Answer:
TELL HIM TO STOP BEING SO CHEAP!!!!!!!!! <3
and i oop-
Step-by-step explanation:
Evaluate -3x3-4x for x= -1.
1
7
-1
ANSWER
The correct a sweet is 7
EXPLANATION
The given algebraic expression is;
[tex]f(x) = - 3 {x}^{3} - 4x[/tex]
To evaluate this function for f means, we should substitute x=-1 wherever we see x in the given expression.
[tex] f( - 1) = - 3 { (-1 )}^{3} - 4( - 1)[/tex]
[tex]f( - 1) = - 3 { (-1 )} - 4( - 1)[/tex]
This simplifies to
[tex]f( - 1) = 3 + 4[/tex]
[tex]f( - 1) = 7[/tex]
The correct answer is 7
the end points of AB are A(2,3) and B(8,1). The perpendicular bisector of AB is CD, and point C lies on AB. The length of CD is square root of 10 units. the coordinates of point C are? the slope of CD is? the possible coordinates of point D are ____ and ?
Answer:
The coordinates of C are (5 , 2)
The slope of CD is 3
The coordinates of D are (6 , 5) and (4 , -1)
Step-by-step explanation:
* Now lets study the problem
- The ends points of line AB are A = 2 , 3) and B = (8 , 1)
- CD is the perpendicular bisector of AB, and C lies on AB
- That means:
# C is the mid-point of AB
# The slope of AB × the slope of CD = -1 (one of them is a multiplicative
inverse and additive inverse of the other)
-Ex: the slope of one is a/b, then the slope of the other is -b/a
* The mid-point between two points (x1 , y1) and (x2 , y2) is:
[(x1 + x2)/2 , (y1 + y2)/2]
∵ C is the mid-point of AB
∴ C = [(2 + 8)/2 , (3 + 1)/2] = [10/2 , 4/2] = (5 , 2)
* The coordinates of C are (5 , 2)
- The slope of a line passing through points (x1 , y1) and (x2 , y2) is:
the slope = (y2 - y1)/(x2 - x1)
∴ The slope of AB = (1 - 3)/(8 -2) = -2/6 = -1/3
∵ CD ⊥ AB
∴ The slope of CD × the slope of AB = -1
∴ The slope of CD = 3
* The slope of CD is 3
- The length of a line passing through points (x1 , y1) and (x2 , y2) is:
the length = √[(x2 - x1)² + (y2 - y1)²]
∵ The length of CD = √10
∵ Point D is (x , y)
∴ (x - 5)² + (y - 2)² = (√10)²
∴ (x - 5)² + (y - 2)² = 10 ⇒ (1)
∵ The slope of CD is (y - 2)/(x - 5) = 3 ⇒ by using cross multiply
∴ (y - 2) = 3(x - 5) ⇒ (2)
- Substitute (2) in (1)
∴ (x - 5)² + [3(x - 5)]² = 10 ⇒ simplify
* [3(x - 5)]² = (3)²(x - 5)² = 9(x - 5)²
∴ (x - 5)² + 9(x - 5)² = 10 ⇒ add the like terms
∴ 10(x - 5)² = 10 ⇒ ÷ 10 both sides
∴ (x - 5)² = 1 ⇒ take √ for both sides
∴ x - 5 = ± 1
∴ x - 5 = 1 ⇒ add 5 to both sides
∴ x = 6
* OR
∴ x - 5 = -1 ⇒ add 5 to both sides
∴ x = 4
- Substitute the values of x in (2)
∴ y - 2 = 3(6 - 5)
∴ y - 2 = 3 ⇒ add 2
∴ y = 5
* OR
∴ y - 2 = 3(4 - 5)
∴ y - 2 = -3 ⇒ add 2
∴ y = -1
* The coordinates of D are (6 , 5) and (4 , -1)
Answer and Step-by-step explanation:
Answer:
The coordinates of C are (5 , 2)
The slope of CD is 3
The coordinates of D are (6 , 5) and (4 , -1)
Step-by-step explanation:
* Now lets study the problem
- The ends points of line AB are A = 2 , 3) and B = (8 , 1)
- CD is the perpendicular bisector of AB, and C lies on AB
- That means:
# C is the mid-point of AB
# The slope of AB × the slope of CD = -1 (one of them is a multiplicative
inverse and additive inverse of the other)
-Ex: the slope of one is a/b, then the slope of the other is -b/a
* The mid-point between two points (x1 , y1) and (x2 , y2) is:
