Answer:
x - 3y = 8.
Step-by-step explanation:
Use the point-slope form of the equation of a line:
y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line.
So substituting the given values:
y - (-2) = 1/3(x - 2)
y + 2 = 1/3x - 2/3 Multiply through by 3:
3y + 6 = x - 2
x - 3y = 6 + 2
x - 3y = 8 <---- Standard Form.
Henry's wage is £450 per week.
He spends 2/5 of his wage on food.
30% goes on the household bills and the rest is saved.
How much does Henry save each week?
Answer:
He saves £135 each week
Step-by-step explanation:
He spends 2/5 of his wage on food
2/5x450=£180
He spends 180£ on food each week
30% of 450 is 135 which he spends on house holdbills. thus, he pays £135 on bills
so his total expenditure is 135+180= £315
he saves the rest which is £135.
thus, your answer is £135
If 0 < f ≤ 90 and cos(22f − 1) = sin(7f + 4), what is the value of f?
f = 3
f = 4
f = 5
f = 6
Answer:
f = 3Step-by-step explanation:
Given the equation cos(22f − 1) = sin(7f + 4), the following steps must be followed in order to get the value of f;
From the trigonometry identity, sin(90-theta) = cos theta.
cos(22f-1) = sin (90-(22f-1))
cos(22f-1) = sin (90-22f+1)
cos(22f-1) = sin (91-22f)... 3
substituting eqn 3 into the original equation given, we will have;
sin (91-22f) = sin(7f + 4)
91-22f = 7f+4
7f+22f = 91-4
29f = 87
f = 87/29
f = 3
A correct option is an option (a)
Given function is,
[tex]cos(22f-1) = sin(7f + 4)[/tex]
As we know the relation,
[tex]cosx=sin(90-x)[/tex]
Now, apply the above relates to the given function.
[tex]cos(22f − 1) = sin(7f + 4)\\sin(90-(22f-1))=sin(7f + 4)\\90-22f+1=7f+4\\-22f-7f=4-91\\-29f=-87\\f=3[/tex]
So, the required value is [tex]f=3[/tex]
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A rectangle has length x+2 and width x+1. Which equation correctly represents the perimeter of the rectangle? 1. 2(x+2)=2x+4 2. 2(2x+3)=4x+6 3. 2(2x+3)=4x+3 4. 2(x+1)=2x+2
Answer:
4x+6
Step-by-step explanation:
P=2L+2W
P= 2(x+2) +2(x+1)
P= 2x+4+2x+2
P= 4x+6
HELP PLEASE. THIS IS ABOUT FUNCTIONS ! EXPLANATION NEEDED PLEASE
Answer:
B
Step-by-step explanation:
Looking at the graph we can see that the function is increasing -4<x<-2 and 0<x2
The graph is increasing when it is going upwards, or has a slope greater than 0
We can see that happening in two places in the function, which are the intervals of the x coordinate in B
Answer:
B
Step-by-step explanation:
The function is increasing - 4 < x < - 2 and 0 < x < 2 and has a slope greater than 0, and it's happening at 2 places on the graph, so it's B
Hope this helps!
What is an equation of the line that passes through the point (8,-8) and is
perpendicular to the line 4x – 3y = 18?
Answer:
y = -3/4x - 2
Step-by-step explanation:
You put the equation in the slope-intercept form. Remember that the perpendicular slope is the negative reciprocal. You plug in the slope and the point into the slope-intercept formula. Solve for b then plug it into the final formula.
The equation of the line that passes through the point (8,-8) and is
perpendicular to the line 4x – 3y = 18 is;
⇒ 3x + 4y = -8
Here,
The point is (8, -8)
And, The equation of line is, 4x - 3y = 18
What is Equation of line?
