This is a translation of one unit up of f(x), and we will get:
f(x) + 1 = 3x + 3
How to find the value of f(x) + 1?
Here we need to learn to rewrite functions:
Here we know that:
f(x) = 3x + 2
And
g(x) = x^2 - x
(we will not use g(x) in this problem)
So, f(x) +1 can be rewritten by just replacing f(x) by the equation above, so we can redefine:
h(x) = f(x) + 1
Now we replace the function f of x to get:
h(x) = 3x + 2 + 1 = 3x + 3
In this way, we conclude that:
f(x) + 1 = 3x + 3
This is a translation of one unit up of f(x).
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The midpoint of \overline{\text{AB}} AB is M(-4, -3)M(−4,−3). If the coordinates of AA are (-1, -2)(−1,−2), what are the coordinates of BB?
The midpoint of AB is M(-4, -3). If the coordinates of A are (−1,−2), then B has coordinates of (-2, -7/3)
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.
Line AB has a midpoint, M.
A is (-1, -2)
B is unknown, M is(−4,−3)
Let's assume straight line of the form y=mx+b, where m is the slope.
Rise = (-3-(-2))= -1
Run = (-4-(-1)) = -3
Slope = (Rise/Run) = (1/3)
The line becomes y=(1/3)x+b
Calculate b, the y-intercept (the value of y when x is 0)
y=(1/3)x+b
-2 = (1/3)(-1)+b
b = -2 + (1/3)
b = -5/3
The equation becomes:
y=(1/3)x - -5/3
Find the value of y for x=-2:
y=(1/3)x - -5/3
y=(1/3)(-2) - 5/3
y= -7/3
B has coordinates of (-2, -7/3)
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The width of a vegetable garden is 1/4 times its length. If the length of the garden is 5 1/2 feet, what is the width in simplest form?
Answer:
W = 11/8 or 1 3/8
Step-by-step explanation:
The width of a vegetable garden is 1/4 times its length. If the length of the garden is 5 1/2 feet, what is the width in simplest form?
W=(1/4)(L)
width is 1/4 length
if the length is 5 1/2 ft
5 1/2 is equivalent to 11/2
W= (1/4)(11/2)
Multiply across.
W = 11/8 or 1 3/8
2(3) 3 as an exponent + 5
Answer: 13
Step-by-step explanation:
A farmer has 30 boxes of eggs.
6 There are 6 eggs in each box.
Write, as a ratio, the number of eggs in three boxes to the total number of eggs.
Give your answer in its simplest form
Answer: 1:15
Step-by-step explanation:
we know that the total number of eggs is the same as the number of eggs in 30 boxes. Hence the ratio will be 2 : 30, and then divide both sides by 2 to get 1 : 15 as the ratio in its simplest terms.
The ratio of the number of eggs in three boxes to the total number of eggs is 1 : 10.
We have,
To find the ratio of the number of eggs in three boxes to the total number of eggs, first, let's calculate the number of eggs in three boxes:
Number of eggs in three boxes
= 3 boxes * 6 eggs per box
= 18 eggs
Now, the ratio of the number of eggs in three boxes to the total number of eggs is:
18 eggs : 30 boxes x 6 eggs per box
18 eggs : 180 eggs
Cancel out the common factors.
1 egg : 10 eggs
So, the simplified ratio is:
1 egg : 10 boxes
Therefore,
The ratio of the number of eggs in three boxes to the total number of eggs is 1 : 10.
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The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55.
The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10.
Work out the cost of
a) 1 kg of turnips.
b) 1 kg of mushrooms.
The cost of one kg of mushroom is $2.90 while the cost of 1 kg of turnips is $1.10
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.
Let x represent the cost of on kg of mushroom and y represent the cost of one kg of turnips.
The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55. Hence:
2x + 2.5y = 8.55 (1)
The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10. Hence:
3x + 4y = 13.10 (2)
From both equations:
x = 2.9, y = 1.1
The cost of one kg of mushroom is $2.90 while the cost of 1 kg of turnips is $1.10
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Factor the expression. 8+27 x³
The factored form of the given expression is (3x+2)(9x²-6x+4).
Given the expression is 27x³+8.
In order to be factor out any polynomial expression, we want to identify firstly the method of factoring to be used in the given expression. We also need to simplify the factors.
We are given the expression 27x³+8.
We want to factor out the given expression.