[(x1 + x2)/2 , (y1 + y2)/2]
∵ C is the mid-point of AB
∴ C = [(2 + 8)/2 , (3 + 1)/2] = [10/2 , 4/2] = (5 , 2)
* The coordinates of C are (5 , 2)
- The slope of a line passing through points (x1 , y1) and (x2 , y2) is:
the slope = (y2 - y1)/(x2 - x1)
∴ The slope of AB = (1 - 3)/(8 -2) = -2/6 = -1/3
∵ CD ⊥ AB
∴ The slope of CD × the slope of AB = -1
∴ The slope of CD = 3
* The slope of CD is 3
- The length of a line passing through points (x1 , y1) and (x2 , y2) is:
the length = √[(x2 - x1)² + (y2 - y1)²]
∵ The length of CD = √10
∵ Point D is (x , y)
∴ (x - 5)² + (y - 2)² = (√10)²
∴ (x - 5)² + (y - 2)² = 10 ⇒ (1)
∵ The slope of CD is (y - 2)/(x - 5) = 3 ⇒ by using cross multiply
∴ (y - 2) = 3(x - 5) ⇒ (2)
- Substitute (2) in (1)
∴ (x - 5)² + [3(x - 5)]² = 10 ⇒ simplify
* [3(x - 5)]² = (3)²(x - 5)² = 9(x - 5)²
∴ (x - 5)² + 9(x - 5)² = 10 ⇒ add the like terms
∴ 10(x - 5)² = 10 ⇒ ÷ 10 both sides
∴ (x - 5)² = 1 ⇒ take √ for both sides
∴ x - 5 = ± 1
∴ x - 5 = 1 ⇒ add 5 to both sides
∴ x = 6
* OR
∴ x - 5 = -1 ⇒ add 5 to both sides
∴ x = 4
- Substitute the values of x in (2)
∴ y - 2 = 3(6 - 5)
∴ y - 2 = 3 ⇒ add 2
∴ y = 5
* OR
∴ y - 2 = 3(4 - 5)
∴ y - 2 = -3 ⇒ add 2
∴ y = -1
* The coordinates of D are (6 , 5) and (4 , -1)
What expression is represented by the factorization below?
(3x+2)(3x - 2)
Answer:
9x^2-4
Step-by-step explanation:
use FOIL
9x²-4 is represented by the factorization.
What is factorization?Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.
Given
(3x+2)(3x - 2)
= 9x² + 6x - 6x -4
= 9x² -4
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The data shows the amounts, in thousands of dollars sold by salespeople in a company.
10, 9, 12, 3, 2, 7, 2, 4, 9, 15, 13, 4, 7, 8
Create a histogram of this data.
To create a histogram, hover over each distance range on the x-axis. Then click and drag up to plot the data.
The histogram would look something like this:
To graph a histogram, find out how many values (on the x-axis) are in a column for a specific value and make the column as high as that value (on the y-axis)Hope I helped and please give me brainliest!
The wind has blown a tree so that it is growing at a 108° angle with the ground. The top of the tree is 75 ft. from the ground. How tall is the tree?
Answer: 78.85 ft
Step-by-step explanation:
Based on the information provided in the exercise, you can draw the right triangle attached, wheree "x" is the height of the tree.
You need to remember the following identity:
[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]
By definition:
[tex]\alpha+108\°=180\°[/tex]
Then, this is:
[tex]\alpha=180\°-108\°\\\alpha =72\°[/tex]
In the right triangle shown in the figure, you can identify:
[tex]opposite=75\\hypotenuse=x[/tex]
Then, you need to substitute the corresponding values into [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]:
[tex]sin(72\°)=\frac{75}{x}[/tex]
Now, you can solve for "x":
[tex]xsin(72\°)=75\\\\x=\frac{75}{sin(72\°)}\\\\x=78.85\ ft[/tex]
PLEASE HELP!!! the plot and table show the total number of people ,p who have bought tickets to a concert ,t ,minutes after they went on sale. the equation to show the relationship between p and t
Answer:
answer is 25t I DID THE TEST!!