The equation of line passes through points (x₁, y₁) and has slope m is;
y - y₁ = m₂ (x - x₁)
Now,
The point is (x₁, y₁) = (8, -8)
And, The equation of line is, 4x - 3y = 18
Put into the slope form as;
4x - 3y = 18
4x - 18 = 3y
y = (4/3)x - 6
Hence, Slope of the given line = 4/3
The slope (m₁) of perpendicular line relationship is;
4/3 * m₂ = -1
m₂ = -3/4
Hence, slope of perpendicular line (m₂) = -3/4
So, The equation of line by using point/slope form is;
y - y₁ = m₂ (x - x₁)
y - (-8) = -3/4 (x - 8)
y + 8 = -3/4 (x - 8)
4 (y + 8) = -3 (x - 8)
4y + 32 = -3x + 24
3x + 4y = -8
Hence, The equation of the line that passes through the point (8,-8) and is perpendicular to the line 4x – 3y = 18 is;
⇒ 3x + 4y = -8
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The five members of the Traynor family each buy train tickets. During the train ride, each family member buys a boxed lunch for $6.50. If the total cost of the trip is $248.50, what is the price of each train ticket?
Answer:
Step-by-step explanation:
it’s B
Bro I don't know haha
What is the completely factored form of x3 – 64x?
Answer:
x( x-8)(x+8)
Step-by-step explanation:
x^3 - 64x
Factor out an x
x( x^2 -64)
This is the difference of squares x^2 -8^2 which is a^2 - b^2 = (a-b)(a+b)
x( x-8)(x+8)
Answer:
[tex]x(x - 8)(x + 8)[/tex]
Step-by-step explanation:
[tex] {x}^{3} - 64x \\ x( {x}^{2} - 64) \\ x( {x}^{2} - {8}^{2} ) \\ = x(x - 8)(x + 8)[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
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Answer:
[tex] \boxed{D. \: (f-g)(x) = {x}^{2} + 4x + 3} [/tex]
Given:
[tex]f(x) =2 {x}^{2} - 5 \\ g(x) = {x}^{2} - 4x - 8[/tex]
To find:
[tex](f - g)(x) = f(x) - g(x)[/tex]
Step-by-step explanation:
[tex] \implies(f - g)x = f(x) - g(x) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (2 {x}^{2} - 5) - ( {x}^{2} - 4x - 8) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (2 {x}^{2} - 5) + (- {x}^{2} + 4x + 8) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 {x}^{2} - 5 - {x}^{2} + 4x + 8 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 {x}^{2} - {x}^{2} + 4x - 5 + 8 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 4x + 8 - 5 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 4x + 3[/tex]
Today you will need to look at the following problem and explain what Susan did incorrectly. You can explain what she did incorrectly and how to do it correctly
Answer:
see below
Step-by-step explanation:
The equation of a circle can be written as
( x-h) ^2 + (y-k) ^2 = r^2
( x-3)^2 + (y+4) ^2 = 36
Rewriting this equation
( x - 3)^2 + ( y - -4)^2 = 6^2
The center is at (3,-4) and the radius is at 6
Susan did not use the formula correctly.
It is x-h and y-k so she needed to rewrite to get the equation in the proper form
Also the radius is r^2 not r/2
Factorize x squared - 1x +10 =0
Answer:
no solution exists:
Step-by-step explanation:
x²−1x+10=0
Step 1: Simplify both sides of the equation.
x²−x+10=0
Step 2: Subtract 10 from both sides.
x²−x+10−10=0−10
x²−x=−10
Step 3: The coefficient of -x is -1. Let b=-1.
Then we need to add (b/2)^2=1/4 to both sides to complete the square.
Add 1/4 to both sides.
x²−x+ 1/4=−10+ 1/4
x²−x+ 1/4=−39 /4
Step 4: Factor left side.
(x -1/2)² = −39 /4
Step 5: Take square root.
x −1 /2 =±√ −39 /4
Step 6: Add 1/2 to both sides.
x =−1/2 + 1/2 = 1/2 ±√ -39/4
x = 1/2 ±√ -39/4
No real solutions.