Applying the sum of two cubes formula x³+y³=(x+y)(x²-xy+y²), we have:
27x³+8=(3x)³+(2)³
27x³+8=(3x+2)(3²x²-3x·2+2²)
27x³+8=(3x+2)(9x²-6x+4)
Hence, the factored form of the given expression 27x³+8 is (3x+2)(9x²-6x+4).
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Fiona is heating water for a science experiment the temperature of the water increases 4/5 of a degree every 2/5 of a minute how much is the temperature of the water increasing per minute.
Answer needed ASAP
thanks
The temperature that water is increasing per minute is 2 degrees.
What is the increase in temperature per minute?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the digit above the line and the denominator is the number below the line. An example of a fraction is 3/7.
The first step is to determine what 2/5 of a minute is equivalent to in seconds.
1 minute = 60 seconds
2/5 x 60 = 24 seconds
The formula that can be used to determine the temperature that water is increasing per minute is :
Temperature increase per minute = (degree it rises to 2/5 of a minute x seconds in a minute) / seconds in 2/4 of a minute
(4/5 x 60) / 24 = 2 degrees
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the table shows a proportional relationship between the millilitres (ml) of red paint and millilitres of yellow paint to make a certain shade of orange.
The department store sells logo t-shirts at an original price of $12.50. Every month that a t-shirt doesn’t sell, the store reduces the price by 25%. Brianna calculated the price after two reductions:
12 dollars and 50 cents minus (12 dollars and 50 cents) (0.25) minus (12 dollars and 50 cents) (0.25) = 6 dollars and 25 cents
What is Brianna’s error?
Answer:
On the second reduction, she reduced 25% of the original T-Shirt's price. She should have reduced the price of the T-Shirt after one reduction.
Step-by-step explanation:
Iggy bought the refrigerator on a payment plan.He paid $150 when he bought it and he agreed to pay $28.50 each month for the next 24 months.
Answer:834$
Step-by-step:150+28.24=834$
$74.95 ladder; 6.5% tax
Answer:
11.5307692308
Step-by-step explanation:
Answer:
Around $79.88
8x = 2
Write down the value of x.
(It’s not 2/8 or 0.25)
Answer:
1/4
Step-by-step explanation:
Get x by itself by dividing both sides by 8
x = 2/8
Reduce
1/4
Answer:
8x=2
/8 /8
Step-by-step explanation:
it is 0.25
8x=2
/8 /8
x=0.25
Please help me calculate the value of y with steps
The value of y in the triangle is 7.5
How to calculate the value of y?The given parameter is the triangle
On the triangle, we have the following equivalent ratio
y : 8 = y + 15 : 20
Express as fraction
y/8 = y + 15/20
Cross multiply
20y = 8y + 90
Collect the like terms
20y - 8y = 90
Evaluate
12y = 90
Divide by 12
y = 7.5
Hence, the value of y in the triangle is 7.5
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The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched a in square feet and the depth of the mulch d in feet. If you need 10 bags to mulch 120ft² to a depth of 3in., how many bags do you need to mulch 200ft² to a depth of 4in ?
To cover 200 ft2 to a depth of 4 inches, we'll need 22(2/9) bags of mulch.
What do we mean by depth?The depth of an object is defined as the distance between its nearest and farthest ends in mathematics. The vertical magnitude of an object is measured by its height. Depth is also a measure of an object's vertical magnitude. These two terms appear to represent the same quantity.So,
When z "varies jointly" with x and y, the following formula can be used to describe it:
z = kxy
Here, we have mulch bags (n) that vary with the area (a) and depth (d), both in feet.
The information provided allows us to calculate the value of k.
n = kad10 = k·(120)(1/4)10/30 = k = 1/3 (divide by the k coefficient)Now we can fill in the blanks with the other values of interest.
n = (1/3)·(200)·(1/3) = 200/9n = 22(2/9)Therefore, to cover 200 ft2 to a depth of 4 inches, we'll need 22(2/9) bags of mulch.
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What is the value of (−12)4?
Answer:
-48
Step-by-step explanation:
[tex](-12)4\\(-12) \times 4\\= -48[/tex]
Answer: -48
Step-by-step explanation:
negative x negative x negative x negative = negative
12 x 4 = 48
remember the answer needs to be a negative
(-12)4 = -48
Question 10: Neil writes down four numbers with a sum of 50.
All the numbers have two decimal places and no two numbers are the same.
Write down four possible numbers Neil could have written down.