Answer: 25F i did the test
Step-by-step explanation:
The graph of the function f (x) is shown below. When f(x)=0,x=?
Answer:
0
Step-by-step explanation:
From the graph of the function f(x) we have:
When f(x)=0 , x= -1.8
Step-by-step explanation:By looking at the graph we observe that the graph first increases in the interval (-∞,-1.2) and then it decreases in the interval (-1.2,0.6) and then again it increases in the interval (0.6,∞).
Hence, the graph of the function is neither strictly increasing nor strictly decreasing in the whole of the real line.
Also, when x=0 the value of the function is: f(x)=5
( Since, the graph passes through the point (0,5) )
Also, when f(x)=0
then x= -1.8
( Since, the graph of the function passes through the point (-1.8,0) )
A company models its net income, in thousands of dollars, with the function f(x) = 9x2 - 54x - 144, where x is the number of units of its product sold.
How many units of its product does the company need to sell in order for the net income to equal $0?
Answer:
x=9 and x=-2
Step-by-step explanation:
GFC = 9 => 9(x²-6x-16) =0
9(x-8)(x+2) = 0
x-b=0 x+2= 0
x=8 and x = -2
Solving the quadratic equation, it is found that the company needs to sell 8 products for the net income to be equal $0.
What is the quadratic equation for the net income of the company?It is given by:
f(x) = 9x² - 54x - 144.
It can be simplified as follows:
f(x) = 9(x² - 6x - 16)
Then:
f(x) = 9[(x + 2)(x - 8)]
It has a net income equals to 0 when:
f(x) = 0, hence:
x + 2 = 0 -> x = -2.x - 8 = 0 -> x = 8.The amount of products sold is positive, hence, the company needs to sell 8 products for the net income to be equal $0.
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A family has two cars. The first car has a fuel efficuency of 15 miles per gallon of gas and the second has a fuel efficiency of 35 miles per gallon of gas. During one particular week, the two cars went a combined total of 1925 miles, for a total gas consumtion of 75 gallons. How many gallons were consumed by each of the two cars that week?
Answer:
x= 35 gallons consumed by 1st car
and y= 40 gallons consumed by 2nd car
Step-by-step explanation:
Fuel efficiency of 1st car = 15 miles per gallon
Fuel efficiency of 2nd car = 35 miles per gallon
Let x= gallons consumed by 1st car
and y= gallons consumed by 2nd car
Total gallons consumed by both cars = 75
so, we can write
x + y = 75
Miles covered by both cars = 1925 miles
and we know, Fuel efficiency of 1st car = 15 miles per gallon
Fuel efficiency of 2nd car = 35 miles per gallon
we can write the equation as
15 x + 35 y = 1925
where x and y are gallons consumed by 1st and 2nd car.
We have two equation now,
x + y = 75 (1)
15 x + 35 y = 1925 (2)
Multiplying eq(1) with 15 and subtracting eq (1) and 2
15 x + 15 y = 1125
15 x + 35 y = 1925
- - -
_______________
0 - 20 y = -800
y= -800 / -20
y = 40
Putting value of y in equation 1
x + y = 75
x + 40 = 75
x= 75 - 40
x = 35
x= 35 gallons consumed by 1st car
and y= 40 gallons consumed by 2nd car
The first car consumed 50 gallons of gas and the second car consumed 25 gallons of gas that week.
Explanation:Let's denote the number of gallons consumed by the first car as x and the number of gallons consumed by the second car as y. Then, we have the following two equations based on the mileage and the total gas consumption:
The total distance covered by the two cars is given by: 15x + 35y = 1925 The total gas consumption by the two cars is: x + y = 75
To solve these two equations, you can first solve the second equation for x, x = 75 - y, and then substitute it into the first equation: 15(75 - y) + 35y = 1925. This gives you y = 25. So, the second car consumed 25 gallons of gas. As the total gas consumption is 75 gallons, the first car must have consumed 75 - 25 = 50 gallons of gas.