Which of the following is an equivalent equation to find w
[tex]answer \\ w = \frac{ {8x}^{2} - 2y }{y} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
A bag has the following 10 colored stones in it. There are 2 red, 2 blue, 1 orange, 2 purple and 3 green stones. What is the probability of a green stone?
Answer:
30%
Step-by-step explanation:
Think of the 10 as 100%. 2 as 20% and so on. The green makes up 30%.
What is the measure of RST?
Answer:
The answer is D.
Step-by-step explanation:
You have to divide it by 2 :
∠RST = ∠ROT ÷ 2
= 46° ÷ 2
= 23°
O represents the centre of circle.
(Correct me if I am wrong)
Answer:
D. 23°
Step-by-step explanation:
The measure of central angle is twice the angle of circumference lying on the same arc. So,
<RT = 2(<RST)
<RST = <RT/2
<RST = 46/2
<RST = 23°
Find the equation of the circle whose center and radius are given. center ( 7, -3), radius = √7
Answer & Step-by-step explanation:
The equation of a circle is...
[tex](x-x1)^2+(y-y1)^2=r^2[/tex]
So all we have to do is plug in the numbers we are given.
So, the equation of the circle is (x - 7)² + (y + 3)² = √7²
Answer:
[tex](x - 7)^{2} + (y + 3)^{2} = 7[/tex]
Step-by-step explanation:
Just finished this quiz and checked the answer key.
Hope this helps
does anyone know the bottom answer please
Answer:
6000000 divided by 10 = 600000
Step-by-step explanation:
Your answer should make sense
What is the probability that a card drawn randomly from a standard deck of 52 cards is a nine? Express your answer as a fraction in lowest
terms or a decimal rounded to the nearest millionth.
Answer:
1/13
Step-by-step explanation:
There are 4 nines in a deck so the probability is 4/52 = 1/13
The probability that a card drawn randomly from a standard deck of 52 cards is a nine is 1/13.
What is Probability?
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, Total outcomes = 52 cards
Number of cards which contain 9 = 4 cards
Probability = favorable outcomes/ total outcomes
= 4 / 52
= 1/13
Thus, The probability that a card drawn randomly from a standard deck of 52 cards is a nine is 1/13.
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What is -3 1/2 ÷ 4/9 = ???
Answer: -7.875
Step-by-step explanation:
Amanda has at most $40 to spend on flowers. She wants to buy a pair of red rose flowers for $18 dollars and spend the rest on lily flower. Each lily flower costs $11. Write an inequality for the number of lily flowers she can purchase
Answer:
x ≤ 2
Step-by-step explanation:
2 red rose cost $ 18
x flowers cost $ 11x
"At most " means ≤.
11x + 18 ≤ 40
11x ≤ 40 - 18
11x ≤ 22
x ≤ 2
Using inequality we know that Amanda can purchase 2 lily flowers.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity.So, the inequality can be:
Monet Amanda can spend is $40.She purchased a pair of roses worth $18.Rest we want to wants to buy lily, which costs $11 each.Now, the inequality will be:
Let, the number of lilies is x and Amanda purchases 2 lilies:
18 + 2x ≤ 4018 + 2(11) ≤ 4018 + 22 ≤ 4040 = 40Therefore, using inequality we know that Amanda can purchase 2 lily flowers.
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what are the domain and range of the function on the graph
In QRS m Q = 80 degrees m R = 65 degrees m S = 35 degrees which side of the QRS is the longest
Answer: RS
Step-by-step explanation:
A greater angle of a triangle is opposite a greater side. If angle Q is greater than angle R, then side RS is greater than side QS.
Because Q is the larger angle in the triangle, Then RS is the longest side.
I need help pleaseeee
Answer:
8.4375
Step-by-step explanation:
multiply 2.5 times 2.25 times 1.5
lenght x width x height
A dolphin jumps 3 feet above sea level to go through a ring. The dolphin starts at the opposite distance below sea level. How far does the dolphin travel from its starting position to the top of it's jump?
