You must not use any circle theorems in your proof.
Answer:
Kindly refer to explanation.
Step-by-step explanation:
Given that:
A,B and C are 3 points on circumference of circle with centre O.
AOB is diameter.
Kindly refer to the attached image.
To prove:
[tex]\angle ACB = 90^\circ[/tex]
Solution:
Let [tex]\angle A = x[/tex] and [tex]\angle B = y[/tex].
Construction: Join point A with centre O.
Considering [tex]\triangle AOC[/tex]:
Side AO = OC because both are the radius.
Angles opposite to equal sides in a triangle are equal.
Therefore, [tex]\angle ACO=\angle A=x[/tex]
Considering [tex]\triangle BOC[/tex]:
Side BO = OC because both are the radius.
Angles opposite to equal sides in a triangle are equal.
Therefore, [tex]\angle BCO=\angle B=y[/tex]
[tex]\angle ACB = \angle ACO + \angle BCO = x+y[/tex] ...... (1)
Now, in [tex]\triangle ABC:[/tex]
Using angle sum property of triangle:
[tex]\angle A + \angle B + \angle ACB =180^\circ\\\Rightarrow x+y+x+y=180^\circ\\\Rightarrow 2(x+y)=180^\circ\\\Rightarrow x+y=90^\circ[/tex]
By equation (1):
[tex]\angle ACB = 90^\circ[/tex]
Hence proved.
sweet t is making a double batch of Pupcakes. he puts them in the oven at 6:50. they need to bake for 25 minutes
i would love to help but i just need free points
Step-by-step explanation:
what is the inverse function of c(n) = 4n + 20? show your work
Answer:
c(n) = 4n +20
let m = c(n)
m= 4n +20
make n the subject
m -20 =n
4.
inverse function of c(n)= n-20
4
It is a must that one replaces the m with the n in order to get the final answer
What is the rate of change of y with respect to x for 25x-4y=50
Answer:
The rate of change is y with respect to x is [tex]\frac{25}{4}[/tex]
Step-by-step explanation:
Given
[tex]25x - 4y = 50[/tex]
Required
Determine the rate of change of y w.r.t x
[tex]25x - 4y = 50[/tex]
First, make y subject of formula
[tex]4y = 25x- 50[/tex]
Divide through by 4
[tex]y = \frac{25x}{4} - \frac{50}{4}[/tex]
[tex]y = \frac{25x}{4} - 12.5[/tex]
Next, we differentiate the above w.r.t to x
The result of the differentiation is the solution to the question
[tex]y' = 1 * \frac{25x^{1-1}}{4} -0[/tex]
[tex]y' = 1 * \frac{25x^0}{4}[/tex]
[tex]y' = 1 * \frac{25*1}{4}[/tex]
[tex]y' = \frac{25}{4}[/tex]
Hence, the rate of change is y with respect to x is [tex]\frac{25}{4}[/tex]
By calculating derivative of y with respect to x we got rate of change of y with respect to x for 25x-4y=0 is 25/4
What is derivative?Rate of change of a function with respect to a variable is called derivative of that function with respect to that variable .
Here given relation is 25x-4y=0
[tex]\Rightarrow 4y=25x\\\\\Rightarrow y=\frac{25x}{4}[/tex]
We have to calculate rate of change of y with respect to x so we will calculate derivative of y with respect to x.
we can calculate derivative of y with respect to x as
[tex]\frac{dy}{dx}= \frac{d}{dx} (\frac{25x}{4})\\\\[/tex]
As 25/4 is constant we can take it out from derivative function as it is
[tex]\frac{dy}{dx}= (\frac{25}{4})\frac{dx}{dx}\\\\[/tex]
And we know derivative of a variable with respect to itself is 1
so
[tex]\frac{dy}{dx}= (\frac{25}{4})\times 1\\\\ \frac{dy}{dx}= \frac{25}{4}[/tex]
By calculating derivative of y with respect to x we got rate of change of y with respect to x for 25x-4y=0 is 25/4
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Can someone help me please
Answer:
a. angle 6 and angle 7
b. angle 6 and angle 8
c. angle 3 and angle 1
Step-by-step explanation:
linear pair is two angles that share a base and and add up to 180
vertical angles is the pair of opposite angles formed by two intersecting lines
congruent is the same measure
Answer:
see explanation
Step-by-step explanation:
(a)
A linear pair of angles, are adjacent to each other and sum to 180°
There are 8 linear pairs in the diagram, they are
1 and 2 / 2 and 3 / 3 and 4 / 4 and 1 / 5 and 6 / 6 and 7 / 7 and 8 / 8 and 5
(b)
There are 4 vertical angles in the diagram
1 and 3 / 2 and 4 / 5 and 7 / 6 and 8
Note that vertical angles are congruent
Other congruent angles are
2 and 6 / 3 and 7 / 1 and 5 / 4 and 8 ( All corresponding angles )
4 and 6 / 3 and 5 ( are Alternate angles )
Which of the following is a rational number?