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Simplify the expression using long division. (10x2 – 85x – 10) ÷ (x – 8) Question 7 options: quotient 10x – 5 and remainder –50 quotient 10x – 85 and remainder 8 quotient 10x – 5 and remainder –30 quotient 10x + 5 and remainder 30
Answer:
The quotient is (10x - 5) and the reminder is -50 ⇒ 1st answer
Step-by-step explanation:
* Lets solve the long division by easiest way
∵ (10x² - 85x - 10)/(x - 8)
∵ (10x² - 85x - 10) is the dividend
∵ (x - 8) is the divisor
- Divide the first term of the dividend by the first term of the divisor
∴ 10x² ÷ x = 10x ⇒ first term of the quotient
- Multiply 10x by the the divisor
∴ 10x(x - 8) = 10x² - 80x
- Subtract the answer from the dividend
∴ (10x² - 85x - 10) - (10x² - 80x) =
# 10x² - 10x² = 0
# -85x - -80x = -85x + 80x = -5x
# -10
∴ (10x² - 85x - 10)/(x - 8) = 10x + (-5x - 10)/(x - 8)
* Repeat the same steps again with the new dividend -5x - 10
- Divide the first term of the dividend by the first term of the divisor
∴ -5x ÷ x = -5 ⇒ second term of the quotient
- Multiply -5 by the divisor
∴ -5(x - 8) = -5x + 40
- Subtract the answer from the dividend
∴ (-5x - 10) - (-5x + 40) =
# -5x - -5x = -5x + 5x = 0
# -10 - 40 = -50
∴ (-5x - 10)/(x - 8) = -5 + -50/(x - 8)
∴ (10x² - 85x - 10)/(x - 8) = 10x - 5 + -50/(x - 8)
- The quotient is the answer of the division
∴ The quotient is (10x - 5) and the reminder is -50
Answer:
The quotient is 10x - 5 and the reminder is -50
Step-by-step explanation:
What is the measure of angle F?
100
130
140
150
Answer:
140
Step-by-step explanation:
The sum of angles is 360.
9x+14x+4x+90 = 360 => 27x+90 = 360 => 27x = 270 => x = 10 => 14x = 140 => the angle is 140
The measure of angle F is 140
What is a right-angled trapezoid?Two consecutive right angles make up a right trapezoid, also known as a right-angled trapezoid. The trapezoidal rule employs right trapezoids to calculate the areas under a curve. An obtuse trapezoid has one acute and one obtuse angle on each base, whereas an acute trapezoid has two consecutive acute angles on its longer base edge.
Given
Sum of all angles of trapezoid = 360
9x + 14x + 4x+ 90 = 360
27x + 90 = 360
27x = 270
x = 10
F = 14x = 14* 10 = 140
Therefore, The measure of angle F is 140.
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Which expression represents the volume, in cubic units, of the composite figure?
(52)(13) – (52)(12)
(52)(13) – (52)(25)
(52)(13) + (52)(12)
(52)(13) + (52)(25)
Answer:
C. [tex]\pi (5^{2} )(13)+\frac{1}{3} \pi (5^{2} )(12)[/tex]
Step-by-step explanation:
Edge 2021
The volume of the composite figure is given by the expression π(5²)(13) + (1/3)π(5²)(12)
What is volume?
Volume is the amount of space occupied by a three dimensional shape or object.
The volume of the composite figure = volume of cylinder + volume of cone.
Hence:
The volume of the composite figure = π(5²)(13) + (1/3)π(5²)(25 - 13)
The volume of the composite figure = π(5²)(13) + (1/3)π(5²)(12)
The volume of the composite figure is given by the expression π(5²)(13) + (1/3)π(5²)(12)
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Describe a relationship that the graph may represent
Answer:
an increase then a pause then anotha increase
Step-by-step explanation:
What scale factor was applied to the first
rectangle to get the resulting image?
Enter your answer as a decimal in the box
Answer:
The scale factor is [tex]0.25[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional , and this ratio is called the scale factor
Let
z----> the scale factor
x ----> the corresponding side of the resulting image
y-----> the corresponding side of the first rectangle
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=1.5\ units[/tex]
[tex]x=6\ units[/tex]
substitute
[tex]z=\frac{1.5}{6}=0.25[/tex]
Answer:
0.25
Step-by-step explanation:
z=\frac{1.5}{6}=0.25
Please help please is this wrong?
that is incorrect. you would have to do $3.00 divided by 60 which is equal to 0.05. therefore, each crayon costs 0.05. the way you can check that this is right is to do 0.05 multiplied by 60 which will get you to $3.00
Answer:
3.00 is the correct answer
If the great circle circumference of a sphere is 16pie yards, find its surface area
Answer:
Step-by-step explanation:
The circumference of a circle = 2*pi * r
so 16 pi yards = 2 * pi * r
Divide both sides by 2
16 pi/2 = 2*pi * r /2
8*pi = pi * r
Divide both sides by pi
8 * pi / pi = pi * r / pi
r = 8
====================
Surface Area = 4 pi * r^2
r = 8
Surface Area = 4 * pi * 64
Surface Area = 256 * pi
The surface area of the sphere is [tex]\( 256\pi \)[/tex] square yards.