Answer:
15-10-11-14
Step-by-step explanation:
15+10= 25
25+11= 36
36+14= 50
igcse math (quadratic functions)
given the equation: x^2 + 5x - 14
use the discriminant to decide if there are two real and different roots, two equal roots or no real roots
Answer:
2 real different roots
Step-by-step explanation:
Discriminant determines the number of real solutions of a quadratic equation. The formula of discriminant goes by:
[tex]\displaystyle{D = b^2-4ac}[/tex]
The formula is derived from a quadratic formula which is:
[tex]\displaystyle{x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]
The expression inside the square root is discriminant. The discriminant says that:
There are 2 real different roots if the discriminant (D) is greater than 0. (D > 0)There is 2 real double roots (same roots) if the discriminant (D) is equal to 0. (D = 0)There are no real roots (imaginary or complex roots) if the discriminant (D) is less than 0. (D < 0)From the equation [tex]\displaystyle{x^2+5x-14}[/tex], determine the coefficients of equation:
a = 1b = 5c = -14Therefore, substitute the coefficients’ values in the discriminant:
[tex]\displaystyle{D=5^2-4(1)(-14)}\\\\\displaystyle{D=25-4(-14)}\\\\\displaystyle{D=25+56}\\\\\displaystyle{D=81}[/tex]
Since the discriminant is greater than 0, we can conclude that this equation will have 2 real different roots.
Row a in a certain section in a football stadium has 10 seats. each row behind row a is labeled alphabetically (b, c, d, and so on) and has 6 more seats than the row immediately in front of it.how many seats are in row g of this section of the stadium?
The total number of seats in row g is 224.
Number of seats in a row a = 10
Number of seats in row b = 16
Number of seats in row c = 22
The common difference is d.
d = (22-16) = 6
The first term is a.
a = 10
The total number of rows is n.
n = 7
[tex]a _{n} = a + (n - 1)d[/tex]
[tex]a _{n} = 10 + (7 - 1)6[/tex]
= 46
The total number of seats in row g is,
[tex]S _{n} = \frac{n}{2} (a + a _{n})[/tex]
[tex]S _{n} = \frac{8}{2} (10 + 46)[/tex]
= 224
Therefore, the total number of seats in row g is 224.
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Find the slope of the line that goes through the points (–4, 1) and (8, –5).
Answer:
[tex]\frac{-1}{2}[/tex]
Step-by-step explanation:
Slope is the change in y over the change in x.
The ordered pair is in the form (x,y). The first number is the x value and the second number is the y value.
for y;
-5 - 1 = -6
for x:
8 - (-4)
8 + 4
12
[tex]\frac{-6}{12}[/tex] Which is the same as [tex]\frac{-1}{2}[/tex] if we divide the top and bottom by 6
In the first quadrant, you start at (6, 3)
and move 2 units left
What point will you end up on?
Answer: the answer is (6,1)
Step-by-step explanation:
Answer:
(4, 3)
Step-by-step explanation:
If you are moving 2 units left, the x coordinate is shifted to the left by 2 units, the y coordinate remains the same.
A shift to the left means a decrease in the x-coordinate value so new
x-coordinate is 6- 2 = 4 , y coordinate is still 3 so you end up at point (4, 3)
Which relation is a function?
Using the vertical line test, we conclude that the relation that is a function is the bottom right one.
Which of the graphed relations is a function?
A relation is a function only if all the inputs are mapped into a single output.
If we have the graph of a relation, it only will be a function if it passes the vertical line test.
This means that if we draw any vertical line on the coordinate axis, and it intercepts the graph of the relation more than once, then it is not a function.
With that we can see that the first 3 options are not functions, and the last one (bottom right) it is a function.
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Doy muchos puntos pls ayuda
Answer:
5. 18%
6. 5.25% o 5.3 o 5
7. 33.33%
8. 2005-2010
if a one time deposit of $1000 in invested at age 25 with 12% annual interest rate, how much will be in the account at age 65 (40 years later)?
The amount in the account after 40 years will be $5800.
How to illustrate the information?It should be noted that the interest is calculated as:
= (Principal × Rate × Time) / 100
= ($1000 × 12 × 40) / 100
= $480000 / 100
= $4800
Therefore, the amount in the account after 40 years will be:
= Principal + Interest
= $1000 + $4800
= $5800
Therefore, the amount in the account after 40 years will be $5800.
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Multiply and simplify. √8 x² . √2 x²
The simplest form of the expression is 4 x² .