Answer:
6 feet
Step-by-step explanation:
The dolphin jumps 3 feet above sea level and it starts from the opposite distance below sea level.
This means that it starts from 3 feet below sea level.
The total distance the dolphin travels from its starting point to the top of the jump is therefore:
3 + 3 = 6 feet
Answer 5, 6 , and 7 by today please.
Answer:
Step-by-step explanation:
5. a) ∠1 and ∠2 are remote interior angles of ∠ACD so that means that ∠ACD = ∠1 + ∠2
b) Because an exterior angle is the sum of its two remote interior angles it makes sense that an exterior angle is greater in measure than either of its remote interior angles.
6. BD = DB Reflexive property
∠3 = ∠5, ∠4 = ∠6 Alt. int. angles
ΔADB = ΔCDB ASA
7. AB = BC Def. of midpoint
∠1 = ∠2 Given
∠BAE = ∠CBD Corresponding angles
ΔBAE = ΔCBD ASA
∠D = ∠E CPCTC
Which of the following is the correct factored form of the given equation?
4x2 - 11x + 6 = 0
(2x + 3)(2x + 2) = 0
(2x - 3)(2x - 2) = 0
(4x - 3)(x - 2) = 0
Answer:
[tex](4x - 3)(x - 2) = 0[/tex]
Last answer is correct
Step-by-step explanation:
[tex]4 {x}^{2} - 11x + 6 = 0 \\ 4 {x}^{2} - 8x - 3x + 6 = 0 \\ 4x(x - 2) - 3(x - 2) = 0 \\ (4x - 3)(x - 2) = 0[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
who can solve ? 9y < -3
Answer:
y< -1/3
Step-by-step explanation:
To solve the inequality, we must get the variable, y, by itself.
9y< -3
Perform the opposite of what is being done to the equation, to both sides.
y is being multiplied by 9. The opposite of multiplication is division. Therefore, divide both sides by 9.
9y/9 < -3/9
y< -3/9
-3/9 can be reduced. 3 can be divided evenly into both the numerator (top number) and denominator (bottom number).
y< (-3/3) / (9/3)
y< -1/3
I’ll mark you brainliest! What is the answer???
Answer:
A
Step-by-step explanation:
[tex]f(x)=9(3)^x \\\\\\f(-3)=9(3)^{-3}= \\\\\\9\left(\dfrac{1}{3^3} \right)= \\\\\\9\left(\dfrac{1}{27} \right)= \\\\\\\dfrac{9}{27}= \\\\\\\dfrac{1}{3}[/tex]
Hope this helps!
the middle number; put the values in order from lowest to highest, then find the number that is exactly in the middle
2x - 4(4x - 8) = -94 solve for x
Answer:
x =9
Step-by-step explanation:
2x - 4(4x - 8) = -94
Distribute
2x - 16x +32 = -94
Combine terms
-14x +32 = -94
Subtract 32 from each side
-14x+32-32 = -94-32
-14x =-126
Divide each side by 14
-14x/-14 = -126/-14
x =9
Answer:
9
Step-by-step explanation:
Looking at the histogram, where would the median fall?
Answer:
The median would be found in the middle of the histogram
Step-by-step explanation:
It looks like 70-79, would fall in being the median because it is in the middle and it has the most results. In this case, I think it 70-79.
Hope this helps.
Answer:
70-79
Step-by-step explanation:
I took the test :)
I WILL MARK AS BRAINLIST
Answer:
18 square meters
Step-by-step explanation:
Answer:
7.5 square meterssolution,
The given figure if a Trapezium whose parallel sides are of 3 m and 2 m respectively.
Distance between the parallels sides
i.e. height is 3 m
Now,
[tex]area = \frac{1}{2} \times sum \: of \: parallel \: sides \times height \\ = \frac{1}{2} \times (3 + 2) \times 3 \\ = \frac{1}{2} \times 5 \times 3 \\ = \frac{15}{2} \\ = 7.5 \: {m}^{2} [/tex]
Hope this helps...
Good luck on your assignment...