Answer:
B.)
Step-by-step explanation:
A rational number is a number with no repeating decimals or decimals that go on “forever” like pi. An expample of a rational number is 2 where 2.3333333... is not a rational number. Pi isn’t a rational number either since forth there is no known end to that.
So, when solved:
A.) = 1.58113883... (irrational)
B.) = -8 (rational)
C.) = 8.94427191... (irrational)
D.) = 3.794733192... (irrational)
I hope you see the pattern. Hope this helps!
Given the sum of the interior angles of a polygon, tell the number of sides of the polygon.
If the interior angle sum is 360°, the polygon has _
sides.
If the interior angle sum is 540°, the polygon has _
sides.
If the interior angle sum is 900°, the polygon has _
sides.
If the interior angle sum is 1260°, the polygon has _
sides.
Answer:
[tex] \underline{the \: sides \: are} \: \to \\ \underline{ \boxed{ n= 4}} \\ \: \underline{ \boxed{ n= 5}} \\ \:\underline{ \boxed{ n= 7}} \\ \: \underline{ \boxed{ n= 9}} \\ \: [/tex]
Step-by-step explanation:
[tex] \\ the \: sum \:o f \: the\: interior \: angles \: of \: aregular \: polygon \: \\ is \: generaly \: given \: by \to \: 180(n - 2)\\ \underline{ \boxed {case \:( 1) \to}} \\ If \: the \: interior \: angle \: sum \: is \: 360°, \\ then : \: the \: polygon \: has \to \: \\ 180(n - 2) = 360 \\ n - 2 = 2 \\ \underline{ \boxed{ n= 4}} \\ \: \underline{ \boxed {case \:( 2) \to}} \\ If \: the \: interior \: angle \: sum \: is \: 540°, \\ then : \: the \: polygon \: has \to \: \\ 180(n - 2) = 540 \\ n - 2 = 3 \\ \underline{ \boxed{ n= 5}} \\ \: \underline{ \boxed {case \:( 3) \to}} \\ If \: the \: interior \: angle \: sum \: is \: 900°, \\ then : \: the \: polygon \: has \to \: \\ 180(n - 2) = 900 \\ n - 2 = 5 \\ \underline{ \boxed{ n= 7}} \\ \: \underline{ \boxed {case \:(final ) \to}} \\ If \: the \: interior \: angle \: sum \: is \: 1260°, \\ then : \: the \: polygon \: has \to \: \\ 180(n - 2) = 1260 \\ n - 2 = 7\\ \underline{ \boxed{ n= 9}} \\ \: [/tex]
♨Rage♨
Answer:
4,5,7,9
Step-by-step explanation:
Got it right on edge
The number of sticks of gum varies directly as the number of packages. There are 36 sticks of gum in 2 packages. Suppose you have 5 packages of gum. Write and solve a direct variation equation to determine how many sticks you have
Answer:
36 x 2 = 72
36 divide by 2 = 18
72+18=90
90 is the answer
Step-by-step explanation:
Write an equation in point-slope form for the line that passes through the point with the given slope. point: (-1, 5) and m=-4
Answer:
y - 5 = -4(x + 1)
Step-by-step explanation:
The point-slope form is y - k = m(x - h). The point is (h, k): (-1, 5) and the slope is -4.
Here we have y - 5 = -4(x + 1)
The required point-slope form of the equation of the line is y - 5 = -4(x + 1).