Expressions in science are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by degree operator in between.Simplifying expressions mean editing an analogous math expression with no like terms and through a compact manner.To change expressions, we tend to tend to combine all kind terms and solve all the given brackets, if any, and then inside the simplified expression, we tend to are about to be alone left with not like terms that cannot be reduced any.We have given an expression √8 x² . √2 x² . .....(1)
On multiplying , we get
√8 x² . √2 x² = √16 x⁴
On simplifying , we get
√16 x⁴ = √ 4 × 4 × x² × x²
= 4 x²
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Motorcycle A can reach a top speed of 140 miles per hour motorcycle B can reach a top speed of 200 feet per second which motorcycle has a greater top speed
Motorcycle A has a greater top speed.
What unit conversion?A unit conversion expresses the same property as a different unit of measurement.
given:
Motorcycle A can reach a top speed of 140 miles per hour.
Motorcycle B can reach a top speed of 200 feet per second
Now,
1 miles/h = 1.46667 feet/sec
140 miles/h = 140*
= 205.333 feet/sec
So, Motorcycle A can reach a top speed of 205.333 feet/sec.
Hence, Motorcycle A has a greater top speed
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What is each expression written as a single natural logarithm?
(c) 3 ln x+2 ln y+ln 5
According to the question, to write the solution for the logarithmic function, the concept of indices is also needed.
Therefore, the given expression is [tex]3 ln x+2 ln y = ln5[/tex]
The values get multiplied in addition. Therefore, the above expression can be written as: [tex]ln(x^{3} )+ln(y^{2} )+ln5[/tex]
Expression = [tex]ln(x^{3} )+ln(y^{2} )+ln5[/tex]
Using logarithmic definition, we can write:
[tex]ln(x^{3} )+ln(y^{2} )+ln5\\ln(5x^{3} y^{2} )[/tex]
The solution for the given expression is [tex]ln(5x^{3}y^{2} )[/tex]
What is logarithmic function?
In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.
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Let g(x)=5 x-2 and h(x)=x²+1 . Find the value of each expression. (h⁰g)(0)
The value of the expression ( h o g)(0) is 5.
When two functions say f and g, are composed in such a way that h(x) = g(f(x)), a new function, h, is created. In this case, the function of g is being applied to the function of x. So, in essence, the output of one function is applied to the result of another.
Consider the two functions,
g(x) = 5x - 2 and h(x) = x² + 1
So,
( h o g)(x) = h(g(x))
( h o g)(x) = ( 5x - 2 )² + 1
( h o g)(x) = 25x² - 20x + 4 + 1
( h o g)(x) = 25x² - 20x + 5
( h o g)(0) = 25 × (0)² - 20 × (0) + 4 + 1
( h o g)(0) = 0 - 0 + 4 + 1
( h o g)(0) = 5
The value of the expression ( h o g)(0) is 5.
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Which of the following vertices would minimize the objective function N = 7x + 2y?
A. (4,0)
B. (6,3)
C. (3,9)
D. (0,12)
Check the picture below.
Please help fast thank you!
Answer:
-3.78= (-1.2y)+(-4.2y)
y= 0.7
Step-by-step explanation:
-3.78= (-1.2y)+(-4.2y)
-3.78= -5.4y
/-5.4 /-5.4
y=0.7
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The equation of the inverse function of the function f(x) = x^2 - x - 2 is f'1(x) = 0.5 + √x + 2.25
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function
How to determine the inverse function?The function f(x) is given as
f(x) = x^2 - x - 2
Start by expressing the above function in vertex form
Using a graphing calculator, we have
f(x) = (x - 0.5)^2 - 2.25
As a general rule, we start by writing f(x) as a variable (say f(x) = y).
So, the equation of the function becomes
y = (x - 0.5)^2 - 2.25
The next step is to switch/swap the positions of x and y in the above equation y = (x - 0.5)^2 - 2.25
The equation becomes
x = (y - 0.5)^2 - 2.25
Add 2.25 to both sides
So, we have
(y - 0.5)^2 = x + 2.25
Take the square root of both sides
y - 0.5 = √x + 2.25
Add 0.5 to both sides
So, we have
y = 0.5 + √x + 2.25
Express as an inverse function
f'1(x) = 0.5 + √x + 2.25
Hence, the inverse function of the function f(x) = x^2 - x - 2 is f'1(x) = 0.5 + √x + 2.25
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