To find the surface area of a sphere given its great circle circumference, we can use the relationship between the circumference and the radius of the sphere.
The formula for the circumference of a great circle of a sphere is:
[tex]\[ C = 2\pi r \][/tex]
We can solve for the radius r
[tex]\[ 16\pi = 2\pi r \][/tex]
r = 8
Next, we use the formula for the surface area A of a sphere:
[tex]\[ A = 4\pi r^2 \][/tex]
Substitute r = 8 into the formula:
[tex]\[ A = 4\pi (8)^2 \][/tex]
[tex]\[ A = 256\pi \][/tex]
Therefore, the surface area of the sphere is [tex]\[ A = 256\pi \][/tex] square yards.
Do the following scenarios model the equation y = 2x + 5?
There are initially 5 chickens on the farm. Each month thereafter the number of chickens is 2 times the number in the month before
Select a Value
Nina earns $2.00 for each Enjoy the City book she sells. Each time she sells a book she also gets a five-dollar tip.
Select a Value
The temperature at 8:00 AM is 5 degrees Celsius and increases 2 degrees per hour.
Select a Value
5433397.2694
The provided scenario that relates to the equation y = 2x + 5 involves starting with 5 chickens on a farm and then doubling the number each month.
For the farm scenario with chickens, the number of chickens each month is not 2 times the number in the month before plus five, but rather 2 times the previous month's number. This does not fit the equation y = 2x + 5, where x would represent time in months and y would represent the total number of chickens.
In Nina's book-selling scenario, for each book she sells, she earns $2 plus a $5 tip. This fits the equation perfectly, where x represents the number of books Nina sells and y represents her total earnings. So, for Nina's scenario, Yes, it models the equation.
The temperature scenario also fits the equation y = 2x + 5, where x represents the number of hours after 8:00 AM and y represents the temperature in degrees Celsius. Thus, for every hour, the temperature increases by 2 degrees, starting from 5 degrees at 8:00 AM. So, for the temperature scenario, Yes, it models the equation.
Solve for x. x2 = 64
Answer:
32 × 2 = 64
Step-by-step explanation:
x is being multiplied by 2 so it would be half of 64.
Answer:
x = ± 8
Step-by-step explanation:
Given
x² = 64 ( take the square root of both sides )
x = ± [tex]\sqrt{64}[/tex] = ± 8 ← note plus or minus
[ since 8² = 64 and (- 8)² = 64 ]
Draw a square. Place a counter on each corner, or vertex of the square that you drew.Write how many corners, or vertices.
Answer:
4
Step-by-step explanation:
Count
could I get some help in here
Answer:
98 ft²
Step-by-step explanation:
There are a couple of ways you can think about this one. Perhaps easiest is to treat it as a square with a triangle cut out of it. The cutout triangle has a base (across the top) of 14 ft and a height of 14 ft, so its area is ...
A = (1/2)(14 ft)(14 ft) = 98 ft²
Of course the area of the square from which it is cut is ...
A = (14 ft)² = 196 ft²
So, the net area of the two triangles shown is ...
A = (196 ft²) - (98 ft²) = 98 ft²
_____
Another way to work this problem is to attack it directly. Let the base of the left triangle be x. Then the base of the right triangle is 14-x, and their total area is ...
A = A1 + A2 = (1/2)(x ft)(14 ft) + (1/2)((14-x) ft)(14 ft)
We can factor out 7 ft to get ...
A = (7 ft)(x ft + (14 -x) ft)
A = (7 ft)(14 ft) = 98 ft²
Need help with this circumference question
Hold on I have that answer
Answer:
The numerical value of circumference is greater than the numerical value of area
Step-by-step explanation:
Given
circumference= 2π
formula for circumference of circle is 2πr
hence r of given circle is 1
formula for area of circle is πr^2
putting r=1 in above equation
Area of given circle= π(1)^2
= π
As 2π>π
The numerical value of circumference is greater than the numerical value of area!