Given that, To determine an equation in point-slope form for the line that passes through the point with the given slope. point: (-1, 5) and m=-4.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The point-slope of the equation of the line is given by,
y - y₁ = m(x - x₁)
Put the values in the above equation of the line
y - 5 = -4 (x - (-1))
y - 5 = -4 (x + 1)
Thus, the required point-slope form of the equation of the line is y - 5 = -4(x + 1).
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What is the slope of the line (-3,0) and (0,-4)
The prime factorization of 2020 is 2² × 5¹ × 101¹. How many different whole numbers are factors of 2020?
Answer:
4
Step-by-step explanation:
1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010
PLEASE HELP!! (Give reasonable answer)
Answer: B
Step-by-step explanation: You just multiplying 25 with 10 and w which can be simplified as 24(w+10) and adding with the 13.5 x 10 and 13.5 x w, which can be simplified as 13.5(10+w)
Given m∥n, find the value of x and y.
Answer:
x=15
y=63
Step-by-step explanation:
Ivian scores 58 out of 80 marks in a maths test what is his score as a percentage
Answer:
72.5%
Step-by-step explanation:
Lets make his score a percentage: 58/80
Now covert it to a percentage: 58/80 = x/100
Cross multiply: 80x = 5800, x = 145/2
Divide 145 by 2: 72 1/2
Answer is 72.5%
I hope this helped, please mark Brainliest, thank you!
What is rhe vertex of this parabola ?????? HELP
Answer:
The vertex is (3,1)
Step-by-step explanation:
Brainliest please
A pet store has 8 dogs, 12 turtle, and 3 cats. Write a ratio for each of the following situations.
Turtles to dogs and cats:
dogs to turtles
Answer:
Turtles to dogs and cats: 12,8,3
dogs to turtles: 8,12
PLEASE HELP An algebraic ___ is a mathematical phrase
With numbers, variables, operations for days.
is it coefficient , expression or evaluate
Answer:
Expression
Step-by-step explanation:
The definition of an Algebraic Expression is this:
Algebra is an interesting and enjoyable branch of mathematics in which numbers, shapes, and letters are used to express problems.
It can not be an Algebraic Equation because that only includes one variable.
I Hope That This Helps! :)
Will give brainliest if correct
Answer:
y=4
x=2
Step-by-step explanation:
y=4
x=2
I think it's right..
Hope I helped!
Answer:
x - intercept = 2
y - intercept = 4
Bridgette has $1,000 to invest. She has two different investment options, shown in the table below. Each option would give her a different value over three years.
Number of Years 1 2 3
Option A (amount in dollars) 1100 1200 1300
Option B (amount in dollars) 1100 1210 1331
Part A: What type of function, linear or exponential, would be best to describe the value of the investment over a fixed number of years using Option A? Explain your answer.
Part B: Write a function, a(t), to describe the value of the investment, in dollars, of Option A after t years.
Part C: What type of function, linear or exponential, would be best to describe the value of the investment over a fixed number of years using Option B? Explain your answer.
Part D: Write a function, b(t), to describe the value of the investment, in dollars, of Option B after t years.
Part E: Bridgette wants to invest in whichever option would increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Bridgette's investment after 20 years if she uses Option A over Option B? Explain your answer, and show the investment value after 20 years for each option.
Answer/Step-by-step explanation:
Part A: The function that would best describe Option A is a linear function. This is because an increase in x would have a corresponding additive increase in y. With each increasing year, the value of Option A increases by $100. This is how we know Option A would be a linear function.
Part B: a(t) = y.
a(t) = a + 100t
Part C: The function that would best describe Option B is an exponential function. Unlike linear functions, an increase in x would have a corresponding multiplicative increase in y. Each value of Option B shares a common ratio of 1.1.
Part D: b(t) = y.
b(t) = b(1.1)^t
Part E: a(20) = a + 100(20)
1100 + 2000 = 3100
b(20) = b(1.1)^20
1100(1.1)^20
= 7400
There is definitely a significant difference between the value of Bridgette’s investment in both options. The difference between the values of each option after 20 years is 4300. Bridgette is better off using Option B if she wants more money at the end.
Hope this helps!
A recipe for 4 cups of trail mix calls for 2··3cup of raisins. Aniyah has 1 1··2cups of raisins. Does Aniyah have enough raisins to make 14 cups of the trail mix? If not, how many more cups of raisins does Aniyah need?