In the diagram, the radius of the outer circle is 2x cm and
the radius of the inside circle is 6 cm. The area of the
shaded region is 200π cm.
What is the value of x?
Area shaded = Area big circle- Area of small circle;
200 pi= pi•(2x)^2 -pi•6^2;
200pi= pi•4x^2 -pi•36;
200pi=pi•4(x^2 -9) divide both sides by 4pi;
50=x^2 -9; So x=sqrt(59)~7.68cm
how to divide decimals
Answer:
It is easy to divide decimals
Step-by-step explanation
To do it
First: Take an example 5/0.2
Second: Make the division more easier by multiplying the denominator and numerator by 10 ( the number of zeros vary according to the number of places in the decimal part, for example if there where three places in the decimal side the use 1000 to multiply, look at the numer of the decimal places and the numer of zeros in the number to multiply). 5*10/0.2*10 = 50/2
Third: Now divide it normaaly in the example we get 25 as the answer.
I hope you liked the answer.
You need to determine the total distance each hiker will hike.
And
Determine the number off gallons of water each hiker will bring.
Explain
Use picture
so, on the way over the hikers will hike 2 miles, rest and then go the rest of 1¾ miles, meaning on the way over they'll hike 2 + 1¾ miles.
[tex]\bf \stackrel{mixed}{1\frac{3}{4}}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}} \\\\[-0.35em] ~\dotfill\\\\ 2+\cfrac{7}{4}\implies \cfrac{2}{1}+\cfrac{7}{4}\implies \cfrac{(4)2+(1)7}{4}\implies \cfrac{8+7}{4}\implies \cfrac{15}{4}[/tex]
then on the way back, we know is -1/2 less than on the way over, that means the way back is (15/4) - (1/2)
[tex]\bf \cfrac{15}{4}-\cfrac{1}{2}\implies \cfrac{(1)15-(2)1}{4}\implies \cfrac{13}{4} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{total hiked distance}}{\stackrel{\textit{on the way over}}{\cfrac{15}{4}}+\stackrel{\textit{on the way back}}{\cfrac{13}{4}}}\implies \cfrac{(1)15+(1)13}{4}\implies \cfrac{28}{4}\implies 7[/tex]
we know is 1/4 for 1 mile, than how many for 7 miles?, well is just their product
[tex]\bf \cfrac{1}{4}\cdot 7\implies \cfrac{7}{4}\implies 1\frac{3}{4}[/tex]
Given the quadratic equation below, determine which it could represent.
X^2-4x=60
A: A wall in Liza's bedroom has an area of 60 square feet. She covers 4 square feet of the wall with a poster.
B: on Tuesday, a packaging company packed 4 fewer boxes of cashews than they did on Monday. They packed a total of 60 boxes.
C: In a meeting room for a business event, there are 4 fewer chairs laid out in each row than the number of rows. The total number of chairs in the room is 60.
D:Mr.Bass is 4 years older than his sister. The total of their ages is 60 years.
Answer:
C
Step-by-step explanation:
Correct option is C.
Let x be the number of rows in a meeting room. If there are 4 fewer chairs laid out in each row than the number of rows, then in each row there are x-4 chairs.
The total number of chairs is
[tex]x(x-4)[/tex]
The total number of chairs in the room is 60. Hence,
[tex]x(x-4)=60[/tex]
graph the inequality y<2|x-1|-2
Answer:
y<2x-4
y<-2x
Step-by-step explanation:
Since we are dealing with and inequality we need to remember the following tips.
We no obtain values from inequalities, we obtain ranges.
If y<f(x), the range of variable y resides below de graph of f(x), but if y>f(x), the range is above.
y<2|x-1|-2
Gives two functions.
first'
y<2(x-1)-2 if x>1 and
y<-2(x-1)-2 if x<1
First equation turns in y<2x-4 and the second y<-2x
Two line going in different directions
six is what fraction of 15? Six is what percent of 15?
Six Is 2/5 Of 15
6 Is 40% Of 15
Answer:
2/5, 40%
Step-by-step explanation:
When we ask "six is what fraction of 15?", we're asking this: how much of 15 does 6 take up? Just looking at a picture of it, if we have 15 pieces of a whole cake, 6 of those pieces take up a little less than half of that total. We represent this with the fraction 6/15. Now, 6 and 15 have something in common, too: they can both be divided by 3. Take a look at the second picture now. Notice that when we divide the total number of parts and the number of pieces by the same number, the amount those pieces take up stays exactly the same. Since 6 divided by 3 is 2 and 15 divided by 3 is 5, we can say that 6/15 = 2/5, and we can't go any further than that.
Percents are just a special kind of fraction; ones that have 100 in their denominator (the word "percent" literally means "for each 100"). We also have a special way of writing percents: 6/100 would be written as 6%, 50/100 would be 50%, and 100/100 would be 100%.
Remember when I showed how fractions can be equal to each other if you can divide both number by the same thing? You can do the same thing in the other direction: you can create equivalent fractions by multiplying both numbers by the same number.
So, we want to go from 2/5 to ?/100 (we don't know what number ? is yet!) but how do we get there? Well, remember, for two fractions to be equal, you have to multiply both the top and bottom by the same number. Whatever we multiply 5 by to get 100, we'll have to multiply 2 by to get that ?
Well 5 × 20 = 100, so 20 seems to fit the bill, and multiplying 2 × 20 gets us 40, making our fraction 2/5 = 40/100, which we'd write as 40%.
So 6 is 2/5 of 15, which is the same as 40% of 15!
Select the functions that have a value of 0.
sin270
cos90
tan0
csc(-180)
cos(-90)
cot270
Answer:
cos90° = 0°, tan0° = 0°,cos(-90°) = 0°, cot270° = 0°Step-by-step explanation:
[tex]k\in\mathbb{Z}\\\\\sin x=0\iff x=180^ok\\\\\cos x=0\iff x=90^o+180^ok\\\\\tan x=0\iff x=180^ok\\\\\cot x=0\iff x=90^o+180^ok\\\\\csc x\neq0\ \text{for}\ x\in\mathbb{R}-\{180^ok\}\\========================\\\\\sin270^o\neq0\\\\\cos90^o=\cos(90^o+180^o\cdot0)=0\\\\\tan0^o=\tan(180^o\cdot0)=0\\\\\csc(-180^o)\neq0\\\\\cos(-90^o)=\cos(90^o-180^o)=\cos(90^o+180^o\cdot(-1))=0\\\\\cot270^o=\cot(90^o+180^o)=0[/tex]
Answer:
cos90° = 0°, tan0° = 0°,cos(-90°) = 0°, cot270° = 0°
Step-by-step explanation:
Given vector u = (4,-3) and the graph of vector v, find v - 3u and express the result of terms in i and j
Answer: First option
v-3u = 11 j
Step-by-step explanation:
To find the components of the vector v, you must locate the initial and final points of the vector on the graph.
Final point
(7, 2)
Initial point
(-5, 0)
Then the vector v will have the following components:
[tex]v = (7 - (- 5)) i + (2-0) j\\\\v = (7 + 5) i + 2j\\\\v = 12i + 2j[/tex]
Now multiply the vector u by -3
[tex]u = (4, -3)\\\\u =4i -3j\\\\-3u = -12i + 9j[/tex]
Now add both vectors.
[tex]v-3u = (12-12) i + (2 + 9) j\\\\v-3u = 0i + 11j\\\\v-3u = 11j[/tex]
solve this equation for x 0.95 = log x
Answer:
8.91
Step-by-step explanation:
Given: 0.95 = log x,
we can conclude that:
0.95 log x
10 = 10
0.95
which in turn is equivalent to x = 10 whose value is 8.91
Final answer:
To solve 0.95 = log x, we apply the inverse of the logarithmic function, raising 10 to the power of 0.95 to find that x ≈ 8.9125.
Explanation:
To solve the given equation 0.95 = log x, we need to understand that 'log' usually refers to a logarithm with base 10, unless otherwise stated. To find the value of x, we must revert the logarithmic equation back to its exponential form. In this case, we are finding the power to which 10 must be raised to give the value x.
The inverse operation for a base 10 logarithm is raising 10 to the power of whatever the logarithm equals. Applying this principle to our equation, we have:
x = 100.95
Using a calculator, we would get:
x ≈ 8.9125