Answer:
Aniyah does not have enough for 14 cups, and needs 1 1/6 more.
Using the required arithmetic concept, we can conclude that Aniya needs 7/6 more cups.
Representing the problem thus:
4 cups of trail = 2/3 cups of raisins
14 cups of trails = x
Cross multiply
4x = (2/3) × 14
4x = 28/3
x = (28/3) ÷ 4
x = (28/3) × (1/4)
x = 7/3
Cups of raisins Aniya has = 1 1/2 = 3/2
Extra cups needed = 7/3 - 3/2 = 7/6 cups
Therefore, Aniya does not have enough, she needs 7/6 more cups.
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Does the set of ordered pairs
represent a function ? Explain.
(7, 8), (9, 10), (0, 1), (-2, -1),
(9,8)
Answer:no
Step-by-step explanation:
Because there’s two number 9’s for the x values
Answer:
no because x = 9 has two y coordintates, and in a function every x value can only have one y value.
Step-by-step explanation:
egadar amd fred share cupcakes in the ratio 3:1 if edgar gets 9 cakes how many does fred get(pleez someone anwer my question
Answer:
3
Explanation:
For every 3 cupcakes that Edgar gets, Fred gets 1. So, if Edgar gets 9, Fred gets 3.
The table shows the number of coins Kaitlyn has.
penny
4
nickel
9
dime
3
quarter
5
Write the ratio of dimes to all coins that Kaitlyn has as a
fraction in simplest form.
again i need some help with this :D
Answer:
v + u - 4
Step-by-step explanation:
A construction crew has repaired 1.37 miles of a highway. The total length of the highway to be repaired is 7.9. How many miles are left to be repaired?
Answer:
Part A: m+1.37=7.9
Part B: 6.53 miles are left to be repaired.
Step-by-step explanation:
Given,
Length of repaired part = 1.37 miles
Total length to be repaired = 7.9 miles
Miles left to be repaired = m
Part A:
Create an equation to show the relationship between the number of miles repaired and the number of miles left to be repaired, m.
Miles left to be repaired + Length of repaired part = Total length to be repaired
m+1.37=7.9
Part B
How many miles are left to be repaired?
Subtracting 1.37 from both sides
6.53 miles are left to be repaired.
Keywords: length, subtraction
Step-by-step explanation:
Choose the correct pair of expressions to complete the solution of sin r +
37
2
2.
O COS X, 0
O -sin x,-1
O sin x,-1
O-COS X, 0
Answer:
sin x, –1
Step-by-step explanation:
did on edge
The perimeter of a rectangular playground can be no greater than 120 meters. The width of the playground cannot exceed 22 meters. What are the possible lengths of the playground?
Answer:
because The perimeter of a rectangular playground can be no greater than 120 meters, The width of the playground cannot exceed 22 meters
=> the length of the playground cannot exceed: (120/2)-22= 38(meters)
Step-by-step explanation:
Make t the subject of the formula
t = (3m -1) / (m - 1)
What is subject of formula?The subject of a formula is the variable that is being worked out. It can be recognized as the letter on its own on one side of the equals sign.
In order to change the subject of a formula, or rearrange a formula, items in the formula need to be rearranged so a different variable is the subject. Knowledge of solving equations and inverse operations is very useful.
Given formula.
m = t + 1 / t - 3
m ( t - 3) = t - 1
mt - 3m = t - 1
mt - t = 3m - 1
t(m - 1) = (3m - 1)
t = (3m -1) / (m - 1)
Hence, the formula becomes t = (3m -1) / (m - 1).
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From 1990 to 1996, the consumption of poultry per capita is modeled by: y=-.2125t^2 + 2.615t+56.33 where t=0 corresponds to 1990. What was the per capita poultry consumption in 1992?
Answer:
60.71
Step-by-step explanation:
Given that:
Consumption of poultry per capita is modeled by:
y=-.2125t^2 + 2.615t+56.33 ; t = 0 corresponds to 1990
Per capita poultry consumption in 1992;
1992 ; t = 2
y=-.2125t^2 + 2.615t+56.33
Put t = 2 in the equation
y=-.2125(2)^2 + 2.615(2) +56.33
y = -.2125(4) + 2.615(2) + 56.33
y = - 0.85 + 5.23 + 56.33
y = 60.71